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+ 1998 and references therein): a fat spectrum up to a break frequency in the vicinity of a few Iz aud spectrum falling steeply thereafter., 1998 and references therein): a flat spectrum up to a break frequency in the vicinity of a few Hz and spectrum falling steeply thereafter.
+ The narrow quasi-periodic oscillation (QPO) along with its first harmonic. seen durius the other low-hard states of CRS 1915|105 (Paul et al.," The narrow quasi-periodic oscillation (QPO) along with its first harmonic, seen during the other low-hard states of GRS 1915+105 (Paul et al."
+ 1997: Morgan et al., 1997; Morgan et al.
+ 1997). is evident in the PDS.," 1997), is evident in the PDS."
+ Iu the ligh state the PDS is a featureless power-law above 0.2 IIz., In the high state the PDS is a featureless power-law above 0.2 Hz.
+ In the high state of July 20. however. there is a low frequency QPO at 0.13 Iz.," In the high state of July 20, however, there is a low frequency QPO at 0.13 Hz."
+ The salieut. features of the PDS in the two states are even in Table 2., The salient features of the PDS in the two states are given in Table 2.
+ To hiehlieht the differences iu tlhe PDS at the low and high frequencics. we have fitted the PDS with a power-lav and a Lorentzian (whenever a OPO is present) in the frequency ranges 0.1 1 Uz aud 1 10," To highlight the differences in the PDS at the low and high frequencies, we have fitted the PDS with a power-law and a Lorentzian (whenever a QPO is present) in the frequency ranges 0.1 $-$ 1 Hz and 1 $-$ 10"
+is approximated by another log-linear with slope -0.16 (thick dashed line).,is approximated by another log-linear with slope -0.16 (thick dot-dashed line).
+" This translates into a difference in the FP slope from our fiducial case around Py,27 of just about3%.. much less than the statistical uncertainties."," This translates into a difference in the FP slope from our fiducial case around $\Gamma_{\rm m}
+\simeq 7$ of just about, much less than the statistical uncertainties."
+ Similar is the case when different cut-off angles are considered., Similar is the case when different cut-off angles are considered.
+ In the lower panel of Fig., In the lower panel of Fig.
+" Al) we show how the observed correlations are skewed due to relativistic beaming when 6,=10 ¢dot-dashed contours and thick. dot-dashed line) or ϐ,=20° (dashed contours and thick dashed line).", \ref{fig:fp_gamma} we show how the observed correlations are skewed due to relativistic beaming when $\theta_c=10^{\circ}$ (dot-dashed contours and thick dot-dashed line) or $\theta_c=20^{\circ}$ (dashed contours and thick dashed line).
+" Also in these cases the difference with respect to our fiducial ease corresponds to a difference in the ""corrected"" FP coefficients of less than ~3% at Ly,&7."," Also in these cases the difference with respect to our fiducial case corresponds to a difference in the “corrected” FP coefficients of less than $\sim$ at $\Gamma_{\rm m}
+\simeq 7$."
+ In summary. for any value of mean jet Lorentz factor of the sampled AGN. Li. we have shown that it is possible to derive statistically an intrinsic (un-boosted) radio core luminosity based on the observed hard X-ray one. Lx and on the black hole mass. App according to: where we have defined the new constant cen by.," In summary, for any value of mean jet Lorentz factor of the sampled AGN, $\Gamma_{\rm m}$, we have shown that it is possible to derive statistically an intrinsic (un-boosted) radio core luminosity based on the observed hard X-ray one, $L_{\rm
+X}$ and on the black hole mass, $M_{\rm BH}$ according to: where we have defined the new constant $c_{\rm R}=\xi_{\rm RR}b_{\rm
+R}+b_{\rm RR}$ ."
+ The term in the first parenthesis in the right hand side thus represents our simple way to estimate the relativistic beaming bias introduced in the samples used originally to define the FP relation., The term in the first parenthesis in the right hand side thus represents our simple way to estimate the relativistic beaming bias introduced in the samples used originally to define the FP relation.
+ Its numerical value do indeed depends on the assumptions of our fiducial Monte Carlo model. but to an extent that is negligible when compared to the statistical uncertainties on the FP parameters themselves.," Its numerical value do indeed depends on the assumptions of our fiducial Monte Carlo model, but to an extent that is negligible when compared to the statistical uncertainties on the FP parameters themselves."
+ This above relation. then allows a meaningful statistical test of the intrinsic correlation between radio core luminosity and kinetic power of AGN jets. as we show in section 3..," This above relation, then allows a meaningful statistical test of the intrinsic correlation between radio core luminosity and kinetic power of AGN jets, as we show in section \ref{sec:rad}."
+the 83D A and £ values and the tomographic r and { values.,the 3D $k$ and $\ell$ values and the tomographic $r$ and $\ell$ values.
+ We will discuss the Limber approximation further in Section 4., We will discuss the Limber approximation further in Section \ref{Tomography from 3D Cosmic Shear}.
+ In Figure 4 we show the elect of the Limber approximation on the 3D cosmic shear power spectrum., In Figure \ref{limberplot} we show the effect of the Limber approximation on the 3D cosmic shear power spectrum.
+ Me find that the Limber approximation is a remarkably good approximation to the full caleulation for scales £z100. with residuals of ~10+ over all radial and azimuthal scales.," We find that the Limber approximation is a remarkably good approximation to the full calculation for scales $\ell\gs 
+100$, with residuals of $\sim 10^{-4}$ over all radial and azimuthal scales."
+ The break at koμοι In the power spectra at each f£. caused. by the Bessel function inequality ji(Ar()~0. ds reproduced through the inequality expressed. after equation (14)).," The break at $k\sim \ell/r_{\rm max}$ in the power spectra at each $\ell$, caused by the Bessel function inequality $j_{\ell}(kr \ls \ell)\sim 0$, is reproduced through the inequality expressed after equation \ref{l2}) )."
+ For larger scales (<100. there is a larger effect on the power spectrum.," For larger scales $\ell < 100$, there is a larger effect on the power spectrum."
+ In Figure 5 we show the elect of the Limber approximation on the expected. cosmological errors., In Figure \ref{limberfisherplot} we show the effect of the Limber approximation on the expected cosmological errors.
+ We find that in most parameter combinations some information is inevitably lost. through the largest scales being down weighted. the increase in errors is between 1 30% with an average increase of ~ LOK.," We find that in most parameter combinations some information is inevitably lost, through the largest scales being down weighted, the increase in errors is between $1$ $30\%$ with an average increase of $\sim 10\%$ ."
+ We conclude that the Limber approximation is adequate for forecasting purposes. but if computer time allows. it is preferable to use the full expressions in data analysis.," We conclude that the Limber approximation is adequate for forecasting purposes, but if computer time allows, it is preferable to use the full expressions in data analysis."
+ We now approximate the 3D. shear fick further and. show how in the discrete real-space limit the tomographic power spectra can be reproduced., We now approximate the 3D shear field further and show how in the discrete real-space limit the tomographic power spectra can be reproduced.
+ There have been some implicit references to this derivation. for example in Hu (1999). here we will show explicitly how the 3D shear field is related to the tomographic power spectrum.," There have been some implicit references to this derivation, for example in Hu (1999), here we will show explicitly how the 3D shear field is related to the tomographic power spectrum."
+ Weak lensing tomography is a flavour of 3D weak lensing in which the angular anc redshilt information of each. galaxy is used., Weak lensing tomography is a flavour of 3D weak lensing in which the angular and redshift information of each galaxy is used.
+ The practical distinction between 31) cosmic shear and tomography is that tomography divides the redshift range into a series of bins and the 2D shear transform in each bin is constructed., The practical distinction between 3D cosmic shear and tomography is that tomography divides the redshift range into a series of bins and the 2D shear transform in each bin is constructed.
+ The auto (in à single bin) and cross (between bins) power spectra are used. to constrain cosmological parameters., The auto (in a single bin) and cross (between bins) power spectra are used to constrain cosmological parameters.
+ Given the expressions in equations (14)) to (17)) we can now derive the weak lensing tomographie power spectra clirecthy from the 3D shear field., Given the expressions in equations \ref{l2}) ) to \ref{l4}) ) we can now derive the weak lensing tomographic power spectra directly from the 3D shear field.
+" Lo Appendix Bowe show how the 3D cosmic shear power spectrum using the Limber approximation can be written as where we define a weight factor as where 7=(Gb; and ptrz])=ptrz]lezs]) is the redshift probability distribution. equivalent to p(z|2,) in equation (12))."," In Appendix B we show how the 3D cosmic shear power spectrum using the Limber approximation can be written as where we define a weight factor as where $r_i = \ell/k_i$ and $p(r[z])=p(r[z]|r[z_p])$ is the redshift probability distribution, equivalent to $\bar p(z|z_p)$ in equation \ref{Gcont}) )."
+ We condense the notation here and in Appendix B to match the literature for the tomographic case., We condense the notation here and in Appendix B to match the literature for the tomographic case.
+ This is still a full 3D estimator where rj=rsp) and po= can take any value. and in practice would be a sum over all galaxy pairs.," This is still a full 3D estimator where $r_1=r(z_1)$ and $r_2=r(z_2)$ can take any value, and in practice would be a sum over all galaxy pairs."
+ This is a key result. of this article. using only two integrals a full 3D shear power spectrum can be computed from the 3D matter power spectrum (as simple as the standard tomographic approximation).," This is a key result of this article, using only two integrals a full 3D shear power spectrum can be computed from the 3D matter power spectrum (as simple as the standard tomographic approximation)."
+ Inspection of the previous equations shows that they are the usual expressions for the (auto- or cross-) power spectrum of tomography. from which we see that. under the Limber approximation. tomography samples discrete sets of physical wavenumbers. in an £-dependent way: for shells at distances πι...," Inspection of the previous equations shows that they are the usual expressions for the (auto- or cross-) power spectrum of tomography, from which we see that, under the Limber approximation, tomography samples discrete sets of physical wavenumbers, in an $\ell$ -dependent way: for shells at distances $r_i$, $k = \ell/r_i$."
+ 1n summary to convert from 3D cosmic shear to weak lensing omography we see that the following three steps must be aken The second step is benign in that no information. should be lost. however the first and third steps do result. in information loss (see Section 3.1. and 4.1)).," In summary to convert from 3D cosmic shear to weak lensing tomography we see that the following three steps must be taken The second step is benign in that no information should be lost, however the first and third steps do result in information loss (see Section \ref{Convergence of the 3D Cosmic Shear} and \ref{Comparison
+ to 3D shear}) )."
+ Interestingly [or à specific redshift bin (r) and a specific azimuthal {- the tomographic approximation only probes a single physical &-mode A=(fr from the full 3D shear field: in contrast in 3D cosmic shear we have control over the & and { modes over the whole redshift range., Interestingly for a specific redshift bin $r$ ) and a specific azimuthal $\ell$ -mode the tomographic approximation only probes a single physical $k$ -mode $k=\ell/r$ from the full 3D shear field; in contrast in 3D cosmic shear we have control over the $k$ and $\ell$ modes over the whole redshift range.
+ Clearly by fixing the distances of the tomographic binning. we lose some [lexibilitv over the physical wavenumbers probed. so there is a risk that either not all useful modes ave included. (increasing statistical errors). or that. for the nearby shells. the physical wavenumber range sampled extends to too high. a value of A. where theoretical uncertainties become a potential source of svstematic error.," Clearly by fixing the distances of the tomographic binning, we lose some flexibility over the physical wavenumbers probed, so there is a risk that either not all useful modes are included (increasing statistical errors), or that, for the nearby shells, the physical wavenumber range sampled extends to too high a value of $k$, where theoretical uncertainties become a potential source of systematic error."
+ None of this is a fundamental problem for tomography: it simply requires that the £ range chosen should be redshilt- increasing Ax=σι for the distant shells. and reducing it for nearby. shells.," None of this is a fundamental problem for tomography; it simply requires that the $\ell$ range chosen should be redshift-dependent – increasing $\ell_{\rm max}=r[z]k_{\rm max}$ for the distant shells, and reducing it for nearby shells."
+ In a similar manner to Section 2. we can also keep, In a similar manner to Section \ref{Photometric 3D Shear Estimator} we can also keep
+Ideally we would like to use the muicrolensing flux ratios to constrain the size of the quasar as a functiou of waveleneth: however. only weak constraints can be derived without a detection of time variability due to microlensing (?)..,"Ideally we would like to use the microlensing flux ratios to constrain the size of the quasar as a function of wavelength; however, only weak constraints can be derived without a detection of time variability due to microlensing \citep{Wyithe2002}."
+ Iustead we use a senmi-enpircal model for the infrared SED topredict what the flux ratios should be as a function of waveleneth and compare these predictions with the observed flux ratios to confirm the plausibility of this model., Instead we use a semi-empirical model for the infrared SED to what the flux ratios should be as a function of wavelength and compare these predictions with the observed flux ratios to confirm the plausibility of this model.
+ We coustructed a semi-cimpirical model for the flux ratios to compare to the observed IRAC flux ratios as follows., We constructed a semi-empirical model for the flux ratios to compare to the observed IRAC flux ratios as follows.
+ We asstune that the spectra cousists of a power-law component due to an accretion disk (we are modchne the region from Ο.Ε LOgam which is well longward of the peak of the disk spectrum and is only a decade in frequency. so a power-law should be an adequate approximation of a disk spectrum) aud a sinele-temperature thermal dust cussion component. representing the inner edge of the a dusty torus.," We assume that the spectrum consists of a power-law component due to an accretion disk (we are modeling the region from $0.4 - 4.0 \mu$ m which is well longward of the peak of the disk spectrum and is only a decade in frequency, so a power-law should be an adequate approximation of a disk spectrum) and a single-temperature thermal dust emission component, representing the inner edge of the a dusty torus."
+ We fit the spectral cnerey distribution from 0.1 to. L0 nücrous in the rest frame with these two compoucuts. determining their relative streneth at cach wavelength.," We fit the spectral energy distribution from 0.4 to 4.0 microns in the rest frame with these two components, determining their relative strength at each wavelength."
+ The best fit is shown in Figure 8: the model provides a good fit to the four IRAC data points., The best fit is shown in Figure \ref{fig:q2237sed}; the model provides a good fit to the four IRAC data points.
+ We have not attempted to correct for mücroleusiug. nor possible time-variability as the SED data are not simultaneous.," We have not attempted to correct for microlensing, nor possible time-variability as the SED data are not simultaneous."
+ However. this will likely have a sinall effect on the SED as suunnaiug over all four images reduces the impact of mucroleusing aud im the infrared quasars are weakly variable.," However, this will likely have a small effect on the SED as summing over all four images reduces the impact of microlensing and in the infrared quasars are weakly variable."
+ With these two fts we determined the minima possible source sizes to reproduce the observed fux with thermal enission as follows., With these two fits we determined the minimum possible source sizes to reproduce the observed flux with thermal emission as follows.
+" For the power-law component. we assumed a disk ecometry with a temperature that is à power-law in radius. re finding Toxe99, and found that tbe hal£-light radius should scale with waveleugtli as where A is measured iu microns iu the rest frame of the quasar."," For the power-law component, we assumed a disk geometry with a temperature that is a power-law in radius, $r$, finding $T \propto r^{-0.66}$, and found that the half-light radius should scale with wavelength as where $\lambda$ is measured in microns in the rest frame of the quasar."
+" At this radius the standard disk model is well outside the immer edee and thus is expected to lave a temperature dependence of Toxà7/73, which is close to the measured dependence."," At this radius the standard disk model is well outside the inner edge and thus is expected to have a temperature dependence of $T \propto r^{-3/4}$, which is close to the measured dependence."
+ We asstuned that the dust component either las an ciissivity described by optically-thin interstellar medii (ISM) dust with the model of ? or cuits as au optically-thick blackbody (BB)., We assumed that the dust component either has an emissivity described by optically-thin interstellar medium (ISM) dust with the model of \citet{Draine2003} or emits as an optically-thick blackbody (BB).
+ These two extremes were chosen to bracket the range of possible behaviors for the hottest dust at the inner edge of the torus (we did not use the best-fit Fritz model due to the differcut peak waveleneth)., These two extremes were chosen to bracket the range of possible behaviors for the hottest dust at the inner edge of the torus (we did not use the best-fit Fritz model due to the different peak wavelength).
+ We found best-fit temperatures of the dust of 1168 In (ISM), We found best-fit temperatures of the dust of 1168 K (ISM)
+The theoretical approach presented here allows us to determine the spectrum and the anisotropy in the particle distribution for arbitrary shock velocity ancl arbitrary scattering properties of the fluid.,The theoretical approach presented here allows us to determine the spectrum and the anisotropy in the particle distribution for arbitrary shock velocity and arbitrary scattering properties of the fluid.
+ In (his section we show that we can reproduce the results expected in (he non-relativistic limit., In this section we show that we can reproduce the results expected in the non-relativistic limit.
+ We calculated the spectral slope and (he angular part of the distribution function for several values of the shock velocity and shock compression factor r., We calculated the spectral slope and the angular part of the distribution function for several values of the shock velocity and shock compression factor $r$.
+ We also calculated (he return. probability [rom the downstream and upstream sections., We also calculated the return probability from the downstream and upstream sections.
+" The expected return. probability in the Newtonian limit is 77opπαdug. very. accurately reproduced by our calculation. for instance for uy107 (DPZ,=0.96) and for uy=2x103 (P!,— 0.92)."," The expected return probability in the Newtonian limit is $P_{ret}^d=1-4 u_d$, very accurately reproduced by our calculation, for instance for $u_d=10^{-2}$ $P_{ret}^d = 0.96$ ) and for $u_d=2\times 10^{-2}$ $P_{ret}^d =
+0.92$ )."
+ In all cases that we considered. the condition is confirmed for any value of jy within a part in 103.," In all cases that we considered, the condition is confirmed for any value of $\mu_0$ within a part in $10^4$."
+ As a matter of fact. we checked. (hat the above equality is satisfied in all cases we studied. relativistic or otherwise.," As a matter of fact, we checked that the above equality is satisfied in all cases we studied, relativistic or otherwise."
+ The slope of the spectrum of accelerated particles for u=3x107? and uy=107 (compression [actor 3) as calculated wilh our approach is 4.5. in agreement wilh the theoretical prediction (Bell 1973).," The slope of the spectrum of accelerated particles for $u=3\times
+10^{-2}$ and $u_d=10^{-2}$ (compression factor 3) as calculated with our approach is 4.5, in agreement with the theoretical prediction (Bell 1978)."
+ We obtain the same slope in botli cases of small pitch angle scattering with &=0.01 and large angle scattering. that we simulate by choosing ¢=100 (but any large value gives (he same result).," We obtain the same slope in both cases of small pitch angle scattering with $\sigma=0.01$ and large angle scattering, that we simulate by choosing $\sigma=100$ (but any large value gives the same result)."
+ The [act that in the newtonian limit the slope of the spectrum does not depend on the scattering properties of the fIuid is also in agreement with the theoretical prediction of Bell (1978)., The fact that in the newtonian limit the slope of the spectrum does not depend on the scattering properties of the fluid is also in agreement with the theoretical prediction of Bell (1978).
+" It is worth stressing that (his universality in the spectrum of the accelerated.particles does not reflect in the universality of the return probabilities 7; and P,.", It is worth stressing that this universality in the spectrum of the acceleratedparticles does not reflect in the universality of the return probabilities $P_d$ and $P_u$.
+ In Fig., In Fig.
+ 1 we plot μμ.) ancl Pug.ji) as fncetions of ji for the values of ji inclicatecl in the figure ancl assuming «4=0.03.440.01 and a=0.01.," \ref{fig:PdPu001} we plot $P_d(\mu_0,\mu)$ and $P_u(\mu_0,\mu)$ as functions of $\mu$ for the values of $\mu_0$ indicated in the figure and assuming $u=0.03,u_d=0.01$ and $\sigma=0.01$."
+ The same functions are plotted in Fig., The same functions are plotted in Fig.
+ 2 for the case of large angle scattering (a= 100)., \ref{fig:PdPu100} for the case of large angle scattering $\sigma=100$ ).
+ As stressed. above. our method is based on the introduction of the (wo probability clistvibutions £2 and {η (hat can be calculated by solving (wo integral equations. Eqs. (16))," As stressed above, our method is based on the introduction of the two probability distributions $P_d$ and $P_u$ , that can be calculated by solving two integral equations, Eqs. \ref{eq:Pd}) )"
+velocitv of the two cvlinders). as only differential rotation plavs a role in the generation ol turbulence.,"velocity of the two cylinders), as only differential rotation plays a role in the generation of turbulence."
+" Defining w=v—Qyre,. and ©=0—Ouf (so that w and © are the velocity and azimuthal coordinate in (he rotating frame. respectively). the Navier-Stokes equation for w=(iw.ie.ete.) becomes where w.V'w=(w.Vie,je,+(w.Vi4)e;(w.Vi.)e.."," Defining ${\bf w}={\bf v}-\Omega_0 r
+{\bf e}_{\phi}$, and $\phi=\theta-\Omega_0 t$ (so that ${\bf w}$ and $\phi$ are the velocity and azimuthal coordinate in the rotating frame, respectively), the Navier-Stokes equation for ${\bf w}=(w_r,\ w_\phi,\ w_z)$ becomes where ${\bf w}.\nabla'{\bf w}\equiv({\bf w}.\nabla w_r)
+{\bf e}_r+({\bf w}.\nabla w_{\phi}) {\bf e}_{\phi}+({\bf w}.\nabla
+w_z) {\bf e}_z$."
+ For future reference. I refer to (he terms (5/r and 2w;ico/r as “geometric ternis. as they arise because of the cylindricalgeonietrv.," For future reference, I refer to the terms $w_{\theta}^2/r$ and $2w_rw_\theta/r$ as “geometric terms"", as they arise because of the cylindrical."
+. For these flows. (he rotation parameter defined in Eq. (5))," For these flows, the rotation parameter defined in Eq. \ref{Ro}) )"
+ reads where g=—(r/Q)(dQ/dr) is the parameter defined by Balbusοἱaf(1996). to characterize rotation profiles., reads where $q\equiv -(r/\Omega)(d\Omega/dr)$ is the parameter defined by \citet{BHS96} to characterize rotation profiles.
+ The flow is stable according to Ravleigl’s criterion when 4<2. ie. wheΕν S«—1. quite similarly (ο rotating Couette and [ree flows. allhough (hie processes (hroug[un which instability occurs are dillerent.," The flow is stable according to Rayleigh's criterion when $q<2$, i.e. when $S<-1$, quite similarly to rotating Couette and free flows, although the processes through which instability occurs are different."
+ Note also that Eqs. (4)), Note also that Eqs. \ref{NSR}) )
+ and (3)) diller only through the geometric and centrifugal terms., and \ref{NSCT}) ) differ only through the geometric and centrifugal terms.
+ The fact that the minimum Revnolds nunber for developed (turbulence is identical in plane Couette and. Couette-Tavlor flows with Ar/rX1/20 and the inner evlinder at rest can be understood in the following wav., The fact that the minimum Reynolds number for developed turbulence is identical in plane Couette and Couette-Taylor flows with $\Delta r/r\lesssim 1/20$ and the inner cylinder at rest can be understood in the following way.
+ First. the advection term Gvhichli is the source of the turbulence cascade as indicated by the very existence of the Revnolds imunber) dominates over (he geometric terms when rAQ/ArorAQ/r. ie. Ar/r<1.," First, the advection term (which is the source of the turbulence cascade as indicated by the very existence of the Reynolds number) dominates over the geometric terms when $r\Delta\Omega/\Delta r\gg r\Delta\Omega/r$, i.e. $\Delta r/r\ll 1$."
+ Second. AQ=© (one cvlinder being at rest). so that the Coriolis term is also very small compared to the advection term. and Eq. (8))," Second, $\Delta\Omega=\Omega$ (one cylinder being at rest), so that the Coriolis term is also very small compared to the advection term, and Eq. \ref{NSCT}) )"
+ nearly reduces to Eq. (1))., nearly reduces to Eq. \ref{NSC}) ).
+ Note furthermore that the Coriolis force does nol appear to significantly affect (he minimal lRevnolds number for the onset of turbulence for the values of q of interest here (Le. q>1 log~1 - 2). both in the limiting plane Couette regime and in the rotation regime. as exemplified bv the data of Wendt(1933). Lor nearly neutral flows. which follow the same law for the minimal Revnolds number. down to the plane Couette limit.," Note furthermore that the Coriolis force does not appear to significantly affect the minimal Reynolds number for the onset of turbulence for the values of $q$ of interest here (i.e., $q\gg 1$ to $q\sim 1$ - $2$ ), both in the limiting plane Couette regime and in the rotation regime, as exemplified by the data of \citet{Wen33} for nearly neutral flows, which follow the same law for the minimal Reynolds number, down to the plane Couette limit."
+(2002. 2004).,"(2002, 2004)."
+ It is easy to show that C(p) is related: to the Cp) through the relation Cp)|lífüol=ερ)., It is easy to show that $U(p)$ is related to the $\hat{U}(p)$ through the relation $\hat U(p)+1/R_tot = U(p)$.
+ The dotted. and. dashed. lines are. the results. obtained with the caleulation of Alalkoyv (1997) with a Bohm aud Ixolmogorov. cillusion respectively., The dotted and dashed lines are the results obtained with the calculation of Malkov (1997) with a Bohm and Kolmogorov diffusion respectively.
+ For Bohm clilfusion the two approaches give very similar results., For Bohm diffusion the two approaches give very similar results.
+ For Ixolmogorov diffusion the dilferencies are larger. as expected.," For Kolmogorov diffusion the differencies are larger, as expected."
+ In Fig., In Fig.
+ 5 we plot the spectra of the accelerated particles. as obtained in this paper (solid line) and for a Bohm (dotted line) and Ixolmosgorov. (dashed line) diffusion coellicient. as derived by carving out the caleulation of Malkov. (1997).," \ref{fig:malk_spec} we plot the spectra of the accelerated particles, as obtained in this paper (solid line) and for a Bohm (dotted line) and Kolmogorov (dashed line) diffusion coefficient, as derived by carrying out the calculation of Malkov (1997)."
+ We recall that from the theoretical point of view the ohm dilfusion is in lact what should. be expected. in the proximity of a shock if the turbulence. necessary for. the acceleration is strong and generated by the same cosmic ravs that are being accelerated (Lagage Cesarsky 1983)., We recall that from the theoretical point of view the Bohm diffusion is in fact what should be expected in the proximity of a shock if the turbulence necessary for the acceleration is strong and generated by the same cosmic rays that are being accelerated (Lagage Cesarsky 1983).
+ In this perspective. we look at the results illustrated in this section as very encouraging in using the approach presented in Blasi (2002. 2004). since it is simple and at the same time accurate in reproducing the major physical aspects of particle acceleration at cosmic ray modified shocks.," In this perspective, we look at the results illustrated in this section as very encouraging in using the approach presented in Blasi (2002, 2004), since it is simple and at the same time accurate in reproducing the major physical aspects of particle acceleration at cosmic ray modified shocks."
+ The presence of multiple solutions is typical of many non-linear problems anc should not be surprising from the mathematical point of view., The presence of multiple solutions is typical of many non-linear problems and should not be surprising from the mathematical point of view.
+ In terms of physical understanding however. multiple solutions may be disturbing.," In terms of physical understanding however, multiple solutions may be disturbing."
+ The typical situation that takes place in nature when multiple solutions appear in the description of other non linear svstems is that (at least) one of the solutions is unstable and the svstem in a stable solution when perturbed., The typical situation that takes place in nature when multiple solutions appear in the description of other non linear systems is that (at least) one of the solutions is unstable and the system in a stable solution when perturbed.
+ The stable solutions are the only ones that are physically meaningful., The stable solutions are the only ones that are physically meaningful.
+ Some attempts to. investigate the stability of cosmic ray modified shock waves have been mace by Mond Drury (1998) and Toptyein (1999). but all of them refer to the two-Luicl models.," Some attempts to investigate the stability of cosmic ray modified shock waves have been made by Mond Drury (1998) and Toptygin (1999), but all of them refer to the two-fluid models."
+ A step forward is being carried out by Blasi Vietri (in preparation) in the context of kinetic mocels., A step forward is being carried out by Blasi Vietri (in preparation) in the context of kinetic models.
+ In acicdition to the stability. another issue that enters the physical. description of our problem is the identification of possible processes that determine some tvpe of backreaction on the system.," In addition to the stability, another issue that enters the physical description of our problem is the identification of possible processes that determine some type of backreaction on the system."
+ Ht may be expected that when some types of processes of self-regulation are included. the phenomenon of multiple solutions is reduced.," It may be expected that when some types of processes of self-regulation are included, the phenomenon of multiple solutions is reduced."
+ In this section we investigate, In this section we investigate
+IW Pup CUP 36762) is a relatively Taint (Via;=10.36) contact binary which has not had any photometric or radial velocity observations.,HI Pup (HIP 36762) is a relatively faint $V_{\rm max}=10.36$ ) contact binary which has not had any photometric or radial velocity observations.
+ Discovered in 1949. (he svstem was Classified ancl its light curve constructed from photographic observations by Hoffineister (1956).," Discovered in 1949, the system was classified and its light curve constructed from photographic observations by \citet{hoff56}."
+. Sahade&DerónDavila(1963). suggested (hat it is a possible member of the open cluster Cr 173. but this matter has not been established vet.," \citet{sahade63} suggested that it is a possible member of the open cluster Cr 173, but this matter has not been established yet."
+ The Tveho-2 mean B-W=0.51 corresponds to a spectral type about FOV. but there exist no direct classifications of the star.," The Tycho-2 mean $B-V=0.51$ corresponds to a spectral type about F6V, but there exist no direct classifications of the star."
+ A companion with 8—V=1.68 (approximately M3V) is located 52 arcsec away (ESA1997).. but the star is not included as a visual double svstem in the WDS Catalog.," A companion with $B-V =1.68$ (approximately M3V) is located 52 arcsec away \citep{hip}, but the star is not included as a visual double system in the WDS Catalog."
+ We have only 5 radial velocity observations for HI Pup. so the radial velocity orbit must be considered very preliminary.," We have only 5 radial velocity observations for HI Pup, so the radial velocity orbit must be considered very preliminary."
+" The mass ratio is small. qi,=0.19a0.06."," The mass ratio is small, $q_{\rm sp}=0.19 \pm 0.06$."
+ TZ Pvx (HIP. 42619) was discovered as a variable star by Strohmeier(1966). who determined the orbital period to be 0.697 davs (Strolimeier1961b)., TZ Pyx (HIP 42619) was discovered as a variable star by \citet{stroh66} who determined the orbital period to be 0.697 days \citep{stroh67b}.
+. Later Llipparcos observations (ESA1997) showed that the binary has an orbital period of 2.3 days with a light curve showing relatively short. well defined eclipses.," Later Hipparcos observations \citep{hip}
+ showed that the binary has an orbital period of 2.3 days with a light curve showing relatively short, well defined eclipses."
+" It is definitely a detached binary with well separated. components. vet the star still appears as a W UMa-tyvpe binary in the Simbad database with the spectral (ype as an uncertain A. The Tyeho-2 photometric data. 0.27. suggest a spectral type A3/9V at Vi,=10.63."," It is definitely a detached binary with well separated components, yet the star still appears as a W UMa-type binary in the Simbad database with the spectral type as an uncertain A. The Tycho-2 photometric data, $B-V=0.27$ , suggest a spectral type A8/9V at $V_{\rm max}=10.68$."
+ Our radial velocity orbit is the best among this group of targets. mostly because of sharp signabures in the broadening functions which were easy (o measure for radial velocities.," Our radial velocity orbit is the best among this group of targets, mostly because of sharp signatures in the broadening functions which were easy to measure for radial velocities."
+ The Mass ratio is very close to unitv. ονdu=0.9652:0.020. with the slightlySuet less-niassive component (the one showing the larger semi-amplitude) giving a mareinally stronger signature in ihe DF's.," The mass ratio is very close to unity, $q_{\rm sp}=0.965 \pm 0.020$, with the slightly less-massive component the one showing the larger semi-amplitude) giving a marginally stronger signature in the BF's."
+ The current paper is the second and last of the (wo papers describing a short program of radial velocity observations of southern contact binary stus conducted at the European Southern observatory in December 1996 and. August 1998., The current paper is the second and last of the two papers describing a short program of radial velocity observations of southern contact binary stars conducted at the European Southern observatory in December 1996 and August 1998.
+ Paper I eave the full background and explanations for the rationale of this program. and contained results for 17 targets observable in the August season in 1998.," Paper I gave the full background and explanations for the rationale of this program, and contained results for 17 targets observable in the August season in 1998."
+of its counterpart can be estimated. from the reddening clerived from the measurement and ealaxy counts.,of its counterpart can be estimated from the reddening derived from the measurement and galaxy counts.
+" From the reddening map in Burstein Leiles (1982) we obtain a colour excess EGD13)zm0.054 for a halo source at §=46728584"" and b=36711573"".", From the reddening map in Burstein Heiles (1982) we obtain a colour excess $E(B-V) \approx 0.054$ for a halo source at $l = 46^{\circ} 28' 58.4''$ and $b = -36^{\circ} 11' 57.3''$.
+" ""Ehe corresponding extinctions are chyzm(Q.17. chy&O.1l and cl,=0.09."," The corresponding extinctions are $A_V \approx 0.17$, $A_R \approx 0.11$ and $A_I \approx 0.09$."
+" Llence. the extinction-corrected magnitudes of a 0.7 AL. star at a distance of 15 kpe are m,zz22.0. m,c22.2 and m,2 21.5."," Hence, the extinction-corrected magnitudes of a 0.7 $_\odot$ star at a distance of 15 kpc are $m_{_V} \approx 22.9$, $m_{_R} \approx 22.2$ and $m_{_I} \approx 21.7$ ."
+ From the PCA count rates and the distance estimate (5.15 kpc). we obtain an estimate of ~10ores for the X-ray luminosity during ALJD zz24505)9)2451105.," From the PCA count rates and the distance estimate $5 - 15$ kpc), we obtain an estimate of $\sim 1 \times 10^{37}~{\rm erg\,s^{-1}}$ for the X-ray luminosity during MJD $\approx 2450995 - 2451105$."
+ A fraction (OS)(πα) of the N-ravs would intercept the companion star. where [ο is the radius of the companion star and e the orbital separation.," A fraction $(\pi
+R_2^2)/(4 \pi a^2)$ of the X-rays would intercept the companion star, where $R_2$ is the radius of the companion star and $a$ the orbital separation."
+ I£ we substitute the values of {ο and Mo calculated. in. £44. this corresponcls o à fraction of ~3 per cent.," If we substitute the values of $R_2$ and $M_2$ calculated in 4, this corresponds to a fraction of $\sim 3$ per cent."
+" Therefore. energy. will be deposited into the companion star's atmosphere at a rate of 5.LO35eres""."," Therefore, energy will be deposited into the companion star's atmosphere at a rate of $\sim 5 \times
+10^{35}~{\rm erg\,s^{-1}}$."
+ Xn unheated 0.7- M. main-sequence. star as à bolometric luminosity of about 1.1075eres+ and an ellective surface temperature of about 4800 Ix. The intrinsic uminositv of the companion star is therefore much lower han the power of the intercepted X-rays.," An unheated 0.7 $_\odot$ main-sequence star has a bolometric luminosity of about $1 \times 10^{33}~{\rm erg\,s^{-1}}$ and an effective surface temperature of about 4800 K. The intrinsic luminosity of the companion star is therefore much lower than the power of the intercepted X-rays."
+ We suppose that a cquasi-edquilibrium state is set up at the heated surface of the companion star such that the rate of energy. radiated away is the same as the rate of energy. deposited., We suppose that a quasi-equilibrium state is set up at the heated surface of the companion star such that the rate of energy radiated away is the same as the rate of energy deposited.
+ The effective surface temperature of the irraciatively-heatecl atmosphere of the companion star could then reach 20000 Ix. During our observations. the svstem was in the process of returning to its quiescent state.," The effective surface temperature of the irradiatively-heated atmosphere of the companion star could then reach 20000 K. During our observations, the system was in the process of returning to its quiescent state."
+ On August 23. the ASAI count rate had. already dropped to the pre-outburst level (Fig., On August 23 the ASM count rate had already dropped to the pre-outburst level (Fig.
+ 1). which may. be considered. consistent. with zero.," 1), which may be considered consistent with zero."
+ Although the X-ray activity seemed. to have ceased. the accretion disc hack not completely. dissipated. ancl the companion star's atmosphere hack not completely cooled down.," Although the X-ray activity seemed to have ceased, the accretion disc had not completely dissipated, and the companion star's atmosphere had not completely cooled down."
+ Our photometric data obtained on August 19 and 20 show that the minimum brightness in the W-. 2 and {- light-curves was V.2:20.8. 220.5 and {zz20.5.," Our photometric data obtained on August 19 and 20 show that the minimum brightness in the $V$ -, $R$ - and $I$ -band light-curves was $V \approx 20.8$, $R \approx 20.5$ and $I \approx 20.5$."
+ The V-band brightness continued to drop and reached 21.4 mag on August 23., The $V$ -band brightness continued to drop and reached 21.4 mag on August 23.
+ The star was finally not visible in the D-. H- and V-band data that we obtained on August 25 and 26 tthe #-bancl brightness of 21.5 mage on August 26 and 27. Zurita Casares 1998. which would imply a distance of 11 kpc if it is taken as the quicscent brightness of the companion star).," The star was finally not visible in the $B$ -, $R$ - and $V$ -band data that we obtained on August 25 and 26 the $R$ -band brightness of 21.5 mag on August 26 and 27, Zurita Casares 1998, which would imply a distance of $\sim 11$ kpc if it is taken as the quiescent brightness of the companion star)."
+ The optical brightness of RATE 058 was observed to decline at a rate of 0.1 magd+ in carly August (Zurita. Casares Hyvnes 1998).," The optical brightness of RXTE $-$ 058 was observed to decline at a rate of 0.1 ${\rm mag\,d^{-1}}$ in early August (Zurita, Casares Hynes 1998)."
+ We observed a decline rate 0.200+0.001magd in the V-band. brightness between August IS and 20.," We observed a decline rate $0.200 \pm 0.001\,{\rm mag\,d^{-1}}$ in the $V$ -band brightness between August 18 and 20."
+ X decline is also seen in our Z?- and I-band data but at less rapid rates of 0.085+0.002magd and 0.020+0.010magd respectively.," A decline is also seen in our $R$ - and $I$ -band data but at less rapid rates of $0.085 \pm 0.002\,{\rm
+mag\,d^{-1}}$ and $0.020 \pm 0.010\,{\rm mag\,d^{-1}}$ respectively."
+ (X. linear decline in brightness is equivalent to an exponential decline in luminosity., A linear decline in brightness is equivalent to an exponential decline in luminosity.
+ The faster decline in the Y magnitude may indicate the fading or dissipation of the accretion disc (which was bluer than the companion star) after mass transfer ceased. in addition to the cooling of the atmosphere of the companion star.," The faster decline in the $V$ magnitude may indicate the fading or dissipation of the accretion disc (which was bluer than the companion star) after mass transfer ceased, in addition to the cooling of the atmosphere of the companion star."
+ The photometric data also show hints of an ellipsoidal modulation around. phase 0.5. which became more evident in our later observations.," The photometric data also show hints of an ellipsoidal modulation around phase 0.5, which became more evident in our later observations."
+ As we show in Fig., As we show in Fig.
+ 3. the V-band light-curve deviates from a sinusoidal-Iike curve by developing first a Hat top around phase 0.5 on August 18. and then à local minimum on August 20.," 3, the $V$ -band light-curve deviates from a sinusoidal-like curve by developing first a flat top around phase 0.5 on August 18, and then a local minimum on August 20."
+ We attribute the eradual development of the secondary. mininium. at. phase 0.5 to the fading of the accretion disk. which reveals the ellipsoidal modulation of the companion star.," We attribute the gradual development of the secondary minimum at phase 0.5 to the fading of the accretion disk, which reveals the ellipsoidal modulation of the companion star."
+ We carried. out a svnergetic study of the X-ray transient RATE 0585., We carried out a synergetic study of the X-ray transient RXTE $-$ 058.
+ The photometric observations were carried out from 1998 August 14 to 26. when the svstem was in transition from the outburst to the quiescent state.," The photometric observations were carried out from 1998 August 14 to 26, when the system was in transition from the outburst to the quiescent state."
+ data were obtained in the V. 2 and £ bands. which show approximately sinusoidal oscillations with a linear brightness decline when folded: on a period of 0.24821. d. The rate of decline measured from the V brightness during our observations was 0.20040.001magd.+. more rapid than that the rate of 0.085£0.002magd.+ for the & brightness and of 0.020270010magd.+ for the £ brightness.," High-quality data were obtained in the $V$, $R$ and $I$ bands, which show approximately sinusoidal oscillations with a linear brightness decline when folded on a period of 0.24821 d. The rate of decline measured from the $V$ brightness during our observations was $0.200 \pm 0.001\,{\rm mag\,d^{-1}}$, more rapid than that the rate of $0.085 \pm 0.002\,{\rm mag\,d^{-1}}$ for the $R$ brightness and of $0.020 \pm 0.010\,{\rm mag\,d^{-1}}$ for the $I$ brightness."
+ Tho folded light-curves deviate significantly. from a sinusoidal curve around phase 0.5. showing hints of ellipsoidal mocdulations. which tend to become progressively more evident.," The folded light-curves deviate significantly from a sinusoidal curve around phase 0.5, showing hints of ellipsoidal modulations, which tend to become progressively more evident."
+ This sugeests the presence of a fading accretion disc as well as an irraciativelv-heatecd companion star., This suggests the presence of a fading accretion disc as well as an irradiatively-heated companion star.
+ We thank Allvn Tennant. Helen Johnston. Mike Dessell and Peter Wood for discussions. and. Don Melrose. ancl John Greenhill for their commentson the manuscript.," We thank Allyn Tennant, Helen Johnston, Mike Bessell and Peter Wood for discussions, and Don Melrose and John Greenhill for their commentson the manuscript."
+ We also thank John Greenhill and Jorge Casares for their sharing some of the data obtained by the UTas. L-m telescope., We also thank John Greenhill and Jorge Casares for their sharing some of the data obtained by the UTas 1-m telescope.
+ KW acknowledges the support. from the ARC through an Australian Research Fellowship., KW acknowledges the support from the ARC through an Australian Research Fellowship.
+ This work is partially supported by the URC. University of Sydney.," This work is partially supported by the URG, University of Sydney."
+interface fluxes. PF;i.,interface fluxes $F_{i+\frac{1}{2}}$.
+ In general. an initial discontinuity at 7+ due to U; and U;4 will evolve into four piecewise constant states separated by three waves.," In general, an initial discontinuity at $i+\frac{1}{2}$ due to $U_{i}$ and $U_{i+1}$ will evolve into four piecewise constant states separated by three waves."
+" The left-most and waves nav be either shocks or rarefaction waves. while the middle wave is always a contact. discontinuity,"," The left-most and right-most waves may be either shocks or rarefaction waves, while the middle wave is always a contact discontinuity."
+ The determination of these [our piecewise constant states can. in eeneral. be achieved only by iterativelv solving nonlinear equations.," The determination of these four piecewise constant states can, in general, be achieved only by iteratively solving nonlinear equations."
+ Thus (hie computation of the fluxes necessitates a step which can be computationally expensive., Thus the computation of the fluxes necessitates a step which can be computationally expensive.
+ For this reason much attention has been eiven to approximate. but sufficiently accurate. techniques.," For this reason much attention has been given to approximate, but sufficiently accurate, techniques."
+ One notable method is that due to Wartenetal.(1983.IILE).. in which the middle wave. ancl the two constant states that it separates. are replaced by a single piecewise constant state.," One notable method is that due to \citet[HLL]{hlv}, in which the middle wave, and the two constant states that it separates, are replaced by a single piecewise constant state."
+ One benefit of this approximation. which smears the contact discontinuitv somewhat. is io eliminate the iterative step. (hus sienilicantlv improving efficiency.," One benefit of this approximation, which smears the contact discontinuity somewhat, is to eliminate the iterative step, thus significantly improving efficiency."
+ However. the IILL method requires accurate estimates of the wave speeds for the left- and right-moving waves.," However, the HLL method requires accurate estimates of the wave speeds for the left- and right-moving waves."
+ EFinfeldt(1988). analvzed the HLL method and found good estimates for the wave speeds., \citet{ein} analyzed the HLL method and found good estimates for the wave speeds.
+ The resulting method combining the original ILL method with Einfeldts improvements (the IILLE method). has been taken as a starting point for our simulations.," The resulting method combining the original HLL method with Einfeldt's improvements (the HLLE method), has been taken as a starting point for our simulations."
+ In our implementation we use wave speed estimates based on a simple application of the relativistic addition of velocities formula for the individual components of the velocities. and the relativistic sound speed ο. assuming that the waves can be decomposed into components moving perpendicular io the three coordinate directions.," In our implementation we use wave speed estimates based on a simple application of the relativistic addition of velocities formula for the individual components of the velocities, and the relativistic sound speed $c_s$, assuming that the waves can be decomposed into components moving perpendicular to the three coordinate directions."
+" In order to compute the pressure p and sound speed c; we need (he rest. [rame mass density » and energy density ο,", In order to compute the pressure $p$ and sound speed $c_s$ we need the rest frame mass density $n$ and energy density $e$.
+ However. these quantiües are nonlinearly coupled to the components of the velocity as well as to the laboratory [rame variables via (he Lorentz transformation: where >=(1—07)LV? is the Lorentz factor and (?=(07)?+(09)?(i)?.," However, these quantities are nonlinearly coupled to the components of the velocity as well as to the laboratory frame variables via the Lorentz transformation: where $\gamma = ( 1 - v^2 )^{-1/2}$ is the Lorentz factor and $v^2 =
+(v^{x})^2 + (v^{y})^2 + (v^{z})^2$."
+ Whenthe acdiabaticindex is constant it is possible to reduce (he computation of n. e. οὖν e aad e to," Whenthe adiabaticindex is constant it is possible to reduce the computation of $n$ ,$e$ , $v^{x}$ , $v^{y}$ and $v^{z}$ to"
+configurations that are unlikely to occur in the negative specific heat branch are those with very negative values of TT.,configurations that are unlikely to occur in the negative specific heat branch are those with very negative values of $W_*$.
+ Since the absolute value of TT. depends on the Inverse separation between particles. such configurations will have particles that are very close to cach other. aud therefore are likely to be uustable to mergers.," Since the absolute value of $W_*$ depends on the inverse separation between particles, such configurations will have particles that are very close to each other, and therefore are likely to be unstable to mergers."
+ Together with the roughly 20% statistical variation over time of c about c. any configuration with a value of c iu the negative specific heat brauch may be a chance configuration of a cluster that has a negative specific heat.," Together with the roughly $20\%$ statistical variation over time of $\psi$ about $\overline{\psi}$, any configuration with a value of $\psi$ in the negative specific heat branch may be a chance configuration of a cluster that has a negative specific heat."
+ Since the 6.N-dimeusional phase space configuration of subcelusters im a cell is directly related to tlic cells potential aud kinetic euereies aud thus its virial ratio. we cau use the theory to study the internal structure and shapes within a cell.," Since the $6N$ -dimensional phase space configuration of subclusters in a cell is directly related to the cell's potential and kinetic energies and thus its virial ratio, we can use the theory to study the internal structure and shapes within a cell."
+ To do this. we relate the euergey calculated froii the observed iustautauceous pliase space configuration to the ensemble average euereics in quasi-equilibriuni," To do this, we relate the energy calculated from the observed instantaneous phase space configuration to the ensemble average energies in quasi-equilibrium."
+ This hiehlliehts the fact that chisters of ealaxics are not iu strict equilibrimm and hence their poteutial and kinetic cuergies fluctuate about the eusenible average cnerey., This highlights the fact that clusters of galaxies are not in strict equilibrium and hence their potential and kinetic energies fluctuate about the ensemble average energy.
+ The spatial configurations of clusters change as a result of these fluctuations., The spatial configurations of clusters change as a result of these fluctuations.
+ Because the average thermocdvuamic quantities of an eusenible of cells iu quasiequilibriuumi change very slowly compared to the ανασα timescale of a single cell. the quasi-equilibriuim energies are approximately time averages.," Because the average thermodynamic quantities of an ensemble of cells in quasi-equilibrium change very slowly compared to the dynamical timescale of a single cell, the quasi-equilibrium energies are approximately time averages."
+ We use the spectrum of fluctuations to determine the probability that a cell may have a particular mstantaneous virial ratio., We use the spectrum of fluctuations to determine the probability that a cell may have a particular instantaneous virial ratio.
+ This is a uccessary but not sufficient coudition for a cell to lave a given configuration., This is a necessary but not sufficient condition for a cell to have a given configuration.
+ To compare different coufigurationus. we therefore compare the probability that a cell has a virial ratio which could eive rise to a given configuration.," To compare different configurations, we therefore compare the probability that a cell has a virial ratio which could give rise to a given configuration."
+ Based on the range of fluctuations in virial ratio observed in N-body simulations by Aarsetl&Saslaw (1972). we conclude that cells that have a ποσανο specific leat may have almost anv spatial configuration.," Based on the range of fluctuations in virial ratio observed in $N$ -body simulations by \citet{1972ApJ...172...17A}, we conclude that cells that have a negative specific heat may have almost any spatial configuration."
+ These configurations are likely to be chance configurations of fuctuating cells that are nearly vinalized., These configurations are likely to be chance configurations of fluctuating cells that are nearly virialized.
+ Cells with positive specific heat have a rauge of eucreies corresponding to fewer spatial configurations., Cells with positive specific heat have a range of energies corresponding to fewer spatial configurations.
+ Iu our comparisons between line aud rug configurations. the probability that a cell will have a line coufiguration rather than a ring configuration varies depending ou the clustering parameter 6 and the nuuber JN of subclusters in the cell.," In our comparisons between line and ring configurations, the probability that a cell will have a line configuration rather than a ring configuration varies depending on the clustering parameter $b$ and the number $N$ of subclusters in the cell."
+ Therefore we prescut the following procedure for comparing the shapes of two clusters: The first step is to define a region of space that covers the cluster., Therefore we present the following procedure for comparing the shapes of two clusters: The first step is to define a region of space that covers the cluster.
+ The size aud shape of this region of space define the cell size., The size and shape of this region of space define the cell size.
+ Within the cell. identity the subelusters whose masses are within an order of niaenitude of the largest subchister.," Within the cell, identify the subclusters whose masses are within an order of magnitude of the largest subcluster."
+ The positions of these subclusters aro directly related to the scaled potential energy Ws of the claster., The positions of these subclusters are directly related to the scaled potential energy $W_*$ of the cluster.
+ Frou the observed W. or the peculiar velocity information. estimate the virial ratio c.," From the observed $W_*$ or the peculiar velocity information, estimate the virial ratio $\psi$."
+ The next step is to use the cell size to calculate the ΠΟ aud variance of the counts-in-cclls distribution of similarly-sized subclusters for a larger saurple to obtain the clustering parameter b (e.g. Sivakotf&Saslaw2005:Yaug&Saslaw 2011)).," The next step is to use the cell size to calculate the mean and variance of the counts-in-cells distribution of similarly-sized subclusters for a larger sample to obtain the clustering parameter $b$ (e.g. \citealt{2005ApJ...626..795S,2011ApJ...729..123Y}) )."
+ Then using the observed paramcters c and b. calculate the probability of finding a cell with a similar virial ratio using equation(78).," Then using the observed parameters $\psi$ and $b$, calculate the probability of finding a cell with a similar virial ratio using equation."
+. This probability should then be compared to a reference cell that has a different structure to deteriuiue the relative probabilities of different configurations., This probability should then be compared to a reference cell that has a different structure to determine the relative probabilities of different configurations.
+ Although the configurations that we use here are highly idealized. our comparison of a line aud a ring configuration is generallv consistent with observations of the cosmic web.," Although the configurations that we use here are highly idealized, our comparison of a line and a ring configuration is generally consistent with observations of the cosmic web."
+ This simple test of our theory gives a reasonable result., This simple test of our theory gives a reasonable result.
+ We intend to make more detailed comparisons with observations and more realistic cases which may include dark matter in a forthcoming paper., We intend to make more detailed comparisons with observations and more realistic cases which may include dark matter in a forthcoming paper.
+ We wish to acknowledge the preliminary work of Chuah Boon Leng who helped explore some of the concepts discussed in this paper., We wish to acknowledge the preliminary work of Chuah Boon Leng who helped explore some of the concepts discussed in this paper.
+ We also wish to thank Phil Chan and Bernard Leong for many helpful discussions on this topic., We also wish to thank Phil Chan and Bernard Leong for many helpful discussions on this topic.
+ To illustrate the effect of having multiple mass compouents iu a cluster. we consider the case where a cluster has two populations of subclusters.," To illustrate the effect of having multiple mass components in a cluster, we consider the case where a cluster has two populations of subclusters."
+ For simplicity. we assume that these subclusters are poiut masses. and the masses of cach subchister are iy and ie with 227ny for subchisters iu each population.," For simplicity, we assume that these subclusters are point masses, and the masses of each subcluster are $m_1$ and $m_2$ with $m_2 > m_1$ for subclusters in each population."
+ Iu such a cluster. we can consider the interactions of particles from each population such that the total potential of the cluster is (c.f.," In such a cluster, we can consider the interactions of particles from each population such that the total potential of the cluster is (c.f."
+ Equation 503) where the superscripts denote members of the different populations. aud x denotes position.," Equation \ref{eq-PEBinary}) ) where the superscripts denote members of the different populations, and $\mathbf{x}$ denotes position."
+ The three terms iu equation come from considering each mass component as a separate system. and adding their mutual iuteractious.," The three terms in equation come from considering each mass component as a separate system, and adding their mutual interactions."
+ Therefore. equation is similar in form to equation(50).. even though we do not place any constraints on tle positions of mdividual particles.," Therefore, equation is similar in form to equation, even though we do not place any constraints on the positions of individual particles."
+ We can take the average of the sums in equation such that where Ny aud No are the mumbers of particles in cach population. and (1/7515 is the average inverse separation between members of population 1.," We can take the average of the sums in equation such that where $N_1$ and $N_2$ are the numbers of particles in each population, and $\langle 1/r^{(1)} \rangle$ is the average inverse separation between members of population 1."
+ Iu the case where both populations are similarly distributed throughout the cell. the," In the case where both populations are similarly distributed throughout the cell, the"
+"Each of our hierarchical models shows a very wide range of extinction optical depths }} and scattering (7,4)) when the nebula is viewed from various directions.",Each of our hierarchical models shows a very wide range of extinction optical depths ) and scattering ) when the nebula is viewed from various directions.
+ The ancl Observed for a reflection nebula represent a view of the dust [rom one direction., The and observed for a reflection nebula represent a view of the dust from one direction.
+ There is a very wide range of optical properties (à.g) that can [it a given observation.," There is a very wide range of optical properties $a,\,g$ ) that can fit a given observation."
+ Will one or more hierarchical models we can fit the best observed UV reflection nebula.7023.. with albedos > 0.5 over the range of g thal we tested (0.6 /— 0.85) and with a variety of averaged optical depths through the mocel.," With one or more hierarchical models we can fit the best observed UV reflection nebula, with albedos $\ge$ 0.5 over the range of $g$ that we tested (0.6 – 0.85) and with a variety of averaged optical depths through the model."
+ In general. reflection nebulae have substantial optical depths ~ 1—3) otherwise. the scattered Iuxes are too faint.," In general, reflection nebulae have substantial optical depths $\sim1-3$ ); otherwise, the scattered fluxes are too faint."
+ At substantial optical depths. uniform models ean underestimate the albedo rather severely because they overestimate the scattered light.," At substantial optical depths, uniform models can underestimate the albedo rather severely because they overestimate the scattered light."
+ Unless the star happens to be embedded within a dense clump. radiation can leak oul of hierarchical clumps much more easily than from uniform dust.," Unless the star happens to be embedded within a dense clump, radiation can leak out of hierarchical clumps much more easily than from uniform dust."
+ The Diffuse Galactic Light (DGL) has been interpreted (IIenry. 2002) with a recipe that predicts much more scattering Irom each star than our models. resulting in a low estimates ol the UV albedo.," The Diffuse Galactic Light (DGL) has been interpreted (Henry 2002) with a recipe that predicts much more scattering from each star than our models, resulting in a low estimates of the UV albedo."
+ Murthy et al. (, Murthy et al. (
+1991) failed to detect UV. DGL. but our fractal models olten have many directions from whieh the star and scattered light are very faint.,"1991) failed to detect UV DGL, but our fractal models often have many directions from which the star and scattered light are very faint."
+ Thus. we do not believe that the faintness of the DGL in particular directions necessarily signifies a low albedo.," Thus, we do not believe that the faintness of the DGL in particular directions necessarily signifies a low albedo."
+ The determination of both @ and g depends upon the variation of reflected intensity across the face of a centrally illuminated reflection nebula. while we have only considered the [αν of the seattered light.," The determination of both $a$ and $g$ depends upon the variation of reflected intensity across the face of a centrally illuminated reflection nebula, while we have only considered the flux of the scattered light."
+ We feel that if the flux is as weakly constrained as our models show. (he intensity will be similarly subject to variation because of the unknown placement of the star relative to the surrounding dust.," We feel that if the flux is as weakly constrained as our models show, the intensity will be similarly subject to variation because of the unknown placement of the star relative to the surrounding dust."
+ Even the relative variation of albedo with wavelength is difficult to determine from reflection nebulae if there are significant changes in opacitv among the waveleneths., Even the relative variation of albedo with wavelength is difficult to determine from reflection nebulae if there are significant changes in opacity among the wavelengths.
+ The problem is that Che geometry is not really the same when the opacity changes., The problem is that the geometry is not really the same when the opacity changes.
+ As opacity per IL atom increases. opticallv thin chunps become thick and scatter light with a different eeonmeltrical arrangement. so the geometry of the nebula depends on wavelength.," As opacity per H atom increases, optically thin clumps become thick and scatter light with a different geometrical arrangement, so the geometry of the nebula depends on wavelength."
+ Our overall assessment is that the optical properties of grains are probably as well constrained by (heorv as by observations., Our overall assessment is that the optical properties of grains are probably as well constrained by theory as by observations.
+ This statement is made in spite of well-known uncertainties in the theory of interstellar grains., This statement is made in spite of well-known uncertainties in the theory of interstellar grains.
+ These uncertainties are major: whether (vpical large grains are chemically homogeneous (e.g.. silicate or carbonaceous) or composite. whether grains contain voids. or if grains have very loose (“fractal”) structure.," These uncertainties are major: whether typical large grains are chemically homogeneous (e.g., silicate or carbonaceous) or composite, whether grains contain voids, or if grains have very loose (“fractal”) structure."
+ However. theory does not permit the large range of possible albedos provided bv reflection nebulae.," However, theory does not permit the large range of possible albedos provided by reflection nebulae."
+ Al fist glance. various theories seem quite different.," At first glance, various theories seem quite different."
+ Weingartner Draine (2001) have, Weingartner Draine (2001) have
+The VVDS-Deep sample is magnitude limited in the Iap band with 17.5€Ine<24 and covers an area of 0.49 deg? without any color or shape restrictions imposed.,"The VVDS-Deep sample is magnitude limited in the $I_{AB}$ band with $17.5 \le I_{AB} \le 
+ 24$ and covers an area of 0.49 $deg^2$ without any color or shape restrictions imposed."
+" ''he spectroscopic observations were taken with the Visible Multiple-Object Spectrograph (VIMOS, Le Févvre et al."," The spectroscopic observations were taken with the Visible Multiple-Object Spectrograph (VIMOS, Le Fèvvre et al."
+" 2003) at the ESO VLT, whereas the Virmos Deep Imaging survey (VDIS) BVRI photometric data (LeFévreetal.2004) was obtained with the wide field 12k mosaic camera at the CFHT (Canada-France-Hawaii telescope) and is complete and free from surface brightness selection effects (McCrackenetal.2003)."," 2003) at the ESO VLT, whereas the Virmos Deep Imaging survey (VDIS) BVRI photometric data \citep{lef04} was obtained with the wide field 12k mosaic camera at the CFHT (Canada-France-Hawaii telescope) and is complete and free from surface brightness selection effects \citep{mcc03}."
+". 'The sample contains 6582 galaxies with secure redshifts, ie. known at a confidence level >80%."," The sample contains 6582 galaxies with secure redshifts, i.e. known at a confidence level $\ge 80 \%$."
+ These galaxies have a mean redshift of z = 0.83., These galaxies have a mean redshift of z $\approx$ 0.83.
+ Fig., Fig.
+" 1 shows the absolute magnitude of these galaxies as a function of redshift alongwith the different luminosity-threshold subsamples selected, where the luminosity threshold is assumed to evolve according to the relation Mp(z)=—1.15z+Mp(z0)."," \ref{FigMvsZ} shows the absolute magnitude of these galaxies as a function of redshift alongwith the different luminosity-threshold subsamples selected, where the luminosity threshold is assumed to evolve according to the relation $M_B(z)
+ = -1.15z + M_B(z=0)$."
+" The factor of ’-1.15’ arises from the redshift evolution of the characteristic absolute magnitude, Mg, of galaxies as measured in the luminosity function."," The factor of '-1.15' arises from the redshift evolution of the characteristic absolute magnitude, $M_B^*$, of galaxies as measured in the luminosity function."
+ This value has been determined using the luminosity function measurements obtained within the same sample by Ilbert et al. (, This value has been determined using the luminosity function measurements obtained within the same sample by Ilbert et al. (
+2005).,2005).
+" An evolving luminosity threshold needs to be taken into consideration when comparing samples at different epochs, as it provides us with statistically similar samples at different redshifts, having similar evolved luminosities."," An evolving luminosity threshold needs to be taken into consideration when comparing samples at different epochs, as it provides us with statistically similar samples at different redshifts, having similar evolved luminosities."
+" Assuming that the global evolution of galaxies has as a main consequence to increase the global luminosity of galaxies, we follow the evolution of galaxies with similar properties on average."," Assuming that the global evolution of galaxies has as a main consequence to increase the global luminosity of galaxies, we follow the evolution of galaxies with similar properties on average."
+ This falls within the boundaries of standard practice of galaxy evolution studies., This falls within the boundaries of standard practice of galaxy evolution studies.
+" As our subsamples are nearly volume complete, and as we are using all types of galaxies together, we may follow the global increase in the halo mass of an average galaxy."," As our subsamples are nearly volume complete, and as we are using all types of galaxies together, we may follow the global increase in the halo mass of an average galaxy."
+" However, we do recognize that this way of selecting galaxies does not garantee to follow the exact same population with cosmic time."," However, we do recognize that this way of selecting galaxies does not garantee to follow the exact same population with cosmic time."
+" Unfortunately, there is no single prescription enabling to tag galaxies and exactly follow their precursors / descendants."," Unfortunately, there is no single prescription enabling to tag galaxies and exactly follow their precursors / descendants."
+" Indeed, if this were possible it would be the solution to galaxy evolution."," Indeed, if this were possible it would be the solution to galaxy evolution."
+" To try to quantify the impact of our selection on the average halo mass, we have used the Millennium simulation."," To try to quantify the impact of our selection on the average halo mass, we have used the Millennium simulation."
+ This will be further discussed in the next section., This will be further discussed in the next section.
+" Samples using a similar type of selection, i.e. using ]uminosity thresholds, have been extensively studied within a theoretical framework (Zehavietal.2005;Coil2006;Conroyetal.2006;Zheng 2007)."," Samples using a similar type of selection, i.e. using luminosity thresholds, have been extensively studied within a theoretical framework \citep{zeh05, coi06, con06, zhe07}."
+". The corresponding HOD parametrisation requires fewer parameters to be fitted as compared to differential, luminosity binned samples."," The corresponding HOD parametrisation requires fewer parameters to be fitted as compared to differential, luminosity binned samples."
+" However, this means that one is biased towards increasingly brighter galaxies at higher redshifts, simply due to the fact that the sample is selected in apparent magnitude."," However, this means that one is biased towards increasingly brighter galaxies at higher redshifts, simply due to the fact that the sample is selected in apparent magnitude."
+" As can be seen in Fig. 1,"," As can be seen in Fig. \ref{FigMvsZ},"
+ there is a change of about 5 in the B-band absolute magnitude over the redshift, there is a change of about 5 in the B-band absolute magnitude over the redshift
+ü The search for extrasolar planets has garnered enormous attention in recent vears. due primarily to the successtul Huplementation of radial velocity searches (Alavor& 1995.. Marev&Butler 1996)).," The search for extrasolar planets has garnered enormous attention in recent years, due primarily to the successful implementation of radial velocity searches \cite{mandq1995}, \cite{mandb1996}) )."
+ These searches have led to the discovery of a population of massive. close-in planets with orbital separations of e<0.1AU.," These searches have led to the discovery of a population of massive, close-in planets with orbital separations of $a \la 0.1~\au$."
+ Recently. it was discovered that one such planet. the companion to IID 209158. also trausits its parent star (Clarbouneauetal. 2000: Παινetal. 2000)). vielding a measurement of the lass. radius. aud deusitv of the companion.," Recently, it was discovered that one such planet, the companion to HD 209458, also transits its parent star \cite{charbon2000}; \cite{henry2000}) ), yielding a measurement of the mass, radius, and density of the companion."
+ Clearly. transit observations can be used to extract additional information about known companions.," Clearly, transit observations can be used to extract additional information about known companions."
+ Thediscovery of an extrasolar —planet using transits. however. has remained elusive.," The of an extrasolar planet using transits, however, has remained elusive."
+ There are two primary difficultics with detecting plauets with trausits., There are two primary difficulties with detecting planets with transits.
+" First. the photometric requireiieuts are quite stringent: a planct of radius. fh,Ry (ποσο Ry isthe radius of Jupiter) transiting an primary of radius AH.=HR. would produce a fractional deviation of z1% during the course of the transit."," First, the photometric requirements are quite stringent: a planet of radius $\rp\le\rjup$ (where $\rjup$ isthe radius of Jupiter) transiting an primary of radius $\rs=\rsun$ would produce a fractional deviation of $\la 1\%$ during the course of the transit."
+ Second. the probability that a planet will trausit its parent is small: for a planet with separation z0.05AU orbiting a star with AR.=R.. the probability is <10.," Second, the probability that a planet will transit its parent is small: for a planet with separation $\ge 0.05~\au$ orbiting a star with $\rs=\rsun$, the probability is $\la 10\%$."
+ Several methods for dealing will the small probability have been proposed., Several methods for dealing will the small probability have been proposed.
+ For instance. one can monitor eclipsing binary stars. where the orbital plane is known to be (nearly) perpendicular to the sky (Deceetal. 1998)).," For instance, one can monitor eclipsing binary stars, where the orbital plane is known to be (nearly) perpendicular to the sky \cite{deeg}) )."
+ Another wav of overcoming this small probability is to siuplv mouitor many stars sinultaneouslv., Another way of overcoming this small probability is to simply monitor many stars simultaneously.
+ This can be doue by euiploviug a camera with a laree field-of-view. or by inonitoring very deuse stellar fields.," This can be done by employing a camera with a large field-of-view, or by monitoring very dense stellar fields."
+ Were I focus on the latter possibility., Here I focus on the latter possibility.
+ Specifically I determine the uuuber of planets that imieht be detected in a campaign monitorine stars toward the Galactic bulee., Specifically I determine the number of planets that might be detected in a campaign monitoring stars toward the Galactic bulge.
+" The dux of a star beiug occulted by a plauct is given by. where Fy is the unocculted flux of the star. Fy, is the total flux from auv unrelated sources. aud ó(£) is the fractional deviation of the flux due to the transit. which depends on the radius of the plauct relative to the star. the inclination angle. 7. aud the lamh-darkening of the star (Sackett 1999))."," The flux of a star being occulted by a planet is given by, where $F_0$ is the unocculted flux of the star, $F_b$ is the total flux from any unrelated sources, and $\delta(t)$ is the fractional deviation of the flux due to the transit, which depends on the radius of the planet relative to the star, the inclination angle, $i$, and the limb-darkening of the star \cite{sackett1999}) )."
+" For a small planet «f.) aud no liuib-darkeniug. ó=(RV/Rοι.r)Lwhere(74, O7) is the step functiou. and 7 is à normalized tine. 7=(f.ty)/fr."," For a small planet $\rp \ll \rs$ ) and no limb-darkening, $\delta=(\rp/\rs)^2\Theta(1-\tau)$, where $\Theta(x)$ is the step function, and $\tau$ is a normalized time, $\tau \equiv {({ t-t_0}) / \tt}$."
+" Tere fy is the time of the midpoint of the transit. aud fT is one-half the transit duration. which for circular orbits 15. Tu reality. 6 depends very scusitively on 74, aud cosi. and less so on the liiib-darkeniug."," Here $t_0$ is the time of the midpoint of the transit, and $\tt$ is one-half the transit duration, which for circular orbits is, In reality, $\delta$ depends very sensitively on $\rp$ and $\ci$, and less so on the limb-darkening."
+ I will therefore use the explicit form for ó eiven iu Sackett (1999). but πιο uo Iuub-darkening.," I will therefore use the explicit form for $\delta$ given in Sackett (1999), but assume no limb-darkening."
+" Since the proposed search for plauets will be carried out iu dense stellar fields. and transits produce time-dependent varlatious in the flux of the stars. the data will likely be reduced with inage-ubtraction techniques (Tomancy&Crotts 1996.. Alard&Lupton 0051),"," Since the proposed search for planets will be carried out in dense stellar fields, and transits produce time-dependent variations in the flux of the stars, the data will likely be reduced with image-subtraction techniques \cite{tandc1996}, , \cite{andlup1998}) )."
+ With imaee-subtraction. oue mcasures only the time variable portion of the 8ux. F(t)=Fy|étt)].," With image-subtraction, one measures only the time variable portion of the flux, ${\tilde F(t)}=F_0[\delta(t)]$."
+ There are three requirements to detect a plauet of separation e aud radius Πρ around a star of mass M. radius ΠΠ. aud flux Fy.," There are three requirements to detect a planet of separation $a$ and radius $\rp$ around a star of mass $M$, radius $\rs$ and flux $F_0$ ."
+ These are: (1) the planet must transit the star. (2) at least two transits nist occur duiug the time when observations are made. aud(3) the transit must cause a detectable deviation in the lieht curve.," These are: (1) the planet must transit the star, (2) at least two transits must occur during the time when observations are made, and(3) the transit must cause a detectable deviation in the light curve."
+ If the, If the
+outo massive syste.,onto massive systems.
+ Timing our attention to the evolution of the maxima stellar mass. as shown iu the bottom panels. similar treuds are apparent.," Turning our attention to the evolution of the maximum stellar mass, as shown in the bottom panels, similar trends are apparent."
+ While the maxiuun mass in the cooling moclel iucreases monotonically. the ACN feedback model is divided iuto two regions: oue at high redshift in which the maxim stellar mass mereases aloug with the nonlinear lass scale. and one at low redshift in which the maxi stellar mass stays fixed as the scale at which new ealaxics are formuug becomes snaller.," While the maximum mass in the cooling model increases monotonically, the AGN feedback model is divided into two regions: one at high redshift in which the maximum stellar mass increases along with the nonlinear mass scale, and one at low redshift in which the maximum stellar mass stays fixed as the scale at which new galaxies are forming becomes smaller."
+ The general properties of cooling aud ACN feedback iodels are sununuarized iu Table 1., The general properties of cooling and AGN feedback models are summarized in Table 1.
+" Finally, we poiut out that not only the temporal. but thespatial distribution of AGN in our feedback model is suggestive of recent observations."," Finally, we point out that not only the temporal, but the distribution of AGN in our feedback model is suggestive of recent observations."
+ Usiug over 20.000 ealaxies from the 2dF QSO Redshift Survey. Croom (2005) have studied the spatial clustering of QSOs near the characteristic scale in the optical Iuninositv function.," Using over 20,000 galaxies from the 2dF QSO Redshift Survey, Croom (2005) have studied the spatial clustering of QSOs near the characteristic scale in the optical luminosity function."
+" ""They measure bias values which. when converted iuto (+) values using standard expressious (Mo White 1996). evolve frou 2.5characte0.9 at 2=2.18 clown to 1.1€0.2 at dowusizine=0.56.The ristic scale of low-redshift Αν is from the rarest to the most. common objects. spreading the heated eas that extinguishes the formation of galaxies to this dax."," They measure bias values which, when converted into $\nu(z)$ values using standard expressions (Mo White 1996), evolve from $2.5 \pm 0.2$ at $z=2.48$ down to $1.1 \pm 0.2$ at $z=0.56.$ The characteristic scale of low-redshift AGN is downsizing from the rarest to the most common objects, spreading the heated gas that extinguishes the formation of galaxies to this day."
+ We thank Biman Nath. Chis Reynolds. and Toimasso Treu for helpful comments.," We thank Biman Nath, Chris Reynolds, and Tomasso Treu for helpful comments."
+ This work was initiated duriug a visit bv JS to the KITP as part of the Galaxs-ICM Tuteractious Program., This work was initiated during a visit by JS to the KITP as part of the Galaxy-IGM Interactions Program.
+ ES was supported by the NSF under erant PITY99-07919., ES was supported by the NSF under grant PHY99-07949.
+"The minimum photon energy needed to produce muons with energy E, in the atmosphere is E75,~10xΕμ.",The minimum photon energy needed to produce muons with energy $E_{\mu}$ in the atmosphere is $E_{\gamma th} \sim 10 \times E_{\mu}$.
+" In the Tupi experiment the muon energy threshold is estimated as Ej,~0.1GeV.", In the Tupi experiment the muon energy threshold is estimated as $E_{\mu} \sim 0.1GeV$.
+" It means that the minimum proton energy is Ez,~1.0GeV.", It means that the minimum proton energy is $E_{\gamma th} \sim 1.0GeV$.
+" However, Monte Carlo results Porieretal.(2002) showed that an effective photon energy threshold for muon production in the atmosphere is E44,~10GeV (see Fig. 5))."," However, Monte Carlo results \cite{poirier02} showed that an effective photon energy threshold for muon production in the atmosphere is $E_{\gamma th}\sim 10 GeV$ (see Fig. \ref{fig5}) )."
+" The specific yield function, i.e. the number of muons at sea level per photon, as a function of photon energy near the vertical direction, is determined according to the FLUKA Monte Carlos results Porieretal.(2002)."," The specific yield function, i.e. the number of muons at sea level per photon, as a function of photon energy near the vertical direction, is determined according to the FLUKA Monte Carlos results \cite{poirier02}."
+". This FLUKA result can be described by the following fit Ay=(6.16==0.60)x1075, y=1.183+0.014, Eo=7.13+0.56 GeV, A=1.5840.12."," This FLUKA result can be described by the following fit where $A_\mu = (6.16 \pm 0.60) \times 10^{-5}$, $\nu=1.183 \pm 0.014$, $E_0=7.13 \pm 0.56$ GeV, $\lambda=1.58 \pm
+0.12$."
+" We whereassumed that at the top of the atmosphere the energy spectrum of the arrived photons (from GRB) with E.> 10GeV) can be expressed by a single power law function The total number of muons with energies above Εμ covering an effective area Serf at the sea level, during time T, is a convolution between Eq.2 (or Eq.3) and Eq.4,"," We assumed that at the top of the atmosphere the energy spectrum of the arrived photons (from GRB) with $E_{\gamma}\geq 10GeV$ ) can be expressed by a single power law function The total number of muons with energies above $E_{\mu}$ covering an effective area $S_{eff}$ at the sea level, during time T, is a convolution between Eq.2 (or Eq.3) and Eq.4,"
+"by the Chandra observatory, and computed the frequency band-averaged SZ flux decrement in the frequency interval [86 GHz, 94 GHz].","by the Chandra observatory, and computed the frequency band-averaged SZ flux decrement in the frequency interval [86 GHz, 94 GHz]."
+ The ALMA telescope will observe at a frequency 90 GHz with higher sensitivity and resolution than that of the GBT; comparison the sensitivity of the GBT with the ALMA telescope has already been, The ALMA telescope will observe at a frequency 90 GHz with higher sensitivity and resolution than that of the GBT; comparison the sensitivity of the GBT with the ALMA telescope has already been.
+ In Fig., In Fig.
+" [I] we show thestudied]. dependence of the generalized spectral function G(x,T.) at a frequency 90 GHz (x=1.59), derived from Eq. (5))"," \ref{Fig90} we show the dependence of the generalized spectral function $G(x, T_{\mathrm{e}})$ at a frequency 90 GHz (x=1.59), derived from Eq. \ref{G}) )"
+ on temperature., on temperature.
+ We find that the absolute value of the generalized spectral function at a frequency 90 GHz significantly (and monotonically) decreases with electron temperature., We find that the absolute value of the generalized spectral function at a frequency 90 GHz significantly (and monotonically) decreases with electron temperature.
+ The Kompaneets approximation is valid when the change of a photon frequency due to Compton scattering is much smaller than an initial photon frequency Av/v«1., The Kompaneets approximation is valid when the change of a photon frequency due to Compton scattering is much smaller than an initial photon frequency $\Delta\nu/\nu\ll1$.
+" Since the average photon frequency change per inverse Compton scattering equals Av/v=4kyT./(m.c?) (for non-relativistic electrons, see, e. g., Rybicki Lightman 1979), the Kompaneets approximation is invalid when kyT,=(mec?)/4, i.e. when kyT,~128keV."," Since the average photon frequency change per inverse Compton scattering equals $\Delta\nu/\nu=4k_{\mathrm{b}} T_{\mathrm{e}}/(m_{\mathrm{e}}
+c^2)$ (for non-relativistic electrons, see, e. g., Rybicki Lightman 1979), the Kompaneets approximation is invalid when $k_{\mathrm{b}} T_{\mathrm{e}}\simeq (m_{\mathrm{e}}c^2)/4$, i.e. when $k_{\mathrm{b}} T_{\mathrm{e}}\simeq 128 \mathrm{keV}$."
+" Thus, strong deviations from the intensity value (and from the spectral function value of g(1.59)& —3.28) derived in the Kompaneets approximation arise at high temperatures."," Thus, strong deviations from the intensity value (and from the spectral function value of $g(1.59)\approx-3.28$ ) derived in the Kompaneets approximation arise at high temperatures."
+" The given estimate of the regime of breakdown of the Kompaneets approximation is an approximation and significant deviations (although not of order unity) take place at much lower temperatures, even at 30 keV (e.g. Fabbri 1981)."," The given estimate of the regime of breakdown of the Kompaneets approximation is an approximation and significant deviations (although not of order unity) take place at much lower temperatures, even at 30 keV (e.g. Fabbri 1981)."
+" An interesting feature of the SZ effect is that at frequency 217 GHz (x=3.83) where the SZ effect in the framework of the Kompaneets approximation is zero, the SZ effect from an AGN cocoon is dominated by the high temperature electron component (Τε>10° K)."," An interesting feature of the SZ effect is that at frequency 217 GHz (x=3.83) where the SZ effect in the framework of the Kompaneets approximation is zero, the SZ effect from an AGN cocoon is dominated by the high temperature electron component $T_{\mathrm{e}}\gg 10^8$ K)."
+" Therefore, the SZ effect at frequency 217 GHz is an interesting tool for analyzing the hot electron component in AGN cocoons."," Therefore, the SZ effect at frequency 217 GHz is an interesting tool for analyzing the hot electron component in AGN cocoons."
+ Note that Colafrancesco (2005) has considered a measurement of the SZ effect at a frequency 217 GHz to analyze a non-thermal electron component in radio lobes., Note that Colafrancesco (2005) has considered a measurement of the SZ effect at a frequency 217 GHz to analyze a non-thermal electron component in radio lobes.
+" Since the value of G(3.83,Τε) is small when the temperature is either much lower than 10? K or higher than 1010 K, we conclude that this function should have an absolute maximum at an intermediate temperature."," Since the value of $G(3.83,
+T_{\mathrm{e}})$ is small when the temperature is either much lower than $10^{8}$ K or higher than $10^{10}$ K, we conclude that this function should have an absolute maximum at an intermediate temperature."
+" Dependence of the generalized spectral function G(x,Τε) at a frequency 217 GHz (x=3.83) on temperature derived from Eq. (6))"," Dependence of the generalized spectral function $G(x,
+T_{\mathrm{e}})$ at a frequency 217 GHz (x=3.83) on temperature derived from Eq. \ref{G}) )"
+ is shown in Fig. D]., is shown in Fig. \ref{Fig217}.
+" The extremum of a curve G(3.83,Το) is at a temperature T,~160 keV (51.9x10? K) which is in the temperature range found from numerical simulations of cocoons."," The extremum of a curve $G(3.83, T_{\mathrm{e}})$ is at a temperature $T_{\mathrm{e}}\approx 160$ keV $\approx 1.9\times10^9$ K) which is in the temperature range found from numerical simulations of cocoons."
+ Therefore analysis of the SZ effect at this frequency should be a promising way of demonstrating the existence of an electron component at high temperature., Therefore analysis of the SZ effect at this frequency should be a promising way of demonstrating the existence of an electron component at high temperature.
+ Note that combined generalized functions defined in Sect., Note that combined generalized functions defined in Sect.
+ 2.2 are also shown in Fig. D]., 2.2 are also shown in Fig. \ref{Fig217}.
+ Measurements at the frequency of 217 GHz are sensitive to the spectral response of the detectors., Measurements at the frequency of 217 GHz are sensitive to the spectral response of the detectors.
+ In Appendix B we show how the broad detector spectral response impacts on the possibility of an analysis of high temperature plasmas., In Appendix B we show how the broad detector spectral response impacts on the possibility of an analysis of high temperature plasmas.
+ In Sect., In Sect.
+" 2.2, we investigate the possibility of constraining the properties of high energy particle populations by means of SZ intensity measurements at two frequencies."," 2.2, we investigate the possibility of constraining the properties of high energy particle populations by means of SZ intensity measurements at two frequencies."
+ Measurements of the SZ effect at a frequency 217 GHz is a unique way of revealing a population of mildly relativistic electrons in AGN cocoons if the intensity distortion is observed at a single frequency., Measurements of the SZ effect at a frequency 217 GHz is a unique way of revealing a population of mildly relativistic electrons in AGN cocoons if the intensity distortion is observed at a single frequency.
+" We propose below a new method for excluding the contribution from the low energy, non-relativistic electrons to the SZ effect by means of observations at two frequencies."," We propose below a new method for excluding the contribution from the low energy, non-relativistic electrons to the SZ effect by means of observations at two frequencies."
+" By αι,Χο,Το), we denote a combined generalized spectral function which corresponds to a relativistic contribution to the generalized function at a frequency x; taking into account a measurement at a frequency x2 and is defined as At low temperatures T,«105 K, the limiting case http://safe.nrao.edu/wiki/bin/view/GBT/GBTSensitivityComparison(1) holds (see Sect."," By $C (x_{1}, x_{2}, T_{e})$, we denote a combined generalized spectral function which corresponds to a relativistic contribution to the generalized function at a frequency $x_{1}$ taking into account a measurement at a frequency $x_{2}$ and is defined as At low temperatures $T_{\mathrm{e}}\ll 10^8$ K, the limiting case (1) holds (see Sect."
+" 2.1) and, therefore the combined"," 2.1) and, therefore the combined"
+We have searched for quiescent. persistent. radio emission from the northern hemisphere supersoft X-ray sources. and taken a high resolution image of the one known source with emission.,"We have searched for quiescent, persistent radio emission from the northern hemisphere supersoft X-ray sources, and taken a high resolution image of the one known source with emission."
+ We have improved the radio positions. source size and Hux from the persistent emitter AG Dra with MIEILIN.," We have improved the radio positions, source size and flux from the persistent emitter AG Dra with MERLIN."
+ The core is resolved at the milliaresee scale into two components with a combined [lux of  1000 μ.]ν., The core is resolved at the milliarcsec scale into two components with a combined flux of $\sim$ 1000 $\umu$ Jy.
+ Lt is possible that the core detected in the VLA image has significant nebulosity and is resolved out. by the higher ALERLIN resolution., It is possible that the core detected in the VLA image has significant nebulosity and is resolved out by the higher MERLIN resolution.
+ A possible south component. detected: by the VLA was unconfirmed. although this could be due to it having a Hux lower than the noise in the ALERLIN image. or also being resolved out.," A possible south component detected by the VLA was unconfirmed, although this could be due to it having a flux lower than the noise in the MERLIN image, or also being resolved out."
+ No new emission was detected from RN JOOL9S|2156 To Pyx and V1974 Cvgni down to a la RAIS noise level of around .20 [Jy n.," No new emission was detected from RX J0019.8+2156, T Pyx and V1974 Cygni down to a $\sigma$ RMS noise level of around 20 $\umu$ Jy $^{-1}$."
+ No. emissionos was detected from⋅ any oeviouslv known Galactic or extragalactic source in the 3. 104 square aresec fields imaged. and we place upper-IHimits o radio emission from these sources.," No emission was detected from any previously known Galactic or extragalactic source in the 3, 104 square arcsec fields imaged, and we place upper-limits to radio emission from these sources."
+ We have investigated: possible causes of radio emission rom a wind environment. both directly from the secondary star. and also as à consequence of the high X-ray. luminosity. rom the WD.," We have investigated possible causes of radio emission from a wind environment, both directly from the secondary star, and also as a consequence of the high X-ray luminosity from the WD."
+" A total of 17 new point-sources were imaged with Iuxes oetween LOL) and 1500 s an estimate to the density of sources with a flux > ""0 b. wy of2) per square degree. at 5 Cillz. in this region sky."," A total of 17 new point-sources were imaged with fluxes between 100 and 1500 $\umu$ Jy giving an estimate to the density of sources with a flux $>$ 100 $\umu$ Jy of 200 per square degree, at 5 GHz, in this region of the sky."
+ RNO wishes to thank the hospitality of the ALERLIN national facility at the Jodrell Bank Observatory. especially ‘Yom Muxlow.," RNO wishes to thank the hospitality of the MERLIN national facility at the Jodrell Bank Observatory, especially Tom Muxlow."
+ SC acknowledges support from erant. F/00-A from the Leverhulme Trust., SC acknowledges support from grant F/00-180/A from the Leverhulme Trust.
+ The tional liadio Astronomy Observatory ds à facility of theNational Science Foundation operated: under cooperative agreement by Associateck Universities. Inc. ALERLIN is a national facility operated by the University of Manchester on behalf of PPARC.," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. MERLIN is a national facility operated by the University of Manchester on behalf of PPARC."
+ This research has mace use of the SIMIAD database. operated at CDS. Strasbourg. France," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France"
+Classification. ⊲⋅⊀⊀in astronomy has ο to many advances which. iive revealed important. informationun. about the UniverseD. in. which. we live.,Classification in astronomy has led to many advances which have revealed important information about the Universe in which we live.
+. For. example. the classification⊲⋅⊀ of stars w their. colours ancl brightnesses. in. the Llertzsprung-; wor . ↘⊔⊳∖⊳∖∢⋅⊔∖↓∐↘∃∠⊔⋜↧⋏∙≟↓⋅⋜⋯↓↓∢⊾∠⇂⋯⋜⋯⊔⊔∠⇂⋖⊾↓⋅⊳∖⇂⋜⋯∠⊔⊔⋏∙≟∪⇂⊳∖∩⋅∐⋜⊔⋅⋅ structure and. evolution.," For example, the classification of stars by their colours and brightnesses in the Hertzsprung-Russel (HR) diagram led to an understanding of stellar structure and evolution."
+. sThe It undiagram continues. to »: employed as a means to to determine. the ages and metallicitesD. of. stellar populations.. whether they are simple. stellar populations. as in globular clusters. or in composite »opulations. such as dwarf galaxies (?2?27)..," The HR diagram continues to be employed as a means to to determine the ages and metallicites of stellar populations, whether they are simple stellar populations, as in globular clusters, or in composite populations, such as dwarf galaxies \citep{Dolphin2003, 
+Monelli2010, Williams2010}."
+ Even when it is impossible to resolve stars. entire galaxies are classified w their colours and magnitudes.," Even when it is impossible to resolve stars, entire galaxies are classified by their colours and magnitudes."
+ However. galaxies display resolved structure anc morphology that stars do not. and using this morphology can reveal much about the evolution of galaxies.," However, galaxies display resolved structure and morphology that stars do not, and using this morphology can reveal much about the evolution of galaxies."
+ Early methods. used. for the classification of galaxies were based on morphology., Early methods used for the classification of galaxies were based on morphology.
+ The ? Classification System is a method. used to categorise. galaxies. by their. morphology. ancl although it: has been the dominant: morphological. tool since. the mid-1920s.:5 over time. it. has proven to be deficientD. . ↓⊔⊳∖∢⊾∖⇁⋖⋅↓⋅⋜↧," The \citet{Hubble1926} Classification System is a method used to categorise galaxies by their morphology, and although it has been the dominant morphological tool since the mid-1920s, over time it has proven to be deficient in several areas."
+↓⋜⊔⋅��⊾⋜↧⊳∖⊳⇀∖↓≻↓⋅∪⊔∐⊔∢⋅⊔↿∠⊔⊳∖⋯⇂∖⇁⋜⋯↿⋜↧⋏∙≟∢⊾∩⊓∼↓⋜↧⊳∖⊳∖↓⇂∙∖⇁↓⊔⋏∙≟. . VEN ealaxies. based on their. morphological. features⋅ alone is. that it Do.is subjective⊲⊀ with. respect to distance: (or resolution). ancl inclination., A prominent disadvantage to classifying galaxies based on their morphological features alone is that it is subjective with respect to distance (or resolution) and inclination.
+"⋠⋠⋠ Furthermore∖ it⋠ has led to the grouping⋠ of⋅ a wide⋠ range of⋅ asymmetric. galaxies. as simply. .""irregularL", Furthermore it has led to the grouping of a wide range of asymmetric galaxies as simply “irregular”.
+ As both ground- and space-based imaging has improved. and we probe higher redshifts. it has become apparent that classilving galaxies as “irregular” means ignoring a vast amount of. morphological information.," As both ground- and space-based imaging has improved, and we probe higher redshifts, it has become apparent that classifying galaxies as “irregular” means ignoring a vast amount of morphological information."
+ ? attempted. to improve upon the 7 Classification System bv introducing “later ἵνρο as a sub-class of galaxies: however. this system still refers to. local. axisvmametric ealaxies as reference points. and. again. was based solely on morphology.," \citet{deVaucouleurs1959} attempted to improve upon the \citet{Hubble1926} Classification System by introducing “later types” as a sub-class of galaxies; however, this system still refers to local, axisymmetric galaxies as reference points, and, again, was based solely on morphology."
+(sceBeckert&Duschl2004).. one finds an upper limit for the cloud size and a corresponding mass llere c is the cloud-internal speed. of pressure waves which is of the order of Tkms+.,"\citep[see][]{Bec04}, one finds an upper limit for the cloud size and a corresponding mass Here $c_{\rm s}$ is the cloud-internal speed of pressure waves which is of the order of $1\,{\rm km\,s^{-1}}$."
+ We use this value as the unit for ὃς in the following., We use this value as the unit for $\csound$ in the following.
+ This speed. characterizes the cloud. internal pressure whichis required to balance. self-gravity. and can be understood. as the speed. of supersonic turbulence in the clouds.," This speed characterizes the cloud internal pressure whichis required to balance self-gravity, and can be understood as the speed of supersonic turbulence in the clouds."
+ Alternatively. the clouds may be magnetically supported+.," Alternatively, the clouds may be magnetically supported."
+ Due to their large cross section. these clouds dominante the absorption. scattering. and. LR re-emission.," Due to their large cross section, these clouds dominante the absorption, scattering, and IR re-emission."
+ From the relations for Z4 and. Aa. we get an upper envelope for the opacity of Hep=OTAyon(eMIT).," From the relations for $\Rcl$ and $\Mcl$, we get an upper envelope for the opacity of $\kappa_{\rm cl}= 0.7\kappa_0 \cdot \rpc^{3/2}/(\csound \Msev^{1/2})$."
+ The distance from the black hole re is measured in pc and the speed c in km +., The distance from the black hole $\rpc$ is measured in pc and the speed $c_{\rm s}$ in km $^{-1}$.
+ For clouds smaller than the shear limit. the opacity ποxLy becomes smaller.," For clouds smaller than the shear limit, the opacity $\kappa_{\rm cl}\propto \Rcl$ becomes smaller."
+ With Eqn. (1)).," With Eqn. \ref{Ledd_classic}) ),"
+ we obtain the IEddington limit for clouds in a clumipy torus. which are directly exposed to the primary ACN radiation. This is of the same order as in the classical Eddington limit (Eqn. 2))," we obtain the Eddington limit for clouds in a clumpy torus, which are directly exposed to the primary AGN radiation, This is of the same order as in the classical Eddington limit (Eqn. \ref{Ledd_std}) )"
+ and is consistent with observed ACN luminosities and. black hole masses., and is consistent with observed AGN luminosities and black hole masses.
+ Since LopXxX5s+ the Ecelington limit lor small clouds is even Larger than in Eqn. (7)).," Since $\Ledd \propto \kappa^{-1}$, the Eddington limit for small clouds is even larger than in Eqn. \ref{Ledd_clumpy}) )."
+ Eqn.: - (7)), Eqn. \ref{Ledd_clumpy}) )
+ shows that LiiilixrBIDο This o, shows that $\Lecl \propto r^{-3/2}$.
+culosimplies. that at larger distances. ποσαν>αποe clouds which are directly exposedὃν to the AGN radiation. become unbound by the raciation pressure.," This implies that at larger distances, self-gravitating clouds which are directly exposed to the AGN radiation become unbound by the radiation pressure."
+ Εις. distant clouds have to be shielded against the AGN radiation by clouds at. small radii.," Thus, distant clouds have to be shielded against the AGN radiation by clouds at small radii."
+ As a consequence. there should be no significant vertical Daring for a clumpy torus: i.e... we expect ἐνzconst.," As a consequence, there should be no significant vertical flaring for a clumpy torus; i.e., we expect $H/r\approx{\rm const}$."
+ Further consequences of this behaviour will be discussed in Sect. ??.., Further consequences of this behaviour will be discussed in Sect. \ref{Lhigh}.
+ In the previous section. we argued that the Eddington imit for clumpwv dust tori is well in agreement with the range of observed AGN luminosities and black hole masses.," In the previous section, we argued that the Eddington limit for clumpy dust tori is well in agreement with the range of observed AGN luminosities and black hole masses."
+ To be clumpy. a torus requires a small volume filling factor by<< or the dusty clouds.," To be clumpy, a torus requires a small volume filling factor $\pv\ll1$ for the dusty clouds."
+" In the context of a SA model. BeckertDuschl(2004) find a mass transport rate through the orus Adpagusπμ, where v=IG-a is the elective viscosity for a torus and X is the surface H7Ok&Rdensity."," In the context of a SA model, \citet{Bec04} find a mass transport rate through the torus $\Mdtor = 3 \pi \nu \Sigma$, where $\nu= \frac{\tau}{1+\tau^2} H^2 \Omega_{\rm Kepler}$ is the effective viscosity for a torus and $\Sigma$ is the surface density."
+ For an obscuring torus. the scale height. 44. cannot be smaller than the mean free path of clouds. {4ft=(4/34ὧν.," For an obscuring torus, the scale height, $H$, cannot be smaller than the mean free path of clouds $H \ge l = (4/3)R_{\rm cl}/\pv$."
+ Otherwise the torus would become transparent for GIN photons., Otherwise the torus would become transparent for AGN photons.
+ The parameter 7 in the viscosity. prescription measures the ratio 7=f/f., The parameter $\tau$ in the viscosity prescription measures the ratio $\tau=l/H$.
+ Phe ecometric thickness of the torus and the viscosity is maximised for 7=1., The geometric thickness of the torus and the viscosity is maximised for $\tau = 1$.
+ For ff/ the cloud density in the torus growth rapidly and the torus would collapse to a thin disk., For $H \gg l$ the cloud density in the torus growth rapidly and the torus would collapse to a thin disk.
+ We therefore adopt Lf=f for a working mocel., We therefore adopt $H=l$ for a working model.
+ After replacing the mean free path by the appropriate expression from Beckert&Duschl(2004)... we eet d in terms of Aqua The volume filling factor only depends on the mass transport rate through the torus. which we parametrized by Alans=O41.veLas:(gr/0.05)+ (soe Sect; 2)).," After replacing the mean free path by the appropriate expression from \citet{Bec04}, we get $\pv$ in terms of $\Mdtor$, The volume filling factor only depends on the mass transport rate through the torus, which we parametrized by $\Mdtor=0.4\,\Msy\times L_{45}\cdot(\eta\tau/0.05)^{-1}$ (see Sect. \ref{EddLimTor}) )."
+ ὃν substituting Aa we obtain ahard lower luminosity for the existence of an obscuring torus according to the SA model. at which dy=1.," By substituting $\Mdtor$, we obtain ahard lower luminosity for the existence of an obscuring torus according to the SA model, at which $\pv=1$."
+ For clumpy obscuring tori as described. it is necessary that the ACN luminosity is £7» dine ," For clumpy obscuring tori as described, it is necessary that the AGN luminosity is $L\gg L_{\rm low}$ ."
+WEL&Ling. the volume filling factor becomes ο...," If $L \ga L_{\rm low}$, the volume filling factor becomes $\pv\rightarrow1$."
+ At this point. theSA model would require that the torus collapses to a geometrically thin disk.," At this point, theSA model would require that the torus collapses to a geometrically thin disk."
+ As a consequence. most of the cust would be driven away (see Sect. 22)).," As a consequence, most of the dust would be driven away (see Sect. \ref{sdd}) )."
+ Lt is. however. known that this situation can be avoided: Lower Iuminosities &o along with lower accretion rates.," It is, however, known that this situation can be avoided: Lower luminosities go along with lower accretion rates."
+ Vollmeretal.(2004) showed that for low mass accretion rate. a ¢lumpy ancl almost transparent (f>> Lf) circumnuclear clisk (CND) can form similar to what hasbeen found around the central black hole in our Galaxy (Ciüstenetal. 1987)..," \citet{Voll04} showed that for low mass accretion rate, a clumpy and almost transparent $l \gg H$ ) circumnuclear disk (CND) can form similar to what hasbeen found around the central black hole in our Galaxy \citep{Gue87}. ."
+ Phe cüllerence between the clumpy torus and the CND is that the latter one loses most of its obscuration properties while there can still be LR. reprocessing., The difference between the clumpy torus and the CND is that the latter one loses most of its obscuration properties while there can still be IR reprocessing.
+ Several observational studies show that at/ about 1077ergs tthe Lia Lsun- or Lx Lsun-relation show a significant change in behaviour compared to. higher luminosities (e...Lutzetal.2004:Llorstct2006).," Several observational studies show that at about $10^{42}\,\ergs$, the $L_{\rm bol}-L_{\rm MIR}$ - or $L_{\rm X}-L_{\rm MIR}$ -relation show a significant change in behaviour compared to higher luminosities \citep[e.g.,][]{Lut04,Hor06}."
+. Apparently. the main source of MIIU emission at Lo—1077ergs is not the proposed. geometrically thick torus anymore.," Apparently, the main source of MIR emission at $L\sim10^{42}\,\ergs$ is not the proposed, geometrically thick torus anymore."
+ AX similar low-luminosity limit has been found for models where the cust clouds are not. produced in a torus but released into a wind from an aceretion disk(Elitzur&Shlosman 2006)., A similar low-luminosity limit has been found for models where the dust clouds are not produced in a torus but released into a wind from an accretion disk\citep{Eli06}.
+. Phe eutolT at lower Iuminositios is a result of the fact that the mass outflow rate in the wind cannot exceed the mass acerction rate in the disk., The cutoff at lower luminosities is a result of the fact that the mass outflow rate in the wind cannot exceed the mass accretion rate in the disk.
+ Taking the same T and g as used in Elitzur&Shlosman (2006). we obtain Lys—20007eres ," Taking the same $\tau$ and $\eta$ as used in \citet{Eli06}, , we obtain $L_{\rm low}=2\times10^{42}\,\ergs$ ."
+In Sect. ??7.. ," In Sect. \ref{clumpytorus}, ,"
+we have shown that the Eddington luminosity ⋠⋠⋅for clouds in. the clumpy torus.ili £44. depends on the cloud-ACN distance as r ," we have shown that the Eddington luminosity for clouds in the clumpy torus,$\Lecl$ , depends on the cloud-AGN distance as $r^{-3/2}$ ."
+A large [fraction, A large fraction
+decrement as the only likely explanation.,decrement as the only likely explanation.
+ This assumption is at odds. with the standard. AGN unified model. and deserves some further discussion., This assumption is at odds with the standard AGN unified model and deserves some further discussion.
+ In what follows we address 10 question on whether 111320|551 is consistent with an bsorbed/reddened type Ll Sevfert or not., In what follows we address the question on whether H1320+551 is consistent with an absorbed/reddened type 1 Seyfert or not.
+ Word et al (1988) studied the Balmer decrement of rw tvpe L AGN in the Piecinotti ct al (1982) sample., Ward et al (1988) studied the Balmer decrement of the type 1 AGN in the Piccinotti et al (1982) sample.
+ The eood linear correlation. between Balmer decrement versus 10 ratio between 2-10 keV luminosity (mostly. unallected ον reddening/absorption) and 11:3 luminosity (a &ood tracer NW absorption) prompted Ward. ct al. (1988) to. suggest wt Balmer decrement is determined by nuclear reddening. rather than being intrinsic to the DL1It (see their fig.," The good linear correlation between Balmer decrement versus the ratio between 2-10 keV luminosity (mostly unaffected by reddening/absorption) and $\beta$ luminosity (a good tracer of absorption) prompted Ward et al (1988) to suggest that Balmer decrement is determined by nuclear reddening, rather than being intrinsic to the BLR (see their fig."
+ 4)., 4).
+ Thev also find an approximately constant 2-10 keV to Ia ratio for the sample (see their Fig., They also find an approximately constant 2-10 keV to $\alpha$ ratio for the sample (see their Fig.
+ 5)., 5).
+ In fact. Ward ct al (1988) conclude that in spite of the extreme conditions of he BLR. the intrinsic Balmer clecrement is ~3.5 for the vpe 1 AGNs.," In fact, Ward et al (1988) conclude that in spite of the extreme conditions of the BLR, the intrinsic Balmer decrement is $\sim 3.5$ for the type 1 AGNs."
+ Now. 111320|551 has a Balmer clecrement which is more han half à decade larger than what would. be expected rom its 2-10 keV to L3 ratio.," Now, H1320+551 has a Balmer decrement which is more than half a decade larger than what would be expected from its 2-10 keV to $\beta$ ratio."
+ Reddening correction will not ing this into agreement with the Sevfert Ls. as both the Balmer decrement and the X-ray. to 11.1 ratio will decrease if reddening corrected.," Reddening correction will not bring this into agreement with the Seyfert 1s, as both the Balmer decrement and the X-ray to $\beta$ ratio will decrease if reddening corrected."
+ On the contrary. the 2-10 keV. to llo ratio is entirely consistent with that of the Sevfert s.," On the contrary, the 2-10 keV to $\alpha$ ratio is entirely consistent with that of the Seyfert 1s."
+ All that means that the large BLE. decrement for this particular Seyfert 1.8/1.9. together with its unabsorbecl X-rav spectrum cannot be explained as a Sevfert 1 AGN viewed through obscuring material.," All that means that the large BLR decrement for this particular Seyfert 1.8/1.9, together with its unabsorbed X-ray spectrum cannot be explained as a Seyfert 1 AGN viewed through obscuring material."
+" XMM-Newton X-ray observations of the 111320|551. which is classified by its optical spectrum as a type L1.8/1.9 ACN, reveal no absorption."," XMM-Newton X-ray observations of the H1320+551, which is classified by its optical spectrum as a type 1.8/1.9 AGN, reveal no absorption."
+ Lf the non-simultaneous optical ancl X-ray observations both trace the true state of this source. we conclude that the large Balmer decrement of the BLR. which determines its 1.8/1.9 spectroscopic type. is not due to reddening by clusty absorbing material along the line of sight.," If the non-simultaneous optical and X-ray observations both trace the true state of this source, we conclude that the large Balmer decrement of the BLR, which determines its 1.8/1.9 spectroscopic type, is not due to reddening by dusty absorbing material along the line of sight."
+" A variety of models can explain a large intrinsic value of the Balmer decrement. among them the failure of the standard. “case Bo recombination"" and/or optically thick BLR clouds."," A variety of models can explain a large intrinsic value of the Balmer decrement, among them the failure of the standard “case B recombination” and/or optically thick BLR clouds."
+ In any case. the AGN unified mocoel fails completely in this source.," In any case, the AGN unified model fails completely in this source."
+ Regardless on whether the unusual opticalN-rav absorption properties of 111320|551 are due to variations or not. they raise an important issue for unified ACN models for the N-rav. background.," Regardless on whether the unusual optical/X-ray absorption properties of H1320+551 are due to variations or not, they raise an important issue for unified AGN models for the X-ray background."
+ 1113201551 is a source with a relatively soft. unabsorbed N-rav. spectrum that. ds expected to typically have a type LXGN optical counterpart., H1320+551 is a source with a relatively soft unabsorbed X-ray spectrum that is expected to typically have a type 1 AGN optical counterpart.
+ Llowever. we identify it with a Sevfert. 1.8/1.9.. breaking again the one-to-one identification between X-ray absorption and optical obscuration that the NLRB models use.," However, we identify it with a Seyfert 1.8/1.9, breaking again the one-to-one identification between X-ray absorption and optical obscuration that the XRB models use."
+ Similarly. other relatively soft X-ray sources with no X-ray absorption might have optical counterparts which deviate from the standard: Sevfert 1 character.," Similarly, other relatively soft X-ray sources with no X-ray absorption might have optical counterparts which deviate from the standard Seyfert 1 character."
+ LE the DLIU properties are not alwavs linked to the absorption clisplaved by ACN. then Seyfert 1.8/1.9/2. galaxies might appear as optical counterparts of soft. X-ray selected sources as well as type 1 Sevferts often appear as optical counterparts to hard. X-ray SOULCOS.," If the BLR properties are not always linked to the absorption displayed by AGN, then Seyfert 1.8/1.9/2 galaxies might appear as optical counterparts of soft X-ray selected sources as well as type 1 Seyferts often appear as optical counterparts to hard X-ray sources."
+ We are grateful to Steve Sembay and Martin Turner for help with EPIC calibration issues., We are grateful to Steve Sembay and Martin Turner for help with EPIC calibration issues.
+ Phe referee is also thanked for important suggestions on the original version of this paper., The referee is also thanked for important suggestions on the original version of this paper.
+ The WIUE telescope is operated on the island of La Palma by the Isaac Newton Croup of Telescopes in the spanish Observatorio del Roque de Los Muchachos of the Instituto de sica de Canarias., The WHT telescope is operated on the island of La Palma by the Isaac Newton Group of Telescopes in the spanish Observatorio del Roque de Los Muchachos of the Instituto de sica de Canarias.
+ Partial financial support for this work was provided by the Spanish Ministry of Science and Technology uncler project AY.A2000-1690., Partial financial support for this work was provided by the Spanish Ministry of Science and Technology under project AYA2000-1690.
+and extend our use of clusters as tools for cosmology (Haiman.Mohr.&Holder2001).,and extend our use of clusters as tools for cosmology \citep{hai01}.
+. At the lower end of the mass scale. Chandra anc XMM-Nesston will permit the poorer. lower luminosity clusters anc groups (svstems wilh temperatures <2 keV) to be systematically detected for the first time to redshilis of a lew tenths.," At the lower end of the mass scale, Chandra and XMM-Newton will permit the poorer, lower luminosity clusters and groups (systems with temperatures $<2$ keV) to be systematically detected for the first time to redshifts of a few tenths."
+ Previous survevs for these svstems have often had to rely on prior optical catalogs. complicating the estimation of statistical completeness and bias (Aluichaev&Zabludolf1995).," Previous surveys for these systems have often had to rely on prior optical catalogs, complicating the estimation of statistical completeness and bias \citep{mul98}."
+. A common aspect of X-ray group and cluster surveys has been the frequent. (although nol universal) choice of a pass-band trom 0.5-2keV. Such a band typically helps minimize the contribution of soft Galactic emission. and harder particle background. while maximizing sensitivitv to general cluster emission (MeLEucdyοἱal.1993:Rosatiet1995).," A common aspect of X-ray group and cluster surveys has been the frequent (although not universal) choice of a pass-band from 0.5-2keV. Such a band typically helps minimize the contribution of soft Galactic emission, and harder particle background, while maximizing sensitivity to general cluster emission \citep{mch98,ros95}."
+. Previous imaging X-rav observatories have also not had the good spectral resolution of Chandra or XMM-Newton. so the choice of band was less controllable.," Previous imaging X-ray observatories have also not had the good spectral resolution of Chandra or XMM-Newton, so the choice of band was less controllable."
+ In this short paper I present a set of simple calculations aimed at determining a set of optimal pass-bands for thermal plasmas over a range of temperatures and redshifts., In this short paper I present a set of simple calculations aimed at determining a set of optimal pass-bands for thermal plasmas over a range of temperatures and redshifts.
+ I also demonstrate the relationship to the commonly used 0.5-2 keV band. and argue that [uture survevs of cooler svstems must take the band-pass explicitly into account. or risk seriously biasing (heir estimates of the space density of such svstenis.," I also demonstrate the relationship to the commonly used 0.5-2 keV band, and argue that future surveys of cooler systems must take the band-pass explicitly into account, or risk seriously biasing their estimates of the space density of such systems."
+ The signal-to-noise criterion | use here is S/VN. where S is the source photon count. AN is the appropriate backeround count.," The signal-to-noise criterion I use here is $S/\sqrt N$, where $S$ is the source photon count, $N$ is the appropriate background count."
+ This is chosen as a decent. approximation to the various [forms ol detection significance criteria used in X-ray survevs [or extended. sources., This is chosen as a decent approximation to the various forms of detection significance criteria used in X-ray surveys for extended sources.
+ Typically. a mean background count per skv area is estimated. and the deviation of the count rale in a given area. minus the background. is compared to the statistical (usually. Poisson) fInetuation in the background over that area.," Typically, a mean background count per sky area is estimated, and the deviation of the count rate in a given area, minus the background, is compared to the statistical (usually Poisson) fluctuation in the background over that area."
+ A typical background spectrum is derived across the full instrument. band-pass by combining high Galactic latitude data (<nif>~1x 107!) in which bright sources and periods of high particle background (flares) have heen removed.," A typical background spectrum is derived across the full instrument band-pass by combining high Galactic latitude data $<nH>\sim 1\times
+10^{21}$ ) in which bright sources and periods of high particle background (flares) have been removed."
+ For Chandra. the data was culled by combining archival fields ancl (he online background data.," For Chandra, the data was culled by combining archival fields and the online background data."
+ Similarly. for NMM. archival PV data and online background data was utilized.," Similarly, for XMM, archival PV data and online background data was utilized."
+ The background spectrum is derived by binning photons from the entire field-of-view and perlorming a simple. linear.," The background spectrum is derived by binning photons from the entire field-of-view and performing a simple, linear,"
+because By= Oat r=BD),because $B_\theta \ne 0$ at $r=R(t)$.
+ Phe shell and (lux rope solutions have perfectly rellecting solutions in which the total energy in rcAF) is conserved., The shell and flux rope solutions have perfectly reflecting solutions in which the total energy in $r<R(t)$ is conserved.
+ I. means that the solutions are energy eigenstates of the svstem., It means that the solutions are energy eigenstates of the system.
+ The eigenstates can be obtained by adjusting the parameter A., The eigenstates can be obtained by adjusting the parameter $k$.
+ In this paper. we obtained solutions for freely expanding magnetic loops. te. Def)!=0.," In this paper, we obtained solutions for freely expanding magnetic loops, i.e., $Dv / Dt = 0$."
+ We assumed that the magnetic loops have sulliciently large energy to drive the expansion., We assumed that the magnetic loops have sufficiently large energy to drive the expansion.
+ When the ux function ;l increases with time. the toroidal magnetic fieles will also increase with time.," When the flux function $\tilde{A}$ increases with time, the toroidal magnetic fields will also increase with time."
+ Phe toroidal magnetic fields will then allect the dynamics through the magnetic pressure., The toroidal magnetic fields will then affect the dynamics through the magnetic pressure.
+ Such solutions can describe the accelerating magnetic loops., Such solutions can describe the accelerating magnetic loops.
+ Magnetic fields can be expressed as the sum of the Fourier modes in the polar angle., Magnetic fields can be expressed as the sum of the Fourier modes in the polar angle.
+ Phe modes and their amplitudes should be determined at the boundary where the magnetic twist is injected on the surface of the star., The modes and their amplitudes should be determined at the boundary where the magnetic twist is injected on the surface of the star.
+" H0 is not shown but we can construct more complex solutions that the poloidal magnetic fields are expressed by the sum of the Fourier modes. i... .1xsin""@ "," It is not shown but we can construct more complex solutions that the poloidal magnetic fields are expressed by the sum of the Fourier modes, i.e., $\tilde A \propto \sin^n \theta$."
+In actual explosion. the opening angle of the expanding magnetic loops depends on the location at which the magnetic twist is injected on the surface of the central star.," In actual explosion, the opening angle of the expanding magnetic loops depends on the location at which the magnetic twist is injected on the surface of the central star."
+ Such a solution may be expressed as the sum of the Fourier nmiocdes for the poloidal and toroidal magnetic fields., Such a solution may be expressed as the sum of the Fourier modes for the poloidal and toroidal magnetic fields.
+ We should note that SCR Mares are not necessarily axisvmmetric., We should note that SGR flares are not necessarily axisymmetric.
+ Models including the non-axisvmmetrically expanding magnetic loops will be a subject of future works., Models including the non-axisymmetrically expanding magnetic loops will be a subject of future works.
+ We are erateful to the anonymous referee for constructive comments improving the paper., We are grateful to the anonymous referee for constructive comments improving the paper.
+ Fruitful discussions with Tomovuki Ianawa. Akira Mizuta. and Tomohisa Ixawashima at Chiba University are greatly appreciated.," Fruitful discussions with Tomoyuki Hanawa, Akira Mizuta, and Tomohisa Kawashima at Chiba University are greatly appreciated."
+ This work was supported by the Grants-in-Aid for Scientific Research of Ministry of Education. Culture. Sports. Science. and Technology (11:20340040).," This work was supported by the Grants-in-Aid for Scientific Research of Ministry of Education, Culture, Sports, Science, and Technology (RM:20340040)."
+pulse is extracted. trom the reference signal bv a high speed (lip-flop ancl fed into a field xoerammable eate array (FPGA).,pulse is extracted from the reference signal by a high speed flip-flop and fed into a field programmable gate array (FPGA).
+ This FPGA develops all of the various timing signals used in the antenna., This FPGA develops all of the various timing signals used in the antenna.
+ There are two tvpes of svnthesizers in the svstem (Figure 3))., There are two types of synthesizers in the system (Figure \ref{fig:if}) ).
+ The LO signals to the receivers and/or converters for all bands except X-band are produced. by a conventional Yttrium Iron Garnet (YIG) oscillator that is phase locked to a harmonic of the 512 MIIz relerence. offset bv the 128 MlIIz reference. which produces tones in the Lrequency range of 11.776 Gllz to 19.968 GIIz in 256 MlIz steps.," The LO signals to the receivers and/or converters for all bands except X-band are produced by a conventional Yttrium Iron Garnet (YIG) oscillator that is phase locked to a harmonic of the 512 MHz reference, offset by the 128 MHz reference, which produces tones in the frequency range of 11.776 GHz to 19.968 GHz in 256 MHz steps."
+ Since the outputs of these svnthesizers are used as the first (and in some cases second) LO. the svuthesizers ave designed to produce exceptionally clean. low phase noise CW signals with minimal harmonics.," Since the outputs of these synthesizers are used as the first (and in some cases second) LO, the synthesizers are designed to produce exceptionally clean, low phase noise CW signals with minimal harmonics."
+ This is especially critical flor the Ix. Ίνα and Q band receivers where the LO is multiplied by an additional factor of two or three inside the receiver.," This is especially critical for the K, Ka and Q band receivers where the LO is multiplied by an additional factor of two or three inside the receiver."
+ The LO signals to the main downconverters are generated by the second (wpe of saithesizers (FigureES 3))., The LO signals to the main downconverters are generated by the second type of synthesizers (Figure \ref{fig:if}) ).
+ These units are unique microwave svnthesizers based on two YIG oscillators and two direct digital svnthesizer (DDS) chips., These units are unique microwave synthesizers based on two YIG oscillators and two direct digital synthesizer (DDS) chips.
+ The svnthesizers produce tones in the Irequency range of 10.8 Gllz to 14.3 Giz in microhertz steps., The synthesizers produce tones in the frequency range of 10.8 GHz to 14.8 GHz in microhertz steps.
+ The design of this svnüthesizer was verv challenging because the phase of ils output signal was required to be controllable as the lrequencey is changed., The design of this synthesizer was very challenging because the phase of its output signal was required to be controllable as the frequency is changed.
+ The fine tuning requirement for (he svnthesizer was necessary for the transition mode operation of the EVLA system., The fine tuning requirement for the synthesizer was necessary for the transition mode operation of the EVLA system.
+ In this mode. the very fine tuning capability of the svnthesizer is used to produce a differential rate between antennas to allow the interlerometer [ringes to track (he source.," In this mode, the very fine tuning capability of the synthesizer is used to produce a differential rate between antennas to allow the interferometer fringes to track the source."
+ The EVLA data transmission svstem (DTS) dieitizes the IF signals at the antennas and transmits them to the correlator located in the central control building., The EVLA data transmission system (DTS) digitizes the IF signals at the antennas and transmits them to the correlator located in the central control building.
+ The DTS consists of a formatter module in the antenna. optical fibers between (he antenna and the control building. and deformatters in the control building (Figure 5)).," The DTS consists of a formatter module in the antenna, optical fibers between the antenna and the control building, and deformatters in the control building (Figure \ref{fig:dts}) )."
+ The deformatters also include signal processing circuiüry and cdigitial-Lo-analog converters to allow (he digital data produced bv the EVLA antennas to be processed bv the analog inputs to the existing VLA correlator during the (transition period., The deformatters also include signal processing circuitry and digitial-to-analog converters to allow the digital data produced by the EVLA antennas to be processed by the analog inputs to the existing VLA correlator during the transition period.
+ The data path from the antenna to the control building can be summarized as follows., The data path from the antenna to the control building can be summarized as follows.
+ An EVLA receiver can provide an instantaneous bandwidth of up to 3 GlIz in each of two polarizations., An EVLA receiver can provide an instantaneous bandwidth of up to 8 GHz in each of two polarizations.
+ The receiver output is partitioned into eight. 2 Giz wide. IF bands bv the svstem (Figure 5 shows (wo of the eight bands).," The receiver output is partitioned into eight, 2 GHz wide, IF bands by the LO-IF system (Figure \ref{fig:dts} shows two of the eight bands)."
+ Each IF band can be sampled with 4 Gllz, Each IF band can be sampled with 4 GHz
+2010)).,).
+" The leus galaxy redshift (τη) range is 0.05<2,<0.5. with a median of uo0.2."," The lens galaxy redshift $z_{l}$ ) range is $0.05\leq z_l\leq
+0.5$, with a median of $z_{l} \sim 0.2$."
+ Our ο is selected: 1) to have a measured Dumstem radius in Table 3 of A|09. 2) to be classified as elliptical or SU. 3) to have a measured V-band effective radius (anecasured at the intermediate axis).," Our sample is selected: 1) to have a measured Einstein radius in Table 3 of A+09, 2) to be classified as elliptical or S0, 3) to have a measured $V$ -band effective radius (measured at the intermediate axis)."
+ Of the 85 lenses from this latest SLACS release. 66 passed our selection criteria.," Of the 85 lenses from this latest SLACS release, 66 passed our selection criteria."
+ Asa lc0 comparison sample. we use the collection of 330 ETCs over the same mass rauge analyzed iu T|09 and NRTLO.," As a $z\sim0$ comparison sample, we use the collection of 330 ETGs over the same mass range analyzed in T+09 and NRT10."
+ To estimate stellar qmass-to-light ratios (Y.) aud star formation bistorics. we analyze spectral energy distributions (SEDs) based on broad-baud Sloan Digital Sky Survey (SDSS) photometry (uameh. grit).," To estimate stellar mass-to-light ratios $\Upsilon_\star$ ) and star formation histories, we analyze spectral energy distributions (SEDs) based on broad-band Sloan Digital Sky Survey (SDSS) photometry (namely, $ugriz$ )."
+ Our general procedure is to adopt a set of syvuthetic spectra from the prescription of Druzual&Charlot(2003).. a uuiform ietallicity Z. an age f characterizing the time of star formation onset. and au exponcutially declining star formation rate with timescale 7.," Our general procedure is to adopt a set of synthetic spectra from the prescription of \citet{BC03}, a uniform metallicity $Z$, an age $t$ characterizing the time of star formation onset, and an exponentially declining star formation rate with timescale $\tau$."
+ For cach galaxy. Z.t. aud 7 are fitted parameters. with the determined Y. based on a EKroupa(2001) IME: uncertainties ou the estimated parameters have been quantified via Moute Carlo simulations: further details are provided iu T109 aud NRTIO alone wit1 explorations of «ποιατς uncertainties and degencracjes.," For each galaxy, $Z$ , $t$, and $\tau$ are fitted parameters, with the determined $\Upsilon_{\star}$ based on a \citet{Kroupa01} IMF; uncertainties on the estimated parameters have been quantified via Monte Carlo simulations: further details are provided in T+09 and NRT10 along with explorations of systematic uncertainties and degeneracies."
+ The oulv change here is to shift the spectral resonses of the SDSS flters to correspond to the lous redshifts before couvolving with the model SEDs., The only change here is to shift the spectral responses of the SDSS filters to correspond to the lens redshifts before convolving with the model SEDs.
+ We ave checked that inposiug restrictions on Z or r. or adosting the stellar populations results from A|}09 or Cailoetal.(2009).. does not qualitatively affect the resuls described below.," We have checked that imposing restrictions on $Z$ or $\tau$, or adopting the stellar populations results from A+09 or \citet{Grillo+09}, does not qualitatively affect the results described below."
+ We derive the deprojected total mass from dyaiunies and lensing observables. and separate the DAL from the stellar componcuts using the stellar mass estimates discussed in the previous section.," We derive the deprojected total mass from dynamics and lensing observables, and separate the DM from the stellar components using the stellar mass estimates discussed in the previous section."
+ We adopt the stellar effective radius. aas the fiducial reference poiut for mass comparisons., We adopt the stellar effective radius as the fiducial reference point for mass comparisons.
+ For the leus galaxies. is measured. in. the V-baud. corresponcdiug approximately to the rest-frame D-bandused for the local galaxies.," For the lens galaxies, is measured in the $V$ -band, corresponding approximately to the rest-frame $B$ -bandused for the local galaxies."
+ Iu both galaxy samples. the mass constraints are ecnerally based on icasurements at sanaller radii (~OLR aud ~O.5 Rog. respectively). aud therefore some extrapolation is required.," In both galaxy samples, the mass constraints are generally based on measurements at smaller radii $\sim 0.1 \Re$ and $\sim 0.5 \Re$ , respectively), and therefore some extrapolation is required."
+ For the total lass distribution we adopt a singular isothermal sphere (SIS) with density p(r)=σαι.(2xGi?) (o.@. etal— 2006.. Cavazzictal.—.(2007.. IKoopiuausetal. 20093). where oup is an unknown normalization to be determined by fitting the observables.," For the total mass distribution we adopt a singular isothermal sphere (SIS) with density $\rho(r) = \sigma_{\rm SIS}^{2} / (2 \pi G
+r^{2})$ (e.g. \citealt{SLACS3}, , \citealt{Gavazzi07}, \citealt{Koopmans+09}) ), where $\sigma_{\rm SIS}$ is an unknown normalization to be determined by fitting the observables."
+ For the stars. we adopt a constant-Y. mass profile based on the (1990) model.," For the stars, we adopt a $\Upsilon_*$ mass profile based on the \citet{H90} model."
+" To estimate dynamical masses we have used the SDSS stellar velocity dispersious σωμα. nieasured within a circulus aperture of R4,=1.5%."," To estimate dynamical masses we have used the SDSS stellar velocity dispersions $\sigma_{\rm SDSS}$ , measured within a circular aperture of $R_{\rm ap} = 1.5''$."
+" Briefly, we have adopted the spherical Jeaus equation to derive the surface brightuess weighted velocity dispersion 0,318 within R4, (see T|09 for further details}. to be matched to Capss."," Briefly, we have adopted the spherical Jeans equation to derive the surface brightness weighted velocity dispersion $\sigma_{\rm ap,SIS}$ within $R_{\rm ap}$ (see T+09 for further details), to be matched to $\sigma_{\rm SDSS}$."
+ As discussed in T]09. there is some deeree of svsteiiatic uncertainty from asswuptions of sphericity and orbital isotropy. which we can now check in the case of the lenses by using the independent leusine- asses (Gvhieh do have their own uncertainties from mass-sheoet deeeueracies).," As discussed in T+09, there is some degree of systematic uncertainty from assumptions of sphericity and orbital isotropy, which we can now check in the case of the lenses by using the independent lensing-based masses (which do have their own uncertainties from mass-sheet degeneracies)."
+" For the lensing mass estimates. we have used the Einstein radiusRe. to derive a model independent measurement of projected inass (νο). withinfig. since Mg=Afni(RE)zBNet. where Meat=eD,IxGD;Dji,. with Dy. D; aud Dj, the observer - source. observer - lens aud leus - source comoving aueular diameter distances. respectively,"," For the lensing mass estimates, we have used the Einstein radius, to derive a model independent measurement of projected mass $M_{\rm proj}$ ) within, since $M_{E}=M_{\rm proj}(\RE) = \pi
+\RE^{2} \Sigma_{\rm crit}$, where $\Sigma_{\rm crit} = c^{2}
+D_{s}/4 \pi G D_{l} D_{ls}$ , with $D_{s}$, $D_{l}$ and $D_{ls}$ the observer - source, observer - lens and lens - source comoving angular diameter distances, respectively."
+ Finally we match the svediction of the SIS model projected mass. Muisis with Mr to have a further coustraiut on the ouly free uodel parazuueter for cach galaxy. yyy.," Finally we match the prediction of the SIS model projected mass, $M_{proj,SIS}$ with $M_{E}$ to have a further constraint on the only free model parameter for each galaxy, $\sigma_{\rm SIS}$."
+" The best fitted ayy can be derived indepeudently usine either technique to estimate the best 3D deprojected uass profile which we extrapolate to r=Ruy to obtain our reference mass values,", The best fitted $\sigma_{\rm SIS}$ can be derived independently using either technique to estimate the best 3D deprojected mass profile which we extrapolate to $r = \Re$ to obtain our reference mass values.
+ Using this approach. we fud hat lensing and dvuamics provide consistent results. nodulo a ~ (and a scatter of ~25%) higher mass roni dvnanucs. correspouding to a change of 0.03+0.10 in fp.," Using this approach, we find that lensing and dynamics provide consistent results, modulo a $\sim$ (and a scatter of $\sim 25\%$ ) higher mass from dynamics, corresponding to a change of $0.03 \pm 0.10$ in $f_{\rm DM}$."
+" Thus. we adopt a combination of the coustraiuts or our final masses. by minimizing with respect to 31a a combined \? function including oue term for dynamics and one for lensing observables. given by where 6, aud 6) ave the wmucertaitics ou typsyy ancl Alp. respectively9."," Thus, we adopt a combination of the constraints for our final masses, by minimizing with respect to $\sigma_{\rm SIS}$ a combined $\chi^2$ function including one term for dynamics and one for lensing observables, given by where $\delta_{d}$ and $\delta_{l}$ are the uncertainties on $\sigma_{\rm SDSS}$ and $M_{E}$, respectively."
+ Tn the following we will focus ou the central 3D deprojected aand the mean DAI density withinRuy. defined as (pom=Mpw/tl3aRug?)j where Mp=AeAL at is the DAL mass.," In the following we will focus on the central 3D deprojected and the mean DM density within, defined as $\langle \rho_{\rm
+DM}\rangle= M_{\rm DM}/(4/3 \pi \Re^3)$ where $M_{\rm DM}=M_{\rm
+tot}-M_\star$ at is the DM mass."
+ Asin T00 and NRTLO. to interpret the observational results. we construct a series of tov mass models based ou ACDAL cosmological simulations.," Asin T+09 and NRT10, to interpret the observational results, we construct a series of toy mass models based on $\Lambda$ CDM cosmological simulations."
+" For cach biu in M,. we use the average Rog-age relations from 1ο combined. leus|local sample. ancl pareuneterize the virial DM mass by a star formation efficicuev egg=ALOna MU). where O44=O17 (Sperecletal. 2007)) is the barvou densityparaucter."," For each bin in $M_\star$, we use the average $\Re$ -age relations from the combined lens+local sample, and parameterize the virial DM mass by a star formation efficiency $\epsilon_{\rm SF}=M_\star/(\Omega_{\rm bar} M_{\rm tot})$ , where $\Omega_{\rm bar}=0.17$ \citealt{WMAP2}) ) is the baryon densityparameter."
+ The halo deusitics are initially characterized as Navarroοal.(1997). profiles following al average nanss-concentraion relation. adjusted by (1| for the leus galaxies.," The halo densities are initially characterized as \citet{NFW} profiles following an average mass-concentration relation, adjusted by $(1+z)^{-1}$ for the lens galaxies."
+ A recipe for AC frou barvou settling isthen applied (Guedinetal. 2001)..., A recipe for AC from baryon settling isthen applied \citep{Gnedin+04}. .
+ The tov models for egg=0.03.0.1.L3 ave shown iu th. Fies.," The toy models for $\eSF = 0.03,0.1,0.3$ are shown in both Figs."
+ aud 3..,\ref{fig: fig1} and \ref{fig: fig3}..
+"where L, is the luminosity of the star, a is the semi-major axis of the orbit and e is the eccentricity of the orbit.","where $L_*$ is the luminosity of the star, $a$ is the semi-major axis of the orbit and $e$ is the eccentricity of the orbit."
+ T'his analysis was performed on all planets that met our average incident flux cut (F)<2x105 erg s? cm? and had a mass greater than 20 Ma-since our model is primarily designed to describe giants with masses greater than Neptune., This analysis was performed on all planets that met our average incident flux cut $\langle F \rangle < 2 \times 10^8$ erg $^{-2}$ $^{-2}$ and had a mass greater than 20 $M_{\oplus}$ –since our model is primarily designed to describe giants with masses greater than Neptune.
+ Note these heavy element masses should be taken asmasses since if the planet is internally heated or if higher atmospheric opacities (due to metal-enhanced atmospheres), Note these heavy element masses should be taken as since if the planet is internally heated or if higher atmospheric opacities (due to metal-enhanced atmospheres)
+Iu the high pattern speed limit (model 05E). the orbital structure maplies iuner bar that is short. round aud cau trap a good fraction of stars.,"In the high pattern speed limit (model 05E), the orbital structure implies inner bar that is short, round and can trap a good fraction of stars."
+ As pointed out iu Section 3.1.3. its end dis not well defined. and the transition region to the outer bar maw look like an isophotal twist (Figure 2. top panels).," As pointed out in Section 3.1.3, its end is not well defined, and the transition region to the outer bar may look like an isophotal twist (Figure 2, top panels)."
+ The size of this transition zone increases with immer bars pattern speed (see left-hand cols of Figure 3 for models 05 aud O5E). and one may expect that at still higher pattern sxeeds the morphology im the inner bar region is dominated by the isoplotal twist.," The size of this transition zone increases with inner bar's pattern speed (see left-hand columns of Figure 3 for models 05 and 05E), and one may expect that at still higher pattern speeds the morphology in the inner bar region is dominated by the isophotal twist."
+ Iu the low pattern speed iuit (nodel 02). the orbital structure nuplies iuuner bar that is lone. eccentric aud can trap onlv a sinall fraction of stars.," In the low pattern speed limit (model 02), the orbital structure implies inner bar that is long, eccentric and can trap only a small fraction of stars."
+ Such bar has a well defined eud iu terms ο Sorbits that support it. but as these orbits do not trap sars well. the bars cud may uot be defined that well in stellar distribution.," Such bar has a well defined end in terms of orbits that support it, but as these orbits do not trap stars well, the bar's end may not be defined that well in stellar distribution."
+ Further decreasing of pattern speed of the iuner bar erases the supporting orbits abruptly aid completely., Further decreasing of pattern speed of the inner bar erases the supporting orbits abruptly and completely.
+" Thus there is a well defined lowest possibο, critical pattern speed of the inner bar."," Thus there is a well defined lowest possible, critical pattern speed of the inner bar."
+ For pattern speeds lower than that. there are still regular orbits within the iuuer bar. but their appearance is dramatically different. aud they no longer support the shape of the immer bar.," For pattern speeds lower than that, there are still regular orbits within the inner bar, but their appearance is dramatically different, and they no longer support the shape of the inner bar."
+ Most of thei remain xrpeudieular to the immer bar., Most of them remain perpendicular to the inner bar.
+ If the presence of such orbits were a mere cousequence of this bar having an ILR. they should be also preseut in models 01. 03 ane I2. as all these models have an ILR (see fig.9 in ΑΤΑΟΣ).," If the presence of such orbits were a mere consequence of this bar having an ILR, they should be also present in models 04, 03 and 02, as all these models have an ILR (see fig.9 in MA08)."
+ We searched for such orbits in those models. but we di rot flucl au.," We searched for such orbits in those models, but we did not find any."
+ Also. if the structure of the immer aud the outer bar were simular. families of orbits both parallel aux xrpeudieular to the bar should coexist within the same uodoel. which is not the case in our models.," Also, if the structure of the inner and the outer bar were similar, families of orbits both parallel and perpendicular to the bar should coexist within the same model, which is not the case in our models."
+ The abrupt disappearance. at low pattern speeds. of orbits aligue with the ner bar. aud their replacement throughout the extent of the bar by orbits perpendicular to it. which were abseut at higher pattern speeds. reflects the nonlinear interaction between the bars in doubly barred galaxies.," The abrupt disappearance, at low pattern speeds, of orbits aligned with the inner bar, and their replacement throughout the extent of the bar by orbits perpendicular to it, which were absent at higher pattern speeds, reflects the nonlinear interaction between the bars in doubly barred galaxies."
+ The value of the critical pattern speed found im this paper is specific to the set of models considered here. aud it is uot clear by what plysical mechanisin it is determined.," The value of the critical pattern speed found in this paper is specific to the set of models considered here, and it is not clear by what physical mechanism it is determined."
+ It is close to twice the pattern speed of the outer har. and one can hypothesize that the low-order resonance between the bars destroys the support of the inner bar.," It is close to twice the pattern speed of the outer bar, and one can hypothesize that the low-order resonance between the bars destroys the support of the inner bar."
+" However, no transition in orbital structure is seen when the pattern speed of the inner bar is three times that of the outer bar."," However, no transition in orbital structure is seen when the pattern speed of the inner bar is three times that of the outer bar."
+ Receutly a iiethod. has been proposed for extracting inner bars from observations of carly-type spirals by modelling aud subtracting the disk. bulge aud the outer bar.," Recently a method has been proposed for extracting inner bars from observations of early-type spirals by modelling and subtracting the disk, bulge and the outer bar."
+ The results for two ealaxics have already Όσοι presented (Exwin 2010)., The results for two galaxies have already been presented (Erwin 2010).
+ The two extracted mner bars are quite differcut from cach other., The two extracted inner bars are quite different from each other.
+ One (in NGC 1513) contains a small fraction ofthe total stellar elit )). its eccentricity is hieh (axial ratio of 1). and its extent rather well defined. with isophotes aligued throughout the bar.," One (in NGC 1543) contains a small fraction of the total stellar light ), its eccentricity is high (axial ratio of 4), and its extent rather well defined, with isophotes aligned throughout the bar."
+ The other bar (ii NGC 2859). to the coutrary. contaius a mmch larger fraction of the total helt ). its eccentricity is lower (axial ratio of 2). iud its outer part smoothly turus mto a region of twisted isophotes outside it. which at larger radii become round and similar to those of the subtracted components of the galaxy iu the sine region.," The other bar (in NGC 2859), to the contrary, contains a much larger fraction of the total light ), its eccentricity is lower (axial ratio of 2), and its outer part smoothly turns into a region of twisted isophotes outside it, which at larger radii become round and similar to those of the subtracted components of the galaxy in the same region."
+ Based ou our knowledge of single bars. one should not necessarily expect correlatious between the three characteristics above (eccentricifv. luass. and outer isophotal shape).," Based on our knowledge of single bars, one should not necessarily expect correlations between the three characteristics above (eccentricity, mass, and outer isophotal shape)."
+ It is therefore siguificaut that iu the observations they correlate iu the same way as 1n our two models of extreme pattern speeds., It is therefore significant that in the observations they correlate in the same way as in our two models of extreme pattern speeds.
+ Orbits supporting the slowly rotating ΠΙΟ bar iu our models map onto looS that are eccentric. hence large axial ratio of such a bar. but they do uot trap stars well. hence simall mass fraction in the bar.," Orbits supporting the slowly rotating inner bar in our models map onto loops that are eccentric, hence large axial ratio of such a bar, but they do not trap stars well, hence small mass fraction in the bar."
+ We also showed that because of its orbital structure the extent of a slow bar is well defined., We also showed that because of its orbital structure the extent of a slow bar is well defined.
+ The inner bar in NGC 15[3 is eccentric. contaius small iiass raction and has a well defined exteut. which suggests at it rotates slowly in the seuse that its pattern specd is close to the lowest possible onc.," The inner bar in NGC 1543 is eccentric, contains small mass fraction and has a well defined extent, which suggests that it rotates slowly in the sense that its pattern speed is close to the lowest possible one."
+ Ou the other haud. iu our models orbits supporting ie -inner bar of hieh patteru speed nap onto loops jit become increasingly round as the pattern speed of 15 bar increases. therefore the observed axial ratio of wat bar should be small.," On the other hand, in our models orbits supporting the inner bar of high pattern speed map onto loops that become increasingly round as the pattern speed of the bar increases, therefore the observed axial ratio of that bar should be small."
+ These orbits trap stars very eficicuth. heuce the majority of the stars within the extent of the bar follow that bar aud the mass fraction in the bar is large.," These orbits trap stars very efficiently, hence the majority of the stars within the extent of the bar follow that bar and the mass fraction in the bar is large."
+ Outer loops of fast rotating iuner wars become monotomically rounder as their major axes increase. and cuter a transition region that looks like au isophotal twist. so that the end of the bar is not well defined.," Outer loops of fast rotating inner bars become monotonically rounder as their major axes increase, and enter a transition region that looks like an isophotal twist, so that the end of the bar is not well defined."
+ The inner bar of NGC 2859 is less eccentric han in NGC 15123. contains a high mass fraction aud is urrounded by au isophotal twist which sugeests that he angular velocity of the iuuer bar in NGC 2859 is considerable larger than its lowest clvnamically possible value. and that the structure of this iuner bar is close to he structure iu models of fast inner bars preseuted here.," The inner bar of NGC 2859 is less eccentric than in NGC 1543, contains a high mass fraction and is surrounded by an isophotal twist which suggests that the angular velocity of the inner bar in NGC 2859 is considerably larger than its lowest dynamically possible value, and that the structure of this inner bar is close to the structure in models of fast inner bars presented here."
+ Thus. we propose that from the morphology of extracted iuuer bars we can discriminate between slow xus. Whose pattern speed is close to the minimal dynamically possible value. aud fast bars. whose patter speed is cousicderably above this limit (possibly two nues higher).," Thus, we propose that from the morphology of extracted inner bars we can discriminate between slow bars, whose pattern speed is close to the minimal dynamically possible value, and fast bars, whose pattern speed is considerably above this limit (possibly two times higher)."
+ This distinction can be based on the characteristics listed imm Table 2., This distinction can be based on the characteristics listed in Table 2.
+ Note that by slow and fast immer bars we do not mean the ratio of the cheth of the bar to its corotation radius. which iu our models is virtually coustaut.," Note that by slow and fast inner bars we do not mean the ratio of the length of the bar to its corotation radius, which in our models is virtually constant."
+" Our slow bars lave oittern speeds in a range whose lower lait is set bv 10 orbital support for the iuner bar. while our fast bars vecolme increasingly rounder as their angular velocity Increases, and eventually they caunot be distinguished Toni axisviunetrie components of the galaxy."," Our slow bars have pattern speeds in a range whose lower limit is set by no orbital support for the inner bar, while our fast bars become increasingly rounder as their angular velocity increases, and eventually they cannot be distinguished from axisymmetric components of the galaxy."
+Active Galactic Nuclet (AGNs) show significant variability over a large range of timescales.,Active Galactic Nuclei (AGNs) show significant variability over a large range of timescales.
+ Usually. a variety of information can be extracted from the data with statistical methods based on Fourier techniques.," Usually, a variety of information can be extracted from the data with statistical methods based on Fourier techniques."
+ In the X-ray domain. for example. variability iu acereting compact objects has commonly been described by means of power spectral densities (PSD). characterizing the. amount of variability power P(w) as a function of temporal frequencies ω. or timescales 1/« (e.g.. van der Klis 1997).," In the X-ray domain, for example, variability in accreting compact objects has commonly been described by means of power spectral densities (PSD), characterizing the amount of variability power $P(\omega)$ as a function of temporal frequencies $\omega$, or timescales $1/\omega$ (e.g., van der Klis 1997)."
+ For (Seyfert) AGNs the resultant PSDs quite often appear to follow power laws P(w)«qw. which on long timescales (small frequencies) are approximately described by f£ close to | (flicker noise). but break to a steeper slope (= 2) on timescales shorter than à break timescale tp.," For (Seyfert) AGNs the resultant PSDs quite often appear to follow power laws $P(\omega)\propto \omega^{-\beta}$, which on long timescales (small frequencies) are approximately described by $\beta$ close to $1$ (flicker noise), but break to a steeper slope $\geq 2$ ) on timescales shorter than a break timescale $t_B$."
+ Active Galactic Nuclei thus vary more strongly towards lower frequencies (longer timescales)., Active Galactic Nuclei thus vary more strongly towards lower frequencies (longer timescales).
+ Recent studies have shown that the X-ray PSDs of AGNs can be qualitatively similar to the high state of black hole X-ray binary systems (e.g.. McHardy et al.," Recent studies have shown that the X-ray PSDs of AGNs can be qualitatively similar to the high state of black hole X-ray binary systems (e.g., McHardy et al."
+ 2004. 2006).," 2004, 2006)."
+ Based on these and other similarities. AGNs have sometimes been interpreted as scaled-up Galactic black hole In the very-high-energy (VHE) domain. the experimental situation is usually much less favorable.," Based on these and other similarities, AGNs have sometimes been interpreted as scaled-up Galactic black hole In the very-high-energy (VHE) domain, the experimental situation is usually much less favorable."
+ However. one object where it became recently possible to employ similar analysis techniques is the TeV blazar PKS 2155-304 (z= 0.116).," However, one object where it became recently possible to employ similar analysis techniques is the TeV blazar PKS 2155-304 $z=0.116$ )."
+ Usually detected only with a low VHE flux of ~10% of the Crab nebula. PKS 2155-304 underwent a dramatic outburst in July 2006. with VHE flux levels varying between | and 15 Crab units. allowing an unprecedented variability analysis (Aharonian et al.," Usually detected only with a low VHE flux of $\sim 10\%$ of the Crab nebula, PKS 2155-304 underwent a dramatic outburst in July 2006, with VHE flux levels varying between 1 and 15 Crab units, allowing an unprecedented variability analysis (Aharonian et al."
+ 2007; Abramowski et al., 2007; Abramowski et al.
+ 2010; Degrange et al., 2010; Degrange et al.
+ 2008)., 2008).
+ The Fourier analysis of its WHE light curve of. e.g.. MJD 53944 indicates a red (Brownian) noise-type VHE PSD with an exponent close to 2 within the frequency range [1077 Hz. 107 Hz] (Aharonian et al.," The Fourier analysis of its VHE light curve of, e.g., MJD 53944 indicates a red (Brownian) noise-type VHE PSD with an exponent close to 2 within the frequency range $[10^{-4}$ Hz, $10^{-2}$ Hz] (Aharonian et al."
+ 2007)., 2007).
+ Similar results have been obtained in X-rays (1.5-10 keV) with BeppoSAX in 1996 and 1997 (Zhang et al., Similar results have been obtained in X-rays (1.5-10 keV) with BeppoSAX in 1996 and 1997 (Zhang et al.
+ 1999)., 1999).
+ Moreover. similar to findings in the X-ray domain (Zhang et al.," Moreover, similar to findings in the X-ray domain (Zhang et al."
+" 1999, 2005). where linear relations between (absolute) rms variability amplitude and (mean) X-ray flux have been previously reported. a significant rms-flux correlation has been observed in the VHE data set (Degrange et al."," 1999, 2005), where linear relations between (absolute) rms variability amplitude and (mean) X-ray flux have been previously reported, a significant rms-flux correlation has been observed in the VHE data set (Degrange et al."
+ 2008)., 2008).
+ This is known to be characteristic of a non-linear. log-normal stochastic process where the relevant. normally distributed variable 1$ the logarithm of the flux logCX). and not just the flux itself (see Uttley et al.," This is known to be characteristic of a non-linear, log-normal stochastic process where the relevant, normally distributed variable is the logarithm of the flux $\log(X)$, and not just the flux itself (see Uttley et al."
+ 2005 for a general treatment. and Superina et al.," 2005 for a general treatment, and Superina et al."
+ 2008 for application to PKS 2155)., 2008 for application to PKS 2155).
+ A log-normal distribution can be thought of as the result of many multiplicative random effects. whereas additive effects would give rise to a normal (Gaussian) distribution.," A log-normal distribution can be thought of as the result of many multiplicative random effects, whereas additive effects would give rise to a normal (Gaussian) distribution."
+ Dideed. if the variability would be caused merely by an additive stochastic process. the fluxes would be normally distributed and no linear rms-flux relation would be expected. becatse all Fourier. coefficients. would be statistically. independert.," Indeed, if the variability would be caused merely by an additive stochastic process, the fluxes would be normally distributed and no linear rms-flux relation would be expected, because all Fourier coefficients would be statistically independent."
+ Therefore. the finding that the variations on short timescales (determining the rms) decrease in amplitude when the long timescale variations (determining the mean flux) decrease. indicates that the process driving the variations is a multiplicative process (as 1n a cascade) and not just an additive one (e.g.. shot-noise). nor one resulting from independent variations in many separate regions (Uttley et al.," Therefore, the finding that the variations on short timescales (determining the rms) decrease in amplitude when the long timescale variations (determining the mean flux) decrease, indicates that the process driving the variations is a multiplicative process (as in a cascade) and not just an additive one (e.g., shot-noise), nor one resulting from independent variations in many separate regions (Uttley et al."
+ 2005: McHardy In acereting galactic black hole (BH) systems. these variations have been frequently related to small. independent fluctuations 1n the accretion rate. occurring on local viscous timescale {μι over a range of disk radi r that are large compared to the inner radius of the disk (Lyubarskii. 1997; King et al.," 2005; McHardy In accreting galactic black hole (BH) systems these variations have been frequently related to small, independent fluctuations in the accretion rate, occurring on local viscous timescale $t_{\rm visc}(r)$ over a range of disk radii $r$ that are large compared to the inner radius of the disk (Lyubarskii 1997; King et al."
+ 2004: Arevalo Uttley 2006)., 2004; Arevalo Uttley 2006).
+ If not damped. these fluctuations can propagate inwards and couple together in à way to produce the multiplicative characteristics. noted above.," If not damped, these fluctuations can propagate inwards and couple together in a way to produce the multiplicative characteristics noted above."
+ Any emission process linked to the the innermost region (e.g.. as X-ray production or jet launching site) may then eventually be modulated over a frequency interval ranging from the inverse accretion time hear the outer to the one at the innermost disk radius. respectively.," Any emission process linked to the the innermost region (e.g., as X-ray production or jet launching site) may then eventually be modulated over a frequency interval ranging from the inverse accretion time near the outer to the one at the innermost disk radius, respectively."
+ While this scenario sounds very attractive (cf., While this scenario sounds very attractive (cf.
+ also Giebels Degrange 2009 for BL Lac). a generalization to a supermassive source like PKS 2155-304 seems challenging given the detected VHE minimum variability (doubling) timescale of 4.~200 sec.," also Giebels Degrange 2009 for BL Lac), a generalization to a supermassive source like PKS 2155-304 seems challenging given the detected VHE minimum variability (doubling) timescale of $t_v \sim 200$ sec."
+ As we show below. a consistent approach along this line may require the presence of a putative binary BH system in PKS 2155-304 (cf.," As we show below, a consistent approach along this line may require the presence of a putative binary BH system in PKS 2155-304 (cf."
+Polu-aiug galaxies (PRC) are peculiar objects iu which a polar or very inclined ving surround the host galaxy.,Polar-ring galaxies (PRG) are peculiar objects in which a polar or very inclined ring surround the host galaxy.
+ Thev teach us a lot on galaxy formation., They teach us a lot on galaxy formation.
+" At least two niain scenarios are invoked to form these svstenmis either the major merecr scenario. with a head-on mereiue of two galaxies with their disks oriented. perpendicularly (οιο, Bekki 1998). or the accretfion scenario. where a ga-Yich donor loses matter to form the rug (e.e.. Scloweizer et al."," At least two main scenarios are invoked to form these systems: either the major merger scenario, with a head-on merging of two galaxies with their disks oriented perpendicularly (e.g., Bekki 1998), or the accretion scenario, where a gas-rich donor loses matter to form the ring (e.g., Schweizer et al."
+ 1983. Reshetuikov Sotuikova 1997).," 1983, Reshetnikov Sotnikova 1997)."
+ The accretion scenario itself could either correspond to a sil colupanion being disrupted durius a niünor merecr. or a major chcounter with tidal mass transfer from a massive donor to the host (Bowrnaud Combes 2003. hereafter BC03).," The accretion scenario itself could either correspond to a small companion being disrupted during a minor merger, or a major encounter with tidal mass transfer from a massive donor to the host (Bournaud Combes 2003, hereafter BC03)."
+ In previous simmlations. BCO3 have shown that the accretion scenario offers more chances to form the observed svstenmis. aud that a discriminating characteristic can be the existence. in the merecr scenario. of a diffuse stellar backerouud around the polarring svstem.," In previous simulations, BC03 have shown that the accretion scenario offers more chances to form the observed systems, and that a discriminating characteristic can be the existence, in the merger scenario, of a diffuse stellar background around the polar-ring system."
+ Iu the accretion scenario. the matter is not as much dispersed spatially.," In the accretion scenario, the matter is not as much dispersed spatially."
+ It is naportaut ο test on several πο]ουρανος polar-rving systems the possible scenarios. aud the prescut system offers a good example.," It is important to test on several well-observed polar-ring systems the possible scenarios, and the present system offers a good example."
+ The southerm peculiar ealaxy AAD 1931-563. was classified by Whitmore et al. (, The southern peculiar galaxy AM 1934-563 was classified by Whitmore et al. (
+1990) (PRC. polar rines catalogue) as a good candidate for polarring galaxics. (,"1990) (PRC, polar rings catalogue) as a good candidate for polar-ring galaxies. ("
+The object name is PRC B-18 according to the PRC.),The object name is PRC B-18 according to the PRC.)
+" The füut extended feature crosses the iain ealaxy (disturbed edge-on galaxy with inclined. dust lane) at au anele of about GO"" from the major axis (Figs.", The faint extended feature crosses the main galaxy (disturbed edge-on galaxy with inclined dust lane) at an angle of about $^{\rm o}$ from the major axis (Figs.
+ 1 aud 2)., 1 and 2).
+ Both components the main body aud the suspected rine are slightly S-shaped., Both components – the main body and the suspected ring – are slightly S-shaped.
+ ANT 1931-563 has two nearby coupanious of similar size and magnitude (Fies., AM 1934-563 has two nearby companions of similar size and magnitude (Figs.
+ 1 aud 2)., 1 and 2).
+ These are POC 100092 (NW conipanuion) and POC 390718 {5 conrpaniion). both of unknown redshift.," These are PGC 400092 (NW companion) and PGC 399718 (S companion), both of unknown redshift."
+ Other galaxies of comparable iaeuitudes are located about 10 N of AM 1931-563 and belong to the AM. 1931-562 exoup of ealaxies., Other galaxies of comparable magnitudes are located about $'$ N of AM 1934-563 and belong to the AM 1934-562 group of galaxies.
+ AMO 1931-563. is an almost unexplored galaxy., AM 1934-563 is an almost unexplored galaxy.
+ Deshetnikov et al. (, Reshetnikov et al. (
+2001) have found fast rotation of the eas in the central region of the ealaxy. as far as sigus of Sv2 or LINER activity.,"2001) have found fast rotation of the gas in the central region of the galaxy, as far as signs of Sy2 or LINER activity."
+ van Del et al. (, van Driel et al. (
+2002) have detected the 21-cii HI liue cussion toward AM. 1931-563 but the observed III xofile can be confused with another galaxy of the triplet.,2002) have detected the 21-cm HI line emission toward AM 1934-563 but the observed HI profile can be confused with another galaxy of the triplet.
+ We present here new photometric aud spectroscopic data for AAT 1931-563 and two companion galaxies., We present here new photometric and spectroscopic data for AM 1934-563 and two companion galaxies.
+ The ιο data reveal that the three galaxies forma a plivsical viplet., The new data reveal that the three galaxies form a physical triplet.
+ Global observational structure and kinematies of ANTI 1931-563 allow to conclude that this ealaxy is a real x»bur-riug galaxy with a spiral host and inclined rine/cdisk structure., Global observational structure and kinematics of AM 1934-563 allow to conclude that this galaxy is a real polar-ring galaxy with a spiral host and inclined ring/disk structure.
+ We also moclel our observations usiue N-body miuerical siuulations., We also model our observations using N-body numerical simulations.
+ We study different formation scenarios for this polar ring. aud fud that ouly one is likely o reproduce the observed properties of AM 1931-563.," We study different formation scenarios for this polar ring, and find that only one is likely to reproduce the observed properties of AM 1934-563."
+ We hen couclude that this polar ring las been formed bv idal accretion of material frou a eas-vich ealaxy. that uav still be observed today in the triplet.," We then conclude that this polar ring has been formed by tidal accretion of material from a gas-rich galaxy, that may still be observed today in the triplet."
+ Let us stress hat AAD 1931-563. with its massive spiral lost. is peculiar among PRs. which most frequently have a small carly-vpe hosts (often SOs).," Let us stress that AM 1934-563, with its massive spiral host, is peculiar among PRGs, which most frequently have a small early-type hosts (often S0s)."
+ Thus. we study the formation of ANL 1931-563 in particular. aud do uot pretend that our results will strictly extent to PRCs in general. even if may PRGs have probably formed through the same accretion mechamisi (see Ὀς09).," Thus, we study the formation of AM 1934-563 in particular, and do not pretend that our results will strictly extent to PRGs in general, even if many PRGs have probably formed through the same accretion mechanism (see BC03)."
+ The observations that have beeu made are preseuted iu Sect., The observations that have been made are presented in Sect.
+ 2., 2.
+ Their results are analyzed in Sect., Their results are analyzed in Sect.
+ 3., 3.
+ Iu Sect., In Sect.
+ 1 we model this svstem. and discuss its formation mechlanisu.," 4, we model this system, and discuss its formation mechanism."
+ The photometric observations were performed with the l.Gau telescope at the ΟΡΙΟ (AICT/LNA). Brasil ou Aueust 2002.," The photometric observations were performed with the 1.6-m telescope at the OPD (MCT/LNA), Brasil on August 2002."
+ The telescope was equipped with direct Huaging camera 11 and a thick. back-alluuinated," The telescope was equipped with direct imaging camera 1 and a thick, back-illuminated"
+or escaping along open magnetic field lines via direct electron measurements near the Earth (see777.[orareview)..,"or escaping along open magnetic field lines via direct electron measurements near the Earth \citep[see][for a review]{Aschwanden02,BrownKontar05,Benz08}."
+ The first in-situ observations of energetic particles (72) opened up the non-electromagnetic window of flare accelerated. particle observations.," The first in-situ observations of energetic particles \citep{vanAllen65}
+ opened up the non-electromagnetic window of flare accelerated particle observations."
+ Solar impulsive electron events detected in-situ generally clisplay broken power-law energy distributions with lower energies having softer spectra (7).., Solar impulsive electron events detected in-situ generally display broken power-law energy distributions with lower energies having softer spectra \citep{Lin85}.
+ These events also show near time-ol-I[light velocity dispersion and a beamed pitch-angle distribution (e.g.???)..," These events also show near time-of-flight velocity dispersion and a beamed pitch-angle distribution \citep[e.g.][]{Lin85,Krucker_etal1999,Krucker_etal07}."
+ From (his evidence. it is often believed that such electrons propagate scatter-Dree [rom the Sun to the Earth (e.g.?)..," From this evidence, it is often believed that such electrons propagate scatter-free from the Sun to the Earth \citep[e.g.][]{Wang_etal06}."
+ The observed. correlation between (he spectral indices of energetic electrons at the Sun ου data and (he Earth trom in-situ data (??) is often viewed as an additional support for {his model.," The observed correlation between the spectral indices of energetic electrons at the Sun from X-ray data and the Earth from in-situ data \citep{Lin85,Krucker_etal07} is often viewed as an additional support for this model."
+ At the same time. impulsive solar energetic electron events are closely related observalionally (e.g.2??7?77) and theoretically (22277???) to Type II solar radio bursts.," At the same time, impulsive solar energetic electron events are closely related observationally \citep[e.g.][]{Li_etal1981,Ergun_etal98,Gosling_etal2003,Cane2003,Krucker_etal07}
+ and theoretically \citep{GZ1958,Zaitsev_etal72,Grognard1982,Melrose90,Melnik99,Kontar01a,Ledenev04}
+ to Type III solar radio bursts."
+ The stzncdaid model of Type HI solar radio bursts (7). suggests that electron. beams propagating in the ambient solar wind plasma from the Sun (to the Earth can excite Langmuir waves. which in turn generate escaping plasma radio emission (see7.lorareview)...," The standard model of Type III solar radio bursts \citep{GZ1958}
+ suggests that electron beams propagating in the ambient solar wind plasma from the Sun to the Earth can excite Langmuir waves, which in turn generate escaping plasma radio emission \citep[see][for a review]{Melrose_85}."
+ Ii a treatment assuming travel along magnetic field lines. as faster electrons outpace slower electrons a positive gradient is formed in velocity space.," In a one-dimensional treatment assuming travel along magnetic field lines, as faster electrons outpace slower electrons a positive gradient is formed in velocity space."
+ Η (his positive gradient gets large enough to start the generation of waves. electron energy is resonantly transferred to Langmuir waves in (he background plasma.," If this positive gradient gets large enough to start the generation of waves, electron energy is resonantly transferred to Langmuir waves in the background plasma."
+ This transler of energv reduces the gradient in velocitv. space forming; a plateau (??)..," This transfer of energy reduces the gradient in velocity space forming a plateau \citep{Vedenov_etal1962,Drummond_Pines1962}."
+ For a spatially limited electron beam cloud. the plasma waves generated al the front. of the cloud. are absorbed by the electron beam al the back allowing the electrons to travel through the corona with small energy losses aud with a velocity that decreases with time due to plasma inhomogeneity (?)..," For a spatially limited electron beam cloud, the plasma waves generated at the front of the cloud are absorbed by the electron beam at the back allowing the electrons to travel through the corona with small energy losses and with a velocity that decreases with time due to plasma inhomogeneity \citep{Kontar01a}."
+ Although this broad picture is often supported by observations. the detailed picture of electron transport and plasma radio emission is far from well-understood.," Although this broad picture is often supported by observations, the detailed picture of electron transport and plasma radio emission is far from well-understood."
+ This is largely due to electron beam propagation and radio emission being essentially a non-linear multi-scale problem. aud is the solar imp," This is largely due to electron beam propagation and radio emission being essentially a non-linear multi-scale problem, and is the subject of a large number of ongoing simulation efforts \citep[e.g.][]{Melnik99,Kontar01a,KontarPecseli02,Ledenev04,Li_etal2006,2008ApJ...677..676G}."
+ulsive electron events can span a broad range of energies. [rom a lew keV to hundreds of keV. (?)..," Solar impulsive electron events can span a broad range of energies, from a few keV to hundreds of keV \citep{Lin_etal1996}."
+ Their energy distribution forms a broken power-law spectrum with the break enerey in deca-keV range., Their energy distribution forms a broken power-law spectrum with the break energy in deca-keV range.
+ Despite often showing the near time-ol-Ilight. dispersion. lower energv electrons appear to arrive sooner (han expected [rom a scatter-Iree mocel (7?)..," Despite often showing the near time-of-flight dispersion, lower energy electrons appear to arrive sooner than expected from a scatter-free model \citep{Wang_etal06}."
+ Since the low energy electrons of a few keV should lose their energy collisionally in the low corona. these electrons are believed to be accelerated high in the corona (?)..," Since the low energy electrons of a few keV should lose their energy collisionally in the low corona, these electrons are believed to be accelerated high in the corona \citep{Lin_etal1996}."
+ Recent time-ol- analvsis (7) assuming scatter-[ree propagation of solar energetic electrons suggests the existence of two electron populations. one low energy beam injected before the start οἱ the tvpe HIE burst and one high energy beam injected alter the tvpe II burst.," Recent time-of-injection analysis \citep{Wang_etal06} assuming scatter-free propagation of solar energetic electrons suggests the existence of two electron populations, one low energy beam injected before the start of the type III burst and one high energy beam injected after the type III burst."
+ In this Letter. we investigate the electron propagation from the Sun to the Earth taking," In this Letter, we investigate the electron propagation from the Sun to the Earth taking"
+observed Lya region and (4) consistency of the scale factor-derived distance with the adopted distance or distance constraint.,observed $\alpha$ region and (4) consistency of the scale factor-derived distance with the adopted distance or distance constraint.
+ In other words. the fitting solution may not necessarily be the model with the lowest 47 value but rather all other available constraints are used such as constraints on the distance. reliable svstem parameters if available. absorption line fits. especially (he να wings but sometimes even Si II. Si HI. C III. C II. si IV and $i II when (hese features are in absorption aud do not have an origin in a wind or corona.," In other words, the fitting solution may not necessarily be the model with the lowest $\chi^{2}$ value but rather all other available constraints are used such as constraints on the distance, reliable system parameters if available, absorption line fits, especially the $\alpha$ wings but sometimes even Si II, Si III, C III, C II, Si IV and Si II when these features are in absorption and do not have an origin in a wind or corona."
+ We also search for anv statistically significant improvement in the fitting by combining white dwarf models and disk models together using a X7 minimization routine called DISKFIT., We also search for any statistically significant improvement in the fitting by combining white dwarf models and disk models together using a $\chi^{2}$ minimization routine called DISKFIT.
+ Once again. we find the minimum 4? value achieved for the combined models. and check the combined model consistency. wilh the observed continuum slope and Lya region. aud consistency of the scale factor-derived distance wilh the adopted clistance or distance constraints.," Once again, we find the minimum $\chi^{2}$ value achieved for the combined models, and check the combined model consistency with the observed continuum slope and $\alpha$ region, and consistency of the scale factor-derived distance with the adopted distance or distance constraints."
+ For the white dwarl radii. we use the mass-radius relation from (he evolutionary model grid of for C-O cores.," For the white dwarf radii, we use the mass-radius relation from the evolutionary model grid of \citet{Wood1990} for C-O cores."
+ For a non-magnetic nova-like variable during its high state. it is reasonable to expect that a steady state optically Chick accretion disk might provide a successful fit (see (2003))).," For a non-magnetic nova-like variable during its high state, it is reasonable to expect that a steady state optically thick accretion disk might provide a successful fit (see \citet{Hamilton2008}) )."
+ This was our intial expectation lor all three nova-likes. DIx Lyn. V380 Oph and V751 Cveni.," This was our intial expectation for all three nova-likes, BK Lyn, V380 Oph and V751 Cygni."
+ For BI. Lyn. the most striking feature of its spectrum is the sharp. narrow Lya line in combination with a steeply rising continu.," For BK Lyn, the most striking feature of its spectrum is the sharp, narrow $\alpha$ line in combination with a steeply rising continuum."
+ The narrowness of the Lya ancl steep continuum slope suggested (he possiblity (hat the FUV flux originates [rom a hot white cwarf photosphere., The narrowness of the $\alpha$ and steep continuum slope suggested the possiblity that the FUV flux originates from a hot white dwarf photosphere.
+ But a fit to the the continuum slope with a hot photosphere αἱ T=300001. and a nominal white dwarl gravity of log e=8.0. vields a svnthetüie Ίωνα absorption feature which is [ar (oo broad.," But a fit to the the continuum slope with a hot photosphere at T=30000K and a nominal white dwarf gravity of log g=8.0, yields a synthetic $\alpha$ absorption feature which is far too broad."
+ ILowever. a narrower prolile is obtained bv increasing the effective temperature and/or lowering the gravitv.," However, a narrower profile is obtained by increasing the effective temperature and/or lowering the gravity."
+ The continuum slope and narrow Lya feature of the observed spectrum can be matched with a white dwarf photosphere with T-—380001Ix. aud log g—T., The continuum slope and narrow $\alpha$ feature of the observed spectrum can be matched with a white dwarf photosphere with T=38000K and log g=7.
+ A surface gravity Chis low would not be inconsistent with the low white dwarl mass derived by Dobrzveka&Lowell(1992)., A surface gravity this low would not be inconsistent with the low white dwarf mass derived by \citet{Dobrzycka1992}.
+. However. the distance implied by the fit is 1200 pc while the stellar radius approached (hat of a hot subclwarl," However, the distance implied by the fit is 1400 pc while the stellar radius approached that of a hot subdwarf."
+ Moreover. the V-band magnitude ol this model fit is 20.6. which is about [ive magnitudes fainter than the observed magnitude.," Moreover, the V-band magnitude of this model fit is 20.6, which is about five magnitudes fainter than the observed magnitude."
+ The narrowness of the Lya prolile also suggested (he possibility that it is of interstellar origin., The narrowness of the $\alpha$ profile also suggested the possibility that it is of interstellar origin.
+ First. if the svstem were being viewed at low inclination. then the emission lines which are presumed to be formed in the disk. would not be as broad as observed.," First, if the system were being viewed at low inclination, then the emission lines which are presumed to be formed in the disk, would not be as broad as observed."
+ This makes il likely that the narrow Lya absorption. given that it is not cue to a low gravity white dwarl," This makes it likely that the narrow $\alpha$ absorption, given that it is not due to a low gravity white dwarf"
+it is interesting to examine whether such a possibility could be acceptable using additional constraints.,it is interesting to examine whether such a possibility could be acceptable using additional constraints.
+ CMB is known to provide such constraints on the quintessence scenario. eg (?22)..," CMB is known to provide such constraints on the quintessence scenario, eg \citep{spergel03,nous2003,odman2004}."
+ We therefore examine CMB constraints on the type of models introduced above. although we leave to a future work a full investigation of the constraints that can be set on this type of model.," We therefore examine CMB constraints on the type of models introduced above, although we leave to a future work a full investigation of the constraints that can be set on this type of model."
+ We use the WMAP 3 data-set. as well as CBI. VSA and Boomerang data at small scales. and a version of the CAMB cosmological code (2) that we have modified.," We use the WMAP 3 data-set, as well as CBI, VSA and Boomerang data at small scales, and a version of the CAMB cosmological code \citep{CAMB} that we have modified."
+ Modifications of the code are straightforward since its public version includes models with constant We In which we have implemented the energy density ροίς) and the pressure Po) as a function of redshift., Modifications of the code are straightforward since its public version includes models with constant $w_\QUINT$ in which we have implemented the energy density $\rho_\QUINT (z)$ and the pressure $P_\QUINT(z)$ as a function of redshift.
+ Our ansatz for the equation of state parameter wo(z) allows us to integrate the conservation equation to obtain an analytical form for po(z)!., Our ansatz for the equation of state parameter $w_\QUINT(z)$ allows us to integrate the conservation equation to obtain an analytical form for $\rho_\QUINT(z)$.
+. The angular power spectrum of CMB fluctuations in the presence of dark energy is modified mainly through the modification of the angular distance (?) (see Fig., The angular power spectrum of CMB fluctuations in the presence of dark energy is modified mainly through the modification of the angular distance \citep{bl84} (see Fig.
+ 3 ?)., \ref{fig:cmbCl} ).
+ Although a strong dependence appears. this is. partially lost through parameter degeneracies which strongly weaken the final constraints.," Although a strong dependence appears, this is partially lost through parameter degeneracies which strongly weaken the final constraints."
+ In addition. ISW will contribute to lower levels as the transition is assumed at lower redshift. and this effect contributes to modify the angular power spectrum of the CMB fluctuations.," In addition, ISW will contribute to lower levels as the transition is assumed at lower redshift, and this effect contributes to modify the angular power spectrum of the CMB fluctuations."
+ We have investigated the CMB constraints on models with rapid transitions described by Eq. 2.., We have investigated the CMB constraints on models with rapid transitions described by Eq. \ref{wqz}. .
+ Γ was set to 10., $\Gamma$ was set to 10.
+ We have checked that varying E above 5 produces no appreciable differences., We have checked that varying $\Gamma$ above 5 produces no appreciable differences.
+ The other parameters that were left free are the Hubble constant Ho. the dark energy density at the present day Qo. the index of the primordial spectrum 7. the amplitude of fluctuations ος and the transition epoch aq=1/(1+τι).," The other parameters that were left free are the Hubble constant $H_0$, the dark energy density at the present day $\Omega_\QUINT$, the index of the primordial spectrum $n$, the amplitude of fluctuations $\sigma_8$ and the transition epoch $a_\TRANS = 1 / (1 + z_\TRANS)$."
+" From the contours obtained in figure 4.. one can see that the constraints that can be set on the transition redshift z, from the CMB are rather stringent. z;>0.54 (lo on one parameter) when Qo represents less than 50% of the total density."," From the contours obtained in figure \ref{fig:CD2}, one can see that the constraints that can be set on the transition redshift $z_\TRANS $ from the CMB are rather stringent, $z_\TRANS > 0.54 $ $\sigma$ on one parameter) when $\Omega_\QUINT$ represents less than $50\%$ of the total density."
+" These constraints being slightly dependent on Ho we have also examined whether a combination of CMB and supernova data allows to improve the transition epoch constraints. but although the SNIa data restricted the dark energy density much more around Og~0.7. the final constraints do not represent a significant improvement: the final constraint I8 z,>0.66 (26 on one parameter)."," These constraints being slightly dependent on $H_0$ we have also examined whether a combination of CMB and supernova data allows to improve the transition epoch constraints, but although the SNIa data restricted the dark energy density much more around $\Omega_\QUINT \sim 0.7$, the final constraints do not represent a significant improvement: the final constraint is $z_\TRANS > 0.66 $ $\sigma$ on one parameter)."
+ Some different dark energy models could in principle lead to different conclusions in the case where the sound speed varies in a way that significantly affects the integrated. Sachs-Wolfe effect on large angular scales. even though no such model was found in our analysis.," Some different dark energy models could in principle lead to different conclusions in the case where the sound speed varies in a way that significantly affects the integrated Sachs-Wolfe effect on large angular scales, even though no such model was found in our analysis."
+ Clearly. better constraints could be obtained from additional data of cosmological relevance. but this is beyond the scope of the present paper.," Clearly, better constraints could be obtained from additional data of cosmological relevance, but this is beyond the scope of the present paper."
+ In order to distinguish quintessence models from a pure cosmological constant. it is crucial to be able to track the dark energy evolution as early as possible.," In order to distinguish quintessence models from a pure cosmological constant, it is crucial to be able to track the dark energy evolution as early as possible."
+ The main impact of darkenergy comes from its influence on the expansion rate of the universe., The main impact of darkenergy comes from its influence on the expansion rate of the universe.
+ An important question is therefore until what epoch, An important question is therefore until what epoch
+convolved with a Gaussian of full width half maximum + pixels (850. μπι) or 3 pixels (450 sem) giving final resolutions of 14.2 (850 jim) and 8.6 aresees (450 fam).,convolved with a Gaussian of full width half maximum 4 pixels (850 $\mu$ m) or 3 pixels (450 $\mu$ m) giving final resolutions of $14.2$ (850 $\mu$ m) and $8.6$ arcsecs (450 $\mu$ m).
+ The convolved maps with signal-to-noise (S/N) contours are shown in reftig:allmaps.., The convolved maps with signal-to-noise (S/N) contours are shown in \\ref{fig:allmaps}.
+ We observed each field with the IRAC (at 4.5 and 8.0 jim) and MIPS (at 24 jim) cameras on-board theTelescope., We observed each field with the IRAC (at 4.5 and 8.0 $\mu$ m) and MIPS (at 24 $\mu$ m) cameras on-board the.
+ IRAC observations were made between 2005 March and 2005 July while the MIPS observations were made between 2005 March and 2005 December., IRAC observations were made between 2005 March and 2005 July while the MIPS observations were made between 2005 March and 2005 December.
+ For the IRAC observations we used 5-pt Gaussian dithers with frame times of 100 or 200s depending on the predicted brightness of the target., For the IRAC observations we used 5-pt Gaussian dithers with frame times of 100 or 200s depending on the predicted brightness of the target.
+ Frame times for the MIPS observations were between 3 and 10 s. These observations are summarised in Table 3.., Frame times for the MIPS observations were between 3 and 10 s. These observations are summarised in Table \ref{table:spitlog}.
+ The IRAC frames were processed by the Science Center using the standard pipeline version S1:4.0.0., The IRAC frames were processed by the Science Center using the standard pipeline version S14.0.0.
+ The images were then cropped to only include the region of constant exposure time: this allows catalogues to be constructed from regions with similar noise properties., The images were then cropped to only include the region of constant exposure time; this allows catalogues to be constructed from regions with similar noise properties.
+ Source extraction was performed with (Bertin Arnouts 1996) with a fixed aperture of 3.5” and a local background fit., Source extraction was performed with (Bertin Arnouts 1996) with a fixed aperture of $3.5^{\prime\prime}$ and a local background fit.
+ Aperture corrections of 1.6 and 2.13 were applied to the 4.5 and 8.0 jim flux densities respectively. in accord with the values determined from theSpicer First Look Survey (Lacy et al.," Aperture corrections of $1.6$ and $2.13$ were applied to the 4.5 and 8.0 $\mu$ m flux densities respectively, in accord with the values determined from the First Look Survey (Lacy et al."
+ 2005)., 2005).
+ For MIPS observations. the 24 ;7m BCD images were fitted with a plane after first masking out the bright objects.," For MIPS observations, the $24~\mu$ m BCD images were fitted with a plane after first masking out the bright objects."
+ This plane was then subtracted from each. BCD frame resulting in a flat background image., This plane was then subtracted from each BCD frame resulting in a flat background image.
+ These images were then combined with the task using the astrometric solution from each individual BCD image., These images were then combined with the task using the astrometric solution from each individual BCD image.
+ This procedure resulted in a much improved 24 j/m image. free of the jail-bar pattern common to the PBCD images supplied from theSpizer pipeline.," This procedure resulted in a much improved 24 $\mu$ m image, free of the jail-bar pattern common to the PBCD images supplied from the pipeline."
+ Again. only the central 3.3 aremin? region of the images was used to detect sources.," Again, only the central $3\times 3$ $^2$ region of the images was used to detect sources."
+ We used to find sources and thePHOT script in IDL to measure their flux density within a 13 aresec radius aperture., We used to find sources and the script in IDL to measure their flux density within a $13$ arcsec radius aperture.
+ All flux densities were then subjected to an aperture correction of 1.167 (see Seymour et al., All flux densities were then subjected to an aperture correction of 1.167 (see Seymour et al.
+ 2007)., 2007).
+ Our philosophy is to match our analysis as closely as possible to that performed by the SHADES consortium (Coppin et al., Our philosophy is to match our analysis as closely as possible to that performed by the SHADES consortium (Coppin et al.
+ 2006) thus allowing a direct comparison of the number counts determined for blank fields and those in the highly biased regions of the Universe surrounding our QSOs., 2006) thus allowing a direct comparison of the number counts determined for blank fields and those in the highly biased regions of the Universe surrounding our QSOs.
+ Most of the analysis in this section pertains to the 850. jam data., Most of the analysis in this section pertains to the 850 $\mu$ m data.
+ For the 450 jim data we extract a catalogue at a fixed. S/N threshold but do not compute number counts., For the 450 $\mu$ m data we extract a catalogue at a fixed S/N threshold but do not compute number counts.
+ We adopt the source extraction algorithm described by Scott et, We adopt the source extraction algorithm described by Scott et
+"posterior distribution of 0 aud c is Πωαο, poe.110.0) is given by Equation (11)). and pf=10.0) is the probability of including a source in one’s sample. given the model parameters. 0 and (0 I have left off the subscripts for the data poiuts in Equation (11)) because the iuteerals are the same for each (rj.d;£j.4).","posterior distribution of $\theta$ and $\psi$ is Here, $p(x_i,y_i|\theta,\psi)$ is given by Equation \ref{eq-obslik2}) ), and $p(I=1|\theta,\psi)$ is the probability of including a source in one's sample, given the model parameters, $\theta$ and $\psi$: I have left off the subscripts for the data points in Equation \ref{eq-detprob}) ) because the integrals are the same for each $(x_j,y_j,\xi_j,\eta_j)$."
+ IE one asstunes the Gaussian mixture model of Sections L1 and L3.. then ple.gil.c) is eiven by Equations (16)) or (30)).," If one assumes the Gaussian mixture model of Sections \ref{s-normreg} and \ref{s-multreg}, then $p(x_i,y_i|\theta,\psi)$ is given by Equations \ref{eq-bobslik}) ) or \ref{eq-mobslik}) )."
+ The posterior mode can then be used as au estimate of 0 aud c. which is found by maximizing Equation (10)).," The posterior mode can then be used as an estimate of $\theta$ and $\psi$, which is found by maximizing Equation \ref{eq-trunclik}) )."
+ Iu addition to issues related to the sample selection method. if is Common in astronomical data to have nou-detections.," In addition to issues related to the sample selection method, it is common in astronomical data to have non-detections."
+ Such uou-detections are referred to as ‘censored’ data. and the standard procedure is to place an upper and/or lower limit ou the censored data poit.," Such non-detections are referred to as `censored' data, and the standard procedure is to place an upper and/or lower limit on the censored data point."
+ Methods of data analysis for ceusored data have been reviewed aud proposed in the astronomical literature. (e.g...Feigelson&Nelson1985:Sclunitt1985:Magshall1992:Αίας&Siebert 1996).. and Isobeetal.(1986). describe censored regression when the variables are measured without error.," Methods of data analysis for censored data have been reviewed and proposed in the astronomical literature, \citep[e.g.,][]{feig85,schmitt85,marsh92,akritas96}, and \citet{isobe86} describe censored regression when the variables are measured without error."
+ See Feigelsou(1992). for a review of censored. data in astronomy., See \citet{feig92} for a review of censored data in astronomy.
+ To facilitate the inclusiou of censored data. [introduce au additional indicator variable. D. indicating whether a data poiut is censored or not on the depeudent variable.," To facilitate the inclusion of censored data, I introduce an additional indicator variable, $D$, indicating whether a data point is censored or not on the dependent variable."
+ Tf y; is detected. then D;=1. else if y; is censored then D;= 0.," If $y_i$ is detected, then $D_i = 1$, else if $y_i$ is censored then $D_i = 0$ ."
+ It is commonly the case that a source is cousidered “detected if its iieasured fiux falls above some iuultiple of the background5 noise level. sav 3o.," It is commonly the case that a source is considered `detected' if its measured flux falls above some multiple of the background noise level, say $3\sigma$."
+ Then. in this case. the probability of detecting the source given the measured source flux y; is p(D;—Uys)= 1f uy;>36. and p(D;=Oly) Lif yy<30.," Then, in this case, the probability of detecting the source given the measured source flux $y_i$ is $p(D_i=1|y_i) = 1$ if $y_i > 3\sigma$, and $p(D_i=0|y_i) = 1$ if $y_i < 3\sigma$."
+ Since source detection depeuds ou the measured flix. some sources with iutrinsie flux y above the flux limit will have a measured fiux y that falls below the flux limit.," Since source detection depends on the measured flux, some sources with intrinsic flux $\eta$ above the flux limit will have a measured flux $y$ that falls below the flux limit."
+ Similarly. some sources with iutriusic flux below the flux Limit will have a imieasured fiux above the flix lint.," Similarly, some sources with intrinsic flux below the flux limit will have a measured flux above the flux limit."
+ Tassie that a sample ds selected based on the independeut variables. ie. μονο)=pe).," I assume that a sample is selected based on the independent variables, i.e., $p(I|x,y) = p(I|x)$."
+ It is ifhcult to duagine obtaining a censored sample if the sample is selected based ou its dependent variable. as μαome of the values of y are censored aud thus unknown.," It is difficult to imagine obtaining a censored sample if the sample is selected based on its dependent variable, as some of the values of $y$ are censored and thus unknown."
+ Therefore. I ouly investigate the effects of ceusoriug on y When the probability that a source is included in the sample is independent of y. given we.," Therefore, I only investigate the effects of censoring on $y$ when the probability that a source is included in the sample is independent of $y$, given $x$."
+ Ta addition. I o not address the issue of censoring on the independent variable.," In addition, I do not address the issue of censoring on the independent variable."
+ Although such methods can be developed. --- is probably simpler to just omit such data as inference on the regression paramicters is unaffected when a sample is selected based oulv ou the independent variables (cf. 5.1.1)).," Although such methods can be developed, it is probably simpler to just omit such data as inference on the regression parameters is unaffected when a sample is selected based only on the independent variables (cf., \ref{s-seffects_x}) )."
+ The observed data Likelihood for au a-selected sample isgiveu by Equation (39))., The observed data likelihood for an $x$ -selected sample isgiven by Equation \ref{eq-indlik}) ).
+ We can modifv this likelihood. to account for censored y by including the indicator variable D and again inteerating over the mussing data:, We can modify this likelihood to account for censored $y$ by including the indicator variable $D$ and again integrating over the missing data:
+non-barvonie compact objects (ο explain microlensing events.,non-baryonic compact objects to explain microlensing events.
+" This conclusion will be made much stronger if larger future quasar samples demonstrate the limit on ο, to be <0.01. the fraction of barvons unexplained in the current. census (?).."," This conclusion will be made much stronger if larger future quasar samples demonstrate the limit on $\Omega_c$ to be $\lesssim
+0.01$, the fraction of baryons unexplained in the current census \citep{misc:silk-baryons}."
+" Also below this threshold. microlensing by ordinary stars in galaxies may become more significant. since ο,zz0.006 (7)."," Also below this threshold, microlensing by ordinary stars in galaxies may become more significant, since $\Omega_\ast \approx 0.006$ \citep*{misc:baryon-budget}."
+ There are some important points to keep in mind when considering (hie analvsis leading to these constraints., There are some important points to keep in mind when considering the analysis leading to these constraints.
+ The first is that. because the three sets of emission lines are [rom only one sample of quasars. the constraints are independent and cannot in general be combined io derive a stronger limit.," The first is that, because the three sets of emission lines are from only one sample of quasars, the constraints are independent and cannot in general be combined to derive a stronger limit."
+ Rather the three sets of limits serve in some sense as checks on one another., Rather the three sets of limits serve in some sense as checks on one another.
+ The second point concerns the absence of quoted lower limits., The second point concerns the absence of quoted lower limits.
+" While ihe maxinmm-likelihood analysis formally. produces a nonzero most-likely value for ©, in sole cases. along with a lower limit. this should not be interpreted as an unambiguous detection of compact dark matter."," While the maximum-likelihood analysis formally produces a nonzero most-likely value for $\Omega_c$ in some cases, along with a lower limit, this should not be interpreted as an unambiguous detection of compact dark matter."
+ It may very. well be Chat the intrinsic distribution at low equivalent widths departs from a simple lognormal: (his could be easily be misconstrued as evidence for lensing at low O.., It may very well be that the intrinsic distribution at low equivalent widths departs from a simple lognormal; this could be easily be misconstrued as evidence for lensing at low $\Omega_c$.
+ Another wav of saving this is that because probability must be non-negative. anv departure [rom the exponentially small intrinsic probability at low equivalent width will result in a positive detection of compact dark matter. real or not.," Another way of saying this is that because probability must be non-negative, any departure from the exponentially small intrinsic probability at low equivalent width will result in a positive detection of compact dark matter, real or not."
+ The other side of this argument is that if the actual unleused distribution does in fact have some probability al low equivalent widths not represented in the model. then the limits from the simple lognormal-based model will necessarily be conservative.," The other side of this argument is that if the actual unlensed distribution does in fact have some probability at low equivalent widths not represented in the model, then the limits from the simple lognormal-based model will necessarily be conservative."
+ A large source of svstematic uncertainty in (his analvsis is the Daldwin effect. which deserves a much more thorough treatment (han was possible in this paper.," A large source of systematic uncertainty in this analysis is the Baldwin effect, which deserves a much more thorough treatment than was possible in this paper."
+ The requirements of an acdequately parameterized distribution has led to (he introduction of a number of (?).. (D.VandenBerk2003.privatecommunication).. ?..," The maximum-likelihood requirements of an adequately parameterized distribution has led to the introduction of a number of \citep{sdss:qso-belr-shifts}. \citetext{D. Vanden Berk 2003,
+ private communication}. \citet{lens:press-gunn},"
+stals were eliuinated because of their large proper motions. which would skew the zero point of the proper motions.,"stars were eliminated because of their large proper motions, which would skew the zero point of the proper motions."
+" The ""eSlt of steps 1 — Y was a set of parallaxes. proper motious. aud formal errors for all he stals whic ilad been measured in each Ποιά."," The result of steps 1 – 7 was a set of parallaxes, proper motions, and formal errors for all the stars which had been measured in each field."
+ Table 2 (available in full in the electronic versiol of this paper) presents this information. aloug with the celestial coordinates. V. aid V=f anaguitueS. RMS residuas of the fits. aud statistical weights.," Table 2 (available in full in the electronic version of this paper) presents this information, along with the celestial coordinates, $V$ and $V-I$ magnitudes, RMS residuals of the fits, and statistical weights."
+ A COLοςion to absolute parallax was estimated as follows., A correction to absolute parallax was estimated as follows.
+ For each star ied for the reference frame. a «lstance was estimated from the measred £ au V—TJ color. using typical maln-sequeice values ta)lated by Pickles(1998)..," For each star used for the reference frame, a distance was estimated from the measured $I$ and $V-I$ color, using typical main-sequence values tabulated by \citet{pickles}."
+ The straigit mean of the estimated refe'euce-star parallaNOS was usec to correct the relative parallax ¢» absolute., The straight mean of the estimated reference-star parallaxes was used to correct the relative parallax to absolute.
+ Reddeuiug of lie refereuce stars was IOl taken Ito accoLit. nor was the possibility that they uight be giants. which we cauιοί exclude.," Reddening of the reference stars was not taken into account, nor was the possibility that they might be giants, which we cannot exclude."
+ At hieh latitudes. οiauts of the apparent 1uagnitL(e of the refereice stars would be far out iu the alo ancl hence unliselypriori at lower latitucles. where many more rele‘ence stars were avallabe. a few Wus-1ceutified giants w«jid lead to a slig|t overestimation of the very stall «'Orrection.," At high latitudes, giants of the apparent magnitude of the reference stars would be far out in the halo and hence unlikely; at lower latitudes, where many more reference stars were available, a few mis-identified giants would lead to a slight overestimation of the very small correction."
+" The use of £1iagnitucdes mitigaed the ellects of vbsorption to sole extent: in aly Case. ulaccouatecd-for extluction would somew""hat couuter-iutuively tend to make the stars appear ck»er than their true clistalces. because the ‘ecldlening woul uake the stars appear later-tvpe. aid |ence absolutely fainte ‘ancl hence closer than their true ¢]stance."," The use of $I$ magnitudes mitigated the effects of absorption to some extent; in any case, unaccounted-for extinction would somewhat counter-intuitively tend to make the stars appear closer than their true distances, because the reddening would make the stars appear later-type, and hence absolutely fainter, and hence closer than their true distance."
+ Tje extinction would also make le slars appear fainter (and. hence fartler away). but Ie former effect more than compeus:ves for the latter.," The extinction would also make the stars appear fainter (and hence farther away), but the former effect more than compensates for the latter."
+ Accordinely. this estimate is in ellec ali 1pper limit to the correction.," Accordingly, this estimate is in effect an upper limit to the correction."
+ Tle COLrrecious were in all Cases stuall. of order 1 1jas. aud the unce‘tainty in the correction was iguorect.," The corrections were in all cases small, of order 1 mas, and the uncertainty in the correction was ignored."
+ The number of stars measured i1 each field was large enough to allow au alter.ate calculation of the parallax error. as follows.," The number of stars measured in each field was large enough to allow an alternate calculation of the parallax error, as follows."
+ A se olsars was Chosen for proximity οἱ the sky aid similarity in brightuess. aud the scatter of the fitted parallaxes o -AMliese stars was take Las au alterlale allax uncertainty.," A set of stars was chosen for proximity on the sky and similarity in brightness, and the scatter of the fitted parallaxes of these stars was taken as an alternate parallax uncertainty."
+ The magnitude and. radius wiudow was adjisted o include ~10 stars ο: ore in the sample: typically stars within 3 arciiin aud xL mage of the program star were included. but this varied witely based on how mauy stars were available.," The magnitude and radius window was adjusted to include $\sim 10$ stars or more in the sample; typically stars within 3 arcmin and $\pm 1$ mag of the program star were included, but this varied widely based on how many stars were available."
+ T10 scater was computed both arolic Zero aud around the stars’ pl1oloLjetric parallaxes. ut the shotomeric parallax adjustimeuts we'e small ellois0h. aud the errors large enough. that tiis inade little clierence in. practice.," The scatter was computed both around zero and around the stars' photometric parallaxes, but the photometric parallax adjustments were small enough, and the errors large enough, that this made little difference in practice."
+ This measure of parallax 1ucertaluty weis swally somewliat greater 1 li1ο fit. errors above. but they were uot dram:ically larger. indjcatiiig that the fit eVOrs were dt 00 far olf.," This measure of parallax uncertainty was usually somewhat greater than the fit errors above, but they were not dramatically larger, indicating that the fit errors were not too far off."
+ Nonetheless. these meast are probably more faithful indicators of the rue external error. aud they were tsel in the dista estiuates given later. except in those cases 1 which the estimated external erroFr wasfess than fortral error. which could happen because o “the sinall nuiyer of stars involved.," Nonetheless, these measures are probably more faithful indicators of the true external error, and they were used in the distance estimates given later, except in those cases in which the estimated external error was than the formal error, which could happen because of the small number of stars involved."
+ The scater arouud the parallax and proper motion fits for the best. stablest comparison stars is around 6 uas (vector rius error).," The scatter around the parallax and proper motion fits for the best, stablest comparison stars is around 6 mas (vector rms error)."
+ This is abou double the error obtained at USNO with a similar CCD and slightly poorer unage scale (Dalinetal.2002)., This is about double the error obtained at USNO with a similar CCD and slightly poorer image scale \citep{dahn02}.
+. The short exposure times used in the oesent study may coutribute to tlis in the following, The short exposure times used in the present study may contribute to this in the following
+Classical Be stars cau share many similar observational features with ILA&eDe star aud are likely to be more prevalent in the Galaxy. aud SAIC/LAIC. eiveu the short pre-inain sequence lifetimes of iuterinediate-niass stars.,"Classical Be stars can share many similar observational features with HAeBe star and are likely to be more prevalent in the Galaxy and SMC/LMC, given the short pre-main sequence lifetimes of intermediate-mass stars."
+ Thus. establishing that ESIIC. and ΕΠΟ stars are in fact pre-1uain sequence objects requires clear evidence that their observed behavior is iucousisteut with that expected from classical De stars.," Thus, establishing that ESHC and ELHC stars are in fact pre-main sequence objects requires clear evidence that their observed behavior is inconsistent with that expected from classical Be stars."
+ Figure 2 illustrates that the IR colors of mown SMC/LMC. classical Be stars share COMMLOL parameter space both with maux ESIIC/ELIIC stars and with some Calactic WAcBe stars., Figure \ref{2cdfig} illustrates that the IR colors of known SMC/LMC classical Be stars share common parameter space both with many ESHC/ELHC stars and with some Galactic HAeBe stars.
+ Moreover. deWitetal.(2005) show that this degeneracy persists after corrections are made to ceredden the colors of Galactic ILÀAeDe stars to attempt to match the lower metallicity content of the Magellanic Clouds.," Moreover, \citet{dew05} show that this degeneracy persists after corrections are made to deredden the colors of Galactic HAeBe stars to attempt to match the lower metallicity content of the Magellanic Clouds."
+ Thus the magnitude of he near-IR excess associated with ESIIC aud ELIIC stars alone is insufficient to conclusively cletermine whether hese objects are ITAcBe stars or classical Be stars., Thus the magnitude of the near-IR excess associated with ESHC and ELHC stars alone is insufficient to conclusively determine whether these objects are HAeBe stars or classical Be stars.
+ Some aspects of the maguitude and time-scale of the shotometric variability exhibited by ILA&eDe stars aud classical Be stars cau be used to help identity the nature of ELIIC aud ESIC stars., Some aspects of the magnitude and time-scale of the photometric variability exhibited by HAeBe stars and classical Be stars can be used to help identify the nature of ELHC and ESHC stars.
+ Classical Be stars are known o aperiodically exhibit dramatic eveuts whereby thev completely lose their disks or regenerate a new disk frou a disk-less stage (normal D to Be to normal D transitious: Underhill&Doazan1982:MeSwiiuctal.2009:Wis-niewskietal.2010:Draper 2011)).," Classical Be stars are known to aperiodically exhibit dramatic events whereby they completely lose their disks or regenerate a new disk from a disk-less stage (normal B to Be to normal B transitions; \citealt{und82,mcs09,wis10,dra11}) )."
+ During these eveuts the stars optical photometry has been observed to change ~0.5 (Bjorkmanetal.2002) to ~0.7 magnitudes (IIlununel1998:Gaudetetal.2002:Miroshuicheukoal. 2003).," During these events the stars optical photometry has been observed to change $\sim$ 0.5 \citep{bjo02} to $\sim$ 0.7 magnitudes \citep{hum98,gan02,mir03}."
+. .J.ILI&-baud. brishtuess variatious of <0.5 (0.95 imaenuitudes have been reported by Ashoketal.(1981). aud Doueherty&Tavlor(1991) over time-scales of huudreds of davs to tens of vears: the largest of these IR variations Likely correspond to large disk loss/disk-renewal eveuts.," J,H,K-band brightness variations of $<$ 0.5 - $\sim$ 0.95 magnitudes have been reported by \citet{ash84} and \citet{dou94} over time-scales of hundreds of days to tens of years; the largest of these IR variations likely correspond to large disk loss/disk-renewal events."
+ Dougherty&Tavlor(1991) Sugeest that a 70.5 magnitude variation corresponds to a change in the density of au optically thin disk of a, \citet{dou94} suggest that a $\sim$ 0.5 magnitude variation corresponds to a change in the density of an optically thin disk of a
+The identification. of possible dvnamical familics )etween the irregular satellites of the giant planets had oen a common task to all the studies. performed. on he subject.,The identification of possible dynamical families between the irregular satellites of the giant planets had been a common task to all the studies performed on the subject.
+ Lhe existence of collisional families could. in winciple be explained by invoking the effects. of impacts »tween pairs of satellites ancl between satellites and roclies on heliocentric orbits., The existence of collisional families could in principle be explained by invoking the effects of impacts between pairs of satellites and between satellites and bodies on heliocentric orbits.
+ “Lhe impact rate between satellite pairs is low even on timescales of the order of the Solar System age. with the only ex‘option of impacts amongst the most massive irregular satellites.," The impact rate between satellite pairs is low even on timescales of the order of the Solar System age, with the only exception of impacts amongst the most massive irregular satellites."
+ The eravitational interactions between the giant. planets and the planctesimals in the early. Solar System may have pushe some of them in planetcrossing orbits., The gravitational interactions between the giant planets and the planetesimals in the early Solar System may have pushed some of them in planet–crossing orbits.
+ This process is still active at the present time and C'entaurs may cross the Ην sphere of the planets., This process is still active at the present time and Centaurs may cross the Hill's sphere of the planets.
+ However. Zahnleetal.(2003) showed that the present. Dux. of bodies. combined. with the small size of irregular satellites. is unable to supply an adequate impact. rate.," However, \cite{zah03} showed that the present flux of bodies, combined with the small size of irregular satellites, is unable to supply an adequate impact rate."
+ ΙΓ collisions between planetesimals and satellites are responsible for the formation of families. these events should. date back sometime between the formation of the giant planets ancl the Late Heavy. The possible existence of dynamical families in. the Saturn satellite system has been explored by using cilferent approaches.," If collisions between planetesimals and satellites are responsible for the formation of families, these events should date back sometime between the formation of the giant planets and the Late Heavy The possible existence of dynamical families in the Saturn satellite system has been explored by using different approaches."
+ Photometric comparisons has been exploited ov Gravetal.(2003):&Holman(2004):Burattietal.(2005). anc were limited. to a few bright objects.," Photometric comparisons has been exploited by \cite{gra03,gra04,bea05} and were limited to a few bright objects."
+ Dynamical methods have been used by Crayetal.(2003):resvornyetal.(2003):Grav&LHolman(2004) but on he limited sample (about one third of the presently known population) of irregular satellites available at that ime.," Dynamical methods have been used by \cite{gra03,nes03,gra04} but on the limited sample (about one third of the presently known population) of irregular satellites available at that time."
+ These methods aimed to identify those satellites which could. have originated. from a common parent body ollowing one or more breakup events., These methods aimed to identify those satellites which could have originated from a common parent body following one or more breakup events.
+ The identification was based on the evaluation through Gauss equations of he dispersion in orbital element space due to the collisional ejection velocities., The identification was based on the evaluation through Gauss equations of the dispersion in orbital element space due to the collisional ejection velocities.
+ In this paper we apply the (hereinafter UCAL)) described. in Zappaláetal.(1990.1904). to the irregular satellites of Saturn.," In this paper we apply the (hereinafter ) described in \cite{zap90,zap94} to the irregular satellites of Saturn."
+ HCM is a clusterdetection algorithm which looks for groupings within a population of minor bodies with small nearestneighbour distances in orbital clement space., HCM is a cluster–detection algorithm which looks for groupings within a population of minor bodies with small nearest–neighbour distances in orbital element space.
+ These distances are translated. into cillerences in. orbita velocities via Gauss equations and. the membership to a cluster or [αν is defined by giving a limiting velocity dillerence (cutoll)., These distances are translated into differences in orbital velocities via Gauss equations and the membership to a cluster or family is defined by giving a limiting velocity difference (cutoff).
+ Nesvornyetal.(2003). adopted a cutoll velocity. value of LOO m/s according to hycrocode mocels (Benz&Aspaugh1999)., \cite{nes03} adopted a cutoff velocity value of $100$ m/s according to hydrocode models \citep{ben99}.
+. Llere we prefer to relax this value to 200 m/s considering the possible range of variability of the mean orbital elements. because of dynamical. effects., Here we prefer to relax this value to $200$ m/s considering the possible range of variability of the mean orbital elements because of dynamical effects.
+ The results we obtained are summarised in table 3 anc interpreted as in the By inspecting our data. we conclude that. as already argued by Nesvornyetal.(2003)... the velocity. dispersion of prograde ancl retrograde. satellites (about 500. m/s [or progrades and more than GOO mj/s for retrogracles) makes extremely implausible that cach of the two groups originated by a single. parent body.," The results we obtained are summarised in table \ref{families} and interpreted as in the By inspecting our data, we conclude that, as already argued by \cite{nes03}, the velocity dispersion of prograde and retrograde satellites (about $500$ m/s for progrades and more than $600$ m/s for retrogrades) makes extremely implausible that each of the two groups originated by a single parent body."
+ In. addition. the classification in dynamical groups based. on the values. of he orbital inclination originally proposed. by Cladimanal.(2001). and. reported by other authors (see Sheppare(2006) and references within) is probably misleading.," In addition, the classification in dynamical groups based on the values of the orbital inclination originally proposed by \cite{gla01} and reported by other authors (see \cite{she06} and references within) is probably misleading."
+" ""roerade satellites like Ixiviuq. LDiraq. Siarnaq ancl Paaliac do share the same inclination but. as à group. they have a velocity. dispersion of over 450 m/s. hardly deriving rom the breakup of a single. parent. body."," Prograde satellites like Kiviuq, Ijiraq, Siarnaq and Paaliaq do share the same inclination but, as a group, they have a velocity dispersion of over $450$ m/s, hardly deriving from the breakup of a single parent body."
+ Lhe enlarge population of retrograde satellites we have analysed show hat the clustering around a single inclination and their association to Phoebe (Cladmaneal.2001) is not an indication of à common origin., The enlarged population of retrograde satellites we have analysed show that the clustering around a single inclination \citep{gla01} and their association to Phoebe \citep{gla01} is not an indication of a common origin.
+ The required velocity dispersion is in fact about 650 We found. two potential dynamical. familics between the prograde satellites: the couple WiviucLiraq and what we term asfamily. composed of Alhiorix. Erriapo. Jarvos and 8/2004 S11.," The required velocity dispersion is in fact about $650$ We found two potential dynamical families between the prograde satellites: the couple Kiviuq–Ijiraq and what we term as, composed of Albiorix, Erriapo, Tarvos and S/2004 S11."
+ The analysis of the retrograde satellites is more complex., The analysis of the retrograde satellites is more complex.
+ There are three possible groups each composed of three. satellites and two others. by two satellites. all characterised by acceptable values of the velocity dispersion. (between 100. and. 170. m/s)," There are three possible groups each composed of three satellites and two others by two satellites, all characterised by acceptable values of the velocity dispersion (between $100$ and $170$ m/s)."
+ A sixth possible group satisfying our acceptance criterion is composed of Narvi and 8/2004 S18. but its interpretation is quite tricky.," A sixth possible group satisfying our acceptance criterion is composed of Narvi and S/2004 S18, but its interpretation is quite tricky."
+ This group shows a high velocity dispersion. at the upper limit of our range. but the dynamical evolution of both satellites is uncertain on a timescale of 10. vears.," This group shows a high velocity dispersion, at the upper limit of our range, but the dynamical evolution of both satellites is uncertain on a timescale of $10^{9}$ years."
+ The orbits of both bodies have the most extreme values of inclination among all retrograde satellites., The orbits of both bodies have the most extreme values of inclination among all retrograde satellites.
+ Our numerical experiments with test particles showed that for such bodies the cecentricity dis. strongly coupled to the inclination (sce fie. 27))., Our numerical experiments with test particles showed that for such bodies the eccentricity is strongly coupled to the inclination (see fig. \ref{forced-e}) ).
+ In our simulations. initially circular. orbits became highly eccentric in less than LO? vears.," In our simulations, initially circular orbits became highly eccentric in less than $10^{6}$ years."
+ Lt is possible that Narvi ane 5/2004 SIS had. similar orbits in the past which later civerged due to the inclinationeecentricity Some of our candidate Families merge at higher values of the velocity dispersion forming bigeer groups we calledclusters., It is possible that Narvi and S/2004 S18 had similar orbits in the past which later diverged due to the inclination–eccentricity Some of our candidate families merge at higher values of the velocity dispersion forming bigger groups we called.
+ Phe most relevant one is that termed. as cluster A jn table 3.., The most relevant one is that termed as cluster A in table \ref{families}.
+ It is made of two thiree-body. families and an incliviclual satellite and it is defined at à velocity cut.oll of 150 m/s. At à velocity cut.olf of 202 m/s cluster A moerges with the twoΡον family related to 8/2004 S15 forming cluster D. Confirming these dynamical groups by comparing their colour. indices is a οποια task because of the limited amount of data available in the literature., It is made of two three-body families and an individual satellite and it is defined at a velocity cut–off of $150$ m/s. At a velocity cut–off of $202$ m/s cluster A merges with the two–body family related to S/2004 S15 forming cluster B. Confirming these dynamical groups by comparing their colour indices is a difficult task because of the limited amount of data available in the literature.
+ The only spectrophotometric cata concerning Saturn's retrograde satellites are those of Phoebe and Ymir. which. according to our analysis. are separated. by a velocity dispersion of more than GOO m/s. Phoebe appears to have colours not compatible with any other irregular satellite of the system. supporting our claim that Phoebe is not related to the rest of Saturn's present population of irregular The situation looks more favourable for prograde families: the colours of three members of the possible Albiorix family are available. with two sets of data for Albiorix itself.," The only spectrophotometric data concerning Saturn's retrograde satellites are those of Phoebe and Ymir, which, according to our analysis, are separated by a velocity dispersion of more than $600$ m/s. Phoebe appears to have colours not compatible with any other irregular satellite of the system, supporting our claim that Phoebe is not related to the rest of Saturn's present population of irregular The situation looks more favourable for prograde families: the colours of three members of the possible Albiorix family are available, with two sets of data for Albiorix itself."
+ The colour data are reported in table 4 with the corresponding le errors., The colour data are reported in table \ref{family-colour} with the corresponding $1\sigma$ errors.
+ These data seem. to be compatible with the hypothesis of a common origin of the eroup at a 37 level., These data seem to be compatible with the hypothesis of a common origin of the group at a $3\sigma$ level.
+(Watson 11995).,(Watson 1995).
+ The observed variation of the light curves with the colour ratios suggests that the absorption process is likely to be bouncd-free absorption of the Balmer continuum., The observed variation of the light curves with the colour ratios suggests that the absorption process is likely to be bound-free absorption of the Balmer continuum.
+ This is predominantly in the U-band. and the variations in the colour ratios and light curves are explained by variations in the amount and density of material confined by the magnetic Ποιά Hines of the white ciwart.," This is predominantly in the U-band, and the variations in the colour ratios and light curves are explained by variations in the amount and density of material confined by the magnetic field lines of the white dwarf."
+ The phase of the onset of the trough is later than that of the pre-eclipse dip seen in the light curves of HU «qe Allin 11999: Bridge 22002). which was identified as the eclipse of the accretion region by the strongly collimated. accretion. stream.," The phase of the onset of the trough is later than that of the pre-eclipse dip seen in the light curves of HU Aqr (Harrop-Allin 1999; Bridge 2002), which was identified as the eclipse of the accretion region by the strongly collimated accretion stream."
+ “This phase is determined by the geometry of the field. lines carrving the acereting material. so a cillerence between systems is not unexpected.," This phase is determined by the geometry of the field lines carrying the accreting material, so a difference between systems is not unexpected."
+ While the onset of the trough feature is Consistent with an eclipse caused. by the accretion stream. an extended accretion curtain would cause absorption over an extended phase range (previous section) and. produce the observed Hat light curves during the trough (Figures E: and 2)).," While the onset of the trough feature is consistent with an eclipse caused by the accretion stream, an extended accretion curtain would cause absorption over an extended phase range (previous section), and produce the observed flat light curves during the trough (Figures \ref{fig:whitelight} and \ref{fig:UBVRcurves}) )."
+ The extent of this accretion curtain can be estimated using the eclipse light curve features and the ecometric model introduced earlier., The extent of this accretion curtain can be estimated using the eclipse light curve features and the geometric model introduced earlier.
+" A value of 4, can be estimated by varying the parameter until the field lines begin to eclipse the accretion region. at the phase set by the start of the trough in the ligh curve."," A value of $R_{\mu}$ can be estimated by varying the parameter until the field lines begin to eclipse the accretion region, at the phase set by the start of the trough in the light curve."
+" For those eveles with brighter streams and accretion regions. where the onset of the trough is earlier. we finc values of £2,~Ode (lor 5=65) and 0.19 (for 7= Ls"")."," For those cycles with brighter streams and accretion regions, where the onset of the trough is earlier, we find values of $R_{\mu}\sim0.14a$ (for $\beta=65^{\circ})$ and $0.19a$ (for $\beta=18^{\circ}$ )."
+" For those eveles where the onset of the trough is later a 6=0.90. we find 2,~0.16a (for 3= 65) and 0.22« (for j— ISO."," For those cycles where the onset of the trough is later at $\phi=0.90$, we find $R_{\mu}\sim0.16a$ (for $\beta=65^{\circ}$ ) and $0.22a$ (for $\beta=18^{\circ}$ )."
+ The outer edge of the curtain. where materia ireads closest to the secondary. can be estimated from. 1e end of the egress of bright. stream material around © = 1.1. and is independent. of 3.," The outer edge of the curtain, where material threads closest to the secondary, can be estimated from the end of the egress of bright stream material around $\phi$ = 1.1, and is independent of $\beta$."
+ This assumes there is no significant continuum emission from the ballistic section of 10 accretion stream. where material is expected to be faint nd cooling as it falls.," This assumes there is no significant continuum emission from the ballistic section of the accretion stream, where material is expected to be faint and cooling as it falls."
+ For those eveles where the bright gaream egress is clearly seen. we find a value of ~θεα.," For those cycles where the bright stream egress is clearly seen, we find a value of $\sim0.42a$."
+ For rose evcles with Lauter streams the egress ofthe stream is =[udot seen., For those cycles with fainter streams the egress of the stream is not seen.
+ We therefore infer that brighter streams result in a wider accretion curtain. with more material in the accretion gaream penetrating further into the magnetosphere.," We therefore infer that brighter streams result in a wider accretion curtain, with more material in the accretion stream penetrating further into the magnetosphere."
+ For faint stream eveles a decline in [ux is seen immecdiately before the eclipse of the accretion region (see Section 3.2))., For faint stream cycles a decline in flux is seen immediately before the eclipse of the accretion region (see Section \ref{sec:streameclipse}) ).
+ This could be due to the eclipse of stream material which is threacing early in the trajectory. and which should emit through magnetic heating.," This could be due to the eclipse of stream material which is threading early in the trajectory, and which should emit through magnetic heating."
+ Alternatively the decline could be caused by absorption by material along the line of sight to the white dwarl and accretion region (see Section 4.3))., Alternatively the decline could be caused by absorption by material along the line of sight to the white dwarf and accretion region (see Section \ref{sec:trough}) ).
+ The trough is absent in. the observations οἱ temillard ((1991) ancl SMO97., The trough is absent in the observations of Remillard (1991) and SM97.
+ “Phe stream also appears to be fainter in both previous observations. although this may be due to 16 poorer sampling.," The stream also appears to be fainter in both previous observations, although this may be due to the poorer sampling."
+ The lack of a bright stream may. be 1e cause of this absence of a trough in their light curves. if 1e two are linked as we suggest.," The lack of a bright stream may be the cause of this absence of a trough in their light curves, if the two are linked as we suggest."
+" An extended: accretion curtain with material. being weacded at dillerent Z6, would allow material to accrete over uj extended. region on the white dwarf.", An extended accretion curtain with material being threaded at different $R_{\mu}$ would allow material to accrete over an extended region on the white dwarf.
+ The foot points of 1e field lines form an arc shape on the white dwarf surface., The foot points of the field lines form an arc shape on the white dwarf surface.
+ uluch an extended accretion region would be consistent with 10 optical1 evelotron models of SM97 which show evidence or an accretion arc or ribbon., Such an extended accretion region would be consistent with the optical cyclotron models of SM97 which show evidence for an accretion arc or ribbon.
+ We have analysed the first high signal-to-noise ratio and hieh time resolution data of EP Dra taken on two consecutive nights at the WITT using S-Came2., We have analysed the first high signal-to-noise ratio and high time resolution data of EP Dra taken on two consecutive nights at the WHT using S-Cam2.
+ The eclipse light curves show variability in the accretion stream and accretion region over the timescale of the orbital period., The eclipse light curves show variability in the accretion stream and accretion region over the timescale of the orbital period.
+ We see no direct evidence in the light curves for the expected. rapid. eclipse of a small accretion region on the white cwark, We see no direct evidence in the light curves for the expected rapid eclipse of a small accretion region on the white dwarf.
+ The rapid eclipse seen in the light curves is à combination of emission from the white chwarl photosphere and the accretion region., The rapid eclipse seen in the light curves is a combination of emission from the white dwarf photosphere and the accretion region.
+ We see evidence for the variability of the aceretion region from the variation in brightness of the rapid eclipse ingress with the varving aceretion stream brightness., We see evidence for the variability of the accretion region from the variation in brightness of the rapid eclipse ingress with the varying accretion stream brightness.
+ Variability seen in the light curves on a longer timescale is inlluenced to some extent by evelotron beaming., Variability seen in the light curves on a longer timescale is influenced to some extent by cyclotron beaming.
+ However from the colour dependence. there is. probably also a contribution from absorption. and this is seen às a trough in the light curves of the second. night.," However from the colour dependence, there is probably also a contribution from absorption, and this is seen as a trough in the light curves of the second night."
+ We attribute the absorption to. bound-free. absorption by material in an extended. acerction curtain obscuring the accretion region ancl white dwarf., We attribute the absorption to bound-free absorption by material in an extended accretion curtain obscuring the accretion region and white dwarf.
+ Phere may also be significant absorption by material located close to the white dwarf above the accretion reeion., There may also be significant absorption by material located close to the white dwarf above the accretion region.
+ Accreting material is threaded. onto many field. lines along the accretion stream trajectory. ancl the location in phase of the onset of the trough or absorption dip provides an estimate of the location of the edge of the accretion curtain.," Accreting material is threaded onto many field lines along the accretion stream trajectory, and the location in phase of the onset of the trough or absorption dip provides an estimate of the location of the edge of the accretion curtain."
+ Variations in the brightness of the accretion stream seen after the ingress of the white cwarl and the accretion region are caused by a change in the location of bright stream material in the accretion curtain and/or a change in the extent of the curtain., Variations in the brightness of the accretion stream seen after the ingress of the white dwarf and the accretion region are caused by a change in the location of bright stream material in the accretion curtain and/or a change in the extent of the curtain.
+ From the extent of the accretion curtain we infer the presence of an extended. accretion arc at the foot points of the acereting field. lines. however this region is still small compared with the size of the white cart.," From the extent of the accretion curtain we infer the presence of an extended accretion arc at the foot points of the accreting field lines, however this region is still small compared with the size of the white dwarf."
+ We acknowledge the contributions of other members of the Research and. Seientifie Support Department of, We acknowledge the contributions of other members of the Research and Scientific Support Department of
+—,.
+ Allowing for enerev-clepenclent diffusion. we get. inserting into(38).. Εν 12 Ey 4)4.," Allowing for energy-dependent diffusion, we get, inserting into, -1 ) ( - E_0 )."
+ As in the ease of(40)... also does not depend on the magnitude of the cdilfision coefficient. only on the distance r; to the source. ancl via(36).. on the Gime since the injection of the particles into the ISM.," As in the case of, also does not depend on the magnitude of the diffusion coefficient, only on the distance $r_i$ to the source, and via, on the time since the injection of the particles into the ISM."
+ In the limit of E—0. reduces to(40).," In the limit of $E\rightarrow 0$, reduces to."
+. We calculated (the contribution from Geminea and BOGSG+14 (o the positron LIS [or distances of ppc (Caraveoetal.1996) and ppc (Manchesteretal.2005) respectively (assuming 7— 2Okvr and J= 60kvr). in addition to the expected anisotropies in the positron LIS.," We calculated the contribution from Geminga and B0656+14 to the positron LIS for distances of pc \citep{C96} and pc \citep{atnf} respectively (assuming $T\,=\,20\,$ kyr and $T\,=\,60\,$ kyr), in addition to the expected anisotropies in the positron LIS."
+ The results for birth periods of 4d0nmuns and GOmams are plotted in (he left panels of Figs., The results for birth periods of ms and ms are plotted in the left panels of Figs.
+ 1 and 2.. where we compare our calculations with the measurements from Doezioetal.(2000) and DuVernoisetal.(2001)..," \ref{fig:geminga} and \ref{fig:bo656}, where we compare our calculations with the measurements from \citet{2000ApJ...532..653B} and \citet{2001ApJ...559..296D}."
+ We have shown that one can expect a non-negligible Cli positron component in the LIS from nearby pulsars that may become dominant above several GeV. in agreement with Ἀίοναetal.(1995) who showed that the high-energv positron LIS may be explained by a voung. nearby source.," We have shown that one can expect a non-negligible CR positron component in the LIS from nearby pulsars that may become dominant above several GeV, in agreement with \citet{1995PhRvD..52.3265A} who showed that the high-energy positron LIS may be explained by a young, nearby source."
+ In (he context of our model. we are able to constrain the permissible pulsar birth period. £2). depending on the magnitude of the interstellar diffusion coefficient.," In the context of our model, we are able to constrain the permissible pulsar birth period $P_0$, depending on the magnitude of the interstellar diffusion coefficient."
+ For the two nearest pulsars with characteristic ages in the range vvr to vvr. Geminga and D06564-14. we show that in particular lor D0656--14 one can expect. in the absence of a backeround flux. an anisotropy in the positron LIS of up to almost3%.. significantly larger than the expected value of 220.257€ [or Geminga.," For the two nearest pulsars with characteristic ages in the range yr to yr, Geminga and B0656+14, we show that in particular for B0656+14 one can expect, in the absence of a background flux, an anisotropy in the positron LIS of up to almost, significantly larger than the expected value of $\approx$ for Geminga."
+ As shown in Figs., As shown in Figs.
+ 1. and 2.. the observed anisotropy also gives an estimate of the contribution of (he pulsar to the positron LIS.," \ref{fig:geminga} and \ref{fig:bo656}, the observed anisotropy also gives an estimate of the contribution of the pulsar to the positron LIS."
+ On the, On the
+orotherwise only Dey;4 and use,There are several other for which we consider the following truncation.
+ 2 > Dp ⋅⋡↴⋟∖⊽∩∐⋜↙∫⋟3 Sul aglr ga)⋅↽↴∩≼←⋟⋅+, We refer the reader to \cite{allrpaper} for a discussion.
+ ; ↜∣ hy)1ro which(3), This implies where $R$ is the Ricci scalar.
+ Sane↜∣ a σα(r+hk a sufficientapproximation since Y alwavs comeswith a [actor of e. Theevent horizonis," For our ansatz to constitute a solution, it must satisfy the equations of motion for the, the moduli $Y^I$,the auxiliary field $T_{01}^-$, as well as the fields $A_a$, and either $V_a$ or $D$ depending on the compensating multiplet used."
+ locatedal r = innerhorizonal tobe valid.we require ..ο forall£-functions for r 2jrWewere not ablet," In the cases that we solved, we observed that when using the hypermultiplet compensating multiplet, the equation of motion for $D$ has an overall factor of $(k^3-k_0)^2$, after substituting the ansatz."
+o extendthis requirement Although the approximation breaksdownat," For $k^3=k_0$, one has to take this limit only after solving the equations of motion, in order not to lose a constraint."
+ the innerhorizon. the solutions are valid inthe physical regionof," The Einstein-Hilbert term in the Lagrangian, determines that “Newton's constant” is given by the unscaled Kähhler potential: Usually one fixes $G_N=1$ as the dilatational $D$ -gauge choice."
+ interest. [romthe eventhorizon," This, however, is too restrictive and does not always allow a solution."
+ to infinity.Ir addition we setthe boundary," Therefore $G_N$ is a function of the radial coordinate, resembling the case of dilaton gravity."
+" conditions: lim,ος £(r)—0.", The metric in the Einstein frame is given by $g^E_{\mu\nu}=G_N^{-1}g_{\mu\nu}$.
+ This givesan asvinploticallyflat solution. The equations of motionfor the vectorfield strengths were derivedin Fy) iB EDT = (iGo," The ADM mass (in Planck units) for a non-normalized metric is given by One may see this by applying the coordinate transformation $t\rightarrow(-g^E_{tt}(\infty))^{-1/2}t,~r\rightarrow g^E_{rr}(\infty)^{-1/2}r$ to get the conventionally normalized line element."
+HF+5 (Εν+FaAES iF. SE, The central charge is given by
+HF+5 (Εν+FaAES iF. SEA, The central charge is given by
+ (2???) (e.g.222?)..," $0 < z \lesssim
+1$ \citep{CFRS95,ECBHG96,LYCE97,CNOC299} \citep[e.g.\ ][]{KIFD01,DFKI01,Vogtetal96,BZB96}."
+ (??2?) K- (999)..," \citep{KWG93,SP99,CLBF00} $K$ \citep{RR93,KC98a,BE00}."
+ K-band ~3 K-band ? ~5000 2)). 3)) A-band (84)). (35)). £25;=0.3.Q4=0.7 Hy=100//kms7!Mpe7!. Ji=0.60 /i ," $K$ $\sim 3$ $K$ \citet{MUNICS1} $\sim 5000$ \ref{s:sample}) \ref{s:photred}) $K$ \ref{s:integ_mf}) \ref{s:discuss}) $\Omega_M = 0.3$$\Omega_{\Lambda} = 0.7$ $H_0 = 100\ h\ \mathrm{km\ 
+ s^{-1}\ Mpc^{-1}}$ $h = 0.60$ $h$ "
+were obtained by Schwarz et al. (,were obtained by Schwarz et al. (
+2004) to determine the orbital period of the svslem.,2004) to determine the orbital period of the system.
+ They [found a period of 1.7 hours from the fit to the radial velocity curve as determined from the convolution of double Gaussians (o the line profiles (Schafter 1985)., They found a period of 1.7 hours from the fit to the radial velocity curve as determined from the convolution of double Gaussians to the line profiles (Schafter 1985).
+ Unlortunately the derived. period was similar in length to the total observing time and couldn't be classified as a definite period due to undersampling., Unfortunately the derived period was similar in length to the total observing time and couldn't be classified as a definite period due to undersampling.
+" Nevertheless the Ila emission showed a clear periodic change in its blue and red components during the observing run which supported a short orbital period (tvpical of WZ See svstems,", Nevertheless the $\alpha$ emission showed a clear periodic change in its blue and red components during the observing run which supported a short orbital period typical of WZ Sge systems.
+ An optically thin disk. showing the WD absorption. is indicative of a short period. low-ii2 svstem (i.e. below (he period eap).," An optically thin disk, showing the WD absorption, is indicative of a short period, $\dot{m}$ system (i.e. below the period gap)."
+ Likewise. (he lack of an accretion disk in the optical spectrum placed a firm upper limit of 3 hours on the orbital period of PQ And.," Likewise, the lack of an accretion disk in the optical spectrum placed a firm upper limit of 3 hours on the orbital period of PQ And."
+ schwarz et al., Schwarz et al.
+ also determined the effective temperature and surface gravity of the white dwarl (WD) using svnthetic spectra from model atmospheres., also determined the effective temperature and surface gravity of the white dwarf (WD) using synthetic spectra from model atmospheres.
+" The best fits gave T,y; = 12.000 zx 1.000 Α΄ and log(g) = 7.7 + 0.3 (egs units) which placed PQ And in the region of the ZZ Celi instability strip (Bergeron el al."," The best fits gave $_{eff}$ = 12,000 $\pm$ 1,000 K and $g$ ) = 7.7 $\pm$ 0.3 (cgs units) which placed PQ And in the region of the ZZ Ceti instability strip (Bergeron et al."
+ 1995: 2004)., 1995; 2004).
+ Thev noted that with its low accretion rate. PQ And was an excellent candidate {ο search [or non-racial oscillations which have recently been observed in other WZ Sge novae.," They noted that with its low accretion rate, PQ And was an excellent candidate to search for non-radial oscillations which have recently been observed in other WZ Sge novae."
+ In (his paper we present the results of a photometric campaign {ο search [or non-radial pulsations in PQ And., In this paper we present the results of a photometric campaign to search for non-radial pulsations in PQ And.
+ Section 2 provides details of the observations., Section 2 provides details of the observations.
+ The analvsis of the data are given in Section 3 and our conclusions follow in Section 4., The analysis of the data are given in Section 3 and our conclusions follow in Section 4.
+ Our photometric observations were carried out using the Orthogonal Parallel Transfer Tinaging Camera (OPTIC. see Howell et al. 2003) at the WIYN observatory 3.5-in telescope located on Wilt Peak.," Our photometric observations were carried out using the Orthogonal Parallel Transfer Imaging Camera (OPTIC, see Howell et al, 2003) at the WIYN observatory 3.5-m telescope located on Kitt Peak."
+ OPTIC is (he only prototvpe orthogonal (ransler CCD imager operating (see Tonrv el al..," OPTIC is the only prototype orthogonal transfer CCD imager operating (see Tonry et al.,"
+ 2002) and consists of two 2IX by 4x CCLD-28 OTCCDs in a single dewar mounted adjacent to each other with a small gap in between the chips., 2002) and consists of two 2K by 4K CCID-28 OTCCDs in a single dewar mounted adjacent to each other with a small gap in between the chips.
+ OPTIC is controlled by standard. SDSU-2 electronics running custom mierocode and reads out (he two OTCCDs via 4 video channels. one located in each corner of the device.," OPTIC is controlled by standard SDSU-2 electronics running custom microcode and reads out the two OTCCDs via 4 video channels, one located in each corner of the device."
+ OPTIC has a read noise of <4 electrons when read at a normal rate of 160 kpix/sec and a gain of 1.45 e/ADU., OPTIC has a read noise of $<$ 4 electrons when read at a normal rate of 160 kpix/sec and a gain of 1.45 e/ADU.
+ We used OPTIC in conventional mode placing the target star and all comparison stars of interest in one of the CCDs., We used OPTIC in conventional mode placing the target star and all comparison stars of interest in one of the CCDs.
+ Two {ime series data seis. were obtained. the first was on the night of 1H September 2004 UT and the second on 13 October 2004 UT.," Two time series data sets were obtained, the first was on the night of 14 September 2004 UT and the second on 13 October 2004 UT."
+ The September observations consisted of ~125. 45 second observations using a Johnson V filter.," The September observations consisted of $\sim$ 125, 45 second observations using a Johnson V filter."
+ The CCD was binned 2 X 2 (the seeing on this night was 1.67) and the readout (ime was 8 seconds.," The CCD was binned 2 X 2 (the seeing on this night was 1.6"") and the readout time was 8 seconds."
+ The October observations consisted of ~100 60 second V-band integrations using 1 X 1 binning (reaclout time was 24 seconds) and {he seeing was 0.5*," The October observations consisted of $\sim$ 100 60 second V-band integrations using 1 X 1 binning (readout time was 24 seconds) and the seeing was 0.5""."
+ The data were reduced using the standard IRAF packages., The data were reduced using the standard IRAF packages.
+ Relative photometry was performed using four different background stars as references., Relative photometry was performed using four different background stars as references.
+ Figure 1 shows a plot of ihe magnitude difference as a function of time for both nights., Figure 1 shows a plot of the magnitude difference as a function of time for both nights.
+ The squares represent, The squares represent
+older starbursts are related to galactic mergers themselves or to the putative coalescence of the central black holes in post-merger galaxies.,older starbursts are related to galactic mergers themselves or to the putative coalescence of the central black holes in post-merger galaxies.
+ The latter possibility can be viably tested by comparing the starburst ages to the dynamic ages of the active and passive lobes in the X-shaped objects., The latter possibility can be viably tested by comparing the starburst ages to the dynamic ages of the active and passive lobes in the X-shaped objects.
+ The KS-test applied to the distributions of the most recent starburst ages gives a statistical significance of 2.30 for the two samples being different., The KS-test applied to the distributions of the most recent starburst ages gives a statistical significance of $\sigma$ for the two samples being different.
+" To account for a possible dependence of this difference on the galactic type, we apply the KS-test to the X-shaped sample and the subsample of control ellipticals."," To account for a possible dependence of this difference on the galactic type, we apply the KS-test to the X-shaped sample and the subsample of control ellipticals."
+ The results of the test show that the starburst ages of the X- sources and the control ellipticals are still different at a statistical significance of 2.1o., The results of the test show that the starburst ages of the X-shaped sources and the control ellipticals are still different at a statistical significance of $\sigma$.
+" In Fig. 8,,"," In Fig. \ref{fig9},"
+ histograms of the logarithm of the ratio of the dynamic age and most recent starburst age are plotted for the X-shaped sources and control sources of Region 0., histograms of the logarithm of the ratio of the dynamic age and most recent starburst age are plotted for the X-shaped sources and control sources of Region 0.
+" The mean logarithmic ratios are —1.29+0.23 and —0.14+0.18 for the X-shaped objects and the control sample, respectively."," The mean logarithmic ratios are $-1.29 \pm 0.23$ and $-0.14
+\pm 0.18$ for the X-shaped objects and the control sample, respectively."
+" The X-shaped sources tend to have starburst ages that are older than the dynamic ages of the radio lobes, while in both the control sample and the control subsample of ellipticals these ages are comparable."," The X-shaped sources tend to have starburst ages that are older than the dynamic ages of the radio lobes, while in both the control sample and the control subsample of ellipticals these ages are comparable."
+ The starburst activity in X-shaped sources is therefore likely not related to the active lobes., The starburst activity in X-shaped sources is therefore likely not related to the active lobes.
+ The KS-test shows that the ratio distributions are different at a statistical significance of 2.8σ., The KS-test shows that the ratio distributions are different at a statistical significance of $\sigma$.
+ This difference in the starburst/dynamic age ratios may support the scenario in which the active lobes of the X-shaped sources are due to a possible reorientation caused by a black hole merger (Merritt Ekers 2002)) that leaves the old low-surface-brightness lobes inactive., This difference in the starburst/dynamic age ratios may support the scenario in which the active lobes of the X-shaped sources are due to a possible reorientation caused by a black hole merger (Merritt Ekers \cite{merritt}) ) that leaves the old low-surface-brightness lobes inactive.
+" Assuming that the low-surface-brightness lobes became inactive when the high-surface ones were activated, the dynamic age of the passive lobes during their active stage can be determined using Eq. 5.."," Assuming that the low-surface-brightness lobes became inactive when the high-surface ones were activated, the dynamic age of the passive lobes during their active stage can be determined using Eq. \ref{wings}."
+ The ratio of the total dynamic age of the active plus passive lobes to the starburst age is plotted in Fig., The ratio of the total dynamic age of the active plus passive lobes to the starburst age is plotted in Fig.
+" 8 (second panel), and it indicates that the starburst age still remains older than the total dynamic age of the lobes."," \ref{fig9} (second panel), and it indicates that the starburst age still remains older than the total dynamic age of the lobes."
+" This suggests that the starburst activity in X-shaped sources had occured before the possible reorientation owing to a black hole merger, and it may have been related to the galactic merger itself."," This suggests that the starburst activity in X-shaped sources had occured before the possible reorientation owing to a black hole merger, and it may have been related to the galactic merger itself."
+" Instead of analyzing all the X-shaped sources with optical spectra available, we can constrain the X-shaped sample to only the X-shaped radio galaxies included in the bona fide sample of Landt et al. (2010))."," Instead of analyzing all the X-shaped sources with optical spectra available, we can constrain the X-shaped sample to only the X-shaped radio galaxies included in the bona fide sample of Landt et al. \cite{landt2010}) )."
+" This implies taking out 10 of the 29 X-shaped sources included in our sample, which leads to a 50% increase in the statistical erros, but does not change the obtained results."," This implies taking out 10 of the 29 X-shaped sources included in our sample, which leads to a $\%$ increase in the statistical erros, but does not change the obtained results."
+" The statistical studies would be improved, on the other hand, by the addition of more X-shaped radio sources to the sample."," The statistical studies would be improved, on the other hand, by the addition of more X-shaped radio sources to the sample."
+ This will be done with the availability of new optical spectra., This will be done with the availability of new optical spectra.
+One of the fundamental problems in (he search for exoplanets via transits is (he relatively small fraction of svstems exhibiting periodic (ransils that are found {ο be caused by exoplanets alter lollow-up observations reveal the nature of the orbiting body.,One of the fundamental problems in the search for exoplanets via transits is the relatively small fraction of systems exhibiting periodic transits that are found to be caused by exoplanets after follow-up observations reveal the nature of the orbiting body.
+ The process of verification consumes a great deal of telescope time on top-class instruments., The process of verification consumes a great deal of telescope time on top-class instruments.
+ This process would be, This process would be
+orders of magnitude shorter than a usual OSSE exposure.,orders of magnitude shorter than a usual OSSE exposure.
+ OSSE observed GRO J1655-40 during the 1996 outburst VHS when the source was very variable on time scales of hours and longer., OSSE observed GRO J1655-40 during the 1996 outburst VHS when the source was very variable on time scales of hours and longer.
+ In this case the long accumulation time can result in a biases in the observed spectral shape., In this case the long accumulation time can result in a biases in the observed spectral shape.
+ We suggest that the presence of the extended power law up to ~700 keV in OSSE spectra can be a result of the long accumulation time scale when specific details of the spectra can be biased particularly at high energies., We suggest that the presence of the extended power law up to $\sim 700$ keV in OSSE spectra can be a result of the long accumulation time scale when specific details of the spectra can be biased particularly at high energies.
+" Despite the fact that HEXTE is not sensitive above 300 keV, it is able to sample the source spectrum with much more detailed temporal resolution."," Despite the fact that HEXTE is not sensitive above 300 keV, it is able to sample the source spectrum with much more detailed temporal resolution."
+ Our analysis of the PCA/HEXTE from XTE 1550-564 indicates that VHS spectra do show exponential turnover at energies about 200 keV Fig. , Our analysis of the PCA/HEXTE from XTE 1550-564 indicates that VHS spectra do show exponential turnover at energies about 200 keV (see Fig. \ref{cutoff_vs_index_1998}) ).
+"Moreover, our results clearly show that the (seecutoff energy4)). changes gradually from the LHS through the IS towards the HSS."," Moreover, our results clearly show that the cutoff energy changes gradually from the LHS through the IS towards the HSS."
+ It is worth noting that Mottaetal. concluded that the cutoff power law in the PCA/HEXTE(2009) spectrum of GX 339-4 is most likely due to one spectral component., It is worth noting that \citet{motta} concluded that the cutoff power law in the PCA/HEXTE spectrum of GX 339-4 is most likely due to one spectral component.
+" These facts indicate strongly that HEXTE more be more reliable source of information on the hard tails of X-ray spectra, at least, up to 300 keV than OSSE."," These facts indicate strongly that HEXTE more be more reliable source of information on the hard tails of X-ray spectra, at least, up to 300 keV than OSSE."
+" In fact, there are more physical arguments in favor of the versus OSSE observations of the hard X-ray tails in PCA/HEXTEBH X-ray binaries."," In fact, there are more physical arguments in favor of the PCA/HEXTE versus OSSE observations of the hard X-ray tails in BH X-ray binaries."
+" Specifically, the dynamical time scale which is related to the magneto-acoustic oscillations of the Compton cloud (CC) is ta~ where L.. is the CC size and V, is the magnetoacoustic2Lec/Va velocity [see e.g. Titarchuk&Sha- (2005)]."," Specifically, the dynamical time scale which is related to the magneto-acoustic oscillations of the Compton cloud (CC) is $t_d\sim 2L_{cc}/V_a$ where $L_{cc}$ is the CC size and $V_a$ is the magnetoacoustic velocity [see e.g. \cite{ts05}] ]."
+" With the assumption that the characteristicCC size L4. in the HSS is of the order of (5—10)(3Rs)~108(m/10), where Rg=3x is the Schwarchild radius, m is a BH mass in solar units, V,~10'(kT,/1 keV) cm s-!, KT. is Compton cloud temperature, we obtain that tg~20[(m/10)/(kT./lkeV)| s. Thus, the dynamical time scale of the Compton cloud £4 is only one order magnitude140.AAA shortera than the PCA/HEXTE spectrum accumulation time of ~105 s and we rather believe that the PCA/HEXTE spectra including its turnover more precisely describe the shape of the emergent spectra than that by the OSSE spectrahigh/soft averaged over 2 magnitudes longer periods."," With the assumption that the characteristicCC size $L_{cc}$ in the HSS is of the order of $(5-10) (3 R_S) \sim 10^8(m/10)$, where $R_S=3\times 10^5m$ is the Schwarchild radius, $m$ is a BH mass in solar units, $V_a\sim 10^7 (kT_e/1$ keV) cm $^{-1}$, $kT_e$ is Compton cloud temperature, we obtain that $t_d\sim 20[(m/10)/(kT_e/1$ keV)] s. Thus, the dynamical time scale of the Compton cloud $t_d$ is only one order magnitude shorter than the PCA/HEXTE spectrum accumulation time of $\sim 10^3$ s and we rather believe that the PCA/HEXTE spectra including its turnover more precisely describe the shape of the high/soft emergent spectra than that by the OSSE spectra averaged over 2 magnitudes longer periods."
+ We present further observational evidence supporting the theory of the bulk motion (converging) flow near accreting black holes., We present further observational evidence supporting the theory of the bulk motion (converging) flow near accreting black holes.
+" We show that when sufficient cooling is provided by the mass supply from the donor star, the Comptonizing media is completely cooled down and the origin of the extended cutoff power law is due to non-thermal bulk motion process."," We show that when sufficient cooling is provided by the mass supply from the donor star, the Comptonizing media is completely cooled down and the origin of the extended cutoff power law is due to non-thermal bulk motion process."
+ The energy of the high energy cutoff observed during 1998 outbursts from XTE J1550-564 (as well as during 2007 outburst from GX 339-4 reported by Mottaetal. (2009))) behaves in striking agreement with the bulk motion scenario., The energy of the high energy cutoff observed during 1998 outbursts from XTE J1550-564 (as well as during 2007 outburst from GX 339-4 reported by \citet{motta}) ) behaves in striking agreement with the bulk motion scenario.
+ Combined with the previously reported effect of index saturation in BH X-ray binaries (Shaposhnikov&Titarchuk2009) the cutoff energy behavior provides robust observational signature of the bulk motion region near the accreting object., Combined with the previously reported effect of index saturation in BH X-ray binaries \citep{st09} the cutoff energy behavior provides robust observational signature of the bulk motion region near the accreting object.
+" As a direct consequence of the specific drain properties of the BH, this signature presents the most direct observational evidence of the existence of the astrophysical black holes."," As a direct consequence of the specific drain properties of the BH, this signature presents the most direct observational evidence of the existence of the astrophysical black holes."
+ The RXTE data for this work was aquired through HEASARC., The data for this work was aquired through HEASARC.
+ Authors acknowledge the support of this research by NASA grant NNX09AF02G., Authors acknowledge the support of this research by NASA grant NNX09AF02G.
+characteristic of accretion on a putative compact object and is. for now. the main reason to assune that SPAT are binary svstenus.,"characteristic of accretion on a putative compact object and is, for now, the main reason to assume that SFXT are binary systems."
+ As the sources are flaring at most once per dav. their average lard X-ray Iuuiuositv is very low. reaching (0.2Ls1024 erg/s.," As the sources are flaring at most once per day, their average hard X-ray luminosity is very low, reaching $(0.2-4)\times 10^{34}~\rm{erg/s} $ ."
+ It is therefore very unlikely that those systenis have average orbital raclius lower than 1tHanie ~10R.., It is therefore very unlikely that those systems have average orbital radius lower than $10^{13}~\rm{cm}$ i.e. $\sim 10~R_*$.
+ One expects orbital periods larger than 15 davs and underflow Roche lobe systems (note that no orbital period has vet been derived in any of these systenis)., One expects orbital periods larger than 15 days and underflow Roche lobe systems (note that no orbital period has yet been derived in any of these systems).
+ The average hard Nay huuinosity of the SENT svstems in quiescence is <6.6&1075ere/s (which corresponds to 0.2 cet/s)., The average hard X-ray luminosity of the SFXT systems in quiescence is $< 6.6 \times 10^{33}~\rm{erg/s}$ (which corresponds to 0.2 ct/s).
+ This is au upper Πιτ as the mosaics used to measure those quiesceut fiuxes most probably coutain faint flares. not detected dunues single poiutines.," This is an upper limit as the mosaics used to measure those quiescent fluxes most probably contain faint flares, not detected during single pointings."
+ The INTEGRAL data alone do not exclude that there is no quiescent hard N-ray ΕΜ xvsteuis., The INTEGRAL data alone do not exclude that there is no quiescent hard X-ray emission in these systems.
+ The interaction of a compact object with a dense chup formed in the wind of a massive companion leads to lucreased accretion rate and hard ταν cussion (7?).., The interaction of a compact object with a dense clump formed in the wind of a massive companion leads to increased accretion rate and hard X-ray emission \citep{Leyder2007}.
+" The free-fall time from the accretion radius 2,=2«1010cni towards the compact object is of the order of (2.3)ς10%s", The free-fall time from the accretion radius $R_a = 2\times 10^{10}~ \rm{cm}$ towards the compact object is of the order of $(2-3)\times10^2~\rm{s}$.
+ As the intrinsic aneular momenta of the accreted σας is πα (2). the Πα is mostly radial (down to the Compton radius) aud proceeds at the Dondi-ITovle accretion rate., As the intrinsic angular momentum of the accreted gas is small \citep{Illarionov2001} the infall is mostly radial (down to the Compton radius) and proceeds at the Bondi-Hoyle accretion rate.
+ The accretion could slow down if the wind clumps have internal turbulence or harbor significant intrinsic aneular ποιοιτα (77).," The accretion could slow down if the wind clumps have internal turbulence or harbor significant intrinsic angular momentum \citep{Theuns1996,Krumholz2005}."
+ This is however uulikelv iu a lighly supersonic wind. aud supported by the very sharp N-rayv Hare cutoff observed ou time scale of the order of few 100 sin some of these systems (27)..," This is however unlikely in a highly supersonic wind, and supported by the very sharp X-ray flare cutoff observed on time scale of the order of few 100 s in some of these systems \citep{ZuritaWalter2007, gonzalez04aa}."
+ With a duration of fj;=2LO ks. the observed short rard N-ray fares are siguificautly longer than the frec-fall ine.," With a duration of $t_{fl}=2-10$ ks, the observed short hard X-ray flares are significantly longer than the free-fall time."
+" The flare duration is therefore very probably linked with the thickness of the clumps which. for a clump radial velocity V,=105cns. is ha=Vy\tH~(210)«10H cu."," The flare duration is therefore very probably linked with the thickness of the clumps which, for a clump radial velocity $V_{cl}=10^8 ~\rm{cm/s}$, is $h_{cl} = V_{cl} \times t_{fl} \sim (2-10) \times 10^{11}~\rm{cm}$ ."
+ The average hard A-rav Iuninositv resulting frou an interaction between the compact object aud the chimp cau be evaluated as Ly=6€δωJDέμ Gvhere €~ 0.1) aud the mass of a clump can then be estimated as where Ry is the radius of the clump perpendicular to the radial distance., The average hard X-ray luminosity resulting from an interaction between the compact object and the clump can be evaluated as $L_X = \epsilon~M_{acc}c^2/t_{fl}$ (where $\epsilon\sim0.1$ ) and the mass of a clump can then be estimated as where $R_{cl}$ is the radius of the clump perpendicular to the radial distance.
+" In the case of a spherical clump. If N is the rate of chuups emitted by the star. the observed hard Nav fhue rate is given by Thed rate ofH niasz-loss iu+ the form. of. wind. chumps can then be estimated as For ao =l velocity law aud spherical clumps. the munber of chumps located between 1.0572 aud H4, cal be evaluated as where t(r) is the wind flight time (?).."," In the case of a spherical clump, If $\dot{N}$ is the rate of clumps emitted by the star, the observed hard X-ray flare rate is given by The rate of mass-loss in the form of wind clumps can then be estimated as For a $\beta=1$ velocity law and spherical clumps, the number of clumps located between $1.05R_*$ and $R_{orb}$ can be evaluated as where t(r) is the wind flight time \citep{Hamann2001}."
+ Assuming spherical chuups. the chunpdensity at the orbital radius is py=weanLy-)τνag10ll©GaycllB and the corresponding (homogeneous wind cdoensitv is pn—o—ME-LLqpVa).(10d1loseL;uua3umx)yr1.5«10σσ ?.," Assuming spherical clumps, the clumpdensity at the orbital radius is $\rho_{cl}=\left(\frac{L_X}{10^{36}~\rm{erg/s}}\right) ~7\times 10^{-14} ~\rm{g~cm}^{-3}$ and the corresponding homogeneous wind density is $\rho_h=\dot{M}_{cl}/(4\pi~R_{orb}^2~V_{cl})=
+\left(\frac{10~\rm{d}}{T}\frac{L_X}{10^{36}~\rm{erg/s}}\frac{t_{fl}}{3~\rm{ks}}\right)
+~1.5\times 10^{-15}~\rm{g~cm}^{-3}$ ."
+ The ehuup voluue filling factor at the orbital radius is fy=‘=](445)f0.02.E and (<4)15«1022 an.," The clump volume filling factor at the orbital radius is $
+f_V = \frac{\rho_h}{\rho_{cl}} = 
+\left(\frac{10~\rm{d}}{T}\frac{t_{fl}}{3~\rm{ks}}\right)
+~0.02$ and the corresponding porosity length \citep{owocki2006,OskinovaHamannFeldmeier2007} is $h=\frac{R_{cl}}{f_V}=
+\left(\frac{T}{10~\rm{d}}\right)
+~15\times 10^{12} ~\rm{cm}$ ."
+" Tt the deusitv+ of. a clump decreases withB radiusH as rrD7Ἱ andl its mass remains constant. the averaged hionnogeuceous wind deusitv within A4, is pj=NALA(imYu)Hobosfuz)=7.10+5οxem3? aud the average↜ chup. volume filling factor aud porosity leugth could be estimated. as 0.1. and 3.<10132cui respectively."," If the density of a clump decreases with radius as $r^{-2\beta}$ and its mass remains constant, the averaged homogeneous wind density within $R_{obs}$ is $\overline{\rho_{h}}=N M_{cl}/(\frac{4}{3}\pi 
+R_{orb}^3
+) = 
+\left(\frac{10~\rm{d}}{T}\frac{L_X}{10^{36}~\rm{erg/s}}\frac{t_{fl}}{3~\rm{ks}}\right)
+~7\times 10^{-15} ~\rm{g~cm}^{-3}$ and the average clump volume filling factor and porosity length could be estimated as 0.1 and $3\times10^{12} ~\rm{cm}$, respectively."
+. The variety of ty. T aud Εμ tha are observed probably reflects a rauge of clump parameters aud orbital radii.," The variety of $t_{fl}$, $T$ and $F_{fl}$ that are observed probably reflects a range of clump parameters and orbital radii."
+ Several of the average clump parameters estimated above. im particular the chuup deusitv. filling factor aud porosity leugth do uot depend ou the orbital radius. which is unknown. and only slowly depend on the observed quautitics.," Several of the average clump parameters estimated above, in particular the clump density, filling factor and porosity length do not depend on the orbital radius, which is unknown, and only slowly depend on the observed quantities."
+ These average parameters match the macro-clumping scenario proposed bv ? to reconcile clunipiug auc niass-loss rates.," These average parameters match the macro-clumping scenario proposed by \cite{OskinovaHamannFeldmeier2007}
+ to reconcile clumping and mass-loss rates."
+" Their model depeuds on a free parameter Ly=Liga?Vir)Voxj3)E?, where Lir) is the chump separation in unit of A..."," Their model depends on a free parameter $L_0=L(r) (r^2V(r)/V(\infty))^{-1/3}$, where $L(r)$ is the clump separation in unit of $R_*$."
+ Our average clumping parameters correspond to Ly=0.35., Our average clumping parameters correspond to $L_0=0.35$.
+ The muuber of clumps derived above is also comparable to evaluations by ? and ??..," The number of clumps derived above is also comparable to evaluations by \cite{Lepine1999} and \cite{OskinovaFeldmeierHamann2006, OskinovaHamannFeldmeier2007}."
+ The ποιο filling factor and the clamp mass-loss rate are also sinular to those derived bv ?. from the study of ultraviolet and optical line profiles iu two super-elaut stars., The volume filling factor and the clump mass-loss rate are also similar to those derived by \cite{Bouret2005} from the study of ultraviolet and optical line profiles in two super-giant stars.
+ The cohunu density through a clump can also be estimated as Nyy=can(wt:un)5«102o02 3.," The column density through a clump can also be estimated as $N_H = \frac{M_{cl}}{R_{cl}^2m_p}=
+\left(\frac{L_X}{10^{36}\rm{erg/s}}\frac{t_{fl}}{3\rm{ks}}\right)
+~5\times 10^{22}\rm{cm}^{-2}$ ."
+ The chumps remain optically thin iu tle N-ravs., The clumps remain optically thin in the X-rays.
+ The activity surrounding some of the most significant flares unav be related to tidal effects on the clumps themself aud induced turbulence., The activity surrounding some of the most significant flares may be related to tidal effects on the clumps themself and induced turbulence.
+ The long flare that has, The long flare that has
+p(r)οςr .,"$\rho(r) \propto
+r^{-\gamma}$ ."
+ 7 defines an upper limit to the slope; a steeper slope would require more mass interior to r than is measured., $\gamma$ defines an upper limit to the slope; a steeper slope would require more mass interior to $r$ than is measured.
+ We note that this measure was used by ? for resimulated haloes of different masses but comparable particle resolution in their study of the universality of the mass profile., We note that this measure was used by \citet{2004MNRAS.349.1039N} for resimulated haloes of different masses but comparable particle resolution in their study of the universality of the mass profile.
+" In we plot the radial variation of + for all haloes that satisfy the FigureselectionB] criteria of and are in the same mass- as those used in D.2]colour-coded according to the spectral index n of the model insectionB.3},which they form."," In Figure \ref{fig:maxslope_rr2} we plot the radial variation of $\gamma$ for all haloes that satisfy the selection criteria of \ref{sec:halo_selection} and are in the same mass-range as those used in section \ref{sec:fitting}, colour-coded according to the spectral index $n$ of the model inwhich they form."
+" Note that we have normalised these profiles to r_2, the radius at which the differential mass profile pr? reaches a maximum."," Note that we have normalised these profiles to $r_{-2}$, the radius at which the differential mass profile $\rho\,r^2$ reaches a maximum."
+" For a NFW profile, r_2 is identical to the scale radius rs and so it provides an attractive non-parametric measure ofconcentration}."," For a NFW profile, $r_{-2}$ is identical to the scale radius $r_s$ and so it provides an attractive non-parametric measure of."
+" When normalising the radius in this manner, we find excellent agreement between the average shapes of the Υ profiles between the different n models."," When normalising the radius in this manner, we find excellent agreement between the average shapes of the $\gamma$ profiles between the different $n$ models."
+" However, the scatter between profiles within a given simulation is significant (cf."," However, the scatter between profiles within a given simulation is significant (cf."
+" upper panel of figure)), which strengthens our argument that it is essential to use a statistical sample of haloes when discussing the asymptotic inner slope."," upper panel of figure \ref{fig:maxslope_rr2}) ), which strengthens our argument that it is essential to use a statistical sample of haloes when discussing the asymptotic inner slope."
+" It is noticeable that the average profile in each model we have looked at continues to becomes shallower with decreasing radius, without showing evidence for convergence to an asymptotic value (c.f.?).."," It is noticeable that the average profile in each model we have looked at continues to becomes shallower with decreasing radius, without showing evidence for convergence to an asymptotic value \citep[c.f.][]{2004MNRAS.349.1039N}."
+ We find similar behaviour when considering only haloes in the high-mass This figure also confirms our suspicion that it is the scale radius r_2 or concentration cvi;=Tvir/7—2 rather than the slope α that varies with n., We find similar behaviour when considering only haloes in the high-mass This figure also confirms our suspicion that it is the scale radius $r_{-2}$ or concentration $c_{\rm vir}=r_{\rm vir}/r_{-2}$ rather than the slope $\alpha$ that varies with $n$.
+ We find that haloes forming in the n=—0.5 model tend to be more concentrated (cf., We find that haloes forming in the $n=-0.5$ model tend to be more concentrated (cf.
+ figure Al below)than haloes forming in runs with steeper spectral indices., figure \ref{fig:concentration} below)than haloes forming in runs with steeper spectral indices.
+ Therefore fits with a generalised NFW profile (cf., Therefore fits with a generalised NFW profile (cf.
+" equation [9)) tend to favour smaller values of a for steeper n because these haloes tend to be less concentrated, and so we resolve the profile to smaller fractions of r_—2, Where the flattening of the profile is more apparent."," equation \ref{eq:extend_nfw}) ) tend to favour smaller values of $\alpha$ for steeper $n$ because these haloes tend to be less concentrated, and so we resolve the profile to smaller fractions of $r_{-2}$, where the flattening of the profile is more apparent."
+ Therefore a shallower effective slope a will tend to be preferred., Therefore a shallower effective slope $\alpha$ will tend to be preferred.
+ It is a relatively straightforward exercise to obtain expressions for equation [T1] for the NFW profile and the ? profile., It is a relatively straightforward exercise to obtain expressions for equation \ref{eq:maxslope} for the NFW profile and the \citet{1998ApJ...499L...5M} profile.
+" Two other analytical model profiles have been promisingly applied to halo density profiles, the ? and ? profiles, which provide better fits than the NFW profile."," Two other analytical model profiles have been promisingly applied to halo density profiles, the \citet{1965Einasto} and \cite{1997A&A...321..111P} profiles, which provide better fits than the NFW profile."
+" ? argue that the Einasto model performed best in fitting halo profiles, followed closely by the Prugniel-Simien model."," \citet{2006AJ....132.2685M}
+ argue that the Einasto model performed best in fitting halo profiles, followed closely by the Prugniel-Simien model."
+ Expressions for Υ for the Einasto and Prugniel-Simien models are given in the Appendix [B]., Expressions for $\gamma$ for the Einasto and Prugniel-Simien models are given in the Appendix \ref{app:maximumslope}.
+ In the lower panel of figure B] we over-plot the averaged -curves with the theoretical predictions derived for the four analytic profiles mentioned above., In the lower panel of figure \ref{fig:maxslope_rr2} we over-plot the averaged $\gamma$ -curves with the theoretical predictions derived for the four analytic profiles mentioned above.
+ We find that the Moore profile is unable to reproduce the observed behaviour., We find that the Moore profile is unable to reproduce the observed behaviour.
+" The NFW profile is consistent with our data for the 512-0.50 and 512-1.50 runs, but it fails to reproduce the continual flattening of  to small radii."," The NFW profile is consistent with our data for the 512-0.50 and 512-1.50 runs, but it fails to reproduce the continual flattening of $\gamma$ to small radii."
+" In contrast, both the Einasto and Prugniel-Simien profiles capture the behaviour of our data well at small "," In contrast, both the Einasto and Prugniel-Simien profiles capture the behaviour of our data well at small ."
+"Interestingly we note that all of the analytical profiles tend to radij].overestimate the slope of the density profile at large r/r_2, which appears to roll over and flatten off."," Interestingly we note that all of the analytical profiles tend to overestimate the slope of the density profile at large $r/r_{-2}$, which appears to roll over and flatten off."
+" This is most apparent for the data points from the n=—0.5 In Figure we make explicit the connection between r..» and the concentrationA] cyir=Tvir/r—2, showing how cvi, varies with halo mass (given by the number of particles within the virial radius Nyir; upper panel), and the spectral index n (lower panel)."," This is most apparent for the data points from the $n=-0.5$ In Figure \ref{fig:concentration} we make explicit the connection between $r_{-2}$ and the concentration $c_{\rm vir}=r_{\rm
+ vir}/r_{-2}$, showing how $c_{\rm vir}$ varies with halo mass (given by the number of particles within the virial radius $N_{\rm vir}$; upper panel), and the spectral index $n$ (lower panel)."
+" A similar figure can befound in ?,, who looked at scale-free models with spectral indices of n=—0.5,—1.0, —1.5, but who derived their concentrations from fits ofNFW profiles."," A similar figure can befound in \cite{1997ApJ...490..493N}, , who looked at scale-free models with spectral indices of $n=-0.5, -1.0, -1.5$ , but who derived their concentrations from fits ofNFW profiles."
+" Although our concentrations are calculated in a non-parametric manner, it is reassuring that we see a similar trend to that reported in ?.."," Although our concentrations are calculated in a non-parametric manner, it is reassuring that we see a similar trend to that reported in \cite{1997ApJ...490..493N}. ."
+Data from global helioseismologv. (Thompsonetal.2003) have shed some light on ihe internal rotation of the sun.,Data from global helioseismology \citep{Thompson03} have shed some light on the internal rotation of the sun.
+ Throughout the convective envelope. the rotation rate decreases monotonicallv Coward (he poles.," Throughout the convective envelope, the rotation rate decreases monotonically toward the poles."
+ Near the base of the convection zone. there is a sharp (transition between differential rotation in the convective envelope and. nearly uniform rotation in the radiative interior.," Near the base of the convection zone, there is a sharp transition between differential rotation in the convective envelope and nearly uniform rotation in the radiative interior."
+ This (ransition region has become known as the, This transition region has become known as the
+in OSC'A (no focal or Lvot mask) is illustrated in Fig. 7..,in OSCA (no focal or Lyot mask) is illustrated in Fig. \ref{aperture}.
+ The normalised. peak intensity ratio of the PSE produced bv this aperture compared to the same aperture without segmentation (with no phase mismatching) is 0.97., The normalised peak intensity ratio of the PSF produced by this aperture compared to the same aperture without segmentation (with no phase mismatching) is 0.97.
+ From this simple calculation it is seen that a scementec AO system is of lower contrast by design compared to a continuous [ace-sheet mirror., From this simple calculation it is seen that a segmented AO system is of lower contrast by design compared to a continuous face-sheet mirror.
+ Llowever. the loss in performance when using a coronagraph with a segmentecl mirror is much more than34.," However, the loss in performance when using a coronagraph with a segmented mirror is much more than."
+. The reason for this is can be seen by examining the distribution of light in the pupil plane after the application of the focal stop. an example is given in Fig. 9((," The reason for this is can be seen by examining the distribution of light in the pupil plane after the application of the focal stop, an example is given in Fig. \ref{pupil_phase}( ("
+a).,a).
+ For the case of a Gaussian focal plane mask applied. to the PSE obtained by using the aperture in Vig. ΤΡ]. , For the case of a Gaussian focal plane mask applied to the PSF obtained by using the aperture in Fig. \ref{aperture}( (
+it is found that of the total light in the pupil is clistributecl about the segment. edges.,"b), it is found that of the total light in the pupil is distributed about the segment edges."
+ So if à normal Lyot mask is used here (primary. secondary. ancl vane masking) a significant proportion of the light from that remaining of the masked star will stav in the final image. thus reducing the suppression performance.," So if a normal Lyot mask is used here (primary, secondary and vane masking) a significant proportion of the light from that remaining of the masked star will stay in the final image, thus reducing the suppression performance."
+ The use of a more complex Lyot mask which masks the individual mirror segments as well as the telescope primary and secondary gives improved suppression performance compared to a Lvot mask which only masks the telescope primary and secondary., The use of a more complex Lyot mask which masks the individual mirror segments as well as the telescope primary and secondary gives improved suppression performance compared to a Lyot mask which only masks the telescope primary and secondary.
+ The individual segments in NAOALL are T.6mim across with a ~0.loim gap between each one., The individual segments in NAOMI are 7.6mm across with a $\sim$ 0.1mm gap between each one.
+ The ratio of gap to segment size is the same order of magnitude to those proposed. lor future. segmented extremely large telescopes (ELS). ic. lim segments with IO0mm gaps.," The ratio of gap to segment size is the same order of magnitude to those proposed for future segmented extremely large telescopes (ELTs), i.e. 1m segments with 10mm gaps."
+ Hence these results have relevance for high contrast imaging with 1911»., Hence these results have relevance for high contrast imaging with ELTs.
+ To model the effect of the gaps between the NAOALL segments more pixels are required across the aperture., To model the effect of the gaps between the NAOMI segments more pixels are required across the aperture.
+ The results shown in Fig., The results shown in Fig.
+ S were obtained using 1024. pixels across the aperture diameter with a 2 pixel ga ονου the mirror segments.," \ref{grid_plot}
+ were obtained using 1024 pixels across the aperture diameter with a 2 pixel gap between the mirror segments."
+ Due to the size of this array this was à static simulation (i.e. not an AO simulation). a 2 times padding factor was used in the FETs.," Due to the size of this array this was a static simulation (i.e. not an AO simulation), a 2 times padding factor was used in the FFTs."
+ The lines show the mean trends (a convolution filter has been applied to flatten out the high frequeney periodicity) that the segementect aperture produces., The lines show the mean trends (a convolution filter has been applied to flatten out the high frequency periodicity) that the segmented aperture produces.
+ In the high contrast. direction (45° to image axes) the benefit is most evident at. distance 75 aresec [from the centre. reducing counts by 2. orders. of magnitude.," In the high contrast direction $45^\circ$ to image axes) the benefit is most evident at distance $>5$ arcsec from the centre, reducing counts by 2 orders of magnitude."
+ For the racial averaged lines (which include the bright axial dilfraction peaks) the benefit of the grid. Lyot mask is noticeable from 1 arcsec., For the radial averaged lines (which include the bright axial diffraction peaks) the benefit of the grid Lyot mask is noticeable from 1 arcsec.
+ For the full AO simulations (with 256 pixels across the aperture. 4. padding and no gaps). the clleet of phase mismatching between the segments can be seen as an about the segments in the pupil plane subsequent to the application of the occulting mask. as shown in Fig. 9((," For the full AO simulations (with 256 pixels across the aperture, $4\times$ padding and no gaps), the effect of phase mismatching between the segments can be seen as an about the segments in the pupil plane subsequent to the application of the occulting mask, as shown in Fig. \ref{pupil_phase}( ("
+d).,d).
+" Segments with the greatest intensity are those that are ""turned off and so have the greatest phase step between them and adjacent segments.", Segments with the greatest intensity are those that are `turned off' and so have the greatest phase step between them and adjacent segments.
+ Taking gaps and. phase errors between segments into consideration the benefit of a Lyot mask which masks the individual mirror segments becomes apparent., Taking gaps and phase errors between segments into consideration the benefit of a Lyot mask which masks the individual mirror segments becomes apparent.
+ A Lyot mask matched to the NAOMIE mirror segments under sizing of segments) was created with OSCA (shown in Fig., A Lyot mask matched to the NAOMI mirror segments under sizing of segments) was created with OSCA (shown in Fig.
+ 2. (inset top. left-hand mask)) but is as vet untested on-sky.," \ref{lyot} (inset top, left-hand mask)) but is as yet untested on-sky."
+ The mask requires very careful alignment and there has been insullicient. commissioning time to trial this new mask., The mask requires very careful alignment and there has been insufficient commissioning time to trial this new mask.
+ Telescope schedules allowing. trials may. be performed towards the end of 2005.," Telescope schedules allowing, trials may be performed towards the end of 2005."
+ Aspatially filtered collimated 613nm laser beam and a series of lenses and masks were arranged in the laboratory to simulate an ideal coronagraphic svstem., A spatially filtered collimated 613nm laser beam and a series of lenses and masks were arranged in the laboratory to simulate an ideal coronagraphic system.
+ A simple iris was used. for the entrance. aperture and. another one at dizuneter to act as the Lyot mask., A simple iris was used for the entrance aperture and another one at diameter to act as the Lyot mask.
+ Images were recorded at the final focus for a variety of different occulting spots using a Santa Barbara Instrument. Croup (SBLC) camera. this consists of a 3755242 pixel. Pelticr-coolec CCD.," Images were recorded at the final focus for a variety of different occulting spots using a Santa Barbara Instrument Group (SBIG) camera, this consists of a $375\times242$ pixel, Peltier-cooled CCD."
+ The usual calibrations were taken - dark frames and background images between every image., The usual calibrations were taken - dark frames and background images between every image.
+ These tests were performed. after OSCA had. been galipped to the WIEEF., These tests were performed after OSCA had been shipped to the WHT.
+. Phe Gaussian masks were 'ominmissioned. at a later date anc a method. to compare rem. to the standard. masks on OSCA was devised., The Gaussian masks were commissioned at a later date and a method to compare them to the standard masks on OSCA was devised.
+ The lithography5 template plate was used in 1place of a 0.5 aresec isc occulting mask. approximately the same as the full-width half-maximum of the Gaussian masks.," The lithography template plate was used in place of a 0.5 arcsec disc occulting mask, approximately the same as the full-width half-maximum of the Gaussian masks."
+ The ND value X this mask was also closely matched to the max ND level at 16 peak of the Gaussian mask so ollered a good comparison between the two dilferent shapes of mask., The ND value of this mask was also closely matched to the max ND level at the peak of the Gaussian mask so offered a good comparison between the two different shapes of mask.
+ The 1.0 aresee mask tested here was a spare from OSCA and had an ND level of 245.5 (compared to 72.5 for the 0.5 aresee mask ancl Gaussian) at this wavelength., The 1.0 arcsec mask tested here was a spare from OSCA and had an ND level of $\sim$ 5.5 (compared to $\sim$ 2.5 for the 0.5 arcsec mask and Gaussian) at this wavelength.
+ Images were taken at the focus for all 3 cülferent occulting masks. both with and without the Lyot mask.," Images were taken at the focus for all 3 different occulting masks, both with and without the Lyot mask."
+ The images were reduced (dark and background subtracted auc scaled for exposure dilferences) and then radial averages were plotted about the PSE peak., The images were reduced (dark and background subtracted and scaled for exposure differences) and then radial averages were plotted about the PSF peak.
+ Fig., Fig.
+ 10. shows the racial averages of the 3 dillerent masks using the same Lyot mask., \ref{lab_masks} shows the radial averages of the 3 different masks using the same Lyot mask.
+ The 1.0 arcesec mask performs best of all. entirely due to its much larger size (covers 4. the area thus removing much more of the PSE) anc greater opacity.," The 1.0 arcsec mask performs best of all, entirely due to its much larger size (covers $4\times$ the area thus removing much more of the PSF) and greater opacity."
+ Comparing the other two masks which diller mainly in their shape rather than any other factors it can be seen that as the simulations predicted. the Gaussian shaped mask provides ereater suppression closer in to the centre than the disc mask does.," Comparing the other two masks which differ mainly in their shape rather than any other factors it can be seen that as the simulations predicted, the Gaussian shaped mask provides greater suppression closer in to the centre than the disc mask does."
+ Fie., Fig.
+ LL shows the significant ellect adding a Lyot stop has on the suppression with the Gaussian mask. the CCD count at LO pixels from the centre is 5«107. compared to 1.2.104 for the 0.50 aresce dise.," \ref{gausa_graph} shows the significant effect adding a Lyot stop has on the suppression with the Gaussian mask, the CCD count at 10 pixels from the centre is $5\times10^3$, compared to $1.2\times10^4$ for the 0.50 arcsec disc."
+ Without a Lyot stop the value at. 10 pixels from the centre for the Gaussian mask is, Without a Lyot stop the value at 10 pixels from the centre for the Gaussian mask is
+description of the functional form of the above operators is given.,description of the functional form of the above operators is given.
+ The current version of the code uses also some improvements over MK95., The current version of the code uses also some improvements over MK95.
+ Thus for synchrotron radiatior relativistic electrons emit the full photon spectrum (see.e.g.?) instead of the delta-function approximation used in MK95.," Thus for synchrotron radiation relativistic electrons emit the full photon spectrum \citep[see, e.g.][]{blum70} instead of the delta-function approximation used in MK95."
+ Also. for inverse Compton scattering. while the electro: cooling still uses the technique described in MK95. the electro emissivity uses relation (2.48) of ?..," Also, for inverse Compton scattering, while the electron cooling still uses the technique described in MK95, the electron emissivity uses relation (2.48) of \citet{blum70}."
+ Numerical tests have shown that this approach balances electron energy losses anc total photon radiated power to within 90% of each other., Numerical tests have shown that this approach balances electron energy losses and total photon radiated power to within $\%$ of each other.
+ Furthermore. departing from the approach of MK97. we implement an acceleration term in the electron kinetic equatior which is characterized by an appropriate timescale (έως) anc is accompanied by a term which deseribes particle injectior at some low energy (first term in RHS of Eq.," Furthermore, departing from the approach of MK97, we implement an acceleration term in the electron kinetic equation which is characterized by an appropriate timescale $\tacc$ ) and is accompanied by a term which describes particle injection at some low energy (first term in RHS of Eq."
+ ?? where Q(r) is the rate of electrons which are injected at low energies yoHt;c)., \ref{eq1} where $Q(t)$ is the rate of electrons which are injected at low energies $\gamma_0m_\mathrm{e}c^2$ ).
+ This modification allows us to follow particles as they accelerate from low to high energies., This modification allows us to follow particles as they accelerate from low to high energies.
+ Note that this approach is similar to the one taken in KRM., Note that this approach is similar to the one taken in KRM.
+ However. the present work differs from KRM in that we adopt here a one-zone model.," However, the present work differs from KRM in that we adopt here a one-zone model."
+ There are six parameters that are required to specify the source in a stationary state., There are six parameters that are required to specify the source in a stationary state.
+ These include 1., These include 1.
+ The Doppler factor 6=[ΓΙ—8cos0)]7!., The Doppler factor $\delta=[\Gamma(1-\beta \cos\theta)]^{-1}$.
+ 2., 2.
+ The radius R of the source (or. equivalently. the crossing time in the rest frame of the source 44= R/c).," The radius $R$ of the source (or, equivalently, the crossing time in the rest frame of the source $\tcross=R/c$ )."
+ 3., 3.
+ The magnetic field strength B., The magnetic field strength $B$.
+ 4., 4.
+" The acceleration timescale ¢,... which by the setup of the problem must obey the relation face>fa."," The acceleration timescale $\tacc$, which by the setup of the problem must obey the relation $\tacc\ge\tcross$."
+ 5., 5.
+ The timescale of particle escape of the system fa..., The timescale of particle escape of the system $\tesc$.
+ 6., 6.
+ The rate of injected electrons Qo — we note. however. that the solution turns to be largely independent of the exact choice of yo as long as this ts not larger than 10.," The rate of injected electrons $Q_0$ – we note, however, that the solution turns to be largely independent of the exact choice of $\gamma_0$ as long as this is not larger than 10."
+" As was shown in KRM this prescription (under. the assumption of synchrotron radiation losses only) leads to an electron distribution function which in steady state reads ""ὃς. for yo€yyu. Where yu, is the Lorentz factor at which electron energy losses balance acceleration."," As was shown in KRM this prescription (under the assumption of synchrotron radiation losses only) leads to an electron distribution function which in steady state reads ) for $\gamma_0\le\gamma\le\gammamax$, where $\gammamax$ is the Lorentz factor at which electron energy losses balance acceleration."
+" For example. in the pure synchrotron case. where5,=torpor with cy the Thomson cross section."," For example, in the pure synchrotron case, where $\beta_s={4\over 3}\sigma_T c {B^2\over{8\pi m_ec^2}}$ with $\sigma_T$ the Thomson cross section."
+ However. the present approach incorporates. in addition to synchrotron. SSC losses which render the derivation of an analytic solution impossible due to complications arising from the Klein-Nishina limit.," However, the present approach incorporates, in addition to synchrotron, SSC losses which render the derivation of an analytic solution impossible due to complications arising from the Klein-Nishina limit."
+ One further notes that for £4: and fa. both independent of energy. as it was assumed in deriving the above solution. the electron distribution function is a power law of index s2-2--(face—fostae (as long as y<< ος," One further notes that for $\tacc$ and $\tesc$ both independent of energy, as it was assumed in deriving the above solution, the electron distribution function is a power law of index $s=-2-({\tacc-\tesc})/{\tesc}$ (as long as $\gamma<<\gammamax$ )."
+ note also that tests on the code in the pure synchrotron loss case have shown that the electron distribution above yy; does not drop to zero abruptly. but rather. due to numerical diffusion. a very steep power law ts produced.," We note also that tests on the code in the pure synchrotron loss case have shown that the electron distribution above $\gammamax$ does not drop to zero abruptly, but rather, due to numerical diffusion, a very steep power law is produced."
+ The above description changes during a flare: Assume that the system has reached some stationary state., The above description changes during a flare: Assume that the system has reached some stationary state.
+ If this ts perturbed in some way. 1.9. by injecting an increased number of particles in the acceleration mechanism for some time interval Ar. then a wave of fresh particles will move to high energies.," If this is perturbed in some way, i.e. by injecting an increased number of particles in the acceleration mechanism for some time interval $\Delta\tau$, then a wave of fresh particles will move to high energies."
+ Assuming that the episode starts at some instant. fo. then at each time ¢>f+Ar the fresh particles will have Lorentz factors Yniin()€YYnaa(O with Yana=yortntaec and γη)=yoeUnATVface.," Assuming that the episode starts at some instant $t_0$, then at each time $t>t_0+\Delta\tau$ the fresh particles will have Lorentz factors $\gamflmn(t)\le\gamma\le\gamflmx(t)$ with $\gamflmx(t)=\gamma_0e^{(t-t_0)/\tacc}$ and $\gamflmn(t)=\gamma_0e^{(t-t_0-\Delta\tau)/\tacc}$."
+ This relation holds as long as YoanaxSYmas, This relation holds as long as $\gamflmx\le\gammamax$.
+ AS the time evolving particle distribution will have a higher amplitude than the steady state one. this will cause a flare in photons which will relax back to the pre-flare state once particles of Lorentz factor yg start becoming of order yis.," As the time evolving particle distribution will have a higher amplitude than the steady state one, this will cause a flare in photons which will relax back to the pre-flare state once particles of Lorentz factor $\gamflmn$ start becoming of order $\gammamax$."
+ Ht is interesting to note that as losses do not come solely from synchrotron radiation but from SSC as well. the flaring event could have an impact on the determination of yq.," It is interesting to note that as losses do not come solely from synchrotron radiation but from SSC as well, the flaring event could have an impact on the determination of $\gammamax$."
+" More specifically. the presence of extra photons during a flare in the system will increase the total electron energy losses and. depending on the specific conditions. could cause yy, to drop."," More specifically, the presence of extra photons during a flare in the system will increase the total electron energy losses and, depending on the specific conditions, could cause $\gammamax$ to drop."
+ We begin by using the model described in the previous section to fit the X/TeV data as given in Fig., We begin by using the model described in the previous section to fit the X/TeV data as given in Fig.
+ 21 of Ἱ.(July 9. 2005. observations).," 21 of \citet{albert07} (July 9, 2005, observations)."
+ We have solved the set of stiff differential equations (??)) and (22)) using the numerical techniques às these were described and tested in MK95., We have solved the set of stiff differential equations \ref{eq1}) ) and \ref{eq2}) ) using the numerical techniques as these were described and tested in MK95.
+ The parameters used for the steady state fit are R=1.510U em. ó=60. B=05 G. fae=NOa. foe=4.17%. yo=10° and Q=510° em see7ere7!.," The parameters used for the steady state fit are $R=1.5~10^{14}$ cm, $\delta=60$, $B=0.5$ G, $\tacc=3\tcross$, $\tesc=4.17\tcross$, $\gamma_0=10^{0.05}$ and $Q=5~10^6$ $^{-3}$ $^{-1}$ $^{-1}$."
+" The cosmological parameters used are Hy=70kms!Μρο. Q,=0.7 and Q=0.3."," The cosmological parameters used are $H_0=70\ \mathrm{km}\ \mathrm{s}^{-1}\
+\mathrm{Mpc}^{-1}$, $\Omega_\Lambda=0.7$ and $\Omega=0.3$."
+ The spectrum is shown with solid line in Fig. ].., The spectrum is shown with solid line in Fig. \ref{fig1}.
+" The resulting electron distribution function is a power-law of slope s=—1.7 up to an energy Yu,=210°.", The resulting electron distribution function is a power-law of slope $s=-1.7$ up to an energy $\gammamax= 2~ 10^5$.
+ Perturbing the steady state as given above we found that a change in. Q(r) always produces a hard lag flare as the one observed., Perturbing the steady state as given above we found that a change in $Q(t)$ always produces a hard lag flare as the one observed.
+ However. this method of simulating a flaring activity causes the flux in each energy band to increase approximately by the same amplitude — see ?..," However, this method of simulating a flaring activity causes the flux in each energy band to increase approximately by the same amplitude – see \citet{mamo09}."
+ If. as the observations seem to suggest. the flare is becoming harder as well. 1.e. more flux is emitted in the higher energy bands. then in order to get à fit to the TeV lighteurve one needs. in addition. to decrease foe and/or B during the flaring episode.," If, as the observations seem to suggest, the flare is becoming harder as well, i.e. more flux is emitted in the higher energy bands, then in order to get a fit to the TeV lightcurve one needs, in addition, to decrease $\tacc$ and/or $B$ during the flaring episode."
+ This can be explained from an inspection of rel. (, This can be explained from an inspection of rel. (
+4).,4).
+ A spectral hardening of the flare requires an increase of yj; during the episode and this can be achieved. within the context of the present model. only by reducing one. or both. of the aforementioned parameters.," A spectral hardening of the flare requires an increase of $\gammamax$ during the episode and this can be achieved, within the context of the present model, only by reducing one, or both, of the aforementioned parameters."
+ Figures 2 and 3 depict the lightcurves resulting from such a flaring episode., Figures 2 and 3 depict the lightcurves resulting from such a flaring episode.
+ Here the observed flare comes from an impulsive change of Q by a factor of ~13 for Ar=If anda decrease of f; and B by a factor of 1.7 for Ar=30f4 which Is approximately equal to the duration of the flaring episode. i.e. to the time needed for the injected particles to reach yy.," Here the observed flare comes from an impulsive change of $Q$ by a factor of $\sim13$ for $\Delta\tau=1t_\mathrm{cr}$ and a decrease of $\tacc$ and $B$ by a factor of 1.7 for $\Delta\tau=30t_\mathrm{cr}$ which is approximately equal to the duration of the flaring episode, i.e. to the time needed for the injected particles to reach $\gammamax$ ."
+ In order to keep the spectral slope unchanged (see rel., In order to keep the spectral slope unchanged (see rel.
+ 3) we also vary fa. by the same factor., 3) we also vary $\tesc$ by the same factor.
+ Fig., Fig.
+ 2 shows the lightcurve at the lowest energy range (0.15-0.25 TeV) of the MAGIC, 2 shows the lightcurve at the lowest energy range (0.15-0.25 TeV) of the MAGIC
+nunodel is appropriate for the prototvpe lywpernova SN L998Dw Cwamoto et 11998: Ναι et22001),model is appropriate for the prototype hypernova SN 1998bw (Iwamoto et 1998; Nakamura et.
+2.. Teh/WolfRavet stars are known to lose a substantial fraction of their cuvelopes in a stellar wind., Helium/Wolf-Rayet stars are known to lose a substantial fraction of their envelopes in a stellar wind.
+ To take this iuto account. we assume that the helimu star has lost au amount AM.=g(MA.Mp) before the explosion. where Af is the initial mass| of the compact reninaut (neutron star or black hole).," To take this into account, we assume that the helium star has lost an amount $\Delta M_{\rm He}
+= g\, (M_{\rm He}^0-M_{\rm BH}^0)$ before the explosion, where $M_{\rm BH}^0$ is the initial mass of the compact remnant (neutron star or black hole)."
+ We use the parameter g to vary the total amount of wind mass loss before the supernova., We use the parameter $g$ to vary the total amount of wind mass loss before the supernova.
+ At the time of the explosion. the masses of the primacy and secondary are Mg aud AL. respectively.," At the time of the explosion, the masses of the primary and secondary are $M_{\rm He}$ and $M_2^0$, respectively."
+ When the primary collapses. it first forms a compact remnant of ass Alf).," When the primary collapses, it first forms a compact remnant of mass $M_{\rm
+BH}^0$."
+" The rest of the envelope is assumed to be ejected initially, but part of it (Menace) Will subsequently: fall back. either because it did not achieve escape velocity or was pushed back by a reverse shock in the euvelope (see Woosley Weaver 1995)."," The rest of the envelope is assumed to be ejected initially, but part of it $M_{\rm fallback}$ ) will subsequently fall back, either because it did not achieve escape velocity or was pushed back by a reverse shock in the envelope (see Woosley Weaver 1995)."
+" The fallback matter inereases the mass of the compact remmant to Af, (udeed. it may be this fallback that leads to the conversion of the compac remnant into a black hole)."," The fallback matter increases the mass of the compact remnant to $M_{\rm BH}^1$ (indeed, it may be this fallback that leads to the conversion of the compact remnant into a black hole)."
+ Figure 3a schematically illustrates the definition of these various mass parameters., Figure 3a schematically illustrates the definition of these various mass parameters.
+ Tu the simple model we consider first. we assiuune that of the matter that falls back has moved bevoud the position of the secondary (n 3.2 we shall critically assess this assuniptiou).," In the simple model we consider first, we assume that of the matter that falls back has moved beyond the position of the secondary (in 3.2 we shall critically assess this assumption)."
+ Therefore. the secondary can be pollutefice with supernova material. first bv all the materia hat is ejected and then bv material that fallsρα back.," Therefore, the secondary can be polluted with supernova material, first by all the material that is ejected and then by material that falls back."
+" We asstune that the fraction of matter that is captured is given w the geometric fraction of the secondary (10μη,x 0.03. where RY=OsR.(ALYALT ds the radius of the secondary aud ay the initial orbital separation) nues some efficiency factor f. where we assume ciffereut cficiency factors for matter that passes the secoucdary in the initial ejection (fjccrion) aud for matter that falls ack feattback)."," We assume that the fraction of matter that is captured is given by the geometric fraction of the secondary $[R_2^0/2 a_0]^2\simeq 0.01\,$ $\,$ 0.03, where $R_2^0 =
+0.8\Rs\,(M_2^0/\Ms)^{0.8}$ is the radius of the secondary and $a_0$ the initial orbital separation) times some efficiency factor $f$, where we assume different efficiency factors for matter that passes the secondary in the initial ejection $f_{\rm ejection}$ ) and for matter that falls back $f_{\rm fallback}$ )."
+ The efficiency factors can be much smaller han 1. for example. if the supernova leads to stripping of inatter from the secoudarv {(Alavietta. Burrows. Fivecll 2000 and 3.1). or larger than 1 if eravitational ocusing is duportant.," The efficiency factors can be much smaller than 1, for example, if the supernova leads to stripping of matter from the secondary (Marietta, Burrows, Fryxell 2000 and 3.1), or larger than 1 if gravitational focusing is important."
+ The latter requires that the relative velocity of the material is less than the escape velocity of he secondary and can plausibly only occur for fallback. uaterial., The latter requires that the relative velocity of the material is less than the escape velocity of the secondary and can plausibly only occur for fallback material.
+ We also take iuto account the pollution of the secondary that has occurred before the supernova because of the capture of wind material by the secondary (where we assunie a capture efficiency of 1)., We also take into account the pollution of the secondary that has occurred before the supernova because of the capture of wind material by the secondary (where we assume a capture efficiency of 1).
+ The matter that is captured by the secondary. has a much arecr nean molecular weielit than the composition of the secondary. a relatively unevolved star at this stage.," The matter that is captured by the secondary has a much larger mean molecular weight than the composition of the secondary, a relatively unevolved star at this stage."
+ This is secularlv unstable aud leads to thermohaline mixing iu he secondary (0.8.. Ixippeulalin. Ruscheuplatt Thomas 1980).," This is secularly unstable and leads to thermohaline mixing in the secondary (e.g., Kippenhahn, Ruschenplatt Thomas 1980)."
+ Since the time scale for thermohaline wining is short compared to the evolutionary time scale of the secondary. we assume that the material captured x the secondary is completely mixed with the rest of the star after the supernova.," Since the time scale for thermohaline mixing is short compared to the evolutionary time scale of the secondary, we assume that the material captured by the secondary is completely mixed with the rest of the star after the supernova."
+ Iu order to be able to follow the post-superuova evolution. we assume that the pre-supernova system is circular aud that the supernova explosion is spherically svuuimetric in the frame of the primary.," In order to be able to follow the post-supernova evolution, we assume that the pre-supernova system is circular and that the supernova explosion is spherically symmetric in the frame of the primary."
+ It is then straightforward to estimate the post-supernova paraiecters of the svstenm (ve follow Brandt Podsiadlowski 1995. but for otler equivalent treatiuents; see. e.g... Dhattacharya van deu Heuvel 1991: Nelemans et 11999).," It is then straightforward to estimate the post-supernova parameters of the system (we follow Brandt Podsiadlowski 1995, but for other equivalent treatments, see, e.g., Bhattacharya van den Heuvel 1991; Nelemans et 1999)."
+ The ecceutzricitv of the post-supernova binary is giveu by where AMax=Mp.Mig. the post-supernova major axis by where eg is the initial orbital separation.," The eccentricity of the post-supernova binary is given by where $\Delta
+M_{\rm SN}\equiv M_{\rm He}-M_{\rm BH}^1$, the post-supernova semi-major axis by where $a_0$ is the initial orbital separation."
+" The post-supernova svsteni kick velocity can be obtained frou equation (2.10) in Brandt Podsiadlowski (1995) as where e¢!), ds the pre-supernova orbital velocity of the system.", The post-supernova system kick velocity can be obtained from equation (2.10) in Brandt Podsiadlowski (1995) as where $v_{\rm orb}^0$ is the pre-supernova orbital velocity of the system.
+ Here we have neglected. the simall change iu the uass of the secoudary due to the capture of ejected uaterial from the primary (typically ~0.2M LJ. as well as any kick associated with the interaction of the superuova fast wave with the secoudary (see Marietta et 22000).," Here we have neglected the small change in the mass of the secondary due to the capture of ejected material from the primary (typically $\sim 0.2\Ms$ ), as well as any kick associated with the interaction of the supernova blast wave with the secondary (see Marietta et 2000)."
+ After the supernova. the binary parameters will coutinue o evolve.," After the supernova, the binary parameters will continue to evolve."
+ The svstem will first re-cireularize. obtaining a jew orbital separation Once the secondary starts to fill(1 its Roche lobe. it will start o lose mass. of which a fraction οὐ will be accreted by the mumary. while the rest will be ejected from the svstem.," The system will first re-circularize, obtaining a new orbital separation Once the secondary starts to fill its Roche lobe, it will start to lose mass, of which a fraction $\beta$ will be accreted by the primary, while the rest will be ejected from the system."
+ We asstune that the matter that is lost from the svsteni carries away the same specific augular momenta as the primary (see. e... Podsiadlowski Rappaport. Pfall 2001).," We assume that the matter that is lost from the system carries away the same specific angular momentum as the primary (see, e.g., Podsiadlowski Rappaport, Pfahl 2001)."
+ This is appropriate if the mass loss occurs from a region near the primary. as sugeested by the relativistic jets observed from Nova Sco (IIjelliiiug Rupen 1995).," This is appropriate if the mass loss occurs from a region near the primary, as suggested by the relativistic jets observed from Nova Sco (Hjellming Rupen 1995)."
+ Even though this model is still relatively simple (for example. it docs not take iuto account a kick due to an asvuuuetric explosion). it still contains a large umber of essentially unspecified parameters Whe AM: Misglback- Faeenions νοκ. Ge J}.," Even though this model is still relatively simple (for example, it does not take into account a kick due to an asymmetric explosion), it still contains a large number of essentially unspecified parameters $M_{\rm He}^0$, $M_{\rm BH}^0$, $M_{\rm fallback}$, $f_{\rm
+ejection}$, $f_{\rm fallback}$, $g$, $\beta$ )."
+" For givou values of fojection aud füdbaee We have sampled all the other parzuceters iu a failv svsteimnatic and comprehensive fashion. although we eoncrally do not change the present masses of tle Nova Sco comiponeuts, but keep them fixed at amd. AL."," For given values of $f_{\rm ejection}$ and $f_{\rm fallback}$, we have sampled all the other parameters in a fairly systematic and comprehensive fashion, although we generally do not change the present masses of the Nova Sco components, but keep them fixed at and ,."
+..respectively... In practice. we proceed iu he following wav.," In practice, we proceed in the following way."
+ For each of the 7 superuova imoclels (ie. each combination of helium star mass aud explosion energv). we systematically vary the initial black-hole Lass. Mii the fallback amass. AJggnaae the wind-loss xuaneter. g. aud the mass-accretion parameters. 3 (the atter two are varied from 0 to 1).," For each of the 7 supernova models (i.e., each combination of helium star mass and explosion energy), we systematically vary the initial black-hole mass, $M_{\rm BH}^0$, the fallback mass, $M_{\rm fallback}$, the wind-loss parameter, $g$, and the mass-accretion parameters, $\beta$ (the latter two are varied from 0 to 1)."
+ Mavine fixed these waraluctors. we can use the present orbital period aud nasses to reconstruct the pre-superhova lasses aud pre- orbital period using the formalisinoutlined above.," Having fixed these parameters, we can use the present orbital period and masses to reconstruct the pre-supernova masses and pre-supernova orbital period using the formalismoutlined above."
+ If this recoustruction shows that the radius of the, If this reconstruction shows that the radius of the
+computed. for dillerent assumptions of smooth matter density. photometric error. ancl direction. of the galactic transverse velocity.,"computed for different assumptions of smooth matter density, photometric error, and direction of the galactic transverse velocity."
+ Since the probability functions referred to above were computed from. a derivative analysis. the statistics that we compute in this paper are quantitatively similar for the different possible models.," Since the probability functions referred to above were computed from a derivative analysis, the statistics that we compute in this paper are quantitatively similar for the different possible models."
+ “Pherefore we present only results from models with no smooth matter. a transverse velocity direction along the image C-D axis and simulated: photometric errors assigned according to à Gaussian distribution with half widths of @=AAL/2 in images A and D. and 8$=AA in images C and D. Both the microlensing rate cue to a transverse velocity. (ee.," Therefore we present only results from models with no smooth matter, a transverse velocity direction along the image C-D axis and simulated photometric errors assigned according to a Gaussian distribution with half widths of $\sigma=\Delta M/2$ in images A and B, and $\sigma=\Delta M$ in images C and D. Both the microlensing rate due to a transverse velocity (eg."
+ Witt. Iaiser Refsdal 1903). as well as the corresponding rate due to proper motions (WAWLO0a) are not functions of the details of the microlens mass distribution. but rather are only dependent. on the mean microlens mass.," Witt, Kaiser Refsdal 1993), as well as the corresponding rate due to proper motions (WWT00a) are not functions of the details of the microlens mass distribution, but rather are only dependent on the mean microlens mass."
+ We therefore limit our attention to models in which all the microlenses have the same mass since the results obtained will be applicable to other models with different forms for the mass function., We therefore limit our attention to models in which all the microlenses have the same mass since the results obtained will be applicable to other models with different forms for the mass function.
+ The determination. of probability for. the quantity ΓΕΝim) from the OQ2237|0305 monitoring data is quite robust., The determination of probability for the quantity $v_{eff}\sqrt{\langle m\rangle}$ from the Q2237+0305 monitoring data is quite robust.
+ However the probability for the source size Is derived from a single poorly sampled. LATE., However the probability for the source size is derived from a single poorly sampled HME.
+ The small number of observations cleseribing the LOSS peak (ία et al., The small number of observations describing the 1988 peak (Irwin et al.
+ 1989: Corrigan et al 1991) introduces the potential for a systematic error in the source size equal to the ratio of the true event length. and the inferred. event. length. of ~52 days. (twice the estimated rise time)., 1989; Corrigan et al 1991) introduces the potential for a systematic error in the source size equal to the ratio of the true event length and the inferred event length of $\sim 52$ days (twice the estimated rise time).
+ This can be compared to the  100 dav separation of the two points that provide an on the event duration., This can be compared to the $\sim$ 100 day separation of the two points that provide an on the event duration.
+ The resulting systematic error in the estimate of source size is therefore smaller than a [actor of ~2., The resulting systematic error in the estimate of source size is therefore smaller than a factor of $\sim 2$.
+ In addition there may also be à component of svstematic error from the assumption that the LOSS peak was due to a single caustic crossing., In addition there may also be a component of systematic error from the assumption that the 1988 peak was due to a single caustic crossing.
+ “Phe statistics presented in the following sections are therefore computed assuming prior probabilities for S assuming no systematic error. and systematic errors of 2 and 5 in 5: and Our source size estimate was mace from cata collected in the 1t and r bands. while the OGLE light-curves showing the features that we wish to investigate are in the V band.," The statistics presented in the following sections are therefore computed assuming prior probabilities for $S$ assuming no systematic error, and systematic errors of $\times 2$ and $\times 5$ in $S$: and Our source size estimate was made from data collected in the R and r bands, while the OGLE light-curves showing the features that we wish to investigate are in the V band."
+ This introduces the possibility for another source of systematic error if the source has significantly dillerent sizes in the It/r ancl V bands., This introduces the possibility for another source of systematic error if the source has significantly different sizes in the R/r and V bands.
+ To investigate individual ΗΛΙΟΣ we must look at light- statistics for single images., To investigate individual HMEs we must look at light-curve statistics for single images.
+ Therefore unlike the calculation of ps. pe and pi. which used. difference light- intrinsic source variation may be important.," Therefore unlike the calculation of $p_{s}$, $p_{v}$ and $p_{m}$, which used difference light-curves, intrinsic source variation may be important."
+ This cannot be directly. measured. however in Wvithe. Webster. Turner Agol (2000). (hereafter WAWLAOO) limits are placed on the intrinsic variability power-spectreum and it is shown that intrinsic variability should not be an important consideration curing LEMEs.," This cannot be directly measured, however in Wyithe, Webster, Turner Agol (2000) (hereafter WWTA00) limits are placed on the intrinsic variability power-spectrum and it is shown that intrinsic variability should not be an important consideration during HMEs."
+2004).,.
+. This work is supported by a RGC erant of the Hong Kong government of the SAR of China., This work is supported by a RGC grant of the Hong Kong government of the SAR of China.
+ The authors would like to thank to the anonvinous referee for comments that helped io improve (he manuscript., The authors would like to thank to the anonymous referee for comments that helped to improve the manuscript.
+the fit.,the fit.
+ Fixed mass constraints are straightforward to implement., Fixed mass constraints are straightforward to implement.
+ The total gravitating mass within the radius r is simply where is the volume of the spherical shell lying inside r., The total gravitating mass within the radius $r$ is simply where is the volume of the spherical shell lying inside $r$.
+" For a fixed mass, M(r), provided that V;(«r)Z0, this is equivalent to which may be used as a constraint on py."," For a fixed mass, $M(r)$ , provided that $V_k(<r) \ne 0$, this is equivalent to which may be used as a constraint on $\rho_k$."
+" If py bumps up against a further constraint(e.g.,, it goes to zero, or it becomes non-monotonic when the monotonic condition is that constraint must take precedence."," If $\rho_k$ bumps up against a further constraint, it goes to zero, or it becomes non-monotonic when the monotonic condition is applied), that constraint must take precedence."
+ The fixed mass constraint can then be applied to another shell., The fixed mass constraint can then be applied to another shell.
+" In cases applied),where densities of adjacent shells have to be tied to maintain the monotonic constraint, the fixed mass constraint can be applied to a group of shells with the same gravitating mass density (in equation 12,, V,(<r) is replaced by the total volume inside r for the group of tied shells and the sum must exclude all shells of that group)."," In cases where densities of adjacent shells have to be tied to maintain the monotonic constraint, the fixed mass constraint can be applied to a group of shells with the same gravitating mass density (in equation \ref{eq:mcons}, $V_k(<r)$ is replaced by the total volume inside $r$ for the group of tied shells and the sum must exclude all shells of that group)."
+" In general, managing constraints that may conflict with one another is complex."," In general, managing constraints that may conflict with one another is complex."
+" In an attempt to minimize such conflicts, the fixed mass constraint was applied to the shell with the largest volume, Vi(«r), since that choice makes po; least sensitive to o; (under the constraint, dpi=—YidpiVi(r)/Vk(« η)."," In an attempt to minimize such conflicts, the fixed mass constraint was applied to the shell with the largest volume, $V_k(<r)$, since that choice makes $\rho_k$ least sensitive to $\rho_i$ (under the constraint, $d\rho_k = - \sum_{i \ne k} d\rho_i V_i(<r) / V_k(<r)$ )."
+" Much the same issues apply for determining confidence ranges for the mass at a fixed overdensity, rather than at a fixed radius."," Much the same issues apply for determining confidence ranges for the mass at a fixed overdensity, rather than at a fixed radius."
+" Specifying the overdensity determines the relationship between r and M(r)(i.e, M(r)=4rpr?/3, where the overdensity, p, is so that r and V;(<r) vary as M varies."," Specifying the overdensity determines the relationship between $r$ and $M(r)$, $M(r) = 4\pi \rhobar r^3/3$, where the overdensity, $\rhobar$, is fixed), so that $r$ and $V_i(<r)$ vary as $M$ varies."
+" However, since r remains fixed for a fixed mass, the remainder of the discussionfixed), above is unaltered."," However, since $r$ remains fixed for a fixed mass, the remainder of the discussion above is unaltered."
+ Fig., Fig.
+ 5 compares values of Msoo determined from the model to those obtained by ? using essentially the same spectra., \ref{fig:m500} compares values of $M_{500}$ determined from the model to those obtained by \citet{vkf06} using essentially the same spectra.
+" The figure shows confidence ranges (Ax?— 2.706) for both the case where the gravitating matter density is unconstrained fit blue, confidence range green) and when it is constrained to be monotonically decreasing fit red, confidence (bestrange"," The figure shows confidence ranges $\Delta\chi^2 = 2.706$ ) for both the case where the gravitating matter density is unconstrained (best fit blue, confidence range green) and when it is constrained to be monotonically decreasing (best fit red, confidence range black)."
+" Plainly, the model does not place tight limits onvalues of Msoo for the (bestsample clusters."," Plainly, the model does not place tight limits onvalues of $M_{500}$ for the sample clusters."
+" For the unconstrainedblack). fits, the confidence intervals typically extend over a factor of ~3.5 in mass."," For the unconstrained fits, the confidence intervals typically extend over a factor of $\sim 3.5$ in mass."
+The PSPM pulsar backend is à 2 x 128 x 60 ΚΙ. computer controlled processor designed to conduct fast sampled pulsar searches aud precision timing measurements.,"The PSPM pulsar backend is a 2 $\times$ 128 $\times$ 60 kHz, computer controlled processor designed to conduct fast sampled pulsar searches and precision timing measurements."
+ Technical details of the backend are given in Cacwell (1997)., Technical details of the backend are given in Cadwell (1997).
+ I1 the timing mode. the dual-polarization. left- aud vieht-cireularly polarized signals were added together. smoothed with appropriate lime constants ranging from 32 yrs to TOO ps. 4-bit quantized. and averaged svuchronously with the Doppler-shilted pulsar period.," In the timing mode, the dual-polarization, left- and right-circularly polarized signals were added together, smoothed with appropriate time constants ranging from 32 $\mu$ s to 700 $\mu$ s, 4-bit quantized, and averaged synchronously with the Doppler-shifted pulsar period."
+ The average pulse profiles. with the number of phase bins chosen to ensure an approximately one milliperiod (ime resolution. were (ime-tagged using the observatorv's hvdrogen-maser clock anc stored. for further analvsis.," The average pulse profiles, with the number of phase bins chosen to ensure an approximately one milliperiod time resolution, were time-tagged using the observatory's hydrogen-maser clock and stored for further analysis."
+ À typical integration time for each profile was 180 s. For the purpose of single pulse analvsis. the data were (aken in the search mode by continuously sampling the polarization summed signal al SO. yes intervals using a 100 jes post-detection time constant.," A typical integration time for each profile was 180 s. For the purpose of single pulse analysis, the data were taken in the search mode by continuously sampling the polarization summed signal at 80 $\mu$ s intervals using a 100 $\mu$ s post-detection time constant."
+ In (his case. the phasing of the single pulses was accomplished in (he off-line analysis.," In this case, the phasing of the single pulses was accomplished in the off-line analysis."
+ The topocentrie times-of-azrival (TOA) of pulses were calculated by eross-correlating the average pulses with high signal-to-noise template profiles., The topocentric times-of-arrival (TOA) of pulses were calculated by cross-correlating the average pulses with high signal-to-noise template profiles.
+ For each pulsar. the standard timing analvsis package TEMPO (http://www.pulsar.princeton.edu/) was then emploved to convert the TOAs to the solar svstem barveenter using the JPL DE200 ephemeris (Stanclish. 1990) and to perform least-squares fits of appropriate üming models to the data.," For each pulsar, the standard timing analysis package TEMPO (http://www.pulsar.princeton.edu/) was then employed to convert the TOAs to the solar system barycenter using the JPL DE200 ephemeris (Standish, 1990) and to perform least-squares fits of appropriate timing models to the data."
+ In the case of slow pulsars. the models included (he pulsar rotation period P ancl ils slowdown rate P.celestial coordinates aoon aC Oyoo. 2nd Che dispersion measure DAL.," In the case of slow pulsars, the models included the pulsar rotation period $P$ and its slowdown rate $\dot P$,celestial coordinates $\alpha_{J2000}$ and $\delta_{J2000}$, and the dispersion measure $DM$."
+ For P5hR J17092-2313. the additional model parameters were the pulsars proper motion and the live Keplerian elements of its binary orbit.," For PSR J1709+2313, the additional model parameters were the pulsar's proper motion and the five Keplerian elements of its binary orbit."
+ The proper motion was also included in the timing model lor PSR J0538—2817. in which case the fitting of astrometric parameters was carried out in ecliptic coordinates. because of the pulsars proximity (o the ecliptic plane (see also lxramer et. al.," The proper motion was also included in the timing model for PSR J0538+2817, in which case the fitting of astrometric parameters was carried out in ecliptic coordinates, because of the pulsar's proximity to the ecliptic plane (see also Kramer et al."
+ 2003)., 2003).
+ The timine results for (wo of the 13 pulsars presented in this paper. PSR. J110940-2313 and PSR JO538+2817. are discussed separately in this Section. because of their respective meniberships of the millisecond pulsar population aud (he group of voung pulsars associated with supernova remnants.," The timing results for two of the 18 pulsars presented in this paper, PSR J1709+2313 and PSR J0538+2817, are discussed separately in this Section, because of their respective memberships of the millisecond pulsar population and the group of young pulsars associated with supernova remnants."
+ A joint discussion is presented for the remaining sources. lor which the basic Giming model was sullicient to describe (heir properties.," A joint discussion is presented for the remaining sources, for which the basic timing model was sufficient to describe their properties."
+ The pulse widths and flux densities of the 18 pulsars were measured [following the procedures described by Camilo aud Nice (1995) and Lorimer. Camilo aud. Xilouris (2002).," The pulse widths and flux densities of the 18 pulsars were measured following the procedures described by Camilo and Nice (1995) and Lorimer, Camilo and Xilouris (2002)."
+" The widths listed in Tables 1-3 are given as the equivalent width i (the width of a pulse. having the same area and height as the profile). ρω. ancl ie, measured at the"," The widths listed in Tables 1-3 are given as the equivalent width $w_e$ (the width of a top-hat pulse, having the same area and height as the profile), $w_{50}$ and $w_{10}$ measured at the"
+ , 
+Sy was checked by comparing the integral form to the asymptotic form mentioned in Section 2.1.. finding good agreement.,"$S_3$ was checked by comparing the integral form to the asymptotic form mentioned in Section \ref{numsol}, finding good agreement."
+ This shows that using the compactified coordinate introduced in CST allows a very accurate numerical determination of relatively order multipoles., This shows that using the compactified coordinate introduced in CST allows a very accurate numerical determination of relatively high-order multipoles.
+ The last column gives the value of the “quadrupole” parameter b (in km) for which the analytic solution provides a good approximation of the numerical spacetime., The last column gives the value of the “quadrupole” parameter $b$ (in km) for which the analytic solution provides a good approximation of the numerical spacetime.
+ When matching the quadrupole moment of the numerical and analytic spacetimes is not possible. the corresponding entry is omitted.," When matching the quadrupole moment of the numerical and analytic spacetimes is not possible, the corresponding entry is omitted."
+ More details on the procedure we followed to obtain the values listed in this column will be given in section 4.., More details on the procedure we followed to obtain the values listed in this column will be given in section \ref{match}.
+ In this section we summarize the properties of the vacuum analytic solution obtained by Manko (000b)., In this section we summarize the properties of the vacuum analytic solution obtained by Manko (2000b).
+ We will concentrate in particular on the multipolar structure of the solution. since our ultimate purpose will be to reproduce accurately the first few multipoles of the numerical spacetimes we discussed in the previous section.," We will concentrate in particular on the multipolar structure of the solution, since our ultimate purpose will be to reproduce accurately the first few multipoles of the numerical spacetimes we discussed in the previous section."
+ In the vacuum region surrounding a stationary and axisymmetric star. the spacetime only depends on three metric functions (while four metric functions are needed for the interior).," In the vacuum region surrounding a stationary and axisymmetric star, the spacetime only depends on three metric functions (while four metric functions are needed for the interior)."
+ The most general form of the metric (Papapetrou 1953) isent rho, The most general form of the metric (Papapetrou 1953) is ^2.
+-à Here /. w and y are functions of the quasi-cylindrical WevI-Lewis-Papapetrou coordinates (p.=).," Here $f$ , $w$ and $\gamma$ are functions of the quasi-cylindrical Weyl-Lewis-Papapetrou coordinates $(\tilde
+\rho,~\tilde z)$."
+ Starting from this metric one can write down the vacuum Einstein-Maxwell equations as two equations for two complex potentials “ and Φ. following a procedure due to Ernst (1968).," Starting from this metric one can write down the vacuum Einstein-Maxwell equations as two equations for two complex potentials ${\cal E}$ and $\Phi$, following a procedure due to Ernst (1968)."
+ The equations are: (Re “yk5 (Re 7yb=(VE Once the potentials are known. the metric ean be reconstructed.," The equations are: (Re = (Re = Once the potentials are known, the metric can be reconstructed."
+ Sibgatullin (1991) devised a powerful procedure for reducing the solution of the Ernst equations to simple integral equations., Sibgatullin (1991) devised a powerful procedure for reducing the solution of the Ernst equations to simple integral equations.
+" Basically. one starts with a choice for the values of the Ernst potentials on the symmetry axis 00.2). 00.5). solves two complex-valued integral equations. and checks that the obtained solution satisties the expression of the Ernst potentials in terms of physical multipoles: ame quzU(48) The real parts of 77, are the mass multipoles. the imaginary parts of az, are the current multipoles. the real parts of g, are the electric multipoles and the imaginary parts of gy, are the magnetic multipoles."," Basically, one starts with a choice for the values of the Ernst potentials on the symmetry axis z), z), solves two complex-valued integral equations, and checks that the obtained solution satisfies the expression of the Ernst potentials in terms of physical multipoles:, m_n q_n The real parts of $m_n$ are the mass multipoles, the imaginary parts of $m_n$ are the current multipoles, the real parts of $q_n$ are the electric multipoles and the imaginary parts of $q_n$ are the magnetic multipoles."
+ After more than ten years of work in the field. Manko 000b) were finally able to find a vacuum solution involving five parameters (mass. angular momentum. charge. magnetic dipole moment and mass quadrupole moment) which ean be expressed in erms of relatively simple rational functions.," After more than ten years of work in the field, Manko (2000b) were finally able to find a vacuum solution involving five parameters (mass, angular momentum, charge, magnetic dipole moment and mass quadrupole moment) which can be expressed in terms of relatively simple rational functions."
+ We are particularly interested in solutions having no charge or magnetic dipole moment., We are particularly interested in solutions having no charge or magnetic dipole moment.
+ If we denote by M the gravitational mass of the star. by a the specitic angular momentum (¢=J/M). and introduce a xrameter P. which can be related to the mass quadrupole moment. heir choice for the axis values of the Ernst potentials is: with where r2—p>(2L4)? and 8.The inverse transformation between the two sets of coordinates Is στκά," If we denote by $M$ the gravitational mass of the star, by $a$ the specific angular momentum $a=J/M$ ), and introduce a parameter $b$ which can be related to the mass quadrupole moment, their choice for the axis values of the Ernst potentials is: with, , where $r_\pm=\sqrt{\tilde\rho^2+(\tilde z\pm k)^2}$ and .The inverse transformation between the two sets of coordinates is z=kxy."
+ The metric is then written aswith, The metric is then written aswith
+orbit-averaged radius can be parametrized as This power law relation reflects typical energy and eccentricity distributions of particles in halos.,orbit-averaged radius can be parametrized as This power law relation reflects typical energy and eccentricity distributions of particles in halos.
+" We take the pivot radius to be ro=0.03299p,A, which ? showed to minimize the correlation of Αρ and w."," We take the pivot radius to be $r_0 = 0.03 \, r_\mathrm{200b,A}$, which \cite{2011GnedinContraction} showed to minimize the correlation of $A_0$ and $w$ ."
+ The best-fit parameters Ag and w can vary from halo to halo., The best-fit parameters $A_0$ and $w$ can vary from halo to halo.
+ The SAC model corresponds to Αρ=1 and w=1., The SAC model corresponds to $A_0=1$ and $w=1$.
+ The amount of contraction typically increases with decreasing values of Αρ and increasing values of w., The amount of contraction typically increases with decreasing values of $A_0$ and increasing values of $w$.
+ We use a modified version of the code that determines the best-fit values for Ap and w by comparing the prediction to the measured dark matter profile in the dissipational simulation., We use a modified version of the code that determines the best-fit values for $A_0$ and $w$ by comparing the prediction to the measured dark matter profile in the dissipational simulation.
+ The fitting procedure is described in ?.., The fitting procedure is described in \cite{2011GnedinContraction}.
+ Figure 14 shows the best-fit parameters for our selected halos at z22., Figure \ref{fig:contra_A_w} shows the best-fit parameters for our selected halos at $z \approx 2$.
+" The majority of the halos are clustered around Agz2.3, wc0.7, but some show substantial scatter."," The majority of the halos are clustered around $A_0 \approx 2.3$, $w \approx 0.7$, but some show substantial scatter."
+" For each individual halo, the MAC model provides an excellent fit of the dark matter profile, with the median fractional mass error of (averaged over all "," For each individual halo, the MAC model provides an excellent fit of the dark matter profile, with the median fractional mass error of (averaged over all bins)."
+"Overall, the level of contraction is weaker than predictedbins). by the SAC model, confirming the conclusion of ?.."," Overall, the level of contraction is weaker than predicted by the SAC model, confirming the conclusion of \cite{2011GnedinContraction}."
+ Dashed lines in Figure 14 illustrate the strength of halo contraction in comparison to the SAC model., Dashed lines in Figure \ref{fig:contra_A_w} illustrate the strength of halo contraction in comparison to the SAC model.
+" Let us define the mass enhancement ratio at radius r: Fy(r)= Mpw,;(r)/Mpw,(r)."," Let us define the mass enhancement ratio at radius $r$: $F_M(r) \equiv M_{{\rm DM},f}(r) / M_{{\rm DM},i}(r)$ ."
+" Each line corresponds to a fixed fraction of this enhancement factor relative to its value in the SAC model: fas(r)=Fy(r|Ao,w)/Fu(r|1,1) 1, 0.5, and 0.3, respectively."," Each line corresponds to a fixed fraction of this enhancement factor relative to its value in the SAC model: $f_M(r) \equiv F_M(r|A_0,w)/F_M(r|1,1) = 1$ , 0.5, and 0.3, respectively."
+" The radius at which these fractions are evaluated is r=0.005r2oop,A, near our resolution limit."," The radius at which these fractions are evaluated is $r = 0.005\, r_\mathrm{200b,A}$, near our resolution limit."
+" For most of the halos, the mass enhancement factor at this radius is to of the value expected in the SAC model."," For most of the halos, the mass enhancement factor at this radius is to of the value expected in the SAC model."
+ Figure 14 also shows the evolution of the main halo over time in the space of the model parameters., Figure \ref{fig:contra_A_w} also shows the evolution of the main halo over time in the space of the model parameters.
+" It starts with relatively strong contraction, reaches a peak value around the cosmic time 1.3 Gyr, recedes until 1.8 Gyr, then reaches another peak, and finally settles into a quasi-steady state at Ag~2.4, w&0.5."," It starts with relatively strong contraction, reaches a peak value around the cosmic time 1.3 Gyr, recedes until 1.8 Gyr, then reaches another peak, and finally settles into a quasi-steady state at $A_0 \approx 2.4$, $w \approx 0.5$."
+ The two bouts of strongest contraction (when w is highest and Αρ is lowest) do not correspond to the epoch of the peak of star formation following a major merger around t=1.6 Gyr., The two bouts of strongest contraction (when $w$ is highest and $A_0$ is lowest) do not correspond to the epoch of the peak of star formation following a major merger around $t \approx 1.6$ Gyr.
+" Instead, the first bout precedes the merger and the second happens after the system reaches new dynamical equilibrium."," Instead, the first bout precedes the merger and the second happens after the system reaches new dynamical equilibrium."
+ The exact correlation with the dynamical state is not straightforward or very strong., The exact correlation with the dynamical state is not straightforward or very strong.
+ At lower redshift the contraction effect stabilizes and is still significant., At lower redshift the contraction effect stabilizes and is still significant.
+ The structure of the halo is affected by the evolution of its angular momentum., The structure of the halo is affected by the evolution of its angular momentum.
+ We find that baryon dissipation dramatically affects the angular momentum profile of the inner halo., We find that baryon dissipation dramatically affects the angular momentum profile of the inner halo.
+" At a fixed radius, the total angular momentum Lpw (and the specific angular momentum per unit mass, increases with time simply because more mass accumulatesJpM) as the gas falls in and halo contracts."," At a fixed radius, the total angular momentum $L_{\mathrm{DM}}$ (and the specific angular momentum per unit mass, $J_{\mathrm{DM}}$ ) increases with time simply because more mass accumulates as the gas falls in and halo contracts."
+" However, in the idealized scenario of particles on circular orbits and spherical shells that do not cross, the angular momentum of each lagrangian shell with enclosed mass Μην is conserved, J§\(Mpm)=GM(r)rconst."," However, in the idealized scenario of particles on circular orbits and spherical shells that do not cross, the angular momentum of each lagrangian shell with enclosed mass $M_{\mathrm{DM}}$ is conserved, $J^2_{\mathrm{DM}}(M_{\mathrm{DM}}) = G M(r) r = \mathrm{const}$."
+" As the enclosed baryon mass increases, the shell moves inward but retains the angular momentum profile "," As the enclosed baryon mass increases, the shell moves inward but retains the angular momentum profile $J_{\mathrm{DM}}(M_{\mathrm{DM}})$."
+This is a test of the foundation of the halo Jpm(Mpm).contraction model., This is a test of the foundation of the halo contraction model.
+" In this section we consider the evolution (in time and between the runs A and B) of theangular momentum of the same spherical shells, that is, the same enclosed amount of material."," In this section we consider the evolution (in time and between the runs A and B) of theangular momentum of the same spherical shells, that is, the same enclosed amount of material."
+" Relative to the dissipationless case, the inner dark matter shells gain a lot of angular momentum."," Relative to the dissipationless case, the inner dark matter shells gain a lot of angular momentum."
+ Figure, Figure
+the VLTI/AMBER instrument. we propose here to revisit the system along two directions.,"the VLTI/AMBER instrument, we propose here to revisit the system along two directions."
+ In Sect. 2..," In Sect. \ref{AaAborbit},"
+ we describe our new VLTI/AMBER interferometric data. as well as our re-analysis of the spectroscopic and photometric data previously used in Paper II.," we describe our new VLTI/AMBER interferometric data, as well as our re-analysis of the spectroscopic and photometric data previously used in Paper II."
+ Sect., Sect.
+ 2.2 is dedicated to the description of our self-consistent model. and the derivation of an improved orbital solution. physical parameters as well as an independent distance.," \ref{modelfitting} is dedicated to the description of our self-consistent model, and the derivation of an improved orbital solution, physical parameters as well as an independent distance."
+ In Sect., In Sect.
+ 3 we employ NACO astrometry of the visual 0 VVel A-B binary to obtain an improved orbital solution., \ref{ABorbit} we employ NACO astrometry of the visual $\delta$ Vel A-B binary to obtain an improved orbital solution.
+ Compared to our work presented in Paper IL. this new analysis result is a clearer view and better confidence in the derived. fundamental parameters of the system (for all three components). thanks to the redundant nature of our data and our independent determination of the distance.," Compared to our work presented in Paper II, this new analysis result is a clearer view and better confidence in the derived fundamental parameters of the system (for all three components), thanks to the redundant nature of our data and our independent determination of the distance."
+ AMBER (Petrov et al. 2007))," AMBER (Petrov et al. \cite{petrov07}) ),"
+ the three-telescope beam combiner of the VLTI. has the proper angular resolutior to resolve the Aa-Àb pair.," the three-telescope beam combiner of the VLTI, has the proper angular resolution to resolve the Aa-Ab pair."
+ This. instrument combines simultaneously 3 ATs (Auxiliary Telescopes) or 3 UTs (Unit Telescopes) of the VLT and operates in the near infrared (H and K band)., This instrument combines simultaneously 3 ATs (Auxiliary Telescopes) or 3 UTs (Unit Telescopes) of the VLT and operates in the near infrared (H and K band).
+ It has a choice of spectral resolutions of R~35. R~1500 or R~15000.," It has a choice of spectral resolutions of $R\sim35$, $R\sim1500$ or $R\sim15000$."
+ For this study. we hac data in low resolution (ΠΚ bands at R~ 35) and medium resolution (H or K band. at R~ 1500).," For this study, we had data in low resolution (H+K bands at $R\sim35$ ) and medium resolution (H or K band, at $R\sim1500$ )."
+ We used baselines of the order of mm in order to obtain spatial resolution in the milli-aresecond regime., We used baselines of the order of m in order to obtain spatial resolution in the milli-arcsecond regime.
+ These interferometric data have been collected in a dedicated program (ESO program 076.D-0782). as well as during Guaranteed Time (GTO) from Arcetri Observatory.," These interferometric data have been collected in a dedicated program (ESO program 076.D-0782), as well as during Guaranteed Time (GTO) from Arcetri Observatory."
+ We present here a reduction of these data., We present here a reduction of these data.
+ We reduced the data using the AMBER reduction package (Chelli et al. 2009..," We reduced the data using the AMBER reduction package (Chelli et al. \cite{chelli09},"
+ Tatulli et al. 2007)), Tatulli et al. \cite{tatulli07}) )
+ and performed the calibration using stellar calibrators chosen in the catalogue by Mérrand et al. (2005)), and performed the calibration using stellar calibrators chosen in the catalogue by Mérrand et al. \cite{merand05}) )
+ and a custom software which estimates and interpolates the transfer function of the instrument., and a custom software which estimates and interpolates the transfer function of the instrument.
+ For each night. we derived the separation of Aa and Ab using a ye map as a function of the separation vector (two parameters).," For each night, we derived the separation of Aa and Ab using a $\chi^2$ map as a function of the separation vector (two parameters)."
+ The other parameters. such as flux ratio or individual diameters. were set using simple hypothesis and their choice did not affect significantly our final estimated angular separations.," The other parameters, such as flux ratio or individual diameters, were set using simple hypothesis and their choice did not affect significantly our final estimated angular separations."
+ The resulting separation vectors are listed in Table 1. in coordinate towards East and North (which correspond to the # and v axes in the projected baselines map)., The resulting separation vectors are listed in Table \ref{tab:AMBER_positions} in coordinate towards East and North (which correspond to the $u$ and $v$ axes in the projected baselines map).
+ The error bars on this vectors were estimated in the y map., The error bars on this vectors were estimated in the $\chi^2$ map.
+ We used the photometric data from the SMEL satellite. presented in Paper Il.," We used the photometric data from the SMEI satellite, presented in Paper II."
+ The available quantity is the relative flux normalized to the value outside of the eclipses. since there was no absolute calibration of SMEI data available.," The available quantity is the relative flux normalized to the value outside of the eclipses, since there was no absolute calibration of SMEI data available."
+ We corrected for the presence of the B component which is 1n the field of view of SMEI., We corrected for the presence of the B component which is in the field of view of SMEI.
+ From our model of B. the expectec flux ratio between B and Aab is in the SMEI bandpass.," From our model of B, the expected flux ratio between B and Aab is in the SMEI bandpass."
+ The transmission of the instrument has a triangular shape that peaks at nnm. with a quantum efficiency around47%.. and falls to =5% at 430nnm towards the blue. and nnm towards the red (Spreckley Stevens 2008)).," The transmission of the instrument has a triangular shape that peaks at nm, with a quantum efficiency around, and falls to $\approx5\%$ at nm towards the blue, and nm towards the red (Spreckley Stevens \cite{spreckley08}) )."
+ We removed this contribution which. if not taken into account. would result in an underestimation of the depth of the eclipses.," We removed this contribution which, if not taken into account, would result in an underestimation of the depth of the eclipses."
+ We also incorporated to our photometric dataset the photometric measurement we derived of Aab in the K band (Paper D., We also incorporated to our photometric dataset the photometric measurement we derived of Aab in the K band (Paper I).
+ We use this value in our fit as the only constraint in term of absolute photometry., We use this value in our fit as the only constraint in term of absolute photometry.
+ The observables we derived from the visible spectroscopic data are the broadening functions (BF) presented in paper II (see this reference for more explanations)., The observables we derived from the visible spectroscopic data are the broadening functions (BF) presented in paper II (see this reference for more explanations).
+ These functions contain a lot of information: not only do they contain the radial velocities that result from the orbital motion. but also the broadening due to the stellar rotation and the flux ratio in the considered band.," These functions contain a lot of information: not only do they contain the radial velocities that result from the orbital motion, but also the broadening due to the stellar rotation and the flux ratio in the considered band."
+ From the observed BF. it is possible to derive the vsin? from the two components.," From the observed BF, it is possible to derive the $v\sin i$ from the two components."
+ After a few experimentations using the stellar surface model we are going to present later. we found that the following function parameterizes well the BF for a star seen from the equator: where « is the only parameter constraining the gravity darkening and vo ts the velocity offset.," After a few experimentations using the stellar surface model we are going to present later, we found that the following function parameterizes well the BF for a star seen from the equator: where $\alpha$ is the only parameter constraining the gravity darkening and $v_0$ is the velocity offset."
+ The function is defined for |v—vol€vsini only. and its value ts O otherwise.," The function is defined for $|v-v_0| \leq v \sin i$ only, and its value is 0 otherwise."
+ Using this analytical model and a global fit. we estimated vsini for each component and the radial velocities for each epoch (see Fig.," Using this analytical model and a global fit, we estimated $v\sin i$ for each component and the radial velocities for each epoch (see Fig."
+ | and 2. for the quality of the fit)., \ref{fig:AaAb_BF1} and \ref{fig:AaAb_BF2} for the quality of the fit).
+ We found vsini to be 143.5+0.2 km/s and 149.6+0.2 km/s for Aa and Ab respectively., We found $v\sin i$ to be $143.5\pm0.2$ km/s and $149.6\pm0.2$ km/s for Aa and Ab respectively.
+" Incidentally. we find αι20.460+0.003 and ay,=0.451+ 0.003."," Incidentally, we find $\alpha_a = 0.460\pm0.003$ and $\alpha_b=0.451\pm0.003$ ."
+ The rotation rate value is relatively independent of the actual gravity darkening (parameterized here by a) since it is set by the width of the broadening function. not its shape.," The rotation rate value is relatively independent of the actual gravity darkening (parameterized here by $\alpha$ ) since it is set by the width of the broadening function, not its shape."
+ For our fit of the orbit and the stellar parameters. we do not use the center-to-limb darkening we derive here from the," For our fit of the orbit and the stellar parameters, we do not use the center-to-limb darkening we derive here from the"
+"where we have introduced. p;=pop, and go as the angular part of οί]. g(8)/po..","where we have introduced $\bar{\rho}_{J}=\bar{\rho}_{\theta} \bar{\rho}_{r}$ and $g_{\theta}$ as the angular part of $g(\theta)$, $g(\theta)/\bar{\rho}_{0}$."
+" The full solution. can be seen to depend only on the two parameters py and py. normalisation constants for the densities of the background state and the perturbation. with the velocities of the perturbation solution depending only. and. linearly. on the ratio Q=2!""pa/po. which is expected to be small. bevond natural dependences on the physical parameters of the problem. AZ and c."," The full solution can be seen to depend only on the two parameters $\bar{\rho}_{0}$ and $\bar{\rho}_{J}$, normalisation constants for the densities of the background state and the perturbation, with the velocities of the perturbation solution depending only, and linearly, on the ratio $Q=2^{1/2} \bar{\rho}_{J} / \bar{\rho}_{0}$, which is expected to be small, beyond natural dependences on the physical parameters of the problem, $M$ and $c$."
+ We see form eq.(45) that the angular velocity will be zero only for 6=x/2. 6=0 and 6=x.," We see form eq.(45) that the angular velocity will be zero only for $\theta=\pi/2$, $\theta=0$ and $\theta=\pi$."
+ Thus. movement along the plane of the disk will remain along the plane. but also. along the poles movement will be exclusively racial.," Thus, movement along the plane of the disk will remain along the plane, but also, along the poles movement will be exclusively radial."
+ This last point. together with the positive sign of the racial velocity along the poles. provides for a well collimated jet along the poles.," This last point, together with the positive sign of the radial velocity along the poles, provides for a well collimated jet along the poles."
+ From eq.(44) we see that one has only to ask for a background state where matter is concentrated on the plane of the disk with relatively empty. poles. c.g. g(9)-0 for 8:0 and @»zx. in order to obtain extremely large. ejection velocities along the poles.," From eq.(44) we see that one has only to ask for a background state where matter is concentrated on the plane of the disk with relatively empty poles, e.g. $g(\theta) \rightarrow 0$ for $\theta \rightarrow 0$ and $\theta \rightarrow \pi$, in order to obtain extremely large ejection velocities along the poles."
+ The axial symmetry. condition imposed. on eq.(34) guarantees both axial svmmetry and svimnmetry above and below the plane of the disk for the full solution., The axial symmetry condition imposed on eq.(34) guarantees both axial symmetry and symmetry above and below the plane of the disk for the full solution.
+ We see also that if one takes higher orders for m. the index of the Legendre polvnomial solution to. eq.(33). one obtains increasingly more critical angles at positions intermediary between 0 and 7/2231 which the angular velocity &oes to zero.," We see also that if one takes higher orders for $m$, the index of the Legendre polynomial solution to eq.(33), one obtains increasingly more critical angles at positions intermediary between $0$ and $\pi/2$ at which the angular velocity goes to zero."
+ In Lact. more complex geometries and asymmetric jets appear. as inferred observationally by e.g. Ferreira ct al. (," In fact, more complex geometries and asymmetric jets appear, as inferred observationally by e.g. Ferreira et al. ("
+2006). if m ds taken as an arbitrary real number.,"2006), if $m$ is taken as an arbitrary real number."
+ However. modelling a situation where a polar jet dominates the ejection identifies m=2 as the leacling order.," However, modelling a situation where a polar jet dominates the ejection identifies $m=2$ as the leading order."
+ Notice that the qualitative behaviour of the solution is guaranteed by the cxactness of the angular solution. the approximation r«2GAL/e= used. for solving the radial ooblem. will only introduce an error in the actual values of the radial velocities outside of ik«26MC. but will not change the fact that velocities will be of radial infall along he plane of the disk. €=z/2. and of radial outLow along the voles (where the background solution becomes very small). he jet solution for 6= 0.7.," Notice that the qualitative behaviour of the solution is guaranteed by the exactness of the angular solution, the approximation $r<2GM/c^{2}$ used for solving the radial problem will only introduce an error in the actual values of the radial velocities outside of $r<2GM/c^{2}$, but will not change the fact that velocities will be of radial infall along the plane of the disk, $\theta=\pi/2$, and of radial outflow along the poles (where the background solution becomes very small), the jet solution for $\theta=0,\pi$ ."
+" The two constants of the problem. po and py. can now »e caleulated once a choice of g(8) is specified. [rom the two conditions: where 6, is a suitable angle. defining the opening of the jet. in all likelihood. very small. as will be see in the Following section."," The two constants of the problem, $\bar{\rho}_{0}$ and $\bar{\rho}_{J}$, can now be calculated once a choice of $g(\theta)$ is specified, from the two conditions: where $\theta_{J}$ is a suitable angle defining the opening of the jet, in all likelihood very small, as will be see in the following section."
+" In. the above equations AL, gives the matter acerction rate onto the central star. and M; the matter ejection rate due to the jet."," In the above equations $\dot{M}_{a}$ gives the matter accretion rate onto the central star, and $\dot{M}_{j}$ the matter ejection rate due to the jet."
+" Dimensionallv. the two cquantities above will scale as: where C, and €'; are two dimensionless constants which will depend on the choice of go. and which would be expected to x of order 1."," Dimensionally, the two quantities above will scale as: where $C_{a}$ and $C_{j}$ are two dimensionless constants which will depend on the choice of $g_{\theta}$, and which would be expected to be of order 1."
+ Qualitatively. this twpe of model naturally furnishes a ight clisk-jet connection οι.," Qualitatively, this type of model naturally furnishes a tight disk-jet connection (c.f."
+ eq., eq.
+ 44) c.g. as now firmly established in microquasars and AGN jets (see c.g. Marscher ot al.," 44) e.g., as now firmly established in microquasars and AGN jets (see e.g. Marscher et al."
+ 2002. Chatterjee et al.," 2002, Chatterjee et al."
+ 2009)., 2009).
+ In the above systems rusts of enhanced. jet activity are seen to follow temporal dips in disk luminosity output after small characteristic delav times., In the above systems bursts of enhanced jet activity are seen to follow temporal dips in disk luminosity output after small characteristic delay times.
+ La the present model. such a situation would » expected if the critical radius for transition to racial Low in the disk macle a sudden transition to higher values.," In the present model, such a situation would be expected if the critical radius for transition to radial flow in the disk made a sudden transition to higher values."
+" Again. he drop in disk output might not reflect the disk material disappearing (in this case being swallowed by the central jack hole. as sometimes proposed). but simply facing from view as heating mechanisms shut down. then naturally enhancing jet activity as the ellective AL, increases."," Again, the drop in disk output might not reflect the disk material disappearing (in this case being swallowed by the central black hole, as sometimes proposed), but simply fading from view as heating mechanisms shut down, then naturally enhancing jet activity as the effective $\dot{M}_{a}$ increases."
+ In order to present a sample of the trajectories expected in the mocel we turn to the full solution to the problem. eqs.(21) and (22). but written in dimensionless form: The above remain in spherical coordinates. where rev(CAL and T—το)όλ.," In order to present a sample of the trajectories expected in the model, we turn to the full solution to the problem, eqs.(21) and (22), but written in dimensionless form: The above remain in spherical coordinates, where ${\cal R} = r c^{2}/GM$ and ${\cal T}=t c^{3}/GM$."
+ A choice of Q and go now allows to numerically integrate trajectories., A choice of $Q$ and $g_{\theta}$ now allows to numerically integrate trajectories.
+" We take Q=5.10 aud with &,=0.38 radians. or about 22 degrees."," We take $Q=5 \times 10^{-2}$, and with $\theta_{0} = 0.38$ radians, or about 22 degrees."
+ This values is far [from representing an extremely. Lattened disk. and hence one which does not force the jet solution. see edq.(44).," This values is far from representing an extremely flattened disk, and hence one which does not force the jet solution, see eq.(44)."
+ With these parameters. and. initial conditions specified in dimensionless cvlindrical coordinates as /7=2 and Z ranging from O.4 to LA. we solve eqs.(50) and (51) through a finite dillerences scheme to plot figure 1.," With these parameters, and initial conditions specified in dimensionless cylindrical coordinates as $R=2$ and $Z$ ranging from 0.4 to 1.4, we solve eqs.(50) and (51) through a finite differences scheme to plot figure 1."
+ For this case. he two lowermost curves present trajectories. which all urn downwards to converge onto the central star.," For this case, the two lowermost curves present trajectories which all turn downwards to converge onto the central star."
+ These are solutions which essentially follow the background state. infalling onto the bottom of the potential well.," These are solutions which essentially follow the background state, infalling onto the bottom of the potential well."
+ As one raises he initial value of Z however. a threshold. is crossed. and curves of a very dillerent. tvpe ensue. the six upper jet rajectories shown in figure 1.," As one raises the initial value of $Z$ however, a threshold is crossed and curves of a very different type ensue, the six upper jet trajectories shown in figure 1."
+ We see the large pressure eracicnts associated with the distribution of matter in the xickeround solution acting to break the fall of the incoming material. turn it back. and then accelerate it vertically hrough the vertical density eracients.," We see the large pressure gradients associated with the distribution of matter in the background solution acting to break the fall of the incoming material, turn it back, and then accelerate it vertically through the vertical density gradients."
+ These jet trajectories resent a relatively constant thickening at the base of the jet of order 4?20.5. which then rapidly diminishes with height o eventually vield an extremely collimated structure which rapiclly narrows to below the resolution limit of the solution. notice the horizontal displacement of the verticalaxis.," These jet trajectories present a relatively constant thickening at the base of the jet of order $R=0.5$, which then rapidly diminishes with height to eventually yield an extremely collimated structure which rapidly narrows to below the resolution limit of the solution, notice the horizontal displacement of the verticalaxis."
+ Note also that although the region. bevond R=2 lies outside the approximation of the radial solution. the," Note also that although the region beyond ${\cal R}=2$ lies outside the approximation of the radial solution, the"
+We implement these (Gransforms for double precision complex-valued functions on the sphere.,We implement these transforms for double precision complex-valued functions on the sphere.
+ A C library is available [rom theauthors!., A C library is available from the.
+". In this implementation. the equiangular (Equidistant Cvlindrical Projection or EC'P) pixelization is described by parameters ;V,, and Ny. describing the number of pixels in each direction."," In this implementation, the equiangular (Equidistant Cylindrical Projection or ECP) pixelization is described by parameters $N_\phi$ and $N_\theta$, describing the number of pixels in each direction."
+ The first pixel column is centered al ó=0., The first pixel column is centered at $\phi = 0$.
+ The first and last rows each contain redundant. pixels at the poles. 9=0 and 4=x. respectivelv.," The first and last rows each contain redundant pixels at the poles, $\theta = 0$ and $\theta = \pi$, respectively."
+ The FFT portions of the computation use the FFTW and are most eíficient when (he dimensions of the 6-extended map (appendix D)) are are powers οἱ two., The FFT portions of the computation use the FFTW and are most efficient when the dimensions of the $\theta$ -extended map (appendix \ref{quadrature}) ) are are powers of two.
+" The dimensions of the extended map in our implementation are NV, aud 26V;—1).", The dimensions of the extended map in our implementation are $N_\phi$ and $2 (N_\theta - 1)$ .
+ To support a function with limited bandwidth /<L requires NV.Ny>2L+I.," To support a function with limited bandwidth $l \leq L$ requires $N_\phi, N_\theta \geq 2 L+1$."
+ We verilied (he accuracy of our method in two wavs., We verified the accuracy of our method in two ways.
+ First. for selected low multipoles. we checked our transforms against (he analv(üc expressions for single spin spherical harmonics [rom?.," First, for selected low multipoles, we checked our transforms against the analytic expressions for single spin spherical harmonics from."
+. Second. we showed that our transforms are extremely accurate by comparing the spherical harmonic coefficients from a backward-forward transform pair to the original coefficients (Fig. 1)).," Second, we showed that our transforms are extremely accurate by comparing the spherical harmonic coefficients from a backward-forward transform pair to the original coefficients (Fig. \ref{fig:accuracy}) ),"
+ up to a baud-limit of L=4096., up to a band-limit of $L=4096$.
+" We plot the rms of the relative difference between the original (καν) and recovered (ἄν) harmonic coefficients. simTsln,|/f/|s@im|. For Gaussian random white noise. showing tvpical errors of ~1015 which increase roughly. proportional to the band limit."," We plot the rms of the relative difference between the original $_sa_{lm}$ ) and recovered $_s\hat{a}_{lm}$ ) harmonic coefficients, $|_sa_{lm} - _s\hat{a}_{lm}|/|_sa_{lm}|$, for Gaussian random white noise, showing typical errors of $\sim 10^{-13}$ which increase roughly proportional to the band limit."
+ Comparison of (ie maximun relative errors shows that these transforms are 3-4 orders of magnitude more accurate than the (already veryaccurate) s=0.£2 (transforms from onto a similar grid.," Comparison of the maximum relative errors shows that these transforms are 3-4 orders of magnitude more accurate than the (already veryaccurate) $s=0,\pm2$ transforms from onto a similar grid."
+Gyr alter simultaneous mass loss and evolution of the EGP.,Gyr after simultaneous mass loss and evolution of the EGP.
+ In all cases. the mass functions are normalized (o univ al AJ=1 Mj.," In all cases, the mass functions are normalized to unity at $M = 1$ $M_J$."
+ For fixed total initial mass of the ensemble. all subsequent mass functions would plot below the IME due to mass loss. with the strongest deviations at the lowest mass.," For fixed total initial mass of the ensemble, all subsequent mass functions would plot below the IMF due to mass loss, with the strongest deviations at the lowest mass."
+ However. we renormalize the theoretical curves to 11M; for comparison with the observed mass function data points.," However, we renormalize the theoretical curves to 1 $M_J$ for comparison with the observed mass function data points."
+ We denote by ~Lanuner Model the evaporation theory of Lanmmieretal.(2003). as incorporated in the predictions of Baralleοἱal.(2004).," We denote by “Lammer Model” the evaporation theory of \citet{lam03}
+ as incorporated in the predictions of \citet{bar04}."
+.. We do not separately simulate (he implications of more moderate mass-loss rates investigated in more recent. publications (Baralfeetal.2006:Alibert2006) because these are bounded by the (2004) rates and the Watson model.," We do not separately simulate the implications of more moderate mass-loss rates investigated in more recent publications \citep{bar06,ali06} because these are bounded by the \citet{bar04} rates and the Watson model."
+ In agreement with the findings of (2006).. 5-Gvr mass functions corresponding to the Lammmner model show the strongest effect ol mass loss.," In agreement with the findings of \citet{hub06}, 5-Gyr mass functions corresponding to the Lammer model show the strongest effect of mass loss."
+ At the smallest orbital radius investigated. «=0.023 AU. the predicted 5-Gvr nass [function (solid curve) has a positive slope for the entire mass interval plotted in Fig.," At the smallest orbital radius investigated, $a=0.023$ AU, the predicted 5-Gyr mass function (solid curve) has a positive slope for the entire mass interval plotted in Fig."
+ 1. while the IME has a negative slope.," 1, while the IMF has a negative slope."
+ This behavior occurs because mass loss biased to the owest-mss EGPs rapidly depletes their larger initial numbers., This behavior occurs because mass loss biased to the lowest-mass EGPs rapidly depletes their larger initial numbers.
+" Ixdeed. the mass Dunction plotted is almost entirely populated by remnants of EGPs with initial masses Aj>3—4 M, see Fig."," Indeed, the mass function plotted is almost entirely populated by remnants of EGPs with initial masses $M_0 > 3-4$ $M_J$ (see Fig."
+ 7 of Hubbardetal. (2006)))., 7 of \citet{hub06}) ).
+ For the largest orbital radii investigated. @=0.057 AU. alter 5 Gvr there a peak in the mass distribution at M~2.3 Mj.," For the largest orbital radii investigated, $a=0.057$ AU, after 5 Gyr there a peak in the mass distribution at $M \sim 2.3$ $M_J$."
+ In contrast. (he Watson model predicts essentiallv no deviation of the mass function from the IMFE for M>1 Mj.," In contrast, the Watson model predicts essentially no deviation of the mass function from the IMF for $M > 1$ $M_J$."
+ However. as we see from the curves in Fig.," However, as we see from the curves in Fig."
+" 1. lor M<1 AL, ihe Watson model predicts significant deviations [rom the IME. with a maximum at about one Saturn mass for α=0.057 AU and at even higher masses for smaller orbital radii."," 1, for $M < 1$ $M_J$ the Watson model predicts significant deviations from the IMF, with a maximum at about one Saturn mass for $a=0.057$ AU and at even higher masses for smaller orbital radii."
+ The database [from which weconstruct the mass function for highlv-irradiated EEGPs comprises ~40 objects (Table 1)., The database from which weconstruct the mass function for highly-irradiated EGPs comprises $\sim40$ objects (Table 1).
+ These objects were selected from the list of all reported LEGPs (Schneider2006) according to the criteria 0.2 M;<Msin?<5 Mj and ax0.07 AU., These objects were selected from the list of all reported EGPs \citep{sch06} according to the criteria $0.2$ $M_J \le M \sin i \le 5$ $M_J$ and $a \le 0.07$ AU.
+" We selected a central mass bin of width 0.3 Aly. according to 0.9 A/,<Msini1.2 "," We selected a central mass bin of width $0.3$ $M_J$ , according to $0.9$ $M_J \le M \sin i < 1.2$ "
+ddata capable of distinguishing between absorbers with differing (low) redshifts.,data capable of distinguishing between absorbers with differing (low) redshifts.
+ Most of the clusters in our sample do not require an extra absorption component to be modelled successfully., Most of the clusters in our sample do not require an extra absorption component to be modelled successfully.
+ Model fits for each cluster are shown in Table 2.., Model fits for each cluster are shown in Table \ref{tab:fits}.
+ OF the 20 clusters in (he sample. 12 can be fit with a one- or (vo-component model with the intervening column set lo the Galactic Ay value. and (hus require no exira absorption component.," Of the 20 clusters in the sample, 12 can be fit with a one- or two-component model with the intervening column set to the Galactic $\NHxo$ value, and thus require no extra absorption component."
+ Figure shows an acceptable model spectrum. convolved with the PSPC instrument. profile. for Coma (Abell 1656). a cluster in the direction of low Galactic absorption.," Figure \ref{f1}
+ shows an acceptable model spectrum, convolved with the PSPC instrument profile, for Coma (Abell 1656), a cluster in the direction of low Galactic absorption."
+ The model used here consists of one enission component al a temperature of 8.0 keV. with a Galactic column set to 0.60x10777.. a value determined [rom fits to the X-ray emission more than 6’ minutes from the emission center. (," The model used here consists of one emission component at a temperature of 8.0 keV, with a Galactic column set to $0.60\tenup{20}$, a value determined from fits to the X-ray emission more than $6^{\prime}$ minutes from the emission center. ("
+"A nearby region was determined by AB to have a columΕν of 0.78x10?""?..",A nearby region was determined by AB to have a column of $0.78\tenup{20}$.
+ Both of these values deviate from the 21 em column of bv more than the expected see AB [or a diseussion.), Both of these values deviate from the 21 cm column of \citet{hb} by more than the expected – see AB for a discussion.)
+" Figure 2 shows the fit lor Abell 2657. which lies in a direction of relatively large Galactic column CN,—1.13x1074 7))."," Figure \ref{f2} shows the fit for Abell 2657, which lies in a direction of relatively large Galactic column $\NHxo = 1.13\tenup{21}$ )."
+" This model also uses a single emission component (T=3.4 keV). with the column set to the value derived for an annulus 3-6""."," This model also uses a single emission component $T = 3.4$ keV), with the column set to the value derived for an annulus $^{\prime}$."
+ For the 8 clusters that cannot be fit adequately using ἂν from AB. we allow the Galactic column to vary in order (o ascertain whether extra absorption is required.," For the 8 clusters that cannot be fit adequately using $\NHxo$ from AB, we allow the Galactic column to vary in order to ascertain whether extra absorption is required.,"
+fil(e... NZ« 1.26) cluster., $\chi^2_r < 1.26$ ) .
+ In (ree of (hese clusters. however. the fits are only marginally unacceptable.," In three of these clusters, however, the fits are only marginally unacceptable."
+ Abell 85 (42= 1.307: Figure 3)) requires absorption about higher than the Galactic Ay value at a significance of about 1.56. rather weak evidence for an absorption component local to the cluster.," Abell 85 $\chi^2_r = 1.307$ ; Figure \ref{f3}) ) requires absorption about higher than the Galactic $\NHxo$ value at a significance of about $\sigma$, rather weak evidence for an absorption component local to the cluster."
+ The best fit for Abell 496 (42=1.273: Figure 4)) requires a Galactic cohunn which is about than the nominal Vy value ad about the 2.60 level., The best fit for Abell 496 $\chi^2_r = 1.273$; Figure \ref{f4}) ) requires a Galactic column which is about than the nominal $\NHxo$ value at about the $2.6\sigma$ level.
+ The brighter of the two emission peaks in Abell 2256 ean be fit equally well using either the Galactie cohunn from AB or by allowing Ny to vary., The brighter of the two emission peaks in Abell 2256 can be fit equally well using either the Galactic column from AB or by allowing $\NHxo$ to vary.
+ In the latter case the resulting column islower. but bv less than (less than lo significance).," In the latter case the resulting column is, but by less than (less than $1\sigma$ significance)."
+ The difference between the Ny fit in the center and in the outer parts of each cluster is expected [rom normal fluctuations of Galactic Vy) on these angular scales. which are typically al the level (Crovisier&Dickey1983:Schlegel.FinkbeinerDavis1998:&Dregman 1999a).," The difference between the $\NHxo$ fit in the center and in the outer parts of each cluster is expected from normal fluctuations of Galactic $\NHoo$ on these angular scales, which are typically at the level \citep{cd,sfd,ab_a}."
+. Alternatively. thev may be the result of small calibration errors in the PSPC response matrices (Prieto.Hasinger&Snowden1994).," Alternatively, they may be the result of small calibration errors in the PSPC response matrices \citep{phs}."
+. Neither Abell 35 nor Abell 496 shows a svstematic fluctuation in its residuals. whichwould undermineconfidence in the choice of models used. but the nominal uncertainty in each channel is perhaps (oo small.," Neither Abell 85 nor Abell 496 shows a systematic fluctuation in its residuals, whichwould undermineconfidence in the choice of models used, but the nominal uncertainty in each channel is perhaps too small,"
+3«logtafCyr1)1.67 with a step of 0.033 in both directions.,$-3<\log(\alpha/\Gyr^{-1})<-1.67$ with a step of $0.033$ in both directions.
+ This map is then smoothed to the resolution of 0.1. O.Lin order to minimise the stochastic ellects due to the probability distribution function (eq. 1)), This map is then smoothed to the resolution of $0.1\times0.1$ in order to minimise the stochastic effects due to the probability distribution function (eq. \ref{probeject}) )
+ used to build our nmiocdels., used to build our models.
+ As in the case of a pure fountain. different residuals eive dillerent results.," As in the case of a pure fountain, different residuals give different results."
+" Regardless of à ancl fii. absolute and squared. differences have lower values for ,=SOkms while relative residuals favour fy=GOkmsJ|."," Regardless of $\alpha$ and $f_{\rm ion}$, absolute and squared differences have lower values for $h_{\rm v}=80\kms$, while relative residuals favour $h_{\rm v}=60\kms$."
+ Hence we set our kick velocity in the middle ane focus on mocdels with hh.=70kms, Hence we set our kick velocity in the middle and focus on models with $h_{\rm v}=70\kms$.
+ The first three panels in figure 5 show the residual maps obtained with h.=7Okms+ for different ἵνρος of residuals., The first three panels in figure \ref{residuals} show the residual maps obtained with $h_{\rm v}=70\kms$ for different types of residuals.
+ In each panel all values are divided. by the respective minimum. thus they are dimensionless and z1.," In each panel all values are divided by the respective minimum, thus they are dimensionless and $\ge1$."
+ Combining these three panels we obtain the fourth (rightmost) panel. which is the sum of the previous three divided. by the resulting minimum. which occurs at fi;=0.3 and log(a)= (so à=6.3Gvyr. +).," Combining these three panels we obtain the fourth (rightmost) panel, which is the sum of the previous three divided by the resulting minimum, which occurs at $f_{\rm ion}=0.3$ and $\log(\alpha)=-2.2$ (so $\alpha=6.3\Gyr^{-1}$ )."
+ For this best model the mass of the hhalo is 2.To10734..., For this best model the mass of the halo is $2.7\times10^8 M_{\odot}$.
+ Vable 1. [ists the parameters., Table \ref{tModels} lists the parameters.
+ Phe middle column of Fig., The middle column of Fig.
+ 6 shows that the mocel with coronal condensation reproduces the emission near the anticentre better than the pure fountain mocdel., \ref{fBestModels} shows that the model with coronal condensation reproduces the emission near the anticentre better than the pure fountain model.
+ The open arrows (latitudes 6= #30°) indicate other regions where the inclusion of coronal condensation improves the fit to the data.," The open arrows (latitudes $b=\pm 30
+\de$ ) indicate other regions where the inclusion of coronal condensation improves the fit to the data."
+ These are regions in which iis llowing out from the inner disc. and the pure fountain provides too much emission.," These are regions in which is flowing out from the inner disc, and the pure fountain provides too much emission."
+ For our best-litting value of a. the condensation rate of coronal gas into the clouds’ wakes is M—16A.ve+," For our best-fitting value of $\alpha$, the condensation rate of coronal gas into the clouds' wakes is $\dot M=1.6\moyr$."
+ Correcting this value for the content increases the condensation rate to 2.3AL.vr.+., Correcting this value for the content increases the condensation rate to $2.3\moyr$.
+ Ehis value is remarkably close to the CGalaxv SER. which we assume to be ~BAL.vr (2?) of whichs ~LAL.ve+ should be accounted [or bv gas ejected from stars in the disc.," This value is remarkably close to the Galaxy's SFR, which we assume to be $\sim3\moyr$ \citep{Diehl+06}, of which $\sim1\moyr$ should be accounted for by gas ejected from stars in the disc."
+ We consider it hiehly significant that AL deduced from an ssurvev should. agree so well with that required to sustain the SER. which is obtained without reference toLLL.," We consider it highly significant that $\dot M$ deduced from an survey should agree so well with that required to sustain the SFR, which is obtained without reference to."
+ The exact value of the condensation rate M. depends on several factors., The exact value of the condensation rate $\dot M$ depends on several factors.
+ An important parameter is the value of tin Coq. 5)).," An important parameter is the value of $v_{\rm lag}$ (eq. \ref{vphiambient}) ),"
+ which regulates the rotation of the corona and therefore the ellicieney of both the drag (aesx Pus) and the condensation (?).., which regulates the rotation of the corona and therefore the efficiency of both the drag $t_{\rm drag}\propto v_{\rm lag}^{-1}$ ) and the condensation \citep{Marinacci+11}.
+" Llowever. experiments show that the dependence of AL on the adopted value of Pia is not strong: (rq.5Okms+.Fass=1200 vields Al=28M.ye+ (9ΛΙ.ve when corrected. Myr).for. Le). while (0,=l100kmsἄνπμ600 Myr) vields AL=LOALvr+ (LAAL.ve when corrected for He)."," However, experiments show that the dependence of $\dot M$ on the adopted value of $v_{\rm lag}$ is not strong: $v_{\rm lag}=50 \kms,\,t_{\rm drag}=1200\Myr)$ yields $\dot M=2.8\moyr$ $3.9\moyr$ when corrected for He), while $v_{\rm lag}=100 \kms,\,t_{\rm drag}=600\Myr$ ) yields $\dot M=1.0\moyr$ $1.4\moyr$ when corrected for He)."
+ lt is interesting to note that AI depends very. little on. the criterion used to minimise the residuals., It is interesting to note that $\dot M$ depends very little on the criterion used to minimise the residuals.
+ Although the three criteria. vield rather dillerent values for the best-fitting à (see relresicluals) ). Al only varies between 1.5 and M.ve+ eiven that the halo masses also vary between the three models.," Although the three criteria yield rather different values for the best-fitting $\alpha$ (see \\ref{residuals}) ), $\dot M$ only varies between 1.5 and $\moyr$ given that the halo masses also vary between the three models."
+ Our parametrisation assumes that a is spatially constant., Our parametrisation assumes that $\alpha$ is spatially constant.
+ Fortunately. the density of the corona should not vary too much in the regions where the interaction. with the fountain is efficient. (2).. so spatial variation of à is not expected to eive significantly cilferent results.," Fortunately, the density of the corona should not vary too much in the regions where the interaction with the fountain is efficient \citep{Marinacci+11}, so spatial variation of $\alpha$ is not expected to give significantly different results."
+ On the whole. the dynamical modelling of the Galactic thalo performed in this work is a success.," On the whole, the dynamical modelling of the Galactic halo performed in this work is a success."
+ The results are consistent with the conclusions METLI drew from their kinematic models., The results are consistent with the conclusions MF11 drew from their kinematic models.
+ Γον found. negative values for both the average vertical and the racial velocities of the halo material. and. deduced that ejected clouds must be partially ionised (but in a fraction larger than our current determination).," They found negative values for both the average vertical and the radial velocities of the halo material, and deduced that ejected clouds must be partially ionised (but in a fraction larger than our current determination)."
+ Our dynamical analysis identifies these properties as arising rom the sharing of angular momentum with gas accreted rom the lagging corona., Our dynamical analysis identifies these properties as arising from the sharing of angular momentum with gas accreted from the lagging corona.
+ Finally. our Galactic fountain is dynamically sustainable.," Finally, our Galactic fountain is dynamically sustainable."
+" Lt requires a rate of kinetic-energy injection equal to 6.2lO""anergs"". which. with. à supernova rate 0.08M.vr"" and an energv per supernova of 1.107org corresponds to an ellicieney o£ aboutTA."," It requires a rate of kinetic-energy injection equal to $6.2\times10^{39}{\rm erg}\,{\rm s}^{-1}$, which with a supernova rate $\,=0.03 \moyr$ and an energy per supernova of $1\times10^{51} {\rm erg}$ corresponds to an efficiency of about."
+ Now that we have a model that reproduces all the main features of the LAB datacube. we can investigate in detail the physical properties of the Galaxys extraplanar Πάνος.," Now that we have a model that reproduces all the main features of the LAB datacube, we can investigate in detail the physical properties of the Galaxy's extraplanar layer."
+ Fig., Fig.
+ 7 shows the rotation curve of the Galaxys extra-planar eas at clillerent distances [rom the plane as a function of /?., \ref{rotCurve} shows the rotation curve of the Galaxy's extra-planar gas at different distances from the plane as a function of $R$.
+ These values were derived from our best model by simply taking the weighted. mean of the azimuthal components of the velocities of the particles at. different heights., These values were derived from our best model by simply taking the weighted mean of the azimuthal components of the velocities of the particles at different heights.
+ As expected. the halo gas is lagging the rotation of the disc (black curve).," As expected, the halo gas is lagging the rotation of the disc (black curve)."
+ Roughly of this lag is due to gravity (FPBOG) whilst the other half is produced by a combination of the interaction with the corona ancl the phase-change., Roughly of this lag is due to gravity (FB06) whilst the other half is produced by a combination of the interaction with the corona and the phase-change.
+ At oy the gradient is about —1.33Likmsakpe locinexcellent agreement with the average value derived. in the inner, At $R_0$ the gradient is about $-14.3\pm1.1\kmskpc$ inexcellent agreement with the average value derived in the inner
+first. in Sect.,"first, in Sect."
+ 2. discuss some features of the Bianchi tvpe-I universe filled with a fluid that wields an usotropic EoS parameter.," 2, discuss some features of the Bianchi type-I universe filled with a fluid that wields an anisotropic EoS parameter."
+ We define the effective energv deusitv as the sui of the cucrey density of the fluid aud the anisotropy cucrey density. auc specialize the discussion to the models that exhibit de Sitter voluuetiic expansion due to the constan effective energy density.," We define the effective energy density as the sum of the energy density of the fluid and the anisotropy energy density, and specialize the discussion to the models that exhibit de Sitter volumetric expansion due to the constant effective energy density."
+ We then. iu Sect.," We then, in Sect."
+ 3. examine the solutions for a LRS Bianchi type-I space-time. where je universe exhibits de Sitter volumetric expausiou πι the presence of a hypothetical fiid. that has con obtained by miuunuallv altering the conventional vacuunm energy. aud we present two exact models.," 3, examine the solutions for a LRS Bianchi type-I space-time, where the universe exhibits de Sitter volumetric expansion in the presence of a hypothetical fluid, that has been obtained by minimally altering the conventional vacuum energy, and we present two exact models."
+ In the first model. iu Sect.," In the first model, in Sect."
+ 3.1. the directional EoS parameter on the .c axis is assiunued to be -1. while the ones on he other axes aud the euergv deusitv of the fuid are allowed to be functions of time.," 3.1, the directional EoS parameter on the $x$ axis is assumed to be -1, while the ones on the other axes and the energy density of the fluid are allowed to be functions of time."
+ In the second model. iu Sect.," In the second model, in Sect."
+ 3.2. the cuerey density of the fluid is assumed to 0 constant. while the directional EoS parauicters are allowed to be functions of time.," 3.2, the energy density of the fluid is assumed to be constant, while the directional EoS parameters are allowed to be functions of time."
+ We consider the diagonal metric of the spatially flat. homogencous but anisotropic Bianchi tvpe-I space- where A. Bit) aud C(t) are the directional scale factors. functions of the cosmic time. f.," We consider the diagonal metric of the spatially flat, homogeneous but anisotropic Bianchi type-I space-time, where $A(t)$, $B(t)$ and $C(t)$ are the directional scale factors, functions of the cosmic time, $t$."
+" Within the framework of the metric given by (1). the enerevauonieutum tensor of a fluid can be written. most eenerallv. in anisotropic diagonal form as follows: The Einstein feld equations. in natural units Laude= 1). are where fpe AS the aetric teusor: nutu-1 (af=(1.0.0.0) is the four-velocity vector): Rin is the Ricei tensor: Ris the Ricci scalar. T,, is the cucrey-moment tensor."," Within the framework of the metric given by (1), the energy-momentum tensor of a fluid can be written, most generally, in anisotropic diagonal form as follows: The Einstein field equations, in natural units $8\pi G=1$ and $c=1$ ), are where $g_{\mu\nu}$ is the metric tensor; $g_{\mu\nu}u^{\mu}u^{\nu}=1$ $u^{\mu}=(1,0,0,0)$ is the four-velocity vector); $R_{\mu\nu}$ is the Ricci tensor; $R$ is the Ricci scalar, ${T}_{\mu\nu}$ is the energy-momentum tensor."
+ Iu a comoving coordinate system. the Eiusteiu field equations (3). for the Biauchi tvpe-I space-time (1) iu case of the anisotropic enerevanonmentuni tensor given by (2). read where au overdot denotes d/df.," In a comoving coordinate system, the Einstein field equations (3), for the Bianchi type-I space-time (1) in case of the anisotropic energy-momentum tensor given by (2), read where an overdot denotes $d/dt$ ."
+ The directional ITubble parameters. which determine the expansion rates of the universe in the directions of ss yaud τν for the metric eiven in (1) can be defined as respectively. aud then the mean IIubble parameter. which determines the vohunetric expansion rate of the universe. can be given as where V=ABC is the volue of the universe.," The directional Hubble parameters, which determine the expansion rates of the universe in the directions of $x$, $y$ and $z$, for the metric given in (1) can be defined as respectively, and then the mean Hubble parameter, which determines the volumetric expansion rate of the universe, can be given as where $V=ABC$ is the volume of the universe."
+" The anisotropy of the expansion can be parametrized by using the directional Ποιο parameters (8) aud the mean Hubble parameter (9) of the expansion. where I7; (121.2.3) represents the directional Dibble paralucters iu the directions of c; y aud τν respectively,"," The anisotropy of the expansion can be parametrized by using the directional Hubble parameters (8) and the mean Hubble parameter (9) of the expansion, where $H_{i}$ (i=1,2,3) represents the directional Hubble parameters in the directions of $x$, $y$ and $z$, respectively."
+ A=0 corresponds to isotropic expansion., $\Delta=0$ corresponds to isotropic expansion.
+ The Bianchi type-I universe approaches spatial isotropy if A>0. Voqo and T>0 as fooqox (see Collins& for details).," The Bianchi type-I universe approaches spatial isotropy if $\Delta\rightarrow 0$, $V\rightarrow +\infty$ and ${T}^{00}>0$ as $t\rightarrow+\infty$ (see \citealt{collins73} for details)."
+ The anisotropy parameter of the expansion can also be eiven in tenus ofthe components of the cucrev- tensor (2) aud the mean Dubble parameter (9) bv usingS the evolution equatious| (5)-(7):, The anisotropy parameter of the expansion can also be given in terms ofthe components of the energy-momentum tensor (2) and the mean Hubble parameter (9) by using the evolution equations (5)-(7);
+"from Milleretal.(2004) are calculated for spherical top- filtering, giving 6,<0.44 for 1001: Mpc diameters and δᾳ«0.17 for 200h~* Mpc diameters.","from \citet{Miller2004} are calculated for spherical top-hat filtering, giving $\delta_q < 0.44$ for $h^{-1}$ Mpc diameters and $\delta_q < 0.17$ for $h^{-1}$ Mpc diameters."
+" This paper has re-examined the Clowes&Campusano(1991) LQG, originally known with 18 members, using data from the SDSS DR7QSO catalogue."," This paper has re-examined the \citet{Clowes1991} LQG, originally known with 18 members, using data from the SDSS DR7QSO catalogue."
+" It is found as the unit U1.28 of 34 100Mpc-linked quasars, with mean redshift 2=1.28."," It is found as the unit U1.28 of 34 100Mpc-linked quasars, with mean redshift $\bar{z} = 1.28$."
+" While the western, northern and southern boundaries remain essentially unchanged, apart from two compact clumps to the north and south-west, there is an extension eastwards, beyond the original survey, of ~2°."," While the western, northern and southern boundaries remain essentially unchanged, apart from two compact clumps to the north and south-west, there is an extension eastwards, beyond the original survey, of $\sim 2^\circ$."
+" A new LQG, Ul1.11, was discovered in the same direction — 1.97° from U1.28."," A new LQG, U1.11, was discovered in the same direction — $^\circ$ from U1.28."
+ It has 38 members and mean redshift 2=1.11., It has 38 members and mean redshift $\bar{z} = 1.11$.
+" A third candidate, U1.54, in the same direction at 1.62° from U1.28, appeared statistically insignificant, although it is a rediscovery of a known (marginal) LQG (Newmanetal.1998;Newman1999)."," A third candidate, U1.54, in the same direction at $^\circ$ from U1.28, appeared statistically insignificant, although it is a re-discovery of a known (marginal) LQG \citep{Newman1998, Newman1999}."
+". We have also presented the “CHMS method"" for assessing the statistical significance and overdensity of groups such as LQGs that have been found by linkage of points.", We have also presented the “CHMS method” for assessing the statistical significance and overdensity of groups such as LQGs that have been found by linkage of points.
+" Attention was first drawn to peculiarities in this area of sky by Cannon Oke (~ 1980, private communication) who, in the early days of quasar surveys, noted the unusual ease with which they could find the then hard-to-find quasars with z~ 1.6."," Attention was first drawn to peculiarities in this area of sky by Cannon Oke $\sim$ 1980, private communication) who, in the early days of quasar surveys, noted the unusual ease with which they could find the then hard-to-find quasars with $z \sim$ 1.0-1.6."
+" It may be that, now we know there are not one but two LQGs of unusually high membership in this direction, we finally have the complete explanation of their result."," It may be that, now we know there are not one but two LQGs of unusually high membership in this direction, we finally have the complete explanation of their result."
+" A simple measure of the characteristic size of the LQGs, which takes no account of morphology, is the cube root of the corrected CHMS volumes, giving 350,380 Mpc for"," A simple measure of the characteristic size of the LQGs, which takes no account of morphology, is the cube root of the corrected CHMS volumes, giving $\sim 350, 380$ Mpc for"
+"simulations with two different kinds of forcing, finding that for the same Mach number compressive driving leads to a significantly steeper power spectrum than the one obtained with solenoidal forcing.","simulations with two different kinds of forcing, finding that for the same Mach number compressive driving leads to a significantly steeper power spectrum than the one obtained with solenoidal forcing."
+" In an attempt to understand available observations, Hodge Deshpande (2006) presented a simplified model in which the complex distribution of atomic hydrogen is determined only by the superposition of voids generated by supernovae, either with or without kinematical effects."," In an attempt to understand available observations, Hodge Deshpande (2006) presented a simplified model in which the complex distribution of atomic hydrogen is determined only by the superposition of voids generated by supernovae, either with or without kinematical effects."
+ They obtain a velocity spectrum with a power law behavior close to the Kolmogorov spectrum and a (column)density spectrum with a slope of -3.4 for the nonkinematical case., They obtain a velocity spectrum with a power law behavior close to the Kolmogorov spectrum and a (column)density spectrum with a slope of -3.4 for the nonkinematical case.
+ For their kinematical case the density power spectrum does not develop a range with a power law behavior., For their kinematical case the density power spectrum does not develop a range with a power law behavior.
+ The case of density fluctuations from magnetized isothermal turbulence has been recently studied in detail by Kowal et al. (, The case of density fluctuations from magnetized isothermal turbulence has been recently studied in detail by Kowal et al. (
+"2007) whose results for the power spectrum show that for subsonic turbulence, the slope presents slight changes with the sonic Mach number, while when motions become supersonic, the presence of pronounced small scale structure produces a flattening of the spectra, as in the non magnetized case (Kim Ryu 2005).","2007) whose results for the power spectrum show that for subsonic turbulence, the slope presents slight changes with the sonic Mach number, while when motions become supersonic, the presence of pronounced small scale structure produces a flattening of the spectra, as in the non magnetized case (Kim Ryu 2005)."
+ This behavior is observed for superalfvénnic as well as for sublfavénnic simulations., This behavior is observed for superalfvénnic as well as for sublfavénnic simulations.
+" The HI density distribution is however strongly influenced by the presence of the isobaric mode of thermal instability (TI, Field 1965) and the interplay between this instability and turbulence has important consequences on the formation of atomic as well as molecular interstellar structure (e.g. Hennebelle et al."," The HI density distribution is however strongly influenced by the presence of the isobaric mode of thermal instability (TI, Field 1965) and the interplay between this instability and turbulence has important consequences on the formation of atomic as well as molecular interstellar structure (e.g. Hennebelle et al."
+ 2009)., 2009).
+" The density spectrum for cooling thermally bistable turbulent gas has been presented by Hennebelle Audit (2007), who found a -0.4 slope for the integrated spectrum."," The density spectrum for cooling thermally bistable turbulent gas has been presented by Hennebelle Audit (2007), who found a -0.4 slope for the integrated spectrum."
+" However, the behavior of the density power spectrum of thermally unstable gas in different turbulent conditions and in particular its behavior for distinct values of the sonic Mach number, has not been addressed."," However, the behavior of the density power spectrum of thermally unstable gas in different turbulent conditions and in particular its behavior for distinct values of the sonic Mach number, has not been addressed."
+ Although the driving mechanisms for interstellar turbulence remain a matter of debate (Mac Low Klessen 2004; Brunt et al., Although the driving mechanisms for interstellar turbulence remain a matter of debate (Mac Low Klessen 2004; Brunt et al.
+ 2009; Federrath et al., 2009; Federrath et al.
+" 2010), recent observational results (Tamburro et al."," 2010), recent observational results (Tamburro et al."
+ 2009) using a sample of galaxies from the HI Nearby Galaxy Survey show that all the studied galaxies exhibit a systematic radial decline in the HI line width which implies a radial decline in kinetic energy density of HI., 2009) using a sample of galaxies from the HI Nearby Galaxy Survey show that all the studied galaxies exhibit a systematic radial decline in the HI line width which implies a radial decline in kinetic energy density of HI.
+" Previous reports of the same behavior can be found, for example for NGC1058 (Petric Rupen 2007), NGC5474 (Rownd et al."," Previous reports of the same behavior can be found, for example for NGC1058 (Petric Rupen 2007), NGC5474 (Rownd et al."
+" 1994), or NGC6946 (Boulanger Viallefond 1992)."," 1994), or NGC6946 (Boulanger Viallefond 1992)."
+ In this work we present a numerical study of the density power spectrum for cooling turbulent gas in physical conditions similar to those in the interstellar atomic gas., In this work we present a numerical study of the density power spectrum for cooling turbulent gas in physical conditions similar to those in the interstellar atomic gas.
+ The outline of the paper is the following., The outline of the paper is the following.
+" In 8?? we describe the model, in §?? we present results concerning the effects of varying the sonic Mach number on the density and velocity power spectra."," In \ref{sec:model} we describe the model, in \ref {sec:results} we present results concerning the effects of varying the sonic Mach number on the density and velocity power spectra."
+ For the former we study the whole gas distribution as well as the behavior of gas at specific temperature intervals., For the former we study the whole gas distribution as well as the behavior of gas at specific temperature intervals.
+" Then, in §?? we discuss these results in the context of previous work and finally in §?? we give a summary and some conclusions."," Then, in \ref{sec:disc} we discuss these results in the context of previous work and finally in \ref{sec:conc} we give a summary and some conclusions."
+ We solve the hydrodynamic equations in three dimensions to simulate a cubic region of 100 pc on a side with periodic boundary conditions., We solve the hydrodynamic equations in three dimensions to simulate a cubic region of 100 pc on a side with periodic boundary conditions.
+ The equations are solved using a total variation diminishing scheme with a linearized Riemann solver (Roe 1981; Harten 1983; Kim et al., The equations are solved using a total variation diminishing scheme with a linearized Riemann solver (Roe 1981; Harten 1983; Kim et al.
+ 1999)., 1999).
+ 'The energy equation includes a constant background heating rate and a radiative cooling function with a piece-wise power-law dependence on the temperature obtained by Sánnchez-Salcedo et al. (, The energy equation includes a constant background heating rate and a radiative cooling function with a piece-wise power-law dependence on the temperature obtained by Sánnchez-Salcedo et al. (
+"2002) as afit of the standard P vs. p curve of Wolfire et ((1995) at constant heating rate, Το.","2002) as afit of the standard $P$ vs. $\rho$ curve of Wolfire et (1995) at constant heating rate, $\Gamma_0$."
+" In thermal equilibrium conditions this curve implies that the gas is thermally unstable under the isobaric mode for 313K«T<6102K, and marginally stable for 141K«T313K."," In thermal equilibrium conditions this curve implies that the gas is thermally unstable under the isobaric mode for $313\;{\rm K}< T <6102\;{\rm K}$, and marginally stable for $141\;{\rm K}< T <313\;{\rm K}$."
+" The corresponding thermal equilibrium densities are n=0.60, 3.2 and 7.1 cm-?, for T=6102, 313 and 141 K, respectively."," The corresponding thermal equilibrium densities are $n = 0.60$, 3.2 and 7.1 $^{-3}$, for $T=6102$, 313 and 141 K, respectively."
+" For the fit, the assumed value of the heating rate is Το=2.51x107?89ergs-!H7! (where H7! means per hydrogen atom mass)."," For the fit, the assumed value of the heating rate is $\Gamma_0= 2.51\times 10^{-26} {\rm erg s}^{-1}{\rm H}^{-1}$ (where $^{-1}$ means per hydrogen atom mass)."
+" 'The random turbulent forcing is done in Fourier space at a specified narrow wave-number band, 1l€k<2, where k= \/k2+k2+k?2."," The random turbulent forcing is done in Fourier space at a specified narrow wave-number band, $1 \leq k \leq 2$, where $k \equiv \sqrt{k_x^2 + k_y^2 + k_z^2}$ ."
+" The turbulent driving is solenoidal, with the Gaussian deviates having zero mean and unitary standard"," The turbulent driving is solenoidal, with the Gaussian deviates having zero mean and unitary standard"
+PACS 160 um fluxes (Sect. 2)).,PACS 160 $\mu$ m fluxes (Sect. \ref{sec:data}) ).
+" At z—2, the rest-frame wavelengths are shorter than 10 wm and 24 um fluxes probe the IR emission at the edge of the relevant range, far from the SED peak, making them sensitive to extrapolation errors."," At $\sim$ 2, the rest-frame wavelengths are shorter than 10 $\mu$ m and 24 $\mu$ m fluxes probe the IR emission at the edge of the relevant range, far from the SED peak, making them sensitive to extrapolation errors."
+" In addition, at these wavelengths polycyclic aromatic hydrocarbon (PAH) emissions contribute significantly and the ratio of their fluxes to LIR may create significant scatter."," In addition, at these wavelengths polycyclic aromatic hydrocarbon (PAH) emissions contribute significantly and the ratio of their fluxes to LIR may create significant scatter."
+ PACS 160 um fluxes probe the emission much closer to the SED peak and are unaffected by the above issues., PACS 160 $\mu$ m fluxes probe the emission much closer to the SED peak and are unaffected by the above issues.
+" In Fig. 1,,"," In Fig. \ref{fg:L24vsL160},"
+ we plot LIR as derived from 160 jum versus that derived from 24 um for 1.5«z«2.5., we plot LIR as derived from 160 $\mu$ m versus that derived from 24 $\mu$ m for $<$ $<$ 2.5.
+ Individual sources are detected starting at LIR(160 um)»6x10!! Lo at redshifts close to z~1.5., Individual sources are detected starting at LIR(160 $\mu$ $>6\times 10^{11}$ $_{\odot}$ at redshifts close to $\sim$ 1.5.
+ The 24 um sources without a PACS detection (and no X-ray counterpart) are stacked in luminosity bins as indicated by the bars in the figure., The 24 $\mu$ m sources without a PACS detection (and no X-ray counterpart) are stacked in luminosity bins as indicated by the bars in the figure.
+" Since we stack in luminosity and not flux bins, the typical redshifts of sources in a given stack are higher than those of detections with similar LIR(160 jm), which is one reason why not all sources in the luminosity bin are detected."," Since we stack in luminosity and not flux bins, the typical redshifts of sources in a given stack are higher than those of detections with similar LIR(160 $\mu$ m), which is one reason why not all sources in the luminosity bin are detected."
+" It is clear that while there is some scatter, for most sources LIR(24 um) is higher than LIR(160 um)."," It is clear that while there is some scatter, for most sources LIR(24 $\mu$ m) is higher than LIR(160 $\mu$ m)."
+ Figure 2 plots the LIR(24 jum) to LIR(160 um) ratio as a function of LIR(24 um)., Figure \ref{fg:L24overL160} plots the LIR(24 $\mu$ m) to LIR(160 $\mu$ m) ratio as a function of LIR(24 $\mu$ m).
+" The detections appear to show a linear trend, but this is mostly due to a selection effect."," The detections appear to show a linear trend, but this is mostly due to a selection effect."
+" The combined mean for the detection and non-detections (detected in stacks) is much higher and the individual detections represent a fraction of the distribution for which at a given LIR(24 um), LIR(160 um) is high enough to be detected."," The combined mean for the detection and non-detections (detected in stacks) is much higher and the individual detections represent a fraction of the distribution for which at a given LIR(24 $\mu$ m), LIR(160 $\mu$ m) is high enough to be detected."
+" There is a weak 24 um luminosity dependence and the mean of the excess increases with LIR(24 um), at least for log LIR(24 um)»12.2."," There is a weak 24 $\mu$ m luminosity dependence and the mean of the excess increases with LIR(24 $\mu$ m), at least for $\log$ LIR(24 $\mu$ $>12.2$."
+" Below this luminosity, it is harder to determine the slope, but the stack indicates that it may flatten out."," Below this luminosity, it is harder to determine the slope, but the stack indicates that it may flatten out."
+" Though large fraction of the sample relies on photometric redshifts, errorsa in redshifts will move the points in LIR(24ym), but will have a much smaller effect on the LIR ratio."," Though a large fraction of the sample relies on photometric redshifts, errors in redshifts will move the points in $\mu$ m), but will have a much smaller effect on the LIR ratio."
+ The red arrows at the top-left of Fig., The red arrows at the top-left of Fig.
+" 2 demonstrate how the typical phot-z errors, propagated into the quantities plotted in the figure, will affect the values."," \ref{fg:L24overL160} demonstrate how the typical phot-z errors, propagated into the quantities plotted in the figure, will affect the values."
+ The photo-z induced dispersion is directed along the diagonal trend of detected sources and probably contributes to this pattern with the selection effects., The photo-z induced dispersion is directed along the diagonal trend of detected sources and probably contributes to this pattern with the selection effects.
+ X-ray AGNs do not appear to differ from the rest of the sample in Figs., X-ray AGNs do not appear to differ from the rest of the sample in Figs.
+" 1 and 2,, except perhaps for the one source with the highest luminosity."," \ref{fg:L24vsL160} and \ref{fg:L24overL160}, except perhaps for the one source with the highest luminosity."
+ This source also exhibits a very clear power-law SED in the mid-IR., This source also exhibits a very clear power-law SED in the mid-IR.
+" For sources completely dominated by the AGN, fitting a CE01 SED to the 24 um emission is clearly inappropriate."," For sources completely dominated by the AGN, fitting a CE01 SED to the 24 $\mu$ m emission is clearly inappropriate."
+" Even though we can only produce one AGN stack that results in a good detection (Fig. 1)),"," Even though we can only produce one AGN stack that results in a good detection (Fig. \ref{fg:L24vsL160}) ),"
+ the mean luminosity is similar to that of the SFG stacks., the mean luminosity is similar to that of the SFG stacks.
+" This can be interpreted in two ways: either the flux at 6.8<2A9.6 um rest frame is dominated by the starburst emission at all the luminosities considered here, or the flux excess in all sources is due to an AGN, which is obscured in most."," This can be interpreted in two ways: either the flux at $6.8<\lambda<9.6$ $\mu$ m rest frame is dominated by the starburst emission at all the luminosities considered here, or the flux excess in all sources is due to an AGN, which is obscured in most."
+" The latter claim and the relatively tight LIR(24 um)/LIR(160 um) ratio would imply a tight relation between the AGN luminosity and the galaxy's starburst component FIR luminosity, which is not observed (??).."," The latter claim and the relatively tight LIR(24 $\mu$ m)/LIR(160 $\mu$ m) ratio would imply a tight relation between the AGN luminosity and the galaxy's starburst component FIR luminosity, which is not observed \citep{Lutz10, Shao10}."
+" We conclude that while a hidden AGN may contribute to the scatter, it is not likely to be the main cause of the general 24 uum excess."," We conclude that while a hidden AGN may contribute to the scatter, it is not likely to be the main cause of the general 24 $\mu$ m excess."
+" Enhanced emission (relative to local galaxy SEDs) in PAH features between 6.2—8.6 um, that enter the 24 ym filter at z=1.5 is a more plausible explanation."," Enhanced emission (relative to local galaxy SEDs) in PAH features between 6.2–8.6 $\mu$ m, that enter the 24 $\mu$ m filter at z=1.5 is a more plausible explanation."
+" These new results corroborate the main findings of ?,, based on 16, 24, 70 um, and SCUBA 850 um observations."," These new results corroborate the main findings of \citet{Murphy09}, based on 16, 24, 70 $\mu$ m, and SCUBA 850 $\mu$ m observations."
+" For z~2 galaxies, they find that SFRs using only 24 um are overestimated by a factor of 5 and conclude that a hidden AGN can only account for a fraction of this excess. ?,, usingSpitzer"," For $\sim$ 2 galaxies, they find that SFRs using only 24 $\mu$ m are overestimated by a factor of 5 and conclude that a hidden AGN can only account for a fraction of this excess. \citet{Papovich07},"
+" 24, 70 and 160 um stacked fluxes also find that LIR(24 um) is in excess."," using 24, 70 and 160 $\mu$ m stacked fluxes also find that LIR(24 $\mu$ m) is in excess."
+" At the high end, they find 24 um overestimates LIR by a factor of 2-10."," At the high end, they find 24 $\mu$ m overestimates LIR by a factor of 2–10."
+ They too conclude that X-ray sources have a 24 um excess similar to SFGs without X-ray counterparts., They too conclude that X-ray sources have a 24 $\mu$ m excess similar to SFGs without X-ray counterparts.
+ The UV continuum at wavelengths longer thanthe Lyman edge can be used as a SFR indicator., The UV continuum at wavelengths longer thanthe Lyman edge can be used as a SFR indicator.
+" The UV emission is dominated by young, massive, and short-lived stars and a SFR that is required to sustain their population can be calculated."," The UV emission is dominated by young, massive, and short-lived stars and a SFR that is required to sustain their population can be calculated."
+" The SFR(UV) is sensitive to the attenuation correction used, which varies significantly in the UV between different extinction"," The SFR(UV) is sensitive to the attenuation correction used, which varies significantly in the UV between different extinction"
+We have presented additional ancl extensive CCD observations of IKPD 0422|5421.,We have presented additional and extensive CCD observations of KPD 0422+5421.
+ We have discovered. tha the light curve of this binary star contains two clistinc signals. the 2.16 hour ellipsoidal modulation and a non-sinusoidal modulation at 7.8 hours.," We have discovered that the light curve of this binary star contains two distinct signals, the 2.16 hour ellipsoidal modulation and a non-sinusoidal modulation at 7.8 hours."
+ This extra modulation appears to be intrinsic to. WKPD 0422]5421. and is no an artifact of the observation or analvsis., This extra modulation appears to be intrinsic to KPD 0422+5421 and is not an artifact of the observation or analysis.
+ We remove: this 7.8 hour modulation from the light curve and. fole the detrended: curve on the orbital period. to obtain the underbing ellipsoidal light curve., We removed this 7.8 hour modulation from the light curve and folded the detrended curve on the orbital period to obtain the underlying ellipsoidal light curve.
+ “Phis folded. light. curve now clearly shows the signature of the transit of the white chvarl across the face of the sdB star and the signature of the total eclipse of the white dwarf (although the latter feature is somewhat noisier than the former feature)., This folded light curve now clearly shows the signature of the transit of the white dwarf across the face of the sdB star and the signature of the total eclipse of the white dwarf (although the latter feature is somewhat noisier than the former feature).
+ We moclelled the ellipsoidal light curve with the W-D code and derived values of the inclination. the mass ratio. and the © potentials. ancl used a Monte Carlo code to compute the uncertainties in the parameters.," We modelled the ellipsoidal light curve with the W-D code and derived values of the inclination, the mass ratio, and the $\Omega$ potentials, and used a Monte Carlo code to compute the uncertainties in the parameters."
+ The marginal distributions of the component masses as computed with the Monte Carlo code have large “tails”. hence the parameters have relatively large uncertainties.," The marginal distributions of the component masses as computed with the Monte Carlo code have large “tails”, hence the parameters have relatively large uncertainties."
+" Lowe apply an additional constraint and require the white dwarf's radius and mass to be consistent with the theoretical mass-racius relation. we find the derived system, parameters have much smaller uncertainties."," If we apply an additional constraint and require the white dwarf's radius and mass to be consistent with the theoretical mass-radius relation, we find the derived system parameters have much smaller uncertainties."
+ Using he white dwarf mass-radius constraint we find that the mass of the sdB star is somewhat lower than the value determined WOW and is much closer to the “canonical” mass or extended horizontal branch stars., Using the white dwarf mass-radius constraint we find that the mass of the sdB star is somewhat lower than the value determined KOW and is much closer to the “canonical” mass for extended horizontal branch stars.
+ The total mass of the system appears to be less than 1.42A4. with high confidence (99.99 per cent).," The total mass of the system appears to be less than $1.4\,M_{\odot}$ with high confidence (99.99 per cent)."
+ We also find that the white dwarf is much iotter (and hence much vounger) than found by IKOW., We also find that the white dwarf is much hotter (and hence much younger) than found by KOW.
+ The resolved: eclipse. profiles allow us to determine the phase accurately. which in turn may allow for the measurement of the orbital period derivative after a reasonable amount of ime.," The resolved eclipse profiles allow us to determine the phase accurately, which in turn may allow for the measurement of the orbital period derivative after a reasonable amount of time."
+ Our basic picture of the WKWPD 042215421. binary is secure. iit contains an sdB star with a mass close to 5M. paired with a nearly equally massive white dwarf.," Our basic picture of the KPD 0422+5421 binary is secure, it contains an sdB star with a mass close to $0.5\,M_{\odot}$ paired with a nearly equally massive white dwarf."
+ Additional spectroscopic observations should be done to improve the determination of the velocity. amplitude of he sdD star. to determine its rotational velocity. and to refine the measurements of its ellective temperature. surface eravity. and metallicity (a good measurement of the Le abundance is needed. for a precise determination of log g).," Additional spectroscopic observations should be done to improve the determination of the velocity amplitude of the sdB star, to determine its rotational velocity, and to refine the measurements of its effective temperature, surface gravity, and metallicity (a good measurement of the He abundance is needed for a precise determination of $\log g$ )."
+ An improved. dy-velocity. for the sdB star would result in a more precisely determined: mass function. which in turn would. result in. better cetermined masses.," An improved $K$ -velocity for the sdB star would result in a more precisely determined mass function, which in turn would result in better determined masses."
+ Accurate values of Vicisin; and logg could be used to reduce the uncertainty in the mass of the sdB star. independent: of the white dwarf mass-racius relation.," Accurate values of $V_{\rm rot}
+\sin i$ and $\log g$ could be used to reduce the uncertainty in the mass of the sdB star, independent of the white dwarf mass-radius relation."
+ Further photometric observations should) be done in several colours to verily that the 7.8 hour modulation is coherent ancl to see if its character depends on the bandpass. to better sample the ingress and egress phases of the eclipse profiles. and. to provide additional phase determinations so that the change in the period can be tracked over time.," Further photometric observations should be done in several colours to verify that the 7.8 hour modulation is coherent and to see if its character depends on the bandpass, to better sample the ingress and egress phases of the eclipse profiles, and to provide additional phase determinations so that the change in the period can be tracked over time."
+ We are pleased to thank the Whitt Peak director. Richard Green for the generous allocation of a fourth night. of observing time and Doug Williams for his able assistance at the telescope., We are pleased to thank the Kitt Peak director Richard Green for the generous allocation of a fourth night of observing time and Doug Williams for his able assistance at the telescope.
+ We thank Chris Ixoen for reading an earlier version of this paper and the referee. for a detailed. and helpful report., We thank Chris Koen for reading an earlier version of this paper and the referee for a detailed and helpful report.
+Phere are 303 maser sites that show more than one peak in the maser spectrum (we refer to such single »eaks in the spectrum as maser spots).,There are 303 maser sites that show more than one peak in the maser spectrum (we refer to such single peaks in the spectrum as maser spots).
+ Of these sites with more than one maser spot. the widest. velocity. distribution is exhibited by 0.40. overkms.," Of these sites with more than one maser spot, the widest velocity distribution is exhibited by $-$ 0.40, over."
+. Phis maser site was previously reported by. Walshοἱ (2009).. based on LIOPS data. and is a water fountain associated with a post-AGB star.," This maser site was previously reported by \citet{walsh09}, based on HOPS data, and is a water fountain associated with a post-AGB star."
+ Subsequent. observations »v Walshetal.(2009) found maser emission over an even wider range ofkms., Subsequent observations by \citet{walsh09} found maser emission over an even wider range of.
+ In total. there are. 14 maser sites with maser spots spread over a velocity range greater thankms.," In total, there are 14 maser sites with maser spots spread over a velocity range greater than."
+.. Phe median velocity spread iskms., The median velocity spread is.
+ “Phe distribution of velocity. spreads. of maser sites with multiple maser spots can be seen in Figure 7.., The distribution of velocity spreads of maser sites with multiple maser spots can be seen in Figure \ref{vel_spread}.
+ The Figure shows that the occurrence of maser sites with hieh velocity features is relatively rare. but there is a population of about of maser sites with maser spots that span velocity ranges ercater thankms.," The Figure shows that the occurrence of maser sites with high velocity features is relatively rare, but there is a population of about of maser sites with maser spots that span velocity ranges greater than."
+ When comparing the line FILM of maser spots. we find that | 0.20 exhibits the widest FWILAM ofkms.," When comparing the line FWHM of maser spots, we find that $+$ 0.20 exhibits the widest FWHM of."
+ Llowever. because maser sites usually consist. of multiple peaks in the spectrum. it is likely that any single peak may comprise multiple unresolved components in the spectrum.," However, because maser sites usually consist of multiple peaks in the spectrum, it is likely that any single peak may comprise multiple unresolved components in the spectrum."
+" ""This is likely to be the case for | 0.20 whose maser emission is very weak and dominated by noise. possibly masking multiple components."," This is likely to be the case for $+$ 0.20 whose maser emission is very weak and dominated by noise, possibly masking multiple components."
+ The median line FWHIAL is and of mascr spots are no broader thankms., The median line FWHM is and of maser spots are no broader than.
+ In Table 2.. the last column indicates whether a miaser site is coincident with the position and shows similar spectral features to the maser emission from a known evolved star.," In Table \ref{330masers}, the last column indicates whether a maser site is coincident with the position and shows similar spectral features to the maser emission from a known evolved star."
+ “Phere are 15 maser sites so far associated with evolved stars., There are 15 maser sites so far associated with evolved stars.
+ Due to the 27 beam of the Mopra observations. we awail higher resolution observations to associate all miasers with a particular class of astrophysical object.," Due to the $^\prime$ beam of the Mopra observations, we await higher resolution observations to associate all masers with a particular class of astrophysical object."
+ Phere are certainly known evolved stars within 2.2% of masers which we have not vet associated because we cannot compare our maser spectrum to a previously published spectrum., There are certainly known evolved stars within $^\prime$ of masers which we have not yet associated because we cannot compare our maser spectrum to a previously published spectrum.
+ We thus expect there to be more associations with evolved stars to be uncovered. but with the majority of maser sites associated with star forming regions.," We thus expect there to be more associations with evolved stars to be uncovered, but with the majority of maser sites associated with star forming regions."
+ See refsecelat— for. further evidence that leacs us to this expectation., See \\ref{secglat} for further evidence that leads us to this expectation.
+ We plan to conduct. Follow up observations of the maser sites with the APCA. which will give us high positional accuracy. allowing us to identify the majority of maser sites with known astrophysical objects.," We plan to conduct follow up observations of the maser sites with the ATCA, which will give us high positional accuracy, allowing us to identify the majority of maser sites with known astrophysical objects."
+ We expect the noise level in our spectra to vary by about a factor of two because observations were mace at a range of elevations and weather conditions. which gave rise to svstenir temperature variations in the range 50 to Kk. In order to determine the sensitivity limits of the water maser data. we measure the rms noise levels lor cach quarter-square-degree.," We expect the noise level in our spectra to vary by about a factor of two because observations were made at a range of elevations and weather conditions, which gave rise to system temperature variations in the range 50 to K. In order to determine the sensitivity limits of the water maser data, we measure the rms noise levels for each quarter-square-degree."
+ This is done by taking a single channel from the data cube where no emission is expected (typically a channel at a velocity of was used)., This is done by taking a single channel from the data cube where no emission is expected (typically a channel at a velocity of was used).
+ Then the rms noise is measured for each quarter-squarc-deerce using the taskIMsrars., Then the rms noise is measured for each quarter-square-degree using the task.
+ We also checked the noise levels at cilferent parts of cach zoom band and found that the noise does not vary significantly within each zoom., We also checked the noise levels at different parts of each zoom band and found that the noise does not vary significantly within each zoom.
+ This is done for each of the LPs containing maser. NIL; (1.1). HCCCN (32) and L690 emission.," This is done for each of the IFs containing maser, $_3$ (1,1), HCCCN (3–2) and $\alpha$ emission."
+ These IPs were chosen because they contain the most important emission lines in the survey ancl because they sample close to the full range of frequencies observed. in HOPS. from (611 (11690) to GCGLIz (HOCCN (32)).," These IFs were chosen because they contain the most important emission lines in the survey and because they sample close to the full range of frequencies observed in HOPS, from GHz $\alpha$ ) to GHz (HCCCN (3--2))."
+ Figure 8 shows histograms of the noise levels measured or each of the Les., Figure \ref{noisefig} shows histograms of the noise levels measured for each of the IFs.
+ The rms noise levels are. typically around 0.15 to WI in terms of main beam brightness emperature., The rms noise levels are typically around 0.15 to K in terms of main beam brightness temperature.
+ We show the maser rms noise level in erms of Jy. as this is a more typical intensity scale used for masers (assuming 1)," We show the maser rms noise level in terms of Jy, as this is a more typical intensity scale used for masers (assuming $^{-1}$ )."
+ For masers. we find he rms noise level is below 2v for of the survey and xdlow 1.4.4] for of the survey.," For masers, we find the rms noise level is below Jy for of the survey and below Jy for of the survey."
+ The full range of noise evels varies by à factor out we find that of the maser observations are characterised by à rms noise evel between 1 anc Jy.," The full range of noise levels varies by a factor of 2.9, but we find that of the maser observations are characterised by a rms noise level between 1 and Jy."
+ We find that of the rms noise levels in the ος containing NIL; (1.1). 1690 and WOCCCN (32) emission are xtween 0.12 and INK. Thus. we consider that the rms noise levels in the survey are well characterised by variation of a factor of two. but note that approximately of the rms noise levels in the survey lie outside this ranec.," We find that of the rms noise levels in the IFs containing $_3$ (1,1), $\alpha$ and HCCCN (3–2) emission are between 0.12 and K. Thus, we consider that the rms noise levels in the survey are well characterised by variation of a factor of two, but note that approximately of the rms noise levels in the survey lie outside this range."
+"atmosphere fit for the 5.74 hour bursts (see Table 1), and a low solar H/He abundance model for the 4.07 hr bursts in metallicitywhich we use the same value of A determined by the pure He atmosphere fit, but decrease the derived Fgaa by a factor of 1+X=1.7 to account for the difference in Eddington flux with composition.","atmosphere fit for the 5.74 hour bursts (see Table 1), and a low metallicity solar H/He abundance model for the 4.07 hr bursts in which we use the same value of $A$ determined by the pure He atmosphere fit, but decrease the derived $F_{\rm Edd}$ by a factor of $1+X=1.7$ to account for the difference in Eddington flux with composition."
+ This shows that the in {ο in going from pure He to solar plotH composition is changeenough to account for the variation in K observed., This plot shows that the change in $f_c$ in going from pure He to solar H composition is enough to account for the variation in $K$ observed.
+" However, the solar composition model does not match the 4.07 hr data in terms of location on the F/Fgaa axis."," However, the solar composition model does not match the 4.07 hr data in terms of location on the $F/F_{\rm Edd}$ axis."
+" Another way to say it is that if we fit the 4.07 hr data with a solar composition model, the required Fgaq would be larger than for the 5.74 hr data, instead of being a factor 1+X times smaller, as is required for simultaneous fits."," Another way to say it is that if we fit the 4.07 hr data with a solar composition model, the required $F_{\rm Edd}$ would be larger than for the $5.74$ hr data, instead of being a factor $1+X$ times smaller, as is required for simultaneous fits."
+" Furthermore, we see in the lower panel of Figure 4 that reducing the derived Fgaa by a factor of 1+X=1.7 for the 4.07 hr bursts implies that the peak flux for those bursts exceeds the limit, which is known not be the case."," Furthermore, we see in the lower panel of Figure \ref{fig:varycomposition} that reducing the derived $F_{\rm Edd}$ by a factor of $1+X=1.7$ for the 4.07 hr bursts implies that the peak flux for those bursts exceeds the Eddington limit, which is known not be the case."
+ Therefore a consistent Eddingtonexplanation of the variation in K in terms of changing H fraction at the photosphere is not possible., Therefore a consistent explanation of the variation in $K$ in terms of changing H fraction at the photosphere is not possible.
+ We have compared lightcurve and spectral models with observations of Type I X-ray bursts from1826—24., We have compared lightcurve and spectral models with observations of Type I X-ray bursts from.
+. Here we summarize the main conclusions and discuss our results further., Here we summarize the main conclusions and discuss our results further.
+ A is that in the burst emission enters as an generaladditionalpoint uncertainty in anisotropyany derived quantity that depends on distance., A general point is that anisotropy in the burst emission enters as an additional uncertainty in any derived quantity that depends on distance.
+" Since it changes the relation between the source luminosity and observed flux, the anisotropy parameter £y (defined in $3) always enters in combination with distance as 1/2d."," Since it changes the relation between the source luminosity and observed flux, the anisotropy parameter $\xi_b$ (defined in 3) always enters in combination with distance as $\xi_b^{1/2} d$."
+" Even in⋅ cases where distance⋅ to a source can be accurately& determined, the anisotropy introduces an effective uncertainty of up to a factor of20-30%."," Even in cases where distance to a source can be accurately determined, the anisotropy introduces an effective uncertainty of up to a factor of."
+. Anisotropy could be a smaller effect for PRE bursts if the inner disk is disrupted during the burst and intercepts a smaller amount of radiation than a disk extending all the way to the stellar surface., Anisotropy could be a smaller effect for PRE bursts if the inner disk is disrupted during the burst and intercepts a smaller amount of radiation than a disk extending all the way to the stellar surface.
+" Nonetheless, it remains a source of systematic error on derived neutron star radii that needs to be investigated further."," Nonetheless, it remains a source of systematic error on derived neutron star radii that needs to be investigated further."
+" For1826—24,, the limit i<70° from Homer et al. ("," For, the limit $i<70^\circ$ from Homer et al. ("
+1998) gives 6?=0.9-1.2.,1998) gives $\xi_b^{-1/2}=0.9$ $1.2$.
+" Given this uncertainty and the fact that the distance to iis not well constrained, we focused on deriving limits on M and R that are independent of distance and anisotropy."," Given this uncertainty and the fact that the distance to is not well constrained, we focused on deriving limits on $M$ and $R$ that are independent of distance and anisotropy."
+ The first of these constraints comes from using the model lightcurve from Heger et al. (, The first of these constraints comes from using the model lightcurve from Heger et al. (
+2007) to fix the overall luminosity scale of the observed bursts.,2007) to fix the overall luminosity scale of the observed bursts.
+ We showed that this leads to a distance and anisotropy independent relation between the redshift 1+z and color correction factor f. (eq. [5]]), We showed that this leads to a distance and anisotropy independent relation between the redshift $1+z$ and color correction factor $f_c$ (eq. \ref{eq:fczcorr}] ])
+ that depends weakly on the measured normalization K and the ratio of observed and model peak fluxes., that depends weakly on the measured normalization $K$ and the ratio of observed and model peak fluxes.
+" For a color correction between 1.4 and 1.5, which spans the range of values in Fig."," For a color correction between 1.4 and 1.5, which spans the range of values in Fig."
+ 2 of Suleimanov et al. (, 2 of Suleimanov et al. (
+"2011) for example, the inferred redshift is between z=0.19 and 0.28.","2011) for example, the inferred redshift is between $z=0.19$ and $0.28$."
+ The second constraint comes from comparing the spectral evolution during the cooling tail with the spectral models of Suleimanov et al. (, The second constraint comes from comparing the spectral evolution during the cooling tail with the spectral models of Suleimanov et al. (
+"2011b), which determines the Eddington flux Faq and the quantity A=K-!//f..","2011b), which determines the Eddington flux $F_{\rm Edd}$ and the quantity $A=K^{-1/4}/f_c$."
+ AS noted by Suleimanov et al. (, As noted by Suleimanov et al. (
+"2011b), for a given set of measured Fgaq, A parameters, there is an upper limit to the distance of the source beyond which there is no solution for M and R.","2011b), for a given set of measured $F_{\rm Edd}$ , $A$ parameters, there is an upper limit to the distance of the source beyond which there is no solution for $M$ and $R$."
+" We point out here that measuring A and [ται also places an upper limit on R,,=R(1+z) (and therefore upper limits on M and R for a given source).", We point out here that measuring $A$ and $F_{\rm Edd}$ also places an upper limit on $R_\infty=R(1+z)$ (and therefore upper limits on $M$ and $R$ for a given source).
+ This limit is independent of distance and anisotropy and depends only on the measured values of A and Fgaq and the surface fraction., This limit is independent of distance and anisotropy and depends only on the measured values of $A$ and $F_{\rm Edd}$ and the surface hydrogen fraction.
+" For1826—24,, atmospheric models withhydrogen solar hydrogen fractions give Rx,« 9.0-13.2 km (Table 1)) which implies a neutron star mass M< 1.2-1.7Mo and R«6.8-11.3 km assuming a lower mass limit of 1Mo."," For, atmospheric models with solar hydrogen fractions give $R_\infty<9.0$ $13.2$ km (Table \ref{tab:fcfits}) ) which implies a neutron star mass $M<1.2$ $1.7\ M_\odot$ and $R< 6.8$ $11.3\ {\rm km}$ assuming a lower mass limit of $1\ M_\odot$."
+" The corresponding distance limits are d< 4.0-5.6kpc£j"".", The corresponding distance limits are $d<4.0$ $5.6\ {\rm kpc}\ \xi_b^{-1/2}$.
+" Uncertainties associated with absolute flux calibration do not affect our results; they are equivalent to an incorrect measurement of the distance to the source, which our constraints are independent of."," Uncertainties associated with absolute flux calibration do not affect our results; they are equivalent to an incorrect measurement of the distance to the source, which our constraints are independent of."
+ The constraints on M and R are summarized in Figure 5.., The constraints on $M$ and $R$ are summarized in Figure \ref{fig:mr}.
+" We show the limits on Ra; from Table 1 for all the solar hydrogen uppercomposition models each plotted at the respective surface gravity and the pure Helium model with logg=14.3, and the redshift range 14z= 1.16-1.31 from (5)) with f.= 1.4—1.5 and a uncertainty in the ratio equationFops/Fmodel."," We show the upper limits on $R_\infty$ from Table \ref{tab:fcfits} for all the solar hydrogen composition models each plotted at the respective surface gravity and the pure Helium model with $\log g=14.3$, and the redshift range $1+z=1.16$ $1.31$ from equation \ref{eq:fczcorr}) ) with $f_c=1.4$ $1.5$ and a uncertainty in the ratio $F_{\rm obs}/F_{\rm model}$."
+ The limits on radii for the solar hydrogen composition are comparable to but little lower than current theoretical expectations based on adense matter calculations which have radii of 10—13 km for neutron star equations of state that reach a maximum mass >2M. (Hebeler et al., The limits on radii for the solar hydrogen composition are comparable to but a little lower than current theoretical expectations based on dense matter calculations which have radii of 10–13 km for neutron star equations of state that reach a maximum mass $>2 M_\odot$ (Hebeler et al.
+" 2010; Gandolfi, Carlson, Reddy 2011)."," 2010; Gandolfi, Carlson, Reddy 2011)."
+ The mass-radius relation found in Steiner et al. (, The mass-radius relation found in Steiner et al. (
+"2010), derived from a set of photospheric radius expansion X-ray bursts and hydrogen atmosphere fits for transiently accreting neutron stars in quiescence, also lies at slightly larger radii than our R., limits for solar ","2010), derived from a set of photospheric radius expansion X-ray bursts and hydrogen atmosphere fits for transiently accreting neutron stars in quiescence, also lies at slightly larger radii than our $R_\infty$ limits for solar composition."
+It should be noted that Suleimanov et al. (, It should be noted that Suleimanov et al. (
+2011a) call into composition.question the results of Steineret al. (,2011a) call into question the results of Steineret al. (
+"2010) by suggesting that ""short"" PRE bursts should be excluded from analysis as they show smaller blackbody normalizations in the burst tail and also do not follow the theoretically",2010) by suggesting that “short” PRE bursts should be excluded from analysis as they show smaller blackbody normalizations in the burst tail and also do not follow the theoretically
+that the statistical determination of the ellective transverse velocity will be aided when monitoring data from a longer period becomes available.,that the statistical determination of the effective transverse velocity will be aided when monitoring data from a longer period becomes available.
+ The narrowing of the probability for the cllective transverse velocity will in turn provice tighter limits on the mean microlens mass and source size., The narrowing of the probability for the effective transverse velocity will in turn provide tighter limits on the mean microlens mass and source size.
+ At a known transverse velocity. the component of uncertainty due to the range of event lengths that can be produced by a source will be reduced upon the observation of more ILME clurations.," At a known transverse velocity, the component of uncertainty due to the range of event lengths that can be produced by a source will be reduced upon the observation of more HME durations."
+ Phus the extent of the contours in Fig., Thus the extent of the contours in Fig.
+ 5. will be reduced as more monitoring data becomes available., \ref{contour} will be reduced as more monitoring data becomes available.
+ The authors would like to thank Chris Fluke for helpful discussions., The authors would like to thank Chris Fluke for helpful discussions.
+ This work was supported. in part by NSE erant. ASTOS-02802., This work was supported in part by NSF grant AST98-02802.
+ JSDW acknowledges the support of an Australian Posteracuate award and a Melbourne University Overseas Research Expericnce Award., JSBW acknowledges the support of an Australian Postgraduate award and a Melbourne University Overseas Research Experience Award.
+out. by a referee. it should. perhaps be noted that the List of red. clump stars given in Paezvisski Stanek. (1998) exeluded any objects with more than error in their (original) Llipparcos parallaxes.,"out by a referee, it should perhaps be noted that the list of red clump stars given in Paczyńsski Stanek (1998) excluded any objects with more than error in their (original) Hipparcos parallaxes."
+ As our selection from their ist was not. based. on parallax. our subsample of 226 stars shares this cutoll," As our selection from their list was not based on parallax, our subsample of 226 stars shares this cutoff."
+ Our sample also necessarily shares heir definition. of the red clump in colour. ancl absolute maenitucle., Our sample also necessarily shares their definition of the red clump in colour and absolute magnitude.
+" Standard: stars from the Carter [ist were observed requentIy. with preference given to observing standard ancl »rogram stars at comparable airmass. while minimising the angular distance between standard. ancl program, stars on he skv."," Standard stars from the Carter list were observed frequently, with preference given to observing standard and program stars at comparable airmass, while minimising the angular distance between standard and program stars on the sky."
+ Phe resulting mean Εν magnitudes (transformed o the 2ALASS system) can be found in Table 1: (complete version online). where the transformations from the Carter (1990) svstem to 24LASS have been taken from the 2ALASS website (Carpenter 2003).," The resulting mean JHK magnitudes (transformed to the 2MASS system) can be found in Table 1 (complete version online), where the transformations from the Carter (1990) system to 2MASS have been taken from the 2MASS website (Carpenter 2003)."
+ Of the 226 program. stars. 85 were observed more tiui once.," Of the 226 program stars, 85 were observed more than once."
+ From this subsaniple we rave calculated. the internal standard deviation of a single observation to be 0.008 in J and 0.006 in LE and Ex. while the internal mean stancaux error for the 85 stars with multiple observations is 0.005 in J and 0.004 in II and Wk. The mean stancaurd error fw the entire sample (including stars observed only once) is hus about 0.007 in J and 0.005 in LI and dx. The error. introduced. by. standardisation. is [largely included in the above. since the second and any acdclitiona observations of a particular red. clump star will in genera not have been stancdardised using exactly the same choice of standards as for the first observation of that star.," From this subsample we have calculated the internal standard deviation of a single observation to be 0.008 in J and 0.006 in H and K, while the internal mean standard error for the 85 stars with multiple observations is 0.005 in J and 0.004 in H and K. The mean standard error for the entire sample (including stars observed only once) is thus about 0.007 in J and 0.005 in H and K. The error introduced by standardisation is largely included in the above, since the second and any additional observations of a particular red clump star will in general not have been standardised using exactly the same choice of standards as for the first observation of that star."
+ Llow large is the error introduced by random. errors in the standards used?, How large is the error introduced by random errors in the standards used?
+ A comparison of the Carter (1990) a CIT standards can be used to estimate the error introduce by standardisation., A comparison of the Carter (1990) and CIT standards can be used to estimate the error introduced by standardisation.
+ Assuming equal errors in both stanclarc sets. the transformation equations given by Laney Stobie (1993) imply à mean error in Ll and Woof approximately 0.006.," Assuming equal errors in both standard sets, the transformation equations given by Laney Stobie (1993) imply a mean error in H and K of approximately 0.006."
+ Ln general. there will be two standards involved. in stanclarclising a given programme star. thereby reducing the stancdarcdisation error to roughly 0.004. which suggests that random. errors ancl stancarclisation errors are of about the same magnitude.," In general, there will be two standards involved in standardising a given programme star, thereby reducing the standardisation error to roughly 0.004, which suggests that random errors and standardisation errors are of about the same magnitude."
+ Our precision and accuracy should be more than adequate for the present. purpose., Our precision and accuracy should be more than adequate for the present purpose.
+ The absolute magnitudes given in Table 1 for our sample of nearby red clump stars were derived. using the current, The absolute magnitudes given in Table 1 for our sample of nearby red clump stars were derived using the current
+ry<25kpeh! and relative radial velocities AV«350kms''.,"$r_{p}< 25 \rm \,kpc \,h^{-1}$ and relative radial velocities $\Delta V < 350 \rm \,km \,s^{-1}$."
+ According to these prescriptions. we have constructed a catalog of close pairs from the SDSS-DR7 and following Alonso et al. (," According to these prescriptions, we have constructed a catalog of close pairs from the SDSS-DR7 and following Alonso et al. ("
+2007) these pairs were classified according to the level of morphological disturbance associated to the interaction.,2007) these pairs were classified according to the level of morphological disturbance associated to the interaction.
+ In an attempt to explore the physical mechanisms that may affect the star formation activity. we have analyzed galaxy luminosities. spectral indicators of stellar populations. and colors.," In an attempt to explore the physical mechanisms that may affect the star formation activity, we have analyzed galaxy luminosities, spectral indicators of stellar populations, and colors."
+ We use K-corrections of the publicly available code deseribed in Blanton Γονείς (2007) 2)) as a calibration for our k-corrected magnitudes., We use K-corrections of the publicly available code described in Blanton Roweis (2007) ) as a calibration for our k-corrected magnitudes.
+ This paper is structured as follows: Section 2 describes the procedure used to construct the catalog and explain the process of classification and depuration of pair galaxies., This paper is structured as follows: Section 2 describes the procedure used to construct the catalog and explain the process of classification and depuration of pair galaxies.
+ In. Section 3 we study and characterize the effects of major and minor interactions and we discuss the dependence of star formation on colors and stellar population age., In Section 3 we study and characterize the effects of major and minor interactions and we discuss the dependence of star formation on colors and stellar population age.
+ In Section 4. we summarize our main conclusions.," In Section 4, we summarize our main conclusions."
+ The Sloan Digital Sky Survey. (SDSS. York et al.," The Sloan Digital Sky Survey (SDSS, York et al."
+ 2000) is the largest galaxy survey at the present., 2000) is the largest galaxy survey at the present.
+ It uses a 2.5m telescope (Gunn et al., It uses a 2.5m telescope (Gunn et al.
+ 2006) to obtain photometric and spectroscopy data that will cover approximately one-quarter of the celestial sphere and collect spectra of more than one million objects., 2006) to obtain photometric and spectroscopy data that will cover approximately one-quarter of the celestial sphere and collect spectra of more than one million objects.
+ The seven data release imaging (DR7. Abazajan et al.," The seven data release imaging (DR7, Abazajian et al."
+ 2009) comprises 11663 square degrees of sky imaged in five wave-bands (1. g. r. i and z) containing photometric parameters of 357 million objects.," 2009) comprises 11663 square degrees of sky imaged in five wave-bands $u$, $g$, $r$, $i$ and $z$ ) containing photometric parameters of 357 million objects."
+ Within. the survey. area. DR7 includes spectroscopic. data covering 9380 square degrees with 929555 spectra of galaxies.," Within the survey area, DR7 includes spectroscopic data covering 9380 square degrees with 929555 spectra of galaxies."
+ DR7 therefore represents the final data set released with the original targeting and galaxy selection (Etsenstein et al., DR7 therefore represents the final data set released with the original targeting and galaxy selection (Eisenstein et al.
+ 2001. Strauss et al.," 2001, Strauss et al."
+ 2002)., 2002).
+ The main galaxy sample is essentially a magnitude limited spectroscopic sample (Petrosian magnitude) 417.77. mostof galaxiesspanaredshiftrange0 0.25 shifto withamedianred fO.1CS traussetal.," The main galaxy sample is essentially a magnitude limited spectroscopic sample (Petrosian magnitude) $ < 17.77$, most of galaxies span a redshift range $0 < z < 0.25$ with a median redshift of 0.1 (Strauss et al."
+2002)., 2002).
+ WeconsideredauglgntaiadprocedureWeb tian i0.1. inordertoavoidstrongincompletene ssatla ," We considered a shorter redshift range, $z<0.1$, in order to avoid strong incompleteness at larger distances (Alonso et al."
+, 2006).
+We build a Galaxy Pair Catalog (GPC) from the SDSS-DR7. following our previous works (Alonso et al.," We build a Galaxy Pair Catalog (GPC) from the SDSS-DR7, following our previous works (Alonso et al."
+" 2007). requiring members to have relative projected separations. 7,«25kpch! and relative radial velocities. AV<350kms7! within redshifts ><0.1."," 2007), requiring members to have relative projected separations, $r_{p}< 25 \rm \,kpc \,h^{-1}$ and relative radial velocities, $\Delta V< 350 \rm \,km \,s^{-1}$ within redshifts $z<0.1$."
+ The number of pairs satisfying these criteria is 5579., The number of pairs satisfying these criteria is 5579.
+ We exclude AGNs for our sample. which could affect our interpretation of the results due to contributions from their emission line spectral features.," We exclude AGNs for our sample, which could affect our interpretation of the results due to contributions from their emission line spectral features."
+ We have also removed false identifications (mostly parts of the same galaxy) and objects with large magnitude uncertainties., We have also removed false identifications (mostly parts of the same galaxy) and objects with large magnitude uncertainties.
+ With these restrictions. our final pair catalog in the SDSS-DR7 comprises 1959 reliable close galaxy pairs with ς<O.1.," With these restrictions, our final pair catalog in the SDSS-DR7 comprises 1959 reliable close galaxy pairs with $z<0.1$."
+ In Table | we summarize this results., In Table 1 we summarize this results.
+ As discussed in Alonso et al. (, As discussed in Alonso et al. (
+2006). the effects of incompleteness or aperture (e.g see also Balogh et al.2004) do not introduce important bias in the galaxy pair catalogs.,"2006), the effects of incompleteness or aperture (e.g see also Balogh et al.2004) do not introduce important bias in the galaxy pair catalogs."
+ We classified all galaxies in the pair catalog taking into account the eye-ball detection of features characteristics of interactions. using the photometric SDSS-DR7.," We classified all galaxies in the pair catalog taking into account the eye-ball detection of features characteristics of interactions, using the photometric SDSS-DR7."
+ We defined two categories: Disturbed and Nondisturbed pairs., We defined two categories: $Disturbed$ and $Non\ disturbed$ pairs.
+ Disturbed pairs are sub-classified as merging (M. pairs with evidence of an ongoing merging process) and tidal (7. pairs with signs of tidal interactions but not necessarily merging).," $Disturbed$ pairs are sub-classified as merging $M$, pairs with evidence of an ongoing merging process) and tidal $T$, pairs with signs of tidal interactions but not necessarily merging)."
+ Nondisturbed (N) pairs showing no evidence of distorted morphologies., $Non\ disturbed$ $N$ ) pairs showing no evidence of distorted morphologies.
+ Fig., Fig.
+ |] shows images of typical examples of pair galaxies for different visual classification: M. 7 and N.," \ref{ej} shows images of typical examples of pair galaxies for different visual classification: $M$ , $T$ and $N$."
+ Forthe pair catalog we calculate the percentage of these three categories defined above., Forthe pair catalog we calculate the percentage of these three categories defined above.
+ As we can notice from Table 2. we find that about 10 % of galaxy pairs are classified as M. 30 % as T and 60 % as N. these percentages do not depend on redshift.," As we can notice from Table 2, we find that about 10 $\%$ of galaxy pairs are classified as $M$, 30 $\%$ as $T$ and 60 $\%$ as $N$, these percentages do not depend on redshift."
+ The visual inspection was performed by one of the authors in order to maintain a unified eriteria., The visual inspection was performed by one of the authors in order to maintain a unified criteria.
+ The reliability of the classification was addressed by the comparison with the classification of a subsample of pairs by another author., The reliability of the classification was addressed by the comparison with the classification of a subsample of pairs by another author.
+ This allows us to quantify the uncertainty in the ge , This procedure allows us to quantify the uncertainty in the classification (see table 2).
+We show in Fig., We show in Fig.
+" 2. the z. M, and log(23) distributions (upper. medium and lower panels. respectively) for M. 7 and N systems (solid. dashed and dot-dashed lines. respectively)."," \ref{histz1} the z, $M_r$ and $\Sigma_5$ distributions (upper, medium and lower panels, respectively) for $M$, $T$ and $N$ systems (solid, dashed and dot-dashed lines, respectively)."
+ It can be appreciated that the galaxies of the different pair interaction categories show similar redshift trends., It can be appreciated that the galaxies of the different pair interaction categories show similar redshift trends.
+ The middle panel show that the luminosity distributions. of the three interaction categories are comparable albeit with a small trend for higher luminosities in the M and 7 samples., The middle panel show that the luminosity distributions of the three interaction categories are comparable albeit with a small trend for higher luminosities in the $M$ and $T$ samples.
+ The lower panel shows that the log(Xs) distributions of M. 7 and N pairs are remarkably similar.," The lower panel shows that the $\Sigma_5$ ) distributions of $M$, $T$ and $N$ pairs are remarkably similar."
+ This provides an important result regarding the local enviroment of galaxies undergoing merger process in the present universe., This provides an important result regarding the local environment of galaxies undergoing merger process in the present universe.
+"A net flux of particles ¢.5-(p) escaping the system from this boundary is expected to grant the achievement of a stationary configuration, as discussed in |Caprioli,Blasi,Amato}(2009b).","A net flux of particles $\phi_{esc}(p)$ escaping the system from this boundary is expected to grant the achievement of a stationary configuration, as discussed in \cite{escape}."
+. An excellent approximate solution of Eq., An excellent approximate solution of Eq.
+ is found to be: where embeds all the information on the escape flux and the CR distribution function at the shock position [ο(0) can be implicitly written as Here we introduced the normalized fluid velocity U=u/ug and the compression ratios at the subshock Rup=1/19 and between zo and downstream Rig¢=10/10., \ref{diffconvstat} is found to be: where embeds all the information on the escape flux and the CR distribution function at the shock position $f_{sh}(p)$ can be implicitly written as Here we introduced the normalized fluid velocity $U=u/u_{0}$ and the compression ratios at the subshock $\Rs=u_{1}/u_{2}$ and between $x_{0}$ and downstream $\Rt=u_{0}/u_{2}$.
+" The solution of the problem is found using a recursive method, starting from a guess for Uy=Rew/Riot (the compression ratios are linked together by Eq. 28)."," The solution of the problem is found using a recursive method, starting from a guess for $U_{1}=\Rs/\Rt$ (the compression ratios are linked together by Eq. \ref{rsrtTH}) ),"
+" along with a guess for the CR distribution function at the shock and the escape flux |Caprioli,Blasi, Amato|2009b)..", along with a guess for the CR distribution function at the shock and the escape flux \citep[the test-particle solution of][]{escape}.
+" The steps above are iterated, leaving U; unchanged until convergence is reached, uuntil the factor normalizing [δει does not change between one step and the following: in"," The steps above are iterated, leaving $U_{1}$ unchanged until convergence is reached, until the factor normalizing $P_{c,1}$ does not change between one step and the following: in"
+"actually is a blend of two stars. as cliscussecl In this section we want to re-investigate this problem. by using our CDVA data combined with near Hi 11ήν1, data from Tapia et al (1988) and spectral classifications from. Xlorrell οἱ al (1988).","actually is a blend of two stars, as discussed In this section we want to re-investigate this problem by using our $UBVRI$ data combined with near IR $JHKL$ data from Tapia et al (1988) and spectral classifications from Morrell et al (1988)."
+ (BY data can be used. to derive an estimate of the fy parameter. defined as the ratio of the total to selective absorption EBENVas bv means of the variable extinction method. (see. for instance. Johnson 1966a)," $UBV$ data can be used to derive an estimate of the $R_V$ parameter, defined as the ratio of the total to selective absorption $\frac{A_V}{E(B-V)}$, by means of the variable extinction method (see, for instance, Johnson 1966a)."
+ This method requires also the Knowledge of the absolute magnitude and intrinsic colors of individual member stars., This method requires also the knowledge of the absolute magnitude and intrinsic colors of individual member stars.
+ We use the empirical ZAAIS taken from Schmidt-Ixaler (1982) to derive absolute magnitude and intrinsic The result is shown in Fig., We use the empirical ZAMS taken from Schmidt-Kaler (1982) to derive absolute magnitude and intrinsic The result is shown in Fig.
+ 10. where all the probable photometric members selected in the previous Section have been considered.," 10, where all the probable photometric members selected in the previous Section have been considered."
+ The least squares fit through the data provides Ay52.8000.28., The least squares fit through the data provides $R_V~=~2.89\pm0.28$.
+ Phe absolute distance modulus. defined as the ordinate for E(BV) = 0. turns out to be QnAly=11.90d0.25. which implies a clistance from the Sun of 2440.3 The reported. errors are the results of the linear. fit. obtained by assuming that both the color. excesses and the magnitueds have their. uncertainty.," The absolute distance modulus, defined as the ordinate for $(B-V)$ = 0, turns out to be $(m-M)_0~=~11.90\pm0.25$, which implies a distance from the Sun of $2.4\pm0.3$ The reported errors are the results of the linear fit, obtained by assuming that both the color excesses and the magnitueds have their uncertainty."
+ However. due to the small range in color excess. the result we obtained has to be considered. -with some caution- as nomore than an inclication.," However, due to the small range in color excess, the result we obtained has to be considered -with some caution- as nomore than an indication."
+ To obtain another estimate of Z2 we combine our CDVIH photometry with the near Ht photometry in the {1ήν. bands from “Tapia et al (1988)., To obtain another estimate of $R_V$ we combine our $UBVRI$ photometry with the near IR photometry in the $JHKL$ bands from Tapia et al (1988).
+ We have 30 stus in common. but we perform our analvsis onky by considering the star having spectral classification.," We have 30 stars in common, but we perform our analysis only by considering the star having spectral classification."
+ Basically. there are two methods to derive ancl estimate of Ay from near IR The first method. is based on the following approximate relation reported. by Whittet (1990).," Basically, there are two methods to derive and estimate of $R_V$ from near IR The first method is based on the following approximate relation reported by Whittet (1990)."
+ We use Weener (1994) intrinsic colour indices to derive the color excess E(BV) and L(VAx)., We use Wegner (1994) intrinsic colour indices to derive the color excess $(B-V)$ and $(V-K)$.
+ The mean value for the stars in Table 2 turns out to be in fine agreement with the variable extinction The second. method (6) makes use of the extinction, The mean value for the stars in Table 2 turns out to be in fine agreement with the variable extinction The second method makes use of the extinction
+asstued to be solar (Asplundetal.2009) with a 25 of depletion for elements heavier than Ie. aud assume hat initially all the clemeuts are in atomic form. either jeutral or ionized.,"assumed to be solar \citep{asp09} with a 25 of depletion for elements heavier than He, and assume that initially all the elements are in atomic form, either neutral or ionized."
+ The chemical network comprises 2307 Sas plase reactions whose rate constants have Όσσα nostly taken from Agüudez&Cernicharo(2006) and Yoni the UMIST database for (Woodalletal.2007).. some of them revised according o the most recent literature on chemical kinetics.," The chemical network comprises 2307 gas phase reactions whose rate constants have been mostly taken from \citet{agu06} and from the UMIST database for \citep{woo07}, some of them revised according to the most recent literature on chemical kinetics."
+ The shotoclissociation rates of Ts aud CO have been takeu your Leeetal.(1996)., The photodissociation rates of $_2$ and CO have been taken from \citet{lee96}.
+. The adopted visual extinction is 0.5 inag aud the cosumüc-ray ionization rate per IL nolecule is «10 I 1l, The adopted visual extinction is 0.5 mag and the cosmic-ray ionization rate per $_2$ molecule is $\times$ $^{-17}$ $^{-1}$.
+ We do not consider grain surface reactions except for the formation of IT». which is assumed to oceur with a rate constaut of 3410.1 o? +. the canonical value in typical diffuse clouds (Jura L975).," We do not consider grain surface reactions except for the formation of $_2$, which is assumed to occur with a rate constant of $\times$ $^{-17}$ $^3$ $^{-1}$, the canonical value in typical diffuse clouds \citep{jur75}."
+ This quite standard chemical network is completed by adding the reactions of vibrationally excited IT» detailed in Table ??7.., This quite standard chemical network is completed by adding the reactions of vibrationally excited $_2$ detailed in Table \ref{table-h2-reac}.
+" Thus. Πω (ο= 1) is meluded as a new chemical species with a fractional abundance £. relative to eround state IT». which is kept fixed at four different values (0. © 7; and 4), incdependecutly of the miechanisui responsible of the excitation of Πω."," Thus, $_2$ $v=1$ ) is included as a new chemical species with a fractional abundance $f^*$, relative to ground state $_2$, which is kept fixed at four different values (0, $^{-6}$, $^{-5}$, and $^{-4}$ ), independently of the mechanism responsible of the excitation of $_2$."
+ The αλλοι of Πο (ο7 1) is nmuportaut for roactious (2]) aud (3)) so that we also consider IT; iu the 6=2 aud c=3 states with populations which are 1/3 aud 1/9 respectively of that in the e=1 state. values typically attained in interstellar clouds with an imiportaut fraction of vibrationally excited IT» (e.g. vanDishoeck&Blacks1986:Moveretal. 2001)).," The amount of $_2$ $v>1$ ) is important for reactions \ref{reac-h2+heplus}) ) and \ref{reac-h2+o}) ) so that we also consider $_2$ in the $v=2$ and $v=3$ states with populations which are 1/3 and 1/9 respectively of that in the $v=1$ state, values typically attained in interstellar clouds with an important fraction of vibrationally excited $_2$ (e.g. \citealt{van86,mey01}) )."
+ In these exploratory mocdols we do not distinguish between the different reactivity of IT. in the various rotational levels of the erouud vibrational state., In these exploratory models we do not distinguish between the different reactivity of $_2$ in the various rotational levels of the ground vibrational state.
+ The abundance of various species are found o be sensitive to the fraction of vibrationally excited IT»., The abundance of various species are found to be sensitive to the fraction of vibrationally excited $_2$.
+ Iu Fig., In Fig.
+ 2 we plot the steady. state abundance of some of these species for various fractional abundances of IL; (c= 1) as a function of the Ην ratio., \ref{fig-abun} we plot the steady state abundance of some of these species for various fractional abundances of $_2$ $v=1$ ) as a function of the $n_{\rm H}/\chi$ ratio.
+ The steady state abundances are found to depend on this latter ratio rather than on either vy or x., The steady state abundances are found to depend on this latter ratio rather than on either $n_{\rm H}$ or $\chi$.
+ For the results shown in Fig., For the results shown in Fig.
+ 2. a deusity of hvdrogen nuclei of 107 cm has been adopted. so that the FUW field streneth has been varied.," \ref{fig-abun} a density of hydrogen nuclei of $^3$ $^{-3}$ has been adopted, so that the FUV field strength has been varied."
+ Reactions of vibrationally excited IT» have a larecr impact on the chemistrv at low temperatures. since as cliscussed previously the rate coustaut enlaucemoeut Ak of the various reactious is larger.," Reactions of vibrationally excited $_2$ have a larger impact on the chemistry at low temperatures, since as discussed previously the rate constant enhancement $\Delta k$ of the various reactions is larger."
+ The results shown in Fig., The results shown in Fig.
+" 2. correspond to a relatively low teiiperature of 100 EK. The molecule whose abundance is more affected by the reactions of vibrationally excited IT» is the metlovlicdvue cation (CII! which for fractional abundances of IT;(6 = 1) above 10).*—© is readily formed by the reaction between Hate= 1) aud οὐ),"," \ref{fig-abun} correspond to a relatively low temperature of 100 K. The molecule whose abundance is more affected by the reactions of vibrationally excited $_2$ is the methylidyne cation $^+$ ), which for fractional abundances of $_2$ $v=1$ ) above $10^{-7}-10^{-6}$ is readily formed by the reaction between $_2$ $v=1$ ) and $^+$."
+ The steady state abuudauce of CIT! approximately scales with the fraction of Il(e = 1) and reaches its παΙΙ abundance for oqp/X ratios in the range 100., The steady state abundance of $^+$ approximately scales with the fraction of $_2$ $v=1$ ) and reaches its maximum abundance for $n_{\rm H}/\chi$ ratios in the range $-$ 100.
+ By ruuuiug models at different kinetic temperatures we find that above 500 I& the reaction between Ποο= 0) aud C! starts to proceed and the abundance of CII! depends to a πιοlesser extent on the fraction of vibrationally excited IT»., By running models at different kinetic temperatures we find that above $-$ 500 K the reaction between $_2$ $v=0$ ) and $^+$ starts to proceed and the abundance of $^+$ depends to a muchlesser extent on the fraction of vibrationally excited $_2$.
+ The abundances of CIL] and CIE] are strongly linked to that of CII! by the chain of exothermic reactions which stops at CTL. as this species docs not react fast with Πο.," The abundances of $_2^+$ and $_3^+$ are strongly linked to that of $^+$ by the chain of exothermic reactions which stops at $_3^+$, as this species does not react fast with $_2$."
+ Therefore. iu those conditious iu which CIE! reaches a relatively high abundance. CIE] aud CIL] do so (see Fig. 2)).," Therefore, in those conditions in which $^+$ reaches a relatively high abundance, $_2^+$ and $_3^+$ do so (see Fig. \ref{fig-abun}) )."
+ Some other species such as CIT. OIL. and IO also experience a moderate abundauce cuhancement wheu CII! is formed.," Some other species such as CH, OH, and $_2$ O also experience a moderate abundance enhancement when $^+$ is formed."
+ The radical CIL is formed by the dissociative recombination with electrous of the catious and. while OIT aud HT2O. are produced by a sequenceCIS of CILE.reactions that starts with the plotodissociation of CIE! aud production of IL! followed," The radical CH is formed by the dissociative recombination with electrons of the cations $_2^+$ and $_3^+$ , while OH and $_2$ O are produced by a sequence of reactions that starts with the photodissociation of $^+$ and production of $^+$ followed"
+"luminosity of star-forming galaxies mostly originates from the emission of the 7.7um and 8.6um Polycyclic Aromatic Hydrocarbon (PAH) lines, which represent the most prominent features in the mid-IR spectrum of dusty galaxies (e.g.,Laurentetal,2000;Daleαἰ.,2001;Brandletal.,2006;SmithaL, 2007).","luminosity of star-forming galaxies mostly originates from the emission of the $\mu$ m and $\mu$ m Polycyclic Aromatic Hydrocarbon (PAH) lines, which represent the most prominent features in the mid-IR spectrum of dusty galaxies \citep[e.g.,][]{Laurent:00,Dale:01,Brandl:06,Smith:07}."
+". These features are stochastically heated by the radiation field of young stellar populations, and as it was demonstrated by numerous studies of local sources, their luminosity is tightly correlated with the total Infrared luminosity of galaxies, and therefore with their SFR (e.g.,Rousseletal.,2007;Díaz-Santos2008;Goto 2011)."," These features are stochastically heated by the radiation field of young stellar populations, and as it was demonstrated by numerous studies of local sources, their luminosity is tightly correlated with the total Infrared luminosity of galaxies, and therefore with their SFR \citep[e.g.,][]{Roussel:01,Wu:05,Brandl:06,Cal:07,Diaz:08,Goto:11}."
+". Furthermore, observations of distant sources with and more recently withHerschel have revealed that this correlation between the 8um and the total IR luminosity of star-forming galaxies extends up to at least z~2 (Popeetal.2008;RigbyBavouzetMenéndez-Delmestreetal. 2009,, Elbaz et al.,"," Furthermore, observations of distant sources with and more recently with have revealed that this correlation between the $\mu $ m and the total IR luminosity of star-forming galaxies extends up to at least $z \sim 2$ \citealt{Pope:08,Rigby:08,Bavouzet:08,Menendez:09}, Elbaz et al.,"
+" submitted), suggesting that the 8um emission is a fairly good tracer of star-forming activity also in high-redshift galaxies."," submitted), suggesting that the $\mu$ m emission is a fairly good tracer of star-forming activity also in high-redshift galaxies."
+ To convert the observed MIPS-24um fluxes into luminosities at 8um we used the library of IR SED templates of Chary&Elbaz(2001)., To convert the observed $\mu$ m fluxes into luminosities at $\mu$ m we used the library of IR SED templates of \citet{Chary:2001}.
+ In this library the galaxy IR SEDs vary as a function of total IR luminosity (Lip= Ls-1000u4) and for a given redshift the flux density measured at 24m corresponds to a unique monochromatic luminosity at any IR wavelengths., In this library the galaxy IR SEDs vary as a function of total IR luminosity $L_{\rm IR} = L_{8-1000\mu m}$ ) and for a given redshift the flux density measured at $\mu$ m corresponds to a unique monochromatic luminosity at any IR wavelengths.
+ However we stress again that for our current analysis the k-corrections only depend on the shape of these templates between Ag= 8um and Ay=24um/(1-4-z)., However we stress again that for our current analysis the $k$ -corrections only depend on the shape of these templates between $\lambda_0 = 8\mu$ m and $\lambda_1 = 24\mu$ $z$ ).
+" At z~2 they are thus barely sensitive to the choice of SEDs and do not depend on the uncertainties that have been shown to affect the extrapolations of mid-IR fluxes to total IR luminosities (Elbazetal.,2010).", At $z \sim 2$ they are thus barely sensitive to the choice of SEDs and do not depend on the uncertainties that have been shown to affect the extrapolations of mid-IR fluxes to total IR luminosities \citep{Elbaz:10}.
+". In fact we computed the rest-frame 8um luminosities of the MIPS galaxy sample using the libraries of IR SED templates proposed by Dale&Helou (2002),, Lagacheetal.(2004) and Riekeetal.(2009),, and we found virtually no difference with the results obtained with the library of Chary&Elbaz(2001)."," In fact we computed the rest-frame $\mu$ m luminosities of the MIPS galaxy sample using the libraries of IR SED templates proposed by \citet{Dale:2002}, \citet{Lagache:04} and \citet{Rieke:2009}, and we found virtually no difference with the results obtained with the library of \citet{Chary:2001}."
+. This effect will be discussed in more details in a forthcoming paper by Le Floc’h et al. (, This effect will be discussed in more details in a forthcoming paper by Le Floc'h et al. (
+in prep.),in prep.)
+ on the evolution of the mid-IR luminosity function in COSMOS., on the evolution of the mid-IR luminosity function in COSMOS.
+ Based on these 8um luminosities we computed the luminosity functions (LF) associated with our different sub-samples over the 1.7<z2.3 redshift range and we compared these results to the global LF obtained at the same redshifts from the full sample of MIPS sources in COSMOS., Based on these $\mu$ m luminosities we computed the luminosity functions (LF) associated with our different sub-samples over the $1.7<z<2.3$ redshift range and we compared these results to the global LF obtained at the same redshifts from the full sample of MIPS sources in COSMOS.
+ These luminosity functions are illustrated in the top panel of Fig 6.., These luminosity functions are illustrated in the top panel of Fig \ref{fig:LF}.
+" They were estimated using the 1/Vmaz method (Schmidt,1968),, which is advantageous in two ways: no hypothesis on the shape of the LF is needed and the luminosity function is directly measured from the observations."," They were estimated using the $_{max}$ method \citep{Schmidt:68}, which is advantageous in two ways: no hypothesis on the shape of the LF is needed and the luminosity function is directly measured from the observations."
+ For each object we estimated the maximum comoving volume where it can be detected within our given redshift bin (1.7«z 2.3) using, For each object we estimated the maximum comoving volume where it can be detected within our given redshift bin $1.7<z<2.3$ ) using
++) or an equivalent FWIIM of 615 km /. so the line shift is well within the velocity dispersion value).,"$^{-1}$, or an equivalent FWHM of 615 km $^{-1}$, so the line shift is well within the velocity dispersion value)."
+ The OVI A1032 line is visible on both the Lifla and Lif2b channels., The OVI $\lambda$ 1032 line is visible on both the Lif1a and Lif2b channels.
+" NGC 4621: This E5 ealaxy (M59) lies about 3° west of AIST in the Virgo cluster. it has about the average extinction for the Virgo cluster 107"" 7). but it clearly shows Galactic Hà» absorption along with the usual Galactic atomic absorption lines."," NGC 4621: This E5 galaxy (M59) lies about $^{\circ }$ west of M87 in the Virgo cluster, it has about the average extinction for the Virgo cluster $\times$ $^{20}$ $^{-2}$ ), but it clearly shows Galactic $_{2}$ absorption along with the usual Galactic atomic absorption lines."
+ However. (he redshift of the galaxy places both OVI lines in uncontaminated regions aud the spectrum is ol moderately. good S/N (Figure 19).," However, the redshift of the galaxy places both OVI lines in uncontaminated regions and the spectrum is of moderately good S/N (Figure 19)."
+ There is no evidence for emission lines of either OVI line or of ΟΠΠ., There is no evidence for emission lines of either OVI line or of CIII.
+ NGC 4636: This Virgo cluster galaxy. was presented by (2001).. who reported the detection of both OVI lines.," NGC 4636: This Virgo cluster galaxy was presented by \citet{breg01}, who reported the detection of both OVI lines."
+ The width of the emission lines but nol the line strength seems to depend upon the version of the pipeline used: these results employ pipeline version 2.4 (Fieure 20)., The width of the emission lines but not the line strength seems to depend upon the version of the pipeline used; these results employ pipeline version 2.4 (Figure 20).
+ The CII line may be detected. although the centroid is 120 km ! (0.4 A) blueward of the expected line center (the line would have a FWILM of 0.5 aand a flux of 5x10. | erg em7 sect. detected at about the 2c level).," The CIII line may be detected, although the centroid is 120 km $^{-1}$ (0.4 ) blueward of the expected line center (the line would have a FWHM of 0.5 and a flux of $\times$ $^{-15}$ erg $^{-2}$ $^{-1}$, detected at about the $\sigma$ level)."
+ NGC 41649: The redshifted OVI A1032 line would be shifted (1035.8 A) just to the blue side of the Galactie CLL AI036 line (1036.3 A). but there is no evidence for OVI emission above the level of the rather strong stellar continuum. which is similar to the continuum of NGC 1399 (Figure 21).," NGC 4649: The redshifted OVI $\lambda$ 1032 line would be shifted (1035.8 ) just to the blue side of the Galactic CII $\lambda$ 1036 line (1036.3 ), but there is no evidence for OVI emission above the level of the rather strong stellar continuum, which is similar to the continuum of NGC 1399 (Figure 21)."
+ There are moderately strong Galactic Hà» lines ancl atomic absorption lines present. although these do not contaminate the locations of the OVI lines.," There are moderately strong Galactic $_{2}$ lines and atomic absorption lines present, although these do not contaminate the locations of the OVI lines."
+ NGC 4697: The redshift of this galaxy. would place the redshifted OVI A1032 line (1036.2 A) into the strong Galactic CII absorption line (1036.34 A)., NGC 4697: The redshift of this galaxy would place the redshifted OVI $\lambda$ 1032 line (1036.2 ) into the strong Galactic CII absorption line (1036.34 ).
+ There is no strong line to the blue side of the CII line (Figure 22)., There is no strong line to the blue side of the CII line (Figure 22).
+" NGC 5846: This is the optically most Iuminous galaxy in (he center of its group aud it has a moderate amount of extinction 107"" 2). with evidence of absorption from Galactic molecular hydrogen and atomic lines."," NGC 5846: This is the optically most luminous galaxy in the center of its group and it has a moderate amount of extinction $\times$ $^{20}$ $^{-2}$ ), with evidence of absorption from Galactic molecular hydrogen and atomic lines."
+ This is one of the more distant objects. so ihe continuum is fairly Taint but is well-fit bv the stellar continuum of NGC 1399 (Figure 23).," This is one of the more distant objects, so the continuum is fairly faint but is well-fit by the stellar continuum of NGC 1399 (Figure 23)."
+ Both the strong ancl weak redshifted OVI lines appear (o be present. but not in the expected 2:1 ratio (lor OVI A1032 to OVI A038).," Both the strong and weak redshifted OVI lines appear to be present, but not in the expected 2:1 ratio (for OVI $\lambda$ 1032 to OVI $\lambda$ 1038)."
+ The OVI AI032 line is broken up by Galactic molecular absorption features. so il could be significantly stronger.," The OVI $\lambda$ 1032 line is broken up by Galactic molecular absorption features, so it could be significantly stronger."
+ We cannot fit the IH» parameters well enough to make an accurate absorption correction lor the OVI A1032 line., We cannot fit the $_{2}$ parameters well enough to make an accurate absorption correction for the OVI $\lambda$ 1032 line.
+ The usually weaker OVI A1038 line (redshifted to 1043.6. A) falls close to a feature in the detector., The usually weaker OVI $\lambda$ 1038 line (redshifted to 1043.6 ) falls close to a feature in the detector.
+ Whereas this feature is stationary and well-known. we have seen instances of unusual absorption or emission near it. and (his may contribute (ο the strength of this feature.," Whereas this feature is stationary and well-known, we have seen instances of unusual absorption or emission near it, and this may contribute to the strength of this feature."
+ The spectra in the Lil2b channel. while poorer. confirms the presence of the OVI À1032 line but not the OVI A1033 line.," The spectra in the Lif2b channel, while poorer, confirms the presence of the OVI $\lambda$ 1032 line but not the OVI $\lambda$ 1038 line."
+ Consequently. we estimate the OVI Iuminosity [rom," Consequently, we estimate the OVI luminosity from"
+wilh Vj=GCMjs/a.,with $V_{\rm bin}=\sqrt{G\m12/a}$.
+ Figure 2 plots Dy as a [function of V. and Όρων., Figure 2 plots $D_R$ as a function of $V$ and $p_{max}$.
+" The most effective encountersare those with small V. and p,,,,: encounters with impact parameters pXOv23CMyjsa/V. have a closest-approach distance to the binary of r,2a and produce almost no change in (he binarys orientation.", The most effective encountersare those with small $V$ and $p_{max}$; encounters with impact parameters $p\gap \sqrt{2G\m12a}/V$ have a closest-approach distance to the binary of $r_p\gap a$ and produce almost no change in the binary's orientation.
+ Hence Dj reaches a maxinun value al belore levelling olf at larger p., Hence $D_R$ reaches a maximum value at $p\approx \sqrt{2G\m12 a}/V$ before levelling off at larger $p$ .
+ Multiplving (90?) by fj(ey). the distribution of field-star velocities. and integrating dv; eives (AU?)," Multiplying $\langle\delta\vartheta^2\rangle$ by $f_f(\vf)$, the distribution of field-star velocities, and integrating ${\bf dv}_f$ gives $\dv$."
+ We assume a Maxwellian distribution of field star velocities. so that (Nm Ve varthelar).," We assume a Maxwellian distribution of field star velocities, (v_f) = , so that = V^2 ."
+ This can be written in terms of a cdimensionlesscoefficient. L," This can be written in terms of a dimensionlesscoefficient$L$ ,"
+ This can be written in terms of a cdimensionlesscoefficient. L.," This can be written in terms of a dimensionlesscoefficient$L$ ,"
+For a cluster survey. the projected. cluster-centric distance is à convenient parameter to describe the environment of a galaxy. although it may not be entirely. free. [rom introducing potential biases (seeLanectal.2007).,"For a cluster survey, the projected cluster-centric distance is a convenient parameter to describe the environment of a galaxy, although it may not be entirely free from introducing potential biases \cite[see][]{lane07}."
+". In this section. we examine the dependence of stellar population properties of the cluster galaxies on the distance of the ealaxy [rom the cluster centre. which has been taken be at 1A.()2000)—1144""29.57 and |19°50lo21"," In this section, we examine the dependence of stellar population properties of the cluster galaxies on the distance of the galaxy from the cluster centre, which has been taken to be at $11^{h} 44^{m} 29.5^{s}$ and $+19^{\circ} 50^{'} 21^{''}$."
+ We express the cluster-centric radius in terms of the cluster Abell radius. taken to be SO.," We express the cluster-centric radius in terms of the cluster Abell radius, taken to be $80^{'}$."
+ Figure S shows the relationship between the cluster-centric racial cistanee. normalised to the Abell racius of the cluster. anc the integrated. stellar mass (left. panel). the luminositv-weightecl stellar metallicity (middle panel). and the residuals from the bisector Gt of the stellar mass-metallicity relations (right panel).," Figure \ref{resid_proj_RS_SF} shows the relationship between the cluster-centric radial distance, normalised to the Abell radius of the cluster, and the integrated stellar mass (left panel), the luminosity-weighted stellar metallicity (middle panel), and the residuals from the bisector fit of the stellar mass-metallicity relations (right panel)."
+ Galaxies in the sample are separated between those in the red sequence. shown as filled circles. and those in the blue cloud. shown as open circles.," Galaxies in the sample are separated between those in the red sequence, shown as filled circles, and those in the blue cloud, shown as open circles."
+ Galaxies that show signs of the presence of morphological disturbance are. Uageecd with large open triangles., Galaxies that show signs of the presence of morphological disturbance are flagged with large open triangles.
+ The residuals for each subsample are estimated. using the linear least square bisector fit to the mass-metallicity relation. of the subsample., The residuals for each subsample are estimated using the linear least square bisector fit to the mass-metallicity relation of the subsample.
+ In cach panel. the solid line shows the best linear fit for red. sequence galaxies. while the clashed line shows the fit to galaxies in the blue. cloud.," In each panel, the solid line shows the best linear fit for red sequence galaxies, while the dashed line shows the fit to galaxies in the blue cloud."
+ ALL galaxies are assigned equal weight in the fits. since the scatter is primarily intrinsic and the measurement errors similar for the bulk of the points.," All galaxies are assigned equal weight in the fits, since the scatter is primarily intrinsic and the measurement errors similar for the bulk of the points."
+ The slopes ancl the associated errors of the fit to the cluster-centric racial gradients are indicated for both subsamples., The slopes and the associated errors of the fit to the cluster-centric radial gradients are indicated for both subsamples.
+ As expected. more massive red. sequence galaxies [ie preferentially in the core of the cluster.," As expected, more massive red sequence galaxies lie preferentially in the core of the cluster."
+ As red. sequence ealaxies exhibit a clear mass-mectallicity relation. a strong negative luminosityv-weighted metallicity gradient as a function of the cluster-centric distance is present.," As red sequence galaxies exhibit a clear mass-metallicity relation, a strong negative luminosity-weighted metallicity gradient as a function of the cluster-centric distance is present."
+ “Phe metallicity residuals for these galaxies do not show however a statistically significant correlation with the eluster-centric galaxy distance., The metallicity residuals for these galaxies do not show however a statistically significant correlation with the cluster-centric galaxy distance.
+ Because the stellar populations of the cluster red. sequence galaxies follow scaling relations with stellar mass. the residuals from these relations are comparing the inner and outer galaxy. population at [fixed stellar mass.," Because the stellar populations of the cluster red sequence galaxies follow scaling relations with stellar mass, the residuals from these relations are comparing the inner and outer galaxy population at fixed stellar mass."
+ On average. red. sequence galaxies at 40 per cent. of the Abell radius of the cluster are 0.49+0.28 dex poorer than galaxies of similar stellar masses in the cluster core.," On average, red sequence galaxies at 40 per cent of the Abell radius of the cluster are $\sim0.49\pm0.28$ dex poorer than galaxies of similar stellar masses in the cluster core."
+ Similarlv. blue cloud. galaxies show a negative stellar mass &eracient. however the luminositv-weighted metallicity shows no significant correlation with the cluster-centric. radius.," Similarly, blue cloud galaxies show a negative stellar mass gradient, however the luminosity-weighted metallicity shows no significant correlation with the cluster-centric radius."
+ The residuals from the luminositv-weightecl metallicity-mass relation of star-Lorming galaxies show no statistically significant correlation with the projected distance from the cluster centre., The residuals from the luminosity-weighted metallicity-mass relation of star-forming galaxies show no statistically significant correlation with the projected distance from the cluster centre.
+ The lack of a negative correlation for the star forming galaxies could be caused by enhanced star formation. leading to lower luminositv-weighted metallicities (seo section 3.3. above) in higher density regions of the cluster as compared with lower density regions (seeMossetal.1998:Moss&Whittle 2000).," The lack of a negative correlation for the star forming galaxies could be caused by enhanced star formation, leading to lower luminosity-weighted metallicities (see section \ref{mass_met} above) in higher density regions of the cluster as compared with lower density regions \cite[see][]{moss98,mw00}."
+.. Alternatively. given the small size of the our sample. projection effects could cause a dilution of the expected. gradients. although such dilution elfects are expected to be small in the sampled region within hal£ the Abell radii (Mossetal.1998).," Alternatively, given the small size of the our sample, projection effects could cause a dilution of the expected gradients, although such dilution effects are expected to be small in the sampled region within half the Abell radii \citep{moss98}."
+. Finally. neither red. sequence galaxies nor star-forming ealaxies show ¢luster-centric radial &racients for the residual from the relationship between Iuminosity-weighted age and stellar mass. over the radial range covered. by the sample galaxies.," Finally, neither red sequence galaxies nor star-forming galaxies show cluster-centric radial gradients for the residual from the relationship between luminosity-weighted age and stellar mass, over the radial range covered by the sample galaxies."
+ Ellipticals and lenticulars populating the red sequence do appear to be dominated. by different stellar populations (sco Lig., Ellipticals and lenticulars populating the red sequence do appear to be dominated by different stellar populations (see Fig.
+ 3. and 5)) suggesting that they might have experienced: dilferent assembly: histories.," \ref{bmk_jmk} and \ref{mst_age}) ), suggesting that they might have experienced different assembly histories."
+ Lt is legitimate then to check how their stellar population properties taken separately change racially within the cluster., It is legitimate then to check how their stellar population properties taken separately change radially within the cluster.
+ Figure 9 shows the relationships between the eluster-centric distance normalized to the Abell radius of the cluster anc the residuals from the stellar mass-metallicity relations (the upper panel) ancl the stellar mass-age relations (the lower wel) for ellipticals ancl lenticulars in the red sequence shown as open and filled circles respectively., Figure \ref{res_feh_age_ellip_S0} shows the relationships between the cluster-centric distance normalized to the Abell radius of the cluster and the residuals from the stellar mass-metallicity relations (the upper panel) and the stellar mass-age relations (the lower panel) for ellipticals and lenticulars in the red sequence shown as open and filled circles respectively.
+ The fits to the stellar mass vs. metallicity/age relations are done separately or elliptical and lenticular subsamples., The fits to the stellar mass vs. metallicity/age relations are done separately for elliptical and lenticular subsamples.
+ Lhe slopes ancl their associated errors. of the best linear. fits to the relations otween the residuals ancl the normalized: cluster-centric radial distance are indicated., The slopes and their associated errors of the best linear fits to the relations between the residuals and the normalized cluster-centric radial distance are indicated.
+ No statistically significant rends are found between the residuals. from the. mass-metallicity/mass-age relations and the cluster-centric galaxy distance for neither red sequence ellipticals nor lenticulars., No statistically significant trends are found between the residuals from the mass-metallicity/mass-age relations and the cluster-centric galaxy distance for neither red sequence ellipticals nor lenticulars.
+ This indicates that no significant. dillerences in the mean luminosityv-weightecd metallicities anc ages are present. at a fixed stellar mass. between the red sequence galaxy sub- distributed within the 40 per cent of the Abell radius of the cluster covered. by our survey.," This indicates that no significant differences in the mean luminosity-weighted metallicities and ages are present, at a fixed stellar mass, between the red sequence galaxy sub-populations distributed within the 40 per cent of the Abell radius of the cluster covered by our survey."
+ “Lhe lack of, The lack of
+indicating three distinct portions of the spectrua that exhibit a power-law.,indicating three distinct portions of the spectrum that exhibit a power-law.
+ In fact. the two peaks define a frequency “window or baud for au intermediate power-law with a slope between |2 aud 0.11.," In fact, the two peaks define a frequency “window” or band for an intermediate power-law with a slope between $+2$ and $-0.11$ ."
+ Figure 5 shows more SED calculations for à finer exid of > values. focussing on the range of +=1 to 2.," Figure \ref{fig5} shows more SED calculations for a finer grid of $\gamma$ values, focussing on the range of $\gamma=1$ to 2."
+ Iu this rangem intermediate power-law seenientsm persist with windows of about 1 dex in frequeucv., In this range intermediate power-law segments persist with windows of about 1 dex in frequency.
+penc] At +=1 the slope of the intermediate power-law is high at about àz1.6. but with increasing >. the value of à drops.," At $\gamma=1$ the slope of the intermediate power-law is high at about $\alpha\approx 1.6$, but with increasing $\gamma$, the value of $\alpha$ drops."
+ The frequency. wivdows are narrower for 5;=ld aud 2., The frequency windows are narrower for $\gamma=1$ and 2.
+ As seen in Figure L. the SED turnover is smooth and regular for 5 values outside the range of 12.," As seen in Figure \ref{fig4}, the SED turnover is smooth and regular for $\gamma$ values outside the range of 1–2."
+" Ποσο, we come to the interesting conclusion that a rather restricted range of ~ values are suitable for producing intermediate power-laws of significant bandwidth."," Hence, we come to the interesting conclusion that a rather restricted range of $\gamma$ values are suitable for producing intermediate power-laws of significant bandwidth."
+ To illustrate etter how intermediate power-law sceieuts arise. Figure 6 shows a model SED using a value of >=1.5.," To illustrate better how intermediate power-law segments arise, Figure \ref{fig6} shows a model SED using a value of $\gamma=1.5$."
+ The solid line is the SED from the chuup cusemble., The solid line is the SED from the clump ensemble.
+ The dotted lines are for coutyibutious to the net spectrau from chumps of different optical depths (artificially shifted upward for clarity of display)., The dotted lines are for contributions to the net spectrum from clumps of different optical depths (artificially shifted upward for clarity of display).
+ The SEDs of individual clips show a power-law ποσο of f at low frequency and oue of f0.11 at ligh frequency. the two joined by a fairly rapid turnover.," The SEDs of individual clumps show a power-law segment of $f^2$ at low frequency and one of $f^{-0.11}$ at high frequency, the two joined by a fairly rapid turnover."
+ The different combination of clumps with differeut optical depths at the fiducial frequency vy serves to “spread out” the turnovers of the iudividual clump SEDs. so as to produce in the net SED a significant power-law segment that has a slope intermediate betwee- |2 aud 0.11.," The different combination of clumps with different optical depths at the fiducial frequency $\nu_0$ serves to “spread out” the turnovers of the individual clump SEDs, so as to produce in the net SED a significant power-law segment that has a slope intermediate between $+2$ and $-0.11$."
+ Tt is crucial to cousicer how the lower and upper optical depth scales for the clip distribution iuflueuce the SED., It is crucial to consider how the lower and upper optical depth scales for the clump distribution influence the SED.
+ Figure 7. shows more models of the case 5=1.5. now with the upper linüt f» fixed at 100. aud the lower limit f4 varied from 0.0001 to LO as indicated.," Figure \ref{fig7} shows more models of the case $\gamma=1.5$, now with the upper limit $t_2$ fixed at 100, and the lower limit $t_1$ varied from 0.0001 to 10 as indicated."
+ As the lower limit £4 apyroaches the upper luit value. the bandwidth of the intermediate power-law erows progressive voanarrowor. nearly to disappear in the final panel.," As the lower limit $t_1$ approaches the upper limit value, the bandwidth of the intermediate power-law grows progressively narrower, nearly to disappear in the final panel."
+ This is reasonable. because as ty approaches fy. the distribution of chum» optical depths becomes progressively narrower. eventually to approach a à-functiou.," This is reasonable, because as $t_1$ approaches $t_2$, the distribution of clump optical depths becomes progressively narrower, eventually to approach a $\delta$ -function."
+" Figure 8. shows a similar kiud of plot. but now f, is fixed at a value of 0.001. and the upper limit f» is decreased by factors of 10 from 10.000 down to 0.1."," Figure \ref{fig8} shows a similar kind of plot, but now $t_1$ is fixed at a value of 0.001, and the upper limit $t_2$ is decreased by factors of 10 from 10,000 down to 0.1."
+ As fo approaches fy. the intermediate power-law seement again narrows.," As $t_2$ approaches $t_1$, the intermediate power-law segment again narrows."
+ Conelusious from varviug the upper aud lower optical depth limits are as follows. (, Conclusions from varying the upper and lower optical depth limits are as follows. (
+a) When the ratio τοτι is near unity. the resulting SED is esseutially that of a sinele cluup. (,"a) When the ratio $t_2/t_1$ is near unity, the resulting SED is essentially that of a single clump. ("
+b) As the ratio is made large. an intermediate power-law ποσο can arise for certain values of 5. aud large ratios of fo/f4 maximize the frequency window over which this scement persists.,"b) As the ratio is made large, an intermediate power-law segment can arise for certain values of $\gamma$ , and large ratios of $t_2/t_1$ maximize the frequency window over which this segment persists."
+ And (ο) assunmiug asieuificaut power-law sceient exists. changing the individual values of fj aud fo shifts the power-law scement in frequency.," And (c) assuming a significant power-law segment exists, changing the individual values of $t_1$ and $t_2$ shifts the power-law segment in frequency."
+ Increasing το shifts the window to higher frequency. whereas decreasing its value results in : vshift to lower frequeucies.," Increasing $t_2$ shifts the window to higher frequency, whereas decreasing its value results in a shift to lower frequencies."
+ Next. we use the experience gained frou our parameter study to model the spectrun of the WC IIIT reeion W19N-D2 which exhibits an observed radio SED characterize: by a power-law index of |0.9.," Next, we use the experience gained from our parameter study to model the spectrum of the HC HII region W49N-B2 which exhibits an observed radio SED characterized by a power-law index of $+0.9$."
+ The hermal radio source W19A. first observed by. Westerhout (1958). lies at a disance of 11.1 kpc (Cavin. Moran. Rek 1992) and is composed of two main compoucuts WISA-N and W19À-S which are eoncrally referred to simply as WLON aud. W19S. With high spatial resolution. these two nail. colpoucuts rosOve lno inultiple. huuinous radio comipoueuts.," The thermal radio source W49A, first observed by Westerhout (1958), lies at a distance of 11.4 kpc (Gwinn, Moran, Reid 1992) and is composed of two main components W49A-N and W49A-S which are generally referred to simply as W49N and W49S. With high spatial resolution, these two main components resolve into multiple, luminous radio components."
+ Dreher ((1981) aid De Pree ((20WO) τεsolve W19N iuto nine or more very compact aud luminous radio-contiuuunu conpoucuts., Dreher (1984) and De Pree (2000) resolve W49N into nine or more very compact and luminous radio-continuum components.
+ Of the niue sources ideutified bv De Pree ((2060) 1 WION. seven have broad radio recombination lines (>10 kin +) aud visine spectra iu the waveleughn rauge 12 nu to 2 nuu.," Of the nine sources identified by De Pree (2000) in W49N, seven have broad radio recombination lines $\ge 40$ km $^{-1}$ ) and rising spectra in the wavelength range 13 mm to 3 mm."
+ We have selected one of the brightest of these. W19N-D2. from De Pree ((2010) to attempt to ft its SED from 13 nun to 3nua (spectral iudex of a=|0.9).," We have selected one of the brightest of these, W49N-B2, from De Pree (2000) to attempt to fit its SED from 13 mm to 3mm (spectral index of $\alpha = +0.9$)."
+ This compact. Iuninous," This compact, luminous"
+time-scale considered.,time-scale considered.
+ However. the number of mergers per unit time is independent of the time-scale used.," However, the number of mergers per unit time is independent of the time-scale used."
+ The merger rate. defined. as the number of galaxies mereing per unit time and per unit volume. which we denote as(ο). is given by: where roy is the number density of galaxies within a eiven stellar mass range.," The merger rate, defined as the number of galaxies merging per unit time and per unit volume, which we denote as, is given by: where $n_{\rm gm}$ is the number density of galaxies within a given stellar mass range."
+ Although the observational valueol τι is not well constrained ancl there are a few indications that it might not be the same for structural and pair methods (Lotzctal.200Sa:: Ixitzbichler&White 2008)). in general it varies between about 0.4 Civr and 1 Gyr (c.g. Conselice2006a:: Lotzetal. 2008b)).," Although the observational valueof $\tau_{\rm m}$ is not well constrained and there are a few indications that it might not be the same for structural and pair methods \citealt{lotz2008a}; \citealt{manfred2008}) ), in general it varies between about 0.4 Gyr and 1 Gyr (e.g., \citealt{cons2006}; \citealt{lotz2008b}) )."
+" In this work we assume two cillerent values for my. that is my,=0.4 Cyr and mm,1 Cyr. in order to take in to account at first order the possible systematies involved with comparing data with mocels."," In this work we assume two different values for $\tau_{\rm m}$, that is $\tau_{\rm m}=0.4$ Gyr and $\tau_{\rm m}=1$ Gyr, in order to take in to account at first order the possible systematics involved with comparing data with models."
+ The value of τι=0.4 Gyr is based on the sensitivity. of the CAS method. which is believed. to identify galaxies. that have undergone mergers within approximately such a scale.," The value of $\tau_{\rm m}=0.4$ Gyr is based on the sensitivity of the CAS method, which is believed to identify galaxies that have undergone mergers within approximately such a time-scale."
+ The time-scale of Gyr has been suggested by Lotzetal.(2008b) on the basis1 of results of νάνοἄνnamical simulations., The time-scale of 1 Gyr has been suggested by \citet{lotz2008b} on the basis of results of hydro-dynamical simulations.
+ Another issue to address while comparing models with simulations is the minor vs. major merger sensitivity of different methods., Another issue to address while comparing models with simulations is the minor vs. major merger sensitivity of different methods.
+ Pair fractions require. galaxies to have magnitudes within x15 of each other. but do not. provide exact information about the respective galaxy masses.," Pair fractions require galaxies to have magnitudes within $\pm 1.5$ of each other, but do not provide exact information about the respective galaxy masses."
+ Although5 it is usually assumed that the mass ratio in 5galaxy pairs is larger than about 1:4. there might be large variations from pair to pair.," Although it is usually assumed that the mass ratio in galaxy pairs is larger than about 1:4, there might be large variations from pair to pair."
+ As discussed. in Section. 2.1.. the CAS method identifies galaxies that have already. merged.," As discussed in Section \ref{sec21}, the CAS method identifies galaxies that have already merged."
+ This implies that we do not know the progenitor masses. although simulations predict that minor mergers with mass ratios 1:10 or less do not. produce significant. structural asymimetries (Llernandez-Loledoetal...2005: Conselice 200623).," This implies that we do not know the progenitor masses, although simulations predict that minor mergers with mass ratios 1:10 or less do not produce significant structural asymmetries \citealt{hernandez2005}; \citealt{cons2006}) )."
+ The limited information available suggests that the CAS method only picks out major mergers with a mass ratio of about 1:4 or greater. but does not exclude contamination from mergers with smaller mass ratio (.Josceoetal.2009).," The limited information available suggests that the CAS method only picks out major mergers with a mass ratio of about 1:4 or greater, but does not exclude contamination from mergers with smaller mass ratio \citep{jogee2009}."
+. The numerical results presented in this work use the galaxy catalogues of Bertonectal. (2007)... publicly available [rom the Millenniumwebsite!.," The numerical results presented in this work use the galaxy catalogues of \citet{bertone2007}, , publicly available from the Millennium."
+". The Millennium simulation (Springeletal.2005) uses a ACDAL cosmology with parameters Oy,=0.25. 4,=0045. h=0.73. OY=0.15. n=] and oy=0.9."," The Millennium simulation \citep{springel2005} uses a $\Lambda$ CDM cosmology with parameters $\Omega_{\rm m}=0.25$, $\Omega_{\rm b}=0.045$, $h=0.73$, $\Omega_\Lambda=0.75$, $n=1$ and $\sigma_8=0.9$."
+ The Hubble constant is paramoeterised as ify= 1005 kms ! |., The Hubble constant is parameterised as $H_{\rm 0} = 100$ $h^{-1}$ km $^{-1}$ $^{-1}$.
+ The Millennium cosmology. is slightly dillerent. [rom that assumed by the observations. but the uncertainties that may derive from this discrepancy should be negligible in comparison with the uncertainties introduced. for example. by the merging time-scale.," The Millennium cosmology is slightly different from that assumed by the observations, but the uncertainties that may derive from this discrepancy should be negligible in comparison with the uncertainties introduced, for example, by the merging time-scale."
+ For example. at the highest redshifts the ratio of volumes for the model cosmology is higher than the cosmology used in the observations.," For example, at the highest redshifts the ratio of volumes for the model cosmology is higher than the cosmology used in the observations."
+ This volume elfect only inlluences the calculation of the merger rates. and does not alfect the calculation of the merger fractions.," This volume effect only influences the calculation of the merger rates, and does not affect the calculation of the merger fractions."
+ The simulation follows the evolution of about 20 nüllion. galaxies in a region of 500 tAlpe on a side., The simulation follows the evolution of about 20 million galaxies in a region of 500 Mpc on a side.
+ The galaxy catalogues were created using a variation of he semi-analvtic model of DeLucia&Blaizot(2007).. in which supernova feedback is implemented using a dynamical reatment of galactic winds (Bertone.Stochr&White 2005).," The galaxy catalogues were created using a variation of the semi-analytic model of \citet{delucia2007}, in which supernova feedback is implemented using a dynamical treatment of galactic winds \citep{bertone2005}."
+". The model improves the treatment of galaxies with stellar masses AJ,«LOM but somewhat overpredicts he abundance of the most massive galaxies with A,>LottAL..."," The model improves the treatment of galaxies with stellar masses $M_{\star} < 10^{11}$, but somewhat overpredicts the abundance of the most massive galaxies with $M_{\star} > 10^{11}$."
+" For a detailed deseription of the ποσο, we refer the interested reader to the original paper of Bertonectal. (2007)."," For a detailed description of the model, we refer the interested reader to the original paper of \citet{bertone2007}."
+". The merger history of the simulated galaxies is recovered by [ageing"" ealaxies that have undergone mergers and by saving additional information about the time when the mergers occur.", The merger history of the simulated galaxies is recovered by flagging galaxies that have undergone mergers and by saving additional information about the time when the mergers occur.
+" In order to estimate the merger fractions and the merger rates as closely as possible to the observations. we count the number of galaxies Vy, that have merged at least once within a time-scale 74, at redshifts 2 0.0.5. 1. 1.5. 2 and 3."," In order to estimate the merger fractions and the merger rates as closely as possible to the observations, we count the number of galaxies $N_{\rm m}$ that have merged at least once within a time-scale $\tau_{\rm m}$ at redshifts $z=0$, 0.5, 1, 1.5, 2 and 3."
+ The merger fractions are then calculated as in Eq. (2)), The merger fractions are then calculated as in Eq. \ref{mergfrac}) )
+ and the merger rates as in Eq. (4)., and the merger rates as in Eq. \ref{mergerrate}) ).
+" The numerical resolution of the Millennium simulation allows us to correctly track the merging history of galaxies only for M,107n ML...", The numerical resolution of the Millennium simulation allows us to correctly track the merging history of galaxies only for $M_{\star} > 10^{9.5}$ $_{\sun}$ .
+ Accordingly.. our results are not fully reliable below this mass threshold.," Accordingly, our results are not fully reliable below this mass threshold."
+" Nonetheless. in a [ow cases we have chosen to display results for the merger rates and [fractions in the interval LO"" AL,<«107 AL: : the inability of the model to track the merger history ofgalaxies with 10"" AL,« Ὁ Mz translates in to lower predicted: values than in the ideal case where themerger history is fully accounted for."," Nonetheless, in a few cases we have chosen to display results for the merger rates and fractions in the interval $10^9$ $_{\sun}<M_{\star} < 10^{10}$ $_{\sun}$ : the inability of the model to track the merger history ofgalaxies with $10^9$ $_{\sun}<M_{\star} < 10^{9.5}$ $_{\sun}$ translates in to lower predicted values than in the ideal case where themerger history is fully accounted for."
+ Vhis ellect is certainly stronger for minor merger counts. but may also alfect major mergers.," This effect is certainly stronger for minor merger counts, but may also affect major mergers."
+of many data sets that there are artificial spikes in the photometric redshift distribution.,of many data sets that there are artificial spikes in the photometric redshift distribution.
+" These spikes may result from the particular filter/template combination, or may be due to systematic errors in object colors."," These spikes may result from the particular filter/template combination, or may be due to systematic errors in object colors."
+" For instance, if the observed galaxy colors in two closely-spaced filters are systematically too red — due to poor PSF matching or zeropoint errors — then the photometric redshift code may interpret the red colors as being due to bbreaks in the galaxy SEDs, with the effect that many objects will have artificially similar photometric redshifts."," For instance, if the observed galaxy colors in two closely-spaced filters are systematically too red — due to poor PSF matching or zeropoint errors — then the photometric redshift code may interpret the red colors as being due to breaks in the galaxy SEDs, with the effect that many objects will have artificially similar photometric redshifts."
+P(B) =const In order to make an intelligent guess about the B-dependence of 77'(B). we have to invoke our understanding of the field structure at subviscous scales.,"P(B) = In order to make an intelligent guess about the $B$ -dependence of $\tau_r^{-1}(B)$, we have to invoke our understanding of the field structure at subviscous scales."
+ The relaxation term in is due to the suppression of the velocity shear by the Lorentz back reaction., The relaxation term in is due to the suppression of the velocity shear by the Lorentz back reaction.
+" The latter can be thought of as inducing a certain magnetic component u,, of the velocity field. that counterbalances the external shear. so 7(B)αι."," The latter can be thought of as inducing a certain magnetic component $\vum$ of the velocity field that counterbalances the external shear, so $\tau_r^{-1}(B)\sim\nabla\vum$."
+" Since we are considering a viscosity-dominated regime. Vu,, should be estimated by balancing the viscous damping and the magnetic tension: vB."," Since we are considering a viscosity-dominated regime, $\nabla\vum$ should be estimated by balancing the viscous damping and the magnetic tension: ."
+" The characteristic scale of u,, cannot be smaller than the viscous scale: otherwise. u,, would be viscously damped at a shorter time scale than that of the external shear and could not provide an effective counteraction to it."," The characteristic scale of $\vum$ cannot be smaller than the viscous scale: otherwise, $\vum$ would be viscously damped at a shorter time scale than that of the external shear and could not provide an effective counteraction to it."
+ We have. therefore.," We have, therefore,."
+ We emphasizeUh that the own)above relation represents a force balance in a particular fold., We emphasize that the above relation represents a force balance in a particular fold.
+ Now. in a ¢vpical case. the folding structure would imply K~Κιν soDN Btyp.. where Bypicat~Bony d$ the typical value of the back-reacting magnetic field in the system.," Now, in a case, the folding structure would imply $K\sim\kd$, so, , where $\Btyp\sim\Brms$ is the typical value of the back-reacting magnetic field in the system."
+ This regime corresponds to what is sometimes referred to as theeffect (Chandran1998:Kinneyetal. 2000).," This regime corresponds to what is sometimes referred to as the \citep{Chandran_visc_rlx,Kinney_etal}. ."
+". Substituting the expression for 77'(B) into(76).. we find a Gaussian PDF (ef.Boldyrev2001) with Bj,~(62107. which approximately corresponds to magnetic energy equalizing with the energy of the viscous-scale eddies and accounts for the energy equipartition we have seen in our simulations."," Substituting the expression for $\tau_r^{-1}(B)$ into, we find a Gaussian PDF \citep[cf.][]{Boldyrev_alpha} with $\Brms\sim(\kappa_2\nu)^{1/2}$, which approximately corresponds to magnetic energy equalizing with the energy of the viscous-scale eddies and accounts for the energy equipartition we have seen in our simulations."
+ However. these arguments are only appropriate in application to the statistics of the values of the magnetic-field strength. Le. to the of the distribution function. (cf.Boldyrev 2001)..," However, these arguments are only appropriate in application to the statistics of the values of the magnetic-field strength, i.e., to the of the distribution function \citep[cf.][]{Boldyrev_alpha}."
+ In order to understand the(αἱ of the PDF. one must consider events. specifically. the instances (or places) where B tslarge.," In order to understand the of the PDF, one must consider events, specifically, the instances (or places) where $B$ is."
+" In the framework of the ""stretch-and-fold"" small-scale dynamo mechanism. such events can occur if magnetic field gets ""overstretched"" (for instance. because the shear has acted coherently in one direction for an atypically long time)."," In the framework of the “stretch-and-fold” small-scale dynamo mechanism, such events can occur if magnetic field gets “overstretched” (for instance, because the shear has acted coherently in one direction for an atypically long time)."
+" The local relation between the curvature and the field strength associated with it is given by(58).. whence KB~Kk,Bypic"," The local relation between the curvature and the field strength associated with it is given by, whence $KB\sim\kd\Btyp$."
+at- Inserting this into(84).. we findMEBtyp.. which. upon substitution into(76).. gives the exponential tail evidenced by the numertes.," Inserting this into, we find, which, upon substitution into, gives the exponential tail evidenced by the numerics."
+ The persistence of the kinematic curvature statistics 1n the face of nonlinear effects can also be understood in these terms., The persistence of the kinematic curvature statistics in the face of nonlinear effects can also be understood in these terms.
+" Essentially. the tail of the curvature PDF remains unaffected by the back reaction because it describes areas of anomalously large curvature (K>>K,) where. due to the anticorrelation property. the field is weak."," Essentially, the tail of the curvature PDF remains unaffected by the back reaction because it describes areas of anomalously large curvature $K\gg\kd$ ) where, due to the anticorrelation property, the field is weak."
+ On a slightly more quantitative level. we argue that the effect of the back reaction on the curvature can also be modelled by a simple nonlinear relaxation term. as in(69):: = br]] -vK.," On a slightly more quantitative level, we argue that the effect of the back reaction on the curvature can also be modelled by a simple nonlinear relaxation term, as in: = ] -."
+. Here 7:(B) is again estimated via and(58)., Here $\tau_r^{-1}(B)$ is again estimated via and.
+. The nonlinear relaxation term in is then - - vn. where n=K/K.," The nonlinear relaxation term in is then - - , where $\vn=\vK/K$."
+ With this correction. the Fokker-Planck equation for the PDF of curvature becomes KK where à 1s (LEA)a numericalS ePETP-LPD.OO0DOconstant of order unity and. as before. Kis rescaled by K..~ Κων ," With this correction, the Fokker–Planck equation for the PDF of curvature becomes _t P = K, where $\cK$ is a numerical constant of order unity and, as before, $K$ is rescaled by $K_*\sim\kd$ ."
+Itis a straightforward exercise to show that the stationary PDF is now given by P(K) 2 which has the same power tail ~K-' as its kinematic counterpart(54).," It is a straightforward exercise to show that the stationary PDF is now given by P(K) =, which has the same power tail $\sim K^{-13/7}$ as its kinematic counterpart."
+. Finally. we would like to stress the qualitative character of the ideas and results put forward in this section.," Finally, we would like to stress the qualitative character of the ideas and results put forward in this section."
+ A more quantitative nonlinear theory based on these ideas may be feasible. but is left for future work.," A more quantitative nonlinear theory based on these ideas may be feasible, but is left for future work."
+ Another important issue that requires careful quantitative treatment is the role of Ohmic diffusion., Another important issue that requires careful quantitative treatment is the role of Ohmic diffusion.
+ Based on the model of back reaction proposed here. we seem to be able to understand the nonlinear regime without including the resistive terms.," Based on the model of back reaction proposed here, we seem to be able to understand the nonlinear regime without including the resistive terms."
+" These terms arehard totreat analytically due to the usual closure problem associatedwith the diffusionoperator,", These terms arehard totreat analytically due to the usual closure problem associatedwith the diffusionoperator.
+ Numerically.wehave confirmed that," Numerically,wehave confirmed that"
+fi=| Mm above the photosphere [The photosphere is defined here as a layer with Hydrogen numberdensity 1.16»I0cm? (?)]].,$h=1$ Mm above the photosphere [The photosphere is defined here as a layer with Hydrogen numberdensity $1.16\times10^{17}$ $^{-3}$ \citep[][]{vernazza1981}] ].
+ This is the typical hard X-ray source height found i1 footpoints (??)..," This is the typical hard X-ray source height found in footpoints \citep{aschwanden_etal2002,Kontar_etal08}."
+ The energy spectrum for photons has a power law /(e)~€ with a spectral index of y. for energies betweer 3 keV and 300 keV. typical for RHESSI.," The energy spectrum for photons has a power law $I(\epsilon)\sim \epsilon^{-\gamma}$ with a spectral index of $\gamma$, for energies between $3$ keV and $300$ keV, typical for RHESSI."
+ The code accounts for the curvature of the Sun and the photons are assumed to move freely until they reach the photospheric density at a height z«=2—-y-Re. where RS=6.96x1010 em is the solar radius.," The code accounts for the curvature of the Sun and the photons are assumed to move freely until they reach the photospheric density at a height $z_{\odot}=\sqrt{R_{\odot}^{2}-x^2-y^2}-R_{\odot}$, where $R_{\odot}=6.96\times 10^{10}$ cm is the solar radius."
+ Below this level photons can be either scattered or photo-electrically absorbed., Below this level photons can be either scattered or photo-electrically absorbed.
+ Similar to previous MC simulations (??).. the Klein-Nishina cross-section for unpolarized X-ray radiation was used where e; is the initial photon energy. € is the new photon energy. Ας is the angle between the initial and new photon direction and ry=2.82x 107-Fem is the classical electron radius.," Similar to previous MC simulations \citep{BaiRamaty1978,MagdziarzZdziarski95}, the Klein-Nishina cross-section for unpolarized X-ray radiation was used where $\epsilon_0$ is the initial photon energy, $\epsilon$ is the new photon energy, $\theta_s$ is the angle between the initial and new photon direction and $r_0=2.82\times10^{-13}$ cm is the classical electron radius."
+" After a scattering. the new photon energy is just given by e=@/(1+=5(1—-cos4,))."," After a scattering, the new photon energy is just given by $\epsilon=\epsilon_0/(1+\frac{\epsilon_0}{mc^{2}}(1-\cos\theta_s))$."
+ The absorption of X-ray photons. which ts the dominant process below ~10 keV was modeled using modern solar photospherie abundances (?) and cross-sections (??) for the most important elements H. He. C. N. O. Ne. Na. Mg. Al. Si. S. CI. Ar. Ca. Cr. Fe and Ni.," The absorption of X-ray photons, which is the dominant process below $\sim 10 $ keV was modeled using modern solar photospheric abundances \citep{Asplund_etal2009}
+ and cross-sections \citep{Henke_etal1982,Balucinska-ChurchMcCammon1992}
+ for the most important elements H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe and Ni."
+" For X-ray energies >10 keV. photoelectric absorption was approximated as cten)e, (2).."," For X-ray energies $> 10 $ keV, photoelectric absorption was approximated as $\sigma_a(\epsilon_0)\sim \epsilon_0^{-3}$ \citep{MagdziarzZdziarski95}. ."
+ To account for elements with more electrons than Hydrogen. e.g. Helium. Carbon ete. Equation (1) was multiplied by 1.18.," To account for elements with more electrons than Hydrogen, e.g. Helium, Carbon etc, Equation \ref{eq:Klein-Nishina}) ) was multiplied by 1.18."
+ Our simulations differ from previous simulations (e.g.??) because of newer abundances and the inclusion of the curvature of the Sun.," Our simulations differ from previous simulations \cite[e.g.][]{BaiRamaty1978,MagdziarzZdziarski95} because of newer abundances and the inclusion of the curvature of the Sun."
+ The escaping photons are accumulated to create the brightness distribution I(x.v) over a given energy and solid angle.," The escaping photons are accumulated to create the brightness distribution $I(x,y)$ over a given energy and solid angle."
+ The total primary or reflected flux is then just an integral over the correspondirΠα» area /{ένναxdy.," The total primary or reflected flux is then just an integral over the corresponding area $\int I(x,y)dxdy$."
+ Fig., Fig.
+ laa shows the primary and escapirΠα» photon brightness distributions for a source located at the disk centre., \ref{fig1}a a shows the primary and escaping photon brightness distributions for a source located at the disk centre.
+ Similar to the previous results (2) we see that for a compact primary source of size d.=1.54. the back-scattered (albedo) photons are reflected from an area much larger than the primary source.," Similar to the previous results \citep{BaiRamaty1978} we see that for a compact primary source of size $d=1.5h$, the back-scattered (albedo) photons are reflected from an area much larger than the primary source."
+ The reflected photons change the spatial distribution of the observed photons and produce a halo around the primary source., The reflected photons change the spatial distribution of the observed photons and produce a halo around the primary source.
+ Importantly. even a primary point source will be seen as a source of finite size (Fig. 2)).," Importantly, even a primary point source will be seen as a source of finite size (Fig. \ref{fig2}) )."
+ The brightness distribution of a large primary source of d=4.5/1 is less influenced by the reflected photons but nevertheless the source will look larger than it actually ts., The brightness distribution of a large primary source of $d=4.5h$ is less influenced by the reflected photons but nevertheless the source will look larger than it actually is.
+" Using solar disk centered coordinates. the centroid position of the source (X. Y) can be found by calculating the first normalized moment of the distribution (mean) and the normalized variance of the distribution (second moment). Hereafter. following RHESSI measurements (???) we will use source sizes in terms of FWHM (Full Width Half Maximum). EWHM,,=2V2In2o,.."," Using solar disk centered coordinates, the centroid position of the source $\bar{x}$, $\bar{y}$ ) can be found by calculating the first normalized moment of the distribution (mean) and the normalized variance of the distribution (second moment), Hereafter, following RHESSI measurements \citep[][]{Kontar_etal08,dennis2009,Prato_etal2009}
+ we will use source sizes in terms of FWHM (Full Width Half Maximum), $FWHM_{x,y}=2\sqrt{2\ln{2}}\sigma_{x,y}$."
+ The scattered X-ray flux depends on the cosine of heliocentric angle of the source (µ=cos(8)) or equivalently on the position of the source at the solar disk. poo=|-G2+17)/R ," The scattered X-ray flux depends on the cosine of heliocentric angle of the source $\mu \equiv\cos (\theta)$ ) or equivalently on the position of the source at the solar disk, $\mu =\sqrt{1-(x^2+y^2)/R_{\odot}^2}$ ."
+A circular X-ray source located above the centre of the disk will produce a circular albedo patch (Fig., A circular X-ray source located above the centre of the disk will produce a circular albedo patch (Fig.
+ laa)., \ref{fig1}a a).
+ Naturally. the location of the HXR source and albedo patch will coincide at the disk centre. so albedo will not change the source position.," Naturally, the location of the HXR source and albedo patch will coincide at the disk centre, so albedo will not change the source position."
+ However. the albedo will make the source larger than it is actually is (Fig.," However, the albedo will make the source larger than it is actually is (Fig."
+ laa)., \ref{fig1}a a).
+ The albedo contribution becomes asymmetric if the source is located away from the disk centre at a given heliocentric angle ϐ (Fig., The albedo contribution becomes asymmetric if the source is located away from the disk centre at a given heliocentric angle $\theta$ (Fig.
+ Ibb-d)., \ref{fig1}b b-d).
+ Due to the spherical symmetry of the Sun. there are two distinct directions: radial - along the line connecting the centre of the Sun and the X-ray source r. and perpendicular to the radial Ρο.," Due to the spherical symmetry of the Sun, there are two distinct directions: radial - along the line connecting the centre of the Sun and the X-ray source $r$, and perpendicular to the radial $r_\perp$."
+ There ts no change in centroid position in the x».-direction for a spherically symmetric primary source., There is no change in centroid position in the $r_\perp$ -direction for a spherically symmetric primary source.
+ In the r-direction. the albedo causes a centroid shift towards the disk centre that rises from ~Oat jj=1.0 and peaks shortly before falling to - Oagain at uw=0.0.," In the $r$ -direction, the albedo causes a centroid shift towards the disk centre that rises from $\sim 0$ at $\mu=1.0$ and peaks shortly before falling to $\sim 0$ again at $\mu=0.0$."
+ Fig., Fig.
+ | also shows how the source size varies in r_ direction. with the FWHM of the source generally decreasing at lower qi.," \ref{fig1} also shows how the source size varies in $r_{\perp}$ direction, with the FWHM of the source generally decreasing at lower $\mu$."
+ In the radial direction. the FWHM of the total and primary sources decreases close to linear due to a simple projection effect.," In the radial direction, the FWHM of the total and primary sources decreases close to linear due to a simple projection effect."
+ The detailed 3D structure of the source is required before any physically meaningful predictions can be made concerning the change in source size in the radial direction. and this is beyond the scope of the paper.," The detailed 3D structure of the source is required before any physically meaningful predictions can be made concerning the change in source size in the radial direction, and this is beyond the scope of the paper."
+ Therefore. we consider the source sizes in the r_ direction and the source position in the radial direction rather than along the East-West and South-North directions.," Therefore, we consider the source sizes in the $r_{\perp}$ direction and the source position in the radial direction rather than along the East-West and South-North directions."
+ Similar to the spatially integrated albedo (?).. the shift in centroid position and the growth of the source are also energy and ji dependent.," Similar to the spatially integrated albedo \citep{Kontar_etal2006}, , the shift in centroid position and the growth of the source are also energy and $\mu$ dependent."
+ In the following. we consider the position and source size changes for various à) spectra of the primary source. b) primary source size. and c) X-ray directivity (the ratio of downward to upward emitted photons) separately.," In the following, we consider the position and source size changes for various a) spectra of the primary source, b) primary source size, and c) X-ray directivity (the ratio of downward to upward emitted photons) separately."
+ The results are summarized in Fig. 2.. (, The results are summarized in Fig. \ref{fig2}. (
+Fig. 2a-d) -,Fig. \ref{fig2}{ ) -
+ Similar to the spectral results. the albedo contribution from a smaller spectral index produces the largest shift in position and the larger total source size (Fig.," Similar to the spectral results, the albedo contribution from a smaller spectral index produces the largest shift in position and the larger total source size (Fig."
+ 2aa-d)., \ref{fig2}a a-d).
+" An isotropic source of FWHM-4.9” with the smallest modeled spectral index of y2 produces the greatest shift of ~0.5"" at u=0.5—0.6 and ~30 keV. This spectral index also produces the largest source size and has a FWHM~9.5” at =1.0. compared with the other spectral indices of y=3.4 modeled. ("," An isotropic source of $\sim 4.9''$ with the smallest modeled spectral index of $\gamma =2$ produces the greatest shift of $\sim 0.5''$ at $\mu=0.5-0.6$ and $\sim 30$ keV. This spectral index also produces the largest source size and has a $\sim 9.5''$ at $\mu=1.0$, compared with the other spectral indices of $\gamma=3,4$ modeled. ("
+Fig. 2e-h) -,Fig. \ref{fig2}{ ) -
+ For a fixed spectral index of y= 3. all primary source sizes produce the same shift in centroid position.," For a fixed spectral index of $\gamma=3$ , all primary source sizes produce the same shift in centroid position."
+ The maximum shift in position occurs at pe and ~30 keV for all sources (Fig., The maximum shift in position occurs at $\mu=0.5-0.6$ and $\sim30$ keV for all sources (Fig.
+ 2ee.g).," \ref{fig2}e e,g)."
+ Although the FWHM of the total source grows with increasing primary size. it is observed that the relative size of the total to theprimary source is smaller for a larger primary source.," Although the FWHM of the total source grows with increasing primary size, it is observed that the relative size of the total to theprimary source is smaller for a larger primary source."
+ This indicatesthat a larger primary source should have a smaller relative size, This indicatesthat a larger primary source should have a smaller relative size
+cosmic microwave background radiation. which increases stronely with redshift.,"cosmic microwave background radiation, which increases strongly with redshift."
+ This could lead to τα[ους hotspots leadingὃν to their classification as independent: racio sources (e.g. Balelbwin 1982)., This could lead to `tail-less' hotspots leading to their classification as independent radio sources (e.g. Baldwin 1982).
+ The problem would be more acute if there are no detected cores and radio jets., The problem would be more acute if there are no detected cores and radio jets.
+ The objectives of the GM observations were to investigate the possibility of detecting bridges of emission at low frequencies. and/or a radio jet. with the broader goal of developing strategies for identifying high-redshift &imnt. sources.," The objectives of the GMRT observations were to investigate the possibility of detecting bridges of emission at low frequencies, and/or a radio jet, with the broader goal of developing strategies for identifying high-redshift giant sources."
+ The GMIEE observations were mace at 333 and 617. Mllz on 2002 Aug 24 and 2003 Jul 11 respectively., The GMRT observations were made at 333 and 617 MHz on 2002 Aug 24 and 2003 Jul 11 respectively.
+" The CMICE consists of thirty 45-m antennas in an approximate ""Y shape similar to the ουν Large Array but with cach antenna in a fixed position.", The GMRT consists of thirty 45-m antennas in an approximate `Y' shape similar to the Very Large Array but with each antenna in a fixed position.
+" Twelve antennas are randomly placed: within a central 1 km by 1 km square (the “Central Square"") and the remainder form the irregularly shaped. Y (6 on each arm) over a total extent of about 25 km.", Twelve antennas are randomly placed within a central 1 km by 1 km square (the “Central Square”) and the remainder form the irregularly shaped Y (6 on each arm) over a total extent of about 25 km.
+ Further details about the array can be found at the GAIRT website alhttp://www., Further details about the array can be found at the GMRT website at.
+gmrt.ncra.tifr.res.in. Vhe observations were made in the standard fashion. with cach source observation. interspersed. with observations of the phase calibrator.," The observations were made in the standard fashion, with each source observation interspersed with observations of the phase calibrator."
+ The source was observed for about 8 hours at 333 Mllz. although a significant amount of data had to be edited out due to ionospheric disturbances.," The source was observed for about 8 hours at 333 MHz, although a significant amount of data had to be edited out due to ionospheric disturbances."
+" The observations at 61t) MllIz were made in the ""snapshot! mode with only about one hour being spent on the source.", The observations at 610 MHz were made in the `snapshot' mode with only about one hour being spent on the source.
+ The primary [lux density calibrator was 3€286 whose llux density was estimated on the VLA scale., The primary flux density calibrator was 3C286 whose flux density was estimated on the VLA scale.
+ Phe phase calibrator at 333 MlIIz was ὃς298 whose [lux density was estimated to be 29.60.38 Jy. while at 610 MlIE the phase calibrator was J1445|099 with a flux density of 2.394+0.02 Jv.," The phase calibrator at 333 MHz was 3C298 whose flux density was estimated to be $\pm$ 0.3 Jy, while at 610 MHz the phase calibrator was J1445+099 with a flux density of $\pm$ 0.02 Jy."
+ Phe data analyses were done using the Astronomical Image Processing Software (ALPS) of the National Raclio Astronomy Observatory., The data analyses were done using the Astronomical Image Processing Software (AIPS) of the National Radio Astronomy Observatory.
+ The (ΑΔΗ images of 1432]158 at 333 and 617 MlISZ are oxesented in Fig., The GMRT images of J1432+158 at 333 and 617 MHz are presented in Fig.
+ 1., 1.
+ The 333-MlIz image with an angular resolution of 11.74. 10.73 along a position angle of 24 is superimposed on the optical field. showing the radio core to » coincident. with the optical quasar.," The 333-MHz image with an angular resolution of $^{\prime\prime}$ $\times$ $^{\prime\prime}$ 3 along a position angle of $^\circ$ is superimposed on the optical field, showing the radio core to be coincident with the optical quasar."
+" The 617-MlIz image is shown convolved to the same resolution as the 333-MlIIz image with the spectral index image. a. (defined as Sx9g""). tween. 333 and 617 MllIz being shown in grav."," The 617-MHz image is shown convolved to the same resolution as the 333-MHz image with the spectral index image, $\alpha$, (defined as $\propto\nu^\alpha$ ), between 333 and 617 MHz being shown in gray."
+ Both the images show the three main components of the source. the western lobe. the weak nuclear component coincident. with he position of the optical quasar. and the eastern. lobe.," Both the images show the three main components of the source, the western lobe, the weak nuclear component coincident with the position of the optical quasar, and the eastern lobe."
+ The 33-MlIz image shows evidence of a jet-like extension owards the north-western component. but no bridge of emission is seen between the eastern hot-spot and the radio core.," The 333-MHz image shows evidence of a jet-like extension towards the north-western component, but no bridge of emission is seen between the eastern hot-spot and the radio core."
+ While the western hotspot appears to have a tail of emission. extending towards the core. no significant tail is seen in the eastern hotspot at either 333 or 617 MllIz.," While the western hotspot appears to have a tail of emission extending towards the core, no significant tail is seen in the eastern hotspot at either 333 or 617 MHz."
+ These images are consistent with the NVSS anc FIRST images which are shown in Fig., These images are consistent with the NVSS and FIRST images which are shown in Fig.
+ 2., 2.
+" The higher-resolution. FIRST image shows the core to be extended. with a deconvolved angular size of 1.760 1.""0 along a position angle of 117. consistent with the direction of the jet-like structure seen in the 333-AIz image."," The higher-resolution FIRST image shows the core to be extended, with a deconvolved angular size of $^{\prime\prime}$ $\times$ $^{\prime\prime}$ 0 along a position angle of $^\circ$, consistent with the direction of the jet-like structure seen in the 333-MHz image."
+ The observed parameters of J1432|158. from both the GAIRT images as well as from the NVSS and FIRST images αἲ 1400 MlIz are Listed in Table 1. which is arranged as follows.," The observed parameters of J1432+158, from both the GMRT images as well as from the NVSS and FIRST images at 1400 MHz are listed in Table 1, which is arranged as follows."
+ Column 1: Name of the telescope. column 2: frequeney of observations in units of MlIz. columns 3-5: the major ancl minor axes of the restoring beam in arcsec," Column 1: Name of the telescope, column 2: frequency of observations in units of MHz, columns 3-5: the major and minor axes of the restoring beam in arcsec"
+With this approach. the values of the 3D gas density and temperature profiles are computed at Wo=15 radii each.,"With this approach, the values of the 3D gas density and temperature profiles are computed at $N=15$ radii each."
+ Therefore. the total number of parameters to be determined with the maximum likelihood approach is 30.," Therefore, the total number of parameters to be determined with the maximum likelihood approach is 30."
+ In order to optimize the sampling of such a large parameter space. we adopt a Markov Chain Monte Carlo (MCMC) fitting technique (222).," In order to optimize the sampling of such a large parameter space, we adopt a Markov Chain Monte Carlo (MCMC) fitting technique \citep[][]{1993Neal,gilks1996,mackay1996}."
+ What the MCMC computes is the (marginalized) distribution of each parameter of a set. οτε (e. the values of density and temperature into each bin). for which the global (posterior) probability £’Cr). which is proportional to the likelihood function. is known at any point in the parameter space.," What the MCMC computes is the (marginalized) distribution of each parameter of a set, $x_i$ (i.e. the values of density and temperature into each bin), for which the global (posterior) probability $P(x)$, which is proportional to the likelihood function, is known at any point in the parameter space."
+ In the case of an high number of parameters or of a particularly complex ?(.r). this is quite difficult to be done analytically. or simply computationally very expensive.," In the case of an high number of parameters or of a particularly complex $P(x)$, this is quite difficult to be done analytically, or simply computationally very expensive."
+ Instead. the MCMC performs the exploration of the parameter space with a limited computational cost. thanks to an iterative Monte Carlo approach. by sampling the /?(.r) distribution.," Instead, the MCMC performs the exploration of the parameter space with a limited computational cost, thanks to an iterative Monte Carlo approach, by sampling the $P(x)$ distribution."
+ At each iteration. new values of the parameters are drawn from a symmetric proposal distribution. that in our case is a Gaussian. ln (6," At each iteration, new values of the parameters are drawn from a symmetric proposal distribution, that in our case is a Gaussian, x_i)."
+)Here .r; andr; are the entries of two vectors. having 30 components each. which represent the updated and the old values of the fitting parameters. respectively.," Here $x_i$ and $\hat x_i$ are the entries of two vectors, having 30 components each, which represent the updated and the old values of the fitting parameters, respectively."
+ The parameter à; determines the possible range for ας given .F., The parameter $\alpha_i$ determines the possible range for $x_i$ given $\hat x$.
+" After the likelihood function is computed for a new set of parameters .r. these new values are accepted or rejected with a probability (A) given by the so-called Metropolis criterion (23: Cr)where (7°) is the distribution sampled by the MCMC eq.(6)). 0;. à; a; eq.(7)). 0.1<on.«10""em ? 7. ACL) The iterative procedure described above is repeated until a suitable number of new sets of parameters are accepted in the chain (typically zz5«107)."," After the likelihood function is computed for a new set of parameters $x$, these new values are accepted or rejected with a probability (A) given by the so–called Metropolis criterion \citep{metropolis1953}:, where $P(x)$ is the distribution sampled by the MCMC \ref{eq:distr}) $\alpha_i$ $\alpha_i$ $\alpha_i$ \ref{eq:accept}) $0.1 < n_e < 10^{-6}$ $^{-3}$ $n_e^2$ $\Lambda(T)$ The iterative procedure described above is repeated until a suitable number of new sets of parameters are accepted in the chain (typically $\magcir 5\times 10^4$ )."
+ In this condition. the frequency of the occurrence in the chain of the /-th parameter or; approaches its true probability distribution. /?(.r;).," In this condition, the frequency of the occurrence in the chain of the $i$ -th parameter $x_i$ approaches its true probability distribution, $P(x_i)$."
+ Note that each parameter distribution is already marginalized over the distributions of all the other parameters., Note that each parameter distribution is already marginalized over the distributions of all the other parameters.
+ We perform the statistical analysis of the chain by using the code of the COSMOMC package (2)., We perform the statistical analysis of the chain by using the code of the COSMOMC package \citep[]{2002PhRvD..66j3511L}.
+ In addition to a complete statistical analysis of the chain. the code performs a series of convergence tests: the Gelman Rubin R statistics (2).. the Raftery Lewis test (2). and a split-test (which essentially consists in splitting the chain into 2. 3 or + parts and comparing the difference in the parameter quantiles).," In addition to a complete statistical analysis of the chain, the code performs a series of convergence tests: the Gelman Rubin R statistics \citep{gelman1992}, the Raftery Lewis test \citep{raftery1992} and a split–test (which essentially consists in splitting the chain into 2, 3 or 4 parts and comparing the difference in the parameter quantiles)."
+ We check the convergence of our result against all these three tests., We check the convergence of our result against all these three tests.
+ arderito investBrute the presence of possible systematics in the geometrical deprojection technique. we carry out a test on an ideal cluster model.," In order to investigate the presence of possible systematics in the geometrical deprojection technique, we carry out a test on an ideal cluster model."
+" We construct this model cluster by assuming the —-model for the gas density profile. with an effective polytropic equation of state to define the temperature profile: 2 -no(H T T, plan (α (spotsMoy The values of the model parameters are fixed as follows: 3=0.5. ~=1.2 for the effective polytropic index. ng=3-10em ? for central electron number density. 75,=+ keV for the central temperature. r,.=200 kpe for the core radius."," We construct this model cluster by assuming the $\beta$ –model for the gas density profile, with an effective polytropic equation of state to define the temperature profile: n_e = ( 1+ T = T_0 = T_0 ( 1+ The values of the model parameters are fixed as follows: $\beta =
+0.8$, $\gamma =1.2$ for the effective polytropic index, $n_{e0} =
+3\cdot 10^{-3}$ $^{-3}$ for central electron number density, $T_0 =
+4$ keV for the central temperature, $r_c = 200$ kpc for the core radius."
+ The “virial” radius. which represents here the largest cluster-centric distance out to which the profiles are followed. is fixed at ου.=2 Mpc.," The “virial” radius, which represents here the largest cluster-centric distance out to which the profiles are followed, is fixed at $r_{vir} = 2$ Mpc."
+ We assume the cluster to be placed at redshift .=0.1., We assume the cluster to be placed at redshift $z=0.1$.
+ We create tSZ and X-ray images of this model in X-ray and tSZ., We create tSZ and X–ray images of this model in X–ray and tSZ.
+ The maps are composed by a grid 312x512 pixels., The maps are composed by a grid 512x512 pixels.
+ The physical dimension of the pixel is ~16 kpe. which corresponds to an angular scale of + arcsec at this redshift.," The physical dimension of the pixel is $\sim 16$ kpc, which corresponds to an angular scale of $\sim 4$ arcsec at this redshift."
+" In realizing the map of X-ray surface brightness. we adopt for the cooling function the pure bremsstrahlung expression (7)=Αα)Ti)"" where Au=5-10.77 erg/s em."," In realizing the map of X–ray surface brightness, we adopt for the cooling function the pure bremsstrahlung expression $\Lambda (T) = \Lambda_0 (T/T_0)^{0.5}$ where $\Lambda_0 = 5\cdot 10^{-23}$ erg/s ${^3}$."
+ We prefer this simple formula since at this stage our main interest is to investigate the systematics of the deprojection itself. rather than the uncertainties introduced by the dependence of the X-ray emissivity on the temperature (which we expect anyway to be quite small).," We prefer this simple formula since at this stage our main interest is to investigate the systematics of the deprojection itself, rather than the uncertainties introduced by the dependence of the X–ray emissivity on the temperature (which we expect anyway to be quite small)."
+ We adopt the same binning strategy for both the ideal cluster and for the simulated objects. that we shall describe in the next Section.," We adopt the same binning strategy for both the ideal cluster and for the simulated objects, that we shall describe in the next Section."
+" The first bin is taken from r=0 to r=0.05r,;, which always corresponds to 100 Κρο in our set of simulated clusters.", The first bin is taken from $r=0$ to $r=0.05r_{vir}$ which always corresponds to 100 kpc in our set of simulated clusters.
+" Then. we compute the profile in 10 (15) bins out to Hoo G1, which are equally spaced in logarithm."," Then, we compute the profile in 10 (15) bins out to $R_{500}$ $R_{vir}$ ) which are equally spaced in logarithm."
+ This choice represents a good compromise between the needs of accurately resolving the profile and of having an adequate signal-to-noise (S/N 3) in each bin., This choice represents a good compromise between the needs of accurately resolving the profile and of having an adequate signal-to-noise (S/N 5) in each bin.
+ We point out that a proper binning criterion is important in order to get an unbiased reconstruction of the profiles., We point out that a proper binning criterion is important in order to get an unbiased reconstruction of the profiles.
+ One should keep in mind that the spherical shells are assumed to have homogeneous gas density and temperature structures. thusneglectingany internalradialgradient.," One should keep in mind that the spherical shells are assumed to have homogeneous gas density and temperature structures, thusneglectingany internalradialgradient."
+ Onthe other hand. the portion of each shell. which is projected on the corresponding ring in the image. is located at a largerradial distance from the center," Onthe other hand, the portion of each shell, which is projected on the corresponding ring in the image, is located at a largerradial distance from the center"
+"It is generally accepted that there exist two separate classes of black holes (BHs) defined by their mass ranges: stellar-mass BHs of mass 3—20Mg (???) that form through the collapse of massive stars, and supermassive BHs (SMBHs) of mass ~10°—10!M that are found in the centers of most galaxies including the Milky Way (???7)..","It is generally accepted that there exist two separate classes of black holes (BHs) defined by their mass ranges: stellar-mass BHs of mass $\sim3 - 20\, {\rm M_{\odot}}$ \citep{Bolton72, WebMur72, Casares07} that form through the collapse of massive stars, and supermassive BHs (SMBHs) of mass $\sim10^6 - 10^{10}\, {\rm M_{\odot}}$ that are found in the centers of most galaxies including the Milky Way \citep{korm, merritt01, gz2003, miller04}."
+" However, this leaves a gap in the mass range from ~10?—10*Mc which in recent years seems to have been filled by tentative evidence for intermediate-mass black holes (IMBHs) (??).."," However, this leaves a gap in the mass range from $\sim10^2 - 10^4\, {\rm
+M_{\odot}}$ which in recent years seems to have been filled by tentative evidence for intermediate-mass black holes (IMBHs) \citep{zwart99, Grin01}."
+" This evidence consists of dynamical measurements (???),, detection of ultraluminous X-ray sources (ULX) found off-center in galaxies (?),, the anomalously high mass-to-light ratio observed in the centers of some globular clusters (7?)| and the mass segregation quenching in the cores of"," This evidence consists of dynamical measurements \citep{Gebhardt02, gerssen02,
+Van02}, detection of ultraluminous X-ray sources (ULX) found off-center in galaxies \citep{miller04}, the anomalously high mass-to-light ratio observed in the centers of some globular clusters \citep{miller04} and the mass segregation quenching in the cores of"
+with Eq.,with Eq.
+ 1 is that the emission height and the fraction of the polar cap which is active is independent of the pulsar period (e.g. 23)., \ref{EqH} is that the emission height and the fraction of the polar cap which is active is independent of the pulsar period (e.g. \citealt{mr02a}) ).
+ 7. analvsed. published: values for à of several hundred pulsars. showed. they are inconsistent with a random a distribution and concluded that à decreases on a time-scale of ~10* vr.," \cite{tm98} analysed published values for $\alpha$ of several hundred pulsars, showed they are inconsistent with a random $\alpha$ distribution and concluded that $\alpha$ decreases on a time-scale of $\sim10^7$ yr."
+ In contrast. ? concluded that the o distribution is random. provided that the bean was compressed in the alitudinal direction.," In contrast, \cite{mck93} concluded that the $\alpha$ distribution is random, provided that the beam was compressed in the latitudinal direction."
+ In this paper. the issue of beam evolution is approached rom a cillerent angle.," In this paper, the issue of beam evolution is approached from a different angle."
+ We do not rely on polarization data or a p correlation to determine à and 2., We do not rely on polarization data or a $\rho$ correlation to determine $\alpha$ and $\beta$.
+ Rather. we will construct a bean moclel based on the observed. fraction of »ulsars with interpulses and their period. distribution and he observed £2Nó plane is used directly.," Rather, we will construct a beam model based on the observed fraction of pulsars with interpulses and their period distribution and the observed $P-\Delta\phi$ plane is used directly."
+ The interpulse »opulation. the pulse width. measurements and the mocel are described. in sections 2. 3 and 4 respectively.," The interpulse population, the pulse width measurements and the model are described in sections 2, 3 and 4 respectively."
+ The results are presented in section 5 and their implications are discussed. section 6., The results are presented in section 5 and their implications are discussed section 6.
+ The population of pulsars with interpulses is a 1powerfu probe of pulsar beam properties., The population of pulsars with interpulses is a powerful probe of pulsar beam properties.
+ In. the case where an interpulse is seen. with a separation from the main pulse of 1801 in rotational phase. it implies that à must be ~90° and therefore gives à good. count of how many orthogona rotators there are in the population.," In the case where an interpulse is seen, with a separation from the main pulse of $\sim180\degr$ in rotational phase, it implies that $\alpha$ must be $\sim90\degr$ and therefore gives a good count of how many orthogonal rotators there are in the population."
+ We therefore searche he literature to obtain a complete census of the interpulse population., We therefore searched the literature to obtain a complete census of the interpulse population.
+ For this search. we excluded: all millisccone »ulsars and pulsars in eglobular clusters. because the opening angle of the beams of milli-seconcd pulsars are believed to rave a different £2 dependence to that of normal. pulsars (c.g. ?)) and the values for the spin period cerivative (P) of globular cluster pulsars are contaminated by their acceleration in the gravitational Ποιά of the cluster.," For this search, we excluded all millisecond pulsars and pulsars in globular clusters, because the opening angle of the beams of milli-second pulsars are believed to have a different $P$ dependence to that of normal pulsars (e.g. \citealt{kxl+98}) ) and the values for the spin period derivative $\dot{P}$ ) of globular cluster pulsars are contaminated by their acceleration in the gravitational field of the cluster."
+ We started with the catalogue of “Vavlor et. al. (, We started with the catalogue of Taylor et al. (
+1993). which abulatec 14 interpulse pulsars out of a total of 527 objects.,1993) which tabulated 14 interpulse pulsars out of a total of 527 objects.
+ We then examined. all pulse profiles in the major surveys conducted since that time., We then examined all pulse profiles in the major surveys conducted since that time.
+ ‘Table 1 lists the relevant papers. the number of pulsars reported. and the interpulses detected.," Table \ref{TableSurveys} lists the relevant papers, the number of pulsars reported and the interpulses detected."
+ Table 2/— lists the »opulation of pulsars with interpulses., Table \ref{TableInterpulses} lists the population of pulsars with interpulses.
+ The table includes 5 weak interpulses not. previously. detected., The table includes 3 weak interpulses not previously detected.
+ Their. profiles will be presented in a forthcoming publication (?).., Their profiles will be presented in a forthcoming publication \citep{wj08b}.
+ In total here are 27 pulsars with interpulses from. a total sample of 1487 pulsars. i.c. of the population.," In total there are 27 pulsars with interpulses from a total sample of 1487 pulsars, i.e. of the population."
+ We note that he List should not be considered as complete., We note that the list should not be considered as complete.
+ Some objects in the list mav not be orthogonal rotators but are rather aligned rotators with wide beams (see the debate for PSRs 0950|05 and. D1929|10 in ? for example)., Some objects in the list may not be orthogonal rotators but are rather aligned rotators with wide beams (see the debate for PSRs B0950+08 and B1929+10 in \citealt{ew01} for example).
+ On the other rand we may have missed. some interpulse objects because he flux in the interpulse is too weak to be detected., On the other hand we may have missed some interpulse objects because the flux in the interpulse is too weak to be detected.
+ Η the a distribution of pulsars is random. then of he order of of the pulsars can be expected. to. have an interpulse (e.g. 2)).," If the $\alpha$ distribution of pulsars is random, then of the order of of the pulsars can be expected to have an interpulse (e.g. \citealt{gh96}) )."
+ The measured. percentage is lower. indicating a potential problem for such a model.," The measured percentage is lower, indicating a potential problem for such a model."
+ Not only is the percentage of pulsars with interpulses an important clue for beam models. more important still is their period distribution.," Not only is the percentage of pulsars with interpulses an important clue for beam models, more important still is their period distribution."
+ This distribution is shown in Fie., This distribution is shown in Fig.
+ 1l as a cumulative distribution (thick solid. histogram)., \ref{Fig_ip_period} as a cumulative distribution (thick solid histogram).
+ The distribution indicates the fraction of pulsars with interpulses y which have a period less than or., The distribution indicates the fraction of pulsars with interpulses $y$ which have a period less than $x$.
+ Compared with the period. distribution. of all normal (i.e. non-millisecond) pulsars (lowest thick curve of Fig. 1)), Compared with the period distribution of all normal (i.e. non-millisecond) pulsars (lowest thick curve of Fig. \ref{Fig_ip_period}) )
+ there are relatively many more short period pulsars with interpulses., there are relatively many more short period pulsars with interpulses.
+ In this paper we will trv to construct a ecometrical mocel which can account, In this paper we will try to construct a geometrical model which can account
+spectrumm. which we use to determine spectroscopic stellar parameters.,"m, which we use to determine spectroscopic stellar parameters."
+estimated as a fraction of the integrated tas in the wavelength rauge 1120 AA.,estimated as a fraction of the integrated flux in the wavelength range $1420 - 1470$ .
+ The Daliner continuum enission contributes approximately 1.6+0.7 he Fe emissiou amounts to 1.7£0.1 Iu spite of this mall contributions. the estimate of the Fe line eissiou. improves especially the ueasuremients of Ngn|ATT50 and lines such as nA1610 near the AT600 feature (Laor et 1499L: Vestereaard Wilkes 2001).," The Balmer continuum emission contributes approximately $1.6\pm 0.7$ the Fe emission amounts to $1.7\pm 0.4$ In spite of this small contributions, the estimate of the Fe line emission improves especially the measurements of $\lambda 1750$ and lines such as $\lambda 1640$ near the $\lambda 1600$ feature (Laor et 1994; Vestergaard Wilkes 2001)."
+ The C1IvA1519 line profile was fitted with a broad and narrow Curs component., The $\lambda 1549$ line profile was fitted with a broad and narrow Gaussian component.
+ The approach to recoustruct the oeission line profiles with two Cures; compouecuts was chosen to measure the integrated line flux: however. each individual componcut has no plhvsical meaning bv itself.," The approach to reconstruct the emission line profiles with two Gaussian components was chosen to measure the integrated line flux; however, each individual component has no physical meaning by itself."
+ These components lave been used as a template to measure the other cuaission line fluxes., These components have been used as a template to measure the other emission line fluxes.
+ In using this approach to fit other Cluission lines. the widths of the broad aud narrow component were fixed in velocity space while their streneths were allowed to vary indepeudently.," In using this approach to fit other emission lines, the widths of the broad and narrow component were fixed in velocity space while their strengths were allowed to vary independently."
+ Furthermore. shüfts im velocity. space of cach component were restricted to a range of less than a ew * with respect to CIVALSLO.," Furthermore, shifts in velocity space of each component were restricted to a range of less than a few $^{-1}$ with respect to $\lambda 1549$."
+ Using he components ofthe IvA1519 eiission liue as cluplates is particularly iuportaut for measuring NVAL2LO aud HWAL6LO because they are blended with other emission lines., Using the components ofthe $\lambda 1549$ emission line as templates is particularly important for measuring $\lambda 1240$ and $\lambda 1640$ because they are blended with other emission lines.
+" Furthermore. curploving he line profile as a template provides iieasurements of importaut weak lines like Nün|A1750 aud NAVJATI86 which are usually difficult to measure,"," Furthermore, employing the line profile as a template provides measurements of important weak lines like $\lambda 1750$ and $\lambda 1486$ which are usually difficult to measure."
+ This template-fitting approach is well justified because IvÀ1519. VAL2LO. and WA1610 are all hieh ionization lines (IIIL).," This template-fitting approach is well justified because $\lambda 1549$, $\lambda 1240$, and $\lambda 1640$ are all high ionization lines (HIL)."
+ Figure 1 show typical examples of the debleudiug of the Lva1216 - NvAI210. CI1VA1519 - Πομλίσιο- Orij]AT663. and HJAT750 enissiou line profile complexes. respectively.," Figure 1 show typical examples of the deblending of the $\alpha 1216$ - $\lambda 1240$, $\lambda 1549$ - $\lambda 1640$ - $\lambda 1663$, and $\lambda 1750$ emission line profile complexes, respectively."
+ The measurement of the IV|ATI86. eiission line flux is severely affected by the blue wing of the broad ccomponeut., The measurement of the $\lambda 1486$ emission line flux is severely affected by the blue wing of the broad component.
+ Particularly. for quasars with broad cinission liue profiles. the Iv|AlI8SG line tends to show a low contrast to the outer part of the CALSl9 line profile (see Dietrich Taman 2003. in prep.," Particularly, for quasars with broad emission line profiles, the $\lambda 1486$ line tends to show a low contrast to the outer part of the $\lambda 1549$ line profile (see Dietrich Hamann 2003, in prep."
+ for further discussion)., for further discussion).
+ The v1A1031 cluission line dux has been corrected for Lyo fores absorption shortwiud of the Lye oenüssion line., The $\lambda 1034$ emission line flux has been corrected for $\alpha $ forest absorption shortward of the $\alpha$ emission line.
+" For this correction we assumed that the quasars show an iutrinsic unabsorbed coutimmiun slope of a=146 CF,x9"") for Ax1200 following Telfer et ((2002)."," For this correction we assumed that the quasars show an intrinsic unabsorbed continuum slope of $\alpha = -1.76$ $F_\nu \propto \nu^\alpha$ ) for $\lambda \leq 1200$, following Telfer et (2002)."
+ Provided tha the same fraction of the contimmun aud VIALO3 chussion line flux were absorbed. we estimated a corresponding correction factor.," Provided that the same fraction of the continuum and $\lambda 1034$ emission line flux were absorbed, we estimated a corresponding correction factor."
+ Theintegrate VIALO31 flux was corrected by this factor. which varied fron l.l? to 2.77. with an average of 1.750.12.," Theintegrated $\lambda 1034$ flux was corrected by this factor, which varied from 1.17 to 2.77, with an average of $1.75 \pm 0.42$ ."
+ The uncertainties of the flux measurements were estimated from the iulti-component line fi using the scaled CIAL19 line profile to obtain a luininnun X? of the fit., The uncertainties of the flux measurements were estimated from the multi-component line fit using the scaled $\lambda 1549$ line profile to obtain a minimum $\chi^2$ of the fit.
+ For the strouecr lines like Lyal2l6. NvAI210. SilvAllo2. CivaAls19. and A1909 the errors are of the order of ~10 These errors do not take iuto account the uncertainties introduced by the placemieut of the coutiuuuan.," For the stronger lines like $\alpha 1216$, $\lambda 1240$, $\lambda 1402$, $\lambda 1549$, and $\lambda 1909$ the errors are of the order of $\sim 10$ These errors do not take into account the uncertainties introduced by the placement of the continuum."
+ While the streusth of strong cussion lines like IVA1519 is not chanecd significantly. the emission line fux of weaker lines like Niv|ALLS6 can be uuderestimated by a factor of as much as —2 (Dietrich Taman 2003. in prep.).," While the strength of strong emission lines like $\lambda 1549$ is not changed significantly, the emission line flux of weaker lines like $\lambda 1486$ can be underestimated by a factor of as much as $\sim 2$ (Dietrich Hamann 2003, in prep.)."
+ We calculated. cussion line ratios relating uitrogen lines with lines of helimmm. oxveen. aud carbon to derive the chemical composition of the BELR eas at hieh redshifts.," We calculated emission line ratios relating nitrogen lines with lines of helium, oxygen, and carbon to derive the chemical composition of the BELR gas at high redshifts."
+ These line ratios are used to estimate the chemical abundances cluploving the results of Wamaun et ((2002)., These line ratios are used to estimate the chemical abundances employing the results of Hamann et (2002).
+ They studied in detail the dependence of emission line ratios from the eas metallicity aud the shape of the ionizing continuum., They studied in detail the dependence of emission line ratios from the gas metallicity and the shape of the ionizing continuum.
+" For several mctallicities and continuum shapes. they calculated evids of photoionization models spanning a wide range of density. &,. aud coutimmiun streneth. oy. sine CLOUDY (Ferland et 11998)."," For several metallicities and continuum shapes, they calculated grids of photoionization models spanning a wide range of density, $n_e$, and continuum strength, $\phi _H$, using CLOUDY (Ferland et 1998)."
+ The metallicity was varied from Z/Z..=0.2 to 10 with all of the metals scaled in solar ratios. except οx Z.," The metallicity was varied from $Z/Z_\odot = 0.2$ to $10$ with all of the metals scaled in solar ratios, except $N/O \propto Z$ ."
+ Three different input contiuua were used a broken power-law coutiuuumn with an UV buup (Mathews Ferland 1987). a single power-law contimmun with a= l. aud a segmented power-law that providesthe best match to recent observations (Zheng et 11997: Laor ct 11997).," Three different input continua were used — a broken power-law continuum with an UV bump (Mathews Ferland 1987), a single power-law continuum with $\alpha = -1$ , and a segmented power-law that providesthe best match to recent observations (Zheng et 1997; Laor et 1997)."
+Equations 13. and 11. present a new picture of the stochastic evolution of the binarys eccentricity.,Equations \ref{eqGofx} and \ref{eqDiffeoft} present a new picture of the stochastic evolution of the binary's eccentricity.
+ Often the evolution of a random variable is characterized by Drowniau motion. m which the distribution of the radon variable is set by the lone terii accumulation of many small perturbations.," Often the evolution of a random variable is characterized by Brownian motion, in which the distribution of the random variable is set by the long term accumulation of many small perturbations."
+" The typical value of such a variable erows as the square-root of tine (written V2x£772), aud the probability of finding the svstem very far away from the typical value is exponcutially low."," The typical value of such a variable grows as the square-root of time (written $\sqrt{\langle x^2 \rangle} \propto t^{1/2}$ ), and the probability of finding the system very far away from the typical value is exponentially low."
+ The ecceutricity of the binary evolves differeutly., The eccentricity of the binary evolves differently.
+ The probability of finding the binary with an eccentricity larger than ο) oulv diminishes as a power law (equation 13))., The probability of finding the binary with an eccentricity larger than $e_c(t)$ only diminishes as a power law (equation \ref{eqGofx}) ).
+ Physically. this reflects the probability that the binary received a sinele large perturbation to that state.," Physically, this reflects the probability that the binary received a single large perturbation to that state."
+ The characteristic eccentricity. ~ο) corresponds to the size of the perturbation that occurs with a frequency of about L/f.," The characteristic eccentricity, $\sim e_c(t)$ corresponds to the size of the perturbation that occurs with a frequency of about $1/t$."
+" The linear erowth of ¢,.(¢) demonstrated by equation Ll reveals that the eccentricity of the binary docs not reflect the accumulation of many siuall perturbations. but the single largest perturbation occuring in its history."," The linear growth of $e_c(t)$ demonstrated by equation \ref{eqDiffeoft} reveals that the eccentricity of the binary does not reflect the accumulation of many small perturbations, but the single largest perturbation occurring in its history."
+" This kind of raudonm walk is called a ""Léóvvy flight” (?)..", This kind of random walk is called a “Lévvy flight” \citep{SZF95}.
+ The same analysis applies to the changes inaugulur momeutum of the binary., The same analysis applies to the changes inangular momentum of the binary.
+ Since [Ai]~|Ae]|. it follows that pU)~ple’).," Since $|\Delta \vec i| \sim |\Delta \vec e|$, it follows that $p(i') \sim p(e')$."
+ The evolution of inclination differs oulv in the coefficients that depend on the ecoumietrical configuration of the eucouuter., The evolution of inclination differs only in the coefficients that depend on the geometrical configuration of the encounter.
+ The calculation of the coefficients is described in the Appendix., The calculation of the coefficients is described in the Appendix.
+ The sclfsimiular distribution shape is a function of the dimensionless variable //7.(f). where 4(0) is the time-depeudent characteristic inclination.," The self-similar distribution shape is a function of the dimensionless variable $i/i_c(t)$, where $i_c(t)$ is the time-dependent characteristic inclination."
+" The following equation describes the evolution of /.(f): where we have used 7; to distinguish the timescale at which the inclination of the binary is damped. and (Cj)=0.75. the average of the angular terms im equation ὃν, "," The following equation describes the evolution of $i_c(t)$: where we have used $\tau_{d,i}$ to distinguish the timescale at which the inclination of the binary is damped, and $ \langle C_i \rangle =
+0.75$, the average of the angular terms in equation \ref{eqDeltah}. ."
+"The inclination is always measured relative to the orbital plane at f—ο,", The inclination is always measured relative to the orbital plane at $t=0$.
+ The distribution eiven by equation 13. then describes the probability of the binary being inclined by /=r(f) relative to its original orbital plane., The distribution given by equation \ref{eqGofx} then describes the probability of the binary being inclined by $i=x~ i_c(t)$ relative to its original orbital plane.
+ For many plivsical applications we must cousider a rangeof perturbing masses and velocities aud the effects of collisious onto the binary., For many physical applications we must consider a rangeof perturbing masses and velocities and the effects of collisions onto the binary.
+ In the siuele mass case discussed iu section 3.1.. the imteraction frequency ple) is set bv the likelihood that the binary eucounters a perturber at the impact parameter that causes such a change of €.," In the single mass case discussed in section \ref{secBEecc}, the interaction frequency $p(e')$ is set by the likelihood that the binary encounters a perturber at the impact parameter that causes such a change of $e'$."
+ For perturbers that have differeut masses. the chance of expericncing a perturbation of magnitude ο depends on the combined Likelihood that the perturber has the required mipact parameter and the required mass to excite such a change.," For perturbers that have different masses, the chance of experiencing a perturbation of magnitude $e'$ depends on the combined likelihood that the perturber has the required impact parameter and the required mass to excite such a change."
+ To extend our analysis we set up several pieces of notation., To extend our analysis we set up several pieces of notation.
+" Assunmüng that the mass aud velocity distributions are independent. we cousider Εν.ον)=FrelepjFi,(in,)."," Assuming that the mass and velocity distributions are independent, we consider ${\cal F}(m_p,v_p) = {\cal F}_v(v_p) {\cal F}_m(m_p)$."
+ We restrict our analysis to velocity distributious with a characteristic value. ey. such as a Gaussian distribution.," We restrict our analysis to velocity distributions with a characteristic value, $v_0$ , such as a Gaussian distribution."
+" We consider systems with differential mass spectra characterized by a power law: Jon)x valid frou a WAI Wass yy, tO a WANT sagax."," We consider systems with differential mass spectra characterized by a power law: ${\cal
+ F}_m(m_p) \propto m_p^{-\gamma}$, valid from a minimum mass $m_{\rm
+ min}$ to a maximum $m_{\rm max}$."
+" These functions are consistent with conditions in the m,I&uiper belt. where a power law mass spectrmm aud roughly Caussian velocity spectrmm are observed (?).."," These functions are consistent with conditions in the Kuiper belt, where a power law mass spectrum and roughly Gaussian velocity spectrum are observed \citep{LJ02}."
+ We define the differential mass spectra by where sg is the umber density of bodies larger than mass 9., We define the differential mass spectrum by where $n_0$ is the number density of bodies larger than mass $m_0$.
+ In the literature the differential size spectrum of Iuiper belt objects is characterized as a power law in radius with index q: this is related to our iudex by 5=(gy|24/3.," In the literature the differential size spectrum of Kuiper belt objects is characterized as a power law in radius with index $q$; this is related to our index by $\gamma =
+(q+2)/3$."
+ Iu this section we discuss the ple’) aud pt) that result from several values of 5., In this section we discuss the $p(e')$ and $p(i')$ that result from several values of $\gamma$.
+ The total mass deusitv of perturbers for 5<2 is dominated by the perturbers with the largest mass. nugas," The total mass density of perturbers for $\gamma < 2$ is dominated by the perturbers with the largest mass, $m_{\rm max}$."
+ While perturbations of size e are excited by all of the perturbers. the most likely perturber to cause a perturbation of this streugth is the largest mass perturber.," While perturbations of size $e'$ are excited by all of the perturbers, the most likely perturber to cause a perturbation of this strength is the largest mass perturber."
+ The dvnamics of the binary are then the same as described in section2.1. with Hy=Max., The dynamics of the binary are then the same as described in section\ref{secBEecc} with $m_p=m_{\rm max}$.
+ The power law of ple’)xeὃς based on distant cucouuters. is valid up to the ceceutricity excited by a perturbor of mass nhüjax interacting at à b~ry. or for 6!«Xοmp)(esf0s) (equation 7)).," The power law of $p(e') \propto e'^{-3}$, based on distant encounters, is valid up to the eccentricity excited by a perturber of mass $m_{\rm max}$ interacting at a $b \sim r_b$, or for $e' \ll (m_{\rm
+ max}/m_b)(v_b/v_p)$ (equation \ref{eqDeltae}) )."
+ It is necessary ouly to know the total mass deusitv p of the perturbing sw in order to caleulate the excitation frequency in this scenario. even by equation 11..," It is necessary only to know the total mass density $\rho$ of the perturbing swarm in order to calculate the excitation frequency in this scenario, given by equation \ref{eqPofE}."
+ The powerlaw 5=2 describes a special mass distribution where the frequency of encountenrues the few large perturbers at large impact paraieters is the same as cucounterine the more abundant sialler perturbers at smaller iurpact parameters., The powerlaw $\gamma=2$ describes a special mass distribution where the frequency of encountering the few large perturbers at large impact parameters is the same as encountering the more abundant smaller perturbers at smaller impact parameters.
+ Thus cach logavithimic interval in impact parameter coutributes the same amount to the frequency of perturbations by e. ple.," Thus each logarithmic interval in impact parameter contributes the same amount to the frequency of perturbations by $e'$, $p(e')$."
+ The upper limit of impact parameters that cau coutribute to excitations of a eivou c. however. is given by the maxiniun mass perturber.," The upper limit of impact parameters that can contribute to excitations of a given $e'$ , however, is given by the maximum mass perturber."
+ The total range of contributing imipact parametersthen diminishes as € approaches the eccentricity caused by the largest perturber interacting with b~ ry. etu=GnΕΠΗ)(ep! 0o).," The total range of contributing impact parametersthen diminishes as $e'$ approaches the eccentricity caused by the largest perturber interacting with $b \sim r_b$ , $e'_{\rm max}\equiv (m_{\rm
+ max}/m_b)(v_b/v_0)$ ."
+ Mathematically this behavior is determined by the iutegral of equation 9.. which vields an excitation frequency of:," Mathematically this behavior is determined by the integral of equation \ref{eqRofe},, which yields an excitation frequency of:"
+Screen is centered at around £2.139770.b.=—1720.,"Screen is centered at around $\ell = 139\fdg70, b = -1\fdg20$."
+ There is no counterpart in the 7 map (see Fig. 9).," There is no counterpart in the $I$ map (see Fig. ),"
+ thus the thermal electron density must be very low., thus the thermal electron density must be very low.
+ Polarization observations at other wavelengths are needed to analyze this feature in some detail., Polarization observations at other wavelengths are needed to analyze this feature in some detail.
+ Also the small objects at £=139795.b—2:05 and at ἐξ139220.b.=—3:00 were found to be thermal (Gao et al..," Also the small objects at $\ell = 139\fdg95, b = -2\fdg05$ and at $\ell = 139\fdg20, b = -3\fdg00$ were found to be thermal (Gao et al.,"
+ in prep.), in prep.)
+ and act as Faraday Screens., and act as Faraday Screens.
+ They also can be clearly identified in the PA map (Fig. 9)., They also can be clearly identified in the $PA$ map (Fig. ).
+ G146.4-3.0 is a large Faraday Screen with a diameter of approximately 3°3. centered at /=1640.—3:00.," G146.4-3.0 is a large Faraday Screen with a diameter of approximately $3\fdg3$, centered at $\ell = 146\fdg40, b = -3\fdg00$."
+ This structure shows highly polarized emission in the original PI map at 26 em and becomes depolarized after large-scale polarized emission ts added., This structure shows highly polarized emission in the original $PI$ map at $\lambda$ 6 cm and becomes depolarized after large-scale polarized emission is added.
+ No counterpart can be found in the / map (see Fig. 13)., No counterpart can be found in the $I$ map (see Fig. ).
+ The Ha intensity in this region is in general low and does not show any excess related to this Faraday Screen., The $\alpha$ intensity in this region is in general low and does not show any excess related to this Faraday Screen.
+ A Faraday Screen model fit (Fig. 14), A Faraday Screen model fit (Fig. )
+ results inan average RM«s for the central area of 1° diameter of — 140220 rad m., results inan average $RM_{FS}$ for the central area of $\degr$ diameter of $-140\pm$ 20 rad $^{-2}$ .
+ 26% of total PI in this area originates in front of the Faraday Screen forf = 0.97., 26% of total $PI$ in this area originates in front of the Faraday Screen for $\mathit{f}$ = 0.97.
+ The RM value tis not exceptionally high. but the scatter across the Faraday Screen is large enough to make the object invisible in the 221 em polarizatio survey by Landecker et al. (," The $RM$ value is not exceptionally high, but the scatter across the Faraday Screen is large enough to make the object invisible in the $\lambda$ 21 cm polarization survey by Landecker et al. ("
+2010. submitted). although their survey only covers the northern area of the Faraday Screen.,"2010, submitted), although their survey only covers the northern area of the Faraday Screen."
+ The distance to this prominent Faraday Screen in the 26 cm survey Is not clear., The distance to this prominent Faraday Screen in the $\lambda$ 6 cm survey is not clear.
+" To derive 7, by its free-free £M we used the 3c level of the 216 em / map. means about 1.5 mK Ty. as a brightness temperature upper limit."," To derive $n_{e}$ by its free-free $EM$ we used the $\sigma$ level of the $\lambda$ 6 cm $I$ map, means about 1.5 mK $\rm T_{B}$, as a brightness temperature upper limit."
+" The fitted central By and n, are estimated and shown in Fig.", The fitted central $B_{\parallel}$ and $n_{e}$ are estimated and shown in Fig.
+ as a function of distance., as a function of distance.
+" Note that 2, is always an upper limit. while Bj has to be taken as minimum."," Note that $n_{e}$ is always an upper limit, while $B_{\parallel}$ has to be taken as minimum."
+ The foreground polarized emission of about 26% is small compared to the fraction of about 70% obtained for the LBNe in the Perseus arm (see Sect., The foreground polarized emission of about 26% is small compared to the fraction of about 70% obtained for the LBNe in the Perseus arm (see Sect.
+ 3.4.3)., 3.4.3).
+ Thus the distance to G146.4-3.0 should be small., Thus the distance to G146.4-3.0 should be small.
+ Assuming the polarized emissivity along the line of sight to be the same as to the Perseus LBNe of about 3.4 mK kpe7!. we estimate the distance toFaraday Screen G146.4-3.0 as about 690 pe. which implies a diameter of the Faraday Sereen of about 40 pe.," Assuming the polarized emissivity along the line of sight to be the same as to the Perseus LBNe of about 3.4 mK $^{-1}$, we estimate the distance toFaraday Screen G146.4-3.0 as about 690 pc, which implies a diameter of the Faraday Screen of about 40 pc."
+" Then Bj for its central area is about —8.6 4G and zi, is about 0.5 em.", Then $B_{\parallel}$ for its central area is about $-8.6~\mu$ G and $n_{e}$ is about 0.5 $^{-3}$.
+ However. the local emissivity is known to be two to three times larger than the average emissivity at 2 kpe distance(?).," However, the local emissivity is known to be two to three times larger than the average emissivity at 2 kpc distance."
+ This will reduce the distance and the size of the Faraday Screen accordingly., This will reduce the distance and the size of the Faraday Screen accordingly.
+ For a distance of 280 pe. its size reduces to about 16 pe. 7 increases to about 0.8 em? and By to 213.5μα. re-analyzed the NVSS polarization data.," For a distance of 280 pc, its size reduces to about 16 pc, $n_{e}$ increases to about 0.8 $^{-3}$ and $B_{\parallel}$ to $-13.5~\mu$ G. re-analyzed the NVSS polarization data."
+ RMs for 37543 polarized radio sources were derived., $RM$ s for 37 543 polarized radio sources were derived.
+ We examine our Faraday Screen model resultby checking the RMs in the area of Fig., We examine our Faraday Screen model resultby checking the $RM$ s in the area of Fig.
+13. Two sources are located within the area of the Faraday Screen., Two sources are located within the area of the Faraday Screen.
+ The RMs of the two sources £=146262.b.—2269 and £=146°63.6-3X81 are —151.1:8.2 rad m and —221.948.4 rad m7. respectively.," The $RM$ s of the two sources $\ell = 146\fdg62, b = -2\fdg69$ and $\ell = 146\fdg63, b = -3\fdg81$ are $-151.1\pm$ 8.2 rad $^{-2}$ and $-221.9\pm$ 8.4 rad $^{-2}$ , respectively."
+ For another source at /145761.5b.=—2:9 reported a RM value of 23384515 rad mto from the CGPS. which is the most excessive AM value.," For another source at $\ell = 145\fdg61, b = -2\fdg9$ reported a $RM$ value of $-338\pm$ 15 rad $^{-2}$ from the CGPS, which is the most excessive $RM$ value."
+ Outside the Faraday Sereen area list RMs for 15 sources with an average RM= —75.7430.4 rad m., Outside the Faraday Screen area list $RM$ s for 15 sources with an average $RM = -75.7\pm$ 30.4 rad $^{-2}$.
+ Despite significant scatter the three sources show excessive negative RMs. which seem to beattributed to G146.4-3.0.," Despite significant scatter the three sources show excessive negative $RM$ s, which seem to beattributed to G146.4-3.0."
+ Two coinciding magnetic bubbles of different sizes were identified in the area £ around 165° by from polarization observations with about 1 resolution at 221 em with the DRAO synthesis telescope., Two coinciding magnetic bubbles of different sizes were identified in the area $\ell$ around $165\degr$ by from polarization observations with about $\arcmin$ resolution at $\lambda$ 21 cm with the DRAO synthesis telescope.
+ These bubbles were also seen in the Effelsberg 1.4 GHz polarization data at 9/4resolution., These bubbles were also seen in the Effelsberg 1.4 GHz polarization data at $\farcm4$resolution.
+ The smaller bubble extends from £ 2 164° to 16775 and —2° to 2° in b. while the larger one has about the same projected centre but is approximately 9° in size.," The smaller bubble extends from $\ell$ = $\degr$ to $167\fdg5$ and $-2\degr$ to $\degr$ in $b$ , while the larger one has about the same projected centre but is approximately $\degr$ in size."
+ At 16 em thetwo bubbles become very faint., At $\lambda$ 6 cm thetwo bubbles become very faint.
+ The 221 em map was limited to b= —37. while," The $\lambda$ 21 cm map was limited to $b = -3\degr$ , while"
+"to fall (see, e.g., Fig.","to fall (see, e.g., Fig."
+" 1 in Popielskietal.(2000),, and Fig."," 1 in \citet{po00}, and Fig."
+ 13 in Clementinietal. (2004)))., 13 in \citet{cl04}) ).
+" Two long-period variables, V53 and V65, were found in our study of NGC 1466."," Two long-period variables, $53$ and $65$, were found in our study of NGC 1466."
+" We were unable to determine periods for either of these stars; in fact, we do not have enough light curve information to say for sure that their variability is periodic."," We were unable to determine periods for either of these stars; in fact, we do not have enough light curve information to say for sure that their variability is periodic."
+" Both stars are located near the tip of the giant branch on the CMD, as can be seen in Figure 1, and have several possible periods in the range of 60 to 90 days."," Both stars are located near the tip of the giant branch on the CMD, as can be seen in Figure \ref{cmd}, and have several possible periods in the range of $60$ to $90$ days."
+" V32 appears to be a potential anomalous Cepheid having an average V luminosity that is approximately(AC), 1.2 magnitudes brighter in V than the RR Lyrae stars."," $32$ appears to be a potential anomalous Cepheid (AC), having an average $V$ luminosity that is approximately $1.2$ magnitudes brighter in $V$ than the RR Lyrae stars."
+ The star has a potential period of either 0.331 days or 0.497 days., The star has a potential period of either $0.331$ days or $0.497$ days.
+ The 0.497 day period would be consistent with the period-luminosity diagram for ACs from Pritzletal.(2005)., The $0.497$ day period would be consistent with the period-luminosity diagram for ACs from \citet{pr05}.
+". Based on Equations 2 through 5 in Pritzletal.(2002) and the distance modulus that we derive for NGC 1466, V32 would most likely be a first overtone pulsator."," Based on Equations $2$ through $5$ in \citet{pr02} and the distance modulus that we derive for NGC 1466, $32$ would most likely be a first overtone pulsator."
+" If the 0.331 day period is correct, the star would be too bright to be an AC, based on the period-luminosity diagram, and would most likely be a foreground RR Lyrae."," If the $0.331$ day period is correct, the star would be too bright to be an AC, based on the period-luminosity diagram, and would most likely be a foreground RR Lyrae."
+" The shape of V32’s light curve is similar to an RRab star, which would be inconsistent with a 0.331 day period."," The shape of $32$ 's light curve is similar to an RRab star, which would be inconsistent with a $0.331$ day period."
+" Based on this we feel that the 0.497 day period is correct and that this star is either an AC or, less likely, a foreground RRab."," Based on this we feel that the $0.497$ day period is correct and that this star is either an AC or, less likely, a foreground RRab."
+ Nine variables of unknown classification were found., Nine variables of unknown classification were found.
+" 4 of these stars were only found by ISIS as they were either located in the crowded cluster center (V31, V51, and V54) or near the bright star in the southeast corner of the images (V67)."," $4$ of these stars were only found by ISIS as they were either located in the crowded cluster center $31$, $51$, and $54$ ) or near the bright star in the southeast corner of the images $67$ )."
+" Thus their light curves are in differential fluxes, which does not allow us to obtain positive classifications for them."," Thus their light curves are in differential fluxes, which does not allow us to obtain positive classifications for them."
+" While periods and light curve shape can be used to determine potential classifications, without having a magnitude we cannot distinguish between a cluster RR Lyrae, a foreground RR Lyrae, or an AC, for example."," While periods and light curve shape can be used to determine potential classifications, without having a magnitude we cannot distinguish between a cluster RR Lyrae, a foreground RR Lyrae, or an AC, for example."
+ Notes on the other stars with unknown classification follow. -, Notes on the other stars with unknown classification follow. -
+" V18 (Walker 110) is slightly brighter than the horizontal branch but is very red, B—V=1.27."," $18$ (Walker $110$ ) is slightly brighter than the horizontal branch but is very red, $B-V = 1.27$."
+ It has a period of 0.48 days and an amplitude of 0.15 mag in V., It has a period of $0.48$ days and an amplitude of $0.15$ mag in $V$.
+ Walker(1992) noted that in his images this star had an elongated shape that suggested a likely unresolved companion., \citet{wa92b} noted that in his images this star had an elongated shape that suggested a likely unresolved companion.
+ Our images also show this star to be elongated., Our images also show this star to be elongated.
+" The HST images of Johnsonetal.(1999) were checked in order to investigate the possibility of a close companion, however V18 did not fall within the HST field. -"," The HST images of \citet{jj99} were checked in order to investigate the possibility of a close companion, however $18$ did not fall within the HST field. -"
+ V34 129) is about one magnitude brighter than the RR (WalkerLyrae level and has a B—V=0.70., $34$ (Walker $129$ ) is about one magnitude brighter than the RR Lyrae level and has a $B-V = 0.70$.
+ Wesselink(1971) had labeled this star as a variable but Walker(1992) considered it a constant RHB star., \citet{we71} had labeled this star as a variable but \citet{wa92b} considered it a constant RHB star.
+" The period, 0.61594 days, and light curve shape of this star suggest that it could be an RRab star whose color and brightness are affected by contamination. -"," The period, $0.61594$ days, and light curve shape of this star suggest that it could be an RRab star whose color and brightness are affected by contamination. -"
+ Star V59 is located in the cluster center and has an ISIS light curve that suggests several possible periods., Star $59$ is located in the cluster center and has an ISIS light curve that suggests several possible periods.
+ Its Daophot light curves suggest that it has a similar color to the RR Lyrae stars but is about one magnitude brighter; this is possibly due to contamination., Its Daophot light curves suggest that it has a similar color to the RR Lyrae stars but is about one magnitude brighter; this is possibly due to contamination.
+ Our images and the HST images of Johnsonetal.(1999) confirm the existence of neighbor stars that could be effecting the photometry of V59 through blending., Our images and the HST images of \citet{jj99} confirm the existence of neighbor stars that could be effecting the photometry of $59$ through blending.
+" However, V59 displays a B to V amplitude ratio that is similar to the other RR Lyraes in the cluster (Fig. 9))."," However, $59$ displays a $B$ to $V$ amplitude ratio that is similar to the other RR Lyraes in the cluster (Fig. \ref{bvamp}) )."
+ V59 could also potentially be an AC or a Type II Cepheid. -, $59$ could also potentially be an AC or a Type II Cepheid. -
+ V60 is located in the crowded cluster center and has a clean ISIS light curve that suggests a period of 0.522 days., $60$ is located in the crowded cluster center and has a clean ISIS light curve that suggests a period of $0.522$ days.
+" Its light curve from Daophot suggests a luminosity approximately two magnitudes brighter than the RR Lyrae stars but the light curve is messy, possibly due to blending. -"," Its light curve from Daophot suggests a luminosity approximately two magnitudes brighter than the RR Lyrae stars but the light curve is messy, possibly due to blending. -"
+ Star V62 is located in the cluster center and has a light curve that suggests that it is a variable with a, Star $62$ is located in the cluster center and has a light curve that suggests that it is a variable with a
+If (he II atoms were labeled (his would correspond to a rieht-handed form of the molecule converting into a left-handed form.,If the H atoms were labeled this would correspond to a right-handed form of the molecule converting into a left-handed form.
+ Hence. there are two forms (frameworks) of the NIL; molecule (energy. levels are conventionally labeled as 5 and α or + and -) which can interconvert.," Hence, there are two forms (frameworks) of the $_{3}$ molecule (energy levels are conventionally labeled as $s$ and $a$ or + and -) which can interconvert."
+" Indeed. the interconversion [frequency al 24 GlIIz (s—à transition for J=1. ἐν =1) can be used by radio astronomers to monitor NIL, in dark interstellar elouds (Benson&Alvers1989)."," Indeed, the interconversion frequency at 24 GHz $s-a$ transition for $J=1$, $K=1$ ) can be used by radio astronomers to monitor $_{3}$ in dark interstellar clouds \citep{benmyers89}."
+. In general. this inversion motion doubles vibration-rotation lines (each of the (wo interconverting forms has slightly different energy levels) and leads to the two slightly different band origins listed in Table 1..," In general, this inversion motion doubles vibration-rotation lines (each of the two interconverting forms has slightly different energy levels) and leads to the two slightly different band origins listed in Table \ref{tab1}."
+ NlII4 is an oblate svmimetric top (B=9.9443 |. C=6.196 !) and the fundamental modes are either parallel (7j ancl νο (4— 04) or perpendicular (14 ancl ii. €— a4) depending on whether the infrared transition dipole moment is oscillating parallel or perpendicular to the C3 svimetry axis.," $_{3}$ is an oblate symmetric top $B=9.9443$ $^{-1}$, $C=6.196$ $^{-1}$ ) and the fundamental modes are either parallel $\nu_{1}$ and $\nu_{2}$, $a_{1}-a_{1}$ ) or perpendicular $\nu_{3}$ and $\nu_{4}$, $e-a_{1}$ ) depending on whether the infrared transition dipole moment is oscillating parallel or perpendicular to the $_{3}$ symmetry axis."
+" The rotational quantum munbers J aud A. describe the quantization of the total angular momentum (excluding nuclear spin) and its projection onto the symmetry axis. respectively,"," The rotational quantum numbers $J$ and $K$ , describe the quantization of the total angular momentum (excluding nuclear spin) and its projection onto the symmetry axis, respectively."
+ Rotational selection rules (A/V= 0. A=0.41) for a parallel transition lead to a simpleP. Q. structure (AJ=—1.0.1) with a small A splitting.," Rotational selection rules $\Delta K=0$ , $\Delta J=0,\pm1$ ) for a parallel transition lead to a simple$P$, $Q$ , $R$ structure $\Delta J=-1,0,1$ ) with a small $K$ splitting."
+" The selection rules for perpendicular transitions (Adv=0.41. AJ= 0.41) lead lo a more complex pattern wilh widely spaced Jv structive. organized into Jv sub-bands each with different A""—A” values and P. Q. 2 structure (Bernati2005)."," The selection rules for perpendicular transitions $\Delta K=0,\pm1$, $\Delta J=0,\pm1$ ) lead to a more complex pattern with widely spaced $K$ structure, organized into $K$ sub-bands each with different $K^{\prime}-K^{\prime\prime}$ values and $P$, $Q$, $R$ structure \citep{bernath05}."
+. Over (he vears. numerous studies have been undertaken (o assign the complicated NI; spectrum (Poynter&Margolis1933.1934:Sasadaοἱal.1992:IXleinerelal.2000:Leeset 2008).," Over the years, numerous studies have been undertaken to assign the complicated $_{3}$ spectrum \citep{pandm83, pandm84, sasada92, kleiner99, cottaz00, lees08}."
+". Many studies are of cold NIL, and are useful when studying planetary almospheres in our solar svstem (Brown&Margolis1996).", Many studies are of cold $_3$ and are useful when studying planetary atmospheres in our solar system \citep{brownmarg96}.
+. Some work has been done in determining empirical lower state energies (Brown&Margolis1996)as well as on (he rotation-inversion spectra(Sasadaetal.1992;Yu 2010)..," Some work has been done in determining empirical lower state energies \citep{brownmarg96} as well as on the rotation-inversion spectra\citep{sasada92, yu2010}. ."
+ Recentlythere has been considerable progress in (he variational calculation of vibration-rotation energy levels and, Recentlythere has been considerable progress in the variational calculation of vibration-rotation energy levels and
+"Figure 4 presents an example of the fitting performed with ULySS for the bulge red spectrum because it shows H@ and [OIII]5007, which are the most prominent emission lines we observed.","Figure \ref{fig:emission} presents an example of the fitting performed with ULySS for the bulge red spectrum because it shows $\beta$ and [OIII]5007, which are the most prominent emission lines we observed."
+" A set of suitable absorption line-strength indices are measured over the emission-cleaned spectra of the bulge, inner bar, and outer bar, as well as over the Vazdekisetal.(2010) models."," A set of suitable absorption line-strength indices are measured over the emission-cleaned spectra of the bulge, inner bar, and outer bar, as well as over the \citet{2010MNRAS.404.1639V} models."
+" In order to compare the results of the three components, the galaxy spectra and the SSPs are first degraded to their maximum resolution, given by the higher value of the velocity dispersion profile (c ~180 kmss~*)."," In order to compare the results of the three components, the galaxy spectra and the SSPs are first degraded to their maximum resolution, given by the higher value of the velocity dispersion profile $\sigma\sim$ 180 $^{-1}$ )."
+" All the measurements are performed in the same system, i.e., the one defined by the kinematics of the galaxy in a consistent way."," All the measurements are performed in the same system, i.e., the one defined by the kinematics of the galaxy in a consistent way."
+" We plot the values obtained for an age indicator versus those of a metallicity indicator for the SSP models, in order to obtain model grids such as those shown in Figures 5 and 6.."," We plot the values obtained for an age indicator versus those of a metallicity indicator for the SSP models, in order to obtain model grids such as those shown in Figures \ref{fig:spBB} and \ref{fig:spALL}."
+ These grids are not perfectly orthogonal due to the age-metallicity degeneracy., These grids are not perfectly orthogonal due to the age-metallicity degeneracy.
+ The mean luminosity-weighted ages and metallicities of each structural component of 3357 can then be derived by simply overplotting the observed indices on these grids., The mean luminosity-weighted ages and metallicities of each structural component of 357 can then be derived by simply overplotting the observed indices on these grids.
+" In particular, we computed all the Lick indices included in our spectral range, following the definitions given by Trageretal.(1998).."," In particular, we computed all the Lick indices included in our spectral range, following the definitions given by \citet{1998ApJS..116....1T}."
+" Note that although the index definitions are similar, our model measurements are not in the Lick/IDS resolution and IDS instrumental system, but at constant σ and flux-calibration response curve."," Note that although the index definitions are similar, our model measurements are not in the Lick/IDS resolution and IDS instrumental system, but at constant $\sigma$ and flux-calibration response curve."
+" Since the red pseudo-continuum of the Fe4383 index falls partially out of our blue spectral range, we have defined a new Fe4383°” index (named afterRed,, see Appendix ?? for details)."," Since the red pseudo-continuum of the Fe4383 index falls partially out of our blue spectral range, we have defined a new $^{SR}$ index (named after, see Appendix \ref{sec:apFe} for details)."
+ Table 2 presents the definitions of the new Fe4383°* and the original Lick/IDS Fe4383 index., Table \ref{tab:fe} presents the definitions of the new $^{SR}$ and the original Lick/IDS Fe4383 index.
+" For the bulge red spectrum, we compute the combined Iron-index (Fe) and total metallicity indicator (González1993).."," For the bulge red spectrum, we compute the combined Iron-index $\langle{\rm Fe}\rangle$ and total metallicity indicator \citep{1993PhDT.......172G}."
+" We avoid the use of the Fe5015 index, since it is highly contaminated by the prominent [OIII|5007 emission line."," We avoid the use of the Fe5015 index, since it is highly contaminated by the prominent [OIII]5007 emission line."
+" In addition to the Lick age index-definitions for the Balmer lines (HG, Hy and Hó), we also measure the more powerful Hf, (Cervantes&Vazdekis2009) and He, (Vazdekis&Arimoto1999) indices, which show great abilities to disentangle ages."," In addition to the Lick age index-definitions for the Balmer lines $\beta$, $\gamma$ and $\delta$ ), we also measure the more powerful $\beta_o$ \citep{2009MNRAS.392..691C} and $\gamma_\sigma$ \citep{1999ApJ...525..144V} indices, which show great abilities to disentangle ages."
+ The use of indices with enhanced sensitivity to the age or metallicity represents an advantage to lift the degeneracy between these parameters., The use of indices with enhanced sensitivity to the age or metallicity represents an advantage to lift the degeneracy between these parameters.
+f= fle wr ax.,f_g = f + - _g = f +.
+ The plane-polar components of the velocity of gas at the position of the planetesimal can then be written as Vui eosin where py(r)αρ)ορ).," The plane-polar components of the velocity of gas at the position of the planetesimal can then be written as _r = e_g = ], where $p_g(r) = a_g(r)(1-e_g^2)$."
+ Given that in a two-body system r.=a(1cM|ecosf). the semimajor axis of the gas element can be written as dy =a (4 |) and subsequently ptr) p The dependence on r is given implicitly through the true anomaly f.," Given that in a two-body system $r = a(1-{e^2})/(1+e \cos f)$, the semimajor axis of the gas element can be written as a_g = a ( ), and subsequently p_g(r) = p The dependence on $r$ is given implicitly through the true anomaly $f$."
+ For the purpose of numerical simulations. it proves useful to calculate the contribution of the gas drag to the total acceleration of a planetesimal in Cartesian coordinate system.," For the purpose of numerical simulations, it proves useful to calculate the contribution of the gas drag to the total acceleration of a planetesimal in Cartesian coordinate system."
+ From equation (3)). we can write. re QCvultro (0) go Cell cule," From equation \ref{eq3}) ), we can write, x = - | ( x - ) y = - | ( y - )."
+" To calculate the Cartesian components of v, we note that from Figure |. feo=fy | =arctan(y/r). and therefore the Cartesian components of the gus velocity can be written as. = | eysincy ]U2) = | eyJ ll."," To calculate the Cartesian components of ${\bf v}_g$ we note that from Figure \ref{fig1}, f + = + = (y/x), and therefore the Cartesian components of the gas velocity can be written as, = + e_g ] = + e_g ]."
+" In a precessing disk. the longitude of pericenter σσ is a function of time and can be included in numerical simulations as νο where g, Is the precessional frequency of the disk and zc, is the value of longitude of pericenter at the beginning of the simulations."," In a precessing disk, the longitude of pericenter $\varpi_g$ is a function of time and can be included in numerical simulations as _g = g_g t + where $g_g$ is the precessional frequency of the disk and ${\varpi_g}_0$ is the value of longitude of pericenter at the beginning of the simulations."
+ Finally. in this section we construct a simple analytical model for the differential equations averaged over the short period terms.," Finally, in this section we construct a simple analytical model for the differential equations averaged over the short period terms."
+ In a perturbed two-body problem. the variational equations for (et.€.zc) can be obtained from Gauss! perturbation equations (Roy 2005): f| Ptr plsin f ," In a perturbed two-body problem, the variational equations for $(a,e,\varpi)$ can be obtained from Gauss' perturbation equations (Roy 2005): = + T' (1+e ) ] = + T' + ) ] = + T' (1+r/p) ]."
+"Here # is the eccentric anomaly of the planetesimal. 7?"" is the radial. component of. the acceleration: due to gas drag. and cpl7 is its transverse component."," Here $u$ is the eccentric anomaly of the planetesimal, $R'$ is the radial component of the acceleration due to gas drag, and $T'$ is its transverse component."
+" From equation (3)). these quantities are given by R --C—wual(es 024)(16) T 2-C—w,l(ro — cag)."," From equation \ref{eq3}) ), these quantities are given by R' = | - _g) T' = | - _g) ."
+" Substituting for the components of the planetesimal and gas velocities from equations (5) and (79). expanding to the second order in c and c,. retaining only lowest order terms in à and averaging over the planetesimal's mean anomaly. equations (15)) can be written as που... for the semimajor axis. and di Mobhalf for the Cysecular variables."," Substituting for the components of the planetesimal and gas velocities from equations \ref{eq6}) ) and \ref{eq8}) ), expanding to the second order in $e$ and $e_g$, retaining only lowest order terms in $\alpha$ and averaging over the planetesimal's mean anomaly, equations \ref{eq18}) ) can be written as = (e^2,e_g^2), for the semimajor axis, and = (k-k_g) = (h-h_g), for the secular variables."
+" Here we have adopted the regular variables (&.h)=(ecosc.esinze) for the motion of the planetesimal. and (&,.h,)=(e,cosy.cysinσι) for the gas elements (Paardekooper et al."," Here we have adopted the regular variables $(k,h)=(e \cos {\varpi}, e \sin {\varpi})$ for the motion of the planetesimal, and $(k_g,h_g)=(e_g \cos {\varpi_g}, e_g \sin {\varpi_g})$ for the gas elements (Paardekooper et al."
+ 2008)., 2008).
+ Due to its complicated form. the variational equation for the semimajor axis (179) has been written only to its lowest order terms.," Due to its complicated form, the variational equation for the semimajor axis \ref{eq20bis}) ) has been written only to its lowest order terms."
+" We refer the reader to Gomes (1995) for more a detailed analysis of the complications of deducing an analytical expression for valid for any value of à and eccentricity,", We refer the reader to Gomes (1995) for more a detailed analysis of the complications of deducing an analytical expression for valid for any value of $\alpha$ and eccentricity.
+ Our first analysis is restricted to the dynamics of the planetesimal (around the primary star) without considering the perturbations from. the binary companion., Our first analysis is restricted to the dynamics of the planetesimal (around the primary star) without considering the perturbations from the binary companion.
+ The orbital evolution of the planetesimal will then be governed by the gravitational attraction of the primary star plus the effects of gas drag., The orbital evolution of the planetesimal will then be governed by the gravitational attraction of the primary star plus the effects of gas drag.
+" In all the numerical simulations performed in this section we assume a planetesimal with a bulk density of p,=3 gr/em? and initial orbital elements of «=2 AU. e=0.2 and Ax=120°."," In all the numerical simulations performed in this section we assume a planetesimal with a bulk density of $\rho_p=3$ $^3$ and initial orbital elements of $a=2$ AU, $e=0.2$ and $\Delta \varpi=120^\circ$."
+" The mass of the primary star is chosen as n1y=1.59,U.. equal to the mass of the largest component of -Cephei."," The mass of the primary star is chosen as $m_A = 1.59 M_{\odot}$, equal to the mass of the largest component of $\gamma$ -Cephei."
+ For the gas disk we assume a volumetric density ofp—510 erfem? (value at @=2 AU). consistent with the values adopted by Paardekooper et al. (," For the gas disk we assume a volumetric density of $\rho = 5 \times 10^{-10}$ $^3$ (value at $a=2$ AU), consistent with the values adopted by Paardekooper et al. ("
+2008) for àMMSN.,2008) for aMMSN.
+" Finally. in our simulations both the gas eccentricity c, and the retrograde precession frequency g, are consideredfree parameters."," Finally, in our simulations both the gas eccentricity $e_g$ and the retrograde precession frequency $g_g$ are consideredfree parameters."
+every single nuage pixel because (a) it would add sguificaut. computational overhead relative to the very efficient. Rice compression algoritlun. and (b) true randonimess is not required for this purpose since even crude dithering patterus would stil help o initieate the iueasurement biases iu quantized images.,"every single image pixel because (a) it would add significant computational overhead relative to the very efficient Rice compression algorithm, and (b) true randomness is not required for this purpose since even crude dithering patterns would still help to mitigate the measurement biases in quantized images."
+ Our compromise solution is to calculate a look-up-table of 10000. random ΠΡΟΣ using the above mentioned PRNG. aud hen repeatedly recycle hrough this LUT wheu calculating the amount of dither for cach pixel 1- he image.," Our compromise solution is to calculate a look-up-table of 10000 random numbers using the above mentioned PRNG, and then repeatedly recycle through this LUT when calculating the amount of dither for each pixel in the image."
+ As a precaution against introducing regular cevclical noise patterns iuto the muage. a oseudo vaudoi starting offset is computed cach inue when recvcliug through the LUT.," As a precaution against introducing regular cyclical noise patterns into the image, a pseudo random starting offset is computed each time when recycling through the LUT."
+ Finally. 1 out of a possible 10000 initial seed values for the eutire dithering process is computed based ou the system clock time (or optionally the cliecksiua of the first row of pixel values in the image) to ensure that the same dithering pattern is not repeated in every nuage.," Finally, 1 out of a possible 10000 initial seed values for the entire dithering process is computed based on the system clock time (or optionally the checksum of the first row of pixel values in the image) to ensure that the same dithering pattern is not repeated in every image."
+ This initial seed value is stored in the header of the compressed image for reuse when mncompressing the image., This initial seed value is stored in the header of the compressed image for reuse when uncompressing the image.
+ While quantization| reduces the entropy in the representation of the pixel values (thus nuprovius the image compression ratio) any quantization operation. even with subtractive dithering. modifies the pixel values and thus inherently iucreases the RAIS noise in the pixol-to-pixel variations iu the nuage by au amount eiven by: where the total varianceH 7; PEEin the quanutized- oenage is the sum of the variance o5 2iu the original oenage plus the quantization noise variance. aud where A ds the intensity spacing between the uantized levels.," While quantization reduces the entropy in the representation of the pixel values (thus improving the image compression ratio), any quantization operation, even with subtractive dithering, modifies the pixel values and thus inherently increases the RMS noise in the pixel-to-pixel variations in the image by an amount given by: where the total variance $\sigma_q^2$ in the quantized image is the sum of the variance $\sigma_0^2$ in the original image plus the quantization noise variance, and where $\Delta$ is the intensity spacing between the quantized levels."
+ The factor 1/12 comes from the variance of a uniforiu random distribution with uit width (Janesick2001.alsoseetheappendix+oPaper D).., The factor 1/12 comes from the variance of a uniform random distribution with unit width \citep[also see the appendix to Paper I]{janesick2001}.
+ Substituting A=oyή. the fractional oeicrease in the noise caused by quantizing the oenage can be expressed as Figure 1l shows how the fractional noise ratio (froin equation 10)) and the compression ratio (from equation 63) of an image containing Coussiiuu-distributed noise both depend ou q. To foreshadow the results of the experiments that will be described in 3. this figure shows that q values in the rauge of | to 1 provide a good combination of high conrpression ratio with relatively little added nolse.," Substituting $\Delta = \sigma_0 / q$, the fractional increase in the noise caused by quantizing the image can be expressed as Figure 1 shows how the fractional noise ratio (from equation \ref{eq:fractionalnoise}) ) and the compression ratio (from equation \ref{eq:ratio3}) ) of an image containing Gaussian-distributed noise both depend on q. To foreshadow the results of the experiments that will be described in \ref{s:tests}, this figure shows that q values in the range of 4 to 1 provide a good combination of high compression ratio with relatively little added noise."
+ It should be cautioned that if à floating-poiut inage is repeatedly compressed aud umconmpressed. then the cumulative quantization noise will be eiven bv where N ds the nunber of compression aud unconrression cycles. (," It should be cautioned that if a floating-point image is repeatedly compressed and uncompressed, then the cumulative quantization noise will be given by where N is the number of compression and uncompression cycles. ("
+This assmucs that the dithering is rerandomized dunus cach cycle. which is always the case in our iuplementation of the subtractive clithering algorithun).,"This assumes that the dithering is re-randomized during each cycle, which is always the case in our implementation of the subtractive dithering algorithm)."
+ The auplitude of this effect depends strongly on the q value., The amplitude of this effect depends strongly on the q value.
+ To put this iu practical terms. an duaee can be compressed aud uncompressed at least 16 times using qc 1 before the noise would increase to the same level equivalent to compressing the image ounce with q = 1.," To put this in practical terms, an image can be compressed and uncompressed at least 16 times using q $\geq$ 4 before the noise would increase to the same level equivalent to compressing the image once with q = 1."
+ But if the image is compressed multiple times using gq = 1. the noise would increase to scicutifically unacceptable levels after," But if the image is compressed multiple times using q = 1, the noise would increase to scientifically unacceptable levels after"
+Seven objects form in this simulation.,Seven objects form in this simulation.
+ The first. à 1.31M. star forms at 0.053Myr. and the other six (including two brown dwarfs) form between 0.070 and 0.073Myr.," The first, a $1.31
+M_{\odot}$ star forms at $0.053\,{\rm Myr}\,$, and the other six (including two brown dwarfs) form between 0.070 and $0.073\,{\rm Myr}\,$."
+ Four objects are ejected. and the remaining three stabalise by 0.12Myr into a close binary (component masses 1.31and 0.52M... semi-major axis ¢= 9.8au) and a third relatively high-mass star (0.61M...) in à distant orbit (a800 au) around this binary.," Four objects are ejected, and the remaining three stabalise by $0.12\,{\rm Myr}$ into a close binary (component masses 1.31and $0.52M_{\odot}$, semi-major axis $a=9.8\,{\rm au}$ ) and a third relatively high-mass star $0.61 M_{\odot}$ ) in a distant orbit $a \sim 800\,{\rm au}$ ) around this binary."
+ As the system evolves. the central binary hardens and the more distant companion becomes only very loosely bound with an orbit of a few thousand au.," As the system evolves, the central binary hardens and the more distant companion becomes only very loosely bound with an orbit of a few thousand au."
+ Two other stars. with masses 0.27 and 0.12M/.. are still in the core at 0.3Myr. but both are single.," Two other stars, with masses 0.27 and $0.12 M_{\odot}$ are still in the core at $0.3\,{\rm Myr}\,$, but both are single."
+ This simulation produces four stars. with masses 2.32. 0.74. 0.48 and 0.18A£..," This simulation produces four stars, with masses 2.32, 0.74, 0.48 and $0.18 M_{\odot}$."
+ The first star forms after 0.056Myr. and the other three form in a short burst after ~0.08 Myr.," The first star forms after $0.056\,{\rm Myr}\,$, and the other three form in a short burst after $\sim 0.08\,{\rm Myr}\,$ ."
+ At 0.15Myr thetwo most massive objects form a close. eccentric binary with ¢~18au and ο~0.75. but by 0.3Myr aecretion has significantly softened this binary and α~122àu.," At $0.15\,{\rm Myr}$ thetwo most massive objects form a close, eccentric binary with $a \sim 18\,{\rm au}$ and $e \sim 0.75$, but by $0.3\,{\rm Myr}$ accretion has significantly softened this binary and $a \sim 122\,{\rm au}\,$."
+ Five stars and one brown dwarf form early in this simulation., Five stars and one brown dwarf form early in this simulation.
+ The primary star forms at 0.052Myr and eventually acquires a mass of 1.07M...," The primary star forms at $0.052\,{\rm Myr}$ and eventually acquires a mass of $1.07 M_{\odot}$."
+ The other four stars and the brown dwarf form in a burst between 0.067 and 0.071Myr.," The other four stars and the brown dwarf form in a burst between 0.067 and $0.071\,{\rm Myr}\,$."
+ By 0.20Myr. the primary star has paired up with a 0.66M.. star to form a close binary with ¢=23au and e=0.87.," By $0.20\,{\rm Myr}$, the primary star has paired up with a $0.66 M_{\odot}$ star to form a close binary with $a=23\,{\rm au}$ and $e=0.87$."
+ An unusual second burst of star formation occurs between 0.26 and 0.28Myr. forming another four objects: by 0.3Myr. three have accreted enough material to become stars. and the fourth has been ejected as a brown dwarf.," An unusual second burst of star formation occurs between 0.26 and $0.28\,{\rm Myr}$, forming another four objects; by $0.3\,{\rm Myr}$, three have accreted enough material to become stars, and the fourth has been ejected as a brown dwarf."
+ The three new stars form a very close. but highly unstable. triple. which 1s bound into a quintuple with the main binary system.," The three new stars form a very close, but highly unstable, triple, which is bound into a quintuple with the main binary system."
+ However this quintuple is not expected to survive. and at least one of its components ts likely to be ejected.," However this quintuple is not expected to survive, and at least one of its low-mass components is likely to be ejected."
+ Three stars form. with masses 1.63. 1.56 and 0.83... the first after 0.052Myr. and the others at ~0.075 Myr.," Three stars form, with masses 1.63, 1.56 and $0.83 M_{\odot}$ , the first after $0.052\,{\rm Myr}$, and the others at $\sim 0.075\,{\rm Myr}\,$ ."
+ All three stars rema bound in a triple system: the 1.63 and 0.83M.. stars are in à central close binary with a=13au and e=0.10. while the 1.56M. star is 1n an orbit with à~90au and e=0.09 around this binary.," All three stars remain bound in a triple system; the 1.63 and $0.83 M_{\odot}$ stars are in a central close binary with $a=13\,{\rm au}$ and $e=0.10$, while the $1.56 M_{\odot}$ star is in an orbit with $a \sim 90\,{\rm au}$ and $e=0.09$ around this binary."
+ The outer starin the triple has been able to grow significantly faster than the central stars as. unlike those stars. it does not have to sharematerial falling into its gravitational influerce.," The outer starin the triple has been able to grow significantly faster than the central stars as, unlike those stars, it does not have to sharematerial falling into its gravitational influence."
+ Only two stars are formed. a 2.63M.. star after 0.057Myr. followed by a 1.06M.. star at 0.065Myr.," Only two stars are formed, a $2.63 M_{\odot}$ star after $0.057\,{\rm Myr}$, followed by a $1.06 M_{\odot}$ star at $0.065\,{\rm Myr}$."
+ These stars form and remain imm a wide binary with ¢=280au.," These stars form and remain in a wide binary with $a = 280\,{\rm au}$."
+ Two stars are formed early. a 2.18M. star after 0.057Myr. and a 1.40M.. star after 0.072Myr.," Two stars are formed early, a $2.18 M_{\odot}$ star after $0.057\,{\rm Myr}$, and a $1.40 M_{\odot}$ star after $0.072\,{\rm Myr}$."
+ The evolution is very similar to AOI5 until. at 0.178Myr. a third object forms and is immediately ejected as a brown dwarf.," The evolution is very similar to A015 until, at $0.178\,{\rm Myr}$, a third object forms and is immediately ejected as a brown dwarf."
+ Six stars are formed. the first at 0.051Myr and the other five in a late burst around 0.096Myr.," Six stars are formed, the first at $0.051\,{\rm Myr}$ and the other five in a late burst around $0.096\,{\rm Myr}$."
+" After three stars have been ejected. a massive triple system remains. comprising a close binary (component masses 1.60 and 1.16M... semi-major axis a= 6au) with a third star (0.6444,.) in a wide orbit with around this binary."," After three stars have been ejected, a massive triple system remains, comprising a close binary (component masses 1.60 and $1.16 M_\odot$, semi-major axis $a=6\,{\rm au}$ ) with a third star $0.64 M_{\odot}$ ) in a wide orbit with $a \sim 60\,{\rm au}$ around this binary."
+ Five stars and two brown dwarfs are formed. the first star at 0.055Myr. the other four stars and one brown dwarf between 0.065 to 0.071Myr: the second brown dwarf forms at 0.10Myr and is immediately ejected.," Five stars and two brown dwarfs are formed, the first star at $0.055\,{\rm Myr}$, the other four stars and one brown dwarf between 0.065 to $0.071\,{\rm Myr}$; the second brown dwarf forms at $0.10\,{\rm Myr}$ and is immediately ejected."
+ Three of the stars form a triple with component masses 1.09. 1.03 and 0.69M... but it is very unstable.," Three of the stars form a triple with component masses 1.09, 1.03 and $0.69 M_{\odot}$, but it is very unstable."
+ At 0.20Myr the two most massive stars are in a close binary. with the 0.69M.. star in a more distant orbit.," At $0.20\,{\rm Myr}$ the two most massive stars are in a close binary, with the $0.69 M_{\odot}$ star in a more distant orbit."
+ Then at 0.21Myr there is an interaction which swaps the 0.69M.. star with one of the components of the close binary. and at around 0.26Myr they are swapped back.," Then at $0.21\,{\rm Myr}$ there is an interaction which swaps the $0.69 M_{\odot}$ star with one of the components of the close binary, and at around $0.26\,{\rm Myr}$ they are swapped back."
+ In addition there ts a 0.58M.; star very loosely bound to the triple system., In addition there is a $0.58 M_{\odot}$ star very loosely bound to the triple system.
+ This simulation produces eight objects. five stars and three brown dwarves.," This simulation produces eight objects, five stars and three brown dwarves."
+ The first object forms after 0.057Myr. followed by two bursts. the first of which forms four objects at ~0.064 Myr. and the second of which forms three objects at~0.090 Myr.," The first object forms after $0.057\,{\rm Myr}$, followed by two bursts, the first of which forms four objects at $\sim 0.064\,{\rm Myr}$ , and the second of which forms three objects at$\sim 0.090\,{\rm Myr}$ ."
+ By the end of the simulation there is a massive triple comprising a close binary(component masses 1.27 and Γ.Γ. semi-major axis α=Il au. eccentricity ο= 0.43) with a third star (0.69M..) in a wide orbit (4.~ 80au) around this binary.," By the end of the simulation there is a massive triple comprising a close binary(component masses 1.27 and$1.16 M_\odot$ , semi-major axis $a=11\,{\rm au}$ , eccentricity $e=0.43$ ) with a third star $0.69 M_{\odot}$ ) in a wide orbit $a \sim 80\,{\rm au}$ ) around this binary."
+ A single star is formed at 0.055Myr and reaches a mass of 3.63M.. by 0.3 Myr.," A single star is formed at $0.055\,{\rm Myr}$ and reaches a mass of $3.63 M_{\odot}$ by $0.3\,{\rm Myr}$ ."
+the power ο: the detectioL process.,the power of the detection process.
+ We can preciscly state this difference in ti6 coutext of an example., We can precisely state this difference in the context of an example.
+" Suppose tha we lave a ty""pica case of a source detection problem. where coums are collected in a region contaiunuga putative or ]xsible source aud are compared with counts from a sotree-free region that defines the backerotud."," Suppose that we have a typical case of a source detection problem, where counts are collected in a region containing a putative or possible source and are compared with counts from a source-free region that defines the background."
+ If the sorPEO cOILits exeecd the threshold for detection. the source is cousidered detected.," If the source counts exceed the threshold for detection, the source is considered detected."
+ This detectiou threshold is usually determined by limiting the probability of a false detection., This detection threshold is usually determined by limiting the probability of a false detection.
+ If the threshold were lower. trere would be more false detections.," If the threshold were lower, there would be more false detections."
+ Caven this setup. we nieht ask how bright must a source be iu order to eusure detection.," Given this setup, we might ask how bright must a source be in order to ensure detection."
+ Although statistically there are no euarautees. the wpper limit is the minima xiehtuess that cusures a certaindetection.," Although statistically there are no guarantees, the upper limit is the minimum brightness that ensures a certain."
+ Critically. this value can be computed before 16 source counts are observed.," Critically, this value can be computed before the source counts are observed."
+ I is based on two probabilities. (1) the probability of a false detection which deternunes the detection threshold. aud (2) the minimum probability that a brigh source is detected.," It is based on two probabilities, (1) the probability of a false detection which determines the detection threshold, and (2) the minimum probability that a bright source is detected."
+ Although ie upper huit is primarily of mterest when the observed couuts are less than the detection ireshold. it does not depend ou the observed counts.," Although the upper limit is primarily of interest when the observed counts are less than the detection threshold, it does not depend on the observed counts."
+ This is iu sharp contrast to a coufidence interval for 1e source intensity. that is typically of the forma where 16 estimae and the error bars depend directly on the observed source couuts in the putative source region.," This is in sharp contrast to a confidence interval for the source intensity, that is typically of the form where the estimate and the error bars depend directly on the observed source counts in the putative source region."
+ Of course. the functional form of the confidence interval may be more complicated than iu this example. OS»eciallv in low count settings. but auv reasonable coufidence interval depeuds on the source counts. uulike upper lits.," Of course, the functional form of the confidence interval may be more complicated than in this example, especially in low count settings, but any reasonable confidence interval depends on the source counts, unlike upper limits."
+ The fact that upper limits do uot depeud on the source counts while confidence intervals do should not be viewed as au advantage of one quantity or the other., The fact that upper limits do not depend on the source counts while confidence intervals do should not be viewed as an advantage of one quantity or the other.
+ Rather it reflects their differing goals., Rather it reflects their differing goals.
+ Upper linüts quautifv the power of the detection procedure aud confidence mtervals describe likely values of the source iuteusitv., Upper limits quantify the power of the detection procedure and confidence intervals describe likely values of the source intensity.
+ These distinctions are lighliehted with illustrative examples in rofsecallustex.., These distinctions are highlighted with illustrative examples in \\ref{sec:illustex}.
+ To formalize discussion. suppose that a known source has an iutriusic intensity m a given passbaud of As and that the background intensity under the source is Ap.," To formalize discussion, suppose that a known source has an intrinsic intensity in a given passband of $\lamS$ and that the background intensity under the source is $\lamB$."
+ Further suppose that the source is observed for a duration τς and that vs comnts are collected. aud similarly. a separate mcasurement of the backeround could be made over a duration 7p and vp counts are collected.," Further suppose that the source is observed for a duration $\exptime$ and that $\nS$ counts are collected, and similarly, a separate measurement of the background could be made over a duration $\exptimeB$ and $\nB$ counts are collected."
+ If the backeround counts are collected iu an . ⋜⋯∖⋜↧∣⋮↑∐⊔↸∖↴∖↴↑↕∐∖↴∖↴≺∏∐⋅↸⊳↸∖⋜∐⋅↸∖⋜↧∙−↖↖⇁↸∖↸⊳⋜∐⊔⋅↸∖↕⋜↧↑↸∖↑↕⊔∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺⇂⋯∏∐↑↴∖↴↑∪↑∐↸∖↸∖↘↻↸∖↸⊳↑↸∖≼↧⋯↑↸∖∐↴∖↴↕⊓↸∖↴∖↴∙ .⋅⋅ the background and source regions respectively. where ap aud ης are independent.," If the background counts are collected in an area $\rr$ times the source we can relate the observed counts to the expected intensities, in the background and source regions respectively, where $\nB$ and $\nS$ are independent."
+ For simplicity. we beein bv assuming that Ap is known.," For simplicity, we begin by assuming that $\lamB$ is known."
+ Confideuce intervals give a set of values for the source iuteusitv that are consistent with the observed data., Confidence intervals give a set of values for the source intensity that are consistent with the observed data.
+ They are typically part of the iufereuce problem for the source iuteusitv., They are typically part of the inference problem for the source intensity.
+ The basic strategv is to conrpute anu interval of parameter values so that on repeated observations a certain proportion of the, The basic strategy is to compute an interval of parameter values so that on repeated observations a certain proportion of the
+E=l0keV3028). and Bs0.01: all terms of order 27 or higher can be neglected. as can the term in 1°.,"$E= 10keV = 30E_0$, and $B \backsim 0.01$; all terms of order $B^3$ or higher can be neglected, as can the term in $A^3$."
+ Thus we can salely use the assumption Fo=F in this regime. and (11)) is reasonable.," Thus we can safely use the assumption $F_+ = F_- = F$ in this regime, and \ref{11}) ) is reasonable."
+task.,task.
+ The turbulent convection model we use contains several free parameters., The turbulent convection model we use contains several free parameters.
+ Also. the Cepheid domain extends over a wide range of luminosities in the HR diagram. covering different masses and evolutionary stages.," Also, the Cepheid domain extends over a wide range of luminosities in the HR diagram, covering different masses and evolutionary stages."
+ Consequently. extensive model computations are needed.," Consequently, extensive model computations are needed."
+ Our recent model surveys (Smolee Moskalik 2008b.. Smolee 2009b.. this paper) cover different stellar systems (Galaxy. LMC) and different evolutionary stages (post-main sequence and helium burning objects).," Our recent model surveys (Smolec Moskalik \cite{sm08b}, Smolec \cite{rs09b}, this paper) cover different stellar systems (Galaxy, LMC) and different evolutionary stages (post-main sequence and helium burning objects)."
+ Different. sets of convective parameters were investigated., Different sets of convective parameters were investigated.
+ Ar extensive parameter study was done for F-1O Cepheid models (Smolec Moskalik 2008b))., An extensive parameter study was done for F+1O Cepheid models (Smolec Moskalik \cite{sm08b}) ).
+ For the 10-20 nodels presented here. only a limited study with carefully chosen parameters was possible. owing to the longer computation time needed for these models (see Sect.," For the 1O+2O models presented here, only a limited study with carefully chosen parameters was possible, owing to the longer computation time needed for these models (see Sect."
+ 4.1)., 4.1).
+ Only a few double-periodic models. limited to a narrow period ranges. were found.," Only a few double-periodic models, limited to a narrow period ranges, were found."
+ In particular. we have not found any large domain in which the non-resonant mechanism is the sole cause of the double-mode pulsation.," In particular, we have not found any large domain in which the non-resonant mechanism is the sole cause of the double-mode pulsation."
+ In. most of the observed Cepheids a non-resonant mechanism should be responsible for the simultaneous pulsation in two modes., In most of the observed Cepheids a non-resonant mechanism should be responsible for the simultaneous pulsation in two modes.
+ With purely radiative hydrocodes. non-resonant double-mode models are found only for RR Lyrae stars. and only if the artificial viscosity is significantly reduced (Kovices Buchler 1993)).," With purely radiative hydrocodes, non-resonant double-mode models are found only for RR Lyrae stars, and only if the artificial viscosity is significantly reduced (Kováccs Buchler \cite{kb93}) )."
+ These models are however sensitive to numerical details and their pulsation amplitudes are too high., These models are however sensitive to numerical details and their pulsation amplitudes are too high.
+ On the other hand. several computed resonant radiative beat Cepheid and RR. Lyrae models (Kováces Buchler 1988.. Buchler. Moskalik Kovaecs 1990.. Smolec 2009a)) disagree with the observations.," On the other hand, several computed resonant radiative beat Cepheid and RR Lyrae models (Kováccs Buchler \cite{kb88}, Buchler, Moskalik Kováccs \cite{bmk90}, Smolec \cite{rs09a}) ) disagree with the observations."
+ The inclusior of turbulent convection into pulsation hydrocodes seemec to offer the solution., The inclusion of turbulent convection into pulsation hydrocodes seemed to offer the solution.
+ Using modified convectior model where negative buoyancy effects were excluded (e.g. Kollatth et al. 1998)).," Using modified convection model where negative buoyancy effects were excluded (e.g. Kollátth et al. \cite{koea98}) ),"
+ the Florida-Budapest group published many non-resonant beat Cepheid models (e.g. Kollátth et al. 2002..," the Florida-Budapest group published many non-resonant beat Cepheid models (e.g. Kollátth et al. \cite{koea02},"
+ Buchler 2009)., Buchler \cite{bu09}) ).
+ However. the exclusior of the negative buoyancy is physically not justified and. as show! by Smolee Moskalik (2008b)). it is the main cause of the computed double-mode pulsation.," However, the exclusion of the negative buoyancy is physically not justified and, as shown by Smolec Moskalik \cite{sm08b}) ), it is the main cause of the computed double-mode pulsation."
+ Using the original prescription including the negative buoyancy. we were unable to find any non-resonant F+1O double-mode Cepheid models (Smolee Moskalik 2008b)).," Using the original prescription including the negative buoyancy, we were unable to find any non-resonant F+1O double-mode Cepheid models (Smolec Moskalik \cite{sm08b}) )."
+ In this paper we conducted an additional search for double-periodic Cepheids. including double-overtone (10+20) pulsators.," In this paper we conducted an additional search for double-periodic Cepheids, including double-overtone (1O+2O) pulsators."
+ With our hydrocode. which includes negative buoyancy effects. we found several double-periodic models of both F-1O and 10+20 type.," With our hydrocode, which includes negative buoyancy effects, we found several double-periodic models of both F+1O and 1O+2O type."
+" In the first case. the double-periodic pulsation is most likely caused by the 2w,=Wo+c» resonance."," In the first case, the double-periodic pulsation is most likely caused by the $2\omega_1=\omega_0+\omega_2$ resonance."
+ In the latter case. the exact mechanism cannot be identified beyond doubt.," In the latter case, the exact mechanism cannot be identified beyond doubt."
+ We only note that the 2:1 resonance. Ζω=ws nay be operational in these models.," We only note that the 2:1 resonance, $2\omega_1=\omega_5$ may be operational in these models."
+ The computed models are very interesting., The computed models are very interesting.
+ Their periods and period ratios agree well with the observations., Their periods and period ratios agree well with the observations.
+ Nevertheless. they are restricted to very narrow domains in the HR diagram and offer no general solution to the problem of modelling the beat Cepheid pulsation.," Nevertheless, they are restricted to very narrow domains in the HR diagram and offer no general solution to the problem of modelling the beat Cepheid pulsation."
+ Turbulent convection. Is. an important phenomenon determining the properties of Cepheid envelopes and cannot be neglected in pulsation models., Turbulent convection is an important phenomenon determining the properties of Cepheid envelopes and cannot be neglected in pulsation models.
+ However. the numerical expense of non-linear computations requires relatively simple convective recipes.," However, the numerical expense of non-linear computations requires relatively simple convective recipes."
+ So far. only one-equation models. for the generation of turbulent coavection were implemented in pulsation hydrocodes.," So far, only one-equation models for the generation of turbulent convection were implemented in pulsation hydrocodes."
+ Two stch models were used in the computation of Cepheid modeIs. the (1986)) model and the Stellingwerf model (Stellingwerf 1982.. Bono Stellingwerf 1992)).," Two such models were used in the computation of Cepheid models, the \cite{ku86}) ) model and the Stellingwerf model (Stellingwerf \cite{st82}, Bono Stellingwerf \cite{bos92}) )."
+ Our extersive computations (Smolee Moskalik 2008b.. Smolee 2009b.. this paper) indicate that the original model (1.9. including negative buoyancy) ts incapable of reproducing the najority of the observed beat Cepheids.," Our extensive computations (Smolec Moskalik \cite{sm08b}, Smolec \cite{rs09b}, this paper) indicate that the original model (i.e. including negative buoyancy) is incapable of reproducing the majority of the observed beat Cepheids."
+ In the original Stellingwerf (1982)) model. the negative buoyancy effects were neglected. because in that model the turbulent source function is proportional to square-root of the superadiabatie gradient. $xVY.," In the original Stellingwerf \cite{st82}) ) model, the negative buoyancy effects were neglected, because in that model the turbulent source function is proportional to square-root of the superadiabatic gradient, $S\propto\sqrt{Y}$ ."
+ This makes the original Stellingwerf model very similar to the modified model used in the Florida-Budapest hydrocode. and indeed. as investigated by Buchler Kollatth (2000)) both convection recipes lead to qualitatively the same results.," This makes the original Stellingwerf model very similar to the modified model used in the Florida-Budapest hydrocode, and indeed, as investigated by Buchler Kollátth \cite{bk00}) ) both convection recipes lead to qualitatively the same results."
+ Stellingwerf's (1982)) functional form of the source function was criticised by Gehmeyr Winkler (1992)) who pointed out the arising problems associated with the long time-scale of decay of the turbulent eddies in regions that became convectively stable during pulsation., Stellingwerf's \cite{st82}) ) functional form of the source function was criticised by Gehmeyr Winkler \cite{gw92}) ) who pointed out the arising problems associated with the long time-scale of decay of the turbulent eddies in regions that became convectively stable during pulsation.
+ Bono Stellingwerf (1992)) modified the original Stellingwerf recipe through setting S. o—sgn(Y)vIY].," Bono Stellingwerf \cite{bos92}) ) modified the original Stellingwerf recipe through setting $S\propto{\rm
+sgn}(Y)\sqrt{|Y|}$."
+ With this model for negative buoyancy. plenty of Cepheid models were computed with the Italian code (e.g. Bono. Marconi Stellingwerf 2000)).," With this model for negative buoyancy, plenty of Cepheid models were computed with the Italian code (e.g. Bono, Marconi Stellingwerf \cite{bms00}) )."
+ However. no double-periodic classical Cepheid models were ever found (Bono. private communication).," However, no double-periodic classical Cepheid models were ever found (Bono, private communication)."
+ This supports our results., This supports our results.
+ Including the negative buoyancy in the convective models (both in. and in Stellingwerf models). wide domains of double-periodic pulsation cannot be found.," Including the negative buoyancy in the convective models (both in and in Stellingwerf models), wide domains of double-periodic pulsation cannot be found."
+ We conclude that with the one-equation models used in. non-linear Cepheic modelling. double-periodic Cepheid pulsation cannot be modelled satisfactorily.," We conclude that with the one-equation models used in non-linear Cepheid modelling, double-periodic Cepheid pulsation cannot be modelled satisfactorily."
+ The question of how the hydrocodes should be modified to solve the puzzle of beat Cepheid pulsation is difficult to answer., The question of how the hydrocodes should be modified to solve the puzzle of beat Cepheid pulsation is difficult to answer.
+ A simple convectior model seems the most severe shortcoming of the present hydrocodes., A simple convection model seems the most severe shortcoming of the present hydrocodes.
+ More sophisticated convective recipes are being developed (Stókkl 2008.. Buchler 2009)). however. many problems have to be solved before they can be applied in non-linear modelling.," More sophisticated convective recipes are being developed (Stökkl \cite{stokl}, Buchler \cite{bu09}) ), however, many problems have to be solved before they can be applied in non-linear modelling."
+ Another shortcoming of the present models is the simple structure of the constructed Cepheid envelopes — they are chemically homogeneous anc non-rotating., Another shortcoming of the present models is the simple structure of the constructed Cepheid envelopes – they are chemically homogeneous and non-rotating.
+ Without detailec model computations however. it is hard to judge whether e.g. possible differential rotation could have an effect on modal selection.," Without detailed model computations however, it is hard to judge whether e.g. possible differential rotation could have an effect on modal selection."
+ The treatment of radiatior is also very simple in most of the hydrocodes. re. diffustor approximation is used (our code. the Florida-Budapest code and Italian code).," The treatment of radiation is also very simple in most of the hydrocodes, i.e. diffusion approximation is used (our code, the Florida-Budapest code and Italian code)."
+ However. a more detailed time-dependent treatment did not lead to substantial changes in the computed models (Feuchtinger. Buchler Kollátth 2000)).," However, a more detailed time-dependent treatment did not lead to substantial changes in the computed models (Feuchtinger, Buchler Kollátth \cite{fbk00}) )."
+ Finally. in the present models only radialpulsation is considered.," Finally, in the present models only radialpulsation is considered."
+ Non-radial modes are neglected., Non-radial modes are neglected.
+ There is a growing evidence that, There is a growing evidence that
+below the stronger ones in (hese velocity ranges.,below the stronger ones in these velocity ranges.
+ Our detection limit for absorption leatures is (hus a function of velocity. and is generally higher than that set by the noise.," Our detection limit for absorption features is thus a function of velocity, and is generally higher than that set by the noise."
+ Note that these boxes do not represent velocity ranges over which (he filling is performed., Note that these boxes do not represent velocity ranges over which the fitting is performed.
+ In cases where several line components are blended we perform the fitting of all Gaussian parameters simultaneously over the full velocity range covered by all components. plus some baseline on either side.," In cases where several line components are blended we perform the fitting of all Gaussian parameters simultaneously over the full velocity range covered by all components, plus some baseline on either side."
+ For deep absorption lines such as those found at low latitudes. it is preferable on physical erounds to fit the absorption spectrum wilh a sum of functions which are Gaussian in (he optical depth. 7. rather Chan in the observed absorption. e.," For deep absorption lines such as those found at low latitudes, it is preferable on physical grounds to fit the absorption spectrum with a sum of functions which are Gaussian in the optical depth, $\tau$, rather than in the observed absorption, $e^{-\tau}$."
+7 We could do this by fitting Gaussians to the log of the observed ο7 spectrum. but this amplifies the effect of the noise for the deeper lines: lor a deep lime with noise we can get (1—€7)>1 which causes the Ίου function to diverge.," We could do this by fitting Gaussians to the log of the observed $e^{-\tau}$ spectrum, but this amplifies the effect of the noise for the deeper lines; for a deep line with noise we can get $(1-e^{-\tau})>1$ which causes the log function to diverge."
+ It is better to do the fitting using for the model a sum of functions of the form where the parameters σι. Cy. and o; for each line component / are varied to minimize V? in the usual wav (see table 2. columns 3-5).," It is better to do the fitting using for the model a sum of functions of the form where the parameters $\tau_{0,i}$, $v_{0,i}$ , and $\sigma_{i}$ for each line component $i$ are varied to minimize $\chi^2$ in the usual way (see table 2, columns 3-5)."
+ In spite of the double exponential this is no more diffieult to fit to the data than a sum of ordinary Gaussians. and it provides a better match to the flat tops seen on the deeper lines.," In spite of the double exponential this is no more difficult to fit to the data than a sum of ordinary Gaussians, and it provides a better match to the flat tops seen on the deeper lines."
+ More importantly. (he values of 75; are significantly larger (han the depths of the corresponding Gaussian fits. because of saturation.," More importantly, the values of $\tau_{0,i}$ are significantly larger than the depths of the corresponding Gaussian fits, because of saturation."
+ Thus the derived column densities for the cool gas are larger. often bv a [actor of (wo or more. than what would be obtained from simple Gaussian fits.," Thus the derived column densities for the cool gas are larger, often by a factor of two or more, than what would be obtained from simple Gaussian fits."
+ The fitted parameters are obtained using an interactive program based on the Levenbere-\larquardt method of non-Inear chi-squared minization (Press et al..," The fitted parameters are obtained using an interactive program based on the Levenberg-Marquardt method of non-linear chi-squared minization (Press et al.,"
+ 1992)., 1992).
+ The numbered boxes above the spectra on figures 2-8 indicate the velocity ranges dominated by the different line components (given on Table 2. columns 6 and 7).," The numbered boxes above the spectra on figures 2-8 indicate the velocity ranges dominated by the different line components (given on Table 2, columns 6 and 7)."
+ Weaker components may be hidden below the stronger ones in these velocily ranges., Weaker components may be hidden below the stronger ones in these velocity ranges.
+ Our detection limit for absorption features is (hus a function of velocity. and is generally hieher than that set bv the noise.," Our detection limit for absorption features is thus a function of velocity, and is generally higher than that set by the noise."
+ Note that these boxes do not represent velocity. ranges over Which (he fitting is performed., Note that these boxes do not represent velocity ranges over which the fitting is performed.
+ In cases where several line components are blended we perform the fitting of all Gaussian parameters simultaneously over the full velocity range covered by all components. plus some baseline on either side.," In cases where several line components are blended we perform the fitting of all Gaussian parameters simultaneously over the full velocity range covered by all components, plus some baseline on either side."
+ We cannol estimate the cool phase temperature directly from the widths of the Gaussians. however (μον are fitted. because turbulence and random motions on all scales have the elect of widening the line significantly bevond the thermal width given bythe Maxwellian," We cannot estimate the cool phase temperature directly from the widths of the Gaussians, however they are fitted, because turbulence and random motions on all scales have the effect of widening the line significantly beyond the thermal width given bythe Maxwellian"
+This formula is exact for a uniform noise model (Llivonetal.2002). and is similar to the one used in most. publications.,This formula is exact for a uniform noise model \cite{master} and is similar to the one used in most publications.
+ ]t is in this case à very good approximation even with non-uniform: noise., It is in this case a very good approximation even with non-uniform noise.
+ In the next example however we will show that the formula has to be used with care., In the next example however we will show that the formula has to be used with care.
+ In the figure. the error bars on the estimates are taken from the Fisher matrix ancl the signal-to-noise ratio SYN= lat f=575. In Fig. 14.," In the figure, the error bars on the estimates are taken from the Fisher matrix and the signal-to-noise ratio $S/N=1$ at $\ell=575$ In Fig. \ref{fig:master2},"
+ we have plotted the average of 1000 such simulations. with cdillerent noise and sky realisations.," we have plotted the average of 1000 such simulations, with different noise and sky realisations."
+ From the plot. the method seems to give an unbiased estimate of the power spectrum bins D.," From the plot, the method seems to give an unbiased estimate of the power spectrum bins $D_b$."
+ For the lowest multipoles the estimates are slightly lower than the binned input spectrum., For the lowest multipoles the estimates are slightly lower than the binned input spectrum.
+ This is a result of the slightly skewed probability distribution of €; for small windows at these low multipoles (see Figs 9 and 10))., This is a result of the slightly skewed probability distribution of $\tilde C_\ell$ for small windows at these low multipoles (see Figs \ref{fig:prob5} and \ref{fig:prob15}) ).
+ The probability that the €; at lower multipoles have a value lower than the average (53 is high and the assumption about a Gaussian distribution about this average leads the estimates to be lower., The probability that the $\tilde C_\ell$ at lower multipoles have a value lower than the average $\VEV{\tilde C_\ell}$ is high and the assumption about a Gaussian distribution about this average leads the estimates to be lower.
+ When a bigger area of the sky is available such that several patches can be analvsed jointly to give the full sky power spectrum. this bias seems to disappear.," When a bigger area of the sky is available such that several patches can be analysed jointly to give the full sky power spectrum, this bias seems to disappear."
+ This will be shown in Section (4.1)). In this example one can see that the Lo error bars from Monte Carlo coincide very well with the theoretical error shown as shaded areas from the formula in (Hivonctal. 2002)., This will be shown in Section \ref{sect:multiple}) In this example one can see that the $1\sigma$ error bars from Monte Carlo coincide very well with the theoretical error shown as shaded areas from the formula in \cite{master}. .
+. Note that the error bars on the higher { are smaller than in because the noise model used in that paper was not white., Note that the error bars on the higher $\ell$ are smaller than in \cite{master} because the noise model used in that paper was not white.
+ Also they took into account errors due to map making which is not considered. As a next test. we used a simulation with the same resolution ancl beam. size.," Also they took into account errors due to map making which is not considered As a next test, we used a simulation with the same resolution and beam size."
+ Phe power spectrum was this time a standard CDM power spectrum., The power spectrum was this time a standard CDM power spectrum.
+ We used an axisvmmetric noise model with noise increasing from the centre and outwards to the edges (see Fig. 16))., We used an axisymmetric noise model with noise increasing from the centre and outwards to the edges (see Fig. \ref{fig:noisemap}) ).
+ This is the kind of noise model which could be expected from an experiment scanning on rings. with the rings crossing in the centre.," This is the kind of noise model which could be expected from an experiment scanning on rings, with the rings crossing in the centre."
+ We now use a circular pateh with 18.57 radius and a £344A=15° GaussianGabor, We now use a circular patch with $18.5^\circ$ radius and a $FWHM=15^\circ$ GaussianGabor
+is slightlv different [rom our standard planet search RV reduction pipeline (described in detail in Cochran οἱ al.,is slightly different from our standard planet search RV reduction pipeline (described in detail in Cochran et al.
+ 2004)., 2004).
+ We used the 2 arcsec fiber to feed the light into the IRS., We used the 2 arcsec fiber to feed the light into the HRS.
+" The setting was 760085822"". which corresponds (to a wavelength coverage [rom 4814 toAA.. thus covering the entire I5 spectral range ofAA."," The cross-disperser setting was “600g5822”, which corresponds to a wavelength coverage from 4814 to, thus covering the entire $_2$ spectral range of."
+.. We also used a wider slit to gain a higher throughput for this faint target. reducing the spectral resolving power to /?=A/AA30.000 (instead of our nominal &=60.000).," We also used a wider slit to gain a higher throughput for this faint target, reducing the spectral resolving power to $R =\lambda/\Delta\lambda = 30,\!000$ (instead of our nominal $R=60,\!000$ )."
+ Moreover. two sky fibers allow us (o simultaneously record the skv background. ancl to properly subtract it from our data.," Moreover, two sky fibers allow us to simultaneously record the sky background and to properly subtract it from our data."
+ The CCD was binned 2x2. which vields 4 pixels per resolution element.," The CCD was binned 2x2, which yields 4 pixels per resolution element."
+ This new setup is better suited [ον observations of the faint IxXepler targets., This new setup is better suited for observations of the faint Kepler targets.
+ The exposure (ime for each observation was 1200 seconds., The exposure time for each observation was $1200$ seconds.
+ The mean $/N-ratio of the 24 spectra is 42-6 per resolution element., The mean S/N-ratio of the 24 spectra is $42\pm6$ per resolution element.
+ As higher spectral resolution is advantageous for the template spectrum. we obtained this spectra with 2=60.000 and a longer exposure time of 2100 seconds.," As higher spectral resolution is advantageous for the template spectrum, we obtained this spectrum with $R=60,\!000$ and a longer exposure time of 2700 seconds."
+ We computed precise dillerential RVs with ourzTustral I-cell data modeling algorithm (Endl et al., We computed precise differential RVs with our $_2$ -cell data modeling algorithm (Endl et al.
+ 2000)., 2000).
+ The HET/IIRS BV data are listed in relrvstab.., The HET/HRS RV data are listed in \\ref{rvstab}.
+ The data have an overall rms-scatter of GOms| and average internal errors of PHSms1," The data have an overall rms-scatter of $60~{\rm m\,s}^{-1}$ and average internal errors of $25\pm8~{\rm m\,s}^{-1}$."
+ We performed a period search in our WET RV data set using the classic Lomb-Scargle periodogram (Lomb 1976. Scargle 1982).," We performed a period search in our HET RV data set using the classic Lomb-Scargle periodogram (Lomb 1976, Scargle 1982)."
+ relper displavs the power spectrum over the period range [rom 2 to LOO days., \\ref{per} displays the power spectrum over the period range from 2 to 100 days.
+ The highest peak is located al a period of 4.94 days., The highest peak is located at a period of $4.94$ days.
+ This is an independent confirmation of the transit period., This is an independent confirmation of the transit period.
+ The signal is also statistically highly significant. we estimate a false-alarm-probability (FAP) of less than 10.? using a bootstrap randomization scheme (IXirrster οἱ al.," The signal is also statistically highly significant, we estimate a false-alarm-probability (FAP) of less than $10^{-5}$ using a bootstrap randomization scheme (Kürrster et al."
+ 1997)., 1997).
+ We have also determined line bisectors from the WET spectra., We have also determined line bisectors from the HET spectra.
+ As we could use only the small fraction of the available spectral range that lies outside the I region (5000—6400 AA)) the uncertainties in the bisector velocity span (BVS) are quite large. the average error ol the BYS measurements is $3217 1 and thev have a total rms-scatter of 1," As we could use only the small fraction of the available spectral range that lies outside the $_2$ region $5000-6400$ ) the uncertainties in the bisector velocity span (BVS) are quite large, the average error of the BVS measurements is $43\pm17$ $^{-1}$ and they have a total rms-scatter of $^{-1}$."
+ The bisector measurements are given in re[lbisector.., The bisector measurements are given in \\ref{bisector}.
+ relbvs shows the correlation plot of BVS values versus RV measurements., \\ref{bvs} shows the correlation plot of BVS values versus RV measurements.
+ The linear correlation coefficient is —0.076 corresponds to a probability that the null-hvpothesis ol zero correlation is true., The linear correlation coefficient is $-0.076$ corresponds to a probability that the null-hypothesis of zero correlation is true.
+ This further strengthens the ease that the RY modulation is due {ο an orbiling companion., This further strengthens the case that the RV modulation is due to an orbiting companion.
+ We have also taken 6 spectra between 2010 July and August using the Fibre[ed Eechelle spectrograph (FIES) at the mm Nordic Optical Telescope (NOT) at La Palma. Spain (Djupyik 22010).," We have also taken 6 spectra between 2010 July and August using the FIbre–fed Écchelle Spectrograph (FIES) at the m Nordic Optical Telescope (NOT) at La Palma, Spain (Djupvik 2010)."
+ We used the medium and the high.resolution fibers (173 , We used the medium and the high–resolution fibers $1\farcs3$ 
+(7=77£18 s),$\tau = 77 \pm 18$ s).
+ Thus. the burst appears to cool as it decays. which suggests that the burst is thermonuclear in origin. aud not a sudden burst of accretion (seeLewinetal. 1993).," Thus, the burst appears to cool as it decays, which suggests that the burst is thermonuclear in origin, and not a sudden burst of accretion \citep[see][]{lvt93}."
+. Towever. the burst is weak. reaching a peal flux only 3.5 times that of the persistent enüssion.," However, the burst is weak, reaching a peak flux only 3.5 times that of the persistent emission."
+ For a 2 keV blackbody (e.g.I[kuulkersetal.2002.seealso below)... the peak rate of Ls count + is equivalent to 6«10.19 ere 2 lor 5.1079 σος lat Skpc (28 keV).," For a 2 keV blackbody \citep[e.g.,][see also below]{kul02}, the peak rate of 18 count $^{-1}$ is equivalent to $6 \times 10^{-10}$ erg $^{-2}$ $^{-1}$, or $5 \times 10^{36}$ erg $^{-1}$ at 8kpc (2–8 keV)."
+ The flucuce of the burst is approsimately LOO counts;, The fluence of the burst is approximately 400 counts.
+ This trauslates to 1410.P ere cin2 (2.8 keV. absorbed) assumndue a 2 keV blackbody spectrum aud a d&10°? 2? absorption colui. for au eucrev output of 1075 ere (8 pe).," This translates to $1 \times 10^{-8}$ erg $^{-2}$ (2–8 keV, absorbed) assuming a 2 keV blackbody spectrum and a $1 \times 10^{23}$ $^{-2}$ absorption column, for an energy output of $10^{38}$ erg (8 kpc)."
+ We extracted a spectrum of the first SO 5 of the burst in order to determine the average temperature and solid anele of the emitting area., We extracted a spectrum of the first 80 s of the burst in order to determine the average temperature and solid angle of the emitting area.
+ We used the persistent eunission frou the cutive observation prior to 20 s before the burst as backerouud (e.g..Iuulkersetal.2002).. and modeled the burst as a blackbody absorbed by a 10s1022 2? column of eas and dust usingXSPEC.," We used the persistent emission from the entire observation prior to 20 s before the burst as background \citep[e.g.,][]{kul02}, and modeled the burst as a blackbody absorbed by a $10 \times 10^{22}$ $^{-2}$ column of gas and dust using."
+. The spectrum coutaimed only about 250 counts. so we grouped the spectrum so that each bin contained =20 counts.," The spectrum contained only about 250 counts, so we grouped the spectrum so that each bin contained $\ge 20$ counts."
+ We can only place confidence limits on theapparent temperature of keV. and ou the apparent radius of 0.31.5 kin (at 8 kpc).," We can only place confidence limits on theapparent temperature of 2--8 keV, and on the apparent radius of 0.3–1.5 km (at 8 kpc)."
+ The fit was acceptable. with 4?=6 for 12 degrees of freedom.," The fit was acceptable, with $\chi^2 = 6$ for 12 degrees of freedom."
+ The solid aneles derived frou spectra of N-rav bursts are usually within a factor of two of the expected radius of a neutron star (about10kin:c.g...Napteinetal.etal. 2002).," The solid angles derived from spectra of X-ray bursts are usually within a factor of two of the expected radius of a neutron star \citep[about 10~km; e.g.,][]{kap00,coc01,cor02a,kul02}."
+. The small solid anele from which the burst Cluission originates appears to be the main factor im its relative weakuess compared to previous bursts frou this source (compareCocchictal.1999)., The small solid angle from which the burst emission originates appears to be the main factor in its relative weakness compared to previous bursts from this source \citep[compare][]{coc99}.
+. Iu order to search for variability iu the helt curve aside roni the burst. we removed L10 s of data starting 20 x xior to the burst. filled the eap with the mean count rate. and computed a Fourier Trausforiii of the resulting ight curve.," In order to search for variability in the light curve aside from the burst, we removed 140 s of data starting 20 s prior to the burst, filled the gap with the mean count rate, and computed a Fourier Transform of the resulting light curve."
+ We find broad-band low-frequency variability with a total mus power of rms above the expected Poissou noise between 5.5«10.7 and 0.13. Πε., We find broad-band low-frequency variability with a total rms power of rms above the expected Poisson noise between $5.5 \times 10^{-5}$ and 0.13 Hz.
+ We find 10 evidence for periodic signals over this frequency ranec with a significance ercater than 2-7. aud place a upper iut on anv periodic signal im this range of.. after Incorporating the expected distribution of noise power (Vaughanetal.1991).," We find no evidence for periodic signals over this frequency range with a significance greater than $\sigma$, and place a upper limit on any periodic signal in this range of, after incorporating the expected distribution of noise power \citep{vau94}."
+. oobserved sseveral times as part of a survev of the Galactic Plaue and observations of the bursting pulsar GRO 2s., observed several times as part of a survey of the Galactic Plane and observations of the bursting pulsar GRO $-$ 28.
+ We searched for iiu the three observations taken with the European Photon huaegmg Camera (EPIC) that were in the public archive as of April 2003 (Table 1)., We searched for in the three observations taken with the European Photon Imaging Camera (EPIC) that were in the public archive as of April 2003 (Table \ref{tab:xmm}) ).
+ Data from the two inetal-oxide semiconductor (MOS) CCDs were available frou all three observations. while data frou the pn CCD camera were ouly available on 2001 September 01.," Data from the two metal-oxide semiconductor (MOS) CCDs were available from all three observations, while data from the pn CCD camera were only available on 2001 September 04."
+ The cameras record N-ravs within a calibrated euergv baud of 0.212 keV with an enorgv resolution of L/AEz50 at 6.5 keV. The medi filters were used for all observations., The cameras record X-rays within a calibrated energy band of 0.2–12 keV with an energy resolution of $E/\Delta E \approx 50$ at 6.5 keV. The medium filters were used for all observations.
+ We reduced the data starting with the standard pipcline event lists for each EPIC camera using SAS version 5.1.1., We reduced the data starting with the standard pipeline event lists for each EPIC camera using SAS version 5.4.1.
+ We filtered the data to remove event erades higher than 12. events flagged as bad by the standard processing. aud events below 0.3 keV (as these are likely to be backerouud events).," We filtered the data to remove event grades higher than 12, events flagged as bad by the standard processing, and events below 0.3 keV (as these are likely to be background events)."
+ We then examined the light curve from each observation in order to check for soft protou flares., We then examined the light curve from each observation in order to check for soft proton flares.
+ The eutire exposure on 2001 March 31 was contaminated with such flares. Liiting the usefulucss of the data.," The entire exposure on 2001 March 31 was contaminated with such flares, limiting the usefulness of the data."
+ Flares were also observed on 2001 September 01. so we removed all intervals for which the count rate was 23 staucdare deviations above the mean.," Flares were also observed on 2001 September 04, so we removed all intervals for which the count rate was 3 standard deviations above the mean."
+ We removed 6000 s of faring from the pu data in this manner (resulting in the exposure listed in Table D). aud 3500 s from the MOS data.," We removed 6000 s of flaring from the pn data in this manner (resulting in the exposure listed in Table \ref{tab:xmm}) ), and 3500 s from the MOS data."
+ The field of view of the EPIC cameras are Hu radius. so was near the οσο of the field in all three observations.," The field of view of the EPIC cameras are in radius, so was near the edge of the field in all three observations."
+ wwas not detected by eve. aud uo source at its location was listed in the source catalogs that are produced iu the standard pipeline processing.," was not detected by eye, and no source at its location was listed in the source catalogs that are produced in the standard pipeline processing."
+ We were unable to use the technique applied to the oobservatious to derive au upper limit on the fiux from dauiug the observations for two reasons., We were unable to use the technique applied to the observations to derive an upper limit on the flux from during the observations for two reasons.
+ First. although the width of the halfanaxiunun of the PPSF is only oo0lr-axis. off-axis it is significantly deeraded.," First, although the full-width of the half-maximum of the PSF is only on-axis, off-axis it is significantly degraded."
+" At au offset of ήν, of the photous at 5 keV. are euclosed by the PSF within radii of Πων the pn CCDs aud"," At an offset of , of the photons at 5 keV are enclosed by the PSF within radii of for the pn CCDs and"
+3643 source detections.,3643 source detections.
+" This catalogue was searched with the same criteria as for the X-ray catalogue (1.e. detections within S"" of the candidate positions) and six objects were found.", This catalogue was searched with the same criteria as for the X-ray catalogue (i.e. detections within $8''$ of the candidate positions) and six objects were found.
+ The number of random detections in a 8” radius aperture is 0.026., The number of random detections in a $8''$ radius aperture is $0.026$.
+ Of the six radio detections. one object is GALEX-detected (candidate 173).," Of the six radio detections, one object is GALEX-detected (candidate 173)."
+). The radio fluxes of these sources can be found in Table 5.., The radio fluxes of these sources can be found in Table \ref{xraytab}.
+ Only one source has a detection in both the X-ray and radio data., Only one source has a detection in both the X-ray and radio data.
+ This is 1n. principle not a problem since AGN can be both radio-loud and radio-quiet., This is in principle not a problem since AGN can be both radio-loud and radio-quiet.
+ The radio objects without X-ray detections are more enigmatic. but can be explained by the relatively shallow luminosity limit of the X-ray observations.," The radio objects without X-ray detections are more enigmatic, but can be explained by the relatively shallow luminosity limit of the X-ray observations."
+ If the radio fluxes are converted into star formation rates using the conversion rate of Condon (1992). they correspond to values in the range of ~1001300 M.. + whereas the upper limit to star formation rates in the XMM survey is ~1200 .. yr.+. using the conversion of Ranalli. Comastri Setti (2003).," If the radio fluxes are converted into star formation rates using the conversion rate of Condon (1992), they correspond to values in the range of $\sim 400 - \sim 1300$ $_{\odot}$ $^{-1}$ whereas the upper limit to star formation rates in the XMM survey is $\sim 1200$ $_{\odot}$ $^{-1}$, using the conversion of Ranalli, Comastri Setti (2003)."
+ The AGN fraction of the non-GALEX-detected LAE sample is thus at least Όσοι if 1t 1s assumed that the X-ray and radio objects within 5” of the narrow-band sources are true detections.," The AGN fraction of the non-GALEX-detected LAE sample is thus at least $\sim 5$, if it is assumed that the X-ray and radio objects within $5''$ of the narrow-band sources are true detections."
+ It ts clear that the shallow flux limit to the deepest X-ray band. corresponding to a luminosity of berg 1. ensure many AG of lower luminosities to be undetected. as confirmed by the radio ¢etections without X- counterparts.," It is clear that the shallow flux limit to the deepest X-ray band, corresponding to a luminosity of erg $^{-1}$, ensure many AGN of lower luminosities to be undetected, as confirmed by the radio detections without X-ray counterparts."
+ The AGN fraction should therefore almost certainly be even higher. although we did not detect any ray flux in the mean. stacked total GALEX and non-GALEX-detected sample of 170 objects.," The AGN fraction should therefore almost certainly be even higher, although we did not detect any X-ray flux in the mean, stacked total GALEX and non-GALEX-detected sample of 170 objects."
+ Previous studies of LAEs at higher redshifts exhibited very small AGN contributions. from less tha| one percent in the :~1.5 LAEs studied by Wang et al. (," Previous studies of LAEs at higher redshifts exhibited very small AGN contributions, from less than one percent in the $z \sim 4.5$ LAEs studied by Wang et al. ("
+22004) to ~1l at:~3 as inferred by Gawiser et al. (,2004) to $\sim 1$ at $z \sim 3$ as inferred by Gawiser et al. (
+2007).,2007).
+ Lehmer et al. (, Lehmer et al. (
+"2008) calculated the “AGN fraction function"" of Έναemitters at.~3 both in the field and the overdense region of SSA?2 (Fig.",2008) calculated the “AGN fraction function” of $\alpha$emitters at $z \sim 3$ both in the field and the overdense region of SSA22 (Fig.
+ 3b in their paper)., 3b in their paper).
+ If we convert our (0.5—2.0 keV detection limit to their 832 keV luminosity range. we should expect to detect an AGN fraction of ü.51.59c.. where the lower number is related to their field result and the higher to the SSA2? result.," If we convert our $0.5-2.0$ keV detection limit to their $8-32$ keV luminosity range, we should expect to detect an AGN fraction of $0.5-1.5$, where the lower number is related to their field result and the higher to the SSA22 result."
+ Based on this comprehensive study of X-ray detected Lye emitting AGN. it is clear that the AGN fraction detected here is larger than at Do. as expected from the Lehmer et al. (," Based on this comprehensive study of X-ray detected $\alpha$ emitting AGN, it is clear that the AGN fraction detected here is larger than at $z\sim3$, as expected from the Lehmer et al. ("
+2008) survey.,2008) survey.
+ Ouchi et al. (, Ouchi et al. (
+2008) argued that the missed fraction in AGN X-ray searches among LAEs may be as high as 10%..,2008) argued that the missed fraction in AGN X-ray searches among LAEs may be as high as .
+ We performed the same test as in the Ouchi et al. (, We performed the same test as in the Ouchi et al. (
+2008) publication.,2008) publication.
+ Based, Based
+"Spica, =) and mmy/IHz.","$S_{1.4\,{\rm GHz}}=$ 5 and mJy/Hz."
+ Fie., Fig.
+ 3. shows the ceross correlations for each of the flux density bins for the three LRG samples., \ref{fig:radbin_cfs} shows the cross correlations for each of the flux density bins for the three LRG samples.
+ We do not find the same behaviour in cach LRG sample., We do not find the same behaviour in each LRG sample.
+ In the SDSS sample there is a clear. positive correlation between radio luminosity and the angular correlation amplitude., In the SDSS sample there is a clear positive correlation between radio luminosity and the angular correlation amplitude.
+ As with the difference between the aand ecorrelations. the luminosity dependence is most pronounced at small angular scales (<2 aarcmin).," As with the difference between the and correlations, the luminosity dependence is most pronounced at small angular scales $<$ arcmin)."
+ 1n the PSLAQ sample the lowest [lux density bin is significantly (> 30) lower than the other two subsets Chat essentially [ie on top of each other., In the 2SLAQ sample the lowest flux density bin is significantly $>3\sigma$ ) lower than the other two subsets that essentially lie on top of each other.
+ However. in the highest redshift ssample we find no significant cilference between the three ας bins.," However, in the highest redshift sample we find no significant difference between the three flux bins."
+ Our results. are. broadly consistent with those of 7..., Our results are broadly consistent with those of \citet{don09}.
+ A. the median. redshift of our. samples the Dux density limits we have chosen mumJv. correspond. to logCLiaog/(ONfMz)= 24.3/24.9. 24.7/25.3 and 25.0/25.5 for the SDSS. PSLAQ and ssamples respectively.," At the median redshift of our samples the flux density limits we have chosen mJy correspond to $\log(L_{1.4\,{\rm GHz}}{\rm /(W/Hz)})=$ 24.3/24.9, 24.7/25.3 and 25.0/25.5 for the SDSS, 2SLAQ and samples respectively."
+ Hence our results are consistent with the small-scale radio correlation function increasing for racio luminosities 1077 NWLiz and then Hattening oll., Hence our results are consistent with the small-scale radio correlation function increasing for radio luminosities $\lesssim10^{25}$ W/Hz and then flattening off.
+ Given our three samples span z0.68 to 0.35 (2.3 GCGvr of cosmic time) we are interested in any signs of evolution in the clustering strength of radio LRGs., Given our three samples span $z\sim0.68$ to 0.35 $\sim$ Gyr of cosmic time) we are interested in any signs of evolution in the clustering strength of radio LRGs.
+ To make a [air comparison we make our samples as equivalent as possible in terms of their optical and radio selection., To make a fair comparison we make our samples as equivalent as possible in terms of their optical and radio selection.
+" ?. showed that bv applying magnitude limits of 7...=19.32 and 20.25 to the PSLAQ and ssaniples respectively, they could be mace roughly equivalent to the SDSS sample in terms of their (optical) luminosity distribution ancl space density (given. that the LRG luminosity function does not evolve strongly over this interval: e.g. 2)."," \citet{saw09} showed that by applying magnitude limits of $i_{dev}=19.32$ and $20.25$ to the 2SLAQ and samples respectively, they could be made roughly equivalent to the SDSS sample in terms of their (optical) luminosity distribution and space density (given that the LRG luminosity function does not evolve strongly over this interval; e.g. \citealt{wak08b}) )."
+ They call these optical LAG samples with additional magnitude cuts SDSS*. 29LAQ and AQ.," They call these optical LRG samples with additional magnitude cuts $^*$ , $^*$ and $^*$."
+ la addition. we increase the radio (lux limit of the SDSS* and 28LACQ' samples to 13.8 and mindy respectively. in order to be equivalent to a radio power of ~107572 ANCWV/LHIz at the median. redshift. of each. sample.," In addition, we increase the radio flux limit of the $^*$ and $^*$ samples to 13.8 and mJy respectively, in order to be equivalent to a radio power of $\sim10^{24.72}$ W/Hz at the median redshift of each sample."
+" This results in 3576. 4155. 5089 objects in our radio matched samples we will callSDSS'""."," This results in 3576, 4755, 5089 objects in our radio matched samples we will call, and."
+. aandrs., In Fig.
+ In Fig. 4 we show the cross correlations between the radio matched and optically matehecl samples along with a best-fit double power law in €(r) mapped to w(0) with Limber’s equation., \ref{fig:3s_cfs_lr} we show the cross correlations between the radio matched and optically matched samples along with a best-fit double power law in $\xi(r)$ mapped to $w(\theta)$ with Limber's equation.
+ Again the break in the power law is assumed to be at lf1 MMpe when performing the fit. in addition to which we fix the slope of the large-scale power law to be 54=L8 to facilitate comparisons of the clustering amplitude.," Again the break in the power law is assumed to be at $1h^{-1}$ Mpc when performing the fit, in addition to which we fix the slope of the large-scale power law to be $\gamma=1.8$ to facilitate comparisons of the clustering amplitude."
+ Fig., Fig.
+ 8 shows the large-scale (Lh1 MMpc) clustering amplitude as a function of redshift (squares)., \ref{fig:r0_lr_evol} shows the large-scale $>1h^{-1}$ Mpc) clustering amplitude as a function of redshift (squares).
+ Ehe resultsare consistent with a constant clustering amplitude with little evidence for evolution. 9.. 3., The resultsare consistent with a constant clustering amplitude with little evidence for evolution. \ref{fig:3s_cfs}.
+ ? , \ref{tab:pl_vals_match} \citet{bra05} 
+where AN(Ag./) is the mass function of massive black holes including both active and inactive black holes. <AL(Ma.f) is the mean mass accretion rate for the black holes with A‘. In this work. we neglect the effect of black hole mergers. Le. S(Mi/)— Oin Eq. CIO. ,"where $N(M_{\rm bh},t)$ is the mass function of massive black holes including both active and inactive black holes, $<\dot{M}(M_{\rm
+bh},t)>$ is the mean mass accretion rate for the black holes with $M_{\rm bh}$, In this work, we neglect the effect of black hole mergers, i.e., $S(M_{\rm bh}, t)\equiv 0$ in Eq. \ref{mbhevol}) ),"
+as in most of the previous works2006)., as in most of the previous works.
+. The mean mass accretion rate is where the duty cycle of active black holes is detined as Substituting Eqs. (1 1) , The mean mass accretion rate is where the duty cycle of active black holes is defined as Substituting Eqs. \ref{meanmdot}) )
+and ¢12)) into Eq. (CLO).," and \ref{dutycycle}) ) into Eq. \ref{mbhevol}) ),"
+ we ean rewrite the black hole evolution equation as The AGN LF plays an important role in the study of the cosmological evolution of massive black holes., we can rewrite the black hole evolution equation as The AGN LF plays an important role in the study of the cosmological evolution of massive black holes.
+ The optical quasar LF was adopted in(2002).. however. the optical quasar LF has missed faint AGN (either intrinsic low-luminosity or obscured AGN).," The optical quasar LF was adopted in, however, the optical quasar LF has missed faint AGN (either intrinsic low-luminosity or obscured AGN)."
+ The hard X-ray surveys (~2.LOKeV) can trace the whole AGN population. including obscured type IT AGN.," The hard X-ray surveys $\sim
+2-10$ keV) can trace the whole AGN population, including obscured type II AGN."
+ The hard X-ray LF derived by was used in some works on he cosmological evolution of massive black holes2007)., The hard X-ray LF derived by was used in some works on the cosmological evolution of massive black holes.
+. The number density of Compton-thick AGN is still quite uncertain. which is not included in the hard X-ray LF.," The number density of Compton-thick AGN is still quite uncertain, which is not included in the hard X-ray LF."
+ The contribution of Compton-thick AGN to the black hole evolution was taken into account by multiplying a correction factor of 1.6 independent of the luminosity2006)., The contribution of Compton-thick AGN to the black hole evolution was taken into account by multiplying a correction factor of 1.6 independent of the luminosity.
+". The hard X-ray (>20keV) and the mid-IR (550um) bands are optimal for detection ο"" AGN with column densities ©102!emi+ 2005).."," The hard X-ray $>20~{\rm keV}$ ) and the mid-IR $5-50~\mu{\rm m}$ ) bands are optimal for detection of AGN with column densities $\la
+10^{24}~{\rm cm}^{-1}$ ."
+ The observations with the International Gamma-Ray Astropivsies Laboratory INTEGRAL) and the Swift Burst Alert Telescope (BAT) indicate that the fraction of the absorbed AGN decreases with the 20100 keV luminosity 2006).. which is confirmed by the mid-IR Spitzer observations of 25 luminous and distant quasars2007).," The observations with the International Gamma-Ray Astrophysics Laboratory (INTEGRAL) and the Swift Burst Alert Telescope (BAT) indicate that the fraction of the absorbed AGN decreases with the $20-100$ keV luminosity , which is confirmed by the mid-IR Spitzer observations of 25 luminous and distant quasars."
+. suggested that the fraction of the obscured AGN to the total can be well fitted with where found that the fraction of type II AGN detected in the hard X-ray band can be described by this function (Equation 143) quite well (see Fig., suggested that the fraction of the obscured AGN to the total can be well fitted with where found that the fraction of type II AGN detected in the hard X-ray band can be described by this function (Equation \ref{fobsc}) ) quite well (see Fig.
+ 3 in their paper)., 3 in their paper).
+ suggested that the fraction of Compton-thick to the total also decreases with luminosity and it is less than ~30 per cent based on a variety of very hard X-ray/soft gamma-ray observations on AGN (see their paper for the detailed discussion)., suggested that the fraction of Compton-thick to the total also decreases with luminosity and it is less than $\sim 30$ per cent based on a variety of very hard X-ray/soft gamma-ray observations on AGN (see their paper for the detailed discussion).
+ Motivated by the results of these works. besides the luminosity-independent correction for Compton-thick AGN. we tentatively employ a similar luminosity-dependent correction as that given by(2007).," Motivated by the results of these works, besides the luminosity-independent correction for Compton-thick AGN, we tentatively employ a similar luminosity-dependent correction as that given by."
+..2000). which is the same as that in(2004). while for=0 for luminous AGN.," which is the same as that in, while $f_{\rm CT}\rightarrow 0$ for luminous AGN."
+ In most of the previous works. both the radiative eTicieney Of aa and Eddington ratio À are free parameers. and the comparisons between the BHMF of AGN relics and the measured local BHMF of galaxies always require: trad0.1 and A~12006).," In most of the previous works, both the radiative efficiency of $\eta_{\rm rad}$ and Eddington ratio $\lambda$ are free parameters, and the comparisons between the BHMF of AGN relics and the measured local BHMF of galaxies always require: $\eta_{\rm rad}\sim 0.1$ and $\lambda\sim 1$."
+ As we have derived the mean Eddington ratio distributions as functions of black hole mass and redshift in the last section. there is only one free parameter rq in our calculations for the cosmological evolution of massive black holes.," As we have derived the mean Eddington ratio distributions as functions of black hole mass and redshift in the last section, there is only one free parameter $\eta_{\rm rad}$ in our calculations for the cosmological evolution of massive black holes."
+ The local, The local
+Lévvy-stable distributions have 0<a<2 whereas lor (he Pareto distribution the parameter a is greater (han zero.,Lévvy-stable distributions have $0<\alpha<2$ whereas for the Pareto distribution the parameter $\alpha$ is greater than zero.
+ The resulüng process A(7) will be long-range dependent ancl if the innovations are Lévyy-stable. aud asvanptotically will be in the domain of attraction of a Léevvy-stable distribution if the innovations are Pareto (see 1990).," The resulting process $X(n)$ will be long-range dependent and L\'evvy-stable if the innovations are Lévvy-stable, and asymptotically will be in the domain of attraction of a Lévvy-stable distribution if the innovations are Pareto (see )."
+ Moreover. such FARIAIA processes are asvinplotically self-similar with d—lfo.," Moreover, such FARIMA processes are asymptotically self-similar with $d-1/\alpha$."
+ The Lévyvy-stable distribution. named after the French mathematician Paul Lévvy. who investigated the behavior of sums of independent random variables. is most conveniently described by its characteristic function ó(9) the inverse Fourier (ranslorm of the probability density function.," The Lévvy-stable distribution, named after the French mathematician Paul Lévvy who investigated the behavior of sums of independent random variables, is most conveniently described by its characteristic function $\phi(\theta)$ – the inverse Fourier transform of the probability density function."
+ The most popular form of the characteristic function of a Lévvy-stable random variable is givenby (he expression where 0«a x2. 21€95 lag>0 and µε Rave parameters of this distribution 1994)).," The most popular form of the characteristic function of a Lévvy-stable random variable is givenby the expression where $0<\alpha\leq 2$ , $-1\leq\beta\leq 1$, $\sigma>0$ and $\mu \in {\bf R}$ are parameters of this distribution )."
+ The Pareto distribution. introduced. by the Italian econonmist Villvedo Pareto. is a power law probability. density (hal we represent in the form of fGCr)—αλλor)&1. where A and a are positive constants 2005)).," The Pareto distribution, introduced by the Italian economist Vilfredo Pareto, is a power law probability density that we represent in the form of $f(x)=\alpha\lambda^\alpha(\lambda+x)^{-\alpha-1}$, where $\lambda$ and $\alpha$ are positive constants )."
+ The power-law behavior of the tails implies that the variance is infinite il à.<2., The power-law behavior of the tails implies that the variance is infinite if $\alpha<2$.
+ The tail index (exponent) à. controls the rate of decay of the tail of the distribution function £., The tail index (exponent) $\alpha$ controls the rate of decay of the tail of the distribution function $F$.
+ Alodeling with FARIALA time series with infinite variance allows to take into account heavy (ails., Modeling with FARIMA time series with infinite variance allows to take into account heavy tails.
+ Through a suitable choice of coellicients ο; one can also add long-term memory effects., Through a suitable choice of coefficients $c_{n-j}$ one can also add long-term memory effects.
+ The FARIMA processes is an useful family of models because it offers a lot of flexibility in modeling long-range and short-range dependence by choosing the memory parameter d ancl appropriate autoregressive and moving average coellicient(s in expression (1))., The FARIMA processes is an useful family of models because it offers a lot of flexibility in modeling long-range and short-range dependence by choosing the memory parameter $d$ and appropriate autoregressive and moving average coefficients in expression \ref{eq1}) ).
+ The problem of estimating the exponent in heavsy-tziled data has a long history in statistics because of its practical importance., The problem of estimating the exponent in heavy-tailed data has a long history in statistics because of its practical importance.
+ The presence of heavy tails in data was firstly noted in the work of ((1932)) in his study. of word frequencies in languages., The presence of heavy tails in data was firstly noted in the work of ) in his study of word frequencies in languages.
+ Next. ((1960)) noted their presence in financial data.," Next, ) noted their presence in financial data."
+ Since the early 1970s the behavior has been noted in many other scientific fiekls (see. for example. reviews οἱ1998: 2000)).," Since the early 1970s the heavy-tailed behavior has been noted in many other scientific fields (see, for example, reviews of; )."
+ However. the availability of huge amount of various data poses a set of new challenges for the problem of estimating the tail index.," However, the availability of huge amount of various data poses a set of new challenges for the problem of estimating the tail index."
+ The point is that the data can be contaminated by extraneous oscillations. different noises with finile variance and so on.," The point is that the data can be contaminated by extraneous oscillations, different noises with finite variance and so on."
+ This makes the analvsis of heavy-tailed data more complicated likvinarkmainBoclyCilaGonSt20431994: 2005))., This makes the analysis of heavy-tailed data more complicated ; ).
+ The time series of soft solar emission relates to such problematic data, The time series of soft X-ray solar emission relates to such problematic data
+algorithms were affected. by (hese changes. resulting in the observed. transient features. in magneto(Doppler)grams.,"algorithms were affected by these changes, resulting in the observed transient features in magneto(Doppler)grams."
+ This change in (he line profile may arise due to both thermal effects ancl non-thermal excitation and ionization by the penetrating electron jets produced during the large Lares., This change in the line profile may arise due to both thermal effects and non-thermal excitation and ionization by the penetrating electron jets produced during the large flares.
+ The precipitation of electrons ancl deposition of energy in the chromosphere gives rise to the line source function leading to an increase of the line core emission relative to the far wing and continuum of the Ni line. as suggested bv Dingetal.(2002).," The precipitation of electrons and deposition of energy in the chromosphere gives rise to the line source function leading to an increase of the line core emission relative to the far wing and continuum of the Ni line, as suggested by \citet{Ding2002}."
+. The magnetic (ransients were observed at the locations of anomalous sien reversal of magnetic polarity., The magnetic transients were observed at the locations of anomalous sign reversal of magnetic polarity.
+ Co-temporal enhancement in the measured Doppler velocity also occurred there., Co-temporal enhancement in the measured Doppler velocity also occurred there.
+ Qiu&Gary(2003). suggested that the observed sign reversal is caused by changes in (he line profile related to the non-thermal effects.," \citet{Qiu2003}
+ suggested that the observed sign reversal is caused by changes in the line profile related to the non-thermal effects."
+ But the TFs seen during the X2.2 flare did not show a good correlation with the WAR sources. particularly in the post-peak phase of the flare.," But the TFs seen during the X2.2 flare did not show a good correlation with the HXR sources, particularly in the post-peak phase of the flare."
+ Therefore. energetic injection of electrons alone do not appear to have caused the observed changes in the spectral line in this flare.," Therefore, energetic injection of electrons alone do not appear to have caused the observed changes in the spectral line in this flare."
+ Thermal effects also appear to have contributed to the observed changes as inferred from the observed. association of the TFs wilh the flare ribbons., Thermal effects also appear to have contributed to the observed changes as inferred from the observed association of the TFs with the flare ribbons.
+ We thus conclude (hat (he magnetic and Doppler transients observed during the X2.2 flare of 2011 February 15 were essentially related to the line profile changes., We thus conclude that the magnetic and Doppler transients observed during the X2.2 flare of 2011 February 15 were essentially related to the line profile changes.
+ These changes were reflected in the maps of the AR. in all the Stokes parameters., These changes were reflected in the maps of the AR in all the Stokes parameters.
+ However. thev did not correspond (o a real change occurring in (he photospheric magnetic [Iux or Doppler velocity during the impulsive phase of this. and the other such large. energetic flares.," However, they did not correspond to a `real' change occurring in the photospheric magnetic flux or Doppler velocity during the impulsive phase of this, and the other such large, energetic flares."
+ Both thermal and non-thermal physical processes operating during the flare may have contributed to the transient changes in spectral line profiles., Both thermal and non-thermal physical processes operating during the flare may have contributed to the transient changes in spectral line profiles.
+ Therefore. the observed magnetic ancl velocity transients may be considered to be the observational signatures of these physical processes occurring during the peak phase of the flare.," Therefore, the observed magnetic and velocity transients may be considered to be the observational signatures of these physical processes occurring during the peak phase of the flare."
+ This work utilizes data [rom the Ilelioseismie ancl Magnetic Imager (IIMI) and the Aimospherie Imaging Assembly (ALA) on board Solar Dynamics Observatory (8DO)., This work utilizes data from the Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO).
+ This work also utilizes the X-ray data obtained by Ramaty High-Energv. Solar Spectroscopic Imager (RIIESSI). and LE data from the Solar Optical Telescope (SOT) on board Hinode.," This work also utilizes the X-ray data obtained by Ramaty High-Energy Solar Spectroscopic Imager (RHESSI), and H data from the Solar Optical Telescope (SOT) on board Hinode."
+ We are grateful to S. Couvidat of Stanford. University for providing (he spectral data and helpful discussions., We are grateful to S. Couvidat of Stanford University for providing the spectral data and helpful discussions.
+ We (hank anouvinous referee and Professor Jongchul Chae lor (heir valuable commentis and suggestions that. helped in improving (he manuscript., We thank anonymous referee and Professor Jongchul Chae for their valuable comments and suggestions that helped in improving the manuscript.
+ One of the authors (RAAT) acknowledges support by the National Research Foundation of Korea 0028102) under which a part of (his work was carried out., One of the authors (RAM) acknowledges support by the National Research Foundation of Korea (2011-0028102) under which a part of this work was carried out.
+Several factors are thought to play a role in the development of pulsating Am stars. but stellar rotation is probably one of the most important.,"Several factors are thought to play a role in the development of pulsating Am stars, but stellar rotation is probably one of the most important."
+ Charbonneau&Michaud(1991) showed that Am chemical peculiarity develops in stars that rotate slower than ss! and that the ionisation zone deepens with decreasing rotation., \citet{1991ApJ...370..693C} showed that Am chemical peculiarity develops in stars that rotate slower than $^{-1}$ and that the ionisation zone deepens with decreasing rotation.
+ This was later confirmed by more advanced diffusion model calculations by Talonetal.(2006) and observationally by Fossatietal. (2008).. who found a correlation between Am chemical peculiarities and vsini in Am stars belonging to the Praesepe open cluster.," This was later confirmed by more advanced diffusion model calculations by \citet{2006ApJ...645..634T} and observationally by \citet{2008A&A...483..891F}, who found a correlation between Am chemical peculiarities and $v \sin i$ in Am stars belonging to the Praesepe open cluster."
+ The vast majority of the Am stars already known to pulsate have a rather large vsin/. between 40 and 90 kmss7!. thus avoiding the ionisation zone sinking too deep into the star and therefore allowing the development of pulsation driven by the «-mechanism.," The vast majority of the Am stars already known to pulsate have a rather large $v \sin i$, between 40 and 90 $^{-1}$, thus avoiding the ionisation zone sinking too deep into the star and therefore allowing the development of pulsation driven by the $\kappa$ -mechanism."
+ On the other hand. for the very slowly rotating pulsating Am stars. the pulsation could be laminar.," On the other hand, for the very slowly rotating pulsating Am stars, the pulsation could be laminar."
+ It is therefore likely there are two different mechanisms driving pulsation in Am stars., It is therefore likely there are two different mechanisms driving pulsation in Am stars.
+ Our results show a wide variety of pulsations. from singly periodic to complex multiperiodic. and also some examples of what appear to be hybrid y DDor/ó SSct pulsators.," Our results show a wide variety of pulsations, from singly periodic to complex multiperiodic, and also some examples of what appear to be hybrid $\gamma$ $\delta$ Sct pulsators."
+ This ts similar to the range of behaviour seen m normal abundance OSSet stars. as can be seen in the study ofKepler data by Grigahceneetal.(2010)..," This is similar to the range of behaviour seen in normal abundance $\delta$ Sct stars, as can be seen in the study of data by \cite{2010ApJ...713L.192G}."
+ Those authors reclassified pulsation types with the following scheme: Our results are summarized in Table 3. and the individual classes for each star are given in Table 4.., Those authors reclassified pulsation types with the following scheme: Our results are summarized in Table \ref{class} and the individual classes for each star are given in Table \ref{table:Pulsating Am stars}.
+ The majority of the pulsators we found are 0 SSet stars. with the remaining quarter split between y DDor stars and mostly 0 SSct/y DDor hybrids.," The majority of the pulsators we found are $\delta$ Sct stars, with the remaining quarter split between $\gamma$ Dor stars and mostly $\delta$ $\gamma$ Dor hybrids."
+ Given that the SuperWASP data are affected by daily aliases and systematics at low frequencies. the true number of stars with y DDor pulsations may indeed be higher.," Given that the SuperWASP data are affected by daily aliases and systematics at low frequencies, the true number of stars with $\gamma$ Dor pulsations may indeed be higher."
+ However. given that Am stars are thought to be members of binary systems and tidal effects slow the stellar rotation rate. it 1s possible that some of the low-frequency signatures found in the SuperWASP data are due to ellipsoidal effects in close binaries.," However, given that Am stars are thought to be members of binary systems and tidal effects slow the stellar rotation rate, it is possible that some of the low-frequency signatures found in the SuperWASP data are due to ellipsoidal effects in close binaries."
+ Assuming a rotation limit of ysiné<120kkmss ! for an Am star and a radius of Ro. the shortest period for a binary system containing a tidally-synchronised Am star is ~0.6 dd. Close binary systems with dissimilar components have two maxima and minima per orbital period. and this value dominates over the orbital value in. periodograms.," Assuming a rotation limit of $v \sin i
+\la 120$ $^{-1}$ for an Am star and a radius of $R_{\sun}$, the shortest period for a binary system containing a tidally-synchronised Am star is $\sim$ d. Close binary systems with dissimilar components have two maxima and minima per orbital period, and this value dominates over the orbital value in periodograms."
+ Hence. frequencies X3.3dd! may have arisen due to ellipsoidal variations in close binaries.," Hence, frequencies $\la$ $^{-1}$ may have arisen due to ellipsoidal variations in close binaries."
+ Thus. we caution that some of the stars presented in Table 4+ could have erroneously been classified as having yDDor pulsations.," Thus, we caution that some of the stars presented in Table \ref{table:Pulsating Am stars} could have erroneously been classified as having $\gamma$ Dor pulsations."
+ In addition. it is possible that long-period pulsations in close binaries could be tidally excited al.. 2002).," In addition, it is possible that long-period pulsations in close binaries could be tidally excited \citep{2002MNRAS.333..262H}."
+ It is clear from examination of the data set that the ὃ SSct stars show frequencies ranging from nearly zero d! up to dd!: some stars even show the full range. including frequencies between the mmode and pmmode ranges seen in models.," It is clear from examination of the data set that the $\delta$ Sct stars show frequencies ranging from nearly zero $^{-1}$ up to $^{-1}$; some stars even show the full range, including frequencies between the mode and mode ranges seen in models."
+ These intermediate frequencies are unexplained at present., These intermediate frequencies are unexplained at present.
+ It is clear that the ὁ SSct stars are complex pulsators that show gmmodes. pmmodes. mixed modes and many nonlinear eross terms.," It is clear that the $\delta$ Sct stars are complex pulsators that show modes, modes, mixed modes and many nonlinear cross terms."
+ Whether there are differences between abnormal abundance. slowly rotating Am stars that are 0 SSet stars and the more rapidly rotating. normal abundance 9 SSet stars is yet to be determined.," Whether there are differences between abnormal abundance, slowly rotating Am stars that are $\delta$ Sct stars and the more rapidly rotating, normal abundance $\delta$ Sct stars is yet to be determined."
+ The objects we present here from SuperWASP greatly increases the number of pulsating Am stars for statistical study of this question., The objects we present here from SuperWASP greatly increases the number of pulsating Am stars for statistical study of this question.
+What can we learn from (he GRB IIubble Diagram?,	What can we learn from the GRB Hubble Diagram?
+ We can test the predicted shift ol the Universe from matter to dark-energy. domination in the range 1<z2., We can test the predicted shift of the Universe from matter to dark-energy domination in the range $1<z<2$.
+ We will also look for various predicted quintessence (Weller&Albrecht1999)and non-standard (Mannheunn2002) effects in the range 2<«10., We will also look for various predicted quintessence \citep{wea01} and non-standard \citep{man02} effects in the range $2<z<10$.
+ The typical sizes of these ellects are 0.4 in (he log of the distance around a redshift of 2=3., The typical sizes of these effects are 0.4 in the log of the distance around a redshift of $z=3$.
+ The current. paradigm of cosmology (ihe new inflation perhaps with quintessence) is so new and untested that surprises could easily awail in the unknown regime of z>I., The current paradigm of cosmology (the new inflation perhaps with quintessence) is so new and untested that surprises could easily await in the unknown regime of $z>1$ .
+galaxies.,galaxies.
+" Unfortunately, these outer pixels are also the closest to sky values and suffer from the highest errors."," Unfortunately, these outer pixels are also the closest to sky values and suffer from the highest errors."
+" Thus, technique (1) frequently fails to converge due to noise at low levels."," Thus, technique (1) frequently fails to converge due to noise at low levels."
+" Likewise, technique (3) is error prone due to the sensitivity of exponential fits to noisy outer isophotes."," Likewise, technique (3) is error prone due to the sensitivity of exponential fits to noisy outer isophotes."
+ We found reasonably stable total luminosity values using technique (2) extrapolating the isophotal intensities., We found reasonably stable total luminosity values using technique (2) extrapolating the isophotal intensities.
+" Here the apertures are integrated to a user specified point (typically the point where L=80% Lr), then the mean intensities from the fitted ellipses are used to sum the remaining luminosity."," Here the apertures are integrated to a user specified point (typically the point where $L = 80$ $L_T$ ), then the mean intensities from the fitted ellipses are used to sum the remaining luminosity."
+" For a majority of the galaxies imaged in this study, the total V magnitudes converged using this technique with typical internal errors of 0.06 mags."," For a majority of the galaxies imaged in this study, the total $V$ magnitudes converged using this technique with typical internal errors of 0.06 mags."
+" They are listed in Table 1, errors are assigned based on the error in the sky value (which dominates the noise in LSB images)."," They are listed in Table 1, errors are assigned based on the error in the sky value (which dominates the noise in LSB images)."
+ An external check to the integrated magnitudes is offered by comparison to the LSB sample from Hunter Elmegreen (2006)., An external check to the integrated magnitudes is offered by comparison to the LSB sample from Hunter Elmegreen (2006).
+ There are eight objects in common with that study., There are eight objects in common with that study.
+ Their identifications and apparent magnitudes (corrected for galactic extinction) are shown in Figure 2., Their identifications and apparent magnitudes (corrected for galactic extinction) are shown in Figure 2.
+bolometric correction of ?.. we derive a distance of ppc to 1171028. with an error around ppe if we consider a conservative error in the logy of ddex.,"bolometric correction of \citet[][]{Flower-1996}, we derive a distance of pc to 171028, with an error around pc if we consider a conservative error in the $\log g$ of dex."
+ No reddening corrections were taken mto account in this estimate., No reddening corrections were taken into account in this estimate.
+" The values mentioned above are a bit different from those listed in the ? catalogue (T,6;=5132N. [PeΠΠ=OSL+ 0.02. MAL... and distance of ppc)."," The values mentioned above are a bit different from those listed in the \citet[][]{Nordstrom-2004} catalogue $T_{eff} = 5432\,K$, $[Fe/H]=-0.81\pm0.02$ , $_{\odot}$, and distance of pc)."
+ We noto. rowever. that the photometric calibrations used by Nordstromun et al.," We note, however, that the photometric calibrations used by Nordströmm et al."
+ to derive these parameters Gucluding he absolute maenitudeC» used to derive the distance) are Likely only valid. for nidn-sequeuce stars., to derive these parameters (including the absolute magnitude used to derive the distance) are likely only valid for main-sequence stars.
+ From the TARPS spectra we derived a chromospheric activity index (logRij.1.92. with nus of 0.02) following a procedure similar to the oue presented iu (?)..," From the HARPS spectra we derived a chromospheric activity index $\log{R'_{\rm HK}}=-4.92$, with rms of 0.02) following a procedure similar to the one presented in \citep[][]{Santos-2000a}."
+ From the activity level aux the D.V colour we estimate a rotational period of ddavs (2). aud au age of LCC (2) (oratleastabove2€yr7).," From the activity level and the $B-V$ colour we estimate a rotational period of days \citep[][]{Noyes-1984} and an age of Gyr \citep[][]{Henry-1996} \citep[or at least above 2\,Gyr --][]{Pace-2004}."
+ It is known that thick-«lisk stars have typically higher abundances of alpha elements (?7)..," It is known that thick-disk stars have typically higher abundances of alpha elements \citep[][]{Bensby-2003,Fuhrmann-2004}."
+ To try to access if 1171028 could be a member of this ealactic population. we used the method aud lue-lists described in’? and ? to derive the abundanuces of several alpha aud irou-peek clemeuts for 1171028.," To try to access if 171028 could be a member of this galactic population, we used the method and line-lists described in \citet[][]{Gilli-2006} and \citet[][]{Santos-2006b} to derive the abundances of several alpha and iron-peek elements for 171028."
+ The results. listed iu reftable:clements.. sugeest that this star has typical abuudances of thin disk soblu-tvpo stars (scealso?)..," The results, listed in \\ref{table:elements}, suggest that this star has typical abundances of thin disk solar-type stars \citep[see also][]{Gilli-2006}."
+ In particular. no overabundance of alpha elements ix secu when comparing with stars of similar [Fe/TI].," In particular, no overabundance of alpha elements is seen when comparing with stars of similar [Fe/H]."
+ No trace of the Li Bue at iis found in our S/N500 spectrum of 1171028., No trace of the Li line at is found in our $\sim$ 500 spectrum of 171028.
+ As mentioned above. we obtained 19 accurate radial-velocity measurements of with the TARPS. spectrograph. between October 2001 and April 2007.," As mentioned above, we obtained 19 accurate radial-velocity measurements of with the HARPS spectrograph, between October 2004 and April 2007."
+ The complete radial velocity nuieasuremenuts obtained and the correspondiug errors ire presented in roftableuxv.., The complete radial velocity measurements obtained and the corresponding errors are presented in \\ref{table:rv}.
+" I is worth noticing that the errors quoted in the table. which are used o plot the error bars. refer solely to the instimuental (calibration) aud plhotou-nolse error share of the total error budget (ος, activity and/or stellar oscillations are not considered. eiven the difficulty in having a clear estimate of their influence)."," It is worth noticing that the errors quoted in the table, which are used to plot the error bars, refer solely to the instrumental (calibration) and photon-noise error share of the total error budget (e.g. activity and/or stellar oscillations are not considered, given the difficulty in having a clear estimate of their influence)."
+ Just after the first lucasurements were doue the star was noticed to be radial-welocitv variable., Just after the first measurements were done the star was noticed to be radial-velocity variable.
+ A later analysis of the whole data set revealed the preseuce of a 53s8-dav period radial-velocitv signal., A later analysis of the whole data set revealed the presence of a 538-day period radial-velocity signal.
+ This sigual is best fitted using a I&epleriaun fit with an seumi-uuplitude I& of, This signal is best fitted using a Keplerian fit with an semi-amplitude K of
+curve.,curve.
+" For these we adopt the maximum. velocity. obtained from our Z7, measurement.", For these we adopt the maximum velocity obtained from our $H_{\alpha}$ measurement.
+" We assume that the average distance of the Virgo cluster A (the membership is taken from DBingeeli. Popeseu and Tammann 1993) is 16 Alpe (57,231.02). as derived. from recent primary distance determinations of 4 LIST galaxies with Cepheids (van den Bergh 1996)."," We assume that the average distance of the Virgo cluster A (the membership is taken from Binggeli, Popescu and Tammann 1993) is 16 Mpc $\mu_o$ =31.02), as derived from recent primary distance determinations of 4 HST galaxies with Cepheids (van den Bergh 1996)."
+" We also assume that the clifference of distance moduli between Virgo cluster A and Coma is 3.71 mae: thus flecome 4.03 or Du, 288.3 Alpe (van den Bergh 1996).", We also assume that the difference of distance moduli between Virgo cluster A and Coma is 3.71 mag; thus $\mu_{o~coma}$ =34.73 or $D_{coma}$ =88.3 Mpc (van den Bergh 1996).
+ Given that the average recessional velocity. of Coma corrected for. the motion with respect to. the C'osmic Microwave. Background. (CAIB) is <Vουν = 7185 kms+ (CGiovanelli et al., Given that the average recessional velocity of Coma corrected for the motion with respect to the Cosmic Microwave Background (CMB) is $<V>_{CMB}$ = 7185 $km~s^{-1}$ (Giovanelli et al.
+" 1997). the previous assumptions imply 44,281.35 Kms1Alpe"," 1997), the previous assumptions imply $H_o$ =81.35 $km~s^{-1}~Mpc^{-1}$."
+ Vhe infall velocity. of the Local Group (LO) toward Virgo is taken to be 220 kms (see Federspiel et. al., The infall velocity of the Local Group (LG) toward Virgo is taken to be 220 $km~s^{-1}$ (see Federspiel et al.
+" 1998): velocities with respect to LG centroid. Vices. are thus computed as 15,4 |220."," 1998); velocities with respect to LG centroid, $V_{LG}$, are thus computed as $V_{hel}$ +220."
+ Distances to Virgo cluster earlv- and late-tvpe galaxies are computed. using the FP and TE. relation. respectively.," Distances to Virgo cluster early- and late-type galaxies are computed using the FP and TF relation, respectively."
+ Templates for these relations are obtained from other well studied: clusters. scaled according to the relative distances on the basis of the above assumptions.," Templates for these relations are obtained from other well studied clusters, scaled according to the relative distances on the basis of the above assumptions."
+ An IL band EP template was derived. from ài sample of T4 galaxies in the Coma cluster by Scodeggio et. al. (, An H band FP template was derived from a sample of 74 galaxies in the Coma cluster by Scodeggio et al. (
+1998a).,1998a).
+ The best fit to this relation. obtained. assuming that Coma is at rest in the CMD reference frame (see. for example. Ciovanclli et al.," The best fit to this relation, obtained assuming that Coma is at rest in the CMB reference frame (see, for example, Giovanelli et al."
+ 1997. Scodegeio et al.," 1997, Scodeggio et al."
+" 1997a). is: {ου=S3541.52/oge|0.32544. (with the zero-point adapted to 4,281.35)."," 1997a), is: $logR_e=-8.354+1.52 log \sigma+0.32 \mu_e$ (with the zero-point adapted to $H_o$ =81.35)."
+ The scatter of the template relation. thus the uncertainty on the distance modulus determination ofa single galaxy is 0.45 mag.," The scatter of the template relation, thus the uncertainty on the distance modulus determination of a single galaxy is 0.45 mag."
+ The fit is obtained minimizing the weighted sum of the orthogonal distances of the data points from the plane., The fit is obtained minimizing the weighted sum of the orthogonal distances of the data points from the plane.
+ ‘This is a generalization to 3 dimensions of the maximuni likelihood method. of Press et al. (, This is a generalization to 3 dimensions of the maximum likelihood method of Press et al. (
+1992) (heir ~Litex.” routine). with a modification introclucect to take into account the high degree of covariance shown by the uncertainties on the determination of log [ and yr. (see Scodegeio 1997 for details).,"1992) (their “fitexy” routine), with a modification introduced to take into account the high degree of covariance shown by the uncertainties on the determination of log $R_e$ and $\mu_e$ (see Scodeggio 1997 for details)."
+ Uncertainties on the FP parameters are determined using the statistical jackknife: No sub-sanmiples. cach one composed o£N.1 data-points. are extracted from the original sample of N data-points. rejecting in turn one of the data-points.," Uncertainties on the FP parameters are determined using the statistical jackknife: N sub-samples, each one composed of N–1 data-points, are extracted from the original sample of N data-points, rejecting in turn one of the data-points."
+ The distribution of a certain statistical parameter among those IN. sub-sanmiples is then used. to estimate the uncertainty in the value of that same parameter. without having to assume an a-priori statistical distribution for the parent population of the data-set under examination (see for example Tukey 1958. and Efron 1987).," The distribution of a certain statistical parameter among those N sub-samples is then used to estimate the uncertainty in the value of that same parameter, without having to assume an a-priori statistical distribution for the parent population of the data-set under examination (see for example Tukey 1958, and Efron 1987)."
+ The FP relation of early-type Virgo galaxies is given in Fig., The FP relation of early-type Virgo galaxies is given in Fig.
+ 2a superposed to the fit of the Coma template relation., 2a superposed to the fit of the Coma template relation.
+ The points are coded: according to wether @ is larger or smaller than 100 An5.I., The points are coded according to wether $\sigma$ is larger or smaller than 100 $km~s^{-1}$.
+ Lt is known that uncertainties in the measurement of such low velocity dispersions are larger than in the case of galaxies with higher velocity. dispersion (e.g. Scodegeio et al., It is known that uncertainties in the measurement of such low velocity dispersions are larger than in the case of galaxies with higher velocity dispersion (e.g. Scodeggio et al.
+ 1998b)., 1998b).
+ Lo fact the dispersion of Virgo ealaxies around the template relation is 0.75 mag if e«100 are excluded. significantly larger than that of the template relation.," In fact the dispersion of Virgo galaxies around the template relation is 0.75 mag if $\sigma<100$ are excluded, significantly larger than that of the template relation."
+ If these 12 galaxies are included. the dispersion rises to 0.85 mag. enough to suggest to drop galaxies with σι100 from the following analysis.," If these 12 galaxies are included, the dispersion rises to 0.85 mag, enough to suggest to drop galaxies with $\sigma<100$ from the following analysis."
+ The TE template was derived. combining 73 galaxies from the clusters A262. Cancer. Coma and AL367.," The TF template was derived combining 73 galaxies from the clusters A262, Cancer, Coma and A1367."
+ The clusters were considered to be at rest in the CAIB reference frame., The clusters were considered to be at rest in the CMB reference frame.
+ The galaxies were selected from the αςαν (Zwicky ct al., The galaxies were selected from the CGCG (Zwicky et al.
+" 1961-68) (thus with my,x15.7) according to slightly more restrictive criteria than for the Virgo galaxies.", 1961-68) (thus with $m_p\leq 15.7$ ) according to slightly more restrictive criteria than for the Virgo galaxies.
+ LE band data [or these galaxies were obtained from. Gavazzi Boselli (1996) while the 21cm LIL line cata were collected. from a large number of sources., H band data for these galaxies were obtained from Gavazzi Boselli (1996) while the 21cm HI line data were collected from a large number of sources.
+ Lt is important to stress here that the method. used lor determining the Ll magnitudes of the template galaxies is identical to that used for the Virgo galaxies (see Section 3.2)., It is important to stress here that the method used for determining the H magnitudes of the template galaxies is identical to that used for the Virgo galaxies (see Section 3.2).
+ Galaxies with Def.»0.5 were not used. because the LL line-width in this case could underestimate the galaxy. true rotation velocity.," Galaxies with $DefHI>0.5$ were not used, because the HI line-width in this case could underestimate the galaxy true rotation velocity."
+ Also galaxies with /ogMο«2.2 were not used. to avoid objects whose correction for turbulent motion is relevant.," Also galaxies with $logWc<2.2$ were not used, to avoid objects whose correction for turbulent motion is relevant."
+ We assume that the uncertainty on the measurements of the line width is 10 Amos and that on II band magnitudes is of O.15 mag., We assume that the uncertainty on the measurements of the line width is 10 $km~s^{-1}$ and that on H band magnitudes is of 0.15 mag.
+ The TE relation for the τὸ galaxies used in the derivation of the template is shown in Fig., The TF relation for the 73 galaxies used in the derivation of the template is shown in Fig.
+ 2c., 2c.
+ The best fitting template. obtained. using the bivariate method (Ciovanelli et al.," The best fitting template, obtained using the bivariate method (Giovanelli et al."
+ 1997) is given bv: 44=2.60.7.85LogM, 1997) is given by: $H=-2.60 - 7.85~Log W_c$.
+ The scatter of the FEE template. thus the uncertainty in the distance modulus of the individual galaxies is 0.35 mage.," The scatter of the TF template, thus the uncertainty in the distance modulus of the individual galaxies is 0.35 mag."
+ The the zero point and slope of the TE template relation are found consistent with the parameters of the local TE calibrators., The the zero point and slope of the TF template relation are found consistent with the parameters of the local TF calibrators.
+ The TE relation of Virgo Iate-tvpe galaxies is given in Fig 2b. with the template relation superposed.," The TF relation of Virgo late-type galaxies is given in Fig 2b, with the template relation superposed."
+ The scatter of Virgo galaxies is 0.70 mag. thus significantly larger than that of the template relation.," The scatter of Virgo galaxies is 0.70 mag, thus significantly larger than that of the template relation."
+ We have checked. if to this larger scatter might contribute a not enough conservative threshold on galaxy. inclination (7z30 deg)., We have checked if to this larger scatter might contribute a not enough conservative threshold on galaxy inclination $i>30~deg$ ).
+ However we found that for galaxies with inclination 745deg the scatter remains 0.70 mae., However we found that for galaxies with inclination $i>45~deg$ the scatter remains 0.70 mag.
+ Meanwhile we determined. that the scatter is not alfected by the inclusion of galaxies with, Meanwhile we determined that the scatter is not affected by the inclusion of galaxies with
+The gamma-ray burst (GRB) 050502B was a remarkable event showing a conspicuous X-ray flare lasting from ~ 400 to 1400 s after trigger. with as much energy (~9x107! cem. in the kkeV band) as the prompt emission itself [(8.0+1.0)x1077 erg em. in the kkeV band].,"The gamma-ray burst (GRB) 050502B was a remarkable event showing a conspicuous X-ray flare lasting from $\sim$ 400 to 1400 s after trigger, with as much energy $ \sim 9 \times 10^{-7}$ $^{-2}$, in the keV band) as the prompt emission itself $8.0\pm 1.0) \times 10 ^{-7}$ erg $^{-2}$, in the keV band]."
+ The X-ray light curve also showed later activity and a second less intense flare. followed by a possible jet break at ~1.1»10? ss (?2)..," The X-ray light curve also showed later activity and a second less intense flare, followed by a possible jet break at $\sim1.1 \times 10^{5}$ s \citep{Falcone,Burrows}."
+ Given the exceptionality of this GRB. it is important to study its optical afterglow. searching for properties that may lead to a better understanding of its phenomenology.," Given the exceptionality of this GRB, it is important to study its optical afterglow, searching for properties that may lead to a better understanding of its phenomenology."
+ As expected. when the relativistic jet slows down. the aberration of light due to Special Relativity effects becomes less important. and thus the beaming angle. Q5~1/P. increases within the jet (2)..," As expected, when the relativistic jet slows down, the aberration of light due to Special Relativity effects becomes less important, and thus the beaming angle, $\theta_{\rm b} \sim 1/\Gamma$, increases within the jet \citep {Rhoads}."
+ A jet break occurs when the Lorentz factor is such that I/F>44. resulting in a significant decrease of the afterglow brightness and steepening of the light curve at all wavelengths.," A jet break occurs when the Lorentz factor is such that $1/\Gamma > \theta_{\rm jet}$, resulting in a significant decrease of the afterglow brightness and steepening of the light curve at all wavelengths."
+ In the satellite era (2).. X- light curves are much better sampled than previously. but simultaneous optical and X-ray light curve breaks have been rarely observed.," In the satellite era \citep{Gehrels}, X-ray light curves are much better sampled than previously, but simultaneous optical and X-ray light curve breaks have been rarely observed."
+ For example. from the sample of ?.. with X-Ray Telescope (XRT:?) data for 179 GRBs and 57 pre- and GRBs optical afterglow data. only 7 of them show an achromatic break.," For example, from the sample of \citet{Liang}, with X-Ray Telescope \citep [XRT;] [] {Burrows05} data for 179 GRBs and 57 pre- and GRBs optical afterglow data, only 7 of them show an achromatic break."
+ This apparent lack of jet breaks is still in debate and could be due to a combination of higher redshifts. fainter bursts. larger opening angles. ete.," This apparent lack of jet breaks is still in debate and could be due to a combination of higher redshifts, fainter bursts, larger opening angles, etc."
+ Models that go beyond the fireball external shock afterglow scenario have also been explored. as they include an extra component that can be described as “late prompt emission due to late time activity of long living central engines.," Models that go beyond the fireball external shock afterglow scenario have also been explored, as they include an extra component that can be described as “late prompt"" emission due to late time activity of long living central engines."
+" As discussed by ? and ?.. the lack of achromatic breaks could be explained by the presence of the ""late prompt"" emission,"," As discussed by \citet{Ghisellini} and \citet{Nardini}, the lack of achromatic breaks could be explained by the presence of the “late prompt"" emission."
+ The analysis of GRB 050502B optical data from the mm Telescopio Nazionale Galileo (TNG) was done with focus on correlations between the optical and X-ray afterglow behavior., The analysis of GRB 050502B optical data from the m Telescopio Nazionale Galileo (TNG) was done with focus on correlations between the optical and X-ray afterglow behavior.
+ In the next pages the X-ray light curve is discussed first. following ? as a guideline.," In the next pages the X-ray light curve is discussed first, following \citet{Falcone} as a guideline."
+ Evidence for a jet break and large redshift are presented later in §3., Evidence for a jet break and large redshift are presented later in $\S\ 3$.
+ At 09:25:40 UT. the Swift Burst Alert Telescope (BAT:?) triggered and located GRBOS0502B (?)..," At 09:25:40 UT, the Swift Burst Alert Telescope \citep [BAT;] [] {Barthelmy} triggered and located GRB050502B \citep {Pagani}."
+ The XRT repository indicates that the afterglow of GRB 050502B was observed at the coordinates RA = 09:30:10.11. Dee = +16:59:47.9 (J2000.0). being located within the XRT UVOT-enhanced position [1.4 aresecond radius error circle.," The XRT repository indicates that the afterglow of GRB 050502B was observed at the coordinates RA = 09:30:10.11, Dec = +16:59:47.9 (J2000.0), being located within the XRT UVOT-enhanced position 1.4 arcsecond radius error circle."
+ The detailed TNG I and R bands data. taken on 2005. May 3. 4 and 5 (1. 2 and 3 days after the trigger. respectively). are summarized in Table |.," The detailed TNG $I$ and $R$ bands data, taken on 2005, May 3, 4 and 5 (1, 2 and 3 days after the trigger, respectively), are summarized in Table 1."
+ Raw images were corrected for bad pixels. debiased and fielded in a standard way with IRAF (?)..," Raw images were corrected for bad pixels, debiased and flat-fielded in a standard way with IRAF \citep{Tody}."
+ In addition. the TNG I-band images severely affected by fringing were corrected using standard routines.," In addition, the TNG $I$ -band images severely affected by fringing were corrected using standard routines."
+ Photometry was done also with IRAF. using the USNO-BI.O catalog for calibration purposes. which has a systematic error of 40.2 mmag.," Photometry was done also with IRAF, using the USNO-B1.0 catalog for calibration purposes, which has a systematic error of $\pm 0.2$ mag."
+ In order to calibrate the afterglow photometry. 40 to 50 stars were used per final science image.," In order to calibrate the afterglow photometry, 40 to 50 stars were used per final science image."
+ The TNG photometric uncertainties listed in Table | are statistical only., The TNG photometric uncertainties listed in Table 1 are statistical only.
+ Later in time the Sloan Digital Sky Survey (SDSS) Data Release 6. finally covered the field of view of 0050502B. A cross-calibration between USNO-B1.0 and SDSS catalogs yielded consistent zero points.," Later in time the Sloan Digital Sky Survey (SDSS) Data Release 6, finally covered the field of view of 050502B. A cross-calibration between USNO-B1.0 and SDSS catalogs yielded consistent zero points."
+ Conversion from r to R-band and i to /-band was performed using observations of Landolt standard stars (?) in SDSS fields. following ?..," Conversion from $r$ to $R$ -band and $i$ to $I$ -band was performed using observations of Landolt standard stars \citep {Landolt} in SDSS fields, following \citet {Chonis}. ."
+of the isothermal plasma temperature.,of the isothermal plasma temperature.
+ This comparison assumes the individual observations also correspond (o isothermal plasma: (his is strictly not likely to be (he case ancl we return io this later in Section2.2.2.., This comparison assumes the individual observations also correspond to isothermal plasma; this is strictly not likely to be the case and we return to this later in Section\ref{s:dem}.
+" The theoretical line intensity ratio depends linearly on the assumed Ne/O abundance ratio, and a single theoretical intensity ratio vs temperature locus was found {ο be a poor malch to the observed data for anv single adopted Ne/O abundance ratio."," The theoretical line intensity ratio depends linearly on the assumed Ne/O abundance ratio, and a single theoretical intensity ratio vs temperature locus was found to be a poor match to the observed data for any single adopted Ne/O abundance ratio."
+ In Figure 3. we illustrate this by showing (wo theoretical isothermal intensity ralio curves corresponding to two different Ne/O abundance ratios., In Figure \ref{f:linerats} we illustrate this by showing two theoretical isothermal intensity ratio curves corresponding to two different Ne/O abundance ratios.
+ These curves are analogous to both the upper panel in Figure 1 of Actonetal.(1975).. and the eurves bounding the line (lux ratios in Figure 10 of Alclxenzie&Feldman(1992).," These curves are analogous to both the upper panel in Figure 1 of \citet{Acton.etal:75}, and the curves bounding the line flux ratios in Figure 10 of \citet{McKenzie.Feldman:92}."
+. The Ne/O abundance ratio for (he lower curve (Ne/O-—0.12) is such (hat the theoretical photon intensity ratio reached matches the observed ratio. excluding the most extreme observed. point.," The Ne/O abundance ratio for the lower curve (Ne/O=0.12) is such that the theoretical photon intensity ratio reached matches the observed ratio, excluding the most extreme observed point."
+ The abundance ratio lor the upper curve (Ne/O-—0.17) is such that the theoretical photon intensity ratio reached matches (he observed ratio. again excluding (he most extreme observed point.," The abundance ratio for the upper curve (Ne/O=0.17) is such that the theoretical photon intensity ratio reached matches the observed ratio, again excluding the most extreme observed point."
+ Note that there are still observed. photon intensity ratios that lie below the lower theoretical ratio curve and one that lies slighilv above the upper one: in principle. these could be made to fit within the (wo curves were there to be some source of additional error in (he derived plasma temperatures which allowed the points to be shifted arbitrarily to the left or right.," Note that there are still observed photon intensity ratios that lie below the lower theoretical ratio curve and one that lies slightly above the upper one: in principle, these could be made to fit within the two curves were there to be some source of additional error in the derived plasma temperatures which allowed the points to be shifted arbitrarily to the left or right."
+ In this way. the two curves represent thespread in Ne/O abundance ratio (Ne/O-—0.12 and 0.17) that can match the data.," In this way, the two curves represent the in Ne/O abundance ratio (Ne/O=0.12 and 0.17) that can match the data."
+ The separation of the two curves is much greater (han the statistical errors in the data. and we conclude that the observed intensity ratios cannot be explained by a single Ne/O abundance ratio.," The separation of the two curves is much greater than the statistical errors in the data, and we conclude that the observed intensity ratios cannot be explained by a single Ne/O abundance ratio."
+ The trend of the observed intensities wilh temperature is also much steeper than the theoretical ratio., The trend of the observed intensities with temperature is also much steeper than the theoretical ratio.
+ Hf the observed intensities are [rom isothermal plasma. this indicates a trend of increasing Ne/O abundance ratio wilh temperature.," If the observed intensities are from isothermal plasma, this indicates a trend of increasing Ne/O abundance ratio with temperature."
+ The fields of view of the SOLEX and FCS instruments [rom whieh the observations analvsed here were obtained were l arcmin and 15 arcsec across. respectively. 1992:Schmelzetal. 2005)..," The fields of view of the SOLEX and FCS instruments from which the observations analysed here were obtained were 1 arcmin and 15 arcsec across, respectively \citep{McKenzie.Feldman:92,Schmelz.etal:05b}."
+ It is likely than in regions of this size the observed plasma is not isothermal., It is likely than in regions of this size the observed plasma is not isothermal.
+ Anv deviation Irom isothermality tends to flatten out the theoretical line intensitv ralio curves., Any deviation from isothermality tends to flatten out the theoretical line intensity ratio curves.
+ We investigate (his quantitatively using a model contünuous differential emission measure distribution (DENI)., We investigate this quantitatively using a model continuous differential emission measure distribution (DEM).
+ For the DEM model. we adopted the form Φ(Τ)=n7(T) D where V. is the volume," For the DEM model, we adopted the form $\Phi(T)=n_e^2(T)\frac{dV(T)}{dT}$ , where $V$ is the volume"
+"detector thresholds, giving a much greater change in detection rate with recoil energy compared with the SHM alone.","detector thresholds, giving a much greater change in detection rate with recoil energy compared with the SHM alone."
+ The total rate in a detector using a Ge target is shown in Figure 4 varying pa/pn and Mwrwp., The total rate in a detector using a Ge target is shown in Figure 4 varying $\rhodrat$ and $\MWIMP$.
+ If the detectors threshold is sufficiently low even an extremely conservative dark disk with ρα/ρι=0.1 can be detected., If the detectors threshold is sufficiently low even an extremely conservative dark disk with $\rhodrat=0.1$ can be detected.
+ Current germanium detectors achieve thresholds below 1 keV (Linetal.2008;Aalseth2008).," Current germanium detectors achieve thresholds below 1 keV \citep{Texono,CoGeNT}."
+" The details of the differential rate with energy, as shown in Figure 4, betray both the contribution of the dark disk relative to the SHM and Mwrywyp."," The details of the differential rate with energy, as shown in Figure 4, betray both the contribution of the dark disk relative to the SHM and $\MWIMP$."
+ This introduces a mass-dependend characteristic shape of the differential rate which will improve the constrains on Mwrywyp upon detection., This introduces a mass-dependend characteristic shape of the differential rate which will improve the constrains on $\MWIMP$ upon detection.
+" The motion of the Earth around the Sun gives rise to an annual modulation of the event rate and recoil energy spectrum (Drukier,FreeseandSpergel1986).", The motion of the Earth around the Sun gives rise to an annual modulation of the event rate and recoil energy spectrum \citep{DrukierFreese}.
+". 'The annual modulation is more pronounced for the dark disk, since the relative change to the mean streaming velocity owing to the Earth's motion is larger (~19%)) compared with the SHM (~6%))."," The annual modulation is more pronounced for the dark disk, since the relative change to the mean streaming velocity owing to the Earth's motion is larger $\sim$ ) compared with the SHM $\sim$ )."
+" We show in Figure 3 the residual integrated rates for a liquid xenon detector throughout a year, for three different Mwrywup and two values of pq"," We show in Figure 3 the residual integrated rates for a liquid xenon detector throughout a year, for three different $\MWIMP$ and two values of $\rhodrat$."
+ The residuals are calculated with respect to the mean /pn.counting rates in a given energy region., The residuals are calculated with respect to the mean counting rates in a given energy region.
+ The phase (defined at maximum rate) of the dark, The phase (defined at maximum rate) of the dark
+We have retrieved and combined the NEWSIPS-calibrated IVE data from the short-wavelength camera. including om own IUE observation (SWPOL9L. SWPLOSSO. SWP1682 ΝΤΟ with observation dates UT 1979 April 15. 1980 Dec. 1. 1982 April 21. 1986 Jan. 12 respectively). weielting these according to the square of the signal-to-noise ratio.,"We have retrieved and combined the NEWSIPS-calibrated IUE data from the short-wavelength camera, including our own IUE observation (SWP04942, SWP10850, SWP16824, SWP27517 with observation dates UT 1979 April 15, 1980 Dec. 1, 1982 April 24, 1986 Jan. 12 respectively), weighting these according to the square of the signal-to-noise ratio."
+ All observations were at low dispersion im the luge aperture. eiving a resolution of ~1100 kan + ffrom tto.," All observations were at low dispersion in the large aperture, giving a resolution of $\sim$ 1100 km $^{-1}$ from to."
+1980AÀ... Waveleneth scales were checked using the eeocoronal Lvo luce., Wavelength scales were checked using the geocoronal $\alpha$ line.
+ We have applied an approximate correction for IVE artifacts and the wines of the ecocoronal Lva πιο. by subtracting the SWP artifact spectrum appropriate to point source spectral extractio- as preseuted by Crenshaw. Bruceman. Norman (1990).," We have applied an approximate correction for IUE artifacts and the wings of the geocoronal $\alpha$ line, by subtracting the SWP artifact spectrum appropriate to point source spectral extraction, as presented by Crenshaw, Bruegman, Norman (1990)."
+ By good fortune. the line-ofsight to PERS 10010 happens to pass oulv 31! from the center of the Leo I dwarf spheroidal galaxy. so Bowen et al. (," By good fortune, the line-of-sight to PKS 1004+13 happens to pass only $\arcmin$ from the center of the Leo I dwarf spheroidal galaxy, so Bowen et al. ("
+1997) used this QSO as a background probe of Leo Ts halo.,1997) used this QSO as a background probe of Leo I's halo.
+ They obtained high-resolution 1) HIST CIIRS spectra of PISS 10011123 from tto1562À., They obtained high-resolution $^{-1}$ ) HST GHRS spectra of PKS 1004+13 from to.
+. We have retrieved the IST archival spectra. applving the same wavelength shift as Bowen et al.," We have retrieved the HST archival spectra, applying the same wavelength shift as Bowen et al."
+ to convert to a heliocentric velocity scale., to convert to a heliocentric velocity scale.
+ Both the shape and flux density level of the CIIRS spectrum agree well with the IUE spectra. sugeesting the correctness of the fiux-deusity calibration. despite the possibility of a (Cobserved waveleueth) buup artifact iu the IUE SWP data (INiunev et al.," Both the shape and flux density level of the GHRS spectrum agree well with the IUE spectrum, suggesting the correctness of the flux-density calibration, despite the possibility of a (observed wavelength) bump artifact in the IUE SWP data (Kinney et al."
+ 1991)., 1991).
+ The OST aud coadded IUE spectiuu for 11001113 is shown as the lower spectrum in Figure 1., The HST and coadded IUE spectrum for 1004+13 is shown as the lower spectrum in Figure 1.
+ Beneath is a standard deviation spectrum derived from the scatter among the individual IUE spectra., Beneath is a standard deviation spectrum derived from the scatter among the individual IUE spectra.
+ The svstemic redshift τμ 20.2101 as derived from our aud Stockton Mackeutvs. (1987). imeasured wavelength of the narrow A5007 eniission line., The systemic redshift $z_{\rm em} =$ 0.2401 is derived from our and Stockton MacKenty's (1987) measured wavelength of the narrow $\lambda$ 5007 emission line.
+ Based on this. above the spectzuüii are shown the expected waveleneths of redshifted broad emission lines.," Based on this, above the spectrum are shown the expected wavelengths of redshifted broad emission lines."
+ As noted by Kinucv et al. (, As noted by Kinney et al. (
+"1991): ""Dased on this spectrum alone. 10011130 would not be classified as a QSO because of the very weak Ίσα eunission πο,","1991): “Based on this spectrum alone, 1004+130 would not be classified as a QSO because of the very weak $\alpha$ emission line.”"
+ Even the expected strong A1519 enission is not clearly preseut., Even the expected strong $\lambda$ 1549 emission is not clearly present.
+ To demonstrate the unusual weakness of the broad Lyo emission. we note that its rest equivalent width EW = is the smallest of 19 low-vedshift. radio-loud. loloe-dominant QSOs from the IST archives.," To demonstrate the unusual weakness of the broad $\alpha$ emission, we note that its rest equivalent width EW = is the smallest of 19 low-redshift, radio-loud, lobe-dominant QSOs from the HST archives."
+ The mean for this sample is140AÀ., The mean for this sample is.
+. The next smallest (Live) is for 2288.1. for which strong associated absorption is clearly preseut (Wills et al.," The next smallest $\alpha$ ) is for 288.1, for which strong associated absorption is clearly present (Wills et al."
+ 1995)., 1995).
+ Below. we compare he UV spectra of PIKS11001113 with that of a typical ὀςο.," Below, we compare the UV spectrum of 1004+13 with that of a typical QSO."
+ liunuev oet al (, Kinney et al. (
+1991) noted unresolved absorption eatures at aand that they attributed to VV. and CIIV. doublets at a redshift of 0.21.,1991) noted unresolved absorption features at and that they attributed to V and IV doublets at a redshift of 0.24.
+ The high-resolution. high sigual-to-nolse-ratio GIIRS spectra shows that the componcuts of the AAL238.12 12 doublet are further split aud that there is corresponding strong absorption in VVIAALO32. L038 (Fig.," The high-resolution, high signal-to-noise-ratio GHRS spectrum shows that the components of the $\lambda\lambda$ 1238,1242 doublet are further split and that there is corresponding strong absorption in $\lambda\lambda$ 1032,1038 (Fig."
+ 2a. by.," 2a, b)."
+ These two absorption svstenis are also seen. mt less clearly. du Lye (Fig.," These two absorption systems are also seen, but less clearly, in $\alpha$ (Fig."
+ 2c)., 2c).
+ All these features are also marked beneath the spectrum of Fig., All these features are also marked beneath the spectrum of Fig.
+ 1., 1.
+" These systems iive heliocentric absorption τους]τς of 4, = 0.2361 aud 2387. aud are intrinsically broad = respectively. 7600 kin staand 500 kins 1 ttotal width. representing outflows of 50-50 kins 1 (πιο outflow) to 1200 Ilan s.+."," These systems have heliocentric absorption redshifts of $z_a$ = 0.2364 and 0.2387, and are intrinsically broad – respectively $\sim$ 600 km $^{-1}$ and 500 km $^{-1}$ total width, representing outflows of $\pm$ 50 km $^{-1}$ (no outflow) to 1200 km $^{-1}$."
+ Tt is therefore iof surprising that the corresponding high-ionization enüsson lines should be suppressed over this velocity vanec., It is therefore not surprising that the corresponding high-ionization emission lines should be suppressed over this velocity range.
+ There is no sign of low-ionization absorption at hese redshifts in the broad MgIIIA2798 cenuissou line (Antonucci. Wills. unpublished).," There is no sign of low-ionization absorption at these redshifts in the broad $\lambda$ 2798 emission line (Antonucci, Wills, unpublished)."
+ Both VVI doublets appear optically thick DN~6). with absorbing gas covering only to of the contimmun source (usine the method of Arav ct al.," Both VI doublets appear optically thick ${\tau}_{1034{\rm\AA}} \sim 6$ ), with absorbing gas covering only to of the continuum source (using the method of Arav et al."
+ 1999)., 1999).
+ Thus the absorption is intrinsic to the QSO., Thus the absorption is intrinsic to the QSO.
+ The result for the VV doublets are consistent. but with larger uncertainties.," The result for the V doublets are consistent, but with larger uncertainties."
+ We also note the probable existence of broad absorption troughs at even greater outflow velocities up to 10 0000 liu i4., We also note the probable existence of broad absorption troughs at even greater outflow velocities – up to $\sim$ 000 km $^{-1}$.
+ The waveleneth ranee corresponding to 0 to 100000 kun L| ds indicated by shading in Figure L. for OVVIAI031. πας AI210. AL397. and A1519.," The wavelength range corresponding to 0 to $-$ 000 km $^{-1}$ is indicated by shading in Figure 1, for $\lambda$ 1034, $\alpha$, $\lambda$ 1240, $\lambda$ 1397, and $\lambda$ 1549."
+ The CIIV associated aud broader absorption are visible ou the IVE two-dimensional nuages for the 3 long-exposure spectra., The IV associated and broader absorption are visible on the IUE two-dimensional images for the 3 long-exposure spectra.
+ These BAL-like troughs suggest a reason why the Lya-N A1210 broad enüssion is so weak: it has been suppressed largely by VV absorption., These BAL-like troughs suggest a reason why the $\alpha$ $\lambda$ 1240 broad emission is so weak: it has been suppressed largely by V absorption.
+ The ἵνα BBAL would appear to be much weaker than for the higher ionization species., The $\alpha$ BAL would appear to be much weaker than for the higher ionization species.
+ Above the PIS 1001113 spectrum. we show for comparison a spectrum of the well-known BAL QSO. 00916|301. (I&orista Aray 1997). redshitted to align the broad. absorption features as indicated by the shaded strips.," Above the PKS 1004+13 spectrum, we show for comparison a spectrum of the well-known BAL QSO, 0946+301 (Korista Arav 1997), redshifted to align the broad absorption features as indicated by the shaded strips."
+ Note the suppression of broad Lvo euissiou by the VV DAL for 00916|301., Note the suppression of broad $\alpha$ emission by the V BAL for 0946+301.
+ Ilieher qualitv UV spectroscopy would confini the reality of BALs in PIS 1001]13., Higher quality UV spectroscopy would confirm the reality of BALs in PKS 1004+13.
+" One wav in principle to distinguish absorption from enuüssion. and isolate the absorption spectrum of 11001]13. is to divide by a ""normal QSO spectrin."," One way in principle to distinguish absorption from emission, and isolate the absorption spectrum of 1004+13, is to divide by a `normal' QSO spectrum."
+ We and others (e.g. Wills et al.," We and others (e.g., Wills et al."
+ 1999) have shown that the ereatest spectrüunrto-spectruni differences can be deseribed bw bhunuinositv relationships (the Baldwin effect). depeudeuce ou Boroson aud (σουκ (1992) optical Principal Component 1 (PCT). and radio core-dominauce (Baker Thiustead 1995. Vestereaard 1998).," 1999) have shown that the greatest spectrum-to-spectrum differences can be described by luminosity relationships (the Baldwin effect), dependence on Boroson and Green's (1992) optical Principal Component 1 (PC1), and radio core-dominance (Baker Hunstead 1995, Vestergaard 1998)."
+ Therefore we choose to divide bv a QSO spectrin that is quite siuilu in huuinositv. radio core-donunance. aud in optical PCL properties.," Therefore we choose to divide by a QSO spectrum that is quite similar in luminosity, radio core-dominance, and in optical PC1 properties."
+ We chose3022635. with EW(Lya) =LILA. and EW(CIIV) =86À.. from a sample of radio- QSOs (Wills et al.," We chose, with $\alpha$ ) =, and IV) =, from a sample of radio-loud QSOs (Wills et al."
+ 1995)., 1995).
+ Figure 3 shows the result. and serves to illustrate the approximate streneth of the VV absorption.," Figure 3 shows the result, and serves to illustrate the approximate strength of the V absorption."
+ This techuique would eive au accurate absorption profile only if the template spectrum were an accurate match to the cussion Lue spectrum of PES 10011123. and in the uulikely situation that the absorbing," This technique would give an accurate absorption profile only if the template spectrum were an accurate match to the emission line spectrum of PKS 1004+13, and in the unlikely situation that the absorbing"
+"the passage of the cooling frequency v,. through the observing band or by the core edge becoming visible.",the passage of the cooling frequency $\nu_c$ through the observing band or by the core edge becoming visible.
+ For the former. Aq= 1/Leither if the entire visible region of the fireball is within its core or if the core edge is observable but g>3$.," For the former, $\Delta \alpha = 1/4$ either if the entire visible region of the fireball is within its core or if the core edge is observable but $q > \tilde{q}$."
+ For q« qg. the passage of i. (which decreases in time for a homogeneous medium. but increases if the medium is wind- yields An=(20«ϱδστι.," For $q < \tilde{q}$ , the passage of $\nu_c$ (which decreases in time for a homogeneous medium, but increases if the medium is wind-like) yields $\Delta \alpha = (2-q)/(8-q) < 1/4$."
+" Because 2ó increases with à and à(8)—(1.s).V2«1. when the core edge becomes visible (5(f...0,.)0,.= 1) the core edge is outside the inner disk (0.>(f, ))."," Because $\gamma \delta$ increases with $\delta$ and $\tildelta \, \gamma (\tildelta) = (4-s)^{-1/2} 
+< 1$, when the core edge becomes visible $\gamma (t_c,\theta_c) \theta_c = 1$ ) the core edge is outside the inner disk $\theta_c > \tildelta (t_c)$ )."
+" Therefore GL) satisfies equation 15)). which. together with (f.0.)=0,!. yields For q>4 the light-curve break across t. is Aa=3/1 for a homogeneous medium and Aa=1/2 for a wind. while for q<q the break ts Therefore the maximal light-curve break that a non-spreading. power-law fireball can yield to an observer located with its uniform core ts 2/1 for a homogeneous medium and 1/2 for a wind (Panaitescu. Mésszirros Rees 1998)."," Therefore $\gamma (t_c,\theta_c)$ satisfies equation \ref{rg2}) ), which, together with $\gamma (t_c,\theta_c) = \theta_c^{-1}$, yields For $q > \tilde {q}$ the light-curve break across $t_c$ is $\Delta \alpha = 3/4$ for a homogeneous medium and $\Delta \alpha = 1/2$ for a wind, while for $q < \tilde{q}$ the break is Therefore the maximal light-curve break that a non-spreading, power-law fireball can yield to an observer located with its uniform core is $3/4$ for a homogeneous medium and $1/2$ for a wind (Panaitescu, Mésszárros Rees 1998)."
+ The evolution of the light-curve index o(f). obtained by calculating numerically the integral of equation (8) without the simplifications made subsequently). for an observer is shown im Figure ] for some values of the structural parameter 4.," The evolution of the light-curve index $\alpha (t)$, obtained by calculating numerically the integral of equation \ref{fnu2}) ) without the simplifications made subsequently), for an on-axis observer is shown in Figure 1 for some values of the structural parameter $q$."
+" Before the edge core becomes visible. the index a=a, given by equation (22))."," Before the edge core becomes visible, the index $\alpha = \alpha_1$ given by equation \ref{a1}) )."
+" When the core edge becomes visible. at #—f.~2«10°£, for s=0 and ~110°fa fors=2 (f, being the observer frame deceleration timescale for the fluid moving toward the observer: 0.— 0). the index à increases toward the à» given in equations (25)) and (26) for ¢=1«q and that given in equation (27)) for q=2.3>d."," When the core edge becomes visible, at $t=t_c \sim 2\times 10^3\, t_d$ for $s=0$ and $\sim 4 
+\times 10^3\, t_d$ for $s=2$ $t_d$ being the observer frame deceleration timescale for the fluid moving toward the observer: $\theta=0$ ), the index $\alpha$ increases toward the $\alpha_2$ given in equations \ref{a20}) ) and \ref{a22}) ) for $q = 1 < \tilde{q}$ and that given in equation \ref{a2}) ) for $q = 2, 3 > \tilde{q}$."
+" As shown in Figure |. of the light-curve decay steepening across f,. lasts a factor 4-6 in time for s=0 and a factor 7-10 for s=2."," As shown in Figure 1, of the light-curve decay steepening across $t_c$ lasts a factor 4–6 in time for $s=0$ and a factor 7–10 for $s=2$."
+" The slower transition for a wind- medium is caused by the slower decrease of the fireball Lorentz factor with time. given in equations (14)) and (15)): fors= 0.7x£YS ifsc Gand sx£2 d£ >à. while for s= 2.5x£ll and 4x¢(7, respectively."," The slower transition for a wind-like medium is caused by the slower decrease of the fireball Lorentz factor with time, given in equations \ref{rg1}) ) and \ref{rg2}) ): for $s=0$, $\gamma 
+\propto t^{-3/8}$ if $\delta < \tildelta$ and $\gamma \propto t^{-3/2}$ if $\delta > \tildelta$, while for $s=2$, $\gamma \propto t^{-1/4}$ and $\gamma \propto t^{-1/2}$, respectively."
+ The fireball deceleration being slower for a wind-like medium. it takes a longer time for the core edge to become fully visible. thus the transition between the asymptotic light-curve indices is smoother.," The fireball deceleration being slower for a wind-like medium, it takes a longer time for the core edge to become fully visible, thus the transition between the asymptotic light-curve indices is smoother."
+ Figure | also shows the light-curve steepening for a fireball with 4=x. corresponding to a uniform. collimated outflow with a sharp edge. undergoing lateral spreading.," Figure 1 also shows the light-curve steepening for a fireball with $q=\infty$, corresponding to a uniform, collimated outflow with a sharp edge, undergoing lateral spreading."
+ Due to the widening of the jet aperture. a(f«f.) is not constant. but increases slowly in time.," Due to the widening of the jet aperture, $\alpha (t < t_c)$ is not constant, but increases slowly in time."
+ Furthermore. a(#>f.) Is larger than without lateral spreading. reaching αυ=p (Rhoads 1999).," Furthermore, $\alpha (t \gg t_c)$ is larger than without lateral spreading, reaching $\alpha_2 = p$ (Rhoads 1999)."
+ For a uniform. spreading jet. interacting with a homogeneous medium. the fastest of the analytically expected steepening Aa=pay is acquired over a factor 20 in time if £6.<vy. and 10 if vy.<ν. while for a wind- medium the corresponding factors are 100 and. 1.000. respectively.," For a uniform, spreading jet, interacting with a homogeneous medium, the fastest of the analytically expected steepening $\Delta \alpha = p - \alpha_1$ is acquired over a factor 20 in time if $\nu < \nu_c$ and 10 if $\nu_c < \nu$, while for a wind-like medium the corresponding factors are 100 and 1,000, respectively."
+ Therefore the “jet-break” transition is significantly slower and smoother tf the surrounding medium is the wind that a massive GRB progenitor expelled before the burst (Kumar Panaitescu 2000).," Therefore the ""jet-break"" transition is significantly slower and smoother if the surrounding medium is the wind that a massive GRB progenitor expelled before the burst (Kumar Panaitescu 2000)."
+" For observers located outside the uniform fireball core. the pre-break light-curve fall-off is mitigated as the more energetic ejecta located closer to the fireball axis become visible. therefore the early time light-curve index a, decreases in time (see also the light-curves presented by Granot Kumar 2003 and Wei Jin 2003)."," For observers located outside the uniform fireball core, the pre-break light-curve fall-off is mitigated as the more energetic ejecta located closer to the fireball axis become visible, therefore the early time light-curve index $\alpha_1$ decreases in time (see also the light-curves presented by Granot Kumar 2003 and Wei Jin 2003)."
+" The fireball axis is seen at a time satisfying similar to the time £,. when the core edge becomes visible to an on-axis observer [28]]) but with the core size 0, replaced by the angle 0,4, between the fireball axis and the center — observer line (Rossi. Lazzati Rees 2002)."," The fireball axis is seen at a time satisfying similar to the time $t_c$ when the core edge becomes visible to an on-axis observer ]) but with the core size $\theta_c$ replaced by the angle $\theta_{obs}$ between the fireball axis and the center – observer line (Rossi, Lazzati Rees 2002)."
+" Well after ¢,,. when the beaming factor D is almost the same across the fireball core. the light-curve index for an off-core observer should reach that given in equations (25))-(27)) for an on-axis observer."," Well after $t_a$, when the beaming factor ${\cal D}$ is almost the same across the fireball core, the light-curve index for an off-core observer should reach that given in equations \ref{a20}) \ref{a2}) ) for an on-axis observer."
+" Thus. the fattening of the light-curve fall-off at <f, yields larger light-curve breaks Acq than for an on-axis observer."," Thus, the flattening of the light-curve fall-off at $t< t_a$ yields larger light-curve breaks $\Delta \alpha$ than for an on-axis observer."
+ This is the most important feature arising from the structure of the outflow., This is the most important feature arising from the structure of the outflow.
+" Figure 2 shows the evolution of « obtained from equation (8)) for an off-core observer located at 0,4,=230..", Figure 2 shows the evolution of $\alpha$ obtained from equation \ref{fnu2}) ) for an off-core observer located at $\theta_{obs} = 3 \theta_c$.
+" As can be noticed. a stronger fall-off of the ejecta energy away from the fireball axis à larger parameter 4). leads to à more prominent flattening of the afterglow light-curve at? <fj. where £,—3«10?#,(0=0) for s=0 and ~10#,(00) for s=2."," As can be noticed, a stronger fall-off of the ejecta energy away from the fireball axis a larger parameter $q$ ), leads to a more prominent flattening of the afterglow light-curve at $t < t_a$, where $t_a \sim 3 \times 10^3\, t_d (\theta=0)$ for $s=0$ and $\sim 10^5\, t_d (\theta=0)$ for $s=2$."
+" Also as expected. at ¢“>f£, the index a asymptotically reaches the values for an on-axis observer."," Also as expected, at $t \gg t_a$ the index $\alpha$ asymptotically reaches the values for an on-axis observer."
+" Note that. for the same parameter q. the light-curve break Ao across f, is larger for a homogeneous medium. and that the transition between the lowest value of a and the e» at late time takes about a decade in time for a homogeneous medium and about two decades for a wind-like medium."," Note that, for the same parameter $q$, the light-curve break $\Delta \alpha$ across $t_a$ is larger for a homogeneous medium, and that the transition between the lowest value of $\alpha$ and the $\alpha_2$ at late time takes about a decade in time for a homogeneous medium and about two decades for a wind-like medium."
+ The slow transition in the latter case (see also Dai Gou 2001 and Granot Kumar 2003) suggests that. for a wind-like stratified medium. light-curve breaks arising from the structure of the outflow may be too shallow compared the light-curve steepenings observed in some afterglows. which last less than a decade in time.," The slow transition in the latter case (see also Dai Gou 2001 and Granot Kumar 2003) suggests that, for a wind-like stratified medium, light-curve breaks arising from the structure of the outflow may be too shallow compared the light-curve steepenings observed in some afterglows, which last less than a decade in time."
+" The minimal value ο reached by the light-curve index before the break depends not only on the structural parameter q. às shown in Figure 2. but also on the location of the observer. through the ratio 0,4,θε. and on the slope p of the electron distribution."," The minimal value $\alpha_{min}$ reached by the light-curve index before the break depends not only on the structural parameter $q$, as shown in Figure 2, but also on the location of the observer, through the ratio $\theta_{obs}/\theta_c$, and on the slope $p$ of the electron distribution."
+ As illustrated 1n. Figure 3. the observer location has a much stronger effect on the sharpness of the light-curve break produced by the fireball structure if the external medium is homogeneous.," As illustrated in Figure 3, the observer location has a much stronger effect on the sharpness of the light-curve break produced by the fireball structure if the external medium is homogeneous."
+" In this case. for observer directions further away fromthe fireball axis. 0,,;,, decreases and the transition between ,,;,, and the o» at late times lasts shorter (relative to the break-time ¢,,). the light-curve break becoming sharper."," In this case, for observer directions further away fromthe fireball axis, $\alpha_{min}$ decreases and the transition between $\alpha_{min}$ and the $\alpha_2$ at late times lasts shorter (relative to the break-time $t_a$ ), the light-curve break becoming sharper."
+ Consequently. for a homogeneous medium. higher observer offsets will accommodate easier some of the observed sharp breaks.," Consequently, for a homogeneous medium, higher observer offsets will accommodate easier some of the observed sharp breaks."
+ However. given the expected correlation between the GRB peak flux and the energy of ejecta moving toward the observer. large observer offsets render the burst less likely to be detected.," However, given the expected correlation between the GRB peak flux and the energy of ejecta moving toward the observer, large observer offsets render the burst less likely to be detected."
+ Furthermore. for homogeneous media. as shown in Figure 3. large offsets also yield. pre-break light-curve indices that are too small compared to those observed.," Furthermore, for homogeneous media, as shown in Figure 3, large offsets also yield pre-break light-curve indices that are too small compared to those observed."
+ Taking, Taking
+in Fig. 2..,in Fig. \ref{t_flu}.
+ It is interesting that the £? value (~ 0.01) required to match the observed [O ΠΠ AA1363.5007 line ποβ]ος is unuch lower than that derived from the II Bahucr Jump and |O lines (P=0.015: Liu et al. 20003).," It is interesting that the $t^2$ value $\sim0.01$ ) required to match the observed [O ] $\lambda\lambda4363,5007$ line profiles is much lower than that derived from the H Balmer Jump and [O ] lines $t^2=0.045$; Liu et al. \cite{liubarlow00}) )."
+ This appears to support the idea that the two-abundance uchulaa-componcut model accurately describes he observations. to discount the theory that temperature Huctuations are the cause of the CEL/ORL abuudauce dichotomy.," This appears to support the idea that the two-abundance nebular-component model accurately describes the observations, to discount the theory that temperature fluctuations are the cause of the CEL/ORL abundance dichotomy."
+ These conclusions are. however. arguable since he analysis of [JO 111] AA1363.5007 line profiles cau provide ouly a lower limit to the temperature variations alone the ine of sight (see below).," These conclusions are, however, arguable since the analysis of [O ] $\lambda\lambda4363,5007$ line profiles can provide only a lower limit to the temperature variations along the line of sight (see below)."
+" To study the temperature variations. we define the average temperature των aud the mean square temperature fluctuation parameter H in velocity space by and where eds the velocity along the line of sight. aud T;(c) and £,(11.+) are the electron teniperature deduced from the forbidden line iuteusitv ratio aud the iuteusitv of IDs (xANVNS) at a given velocity. respectively."," To study the temperature variations, we define the average temperature $T_{0,v}$ and the mean square temperature fluctuation parameter $t^2_v$ in velocity space by and where $v$ is the velocity along the line of sight, and $T_{\rm e}(v)$ and $I_v({\rm H}\beta)$ are the electron temperature deduced from the forbidden line intensity ratio and the intensity of $\beta$ $\propto N_{\rm p}N_{\rm e}$ ) at a given velocity, respectively."
+ The iutegratious in the two equatious are over velocity space., The integrations in the two equations are over velocity space.
+ As defined by Eqs. (, As defined by Eqs. (
+"3) aud CL. Zo, and H characterize temperature fluctuations along the line of sight and are simular to those introduced to explain the T.¢ [ο TAIT 1) discrepancy. which are given iu Eqs. (","3) and (4), $T_{0,v}$ and $t^2_v$ characterize temperature fluctuations along the line of sight and are similar to those introduced to explain the $T_{\rm e}$ ([O $T_{\rm e}$ (H ) discrepancy, which are given in Eqs. ("
+1) aud (2).,1) and (2).
+ In Eqs. (, In Eqs. (
+3) ancl (1). we can use Z0NA!). which is the intensity of a CEL used to determine Tite). as weights stead of £T).,"3) and (4), we can use $I_v({\rm X}^{i+})$, which is the intensity of a CEL used to determine $T_{\rm e}(v)$, as weights instead of $I_v({\rm H}\beta)$."
+ However. if significant density variations are preseut aloug the line of sieht. it may be problematic to use fX) since its density depeudences differ in hieh- aud low-density roeglous.," However, if significant density variations are present along the line of sight, it may be problematic to use $I_v({\rm X}^{i+})$ since its density dependences differ in high- and low-density regions."
+ Using Eqs. (, Using Eqs. (
+3) aud (1). we calculated τοι and H for three PNe. IC 2501. IC. 1191. and NCC 2110.,"3) and (4), we calculated $T_{0,v}$ and $t^2_v$ for three PNe, IC 2501, IC 4191, and NGC 2440."
+ Our data were acquired using the Las Campanas Observatory (LOCO) Baade 6.51 telescope with the ΑΠΙΝΤ echelle spectrograph. viclding a resolution of ~25.000 (sce Sharpee et al.," Our data were acquired using the Las Campanas Observatory (LCO) Baade 6.5m telescope with the MIKE echelle spectrograph, yielding a resolution of $\sim25,000$ (see Sharpee et al."
+ 2007— for a detailed description of the observations)., \cite{sharpee07} for a detailed description of the observations).
+ The results are given in Table 1.., The results are given in Table \ref{tab1}.
+" For IC. 1191 and NGC 2110 the values of Ty, aud H are measured using the [O 111] AA1363.5007 lines."," For IC 4191 and NGC 2440 the values of $T_{0,v}$ and $t^2_v$ are measured using the [O ] $\lambda\lambda4363,5007$ lines."
+ For the low-excitation PN IC 2501. the slit was placed on the edge of the compact OF! regions aud the thermal broadening provides a dominant contribution to the profiles of the [ο lines.," For the low-excitation PN IC 2501, the slit was placed on the edge of the compact $^{2+}$ regions and the thermal broadening provides a dominant contribution to the profiles of the [O ] lines."
+" For IC 2501 we obtained Ty, aud fz using iustead the single-ionization lines [N 11] AA75L16678 lines."," For IC 2501 we obtained $T_{0,v}$ and $t^2_v$ using instead the single-ionization lines [N ] $\lambda\lambda5754,6678$ lines."
+ For the calculations. the reddening cocficient and the clectrou deusitics presented by Slarpee et al. (2007))," For the calculations, the reddening coefficient and the electron densities presented by Sharpee et al. \cite{sharpee07}) )"
+ were adopted., were adopted.
+ As depicted in Fig. 3..," As depicted in Fig. \ref{t_v},"
+ the temperature variations in the velocity space are minor for the three PN¢, the temperature variations in the velocity space are minor for the three PNe.
+ Based ou the values of T(O 11]) aud 111 1) oxesented by Sharpee et al. (2007)).," Based on the values of$T_{\rm e}$ ([O ]) and $T_{\rm e}$ (H ) presented by Sharpee et al. \cite{sharpee07}) ),"
+ we determined Ty aud f using Ponuberts formulae (Peiiibert. 1967))., we determined $T_0$ and $t^2$ using Peimbert's formulae (Peimbert \cite{peimbert67}) ).
+ The caleulatious were based ou the assuniption- that the 031uD aud II! regions are identical. which is appropriate for our studied PNe since their O! Οἱ O72!) abundance ratios are consistently lower than 0.1 (Sharpee et al. 2007)).," The calculations were based on the assumption that the $^{2+}$ and $^{+}$ regions are identical, which is appropriate for our studied PNe since their $^{+}$ $^{+}$ $^{2+}$ ) abundance ratios are consistently lower than 0.1 (Sharpee et al. \cite{sharpee07}) )."
+ The resultant Ty aud £7 ave given in Table L.., The resultant $T_0$ and $t^2$ are given in Table \ref{tab1}. .
+ If the discrepancy between {ο mn aud ZI 1) d8 caused by small temperature fluctuations. the £2 measured by. ΤΟ. tu)," If the discrepancy between $T_{\rm e}$ ([O ]) and $T_{\rm e}$ (H ) is caused by small temperature fluctuations, the $t^2$ measured by $T_{\rm e}$ ([O ])"
+"convergence rate for the VST. the constant οἱ) associated to 7! should be set to: The MS-VSTS|IUWT procedure is directly invertible as we have: Setting bY):—sentiMn| if A ds constaut within the support of the filter. Aly),","convergence rate for the VST, the constant $c^{(j)}$ associated to $h^{(j)}$ should be set to: The MS-VSTS+IUWT procedure is directly invertible as we have: Setting $b^{(j)}:=\text{sgn}(\tau_1^{(j)})/\sqrt{|\tau_1^{(j)}|}$, if $\lambda$ is constant within the support of the filter. $h^{(j)}$,"
+ then we have (?):: where ©...) denotes inner product.," then we have \citep{Zhang}: where $\langle . , . \rangle$ denotes inner product."
+ It iue that the detail coefficients issued frou locally homogeneous parts of the signal follow asviuptotieallv a central uormal distribution with an intensitv-Indepenudaut varlance which relics solely on the filter 7 and the curren scale. for a eiven filter Ph., It means that the detail coefficients issued from locally homogeneous parts of the signal follow asymptotically a central normal distribution with an intensity-independant variance which relies solely on the filter $h$ and the current scale for a given filter $h$.
+ Consequently. the stabilized variances and the constants DU el HouNE can all be pre-computed.," Consequently, the stabilized variances and the constants $b^{(j)}$ $c^{(j)}$ $\tau_k^{(j)}$ can all be pre-computed."
+ Let us define] U the stabilizedeq: variance. at seale j for a locallyum homogeneous part of the signal: To compute the σι. bU egy]) we oulv have to know the filters 5.," Let us define $\sigma_{(j)}^2$ the stabilized variance at scale $j$ for a locally homogeneous part of the signal: To compute the $\sigma_{(j)}$, $b^{(j)}$ $c^{(j)}$ $\tau_k^{(j)}$, we only have to know the filters $h^{(j)}$."
+" We compute these filters thanks to the fornmla a;=fl! “ay. DV applying the IUWT to a Dirac mise ay=0,"," We compute these filters thanks to the formula $a_j = h^{(j)} \ast a_0$ , by applying the IUWT to a Dirac pulse $a_0 = \delta$."
+ Then. the 57 are the scaling cocfiicicuts of tle IUWT.," Then, the $h^{(j)}$ are the scaling coefficients of the IUWT."
+ The σι have been precoiiputed for a G-scaled IUWT (Table 1))., The $\sigma_{(j)}$ have been precomputed for a 6-scaled IUWT (Table \ref{sigmaj}) ).
+" We have simulated Poisson images of different constant mtensities A. computed the IUWT with AIS-VSTS on cach image and observed the variation of the normalized value of 0,5) (COG)anular/UTGhbrheoreric al) as a function or each scale j (Fig. 1))."," We have simulated Poisson images of different constant intensities $\lambda$, computed the IUWT with MS-VSTS on each image and observed the variation of the normalized value of $\sigma_{(j)}$ $\mathbf{ (\sigma_{(j)})_{\text{simulated}}} / (\sigma_{(j)})_{\text{theoretical}}$ ) as a function of $\lambda$ for each scale $j$ (Fig. \ref{sigma}) )."
+" We see hat the wavelet coefficients are stabilized when A=0.1 except for the first wavelet scale. which is mostly coustituted of noise,"," We see that the wavelet coefficients are stabilized when $\lambda \gtrsim 0.1$ except for the first wavelet scale, which is mostly constituted of noise."
+ On Fig. 2..," On Fig. \ref{ansc},"
+ we compare the rOesn of MS-VSTS with Anscombe | wavelet shrinkage. on sources of varviug intensities.," we compare the result of MS-VSTS with Anscombe + wavelet shrinkage, on sources of varying intensities."
+ We see that AIS-VSTS works well ou sources of very low 1iteusitics. whereas Anscombe doesu't work when the intensity is too low.," We see that MS-VSTS works well on sources of very low intensities, whereas Anscombe doesn't work when the intensity is too low."
+ As the frst step of the algorithm is an IUNT. we can stabilize each resolution level as in Equation (7)).," As the first step of the algorithm is an IUWT, we can stabilize each resolution level as in Equation \ref{eq27}) )."
+ We then apply the local ridgelet transform: on cach stabilized wavelet baud., We then apply the local ridgelet transform on each stabilized wavelet band.
+ It is not as straightforward as with the IUWT to derive the asvinptotic noise variance in the stabilized curvelet domain., It is not as straightforward as with the IUWT to derive the asymptotic noise variance in the stabilized curvelet domain.
+ Im our experiments. we derived them using simulated Poisson data of stationary intensity level A.," In our experiments, we derived them using simulated Poisson data of stationary intensity level $\lambda$."
+ After having checked that the standard deviation in the curvelet bands becomes stabilized as the iutensitv level increases Qvhich means that the stabilization is working properly). we stored the standard deviation 04 for cach wavelet scale j and cach ridgclet band 1 (Table 2)).," After having checked that the standard deviation in the curvelet bands becomes stabilized as the intensity level increases (which means that the stabilization is working properly), we stored the standard deviation $\sigma_{j,l}$ for each wavelet scale $j$ and each ridgelet band $l$ (Table \ref{tabcurv}) )."
+ Under the hypothesis of homogeneous Poisson intensity. the stabilized wavelet cocfficicuts d; behave like centered Ciaunssian variables of standard deviation oj).," Under the hypothesis of homogeneous Poisson intensity, the stabilized wavelet coefficients $d_j$ behave like centered Gaussian variables of standard deviation $\sigma_{(j)}$."
+ We can detect sienificaut cocticicnts with inary hypothesis testing as in Camssian denoising., We can detect significant coefficients with binary hypothesis testing as in Gaussian denoising.
+ Under the unl hypothesis Hy of homogceucous Poisson intensity. the distribution of the stabilized wavelet cocfficicnut d;|&| at scale { and location index & ean be written as: The rejection of the hypothesis Hy depends on the double-sided p-value: Consequently. to accept or reject Hy. we compare each |/;[k|| with a critical threshold Ko; KR=3.Lor correspouding respectively to significance levels.," Under the null hypothesis $\mathcal{H}_0$ of homogeneous Poisson intensity, the distribution of the stabilized wavelet coefficient $d_j[k]$ at scale $j$ and location index $k$ can be written as: The rejection of the hypothesis $\mathcal{H}_0$ depends on the double-sided p-value: Consequently, to accept or reject $\mathcal{H}_0$, we compare each $|d_j[k]|$ with a critical threshold $\kappa \sigma_j$, $\kappa= 3,4 \text{ or } 5$ corresponding respectively to significance levels."
+ This amonuts to deciding that: Then we have to invert the AIS-VSTS scheme to reconstruct the estimate., This amounts to deciding that: Then we have to invert the MS-VSTS scheme to reconstruct the estimate.
+ Towever. althoughthe direct inversion is possible (Eq. (10))).," However, althoughthe direct inversion is possible (Eq. \ref{eq30}) )),"
+" if can not enarantee a positive intensity estimate. while the Poisson intensity is always nonnegative,"," it can not guarantee a positive intensity estimate, while the Poisson intensity is always nonnegative."
+ À positivity projection can be, A positivity projection can be
+Another property to be explored is the /Balmer ratio which one might expect to depend upon white dwarf mass on 1c basis that accretion onto higher mass white cwarfs will oduce more photons capable of ionisingHe1r.,Another property to be explored is the /Balmer ratio which one might expect to depend upon white dwarf mass on the basis that accretion onto higher mass white dwarfs will produce more photons capable of ionising.
+. In Fig., In Fig.
+ 10 we have plotted those two quantities for those svstems where 15 mass of the white cwarl has been measured., \ref{res:wdheiihr} we have plotted those two quantities for those systems where the mass of the white dwarf has been measured.
+ There is no correlation apparent., There is no correlation apparent.
+ In most cases the measurements of 1e masses of the compact objects have been. performed. by measuring the white dwarf racial velocity. semi-amplituce uid combining it with the radial velocity semi-aumplitude of re companion star., In most cases the measurements of the masses of the compact objects have been performed by measuring the white dwarf radial velocity semi-amplitude and combining it with the radial velocity semi-amplitude of the companion star.
+ Assuming a mass for the donor star depending on its spectral type. a value for the mass of the ‘ompact object is obtained.," Assuming a mass for the donor star depending on its spectral type, a value for the mass of the compact object is obtained."
+ Lt is worth mentioning tha is method is known to produce very uncertain results and that the uncertainties in the mass determinations could completely mask any such a relationship ifit existed., It is worth mentioning that this method is known to produce very uncertain results and that the uncertainties in the mass determinations could completely mask any such a relationship if it existed.
+ When we explore the correlation hxtween the LEW of the Iline versus the mass of the compact object. the mass of the donor star. and the mass ratio of the svstem we reach the same conclusion: there is no correlation between the masses of the components of the binaries and the LEEW.," When we explore the correlation between the EW of the line versus the mass of the compact object, the mass of the donor star, and the mass ratio of the system we reach the same conclusion: there is no correlation between the masses of the components of the binaries and the EW."
+ Ht is worth emphasising again that he values for the white chwarl masses are very uncertain., It is worth emphasising again that the values for the white dwarf masses are very uncertain.
+ Aso we should not orget that the EWs of the lines can change significantly for one system during the outburst. e.g. the I5ENV of U Gem during its Αρνίλίαν 2001 outburst changes rom -l t0 4 throughout the outburst (Steeghs private communication).," Also we should not forget that the EWs of the lines can change significantly for one system during the outburst, e.g. the EW of U Gem during its April/May 2001 outburst changes from -1 to 4 throughout the outburst (Steeghs private communication)."
+ The EW values plotted. here are measured at a particular ime during outburst that is not the same for all the svstenis slotted which again may mask any correlations., The EW values plotted here are measured at a particular time during outburst that is not the same for all the systems plotted which again may mask any correlations.
+ In Fig., In Fig.
+ 11. we present the EW of the [line measured from cach dwarf nova spectrum presented in this paper versus its orbital period (Ritter Ixolb 1998)., \ref{res:heiiewperiod} we present the EW of the line measured from each dwarf nova spectrum presented in this paper versus its orbital period (Ritter Kolb 1998).
+ As there is a correlation between the dwarf nova type ancl its orbital period. we have used different svmbols for U Gena. SU UMa and Z Cam svstems.," As there is a correlation between the dwarf nova type and its orbital period, we have used different symbols for U Gem, SU UMa and Z Cam systems."
+ It is clear that there is no correlation between the orbital. period. of the CV and the strength of the eemission., It is clear that there is no correlation between the orbital period of the CV and the strength of the emission.
+ “Phe orbital periods of 9 of the dwarf. novae presented in this study are unknown and therefore have not been included in this plot., The orbital periods of 9 of the dwarf novae presented in this study are unknown and therefore have not been included in this plot.
+ We already. mentioned in section 4.2 that the EW of one particular line might change consicerably throughout the outburst., We already mentioned in section 4.2 that the EW of one particular line might change considerably throughout the outburst.
+ By introducing the concept of outburst phase. Oo (lime since the start of the outburst divided by the length. of the outburst) we can use our sample of dwarf novae to study whether there is anv relationship between the EW and. FWIIAL of the lines anc the outburst phase at which they were observed.," By introducing the concept of outburst phase, $\phi_{\rm out}$, (time since the start of the outburst divided by the length of the outburst) we can use our sample of dwarf novae to study whether there is any relationship between the EW and FWHM of the lines and the outburst phase at which they were observed."
+ “Phe outburst phases for the dwarf novae observed are given in Table 2.., The outburst phases for the dwarf novae observed are given in Table \ref{res:phase:tab}.
+ Phe top panel of Fig., The top panel of Fig.
+ 12. presents the ENIENM. and EW measured for aandA4686AL., \ref{res:phase} presents the FWHM and EW measured for and.
+ “Pwo values for the FWILAL of aare presented. one was measured when the line was in absorption and the other when the line was in emission or when the absorption line showed an emission core.," Two values for the FWHM of are presented, one was measured when the line was in absorption and the other when the line was in emission or when the absorption line showed an emission core."
+ The bottom panel of Fig., The bottom panel of Fig.
+ 12 shows also the EPWILM and EW for both lines but this time versus the average times between outbursts., \ref{res:phase} shows also the FWHM and EW for both lines but this time versus the average times between outbursts.
+ We calculated these by using VSNIZT lietheurves that span over vears., We calculated these by using VSNET ligthcurves that span over years.
+ One of the dwarf novae. Gly Por. has not been included in this bottom figure because its outburst," One of the dwarf novae, GK Per, has not been included in this bottom figure because its outburst"
+We have analyzed the observations D aud C that are pointed toward the same direction.,We have analyzed the observations B and C that are pointed toward the same direction.
+ Axa first step we have considered the data of the three EPIC cameras. 2 MOS (Turneretal. 2000)) and 1 PN (Strtideretal. 2000)) aud of the B and € observations. separately.," As a first step we have considered the data of the three EPIC cameras, 2 MOS \cite{T++00}) ) and 1 PN \cite{S++00}) ) and of the B and C observations, separately."
+" By cross-matching the iudividual source lists we lave been able to derive: i} the relative spatial registering of the two MOS cameras (their mean relative aliguiment is currently of ~ 1"" with a mus of 37) as well as that of the PN one: ii) a preliminary absolute spatial registering of the MOS cameras that is currently accurate to ~ 3” as measured by the median offset between X-ray aud optical positions.", By cross-matching the individual source lists we have been able to derive: i) the relative spatial registering of the two MOS cameras (their mean relative alignment is currently of $\sim$ $^{\prime\prime}$ with a rms of $^{\prime\prime}$ ) as well as that of the PN one; ii) a preliminary absolute spatial registering of the MOS cameras that is currently accurate to $\sim$ $^{\prime\prime}$ as measured by the median offset between X-ray and optical positions.
+ These latter are taken from the catalogue we lave used for identification purpose., These latter are taken from the catalogue we have used for identification purpose.
+ By cross-imatcling the positions of, By cross-matching the positions of
+where the pressure is denoted by P. the density. p.the velocity e. the corresponding Lorentz factor 5. and the density in the fixed frame p!=p5.,"where the pressure is denoted by $P$, the density $\rho$,the velocity $v$, the corresponding Lorentz factor $\gamma$, and the density in the fixed frame $\rho^\prime = \rho \gamma$."
+ In the shocked ambient medium. the ultra-relativistic equation of state is assumed.," In the shocked ambient medium, the ultra-relativistic equation of state is assumed."
+ Thus 5=4/3 and the energy. densitv € per uni mass is wrillen as e=3/?/p bx neglecting the rest mass energy. density., Thus $\hat{\gamma} = 4/3$ and the energy density $\epsilon$ per unit mass is written as $\epsilon=3P/\rho$ by neglecting the rest mass energy density.
+ These approximations lead to the same equations as presented in Blandford&Mclxee(1976)., These approximations lead to the same equations as presented in \citet{Blandford76}.
+. On the other hand. it is found that the rest mass energy should not be ignored in the shocked ejecta to have a compression shock.," On the other hand, it is found that the rest mass energy should not be ignored in the shocked ejecta to have a compression shock."
+ Otherwise the jump condition would result in an expansion shock for m<1., Otherwise the jump condition would result in an expansion shock for $m<1$.
+ Then the energy density becomes e=P/1[(5—Lip}+1 in (his region and the term including the densitv in (he left hand side of equation (2)) is not neglected., Then the energy density becomes $\epsilon = P/\left\{(\hat{\gamma}-1)\rho\right\} + 1$ in this region and the term including the density in the left hand side of equation \ref{rhydro}) ) is not neglected.
+ The densitv. pressure. and velocity have discontinuities al the shock front.," The density, pressure, and velocity have discontinuities at the shock front."
+ Relations to connect these quantities at both sides of the shock front are given here., Relations to connect these quantities at both sides of the shock front are given here.
+" The mass flux. pu"" and (he energv momentum tensor Z7"" change across the shock propagating at (he velocity ol Vs according to the following formulae. where [F]=Fi.—Fy."," The mass flux $\rho u^\mu$ and the energy momentum tensor $T^{\mu\nu}$ change across the shock propagating at the velocity of $V_2$ according to the following formulae, where $[F]\equiv F_{\rm e} - F_2$."
+ The subscript e refers to values in the freely expanding ejecta at radius fi» defined as while the subscript 2 relers to values in the shocked matter at the same radius fo., The subscript e refers to values in the freely expanding ejecta at radius $R_2$ defined as while the subscript 2 refers to values in the shocked matter at the same radius $R_2$.
+" The variables n,. u. and T"" have been defined as with the metric j/""=diag(—1.1. 1)."," The variables $n_\mu$, $u^\mu$, and $T^{\mu\nu}$ have been defined as with the metric $\eta^{\mu\nu}\equiv{\rm diag}(-1,\,1,\,1,\,1)$ ."
+ Ποιο Ps denotes the Lorentz factor of the shock and is assumed to evolve as a function of time / as, Here $\Gamma_2$ denotes the Lorentz factor of the shock and is assumed to evolve as a function of time $t$ as
+limits. rather (han the SDSS quasar selection.,"limits, rather than the SDSS quasar selection."
+ The first {lis limit for SDSS quasar selection isal? <19.1. where quasars are selected in the ugri color cube (Schneider et al.," The first flux limit for SDSS quasar selection is at $i<19.1$, where quasars are selected in the $ugri$ color cube (Schneider et al."
+ 2005). and ihe 2MASS sample fails to detect the majority of quasars at this SDSS 7 magnitude limit.," 2005), and the 2MASS sample fails to detect the majority of quasars at this SDSS $i$ magnitude limit."
+ About of SDSS quasars are detected in 241ASS., About of SDSS quasars are detected in 2MASS.
+ This is expected since the 2\LASS is a significantly shallower survev than the SDSS survey., This is expected since the 2MASS is a significantly shallower survey than the SDSS survey.
+" We define the “2ATASS sample? as quasars detected in all of the J. H. and dv, bonds. and (he 7A, complete sample” as quasars with A,«15.1 mag."," We define the “2MASS sample” as quasars detected in all of the $J$, $H$ , and $K_s$ bands, and the $K_s$ complete sample” as quasars with $K_s < 15.1$ mag."
+ In 855. we use quasar luminosity functions to model BALQSO fractions above selected absolute magnitude limits.," In 5, we use quasar luminosity functions to model BALQSO fractions above selected absolute magnitude limits."
+ Since 2\TASS cannot detect quasars less luminous than the above limits at high redshifts. we also present results [or a narrower redshift” sample. 1.7<2<2.5.," Since 2MASS cannot detect quasars less luminous than the above limits at high redshifts, we also present results for a “narrower redshift” sample, $1.7 < z < 2.5$."
+ Our results are not sienificantly affected by the choice of sample selection., Our results are not significantly affected by the choice of sample selection.
+ We found 884 quasews in the 221A88 sample with 340 BALQSOs and 544 non-BALQSOs., We found 884 quasars in the 2MASS sample with 340 BALQSOs and 544 non-BALQSOs.
+" In the A, complete sample. we found 245. 99. and 146 quasars for total. BALQSOs. and respectively."," In the $K_s$ complete sample, we found 245, 99, and 146 quasars for total, BALQSOs, and non-BALQSOs, respectively."
+" The DALOSO fraction is 40.4fC in the A, complete sample and 38.5 Livin the 2MASS sample.", The BALQSO fraction is $40.4^{+3.4}_{-3.3}$ in the $K_s$ complete sample and $38.5^{+1.7}_{-1.7}$ in the 2MASS sample.
+" We also tested J and Lf band complete samples. obtaining . ≺∢∪∐⋟∖⊽↕⋟∖⊽∩↲∐↥↕⋅≼↲⋟∖⊽∏∐⋟∖⊽⋅≡↽⊰↙⋅↙↨↕↕↸∕∣≀↧↴∐≺⇂≡↽⊰↱≻⋅↻yeeDey .⋅MG. vespectively,"," We also tested $J$ and $H$ band complete samples, obtaining consistent results, $37.7^{+4.2}_{-4.1}$ and $35.6^{+4.6}_{-4.4}$, respectively."
+ These BALQSO fractions [rom PATASS bands are significantly higher than the in the optical bands (TOG)., These BALQSO fractions from 2MASS bands are significantly higher than the in the optical bands (T06).
+ For example. ⊔∐↲≼∐∐≱≼↲↕⋅≼↲∐≺∢≼↲∣↽≻≼↲↥∖∖↽≼↲≼↲∐⊔∐↲∐≙⊔↽≥⊳↔⊲↻↓≯↕⋅≀↧↴≺∢∐∪∐↕∐∪↕↽≻∐≺∢≀↧↴↥≀↧↴∐≼⇂⊔∐↲∫∖↸∖≺∢∪∐↓↕↽≻↥≼↲∥↲⊳," For example, the difference between the BALQSO fraction in optical and the $K_s$ complete sample is $\sigma$."
+∖⊽≀↧↴↕∐↕↽≻↥≼↲↕⋝∖⊽∔⋅∔⊔⋅ ↴⊺∐↕⋟∖⊽↕⋅≼↲⋟∖⇁∏∐↕⋟∖⊽↕∐∩↲↕⋅≼↲⋟∖⊽∐∐≸≟⋅≀↕⊍∖⊽∖∖⇁≼↲≀↕↴↕⋅≼↲≀↧↴↕⋯↴↥⋡∖↽∠↕∐≸≟⊔∐↲⋟∖⊽≀↧↴∐∐↲↕↽≻≀↧↴↕⋅≼↲," This result is interesting, as we are analyzing the same parent BALQSO catalog used in the optical study."
+↕∐∐↼≚⊔↽≥⊳↔⊲↻≺∢≀↕↴↥≀↕↴↥∪↖≺↽↔↴∏⋟∖⇁≼↲≺⊔∐ ⊔∐↲∪↕↽≻∐≺∢≀↧↴↥⊳∖⇁⊓∐⇂∡∖↽⋅∐↕∐≼∐≺∢≀↧↴∩↲⊳∖⊽⊔⋯↥⊔���↲↕⋅≼↲∐↓≀↧∶∖↽∣↽≻≼↲⊳∖⊽↕≸↽↔↴↕∏⇂∎↓≺∢≀↧, It indicates that there may be significant selection bias against BALQSOs in the optical photometric surveys.
+↴∐↥⊳∖⇁≼↲↥≼↲≺∢∐∪∐∣↽≻↕≀↧↪∖⊽≀↧↴≸↽↔↴≀↧↴↕↕↥⊳∖⇁↥∐≙∟≼↽≥⊳↔⊲↻⊳∖⊽ ∎∐⊔∐↲∪↕↽≻∐≺∢≀↧↴↥↕↽≻∐∪↥∪∐∐↲⊔⋅↕≺∢⋟∖⊽⋯⋅∖↽≼↲⋡∖⇁⋟∖⊽⋅∶∖⋟∖⊽≀, As a corollary the near infrared fraction obtained in this paper ) represents the true fraction of BALQSOs.
+↧↴≺∢∪↕⋅∪∐≀↧↴↕⋅⋡∖↽⊔∐↲∐≼↲≀↧↴↕⋅↕∐↓⋟↕⋅≀↕↴↕⋅≼↲≼⇂↓⋟↕⋅≀↧↴≺∢∐∪∐∪∣↽≻↥≀↕↴↕∐≼↲≺⊔∐ ⊔∐⊳∖⇁↕↽≻≀↧↴↕↽≻≼↲↕⋅⋖↜⊑ ↽⊰⇀↱≻−∔∩↖∕⊓∣⊁⇝⋝↕⋟↕⋅≼↲↕↽≻↕⋅≼↲⋟∖⊽≼↲∐↥⋟∖⊽⊔∐," Alternatively, BALQSOs may be intrinsically brighter in the near infrared bands or a combination of both effects is possible."
+↲⊔⋅⋯↲↓⋟↕⋅≀↧↴≺∢∐∪∐∪↓⋟∐∶∖⊔↽≥⊳↔⊲≼↽⋋∖⊽⋅∶∖∐≼↲↕⋅↕⋯∐∖⇁≼↲↥⋡∖↽⋅∐↼≚⊔↽≥⊳↔⊲↻⋟∖⊽ ⊔≀↧∶∖↽∣↽≻≼↲↕↕∐↕⋅↕∐⊳∖⇁↕≺∢≀↧↴∐⋡∖↽∣↽≻↕⋅↕≸↽↔↴∐∩↲↕⋅↕∐⊔∐↲↕∐↲≀↧↴↕⋅↕∐↓≯↕⋅≀↧↴↕⋅≼↲≺⇂∣↽≻≀↧↴∐≼⇂⊳∖⊽∪↕⋅≀↧↴≺∢∪∐↓∣↽≻∎∐≀↧↴∐∪∐∪↓≯∣↽≻∪⊔⊔↲∐⋡≼↲≺∢↥⋝∖⊽↥⊳∖⊽ ↕↽≻∪⋟∖⊽⋟∖⊽↕∣↽≻↥≼↲⋅∖∖⊽≼↲≼↲⇀↸≀↧↴∐∐∐≼↲⊔∐↲∐⋅≀↧↴≺∢∐∪∐∪↓⋟∐∶∖⊔↽≥⊳↔⊲≼↽⋋∖⊽≀↕⊔∖⊽↓⋟∏∐≺∢∐∪∐⋟∖⊽∪↓⋟≀↧↴↕↽≻↕↽≻≀↕↴↕⋅≼↲↕∐∐↓≀↕↴≸↽↔↴∐∐⋯⇂≼↲⋅≀↧↴∣↽≻⋟∖⊽∪↥∏∩↲ ⊔≀↧↴≸↽↔↴∐∎↥⋯⇂≼↲⋅≀↧↴∐≼⊔⋅≼↲≺⇂⊳∖⇁∐∐≯↥↥∪↕∐∖⇁≼↲⊳∖⇁∐≸≟≀↧↴∩↲⊔∐↲≺∢≀↧↴∏⊳∖⇁≼↲↓⋟∪↕⋅⊔∐↲↕∐≺∢↕⋅≼↲≀↧⊔∖⊽≼↲∪⋟⊔∐↲∐↼≚⊔↽≥⊳↔⊲↻∐⋅≀↧↴≺∢∐∪↥⊳∖⊽ in the 2MASS bands.," We examine the fraction of BALQSOs as functions of apparent magnitude, absolute magnitude, and redshift to investigate the cause for the increase of the BALQSO fractions in the 2MASS bands."
+ In top panels of Fig., In top panels of Fig.
+ 2. and Fig. 3..," \ref{fig:fmag} and Fig. \ref{fig:fabs},"
+" we plot the fraction of BALQSOs against the apparent ancl absolute magnitudes in the 4. g. r. i. z and A, bands . respectively.in the redshift range of 1.7«2<4.38."," we plot the fraction of BALQSOs against the apparent and absolute magnitudes in the $u$, $g$, $r$, $i$, $z$ and $K_s$ bands , respectively,in the redshift range of $1.7 < z < 4.38$."
+ In the bottom panels of Fig., In the bottom panels of Fig.
+ 2. and Fig. 3..," \ref{fig:fmag} and Fig. \ref{fig:fabs},"
+ we also show the same plots in the narrower redshift range of 1.7«z5.2.5., we also show the same plots in the narrower redshift range of $1.7 < z < 2.5$.
+" The J and| // band fractions are verv similar to but slightly below the A, band fractions. and we do notshow them [or claritv reasons."," The $J$ and $H$ band fractions are very similar to but slightly below the $K_s$ band fractions, and we do notshow them for clarity reasons."
+" The K-corrections of the quasars are caleulated assuming a power-law spectral index of a=—0.5 (f,xp. Vauden Berk et al.", The K-corrections of the quasars are calculated assuming a power-law spectral index of $\alpha = -0.5$ $f_\nu \propto \nu^\alpha$ Vanden Berk et al.
+ 2001)., 2001).
+ We did not correct. the, We did not correct the
+be noted that the values of n are different for the erowtl and decay rates).,be noted that the values of n are different for the growth and decay rates).
+ The statistical significances of the regression relations and the values of correlation coefficientsο. are tested using: XD and StudentsJ. Jutf distributions. F-test. standard error aud z-transformatiougf tests (Yule&I&eudall1958).," The statistical significances of the regression relations and the values of correlation coefficients are tested using $\chi^2$ and Student's 't' distributions, F-test, standard error and z-transformation tests \citep{yk58}."
+. Iu Table 1 we have given the aunual values of S¢;. Sp aud S4.," In Table 1 we have given the annual values of $S_G$, $S_D$ and $S_A$."
+ Fig., Fig.
+" 1. shows the plots of the normalized anual values of $4. 8e; aud Sp| voar,"," \ref{fig1} shows the plots of the normalized annual values of $S_A$, $S_G$ and $|S_D|$ year."
+ It may boe worth to note here that in evele 23/5 4 has maxima at vear 2002., It may be worth to note here that in cycle 23 $S_A$ has maximum at year 2002.
+ The maxiuuun of the international sunspot nuuber (not shown here) is at 2000., The maximum of the international sunspot number (not shown here) is at 2000.
+ Receutlv. found that the παπα of coronal mass ejection (CALE) is close to that of the suuspot area.," Recently, found that the maximum of coronal mass ejection (CME) is close to that of the sunspot area."
+ Fie., Fig.
+ 2) shows the correlations between 5e; aud. 94 aud between [Sp]* aud S4* (all these are dividedfof by E101)., \ref{fig2} shows the correlations between $S_G$ and $S_A$ and between $|S_D|$ and $S_A$ (all these are divided by $10^4$ ).
+ These correlations. correlation coeficicuts 5—0.989 and s= 0.991. are very lieh (sigmificaut ou >99.9 confidence level}.," These correlations, correlation coefficients $r = 0.989$ and $r =0.994$ , are very high (significant on $> 99.9$ confidence level)."
+ The slopes of the corresponding linear relationships are aliiostequal (0.097+ 0.001), The slopes of the corresponding linear relationships are almostequal $0.097 \pm 0.001$ )
+I&udritzki et al. (,Kudritzki et al. (
+1995) have defined the Wind momentum Lunminositv Relation (WLR): where II (or Alen 15) Gs called the “imeodified wind momentun”.,1995) have defined the Wind momentum Luminosity Relation (WLR): where $\Pi$ (or $\dot{M} \vinf R_*^{0.5}$ ) is called the “modified wind momentum”.
+ Observations of M aud ος of O superegiauts have shown that log IT is proportional to log £. (see e.g. Puls et al., Observations of $\dot{M}$ and $\vinf$ of O supergiants have shown that log $\Pi$ is proportional to log $L_*$ (see e.g. Puls et al.
+ 1996)., 1996).
+ The WLR max in principle be used as a tool to derive distances to galaxies (see Ixudzitzki et al., The WLR may in principle be used as a tool to derive distances to galaxies (see Kudritzki et al.
+ 1995)., 1995).
+ Iu the theory of liue driven winds. the reciprocal value of we equals (Puls et al.," In the theory of line driven winds, the reciprocal value of $x$ equals (Puls et al."
+ 1996): Tere a and 6 are force multiplier paramcters. describing the radiative Lue acceleration gin. through the stellar wind:where nds the electron density aud Wis the dilution factor.," 1996): Here $\alpha$ and $\delta$ are force multiplier parameters, describing the radiative line acceleration $g_{\rm line}$ through the stellar wind:where $n_{\rm e}$ is the electron density and $W$ is the dilution factor."
+ a corresponds to the power law exponent of the line streneth distribution function controling the relative muuber of strong to weak lines., $\alpha$ corresponds to the power law exponent of the line strength distribution function controlling the relative number of strong to weak lines.
+ If ouly stroug (weak) lines coutribute to the line acceleration force. then a = 1 (0).," If only strong (weak) lines contribute to the line acceleration force, then $\alpha$ = 1 (0)."
+ The predicted value of a is about 0.6., The predicted value of $\alpha$ is about 0.6.
+ The parameter à deseribes the ionization balance of the wind., The parameter $\delta$ describes the ionization balance of the wind.
+ Values for this parameter are usually. between 0.0 aud 0.1., Values for this parameter are usually between 0.0 and 0.1.
+ For a detailed discussion of the parameterisation of the line acceleration. see e.g. CAI. Abbott (1982) aud Iudirizl eta. (," For a detailed discussion of the parameterisation of the line acceleration, see e.g. CAK, Abbott (1982) and Kudritzki et al. ("
+1989).,1989).
+ The importait polit to note here is that possible changes in the slope .r as a function of effecIve telserature reflect the fact that the stellar winds are driven bv different sets of ions. ro. lines of different ious.," The important point to note here is that possible changes in the slope $x$ as a function of effective temperature reflect the fact that the stellar winds are driven by different sets of ions, i.e. lines of different ions."
+ Fiere 5 showstat around the bi-stabilitv jump at Tig & 25 0YO IN. yp for decreasing Tig.," Figure \ref{f_eta} shows that around the bi-stability jump at $\teff$ $\simeq$ 25 000 K, $\eta$ for decreasing $\teff$."
+ This implies that one does not necessarily expect a universal WLR over the conplete spectral range of O. Band A stars; nor does one expect a constaut value of αμ orc for different spectral tvpes.," This implies that one does not necessarily expect a universal WLR over the complete spectral range of O, B and A stars, nor does one expect a constant value of $\alpha_{\rm eff}$ or $x$ for different spectral types."
+ Iu this section we prescut a theoretical mass loss formula for OB stars over the full range in Tag between 50 000 aud 12 500 Ik. The mass-loss rate as a function of four basic parameters will be provided., In this section we present a theoretical mass loss formula for OB stars over the full range in $\teff$ between 50 000 and 12 500 K. The mass-loss rate as a function of four basic parameters will be provided.
+ These parameters are the stellar mass and Iuinosity. effective teniperature and teiinal velocity of the wind.," These parameters are the stellar mass and luminosity, effective temperature and terminal velocity of the wind."
+ To obtain a niass-loss recipe. we have derived interpolation formulae frou the exid of AL calculations preseuted in Sect. 3..," To obtain a mass-loss recipe, we have derived interpolation formulae from the grid of $\mdot$ calculations presented in Sect. \ref{s_massloss}."
+ The fitting procedire was performed using multiple linear regression uehods to derive depoeuceuce cocticicnts., The fitting procedure was performed using multiple linear regression methods to derive dependence coefficients.
+ We have applied this method for the wo ranges in Diy separately., We have applied this method for the two ranges in $\teff$ separately.
+ The first raice is roughly the range for the O-type stars heWCCLL 1. = 50 000 21 30 000 I&. The second range is beWCCLL 1. = 2250 yam 15 000 I&. which is roughly the range for the B-type superejauts.," The first range is roughly the range for the O-type stars between $\teff$ = 50 000 and 30 000 K. The second range is between $\teff$ = 22 500 and 15 000 K, which is roughly the range for the B-type supergiants."
+ The two relations are conneced at the bistability jimp., The two relations are connected at the bi-stability jump.
+ We have already derived the jump parameters for different series of models iu Sect. 3..," We have already derived the jump parameters for different series of models in Sect. \ref{s_massloss},"
+ sO we have knowledge about the position of the jump in η as a functio1 of stellar parameters., so we have knowledge about the position of the jump in $\teff$ as a function of stellar parameters.
+ This will be applied i- the determination of mass loss for stars with temperatures around the bistability jump., This will be applied in the determination of mass loss for stars with temperatures around the bi-stability jump.
+ The first range (roughly the rauge of the O-ype stars) is taken trom Ti4g between 50 000 I& aud 30 010 Tx. Iu this ranec the step size iu effective teniperature equals 5 000 Ix. So. for the first range we have five erid points in Tig.," The first range (roughly the range of the O-type stars) is taken from $\teff$ between 50 000 K and 30 000 K. In this range the step size in effective temperature equals 5 000 K. So, for the first range we have five grid points in $\teff$."
+ Five times 12 series of (£... M... together with three ratios of (ex ος) vields a total of 180 poiuts iu AY for the first ranec.," Five times 12 series of $L_*,M_*$ ), together with three ratios of $\ratio$ ) yields a total of 180 points in $\dot{M}$ for the first range."
+ We have found that for the dependence of AT ou Tig. the fit iuproved if a second order term (log Tia)? was taken into account.," We have found that for the dependence of $\dot{M}$ on $\teff$, the fit improved if a second order term (log $\teff)^{2}$ was taken into account."
+ In fact. this is obvious from the shapes of the plots iu the panels of Fig. 2..," In fact, this is obvious from the shapes of the plots in the panels of Fig. \ref{f_massloss}."
+ The best ft that was found by multiple linear regression is: where M is in M. vro L. aud AL. are in solar units aud Zi is in I&elvi1," The best fit that was found by multiple linear regression is: where $\dot{M}$ is in $\msun$ ${\rm yr}^{-1}$, $L_*$ and $M_*$ are in solar units and $\teff$ is in Kelvin."
+ Note that AL. is the stellar mass nof corrected for electron scattering., Note that $M_*$ is the stellar mass corrected for electron scattering.
+ Iu this range exfe = 2.6., In this range $\ratio$ = 2.6.
+ Equation 12 xediets the calculated miass-loss rates of the 180 models with a root-auean-square (riis) accuracy of 0.061 dex., Equation \ref{eq_Ofit} predicts the calculated mass-loss rates of the 180 models with a root-mean-square (rms) accuracy of 0.061 dex.
+ The fits for the various (£... M.) series are," The fits for the various $L_*,M_*$ ) series are"
+107(34) This ts the result of sampling the average of six points in the white-noise réggime., This is the result of sampling the average of six points in the white-noise réggime.
+" Considering the full plane cir.d) atk=k,and low r gives results which are similar."," Considering the full plane $\alpha(r,\phi)$ at $k=k_\star$and low $r$ gives results which are similar."
+ The coherence length evaluated atthe equilateral line Aeon evolves slowly towards larger scales from keon(y=1)5x107 as r increases., The coherence length evaluated atthe equilateral line $k_\mathrm{Coh}$ evolves slowly towards larger scales from $k_\mathrm{Coh}(r=1)\approx 5\times 10^{-3}$ as $r$ increases.
+ A réggime with Kean)€ky is reached at larger »., A réggime with $k_\mathrm{Coh}(r)\lesssim k_\star$ is reached at larger $r$.
+" The recovered a would grow inaccurate unless &,=Κι. reducing at large 7."," The recovered $\alpha$ would grow inaccurate unless $k_\star=k_\star(r)$, reducing at large $r$."
+ The constant back plane and the white-noise behaviour of the scaling make this bispectrum particularly simple on large scales., The constant back plane and the white-noise behaviour of the scaling make this bispectrum particularly simple on large scales.
+" Approximating 8,07.@)=8.35 and «=0. then. with a pivot Κι) that always remains within Keon(7) produces a good modelof the bispectrum as it is applicable to CMB scales."," Approximating $\mathcal{B}_\star(r,\phi)=8.35$ and $\alpha=0$, then, with a pivot $k_\star(r)$ that always remains within $k_\mathrm{Coh}(r)$ produces a good modelof the bispectrum as it is applicable to CMB scales."
+ However. the rapid decay of Aceon with r. combined with the relative strength of power on small scales compared to large scales. implies that one should be wary of wrapping these fields directly onto the CMB.," However, the rapid decay of $k_\mathrm{Coh}$ with $r$, combined with the relative strength of power on small scales compared to large scales, implies that one should be wary of wrapping these fields directly onto the CMB."
+ Finally the full bispectrum in K.7. space is presented in Figure 19..," Finally the full bispectrum in $k,r,\phi$ space is presented in Figure \ref{3DOut}."
+ This plot shows tsosurfaces of constant amplitude through the bispectrum., This plot shows isosurfaces of constant amplitude through the bispectrum.
+ This figure highlights the simple sheet-like structure of this correlation. the of the bounds of the correlations and the relatively slow decay with increasing r.," This figure highlights the simple sheet-like structure of this correlation, the wedge-shape of the bounds of the correlations and the relatively slow decay with increasing $r$."
+ The auto-correlation of the anisotropic is more interesting in structure than that of the isotropic. pressure., The auto-correlation of the anisotropic is more interesting in structure than that of the isotropic pressure.
+" In amplitude it is similar. and on white-noise scales is Az,=0.97A,. but it has a much more complicated pattern."," In amplitude it is similar, and on white-noise scales is $A_{\tau_S}\approx 0.97A_\tau$, but it has a much more complicated pattern."
+ Figure 3 shows that the signal is negative along the entire colinear line. while it is positive for much of the range of & along the equilateral and degenerate lines.," Figure \ref{LinethroughsN0} shows that the signal is negative along the entire colinear line, while it is positive for much of the range of $k$ along the equilateral and degenerate lines."
+ Even here. though. it is negative on small scales.," Even here, though, it is negative on small scales."
+ The (cE) signal therefore passes between regions of positive and negative power dependant on both ¢ and &., The $\av{\tau_S^3}$ signal therefore passes between regions of positive and negative power dependant on both $\phi$ and $k$.
+ It should be expected that the same is true for varying r and this is confirmed in Figure 6.. which shows the negative region beside the colinear line. which 15 joined by a corresponding region along the squeezed plane.," It should be expected that the same is true for varying $r$ and this is confirmed in Figure \ref{PlanesN0TsTsTs}, which shows the negative region beside the colinear line, which is joined by a corresponding region along the squeezed plane."
+ As expected. away from the degenerate line the squeezed plane has the same general behaviour as the colinear plane.," As expected, away from the degenerate line the squeezed plane has the same general behaviour as the colinear plane."
+ The planes in Figure 6 slowly squeeze a positive region which ts centred approximately around @=2/2., The planes in Figure \ref{PlanesN0TsTsTs} slowly squeeze a positive region which is centred approximately around $\phi=\pi/2$.
+" The coherence length at the equilateral line 18 keg,= 107. again evolving only very slowly with increasing r."," The coherence length at the equilateral line is $k_\mathrm{Coh}\approx 10^{-3}$ , again evolving only very slowly with increasing $r$."
+ From the general arguments above. in the limit of high pr we would expect the bispectrum to tend to the large-scale degenerate solution.," From the general arguments above, in the limit of high $r$ we would expect the bispectrum to tend to the large-scale degenerate solution."
+ In Figure 3. we can see that this is negative. albeit extremely small.," In Figure \ref{LinethroughsN0} we can see that this is negative, albeit extremely small."
+ The central. positive. region is then expected to entirely vanish at the extreme reach of the bispectrum.," The central, positive, region is then expected to entirely vanish at the extreme reach of the bispectrum."
+ As with the isotropic pressure. the signal along the colinear line is well-modelled with statistical realisations. but is extremely noisy on large scales.," As with the isotropic pressure, the signal along the colinear line is well-modelled with statistical realisations, but is extremely noisy on large scales."
+" Figure 17 shows 8,0.) atk,=7.5x107? and demonstrates these features clearly."," Figure \ref{PivotPlanesN0} shows $\mathcal{B}_\star(r,\phi)$ at $k_\star=7.5\times 10^{-5}$ and demonstrates these features clearly."
+ The region of positivity is asymmetric around the equilateral line at 6=27/3 with a tail at r=| extending to reach the degenerate line at ó=π., The region of positivity is asymmetric around the equilateral line at $\phi=2\pi/3$ with a tail at $r=1$ extending to reach the degenerate line at $\phi=\pi$.
+" The bispectrum in general exhibits a characteristic “triple drainpipe"" pattern.", The bispectrum in general exhibits a characteristic “triple drainpipe” pattern.
+ Recovering the scaling relation around the equilateral line gives 1, Recovering the scaling relation around the equilateral line gives .
+"074383) The bispectrum can then be modelled by using 6,(7.6) and α= 0; unfortunately this plane is not immediately amenable to analytic approximation."," The bispectrum can then be modelled by using $\mathcal{B}_\star(r,\phi)$ and $\alpha=0$ ; unfortunately this plane is not immediately amenable to analytic approximation."
+ The full bispectrum in Figure 19. shows the triple-drainpipe extremely clearly. along with its slow decayat high r.," The full bispectrum in Figure \ref{3DOut} shows the triple-drainpipe extremely clearly, along with its slow decayat high $r$ ."
+halo gains most of its angular momentum during the linear regime (?): it has further been shown that contributions from later collapse epochs and non-linear corrections are small The spin parameter A (eq. 1)),halo gains most of its angular momentum during the linear regime : it has further been shown that contributions from later collapse epochs and non-linear corrections are small The spin parameter $\lambda$ (eq. \ref{eq:am:0}) )
+" was introduced by asa convenient dimensionless quantity to characterize the tidal growth of the angular momentum, also through the study of its (PDF), P(A)."," was introduced by as a convenient dimensionless quantity to characterize the tidal growth of the angular momentum, also through the study of its (PDF), $P(\lambda)$."
+" All the quantities entering the definition of λ depend ultimately on the adopted halo finder In order to understand the origin of this deviation, we will first consider the evolution of the spin PDF."," All the quantities entering the definition of $\lambda$ depend ultimately on the adopted halo finder In order to understand the origin of this deviation, we will first consider the evolution of the spin PDF."
+ In Figs —5 we show the evolution of the PDF for different mass intervals., In Figs \ref{fig:lam:mass:z1}- – \ref{fig:lam:mass:z0.1} we show the evolution of the PDF for different mass intervals.
+" We also plot the best-fit lognormal distributions, and in Table 1 we present the parameters of these fits."," We also plot the best-fit lognormal distributions, and in Table \ref{fit_lgn} we present the parameters of these fits."
+" Although the fitting functions of and provide a better fit than a lognormal, the latter is a PDF distribution for the origin of angular momentum, predicted both by tidal torque and merger models."," Although the fitting functions of and provide a better fit than a lognormal, the latter is a PDF distribution for the origin of angular momentum, predicted both by tidal torque and merger models."
+" Thus, we will try to understand the possible physical origin of the from the lognormal distribution."," Thus, we will try to understand the possible physical origin of the from the lognormal distribution."
+" It is apparent from these figures that there is deficit of high-\ haloes (logA/A>1.3+ 221553), at all redshifts, as was observed previously(????)."," It is apparent from these figures that there is deficit of $\lambda$ haloes $\log{\lambda/{\bar{\lambda}}} \ga 1.3 \div 2\,\sigma_{{\rmn \log}\lambda}$ ), at all redshifts, as was observed previously."
+". This feature does not significantly depend on the mass, and in the next section we will argue that it originates from statistical correlations between quantities entering the definition of spin, and from deviations from lognormal behaviour of the energy E. From Table 1 we also notice that themaximum À depends on the mass, being a slowly decreasing function of mass."," This feature does not significantly depend on the mass, and in the next section we will argue that it originates from statistical correlations between quantities entering the definition of spin, and from deviations from lognormal behaviour of the energy $E$ From Table \ref{fit_lgn} we also notice that the $\bar{\lambda}$ depends on the mass, being a slowly decreasing function of mass."
+" This fact has been previously noticed byauthors(????),, but they suggested that the A-M relationship flattens for z<1, while our simulations show instead that also at more recent epochs the relationship holds true."," This fact has been previously noticed by, but they suggested that the $\bar{\lambda}-$ M relationship flattens for $z\la 1$, while our simulations show instead that also at more recent epochs the relationship holds true."
+" Our findings and those of Knebe and Power are different to those of?,, but more consistent with those of?,, who find a very mild decreasing trend."," Our findings and those of Knebe and Power are different to those of, but more consistent with those of, who find a very mild decreasing trend."
+" Finally, we notice an evolution also in the shape of the best-fitting lognormal function, in the sense that the dispersion ojo, seems to increase with decreasing redshift (third column of Table 1))."," Finally, we notice an evolution also in the shape of the best-fitting lognormal function, in the sense that the dispersion $\sigma_{{\rmn log}\lambda}$ seems to increase with decreasing redshift (third column of Table \ref{fit_lgn}) )."
+ We do not have sufficient statistics for z20.1 to determine if in the highest mass bin the high-A deficit and the σιοελ width follow the same, We do not have sufficient statistics for $z\ga 0.1$ to determine if in the highest mass bin the $\lambda$ deficit and the $\sigma_{{\rmn \log}\lambda}$ width follow the same
+The thresholds in all cases seem to be at E/E;~0.8.,The thresholds in all cases seem to be at $E_{\rm p}/E \approx 0.8$.
+" In the Tn=0.33R simulations (fig. 12)),"," In the $r_{\rm n}=0.33R$ simulations (fig. \ref{fig:mmodes-pol-g5}) ),"
+" at 0.8 (and at 0.7), an oscillatory behaviour can be seen in the m=2 mode, indicating stability."," at $0.8$ (and at $0.7$ ), an oscillatory behaviour can be seen in the $m=2$ mode, indicating stability."
+" At 0.9, the m=2 mode is dominant; at 0.944 both m=2 and m=3 grow (the m=4 mode is probably just numerical contamination at these ratios, but will becomeproperly unstable above some threshold in E/ E)."," At $0.9$ , the $m=2$ mode is dominant; at $0.944$ both $m=2$ and $m=3$ grow (the $m=4$ mode is probably just numerical contamination at these ratios, but will becomeproperly unstable above some threshold in $E_{\rm p}/E$ )."
+" Looking at fig. 12,,"," Looking at fig. \ref{fig:mmodes-pol-g5},"
+" where Γι=0.47R, we see that Ej/E=0.7 is clearly stable; at 0.8 the πι=2 appears stable and then unstable — this is probably because the magnetic field is just below the threshold and is taken over it by continuing secular evolution, which weakens the toroidal component faster than the poloidal."," where $r_{\rm n}=0.47R$, we see that $E_{\rm p}/E = 0.7$ is clearly stable; at $0.8$ the $m=2$ appears stable and then unstable – this is probably because the magnetic field is just below the threshold and is taken over it by continuing secular evolution, which weakens the toroidal component faster than the poloidal."
+ It is visible in the plots that at higher poloidal energy ratios that the higher azimuthal modes become unstable., It is visible in the plots that at higher poloidal energy ratios that the higher azimuthal modes become unstable.
+ Similarly we see in fig., Similarly we see in fig.
+ 12 (Τα=0.581) that the stability threshold is very close to 0.8., \ref{fig:mmodes-pol-g5} $r_{\rm n}=0.58R$ ) that the stability threshold is very close to $0.8$.
+" Very clear here is the stability (hence oscillations) of m= at 0.9 but unstable growth at E,/E.=0.944.", Very clear here is the stability (hence oscillations) of $m=3$ at $0.9$ but unstable growth at $E_{\rm p}/E=0.944$.
+" Of course, oscillations3 follow unstable growth when saturation, i.e. a new axisymmetric equilibrium, is reached."," Of course, oscillations follow unstable growth when saturation, i.e. a new non-axisymmetric equilibrium, is reached."
+ A perhaps more elegant way to present the output from the simulations is to plot a map of the field on the surface of the star., A perhaps more elegant way to present the output from the simulations is to plot a map of the field on the surface of the star.
+ Figs., Figs.
+" 15 and 16 are such maps of B,; all are taken from the r/R=0.47 simulations.", \ref{fig:map-07000} and \ref{fig:map-higher} are such maps of $B_r$; all are taken from the $r_{\rm n}/R = 0.47$ simulations.
+ Fig.. 15 follows the evolution in time of three simulations with different Ej/E ratios; by the end of the simulations new equilibria have been reached in the unstable cases., Fig.. \ref{fig:map-07000} follows the evolution in time of three simulations with different $E_{\rm p}/E$ ratios; by the end of the simulations new equilibria have been reached in the unstable cases.
+" These maps confirm that E,/E=0.7 is stable (apart from a small m=4 numerical contamination), that 0.8 is stable at first and then succumbs to the m=2 mode, and that the 0.9 field is unstable mainly to the —2 mode and eventually finds its way into a new equilibrium."," These maps confirm that $E_{\rm p}/E = 0.7$ is stable (apart from a small $m=4$ numerical contamination), that $0.8$ is stable at first and then succumbs to the $m=2$ mode, and that the $0.9$ field is unstable mainly to the $m=2$ mode and eventually finds its way into a new equilibrium."
+ Fig., Fig.
+" 16 shows the equilibria reached in simulations with even higher Ey/E ratios; evidently, the higher the ratio, the more complex the resulting equilibrium."," \ref{fig:map-higher} shows the equilibria reached in simulations with even higher $E_{\rm p}/E$ ratios; evidently, the higher the ratio, the more complex the resulting equilibrium."
+" It seems then that a magnetic field becomes unstable as the poloidal energy fraction exceeds about 80%, and that this threshold depends only weakly on the central concentration of the field (i.e. on ry)."," It seems then that a magnetic field becomes unstable as the poloidal energy fraction exceeds about $80\%$, and that this threshold depends only weakly on the central concentration of the field (i.e. on $r_{\rm n}$ )."
+" Just above this threshold, the only unstable mode is m=2, which is reassuringly well resolved by simulations at this resolution."," Just above this threshold, the only unstable mode is $m=2$, which is reassuringly well resolved by simulations at this resolution."
+" At higher values of E/E higher modes become unstable, which is exactly what we expect because higher azimuthal modes have to do more work against the toroidal field, in proportion to the value of m."," At higher values of $E_{\rm p}/E$ higher modes become unstable, which is exactly what we expect because higher azimuthal modes have to do more work against the toroidal field, in proportion to the value of $m$."
+" Therefore, the m=3 mode becomes unstable with a toroidal field 2/3 the strength of that at the m=2 stability threshold, so that if the m=2threshold is E;/E~ 0.8, then the m= threshold will be at Ej/Ezz1—(1—0.8)(2/3)?=0.911 (ignoring3 the small change in poloidal field strength resulting from the change in /E at constant E)."," Therefore, the $m=3$ mode becomes unstable with a toroidal field $2/3$ the strength of that at the $m=2$ stability threshold, so that if the $m=2$threshold is $E_{\rm p}/E\approx 0.8$ , then the $m=3$ threshold will be at $E_{\rm p}/E \approx 1-(1-0.8)(2/3)^2 = 0.911$ (ignoring the small change in poloidal field strength resulting from the change in $E_{\rm_p}/E$ at constant $E$ )."
+ This can be seen for instance in fig., This can be seen for instance in fig.
+" 14 and E,confirms the m dependence of in (16)).", \ref{fig:mmodes-pol-g90} and confirms the $m$ dependence of in \ref{eq:polfrac}) ).
+package (Pengetal.2002) to perform a conventional two-dimensional Sérrsic profile fit to the observed image.,package \citep{pen02} to perform a conventional two-dimensional Sérrsic profile fit to the observed image.
+ For PSFs we use unsaturated stars brighter than K=22.86 that are not contaminated by nearby sources.," For PSFs we use unsaturated stars brighter than $K =
+22.86$ that are not contaminated by nearby sources."
+ We verify the quality of our stellar PSFs by comparing their radial profiles to each other. and find that the profiles show small variations in half-light radius of order ~2%.," We verify the quality of our stellar PSFs by comparing their radial profiles to each other, and find that the profiles show small variations in half-light radius of order $\sim2\%$."
+ We find no systematic dependence of these variations with magnitude., We find no systematic dependence of these variations with magnitude.
+ In order to estimate the effects of PSF variations on our derived parameters we fit every galaxy using each of the stars separately., In order to estimate the effects of PSF variations on our derived parameters we fit every galaxy using each of the stars separately.
+ We find that the derived total magnitudes. sizes and Sérrsic indices vary by aboutO.1%.. and7%.. respectively.," We find that the derived total magnitudes, sizes and Sérrsic indices vary by about, and, respectively."
+ After fitting a Sérrsic model profile we measure the residual flux profile from the residual image. which is the difference between the observed image and the best-fit PSF-convolved model.," After fitting a Sérrsic model profile we measure the residual flux profile from the residual image, which is the difference between the observed image and the best-fit PSF-convolved model."
+ This is done along concentric ellipses which follow the geometry of the best-fit Sérrsic model., This is done along concentric ellipses which follow the geometry of the best-fit Sérrsic model.
+ The residual flux profile is then added to the best-fit Sérrsic profile. effectively providing a first-order correction to the profile at those locations where the assumed model does not accurately describe the data.," The residual flux profile is then added to the best-fit Sérrsic profile, effectively providing a first-order correction to the profile at those locations where the assumed model does not accurately describe the data."
+ The effective radius is then calculated by integrating the residual-corrected profile out to a radius of approximately 12 areseconds (~100 kpe at z~ 2)., The effective radius is then calculated by integrating the residual-corrected profile out to a radius of approximately 12 arcseconds $\sim100$ kpc at $z\sim2$ ).
+ We note that the residual flux profile is not deconvolved for PSF: however. we show below that this does not strongly affect the accuracy of this method.," We note that the residual flux profile is not deconvolved for PSF; however, we show below that this does not strongly affect the accuracy of this method."
+ Errors in the sky background estimate are the dominant source of uncertainty when deriving surface brightness profiles of faint galaxies to large radi., Errors in the sky background estimate are the dominant source of uncertainty when deriving surface brightness profiles of faint galaxies to large radii.
+ Using the wrong sky value can result in systematic effects., Using the wrong sky value can result in systematic effects.
+ GALFIT provides an estimate of the sky background during fitting., GALFIT provides an estimate of the sky background during fitting.
+ To ensure that this estimate is correct we inspect the residual flux profile of each galaxy at radii between 5and 15 arcsec (approximately 40 to 120 kpe at z2 2)., To ensure that this estimate is correct we inspect the residual flux profile of each galaxy at radii between 5and 15 arcsec (approximately 40 to 120 kpc at $z=2$ ).
+ Using this portion of the residual flux profile we derive à new sky value and adjust the intensity profile accordingly., Using this portion of the residual flux profile we derive a new sky value and adjust the intensity profile accordingly.
+" We use the difference between the minimum and maximum values of the residual flux profile within this range of radii as an estimate of the uncertainty in the sky determination,", We use the difference between the minimum and maximum values of the residual flux profile within this range of radii as an estimate of the uncertainty in the sky determination.
+ In Szomoruetal.(2010) this procedure was tested using simulated galaxies inserted into ΝΕΟΣ data of the HUDF., In \cite{szo10} this procedure was tested using simulated galaxies inserted into WFC3 data of the HUDF.
+ Since the data used in this Paper are shallower we have performed new tests., Since the data used in this Paper are shallower we have performed new tests.
+ We create images of simulated galaxies that consist of two components: one compact elliptical component and a larger. fainter component that ranges from disk-like to elliptical.," We create images of simulated galaxies that consist of two components: one compact elliptical component and a larger, fainter component that ranges from disk-like to elliptical."
+ The axis ratio and position angle of the second component are varied. as are its effective radius and total magnitude.," The axis ratio and position angle of the second component are varied, as are its effective radius and total magnitude."
+ The simulated galaxies are convolved with a PSF (obtained from the data) and are placed in empty areas of the observed Aygo band image., The simulated galaxies are convolved with a PSF (obtained from the data) and are placed in empty areas of the observed $H_{160}$ band image.
+ We then run the procedure described above to extract surface brightness profiles and compare them to the input profiles., We then run the procedure described above to extract surface brightness profiles and compare them to the input profiles.
+ A selection of these simulated profiles is shown in Figure 3.., A selection of these simulated profiles is shown in Figure \ref{fig:test}.
+ The input profiles are shown as solid black lines., The input profiles are shown as solid black lines.
+ The dashed grey lines indicate the two subcomponents of each simulated galaxy., The dashed grey lines indicate the two subcomponents of each simulated galaxy.
+ The directly measured profiles are shown m green., The directly measured profiles are shown in green.
+ The best-fit Sérrsic models are shown 1n blue. and the residual-corrected profiles are shown in red.," The best-fit Sérrsic models are shown in blue, and the residual-corrected profiles are shown in red."
+ The residual-corrected profiles are plotted up to the radius where the uncertainty in the sky determination becomes significant., The residual-corrected profiles are plotted up to the radius where the uncertainty in the sky determination becomes significant.
+ The effectiveness of the residual-correction method is clear: whereas a simple Sérrsic fit in. many cases under- or overpredicts the flux at r>5 kpe. the residual-corrected profiles follow the input profiles extremely well up to the sky threshold (~10 kpe).," The effectiveness of the residual-correction method is clear: whereas a simple Sérrsic fit in many cases under- or overpredicts the flux at $r > 5$ kpc, the residual-corrected profiles follow the input profiles extremely well up to the sky threshold $\sim10$ kpc)."
+ The recovered flux within 10 kpe is on average of the total input flux. with a 1-0 spread of2%.," The recovered flux within 10 kpc is on average of the total input flux, with a $\sigma$ spread of."
+. Recovered effective radii are less accurate. às this quantity depends quite strongly on the extrapolation of the surface brightness profile to radii beyond 10 kpe.," Recovered effective radii are less accurate, as this quantity depends quite strongly on the extrapolation of the surface brightness profile to radii beyond 10 kpc."
+ However. effective radii derived from the residual-corrected profiles are generally closer to the true effective radii than those derived from simple Sérrsic fits.," However, effective radii derived from the residual-corrected profiles are generally closer to the true effective radii than those derived from simple Sérrsic fits."
+ We now use the residual-correction method to derive the surface brightness profiles of the z—2 quiescent galaxies., We now use the residual-correction method to derive the surface brightness profiles of the $z\sim2$ quiescent galaxies.
+ The results are shown in Figure 4.., The results are shown in Figure \ref{fig:profiles}.
+ The SEDs. shown in the top row. illustrate the low levels of UV and IR emission of the quiescent galaxies in our sample.," The SEDs, shown in the top row, illustrate the low levels of UV and IR emission of the quiescent galaxies in our sample."
+ Rest-frame color images are shown in the second row., Rest-frame color images are shown in the second row.
+ These images indicate that the galaxies in this sample generally have compact elliptical morphologies., These images indicate that the galaxies in this sample generally have compact elliptical morphologies.
+ Some galaxies have a nearby neighbor: in these cases we simultaneously fit both objects to account for possible contamination by flux from the companion object., Some galaxies have a nearby neighbor; in these cases we simultaneously fit both objects to account for possible contamination by flux from the companion object.
+ In the third row. best-fit Sérrsic profiles are shown in blue and residual-corrected profiles in red.," In the third row, best-fit Sérrsic profiles are shown in blue and residual-corrected profiles in red."
+ The residual-corrected profiles follow the Sérrsic profiles remarkably well., The residual-corrected profiles follow the Sérrsic profiles remarkably well.
+ Most galaxies deviate slightly at large radii., Most galaxies deviate slightly at large radii.
+ The difference between the best-fit Sérrsic profiles and the residual-corrected profiles are shown in the bottom row., The difference between the best-fit Sérrsic profiles and the residual-corrected profiles are shown in the bottom row.
+ The deviations are generally small within 27: for some galaxies larger deviations occur at larger radii. but in these cases the uncertainty is very high due to the uncertain sky.," The deviations are generally small within $2r_e$; for some galaxies larger deviations occur at larger radii, but in these cases the uncertainty is very high due to the uncertain sky."
+ Overall. the profiles are consistent with simple Sérrsic profiles.," Overall, the profiles are consistent with simple Sérrsic profiles."
+ The profiles are given in Table 2.. and can also be downloaded from In order to investigate whether the profiles of z~2 quiescent galaxies deviate systematically from Sérrsic profiles we plot the difference between the best-fit Sérrsic profile and the residual-corrected flux profile in Figure 5... for all galaxies.," The profiles are given in Table \ref{tab:profiles}, and can also be downloaded from In order to investigate whether the profiles of $z\sim2$ quiescent galaxies deviate systematically from Sérrsic profiles we plot the difference between the best-fit Sérrsic profile and the residual-corrected flux profile in Figure \ref{fig:residuals}, , for all galaxies."
+ Black lines indicate the deviation profiles of individual galaxies. and their mean ts indicated by the red line.," Black lines indicate the deviation profiles of individual galaxies, and their mean is indicated by the red line."
+The excitation temperature provides a strict upper limit to the CMB temperature as other sources may contribute appreciably to the excitation.,The excitation temperature provides a strict upper limit to the CMB temperature as other sources may contribute appreciably to the excitation.
+ In fact. if the absorption is not a spurious effect of the line forest. other mechanisms have to be at play to explain an excitation temperature of at least 19.6 K. The possible excitation mechanisms are reviewed in the next section.," In fact, if the $^*$ absorption is not a spurious effect of the line forest, other mechanisms have to be at play to explain an excitation temperature of at least 19.6 K. The possible excitation mechanisms are reviewed in the next section."
+ The higher fine-structure states of a ground state multiplet can be populated by (1) particle collisions. (2) direct excitation by infrared photons and (3) indirect excitation by ultraviolet photons.," \nocite{Morton91}
+ The higher fine-structure states of a ground state multiplet can be populated by (1) particle collisions, (2) direct excitation by infrared photons and (3) indirect excitation by ultraviolet photons."
+ The equilibrium between the excitation and de-exeitation of the J—1/2.>3/2 fine structure is described by: Here the collision excitation rate 1s expressed as (aejn. where (00) 1s the temperature averaged product between the cross-section and the particle velocityand 5» is the particle density. j= H. ο.ν.," The equilibrium between the excitation and de-excitation of the $ J = 1/2 \rightarrow 3/2$ fine structure is described by: Here the collision excitation rate is expressed as $\langle\sigma v\rangle n$, where $\langle\sigma v\rangle $ is the temperature averaged product between the cross-section and the particle velocityand $n$ is the particle density, $j=$ H, $e,~p$."
+ The direct photon excitation rate is expressed as the product between the Einstein probability coefficient for induced transition (2) and the radiation energy density per frequency interval (C (1794))., The direct photon excitation rate is expressed as the product between the Einstein probability coefficient for induced transition $B$ ) and the radiation energy density per frequency interval $U(\nu_{01})$ ).
+ The UV pumping rate is represented by the coefficient [. which includes the UV energy density term.," The UV pumping rate is represented by the coefficient $\Gamma$, which includes the UV energy density term."
+ :1io is the Einstein probability coefficient for spontaneous transition and for the transition 3/2.» 1/2. A49=2.29«10ὃς | (Nussbaumer&Storey 1981)).," $A_{10}$ is the Einstein probability coefficient for spontaneous transition and for the transition $J = 3/2 \rightarrow 1/2$ , $A_{10}
+= 2.29\times 10^{-6}$ $^{-1}$ \cite{Nussbaumer81}) )."
+ For convenience we can divide both sides of (3) by 440 and rewrite: where 5g;j;j. δη and σε) are respectively the collisional excitation rate. the Einstein probability coefficient for induced transition and the UV pumping rate. all divided by (yy.," For convenience we can divide both sides of (3) by $A_{10}$ and rewrite: where $q_{ij,j}$, $b_{ij}$ and $\gamma_{ij}$ are respectively the collisional excitation rate, the Einstein probability coefficient for induced transition and the UV pumping rate, all divided by $A_{10}$."
+ In order to establish the importance of the various factors in determining the observed population ratio in the fine structure levels ofΗΠ.. we need to evaluate the magnitude of each term in this equation.," In order to establish the importance of the various factors in determining the observed population ratio in the fine structure levels of, we need to evaluate the magnitude of each term in this equation."
+ The particles which may be responsible for collisional excitation are essentially electrons. protons and atomic hydrogen. with different contributions dominating in different temperature and ionization regimes.," The particles which may be responsible for collisional excitation are essentially electrons, protons and atomic hydrogen, with different contributions dominating in different temperature and ionization regimes."
+" The expression for the rate of collisional excitation by electrons is given in Baheall&Wolf(1968) and. by using the detailed computation of the effective collisional strength given in Hayes&Nussbaumer(1984) and Keenanetal.(1986).. one obtains typically quj,=0.15 cui?s.+ for T;.=100 K and qusc0051 c0u8| for T.=10000 K. The excitation rates as a function of electron temperature for neutral hydrogen collisions are also given in Keenanetal.(1986) and for T.=100 Κι =28«10τοις tf for T.=10000 Κι =L5«lo? ανν|."," The expression for the rate of collisional excitation by electrons is given in \cite*{Bahcall68} and, by using the detailed computation of the effective collisional strength given in \cite*{Hayes84} and \cite*{Keenan86}, , one obtains typically $q_{01, e^-} = 0.15$ ${\rm cm^3~s^{-1}}$ for $T_e =
+100$ K and $q_{01, e^-} = 0.051$ ${\rm cm^3~s^{-1}}$ for $T_e = 10\,000$ K. The excitation rates as a function of electron temperature for neutral hydrogen collisions are also given in \cite*{Keenan86} and for $T_e =
+100$ K $q_{01, {\rm H}} = 2.8 \times 10^{-4}$ ${\rm cm^3~s^{-1}}$, for $T_e = 10\,000$ K $q_{01,{\rm H}} = 1.5 \times 10^{-3}$ ${\rm cm^3~s^{-1}}$."
+" The electron collision term will dominate the hydrogen collision term for p,20.002p»gp at 7,LOO K and for n».>0.03vy at Tj.=10000 K. If the plasma ts collisionally ionized the electron collision term will be the dominant one for temperature T>10000 K. when the fraction of ionized hydrogen becomes significant (Baheall&Wolf1968))."," The electron collision term will dominate the hydrogen collision term for $n_e \geq 0.002~n_{\rm H}$ at $T_e =
+100$ K and for $n_e \geq 0.03~n_{\rm H}$ at $T_e = 10\,000$ K. If the plasma is collisionally ionized the electron collision term will be the dominant one for temperature $T > 10\,000$ K, when the fraction of ionized hydrogen becomes significant \cite{Bahcall68}) )."
+" If the absorbing medium is significantly photoionized. and i,=0.03ny, the electron collision term will be the dominant term at any kinetic temperature whereas if phototonization 15 not signficant and ο<0.002my, hydrogen collisions. will dominate."," If the absorbing medium is significantly photoionized and $n_e \geq 0.03~n_{\rm H}$ the electron collision term will be the dominant term at any kinetic temperature whereas if photoionization is not signficant and $n_e <
+0.002~n_{\rm H}$ hydrogen collisions will dominate."
+ The excitation rate for proton collision. becomes comparable to the electron contribution only for temperatures T.>10 K (Baheall&Wolf 1968). but at these temperatures is completely destroyed by collisional ionization (Sutherland&Dopita 1993)).," The excitation rate for proton collision becomes comparable to the electron contribution only for temperatures $T_e \geq
+10^5$ K \cite{Bahcall68}) ), but at these temperatures is completely destroyed by collisional ionization \cite{Sutherland93}) )."
+ We will therefore ignore the proton collision contribution., We will therefore ignore the proton collision contribution.
+" The collisional de-excitation rate is given by: As a first approximation. the collisional de-excitation term on the right hand side of ((4) can be omitted tf,<1 ο «LO? 5m "," The collisional de-excitation rate is given by: As a first approximation, the collisional de-excitation term on the right hand side of (4) can be omitted if $n_e < 1$ $^{-3} $ or $n_{\rm H} < 10^3$ $^{-3} $."
+The photons responsible for directly populating fine structure excited levels have a frequency of 7)=GLO | !. , The photons responsible for directly populating fine structure excited levels have a frequency of $\bar{\nu}_{10} = 64.0$ $^{-1}$ .
+Sources of far-infrared photons are the CMB and thermal dust emission., Sources of far–infrared photons are the CMB and thermal dust emission.
+ Since the CMB radiation has a Black Body spectrum the direct excitation rate from CMB photons can be expressed as: As we have seen. the Big Bang model predicts the CMB temperature to be 11.05 K at this redshift. moreover theupper," Since the CMB radiation has a Black Body spectrum the direct excitation rate from CMB photons can be expressed as: As we have seen, the Big Bang model predicts the CMB temperature to be 11.05 K at this redshift, moreover theupper"
+superposition.,ion.
+ Grids can be produced upon request., Grids can be produced upon request.
+tthe square root of the observed number of compauious to a eiven galaxy. because this will bias the resultingo mica.,"the square root of the observed number of companions to a given galaxy, because this will bias the resulting mean."
+ The statistical variance of the A; estimator comes frou two sources. the clustering of tle galaxies and shot noise.," The statistical variance of the $\Delta_j$ estimator comes from two sources, the clustering of the galaxies and shot noise."
+ The clustering term involves the three-poiut correlation function. with one galaxy. from the spectroscopic sample aud two from the nuaging sample.," The clustering term involves the three-point correlation function, with one galaxy from the spectroscopic sample and two from the imaging sample."
+ If the first of these is at the origin and the latter two are at Fy and ry. then we denote the three-point correlation function as (ηνre).," If the first of these is at the origin and the latter two are at $\bfr_1$ and $\bfr_2$, then we denote the three-point correlation function as $\zeta(\bfr_1,\bfr_2)$."
+ The expected deusities at two points eiven a spectroscopic galaxy at the origin is (Peehles1980) > = o0QZoQZ2) |(18) where £i is the two-point correlation between duaging and spectroscopic ealaxics aud £;; is the correlation of two imaging ealaxies.," The expected densities at two points given a spectroscopic galaxy at the origin is \citep{Pee80}
+ > = (Z_2) ] where $\xiis$ is the two-point correlation between imaging and spectroscopic galaxies and $\xi_{ii}$ is the correlation of two imaging galaxies."
+ The chistering coutribution to the variauce of A; is thou ΕΛ”... ΗΡΕΜΗ zum , The clustering contribution to the variance of $\Delta_j$ is then _j) = d^2R_1 d^2R_2 G(R_1) G(R_2) dZ_1 dZ_2 _2) - ].
+The last term is simply (A;Z2., The last term is simply $\left<\Delta_j\right>^2$.
+" The terms in £i, In equation (??)) iuteerate to zero.", The terms in $\xiis$ in equation \ref{eq:rhoexp}) ) integrate to zero.
+ The à terii involves all three objects. so at the level of approximation in equation (2.1)). we cau assume o(Zi)=ofZ2)oy.," The $\zeta$ term involves all three objects, so at the level of approximation in equation \ref{eq:wdef}) ), we can assume $\phi(Z_1)=\phi(Z_2)=\phi_0$."
+ However. the £;; term represents correlated imagine galaxies that are uncorrelated with the spectroscopic object. so they may have Z far from0 and ofZ)zoy.," However, the $\xi_{ii}$ term represents correlated imaging galaxies that are uncorrelated with the spectroscopic object, so they may have $Z$ far from0 and $\phi(Z)\ne\phi_0$."
+ Iutegratiug over Z will vield the angular correlation of the nuagine catalog., Integrating over $Z$ will yield the angular correlation of the imaging catalog.
+ Indeed. for Zz0. the angular separations implicit in our definition of tle transverse coordinate Rcnrespoud to different plivsical scales.," Indeed, for $Z\ne0$, the angular separations implicit in our definition of the transverse coordinate $\bfR$ correspond to different physical scales."
+ Doing this correctly again vields the augular correlation function., Doing this correctly again yields the angular correlation function.
+ We thus sinplifv equation (??)) to pli)? A? RoG{Ry IGRs) | EI to write C.F)κααπο)|(Gea)νο μοι).," We thus simplify equation \ref{eq:VarCl}) ) to _j) = + )^2 d^2R_2 G(R_1) G(R_2) _2|) to write $\zeta(\bfr_1,\bfr_2) = Q\{\xiis(r_1)\xiis(r_2)+[\xiis(r_1)+\xiis(r_2)]\xi_{ii}(|\bfr_1-\bfr_2)|)\}$ ."
+ The two-dimensional Pouricr transform of G(R) is, The two-dimensional Fourier transform of $G(R)$ is
+"x redshift), we adopt the procedure described in Thomasetal. (2009).","$\times$ redshift), we adopt the procedure described in \cite{thomas09}."
+". The procedure involves the stacking of RA and DEC slices, taken from individual snapshots at different redshifts (or frequency), interpolated smoothly to create a reionization history."," The procedure involves the stacking of RA and DEC slices, taken from individual snapshots at different redshifts (or frequency), interpolated smoothly to create a reionization history."
+ This data cube is then convolved with the point spread function of the LOFAR telescope to simulated the mock data cube of the redshifted 21-cm signal as seen by LOFAR., This data cube is then convolved with the point spread function of the LOFAR telescope to simulated the mock data cube of the redshifted 21-cm signal as seen by LOFAR.
+ For further details on creating this cube refer to Thomasetal.(2009)., For further details on creating this cube refer to \citet{thomas09}.
+. As expected the signatures (both visually and in the r.m.s) of the three scenarios (Fig. 11)), As expected the signatures (both visually and in the r.m.s) of the three scenarios (Fig. \ref{fig:histcomp}) )
+ are markedly different., are markedly different.
+" In the miniqso-only scenario, reionization proceeds extremely quickly and the Universe is almost completely (<xu>= 0.95) reionized by around redshift 7."," In the miniqso-only scenario, reionization proceeds extremely quickly and the Universe is almost completely $<\mathrm{x_{HII}}> = 0.95$ ) reionized by around redshift 7."
+ The case in which stars are the only source see reionization end at a redshift of 6., The case in which stars are the only source see reionization end at a redshift of 6.
+" Also in this case, compared to the previous one, reionization proceeds in a rather gradual manner."," Also in this case, compared to the previous one, reionization proceeds in a rather gradual manner."
+" The hybrid model, as explained previously, interpolates between the previous two scenarios."," The hybrid model, as explained previously, interpolates between the previous two scenarios."
+ The ὁΤι in Fig., The $\delta \mathrm{T_b}$ in Fig.
+" 11 is calculated based on the effectivness of Jo, produced by the source, to decouple the CMB temperature (Tcmp) from the spin temperature (Ts)."," \ref{fig:histcomp} is calculated based on the effectivness of $\mathrm{J_o}$, produced by the source, to decouple the CMB temperature $\mathrm{T_{CMB}}$ ) from the spin temperature $\mathrm{T_s}$ )."
+" This flux, both in spatial extent and amplitude, is obviously much larger in the case of miniqsos compared to that of stars resulting in a markedly higher brightness temperatures in both the miniqso-only and hybrid models when compared to that of the stars."," This flux, both in spatial extent and amplitude, is obviously much larger in the case of miniqsos compared to that of stars resulting in a markedly higher brightness temperatures in both the miniqso-only and hybrid models when compared to that of the stars."
+" However, we know that stars themselves produce Lya radiation in their spectrum."," However, we know that stars themselves produce $\alpha$ radiation in their spectrum."
+" Apart from providing sufficient Lyo flux to their immediate surrounding, this radiation builds up, as the Universe evolves, into a strong background J, (Ciardi&Madau2003),, potentially filling the Universe with sufficient Lyo photons to couple the spin temperature to the kinetic temperature everywhere."," Apart from providing sufficient $\alpha$ flux to their immediate surrounding, this radiation builds up, as the Universe evolves, into a strong background $\mathrm{J_o}$ \citep{ciardi03}, potentially filling the Universe with sufficient $\alpha$ photons to couple the spin temperature to the kinetic temperature everywhere."
+" Thus, we plot in Fig."," Thus, we plot in Fig."
+ 12 the same set of reionization histories as in Fig., \ref{fig:histcompinf} the same set of reionization histories as in Fig.
+" 11 but now assuming that T, coupled to Τι.", \ref{fig:histcomp} but now assuming that $\mathrm{T_s}$ coupled to $\mathrm{T_k}$.
+ Clearly the “cold” regions in the Universe show up as regions with large negative brightness temperature., Clearly the “cold” regions in the Universe show up as regions with large negative brightness temperature.
+ This assumption though is not strictly applicable towards the beginning of reionization., This assumption though is not strictly applicable towards the beginning of reionization.
+ In refsec:stats we quantify the differences in the brightness temperature evolution when this assumption is made., In \\ref{sec:stats} we quantify the differences in the brightness temperature evolution when this assumption is made.
+ It has to be noted that the results we are discussing here are extremely model dependent and any changes to the parametres can influence the results significantly., It has to be noted that the results we are discussing here are extremely model dependent and any changes to the parametres can influence the results significantly.
+" This on the other is the demonstration of the capability and the need for a like"" algorithm to span the enormous parametre space of the astrophysical unknowns in reionization studies.", This on the other is the demonstration of the capability and the need for a like” algorithm to span the enormous parametre space of the astrophysical unknowns in reionization studies.
+" To test the feasibiliy of 21-cm telescopes (specifically LOFAR) in distinguishing observational signatures of different sources of reionization, we need to propagate the cosmological 21-cm maps generated in refsubsec:reionhist using LOFAR’s telescope response."," To test the feasibiliy of 21-cm telescopes (specifically LOFAR) in distinguishing observational signatures of different sources of reionization, we need to propagate the cosmological 21-cm maps generated in \\ref{subsec:reionhist} using LOFAR's telescope response."
+ The point spread function (PSF) of the LOFAR array was constructed according to the latest configuration of the antenna layouts for the LOFAR-EoR experiment., The point spread function (PSF) of the LOFAR array was constructed according to the latest configuration of the antenna layouts for the LOFAR-EoR experiment.
+ The LOFAR telescope will consist of up to 48 stations in The Netherlands of which approximately 22 will be located in the core region (Labropoulosetal.2009)., The LOFAR telescope will consist of up to 48 stations in The Netherlands of which approximately 22 will be located in the core region \citep{panos09}.
+. The core marks an area of 1.7 x 2.3 kilometres and is essentially the most important part of the telescope for an EoR experiment., The core marks an area of 1.7 $\times$ 2.3 kilometres and is essentially the most important part of the telescope for an EoR experiment.
+" The core station consists of two sets of antennae, the Low Band (LBA; 30-90 MHz) and the High BandAntenna (HBA; 110-240 MHz)."," The core station consists of two sets of antennae, the Low Band (LBA; 30-90 MHz) and the High BandAntenna (HBA; 110-240 MHz)."
+" The HBA antennae in the core stations is further split into two “half-stations” of half the collecting area (35-metre diameter), separated by zz 130 metres."," The HBA antennae in the core stations is further split into two “half-stations” of half the collecting area (35-metre diameter), separated by $\approx$ 130 metres."
+ This split further improves the uv-coverage., This split further improves the uv-coverage.
+ For details on the antenna layout and the synthesis of the antenna beam pattern refer to upcoming paper by Labropoulosetal.(2009)., For details on the antenna layout and the synthesis of the antenna beam pattern refer to upcoming paper by \citet{panos09}.
+". In its current configuration, the resolution of the is expected to be around 3 arcmins."," In its current configuration, the resolution of the LOFAR-core is expected to be around 3 arcmins."
+" Thus, as an example at redshift 10, all scales below ~ 800 kpc will be filtered out."," Thus, as an example at redshift 10, all scales below $\approx$ 800 kpc will be filtered out."
+ Fig., Fig.
+ 13 shows this effect for the reionization histories corresponding to Fig. 11.., \ref{fig:histcompafterconv} shows this effect for the reionization histories corresponding to Fig. \ref{fig:histcomp}. .
+ The corresponding changes in the r.m.s of the brightness temperature is also plotted., The corresponding changes in the r.m.s of the brightness temperature is also plotted.
+" We see that, although smoothed to a"," We see that, although smoothed to a"
+is rather siiall. ancl hard to ueasure within typical sinee CCD fields (Villuuiseu.Freucling&DaCosta1997)).,"is rather small, and hard to measure within typical single CCD fields \cite{vil97}) )."
+ Only. with he advent of ep. multicolor galaxy samples and reliable shotometric redshift tecliniques it |as been possissl to detect thi ellect (Herraiz el al.," Only with the advent of deep, multicolor galaxy samples and reliable photometric redshift techniques it has been possible to detect this effect (Herranz et al."
+ 1990)., 1999).
+ To iwlerpre the meastομιομίς of w'yp δι& the caculations mentioned above. it Is necessaryry {ο assulne a certalu sye for the power spectrum.," To interpret the measurements of $w_{fb}$ using the calculations mentioned above, it is necessary to assume a certain shape for the power spectrum."
+ UuortuuateN it is still far rom clear whether tle lost) poptllart a1salz. hat of Peacoc da Doclels (1996)—or v other for that matte—provides au accurate o the LSS (listribL10 (see e.g. Jeusus et al.," Unfortunately it is still far from clear whether the most popular ansatz, that of Peacock and Dodds (1996)—or any other for that matter—provides an accurate fit to the LSS distribution (see e.g. Jenkins et al."
+ 1993)., 1998).
+" It hus «esi‘able to develop inethods wLOSE a»plijon ls not l""udered by Us uncertalty.", It is thus desirable to develop methods whose application is not hindered by this uncertainty.
+ An example is t alistjc A (Van Waerbeke. 1995). wlch combi shear and 1luuber counts itformation. aid can be used jeasure the scale dependence o‘the jas.," An example is the statistic $R$ (Van Waerbeke, 1998), which combines shear and number counts information, and can be used to measure the scale dependence of the bias."
+" The Vaie of A is most independent o ‘the shape of the [)Ower yectrum if the foreeroμις, galaxy disributiML Las a Harrow redshift raige.", The value of $R$ is almost independent of the shape of the power spectrum if the foreground galaxy distribution has a narrow redshift range.
+ Here we show tlat SOLuethi1g slilar can be achieved with wyy. with the aclditioal advantage Oo. being abe 10¢ owlhout tlὁ shear info‘nati in those Cases where he latter is cliflieilt {ο οMalL.," Here we show that something similar can be achieved with $w_{fb}$, with the additional advantage of being able to do without the shear information in those cases where the latter is difficult to obtain."
+" lt folows from the uagnific‘ation biane ect 'anizares 1981. Naraya 1989. Broadhur‘st. Tayor Peacock 1995) trat the surface uunber (ensi Νο backer d populatjon iy is chaeed by the magiiicatior jt. associated ith a foreground ealaxy poplation with nyer density η as gy=(o—1)óp. where gr, is the pertt‘Daion iu Ιe egalaxy surface density ny, (n—nj —]).a is |le logaritlunic slope of tje —nuunber courts aldin le weak leusing regije qi] 0H "," It follows from the magnification bias effect (Canizares 1981, Narayan 1989, Broadhurst, Taylor Peacock 1995) that the surface number density of background population $n_b$ is changed by the magnification $\mu$, associated with a foreground galaxy population with number density $n$ as $g_b =(\alpha-1)\delta \mu$, where $g_b$ is the perturbation in the galaxy surface density $n_b$ $g_b=n_b/<n_b>-1$ ), $\alpha$ is the logarithmic slope of the number counts and in the weak lensing regime $\mu \approx 1+ \delta\mu$, $\delta\mu << 1$."
+ce Jrzztt2n aud &. he couvergelce. is proportioial t> th Jor[9]ec inatter surlace density it [o lal yyXORXSMox05.wl ere o is the clewki jatter surface cle verturion.," Since $\mu\approx 1+2\kappa$ and $\kappa$ , the convergence, is proportional to the projected matter surface density $\Sigma$, it follows that $g_b \propto \delta\kappa \propto \delta\Sigma \propto \Omega\delta$, where $\delta$ is the dark matter surface density perturbation."
+ Therelore wp=~MibeCyd aud assmine linearand determiistic Dias οxOb e is the two-poiut galaxy correla iction for the backgroux »opulations.S. alica he biasing LactOr ec b vow=9buss.," Therefore $w_{fb} \equiv <gg_b>\propto \Omega <g\delta>$ and assuming linearand deterministic bias $w_{fb}\propto\Omega b^{-1}w$ where $w$ is the two-point galaxy correlation function for the background populations, and the biasing factor $b$ is defined by $w=b^2w_{\delta\delta}$."
+ This result. prov W.traightforwarcl. virtually 1uodel iudepeieu inethod to esi ‘allo OQ/b.," This result provides a straightforward, virtually model independent method to estimate the ratio $\Omega/b$."
+ Willianis Irwin 1998 arrive(| to a simileWw expressio Lusing a ple.lOlIneiological appreAC1., Williams Irwin 1998 arrived to a similar expression using a phenomenological approach.
+ ult «Istorsion mehod provides the quaity 8xQQ?5/b (Dekel 1991). so comjuiig both oue car esi d b separately.," The redshift distorsion method provides the quantity $\beta\propto \Omega^{0.6}/b$ (Dekel 1994), so combining both one can estimate $\Omega$ and $b$ separately."
+ e outline of the paper is the following., The outline of the paper is the following.
+ Iu Sec., In Sec.
+ 2 we show rigorousy that under reasonable assumptions ie., 2 we show rigorously that under reasonable assumptions $w_{fb}\propto \Omega b^{-1}w$ .
+ Sec., Sec.
+ 3 explores the application of this method o future aid ougoiug su‘veys aud Sec., 3 explores the application of this method to future and ongoing surveys and Sec.
+ 1 stunina‘ies nain results and conclusions., 4 summarizes our main results and conclusions.
+ Let us cousider two populatious of sources: a backgroiud oue (e.g. quasars or galaxies) aud a foregrouud oue (e.g. galaxies). placed at different distances A with p.d.," Let us consider two populations of sources: a background one (e.g. quasars or galaxies) and a foreground one (e.g. galaxies), placed at different distances $\lambda$ with p.d.f."
+L πλ) aud BA). respectively.,"'s $R_b(\lambda)$ and $R(\lambda)$, respectively."
+ Iu Sanz et al. (, In Sanz et al. (
+"1997). the backgrouid-foreground ¢orrelation wy, was calculaed as a functional of the power spectrum (A.4) of the matter ΠιCctuations at aly time (A is the comoving distance from the observer to an object at recdshift A=d'urqu aud Q< 1.A=0);: where b(A.s0) is the bias [actor lor the foreground galaxies (assumed to be linear. non-stochastic but. possibly redshift and. scale dependent). a, is the slope of the background source number counts aud. is the correlation between the magnification auc the mass density fluctuation.","1997), the background-foreground correlation $w_{fb}$ was calculated as a functional of the power spectrum $P(\lambda , k)$ of the matter fluctuations at any time $\lambda$ is the comoving distance from the observer to an object at redshift $z$, $\lambda=\frac{(1 + \Omega z)^{1/2}-1}{(1 + \Omega z)^{1/2}-1+\Omega}$ and $\Omega<1, \Lambda=0$ ): where $b(\lambda,s\theta )$ is the bias factor for the foreground galaxies (assumed to be linear, non-stochastic but possibly redshift and scale dependent), ${\alpha}_b$ is the slope of the background source number counts and $C_{\mu \delta}(\theta)\equiv 2<\mu (\vec{\phi}) 
+\delta(\vec{\phi} + \vec{\theta})>$ is the correlation between the magnification and the mass density fluctuation."
+" 7,fA) is the lensing window function given by equation (7) in Sanzet al. (", $T_b(\lambda)$ is the lensing window function given by equation (7) in Sanzet al. (
+1997): Ty)j—ShdpgldSQ)/Al(1yur omo ,"1997): $T_b(\lambda )\equiv \frac{1}{\lambda }\int_{\lambda}^1\frac{du}{u}R_b(u) 
+(u - \lambda )\frac{1 - (1 - \Omega )u\lambda }{1 - (1 - \Omega ){\lambda }^2}$ ."
+The augular two point correlation Duuctiou for the foregrouud population : cau be obtained as where «e(0)=<gie)g(o+0)> is the foreground angular galaxy-ealaxy correlation function., The angular two point correlation function for the foreground population $w$ can be obtained as where $w(\theta )\equiv <g(\vec{\phi})g(\vec{\phi} + \vec{\theta})>$ is the foreground angular galaxy–galaxy correlation function.
+to investigate whether the peculiar three-peak structure of this scandium Q/7 signal might be explained in. terms of HFS. within a modeling approach similar to that proposed by Belluzzietal.(2007) for the Bat D> line.,"to investigate whether the peculiar three-peak structure of this scandium $Q/I$ signal might be explained in terms of HFS, within a modeling approach similar to that proposed by \citet{Bel07} for the Ba $_2$ line."
+ It is well-known that hyperfine structure is produced by the influence of the nucleus on the energy levels of the atom., It is well-known that hyperfine structure is produced by the influence of the nucleus on the energy levels of the atom.
+ On the one hand. this influence is related to the nuclei of the various isotopes having slightly different volumes and masses (Isotopic effect). and on the other hand. to the coupling of the nuclear spin Z with the total angular momentum J of the electronic cloud (nuclear spin effect).," On the one hand, this influence is related to the nuclei of the various isotopes having slightly different volumes and masses (isotopic effect), and on the other hand, to the coupling of the nuclear spin $\vec{I}$ with the total angular momentum $\vec{J}$ of the electronic cloud (nuclear spin effect)."
+ We note that it is customary to speak about hyperfine structure when referring to the nuclear spin effect only., We note that it is customary to speak about hyperfine structure when referring to the nuclear spin effect only.
+ In the absence of magnetic fields. using Dirac’s notation. the energy eigenvectors of an atomic system with HFS can be written in the form |cJ7Ff>. where « represents a set of inner quantum numbers (specifying the electronic configuration and. if the atomic system is described by the L-S coupling scheme. the total electronic orbital. and spin angular momenta). F is the quantum number associated with the total angular momentum operator (electronic plus nuclear: &=J+ J). and f is the quantum number associated with the projection of F along the quantization axis.," In the absence of magnetic fields, using Dirac's notation, the energy eigenvectors of an atomic system with HFS can be written in the form $|\, \alpha J I F f \!>$, where $\alpha$ represents a set of inner quantum numbers (specifying the electronic configuration and, if the atomic system is described by the $L$ $S$ coupling scheme, the total electronic orbital, and spin angular momenta), $F$ is the quantum number associated with the total angular momentum operator (electronic plus nuclear: $\vec{F}=\vec{J}+\vec{I}$ ), and $f$ is the quantum number associated with the projection of $\vec{F}$ along the quantization axis."
+ [It is possible to demonstrate that the HFS Hamiltonian. describing the interaction between the nuclear spin and the electronic angular momentum. can be expressed as a series of electric and magnetic multipoles (see.forexam-ple.Kopfermann. 1958).," It is possible to demonstrate that the HFS Hamiltonian, describing the interaction between the nuclear spin and the electronic angular momentum, can be expressed as a series of electric and magnetic multipoles \citep[see, for example,][]{Kop58}."
+. In this investigation. we retain only the first two terms (magnetic-dipole and electric-quadrupole). which are given by where A(a.J.D) and SC.J.D) are the magnetie-dipole and the electric-quadrupole HFS constants. respectively. and where We describe the atomic system by means of the density matrix formalism. a robust theoretical framework very suitable for handling atomic polarization. phenomena (population unbalances and quantum interferences between pairs of magnetic sublevels) that can be induced in the atomic system (for example by an anisotropic incident radiation field).," In this investigation, we retain only the first two terms (magnetic-dipole and electric-quadrupole), which are given by where $\mathcal{A}(\alpha,J,I)$ and $\mathcal{B}(\alpha,J,I)$ are the magnetic-dipole and the electric-quadrupole HFS constants, respectively, and where We describe the atomic system by means of the density matrix formalism, a robust theoretical framework very suitable for handling atomic polarization phenomena (population unbalances and quantum interferences between pairs of magnetic sublevels) that can be induced in the atomic system (for example by an anisotropic incident radiation field)."
+ Since the upper and lower levels of the Sc line at 4247 pertain to singlet terms (this is the only line of the multiplet). we consider a simple two-level model atom with HFS.," Since the upper and lower levels of the Sc line at 4247 pertain to singlet terms (this is the only line of the multiplet), we consider a simple two-level model atom with HFS."
+ Following LandiDeelInnocenti&Landolfi(2004) (hereafter LLO4). we describe the atom through the density matrix elements where p is the density-matrix operator.," Following \citet{LL04} (hereafter LL04), we describe the atom through the density matrix elements where $\hat{\rho}$ is the density-matrix operator."
+ We recall that the diagonal elements represent the populations of the various magnetic sublevels. while the off-diagonal elements represent the quantum interferences. or coherences. between pairs of magnetic sublevels.," We recall that the diagonal elements represent the populations of the various magnetic sublevels, while the off-diagonal elements represent the quantum interferences, or coherences, between pairs of magnetic sublevels."
+ In the following. we work in terms of the so-called spherical statistical tensors.," In the following, we work in terms of the so-called spherical statistical tensors."
+ The conversion of the density matrix elements of Eq. (3)), The conversion of the density matrix elements of Eq. \ref{eq:rhoFFp}) )
+ into the spherical statistical tensor representation is given by the relation, into the spherical statistical tensor representation is given by the relation
+"Compton-y maps. we perform a line-of-sight integration of the electron pressure within a given solid angle. 1e. v=κο}dbl where & is the Boltzmann constant. 12. and 7, are the number density and temperature. respectively.","$y$ maps, we perform a line-of-sight integration of the electron pressure within a given solid angle, i.e. $y = \sigma_{\rmn{T}}\int n_\elct k\,T_\elct/(m_\elct c^2)\, \dd l$, where $k$ is the Boltzmann constant, $n_\elct$ and $T_\elct$ are the number density and temperature, respectively."
+ We construct 1.6° x1.6?and 3.2° x3.2? maps for the 256? and 512° simulations. respectively.," We construct $1.6$ $
+\times 1.6$ and $3.2$ $ \times 3.2$ maps for the $256^3$ and $512^3$ simulations, respectively."
+ Using this method there are large sample variances (?) associated with nearby cluster contamination., Using this method there are large sample variances \citep{2002ApJ...579...16W} associated with nearby cluster contamination.
+ We have quantified their influence on the power spectrum for each of our three physics models by averaging over twelve translate-rotate viewing angles each projected from our ten 256? full hydrodynamical simulations for each of the 33 redshift outputs back to a redshift z=5: the power spectra of which are then added up to yield the total spectrum., We have quantified their influence on the power spectrum for each of our three physics models by averaging over twelve translate-rotate viewing angles each projected from our ten $256^3$ full hydrodynamical simulations for each of the 33 redshift outputs back to a redshift $z=5$; the power spectra of which are then added up to yield the total spectrum.
+ This method of computing the power spectrum has the advantage of taking care of the artificial correlations that oceur because any individual simulation follows the time evolution of the same structure., This method of computing the power spectrum has the advantage of taking care of the artificial correlations that occur because any individual simulation follows the time evolution of the same structure.
+ For the shock heating case. we did ten more hydrodynamical simulations to show that our averaged template had converged (within ~10%)). but note that using only a few boxes can be misleading in terms of rare events.," For the shock heating case, we did ten more hydrodynamical simulations to show that our averaged template had converged (within $\sim$ ), but note that using only a few boxes can be misleading in terms of rare events."
+ The computationally more expensive 512* SZ spectra have the equivalent of 8 256? plus wider coverage. so the 512? shock heating result showngives a reasonable indication of what to expect.," The computationally more expensive $512^3$ SZ spectra have the equivalent of 8 $256^3$ plus wider coverage, so the $512^3$ shock heating result showngives a reasonable indication of what to expect."
+ The other 2 physics single-box cases at 512? are similar to the 256 ensemble means., The other 2 physics single-box cases at $512^3$ are similar to the $256^3$ ensemble means.
+ The analytical approach has the great advantage of including an accurate mean cluster density to high halo masses. but to be usable for SZ power estimation. scaled pressure profiles must also be accurate. à subject we turn to in future work.," The analytical approach has the great advantage of including an accurate mean cluster density to high halo masses, but to be usable for SZ power estimation, scaled pressure profiles must also be accurate, a subject we turn to in future work."
+ For now. we note that using such profiles from our simulations gives good agreement with the average SZ power shown at the low€ where sample variance will be largest.," For now, we note that using such profiles from our simulations gives good agreement with the average SZ power shown at the low$\ell$ where sample variance will be largest."
+ In Fig.3," In Fig.,"
+.. our simulation templates and the KS template shown have excluded structures below >=0.07 to decrease the large sample variance associated with whether a large-ish cluster enters the field-of-view., our simulation templates and the KS template shown have excluded structures below $z = 0.07$ to decrease the large sample variance associated with whether a large-ish cluster enters the field-of-view.
+ Such entities would typically be removed from CMB fields and consideredseparately., Such entities would typically be removed from CMB fields and consideredseparately.
+ The mean Compton y-parameter found in our AGN feedback simulations is one order of magnitude below the COBE FIRAS upper limit of 15x107° (2)., The mean Compton $y$ -parameter found in our AGN feedback simulations is one order of magnitude below the COBE FIRAS upper limit of $15 \times 10^{-6}$ \citep{1996ApJ...473..576F}.
+ We compare the theoretical predictions for the tSZ power spectrum in Fig., We compare the theoretical predictions for the tSZ power spectrum in Fig.
+"3.. Our 312? and 256? shock heating simulations are in agreement with previous SPH simulation power spectra (?.BO205) scaled by C,x(Qul?Que. with the factors determined from our simulations of differing cosmologies."," Our $512^3$ and $256^3$ shock heating simulations are in agreement with previous SPH simulation power spectra \citep[][B0205]{2001ApJ...549..681S} scaled by $C_\ell \propto
+(\Omega_\rmn{b} h)^2 \Omega_\rmn{m} \sigma_8^{7}$, with the factors determined from our simulations of differing cosmologies."
+ The B0205 SZ power shown had a cut at z=0.2. appropriate for CBI fields; using the same cut on a shock heating simulation with the same cosmology that we have done. we get superb agreement.," The B0205 SZ power shown had a cut at $z = 0.2$, appropriate for CBI fields; using the same cut on a shock heating simulation with the same cosmology that we have done, we get superb agreement."
+ The KS and S10 semi-analytic SZ power spectra templates differ substantially from our templates. in particular with higher power at low £: as shown in Fig.2," The KS and S10 semi-analytic SZ power spectra templates differ substantially from our templates, in particular with higher power at low $\ell$: as shown in Fig.,"
+.. the KS pressure profile beyond Rsoo overestimates the pressure relative to both simulations and observations. leading to the modified shape and larger Y4: this behaviour is also shown in ?..," the KS pressure profile beyond $R_{500}$ overestimates the pressure relative to both simulations and observations, leading to the modified shape and larger $Y_{\Delta}$; this behaviour is also shown in \citet{2010arXiv1001.4538K}."
+ The spectrum from S10 is very similar to KS possibly because both assume hydrostatic equilibrium. and a polytropic equation of state with a fixed adiabatic index. Γ~1.1—1.2.," The spectrum from S10 is very similar to KS possibly because both assume hydrostatic equilibrium, and a polytropic equation of state with a fixed adiabatic index, $\Gamma
+\sim 1.1-1.2$."
+ Inside Rago. these assumptions are approximately correct. but they start to fail beyond Roo).," Inside $R_{200}$, these assumptions are approximately correct, but they start to fail beyond $R_{200}$."
+ A demonstration ofthis is the rising of I and of the ratio of kinetic-to-thermal energy K/U shown for our simulations in the bottom panels of Fig., A demonstration ofthis is the rising of $\Gamma$ and of the ratio of kinetic-to-thermal energy $K/U$ shown for our simulations in the bottom panels of Fig.
+3.. The present day (¢=1) internal kinetic energy of a cluster 1s given by K=vj—6+HoGr;X/2. where Ho is the present daySyme Hubble7 constant. v; and x; are the peculiar velocity and comoving position for particle 7. and Ὁ and Xx are the gas-particle-averaged bulk flow and center of mass of the cluster.," The present day $a=1$ ) internal kinetic energy of a cluster is given by $K \equiv \Sigma_i m_{\rmn{gas},i} \left|\bvel_i -
+\bar{\bvel}+ H_0(\vecbf{x}_i-\bar{\vecbf{x}})\right|^2 /2$, where $H_0$ is the present day Hubble constant, $\bvel_i$ and $\vecbf{x}_i$ are the peculiar velocity and comoving position for particle $i$, and $\bar{\bvel}$ and $\bar{\vecbf{x}}$ are the gas-particle-averaged bulk flow and center of mass of the cluster."
+ The additional thermal pressure support we find at large radii from AGN feedback results in the slightly slower rate of K/U growth shown., The additional thermal pressure support we find at large radii from AGN feedback results in the slightly slower rate of $K/U$ growth shown.
+ In all cases the large kinetic contribution shown should be properly treated in future models., In all cases the large kinetic contribution shown should be properly treated in future semi-analytic models.
+ Varying the physics over the three cases for energy injection in our simulations leads to relatively minor differences in Fig., Varying the physics over the three cases for energy injection in our simulations leads to relatively minor differences in Fig.
+ among the power spectra for £€2000., among the power spectra for $\ell \lesssim 2000$.
+ This agreement is due in part to hydrostatic readjustment of the structure so the virial relation holds. which relates the thermal content. hence Y4. to the gravitational energy. which is dominated by the dark matter.," This agreement is due in part to hydrostatic readjustment of the structure so the virial relation holds, which relates the thermal content, hence $Y_{\Delta}$, to the gravitational energy, which is dominated by the dark matter."
+ Our AGN feedback parameters do not lead to dramatic gas expulsions to upset this simple reasoning., Our AGN feedback parameters do not lead to dramatic gas expulsions to upset this simple reasoning.
+ Our radiative cooling template has less power at all scales compared to the shock heating template since baryons are converted into stars predominantly at the cluster centers and the ICM adjusts adiabatically to this change., Our radiative cooling template has less power at all scales compared to the shock heating template since baryons are converted into stars predominantly at the cluster centers and the ICM adjusts adiabatically to this change.
+ Thus. at low / where clusters are unresolved. shock heating and radiative simulations give upper and lower limits. bracketing the AGN feedback case.," Thus, at low $\ell$ where clusters are unresolved, shock heating and radiative simulations give upper and lower limits, bracketing the AGN feedback case."
+ AGN feedback suppresses the core value of the pressure compared to the radiative simulation resulting in less power at (>2000. a trend that is more pronounced at z>| (as shown in Fig. 3)).," AGN feedback suppresses the core value of the pressure compared to the radiative simulation resulting in less power at $\ell > 2000$, a trend that is more pronounced at $z>1$ (as shown in Fig. )."
+ Thus. at these angular scales. the power spectrum probes the shape of the average pressure profile.," Thus, at these angular scales, the power spectrum probes the shape of the average pressure profile."
+ It depends sensitively on the physics of star and galaxy formation e.g.. ?..," It depends sensitively on the physics of star and galaxy formation e.g., \citet{2008ApJ...678..674S}."
+ Over the /-range covered by Planck. these effects are sub-dominant. and serve to highlight the importance of the high-resolution reached by ACT and SPT.," Over the $\ell$ -range covered by Planck, these effects are sub-dominant, and serve to highlight the importance of the high-resolution reached by ACT and SPT."
+ Instead of varying all cosmological parameters on which the thermal and kinetic SZ power spectra. Crisz and Cris. depend. we freeze the shapes by adopting the parameters for our fiducial oy=0.8 (and Ομ=0.03096) model evaluated at 150 GHz. and content ourselves with determining template amplitudes. Ajsz and Aysy. and a total SZ amplitude As: The spectral function for the tSZ (?).. f(v). vanishes at the SZ null at - 220 GHz and we normalize it to unity at v= 150 GHz. so it rises to. 4 at 30 GHz.," Instead of varying all cosmological parameters on which the thermal and kinetic SZ power spectra, $C_{\ell,\mathrm{tSZ}}$ and $C_{\ell,\mathrm{kSZ}}$, depend, we freeze the shapes by adopting the parameters for our fiducial $\sigma_8=0.8$ (and $\Omega_{\rmn{b}}h=0.03096$ ) model evaluated at 150 GHz, and content ourselves with determining template amplitudes, $A_{\mathrm{tSZ}}$ and $A_{\mathrm{kSZ}}$, and a total SZ amplitude $A_{\mathrm{SZ}}$: The spectral function for the tSZ \citep{1970Ap&SS...7....3S}, $f(\nu)$ , vanishes at the SZ null at $\sim$ 220 GHz and we normalize it to unity at $\nu =$ 150 GHz, so it rises to 4 at 30 GHz."
+ Thereforeif we find values of Ας; below unity then either c is smaller than the fiducial cosmological value asderived from the primary CMB anisotropies. or else the theoretical templates overestimate the SZ signal.," Thereforeif we find values of $A_{\mathrm{SZ}}$ below unity then either $\sigma_{8}$ is smaller than the fiducial cosmological value asderived from the primary CMB anisotropies, or else the theoretical templates overestimate the SZ signal."
+ To determine the probability distributions of these amplitudes and other cosmological parameters from current CMB data we adopt Markov Chain Monte Carlo (MCMC) techniques using a modified version of CosmoMC (?).., To determine the probability distributions of these amplitudes and other cosmological parameters from current CMB data we adopt Markov Chain Monte Carlo (MCMC) techniques using a modified version of CosmoMC \citep{2002PhRvD..66j3511L}.
+ We include WMAP7 (?) and. separately. ACT (2) and SPT (?).. ," We include WMAP7 \citep{2010arXiv1001.4635L} and, separately, ACT \citep{2010arXiv1001.2934T} and SPT \citep{2009arXiv0912.4317L}. ."
+"In all cases. we assume spatial fatness and fit for 6 basic cosmological parameters (Qu/r.. Ον. ny. the primordial scalar power spectrum amplitude A,.the Compton depth to re-ionization 7. and the angular parameter characterizing the sound crossing distance at recombination 8)."," In all cases, we assume spatial flatness and fit for 6 basic cosmological parameters $\Omega_{\rmn{b}}h^2$ , $\Omega_{\rmn{DM}}h^2$ , $n_{\rmn{s}}$ , the primordial scalar power spectrum amplitude $A_{\rmn{s}}$ ,the Compton depth to re-ionization $\tau$ , and the angular parameter characterizing the sound crossing distance at recombination $\theta$ )."
+ We also allow for a flat white noise template C; with amplitude A... such as would arise from populations of unresolved point sources.," We also allow for a flat white noise template $C_{\ell,\mathrm{src}}$ with amplitude $A_{\mathrm{src}}$ , such as would arise from populations of unresolved point sources."
+ We marginalize over A. allowing for arbitrary (positive) values.," We marginalize over $A_{\mathrm{src}}$ , allowing for arbitrary (positive) values."
+account.,account.
+ Here we consider the effects of metallicity changes in unevolved systems., Here we consider the effects of metallicity changes in unevolved systems.
+ The effects of a decrease in Z turned out to be small. apart from an increase in luminosity and effective temperature for given mass and mass ratio.," The effects of a decrease in $Z$ turned out to be small, apart from an increase in luminosity and effective temperature for given mass and mass ratio."
+ Figure 19 shows examples in in the period-mass ratio diagram.," Figure \ref{fig19}
+ shows examples in in the period-mass ratio diagram."
+ Results for JJ=LAL: represent very small masses where the difficulties are largest., Results for $M=1M_{\sun}$ represent very small masses where the difficulties are largest.
+ Results for AJ=1.5; represent typical masses., Results for $M=1.8M_{\sun}$ represent typical masses.
+ In both cases the influence of Z is weak only., In both cases the influence of $Z$ is weak only.
+ In particular. apparently the lower limit for the period depends only slightly on Z.," In particular, apparently the lower limit for the period depends only slightly on $Z$."
+ The absence of stable systems with large periods and intermediate or small mass ratios is even more pronounced when Z=0.01., The absence of stable systems with large periods and intermediate or small mass ratios is even more pronounced when $Z=0.01$.
+ We conclude that metallicity effects cannot help to extend the range of stable systems in the period-mass ratio diagram., We conclude that metallicity effects cannot help to extend the range of stable systems in the period-mass ratio diagram.
+ Next we investigate evolutionary effects as the only remaining possibility to extend the range of stable systems., Next we investigate evolutionary effects as the only remaining possibility to extend the range of stable systems.
+" In the component / the simple hydrogen profile will be assumed. depending on the central hydrogen content .V,; and a parameter ος."," In the component $i$ the simple hydrogen profile will be assumed, depending on the central hydrogen content $X_{{\rm c}i}$ and a parameter $x_{\rm c}$."
+ The standard value ος0.0 will be used., The standard value $x_{\rm c}=0.5$ will be used.
+" Effects of changes in.r, will be investigated when analysing individual observed systems in Sect 4..", Effects of changes in $x_{\rm c}$ will be investigated when analysing individual observed systems in Sect \ref{test}.
+" In the general case both components are evolved and the evolutionary status is described by two parameters .X,4.ως "," In the general case both components are evolved and the evolutionary status is described by two parameters $X_{{\rm c}1},X_{{\rm c}2}$."
+"In an approximate treatment evolutionary effects in the secondary can be neglected unless the mass ratio is large. and the evolutionary status is described by one parameter .V,4."," In an approximate treatment evolutionary effects in the secondary can be neglected unless the mass ratio is large, and the evolutionary status is described by one parameter $X_{{\rm c}1}$."
+ Concerning the choice of the circulation function. we checked the invariance and found that the use of the standard circulation function is justified also in evolved systems., Concerning the choice of the circulation function we checked the invariance and found that the use of the standard circulation function is justified also in evolved systems.
+ Evolutionary effects for systems with AJ=11M0.02 are shown in Fig. 20..," Evolutionary effects for systems with $M=1M_{\sun},Z=0.02$ are shown in Fig. \ref{fig20}."
+ Except for the thin solid line all curves have been calculated neglecting evolutionary effects in the secondary., Except for the thin solid line all curves have been calculated neglecting evolutionary effects in the secondary.
+ Heavy lines represent configurations with a given value for VY..., Heavy lines represent configurations with a given value for $X_{{\rm c}1}$.
+ As before. solid/dashed lines represent configurations of positive/negative charge.," As before, solid/dashed lines represent configurations of positive/negative charge."
+ Evolved configurations with very large mass ratios (4.20.8) have been omitted., Evolved configurations with very large mass ratios $q\ga 0.8$ ) have been omitted.
+" With decreasing Y,, the curves are shifting to the right. re. to larger periods. and the extent of stable configurations is increasing."," With decreasing $X_{{\rm c}1}$ the curves are shifting to the right, i.e. to larger periods, and the extent of stable configurations is increasing."
+ Stable evolved systems with very small mass ratios exist for periods larger than about 0.3 days., Stable evolved systems with very small mass ratios exist for periods larger than about 0.3 days.
+ On the dotted curves the angular momentum ts constant., On the dotted curves the angular momentum is constant.
+" Since in the course of evolution .V, decreases and the angular momentum does not increase. the period increases and the mass ratio decreases."," Since in the course of evolution $X_{{\rm c}1}$ decreases and the angular momentum does not increase, the period increases and the mass ratio decreases."
+ The lower limit for the period found in unevolved systems is therefore valid also for evolved systems., The lower limit for the period found in unevolved systems is therefore valid also for evolved systems.
+ In systems with large mass ratios the results are rough only since effects of nuclear evolution in the secondary are neglected., In systems with large mass ratios the results are rough only since effects of nuclear evolution in the secondary are neglected.
+ The influence of these effects can be seen if they are overestimated., The influence of these effects can be seen if they are overestimated.
+ This is the case in the thin solid line. which represents stable configurations with X44Neo=03 and ϱx;0.5.," This is the case in the thin solid line, which represents stable configurations with $X_{{\rm c}1}=X_{{\rm c}2}=0.3$ and $q\la 0.8$."
+ The curves of constant angular momentum for Voy=ο almost coincide with the curves for ο=0.7., The curves of constant angular momentum for $X_{{\rm c}1}=X_{{\rm c}2}$ almost coincide with the curves for $X_{{\rm c}2}=0.7$.
+ Accordingly. the main results obtained neglecting evolutionary effects 1n the secondary (increase of period and decrease of mass ratio in the course of evolution) remain valid if these effects are taken into account.," Accordingly, the main results obtained neglecting evolutionary effects in the secondary (increase of period and decrease of mass ratio in the course of evolution) remain valid if these effects are taken into account."
+ A similar diagram for systems with AJ=1.51; 1s shown in Fig. 21.., A similar diagram for systems with $M=1.8M_{\sun}$ is shown in Fig. \ref{fig21}.
+ Again it can be seen that the evolution (with or without loss of angular momentum) proceeds towards larger periods and smaller mass ratios., Again it can be seen that the evolution (with or without loss of angular momentum) proceeds towards larger periods and smaller mass ratios.
+ Again stable evolved systems with very small mass ratios are found., Again stable evolved systems with very small mass ratios are found.
+ Most important is the result that large periods and small mass ratios are possible among evolved systems., Most important is the result that large periods and small mass ratios are possible among evolved systems.
+ We conclude that the structure of contact binaries depends sensitively on evolutionary effects and that the range of observed systems can be explained only by these effects., We conclude that the structure of contact binaries depends sensitively on evolutionary effects and that the range of observed systems can be explained only by these effects.
+The data was obtained in .hlv 1993 with total of 30 uinutes of iuteeration on Aldl 85 at the frecuencv of 333 MIIz and baudwidth of :3.1 MIIz.,The data was obtained in July 1993 with total of 30 minutes of integration on Abell 85 at the frequency of 333 MHz and bandwidth of 3.1 MHz.
+ For reduction. the NRAÀO-AIPS' software was eiiXoved.," For reduction, the NRAO `AIPS' software was employed."
+ Following the usal xocedure of editing aud amplitude aud phase caibration. he calibrated data was Fourier transformed aud the 343 deeree innage was decouvolute with ‘CLEAN aeonth11.," Following the usual procedure of editing and amplitude and phase calibration, the calibrated data was Fourier transformed and the $3 \times 3$ degree image was deconvoluted with `CLEAN' algorithm."
+ The final iniage was convoluted with a circular restori18o ycaun of GO arcsec (PWIIM) οzuissiaun profile., The final image was convoluted with a circular restoring beam of 60 arcsec (FWHM) gaussian profile.
+ Noteworthy are the strong radio ciission ron the region of VSSRS. he South Blob aud the cD ealaxy at fιο cluster centre.," Noteworthy are the strong radio emission from the region of VSSRS, the South Blob and the cD galaxy at the cluster centre."
+ The PSPC X-ray nap is fully described elsewhere (Pislar et al., The PSPC X-ray map is fully described elsewhere (Pislar et al.
+ 1997)., 1997).
+ We have extracted the spectra for eac ireegion aud used siunultaueouxslv th the LECS aid MECS (units 2 aud 3) data., We have extracted the spectra for each region and used simultaneously both the LECS and MECS (units 2 and 3) data.
+" Following the ""Cookbook” (Fiore et al.", Following the “Cookbook” (Fiore et al.
+ 1999). we have used oulv he data in the 1iterval [0.12.L0] keV. for the LECS aud [1.6510.5] κο* for the MECS.," 1999), we have used only the data in the interval [0.12–4.0] keV for the LECS and [1.65–10.5] keV for the MECS."
+ For cach region we have used a single temperature plasiua. the:sorbed Ravinoιαοι (Ravinoud Sinith 1977) aud the MERKAL (Ixaastra Mewe 1993: Liedahl et al.," For each region we have used a single temperature plasma, the absorbed Raymond-Smith (Raymond Smith 1977) and the MEKAL (Kaastra Mewe 1993; Liedahl et al."
+ 1995) modclels., 1995) models.
+ FecÉ sone regious (centre. South Blob aud VSSRS) w(o lave also modelled the iutracluster ουπια with a ¢'onibiuation of two models: 4ther two MEKAL or a àIEKAL plus a power-law. us to take ito account the nou-thermal eiiission.," For some regions (centre, South Blob and VSSRS) we have also modelled the intracluster medium with a combination of two models: either two MEKAL or a MEKAL plus a power-law, this to take into account the non-thermal emission."
+ The absorption is due to the coll eas iu the line-ofsieht. mainly lvdrogen and heli.," The absorption is due to the cold gas in the line-of-sight, mainly hydrogen and helium."
+ We have used 16 photoelectric absorptio1 cross-sections civen by Baluciuska-Cliaweh AleCanunon (1992)., We have used the photoelectric absorption cross-sections given by Balucinska-Church McCammon (1992).
+ When the coums wore hig renoueh. we also have tried re VMERAL uolel. that is. with a variable individual nndancees rates for the clements that contributed for 1ο N-vay flux at the [0.110.| keV. baud.," When the counts were high enough, we also have tried the VMEKAL model, that is, with a variable individual abundances rates for the elements that contributed for the X-ray flux at the [0.1–10.0] keV band."
+ Unfortunately. uost of the metals do not produce strong chough lines or unanmbieuous detection wih BeppoSAN.," Unfortunately, most of the metals do not produce strong enough lines for unambiguous detection with BeppoSAX."
+ Therefore we rave fixed the abuvance values of Te. C. N. ο. Ne. Na. Me. and Al to 0.32...," Therefore we have fixed the abundance values of He, C, N, O, Ne, Na, Mg, and Al to $Z_{\odot}$."
+ The spectral fits were done using NSPEC v10.0., The spectral fits were done using XSPEC v10.0.
+ The DeppoSAX uarrow field instrmuents have chanuels of equal enerev width. but a spectral resolution that scales roughly with the square root «ot the energy (Boclla 19972).," The BeppoSAX narrow field instruments have channels of equal energy width, but a spectral resolution that scales roughly with the square root of the energy (Boella 1997a)."
+ Therefore. if a spectruni nrust be rebiuued (1i order O Increase the counts per bin). oue should first group he bius tasue iuto account the energy. resolution uon-linearity rather than suuplv erouping the chaunels with sole prescripion.," Therefore, if a spectrum must be rebinned (in order to increase the counts per bin), one should first group the bins taking into account the energy resolution non-linearity rather than simply grouping the channels with some prescription."
+ We have used the appropriate rebiunius cluplate fies luade avalabl| bv the SDC (Fiore et al., We have used the appropriate rebinning template files made available by the SDC (Fiore et al.
+ 1999)., 1999).
+ Ilowever. even with t1ο οucrev-«depenudoeut rebinning. here are sill bius with Ow counts.," However, even with the energy-dependent rebinning, there are still bins with low counts."
+ We have then used he recipe [m]eiveu by Clhurazos> ot al. (, We have then used the recipe given by Churazov et al. (
+1996) based. of the sanoothed rebinued spectrum (available in NSPEC) for computing the statistical weights.,1996) based of the smoothed rebinned spectrum (available in XSPEC) for computing the statistical weights.
+ With this procedure. one can still use least-square nmüniusation fif and  statistics for unbiased parameter and error estimation.," With this procedure, one can still use least-square minimisation fit and $\chi^{2}$ statistics for unbiased parameter and error estimation."
+ Within the unobstructed ficld-ofview of a circle of & arcmin centred at the MECS axis we have our greatest signal to noise ratio aud in this region we cau obtain sole well constrainec meal quantities for Abell 85., Within the unobstructed field-of-view of a circle of 8 arcmin centred at the MECS axis we have our greatest signal to noise ratio and in this region we can obtain some well constrained mean quantities for Abell 85.
+ Usine a AIERAL model. we find a teniperature of 6.6092 keV. an hydrogen coluun depity: Vy-55l0)2100n0U.94yt2 2? aud a nucallicitv of 38dE0.06Z.. (cf.," Using a MEKAL model, we find a temperature of $6.6\pm0.3$ keV, an hydrogen column density $N_{H}=5.5^{+0.9}_{-0.7}10^{20}$ $^{-2}$ and a metallicity of $0.38\pm0.06
+Z_{\odot}$ (cf."
+ Table 2))., Table \ref{tbl:fitsResults}) ).
+ We obtain a senificautlv hieier fenaerature tha1i that obtained with the ROSAT PSPC (Lcx1 keV. Pisar ot al.," We obtain a significantly higher temperature than that obtained with the ROSAT PSPC $4\pm1$ keV, Pislar et al."
+ 1997). but CSSCLLlally the same as the one oMained with ASCA (6.12E0.2 keV. t notice that this is f16 120211 feniperature witli jc15 areuin: Markevich et al.," 1997), but essentially the same as the one obtained with ASCA $6.1\pm0.2$ keV, but notice that this is the mean temperature within $\sim 15$ arcmin; Markevich et al."
+ 1998)., 1998).
+ The columu deusi vds ligher than the Galactic value deduced from IIT data in the fied of view (for exide 3.08.«10296 3 at the position of the VSSRS and 3.58«10?cni. 7? at the position of the cD. Dickey Locknmiau 1990).," The column density is higher than the Galactic value deduced from HI data in the field of view (for example $3.08 \times 10^{20}$ $^{-2}$ at the position of the VSSRS and $3.58 \times 10^{20}$ $^{-2}$ at the position of the cD, Dickey Lockman 1990)."
+ This sugecsts that frere Is an amount of TT contained within the cluster itself., This suggests that there is an amount of HI contained within the cluster itself.
+ The metallicity is we1 coustrained aud has the value eenerally. fou in this type of clusters (c.g. Fukaziwa ο al., The metallicity is well constrained and has the value generally found in this type of clusters (e.g. Fukazawa et al.
+ 1998)., 1998).
+ We have further fitted tlrecla a with a VMEIAL inodel to obtain almucdauces of the individual ictal elemoeuts., We have further fitted the data with a VMEKAL model to obtain abundances of the individual metal elements.
+ The reduced. x? (A?D divide by the umber of degrees of freeOni) Is 8ightly higher for the VMEKAL compared to the MEWKAL model. bit the temperature and hydrogen οςunin density are he same aud we detec the presence of sole metals (cf.," The reduced $\chi^2$ $\chi^2$ divided by the number of degrees of freedom) is slightly higher for the VMEKAL compared to the MEKAL model, but the temperature and hydrogen column density are the same and we detect the presence of some metals (cf."
+ Table 2))., Table \ref{tbl:fitsResults}) ).
+ Ouly the abundances of Ni and Fe are no COupatible with zero at lo level aud. except for these two clements. we can ouly give upper limits for the abulance.," Only the abundances of Ni and Fe are not compatible with zero at $\sigma$ level and, except for these two elements, we can only give upper limits for the abundance."
+ The total N-rav huninositv in fje [0.12.1] keV band is (8.192:0.37)10Πρhey ergses * Linginside a radius of 7705 kpe (5 arcnin) ceutred at the VSSBS »ositiou.," The total X-ray luminosity in the [0.1–2.4] keV band is $(8.49\pm0.37)\
+10^{44}h^{-2}_{50}$ erg $^{-1}$ inside a radius of $770h^{-1}_{50}$ kpc (8 arcmin) centred at the VSSRS position."
+ We take a regiou of 1.9 arcmün (1857.4; kpc) at the position of the cD galaxy located at tιο cluster centre., We take a region of 1.9 arcmin $185 h_{50}^{-1}$ kpc) at the position of the cD galaxy located at the cluster centre.
+ A fit with a siuglec» temperature model slows a siegulficaut increase of the hydrogen coluun deusity aud a decrease of temperature relative to the values obtainec when we fitted the whole cluster., A fit with a single temperature model shows a significant increase of the hydrogen column density and a decrease of temperature relative to the values obtained when we fitted the whole cluster.
+" Iu a previous sπάν, Pislar et al. ("," In a previous study, Pislar et al. ("
+1997) observed a negative correlation between the N-ray eas temperature and Nyy.,1997) observed a negative correlation between the X-ray gas temperature and $N_{\rm H}$.
+ Tere. we observe a unch weaker correlation (Fig. 2)).," Here, we observe a much weaker correlation (Fig. \ref{fig:nH_T_all_centre}) ),"
+ so the effect temperature decrease inwards the ceutre ds probably ree dod is uot an artefact of the fit., so the effect – temperature decrease inwards the centre – is probably real and is not an artefact of the fit.
+ The metallicity is significalv higher in the, The metallicity is significantly higher in the
+log(Lig) [L ..]o-12.3 (see Fig. 2)).,$\log($ $_{IR})$ $_{\odot}$ $\sim12.3$ (see Fig. \ref{fig:sfr_smass}) ).
+ However. studies find that most of the emission (=70%)) in ULIRGs is due to star formation (Farrahetal.2008).. thus these members are likely to have both strong star formation and an AGN component.," However, studies find that most of the emission $\gtrsim70$ ) in ULIRGs is due to star formation \citep{farrah:08}, thus these members are likely to have both strong star formation and an AGN component."
+ Note that at z=1.62. the 7.7j/mm PAH band lies partly in the cchannel.," Note that at $z=1.62$, the $7.7\mu$ m PAH band lies partly in the channel."
+ Because part of the IR luminosity is due to star formation. we include both mmembers in our analysis: repeating our analysis. without these two members confirms that our overall results do not change.," Because part of the IR luminosity is due to star formation, we include both members in our analysis; repeating our analysis without these two members confirms that our overall results do not change."
+" In the cluster core (&,,,;20.5 Mpe). the star formation rate density from the pphotometry alone is ~1700 Mpe7: we stress that this is likely a lower limit given the imaging cannot detect any members with SPR;;=40 yr... ie. with star formation rates typical for IR- galaxies in clusters at z« 1."," In the cluster core $R_{proj}=0.5$ Mpc), the star formation rate density from the photometry alone is $\sim1700$ $^{-2}$; we stress that this is likely a lower limit given the imaging cannot detect any members with $_{IR}\lesssim40$ , i.e. with star formation rates typical for IR-detected galaxies in clusters at $z<1$ ."
+ Only one other galaxy cluster at z=1.46 has a comparably high star formation rate in its core (Hayashietal.2010:Hilton 2010).," Only one other galaxy cluster at $z=1.46$ has a comparably high star formation rate in its core \citep{hayashi:10,hilton:10}. ."
+ In comparison. studies of IR-detected galaxies in clusters at =<| find that star-forming members are strongly segregated at >0.5 Mpe (Geachetal.2006:SaintongeKoyamaA;etal.2008 ).," In comparison, studies of IR-detected galaxies in clusters at $z<1$ find that star-forming members are strongly segregated at $R_{proj}>0.5$ Mpc \citep{geach:06,saintonge:08,koyama:08}. ."
+. Given the high star formation rate in its core. does ffollow the well-established trend at ><| of decreasing star-formation with increasing galaxy density (e.g. 2003)?," Given the high star formation rate in its core, does follow the well-established trend at $z<1$ of decreasing star-formation with increasing galaxy density \citep[e.g.][]{hashimoto:98,ellingson:01,gomez:03}?"
+? Figure 3. compares the relative fraction of star-forming members to passive members as a function of local galaxy density (X) which ts defined by distance to the 10th nearestnetghbor (Dressler1980)., Figure \ref{fig:sfr_density} compares the relative fraction of star-forming members to passive members as a function of local galaxy density $\Sigma$ ) which is defined by distance to the 10th nearest neighbor \citep{dressler:80}.
+. We use star-formation rates derived from the limaging as well as from the SED fitting because the two independent star formation tracers complement each other and provide an important check of our results: The limaging is a robust measure of the dust-obscured star formation but only detects the most active members (= νι) while the SED fitting is sensitive to lower levels of unobscured activity Z5 )., We use star-formation rates derived from the imaging as well as from the SED fitting because the two independent star formation tracers complement each other and provide an important check of our results: The imaging is a robust measure of the dust-obscured star formation but only detects the most active members $\gtrsim40$ ) while the SED fitting is sensitive to lower levels of unobscured activity $\gtrsim$ ).
+ Both star formation tracers confirm that (Fig. 3)).," Both star formation tracers confirm that (Fig. \ref{fig:sfr_density}) ),"
+ te. exactly opposite to that observed in clusters at z«I., i.e. exactly opposite to that observed in clusters at $z<1$.
+ A Spearman rank test supports with >97% confidence (>26 significance) that the relative fraction of IR luminous members increases with increasing galaxy density from ~8% at X—10 gal Mpe™ to ~25% at X>100 gal Mpc., A Spearman rank test supports with $>97$ confidence $>2\sigma$ significance) that the relative fraction of IR luminous members increases with increasing galaxy density from $\sim8$ at $\Sigma\sim10$ gal $^{-2}$ to $\sim25$ at $\Sigma\gtrsim100$ gal $^{-2}$.
+ We stress that excluding the two candidate AGN does not change the trend. and the robustness of this result is underscored by the fact that we see the same trend using the SED-derived rates.," We stress that excluding the two candidate AGN does not change the trend, and the robustness of this result is underscored by the fact that we see the same trend using the SED-derived rates."
+ While studies of galaxies in the field at z—1 (X<10 gal Μρο) find that the star formation-density relation is beginning to turn over at this epoch (Elbazetal.2007:Cooper2008).. this 1s the first confirmation of such a reversal in the significantly higher density environment of galaxy clusters.," While studies of galaxies in the field at $z\sim1$ $\Sigma<10$ gal $^{-2}$ ) find that the star formation-density relation is beginning to turn over at this epoch \citep{elbaz:07,cooper:08}, this is the first confirmation of such a reversal in the significantly higher density environment of galaxy clusters."
+ The measured IR luminosities correspond to specific. star formation rates (star formation rate divided by stellar mass: SSFR) per Gyr of ~1—20: these active members can more than double their stellar masses in the next Gyr (by z— 1.2)., The measured IR luminosities correspond to specific star formation rates (star formation rate divided by stellar mass; SSFR) per Gyr of $\sim1-20$: these active members can more than double their stellar masses in the next Gyr (by $z\sim1.2$ ).
+ However. to reproduce the relatively homogeneous stellar ages measured in massive cluster galaxies at z«| (e.g. these IR luminous members cannot maintain such a high SSER for even a Gyr.," However, to reproduce the relatively homogeneous stellar ages measured in massive cluster galaxies at $z<1$ \citep[e.g.][]{blakeslee:06,tran:07,mei:09}, these IR luminous members cannot maintain such a high SSFR for even a Gyr."
+ The current star formation must be quenched rapidly and any later bursts of activity cannot add a substantial amount of new stars. at least not in the massive members (log(M..) ..]2- 10.6) that must populate a well-defined red sequence by z~0.8.," The current star formation must be quenched rapidly and any later bursts of activity cannot add a substantial amount of new stars, at least not in the massive members $\log($ $_{\ast})$ $_{\odot}$ $>10.6$ ) that must populate a well-defined red sequence by $z\sim0.8$ ."
+" We measure the rest-frame colors (dust-corrected). IR luminosities. star formation rates. and stellar masses. of galaxies inJ0218.3-0510.. a Spitzer-selected cluster at >=1.62. by fitting spectral energy distributions to photometry in 10 bands (0.4,/m« App,«Sym) and with deep umaging."," We measure the rest-frame colors (dust-corrected), IR luminosities, star formation rates, and stellar masses of galaxies in, a Spitzer-selected cluster at $z=1.62$, by fitting spectral energy distributions to photometry in 10 bands $0.4\mu$ $<\lambda_{obs}<8\mu$ m) and with deep imaging."
+ The cluster sample (Ραρ10:Tanakaetal.2010). is composed of 12 spectroscopically confirmed members and 80 members selected from photometric redshifts measured using EAZY (Brammeretal.2008): all members are within Ry;51 Mpe of the massive cluster galaxy located at the peak of the X-ray emission., The cluster sample \citep[Pap10;][]{tanaka:10} is composed of 12 spectroscopically confirmed members and 80 members selected from photometric redshifts measured using EAZY \citep{brammer:08}; all members are within $R_{proj}\lesssim1$ Mpc of the massive cluster galaxy located at the peak of the X-ray emission.
+ The 92 cluster members have a color-stellar mass distribution that is surprisingly similar to that observed in field galaxies at z~2., The 92 cluster members have a color-stellar mass distribution that is surprisingly similar to that observed in field galaxies at $z\sim2$.
+ When corrected for dust. the cluster members define a strong blue sequence and span a range in color. indicating a substantial amount of recent and ongoing star formation in the cluster core.," When corrected for dust, the cluster members define a strong blue sequence and span a range in color, indicating a substantial amount of recent and ongoing star formation in the cluster core."
+ This dramatic level of activity is underscored by the 17 members detected at24jm., This dramatic level of activity is underscored by the 17 members detected at.
+". In the cluster core (&,,,;<0.5 Mpe). the star formation rate density from the IR luminous members alone is ~1700 Mpc: the true value is likely to be higher given that we only include members with SFR;=40 '."," In the cluster core $R_{proj}<0.5$ Mpc), the star formation rate density from the IR luminous members alone is $\sim1700$ $^{-2}$; the true value is likely to be higher given that we only include members with $_{IR}\gtrsim40$ ."
+. These IR luminous members also follow the same ..trend of increasing star formation with stellar mass that Is observed in the field at z—2., These IR luminous members also follow the same trend of increasing star formation with stellar mass that is observed in the field at $z\sim2$.
+ We discover the striking result that the the relative fraction of star-forming galaxies increases with increasing. local galaxy density inJO218.3-0510.. a reversal of the wellestablished trend at lower redshifts and in line with recerPM work at z~1.46 that suggests enhanced star formatio in cluster cores.," We discover the striking result that the the relative fraction of star-forming galaxies increases with increasing local galaxy density in, a reversal of the well-established trend at lower redshifts and in line with recent work at $z\sim1.46$ that suggests enhanced star formation in cluster cores."
+ Measurements using star formation rate: derived from the limaging and from the SED fitting provide independer= confirmation that the relative fraction of star-forming galaxies triples from the lowest to highest density regions., Measurements using star formation rates derived from the imaging and from the SED fitting provide independent confirmation that the relative fraction of star-forming galaxies triples from the lowest to highest density regions.
+ By pushing into the redshift desert ἐς> 1.6). we are able to reach the epoch when massive cluster galaxies are still forming a significant number of their stars.," By pushing into the redshift desert $z\gtrsim1.6$ ), we are able to reach the epoch when massive cluster galaxies are still forming a significant number of their stars."
+ KT acknowledges generous support from the Swiss National Science Foundation (grant PP002-110576)., KT acknowledges generous support from the Swiss National Science Foundation (grant PP002-110576).
+. JSD acknowledges the support of the Royal Society via a Wolfson Research Merit award. and also the support of the European Research Council via the award of an Advanced Grant.," JSD acknowledges the support of the Royal Society via a Wolfson Research Merit award, and also the support of the European Research Council via the award of an Advanced Grant."
+ This work is based in part on data obtained as part of the UKIRT InfraredDeep Sky Survey., This work is based in part on data obtained as part of the UKIRT InfraredDeep Sky Survey.
+ Aportion of the Magellan telescope time was granted by NOAO. through the Telescope System InstrumentationProgram (TSIP:funded by NSF).," Aportion of the Magellan telescope time was granted by NOAO, through the Telescope System InstrumentationProgram (TSIP;funded by NSF)."
+concentrate on the clearing phase (Chambers2001).,concentrate on the clearing phase \citep{cha01}.
+. Thus. wnclerstaucling Chis evolutionary phase requires new calculations (seethediscussioninIxokubo&Ida2002).," Thus, understanding this evolutionary phase requires new calculations \citep[see the discussion in][]{kok02}."
+ llere. we use numerical calculations with a new hybrid n-body coagulation code to investigate (he transition from oligarchic growth to ehaotic growth.," Here, we use numerical calculations with a new hybrid $n$ -body–coagulation code to investigate the transition from oligarchic growth to chaotic growth."
+ Our approach allows us to combine statistical algorithms for the planetesimals with direct i-body integrations of the oligarchs., Our approach allows us to combine statistical algorithms for the planetesimals with direct $n$ -body integrations of the oligarchs.
+ From several simple test cases and complete planet Formation calculations. we show that oligarchic growth becomes chaotic when the orbits of oligarchs begin to overlap.," From several simple test cases and complete planet formation calculations, we show that oligarchic growth becomes chaotic when the orbits of oligarchs begin to overlap."
+ If the surface densitv in oligarchs exceeds a critical value. this transition occurs when the oligarchs contain roughly half of the mass in solids.," If the surface density in oligarchs exceeds a critical value, this transition occurs when the oligarchs contain roughly half of the mass in solids."
+" At 1 AU. the critical initial surface density is X,£z D. 23gcm 2"," At 1 AU, the critical initial surface density is $\Sigma_c \approx$ 2–3 g $^{-2}$."
+ iThus. oligarchst can make the (transitiont fromt oligarchicB. to chaotieB growth in. disks with masses comparable to the minim mass solar nebula. where X& 810 g 7 al 1 AU.," Thus, oligarchs can make the transition from oligarchic to chaotic growth in disks with masses comparable to the minimum mass solar nebula, where $\Sigma \approx$ 8–10 g $^{-2}$ at 1 AU."
+ In disks where the surface density of solids is below the limit for chaotic growth. oligarchs slowly merge to lorm larger objects.," In disks where the surface density of solids is below the limit for chaotic growth, oligarchs slowly merge to form larger objects."
+ Pairwise interactions. instead of large-scale chaos. drive the dynamics of (hese svstems.," Pairwise interactions, instead of large-scale chaos, drive the dynamics of these systems."
+ Milder. slower interactions between oligarchs then produce less massive planets.," Milder, slower interactions between oligarchs then produce less massive planets."
+ We develop (he background for our calculations in 822. describe a suite of caleulations in 833. and conclude with a brief summary and conclusions in 844.," We develop the background for our calculations in 2, describe a suite of calculations in 3, and conclude with a brief summary and conclusions in 4."
+ The evolution [rom planetesimals to planets is marked by several phases — orderly erowth. runaway growth. oligarchie growth. and chaotic growth with clear transitions in the dvnamies and mutual interactions of the ensemble of solid objects.," The evolution from planetesimals to planets is marked by several phases – orderly growth, runaway growth, oligarchic growth, and chaotic growth – with clear transitions in the dynamics and mutual interactions of the ensemble of solid objects."
+ Analvtie derivations and sophisticated coagulation and m-body calculations identifv the physics of these transitions., Analytic derivations and sophisticated coagulation and $n$ -body calculations identify the physics of these transitions.
+ llere. we summarize some basic results to provide (he context for our numerical simulations.," Here, we summarize some basic results to provide the context for our numerical simulations."
+ Most. considerations of planet formation begin with small objects. 5;< 1 km. that contain all of the solid material.," Most considerations of planet formation begin with small objects, $r_i \lesssim$ 1 km, that contain all of the solid material."
+ For (hese sizes. collisional camping aid viscous stirring roughly balance for orbital eccentricity e~10.7.," For these sizes, collisional damping and viscous stirring roughly balance for orbital eccentricity $e \sim 10^{-5}$."
+" The gravitational binding energy. E,~10! erg lis then comparable to the tvpical collision energv at 1 AU. E.~10* 104 ere ο"," The gravitational binding energy, $E_g \sim 10^4$ erg$^{-1}$ , is then comparable to the typical collision energy at 1 AU, $E_c \sim 10^3$ $10^4$ erg $^{-1}$."
+ Both energies are smaller (han the disruption energy (hie collision energv needed to remove half of the mass from the colliding pair of objects — which is Qy>10° ere ! for rocky material (Davisetal.L985:Benz&Asphaug 1999)..," Both energies are smaller than the disruption energy – the collision energy needed to remove half of the mass from the colliding pair of objects – which is $Q_d \gtrsim 10^7$ erg $^{-1}$ for rocky material \citep{dav85,ben99}. ."
+ Thus. collisionsproduce mergers insteacl of debris.," Thus, collisionsproduce mergers instead of debris."
+ re white dwarf is from the spacing of evelotron harmonics.,of the white dwarf is from the spacing of cyclotron harmonics.
+ For the field strengths seen in Polars (2710 200 MG) evelotron harmonics are seen às. broad. humps in optical/LR spectra., For the field strengths seen in Polars $B\sim$ 10--200 MG) cyclotron harmonics are seen as broad humps in optical/IR spectra.
+ The evelotron flux originates from electrons spiraling around the Ποιά lines in the post-shock region above the surface of the white cwarf., The cyclotron flux originates from electrons spiraling around the field lines in the post-shock region above the surface of the white dwarf.
+ “Phese hunmps vary in their intensity and. (to a lesser degree their wavelength) as a function of our viewing angle to the garock region (ie they vary over the orbital phase)., These humps vary in their intensity and (to a lesser degree their wavelength) as a function of our viewing angle to the post-shock region (ie they vary over the orbital phase).
+ There was no obvious sign of evelotron features in our optical spectra., There was no obvious sign of cyclotron features in our optical spectra.
+" To make a more detailed. search for such features we mace a mean ""blue and ""red' spectrum: the mean blue spectrum was mace up of blue. spectra (3800.6800 A) taken on the second night. while the mean red spectrum was mace up of red! spectra. (6000.9800 AY) taken on the first night (on the second night no red. spectra were obtained)."," To make a more detailed search for such features we made a mean `blue' and `red' spectrum: the mean blue spectrum was made up of `blue' spectra (3800–6800 ) taken on the second night, while the mean red spectrum was made up of `red' spectra (6000–9800 ) taken on the first night (on the second night no red spectra were obtained)."
+ We then averaged spectra to give spectra covering the phase range 6=0.050.15. 0.150.25 ete and then normalised these spectra by dividing by the appropriate mean spectrum (we use the ephemeris of Buckley ct al δα which defines 6=0.0 as the center of the eclipse of the white dwarf by the secondary).," We then averaged spectra to give spectra covering the phase range $\phi$ =0.05–0.15, 0.15–0.25 etc and then normalised these spectra by dividing by the appropriate mean spectrum (we use the ephemeris of Buckley et al 1998a which defines $\phi$ =0.0 as the center of the eclipse of the white dwarf by the secondary)."
+ Figure 1. shows these normiatisecl spectra over the binary orbit., Figure \ref{cychumps} shows these normalised spectra over the binary orbit.
+ Phere is no evidence for evelotron features until the phase interval covering ©=0.350.45 when humps are seen at  2500T2O0A., There is no evidence for cyclotron features until the phase interval covering $\phi$ =0.35–0.45 when humps are seen at $\sim$ 5800.
+. 'Phese continue to be seen until ó —0.7., These continue to be seen until $\phi\sim$ 0.7.
+ This is confirmed. if we divide the spectrum covering @=0.350.45 by the spectrum covering Ξ00500.15., This is confirmed if we divide the spectrum covering $\phi$ =0.35–0.45 by the spectrum covering $\phi$ =0.05–0.15.
+ ‘To determine the wavelength of evelotron harmonics for a given magnetic field strength. D. we write we=cD/ím.c (where wy is the fundamental evelotron frequency) as wg=1.3610Be (where Be=D/10 C).," To determine the wavelength of cyclotron harmonics for a given magnetic field strength $B$, we write $\omega_{B}=eB/m_{e}c$ (where $\omega_{B}$ is the fundamental cyclotron frequency) as $\omega_{B}=1.76\times10^{14}B_{7}$ (where $B_{7}=B/10^{7}$ G)."
+ We then use equation (3) of Cropper ct al (1988) and put it in terms of A: ∖∖⊽↓↕⋖⋅↓⋅⋖⋅∕∣∶⋯↴∠⋅⊒∕⋅⋅⊻⊽∶⋅↱≻⊔⋅↓⊻⊽⊳⊻⊽↕≻↕↓↥⊔⊔⊀∐⊳∖∪⇂⋅↓∡∢⊾∖↾⊳⊔↕⊳∖ the evelotron harmonic number and 8 is the viewing angle to the magnetic field angle.," We then use equation (3) of Cropper et al (1988) and put it in terms of $\lambda$: where $\mu=m_{e}c^{2}/kT=511.1/T$, $T$ is in units of keV, $n$ is the cyclotron harmonic number and $\theta$ is the viewing angle to the magnetic field angle."
+ We can now rearrange the above as à [function of À: where À is inA., We can now rearrange the above as a function of $\lambda$: where $\lambda$ is in.
+. To determine the magnetic field strength we searched a range of parameters which gave consecutive harmonics jaced at  58007200A., To determine the magnetic field strength we searched a range of parameters which gave consecutive harmonics placed at $\sim$ 5800.
+. For lower values of 6 the harmonics are blue shifted by a small amount compared to higher values., For lower values of $\theta$ the harmonics are blue shifted by a small amount compared to higher values.
+ For ow magnetic fields (2 —15M€G) the individual harmonics »come indistinguishable and form a continuum., For low magnetic fields $B\sim$ 15MG) the individual harmonics become indistinguishable and form a continuum.
+ Similarly or temperatures Z15keV individual harmonies are not visible., Similarly for temperatures $>$ 15keV individual harmonics are not visible.
+ By comparing the expected wavelength of the iwmonics by eve to the observed. spectrum. we found hat D—42MC. &k1—9keV. and 05-00 gave the best fiU," By comparing the expected wavelength of the harmonics by eye to the observed spectrum, we found that $B$ =42MG, $kT$ =9keV and $\theta$ $^{\circ}$ gave the best `fit'."
+ Assuming that we have correctly identified harmonies at ~ H5s007200A.. we estimate the error on D to be —1 2MG based on our search of the variable parameters.," Assuming that we have correctly identified harmonics at $\sim$ 5800, we estimate the error on $B$ to be $\sim$ 1–2MG based on our search of the variable parameters."
+ The value of B=42\IG found here compares: with B~20ALG estimated by Buckley et al (19982a) [rom a single spectrum of exposure 3000 sec., The value of $B$ =42MG found here compares with $B\sim$ 20MG estimated by Buckley et al (1998a) from a single spectrum of exposure 3000 sec.
+ Their spectrum was not ILux- and they caution that the small-scale variations seen in their spectrum could have been due to other factors rather than evclotron humps., Their spectrum was not flux-calibrated and they caution that the small-scale variations seen in their spectrum could have been due to other factors rather than cyclotron humps.
+ We therefore consider that our estimate of D—42MCG to be more reliable., We therefore consider that our estimate of $B$ =42MG to be more reliable.
+ We will examine this in more detail in i, We will examine this in more detail in \ref{daveb}.
+ We obtained a red spectrum of MN Esa which was centred on the eclipse (figure 2))., We obtained a red spectrum of MN Hya which was centred on the eclipse (figure \ref{eclipse}) ).
+ Although emission lines are visible. this may be due to some pre or post eclipse Lux being recorded.," Although emission lines are visible, this may be due to some pre or post eclipse flux being recorded."
+ Absorption features due to the secondary star are visible at 7150 and. S450hspacelmuam., Absorption features due to the secondary star are visible at 7150 and 8450.
+. However. the low resolution of the spectrum did not permit a detailed: analysis of these. features.," However, the low resolution of the spectrum did not permit a detailed analysis of these features."
+ No secondary features are visible outwith the eclipse., No secondary features are visible outwith the eclipse.
+ To determine the spectral type of the secondary. star we compared its spectrum taken during the eclipse with late vpe spectra kindly supplied by. Dr Robert € Smith., To determine the spectral type of the secondary star we compared its spectrum taken during the eclipse with late type spectra kindly supplied by Dr Robert C Smith.
+ οσο are overlaid in figure 2.., These are overlaid in figure \ref{eclipse}.
+ The depth of the TiO band at 8450 indicates that it is later than AIL. while the lack of a wominent Na Ll feature at suggests that it is earlier than ~AIG.," The depth of the TiO band at 8450 indicates that it is later than M1, while the lack of a prominent Na I feature at suggests that it is earlier than $\sim$ M6."
+ Bearing in mind that some Hux has been recorded which is not due to he secondary (since we observe emission lines). the overall spectral shape is closest to M3.5.," Bearing in mind that some flux has been recorded which is not due to the secondary (since we observe emission lines), the overall spectral shape is closest to M3.5."
+" Using the empirical mass-radius relationship of Patterson (1984). the mass of the secondary. is expected o be 0.31. A. [or an orbital period of 2,523.39. hrs."," Using the empirical mass-radius relationship of Patterson (1984), the mass of the secondary is expected to be 0.31 $M_{\odot}$ for an orbital period of $P_{orb}$ =3.39 hrs."
+ Using the tables of spectral tvpe against stellar mass in Zombeck (1990). we find a spectral type of M3.," Using the tables of spectral type against stellar mass in Zombeck (1990), we find a spectral type of $\sim$ M3."
+ Within he uncertainties involved this is consistent with the spectral vpe determined from the eclipse spectrum., Within the uncertainties involved this is consistent with the spectral type determined from the eclipse spectrum.
+ Using the photometry of Sekiguchi. Nakada Bassctt (1994). where they find my-=18.5 at mid-eclipse. ancl the absolute magnitude of an M3 V. star (Al;=8.71: Bessell 1991). we obtain a distance of 910 pe if zero absorption is assumed.," Using the photometry of Sekiguchi, Nakada Bassett (1994), where they find $m_{Ic}$ =18.5 at mid-eclipse, and the absolute magnitude of an M3 V star $M_{I}$ =8.71: Bessell 1991), we obtain a distance of 910 pc if zero absorption is assumed."
+ However. the X-ray. data obtained. usingROSAL show that the absorption to MN Lva is ~2.5«107 emi? (Buckley et al 1998b).," However, the X-ray data obtained using show that the absorption to MN Hya is $\sim2.5\times10^{20}$ $^{-2}$ (Buckley et al 1998b)."
+ This implies ;4; 20.9 and a distance of 610 pe., This implies $A_{I}$ =0.9 and a distance of 610 pc.
+ For à M4 V. star (A; 29.85: Bessell 1991) we get distance of 360 ancl 540 pe assuming 24;=0.9 ancl ο 0.0 respectively., For a M4 V star $M_{I}$ =9.85: Bessell 1991) we get distance of 360 and 540 pc assuming $A_{I}$ =0.9 and $A_{I}$ =0.0 respectively.
+ We estimate that the distance to MN Ίνα is between 300.2700pc., We estimate that the distance to MN Hya is between 300–700pc.
+where X. v—απ ο” and oó(f.Xx) are. respectively. the Eulerian coordinates. the peculiar velocity. and the peculiar Newtonian gravitational. potential.,"where ${\bf x}$ , ${\bf v}=a(t)\frac{d{\bf x}}{dt}= (v_x, v_y, v_z)$ , and $\phi(t,{\bf x})$ are, respectively, the Eulerian coordinates, the peculiar velocity, and the peculiar Newtonian gravitational potential."
+" The total οποίον density. 4=pe|ipe?2. is celine as the acdelition of the thermal energy. pe. where € ds the specific internal energv. and the kinetic energv (where eo=v;|ey""| 02)."," The total energy density, $E= \rho \epsilon + {1\over 2} \rho v^2$, is defined as the addition of the thermal energy, $\rho\epsilon$, where $\epsilon$ is the specific internal energy, and the kinetic energy (where $v^2 = v_x^2 + v_y^2 + v_z^2$ )."
+ The background. parameters are the scale factor. a. background. density. ου and the Lubble constant. ££.," The background parameters are the scale factor, $a$, background density, $\rho_{_{B}}$ , and the Hubble constant, $H$."
+" Phe density contrast. 9. is defined as ὁ=p/p,—1."," The density contrast, $\delta$, is defined as $\delta=\rho/\rho_{_{B}} - 1$."
+ Pressure eracients and gravitational forces are the responsible for the evolution., Pressure gradients and gravitational forces are the responsible for the evolution.
+ Poisson's equation (4)) is an elliptic equation. and its solution depends on the boundary conditions.," Poisson's equation \ref{poisson1}) ) is an elliptic equation, and its solution depends on the boundary conditions."
+ This equation has to be solved in conjunction with Eqs (1- 3)) to compute the source term. Vo which appears in I5qs (2- 3))., This equation has to be solved in conjunction with Eqs \ref{hydro1}- \ref{hydro3}) ) to compute the source term $\nabla \phi$ which appears in Eqs \ref{hydro2}- \ref{hydro3}) ).
+ An equation of state p=p(p.«) closes the svstem.," An equation of state $p=p(\rho,\epsilon)$ closes the system."
+ In this paper we used an ideal gas equation of state l)e with 4=5/3.," In this paper we used an ideal gas equation of state $p=(\gamma
+-1)\rho\epsilon$ with $\gamma=5/3$."
+" The hydrodynamic equations Eqs (1- 3)) can be rewritten in a slightly cilferent form: where u is the vector of waknowns(conservecl variables): the threeflier functions F""=[f.g.hj in the spatial directions .r.Jy.2. respectively. are defined by and thesources s are where m,=(0|l)e. m,=(8|De, and "," The hydrodynamic equations Eqs \ref{hydro1}- \ref{hydro3}) ) can be rewritten in a slightly different form: where ${\bf u}$ is the vector of (conserved variables): the three functions ${\bf F}^{\alpha} \equiv \{{\bf f},
+{\bf g},{\bf h}\}$ in the spatial directions $x, y, z$, respectively, are defined by and the ${\bf s}$ are where $m_x=(\delta +1)v_x$, $m_y=(\delta +1)v_y$, and $m_z=(\delta
++1)v_z$ ."
+System (5)) is a three-dimensional with sources s(u)., System \ref{hypersys}) ) is a three-dimensional with sources ${\bf s}({\bf u})$.
+ From the numerical point of view ids important to. introduce. the Jacobian matrices associated to the [Duxes: Ivperbolicity demands that any real linear combination of the Jacobian matrices £4 should. be diagonalizable with real eigenvalues (LeVequc 1992)., From the numerical point of view is important to introduce the Jacobian matrices associated to the fluxes: Hyperbolicity demands that any real linear combination of the Jacobian matrices $\xi_{\alpha} {\bf \cal A}^{\alpha}$ should be diagonalizable with real eigenvalues (LeVeque 1992).
+ This is of crucial importance [rom the numerical point of view., This is of crucial importance from the numerical point of view.
+ The spectral. decompositions of the above Jacobian matrices in each direction. ie. the andeigenvectors are explicitly written in Quilis. tikzmarkmainBoedyEndl530°mainBodyStart1531neez Sácez (1996).," The spectral decompositions of the above Jacobian matrices in each direction, i.e., the and are explicitly written in Quilis, Ib\'a\\tikzmark{mainBodyEnd1530}\~\tikzmark{mainBodyStart1531}neez Sáeez (1996)."
+ The sources do not contain any term with cüllerential operators acting on hvdrodyvnamical variables τα., The sources do not contain any term with differential operators acting on hydrodynamical variables ${\bf u}$.
+ ‘This is an important property consistent with the fact that the left. hand. side of ((5)) defines a hyperbolic system of conservation laws., This is an important property consistent with the fact that the left hand side of \ref{hypersys}) ) defines a hyperbolic system of conservation laws.
+ The mathematical properties resulting from the hyperbolic character of the svstem of equations (5)) allow us to design a set of numerical techniques. known asshock-caphiering (URSC)., The mathematical properties resulting from the hyperbolic character of the system of equations \ref{hypersys}) ) allow us to design a set of numerical techniques known as (HRSC).
+ These techniques are the modern implementation of CGiodunov's original method. (Ciodunov 1959. see Laney (1998) for a mocern review on Codunov schemes and. Eulerian methods).," These techniques are the modern implementation of Godunov's original method (Godunov 1959, see Laney (1998) for a modern review on Godunov schemes and Eulerian methods)."
+ The URSC techniques have several key ingredients such as the reconstruction procedure. the Riemann solver. and time advancing schemes which can vary in cillerent implementations.," The HRSC techniques have several key ingredients such as the reconstruction procedure, the Riemann solver, and time advancing schemes which can vary in different implementations."
+ Nevertheless. all of these implementations share the same basic properties: the ability to hanelle shocks. discontinuities and strong eracdientsinthe integrated quantities. and excellent conservation properties.," Nevertheless, all of these implementations share the same basic properties: the ability to handle shocks, discontinuities and strong gradientsinthe integrated quantities, and excellent conservation properties."
+Our basic byelro solver is) based. on a particular implementation of the LERSC methods — see Quilis. Ibá Sáeez (1996) for more details.,"Our basic hydro solver is based on a particular implementation of the HRSC methods – see Quilis, Ib\'a\\tikzmark{mainBodyEnd1696}\~\tikzmark{mainBodyStart1697}neez Sáeez (1996) for more details."
+ The main ingredients of our solver are the following:, The main ingredients of our solver are the following:
+hand. widens the expected. cüstribution of mass ratios but on the other hand decreases the agreement between the expected ancl observed. distribution of chirp masses in the radio.,hand widens the expected distribution of mass ratios but on the other hand decreases the agreement between the expected and observed distribution of chirp masses in the radio.
+ “This conclusions may be verified with the Square Ixilometer Array observations that should reveal many more binary NS systems., This conclusions may be verified with the Square Kilometer Array observations that should reveal many more binary NS systems.
+ The measurement of their masses along with identification of binary NS merger population by the Advanced: LIGO and VIRGO will provide further insight into the properties of the population of binary neutron stars., The measurement of their masses along with identification of binary NS merger population by the Advanced LIGO and VIRGO will provide further insight into the properties of the population of binary neutron stars.
+ This research was supported by the Polish Cirants 1PO03D00530. N203 302335. by the European Ciravitational Observatory grant. EGO-DITU-102-2007. and by the FOCUS Programme of Foundation for Polish Science.," This research was supported by the Polish Grants 1PO3D00530, N203 302835, by the European Gravitational Observatory grant EGO-DIR-102-2007, and by the FOCUS Programme of Foundation for Polish Science."
+Observed star.,observed star.
+ We then discuss the constraints set by abundances derived from 3D model atmospheres and the uncertainties related to 1D or 3D model atmospheres., We then discuss the constraints set by abundances derived from 3D model atmospheres and the uncertainties related to 1D or 3D model atmospheres.
+" The analysis is done in the Dtrans--[Fe/H] plane, using a grid approach to cover the parameter space of the model."," The analysis is done in the -[Fe/H] plane, using a grid approach to cover the parameter space of the model."
+" The parameters that we vary are vri: (from 2x107? to 2x107? Mo yr! ), ZmIII (from 10 to 26), arr (from 0.5 to 5), bir (from 0.03 to 4.9) and the minimum mass of the massive mode, Mir (from 30 to 39 Mo)."," The parameters that we vary are $\nu_{\rm III}$ (from $2 \times 10^{-5}$ to $2 \times10^{-2}$ $_\odot$ $^{-1}$ $^{-3}$ ), $z_{m {\rm III}}$ (from 10 to 26), $a_{\rm III}$ (from 0.5 to 5), $b_{\rm III}$ (from 0.03 to 4.9) and the minimum mass of the massive mode, $M_{\rm III}$ (from 30 to 39 $_\odot$ )."
+" For each model, we calculate the Dtrans-[Fe/H] curve, which is multi-valued for models including PoplII stars."," For each model, we calculate the -[Fe/H] curve, which is multi-valued for models including PopIII stars."
+ The best fit model corresponds to the set of parameters that minimizes a x? on the predicted and observed stellar iron abundance and transition discriminant ((via stellar carbon and oxygen abundances) of a sample of 21 ESO-LP and 3 peculiar stars., The best fit model corresponds to the set of parameters that minimizes a $\chi^2$ on the predicted and observed stellar iron abundance and transition discriminant (via stellar carbon and oxygen abundances) of a sample of 21 ESO-LP and 3 peculiar stars.
+ We consider all parameters within a confidence level (CL) based on this x? to be acceptable., We consider all parameters within a confidence level (CL) based on this $\chi^2$ to be acceptable.
+" Therefore, in all figures, we have displayed CL envelopes that contain the predicted curves of all those acceptable models."," Therefore, in all figures, we have displayed CL envelopes that contain the predicted curves of all those acceptable models."
+" In many models, the iron abundance is monotonically increasing with time, giving a unique correspondance between [Fe/H] and redshift."," In many models, the iron abundance is monotonically increasing with time, giving a unique correspondance between [Fe/H] and redshift."
+" This is the classical view of cosmological chemical evolution, where the oldest stars are the most metal-poor."," This is the classical view of cosmological chemical evolution, where the oldest stars are the most metal-poor."
+" However, in the first metal-free structures, the nucleosynthesis of PoplII stars provide features in the evolution of [Fe/H], so that the previous picture does not necessarily hold."," However, in the first metal-free structures, the nucleosynthesis of PopIII stars provide features in the evolution of [Fe/H], so that the previous picture does not necessarily hold."
+" In that case, not only the abundances of Fe, but also of elements such as C and O are required in order to be able to assign the VMP stars to a particular redshift."," In that case, not only the abundances of Fe, but also of elements such as C and O are required in order to be able to assign the VMP stars to a particular redshift."
+ Each position along the predicted curve Drans//[Fe/H] is associated with a redshift., Each position along the predicted curve /[Fe/H] is associated with a redshift.
+" Following the procedure described above, we search for the position along this curve that minimizes the distance to the observed values for a given star."," Following the procedure described above, we search for the position along this curve that minimizes the distance to the observed values for a given star."
+ This position gives the redshift of formation of this star., This position gives the redshift of formation of this star.
+" The predicted curve depends on the model considered, and therefore different models will associate different redshifts of formation with the same star."," The predicted curve depends on the model considered, and therefore different models will associate different redshifts of formation with the same star."
+" As we repeat this procedure for models that satisfy the CL on the whole sample, we can infer the allowed range of redshift (from the minimum to the maximum redshift) for one specific star."," As we repeat this procedure for models that satisfy the CL on the whole sample, we can infer the allowed range of redshift (from the minimum to the maximum redshift) for one specific star."
+ Models that satisfy a CL limit are included within the envelope shown in (thin black lines)., Models that satisfy a CL limit are included within the envelope shown in (thin black lines).
+ All stars included in our analysis are located along the path defined by the best fit., All stars included in our analysis are located along the path defined by the best fit.
+" As explained in4.2,, G77-61 displays larger errors on its abundance determination."," As explained in, G77-61 displays larger errors on its abundance determination."
+" Yet, it is also located within the envelope (square in 4))."," Yet, it is also located within the envelope (square in )."
+ HE 0557-4840 is located at a somehow low value for [Fe/H]., HE 0557-4840 is located at a somehow low value for [Fe/H].
+" According to the exact value forDtrans,, it could either seat outside the envelope (Dtrans-2.2) or be very close to the edge (Dtrans-3)."," According to the exact value for, it could either seat outside the envelope $\simeq$ -2.2) or be very close to the edge $\simeq$ -3)."
+ The envelope of the PopIII SFR for all allowed models is shown in (shaded area)., The envelope of the PopIII SFR for all allowed models is shown in (shaded area).
+" Some common features can be noted: the massive mode becomes sub-dominant for redshift lower than about 15; on the contrary, it isrequired at a level of 2x10* - 3x1073 Mo yr! Mpc around z~24—28."," Some common features can be noted: the massive mode becomes sub-dominant for redshift lower than about 15; on the contrary, it isrequired at a level of $\times 10^{-4}$ - $3\times10^{-3}$ $_\odot$ $^{-1}$ $^{-3}$ around $z\sim 24-28$."
+ The PopIII SFR cannot be larger than 3ὃx10? Μο yr! Mpc? independently of the redshift., The PopIII SFR cannot be larger than $3\times10^{-3}$ $_\odot$ $^{-1}$ $^{-3}$ independently of the redshift.
+ The envelope of the optical depth history among all models is shown in (light shaded area)., The envelope of the optical depth history among all models is shown in (light shaded area).
+ We verify that all models are compatible with the 1c limit of WMAPS., We verify that all models are compatible with the $\sigma$ limit of WMAP5.
+" As explained in5.1.2,, for a given model, we have assigned a typical redshift, z,, of formation to each individual star."," As explained in, for a given model, we have assigned a typical redshift, $z_\star$, of formation to each individual star."
+" Thus, we can locate each star on a plot of abundances versus redshift, and compare them directly to the predicted evolution."," Thus, we can locate each star on a plot of abundances versus redshift, and compare them directly to the predicted evolution."
+ This is done in using the best fit model (dashed red line)., This is done in using the best fit model (dashed red line).
+ We also show the corresponding CL envelopes for the evolution of the abundances (thin black lines)., We also show the corresponding CL envelopes for the evolution of the abundances (thin black lines).
+ Those envelopes also bracket the errors on the redshift of formation (see [Fe/H] plot in 5))., Those envelopes also bracket the errors on the redshift of formation (see [Fe/H] plot in ).
+ The redshift ranges are given in2., The redshift ranges are given in.
+. We see that CEMP stars are likely to form at high redshift., We see that CEMP stars are likely to form at high redshift.
+" For example, the star HE 13004-0157 (upper triangle in 4)) is found to be formed at z,~11 (for the best fit model)."," For example, the star HE 1300+0157 (upper triangle in ) is found to be formed at $z_\star\sim 11$ (for the best fit model)."
+ HE 130040157 is located along a branch of the evolution where the dilution by IGM accretion is the only important process., HE 1300+0157 is located along a branch of the evolution where the dilution by IGM accretion is the only important process.
+" Then, abundances decrease very slowly and uncertainties on the redshift are of the order of 100 Myr (15«z 20)."," Then, abundances decrease very slowly and uncertainties on the redshift are of the order of 100 Myr $15<z<20$ )."
+" It is interesting to note that the predicted abundances also reproduce the Fe, C and O abundances at this specific redshift."," It is interesting to note that the predicted abundances also reproduce the Fe, C and O abundances at this specific redshift."
+" The star G 77-61 (square), that has a similar iron abundance but a higher carbon abundance, is born earlier (it is located on a different place along the curve Dtrans--[Fe/H]; 4)) at z~ 16."," The star G 77-61 (square), that has a similar iron abundance but a higher carbon abundance, is born earlier (it is located on a different place along the curve -[Fe/H]; ) at $z\sim 16$ ."
+ The exact redshift for HE 1327-2326 and HE, The exact redshift for HE 1327-2326 and HE
+Seintillations of the pulsar signal is a phenomenon that was identified shortly after the discovery of pulsars themselves (Hewish et al. 1968)).,Scintillations of the pulsar signal is a phenomenon that was identified shortly after the discovery of pulsars themselves (Hewish et al. \cite{hewish}) ).
+ From an observer point of view pulsars are point-like sources. and presumably are intrinsically stable sources of radiation.," From an observer point of view pulsars are point-like sources, and presumably are intrinsically stable sources of radiation."
+ Their radiation. however. undergoes scattering process in the interstellar plasma on its way to the observer.," Their radiation, however, undergoes scattering process in the interstellar plasma on its way to the observer."
+ Depending on the strength of the scattering that the radiation of a given pulsar undergoes. the interstellar seintillations (ISS) will result in different phenomena observed for the pulsar (see Lorimer Kramer. 2005.. and the references therein for a recent review).," Depending on the strength of the scattering that the radiation of a given pulsar undergoes, the interstellar scintillations (ISS) will result in different phenomena observed for the pulsar (see Lorimer Kramer, \cite{lori}, and the references therein for a recent review)."
+ For a nearby pulsar. or when the radiation encounters only small amounts of the scattering material (and if the observing frequency is higher than ca.," For a nearby pulsar, or when the radiation encounters only small amounts of the scattering material (and if the observing frequency is higher than ca."
+ | GHz). the disturbances of the wavefront will be minimal. resulting inscintillations.," 1 GHz), the disturbances of the wavefront will be minimal, resulting in."
+ In case of strong scattering (a distant pulsar and/or low observing frequency). the phase perturbations become large. which leads to a strong modulation of the pulsar signal.," In case of strong scattering (a distant pulsar and/or low observing frequency), the phase perturbations become large, which leads to a strong modulation of the pulsar signal."
+ In this one has to take both diffraction and refraction effects into account., In this one has to take both diffraction and refraction effects into account.
+" The arise from small (10°+105 meter) inhomogeneities in the interstellar medium. which introduce observed flux density variations with the timescale that can be estimated às fyssf!?d""* (assuming a Kolmogorov spectrum of the ISM turbulence. see Rickett 1990:; Romani et al. 1986))."," The arise from small $10^6 \div 10^8$ meter) inhomogeneities in the interstellar medium, which introduce observed flux density variations with the timescale that can be estimated as $t_{\rm DISS} \sim f^{1.2} \ d^{0.6}$ (assuming a Kolmogorov spectrum of the ISM turbulence, see Rickett \cite{rick}; Romani et al. \cite{romani}) )."
+ The (ISS; Stieber 1982: Rickett at al. 1984)), The (RISS; Sieber \cite{sieb}; Rickett at al. \cite{rick84}) )
+ arise from larger scale density fluctuations (10=[0 meters)., arise from larger scale density fluctuations $10^{10} \div 10^{13}$ meters).
+ As theories predict. the RISS timescale decreases with observing frequency. roughly as fgiss~fdo.," As theories predict, the RISS timescale decreases with observing frequency, roughly as $t_{\rm RISS} \sim f^{-2.2} \ d^{1.6}$."
+ For any given pulsar the values of the mentioned parameters will hence change with the observational frequency., For any given pulsar the values of the mentioned parameters will hence change with the observational frequency.
+ Starting from very low frequencies. we will have short but increasing DISS timescales. and very long but decreasing RISS timescales. which will be accompanied by increasing RISS modulation (DISS modulation will be always close to unity).," Starting from very low frequencies, we will have short but increasing DISS timescales, and very long but decreasing RISS timescales, which will be accompanied by increasing RISS modulation (DISS modulation will be always close to unity)."
+ The rate at which these parameters change can be used to decide between various theories describing the ISM turbulence spectrum. because their frequency dependence power-law predictions are tied to the model used (see Romani et al. 1986..," The rate at which these parameters change can be used to decide between various theories describing the ISM turbulence spectrum, because their frequency dependence power-law predictions are tied to the model used (see Romani et al. \cite{romani},"
+ Bhat et al. 1999))., Bhat et al. \cite{bhat}) ).
+ As the observing frequency increases. both scintillation timescales should be closer. and the refractive modulation index should increase towards unity (which is best illustrated by Lorimer Kramer. 2005. on their Figure 3.50).," As the observing frequency increases, both scintillation timescales should be closer, and the refractive modulation index should increase towards unity (which is best illustrated by Lorimer Kramer, \cite{lori}, on their Figure 4.5b)."
+ At a certain frequency. called the both timescales become equal. refractive scintillations reach maximum modulation and the character of the scintillations in general changes.," At a certain frequency, called the both timescales become equal, refractive scintillations reach maximum modulation and the character of the scintillations in general changes."
+ This is the frequency at which the transition from the strong to weak scintillation regimes happens., This is the frequency at which the transition from the strong to weak scintillation regimes happens.
+ Most of the pulsar scintillation observations conducted so far were performed at the frequencies of 1.5 GHz and below. there is only a handful of papers describing ISS observations at higher frequencies (Malofeev et al. 1996::," Most of the pulsar scintillation observations conducted so far were performed at the frequencies of 1.5 GHz and below, there is only a handful of papers describing ISS observations at higher frequencies (Malofeev et al. \cite{malo};"
+ Kramer et al. 1997::, Kramer et al. \cite{kram};
+ Shishov et al. 2003)., Shishov et al. \cite{shis}) ).
+ The attempts to estimate the spectrum of the ISM turbulence via the measurement of ISS parameters were limited to the frequency range from cà., The attempts to estimate the spectrum of the ISM turbulence via the measurement of ISS parameters were limited to the frequency range from ca.
+ ~100 MHz to 1.5 GHz., $\sim 100$ MHz to 1.5 GHz.
+ This is both because pulsars are steep spectrum sources and are considerably weaker at higher frequencies. and the increasing DISS timescale which means one needs longer data sets to be able to perform measurements in à way similar to what is done at low frequencies.," This is both because pulsars are steep spectrum sources and are considerably weaker at higher frequencies, and the increasing DISS timescale which means one needs longer data sets to be able to perform measurements in a way similar to what is done at low frequencies."
+ Both of these reasons result in a much longer observing time to be able to obtain reliable measurements., Both of these reasons result in a much longer observing time to be able to obtain reliable measurements.
+ Because there are only few radiotelesopes capable of high-frequency observations. projects like this are very hard to implement.," Because there are only few radiotelesopes capable of high-frequency observations, projects like this are very hard to implement."
+ The way to at least partially overcome these obstacles is to limit the observations to very strong pulsars. which in turn lowers the telescope-size requirements.," The way to at least partially overcome these obstacles is to limit the observations to very strong pulsars, which in turn lowers the telescope-size requirements."
+ One of the best candidates for these observations is definitely PSR BO329—54. the strongest radio pulsar in the northern hemisphere.," One of the best candidates for these observations is definitely PSR B0329+54, the strongest radio pulsar in the northern hemisphere."
+ Owing to its brightness. it was observed by many various ISS projects in the past (see the section in this paper. and Table for a full list of references).," Owing to its brightness, it was observed by many various ISS projects in the past (see the section in this paper, and Table \ref{tab3} for a full list of references)."
+ Amongst them was a project conducted by Malofeev et al. (1996)).," Amongst them was a project conducted by Malofeev et al. \cite{malo}) ),"
+ which involved fairly short (ca., which involved fairly short (ca.
+ 130 minutes) observations at 4.75 and 10.55 GHz. based on which the authors concluded that for PSR B03294-54," 130 minutes) observations at 4.75 and 10.55 GHz, based on which the authors concluded that for PSR B0329+54"
+ils edge.,its edge.
+ This can explain the frequent. observation (hat the ICS is usually not centrally located within slow wind streams (e.g..Durlagaetal.2002).," This can explain the frequent observation that the HCS is usually not centrally located within slow wind streams \citep[e.g.,][]{burlaga02}."
+. Third. the boundary between the S-web laver and (he featureless polar hole region is sharp: il is narrow compared to the width of the S-web.," Third, the boundary between the S-web layer and the featureless polar hole region is sharp; it is narrow compared to the width of the S-web."
+ This can explain the observation that the (transition from slow Co Last wind as measured by (he composition data 15 narrow compared to the slow wind region itself (Zurbuchenetal.1999)., This can explain the observation that the transition from slow to fast wind as measured by the composition data is narrow compared to the slow wind region itself \citep{zurbuchen99}.
+. In order to explore the details of how coronal hole extensions connect to the polar holes. we ealeulated coronal hole areas al different heights in the corona.," In order to explore the details of how coronal hole extensions connect to the polar holes, we calculated coronal hole areas at different heights in the corona."
+ Figure 8 shows the location of a region near longitude 75° and latitude 157 N in which we explored the connection between the low-latitude coronal hole extensions (of negative polarity. shown in blue) in detail.," Figure 8 shows the location of a region near longitude $75^\circ$ and latitude $15^\circ$ N in which we explored the connection between the low-latitude coronal hole extensions (of negative polarity, shown in blue) in detail."
+ It is evident that (he coronal hole extensions in (his region appear disconnected from the north polar hole in the photosphere. but connect with it low in the corona (at heights approximately between 0.01. and 0.028. above the photosphere).," It is evident that the coronal hole extensions in this region appear disconnected from the north polar hole in the photosphere, but connect with it low in the corona (at heights approximately between $0.01R_\odot$ and $0.02R_\odot$ above the photosphere)."
+ Figure 9 shows explicitly how these coronal holes connect in the low corona., Figure 9 shows explicitly how these coronal holes connect in the low corona.
+ The three-dimensional shape of the coronal hole boundary is shown as a green semi-transparent surface in the low corona in the region detailed in Figure 8., The three-dimensional shape of the coronal hole boundary is shown as a green semi-transparent surface in the low corona in the region detailed in Figure 8.
+ This is the boundary between open aud closed Ποια regions., This is the boundary between open and closed field regions.
+ The regions marked by A.B. and C show examples in which the extensions of coronal holes are not connected in (he photosphere. at least by any measurable open-field corridor. but. appear to connect above (he photosphere in the low corona.," The regions marked by A, B, and C show examples in which the extensions of coronal holes are not connected in the photosphere, at least by any measurable open-field corridor, but appear to connect above the photosphere in the low corona."
+ These regions are also indicated in Figure 8 [or ease of cross-relerence., These regions are also indicated in Figure 8 for ease of cross-reference.
+" Despite the fact that (hese coronal holes are ""disconnected"" in the photosphere. they always remain topologically/inked in a singular manner wilh the polar coronal hole. as discussed by Titovetal.(2011)."," Despite the fact that these coronal holes are “disconnected” in the photosphere, they always remain topologically in a singular manner with the polar coronal hole, as discussed by \citet{titov11}."
+. Finally. note that the connections of the high-Q lines between the neighborhood of the ICS and the photosphere ancl low corona that were postulated by the uniqueness conjecture (Antiochosetal.2007) are largely. present. even though the insight from these new MILD simulations has led us to generalize the uniqueness conjecture.," Finally, note that the connections of the $Q$ lines between the neighborhood of the HCS and the photosphere and low corona that were postulated by the uniqueness conjecture \citep{ska07} are largely present, even though the insight from these new high-resolution MHD simulations has led us to generalize the uniqueness conjecture."
+ We have found (hat. in general. coronal hole extensions are sometimes connected to the polar holes in the photosphere via narrow corridors. as originally postulated (Antiochosοἱal.2007).. bul in other instances they are disconnected in the photosphere. but remain topologically linked to the polar holes (Titovetal.2011).," We have found that, in general, coronal hole extensions are sometimes connected to the polar holes in the photosphere via narrow corridors, as originally postulated \citep{ska07}, but in other instances they are disconnected in the photosphere, but remain topologically linked to the polar holes \citep{titov11}."
+. In either case. these connections are responsible for the formation of the S-web.," In either case, these connections are responsible for the formation of the S-web."
+ It should be emphasized that in order to capture (he intricate structure of these connections. very hieh resolution models are recuired (hat can incorporate sone of the complexity of the photospheric magnetic carpet fields.," It should be emphasized that in order to capture the intricate structure of these connections, very high resolution models are required that can incorporate some of the complexity of the photospheric magnetic carpet fields."
+ Given sullicient resolution. the S-web should appear as a generic feature of all quasi-steady models. including (he PESS.," Given sufficient resolution, the S-web should appear as a generic feature of all quasi-steady models, including the PFSS."
+ In fact. the PES models should be more effective than the MIID for studying the complex topology of the S-web. because they allow lor nich higher spatial resolution (han is possible with an MIID code.," In fact, the PFSS models should be more effective than the MHD for studying the complex topology of the S-web, because they allow for much higher spatial resolution than is possible with an MHD code."
+ On the other hand. for quantitative comparison wilh observations. the," On the other hand, for quantitative comparison with observations, the"
+o our initial assumption of a constant Εν.,to our initial assumption of a constant $_b$.
+ “Phis increases rw number of BSs formed from binary star evolution and --mproves the agreement between our model predictions and 16 observations in low-mass clusters., This increases the number of BSs formed from binary star evolution and improves the agreement between our model predictions and the observations in low-mass clusters.
+ This is consistent with the results of Sollimaetal.(2008)., This is consistent with the results of \citet{sollima08}.
+" However. adopting Equation 14. for b, also causes our model to under-predict 1e number of BSs in several high-mass clusters."," However, adopting Equation \ref{eqn:sollima07} for $_b$ also causes our model to under-predict the number of BSs in several high-mass clusters."
+" The best fit to the observations is found. by. adopting 1e relation for fj provided in Equation 14— and setting $507zQd (however we note that a comparably σους agreement is found with a slightlv lower [/""= 0.05).", The best fit to the observations is found by adopting the relation for $_b$ provided in Equation \ref{eqn:sollima07} and setting $_b^{min} = 0.1$ (however we note that a comparably good agreement is found with a slightly lower $_b^{min} = 0.05$ ).
+ This improves the agreement between our mocel predictions and he observations by increasing the number of DSs formed rom binary star evolution in massive clusters., This improves the agreement between our model predictions and the observations by increasing the number of BSs formed from binary star evolution in massive clusters.
+ The result is a good agreement between our model predictions and. the observations in both low- and high-mass cores. as shown in ligure 3..," The result is a good agreement between our model predictions and the observations in both low- and high-mass cores, as shown in Figure \ref{fig:model_best_rmax_sollima_10min_tBS15}."
+ In this case. the best-fitting model. parameters viele the lowest deviance of any of the assumptions so [ar considered.," In this case, the best-fitting model parameters yield the lowest deviance of any of the assumptions so far considered."
+ These best-fitting values suggest that most BSs are formed. from binary star evolution. with a small contribution from 212 collisions being needed. in order to obtain the best possible match to the observations.," These best-fitting values suggest that most BSs are formed from binary star evolution, with a small contribution from 2+2 collisions being needed in order to obtain the best possible match to the observations."
+ Similarly to what was found for our initial assumptions. the ideal contribution from 2| collisions constitutes at most a [ew percent of the predicted. total for most of the clusters in our sample.," Similarly to what was found for our initial assumptions, the ideal contribution from 2+2 collisions constitutes at most a few percent of the predicted total for most of the clusters in our sample."
+ On the other hand. if we change our imposed minimum binary fraction to [7=0.05 we find that a non-negligible (i.e. up to a few tens of a percent) contribution from single-single collisions is needed in several clusters to obtain the best. possible agreement with the observations (which is very nearly as good as was found. using [7= O.1).," On the other hand, if we change our imposed minimum binary fraction to $_b^{min} = 0.05$ we find that a non-negligible (i.e. up to a few tens of a percent) contribution from single-single collisions is needed in several clusters to obtain the best possible agreement with the observations (which is very nearly as good as was found using $_b^{min} = 0.1$ )."
+ All of this shows that. although binary star evolution consistently dominates BS formation in our best-[itting models. at least some contribution from collisions (whether Προ |1 or 2| collisions. or some combination of1|1. 1|2 ancl 2| collisions) also consistently improves the agreement with the observations.," All of this shows that, although binary star evolution consistently dominates BS formation in our best-fitting models, at least some contribution from collisions (whether it be 1+1 or 2+2 collisions, or some combination of 1+1, 1+2 and 2+2 collisions) also consistently improves the agreement with the observations."
+" Moreover. it is interesting to note that an improved agreement with the observations could alternatively be obtained if we keep G7""=0.01 but all or some of £j4. fy)2 and [ο2 increase with increasing cluster mass."," Moreover, it is interesting to note that an improved agreement with the observations could alternatively be obtained if we keep $_b^{min} =
+0.01$ but all or some of $_{1+1}$, $_{1+2}$ and $_{2+2}$ increase with increasing cluster mass."
+ This would also serve to improve the agreement at the hieh-mass end., This would also serve to improve the agreement at the high-mass end.
+ We will return to this in Section 5.., We will return to this in Section \ref{discussion}.
+" Finally. we also tried adopting the observed dependence o, on My: reported in Miloneetal.(2008).. who also found evidence for an anti-correlation. between the core. binary fraction and the total cluster mass."," Finally, we also tried adopting the observed dependence of $_b$ on $_V$ reported in \citet{milone08}, who also found evidence for an anti-correlation between the core binary fraction and the total cluster mass."
+ Despite this change. we consistently find that our results are the same as found when using the empirical binary [raction relation provided in Equation 14..," Despite this change, we consistently find that our results are the same as found when using the empirical binary fraction relation provided in Equation \ref{eqn:sollima07}."
+ We also tried changing our assumption for the average BS lifetime., We also tried changing our assumption for the average BS lifetime.
+ We explored a range of plausible Lifetimes based on values found throughout the literature., We explored a range of plausible lifetimes based on values found throughout the literature.
+ Specifically. we explored the range 0.5-5 Cars.," Specifically, we explored the range 0.5-5 Gyrs."
+ We find that at the low end of this range. our model fits become increasingly. poor.," We find that at the low end of this range, our model fits become increasingly poor."
+In 1964. Refsdal first suggested that time delays between gravitationally lensed images could be used to determine the Hubble constant Ho.,"In 1964, Refsdal first suggested that time delays between gravitationally lensed images could be used to determine the Hubble constant $H_{0}$."
+ The appeal of this method was the fact that it did not depend upon the local distance scale and was a relatively straightforward single-step process., The appeal of this method was the fact that it did not depend upon the local distance scale and was a relatively straightforward single-step process.
+ In addition. the time delay theory upon which it is based was derived from the established theory of general relativity.," In addition, the time delay theory upon which it is based was derived from the established theory of general relativity."
+ Only in recent years. however. with the availability of high resolution radio and optical imaging. has the method begun to yield results.," Only in recent years, however, with the availability of high resolution radio and optical imaging, has the method begun to yield results."
+ When focusing on individual lensing galaxies. a large number of lens modeling studies (e.g. Impey et al.," When focusing on individual lensing galaxies, a large number of lens modeling studies (e.g. Impey et al."
+ 1998; Williams Saha 2000; Winn et al., 1998; Williams Saha 2000; Winn et al.
+ 2002) have obtained values of Ho that have been lower than that from the (Freedman et al., 2002) have obtained values of $H_{0}$ that have been lower than that from the (Freedman et al.
+ 2001) which yields a value of Hy = 72 + 8 kms7!Mpe7!. or indeed the which yields a very similar Ho = 72 € 5 kms!Mpc. although this assumes a flat universe (Spergel et al.," 2001) which yields a value of $H_{0}$ = 72 $\pm$ 8 ${\rm km}\,{\rm s}^{-1}{\rm Mpc}^{-1}$, or indeed the which yields a very similar $H_{0}$ = 72 $\pm$ 5 ${\rm km}\,{\rm s}^{-1}{\rm Mpc}^{-1}$, although this assumes a flat universe (Spergel et al."
+ 2003)., 2003).
+ In particular. a few studies have inferred that if one assumes that lenses have an isothermal mass distribution (flat rotation. curves) the derived value is Hy~SOkms!Mpe. whereas if they assume a constant mass-to-light ratio (M/L). which results in a falling rotation curve. then Hy~7Okms~!Mpe7!. which is in agreement with the finding (Kochanek 2002: others e.g. Impey et al.," In particular, a few studies have inferred that if one assumes that lenses have an isothermal mass distribution (flat rotation curves) the derived value is $H_{0}\sim 50{\rm km}\,{\rm s}^{-1}{\rm Mpc}^{-1}$, whereas if they assume a constant mass-to-light ratio (M/L), which results in a falling rotation curve, then $H_{0}\sim 70 {\rm km}\,{\rm s}^{-1} {\rm Mpc}^{-1}$, which is in agreement with the finding (Kochanek 2002; others e.g. Impey et al."
+ 1998: Rusin et al., 1998; Rusin et al.
+ 2003)., 2003).
+ This constant M/L ratio implies a compact dark matter halo., This constant M/L ratio implies a compact dark matter halo.
+ However. other studies such as weak lensing (e.g. Guzik Seljak 2002). stellar dynamies (Rix et al.," However, other studies such as weak lensing (e.g. Guzik Seljak 2002), stellar dynamics (Rix et al."
+ 1997; Romanowsky Kochanek 1999; Gerhard et al., 1997; Romanowsky Kochanek 1999; Gerhard et al.
+" 2001: Treu Koopmans 2002). and X-ray galaxy measurements (e.g. Fabbiano 1999; Lowenstein White 1999), are consistent with near isothermal density profiles (1.e. extended dark matter halos)."," 2001; Treu Koopmans 2002), and X-ray galaxy measurements (e.g. Fabbiano 1999; Lowenstein White 1999), are consistent with near isothermal density profiles (i.e. extended dark matter halos)."
+ Note however that in the strong lensing regime we are probing the inner few kpe of galaxies (ie. within the Einstein radius). whereas other studies. such as galaxy-galaxy lensing. are sensitive to more extended scales.," Note however that in the strong lensing regime we are probing the inner few kpc of galaxies (i.e. within the Einstein radius), whereas other studies, such as galaxy-galaxy lensing, are sensitive to more extended scales."
+ The aim of this paper is to study whether time delays from multiple image lens systems statistically point towards extended dark matter halos which are inferred from other measurements. when an external prior is adopted for Ho.," The aim of this paper is to study whether time delays from multiple image lens systems statistically point towards extended dark matter halos which are inferred from other measurements, when an external prior is adopted for $H_{0}$."
+ We perform the study without the complexity of detailed lens modeling in an effort to provide insight with a simple model., We perform the study without the complexity of detailed lens modeling in an effort to provide insight with a simple model.
+ The outline of this paper ts as follows., The outline of this paper is as follows.
+ In 322 we introduce two analytic models for the gravitational time delay based upon an SIS potential and general power law potential., In 2 we introduce two analytic models for the gravitational time delay based upon an SIS potential and general power law potential.
+ $33 will discuss the effect of ellipticity and shear on the time delays., 3 will discuss the effect of ellipticity and shear on the time delays.
+ In $44 we discuss the lens sample used as the data set in the Investigation. and i $55 we explain the analysis of this data set and present results.," In 4 we discuss the lens sample used as the data set in the investigation, and in 5 we explain the analysis of this data set and present results."
+ $66 draws some conclusions based upon the findings., 6 draws some conclusions based upon the findings.
+" The light-travel time for an image of a gravitational lens system. is given by (see e.g.Narayan Bartelmann 1997) where z is the redshift of the lensing galaxy. D; and D, are the angular diameter distances to the lens and source respectively. and D,, is the angular diameter distance between the lens and source."," The light-travel time for an image of a gravitational lens system, is given by (see e.g.Narayan Bartelmann 1997) where $z_{l}$ is the redshift of the lensing galaxy, $D_{l}$ and $D_{s}$ are the angular diameter distances to the lens and source respectively, and $D_{ls}$ is the angular diameter distance between the lens and source."
+ The two dimensional vectors @ and f. are the (angular) image and source positions respectively and the effective potential at the locations of images is (0).," The two dimensional vectors $\vec{\theta}$ and $\vec{\beta}$, are the (angular) image and source positions respectively and the effective potential at the locations of images is $\psi(\vec{\theta})$."
+ Note that the light-travel time has a geometrical component and a component due to gravitational time dilation (Shapiro delay) which depends on the gravitational potential., Note that the light-travel time has a geometrical component and a component due to gravitational time dilation (Shapiro delay) which depends on the gravitational potential.
+ Since angular diameter distance scales as c/Ho. where Ho is the Hubble parameter at the present epoch. it follows that to1/Ho.," Since angular diameter distance scales as $c/H_{0}$, where $H_{0}$ is the Hubble parameter at the present epoch, it follows that $t\propto 1/H_{0}$."
+ The time delay between two Images. say A and B. ts the difference in their light-travel time ie. At=£4—fg.," The time delay between two images, say A and B, is the difference in their light-travel time i.e. $\Delta t = t_{A} - t_{B}$."
+ In order to calculate this quantity we must adopt a specific effective potential., In order to calculate this quantity we must adopt a specific effective potential.
+ The singular isothermal sphere (SIS) is a simple yet surprisingly realistic starting point. for modeling lenses., The singular isothermal sphere (SIS) is a simple yet surprisingly realistic starting point for modeling lenses.
+ Its lensing potential has the form: where is a deflection scale determined by the geometry., Its lensing potential has the form: where is a deflection scale determined by the geometry.
+ For a |B|« 5. the SIS produces two collinear images at radit Ry = |B]+5 and," For a $|\beta| < b$ , the SIS produces two collinear images at radii $R_{A}$ = $|\beta| + b$ and"
+width and multiple spectral components.,width and multiple spectral components.
+ Both the Al A1670 and AI526 lines are usually very strong and heavily saturated in DLAs and the high rest frame equivalent widths indicate that this is indeed the case for the absorber towards TXS 03114430., Both the Al $\lambda$ 1670 and $\lambda$ 1526 lines are usually very strong and heavily saturated in DLAs and the high rest frame equivalent widths indicate that this is indeed the case for the absorber towards TXS 0311+430.
+ Conversely. ALSOS is often unsaturated in DLA spectra and can therefore be used to derive an abundance for silicon.," Conversely, $\lambda$ 1808 is often unsaturated in DLA spectra and can therefore be used to derive an abundance for silicon."
+ However. in the present case. the high rest frame equivalent width of the AISOS line suggests that it too is likely to be saturated.," However, in the present case, the high rest frame equivalent width of the $\lambda$ 1808 line suggests that it too is likely to be saturated."
+ Nonetheless. by assuming that the A1808 line is in the linear part of the curve of growth. it is possible to obtain a lower limit on the ccolumn density and hence. on the metallicity of the DLA.," Nonetheless, by assuming that the $\lambda$ 1808 line is in the linear part of the curve of growth, it is possible to obtain a lower limit on the column density and hence, on the metallicity of the DLA."
+ The column density is /N(SilID c2.710 >. giving =—0.48.," The column density is $N$ $\geq 2.7 \times 10^{15}$ $^{-2}$, giving $\geq -0.48$."
+ This is an unusually high metallicity among DLAs. including those in radio-selected QSOs (2)..," This is an unusually high metallicity among DLAs, including those in radio-selected QSOs \citep{akerman05}. ."
+" Among the 104 DLAs at zi,>1.6 in the compilation by ?.. there are only three absorbers with higher values of the silicon abundance."," Among the 104 DLAs at $z_{\rm abs} > 1.6$ in the compilation by \citet{prochaska07}, there are only three absorbers with higher values of the silicon abundance."
+ Our estimates of /V(STIDJ. and hence [Si/H]. may be lower limits. because we have assumed no line saturation and no depletion of Si onto dust grains.," Our estimates of $N$ ), and hence [Si/H], may be lower limits, because we have assumed no line saturation and no depletion of Si onto dust grains."
+ On the other hand. it is possible that we may have over-estimated the equivalent width of the ALSOS absorption line through unrecognised blending with other features in our low resolution GMOS spectrum.," On the other hand, it is possible that we may have over-estimated the equivalent width of the $\lambda 1808$ absorption line through unrecognised blending with other features in our low resolution GMOS spectrum."
+ The work of ? —see. in particular. their Figure 5— shows that in low resolution spectra from the Sloan Digital Sky Survey this effect can lead one to overestimate /V(STID) by as muchas a factor of three.," The work of \citet{herbertfort06} —see, in particular, their Figure 5— shows that in low resolution spectra from the Sloan Digital Sky Survey this effect can lead one to overestimate $N$ ) by as muchas a factor of three."
+ Higher resolution spectra. and observations of other spectral lines such as AÀA2026.2062. should help resolve these ambiguities.," Higher resolution spectra, and observations of other spectral lines such as $\lambda\lambda 2026,2062$, should help resolve these ambiguities."
+ We also examined the GMOS spectrum for. possible absorption at other redshifts and detected a strong ssystem at 2~1.069., We also examined the GMOS spectrum for possible absorption at other redshifts and detected a strong system at $z \sim 1.069$.
+ The large rest frame equivalent widths of the AA2796.2803 doublet C»3 A)) and the A2600 line (~2.3 Ad) in this absorber (see Table 15) imply that it too is likely to be a DLA (?)..," The large rest frame equivalent widths of the $\lambda\lambda$ 2796,2803 doublet $> 3$ ) and the $\lambda$ 2600 line $\sim 2.3$ ) in this absorber (see Table \ref{tab:metals}) ) imply that it too is likely to be a DLA \citep{rao06}."
+ The final 21 em spectra from the October and January observing sessions are shown in panels [A] and [B] of Figure 2.. with the vertical shaded region in each panel markinga frequency," The final 21 cm spectra from the October and January observing sessions are shown in panels [A] and [B] of Figure \ref{fig:21cm}, , with the vertical shaded region in each panel markinga frequency"
+Alost Sevfert galaxies show some spectral lines from forbidden transitions of highly ionised ions in their spectra. e.g. be vu]. Ve xij. Fe xi] and even Fe xiv]] (Penston 1984).,"Most Seyfert galaxies show some spectral lines from forbidden transitions of highly ionised ions in their spectra, e.g. [Fe ], [Fe ], [Fe ] and even [Fe ] \citep{penston}."
+" These emission. lines are often blueshifted with respect to the rest frame of the AGN and have velocity widths which are between those of the Narrow-Line ltegion (NLR). and the Broad-Line Region (BLA. οἱM Appenzeller&Wagner1991... Mullaney.etal.""n ."," These emission lines are often blueshifted with respect to the rest frame of the AGN and have velocity widths which are between those of the Narrow-Line Region (NLR), and the Broad-Line Region (BLR, \citealt{penston}, \citealt{appenzeller}, \citealt{mullaney}) )."
+ In Dsome rare cases many forbidden high ionisation m1Ls) of relatively high equivalent width have been detected., In some rare cases many forbidden high ionisation lines (FHILs) of relatively high equivalent width have been detected.
+ Examples include HE Zw 77 (Osterbrock.1981).. 'l'ololo 0109-383 (ον&Sansom1983). and ESO 138 1 CAlloinetal.1992)," Examples include III Zw 77 \citep{osterbrock2}, Tololo 0109-383 \citep{fosbury} and ESO 138 G1 \citep{alloin}."
+" The physical mechanisms ancl conditions that allow strong FLILLs to be produced have been debated for some ime: whether there is a continuity from the photoionisation orocesses which produce the lower ionisation lines D the LIUC (Ixorista&Ferland1989.. chanimFergusonetal. 1997)).-- or here is an entirely different me for their (c.g. collisional excitation. in a high temperature. gas: ussbaumer&Osterbrock 19702)Given that the transitions associated with many of the FILS have high. critical densities (n2 10"" 7). it has oen sugeested that they may. originate in the innermos orus wall facing the illuminating source."," The physical mechanisms and conditions that allow strong FHILs to be produced have been debated for some time: whether there is a continuity from the photoionisation processes which produce the lower ionisation lines in the NLR \citealt{korista}, \citealt{ferg}) ), or there is an entirely different mechanism for their formation (e.g. collisional excitation in a high temperature gas; \citeauthor{nussbaumer1} \citeyear{nussbaumer1}) ).Given that the transitions associated with many of the FHILs have high critical densities $_c$$>$ $^5$ $^{-3}$ ), it has been suggested that they may originate in the innermost torus wall facing the illuminating source."
+ Studies of the high critical density Fe v11]|AGOSG. emission line across Sevfor galaxies [from tvpes 1-2. including intermediate types. finc hat its strength increases relative to the low ionisation lines rom tvpe 2 to tvpe 1.," Studies of the high critical density [Fe $\lambda$ 6086 emission line across Seyfert galaxies from types 1-2, including intermediate types, find that its strength increases relative to the low ionisation lines from type 2 to type 1."
+ This can be interpreted in terms of he orientation-based. division between Sevfert twpes (e.g. Antonuect 1993)): as the Sevífert tvpe gets closer to à Sever 1. more of the emission from the inner torus becomes visible o the observer (see Murayama&Taniguchi 1998.. Nagaoeal. 20013).," This can be interpreted in terms of the orientation-based division between Seyfert types (e.g. \citealt{ant}) ): as the Seyfert type gets closer to a Seyfert 1, more of the emission from the inner torus becomes visible to the observer (see \citealt{murayama2}, , \citealt{nagao1}) )."
+ Therefore the high critical density lines that are xeferentially emitted by the torus are likely to be stronger, Therefore the high critical density lines that are preferentially emitted by the torus are likely to be stronger
+supposed to be at or near the temperatures mentioned above.,supposed to be at or near the temperatures mentioned above.
+ The observed structures are: Figs., The observed structures are: Figs.
+" laa, b evidence the co-spatiality of the polar-crown material in both the and channels."," \ref{fig:closeup}a a, b evidence the co-spatiality of the polar-crown material in both the and channels."
+ These snapshots highlight: The latter assumption is also supported by the fact that the cavity has been stable for several hours before the eruption., These snapshots highlight: The latter assumption is also supported by the fact that the cavity has been stable for several hours before the eruption.
+" Even if the location is similar, the U-shaped field lines in both channels are not filled by the corresponding plasma in the same manner: in the channel the length along the U-shaped field lines filled by the coronal plasma appears longer than in the channel."," Even if the location is similar, the U-shaped field lines in both channels are not filled by the corresponding plasma in the same manner: in the channel the length along the U-shaped field lines filled by the coronal plasma appears longer than in the channel."
+ It is important to remember here that the observed structure is integrated along the line-of-sight., It is important to remember here that the observed structure is integrated along the line-of-sight.
+ Therefore limited three dimensional depth information can be derived on the polar crown filament solely from this SDO/AIA dataset only., Therefore limited three dimensional depth information can be derived on the polar crown filament solely from this SDO/AIA dataset only.
+" In order to study the dynamics of the eruption, we first look at several snapshots of the cavity to describe the motions and structures of the polar crown filament."," In order to study the dynamics of the eruption, we first look at several snapshots of the cavity to describe the motions and structures of the polar crown filament."
+ We restrict the dynamical study to the and channels in which the U-shaped structures are clearly seen and also for which there is a minimum of confusion with the background emission (see Fig., We restrict the dynamical study to the and channels in which the U-shaped structures are clearly seen and also for which there is a minimum of confusion with the background emission (see Fig.
+" 1cc, d)."," \ref{fig:closeup}c c, d)."
+ Fig., Fig.
+" 2 outlines a series of images at four characteristic times of the cavity evolution: (a) at 00:03 UT when the cavity is stable at a height of 100 Mm above the surface (projection on the plane of the sky), (b) at 03:24 UT in the early phase of the eruption, (c) at 06:51 UT towards the end of cavity eruption within the SDO/AIA field-of-view, (d) at 09:00 UT, a couple of hours after the cavity has moved into the higher part of the corona, and the plasma and magnetic field lines are still in the process of reorganisation and relaxation."," \ref{fig:evol_cav} outlines a series of images at four characteristic times of the cavity evolution: (a) at 00:03 UT when the cavity is stable at a height of 100 Mm above the surface (projection on the plane of the sky), (b) at 03:24 UT in the early phase of the eruption, (c) at 06:51 UT towards the end of cavity eruption within the SDO/AIA field-of-view, (d) at 09:00 UT, a couple of hours after the cavity has moved into the higher part of the corona, and the plasma and magnetic field lines are still in the process of reorganisation and relaxation."
+" The polar crown material is divided into two parts, namely P1 and P2, that are not distinguishable at first (Fig."," The polar crown material is divided into two parts, namely P1 and P2, that are not distinguishable at first (Fig."
+ 2aa) but can be differentiated in the following frames (Fig., \ref{fig:evol_cav}a a) but can be differentiated in the following frames (Fig.
+ 2bb-c by the solid line parallel to the limb)., \ref{fig:evol_cav}b b-c by the solid line parallel to the limb).
+ P1 corresponds to the main part of the eruptive cavity., P1 corresponds to the main part of the eruptive cavity.
+ In Fig., In Fig.
+" 2bb, the plasma contained in U-shaped fied lines starts to move upwards (as indicated by the left arrow) whilst the plasma on the right-hand side exhibits upwards flows along field lines (right arrow)."," \ref{fig:evol_cav}b b, the plasma contained in U-shaped fied lines starts to move upwards (as indicated by the left arrow) whilst the plasma on the right-hand side exhibits upwards flows along field lines (right arrow)."
+ P2 remains stable., P2 remains stable.
+ In Fig., In Fig.
+" 2cc, the plasma in Pl is detached and thus ejected into the high corona."," \ref{fig:evol_cav}c c, the plasma in P1 is detached and thus ejected into the high corona."
+ P2 starts to rise., P2 starts to rise.
+ In Fig., In Fig.
+" 2dd, only the plasma in P2 remains at this height in the corona whilst P1 continues its way out of the corona."," \ref{fig:evol_cav}d d, only the plasma in P2 remains at this height in the corona whilst P1 continues its way out of the corona."
+ The plasma in P2 is flowing down towards the low corona following the field lines in both channels (see arrows)., The plasma in P2 is flowing down towards the low corona following the field lines in both channels (see arrows).
+" From this time series, it is important to notice that the plasma in both EUV channels are located at the same place below the polar crown cavity, and this is only during the eruptive phase that the decoupling between the two is observed."," From this time series, it is important to notice that the plasma in both EUV channels are located at the same place below the polar crown cavity, and this is only during the eruptive phase that the decoupling between the two is observed."
+" Second, we examine the radial evolution of the cavity at three different locations along the width of the cavity by plotting three adjacent time slices (Figs."," Second, we examine the radial evolution of the cavity at three different locations along the width of the cavity by plotting three adjacent time slices (Figs."
+" 3 and 4)): the middle location (2) corresponds to the minimum height of the cavity above the surface at the beginning of the time series, whilst locations (1) and (3) are symmetrically on both sides of the minimum height."," \ref{fig:cut304} and \ref{fig:cut171}) ): the middle location (2) corresponds to the minimum height of the cavity above the surface at the beginning of the time series, whilst locations (1) and (3) are symmetrically on both sides of the minimum height."
+ The cavity appears in the top left corner of the time slices and the bottom of the cavity is first located at about 90 Mm at and 100 Mm at171A.., The cavity appears in the top left corner of the time slices and the bottom of the cavity is first located at about 90 Mm at and 100 Mm at.
+" Even if the motion of the cavity is not entirely in the radial direction, the three time slices show the behaviour of a large portion of the cavity during the eruption: the similar evolution in all three slices supports the assumption that the cavity evolves as a solid body."," Even if the motion of the cavity is not entirely in the radial direction, the three time slices show the behaviour of a large portion of the cavity during the eruption: the similar evolution in all three slices supports the assumption that the cavity evolves as a solid body."
+ We note, We note
+The brute-force algorithm is the simplest and most accurate to implement for ce-cispersion of incoherent data. but is also the least cllicient processing wise.,"The brute-force algorithm is the simplest and most accurate to implement for de-dispersion of incoherent data, but is also the least efficient processing wise."
+" Assuming A’. samples. cach with A. channels. and de-dispersing for Npay DM values. the algorithmic time complexity of the brute force algorithm is OQGN,5NowUINpar)."," Assuming $N_s$ samples, each with $N_c$ channels, and de-dispersing for $N_{DM}$ DM values, the algorithmic time complexity of the brute force algorithm is $\mathcal{O}\left(N_s\times N_c \times
+ N_{DM}\right)$."
+" UNS can be seen as an infinite stream of samples. while IN, and Nowy will usually have a similar value. resulting in approximately AW operations for every input sample."," $N_s$ can be seen as an infinite stream of samples, while $N_c$ and $N_{DM}$ will usually have a similar value, resulting in approximately $N^2$ operations for every input sample."
+ According to (72) there are three main ways in which his algorithm can be parallelized: The current implementation uses a variant of scheme (a). where cach thread sums up the input for a single time sample.," According to \citep{Barsdell2010} there are three main ways in which this algorithm can be parallelized: The current implementation uses a variant of scheme (a), where each thread sums up the input for a single time sample."
+ Due to the kuge number of samples which can fit in GPU memory. cach thread will end up processing more han one sample.," Due to the large number of samples which can fit in GPU memory, each thread will end up processing more than one sample."
+ A wav to envisage this is to imagine the CUDA eric as à sliding window which moves along the input samples at discrete intervals equal to the total number of threads in one row., A way to envisage this is to imagine the CUDA grid as a sliding window which moves along the input samples at discrete intervals equal to the total number of threads in one row.
+ At cach grid. position. threads. are assigned to their respective samples.," At each grid position, threads are assigned to their respective samples."
+ The kernel can process any number of DAL values concurrentIv. and this is done by creating a two-dimensional eric. where each row is assigned a different DAL value [or de-dispersion.," The kernel can process any number of DM values concurrently, and this is done by creating a two-dimensional grid, where each row is assigned a different DM value for de-dispersion."
+ The output of Np time-series. each with iV. samples. is output to the output thread for post-processing.," The output of $N_{DM}$ time-series, each with $N_s$ samples, is output to the output thread for post-processing."
+ This kernel is not. very compute-intensive. performing less than ten Loating point operations per elobal memory read.," This kernel is not very compute-intensive, performing less than ten floating point operations per global memory read."
+ This makes the cde-dispersion. algorithm: For this reason. depending on the way the data are read from the input device. a corner-turn (matrix transpose) night be required in order to store the data in channel order.," This makes the de-dispersion algorithm For this reason, depending on the way the data are read from the input device, a corner-turn (matrix transpose) might be required in order to store the data in channel order."
+ With this memory setup. and having cach thread: process one sample for one DAL value. threads within a half warp (16 threads) will access the input bulfer in a quasi-fully coalescecl manner.," With this memory setup, and having each thread process one sample for one DM value, threads within a half warp (16 threads) will access the input buffer in a quasi-fully coalesced manner."
+ This also applies for storing the result in the output bulfer since all threads within a row will shift by the same amount. resulting in stores which are performed in a coalesced manner as well.," This also applies for storing the result in the output buffer since all threads within a row will shift by the same amount, resulting in stores which are performed in a coalesced manner as well."
+ Shared. memory is also used. to reduce global memory reads., Shared memory is also used to reduce global memory reads.
+ Each output value requires A. additions. and performing these additions in global memory would reduce performance drastically.," Each output value requires $N_c$ additions, and performing these additions in global memory would reduce performance drastically."
+ To counter this. cach thread. is assigned a cell in shared. memory where the additions are performed.," To counter this, each thread is assigned a cell in shared memory where the additions are performed."
+ “Phe final result is then copied to global memory., The final result is then copied to global memory.
+ Subbancl ce-clispersion uses aspects of brute-force de-dispersion. however it is also intlueneec by the tree algorithm. which reuses sums of groups of [frequency channels for different DAL values.," Subband de-dispersion uses aspects of brute-force de-dispersion, however it is also influenced by the tree algorithm, which reuses sums of groups of frequency channels for different DM values."
+ Lt relies on the fact tha acjacent DAL values (given an appropriate DAL step) wil use overlapping samples during the summation. so it splits up the DAL range into several sub-ranges. cach centre around a nominal DAL value.," It relies on the fact that adjacent DM values (given an appropriate DM step) will use overlapping samples during the summation, so it splits up the DM range into several sub-ranges, each centred around a nominal DM value."
+ The bandwidth is also spli into several subbands. resulting in a partitioning of the se of channels.," The bandwidth is also split into several subbands, resulting in a partitioning of the set of channels."
+ Ehe delays corresponding to the nominal D for every channel in a subband. minus the delav at the highest frequency in that subbancl. are subtracted from each subband channel.," The delays corresponding to the nominal DM for every channel in a subband, minus the delay at the highest frequency in that subband, are subtracted from each subband channel."
+ This results in a partially cde-clispersed se of subbancds., This results in a partially de-dispersed set of subbands.
+ This scheme is depicted in figure 3.., This scheme is depicted in figure \ref{subbandDedispFigure}.
+ Norma de-dispersion is then used to generate the de-dispersed time series for the rest of the DAL values within the same D sub-range., Normal de-dispersion is then used to generate the de-dispersed time series for the rest of the DM values within the same DM sub-range.
+ Depending on the number of subbands used. the size of the DAL ranges. as well as other factors. we can limit the error induced in the result by these approximations.," Depending on the number of subbands used, the size of the DM ranges, as well as other factors, we can limit the error induced in the result by these approximations."
+ Further, Further
+αοανν minimum occurred and how different it was [rom previously recorded minima.,activity minimum occurred and how different it was from previously recorded minima.
+ A variety of data [rom the solar interior to the corona has been analvzed to seek the origin ol such an unusually low solar activity for a long duration (e.g.. see articles in Cranmer. ]loeksema Ixohl 2010).," A variety of data from the solar interior to the corona has been analyzed to seek the origin of such an unusually low solar activity for a long duration (e.g., see articles in Cranmer, Hoeksema Kohl 2010)."
+ All of these analvses indicate that the ciurent minimum was nich deeper (han previous ones in modern era., All of these analyses indicate that the current minimum was much deeper than previous ones in modern era.
+ Since the source of solar activitv is believed to lie in ashear laver at the base of the convection zone. known as the tachocline. the analysis of heloseisnuc data is important in order to probe these regions.," Since the source of solar activity is believed to lie in a shear layer at the base of the convection zone, known as the tachocline, the analysis of helioseismic data is important in order to probe these regions."
+ Fortunately. the availability of continuous. consistent helioseisimic data for two consecutive solar minima has provided a unique opportunity to study the changes in the solar interior (hat might have led to (his unusual minimuni.," Fortunately, the availability of continuous, consistent helioseismic data for two consecutive solar minima has provided a unique opportunity to study the changes in the solar interior that might have led to this unusual minimum."
+ Using Dirningham Solar-Oscillation Network (DiSON) frequencies of low-angular degree (f« 3) modes for about three solar eveles. Broomballetal.(2009). found that the frequencies were significantly lower in the extended minimum as compared to those during ihe previous ones.," Using Birmingham Solar-Oscillation Network (BiSON) frequencies of low-angular degree $\ell \le$ 3) modes for about three solar cycles, \citet{bison09} found that the frequencies were significantly lower in the extended minimum as compared to those during the previous ones."
+ Similar results were obtained by Salabertetal.(2009) in an analvsis based on (he data collected by the space-based Global Oscillations at Low Frequencies (GOLF) on board the(SOIIO) spacecraft1995)., Similar results were obtained by \citet{david09} in an analysis based on the data collected by the space-based Global Oscillations at Low Frequencies (GOLF) on board the spacecraft.
+ They further pointed out that evele 24 started in late 2007. despite the absence of anv visible activity on the solar surface.," They further pointed out that cycle 24 started in late 2007, despite the absence of any visible activity on the solar surface."
+ The analvses of modes in intermeciate-degree range between 20 and 150. obtained from the Global Oscillation Network Group (GONG: Harvey (1996))). also showed lower oscillations Irequencies during (he recent minimum (JainTripathyοἱal. 2010).. however these studies did not identify (he minimum as occurring until the end of 2008. leading to an extended phase of low activity.," The analyses of modes in intermediate-degree range between 20 and 150, obtained from the Global Oscillation Network Group (GONG: \citet{harvey96}) ), also showed lower oscillations frequencies during the recent minimum \citep{jain10, sct10b}, however these studies did not identify the minimum as occurring until the end of 2008, leading to an extended phase of low activity."
+ Furthermore. the zonal and meridional flow patterns inferred [rom inverting frequencies also suggested a delaved onset of the new evele.," Furthermore, the zonal and meridional flow patterns inferred from inverting frequencies also suggested a delayed onset of the new cycle."
+ Loweetal.(2009) compared the evolution of the zonal flow pattern in the upper convection zone and suggested that the mid-Iatitude flow baud corresponding to the recent evele moved more slowly towards the equator than was observed, \citet{howe09} compared the evolution of the zonal flow pattern in the upper convection zone and suggested that the mid-latitude flow band corresponding to the recent cycle moved more slowly towards the equator than was observed
+stable circular orbit around a neutron star.,stable circular orbit around a neutron star.
+ In this paper. we revisit (he RATE observations reported by Sannaetal.(2010). focussing on the lower kHz QPO. and apply the same analysis procedures (frequency. αν! correction) as described in Barretetal.(2006)..," In this paper, we revisit the RXTE observations reported by \citet{sanna10mnras}, focussing on the lower kHz QPO, and apply the same analysis procedures (frequency drift correction) as described in \citet{barret06mnras}."
+ The main reason is (hat. despite very [ew detections overall (12 segments of observations in total). the frequency. span of the lower kllz QPO ranges from about 640 Hz to 850 IIz. aud by comparison wilh other sources. this should be sullicient to investigate the drop of its quality factor (no such drop is obvious in Figure 3 of Sannaetal.(2010) who used a different analvsis than Barretοἱal.(2006))).," The main reason is that, despite very few detections overall (12 segments of observations in total), the frequency span of the lower kHz QPO ranges from about 640 Hz to 850 Hz, and by comparison with other sources, this should be sufficient to investigate the drop of its quality factor (no such drop is obvious in Figure 3 of \citet{sanna10mnras} who used a different analysis than \citet{barret06mnras}) )."
+ In the next section. we describe (he re-analvsis of the lower kIIz QPOs reported by to show that the drop of its quality factor and RATS amplitude is indeed observed.," In the next section, we describe the re-analysis of the lower kHz QPOs reported by \citet{sanna10mnras} to show that the drop of its quality factor and RMS amplitude is indeed observed."
+ We then discuss the changes in the properties of the QPOs from NTE J1101.462 as simply related to a likely decrease of the disk thickness between the Z and atoll phases. as previously discussed in (he framework of the tov model presented in Barretetal.(2007).," We then discuss the changes in the properties of the QPOs from XTE J1701–462 as simply related to a likely decrease of the disk thickness between the Z and atoll phases, as previously discussed in the framework of the toy model presented in \citet{barret07mnras}."
+ We follow the definition of the Z and atoll states as in Sannaetal.(2010): the separation is estimated. around the end of April 2007., We follow the definition of the Z and atoll states as in \citet{sanna10mnras}: the separation is estimated around the end of April 2007.
+ We have retrieved from the IEASARC archive science event mode and single bit data recorded by the RATE Proportional Counter Array (PCA)., We have retrieved from the HEASARC archive science event mode and single bit data recorded by the RXTE Proportional Counter Array (PCA).
+ We consider data as segments of continuous observation (an ObsID may contain more than 1 segment)., We consider data as segments of continuous observation (an ObsID may contain more than 1 segment).
+ For each segment. we have computed an average Power Density Spectrum (PDS) with a 1 Iz resolution and an integration time of 16 seconds. using events recorded between 2 and 40 keV. The PDS are normalized according to Leahyetal.(1933).. so that the Poisson noise level is expected to be a constant close to 2.," For each segment, we have computed an average Power Density Spectrum (PDS) with a 1 Hz resolution and an integration time of 16 seconds, using events recorded between 2 and 40 keV. The PDS are normalized according to \citet{Leahy:1983mb}, so that the Poisson noise level is expected to be a constant close to 2."
+ The PDS is then blindly searched for excess power between 500 Iz and 1400 Lz using a scanning technique. as presented in Doirinetal.(2000)..," The PDS is then blindly searched for excess power between 500 Hz and 1400 Hz using a scanning technique, as presented in \citet{Boirin:2000jt}."
+ We have also verified that no significant excesses were detected between 1400 and 2048 Hz., We have also verified that no significant excesses were detected between 1400 and 2048 Hz.
+ This justifies the use of the 1400—2048 Iz range to estimate accurately the Poisson noise level in each observation. which is indeed close (ο 2 in all segments of data.," This justifies the use of the $1400-2048$ Hz range to estimate accurately the Poisson noise level in each observation, which is indeed close to 2 in all segments of data."
+ The excess power is (hen fitted with a Lorentzian with three free parameters: Ireeuency. Full width at half maximum. and amplitude (equal to the integrated power of the Lorentzian).," The excess power is then fitted with a Lorentzian with three free parameters; frequency, full width at half maximum, and amplitude (equal to the integrated power of the Lorentzian)."
+ The Poisson noise level is fitted separately above 1400 Hz., The Poisson noise level is fitted separately above 1400 Hz.
+ confidence errors on each parameter are computed in a standard way. using a A\? of 1.," confidence errors on each parameter are computed in a standard way, using a $\Delta\chi^2$ of $1$ ."
+ Following (2009).. our threshokl for QPOs is relatedto the ratio (hereafter 0) of the Lorentzian amplitude to its Lo ," Following \citet{boutelier09mnras}, our threshold for QPOs is relatedto the ratio (hereafter $R$ ) of the Lorentzian amplitude to its $1\sigma$ "
+xogresses during the last wears.,progresses during the last years.
+ It shows that O4=0 open-universes with Oy«OL are inconsistent with the observations while a flat-universe with Q4=0.6 or with Ου=1 are acceptable., It shows that $\Omega_{\Lambda}= 0$ open-universes with $\Omega_0< 0.4$ are inconsistent with the observations while a flat-universe with $\Omega_{\Lambda}= 0.6$ or with $\Omega_0= 1$ \cite{Gardner1997} are acceptable.
+ Many others good constraints of he value of Qy come from the study of masses couteut in clusters of ealaxics. he largest (well) observed structures in the Universe.," Many others good constraints of the value of $\Omega_0$ come from the study of masses content in clusters of galaxies, the largest (well) observed structures in the Universe."
+" Their barvou fraction inferred from X-ray studies allows to deduce that O4=0.3240.2 19 and heir galaxies velocity fields eive imply that Oy=0.300.1 29., whereas the direct lensing measurements of their total gravitational masses within a radius of 0.5 Mpe gives Oy in the range = 0.2-0.5 (cf Mellier et al. this conference)."," Their baryon fraction inferred from X-ray studies allows to deduce that $\Omega_0 = 0.32 \pm 0.2$ \cite{Whiteetal1993} and their galaxies velocity fields give imply that $\Omega_0 = 0.3 \pm 0.1$ \cite{Carlbergetal1997}, whereas the direct lensing measurements of their total gravitational masses within a radius of 0.5 Mpc gives $\Omega_0$ in the range = 0.2-0.5 (cf Mellier et al, this conference)."
+ With the weak lensing method. higher lensing deusities corresponding to Oy close to 1 cannot be excluded from some teutative measurcients of extremely weak gravitational shear in volume of several Mpe-sizes arouud cluster centers (Mellier ct al.," With the weak lensing method, higher lensing densities corresponding to $\Omega_0$ close to 1 cannot be excluded from some tentative measurements of extremely weak gravitational shear in volume of several Mpc-sizes around cluster centers (Mellier et al.,"
+ this proceeding)., this proceeding).
+" But for such observations the correction of instruuneutal+ distortion. may not vet be fillyB under control 01,22σοι, "," But for such observations the correction of instrumental distortion may not yet be fully under control \cite{bm95}$ $^{\!,\,}$ \cite{kaiseretal95}."
+Surprisingly+sos the lensing results obtained for largescale structures seenis comparable to those coming from the latest interpretation of large cosmic fows '.., Surprisingly the lensing results obtained for largescale structures seems comparable to those coming from the latest interpretation of large cosmic flows \cite{Deckel1997}.
+ Note that the lensing method seems more reliable aud is able to progress siguificautlv iu the near future., Note that the lensing method seems more reliable and is able to progress significantly in the near future.
+ Therefore. the most likely value for Ορ emcereiug frou all these observational: constraints: «cenis equal to 0.3!410.2ne," Therefore, the most likely value for $\Omega_0$ emerging from all these observational constraints seems equal to $0.3^{+0.2}_{-0.1}$."
+ At least. one crucial tests on O4 for flat models is now eicereiue from the observations of higli-z 3uperuovac.," At least, one crucial tests on $\Omega_{\Lambda}$ for flat models is now emerging from the observations of high-z supernovae."
+" It allows in principle the determination of the acceleration paraiucter gq,=0/2.04/2 with an accuracy of 0.2 as soon as we will be able to detect aud observe a sample of SNs at 2> 124.", It allows in principle the determination of the acceleration parameter $q_o= \Omega/2-\Omega_{\Lambda}/2$ with an accuracy of $\pm$ 0.2 as soon as we will be able to detect and observe a sample of SNs at $z > 1$ \cite{GoodbarandPerlmutter1995}.
+ So far. with. a sample of DADSNs only at τς0.1 Perliuitter et al," So far, with a sample of SNs only at $z < 0.4$ Perlmutter et al."
+"""25 note that qy could be actually in- the 0-0.5 interval.", \cite{Pelmutteretal1996} note that $q_0$ could be actually in the 0-0.5 interval.
+. Similarly.aeB Deuder ot al.," Similarly, Bender et al."
+ Dο recently demonstrate that we can actually use cluster ellipticals as cosmological candles., \cite{Benderetal} recently demonstrate that we can actually use cluster ellipticals as cosmological candles.
+ With two clusters at 2=0.375 they tentatively found gy iu the range 0-0.7., With two clusters at $z=0.375$ they tentatively found $q_0$ in the range 0-0.7.
+ It is clear that such new observational tests do not mach favor the Cosmic Concordance paracdigin., It is clear that such new observational tests do not much favor the Cosmic Concordance paradigm.
+ They can progress a lot if suitable telescope tine is given to these programs and we are expecting a lot from them for a direct measurement of du., They can progress a lot if suitable telescope time is given to these programs and we are expecting a lot from them for a direct measurement of $q_0$.
+ Hence. to the light of all these results. it becomes interesting to look at au other set of almost independent tests on O4: the leusine tests.," Hence, to the light of all these results, it becomes interesting to look at an other set of almost independent tests on $\Omega_{\Lambda}$: the lensing tests."
+ The most classical oues concern the frequency of iiultiply imaged quasars. that in fact probes the volume of the Universe per πια redshift at large distance. or the probability distribution of the redshifts and the distribution of the separation of the multiple leused inages which depeud also on O4.," The most classical ones concern the frequency of multiply imaged quasars, that in fact probes the volume of the Universe per unit redshift at large distance, or the probability distribution of the redshifts and the distribution of the separation of the multiple lensed images which depend also on $\Omega_{\Lambda}$ ."
+ Many works were, Many works were
+and [GM trom 2~5 to 2=0.,and IGM from $z\sim 5$ to $z=0$.
+" Specifically. for the ISM we took logy,Z/Z.=-O.8+0.2 at 2—0 and —OQ.9+0.2 at z— L"," Specifically, for the ISM we took $\log_{10}{Z/Z_\mathrm{\odot}}=-0.3\pm 0.2$ at $z=0$ and $-0.9\pm 0.2$ at $z=4$ ."
+"L For the IGM we took. logy,Z/Z.=—2.50.2 at 2—0 and —3.10.2 at z= [L(??2???).."," For the IGM we took, $\log_{10}{Z/Z_\mathrm{\odot}}=-2.5\pm 0.2$ at $z=0$ and $-3.1\pm 0.2$ at $z=4$ \citep{prochaska:03,ledoux:03,songaila:01,schaye:03,aguirre:04}."
+ These constraints are chosen so that the metallicity in the ISM. (IGM) is always largere (sinaller) than in the most (east) metallic DLA., These constraints are chosen so that the metallicity in the ISM (IGM) is always larger (smaller) than in the most (least) metallic DLA.
+ The dominant elfect «X inchcling the massive mode will fall on the metallicity ο ‘the IC] aud will be discussed it sectio 19 beOW., The dominant effect of including the massive mode will fall on the metallicity of the IGM and will be discussed in section 5 below.
+ The results of t 9 ∐↵∖−∐⊔∐∐∐⋅⋅⋅gation are listed in Table 1 sepa‘ately [or each value of Mii., The results of the $\chi^2$ minimization are listed in Table \ref{tab:model0} separately for each value of $M_\mathrm{min}$.
+ Having fixed the onset of star fornation ο correspond to au initial baryo1 [racion of154.. each value of M leads O a distinct 'ecesluft or iuitial star formation.," Having fixed the onset of star formation to correspond to an initial baryon fraction of, each value of $M_\mathrm{min}$ leads to a distinct redshift for initial star formation."
+ This vaue of Zini Is also given in the table., This value of $z_\mathrm{init}$ is also given in the table.
+ In eacl Case. we [οι ida best fit INF slope of ary=1.3.," In each case, we found a best fit IMF slope of $x_1 = 1.3$."
+ lt shouk be remembered that when we add iu the 1lassive noce. jese best! fits have to be modified iu order to take iuto accouut the metals »rocdu«ed by »opulatiou HI stars.," It should be remembered that when we add in the massive mode, these `best' fits have to be modified in order to take into account the metals produced by population III stars."
+ This will affect ouly the efficiency. of the outflow. e. as the otler pameters control the later pliases of evolution.," This will affect only the efficiency of the outflow, $\epsilon$, as the other parameters control the later phases of evolution."
+ Of the sampled values of Αμ. Adinin10: . Was fouuc to givetie best fit.," Of the sampled values of $M_\mathrm{min}$, $M_\mathrm{min} = 10^7$ $_\odot$ was found to give the best fit."
+ However if the observed SER at high redshift (2> 3) has been uixerestiuated. the best fit mocel may be at lower values of Admin.," However if the observed SFR at high redshift $z>3$ ) has been underestimated, the best fit model may be at lower values of $M_\mathrm{min}$."
+ For example. we find that Adin=108 becoijes a better fit if the high redshilt SER data are tucreased by a factor ~3.," For example, we find that $M_\mathrm{min}=10^{6}\ \mathrm{M_{\odot}}$ becomes a better fit if the high redshift SFR data are increased by a factor $\sim 3$."
+ Also show. in the table are the outout. values for the baryon fraction in structures and in stars., Also shown in the table are the output values for the baryon fraction in structures and in stars.
+ Note that noie of the mocels accuratey reproduce the sellar barvou fraction a 2=0.In each case. we over-produce stars at a level of a)»ut lo.," Note that none of the models accurately reproduce the stellar baryon fraction at $z = 0$.In each case, we over-produce stars at a level of about $\sigma$."
+" The results of our best fit mocels are plotted in Figure 3 lor each value Ag, as itdicated in the upper panel.", The results of our best fit models are plotted in Figure \ref{fig:model0SFRZ} for each value $M_\mathrm{min}$ as indicated in the upper panel.
+ Because we have fixed the initial baryon fraction in structures. each valte of. Ay corresponds to a clilferent initial redshift.," Because we have fixed the initial baryon fraction in structures, each value of $M_\mathrm{min}$ corresponds to a different initial redshift."
+ As oie cali see. eachof he moclels gives a satisfactory [it to the global SER. save perhaps the case with Admin=LOM M... T1ο data shown (taken DL ‘om? has," As one can see, eachof the models gives a satisfactory fit to the global SFR, save perhaps the case with $M_\mathrm{min} = 10^{11}$ $_\odot$ The data shown (taken from \citet{hopkins:04} has"
+much a model but. instead. derives from a fit to the observed mass density profile for Dz3 kkpe (see Table 2)).,"much a model but, instead, derives from a fit to the observed mass density profile for $\gtrsim 3$ kpc (see Table \ref{tab:fit_pure_pl}) )."
+ These high Q values thus illustrate furthermore that the evolved. mass density. profile mirrors faithfully the initial one., These high $Q$ values thus illustrate furthermore that the evolved mass density profile mirrors faithfully the initial one.
+ As for the evolved number density. profile. this agrees with the data only if the eglobular cluster svstem started with either a gaussian mass function or à power-law mass spectrum. truncated. at 107 MM.," As for the evolved number density profile, this agrees with the data only if the globular cluster system started with either a gaussian mass function or a power-law mass spectrum truncated at $^5$ $_{\odot}$."
+ In case of a power-law mass spectrum probing down to low cluster mass. the ( values get extremely low. disproving such initial mass spectra.," In case of a power-law mass spectrum probing down to low cluster mass, the $Q$ values get extremely low, disproving such initial mass spectra."
+ This discrepancy. results. from the sharp change experienced. by the slope of the number. density profile (panel h] in Fig. 2)).," This discrepancy results from the sharp change experienced by the slope of the number density profile (panel [h] in Fig. \ref{fig:nD3.5_evol}) ),"
+" leading to a present steepness significantly shallower (o 2.5) than the observed. one (~3.45. see ""Table 2))."," leading to a present steepness significantly shallower $\simeq -2.5$ ) than the observed one $\simeq -3.5$, see Table \ref{tab:fit_pure_pl}) )."
+ As a result. examination of Fig.," As a result, examination of Fig."
+ 2 and Table 4 shows that the comparison of the evolved (i.c... modelled) ancl observed: radial density proliles. manber. enables us to constrain the initial mass spectrum of globular clusters.," \ref{fig:nD3.5_evol} and Table \ref{tab:fit_evol_GCS} shows that the comparison of the evolved (i.e., modelled) and observed radial density profiles, , enables us to constrain the initial mass spectrum of globular clusters."
+ The Q values stronglv favour either an initial gaussian mass function or a power-law with slope of order —1.9 and truncated at large mass. around LO’ MM... that is. an initial mass distribution which is somehow depleted. in low-mass objects.," The $Q$ values strongly favour either an initial gaussian mass function or a power-law with slope of order $-1.9$ and truncated at large mass, around $^5$ $_{\odot}$, that is, an initial mass distribution which is somehow depleted in low-mass objects."
+ In this respect. our results confirm those achieved by Vesperini (1998).," In this respect, our results confirm those achieved by Vesperini (1998)."
+" We now consider the steeper initial spatial distribution. namely n;,;xD.oto."," We now consider the steeper initial spatial distribution, namely $n_{init} \propto D^{-4.5}$."
+ As already suggested by Baunigarclt (1998). there is an excellent. agreement. between the halo number density. profile and its modelled counterpart in the case ofa power-law extending down to MAL.. especially if disc shocking is taken into account.," As already suggested by Baumgardt (1998), there is an excellent agreement between the halo number density profile and its modelled counterpart in the case of a power-law extending down to $_{\odot}$, especially if disc shocking is taken into account."
+ Owing to the large contribution of low-mass clusters. the initially steep profile is turned into a shallower one. thus matching the halo —3.5 slope.," Owing to the large contribution of low-mass clusters, the initially steep profile is turned into a shallower one, thus matching the halo $-3.5$ slope."
+ However. we caution that the evolved. mass density profile does not fit its Old Halo counterpart convincingly in any case.," However, we caution that the evolved mass density profile does not fit its Old Halo counterpart convincingly in any case."
+ The best match is obtained for a globular cluster system with a power-law initial mass spectrum. probing down to low-mass (see Table 4))., The best match is obtained for a globular cluster system with a power-law initial mass spectrum probing down to low-mass (see Table \ref{tab:fit_evol_GCS}) ).
+ Even though such a possibility cannot be ruled out firmly. the goodness-ol-fit is very marginal (QS 0.001).," Even though such a possibility cannot be ruled out firmly, the goodness-of-fit is very marginal $Q \lesssim0.001$ )."
+ This case is therefore much less likely than the one we have previously. discussed. namely. a globular cluster system: whose initial spatial steepness is similar to the present one.," This case is therefore much less likely than the one we have previously discussed, namely, a globular cluster system whose initial spatial steepness is similar to the present one."
+ Baumearelt (1998). himself. noted. the odcditv of. this result as it implies a discrepancy. between the initial slope of the elobular cluster spatial distribution on the one hand and the steepness of the stellar halo density. profile on the other hand., Baumgardt (1998) himself noted the oddity of this result as it implies a discrepancy between the initial slope of the globular cluster spatial distribution on the one hand and the steepness of the stellar halo density profile on the other hand.
+ Indeed. the space-density. of halo RRO Lyrac (Suntzell. Winman Ixraft. 1901) as well as of halo blue horizontal branch stars (Ixinman. Suntzell να 1994) falls olf as D..," Indeed, the space-density of halo RR Lyrae (Suntzeff, Kinman Kraft 1991) as well as of halo blue horizontal branch stars (Kinman, Suntzeff Kraft 1994) falls off as $D^{-3.5}$."
+ Baumgardt (1998) suggests that this cliscrepaney results [rom a varving star cluster to field star formation cllicicney., Baumgardt (1998) suggests that this discrepancy results from a varying star cluster to field star formation efficiency.
+ Considering the 6) values. listed in ‘Table 4.. a much safer conclusion may be that the elobular cluster system started with a space-density scaling as D.757 coupled with either a gaussian mass function or a power-law truncated at 107 MM.," Considering the $Q$ values listed in Table \ref{tab:fit_evol_GCS}, a much safer conclusion may be that the globular cluster system started with a space-density scaling as $D^{-3.5}$ coupled with either a gaussian mass function or a power-law truncated at $^5$ $_{\odot}$."
+ While our simulations start with many thousands of clusters. the survival rates £y (quoted in ‘Table 3 indicate that the initial number of clusters is on the order of that today in case of a gaussian initial mass function or in case of a power-law niass spectrum truncated at LO? MAL..," While our simulations start with many thousands of clusters, the survival rates $F_N$ quoted in Table \ref{tab:frac_surv} indicate that the initial number of clusters is on the order of that today in case of a gaussian initial mass function or in case of a power-law mass spectrum truncated at $10^5$ $_{\odot}$."
+ As for the eaussian initial mass function. we have checked that an initial total number of clusters of 200 only does not introduce a significant scatter in the evolved mass density profile with respect to the size of the error. bars.," As for the gaussian initial mass function, we have checked that an initial total number of clusters of 200 only does not introduce a significant scatter in the evolved mass density profile with respect to the size of the error bars."
+ Using Vesperini llegeie 's (1997) model with dise shocking and considering a slope 5=38.5 for the initial radial distribution. the incomplete emma function for the evolved: mass density profile (λος)=0.2) ranges from 0.3 up to 0.9 (10 random samplings of the gaussian cluster IME).," Using Vesperini Heggie 's (1997) model with disc shocking and considering a slope $\gamma = -3.5$ for the initial radial distribution, the incomplete gamma function for the evolved mass density profile $\Delta log D = 0.2$ ) ranges from 0.3 up to 0.9 (10 random samplings of the gaussian cluster IMF)."
+ We note that these results are obtained in case of a eaussian truncated at in order to avoicl the presence of. clusters significantly1.5126 more massive than is observed today., We note that these results are obtained in case of a gaussian truncated at $_{\odot}$ in order to avoid the presence of clusters significantly more massive than is observed today.
+ Actually. inspection of the luminous mass estimates of the halo elobular clusters shows LO? MM. to be an upper limit to the present-day globular cluster mass.," Actually, inspection of the luminous mass estimates of the halo globular clusters shows $10^6$ $_{\odot}$ to be an upper limit to the present-day globular cluster mass."
+ More massive clusters do actually exist. e.g. w Con. M54 (Sagittarius core). NGC 2419 and a few disc clusters. but none of them are relevant to the present study.," More massive clusters do actually exist, e.g., $\omega$ Cen, M54 (=Sagittarius core), NGC 2419 and a few disc clusters, but none of them are relevant to the present study."
+ Itunning the same simulations in case of a non-trunecated eaussian. the incomplete eamma function tends to ect smaller (i0. down to 0.002 in one case).," Running the same simulations in case of a non-truncated gaussian, the incomplete gamma function tends to get smaller (i.e., down to 0.002 in one case)."
+ This is due to the occasional sampling of very massive (1.0.2 MAL.) clusters. giving rise to an upwards scatter in the outermost least-populated: bins of the mass density profile.," This is due to the occasional sampling of very massive $>$ $_{\odot}$ ) clusters, giving rise to an upwards scatter in the outermost least-populated bins of the mass density profile."
+ As for the case of a power-law mass spectrum truncated at 10 MM... we have evolved. a cluster svsten initially comprising 150 clusters. only.," As for the case of a power-law mass spectrum truncated at $10^5$ $_{\odot}$, we have evolved a cluster system initially comprising 150 clusters only."
+ The incomplete gamma function for the evolved: mass density. profile ranges [rom 0.01 to 0.7 (10 random realisations. of which SN give Q70.1).," The incomplete gamma function for the evolved mass density profile ranges from 0.01 to 0.7 (10 random realisations, of which 8 give $Q > 0.1$ )."
+ This robustness. despite a limited number of clusters. is due to the narrow mass range associated to the truncation at large cluster mass.," This robustness, despite a limited number of clusters, is due to the narrow mass range associated to the truncation at large cluster mass."
+ 1n fact. our results are reminiscent of those obtained » Vesperini (2000. 2001) in the case of globular cluster systems hosted ον elliptical galaxies.," In fact, our results are reminiscent of those obtained by Vesperini (2000, 2001) in the case of globular cluster systems hosted by elliptical galaxies."
+ Investigating the case of a power-law initial mass spectrum extending down to ow-mass combined with a coreless D520 initial. number density profile. Vesperini (2001) noted that the evolutionary »ocesses produce a significant dependence of the average cluster mass on the galactocentric distance in the sense hat clusters located in the inner galactic regions are more massive.," Investigating the case of a power-law initial mass spectrum extending down to low-mass combined with a coreless $D^{-3.5}$ initial number density profile, Vesperini (2001) noted that the evolutionary processes produce a significant dependence of the average cluster mass on the galactocentric distance in the sense that clusters located in the inner galactic regions are more massive."
+ This dependence is equivalent. to the dilference tween the slopesof the evolved mass and number density »ofiles highlighted in the bottom panels of Fig., This dependence is equivalent to the difference between the slopesof the evolved mass and number density profiles highlighted in the bottom panels of Fig.
+ 2., 2.
+ Vesperini κ (2001) result contrasts with several observational stuclies hat fail to find a significant. raclial gradient of the average, Vesperini 's (2001) result contrasts with several observational studies that fail to find a significant radial gradient of the average
+enerev returns (o the disk.,energy returns to the disk.
+ If the mass per unit enerev of tidally disrupted matter is Independent of binding energy. the accretion rate into the disk at radii ~Πρ falls x(/Iy) 77. where ly~Pos(min) (Rees1988:Phinney1989).," If the mass per unit energy of tidally disrupted matter is independent of binding energy, the accretion rate into the disk at radii $\sim R_p$ falls $\propto (t/t_0)^{-5/3}$ , where $t_0 \sim P_{\rm orb}(a_{\rm min})$ \citep{rees88,phinney89}."
+. Lodatoetal.(2009). found that. depending on (he degree of density concentration in the star. (he mass accretion rate might [all more shallowly than this when /=/). but gradually tends toward /77 when i>dg.," \cite{lkp09} found that, depending on the degree of density concentration in the star, the mass accretion rate might fall more shallowly than this when $t \gtrsim t_0$ but gradually tends toward $t^{-5/3}$ when $t \gg t_0$."
+ ME nearly all the matter returning to the disk makes it all the wav to the black hole. the time-dependence of the accretion relevant to the disk aud jet powers should match the time-dependence of the accretion rate reaching the outer disk: il. however. super-Edclinetou conditions lead to a significant Iraction being expelled. the accretion rate reaching the event horizon [alls more slowly because the expelled fraction can also be expected to diminish.," If nearly all the matter returning to the disk makes it all the way to the black hole, the time-dependence of the accretion relevant to the disk and jet powers should match the time-dependence of the accretion rate reaching the outer disk; if, however, super-Eddington conditions lead to a significant fraction being expelled, the accretion rate reaching the event horizon falls more slowly because the expelled fraction can also be expected to diminish."
+ When ti first begins to decrease. the thermal radiation hardly changes because photon-trapping continues (o limit Liga to Lp.," When $\dot m$ first begins to decrease, the thermal radiation hardly changes because photon-trapping continues to limit $L_{\rm therm}$ to $L_E$."
+ Consequently. in the period near and shortly after the peak Iuminositv. the thermal light curve should be almost flat. and only slowly roll over toward (0/14)," Consequently, in the period near and shortly after the peak luminosity, the thermal light curve should be almost flat and only slowly roll over toward $(t/t_0)^{-5/3}$."
+ On the other hand. Lj4 in those sources is xqiii. so the jet power falls. provided the accretion rate reaching (he black hole is truly. super-Ecdington.," On the other hand, $L_{\rm jet}$ in those sources is $\propto q\dot m$, so the jet power falls, provided the accretion rate reaching the black hole is truly super-Eddington."
+ The rate of decrease may be slower than /eeSAR if q increases asm falls., The rate of decrease may be slower than $t^{-5/3}$ if $q$ increases as $\dot m$ falls.
+ With declining mi. the black hole mass at which the flow switches from non-radiative to radiative also decreases.," With declining $\dot m$, the black hole mass at which the flow switches from non-radiative to radiative also decreases."
+ Consequently. even though virtually every source begins in a non-radiative state. those in which the black hole mass is relatively large may ultimately become efficient radiators at later times.," Consequently, even though virtually every source begins in a non-radiative state, those in which the black hole mass is relatively large may ultimately become efficient radiators at later times."
+ When that changeover occurs. the jel power remains constant. while the thermal Iuminositv. begins to fall.," When that changeover occurs, the jet power remains constant, while the thermal luminosity begins to fall."
+ This timescale. when the accretion rate and therefore the thermal luminosity [all below Eddineton. we call /jeqq.," This timescale, when the accretion rate and therefore the thermal luminosity fall below Eddington, we call $t_{\rm Edd}$."
+ It should be emphasized that all of these remarks pertain to thevalue for the jet luminosity: relativistic jets are generically unsteady.so flictuations at the order-unity level should be expected around all thesetrends.," It should be emphasized that all of these remarks pertain to the for the jet luminosity; relativistic jets are generically unsteady,so fluctuations at the order-unity level should be expected around all thesetrends."
+"Assuming a 5 K excitation temperature (the same as for NGC 63341 and an ortho/para ratio of 3. we derive H?CI- column densities of 3.4»10 and 2.2x10 em for the 0 and 62 ss! components. with corresponding H?CI column densities of 4x10' and 2»10"" em.","Assuming a 5 K excitation temperature (the same as for NGC 6334I) and an ortho/para ratio of 3, we derive $_2$ $^+$ column densities of $3.4 \times 10^{13}$ and $2.2 \times 10^{13}$ $^{-2}$ for the 0 and 62 $^{-1}$ components, with corresponding $^{35}$ Cl column densities of $4 \times 10^{13}$ and $2 \times 10^{14}$ $^{2}$."
+ The HCI/H?' CI ratio is ~3.3 in both components., The $^{35}$ $^{37}$ Cl ratio is $\sim$ 3.3 in both components.
+ We estimate the uncertainties in our molecular column density estimates to be of order a factor of ?, We estimate the uncertainties in our molecular column density estimates to be of order a factor of 2.
+ To derive the hydrogen column density in the foreground gas towards Ser B2(S). we use the method employed in Lis et al. (," To derive the hydrogen column density in the foreground gas towards Sgr B2(S), we use the method employed in Lis et al. ("
+2001) to analyze the absorption towards Ser B2(M). based on απά CO absorption data.,"2001) to analyze the absorption towards Sgr B2(M), based on and $^{13}$ CO absorption data."
+ We assume that the foreground absorption is extended and column densities are the same towards Sgr B2(M) and (S)., We assume that the foreground absorption is extended and column densities are the same towards Sgr B2(M) and (S).
+ We derive a total hydrogen nuclei column density of «2x107 em- in the atomic and molecular components in the velocity range —10 to 20 ss! (with a factor of 2 uncertainty)., We derive a total hydrogen nuclei column density of $\sim$$2 \times 10^{22}$ $^{-2}$ in the atomic and molecular components in the velocity range $-10$ to 20 $^{-1}$ (with a factor of 2 uncertainty).
+ The corresponding chlorine content. in the form of H:CI- and HCl. is 7x10? em. implying a CI/H ratio of ~4x107?.," The corresponding chlorine content, in the form of $_2$ $^+$ and HCl, is $7 \times
+10^{13}$ $^{-2}$, implying a Cl/H ratio of $\sim$$4 \times 10^{-9}$."
+ This can be compared to the values measured in the UV in diffuse clouds (e.g.. Sonnentrucker et al.," This can be compared to the values measured in the UV in diffuse clouds (e.g., Sonnentrucker et al."
+ 2006). which are in the range 3x107°—3x 1077.," 2006), which are in the range $3
+\times 10^{-8} - 4 \times 10^{-7}$ ."
+ Therefore the high HCI” column densities we derive here are consistent with the overall chlorine budget. leaving plenty of room for atomic CI and depletion on dust grains.," Therefore the high $_2$ $^+$ column densities we derive here are consistent with the overall chlorine budget, leaving plenty of room for atomic Cl and depletion on dust grains."
+ Our estimates of the H»;CI column densities towards NGC 63341 and Ser B2(S). in excess of 10 em. are significantly higher than those expected for a single dense or diffuse PDR viewed at normal incidence.," Our estimates of the $_2$ $^+$ column densities towards NGC 6334I and Sgr B2(S), in excess of $10^{13}$ $^{-2}$, are significantly higher than those expected for a single dense or diffuse PDR viewed at normal incidence."
+ This might point to some deficiency in the models., This might point to some deficiency in the models.
+ Alternatively. a significant enhancement in the absorbing column density could result if the normal to the trradiated surface were inclined relative to the sight-line. or indeed if multiple PDRs were present along the sight-line. particularly if the radiation field is enhanced. as may be likely for the multiple absorption components seen towards Ser B2.," Alternatively, a significant enhancement in the absorbing column density could result if the normal to the irradiated surface were inclined relative to the sight-line, or indeed if multiple PDRs were present along the sight-line, particularly if the radiation field is enhanced, as may be likely for the multiple absorption components seen towards Sgr B2."
+ Similar discrepancies between models and observations are seen for other reactive ions in massive starforming regions (e.g.. CO toward AFGL 2591: Bruderer et al.," Similar discrepancies between models and observations are seen for other reactive ions in massive starforming regions (e.g., $^+$ toward AFGL 2591; Bruderer et al."
+ 2009)., 2009).
+ We derive an HCI/H>CI ratio of «10 in NGC 63341 and the Ser B2 envelope (assuming that in the case of NGC 63341 the H»CI column density on the back side is the same as that derived in front of the continuum source from our absorption measurements)., We derive an $_2$ $^+$ ratio of $\sim$ 10 in NGC 6334I and the Sgr B2 envelope (assuming that in the case of NGC 6334I the $_2$ $^+$ column density on the back side is the same as that derived in front of the continuum source from our absorption measurements).
+ This is well within the range predicted for dense PDRs (up to ~100 for densities above 10° em7*)., This is well within the range predicted for dense PDRs (up to $\sim$ 100 for densities above $10^6$ $^{-3}$ ).
+ The HCI/H*CT- ratio derived in the foreground gas towards Ser B2(S) at velocities 0—20 kmss7!. ~1. is also consistent with predictions of diffuse cloud models.," The $_2$ $^+$ ratio derived in the foreground gas towards Sgr B2(S) at velocities $0-20$ $^{-1}$, $\sim$ 1, is also consistent with predictions of diffuse cloud models."
+ While a detailed analysis of chlorine chemistry in these and other sources that have been or will be observed using HIFI will be presented in a forthcoming paper. this work clearly demonstrates the outstanding spectroscopic capabilities. of HIFI in the search for new interstellar molecules. particularly hydrides. and in providing robust constraints for astrochemical models of the interstellar medium.," While a detailed analysis of chlorine chemistry in these and other sources that have been or will be observed using HIFI will be presented in a forthcoming paper, this work clearly demonstrates the outstanding spectroscopic capabilities of HIFI in the search for new interstellar molecules, particularly hydrides, and in providing robust constraints for astrochemical models of the interstellar medium."
+"while the expression for vi. is We can see that pl decreases first with pl=pl, then increases with v .","while the expression for $\nu_{\times,>}^{\rm{IC}}$ is We can see that $\nu_{\times}^{\rm{IC}}$ decreases first with $\nu_{\times}^{\rm{IC}}=\nu_{\times,<}^{\rm{IC}}$, then increases with $\nu_{\times}^{\rm{IC}}=\nu_{\times,>}^{\rm{IC}}$ ."
+ The time when 7 reaches its mininnm. pl=pvl. is for p=2.2. ancl for p=2.4.," The time when $\nu_{\times}^{\rm{IC}}$ reaches its minimum, $\nu_{\times,<}^{\rm{IC}}=\nu_{\times,>}^{\rm{IC}}=\nu_{m}^{\rm{IC}}$ , is for $p=2.2$, and for $p=2.4$."
+ The IC component could appear in the X-ray altereglow only if the minimum of VS ds less than v=LOM. Hz. which leads to a lower limit on the ambient density 7.," The IC component could appear in the X-ray afterglow only if the minimum of $\nu_{\times}^{\rm{IC}}$ is less than $\nu=10^{18}\nu_{18}$ Hz, which leads to a lower limit on the ambient density $n$."
+ We obtain the lower limit of n as p —2.2.and ( p =2.4.," We obtain the lower limit of $n$ as for $p=2.2$, and for $p=2.4$."
+This lower limit of » for the emergence of IC. component in the X-ray alterglow in the slow cooling phase is twpically in the range of 1—Lf) * (Sari Esin 2001: Panaitesen Iximar 2000: Zhang Meésszárros 2001)., This lower limit of $n$ for the emergence of IC component in the X-ray afterglow in the slow cooling phase is typically in the range of $1-10$ $^{-3}$ (Sari Esin 2001; Panaitescu Kumar 2000; Zhang Mésszárros 2001).
+" Llowever. the (rue lower limit ol n is even than that eiven in the above equations. since we have neglected the ease of VI>αν, male"," However, the true lower limit of $n$ is even smaller than that given in the above equations, since we have neglected the case of $\nu_{\times}^{\rm{IC}}>\nu_{c}^{\rm{IC}}$."
+rThe spectral segment when pl>vl is oversimplilied by a single power law approximation:, The spectral segment when $\nu_{\times}^{\rm{IC}}>\nu_{c}^{\rm{IC}}$ is oversimplified by a single power law approximation.
+ In fact. the logarithmic term dominates at higher lrequencies.," In fact, the logarithmic term dominates at higher frequencies."
+ The (rue evolution of7 is alwaysdecreasing. although the decreasing rate is slowed at late times (Sari Esin 2001).," The true evolution of$\nu_{\times}^{\rm{IC}}$ is alwaysdecreasing, although the decreasing rate is slowed at late times (Sari Esin 2001)."
+where 7; is the number density of species 7. and where the rate coellicients ; for (he various reactions are listed in table 1..,"where $n_{i}$ is the number density of species $i$, and where the rate coefficients $k_{i}$ for the various reactions are listed in table \ref{chem}."
+ If Is formation via reaction 2. occus much faster than the destruction of 1 by the other reactions. then this reduces to in other words. the Πο formation rate is approximately (he same as the IE. formation rate.," If $\mHt$ formation via reaction \ref{h2f2} occurs much faster than the destruction of $\Hm$ by the other reactions, then this reduces to in other words, the $\mHt$ formation rate is approximately the same as the $\Hm$ formation rate."
+" If, on the other hand. mutual neutralization dominates over HH» formation or photodetachment as a means of removing Il. then equation 1. becomes where 7=ng/ny is the fractional ionization of hydrogen."," If, on the other hand, mutual neutralization dominates over $\mHt$ formation or photodetachment as a means of removing $\Hm$, then equation \ref{general} becomes where $x = n_{\Hp}/n_{\mH}$ is the fractional ionization of hydrogen."
+" As long as noονmy. this equation can be further simplified toComparing this equation with equation 8.. we see (that for a small fractional ionization Ry,xoc. but that once the fractional ionization becomes large enough that mutual neutralization dominates. Z4, becomes independent of the ionization: although increases in wr still increase ihe IL. formation rate. (this is balanced by the increase in the mutual neutralization rate and consequent decrease in the fraction of I1. ions surviving to form Ils."," As long as $n_{\me} \simeq n_{\Hp}$, this equation can be further simplified toComparing this equation with equation \ref{low_x}, we see that for a small fractional ionization $R_{\mHt} \propto x$, but that once the fractional ionization becomes large enough that mutual neutralization dominates, $R_{\mHt}$ becomes independent of the ionization: although increases in $x$ still increase the $\Hm$ formation rate, this is balanced by the increase in the mutual neutralization rate and consequent decrease in the fraction of $\Hm$ ions surviving to form $\mHt$."
+ This change in behaviour occurs lor Iractional ionizations near a critical value c4. defined by The precise value of .r; is somewhat uncertain. due to the significant uncertainty that remains in (he determination of (he mutual neutralization rate.," This change in behaviour occurs for fractional ionizations near a critical value $x_{\rm cr}$, defined by The precise value of $x_{\rm cr}$ is somewhat uncertain, due to the significant uncertainty that remains in the determination of the mutual neutralization rate."
+ In (his paper. I have chosen to adopt the rate listed in Galli&Palla(1995).. which is derived [rom the data of (1910)...," In this paper, I have chosen to adopt the rate listed in \citet{gp}, which is derived from the data of \citet{map}."
+ This is a conservative choice. in (hat it gives the lowest value of ως other possibilities include the rates of Dulev&Williams(1984).. Dalearno&Lepp(1987) ancl CroftetaL.(1999)... with the last-named. being preferred by (he most recent compilation (Leppefαἱ.2002).," This is a conservative choice, in that it gives the lowest value of $x_{\rm cr}$; other possibilities include the rates of \citet{dw}, \citet{dl} and \citet{croft}, with the last-named being preferred by the most recent compilation \citep{lsd}."
+. For the temperature range of interest. the Galli&Palla rate gives us a value ty~5nxI0 7. with only a slight dependence on temperature.," For the temperature range of interest, the \citeauthor{gp} rate gives us a value $x_{\rm cr} \sim 5 \times 10^{-3}$ , with only a slight dependence on temperature."
+ The alternative rates tvpically give values ofc; (hat are factors of a few larger., The alternative rates typically give values of $x_{\rm cr}$ that are factors of a few larger.
+Apart from the Z profile. there could also he uucertainties in the theoretically caleulated values of opacitics.,"Apart from the $Z$ profile, there could also be uncertainties in the theoretically calculated values of opacities."
+ Iu order to obtain constraiuts which are independent of errors iu opacity we can consider X profiles with cocfficicuts im equation (3)) chosen arbitrarily.," In order to obtain constraints which are independent of errors in opacity we can consider $X$ profiles, with coefficients in equation \ref{xbsp}) ) chosen arbitrarily."
+ These arbitrary profiles may not satisfv t1e equations of thermal equilibiun with at1v reasonalie estimate for opacities., These arbitrary profiles may not satisfy the equations of thermal equilibrium with any reasonable estimate for opacities.
+ However. using the iuverted souxd speed aud assiniue the NV and Z profiles. it ds possilie o calculate the temperature profile iside the Sili.," However, using the inverted sound speed and assuming the $X$ and $Z$ profiles, it is possible to calculate the temperature profile inside the Sun."
+" Once these thermal and composition profiles are known. he huninesity iu corresponding scisuiic mode""S Call ο computed."," Once these thermal and composition profiles are known, the luminosity in corresponding seismic models can be computed."
+ Iu order to estimate an upper anit on the yp nuclear reaction rate we can tiv to construct a xofile which generates the minima ΟΠΟΥ03 for the given sound speed aud density profiles., In order to estimate an upper limit on the pp nuclear reaction rate we can try to construct a profile which generates the minimum energy for the given sound speed and density profiles.
+ Since the| sound speed essentially constrains the value of Τμ. where p ds the nean molecular weight of the solar material. it scclus in order to cut down the energv ecucraticon one shotd reduce T as well as µ to keep the ratio coustaut.," Since the sound speed essentially constrains the value of $T/\mu$, where $\mu$ is the mean molecular weight of the solar material, it seems in order to cut down the energy generation one should reduce $T$ as well as $\mu$ to keep the ratio constant."
+ It is clear that the minima value of fis achieved when X=] aud Z=0. Le. when there is no heli or heavy clemeuts prescut in the central region.," It is clear that the minimum value of $\mu$ is achieved when $X=1$ and $Z=0$, i.e. when there is no helium or heavy elements present in the central region."
+ Frou. more detailed calculation of οποίον ecucration rate. we have verified that this is indeed true. altlrough strictly speaking. since the temperature is not ligh enough &Du helium burning reactions. tho nininimn euer‘oy generation occurs When N= 0. when there is no fuel to buru!," From more detailed calculation of energy generation rate, we have verified that this is indeed true, although strictly speaking, since the temperature is not high enough for helium burning reactions, the minimum energy generation occurs when $X=0$ , when there is no fuel to burn!"
+ But even a value of X=0.005 eives much higher euergv eeneration rate as compared to X=1 Zint1ο COLC. because the temperature has to be increwed when X decreases to keep the sound spec constant.," But even a value of $X=0.005$ gives much higher energy generation rate as compared to $X=1-Z$ in the core, because the temperature has to be increased when $X$ decreases to keep the sound speed constant."
+ Further. if tle temperature is regiime to decrease monotonicalv with radial distauce. then even such profiles cau be ruled out.," Further, if the temperature is required to decrease monotonically with radial distance, then even such profiles can be ruled out."
+" ""Thus. leaving aside this uulikely possibility. the muni οποιον generation occurs when X=1 andZ= ) when there is no helinm i the core (Y =())."," Thus, leaving aside this unlikely possibility, the minimum energy generation occurs when $X=1$ and$Z=0$ , when there is no helium in the core $Y=0$ )."
+ For the case of a profile wih X21 aud Z=0 We can CasiVo CLOILIOistrate that he computed Inuinuositv in the resultiug seismic model is about 0οτῆς when re usual nuclear reaction rates are adoptdo, For the case of a profile with $X=1$ and $Z=0$ we can easily demonstrate that the computed luminosity in the resulting seismic model is about $0.617L_\odot$ when the usual nuclear reaction rates are adopted.
+ Now if we increase the pp nuclear reaction rate for obtaining the correct solar Iuninositv with this profile. it t1rus out that 106 CLOSS-S8CCT1n needs to be increased to aout. 1.6255.," Now if we increase the pp nuclear reaction rate for obtaining the correct solar luminosity with this profile, it turns out that the cross-section needs to be increased to about $1.62S_0$."
+ Tt is clear that if the cross-section is lucrceased. bevonud us value it is not possible to find auv X profile (apart roni the one where hydroge Lis almost totalvy exhausted woueghout the solar core). which will simultarcously vield 16 correct sound speed aud Iuuiuositv iu xYsuic models.," It is clear that if the cross-section is increased beyond this value it is not possible to find any $X$ profile (apart from the one where hydrogen is almost totally exhausted throughout the solar core), which will simultaneously yield the correct sound speed and luminosity in seismic models."
+ The exact liuitiug value of the cross-sectiou will depend on the ivered sound speed and deusitv profiles. but as we have seen in the previous section these unucertaiities are very snualdl.," The exact limiting value of the cross-section will depend on the inverted sound speed and density profiles, but as we have seen in the previous section these uncertainties are very small."
+ We can therefore. conclude that any value hieher than 1.65.59 is madiuissible even if aibitrarv errors in opacities are allowed aud the Sun is assted to generate the observed bhuuinositv.," We can therefore, conclude that any value higher than $1.65S_0$ is inadmissible even if arbitrary errors in opacities are allowed and the Sun is assumed to generate the observed luminosity."
+ Au iucrease in tl10 pp uuclear reaction rate bv a actor of 2.9 (Ivanov et al. 1997)), An increase in the pp nuclear reaction rate by a factor of 2.9 (Ivanov et al. \cite{iva97}) )
+ is certainly ruled out by the heloscismuic data., is certainly ruled out by the helioseismic data.
+ Tn fact. iu actual practice even the profile with 17QO considered 1 obtaining this liwit is unacceptable since oue would expect significant amount of ποια to be present in 1C SCdar core.," In fact, in actual practice even the profile with $Y=0$ considered in obtaining this limit is unacceptable since one would expect significant amount of helium to be present in the solar core."
+ If we cousider a profile with Y=0.2. which is still lower hau the expected helium abundance. je liuifing cross-section for the pp reaction drops to 1.275y.," If we consider a profile with $Y=0.2$, which is still lower than the expected helium abundance, the limiting cross-section for the pp reaction drops to $1.27S_0$."
+ It is therefore evident that. amy siguicant Innerease in the pp cross-section is demoustably iucouslsteut with jclioseisiuie coustraiuts.," It is therefore evident that, any significant increase in the pp cross-section is demonstably inconsistent with helioseismic constraints."
+ We would like to a«ld that there is 10 straightforward way to set a lower bouud ou this cross-section from such aianalvsis. as by iucreasing the helm abundance suitably it is possible to reproduce the solar uununositv even Wwien this cross-section 1s significantly reduced. although such xofiles may require macaniissidv aree opacity modifications.," We would like to add that there is no straightforward way to set a lower bound on this cross-section from such an analysis, as by increasing the helium abundance suitably it is possible to reproduce the solar luminosity even when this cross-section is significantly reduced, although such profiles may require inadmissibly large opacity modifications."
+ Iun the foregoi18o discussion we haye allowed for arbitrary errors d sfaukard opacity tables., In the foregoing discussion we have allowed for arbitrary errors in standard opacity tables.
+ Even thoieh such au analysis helps iu ilhstrating that the helioseisinic data are able to put severe constraiits on unclear reaction rates. the resulting boinds on cross-section are hieily conservative and are uulikev to be achieved 1 realistic situations.," Even though such an analysis helps in illustrating that the helioseismic data are able to put severe constraints on nuclear reaction rates, the resulting bounds on cross-section are highly conservative and are unlikely to be achieved in realistic situations."
+ It would be possible to ostain more neaineful bounds if one allows ouly reasouale errors iu opacities., It would be possible to obtain more meaningful bounds if one allows only reasonable errors in opacities.
+" There are two problems with this approach: first. it is 101I to define what is a reasoable error in «ypacity and second. the error in opacities nav have artrary udatioji with temperature aud deusitv. thus liasine it icult to consider all possible variations c""Oh witun the assuned limits."," There are two problems with this approach; first, it is difficult to define what is a reasonable error in opacity and second, the error in opacities may have arbitrary variation with temperature and density, thus making it difficult to consider all possible variations even within the assumed limits."
+" One possibility is to use the procedure outline in the Section 2 with a suitably large value of a n equatio1 (63). to obtain the .X. profile w""ich 2elerates the correct ΠΕ aud requires sone nininiun opacity variation for any specified nuclear reactjon rates."," One possibility is to use the procedure outlined in the Section 2 with a suitably large value of $\alpha$ in equation \ref{chisq}) ), to obtain the $X$ profile which generates the correct luminosity and requires some minimum opacity variation for any specified nuclear reaction rates."
+ We cousider this apxoach later. but before that we adopt a simpler procedure by taking different Z profiles with a large range of Zang to see how the computed Iuninositv varies witι Ζ.," We consider this approach later, but before that we adopt a simpler procedure by taking different $Z$ profiles with a large range of $Z_\mathrm{surf}$ to see how the computed luminosity varies with $Z$."
+11 this process. the opacity cjnges are accounted throug1 changes in Z profiles.," In this process, the opacity changes are accounted through changes in $Z$ profiles."
+ Using the Z profile with diffusion (Proffitt 1991)) scaled to different values of Z4; we cau calculate the X profiles followiic the procedure outlined iu Section 2. with a0 im equation (6)).," Using the $Z$ profile with diffusion (Proffitt \cite{pro94}) ) scaled to different values of $Z_\mathrm{surf}$ we can calculate the $X$ profiles following the procedure outlined in Section 2, with $\alpha=0$ in equation \ref{chisq}) )."
+" The total uuirosity ancl jeutrino fluxes in the resulting seisuiüc 10dels are shown in Fie. δι,", The total luminosity and neutrino fluxes in the resulting seismic models are shown in Fig. \ref{lum}.
+ I is clear that the inteeraec luminosity goes up with Zur as a result of increase in opacitics. mt not very siguificautlv a variation of Zou from 0 o 0.06. results in an increase in the hnimositv frou LSEL. to L.13L..," It is clear that the integrated luminosity goes up with $Z_\mathrm{surf}$ as a result of increase in opacities, but not very significantly – a variation of $Z_\mathrm{surf}$ from 0 to 0.06, results in an increase in the luminosity from $0.87L_\odot$ to $1.13L_\odot$."
+ The range of Z vales covered byhese models is in all probability inuch nore than the expected uncertainties in the Z profile., The range of $Z$ values covered bythese models is in all probability much more than the expected uncertainties in the $Z$ profile.
+ Wit ithe allowance of a factorof two variation Hi Ζ-μνε onegets an error of about iu computed luminosity.," With the allowance of a factorof two variation in $Z_\mathrm{surf}$ , onegets an error of about in computed luminosity."
+ An uncertainty by a factor of two is probably the most that is expected in Z. and hence we have only considered profiles where," An uncertainty by a factor of two is probably the most that is expected in $Z$ , and hence we have only considered profiles where"
+likely to be found in the same halo.,likely to be found in the same halo.
+ This term is determinecl by the couvolution of the dimeusiouless density profile with itsell. For mauy forms of «:(Crc). the angular integration in this equation is analytic. aud A cau be reduced to a simple oue-dimeusioual integral over y.," This term is determined by the convolution of the dimensionless density profile with itself, For many forms of $u(x)$, the angular integration in this equation is analytic, and $\lambda$ can be reduced to a simple one-dimensional integral over $y$."
+ For some special cases. A can even be reduced to an analytic expression.," For some special cases, $\lambda$ can even be reduced to an analytic expression."
+ We leave the detailed results for A to the Appendix., We leave the detailed results for $\lambda$ to the Appendix.
+ Iu &-space. the convolutious in lor £(r) become simple products.," In $k$ -space, the convolutions in for $\xi(r)$ become simple products."
+ Using fy) to denote the Fourier trauslorm of wor). where «(q)={deutr)«HUS ve cap readily transforui into expressions for the mass power spectrum: where the I-halo aud 2-halo terius are To arrive at the last expression above. we have again used the bias model of(10).," Using $\ut(q)$ to denote the Fourier transform of $u(x)$, where $\ut(q) =\int d^3 x\, u(x)\,e^{-i\q\cdot\x} $, we can readily transform into expressions for the mass power spectrum: where the 1-halo and 2-halo terms are To arrive at the last expression above, we have again used the bias model of."
+. For computational efficiency. we find that the algebraic expressions provide excellent fits lor the profiles of Navarro et al. (," For computational efficiency, we find that the algebraic expressions provide excellent fits for the profiles of Navarro et al. ("
+1997) ancl Moore et al. (,1997) and Moore et al. (
+1999). with less than rims error for form [anc less than rms error for form II.,"1999), with less than rms error for form I and less than rms error for form II."
+ The funetioual form is chosen to reproduce the asyinptotie behaviors: 4Izln at small ϱ (with no radial eutolD). and àxq7 (type D) and àxyο (type LD) at large q.," The functional form is chosen to reproduce the asymptotic behaviors: $\ut \sim 4\pi\ln q$ at small $q$ (with no radial cutoff), and $\ut \propto q^{-2}$ (type I) and $\ut \propto q^{-3/2}$ (type II) at large $q$."
+ The two-poiut &£(r) and PEA) can now be computed. analytically from equations (18)) aud (21))., The two-point $\xi(r)$ and $P(k)$ can now be computed analytically from equations \ref{xi2}) ) and \ref{Pk})).
+ The inputs are or (22)) for the halo density. profile «(r) or πα). equations (1)) and (5)) for Ry and 9. for the halo mass function di/dÀ/. and for the halo-halo correlation functiou.," The inputs are or \ref{uq}) ) for the halo density profile $u(x)$ or $\ut(q)$, equations \ref{Rs}) ) and \ref{delbar}) ) for $R_s$ and $\bar\delta$, for the halo mass function $dn/dM$, and for the halo-halo correlation function."
+ Since the halo density profile appears to have a nearly. universal form regardless of background cosmology. £60) aud P(&) depend ou cosinological parameters mainly through ofAL) of aud the halo concentration e(M) or central deusity 0(37). (," Since the halo density profile appears to have a nearly universal form regardless of background cosmology, $\xi(r)$ and $P(k)$ depend on cosmological parameters mainly through $\sigma(M)$ of and the halo concentration $c(M)$ or central density $\deltabar(M)$ . ("
+See Ma Fry 20006 for a more detailed discussion of e(M ).),See Ma Fry 2000c for a more detailed discussion of $c(M)$ .)
+"the reflectivity of the Gold coating was computed by assuming the same surface roughness rms of o = 4À,, regardless of the photon energy and the incidence angle.","the reflectivity of the Gold coating was computed by assuming the same surface roughness rms of $\sigma$ = 4, regardless of the photon energy and the incidence angle."
+" This is not completely correct, because the spectral window of the roughness power spectrum effective for X-ray scattering changes with A, αι, a5», and the size of the region over which the image is integrated."," This is not completely correct, because the spectral window of the roughness power spectrum effective for X-ray scattering changes with $\lambda$ , $\alpha_1$, $\alpha_2$, and the size of the region over which the image is integrated."
+" A variable c, computed from the power spectrum of roughness in a variable frequency range, should be adopted (Spiga et al. 2009))."," A variable $\sigma$, computed from the power spectrum of roughness in a variable frequency range, should be adopted (Spiga et al. \cite{Spiga2009}) )."
+" Nevertheless, this has no relevance to the present comparison and we retain o as a constant."," Nevertheless, this has no relevance to the present comparison and we retain $\sigma$ as a constant."
+" As can be noted from Fig. 8,,"," As can be noted from Fig. \ref{fig:XMM_mir},"
+" the comparison provides a good agreement between the two methods, at all considered energies and off-axis angles."," the comparison provides a good agreement between the two methods, at all considered energies and off-axis angles."
+" The analytical method underestimates the ray-tracing findings by only at most, as foreseen, an amount close to the statistical error for the ray-tracing."," The analytical method underestimates the ray-tracing findings by only at most, as foreseen, an amount close to the statistical error for the ray-tracing."
+ This confirms the correctness of the analytical formula (Eq.(26))) for Wolter-I mirrors within the approximation limits stated in Sect. 2.., This confirms the correctness of the analytical formula \ref{eq:Aeff_fin_offaxis0}) )) for Wolter-I mirrors within the approximation limits stated in Sect. \ref{DC_WI}.
+" Finally, as an application to the hard X-ray band (> 10 keV), we consider the case of a long focal length (f=20 m) X-ray mirror with a wideband multilayer coating."," Finally, as an application to the hard X-ray band $>$ 10 keV), we consider the case of a long focal length $f = 20$ m) X-ray mirror with a wideband multilayer coating."
+" Because of the complex dependence of multilayer reflectivity on the photon energy and the incidence angles, this example places the analytical method to the test, because any departure of the incidence angles from the true values would result in a displacement of the reflectance peaks."," Because of the complex dependence of multilayer reflectivity on the photon energy and the incidence angles, this example places the analytical method to the test, because any departure of the incidence angles from the true values would result in a displacement of the reflectance peaks."
+" As simulation parameters, we assumed Κο=296.2 mm, and L;=Ly300 mm, αρ = 0.106 deg."," As simulation parameters, we assumed $R_0~=~296.2$ mm, and $L_1 = L_2 = 300$ mm, $\alpha_0$ = 0.106 deg."
+" The geometrical area for a source at infinity, would be 5.17 cm?."," The geometrical area for a source on-axis, at infinity, would be 5.17 $^2$."
+" The ratio expressing the departure of the double cone from the Wolter's, L'/ftt, is only1."," The ratio expressing the departure of the double cone from the Wolter's, $L'/f\#$, is only."
+5%.. The multilayer coating is supposed to consist of 200 pairs of Pt/C layers., The multilayer coating is supposed to consist of 200 pairs of Pt/C layers.
+" The layer thickness decreases from the coating surface towards the substrate, according to the well-known power-law for the d-spacing — i.e., the sum of the thicknesses of two adjacent layers — d;=a(b+j) (Joensen 1995)), with j =1, 2,...,, 200 and a, b,c, parameters© with values depending on the desired reflectivity."," The layer thickness decreases from the coating surface towards the substrate, according to the well-known power-law for the d-spacing – i.e., the sum of the thicknesses of two adjacent layers – $d_j = a(b+j)^{-c}$ (Joensen \cite{Joensen}) ), with $j =$ 1, 2, 200 and $a$, $b$,$c$, parameters with values depending on the desired reflectivity."
+" In the present example we adopted a=115.5A, b=0.9, and c=0.27, for a constant thickness ratio of Pt to the d-spacing, Γ=0.35."," In the present example we adopted $a = 115.5~\AA$, $b = 0.9$, and $c = 0.27$, for a constant thickness ratio of Pt to the d-spacing, $\Gamma = 0.35$."
+ The outermost layer is Pt., The outermost layer is Pt.
+" Finally, the surface roughness of the mirror is assumed to have the constant value 7=4A."," Finally, the surface roughness of the mirror is assumed to have the constant value $\sigma = 4~\AA$."
+ The results of this test are shown in Fig., The results of this test are shown in Fig.
+" 9 for a source at infinity, and in Fig."," \ref{fig:comp_infty} for a source at infinity, and in Fig."
+10 for a source at a D~ 102 m distance from the mirror.,\ref{fig:comp_finite} for a source at a $D \simeq$ 102 m distance from the mirror.
+" The results for a 10* ray tracing for each energy value (1 keV steps) are plotted as symbols, whereas the results for the application of Eq. (26))"," The results for a $10^4$ ray tracing for each energy value (1 keV steps) are plotted as symbols, whereas the results for the application of Eq. \ref{eq:Aeff_fin_offaxis0}) )"
+ are plotted as lines., are plotted as lines.
+" The statistical error of the ray-tracing results is of a few percent at low energies and close to at high energies, where the reflectivity is lower."," The statistical error of the ray-tracing results is of a few percent at low energies and close to at high energies, where the reflectivity is lower."
+ We note the excellent matching of peak positions and shapes in both cases., We note the excellent matching of peak positions and shapes in both cases.
+" A mismatch of a few percent can be observed at low energies, even at ὁ=00, which is probably still related to the double cone approximation (Eq. (12)))."," A mismatch of a few percent can be observed at low energies, even at $\delta = \theta =0$, which is probably still related to the double cone approximation (Eq. \ref{eq:F_var}) ))."
+" From these examples, we also note that, even on-axis, the effective area is heavily reduced by the source at a 102 m distance from the mirror."," From these examples, we also note that, even on-axis, the effective area is heavily reduced by the source at a 102 m distance from the mirror."
+" This occurs because 6 = 0.083 deg is close to αρ = 0.106 deg, although still smaller, thus the geometric area is only of the one we would have with D=co (see Eq. (9)))."," This occurs because $\delta$ = 0.083 deg is close to $\alpha_0$ = 0.106 deg, although still smaller, thus the on-axis geometric area is only of the one we would have with $D = \infty$ (see Eq. \ref{eq:vign}) ))."
+" For the case 6 = 0, the effective area also decreases with 9 almost everywhere, as predicted by Eq. (32))."," For the case $\delta$ = 0, the effective area also decreases with $\theta$ almost everywhere, as predicted by Eq. \ref{eq:Ageom_SC3}) )."
+" The opposite effect is observed for a source at a 102 m distance, in agreementwith Eq. (39)),"," The opposite effect is observed for a source at a 102 m distance, in agreementwith Eq. \ref{eq:Ageom_D7}) ),"
+" which predicts an increase in the geometric area with 0 when 6> ao/2, as in the case that we considered.", which predicts an increase in the geometric area with $\theta$ when $\delta>\alpha_0/2$ as in the case that we considered.
+" Finally, we also note how the reflectance features are out when the source moves off-axis, because of the variation in incidence angles over the reflecting surfaces."," Finally, we also note how the reflectance features are when the source moves off-axis, because of the variation in incidence angles over the reflecting surfaces."
+The extremely red galaxies (ERGs) discovered in deep near-infrared (LI). and optical surveys (e.g. AIeCarthy et. al.,"The extremely red galaxies (ERGs) discovered in deep near-infrared (IR) and optical surveys (e.g., McCarthy et al."
+ 1992. Llu Ridgeway 1994) are among the most intriguing objects in the modern cosmology anc their nature is still controversial.," 1992, Hu Ridgway 1994) are among the most intriguing objects in the modern cosmology and their nature is still controversial."
+ They are defined in terms of their very. red optical/near-L1t colours (22Av Sor ντ). are very rare at bright Ix magnitudes while their density approaches 0.5 c 0.1 aremin? at K=20 (MeCracken et al.," They are defined in terms of their very red optical/near-IR colours $R-K>5$ or $I-K>4$ ), are very rare at bright K magnitudes while their density approaches 0.5 $\pm$ 0.1 $^{-2}$ at K=20 (McCracken et al."
+ 2000)., 2000).
+ Such very red. colours can be explained by two mainly opposing scenarios: 1) ERGs can be starburst galaxies hidden by larec amounts of dust. or 2) can be high redshift (2> 1) old ellipticals with intrinsically red spectral energy distributions (SEDs) and large positive k-corrections.," Such very red colours can be explained by two mainly opposing scenarios: 1) ERGs can be starburst galaxies hidden by large amounts of dust, or 2) can be high redshift $z>1$ ) old ellipticals with intrinsically red spectral energy distributions (SEDs) and large positive k-corrections."
+ To know which population is dominant between the ERGs is a crucial test for the models of galaxy formation: the presence of a wicle-spreacl population of high recshift old. ellipticals would. point towards a very carly formation of massive ealaxies in a “monolithic” scenario (Egegen. Lynden-Dell Sandage 1962. Larson 1975). while the presence of numerous dustv starbursts at. intermediate. recdshift is better fitted w the hierarchical scenarios of galaxy formation. (White Frenk 1991. Waullmann. Charlot White 1996).," To know which population is dominant between the ERGs is a crucial test for the models of galaxy formation: the presence of a wide-spread population of high redshift old ellipticals would point towards a very early formation of massive galaxies in a “monolithic"" scenario (Eggen, Lynden-Bell Sandage 1962, Larson 1975), while the presence of numerous dusty starbursts at intermediate redshift is better fitted by the hierarchical scenarios of galaxy formation (White Frenk 1991, Kauffmann, Charlot White 1996)."
+ Both hese populations would have a deep impact on the actual knowledge of the cosmic history of star formation., Both these populations would have a deep impact on the actual knowledge of the cosmic history of star formation.
+ The two populations can in principle be distinguished w several observations: 1) high signal-to-noise spectra can show the presence of emission lines. revealing ongoing star Oorniation activity. or. on the contrary. sharp spectral breaks due to old. stellar populations: 2) sub-mm observations can detect the [ας]. emission. from the hot dust. heated w the starburst: 3) high. resolution optical ancl near-H1 images can reveal the morphology. which is expected to be regular and centrally peaked for old ellipticals and irregular. disturbed. or even double for dusty. starbursts.," The two populations can in principle be distinguished by several observations: 1) high signal-to-noise spectra can show the presence of emission lines, revealing ongoing star formation activity, or, on the contrary, sharp spectral breaks due to old stellar populations; 2) sub-mm observations can detect the far-IR emission from the hot dust heated by the starburst; 3) high resolution optical and near-IR images can reveal the morphology, which is expected to be regular and centrally peaked for old ellipticals and irregular, disturbed or even double for dusty starbursts."
+ In. practice these observations help only in a limited number of cases: 1) the faintness of these objects in the near-LR and especially in the optical (typical magnitudes are K=19 and 11225) makes the spectroscopic observations very dillieult. and many Weck and WLP nights have produced redshifts for just few objects (see below): 2) the best current sub-mm instrument. SCUBA," In practice these observations help only in a limited number of cases: 1) the faintness of these objects in the near-IR and especially in the optical (typical magnitudes are K=19 and R=25) makes the spectroscopic observations very difficult, and many Keck and VLT nights have produced redshifts for just few objects (see below); 2) the best current sub-mm instrument, SCUBA"
+"sspectrim., it ust be «1. where Furthermore. the extrapolation of the cold blackbody component iu the R band must be compatible with our new ""upper limit.",", it must be $R \ll 1$, where Furthermore, the extrapolation of the cold blackbody component in the R band must be compatible with our new upper limit."
+ We have performed the calculation for a luge set of parameters. varving the source distance between 100 aud 500 pe. the B-hane excess f within the 30 luüts (13.3.«F< 35.5). aud considering ο=10. 15. ane 20lau.," We have performed the calculation for a large set of parameters, varying the source distance between $100$ and $500$ pc, the B-band excess $f$ within the $3 \sigma$ limits $13.3\leq f\leq 35.5$ ), and considering $r_O=10$, $15$, and $20$."
+.. We found that the data are quite constraiume: a radius re=15 kan is compatible with the considered rauge of f onlyfor d<200 pe (which implies ry<1.2 kin) aux To=20 eV. Assuniug a smaller radius (ry=I10 kn). the observed excess is ouly compatible with even sinaller distances (~100 pe. corresponding to my=0.6 km) aux Tyx10 eV. On the other haud. assuming a larecr radius (ro=20 kin) the observed excess is compatible with distances up to 300 pe (correspondiug to ryx2 lau) and Jy<15 eV. As an exiuuple. we plotted in Fig.2 a blackbody with T;=11 eV. corresponding to ο=15 kii aud d=150 pe.," We found that the data are quite constraining: a radius $r_O=15$ km is compatible with the considered range of $f$ onlyfor $d\leq 200$ pc (which implies $r_X \leq 1.3$ km) and $T_O \leq 20$ eV. Assuming a smaller radius $r_0=10$ km), the observed excess is only compatible with even smaller distances $\sim 100$ pc, corresponding to $r_X=0.6$ km) and $T_0 \leq 10$ eV. On the other hand, assuming a larger radius $r_O=20$ km) the observed excess is compatible with distances up to 300 pc (corresponding to $r_X \leq 2$ km) and $T_0 \leq 15$ eV. As an example, we plotted in Fig.2 a blackbody with $T_O = 11$ eV, corresponding to $r_O=15$ km and $d=150$ pc."
+" Next. we verified if the inferred size of the hotter caps is compatible with the observed pulsed fraction (PE) where £44; (F,,;,) ave the masini (nininimni) value of the flux along the pulse The PF owas computed munerically by meaus of au IDL script for differcut allowed colubinations of ro. ry and Zo (that is for which the condition A«1l was ict). and assuniüus in all cases Ty=101 eV. We also used two values of the star mass, AJ=d.d.LasAL. to check low seusitive our results are to ecneral relativistic effects (which depend ou the compactness AL/R: e.g Beloborodoy 2002)."," Next, we verified if the inferred size of the hotter caps is compatible with the observed pulsed fraction (PF) where $F_{max}$ $F_{min}$ ) are the maximum (minimum) value of the flux along the pulse The PF was computed numerically by means of an IDL script for different allowed combinations of $r_O$, $r_X$ and $T_O$ (that is for which the condition $R\ll 1$ was met), and assuming in all cases $T_X=104$ eV. We also used two values of the star mass, $M=1.4,\, 1.8\, M_\odot$ to check how sensitive our results are to general relativistic effects (which depend on the compactness $M/R$; e.g Beloborodov 2002)."
+ Since it is always ryS(dre. we took the latter to coincide with the star radius.," Since it is always $r_X\la 0.1 r_O$, we took the latter to coincide with the star radius."
+ Results are shown in Fig.3. where the curve of constant PF (0.0L) is plotted as a function of the two ecometrical aueles. £. the angle between the neutron star spin and magnetic axes. aud Y. he angle between the spin axis and the linc-of-3ighit (LOS). for the case reporxd in Fie.," Results are shown in Fig.3, where the curve of constant PF (0.04) is plotted as a function of the two geometrical angles, $\xi$, the angle between the neutron star spin and magnetic axes, and $\chi$, the angle between the spin axis and the line-of-sight (LOS), for the case reported in Fig."
+ 2., 2.
+ Overplotted to the nunierical contour ds the analytical curve obtained following he method presentec by Beloborodov (2002). aud which is strictly valid ouly for poiut-like caps.," Overplotted to the numerical contour is the analytical curve obtained following the method presented by Beloborodov (2002), and which is strictly valid only for point-like caps."
+ The present analyses coufiris previous findines (Zane et al., The present analyses confirms previous findings (Zane et al.
+ 2008: Sclavope et al., 2008; Schwope et al.
+ 2009)., 2009).
+ One possibility is that either the spin axis is nearly aligued with the magnetic axis. hence the star is a nearly aligued rotator. or the spin axis is nearly aligned with the LOS.," One possibility is that either the spin axis is nearly aligned with the magnetic axis, hence the star is a nearly aligned rotator, or the spin axis is nearly aligned with the LOS."
+ The other possibility is that the spin axis ds slightly nusaligned with respect to both the magnetic axis and the LOS by 5 107., The other possibility is that the spin axis is slightly misaligned with respect to both the magnetic axis and the LOS by $5-10^{\circ}$ .
+ We note that although the nuuerical and analytical curves are qualitatively similar there are quantitative differences., We note that although the numerical and analytical curves are qualitatively similar there are quantitative differences.
+ The allowed rauge iu the two, The allowed range in the two
+chosen such as to represent an initial rins sonic Mach of MM=10.,chosen such as to represent an initial $rms$ sonic Mach of ${\cal M}=10$.
+" The Jeans number of the box is /,,,=4 (i.e.. number of Jeans masses in the box is Mi/Mjsuis=Jbor564)."," The Jeans number of the box is $J_{box}=4$ (i.e., number of Jeans masses in the box is $M_{box}/M_{Jeans,box}=J_{box}^{3}=64$ )."
+" In physical units. the simulation box has a size of L,4=4 pe (thus (he spatial resolution is 4pc/4096~10 pe). an average munber density of my...=500 7. and a temperature of T=11.43 KK which leads to a sound speed of 0.2 km | with a mean molecular weight of M,=2.36 in units of (he proton mass m."," In physical units, the simulation box has a size of $L_{cl}=4$ pc (thus the spatial resolution is $4~{\rm pc}/4096 \sim 10^{-3}$ pc), an average number density of $n_{aver}=500$ $^{-3}$, and a temperature of $T=11.43$ K which leads to a sound speed of $0.2$ km $^{-1}$ with a mean molecular weight of $M_{w}=2.36$ in units of the proton mass $m_{H}$."
+ The free-fall time of the simulation volume is defined as being Upp.)Εκp)U?e2.76x10 vrs. where p is the physical uniform density in thebox!.," The free-fall time of the simulation volume is defined as being $t_{ff,cl}=1/(G~\rho)^{1/2} \sim 2.76 \times 10^{6}$ yrs, where $\rho$ is the physical uniform density in the."
+. The simulations differ bv the strength of the initial magnetic field in the parent cloud. with one simulation being slightly magneticallv-superceritical (run DI). aud the other one sironelv supercritical (run D2).," The simulations differ by the strength of the initial magnetic field in the parent cloud, with one simulation being slightly magnetically-supercritical (run B1), and the other one strongly supercritical (run B2)."
+ Initially the magnetic field has a component only in one direction., Initially the magnetic field has a component only in one direction.
+" The initial magnetic field strength. the mass-to-magnetic flix ratio (in units of the critical value for collapse 44,22(437G)42. Nakano Nakamura and the beta plasma. values are By=14.5.4.6Gh pi,=28.8.8. and 3,=0.1.1. lor simulations Bl. and D2 respectively."," The initial magnetic field strength, the mass-to-magnetic flux ratio (in units of the critical value for collapse $\mu_{cr} \approx (4~\pi^{2}~G)^{-1/2}$, Nakano Nakamura and the beta plasma values are $B_{cl}=14.5, 4.6~\mu G$, $\mu_{cl}=2.8, 8.8$, and $\beta_{p}=0.1, 1$, for simulations B1, and B2 respectively."
+ The Poisson equation is solved. right from the beginning of both simulations. using the conjugate eradient method implemented in RAMSES.," The Poisson equation is solved, right from the beginning of both simulations, using the conjugate gradient method implemented in RAMSES."
+ In this work. we restrict our analvsis to magnetized cloud models since. aside from the now commonly accepted Lact (hat clouds and cores are indeed magnetized (e.g.. Crutcher οἱ al.," In this work, we restrict our analysis to magnetized cloud models since, aside from the now commonly accepted fact that clouds and cores are indeed magnetized (e.g., Crutcher et al."
+ 2004). we have shown in some of our previous work (hat cores formed in magnetized cloud provide the best matel to the available observational constraints such as the exponent of virial paramelter-mass relation of the cores (Dib et al.," 2004), we have shown in some of our previous work that cores formed in magnetized cloud provide the best match to the available observational constraints such as the exponent of virial parameter-mass relation of the cores (Dib et al."
+ 2007a) ancl their lifetimes (Galvánn-Macdrid et al., 2007a) and their lifetimes (Galvánn-Madrid et al.
+" 2007) (particularly for the nearly magneticallv-eritieal cloud),", 2007) (particularly for the nearly magnetically-critical cloud).
+ In order to be able to handle the large data cubes when perlorming the clump finding. we have binned the simulations such as to generate 1024 uniform data cubes for each of ihe ime-steps of the simulations we have analyzed.," In order to be able to handle the large data cubes when performing the clump finding, we have binned the simulations such as to generate $1024^{3}$ uniform data cubes for each of the time-steps of the simulations we have analyzed."
+ Cores are identified on the uniform evids using a chunp-lincing algorithm based on a density threshold. and a [riend-of-Iriend criterion similar to the ones used in Dib et al. (, Cores are identified on the uniform grids using a clump-finding algorithm based on a density threshold and a friend-of-friend criterion similar to the ones used in Dib et al. (
+2007.2003a.2008b). Dib Wim (2007). Audit IIennebelle (2005). and IIlennebelle Audit (2007).,"2007,2008a,2008b), Dib Kim (2007), Audit Hennebelle (2005), and Hennebelle Audit (2007)."
+ We have performed a chimp finding, We have performed a clump finding
+the centroid of the strength in excitation energy (provided that low Iving discrete transitions are well accounted for).,the centroid of the strength in excitation energy (provided that low lying discrete transitions are well accounted for).
+ The strength in the GT resonance was also estimated by FEN in a zeroth order shell model picture., The strength in the GT resonance was also estimated by FFN in a zeroth order shell model picture.
+ In this picture the lowest shell orbitals are filled with nucleons. and the total strength is taken to be the sum of the contributions from each pair of single particle orbitals: Here 1 and [denote initial and final orbitals respectively. Πρ and à» denote the number of particles and holes in (hese orbitals. and AC is the single particle matrix element connecting (he initial and final states.," In this picture the lowest shell orbitals are filled with nucleons, and the total strength is taken to be the sum of the contributions from each pair of single particle orbitals: Here i and f denote initial and final orbitals respectively, $n_p$ and $n_h$ denote the number of particles and holes in these orbitals, and $M^{sp}_{\rm GT}$ is the single particle matrix element connecting the initial and final states."
+ These single particle matrix elements can be found from angular monientuni Considerations and are shown in Table 1 of FENII., These single particle matrix elements can be found from angular momentum considerations and are shown in Table 1 of FFNII.
+ We follow FEN in using the single particle result (Eq. 17)), We follow FFN in using the single particle result (Eq. \ref{spstrength}) )
+ to estimate the total strength., to estimate the total strength.
+ Experimentally it is well established that the axial vector current is renormalized by a factor ol ~(1/1.24) in nuclei., Experimentally it is well established that the axial vector current is renormalized by a factor of $\sim (1/1.24)$ in nuclei.
+ This results in a strength a [actor of (1/1.24)QD»21/2 smaller than shell model calculations give., This results in a strength a factor of $(1/1.24)^2\approx 1/2$ smaller than shell model calculations give.
+ In addition. shell model ealeulations show that residual interaction-induced particle-hole correlations further reduce (he total strength. by a factor of one to a few.," In addition, shell model calculations show that residual interaction-induced particle-hole correlations further reduce the total strength by a factor of one to a few."
+ Typically. these correlations are more important for GT (ransitions. so that the additional quenching is larger lor these transitions.," Typically, these correlations are more important for ${\rm GT^+}$ transitions, so that the additional quenching is larger for these transitions."
+ We adopt a quenching factor of 4 [or GT (vansilions and 3 for GT— (ransitions., We adopt a quenching factor of 4 for ${\rm GT^+}$ transitions and 3 for ${\rm GT^-}$ transitions.
+ These values lor the quenching [actors generally eive strengths within a [actor of two of more detailed strength determinations., These values for the quenching factors generally give strengths within a factor of two of more detailed strength determinations.
+ When the quenchecl value for the strength is less (han one. we assign a configuration mixing strength ol one.," When the quenched value for the strength is less than one, we assign a configuration mixing strength of one."
+ As discussed below. this is roughly consistent with the results of (n.p) experiments for GTI blocked nuclei.," As discussed below, this is roughly consistent with the results of (n,p) experiments for ${\rm GT^+}$ blocked nuclei."
+ FEN estimated the centroid of the GT resonance by considering a zeroth order shell model description for (he spin flip part of (he GT resonance., FFN estimated the centroid of the GT resonance by considering a zeroth order shell model description for the spin flip part of the GT resonance.
+" This configuration was compared with the zeroth order shell model description of the daughter ground state aud assigned an excitation energv Here AL), is the dillerence in single particle energies between the two states (daughter ground state and spin [lip GT resonance state). E, accounts for the difference in pairing energy between the two states. and AF, (taken to be 2 MeV) accounts for the effects of configuration mixing and particle hole repulsion."," This configuration was compared with the zeroth order shell model description of the daughter ground state and assigned an excitation energy Here $\Delta E_{\rm s.p.}$ is the difference in single particle energies between the two states (daughter ground state and spin flip GT resonance state), $\Delta E_{\rm pair}$ accounts for the difference in pairing energy between the two states, and $\Delta E_{\rm ph}$ (taken to be 2 MeV) accounts for the effects of configuration mixing and particle hole repulsion."
+ For 7—15 transitions the energy of the TAS in the daughter is added to eq. 15.., For $T^>\rightarrow T^<$ transitions the energy of the IAS in the daughter is added to eq. \ref{egteqn}. .
+have basically merged to one in all three simulations.,have basically merged to one in all three simulations.
+ By 400 kyr R2 and R5 have become cometary globules rather than pillar-like structures.," By $400\,$ kyr R2 and R5 have become cometary globules rather than pillar-like structures."
+ R5 is also fragmenting — the small protrusion at the top of the dense region eventually detaches from the main clump and is rapidly accelerated., R5 is also fragmenting – the small protrusion at the top of the dense region eventually detaches from the main clump and is rapidly accelerated.
+ R8 at this stage looks completely different to the other models., R8 at this stage looks completely different to the other models.
+ Low density gas has recombined behind the very broad ionisation front formed by gas expansion along the field lines., Low density gas has recombined behind the very broad ionisation front formed by gas expansion along the field lines.
+ The field remains almost unchanged from its initial value even at this late stage., The field remains almost unchanged from its initial value even at this late stage.
+" The field evolution is shown in a more quantitative way in Fig. 4,,"," The field evolution is shown in a more quantitative way in Fig. \ref{fig:R258_Bevo},"
+" where the ratio of the mean (volume averaged) parallel field (|B.|) to perpendicular field (,/B?+B2) is plotted as a function of time for both the full simulation domain and for only those cells with gas density ny>5000cm7°."," where the ratio of the mean (volume averaged) parallel field $\langle\vert B_x\vert\rangle$ to perpendicular field $\langle\sqrt{B_y^2+B_z^2}\rangle$ is plotted as a function of time for both the full simulation domain and for only those cells with gas density $n_{\mathrm{H}}\geq5\,000\,\mathrm{cm}^{-3}$."
+ This ratio changes relatively little in the full domain because ionised gas takes up the overwhelming majority of the simulation volume., This ratio changes relatively little in the full domain because ionised gas takes up the overwhelming majority of the simulation volume.
+" For the dense gas, however, a very strong effect is seen in the evolution as the field strength increases."," For the dense gas, however, a very strong effect is seen in the evolution as the field strength increases."
+ The weak field in model R2 is swept into alignment with the pillar by the dynamics of RDI and the rocket, The weak field in model R2 is swept into alignment with the pillar by the dynamics of RDI and the rocket
+2-dimensional Gaussian ou top of a plane with au arbitrary tilt. arc determined the average FEWIIM for the secondary stars.,"2-dimensional Gaussian on top of a plane with an arbitrary tilt, and determined the average FWHM for the secondary stars."
+ We then refitted all objects keeping the FWIIM fixed at the average. and used the amplitudes of he Gaussians to determine relative magnitudes.," We then refitted all objects keeping the FWHM fixed at the average, and used the amplitudes of the Gaussians to determine relative magnitudes."
+ Finally. the difference with the aperture results for the secondary stars was used to calculate iustruinental magnitudes for stars 1. 7. 8. and 9. and all magnitudes were calibrated using the solutiou found from he Landolt stars.," Finally, the difference with the aperture results for the secondary stars was used to calculate instrumental magnitudes for stars 1, 7, 8, and 9, and all magnitudes were calibrated using the solution found from the Landolt stars."
+ The results are listed in Table1.., The results are listed in Table\ref{tab:phot-astr}.
+ In order to verify our procedures. we also determined £D aud Π iaenitudes for stars 1. 7. 8. and 9 from the stacked images from the 28th. aud 29th separately: these eave consistent results.," In order to verify our procedures, we also determined $B$ and $R$ magnitudes for stars 1, 7, 8, and 9 from the stacked images from the 28th and 29th separately: these gave consistent results."
+ The probability that star Lis a object that happens to be within the backgrounderrorregion0.5arcsec? confidence) ofthe tiniug position of Us abot 1.6.. DO particularly low.," The probability that star 1 is a background object that happens to be within the } error region confidence) of the timing position of is about, i.e., not particularly low."
+ With BoR=0.05+ 0.18. however. star Lis bluer than all other aut stars in the field.," With $B-R=-0.05\pm0.18$ , however, star 1 is bluer than all other faint stars in the field."
+ In our iuages. the bluest other objects have BOR~0.6 (e.g. stars 8 and 9).," In our images, the bluest other objects have $B-R\simeq0.6$ (e.g., stars 8 and 9)."
+ Of jose. there are only a few 7 and the chance coincidence probability is «0.1.," Of these, there are only a few $^{-2}$ and the chance coincidence probability is $<\!0.1\%$."
+ The probability x au object as blue as star Lois lower still aud. jerefore. we believe star lis the optical counterpart oIG.," The probability for an object as blue as star 1 is lower still, and, therefore, we believe star 1 is the optical counterpart to."
+. It is unlikely that the optical cuuission is due to je pulsar or to à neutron-star companion., It is unlikely that the optical emission is due to the pulsar or to a neutron-star companion.
+ Thermal Cluission from a neutron star could reproduce the colors. but it would be much too faint: the kuown sources lave simula magnitudes. but are all nearby (for arecent compilation. see MGenani 1998)).," Thermal emission from a neutron star could reproduce the colors, but it would be much too faint: the known sources have similar magnitudes, but are all nearby (for a recent compilation, see Mignani \cite{mign:98}) )."
+ Noutlermal Cluission cau lead to brighter sources. but only for voung pulsars and ecucrally with colors that are too red.," Nonthermal emission can lead to brighter sources, but only for young pulsars and generally with colors that are too red."
+ This leads us to propose that the companion of lis a nassive white dwarf. aud that star Lis its optical counterpart.," This leads us to propose that the companion of is a massive white dwarf, and that star 1 is its optical counterpart."
+ Iu order to verity whether our observations are consistent with a white-dwarft companion. we necd to estimate the expected brightuess.," In order to verify whether our observations are consistent with a white-dwarf companion, we need to estimate the expected brightness."
+ This is possible using cooling models for white dwarfs. provided we have estimates for the white-dwart mass. composition. and age. as well as for the distance and reddening.," This is possible using cooling models for white dwarfs, provided we have estimates for the white-dwarf mass, composition, and age, as well as for the distance and reddening."
+ We will cliscuss these in turni., We will discuss these in turn.
+ The mass ofthe companion has a strict lower bound white(inferred.dwarfof1.2M... frou timine: §??))., The mass of the white dwarf companion has a strict lower bound of } (inferred from timing; ).
+ Au equally strict upper LAL...isboundof1. set by the Chancrasckhar mass., An equally strict upper bound of } is set by the Chandrasekhar mass.
+ The age of the white dwarf is the sum offax.. the time hat clapsed between the formation of the white dwart and the supernova explosion. aud£pag.. the age of the pulsar (see 822)).," The age of the white dwarf is the sum of, the time that elapsed between the formation of the white dwarf and the supernova explosion, and, the age of the pulsar (see )."
+ An upper limit to Ds se by the total lifetime of au (Afi}) star. Le. fan<<DOM (e.g. Schaller et citeschaa:96)).," An upper limit to is set by the total lifetime of an ) star, i.e., $\tsn<40\un{Myr}{}$ (e.g., Schaller et \\cite{scha&a:96}) )."
+ Au upper limi to ls se bv the characteristic age (but see 827)). Le. fpsnxΤομ=30Myr.," An upper limit to is set by the characteristic age (but see ), i.e., $\tpsr\simlt\taupsr=30\un{Myr}{}$."
+ The cooling age of the white dwarf may equal its actual age. or fo!fax|f£pag<£0 Myr.," The cooling age of the white dwarf may equal its actual age, or $\tcool=\tsn+\tpsr<70\un{Myr}{}$ ."
+ It is quite likely. however. that the white dwarf was reheated," It is quite likely, however, that the white dwarf was reheated"
+"xeseription for determining if two black holes ποσο, aud he frequency of finding halos. creating black holes. aud checking for mereers.","prescription for determining if two black holes merge, and the frequency of finding halos, creating black holes, and checking for mergers."
+ For cach of these aspects we study wo possibilities: a “pessimistic” and au “optimistic” scenario., For each of these aspects we study two possibilities: a “pessimistic” and an “optimistic” scenario.
+ This leads to a total of cight combinations of nodels., This leads to a total of eight combinations of models.
+ For the initial mass of seed black holes. authors who ive performed calculations simular to ours (eg. 7 :7 22) typically choose a constant seed mass of 10AL... and this is the value we will choose for this model.," For the initial mass of seed black holes, authors who have performed calculations similar to ours (e.g., \citealt{booth_cosmological_2009}
+ ; \citealt{sijacki_unified_2007}
+ ; \citealt{di_matteo_direct_2008}) ) typically choose a constant seed mass of $10^{5} \msol$, and this is the value we will choose for this model."
+ The value chosen is typically motivated by a desire not to violate coustraints on the observed black hole 12ass density (€2).. especially when black loles are allowed to accrete a significant portion of their final mass.," The value chosen is typically motivated by a desire not to violate constraints on the observed black hole mass density \citep{shankar_supermassive_2004}, especially when black holes are allowed to accrete a significant portion of their final mass."
+ However. this approach mav have several weakuesses.," However, this approach may have several weaknesses."
+ First. black holes with masses as hiel as 10°AZ. are inferred to exist frou quasar activity at 2—6 (?)..," First, black holes with masses as high as $10^9 \msol$ are inferred to exist from quasar activity at $z \sim 6$ \citep{fan_evolution_2006}."
+" Second. depending ou the frequency of halo Πιοπιο, when iilos are initially detected they may uot have identical nasses, and if whatever plivsical processes which create he observed relations are already present. then the seed lack holes should scale with halo mass."," Second, depending on the frequency of halo finding, when halos are initially detected they may not have identical masses, and if whatever physical processes which create the observed relations are already present, then the seed black holes should scale with halo mass."
+ Finally. at ower redshifts the halo finding algoritlin may spuriously ucree two halos.," Finally, at lower redshifts the halo finding algorithm may spuriously merge two halos."
+ If we instantly merece black holes aud iu he following step the halo fiuder identifies two separate idos. one will be without its black hole.," If we instantly merge black holes and in the following step the halo finder identifies two separate halos, one will be without its black hole."
+" It may be inappropriate to re-seed the halo with a low-mass black role,", It may be inappropriate to re-seed the halo with a low-mass black hole.
+" Alternatively. we may derive the seed black hole mass youn a form of the observed Ady,σ relation."," Alternatively, we may derive the seed black hole mass from a form of the observed $\msig$ relation."
+ This approach may seem tautological: however. accretion aud codback processes may dominate at high redshift aud at scales below which we can resolve (27)..," This approach may seem tautological; however, accretion and feedback processes may dominate at high redshift and at scales below which we can resolve \citep{shankar_demography_2009, merloni_cosmic_2010}."
+" The observed Ati,c relation at 2=O may then siuplv be a consequence of pure increing at late times and large scales.", The observed $\msig$ relation at $z=0$ may then simply be a consequence of pure merging at late times and large scales.
+ Also. this approach may be useful in testing other SMBI-velated processes and relations i groups and clusters.," Also, this approach may be useful in testing other SMBH-related processes and relations in groups and clusters."
+ However. this approach is complicated by the act that calculations of o directly iu simmlatious suffer roni high scatter. especially at high redshift when halos first form and at low redshift when satellite halos may © contaminated by hot particles belonging to a larecr icielibor.," However, this approach is complicated by the fact that calculations of $\sigma$ directly in simulations suffer from high scatter, especially at high redshift when halos first form and at low redshift when satellite halos may be contaminated by hot particles belonging to a larger neighbor."
+ Fortunately. we may seed halos by relating the dack hole mass directly to the halo mass through the observed relation (?):: This relation comes frou observations at ;=0.2 of bulge velocity dispersions and halo masses using eravitational lensing.," Fortunately, we may seed halos by relating the black hole mass directly to the halo mass through the observed relation \citep{bandara_relationship_2009}: This relation comes from observations at $z=0.2$ of bulge velocity dispersions and halo masses using gravitational lensing."
+" These measurements are linked to black hole mass by assmuing the Afi,7 relation of ?:: where oy=200Iansο,", These measurements are linked to black hole mass by assuming the $\msig$ relation of \citet{gultekin_m-sigma_2009}: where $\sigma_0 = 200 \mbox{ km s}^{-1}$.
+ We will asume the relation in Eq.(5)) holds to high redshift., We will assume the relation in \ref{eq:mhalo}) ) holds to high redshift.
+ Figure G shows velocity dispersion as measured iu one of our ruus (detailed below) as a function of mass at 2=0.2., Figure \ref{fig:msigma200} shows velocity dispersion as measured in one of our runs (detailed below) as a function of mass at $z=0.2$.
+ While we agree with observations aud the best fit from a suite of simulations described by ?.. there Is significant scatter. especially at low mass.," While we agree with observations and the best fit from a suite of simulations described by \cite{evrard_virial_2008}, there is significant scatter, especially at low mass."
+" Note that since we are performing dark matter-ouly simulations. we do not directly measure the velocity dispersion of the ealactic central bulge: instead we measure that of the dark matter in the eutire halo. defined by: where e(f) is the scale factor. (V, is the muuber of particles in the halo. ορ, is the jth velocity conipoucut of the ith particle, aud ce; is the jth componueut of the ceuter-ofauass velocity."," Note that since we are performing dark matter-only simulations, we do not directly measure the velocity dispersion of the galactic central bulge; instead we measure that of the dark matter in the entire halo, defined by: where $a(t)$ is the scale factor, $N_p$ is the number of particles in the halo, $v_{i,j}$ is the $j{\rm th}$ velocity component of the $i{\rm th}$ particle, and $\bar v_j$ is the $j{\rm th}$ component of the center-of-mass velocity."
+ Note that velocities iu the sinulation are comoving quantities., Note that velocities in the simulation are comoving quantities.
+ This plot aud other results (as sunniarized bv 7)) indicate that epa aud Thue Agree to Within a factor of order unity. so woe may substitute one for the other.," This plot and other results (as summarized by \citealt{croton_simple_2009}) ) indicate that $\sigma_{\rm DM}$ and $\sigma_{\rm bulge}$ agree to within a factor of order unity, so we may substitute one for the other."
+ Next. we may chauge the prescription for testing black hole mergers.," Next, we may change the prescription for testing black hole mergers."
+ Most approaches to studving the erowtl of SAIBUs rely ou halo merger histories derived from shuulatious (2). oy Press-Schechter models (??)..," Most approaches to studying the growth of SMBHs rely on halo merger histories derived from simulations \citep{micic_supermassive_2007} or Press-Schechter models \citep{menou_merger_2001, volonteri_evolution_2008}."
+ These approaches asstuue that each halo contains a single SMDIT. and whenever two halos merece their respective black holes instantly meree as well.," These approaches assume that each halo contains a single SMBH, and whenever two halos merge their respective black holes instantly merge as well."
+ While this approach is highly optimistic. it does provide an upper μπιτ to predicted merger rates. au important coustraimt on upconune eravitational wave experiments (7).," While this approach is highly optimistic, it does provide an upper limit to predicted merger rates, an important constraint on upcoming gravitational wave experiments \citep{amaro-seoane_topical_2007}."
+ It is also easv to nupleiaent and provides a simple wav to conrpare results from simulations to approaches based ou morecr trees., It is also easy to implement and provides a simple way to compare results from simulations to approaches based on merger trees.
+ However. this approach can lead to spurious black hole merecrs. since halos may temporarily iutersect without mereine.," However, this approach can lead to spurious black hole mergers, since halos may temporarily intersect without merging."
+ We will include this scenario in our study., We will include this scenario in our study.
+ Suberid models used directly im simulations (ec...7) have used a inore sophisticated approach iu iucreme black holes.," Subgrid models used directly in simulations \citep[e.g.,][]{booth_cosmological_2009} have used a more sophisticated approach in merging black holes."
+ Iu these simulations. SMDIIS only moree when they are within some defined distance (for Lagrangian codes. this is typically the softening length) and have relative velocities below some threshold.," In these simulations, SMBHs only merge when they are within some defined distance (for Lagrangian codes, this is typically the softening length) and have relative velocities below some threshold."
+ This is to avoid mereie black holes that are onlv passing by each other aud are not part of a true coalescing system, This is to avoid merging black holes that are only passing by each other and are not part of a true coalescing system.
+ The velocity threshold varies by author. but it is usually taken to be the local eas sound speed or the circular velocity near the larger black holeof tle mereing," The velocity threshold varies by author, but it is usually taken to be the local gas sound speed or the circular velocity near the larger black holeof the merging"
+of the metallicities of carbon stars in the three galaxies. and heuce ¢ cau robustly distinguish between a ligh-mctallicity population aud a low-uctallicity population.,"of the metallicities of carbon stars in the three galaxies, and hence $\zeta$ can robustly distinguish between a high-metallicity population and a low-metallicity population."
+ We find that the metallicity indicator ¢ is differeut for laugh velocity-vesidual stars than for low velocity stars., We find that the metallicity indicator $\zeta$ is different for high velocity-residual stars than for low velocity stars.
+ Specifically. for stars with [Ae]<10 Xmj/sec. we find Q=0.678+0.007 while for |Ac|>10 kin/sec. we have ο=0.662£0.005.," Specifically, for stars with $|\Delta v| < 10 $ km/sec, we find $\zeta=0.678 \pm
+0.007$ while for $|\Delta v| > 10$ km/sec, we have $\zeta=0.662 \pm
+0.005$."
+ These two values of ¢ are different at the confidence level., These two values of $\zeta$ are different at the confidence level.
+" However. since most of the ""low velocity stars chosen this wav are actually from the more numerous thick-disk velocity sample. dividing up the saluple in this wav is not the best wav to measure the metallicity difference."," However, since most of the “low velocity” stars chosen this way are actually from the more numerous thick-disk velocity sample, dividing up the sample in this way is not the best way to measure the metallicity difference."
+ To isolate the thin aud thick disks we modifv equation (1)) to read where ¢; is the mean value ofà for cach population aud a.= 0.0LLis the observed dispersion of¢ iu the sunple for the 103 stars with volocities aud iufrared data.," To isolate the thin and thick disks, we modify equation \ref{twopop}) ) to read where $\bar\zeta_i$ is the mean value of $\zeta$ for each population and $\sigma_\zeta=0.044$ is the observed dispersion of $\zeta$ in the sample for the 103 stars with velocities and infrared data."
+ Note that for stars without infrared data. the last terii is simply sot to unity.," Note that for stars without infrared data, the last term is simply set to unity."
+ We then fud οἱ=0.6632:0.01. 65=0.7002E0.16. and ο=0.0357dO.OLT. Le. a 26 difference. which corresponds to A[Fo/TI|~0.25.," We then find $\bar\zeta_1= 0.663\pm 0.04$, $\bar \zeta_2=0.700\pm 0.16$, and $\bar\zeta_2-\bar\zeta_1=0.037\pm 0.017$, i.e. a $2\,\sigma$ difference, which corresponds to $\Delta {\rm [Fe/H]}\sim 0.25$."
+ Given the combination of different velocities and different inetallieities. we claim that we have detected either two different disks within the LAIC represcuting different ages of stellar populations or a continuous distribution of disk populations with a rauge of ages.," Given the combination of different velocities and different metallicities, we claim that we have detected either two different disks within the LMC representing different ages of stellar populations or a continuous distribution of disk populations with a range of ages."
+ Iu either case. the vouuger populations lave higher metallicity audlower velocity dispersion.," In either case, the younger populations have higher metallicity andlower velocity dispersion."
+ Gould (1995)) showed that for mnücroleusimg within a virialized disk. the microleusiug optical depth is where (is the angle of inclination of the disk with respect o the line of sight. 30°00107 in the case of the LMC.," Gould \cite{gouldvir}) ) showed that for microlensing within a virialized disk, the microlensing optical depth is where $i$ is the angle of inclination of the disk with respect to the line of sight, $30-40 ^\circ$ in the case of the LMC."
+" Iu he case of the carbon stars. the total velocity cispersion is 21lans+ and thus the optical depth due a viialised stellar lation traced by the cavbou stars is 2&10.7. iiuch stnaller than that measured by the NLACTIO. experiment (Alcock 1997)) of 1.2!ud«10""."," In the case of the carbon stars, the total velocity dispersion is $21\,\kms$ and thus the optical depth due a virialised stellar population traced by the carbon stars is $\la 2\times 10^{-8}$, much smaller than that measured by the MACHO experiment (Alcock \cite{macho6yr}) ) of $1.2 ^{+0.4}_ {-0.3} 
+\times 10^{-7}$."
+ Thus. the virialized »pulatiou traced by carbon stars cinnot account for wicrolensing.," Thus, the virialized population traced by carbon stars cannot account for microlensing."
+ However. a virialized population too old to © traced by carbon stars would not be seen im our data (Auboure et 11999).," However, a virialized population too old to be traced by carbon stars would not be seen in our data (Aubourg et 1999)."
+ We have explicitly assuued that hotter. more metal poor population is older than the vounger. metal rich population in analogy with the Milkv Was. eventhough the LMC aay have a different disk heating mechanisi than the \filky Way.," We have explicitly assumed that hotter, more metal poor population is older than the younger, metal rich population in analogy with the Milky Way, eventhough the LMC may have a different disk heating mechanism than the Milky Way."
+ The age-velocity dispersion relation has been coufirimed previously by Iugues. Wood Reid (1991)) aud Schonuuer (1992)).," The age-velocity dispersion relation has been confirmed previously by Hugues, Wood Reid \cite{hughes}) ) and Schommer \cite{sosh}) )."
+ Since we detect a anctallicity difference based ou. our infrared colors within this population. we also determine that some noticeable metal eurichmieut occured during the Carbon star formation epoch.," Since we detect a metallicity difference based on our infrared colors within this population, we also determine that some noticeable metal enrichment occured during the Carbon star formation epoch."
+ The velocity dispersion of the thick disk componeut. 22]ausft. is auch higher thau the thin disk. aud is close to the velocity dispersion of the oldest objects measured in the LMC. ~3014s! (Hugbes. Wood Reid 1901. Schonuuer 1992).," The velocity dispersion of the thick disk component, $22\, \kms$, is much higher than the thin disk, and is close to the velocity dispersion of the oldest objects measured in the LMC, $\sim 30 \kms$ (Hughes, Wood Reid 1991, Schommer 1992)."
+ Thus. we can show that the bulk of disk heating occurred during the Carbou star formation epoch.," Thus, we can show that the bulk of disk heating occurred during the Carbon star formation epoch."
+ The analysis of Gould (1995)) oulv applies to virialized populations., The analysis of Gould \cite{gouldvir}) ) only applies to virialized populations.
+ It is stil possible that an unvirialized population of stars could be causing microlensiug., It is still possible that an unvirialized population of stars could be causing microlensing.
+ Such a population might be a streamer of stellar material pulled out bv tidal interactions between the LMC aud the Milky Way. or between the LMC iud the SAIC (Zhao 1998)).," Such a population might be a streamer of stellar material pulled out by tidal interactions between the LMC and the Milky Way, or between the LMC and the SMC (Zhao \cite{zhao}) )."
+ Zaritsky Lin (1997)) claimed that they may have seen such a streamer in LMC chup giants., Zaritsky Lin \cite{zl97}) ) claimed that they may have seen such a streamer in LMC clump giants.
+ This paper caused nunerous couuter-aremuents which are summarized aud debated in (Zaritsky 1999))., This paper caused numerous counter-arguments which are summarized and debated in (Zaritsky \cite{zsthl99}) ).
+ Thata. Lewis Beaulicu (1998)) examined the velocities of LO chup giauts in the LMC of which 21 were candidate foreground stars according to the criteria of Zavitsky Lin (1997).," Ibata, Lewis Beaulieu \cite{ilb}) ) examined the velocities of 40 clump giants in the LMC of which 24 were candidate foreground stars according to the criteria of Zaritsky Lin )."
+ Ibata et ((1998) found no difference iu the mean velocities of the candidate foreground stars aud the other chunip stars and concluded that these stars did not form a separate kinematic population from the LMC., Ibata et (1998) found no difference in the mean velocities of the candidate foreground stars and the other clump stars and concluded that these stars did not form a separate kinematic population from the LMC.
+ Zaxitskyv (19993) confirmed the results of Ibata et ((1998) using a mich larger sample of 190 caucidate foreerouud chuup stars., Zaritsky \cite{zsthl99}) ) confirmed the results of Ibata et (1998) using a much larger sample of 190 candidate foreground clump stars.
+ However. the carbou-star sample that we analyze here is potentially more seusitive to the presence of tidal streamers than either of these two chuup-star saluples. iu part because it is larger (551 stars) and im part because the velocity errors are nimchi smaller (~kms1).," However, the carbon-star sample that we analyze here is potentially more sensitive to the presence of tidal streamers than either of these two clump-star samples, in part because it is larger (551 stars) and in part because the velocity errors are much smaller $\sim 1\,\kms$ )."
+ We search the data for à non-virialized. kinematically distinct. population (SDP) iu two different wavs.," We search the data for a non-virialized, kinematically distinct population (KDP) in two different ways."
+" First. we ft the residuals to the disk solution to the sun of three Gaussians. two represcuting the LMC. aud oue for the ΙΟΣ,"," First, we fit the residuals to the disk solution to the sum of three Gaussians, two representing the LMC, and one for the KDP."
+ That is. we apply equation (6)) with η=3.," That is, we apply equation \ref{twopopp}) ) with $n=3$."
+ We find a solution which is somewhat better than the two Canssian fit. Ay?=8 for a change of Ldeerees of freedom.," We find a solution which is somewhat better than the two Gaussian fit, $\Delta\chi^2=8$ for a change of 4 degrees of freedom."
+ The offceuter NDP peak is found to be moving towards us at 27lans+ relative to the bulk of the LMC and to contain 63 stars. about of the total.," The off-center KDP peak is found to be moving towards us at $27\,\kms$ relative to the bulk of the LMC and to contain 63 stars, about of the total."
+ Thus. the data Seeost that there may be a IKDP. but at a statistically weal. level of confidence.," Thus, the data suggest that there may be a KDP, but at a statistically weak level of confidence."
+ A Moute Carlo simulation was performed to verify the statistical confidence (details of which are described iu 11.3) which showed that this third burp is only preseut at the confidence level., A Monte Carlo simulation was performed to verify the statistical confidence (details of which are described in 4.3) which showed that this third bump is only present at the confidence level.
+ The fit to the third bump is shown iu Fie 5.., The fit to the third bump is shown in Fig \ref{threepopfig}. .
+ Iu the model considered iu the previous section. the KDP stars have a common motion LAMC.," 	In the model considered in the previous section, the KDP stars have a common motion ."
+ Possibly. the NDP stars are moving steadily away frou," Possibly, the KDP stars are moving steadily away from"
+invvariant value higher than 3. are showing cometary activity.,"variant value higher than 3, are showing cometary activity."
+total of 278 deg?.,total of 278 $^{2}$.
+ The SDSS Fifth Data Release (Acelman-AMeCarthyctal.2007) contains the 57 survev-quality imaging runs that cover Stripe S2. which were observed. as part of regular SDSS-L operations through 2005 June.," The SDSS Fifth Data Release \citep{adelman07} contains the 57 survey-quality imaging runs that cover Stripe 82, which were observed as part of regular SDSS-I operations through 2005 June."
+ We study only those objects observed spectroscopically. as they have been confirmed. as quasars. and. information about their black bole masses can be extracted. directly from their spectra.," We study only those objects observed spectroscopically, as they have been confirmed as quasars, and information about their black hole masses can be extracted directly from their spectra."
+ In this region. 7886 objects have been spectroscopically observed by the SDSS and confirmed to be quasars.," In this region, 7886 objects have been spectroscopically observed by the SDSS and confirmed to be quasars."
+ The majority of these quasars have been imaged by the SDSS between S and 12 times each. with an average of 9.5 (and a maximum of 27) observations per object.," The majority of these quasars have been imaged by the SDSS between 8 and 12 times each, with an average of 9.5 (and a maximum of 27) observations per object."
+ To measure the streneth of the variability. of our full sample and various subsamples. we use a standard formulation of the structure function. (diClementeetal. 190011: where Am(Ar) is the dilference in magnitude between any two observations of a quasar. separated by Ar in the quasars rest Crane. and oF is the square of the uncertainty in that dillerenee (which is equal to the sum of the two individual observations! errors in quadrature).," To measure the strength of the variability of our full sample and various subsamples, we use a standard formulation of the structure function \citep{diclemente96}: where $\Delta{m}(\Delta{\tau})$ is the difference in magnitude between any two observations of a quasar, separated by $\Delta{\tau}$ in the quasars rest frame, and $\sigma_{n}^{2}$ is the square of the uncertainty in that difference (which is equal to the sum of the two individual observations' errors in quadrature)."
+ “Phe units of the structure function are magnitudes., The units of the structure function are magnitudes.
+ The means of these cuantities are taken over 10 bins. ranging from 7 davs to 100 days. of equal width in the logarithm of the time Lag.," The means of these quantities are taken over 10 bins, ranging from 7 days to 700 days, of equal width in the logarithm of the time lag."
+ The structure function can be a useful tool. especially in comparing the relative variability of two. subsamples of quasars. which is the primary approach cniploved in this paper.," The structure function can be a useful tool, especially in comparing the relative variability of two subsamples of quasars, which is the primary approach employed in this paper."
+ However. the structure function is not an ideal measure in a statistical sense.," However, the structure function is not an ideal measure in a statistical sense."
+ It assumes cach point is statistically independent. from. all others. which is clearly not the case. as most quasars contribute more than one data »oint to each bin: this makes à true measurement of the errorquite difficult.," It assumes each point is statistically independent from all others, which is clearly not the case, as most quasars contribute more than one data point to each bin; this makes a true measurement of the errorquite difficult."
+ We follow the Lead of Cristiani.Trentini.LaFranca.&Xndreani(1997). and RenestorlBrunner.&Wil-ite(2006) in estimating the error. by making the (known incorrect) assumption that the individual data points. are independent. and. ignoring covariance between points.," We follow the lead of \citet{cristiani97} and \citet{rengstorf06} in estimating the error, by making the (known incorrect) assumption that the individual data points are independent, and ignoring covariance between points."
+ We hen apply standard error propagation to Equation 1.. using he statistical error in the mean as the uncertainties for JAm(Ar)|) and (02) in cach bin.," We then apply standard error propagation to Equation \ref{sfeq}, , using the statistical error in the mean as the uncertainties for $\langle|\Delta{m(\Delta{\tau})}|\rangle$ and $\langle\sigma_{n}^{2}\rangle$ in each bin."
+ This leads to a slight overestimation of the uncertainty in the structure function (RenestorlBrunner.&\Wilbite2006).. which does. not change any of our results: we defer a complete treatment of the covariance to a later paper.," This leads to a slight overestimation of the uncertainty in the structure function \citep{rengstorf06}, which does not change any of our results; we defer a complete treatment of the covariance to a later paper."
+ Figure 6 shows the structure Function in all five SDSS photometric bands for the full sample of 7.886. quasars.," Figure \ref{Fig3.1} shows the structure function in all five SDSS photometric bands for the full sample of 7,886 quasars."
+ A comparison of these five structure functions shows that quasars are most variable in the wv band. and least variable in the + band.," A comparison of these five structure functions shows that quasars are most variable in the $u$ band, and least variable in the $z$ band."
+ This is as one would expect. since it is well known that quasars vary more at blue wavelengths in the ultraviolet anc optical (sec.e.g...Wilhiteetal.2005).," This is as one would expect, since it is well known that quasars vary more at blue wavelengths in the ultraviolet and optical \citep[see, e.g.,][]{wilhite05}."
+. To characterise these structure functions. we fit à power low to these data of the form: This is done hy fitting a line to the logarithm of these data with the LDL function POLYEITW. weighting the points by the uncertainties caleulated in refs.," To characterise these structure functions, we fit a power low to these data of the form: This is done by fitting a line to the logarithm of these data with the IDL function POLYFITW, weighting the points by the uncertainties calculated in \\ref{sf}."
+ These values are translated. into the corresponding values for a power law fit., These values are translated into the corresponding values for a power law fit.
+ Parameters resulting from fits to the fulbsample structure functions can be found in Table 4.., Parameters resulting from fits to the full-sample structure functions can be found in Table \ref{fullplfittab}.
+ We employ a power law fit largely for historical reasons. as this has often been the functional form of choice (c.g.2004).," We employ a power law fit largely for historical reasons, as this has often been the functional form of choice \citep[e.g.][]{hook94,vandenberk04}."
+. While other functional forms may produce a better fit. in terms of the chi-squarecl parameter. we have found that the relative results in the values of V(Ng=100) are completely unchanged.," While other functional forms may produce a better fit, in terms of the chi-squared parameter, we have found that the relative results in the values of $V(\Delta{\tau}=100)$ are completely unchanged."
+ Thus. we use a power law to fit our structure functions. to allow for comparisons with previous work.," Thus, we use a power law to fit our structure functions, to allow for comparisons with previous work."
+ Using this functional form. the parameter Avy should not be construed as a natural time-scale for variability: it is simply the time at which the structure function reaches a value of one magnitude.," Using this functional form, the parameter $\Delta{\tau}_{0}$ should not be construed as a natural time-scale for variability; it is simply the time at which the structure function reaches a value of one magnitude."
+" For structure functions of roughly equal power law slope (a). however. a lower value of An, corresponds to à greater strength of variability."," For structure functions of roughly equal power law slope $\alpha$ ), however, a lower value of $\Delta{\tau}_{0}$ corresponds to a greater strength of variability."
+ Thus. as seen in Table 4.. values for Am increase as one proceeds reckwared in wavelength. indicating declining variability. as seen in Figure 6..," Thus, as seen in Table \ref{fullplfittab}, values for $\Delta{\tau}_{0}$ increase as one proceeds redward in wavelength, indicating declining variability, as seen in Figure \ref{Fig3.1}."
+" However. in cases where the power law slopes of multiple structure functions are not equal. neither Az, nor à gives a reliable measure of the strength of variability."," However, in cases where the power law slopes of multiple structure functions are not equal, neither $\Delta{\tau}_{0}$ nor $\alpha$ gives a reliable measure of the strength of variability."
+ This can be better achieved by evaluating the function at some chosen value of Ar: we choose a value of 100 davs. as this falls near the centre of the range of time lags sampled bv our data.," This can be better achieved by evaluating the function at some chosen value of $\Delta{\tau}$; we choose a value of 100 days, as this falls near the centre of the range of time lags sampled by our data."
+ We shall. therefore. use the V(;Nz=100) parameter as a proxy for the strength. of variability. when comparing the structure functions for samples constructed bv binning in black hole mass and continuum luminosity.," We shall, therefore, use the $V(\Delta{\tau}=100)$ parameter as a proxy for the strength of variability when comparing the structure functions for samples constructed by binning in black hole mass and continuum luminosity."
+ The uncertainties quoted. for values of V(GNz.=100) in ‘Tables 1: and 3 are obtained by using the uncertainties in Aryand o returned by LDL and employing standard: error propagation., The uncertainties quoted for values of $V(\Delta{\tau}=100)$ in Tables 1 and 3 are obtained by using the uncertainties in $\Delta{\tau}_{0}$and $\alpha$ returned by IDL and employing standard error propagation.
+ A total of 2.531 of our quasars are at a sullicientlv high reclshilt (+ 1.69) such that the entire C line profile is," A total of 2,531 of our quasars are at a sufficiently high redshift $z > 1.69$ ) such that the entire C line profile is"
+excitation in nearby LIRGs (Monreal-Iberoetal. 2010)..,excitation in nearby LIRGs \citep{Monreal10}. .
+ Farageetal.(2010) discovered extended shocks caused by gas accreting onto a giant brightest cluster galaxy (BCG)., \citet{Farage10} discovered extended shocks caused by gas accreting onto a giant brightest cluster galaxy (BCG).
+ Finally Richetal.(2010) found extended shock excitation caused wind in the M82-like galaxy NGC 839., Finally \citet{Rich10} found extended shock excitation caused by a galactic wind in the M82-like galaxy NGC 839.
+" In both byFarageagalacticetal.(2010) and Richetal.(2010),, new slow shock models were employed to analyze the shocked gas."," In both \citet{Farage10} and \citet{Rich10}, new slow shock models were employed to analyze the shocked gas."
+ In all of the above cases shock excitation exhibits characteristics of extended LINER-like emission., In all of the above cases shock excitation exhibits characteristics of extended LINER-like emission.
+ In this paper we present a detailed analysis of the widespread shock excitation in two galaxies drawn from a larger IFU sample of nearby U/LIRGs: the Wide Field Spectrograph (WiFeS) Great Observatory All-Sky LIRG Survey (GOALS) sample., In this paper we present a detailed analysis of the widespread shock excitation in two galaxies drawn from a larger IFU sample of nearby U/LIRGs: the Wide Field Spectrograph (WiFeS) Great Observatory All-Sky LIRG Survey (GOALS) sample.
+" We discuss these two systems, IC 1623 and NGC 3256 in ?? and our observations, data reduction and line-fitting in ??.."," We discuss these two systems, IC 1623 and NGC 3256 in \ref{sample} and our observations, data reduction and line-fitting in \ref{observations}."
+" We the properties of the emission line gas for these two presentsystems in 33, including line ratio maps in ?? and emission line diagnostic diagrams in refdiagnostics.."," We present the properties of the emission line gas for these two systems in \ref{emissionlines}, including line ratio maps in \ref{ratiomaps} and emission line diagnostic diagrams in \\ref{diagnostics}."
+ We discuss the distribution of velocity dispersions for each system in ??.., We discuss the distribution of velocity dispersions for each system in \ref{dispersions}.
+ We combine the observed quantities and use them to separate the shocked gas from the HII region gas and provide an analysis of our results in ??.., We combine the observed quantities and use them to separate the shocked gas from the HII region gas and provide an analysis of our results in \ref{analysis}.
+ In ?? we discuss the implications of our results for the interpretation of emission line spectra and investigate the effect that extended shock excitation can have on derived from single aperture of nearby and quantitieshigh-redshift galaxies., In \ref{discussion} we discuss the implications of our results for the interpretation of emission line spectra and investigate the effect that extended shock excitation can have on quantities derived from single aperture spectra of nearby and high-redshift galaxies.
+ Finally we give our spectraconclusions in 22., Finally we give our conclusions in \ref{conclusion}.
+" Throughout this paper we adopt the cosmological Ho270 km Qy20.72, and (420.28, based on parametersthe five-year WMAP s-'Mpc!,results Hinshawetal.(2009) and consistent with the Armusetal.(2009) summary of the GOALS sample."," Throughout this paper we adopt the cosmological parameters $_{0}$ =70 km $^{-1}$ $^{-1}$, $\Omega_{\mathrm{V}}$ =0.72, and $\Omega_{\mathrm{M}}$ =0.28, based on the five-year WMAP results \citet{Hinshaw09} and consistent with the \citet{armus09} summary of the GOALS sample."
+ Systemic heliocentric velocities adjusted adjusted using the 3-attractor flow model of (2000) are taken from Armusetal.(2009)., Systemic heliocentric velocities adjusted adjusted using the 3-attractor flow model of \citet{Mould00} are taken from \citet{armus09}.
+. The labelsamplesystems analyzed in this paper are drawn froma larger integral field spectroscopic survey of the GOALS sample., The systems analyzed in this paper are drawn from a larger integral field spectroscopic survey of the GOALS sample.
+" GOALS is a multi-wavelength survey of the brightest 60j:m extragalactic sources in the local universe (log(Lrg/ 11.0), with redshifts z « 0.088 and is a complete subsetLo) of the IRAS Revised Bright Galaxy Sample (RBGS) (Sandersetal. 2003)."," GOALS is a multi-wavelength survey of the brightest $\mu$ m extragalactic sources in the local universe $log(L_{IR}/L_{\sun}) > 11.0$ ), with redshifts z $<$ 0.088 and is a complete subset of the IRAS Revised Bright Galaxy Sample (RBGS) \citep{Sanders03}."
+. Objects in GOALS cover the full range of nuclear spectral types and interaction stages and provide excellent nearby laboratories for the study of galaxy evolution., Objects in GOALS cover the full range of nuclear spectral types and interaction stages and provide excellent nearby laboratories for the study of galaxy evolution.
+ We chose IC 1623 and NGC 3256 for a more detailed analysis since they both show evidence of widespread shock excitation., We chose IC 1623 and NGC 3256 for a more detailed analysis since they both show evidence of widespread shock excitation.
+" Table 1 shows the global properties of the two systems, both of which are ongoing mergers of two massive spiral galaxies."," Table 1 shows the global properties of the two systems, both of which are ongoing mergers of two massive spiral galaxies."
+ Both systems are fairly luminous LIRGs and neither shows evidence of an embedded AGN., Both systems are fairly luminous LIRGs and neither shows evidence of an embedded AGN.
+ Archival HST data of the systems is shown in fig. 1.., Archival HST data of the systems is shown in fig. \ref{fig1}.
+ Both systems show a complex optical morphology and contain one galaxy nucleus that is heavily extinguished by dust lanes., Both systems show a complex optical morphology and contain one galaxy nucleus that is heavily extinguished by dust lanes.
+" Both galaxies are classified as close mergers (projected separation between the merging nuclei of less than 10 kpc) when using the scheme of Veilleux&Rupke(2002),, which utilizes classifications based on numerical simulations of mergers (Barnesquist1992, 1996)."," Both galaxies are classified as close mergers (projected separation between the merging nuclei of less than 10 kpc) when using the scheme of \citet{Veilleux02}, which utilizes classifications based on numerical simulations of mergers \citep{Barnes92,Barnes96}."
+. IC 1623 (also commonly referred to as VV 114 and with the IRAS designation IRASF 01053-1746) consists of two galaxies: IC 1623 A in the west and the more heavily obscured IC 1623 B in theeast., IC 1623 (also commonly referred to as VV 114 and with the IRAS designation IRASF 01053-1746) consists of two galaxies: IC 1623 A in the west and the more heavily obscured IC 1623 B in theeast.
+" The dust lane seen in figure 1 covers the eastern nucleus, which is actually brighter in the"," The dust lane seen in figure \ref{fig1} covers the eastern nucleus, which is actually brighter in the"
+together with the divergence constraint V-D=0.,together with the divergence constraint $\divB = 0$.
+ We perturb according to where ¢=>Pfpo is the sound speed., We perturb according to where $c_s^2 = \gamma P_0 / \rho_0$ is the sound speed.
+ Considering only linear terms. the perturbed equations are therefore given by Specifying the perturbation according to we have Considering only waves in the x-direction Ge.," Considering only linear terms, the perturbed equations are therefore given by Specifying the perturbation according to we have Considering only waves in the x-direction (ie."
+" Kk= k,.0. Op. defining the wave speed ¢=w/k and using (A9)) to eliminate D. equation CÀ ΤΟ) gives where b,=O since V-DB—0."," $\bk = [\mathrm{k}_x,0,0]$ ), defining the wave speed $v = \omega/\mathrm{k}$ and using \ref{eq:omegaD}) ) to eliminate $D$ , equation \ref{eq:omegav}) ) gives where $b_x = 0$ since $\divB = 0$."
+" Using these in (Al 13) we have We can therefore solve for the perturbation amplitudes Οιμι0.5, and b. in terms of the amplitude of the density perturbation D and the wave speed ο."," Using these in \ref{eq:omegab}) ) we have We can therefore solve for the perturbation amplitudes $v_x,v_y,v_z,b_y$ and $b_z$ in terms of the amplitude of the density perturbation $D$ and the wave speed $v$."
+ We ti, We find where we have dropped the subscript 0.
+nd which reveals the three wavetypes in MHD.," The wave speed $v$ is found by eliminating these quantities from \ref{eq:vxeqn}) ), giving which reveals the three wavetypes in MHD."
+ The Alfvénn waves are those with, The Alfvénn waves are those with
+stars. In particular. may be observable as pulsars. although none is vel known within 1° radius of the Galactic center (GC).,"stars, in particular, may be observable as pulsars, although none is yet known within $1^\circ$ radius of the Galactic center (GC)."
+ Detection of radio pulsars in the GC region is difficult. because of the severe radio wave scattering by intervening interstellar ionized gas (Cordes Lazio 1997).," Detection of radio pulsars in the GC region is difficult, because of the severe radio wave scattering by intervening interstellar ionized gas (Cordes Lazio 1997)."
+ On the other hand. two of the polarized radio nonthermal filaanents CNTEs: in the Radio Are and G359.96-+0.09) show flat or slightlv rising positive spectral indices a characteristic of Crab-like pulsar wind nebulae (DWNe: e.g.. Anantharamaiah et al.," On the other hand, two of the polarized radio nonthermal filaments (NTFs; in the Radio Arc and G359.96+0.09) show flat or slightly rising positive spectral indices — a characteristic of Crab-like pulsar wind nebulae (PWNe; e.g., Anantharamaiah et al."
+ 1991)., 1991).
+ observations have further revealed various diffuse N-rav. filaments with unusually hard spectra. which are also signatures of PWNe.," observations have further revealed various diffuse X-ray filaments with unusually hard spectra, which are also signatures of PWNe."
+ However. no specific link has so far been proposed between such radio/X-ray features and PWNe.," However, no specific link has so far been proposed between such radio/X-ray features and PWNe."
+ llere we report a strong candidate lor a PWN (hat links an X-ray Cireacl G0.13-0.11 and the prominent NTFs in the Radio Are region (Galactic longitude /zz07.2: 11: Yusel-Zadeh. Morris. Chance 1984).," Here we report a strong candidate for a PWN that links an X-ray thread G0.13-0.11 and the prominent NTFs in the Radio Arc region (Galactic longitude $l \approx 0^\circ.2$; 1; Yusef-Zadeh, Morris, Chance 1984)."
+ This X-ray thread. GO.12-0.11 was first apparent in the images of Yusel-Zadeh et al. (, This X-ray thread G0.13-0.11 was first apparent in the images of Yusef-Zadeh et al. (
+2002).,2002).
+ The diffuse X-ray. emission from the neighboring molecular cloud GO.13-0.13 (Oka et al., The diffuse X-ray emission from the neighboring molecular cloud G0.13-0.13 (Oka et al.
+ 2001) has been further investigated by Yusel-Zacdeh. Law. Wardle (2002).," 2001) has been further investigated by Yusef-Zadeh, Law, Wardle (2002)."
+ Thev considered the X-ray. thread. as part of a large-scale diffuse feature that emits the 6.4-keV. [Inorescent. line. whieh results [rom the filling of IX-shell vacancies of neutral or weaklv-ionized irons (IXovama et al.," They considered the X-ray thread as part of a large-scale diffuse feature that emits the 6.4-keV fluorescent line, which results from the filling of K-shell vacancies of neutral or weakly-ionized irons (Koyama et al."
+ 1996: Wang. Gotthelf. Lang 2002: Wane 2002: Yusel-Zadeh. Law. Warclle 2002).," 1996; Wang, Gotthelf, Lang 2002; Wang 2002; Yusef-Zadeh, Law, Wardle 2002)."
+" Because the prominent X-ray. thread is on the side of the molecular cloud that is opposite to Ser A"". they concluded that the G.4-keV line emission could not represent the reflection of a possible recent radiation burst Ilrom the central massive black hole."," Because the prominent X-ray thread is on the side of the molecular cloud that is opposite to Sgr $^*$, they concluded that the 6.4-keV line emission could not represent the reflection of a possible recent radiation burst from the central massive black hole."
+ However. our examination of related observations shows that the G.4-keV line is clearly not associated with the X-ray thread. C0.13-0.11. although ihe molecular cloud is indeed a strong 6.4-keV line emitter (e.g.. 22: Wang 2002).," However, our examination of related observations shows that the 6.4-keV line is clearly not associated with the X-ray thread G0.13-0.11, although the molecular cloud is indeed a strong 6.4-keV line emitter (e.g., 2; Wang 2002)."
+ We have conducted morphological aud spectral analyses of both GO0.13-0.11 and an embedded point-like source., We have conducted morphological and spectral analyses of both G0.13-0.11 and an embedded point-like source.
+" This X-ray study. together with an investigation of the radio emission from (he region. has led us to conclude that GO.13-0.11 most Likely represents a PWN,"," This X-ray study, together with an investigation of the radio emission from the region, has led us to conclude that G0.13-0.11 most likely represents a PWN."
+ Our study usecl all existing observations of the region around. GO0.13-0.11: (his field is shown in Fie., Our study used all existing observations of the region around G0.13-0.11; this field is shown in Fig.
+ 1 with the important features labelled., 1 with the important features labelled.
+ In addition to the observation (50 ks: Obs., In addition to the cycle-1 observation (50 ks; Obs.
+ ID 329945). which was used in Yusel-Zadeh et al. (," ID 945), which was used in Yusef-Zadeh et al. ("
+2002) ancl Yusel-Zadeh. Law. Wirdle (2002). we included. the recent GC ridge survey data (Obs.,"2002) and Yusef-Zadeh, Law, Wardle (2002), we included the recent GC ridge survey data (Obs."
+ TD 422273. 2216. 2282 and 2284 ~I1 ks each: Wang. Gotthelf. Lang 2002) and the evele-1 observation pointed al Ser À* (50 ks: Obs.," ID 2273, 2276, 2282 and 2284 — $\sim 11$ ks each; Wang, Gotthelf, Lang 2002) and the cycle-1 observation pointed at Sgr $^*$ (50 ks; Obs."
+ ID 42242)., ID 242).
+ The X-ray data calibration. including the CTI correction (Townsley et al.," The X-ray data calibration, including the CTI correction (Townsley et al."
+ 2001). has been described bx Wang. Gotthelf.," 2001), has been described by Wang, Gotthelf,"
+relation between the X-ray and the TeV appearance of sources with jets pointing towards us.,relation between the X-ray and the TeV appearance of sources with jets pointing towards us.
+" ote. however. that an observer may see an imperfect correlation if à) the synchrotron and the z-decay spectra are not observed near their »/£,,-peaks. or b) inverse Compton scattering contributes significantly to the X-ray emission. or c) strong absorption shifts the apparent »7;,-peak of the z""-decay emission."," Note, however, that an observer may see an imperfect correlation if a) the synchrotron and the $\pi^0$ -decay spectra are not observed near their $\nu F_\nu$ -peaks, or b) inverse Compton scattering contributes significantly to the X-ray emission, or c) strong absorption shifts the apparent $\nu F_\nu$ -peak of the $\pi^0$ -decay emission."
+ Correlations between the X-ray and TeV emission of BL Lacertae objects have indeed been observed in case of Mkn 421 (Buckley et al. 1996)), Correlations between the X-ray and TeV emission of BL Lacertae objects have indeed been observed in case of Mkn 421 (Buckley et al. \cite{buc96}) )
+ and Mkn 501 (Catanese et al. 1997..," and Mkn 501 (Catanese et al. \cite{cat97},"
+ Aharonian et al. 1999.," Aharonian et al. \cite {aha99},"
+ and eet al. 1999)).," and et al. \cite{dja99}) ),"
+ but at least for Mkn 421 recent data show that there Is no one-to-one correlation during flares (Catanese et al. 1999))., but at least for Mkn 421 recent data show that there is no one-to-one correlation during flares (Catanese et al. \cite{cat99}) ).
+ The high Lorentz factors in our model imply that the observed emission depends more strongly on the aspect angle than in conventional jet models with D ~10., The high Lorentz factors in our model imply that the observed emission depends more strongly on the aspect angle than in conventional jet models with $\Gamma \simeq $ 10.
+ This is shown in Fig. 5.. ," This is shown in Fig. \ref{specc}, ,"
+which displays the spectral evolution of a source viewed at an aspect angle of 2° (j/20.99939)., which displays the spectral evolution of a source viewed at an aspect angle of $^\circ$ $\mu$ =0.99939).
+ The model parameters have been changed slightly compared with those used for the head-on case (Fig. 4))," The model parameters have been changed slightly compared with those used for the head-on case (Fig. \ref{speca}) ),"
+ mostly to make the source brighter., mostly to make the source brighter.
+ The fundamental difference to the 0.—0° case is. however. that the Doppler factor D increases with decreasing D when BO.," The fundamental difference to the $\theta\simeq 0\degr$ case is, however, that the Doppler factor D increases with decreasing $\Gamma$ when $\mu >\beta$ ."
+ In contrast to Fig. 4..," In contrast to Fig. \ref{speca},"
+ where always D>FL. here D increases from an initial value of ~5 to à maximum of Dax=040)U?~29.," where always $D>\Gamma$, here D increases from an initial value of $\sim 5$ to a maximum of $D_{\rm max}
+=(1-\mu^2)^{-0.5}
+\simeq 29$."
+ As a consequence the apparent evolution of the source spectrum is much slower. and the peak energies are smaller and don't change much during the evolution.," As a consequence the apparent evolution of the source spectrum is much slower, and the peak energies are smaller and don't change much during the evolution."
+ The syichrotron peaks are located in the optical. and the x-ray luminosity is small.," The synchrotron peaks are located in the optical, and the x-ray luminosity is small."
+ Strong TeV emission implies that the systems need to be observed head-o1., Strong TeV emission implies that the systems need to be observed head-on.
+ Even for --200 an aspect angle 0.<1° is required., Even for $\Gamma =200$ an aspect angle $\theta \le 1^\circ$ is required.
+ Viewed at aspect angles of a few degrees the sources look like the typical hard spectrum EGRET sources: the spectrum peaks somewhere in the GeV region. the sources reach their maxinum luminosity when the blast wave has decelerated to Lorentz factors around ~sin0. the luminosity spectrum displays a minimum in the keV to MeV range. and the temporal evolution is slower.," Viewed at aspect angles of a few degrees the sources look like the typical hard spectrum EGRET sources: the spectrum peaks somewhere in the GeV region, the sources reach their maximum luminosity when the blast wave has decelerated to Lorentz factors around $\sim \sin^{-1} \theta$, the luminosity spectrum displays a minimum in the keV to MeV range, and the temporal evolution is slower."
+" The dependence of the vf, peak of the high energy emission on the aspect angle Eq. (102))", The dependence of the $\nu F_\nu$ peak of the high energy emission on the aspect angle Eq. \ref{pimax}))
+" also implies a general relationbetween the observed Lo4,,., and the apparent superluminal velocities in. VLBI images."," also implies a general relationbetween the observed $E_{\rm \pi^0,max}$ and the apparent superluminal velocities in VLBI images."
+ Using Eq. (102)), Using Eq. \ref{pimax}) )
+ we may write, we may write
+out on the folded. profiles mace using only ode ane even period-numbers separately.,out on the folded profiles made using only odd and even period-numbers separately.
+ Both incdepencentLy shower peak aroundDM-15.4. pefee., Both independently showed peak around$\sim$ 15.4 pc/cc.
+ We also carried. out. these searches on two fields observed on the same day just. 20 minutes (in right ascension) prior to and after the fiel containing the candidate., We also carried out these searches on two fields observed on the same day just 20 minutes (in right ascension) prior to and after the field containing the candidate.
+ No sign of dispersed signal arounc this period. was found in either of the fields., No sign of dispersed signal around this period was found in either of the fields.
+ This makes i unlikely that the above detection of a periodic signal couk have been a result of some man-made or svstem originate signal., This makes it unlikely that the above detection of a periodic signal could have been a result of some man-made or system originated signal.
+ Intriguingly. for rest of the 9 observing sessions. neither of the two kinds of searches showed anw significant detection.," Intriguingly, for rest of the 9 observing sessions, neither of the two kinds of searches showed any significant detection."
+ We vill discuss. various possibilities which may have caused. these non-detections. along with the implications of parameters determined from our data (table 1) in the Following section.," We will discuss various possibilities which may have caused these non-detections, along with the implications of parameters determined from our data (table 1) in the following section."
+ In figure 4.. the average profile of the LAT PSI. 1732-3131 at 34.5 MllIZ (solid-line) is compared with the pulse-prolile as seen in gamma-rays (dotted-line) (Ravetal.2011.scetheirfigure 25)..," In figure \ref{j1732_profile}, the average profile of the LAT PSR J1732-3131 at 34.5 MHz (solid-line) is compared with the pulse-profile as seen in gamma-rays (dotted-line) \citep[][see their figure 25]{Ray11}."
+ Phe radio profiles have been aligned with 5. rav profile manually. since the accuracy in the estimated: DM value is not adequate enough for absolute phase-alignment.," The radio profiles have been aligned with $\gamma-$ ray profile manually, since the accuracy in the estimated DM value is not adequate enough for absolute phase-alignment."
+ The apparent similarity. between the profiles at these. two extreme ends of the spectrum is striking. although there are possible cilferences.," The apparent similarity between the profiles at these two extreme ends of the spectrum is striking, although there are possible differences."
+ At radio frequencies. the significant pulsed. emission is confined. to about τος of the period. with possibly bridging emission between the (wo rav components (i.e. between 120 to 220 degrees)," At radio frequencies, the significant pulsed emission is confined to about $70\%$ of the period, with possibly bridging emission between the two gamma-ray components (i.e. between 120 to 220 degrees)."
+" The distribution of single bright pulses (figure 4: see the ""arrow-marks"") in longitude is bimocal rather than uniform. visiting regions near the leading and trailing components of the main broad. pulse in the racdio-profile."," The distribution of single bright pulses (figure \ref{j1732_profile}; see the “arrow-marks”) in longitude is bimodal rather than uniform, visiting regions near the leading and trailing components of the main broad pulse in the radio-profile."
+ Given that 1) no obvious association of these single pulses with any of the known pulsars is apparent (based on DM). 2) the dispersion measure suggested by these bright pulses 15.55+£0.04 pefec) falls within the error limits of that associated. with the periodic signal (15.44-£0.32 pefee). 3) the profile shapes ab these two DAL values are indistinguishable (not shown in ligure 4.. but assessed. separately). and. 4) the position of these pulses are correlated with the outer regions of he pulse-window: it is cillicult to rule out the possibility hat these single pulses share their origin with the perioclic signal.," Given that 1) no obvious association of these single pulses with any of the known pulsars is apparent (based on DM), 2) the dispersion measure suggested by these bright pulses $15.55\pm0.04$ pc/cc) falls within the error limits of that associated with the periodic signal $15.44\pm0.32$ pc/cc), 3) the profile shapes at these two DM values are indistinguishable (not shown in figure \ref{j1732_profile}, but assessed separately), and 4) the position of these pulses are correlated with the outer regions of the pulse-window; it is difficult to rule out the possibility that these single pulses share their origin with the periodic signal."
+ At the same time. the statistics of 10. pulses 1s oo poor to rule out chance segregation in longitude.," At the same time, the statistics of 10 pulses is too poor to rule out chance segregation in longitude."
+ Ciant pulses/radiation spikes are usually seen to confine hemselves within the average pulse window (Lunderenetal.1995:Xblesetal. 1997).," Giant pulses/radiation spikes are usually seen to confine themselves within the average pulse window \citep[][]{L95,Ables97}."
+. Llowever. in the case of 0218|4232 (Ixnightctal.2006).. the giant. pulses concentrate just outside the rising and trailing edges of the broad radio pulse. and those regions match the locations of the peaks in the ligh energy (x-ray) profile.," However, in the case of J0218+4232 \citep{Knight06}, the giant pulses concentrate just outside the rising and trailing edges of the broad radio pulse, and those regions match the locations of the peaks in the high energy (x-ray) profile."
+ H£ our single pulses are real. then heir apparent distribution is reminiscent of the situation in J0218|4232. and the peaks in the eumma-ray. profile could correspond to the single. pulse locations if the eaunma-ravy »ofile was shifted by about 1807 compared to what is shown in figure 4..," If our single pulses are real, then their apparent distribution is reminiscent of the situation in J0218+4232, and the peaks in the gamma-ray profile could correspond to the single pulse locations if the gamma-ray profile was shifted by about $180^{\circ}$ compared to what is shown in figure \ref{j1732_profile}."
+ Given this. and the apparent relative brightness of our single pulses. the possibility of their being giant pulses can not be ruled out.," Given this, and the apparent relative brightness of our single pulses, the possibility of their being giant pulses can not be ruled out."
+ The half-power beam-width at this declinationis almost 35 (in declination)., The half-power beam-width at this declination is almost $^{\circ}$ (in declination).
+ Fherefore. we take the sky temperature estimates at various points across the beam from the higher resolution svnthesis skv-map at 34.5 MlIIZ (Dwarakanath&UdayShankar1990).. and a weighted average of these using a theoretical beam-gain pattern provides us an estimate for the svstem. temperature.," Therefore, we take the sky temperature estimates at various points across the beam from the higher resolution synthesis sky-map at 34.5 MHz \citep{DU90}, and a weighted average of these using a theoretical beam-gain pattern provides us an estimate for the system temperature."
+ For the present. case. dU is estimated to be 570007 IX (receiver temperature Contribution is negligible).," For the present case, it is estimated to be $57000^{\circ}$ K (receiver temperature contribution is negligible)."
+ Using this calibration. ancl assuming an ellective. collecting area of S700mi. (in the direction. of the pulsar) we estimate the average [lux density. (pulse-energy/period) of this pulsar at. 34.5. MllIz to be about 4 Jv.," Using this calibration, and assuming an effective collecting area of $8700 \; {\rm m^2}$ (in the direction of the pulsar) we estimate the average flux density (pulse-energy/period) of this pulsar at 34.5 MHz to be about 4 Jy."
+ Vhe mean [lux density at 34.5 Mllz. combined with the upper limit on the Lux density at 1.4 Gllz (0.2mJv:Camiloetal. 2009). suggests à spectral index à:2.7 assuming no turnover in the spectrum (a tighter upper limit eiven by Rayctal.2011. from a deeper search. suggests. further steeper spectral index).," The mean flux density at 34.5 MHz, combined with the upper limit on the flux density at 1.4 GHz \citep[0.2 mJy;][]{Camilo09}, suggests a spectral index $\alpha\leq -2.7$ assuming no turn-over in the spectrum (a tighter upper limit given by \citealt{Ray11} from a deeper search suggests further steeper spectral index)."
+ Although such a steep spectrum. could. explain the non-detection of the pulsar at higher frequencies. its detection in only one out of ten observing sessions at 34.5 MlIZ necessitates consideration of following possibilities ].," Although such a steep spectrum could explain the non-detection of the pulsar at higher frequencies, its detection in only one out of ten observing sessions at 34.5 MHz necessitates consideration of following possibilities 1."
+ This pulsar may actually be emitting below our detection limit. and favorable refractive scintillation conditions possibly raised. the [lux above our detection limit during one of our observing 2.," This pulsar may actually be emitting below our detection limit, and favorable refractive scintillation conditions possibly raised the flux above our detection limit during one of our observing 2."
+" The source may be an intermittent pulsar or a radio-faint pulsar which comes in ""racio-bright mode once in a while.", The source may be an intermittent pulsar or a radio-faint pulsar which comes in “radio-bright” mode once in a while.
+ In either. of the above possibilities. the spectral steepness mentioned above would be an overestimate.," In either of the above possibilities, the spectral steepness mentioned above would be an overestimate."
+ For DM-15. pc/cc anc location of the pulsar (lLX—17:32:33.54.— Dec--31:31:223.00). the Cordes—Lazio(2002) electron density model LL model) a pulsar distance (dps) of 600+150 pe.," For DM=15.4 pc/cc and location of the pulsar (RA=17:32:33.54, Dec=-31:31:23.00), the \citet{CL02} electron density model L model) a pulsar distance $d_{PSR}$ ) of $600\pm150$ pc."
+ This agrees well with the dpsg estimates of 0.ττatO34 kpe and ONG(ID kpe by WeiWang (2011).. using the correlation between the ganuna-ray emission efficiency. ancl a few pulsar parameters (ecneration-order parameter and ο).," This agrees well with the $d_{PSR}$ estimates of $0.77^{+0.41}_{-0.35}$ kpc and $0.86^{+0.49}_{-0.30}$ kpc by \citet{Wang11}, , using the correlation between the gamma-ray emission efficiency and a few pulsar parameters (generation-order parameter and $B_{LC}$ )."
+ Alternatively. these distance estimates combined with the mocel electron density along the pulsar direction. give consistent DAL value.," Alternatively, these distance estimates combined with the model electron density along the pulsar direction, give consistent DM value."
+brielit regions separated by ~10% au incomplete shell ~30% long in the east. aud an extended (~20ς 10) structure in the west.,"bright regions separated by $\sim 10'$, an incomplete shell $\sim 30'$ long in the east, and an extended $\sim 20'\times 10'$ ) structure in the west."
+ The structure in the west is separated from the ceutral region by a region of weak emissiou where molecular clouds associated with the W51D star-forming region are located., The structure in the west is separated from the central region by a region of weak emission where molecular clouds associated with the W51B star-forming region are located.
+ The systematic judenimg of the N-aax spectrin toward the wes sugeested that the X-ravs are eluitted behiud these molecular clouds., The systematic hardening of the X-ray spectrum toward the west suggested that the X-rays are emitted behind these molecular clouds.
+ The average X-ray spectrum of the SNR was fitted well bv a sinele-temperatiure (Apiz0.29 keV) jeriual plasma model., The average X-ray spectrum of the SNR was fitted well by a single-temperature $k_B T\simeq 0.29$ keV) thermal plasma model.
+ But the energy rauge of the ROSAT detector was uo enough to distinguish us from other cussion models., But the energy range of the ROSAT detector was not enough to distinguish this from other emission models.
+ Iu this paper. we present the results of an y.udv of the W51 complex.," In this paper, we present the results of an study of the W51 complex."
+" The greater (0.710 ""meV) energy coverage of makes it clear that 1ο N-rav oenadssiou from the SNR is of thermal origin.", The greater (0.7–10 keV) energy coverage of makes it clear that the X-ray emission from the SNR is of thermal origin.
+ The newly derived plasma parameters are consistent with the ROSAT results., The newly derived plasma parameters are consistent with the ROSAT results.
+ also reveals hard X-ravs from star-forming regions i W5I. which were not seen by ROSAT.," also reveals hard X-rays from star-forming regions in W51, which were not seen by ROSAT."
+ W51 was observed by October 10. 1995.," W51 was observed by October 10, 1995."
+ Two chips of cach SIS detector were aligned in 2-CCD mode to cover the bright central region revealed by ROSAT. while the CIS detector covered most of the N-rav cluitting region.," Two chips of each SIS detector were aligned in 2-CCD mode to cover the bright central region revealed by ROSAT, while the GIS detector covered most of the X-ray emitting region."
+ Figure 1 shows the positions of SIS aud GIS fields overlaid on the ROSAT image of KKS., Figure 1 shows the positions of SIS and GIS fields overlaid on the ROSAT image of KKS.
+ The data used are the archive data processed by the revision 2 standard sereeniug process., The data used are the archive data processed by the revision 2 standard screening process.
+" The total exposure times after screening were 36.1 ks aud 12.8 ks for SISO and SISL. aud [1.3 ks for both CIS2 and (5,"," The total exposure times after screening were 36.4 ks and 12.8 ks for SIS0 and SIS1, and 44.3 ks for both GIS2 and GIS3."
+ For spatial analysis. we have ecuerated CIS nuages in the cnerev ances: 1.5 keV. 1.52.5 keV. 2.56.0 keV. and 6.010.0 keV. We fist generated a raw CUS nuage for a eiven enerev baud aud divided it wv the blauk-ska COS iuage of the same energv xuxl.," For spatial analysis, we have generated GIS images in the energy bands: 0.7–1.5 keV, 1.5--2.5 keV, 2.5–6.0 keV, and 6.0–10.0 keV. We first generated a raw GIS image for a given energy band and divided it by the blank-sky GIS image of the same energy band."
+ The blauk-skv inage represents the respouse of ταν clescope (XRT) plus CdS for uuiforii background emission., The blank-sky image represents the response of X-ray telescope (XRT) plus GIS for uniform background emission.
+ Therefore. by dividing the raw image by the blauk-sky nuage. the backeround level iu the nuage could be flattened (e.g... Ἱναποία 1998). aud bx subtracting a constant. à backerounud-subtracted nuage was obtained.," Therefore, by dividing the raw image by the blank-sky image, the background level in the image could be flattened (e.g., Kaneda 1998), and by subtracting a constant, a background-subtracted image was obtained."
+ For a test. we applied the technique to a source-free region at (2507 and confirmed that the residual image did not have any systematic eradieut.," For a test, we applied the technique to a source-free region at $\ell\simeq 50^\circ$ and confirmed that the residual image did not have any systematic gradient."
+ The vieuettiug effect for spatially-confined sources. however. is ercater than that for the background because there is uo strav-lieht coming frou outside the field-of-view.," The vignetting effect for spatially-confined sources, however, is greater than that for the background because there is no stray-light coming from outside the field-of-view."
+ We therefore divided the above image by an cHective exposure map Which accounts for the variation of effective area with detector position and cuerey., We therefore divided the above image by an effective exposure map which accounts for the variation of effective area with detector position and energy.
+ We constructed GIS2 aud GIS3 images separately aud added the two after masking out regions near the edge of the field aud around the built-in calibration source., We constructed GIS2 and GIS3 images separately and added the two after masking out regions near the edge of the field and around the built-in calibration source.
+" The images have pixel size of 15""« aud have been smoothed using a Gaussian profile of c=1’.", The images have pixel size of $15''\times 15''$ and have been smoothed using a Gaussian profile of $\sigma=1'$.
+" The count rates in the CGIS2]2 nuages of 0.71.5. 1.52.5. 2.56.0. and 6.010.0 keV are 0.51. 0.61. 0.16. and 1.26 counts respectively,"," The count rates in the GIS2+3 images of 0.7–1.5, 1.5–2.5, 2.5--6.0, and 6.0–10.0 keV are 0.51, 0.64, 0.46, and 0.26 counts $^{-1}$, respectively."
+ huages of wider enerev bands. e.g. 0.72.5 keV. were coustructed w addiug the above images.," Images of wider energy bands, e.g., 0.7–2.5 keV, were constructed by adding the above images."
+ We eenerated SIS nuages in a simular wav. except that they were iot divided by Dblank-sky images because the ackeround intensity was uniforii over the field.," We generated SIS images in a similar way, except that they were not divided by blank-sky images because the background intensity was uniform over the field."
+" SIS nuages have pixel size of 671«G1 and rave been smoothed using a Caussian profile of 9-25"",", SIS images have pixel size of $6\farcsec 4 \times 6\farcsec 4$ and have been smoothed using a Gaussian profile of $\sigma=25\arcsec$.
+ Figure 2a is CIS image of W5l in the total (0.710.0 keV) cnerey band aud shows that the region has a complex. X-ray imorpholosv., Figure 2a is GIS image of W51 in the total (0.7–10.0 keV) energy band and shows that the region has a complex X-ray morphology.
+" This is partly due to the superposition. of uurclated sources, Which can be distinguished by looking at soft and hard N-rav nuages."," This is partly due to the superposition of unrelated sources, which can be distinguished by looking at soft and hard X-ray images."
+ Figures 2b and 2c are CUS nuages of W51 in the soft (0.72.5 keV) and hard (2.56.0 keV) euergv bands., Figures 2b and 2c are GIS images of W51 in the soft (0.7–2.5 keV) and hard (2.5–6.0 keV) energy bands.
+ Figure 2b. which is consistent with the ROSAT image of ο (Fie.," Figure 2b, which is consistent with the ROSAT image of KKS (Fig."
+ 1). shows an extended structure ~20’ loug along the SE-NW= direction at the field ceuter.," 1), shows an extended structure $\sim 20'$ long along the SE-NW direction at the field center."
+ It is composed of two bright regions. regions NN and XS. separated bv ~10.," It is composed of two bright regions, regions XN and XS, separated by $\sim 10'$."
+ XS has a rklee extending to the east., XS has a ridge extending to the east.
+ There is also a bright extended structure in the west. NW.," There is also a bright extended structure in the west, XW."
+ These structures are mainersed in falter diffuse emission., These structures are immersed in fainter diffuse emission.
+ Tn hard X-ravs (Fig., In hard X-rays (Fig.
+ 2c). there are also bright regions aud faint diffuse cussion.," 2c), there are also bright regions and faint diffuse emission."
+ The bright, The bright
+where the state parameter of modified Chaplvein gas ls For the mathematical simplicity. we work out a=l oul.,"where the state parameter of modified Chaplygin gas is For the mathematical simplicity, we work out $\alpha=1$ only."
+ The critical points of the above svsteni are obtainedaine by- puttingine JUπο202mqve$7 which vield The two critical points correspond to the era dominated by dark matter aud MC. type dark energyaud exist forον A>ανπαpy., The critical points of the above system are obtained by putting $\frac{du}{dx}=0=\frac{dv}{dx}$ which yield The two critical points correspond to the era dominated by dark matter and MCG type dark energyand exist for $A>\frac{1}{b-1}$.
+ For the two critical poiuts. the state parameter (9) of the interacting dark energy takes the form which holds ouly when aj.|6;41.," For the two critical points, the state parameter (9) of the interacting dark energy takes the form which holds only when $u_{ic}+v_{ic}\neq1$."
+ We further check the stability of the dynamical system (Eqs. (, We further check the stability of the dynamical system (Eqs. (
+7) aud (8)) about the critical point.,7) and (8)) about the critical point.
+" To do this. we linearize the eoverming equations about the critical point ie. 8=,|du aud e—6.|de. we obtain The subscript e refers to quautities evaluated at the critical poiut of the dvizauical system."," To do this, we linearize the governing equations about the critical point i.e. $u=u_c+\delta u$ and $v=v_c+\delta v$, we obtain The subscript $c$ refers to quantities evaluated at the critical point of the dynamical system."
+" We also calculate the deceleration parameter g-1CIT/TT?). in this model as which can be written in terms of dimensionless density parameter O4,=Puce!pi Clearly in the limit of pj> x. we retrieve the result for the Eiusteiu's eravity as"," We also calculate the deceleration parameter $q=-1-(\dot H/H^2)$, in this model as which can be written in terms of dimensionless density parameter $\Omega_\text{mcg}=\rho_\text{mcg}/\rho$: Clearly in the limit of $\rho_1\rightarrow\infty$ , we retrieve the result for the Einstein's gravity as"
+The simple correlation test tends to report mareinally higher detection levels than the field amplitude aud model colmparisou tests. and the model comparison test similar values as the field amplitude test. which is compatible with the predictious frou the ROC curves in Figure 3..,"The simple correlation test tends to report marginally higher detection levels than the field amplitude and model comparison tests, and the model comparison test similar values as the field amplitude test, which is compatible with the predictions from the ROC curves in Figure \ref{fig:roc}."
+H lu this paper we have extensively reviewed the miierous methods in the literature which are used to detect and measure the presence o ean ISW signal using naps for the CMD and local tracers of nass., In this paper we have extensively reviewed the numerous methods in the literature which are used to detect and measure the presence of an ISW signal using maps for the CMB and local tracers of mass.
+ We notice hat the variety of methods used ca1 leac to cüfferenut aux conflicting conclusions., We noticed that the variety of methods used can lead to different and conflicting conclusions.
+ We also noted two broad classes of nethods: oue which uses the cross-c¢relation spectrum as he measure and the other which 1ses the reconstructec ISW temperature field., We also noted two broad classes of methods: one which uses the cross-correlation spectrum as the measure and the other which uses the reconstructed ISW temperature field.
+ We identified the advantages and cisacdvarages of al nethods used in the literature aud concluded hat: This led us to construct a new and complete method for detecting aud measuring the ISW effect., We identified the advantages and disadvantages of all methods used in the literature and concluded that: This led us to construct a new and complete method for detecting and measuring the ISW effect.
+ The method is παπασος as follows: The method we preseut in this paper makes ouly oue assunption: that the primordial CAIB tempcrature field behaves like a Caussian randoms field., The method is summarised as follows: The method we present in this paper makes only one assumption: that the primordial CMB temperature field behaves like a Gaussian random field.
+" The method is general in that it ""allows! the galaxy field to behave as a lognormal field. but does not automatically asstme that the galaxy field is lognormal."," The method is general in that it `allows' the galaxy field to behave as a lognormal field, but does not automatically assume that the galaxy field is lognormal."
+ We first applied our method to 2\TASS aiD clid simulaions., We first applied our method to 2MASS and Euclid simulations.
+ We find that it is «iffient to detect the ISW VAignificautly usine 2MASS siations. aud fiud ιο diffeveuce between assmnuing the uderlying eaOs:ANY field is Ciussiau or lognormal. aux ouly muild differences depending on the statistical test used.," We find that it is difficult to detect the ISW significantly using 2MASS simulations, and find no difference between assuming the underlying galaxy field is Gaussian or lognormal, and only mild differences depending on the statistical test used."
+ With a Euclid-ike survey. we expect high deteclon evels. even with incomplete Sky coverage - we expeoT σ detection level ux18o he simple correlation methoo xd ~Lia detection evel 1sine the fields amplitude or imehod. comparison οςincpues.," With a Euclid-like survey, we expect high detection levels, even with incomplete sky coverage - we expect $\sim 7 \sigma$ detection level using the simple correlation method, and $\sim 4.7\sigma$ detection level using the fields amplitude or method comparison techniques."
+ These detections levels are the same whether he Iacld galaxy field follows a Causinu or lognormal disτηΊο., These detections levels are the same whether the Euclid galaxy field follows a Gaussian or lognormal distribution.
+ Οιr results also show that the iupaiutius uehod does uo introduce spurious correlations between Laps., Our results also show that the inpainting method does not introduce spurious correlations between maps.
+ We applied tus method to WMADPT aud 2ΔASS data. aud found that or results were comparable with carly cleections of the ISW sienal using 2MÁSS data and lie roughly in the 1.1]2.00 rauge.," We applied this method to WMAP7 and 2MASS data, and found that our results were comparable with early detections of the ISW signal using 2MASS data and lied roughly in the $1.1-2.0\sigma$ range."
+" These resits are also COupatible with the simulations we ran for fιο 2MASS SUEVOY,", These results are also compatible with the simulations we ran for the 2MASS survey.
+ The last test we performed. the model comparison test. ss the inuch more pertinent question of w1οher the data prefers à ACDAM. mode to the null hypothesis (1.6. curvature aud uo dark cucrey).," The last test we performed, the model comparison test, asks the much more pertinent question of whether the data prefers a $\Lambda$ CDM model to the null hypothesis (i.e. no curvature and no dark energy)."
+ Using this test. we fiud allLao detection for rauges f=[2/350] and 1.21.900 for ranges {[2/3100/200). which is sometimes üeher than what was previously reported im using a spectra models courparisou test. withou sparse duuniting or bootstrapping.," Using this test, we find a $1.1-1.8\sigma$ detection for ranges $\ell=[2/3-50]$ and $1.2-1.9\sigma$ for ranges $\ell=[2/3-100/200]$, which is sometimes higher than what was previously reported in using a spectra models comparison test, without sparse inpainting or bootstrapping."
+ À ly-pro«uct of this measurement is he reconstruction of the temperature 1SW feld due to 2ATASS ealanics. recostructed with full sky coverage.," A by-product of this measurement is the reconstruction of the temperature ISW field due to 2MASS galaxies, reconstructed with full sky coverage."
+ By applying OUL nethod to different estinatious of CAIB inaps. we liehlieht the importance of component separation ou the ISW detection.," By applying our method to different estimations of CMB maps, we highlight the importance of component separation on the ISW detection."
+ Tabο δ shows scores between 1.12.00 0i different WMADP maps., Table \ref{tab:resl100} shows scores between $1.1-2.0\sigma$ on different WMAP maps.
+ We were also able to detect the ISW signal at 2.70 using a another lap (not presente in this paper), We were also able to detect the ISW signal at $2.7\sigma$ using a another map (not presented in this paper).
+ The intlucuce of the component separation method ou the quality of the estimation needs to ve nore deeply understood in future works., The influence of the component separation method on the quality of the estimation needs to be more deeply understood in future works.
+With the advent of deep and wide multi-band photometric surveys there has been a resurgence of interest in photometric redshifts as a means of estimating the distance to a range of astrophysical objects.,With the advent of deep and wide multi-band photometric surveys there has been a resurgence of interest in photometric redshifts as a means of estimating the distance to a range of astrophysical objects.
+ Depending on the objects of interest and the information to hand. the derived photometrie redshifts will be of varving precision and accuracy. but all ean be described by a probability density function (PDF).," Depending on the objects of interest and the information to hand, the derived photometric redshifts will be of varying precision and accuracy, but all can be described by a probability density function (PDF)."
+ As our understanding of photometric redshifts improves our confidence in. and ability to characterise. these PDFs. their use in cosmological statistical analyses Is sure to increase.," As our understanding of photometric redshifts improves our confidence in, and ability to characterise, these PDFs, their use in cosmological statistical analyses is sure to increase."
+" In the sense that photo-zs represent color-redshift relations. the use of an of PDFs for a of objects is a decades-old approach (e.g.Koo1999,andreferencestherein)."," In the sense that $z$ s represent color-redshift relations, the use of an of PDFs for a of objects is a decades-old approach \citep[e.g.][and references therein]{Koo99}."
+ An example of this is the selection of cluster galaxies (e.g..viatheRedSequence:Gladders&Yee 2000).," An example of this is the selection of cluster galaxies \citep[e.g., via the Red Sequence;][]{Gla00}."
+. Cluster galaxy selection techniques have. in fact. recently been updated to incorporate full PDFs but approaches that use full PDFs remain rare.," Cluster galaxy selection techniques have, in fact, recently been updated to incorporate full PDFs but approaches that use full PDFs remain rare."
+ Subbaraoetal.(1996) introduced. a method that used Gaussian PDFs to estimate luminosity functions. a problem that ws been studied for more arbitrary PDF shapes by Chenetal.(2003) and Sheth(2007).," \citet{Sub96} introduced a method that used Gaussian PDFs to estimate luminosity functions, a problem that has been studied for more arbitrary PDF shapes by \citet{Che03} and \citet{Sheth07}."
+. Full PDFs are particularly underutilised in clustering work. where the use of broad redshift bins is more wrevalent.," Full PDFs are particularly underutilised in clustering work, where the use of broad redshift bins is more prevalent."
+ By using broad redshift bins to measure photometric clustering one can ameliorate uncertainties in the photo-z “peak”. but typically at the expense of constraining power.," By using broad redshift bins to measure photometric clustering one can ameliorate uncertainties in the $z$ “peak"", but typically at the expense of constraining power."
+ One of the most fundamental statistics of any population of objects. and one which carries much physical information. is the 2-»oint correlation function (e.g.Totsuyi&Kihara1969).," One of the most fundamental statistics of any population of objects, and one which carries much physical information, is the 2-point correlation function \citep[e.g.][]{Tot69}."
+. Provided he redshift distribution of the objects is well known. the underlying 3D clustering can be robustly inferred from the measured clustering in projection (Limber1953).. but the number of objects required increases dramatically when the redshift distribution is broad.," Provided the redshift distribution of the objects is well known, the underlying 3D clustering can be robustly inferred from the measured clustering in projection \citep{Limber}, but the number of objects required increases dramatically when the redshift distribution is broad."
+ For this reason. estimates of the 2-point function can in principle gain tremendously from improved utilization of the redshift information associated with photometric objects.," For this reason, estimates of the 2-point function can in principle gain tremendously from improved utilization of the redshift information associated with photometric objects."
+"and 0.061, respectively.","and 0.061, respectively."
+" This increase of the mean ratio ro» of about and after 3 and GGyr directly reflects variation of the composition and structure of the central stellar layers caused by rotational mixing, which become more visible as the age increases."," This increase of the mean ratio $r_{02}$ of about and after 3 and Gyr directly reflects variation of the composition and structure of the central stellar layers caused by rotational mixing, which become more visible as the age increases."
+ We thus conclude that the increase of the small separation and the ratio ro» discussed above in the case of stellar models computed with the same initial parameters (but sharing different location in the HR diagram) is still clearly observed for models with the same global stellar parameters., We thus conclude that the increase of the small separation and the ratio $r_{02}$ discussed above in the case of stellar models computed with the same initial parameters (but sharing different location in the HR diagram) is still clearly observed for models with the same global stellar parameters.
+" Figure 12. shows that this increase is more pronounced at low frequency, leading to a slightly steeper slope in the ro? versus frequency diagram."," Figure \ref{r02_t3t6} shows that this increase is more pronounced at low frequency, leading to a slightly steeper slope in the $r_{02}$ versus frequency diagram."
+" Thus, in addition to increasing the mean value of the ratio ro», rotational mixing also changes the frequency dependence of ro»."," Thus, in addition to increasing the mean value of the ratio $r_{02}$, rotational mixing also changes the frequency dependence of $r_{02}$."
+ This reflects the effects of rotation on the chemical gradients and in particular the change of the abundance of hydrogen in the central parts of the star (see Fig. 9))., This reflects the effects of rotation on the chemical gradients and in particular the change of the abundance of hydrogen in the central parts of the star (see Fig. \ref{profx}) ).
+" By comparing the asteroseismic properties of models that share the same global stellar parameters, we conclude that rotational mixing is able to increase the mean small separation and ratio ro? without changing the mean large separation."," By comparing the asteroseismic properties of models that share the same global stellar parameters, we conclude that rotational mixing is able to increase the mean small separation and ratio $r_{02}$ without changing the mean large separation."
+" These results are particularly interesting in the context of the asteroseismic calibration of stars for which solar-like oscillations are observed, since all observational constraints (classical as well as asteroseismic) have to be correctly reproduced simultaneously."," These results are particularly interesting in the context of the asteroseismic calibration of stars for which solar-like oscillations are observed, since all observational constraints (classical as well as asteroseismic) have to be correctly reproduced simultaneously."
+ It is long known that meridional circulation. and shear turbulence are actually not sufficient to enforce the near uniformity of the solar rotation profile measured by helioseismology., It is long known that meridional circulation and shear turbulence are actually not sufficient to enforce the near uniformity of the solar rotation profile measured by helioseismology.
+" Indeed, models of solar-type stars including shellular rotation predict an increase in the angular velocity "," Indeed, models of solar-type stars including shellular rotation predict an increase in the angular velocity when the distance to the centre decreases \citep{pin89,cha95,tal97_these,mat98}."
+This is contradicted by helioseismic measurements indicating an approximately constant angular velocity between about and of the total solar radius (???)..," This is contradicted by helioseismic measurements indicating an approximately constant angular velocity between about and of the total solar radius \citep{bro89,kos97,cou03}."
+ Another process is thus expected to intervene in the transport of angular momentum in low-mass stars., Another process is thus expected to intervene in the transport of angular momentum in low-mass stars.
+ Additional clues about the existence and nature of this process come from observations of light element abundances in low-mass stars which are efficiently spun down via magnetic torquing and lie on the cool side of the lithium dip (??)..," Additional clues about the existence and nature of this process come from observations of light element abundances in low-mass stars which are efficiently spun down via magnetic torquing and lie on the cool side of the lithium dip \citep{tal98,tal03}."
+" Two main candidates have been proposed to efficiently extract angular momentum from the central core of a solar-type star, namely magnetic fields (seee.g.319) and travelling internal gravity waves (222222?).."," Two main candidates have been proposed to efficiently extract angular momentum from the central core of a solar-type star, namely magnetic fields \citep[see e.g.][]{mes87,cha93,egg05_mag} and travelling internal gravity waves \citep{scha93,kum97,zah97,cha05,tal05,mat08,mat09}."
+" Since these processes leave slightly different signatures on the angular rotation profiles, it is important to test both of them with asteroseismic techniques."," Since these processes leave slightly different signatures on the angular rotation profiles, it is important to test both of them with asteroseismic techniques."
+" As of now however only the prescription for angular momentum transport by magnetic fields for the Tayler-Spruit dynamo (?) is included in the Geneva stellar evolution code, while the modelling of the transport of angular momentum by internal gravity including recent improvements is currently being implemented in this tool."," As of now however only the prescription for angular momentum transport by magnetic fields for the Tayler-Spruit dynamo \citep{spr02} is included in the Geneva stellar evolution code, while the modelling of the transport of angular momentum by internal gravity including recent improvements is currently being implemented in this tool."
+" We thus present here only models computed with both shellular rotation and magnetic fields as prescribed by the Tayler-Spruit dynamo, which are found to correctly reproduce the helioseismic measurements of the internal rotation of the Sun (?).."," We thus present here only models computed with both shellular rotation and magnetic fields as prescribed by the Tayler-Spruit dynamo, which are found to correctly reproduce the helioseismic measurements of the internal rotation of the Sun \citep{egg05_mag}."
+" This will allow us to investigate the general asteroseismic properties of solar-type stars with quasi-solid body rotation of their radiative interior, even if the theoretical prescription for the dynamo (seee.g.?) as well as its real existence (??) is still a matter of debate."," This will allow us to investigate the general asteroseismic properties of solar-type stars with quasi-solid body rotation of their radiative interior, even if the theoretical prescription for the dynamo \citep[see e.g.][]{den07} as well as its real existence \citep{zah07,gel08}
+ is still a matter of debate."
+ The effects of internal gravity waves on the asteroseismic properties of stellar models as well as the influence of other prescriptions for internal magnetic fields (e.g.?) will be studied in the near future., The effects of internal gravity waves on the asteroseismic properties of stellar models as well as the influence of other prescriptions for internal magnetic fields \citep[e.g.][]{mat05} will be studied in the near future.
+ The main-sequence evolution of a MM; model including both shellular rotation and the Tayler-Spruit dynamo is computed for an initial velocity on the ZAMS of ss-!., The main-sequence evolution of a $_{\odot}$ model including both shellular rotation and the Tayler-Spruit dynamo is computed for an initial velocity on the ZAMS of $^{-1}$.
+ Figure 13 shows the evolutionary tracks in the HR diagram for this model and for the corresponding models computed with rotation only and without rotation., Figure \ref{dhr_magn} shows the evolutionary tracks in the HR diagram for this model and for the corresponding models computed with rotation only and without rotation.
+ All three models include atomic diffusion of helium and heavy elements., All three models include atomic diffusion of helium and heavy elements.
+ The effects of rotation are strongly reduced when the Tayler-Spruit dynamo is included in the computation., The effects of rotation are strongly reduced when the Tayler-Spruit dynamo is included in the computation.
+" Only a slight shift of the track to the blue part of the HR diagram is indeed observed for the model with both rotation and magnetic fields, while the rotating model exhibits a significant increase of the effective temperature."," Only a slight shift of the track to the blue part of the HR diagram is indeed observed for the model with both rotation and magnetic fields, while the rotating model exhibits a significant increase of the effective temperature."
+ These differences observed in the HR diagram can be related to changes in the surface chemical composition, These differences observed in the HR diagram can be related to changes in the surface chemical composition
+the observed x value by (cos(8))! over the [face on x value.,the observed x value by $(\cos(\theta))^{-1}$ over the face on x value.
+ This has three effects on equation 12.., This has three effects on equation \ref{eqn:ar}.
+ The value of x in K(x) should be .rcos(8) since a value wvcos(@) in Che lace on frame appears to be x in the observed [rame., The value of x in K(x) should be $x \cos(\theta)$ since a value $x \cos(\theta)$ in the face on frame appears to be x in the observed frame.
+ Next the radius Ar of the ring spanning A. is now Arcos(#) since Ar is now Arcos(@) in the lace on coordinates.," Next the radius $\Delta r$ of the ring spanning $\Delta x$ is now $\Delta r
+\cos(\theta)$ since $\Delta x$ is now $\Delta x \cos(\theta)$ in the face on coordinates."
+ Finally the projected area is also reduced by cos(@)., Finally the projected area is also reduced by $\cos(\theta)$.
+ This transforms equation 12. to Under the assumption (hat all inclinations are equally probable the range between 0 and 90° is divided into LOO equally spaced angles and equation 19 is summied over all angles., This transforms equation \ref{eqn:ar} to Under the assumption that all inclinations are equally probable the range between 0 and $^{\circ}$ is divided into 100 equally spaced angles and equation \ref{eqn:arth} is summed over all angles.
+ The last 20 angles in the angle distribution are set equal to the 80(h value to recognize the ealaxies have significant thickness which also avoids the singularity at 90° inclination., The last 20 angles in the angle distribution are set equal to the 80th value to recognize the galaxies have significant thickness which also avoids the singularity at $^{\circ}$ inclination.
+ The areas found for each intensity value are divided bv the intensity interval (o determine the caleulated h(x) shown as the solid line in fig. 1.., The areas found for each intensity value are divided by the intensity interval to determine the calculated h(x) shown as the solid line in fig. \ref{fig:hx}.
+ Free parameter values of ó*=000Τη per comoving cubic Megaparsec. m* = 4x10! Np; = 2.0 kpe a = -12 and n = 5 produce a good fil to the observed h(x).," Free parameter values of $\phi^* = 0.007 m^*$ per comoving cubic Megaparsec, m* = $4 \times 10^{10}$ $_{\odot}$, $r_o$ = 2.0 kpc, $\alpha$ = -1.2 and n = 5 produce a good fit to the observed h(x)."
+ It could be asked whether with 5 free parameters can vou alwavs get a good fil?, It could be asked whether with 5 free parameters can you always get a good fit?
+ On the other hand the empirical laws governing the distribution contain these parameters and (their values must be set., On the other hand the empirical laws governing the distribution contain these parameters and their values must be set.
+ That (he values are consistent wilh values (hat one would set à priori in an attempt to model the distributions gives a good indication that the distribution shape is determined by (he empirical laws and assumptions emploved., That the values are consistent with values that one would set a priori in an attempt to model the distributions gives a good indication that the distribution shape is determined by the empirical laws and assumptions employed.
+ Experiments setting one of (he parameters to a mildly nonphlivsical value indicated that no rearrangement of (he remaining parameters could produce an acceptable fit., Experiments setting one of the parameters to a mildly nonphysical value indicated that no rearrangement of the remaining parameters could produce an acceptable fit.
+ The diamonds in fig., The diamonds in fig.
+ l indicate the computed distribution if the correction for critical density is omitted., \ref{fig:hx} indicate the computed distribution if the correction for critical density is omitted.
+ It has a steeper slope than (he observed distribution at low x values., It has a steeper slope than the observed distribution at low x values.
+ No physical combination of free parameters resulted in a shallower slope than the one shown by the diamonds., No physical combination of free parameters resulted in a shallower slope than the one shown by the diamonds.
+ Lowering o in the Schechter mass equation to values that result in a divergent mass in galaxies lowered the slope slightly but was considered non-physical., Lowering $\alpha$ in the Schechter mass equation to values that result in a divergent mass in galaxies lowered the slope slightly but was considered non-physical.
+ The discussions in Wennicutt(1989). and MartinandKennicutt(2001) indicate that there is a critical density that depends on dynamical factors through the Toomre Q [actor ancl possibly the amount of shear in (he galactic rotation., The discussions in \citet{ken89} and \citet{mar01} indicate that there is a critical density that depends on dynamical factors through the Toomre Q factor and possibly the amount of shear in the galactic rotation.
+ The form of the reduction of star formation efficiency utilized in equ., The form of the reduction of star formation efficiency utilized in eqn.
+" 4. is a simple wav of reducing, elliciency al low surface densitv. ie. low x. regions."," \ref{eqn:crit} is a simple way of reducing efficiency at low surface density, i.e. low x, regions."
+The range of critical densities discussed in Martinandουσ(2001) ancl the,The range of critical densities discussed in \citet{mar01} and the
+~0.002 per cent for the dillerence of the white dwarf spin and orbital period.,${\rm \sim0.002}$ per cent for the difference of the white dwarf spin and orbital period.
+ “Phere are four polars which have been Found to show a small (71 percent) degree of asvnchronism., There are four polars which have been found to show a small $\sim$ 1 percent) degree of asynchronism.
+ The polar showing the smallest. V14332 Λα. is 0.28 percent asvnchronous (Geckeler&Staubert1997): over two orders of magnitude greater than V1309 Ori.," The polar showing the smallest, V1432 Aql, is 0.28 percent asynchronous \cite{b13}: over two orders of magnitude greater than V1309 Ori."
+ Our circular polarimetry curves (Figure.e 2) shows clear positive and negative excursions which indicate that V1309 Ori has two accreting poles., Our circular polarimetry curves (Figure 2) shows clear positive and negative excursions which indicate that V1309 Ori has two accreting poles.
+ This is consistent with previous polarisation observations., This is consistent with previous polarisation observations.
+ Phe X-ray data from theROSAL archive suggests that the negative circularly polarised pole is brighter in N-rays., The X-ray data from the archive suggests that the negative circularly polarised pole is brighter in X-rays.
+ Lt is possible that it is bright because of the increased. mass transfer at this pole., It is possible that it is bright because of the increased mass transfer at this pole.
+ Alternatively. it might be due to the fact that the accretion [low to this pole is very inhomogeneous. with the dense parts of the Dow accreting directly into the white dwarf without causing a shock and therefore liberating its energy at κο X-rays.," Alternatively, it might be due to the fact that the accretion flow to this pole is very inhomogeneous, with the dense parts of the flow accreting directly into the white dwarf without causing a shock and therefore liberating its energy at soft X-rays."
+ We note that Stauce et al., We note that Staude et al.
+ (2001). based on opticalUV photometry and optical spectroscopy did not find. any evidence for a second accretion pole. although they could not exclude one.," \shortcite{b42} based on optical/UV photometry and optical spectroscopy did not find any evidence for a second accretion pole, although they could not exclude one."
+ Their modelling predicts that the one accreting pole would show a maximun in the soft X-ray light curve at «p—0.045 and would show a self eclipse at P=0.55., Their modelling predicts that the one accreting pole would show a maximum in the soft X-ray light curve at $\Phi$ =0.045 and would show a self eclipse at $\Phi$ =0.55.
+ Llowever. theROSA data does not confirm this view.," However, the data does not confirm this view."
+ Indeed. we see maximum flux at 6=0.55 and a minimum at Φ--0 019.," Indeed, we see maximum flux at $\phi$ =0.55 and a minimum at $\Phi$ =0.045."
+ The X-ray data does show a dip around 9~=0.7., The X-ray data does show a dip around $\Phi\sim$ =0.7.
+ This is unlikely to be due to absorption of X-rays by the accretion stream since the stream does not eut through our line of sight to the accretion region at this phase., This is unlikely to be due to absorption of X-rays by the accretion stream since the stream does not cut through our line of sight to the accretion region at this phase.
+ Lt is also unlikely that this dip is due to that observation being at a lower accretion state since the same observation shows a peak at oO~=0.6., It is also unlikely that this dip is due to that observation being at a lower accretion state since the same observation shows a peak at $\phi\sim$ =0.6.
+ The cause of the dip in N-rays is unclear but maybe due to a fraction of the accretion region being eclipsed by the white dwarf at these phases., The cause of the dip in X-rays is unclear but maybe due to a fraction of the accretion region being self-eclipsed by the white dwarf at these phases.
+ Along the ballistic [Low. emission extends to Vy~SOO km sft νο200 km | in our maps anc also the mapsof Loarel (1999).," Along the ballistic flow, emission extends to ${\rm V_{x}\sim-800}$ km $^{-1}$, ${\rm V_{y}\sim-200}$ km $^{-1}$ in our maps and also the mapsof Hoard (1999)."
+" “Phe maps of Stauce et al(2001) show the flow extending to V,~100 kms +.", The maps of Staude et \shortcite{b42} show the flow extending to ${\rm V_{y}\sim-100}$ km $^{-1}$.
+ Taking V;.Vy from our maps (giving a velocity of S20 km 1) and using 6= (where e is velocity and rp is distance from the white dwarf). we find that the end of the ballistic [ow R . ↓⊳∖∣⋮∶−≽⊳⋉⋜⋯∠∟≽⋅↖∖↓∪⊥≼⇍⊔↓∠⊔⊳∖⇂⋜⋯⇂⇂↓⋅∪⊔↓↿↓⊔⋅∖∖⊽⊔↿⋖⋅∠⇂∖∖⊽⋜⊔⋅⇂⇂∪↓⋅.vu : ⋅ ⊀ ⋅⋅ ⇀⋃⊓∡∣∶∪⊳∪⋜↧⊔∠⇂∪⊳⊤⇀⋃⋅↓⋅⋖⊾⊳∖," Taking $V_{x}, V_{y}$ from our maps (giving a velocity of 820 km $^{-1}$ ) and using $v=(2GM_{wd}/r)^{1/2}$ (where $v$ is velocity and $r$ is distance from the white dwarf), we find that the end of the ballistic flow is $r$ =2.4 and $2.8\times10^{10}$ cm distant from the white dwarf for $M_{wd}$ =0.6 and respectively."
+"↓≻⋖⊾≼∙↕∖⇁⋖⊾↓∙∖⇁⋡ We can compare these estimates to. the. expected distance from the white dwarf that material ects coupled bv the magnetic field. (2,) using equation (1b) of. Mukai (1955).", We can compare these estimates to the expected distance from the white dwarf that material gets coupled by the magnetic field $R_{\mu}$ ) using equation (1b) of Mukai \shortcite{b23}.
+" We assume B=50 MG. (tvpical of the estimates mace for V1309 Ori). go=3 (the ασας of the stream in units of 10"" em: the value estimated for LU ar. Larrop-Allin et al."," We assume $B$ =50 MG (typical of the estimates made for V1309 Ori), $\sigma_{9}$ =3 (the radius of the stream in units of $10^{9}$ cm: the value estimated for HU Aqr, Harrop-Allin et al."
+ 1999) and Aso 10 (the mass transfer rate in units of 1019 es tL Larrop-Allin et al.," 1999) and $\dot{M}_{16}$ =10 (the mass transfer rate in units of $^{16}$ g $^{-1}$, Harrop-Allin et al."
+ 1997)., 1997).
+" We find that for AL,..,=0.6 and we σοι 2,= 3.4 and 10""Lu em respectively.", We find that for $M_{wd}$ =0.6 and we get $R_{\mu}$ = 3.4 and $\times10^{10}$ cm respectively.
+"M Although there is some considerable degree of uncertainty in how applicable the above formulation for £2), actually is. Ht is interesting that for masses between the predicted value of /?,, is consistent with our Doppler maps."," Although there is some considerable degree of uncertainty in how applicable the above formulation for $R_{\mu}$ actually is, it is interesting that for masses between the predicted value of $R_{\mu}$ is consistent with our Doppler maps."
+ This range of mass is consistent with that estimated. by Staucle ct al. (2001).., This range of mass is consistent with that estimated by Staude et al. \shortcite{b42}.
+ Our photometric observations show evidence for QPOs on time scales of 10 min with amplitudes up to 0.2 magnitudes., Our photometric observations show evidence for QPOs on time scales of 10 min with amplitudes up to 0.2 magnitudes.
+ This compares with 6.7 and 15.5 min: Shafter et al. (1995). , This compares with 6.7 and 15.5 min: Shafter et al. \shortcite{b35}. .
+There are some examples of other AAL Her systems where Ilickering on time scales of few minutes have been observed: 4.5 min in BL Ili (Singh.Agrawal&Riceler 1984)... 4," There are some examples of other AM Her systems where flickering on time scales of few minutes have been observed: 4.5 min in BL Hyi \cite{b39}, , 4 –"
+An absorbe oue temperature plasma model (as used. for the ddata. whici however have lower statistics) does not provide au acceptable description of the Μπροςτα.,"An absorbed one temperature plasma model (as used for the data, which however have lower statistics) does not provide an acceptable description of the spectrum."
+ Nevertheless a two temperature plasma model with a nietal abuance and two plasina temperatures frozen at the values above (Z= O21. kT;1.02 keV aud kT»= 2.82) xovides a eood fit to the ddata (P= 0.72) by letting the two eniüssionu nieasures aud the absxbiue column density vary sce Table 2..," Nevertheless a two temperature plasma model with a metal abundance and two plasma temperatures frozen at the values above $Z = 0.21$ , $kT_1 = 1.02$ keV and $kT_2= 2.82$ ) provides a good fit to the data $P=0.72$ ) by letting the two emission measures and the absorbing column density vary – see Table \ref{tab:xmm74ks_ps}."
+" The fitted values for the two ciuaission measures are LAL,=(L316)<1Q7cnP and EM,=(2.20.1)ς10%αι3, conssteut with the values derived from the προς."," The fitted values for the two emission measures are $E\!M_1 = (4.3 \pm 1.6) \times 10^{53}~{\rm
+cm^{-3}}$ and $E\!M_2 = (2.2 \pm 0.4) \times 10^{53}~{\rm cm^{-3}}$, consistent with the values derived from the spectrum."
+ The relative imodel fiux level is 10Pore (αι the 0.55 7.50 keV baud)., The relative model flux level is $7.3 \times 10^{-13}$ (in the $0.55$ $7.50$ keV band).
+ The value for the absorbing column cdesity (erived in this wav from the ata. ΝΤ)=(1.212:0.09)ς1022 2 is lugher than the value «Cljved froun and a moded with the valie derived frou ddocs uot xovide au accepable description of the data).," The value for the absorbing column density derived in this way from the data, $N({\rm H}) = (1.24\pm
+0.09) \times 10^{22}$ $^{-2}$ is higher than the value derived from (and a model with the value derived from does not provide an acceptable description of the data)."
+ We note thotih hat a systematically ligher value for the alssorbing cohun1 desity derived from ata is consistent with fi6 known presence of (likelv carbon-based) οςontaniuuation on he ACIS chips., We note though that a systematically higher value for the absorbing column density derived from data is consistent with the known presence of (likely carbon-based) contamination on the ACIS chips.
+ This causes additioua ow-energv absortion (up to near the € edge) not accounted for iu the current response matrices (Phwinskyetal. 2003)., This causes additional low-energy absorption (up to near the C edge) not accounted for in the current response matrices \citealp{psm+02}) ).
+ (νο. thiο source variability during these ~61 ks of observaticon. we have investigaed the preseuce of sienificant spectral variation.," Given the source variability during these $\sim 64$ ks of observation, we have investigated the presence of significant spectral variation."
+ We have subdivided the data iuto three iutervals (the first 30 ks. he following l5 ks aud he final 16 ks). €jiosen to ensure saüilar statistics in the resulting speetri," We have subdivided the data into three intervals (the first 30 ks, the following 18 ks and the final 16 ks), chosen to ensure similar statistics in the resulting spectra."
+ As the initial part of the observation is rather heavily couannuated by lich background. a higher raction of it Was ¢iscardecd. aud therefore the first interval 1s sienificautIv longer.," As the initial part of the observation is rather heavily contaminated by high background, a higher fraction of it was discarded, and therefore the first interval is significantly longer."
+ The three spectra were uxxleled with au absorbec two temperature plasma mode., The three spectra were modeled with an absorbed two temperature plasma model.
+ The fitted values of the model parameters are sumuuarised iu Table 2.., The fitted values of the model parameters are summarised in Table \ref{tab:xmm74ks_ps}.
+ As it can be seen by inspecting the tabe. the short terii variability observed iu the svstem V892 Tau caving this fürst oobservation does not appear to be associated with sjeuificaut spectral changes.," As it can be seen by inspecting the table, the short term variability observed in the system V892 Tau during this first observation does not appear to be associated with significant spectral changes."
+ A tine τςsolved spectral analysis was also performed. for the second oobservation of V892 Tau system. when the huge fare took ulace.," A time resolved spectral analysis was also performed for the second observation of V892 Tau system, when the large flare took place."
+ The data were subdivided into tbi intervals: a first 11 ks interval while the source is quiescent. a second Nksiterval while the source counts are rising and the last 10 ks. while the source is at its luminosityΠ," The data were subdivided into three intervals: a first 14 ks interval while the source is quiescent, a second 8 ks interval while the source counts are rising and the last 10 ks, while the source is at its luminosity."
+"ΤΙ), The three sjvectra are shown in Fie. 6."," The three spectra are shown in Fig. \ref{fig:ps_xmm},"
+ aud their parameters are listed in Table 3.., and their parameters are listed in Table \ref{tab:spectra}.
+ As explained at the beeining of this section au absorbed once-teniperature plasina 1ος) provides an acceptable description for all tje three specra derived from this exposure. so we did hot atempted fits with two-tempcrature las| models (whic) were necessary to obtain acceptable fits of the spectra deriος frou he first exposure).," As explained at the beginning of this section an absorbed one-temperature plasma model provides an acceptable description for all the three spectra derived from this exposure, so we did not attempted fits with two-temperature plasma models (which were necessary to obtain acceptable fits of the spectra derived from the first exposure)."
+ Iu aclditicmu. the approacifo flare nrodelling lat woe presen iu Sect.," In addition, the approach to flare modelling that we present in Sect."
+ 1.2.1 relies on single teperature nrunateriz:tion of he Xaav specruli., \ref{sec:flare} relies on single temperature paramaterization of the X-ray spectrum.
+" Nevertheless. or the spectiii derived from the first 1 ks interval of js exposure (corresvonding to the cescent phase). we verified that an absorved two tenmiperature asma model with a metal abundance and two paslua teniperatures yozen at the! values cerived from the first cexposure (Z=0.21 JAD, =1.02 keV ane Ay=2.82) iucdeec fits the spectrum (P0.08)."," Nevertheless, for the spectrum derived from the first 14 ks interval of this exposure (corresponding to the quiescent phase), we verified that an absorbed two temperature plasma model with a metal abundance and two plasma temperatures frozen at the values derived from the first exposure $Z = 0.21$ , $kT_1 = 1.02$ keV and $kT_2= 2.82$ ) indeed fits the spectrum $P=0.08$ )."
+" The Vauc| for the absorling coluum deitv derived im this way Is NUD)=(O.83-E0.08)&1022 2, somewhat lüeher daithe value derived with the one-tempcrature plasina fit (NIT)(0.65x0.06)«1072 7. second line of Tabe 3)). and in beter aerecineut with t1ο value derived Yolu the first cexposure."," The value for the absorbing column density derived in this way is $N({\rm H}) = (0.83\pm 0.08)
+\times 10^{22}$ $^{-2}$, somewhat higher than the value derived with the one-temperature plasma fit $N({\rm H}) = (0.65\pm 0.06) \times
+10^{22}$ $^{-2}$, second line of Table \ref{tab:spectra}) ), and in better agreement with the value derived from the first exposure."
+ This confirms fhe lack of significait spectral variation in the 502 Ta system duriug he quiesceut pla., This confirms the lack of significant spectral variation in the V892 Tau system during the quiescent phase.
+" As can be SCCIL from. Tabe ον, ming the flare the only significant specral variation QCCUIS in the asia teuperature. while the fted values for asorbine μαμα deusitv and plasima metalliciVv remain essentially ichauged."," As can be seen from Table \ref{tab:spectra}, during the flare the only significant spectral variation occurs in the plasma temperature, while the fitted values for absorbing column density and plasma metallicity remain essentially unchanged."
+ The plana teuperaure Increases 1έmht =1.53 keV vefore the flare O AT—ALL during tjo Tsing aAC reluains around tha vaπο afterwards., The plasma temperature increases from $kT = 1.53$ keV before the flare to $kT = 8.11$ during the rising phase and remains around that value afterwards.
+ The d dependent fiux density of the sourcs ln he energy and 0.35Ar. 7.50 keV. gocs youn 6.7hy10 yefore he fare to 1.01011 delving the flare mnaxinuu.," The model dependent flux density of the source, in the energy band $0.35$ $7.50$ keV, goes from $6.7\times 10^{-13}$ before the flare to $1.0\times
+10^{-11}$ during the flare maximum."
+ The peak X-ray Mununositv or the flare is Lx=2«10ere5. hiel but not exceptioally so for stellar N-rav. flares.," The peak X-ray luminosity for the flare is $L_{\rm X} = 2.4 \times 10^{31}$, high but not exceptionally so for stellar X-ray flares."
+ Diving the H8 ks oobservation. V8SO2 Tau (which is well resolved from the apparent companion) presen RESIenificaut variabiitv. with its N-rav flux varving by a actor of 2 in less than 1 ks.," During the 18 ks observation, V892 Tau (which is well resolved from the apparent companion) presents significant variability, with its X-ray flux varying by a factor of 2 in less than 1 ks."
+ This type of variabilits todas never been reported before for a Uerhig Ac star., This type of variability has never been reported before for a Herbig Ae star.
+ UidoutecIv. though. it is he large variation of uninositv of tli V8SO2 Tau svsteim {he large flare) observed with tthat Is nios relarkalhο," Undoubtedly, though, it is the large variation of luminosity of the V892 Tau system (the large flare) observed with that is most remarkable."
+", T LCOScep tpulsive 11se of thesource couts bv a facto rofl Otoeether with the iupulsive rise ofthe asma teniperatur| (from 1.5 to s.l keV) are all consistent with he 1iterxetation of the observed variation iu erus ofa aree coronal flare.", The steep impulsive rise of thesource counts by a factor of 10 together with the impulsive rise ofthe plasma temperature (from 1.5 to 8.1 keV) are all consistent with the interpretation of the observed variation in terms of a large coronal flare.
+March 6.,March 6.
+ The target source wwas positioned at the default position on the back-illuminated S3 chip of the ACIS-S array., The target source was positioned at the default position on the back-illuminated S3 chip of the ACIS-S array.
+ The total usable exposure time was 28.117 s. Figure | shows a smoothed version of the image.," The total usable exposure time was 28,117 s. Figure 1 shows a smoothed version of the image."
+ A total of 260 counts were extracted from a 179 radius circle centered on uusing the CIAO “psextract” script., A total of 260 counts were extracted from a $1\farcs9$ radius circle centered on using the CIAO “psextract” script.
+ A spectral file was produced by grouping at least 20 counts per channel., A spectral file was produced by grouping at least 20 counts per channel.
+" Instrument and mirror response files were generated using the CIAO tools ""makermf"" and “makearf™.", Instrument and mirror response files were generated using the CIAO tools “makermf” and “makearf”.
+ The expected contribution of background to the source spectrum is only ~4 counts. so no background subtraction was performed.," The expected contribution of background to the source spectrum is only $\approx 4$ counts, so no background subtraction was performed."
+ There is no evidence for extended emission (synchrotron nebulosity) associated with this source., There is no evidence for extended emission (synchrotron nebulosity) associated with this source.
+ Figure 2 shows the grouped ACIS spectrum. which is clearly that of an ultrasoft source. as first revealed by theROSAT Survey (Paper II).," Figure 2 shows the grouped ACIS spectrum, which is clearly that of an ultrasoft source, as first revealed by the All-Sky Survey (Paper II)."
+ The fact that the counts are rising down to the lowest energy signifies both a soft intrinsic spectrum and litthe absorbing column., The fact that the counts are rising down to the lowest energy signifies both a soft intrinsic spectrum and little absorbing column.
+ Although the ACIS response below 0.6 keV may not be well calibrated (e.g.. Zavlin et al.," Although the ACIS response below 0.6 keV may not be well calibrated (e.g., Zavlin et al."
+ 2002). we do not have the freedom to exclude these energies from spectral fitting because they contain the majority of our photons.," 2002), we do not have the freedom to exclude these energies from spectral fitting because they contain the majority of our photons."
+ Instead. we proceed with the following analysis based on the current calibration.," Instead, we proceed with the following analysis based on the current calibration."
+ First. we ignore the spectral channel around 0.28 keV. since a deviant point there may be associated with poor instrumental calibration around the carbon K-edge.," First, we ignore the spectral channel around 0.28 keV, since a deviant point there may be associated with poor instrumental calibration around the carbon K-edge."
+ Next. attempts to fit the spectrum using a blackbody or power-law model alone produced unsatisfactory fits. with \-/dof = 10 and 4. respectively.," Next, attempts to fit the spectrum using a blackbody or power-law model alone produced unsatisfactory fits, with $\chi^2$ /dof = 10 and 4, respectively."
+ This result is insensitive to Ny. whether the latter is treated as a free parameter or held fixed at the maximum Galactic value in this direction (4.6[00 em).," This result is insensitive to $N_{\rm H}$, whether the latter is treated as a free parameter or held fixed at the maximum Galactic value in this direction $4.6 \times 10^{20}$ $^{-2}$ )."
+ A two-component model consisting of a blackbody plus a power law produced adequate fits. with reduced \-<1.4 for all values of Nyx4.6&107? em.," A two-component model consisting of a blackbody plus a power law produced adequate fits, with reduced $\chi^2 < 1.4$ for all values of $N_{\rm H} \leq 4.6 \times 10^{20}$ $^{-2}$."
+ However. the small number of photons. extremely soft spectrum. and unknown intervening column density render the blackbody flux and bolometric luminosity highly uncertain even if the instrument response were known accurately.," However, the small number of photons, extremely soft spectrum, and unknown intervening column density render the blackbody flux and bolometric luminosity highly uncertain even if the instrument response were known accurately."
+ Rather than leaving Ny a free parameter in the fits. we explore the effects of assuming particular values of Na ranging from 2.5«10!° em to the maximum Galactic value of 4.6«10-9 em.," Rather than leaving $N_{\rm H}$ a free parameter in the fits, we explore the effects of assuming particular values of $N_{\rm H}$ ranging from $2.5 \times 10^{19}$ $^{-2}$ to the maximum Galactic value of $4.6 \times 10^{20}$ $^{-2}$."
+ Figure 3 shows the corresponding confidence contours., Figure 3 shows the corresponding confidence contours.
+ The best fitted blackbody temperatures for this range of Ny vary from (2.9—3.5)«10? K. with a 1σ upper limit of 5.5«10° K. The high-energy tail that is required to accompany the blackbody component is parameterized às à power-law of photon index 1.6<P2.8 (Io limits). with flux in the 0.2—2.0 keV band of (1.9-2.6)«107 eres em sol.," The best fitted blackbody temperatures for this range of $N_{\rm H}$ vary from $(2.9 - 3.5) \times 10^5$ K, with a $1\sigma$ upper limit of $5.5 \times 10^5$ K. The high-energy tail that is required to accompany the blackbody component is parameterized as a power-law of photon index $1.6 \leq \Gamma \leq 2.8$ $1\sigma$ limits), with flux in the $0.2-2.0$ keV band of $(1.9 - 2.6) \times 10^{-14}$ ergs $^{-2}$ $^{-1}$."
+ We bound the range of plausible distances by assuming a blackbody radius of 10 km for each of the trial values of My., We bound the range of plausible distances by assuming a blackbody radius of 10 km for each of the trial values of $N_{\rm H}$.
+ Under this assumption. 100<d800 pe. and 5<10Ega1.1«10°! eres s7': smaller distance corresponds to smaller temperature.," Under this assumption, $100 \leq d \leq 800$ pc, and $5 \times 10^{30} \leq L_{\rm Bol} \leq 1.1 \times 10^{31}$ ergs $^{-1}$; smaller distance corresponds to smaller temperature."
+ Formally. no lower limit on 7. can be set from the X-ray spectrum alone. although the distance would become unreasonably small for 7.<3\10° K given the lack of optical detection. which sets an additional lower bound on d (see $3).," Formally, no lower limit on $T_{\infty}$ can be set from the X-ray spectrum alone, although the distance would become unreasonably small for $T_{\infty} < 3 \times 10^5$ K given the lack of optical detection, which sets an additional lower bound on $d$ (see 3)."
+" Precise astrometry of the ACIS image in the USNO-A2.0 optical reference frame was achieved by registration of four previously identified. ""bright X-ray sources in Figure | with their optical counterparts on the MDM 2.4m V-band CCD image described in Papers I and IL."," Precise astrometry of the ACIS image in the USNO-A2.0 optical reference frame was achieved by registration of four previously identified, “bright” X-ray sources in Figure 1 with their optical counterparts on the MDM 2.4m $V$ -band CCD image described in Papers I and II."
+ This required a zero-point shift to the aspect solution of 20713 in right ascension and —0739 in declination. which is within specifications.," This required a zero-point shift to the aspect solution of $-0\farcs13$ in right ascension and $-0\farcs39$ in declination, which is within specifications."
+" The corrected position of iis (2000). 18936""132723.5073513005. which should be accurate to 07] relative to our ground-based optical image as indicated by the residual dispersion in X-ray-optical offsets of the identified sources."," The corrected position of is (J2000) $18^{\rm h}36^{\rm m}13.\!^{\rm s}723,
++59^{\circ}25^{\prime}30\farcs05$, which should be accurate to $0\farcs1$ relative to our ground-based optical image as indicated by the residual dispersion in X-ray-optical offsets of the identified sources."
+ We note that this position is only 005 from the HRI position that was determined in a similar manner in Paper IL. confirming that the latter's error circle radius of 3” was conservative.," We note that this position is only $0\farcs5$ from the HRI position that was determined in a similar manner in Paper II, confirming that the latter's error circle radius of $3^{\prime\prime}$ was conservative."
+" The agreement in position between these two X-ray observations that were made 4 years apart already limits any proper motion of the source to <I"" yr !.", The agreement in position between these two X-ray observations that were made 4 years apart already limits any proper motion of the source to $< 1^{\prime\prime}$ $^{-1}$ . } }
+ Stellar occultations observed by (the Visual and Infrared. Mapping Spectrometer, Stellar occultations observed by the Visual and Infrared Mapping Spectrometer
+However. the photospheric abundances of HB stars hotter than about 11500 K are altered by atomic diffusion processes and cannot be used directly to measure the original values.,"However, the photospheric abundances of HB stars hotter than about 11500 K are altered by atomic diffusion processes and cannot be used directly to measure the original values."
+ For instance. Behr (2003) found a depletion in. moderately hot HB stars in several GCs.," For instance, Behr (2003) found a depletion in moderately hot HB stars in several GCs."
+ Moehler et al..," Moehler et al.,"
+ in à series of papers (e.g..Moehleretal..2007) concentrated instead on the hottest part of the HB (and blue-hook stars in the two GCs -c Cen and NGC 2808- where they are present) and found He-enhancement.," in a series of papers \citep[e.g.,][]{moehler07} concentrated instead on the hottest part of the HB (and blue-hook stars in the two GCs $\omega$ Cen and NGC 2808- where they are present) and found He-enhancement."
+ This can be attributed either to pollution from a previous generation or to He flash induced mixing occurring in hot He-flashers. 1.9. those stars experiencing the He flash not at the RGB tip but along the White Dwarf cooling sequence (seeCastellani&Castellani.1993).," This can be attributed either to pollution from a previous generation or to He flash induced mixing occurring in hot He-flashers, i.e. those stars experiencing the He flash not at the RGB tip but along the White Dwarf cooling sequence \citep[see][]{cc93}."
+.. A further discussion of this problem in w Cen can be found in Cassisietal.(2009)., A further discussion of this problem in $\omega$ Cen can be found in \cite{cassisi09}.
+. We have studied in a companion paper (Grattonetal.. the effect of (even a small) difference in He content on the morphology of HBs. and found that He is most probably the third parameter governing the HB. after metallicity and age.," We have studied in a companion paper \citep{gratton10} the effect of (even a small) difference in He content on the morphology of HBs, and found that He is most probably the third parameter governing the HB, after metallicity and age."
+ We refer to that paper for a long and detailed discussion on the effects of He variations. on methods to measure He content (e.g..theR-method:Iben.1968). on comparison between results obtained through different approaches.," We refer to that paper for a long and detailed discussion on the effects of He variations, on methods to measure He content \citep[e.g., the
+R-method:][]{iben}, on comparison between results obtained through different approaches."
+ In the present paper we limit our analysis to the differences in He that can be deduced from RGB stars., In the present paper we limit our analysis to the differences in He that can be deduced from RGB stars.
+ May we use the present analysis. combined with the previous work on the Na-O and other (anticorrelations to try diseriminating between AGB and FRMS as the polluters of the second-generation stars?," May we use the present analysis, combined with the previous work on the Na-O and other (anti)correlations to try discriminating between AGB and FRMS as the polluters of the second-generation stars?"
+ We need to consider that He is produced essentially in MS for both classes of polluters. while there 1s a difference for the other “peculiar” elements (O. Na. Mg. ΑΙ. Si). produced during Hot Bottom Burning or in MS. respectively.," We need to consider that He is produced essentially in MS for both classes of polluters, while there is a difference for the other “peculiar"" elements (O, Na, Mg, Al, Si), produced during Hot Bottom Burning or in MS, respectively."
+ However. we still miss important details of stellar evolution (e.g.. how much He is dredged up in AGB stars. or what is the dependence on metallicity -via rotation- of FRMS). the numbers are still small and the inferences are not conclusive.," However, we still miss important details of stellar evolution (e.g., how much He is dredged up in AGB stars, or what is the dependence on metallicity -via rotation- of FRMS), the numbers are still small and the inferences are not conclusive."
+ We need to further investigate the dependencies of variations of He and those other elements on the stars and cluster properties., We need to further investigate the dependencies of variations of He and those other elements on the stars and cluster properties.
+ In summary. with the present work we have seen that:," In summary, with the present work we have seen that:"
+"The 3D primitive equations. linearized around a uniformly stratified flow (see |?].. |7].. [2] and [?])). read where u. e and ic are the perturbation variables of the three velocity components. ó is the perturbation variable of the pressure. iis the perturbation variable of the temperature: f is (he Coriolis force parameter. NV isthe Brunt (buovancy) frequency. assumed to be constant in the current study: D(u.ο.0.0)=ub,+v8,cO. lor 0—ue. or c.","The 3D primitive equations, linearized around a uniformly stratified flow (see \cite{RTT05b}, , \cite{RTT07}, , \cite{CLRTT07} and \cite{CTT08}) ), read where $u$, $v$ and $w$ are the perturbation variables of the three velocity components, $\phi$ is the perturbation variable of the pressure, $\psi$ is the perturbation variable of the temperature; $f$ is the Coriolis force parameter, $N$ isthe Brunt--V\""aiis\""all\""a (buoyancy) frequency, assumed to be constant in the current study; $B(u,v,w; \theta ) = u\theta_x + v\theta_y+ w\theta_z$ for $\theta = u, v $, or $\psi$."
+ We will consider these equations in the domain M=M'x(—1H.0).=(0.L4)xLa).Ly.Lo.LyLH positive constants.," We will consider these equations in the domain $\M = \M'\times (-H,0), \, \\
+ \M' = (0,L_1)\times (0,L_2),\, L_1, \, L_2, \, L_3 = H$ positive constants."
+ Assuming [Tat bottom and the rieid lid hypothesis. we have The boundary conditions for the other variables will be recalled and discussed below.," Assuming flat bottom and the rigid lid hypothesis, we have The boundary conditions for the other variables will be recalled and discussed below."
+ Following [?] and |?].. we consider the normal mode expansion of the solutions of the svstem (2.," Following \cite{OS78} and \cite{TT03}, we consider the normal mode expansion of the solutions of the system ."
+1).. That is. we lookfor thesolutions written in the following form:," That is, we lookfor thesolutions written in the following form:"
+"however, the binary orbit is altered during mass transfer, so the composition of the accreted material varies because the surface AGB composition varies.","however, the binary orbit is altered during mass transfer, so the composition of the accreted material varies because the surface AGB composition varies."
+" Moreover, the evolution of the AGB star itself may be altered by the presence of a binary companion."," Moreover, the evolution of the AGB star itself may be altered by the presence of a binary companion."
+" Since there are no models presently available that describe both binary and detailed AGB evolution simultaneously, we have defaulted to using the AGB average composition."," Since there are no models presently available that describe both binary and detailed AGB evolution simultaneously, we have defaulted to using the AGB average composition."
+" In principle, it is possible to constrain the initial orbital period of the binary system."," In principle, it is possible to constrain the initial orbital period of the binary system."
+ The system must have been sufficiently wide to allow the primary star to evolve into an AGB star before filling its Roche lobe; this requirement sets a lower limit to the initial orbital period., The system must have been sufficiently wide to allow the primary star to evolve into an AGB star before filling its Roche lobe; this requirement sets a lower limit to the initial orbital period.
+" On the other hand, the efficiency of wind accretion decreases with the distance between the two stars, which implies that the required amount of accreted material may set an upper limit on the initial orbital period."," On the other hand, the efficiency of wind accretion decreases with the distance between the two stars, which implies that the required amount of accreted material may set an upper limit on the initial orbital period."
+" Using the binary evolution code described in Izzardetal. (2006),, we find that the range of initial orbital periods that corresponds to an accretion efficiency >3% in a system with initial masses 0.8 and is between 7 and 27 years."," Using the binary evolution code described in \citet{izzard06}, we find that the range of initial orbital periods that corresponds to an accretion efficiency $>3\%$ in a system with initial masses 0.8 and is between 7 and 27 years."
+" With the binary evolution code described in Izzardetal. (2006), we simulated a population of binaries assuming the Kroupaetal.(1993) initial mass function, a uniform distribution of initial mass ratios, and the (1991) initial period distribution."," With the binary evolution code described in \citet{izzard06}, we simulated a population of binaries assuming the \citet{kroupa93}
+ initial mass function, a uniform distribution of initial mass ratios, and the \citet{duquennoy91} initial period distribution."
+" We find that, of all turn-off and giant CEMP stars formed by mass transfer from an AGB companion, are expected to show an enhanced fluorine abundance of [F/Fe] > +1, have [F/Fe] > +2, and have [F/Fe] >+3."," We find that, of all turn-off and giant CEMP stars formed by mass transfer from an AGB companion, are expected to show an enhanced fluorine abundance of [F/Fe] $>$ +1, have [F/Fe] $>$ +2, and have [F/Fe] $>$ +3."
+ This can be understood qualitatively from the results presented in Fig., This can be understood qualitatively from the results presented in Fig.
+ 1 because AGB stars that produce carbon also produce fluorine., \ref{fig:yields} because AGB stars that produce carbon also produce fluorine.
+" To date, fluorine enhancements have not been reported for other CEMP stars because high-resolution spectra in the 2.4 um band are required, which are not yet available."," To date, fluorine enhancements have not been reported for other CEMP stars because high-resolution spectra in the 2.3-2.4 $\mu$ m band are required, which are not yet available."
+" We predict that fluorine should be found in most CEMP stars that formed via the AGB binary scenario, thus representing a tracer of low-mass AGB pollution in addition to s-process element enhancements."," We predict that fluorine should be found in most CEMP stars that formed via the AGB binary scenario, thus representing a tracer of low-mass AGB pollution in addition to $s$ -process element enhancements."
+" The fluorine abundance in the particular case of HE 1305-0132 appears to be exceptionally high, since we expect only of turn-off and giant CEMP stars to have A(°F)> 44.75, when considering the observational error bar."," The fluorine abundance in the particular case of HE 1305+0132 appears to be exceptionally high, since we expect only of turn-off and giant CEMP stars to have $^{19}$ $ \geq 
++4.75$, when considering the observational error bar."
+" However, we emphasize that many uncertainties play a role in this estimate, both in the assumed distribution functions (which are reasonable for stars in the solar neighbourhood, but not necessarily for halo stars), and in the assumed wind accretion efficiency."," However, we emphasize that many uncertainties play a role in this estimate, both in the assumed distribution functions (which are reasonable for stars in the solar neighbourhood, but not necessarily for halo stars), and in the assumed wind accretion efficiency."
+" The latter is based on the Bondi&Hoyle(1944) prescription, whereas hydrodynamical simulations (Theunsetal.1996;Nagae2004) predict typically lower accretion efficiencies."," The latter is based on the \citet{bondi44} prescription, whereas hydrodynamical simulations \citep{theuns96,nagae04} predict typically lower accretion efficiencies."
+" These uncertainties deserve more attention in a follow-up study (Izzard et al.,"," These uncertainties deserve more attention in a follow-up study (Izzard et al.,"
+ in preparation)., in preparation).
+" Moreover, the theoretical understanding of F production in AGB stars is itself still affected by many uncertainties, as discussed below."," Moreover, the theoretical understanding of F production in AGB stars is itself still affected by many uncertainties, as discussed below."
+" To evaluate AGB model uncertainties we discuss a set of models of and [Fe/H] = —2.3, computed using different physics and nuclear reaction rate assumptions (Table 1))."," To evaluate AGB model uncertainties we discuss a set of models of and [Fe/H] = $-2.3$, computed using different physics and nuclear reaction rate assumptions (Table \ref{tab:uncertain_yields}) )."
+ The first four models in Table | are computed using the codes described in Karakas&Lattanzio(2007).., The first four models in Table \ref{tab:uncertain_yields} are computed using the codes described in \citet{karakas07b}.
+ Model 1 is that used in the previous section for comparison with HE 1305+0132., Model 1 is that used in the previous section for comparison with HE 1305+0132.
+ Model 2 includes a region in which protons from the envelope are mixed down into the top layer of the He- and C-rich intershell (the region between the H and He shells) at the end of each TDU., Model 2 includes a region in which protons from the envelope are mixed down into the top layer of the He- and C-rich intershell (the region between the H and He shells) at the end of each TDU.
+" Proton captures on C generate a “pocket” rich in C, the main neutron source for the S-process in"," Proton captures on $^{12}$ C generate a “pocket” rich in $^{13}$ C, the main neutron source for the $s$ -process in"
+of systems of the type we consider ancl we restrict ourselves to that.,of systems of the type we consider and we restrict ourselves to that.
+ We comment that the equations we solve. incorporating tidal effects. have a radial scale invariance.," We comment that the equations we solve, incorporating tidal effects, have a radial scale invariance."
+ Thus all racii may be mutiplied by some factor f while the timescales are multiplied by 7. The size of the central star has to be sealed by the factor f also., Thus all radii may be mutiplied by some factor $f$ while the timescales are multiplied by $f^{3/2}.$ The size of the central star has to be scaled by the factor $f$ also.
+ Here we shall take the unit of length to be Rie., Here we shall take the unit of length to be $R_{max}$.
+ Then the stellar radius is specified through Ay{ζει The time unit is the period of a circular orbit at uuu. d=eReVOM.;. The interactions amongst the planets lead. to some escaping the system.," Then the stellar radius is specified through $R_*/R_{max}.$ The time unit is the period of a circular orbit at $R_{max},$ $P_0 = 2\pi
+R_{max}^{3/2}/\sqrt{GM_*}.$ The interactions amongst the planets lead to some escaping the system."
+ Objects with positive energy which had reached a distance {μια were considered to be escapers., Objects with positive energy which had reached a distance $\beta R_{max}$ were considered to be escapers.
+ We have considered j—20 and 7=100 which both lead to the same qualitative picture., We have considered $\beta=20$ and $\beta=100$ which both lead to the same qualitative picture.
+ Even the svstems which have a small number of bodies are found to interact strongly ancl to undergo relaxation like a stellar system (Binney Tremanine 1987)., Even the systems which have a small number of bodies are found to interact strongly and to undergo relaxation like a stellar system (Binney Tremanine 1987).
+" For such a system the realaxation time is Llere the root mean square velocity is 0. pis the mass density of interacting bodies assumed. for simplicity to have equal mass νι and A=AL,/A,. Using (=GALSR. NAL,=πιp/3 and adopting the orbital period. P?=2xve this becomes Vhus for Ad,/Ad,—5.010. and /N25 the relaxation ime is about LOO orbits."," For such a system the realaxation time is Here the root mean square velocity is $v,$ $\rho$ is the mass density of interacting bodies assumed for simplicity to have equal mass $M_p$ , and $\Lambda
+=M_*/M_p.$ Using $v^2 = GM_*/R,$ $NM_p= 4\pi R^3 \rho/3 $ and adopting the orbital period $P = 2\pi R/v$ this becomes Thus for $M_p/M_* =5.0\times 10^{-3}$ and $N=5$ the relaxation time is about $100$ orbits."
+ For systems with 7? in the 100 au o 1000 au range this time is around 10P[E v which is within he estimated lifetimes of protostellar disces., For systems with $R$ in the $100$ au to $1000$ au range this time is around $10^{5-6}$ y which is within the estimated lifetimes of protostellar discs.
+ The evolution we obtain is similar to that. undergone ον spherical star clusters (Binney Tremaine 1987)., The evolution we obtain is similar to that undergone by spherical star clusters (Binney Tremaine 1987).
+ The relaxation. due to binary encounters. causes some objects o attain escape velocity while others become more bound.," The relaxation, due to binary encounters, causes some objects to attain escape velocity while others become more bound."
+ Eventually all either escape or end up in extended: orbits. except for one body which takes up all the binding energy.," Eventually all either escape or end up in extended orbits, except for one body which takes up all the binding energy."
+ This is à generic result. provided that close encounters with 1e star can be avoided., This is a generic result provided that close encounters with the star can be avoided.
+ Lowever. for the parameter range of interest such encounters are likely.," However, for the parameter range of interest such encounters are likely."
+ The situation resembles wt of accretion of stars from a spherical star cluster by a Mack hole (eg., The situation resembles that of accretion of stars from a spherical star cluster by a black hole (eg.
+ PrankRees 1976)., FrankRees 1976).
+" At a location with radius H. the fractional volume of phase space containing orbits mt would σος with the star if unperturbed is £2,/22 ( us being the ratio of the square of the angular momentunm xdow which an impact is expected to the square of the mean angular momentum)."," At a location with radius $R,$ the fractional volume of phase space containing orbits that would collide with the star if unperturbed is $\sim R_*/R $ ( this being the ratio of the square of the angular momentum below which an impact is expected to the square of the mean angular momentum)."
+" If an object cannot diffuse out of this volume before impact. the mean time before diffusion into the effective volume produces an impact. for a particular object. is fy. However. the time to dilfuse out of the elective volume Is Ggfh. ME this time is less than the crossing time /,ffe. the expected mean time to impact is fone=(RESR,. his time is just the erossing time divided by the probability of being in the ellective volume of phase space which is regularly sampled: because of the effective cülfusion (see Frank Rees 1976)."," If an object cannot diffuse out of this volume before impact, the mean time before diffusion into the effective volume produces an impact, for a particular object, is $\sim
+t_R.$ However, the time to diffuse out of the effective volume is $\sim (R_* t_R)/R.$ If this time is less than the crossing time $t_c
+\sim R/v,$ the expected mean time to impact is $ t_{enc} = (R
+t_c)/R_*.$ This time is just the crossing time divided by the probability of being in the effective volume of phase space which is regularly sampled because of the effective diffusion (see Frank Rees 1976)."
+ In our calculations the innermost most tightly. bound object. undergoes relaxation or phase space dillusion which can lead to close encounters., In our calculations the innermost most tightly bound object undergoes relaxation or phase space diffusion which can lead to close encounters.
+" For 2=25 au. f,~20 v. and ανοLB.107LL em. us5103 v. Thus we can expect close encounters to occur within the general relaxation process."," For $R=25$ au, $t_c\sim 20$ y, and $R_* \sim 1.5\times 10^{11}$ cm, $t_{enc} \sim 5\times 10^4$ y. Thus we can expect close encounters to occur within the general relaxation process."
+ In some cases these can lead to a strong tical interaction which can circularize the orbit and. potentially leac to the formation of a hot Jupiter’., In some cases these can lead to a strong tidal interaction which can circularize the orbit and potentially lead to the formation of a 'hot Jupiter'.
+ We here describe a sample of our results which illustrate the characteristic behaviour exhibited by the systems we consider., We here describe a sample of our results which illustrate the characteristic behaviour exhibited by the systems we consider.
+ The calculations presented are [isted in table 1.., The calculations presented are listed in table \ref{tab1}.
+" We note that if 42, —100 au. BefRing,—9.396«10 or 1.337101! corresponds to Ry=2 or 3 Ros. respectively. which is the radius of a protostar with a mass around 1 AL: in the early stages."," We note that if $R_{max}$ =100 au, $R_* / R_{max}=9.396\times 10^{-5}$ or $1.337\times10^{-4}$ corresponds to $R_*=2$ or 3 $_{\sun}$, respectively, which is the radius of a protostar with a mass around 1 $_{\sun}$ in the early stages."
+ Run 1 corresponds to à svstem of N=5 planets each raving a mass 510.234. Figure 1. shows plots of afRina in logarithmic scale. where @ denotes the semi-niajor axis. or cach planet in the μπα versus lime (measured in unlts of 2).," Run 1 corresponds to a system of $N=5$ planets each having a mass $5\times 10^{-3} M_*.$ Figure \ref{fig1} shows plots of $a/R_{max}$ in logarithmic scale, where $a$ denotes the semi-major axis, for each planet in the system versus time (measured in units of $P_0$ )."
+ Each line corresponds to a dilferent planet., Each line corresponds to a different planet.
+ Duringhe run 3 planets escape. a line terminating just prior to an escape.," Duringthe run 3 planets escape, a line terminating just prior to an escape."
+" For this case 2,=0 so that there was no idal interaction with the central star.", For this case $R_*=0$ so that there was no tidal interaction with the central star.
+" The initial relaxation ime for this and other similar casesis on the order of 100/1,. in agreement with equation (7))."," The initial relaxation time for this and other similar casesis on the order of $100P_0$ , in agreement with equation \ref{relax1}) )."
+ The evolution of alοRivas. allο) being the pericentre distance and c being the eccentricitv. is also shown in Figure 1..," The evolution of $a(1-e)/R_{max},$ $a(1-e)$ being the pericentre distance and $e$ being the eccentricity, is also shown in Figure \ref{fig1}. ."
+ We, We
+the unieration of the planets can account for a formation on a larger radial range. followed by a conpaction of the configuration of the eiut planets. like in Figure 13..,"the migration of the planets can account for a formation on a larger radial range, followed by a compaction of the configuration of the giant planets, like in Figure \ref{fig:Hayashi}."
+ Then. a fully resonant coufiguration can be achieved. that can be compatible with the Nice model. like iu Morbidellietal.(2007).," Then, a fully resonant configuration can be achieved, that can be compatible with the Nice model, like in \citet{Morby-etal-2007}."
+". Iu addition. the solid uaterial that built the eiauto, planets may conie iot only from the region around their respectiveorbits:: dust drifts isvards in a protoplauctary disk (Weideuschiliug1977).. and simall bodies nigrate as well. so that the giant planets region nay be replenished iu solids by the outer parts of he disk."," In addition, the solid material that built the giant planets may come not only from the region around their respective: dust drifts inwards in a protoplanetary disk \citep{Weiden77}, and small bodies migrate as well, so that the giant planets region may be replenished in solids by the outer parts of the disk."
+ This enables the formation of Jupiter. Saturn. Uranus aud Neptune in a less massive disk than the Desch nebula. to avoid the type III uieration of Jupiter.," This enables the formation of Jupiter, Saturn, Uranus and Neptune in a less massive disk than the Desch nebula, to avoid the type III migration of Jupiter."
+ Iu section 6.. we have secu hat this is possible iu the old Tavashi(1981) jebula.," In section \ref{sec:Hayashi}, we have seen that this is possible in the old \citet{Hayashi1981}
+ nebula."
+ However. there is no reason why the eiaut auets should have formed exactly where thev oxeseutlvorbit: im particular the presence of au outer cold disk of planetesimals (required in the Nice model) is problematic if Neptune formed ονομα 25 AU.," However, there is no reason why the giant planets should have formed exactly where they presently; in particular the presence of an outer cold disk of planetesimals (required in the Nice model) is problematic if Neptune formed beyond 25 AU."
+ Thus. a new construction of a AIMSN is needed. that takes iuto account the Nice uodel and the planetary formation constraints. ike in Desch(2007).. and also the migration of auets and planetesinials.," Thus, a new construction of a MMSN is needed, that takes into account the Nice model and the planetary formation constraints, like in \citet{Desch2007}, and also the migration of planets and planetesimals."
+ lu auv case. our results show that planetary uigration should be iu the construction of a MMSN.," In any case, our results show that planetary migration should be in the construction of a MMSN."
+" The location where the planets form determines the gas density profile of the nebula. which determines the uuerationo, path of the anets. which drives the plauets to à uew position after the disk dissipation."," The location where the planets form determines the gas density profile of the nebula, which determines the migration path of the planets, which drives the planets to a new position after the disk dissipation."
+ This final configuration. and not the initial one. should be compatible with he Nice model (or with the present configuration if one does uot believe that the Nice model is rue).," This final configuration, and not the initial one, should be compatible with the Nice model (or with the present configuration if one does not believe that the Nice model is true)."
+ This idea requires a detailed study. that is vevoud the scope of this paper. but the results oxesented here advocate for such a selt£consisteut construction of the Miunuuni Mass Solar Nebula.," This idea requires a detailed study, that is beyond the scope of this paper, but the results presented here advocate for such a self-consistent construction of the Minimum Mass Solar Nebula."
+ I wish to thank W. Islev. F. Masset. aud A. Morbidelli for discussious. aud W. EKlev for reading this manuscript aud suggestingOO a few inproveienuts.," I wish to thank W. Kley, F. Masset, and A. Morbidelli for discussions, and W. Kley for reading this manuscript and suggesting a few improvements."
+ The computations have beeu performed ou thehpc-bw cluster of the BRecheuzeutruu of the University of Tübbimesen., The computations have been performed on the cluster of the Rechenzentrum of the University of Tübbingen.
+ D. Ditsch is acknowledged for his help with this cluster., B. Bitsch is acknowledged for his help with this cluster.
+ A. Crida acknowledges the support through the German Research Foundation (DFC) eraut KL 650/7., A. Crida acknowledges the support through the German Research Foundation (DFG) grant KL 650/7.
+discussed that DI in the nonlinear stage produces a large-amplitude. localized electrostatic wave which is callecl as the electrostatic solitary wave (ESW) οἱal. 1994).,"discussed that BI in the nonlinear stage produces a large-amplitude, localized electrostatic wave which is called as the electrostatic solitary wave (ESW) \citep{Dav70,Omura94}."
+. Thev also found that the ESW itself is almost stable. but the interaction with other waves in the inhomogeneous shock transition region leads to the dynamical evolution of (he shock energy dissipation.," They also found that the ESW itself is almost stable, but the interaction with other waves in the inhomogeneous shock transition region leads to the dynamical evolution of the shock energy dissipation."
+ Thev discussed that the electrostatic solitary wave (ESW) plays an important role not only on (the rapid electron thermalization but also on the nonthermal electron acceleration. and that the ESWs obtained by the simulation can be compared with observations of the electric field waveform at the Earth's bow shock (Matsumotoetal.1993).," They discussed that the electrostatic solitary wave (ESW) plays an important role not only on the rapid electron thermalization but also on the nonthermal electron acceleration, and that the ESWs obtained by the simulation can be compared with observations of the electric field waveform at the Earth's bow shock \citep{Mat97,Bal98}."
+. IIowever. the actual physics of the nonthermal electron acceleration processes has remained elusive.," However, the actual physics of the nonthermal electron acceleration processes has remained elusive."
+ In (his paper. we study in details (he suprathermal electron. acceleration through the interaction of electrons with ESWs in a transverse. magnetosonie. high Mach number shock.," In this paper, we study in details the suprathermal electron acceleration through the interaction of electrons with ESWs in a transverse, magnetosonic, high Mach number shock."
+ We discuss that the electrons trapped by ESW can resonate with the shock motional electric [ield. aud (he so-called shock surfing mechanism is effective lor producing the non-thermal. high-energv electrons (Hoshino2001:MeClementsetal.2001).," We discuss that the electrons trapped by ESW can resonate with the shock motional electric field, and the so-called shock surfing mechanism is effective for producing the non-thermal, high-energy electrons \citep{Hos01,McC01}."
+. Shock surfing acceleration at quasi-perpendicular shocks is usually considered for ions to be a pre-acceleration mechanism to initiate diffusive shock acceleration (Sagdeev.1966:SagdeevandShapiro1973:SugiharaZankοἱal.1996:LeeetUcerandShapiro 2001).," Shock surfing acceleration at quasi-perpendicular shocks is usually considered for ions to be a pre-acceleration mechanism to initiate diffusive shock acceleration \citep{Sag66,Sag73,Sug79,Kat83,Lem84,Ohs85,Zan96,Lee96,Uce01}."
+. The electrostatic field at the shock front directs upstream. ancl (he ions which energy cannot overcome (he electrostatic potential well are reflected upstream in a super-crilical shock of AM4>2.7.," The electrostatic field at the shock front directs upstream, and the ions which energy cannot overcome the electrostatic potential well are reflected upstream in a super-critical shock of $M_A > 2.7$."
+ In the stancard shock surfing. (he ions are trapped between the shock Iront aud the upstream by the Lorentz force.," In the standard shock surfing, the ions are trapped between the shock front and the upstream by the Lorentz force."
+ During the reflection process. ions travel along the shock [vont and can be accelerated by the motional/convection electric field.," During the reflection process, ions travel along the shock front and can be accelerated by the motional/convection electric field."
+ In this mechanism. however. electrons can be neither reflected nor accelerated.," In this mechanism, however, electrons can be neither reflected nor accelerated."
+ We discuss that a series of large aunplitude electrostatic waves excited by the nonlinear Buneman instability in the shock transition region can play a role of counterpart of the shock [vont potential for the case of the ion shock surfing. ancl those ESWs can elleclively trap electrons.," We discuss that a series of large amplitude electrostatic waves excited by the nonlinear Buneman instability in the shock transition region can play a role of counterpart of the shock front potential for the case of the ion shock surfing, and those ESWs can effectively trap electrons."
+ Then the electron. shock surfing mechanism can be switched on., Then the electron shock surfing mechanism can be switched on.
+ We also propose that for a large Mach number shock with M4> several 10. electrons are likely to be trapped for infinitely long5 (mes. because the electrostatic Loree becomes always larger than the Lorentz force.," We also propose that for a large Mach number shock with $M_A >$ several 10, electrons are likely to be trapped for infinitely long times, because the electrostatic force becomes always larger than the Lorentz force."
+ In this situation. the electrons can be perfectly trapped by EsWs. and can be quickly gain (heir energies until thev obtain the elobal (ransverse shock potential energv.," In this situation, the electrons can be perfectly trapped by ESWs, and can be quickly gain their energies until they obtain the global transverse shock potential energy."
+ We discuss that the shock surfing/surfatron near the shock front region is ihe efficient accelerator for the relativistic electrons., We discuss that the shock surfing/surfatron near the shock front region is the efficient accelerator for the relativistic electrons.
+Weak eravitational lensing has become a powerful tool to sπε] the dark universe. allowing us to place constrains on key cosmological parameters. aud ofíeri1g the possiημίν to place independent conustraiuts ¢ nt10 dark energy equation of state parameter. e (77277?7j.,"Weak gravitational lensing has become a powerful tool to study the dark universe, allowing us to place constraints on key cosmological parameters, and offering the possibility to place independent constraints on the dark energy equation of state parameter, $w$ \citep{lb09,hj08,munshietal08,albrechtetal06,peacocketal06,schneider06,vwm03}."
+ Uitil recently. weak leusiumg studies considerκ. the shear sigjid. and recovered the mass distribution. iu wo duueional projection (see7.forareviewo[weak eusing)..," Until recently, weak lensing studies considered the shear signal, and recovered the mass distribution, in two dimensional projection \citep[see][for a review of weak lensing]{schneider06}."
+ However. with improved data quality auk wide-»uxl pphoonietry. it is now possible to recover tlic Lass ΠΠtkm iu three dineusious by using photomactric redshift information to deproject the lensing signa alo18o he li1C ο Ακ...," However, with improved data quality and wide-band photometry, it is now possible to recover the mass distribution in three dimensions by using photometric redshift information to deproject the lensing signal along the line of sight \citep{sth09, masseyetal07b, masseyetal07a, tayloretal04}."
+ U11ΟΥ the assunptiou of Ciussian noise. various liuear netLaeyds jiwe been developed to recover the 3D natter ΠΠtion. which rely ou the construction of a pseudo-inverse operator to act ou the data. aud which include a renalv function eucocdiis the prior that is to be placed ou the signal (2????7)..," Under the assumption of Gaussian noise, various linear methods have been developed to recover the 3D matter distribution, which rely on the construction of a pseudo-inverse operator to act on the data, and which include a penalty function encoding the prior that is to be placed on the signal \citep{vanderplasetal11, sth09, chk05, tayloretal04, bt03, hk02}."
+" These methods produce promusing results: hoWeVOT, rey show a ΠΟ of problematic arteacts."," These methods produce promising results; however, they show a number of problematic artefacts."
+ Notably. Structures detected usiie these methods are strongY sancaredk along the line «X sight. the detected ampliTLL of the deusitv contrast is damped (in soue cases. ΝΟΥ stronelv). aud the deteced objects are shifted aloug the line of sight relative to heir true positions.," Notably, structures detected using these methods are strongly smeared along the line of sight, the detected amplitude of the density contrast is damped (in some cases, very strongly), and the detected objects are shifted along the line of sight relative to their true positions."
+ Such effects result from the choice of method used: ? vote that thei choice of filter naturally gives rise to a biased solution. aud 2 sugees that linear methods iuight be fufuudauxπιταην liuüted iu the resolution attainable along thie line of sight as a resul of the sieariug effect seen in these methods.," Such effects result from the choice of method used; \cite{sth09} note that their choice of filter naturally gives rise to a biased solution, and \cite{vanderplasetal11} suggest that linear methods might be fundamentally limited in the resolution attainable along the line of sight as a result of the smearing effect seen in these methods."
+ Furthermore. these methods are restriced to deal solely wit1 the overdetermiued inverse problem.," Furthermore, these methods are restricted to deal solely with the overdetermined inverse problem."
+ In other words. the resolution obtainable on the reconstruction of the densi vods liited to be. at best. equal to fhat of the input data.," In other words, the resolution obtainable on the reconstruction of the density is limited to be, at best, equal to that of the input data."
+ Thus. the resolution of the recoustruction is eutirele lamited by the quality of the data ancl its associated uoise levels. with no scope for improvement by judicious choice of inversion or denoising method.," Thus, the resolution of the reconstruction is entirely limited by the quality of the data and its associated noise levels, with no scope for improvement by judicious choice of inversion or denoising method."
+ Tn this paper. we consider the deprojection of the chsing signal alone the line of sight as ai dustance of compressed. seusing. where the seusing operator models he lue-ofsight integration of the matter density ceiving rise to the chsing signal.," In this paper, we consider the deprojection of the lensing signal along the line of sight as an instance of compressed sensing, where the sensing operator models the line-of-sight integration of the matter density giving rise to the lensing signal."
+ For simplicity i iXoemoenutation. and as a proof o: concept of our method. we consider ouly he line of sigh transformation. reducing the 3D weak. eusing problem to a one-dimensional inversion. with cach ine of sight ina i nage treated as indepeudenu.," For simplicity in implementation, and as a proof of concept of our method, we consider only the line of sight transformation, reducing the 3D weak lensing problem to a one-dimensional inversion, with each line of sight in an image treated as independent."
+" We note. rowever, tiat the aleoritlin preseuted here can be cheaply eoneralise to three dimensions."," We note, however, that the algorithm presented here can be cheaply generalised to three dimensions."
+ We ad yptasarse prior on our recoustruction. aud use a state-ofhe art iterative reconstruction aleoritlan draw- frou convex anavais. optimisation methods aud hixinonic analysis set within a compressed scusing framework.," We adopt a sparse prior on our reconstruction, and use a state-of-the art iterative reconstruction algorithm drawn from convex analysis, optimisation methods and harmonic analysis set within a compressed sensing framework."
+ Thiρα enables us to πια a robust estimator of the solution without requinis anv direct prior knowledge of the statistical distriution of the signal., This enables us to find a robust estimator of the solution without requiring any direct prior knowledge of the statistical distribution of the signal.
+ We note that the compressive sensing framework allows us to cousider a- uncderdeternuuec inverse problem. thereby allowing us to obain higher resolution ou our reconstruclous than that provided by the iuput data.," We note that the compressive sensing framework allows us to consider an underdetermined inverse problem, thereby allowing us to obtain higher resolution on our reconstructions than that provided by the input data."
+ This method produces reconstructious with nüninal bias and simearing im redshift space. and with reconstruction amplitudes ~75% of the true amplitude (or Jofer. in some cases}.," This method produces reconstructions with minimal bias and smearing in redshift space, and with reconstruction amplitudes $\sim75\%$ of the true amplitude (or better, in some cases)."
+ This is a significait nuproveieut over current linear inethods. despite the adoption of a simplified. «one-dimensional algorithiu.," This is a significant improvement over current linear methods, despite the adoption of a simplified, one-dimensional algorithm."
+ Iu acicition. ΟΥ method exhibits au apparent increased sensitivity to |ugh redshift structures. as compared with linear methods.," In addition, our method exhibits an apparent increased sensitivity to high redshift structures, as compared with linear methods."
+ Our reconstructions do exhibit ποιο LOISC. with faSC etectious appearing along a Miiber of lines of sight.," Our reconstructions do exhibit some noise, with false detections appearing along a number of lines of sight."
+ However. these tend to be ocalised to. οί or two pixels rather than coherent structures. and we exect jauproved noise control with a ull hrec-diiieusional implementation.," However, these tend to be localised to one or two pixels, rather than coherent structures, and we expect improved noise control with a full three-dimensional implementation."
+ We note that Wwe do uot iuclude photometric redsuft errors ii our simulations and. consequenutl. he simulations shown here should be cousidered to be ideaised.," We note that we do not include photometric redshift errors in our simulations and, consequently, the simulations shown here should be considered to be idealised."
+ 7. have presented a inethod to account for such, \cite{maetal06} have presented a method to account for such
+circular aperture with a size of 4 pixel radius.,circular aperture with a size of 4 pixel radius.
+ The 4 pixel scale encireles TO per cent of the light (at an energy. of 1.5keV) and roughly corresponds to the scale of the wavelet filter used for detection., The 4 pixel scale encircles 70 per cent of the light (at an energy of 1.5keV) and roughly corresponds to the scale of the wavelet filter used for detection.
+ These values are then divided with the corresponding exposure time and are converted to (ux., These values are then divided with the corresponding exposure time and are converted to flux.
+ The area curve is derived. using the merged PN and MOS background and exposure maps where available or the single PN and MOS maps., The area curve is derived using the merged PN and MOS background and exposure maps where available or the single PN and MOS maps.
+ We have checked that the area curve derived above gives reasonable results by estimating the SkkeV logNv* for all the X-ray sources in our fields and comparing with the number counts derived from other surveys (e.8. Manners et al.," We have checked that the area curve derived above gives reasonable results by estimating the keV $\log N -\log
+ S$ for all the X-ray sources in our fields and comparing with the number counts derived from other surveys (e.g. Manners et al."
+ 2003)., 2003).
+ Figure 1. shows the solid angle covered by our survey as a function of the kkeV limiting flux., Figure \ref{area} shows the solid angle covered by our survey as a function of the keV limiting flux.
+ The SDSS is an ongoing imaging and spectroscopic survey which has covered so far (DR-2) =3324deg of the sky.," The SDSS is an ongoing imaging and spectroscopic survey which has covered so far (DR-2) $\approx \rm 3324 \, deg^2$ of the sky."
+ Photometry is performed. in 5 bands (ugriz: Fukugita et al., Photometry is performed in 5 bands $ugriz$; Fukugita et al.
+ 1996: Stoughton et al., 1996; Stoughton et al.
+ 2002) to the limiting magnitude gc 23mmae. providing a uniform and. homogeneous multi-color photometric catalogue.," 2002) to the limiting magnitude $g \approx
+23$ mag, providing a uniform and homogeneous multi-color photometric catalogue."
+ The SDSS spectroscopic observations obtain spectra of galaxies brighter than lv.vmumag as well as of luminous red galaxies with 19.2 mmag (York et al., The SDSS spectroscopic observations obtain spectra of galaxies brighter than $r=17.7$ mag as well as of luminous red galaxies with $r<19.2$ mag (York et al.
+ 2000: Stoughton ct al., 2000; Stoughton et al.
+ 2002)., 2002).
+ We identify the optical counterparts of the X-ray sources following the method of Downes ct al. (, We identify the optical counterparts of the X-ray sources following the method of Downes et al. (
+1986) to calculate the probability. P. that a given candidate is the true identification.,"1986) to calculate the probability, $P$, that a given candidate is the true identification."
+ We apply an upper limit in the search radius. r«Yarcsec and a cutolfin the probability. 2«0.05. to limit the optical identifications to those candidates that are least likelv to be chance coincidences.," We apply an upper limit in the search radius, $r<7\rm\,arcsec$ and a cutoff in the probability, $P<0.05$, to limit the optical identifications to those candidates that are least likely to be chance coincidences."
+" ""Normal. galaxy candidates are selected to have (i) extended optical light profile. ie. resolved (sce Stoughton et al."," `Normal' galaxy candidates are selected to have (i) extended optical light profile, i.e. resolved (see Stoughton et al."
+ 2002). to avoid contamination of the sample by Galactic stars. (ii) X-raytooptical flux ratio log(f/f.)κ2. two orders of magnitude lower than typical AGNs.," 2002), to avoid contamination of the sample by Galactic stars, (ii) X-ray–to–optical flux ratio $\log (f_x / f_o)
+< -2$, two orders of magnitude lower than typical AGNs."
+ The logfx/fi is estimated from the relation The equation above is derived. from the X-raytooptical flux ratio definition of Stocke et al. (, The $\log f_X / f_{o}$ is estimated from the relation The equation above is derived from the X-ray--to--optical flux ratio definition of Stocke et al. (
+1991). that involved. kkeV. ας ancl V-band. magnitude.,1991) that involved keV flux and $V$ -band magnitude.
+ These quantities are converted το O.5-SkkeV flax and. rà band magnitude assuming a mean colour Vo/?=0.7 and a power-law X-ray spectral energy distribution with index |—LS., These quantities are converted to keV flux and $r$ -band magnitude assuming a mean colour $V-R=0.7$ and a power-law X-ray spectral energy distribution with index $\Gamma=1.8$.
+" The sample of ""normal ealaxy candidates is »esented in Table 2...", The sample of `normal' galaxy candidates is presented in Table \ref{sample}.
+ We further exclude from the sample sources with hard X-rav colours (hardness ratio fff ) roughly corresponding to a spectrum with a hydrogen column density higher than 1077em.72 (assuming a power-aw index of P= 1.9).," We further exclude from the sample sources with hard X-ray colours (hardness ratio $HR>0$ ) roughly corresponding to a spectrum with a hydrogen column density higher than $\rm 10^{22} \, cm^{-2}$ (assuming a power-law index of $\Gamma=1.9$ )."
+ The three hard. sources (4477. 15. 28) are most likely associated with low luminosity obscured AGN.," The three hard sources 7, 15, 28) are most likely associated with low luminosity obscured AGN."
+ These are presented. in ‘Table 3.., These are presented in Table \ref{hard}.
+ Note however. that or a [ow sources (2008. 1) I4. 29) we do not have enough photon statistics to pace a stringent constraint on heir N-rav spectrum.," Note however, that for a few sources 08, 10, 14, 29) we do not have enough photon statistics to place a stringent constraint on their X-ray spectrum."
+ We aso exploit the SDSS optical spectroscopic information available for our sources to search or AGN signatures using emission line ratios., We also exploit the SDSS optical spectroscopic information available for our sources to search for AGN signatures using emission line ratios.
+ Sixteen of our galaxies have either a narrow emission line optical spectrum ora Spectral EEnerey. Distribution (SED). as derived from the SDSS colours. consistent with a late-tvpe spectrum.," Sixteen of our galaxies have either a narrow emission line optical spectrum or a Spectral Energy Distribution (SED), as derived from the SDSS colours, consistent with a late-type spectrum."
+ Twelve galaxies either. present only. absorption lines or their SED is Consistent with an earlv-tvpe spectrum., Twelve galaxies either present only absorption lines or their SED is consistent with an early-type spectrum.
+ We employ. the CAIU-PET'T SDSS Value Added Database (VAC )) which provides spectral classifications for the SDSS galaxies using ciagnostic emission line ratios (INH]/IHo. OL]/LL. μήμα. ΟΕμα Miller et. al.," We employ the CMU-PITT SDSS Value Added Database (VAC ) which provides spectral classifications for the SDSS galaxies using diagnostic emission line ratios $\rm [N\,II]/H\alpha$, $\rm
+[O\,III]/H\beta$, $\rm [S\,II]/H\alpha$, $\rm [O\,I]/H\alpha$; Miller et al."
+.. 2003)., 2003).
+ ALL emission line systems in Table ὸ with available spectroscopic classifications have emission-line ratios consistent with star formation activity., All emission line systems in Table \ref{sample} with available spectroscopic classifications have emission-line ratios consistent with star formation activity.
+ However. we note that a number of sources with both absorption (c.g. IL) and. emission-line optical spectra have uncertain. classification based. on one line ratio only. usually Να.," However, we note that a number of sources with both absorption (e.g. $\rm H\beta$ ) and emission-line optical spectra have uncertain classification based on one line ratio only, usually $\rm [N\,II]/H\alpha$."
+ These are marked in Table 2.., These are marked in Table \ref{sample}.
+ The archival X-ray data used here. include: targeted observations of nearby normal galaxies with [ow X-raytooptical Hux ratio., The archival X-ray data used here include targeted observations of nearby normal galaxies with low X-ray--to--optical flux ratio.
+ Such sources have been excluded. from ‘Table 2.., Such sources have been excluded from Table \ref{sample}.
+ Moreover. a number of ‘normal galaxy. candidates although not the prime target of theIXNAZA-Neihon pointing Πο at the same redshift as the prime target. ancl are therefore most likely cürectly associated with it (e.g. cluster or group members).," Moreover, a number of `normal' galaxy candidates although not the prime target of the pointing lie at the same redshift as the prime target and are therefore most likely directly associated with it (e.g. cluster or group members)."
+ These sources are marked. in Table 2. , These sources are marked in Table \ref{sample}. .
+"The final sample of ""normal galaxy candidates that", The final sample of 'normal' galaxy candidates that
+ealaxvs halo. as well as the fraction of iu situ and accreted stars in each observed halo sample.,"galaxy's halo, as well as the fraction of in situ and accreted stars in each observed halo sample."
+" We trace the formation historv of cach star particle located within the virial radius of the main ealaxy at 2=O back to +=6. as well as follow the eas particles from, which the stars have formed."," We trace the formation history of each star particle located within the virial radius of the main galaxy at $z=0$ back to $z=6$, as well as follow the gas particles from which the stars have formed."
+ At each time step output bv the simulation (every 25 My). we identify the dark matter halo to which cach particle belonged usine AIIF?(Cillctal.2001:IKnoliinaun&I&nebe2009).," At each time step output by the simulation (every 25 Myr), we identify the dark matter halo to which each particle belonged using \citep{Gill2004,Knollmann2009}."
+. A star is considered bound to a dark matter halo ouly if it is identified as belonging to that halo for at least two consecutive tine steps;, A star is considered bound to a dark matter halo only if it is identified as belonging to that halo for at least two consecutive time steps.
+ Using this technique we ideutifv του different formation origins: accreted. iu situ. and aüubieuous.," Using this technique we identify three different formation origins: accreted, in situ, and ambiguous."
+ For a detailed description of this procedure. and a diseussion of numerical issues. the reader is referred o Paper 1. We quickly review the three classifications yolow.," For a detailed description of this procedure, and a discussion of numerical issues, the reader is referred to Paper I. We quickly review the three classifications below."
+ Accreted stars formed in halos other than the main ealaxy’s dark matter halo., Accreted stars formed in halos other than the main galaxy's dark matter halo.
+ Through merging. these stars wave become unbound to their progenitors aud now clong to the main galaxy halo.," Through merging, these stars have become unbound to their progenitors and now belong to the main galaxy's halo."
+ The majority of t accreted stars iu the halos of «*h277. h285. aud AAW Wolnass in stars). originated dn 2—3 subhalos. each wi a total mass ofl341019A7...," The majority of the accreted stars in the halos of h277, h285, and MW1 by mass in stars), originated in $2-3$ subhalos, each with a total mass of $1-3 \times 10^{10} M_{\odot}$."
+ The majority of accreted stars in L258. which experiences several major mergers. as discussed in Section 3. originate in three galaxies. with otal masses raueiug from 2.5 to 6 ϱ-- ," The majority of accreted stars in h258, which experiences several major mergers, as discussed in Section 3, originate in three galaxies, with total masses ranging from 2.5 to 6 $\times 10^{10} M_{\odot}$."
+Iu situ stars. on the other haud. formed within the uain galaxy potential well. with their gas progenitors und to the «main galaxy. before their formation.," In situ stars, on the other hand, formed within the main galaxy's potential well, with their gas progenitors bound to the main galaxy before their formation."
+ Paper I found this population formed within the inner ~4 spe of the galaxw’s center before being displaced iuto he kinematic halo component as a result of mergers., Paper I found this population formed within the inner $\sim 4$ kpc of the galaxy's center before being displaced into the kinematic halo component as a result of mergers.
+ Stars which are classified as iuubiguous. 3% of the total alo stars. have au unknown formation history due to the iuited umber of time steps output for cach simulation.," Stars which are classified as ambiguous, $ \sim 3 \%$ of the total halo stars, have an unknown formation history due to the limited number of time steps output for each simulation."
+ This occurs if à gas particle spawns a star particle at approxinatelv the same time that it first becomes bound o the primary., This occurs if a gas particle spawns a star particle at approximately the same time that it first becomes bound to the primary.
+ In such cases it is uncertain whether the star formed in the primary or in its original subhalo., In such cases it is uncertain whether the star formed in the primary or in its original subhalo.
+" All four of the simulated galaxies analyzed in this oper host a stellar halo which contains both accreted and in situ stars,", All four of the simulated galaxies analyzed in this paper host a stellar halo which contains both accreted and in situ stars.
+ While the relative contribution of cach population differs from halo to halo. the presence of stars with a dual origin is a generic feature of the stellar halos surrounding £* galaxies at z=0.," While the relative contribution of each population differs from halo to halo, the presence of stars with a dual origin is a generic feature of the stellar halos surrounding $L^{\star}$ galaxies at z=0."
+ Iu Paper Iwe showed that the fraction of iu situ stars present m a halo depends strongly on the mereing history of the primary galaxy., In Paper I we showed that the fraction of in situ stars present in a halo depends strongly on the merging history of the primary galaxy.
+ The in situ population of galaxies with very active nergiue histories. aud which therefore host massive accreted halos. is diluted iu comparison to the iu situ halo population of galaxies which have not accreted as Inany stars during their lifetimes.," The in situ population of galaxies with very active merging histories, and which therefore host massive accreted halos, is diluted in comparison to the in situ halo population of galaxies which have not accreted as many stars during their lifetimes."
+ As suggested by their in situ fractious. h285 and h258 have much inore active niereime histories than MWT and h277 (Table 2).," As suggested by their in situ fractions, h285 and h258 have much more active merging histories than MW1 and h277 (Table 2)."
+ We now examine the trends iu chemical abundances displaved by the observed. halo stars., We now examine the trends in chemical abundances displayed by the observed halo stars.
+ One expects that the chemical abundance pattern of a stellar population will be set by the star formation history of the galaxy in which the population formec., One expects that the chemical abundance pattern of a stellar population will be set by the star formation history of the galaxy in which the population formed.
+ For this reason we ai to find trends which differeutiate the in situ and accreted populations iu each stellar halo., For this reason we aim to find trends which differentiate the in situ and accreted populations in each stellar halo.
+ These qualitative treuds in inctallicity are robust. aud applicable not just to the Milkv Was. but to Milky Way-iass galaxies witli different mereie histories. as discussed in detail below. and in Section [.," These qualitative trends in metallicity are robust, and applicable not just to the Milky Way, but to Milky Way-mass galaxies with different merging histories, as discussed in detail below, and in Section 4."
+ Massive ealaxics form in deep potential wells. aud consequently have higher star formation rates (SFR) than less massive galaxies. resulting im a mass-metallicity relation (Tremoutietal.2001:Brooks2007:Fin-lator&Davé2008).," Massive galaxies form in deep potential wells, and consequently have higher star formation rates (SFR) than less massive galaxies, resulting in a mass-metallicity relation \citep{Tremonti2004,Brooks2007,Finlator2008}."
+.. With thei hieh SER. massive galaxies will reach higher |Fo/TI] at relatively coustaut [o /Fe] before SNe Ia. begin to contribute. as core-collapse SNe curich the ISM with mostly alpha elements. and little iron or iou-peak elements.," With their high SFR, massive galaxies will reach higher [Fe/H] at relatively constant $\alpha$ /Fe] before SNe Ia begin to contribute, as core-collapse SNe enrich the ISM with mostly alpha elements, and little iron or iron-peak elements."
+ Ta lower mass ealaxies. however. lower SFRs mean that the galaxy cant enrich as much iu Fe before SNe type Ia began to contribute. resulting iu a decrease of ja/Fo] at lower [Fe/TI].," In lower mass galaxies, however, lower SFRs mean that the galaxy can't enrich as much in Fe before SNe type Ia began to contribute, resulting in a decrease of $\alpha$ /Fe] at lower [Fe/H]."
+ Additionally. galaxies with loug star formation histories will form stars out of gas that has been euriched bv both core-collapse SNe and SNe Type Ia. whereas ealaxies with truncated star formation histories will have their abuudance pattern set primarily by core-collapse SNe.," Additionally, galaxies with long star formation histories will form stars out of gas that has been enriched by both core-collapse SNe and SNe Type Ia, whereas galaxies with truncated star formation histories will have their abundance pattern set primarily by core-collapse SNe."
+ These trends are shown in Figure I., These trends are shown in Figure 1.
+ Tf the in situ aud accreted populations each formed at different times. uncer different plosical conditions. we expect to see that reflected in their abundance patterus.," If the in situ and accreted populations each formed at different times, under different physical conditions, we expect to see that reflected in their abundance patterns."
+ We indeed find that iu three of our galaxies (those without a very recent major merger) in situ halo stars at the high |Fe/II] eud of the metallicity distribution πιοο (AIDF) tend to be more alpha rich than the similarly high |Fe/T] accreted stars (Figure 3. discussed in detail below).," We indeed find that in three of our galaxies (those without a very recent major merger) in situ halo stars at the high [Fe/H] end of the metallicity distribution function (MDF) tend to be more alpha rich than the similarly high [Fe/H] accreted stars (Figure 3, discussed in detail below)."
+ At lower [FeTI]. we find that the two »opulations have similar [O/Fe|.," At lower [Fe/H], we find that the two populations have similar [O/Fe]."
+ Because we only follow oxvegenu and iro in these simmlations [O/Fe] serves as our xoxy for [o /Fc]., Because we only follow oxygen and iron in these simulations [O/Fe] serves as our proxy for $\alpha$ /Fe].
+ Before we discuss our fiudiues in detail. it is iniportant o first note that the satellites of the simulated galaxies studied here are brighter. aud heuce are more rich. than those observed iu the Milkv Way (Zolotov[Fe/TI|-etal. 2009).," Before we discuss our findings in detail, it is important to first note that the satellites of the simulated galaxies studied here are brighter, and hence are more [Fe/H]-rich, than those observed in the Milky Way \citep{Zolotov2009}."
+. If the satellites which built up our sinulated stellar halos contained less stellar mass at a given total mass the qualitative chemical abundance patterus for m situ and accreted halo stars diseussed below would not change. as we demonstrate in detail i Section L.," If the satellites which built up our simulated stellar halos contained less stellar mass at a given total mass the qualitative chemical abundance patterns for in situ and accreted halo stars discussed below would not change, as we demonstrate in detail in Section 4."
+ The results in metallicity we discuss. however. are not meant to be absolute. aud the qualitative trends are robust for Alilkv Wavauass galaxies.," The results in metallicity we discuss, however, are not meant to be absolute, and the qualitative trends are robust for Milky Way-mass galaxies."
+" As discussed in Section 2.2. in situ stars formed in the innermost regions of the primary ealaxws darkauatter iio. aud were displaced. into the halo through massive ucrecrs,"," As discussed in Section 2.2, in situ stars formed in the innermost regions of the primary galaxy's dark-matter halo, and were displaced into the halo through massive mergers."
+ Since the redshift of the last significant mecrecr (Table 2) cetermunes the last time at which in situ stars are substantially displaced into the halo. the formation iue of the in situ populations of cach galaxy is quite different.," Since the redshift of the last significant merger (Table 2) determines the last time at which in situ stars are substantially displaced into the halo, the formation time of the in situ populations of each galaxy is quite different."
+ The left panel of Figure 2 shows the time of orlnation for in situ halo stars (solid lines) aud accreted ido stars (dashed lines) in each simulated observed xuuple., The left panel of Figure 2 shows the time of formation for in situ halo stars (solid lines) and accreted halo stars (dashed lines) in each simulated observed sample.
+ Because MW1 and h277 experience their last, Because MW1 and h277 experience their last
+"We knew that. the shape parameter is inversely in proportion to ,/zpy (Pauluhn Solanki 2007) and that the lognormal shape parameter. c. slishtlv changes with a.","We knew that, the shape parameter is inversely in proportion to $\sqrt{\tau{p_f}}$ (Pauluhn Solanki 2007) and that the lognormal shape parameter, $\sigma$, slightly changes with $\alpha$."
+ Although. the sharpness of the distribution indicates that for a higher a. the distribution shape tends to be sharpener as illustrated by the kurtosis increase (Figure 5)).," Although, the sharpness of the distribution indicates that for a higher $\alpha$, the distribution shape tends to be sharpener as illustrated by the kurtosis increase (Figure \ref{fig5}) )."
+ Dazarghan et al. (, Bazarghan et al. (
+2008) used Artificial Neural Networks (ANN) to compare SUMER/SolIO observational time series with simulated (ime series.,2008) used Artificial Neural Networks (ANN) to compare SUMER/SoHO observational time series with simulated time series.
+ In. this paper. a similar method is emploved to determine (he tree kev parameters of SECCIIL/EUVI and SDO/ALA time series.," In this paper, a similar method is employed to determine the three key parameters of SECCHI/EUVI and SDO/AIA time series."
+ The main advantages of the ANN method is that it enables us to obtain quantitative values for all parameters including a. with which Safari et al.(2007) had problem in analvsis.," The main advantages of the ANN method is that it enables us to obtain quantitative values for all parameters including $\alpha$, with which Safari et al.(2007) had problem in analysis."
+ x10M. 10?M... (Gebhardtetal.2000:Ferrarese&Merritt2000).. ανLO?ΑΗ. ," $\times 10^6~M_\odot$ $10^9~M_\odot$ \citep{geb00,fer00}, $\approx 10^5~M_\odot$ "
+the (hermal energy is directly proportional to the hvedrostatic scale height and therefore the temperature.,the thermal energy is directly proportional to the hydrostatic scale height and therefore the temperature.
+ The top pictures of Figure G show that an increase of thermal energy of the plasma causes (he thermal pressure to be more effective in pushing oul against the confining forces of the magnetic field., The top pictures of Figure \ref{tspot} show that an increase of thermal energy of the plasma causes the thermal pressure to be more effective in pushing out against the confining forces of the magnetic field.
+ The more even spread of mass across the concave-upward [oor of (he magnetic configuration imposes less stress on (he magnetic field al y=0 and allows (he prominence plasma to sit higher in (he atmosphere (han in cases with lower temperature., The more even spread of mass across the concave-upward floor of the magnetic configuration imposes less stress on the magnetic field at $y=0$ and allows the prominence plasma to sit higher in the atmosphere than in cases with lower temperature.
+ The effect of this on the characteristic scale leneth of both the plasma distribution aud the magnetic structure itself are clearly visible in (he top two pictures., The effect of this on the characteristic scale length of both the plasma distribution and the magnetic structure itself are clearly visible in the top two pictures.
+ The bottom two pictures show examples with colder plasma but. with significant axial magnetic [lux density - they have axial [Iux profiles derived [rom (hat of model b of Section while the magnitudes of their py proliles are similar to those of the top pictures., The bottom two pictures show examples with colder plasma but with significant axial magnetic flux density - they have axial flux profiles derived from that of model b of Section \ref{nlff} while the magnitudes of their $p_0$ profiles are similar to those of the top pictures.
+ These stronger magnetic structures are able to accommocdate cold plasma without sienilicant changes in (heir magnetic fields., These stronger magnetic structures are able to accommodate cold plasma without significant changes in their magnetic fields.
+ In realitw prominences have tvpical hydrostatic scale height of a few hundred km while flux ropes are of order 10 Mam across., In reality prominences have typical hydrostatic scale height of a few hundred km while flux ropes are of order 10 Mm across.
+ The bottom left picture shows the model closest to these parameter values., The bottom left picture shows the model closest to these parameter values.
+ To demonstrate the flexibility of the solution method. we show an example with two separate prominence concentrations in a sinele flix rope.," To demonstrate the flexibility of the solution method, we show an example with two separate prominence concentrations in a single flux rope."
+ Curve c in Figure 5. is. This polynomial has double roots at &=3/10 and 3/20 and has the same value and derivative at @=0 as3/10—c.," Curve c in Figure \ref{Pi2s} is, This polynomial has double roots at $\psi =3/10$ and $3/20$ and has the same value and derivative at $\psi =0$ as$3/10 -\psi$."
+ The corresponding prominence model is plotted in Figure 7.., The corresponding prominence model is plotted in Figure \ref{double}. .
+ A narrow evacuated channel. corresponding to the first zero of po(i). separates à rounded blob of plasma above and a curved sheet below.," A narrow evacuated channel, corresponding to the first zero of $p_0 (\psi )$, separates a rounded blob of plasma above and a curved sheet below."
+ Further complexity is introduced by an ambient atmosphere populated by a hot plasma in a non-force-free magnetic field., Further complexity is introduced by an ambient atmosphere populated by a hot plasma in a non-force-free magnetic field.
+ Figure 8. shows a model which exploits the non-isothermal aspect of Equation (13))., Figure \ref{noniso} shows a model which exploits the non-isothermal aspect of Equation \ref{nonisogs}) ).
+ A v-cependent temperature profile is imposed so that a hot corona and a cool. dense prominence can be modeled together in a sell-consistent way.," A $\psi$ -dependent temperature profile is imposed so that a hot corona and a cool, dense prominence can be modeled together in a self-consistent way."
+ The variation of the hydrostatic scale height A(o). proportional to the temperature. wilh o within (he flux contour e=3/2 is described by This profile is eraphed inthe left panel of Figure 8..," The variation of the hydrostatic scale height $\Lambda (\psi )$, proportional to the temperature, with $\psi$ within the flux contour $\psi =3/2$ is described by This profile is graphed inthe left panel of Figure \ref{noniso}. ."
+ The scale height therefore ranges, The scale height therefore ranges
+wilh a size between e and a+da is og(r).N(a)ada.,with a size between $a$ and $a + da$ is $\sigma_0(r)N(a)a^{3}da$.
+ The size distribution. initially independent of disk radius. is (wpically assumed to be a simple powerlaw. αλαα. with upper and lower size cutolfs. cas and egg.," The size distribution, initially independent of disk radius, is typically assumed to be a simple powerlaw, $N(a) \propto a^{-s}$, with upper and lower size cutoffs, $a_{\rm
+max}$ and $a_{\rm min}$."
+ The mass distribution is tilted towards large (small) particles is <dt(s> 4)., The mass distribution is tilted towards large (small) particles if $s<4$ $s>4$ ).
+ Particles of a given size evolve according to (25)). and integration over (he size distribution vields the total surface density: where we must now take into account the dependence of Ry ou particle size via (he drift speed.," Particles of a given size evolve according to \ref{gen}) ), and integration over the size distribution yields the total surface density: where we must now take into account the dependence of $R_{\rm i}$ on particle size via the drift speed."
+" Care must be taken in evaluating this integral since the upper size cutoff. a,,44. varies with f? and /. because of the requirement that material not come from beyond. a certain racius."," Care must be taken in evaluating this integral since the upper size cutoff, $a_{\rm max}$, varies with $R$ and $t$, because of the requirement that material not come from beyond a certain radius."
+ Even for the case of a disk with no sharp edge. equ. (001).," Even for the case of a disk with no sharp edge, eqn. \ref{sige2}) ),"
+ a eutol must be placed at some large finite disk radius because. when d>1. material formally dirilts in from infinity in a [inite time.," a cutoff must be placed at some large finite disk radius because, when $d > 1$, material formally drifts in from infinity in a finite time."
+ This effect is not physical since Chie formula for the drift speed must be modified when it exceeds the sound speed. which occurs bevond 500 AU for millimeter sized solids.," This effect is not physical since the formula for the drift speed must be modified when it exceeds the sound speed, which occurs beyond $500$ AU for millimeter sized solids."
+ An insignificant. amount of material lies at such radii. and we may eliminate the mathematical problem by imposing a cutoll," An insignificant amount of material lies at such radii, and we may eliminate the mathematical problem by imposing a cutoff."
+ Our final results are insensitive to (he location of the cutoll as long as i( is imposed in the exponential tail. r>ry.," Our final results are insensitive to the location of the cutoff as long as it is imposed in the exponential tail, $r > r_0$."
+ The numerical integrations were performed using a fifth order Rombere method to deal with the laree derivatives present in the kernel., The numerical integrations were performed using a fifth order Romberg method to deal with the large derivatives present in the kernel.
+ Figs., Figs.
+ A and À show the time evolution of ihe enhancement ο./)/X(r.0) of particles with a distribution of sizes ancl masses (hat is characteristic of chonclrules: eg;=.01 mm. (yas=1 mm. s=3.," \ref{fig:distH} and \ref{fig:distAf} show the time evolution of the enhancement $\Sigma(r,t)/\Sigma(r,0)$ of particles with a distribution of sizes and masses that is characteristic of chondrules: $a_{\rm min} = .01$ mm, $a_{\rm max} = 1$ mm, $s = 3$."
+" We again use (30)) lor Mr.0). with r,=250 AU. with the gas disks following models II and Af."," We again use \ref{sige2}) ) for $\Sigma(r,0)$, with $r_{\rm o} = 250$ AU, with the gas disks following models H and Af."
+ The main effect of introducing a size distribution is to reduce ancl broaden the amount of concentration since particles of dillerent sizes drift at different rates., The main effect of introducing a size distribution is to reduce and broaden the amount of concentration since particles of different sizes drift at different rates.
+" In order to determine whether the concentration due to gas drag only is enough to vield GI according to the saturation mechanism of relseczZGl]. we need to make choices about an initial, size distribution of particles.", In order to determine whether the concentration due to gas drag only is enough to yield GI according to the saturation mechanism of \\ref{sec:ZGI} we need to make choices about an “initial” size distribution of particles.
+ If the parücles are uniformly sized (a false assumption) then enhancement [actors are much larger than required for GI., If the particles are uniformly sized (a false assumption) then enhancement factors are much larger than required for GI.
+ Here we make a more reasonable assumption (hat initially (he clisk contains solar abundances of matrix material with a size distribution: 0.1jm«amm , Here we make a more reasonable assumption that initially the disk contains solar abundances of matrix material with a size distribution: $0.1~\mu{\rm m} < a < 0.1~{\rm mm}$ 
+"In spite of our high-precision and temporal cadency of our RV measurements, we found no evidence for the planetary signal reported by ?..","In spite of our high-precision and temporal cadency of our RV measurements, we found no evidence for the planetary signal reported by \cite{2009arXiv0912.2773H}."
+" Instead of an orbit with peak-to-peak amplitude of mm/s and period of ddays, we detected an RV signal with peak-to-peak variation of mm/s and a periodicity of 2.8 days."," Instead of an orbit with peak-to-peak amplitude of m/s and period of days, we detected an RV signal with peak-to-peak variation of m/s and a periodicity of 2.8 days."
+" Moreover, the amplitude of this signal is not constant, doubling from the first campaign to the second one."," Moreover, the amplitude of this signal is not constant, doubling from the first campaign to the second one."
+ We tried to quantify the likelihood that our points were derived from the announced orbit., We tried to quantify the likelihood that our points were derived from the announced orbit.
+" Since the error propagation on the Tp makes the prediction of an accurate phase impossible, we proceeded as follows."," Since the error propagation on the $_0$ makes the prediction of an accurate phase impossible, we proceeded as follows."
+" We considered a set of 28 data points randomly distributed over the entire phase, and calculated the RV for each point, and the r.m.s."," We considered a set of 28 data points randomly distributed over the entire phase, and calculated the RV for each point, and the r.m.s."
+ of the set of measurements., of the set of measurements.
+" Note that there is no instrumental error added to the curve, so this provides a lower limit to the r.m.s."," Note that there is no instrumental error added to the curve, so this provides a lower limit to the r.m.s."
+ The simulation was repeated 0000 times., The simulation was repeated 000 times.
+" All values were well in excess of the measured RV of mm/s r.m.s.,"," All values were well in excess of the measured RV of m/s r.m.s.,"
+ and we concluded then that the probability that the two data sets are compatible is lower than 107., and we concluded then that the probability that the two data sets are compatible is lower than $^{-4}$.
+" Two arguments point towards a photospheric origin for the RV variations: The hypothesis that the RV on 11790 was rooted on stellar phenomena was discarded by ?,, who detected a RV signal with a periodicity different from the rotational period."," Two arguments point towards a photospheric origin for the RV variations: The hypothesis that the RV on 1790 was rooted on stellar phenomena was discarded by \cite{2009arXiv0912.2773H}, who detected a RV signal with a periodicity different from the rotational period."
+The unit of the age ancl lookback time. fy. is 10? vears.,"The unit of the age and lookback time, $t_{9}$, is $10^{9}$ years."
+ The 5goal of this investigation5 is (to re-construct the Macau plot from local observations., The goal of this investigation is to re-construct the Madau plot from local observations.
+ This is done by using5 the above model to chemically evolve a representative co-moving5 volume of the universe to form what will be a representative or composite galaxy., This is done by using the above model to chemically evolve a representative co-moving volume of the universe to form what will be a representative or composite galaxy.
+" It may be more (han fortuitous that Baldry et ((2002) showed (hat the averaged spectra of 2DE ealaxies as a [function of redshift resemble what would be a present dav Sb-Sbe galaxy. (ie. similar (ο M31 and the Milkv. Waa. galaxies on which our model has been ""calibrated)."," It may be more than fortuitous that Baldry et (2002) showed that the averaged spectra of 2DF galaxies as a function of redshift resemble what would be a present day Sb-Sbc galaxy (i.e. similar to M31 and the Milky Way, galaxies on which our model has been `calibrated')."
+ The starting point is to define a representative co-moviung volume of the universe which we lake to be 100 Mpc., The starting point is to define a representative co-moving volume of the universe which we take to be 100 $^{3}$.
+ The volume assumed is arbitrary and has no effect on the final result., The volume assumed is arbitrary and has no effect on the final result.
+ ILowever. we note that 6”E of a generic galaxy. Iuminosty. function is ~0.01Mpeo implving a volume per L* galaxy of 1001pe.," However, we note that $\phi^{*}$ of a generic galaxy luminosty function is $\sim0.01 Mpc^{-3}$ , implying a volume per $L^{*}$ galaxy of $100 Mpc^{3}$."
+" Given Oh?=0.0224 [rom WMAP (Spergel οἱ 22003). this volume encloses a barvonic mass of 6.22x10!. ML,."," Given $\Omega_{b}h^{2}=0.0224$ from WMAP (Spergel et 2003), this volume encloses a baryonic mass of $^{11}$ $_{\odot}$."
+ While as vel we have no wav of knowing the mass in remnants left from a Population H1 phase. it is assumed that within this volume there is at least 1.2x10! M. of gas which has been enriched during this earlier phase ο —4.0.," While as yet we have no way of knowing the mass in remnants left from a Population III phase, it is assumed that within this volume there is at least $1.2\times10^{11}$ $_{\odot}
+$ of gas which has been enriched during this earlier phase to $=-4.0$."
+" These numbers make up the M, Αμ M, (ved) and Zi of our model.", These numbers make up the $_{t}=$ $_{t}$ $_{t}$ (red)) and $_{0}$ of our model.
+ To form what will be the main spheroidal component. we assign the parameters shown in Table 1.," To form what will be the main spheroidal component, we assign the parameters shown in Table 1."
+ As can be seen from the fourth column. most of the parameters are observationally constrained.," As can be seen from the fourth column, most of the parameters are observationally constrained."
+" The cluster parameters. log Z./Z. anda. come from Cote's discussion. and the ratio of M;(blue) to Al, (red) is the same value deduced [rom the discussion in 322.3 of the M31 halo [rom observations bv Durrell et al."," The cluster parameters, log $Z_{c}/Z_{\odot}$ and $\sigma$, come from Cote's discussion, and the ratio of $_{t}$ (blue) to $_{t}
+$ (red) is the same value deduced from the discussion in 2.3 of the M31 halo from observations by Durrell et al."
+ The adopted value of the vield. p=0.013 (log(p/Z.)= —0.11). is determined from a study of Galactic bulge stars (Zoccali et 22003) which will be discussed in more detail in (he next section.," The adopted value of the yield, $=0.013$ $_{\odot})=-0.11$ ), is determined from a study of Galactic bulge stars (Zoccali et 2003) which will be discussed in more detail in the next section."
+ It should be noted that observational evidence suggests that field. halo. cluster stars. thick. disk. ancl bulge stars all exhibit an enhanced oxvgen to iron abunclance ratio (e.g. Prochaska et 22000).," It should be noted that observational evidence suggests that field halo, cluster stars, thick disk, and bulge stars all exhibit an enhanced oxygen to iron abundance ratio (e.g. Prochaska et 2000)."
+ This provides the justification for modelling the evolution of the iron abundance under theinstantaneous recycling approximation., This provides the justification for modelling the evolution of the iron abundance under theinstantaneous recycling approximation.
+ Using the parameters given above and equation (16) to caleulate the SFR. the results," Using the parameters given above and equation (16) to calculate the SFR, the results"
+flares having similar total energy as reported here.,flares having similar total energy as reported here.
+" The variations detected by Tofflemireetal.(2011) and Davenportetal.(2011) are smaller than the formal uncertainty quoted with the 2MASS magnitudes (20-30 millimags), so we assume that the variation between the published 2MASS magnitudes and the magnitudes of the M dwarfs during our observing was negligible."," The variations detected by \citet{Tofflemire2011} and \citet{Davenport2011} are smaller than the formal uncertainty quoted with the 2MASS magnitudes (20-30 millimags), so we assume that the variation between the published 2MASS magnitudes and the magnitudes of the M dwarfs during our observing was negligible."
+" For two nights, we used the DAO 1.8-m telescope with the SITe5 CCD and spectrograph to observe EV Lac during a coordinated campaign with the telescopes at APO."," For two nights, we used the DAO 1.8-m telescope with the SITe5 CCD and spectrograph to observe EV Lac during a coordinated campaign with the telescopes at APO."
+ Our setup resulted in a spectral resolution of R~750 and wavelength coverage from3550A—4700A., Our setup resulted in a spectral resolution of $\sim$ 750 and wavelength coverage from.
+". We measured Ca II K, He I MAT1À,, and the Hydrogen Balmer series Hy and Hd."," We measured Ca II K, He I $\lambda$, and the Hydrogen Balmer series $\gamma$ and $\delta$."
+ Exposure times for EV Lac ranged from 60 to 420 seconds., Exposure times for EV Lac ranged from 60 to 420 seconds.
+" Due to these relatively long integration times, additional cosmic ray cleaning was performed with the LACOSMIC utility (vanDokkum2001)."," Due to these relatively long integration times, additional cosmic ray cleaning was performed with the LACOSMIC utility \citep{van-Dokkum2001}."
+". The spectra were wavelength-calibrated with a FeAr lamp and flux-calibrated using data from the standard star G191B2B, then spectrophotometrically calibrated by normalizing to the simultaneous U-band data."," The spectra were wavelength-calibrated with a FeAr lamp and flux-calibrated using data from the standard star G191B2B, then spectrophotometrically calibrated by normalizing to the simultaneous $U$ -band data."
+ Equivalent widths are not useful for blue flare spectra because of the changes in the surrounding continuum flux during the flare., Equivalent widths are not useful for blue flare spectra because of the changes in the surrounding continuum flux during the flare.
+" Instead, we measured absolute line fluxes directly from the data."," Instead, we measured absolute line fluxes directly from the data."
+ The values we use during the flare have the quiet line flux subtracted., The values we use during the flare have the quiet line flux subtracted.
+" Flares are most easily seen at blue and ultraviolet wavelengths, where the hot, white-light continuum emission from the flare is in high contrast to the small amount of flux emitted from cool M dwarf photospheres (Lacyetal.1976;Hawley&Pettersen1991)."," Flares are most easily seen at blue and ultraviolet wavelengths, where the hot, white-light continuum emission from the flare is in high contrast to the small amount of flux emitted from cool M dwarf photospheres \citep{Lacy1976,Hawley1991}."
+". To identify as many flares as possible, we used the bluest band of photometry available."," To identify as many flares as possible, we used the bluest band of photometry available."
+" This was typically u, but for some nights only U was available, and VB 8 was too faint to observe in U or u, so we used g-band data."," This was typically $u$, but for some nights only $U$ was available, and VB 8 was too faint to observe in $U$ or $u$, so we used $g$ -band data."
+ The band used to identify flares for each set of observations is given in Table 2.., The band used to identify flares for each set of observations is given in Table \ref{tab:obs}.
+" Photometrically, flares are observed as excursions above the mean quiescent value of the star’s flux, which can be any size or shape."," Photometrically, flares are observed as excursions above the mean quiescent value of the star's flux, which can be any size or shape."
+" Realistically, flare detection must take into account small variations in the continuum caused by observational effects and so a minimum duration and energy above the observed quiescent value is required."," Realistically, flare detection must take into account small variations in the continuum caused by observational effects and so a minimum duration and energy above the observed quiescent value is required."
+" To identify individual flares, we used the custom IDL code discussed in Hilton which selects peaks that have at least three consecutive(2011),, epochs more than 3 standard deviations above the local quiescent light curve."," To identify individual flares, we used the custom IDL code discussed in \citet{Hilton2011phd}, which selects peaks that have at least three consecutive epochs more than 3 standard deviations above the local quiescent light curve."
+ At least one of those epochs must be 5 sigma above quiescence., At least one of those epochs must be 5 sigma above quiescence.
+ We reviewed each flare by eye to confirm that the deviations from the mean were not caused by bad photometry., We reviewed each flare by eye to confirm that the deviations from the mean were not caused by bad photometry.
+" Over the course of 48.9 hours of observations on four different stars, we observed a total of 16 flares, which are listed per star in Table and per night in Table 2.."," Over the course of 48.9 hours of observations on four different stars, we observed a total of 16 flares, which are listed per star in Table \ref{tab:targ} and per night in Table \ref{tab:obs}."
+ Figure 2 shows the energy and peak magnitude of each flare., Figure \ref{fig:chfl} shows the energy and peak magnitude of each flare.
+" To identify flares which had associated IR line emission, we examined the measured EWs of P@ and He I \10830A as a function of time during the flare."," To identify flares which had associated IR line emission, we examined the measured EWs of $\beta$ and He I $\lambda$ as a function of time during the flare."
+" We found that the three most energetic flares, which"," We found that the three most energetic flares, which"
+Our understanding of the cosmic star formation history (SFH) of galaxies has progressed significantly over the past decade (e.g..Hopkins2004:&Beacom2006).,"Our understanding of the cosmic star formation history (SFH) of galaxies has progressed significantly over the past decade \citep[e.g.,][]{Hop:04,HB:06}."
+. In the same time the space density of neutral hydrogen gas has been measured over the majority of cosmic history (seeFigure8ofLahetal. 2007)., In the same time the space density of neutral hydrogen gas has been measured over the majority of cosmic history \citep[see Figure~8 of][]{Lah:07}.
+. The evolution of the atomic hydrogen (HI) in the universe will be comprehensively determined within the next few years by extremely sensitive surveys with the next generation of radio telescope instrumentation (e.g..vanderHulstetal.2004:Rawlings2004;Johnston 2005). and it is timely to consider mechanisms associated with this evolution.," The evolution of the atomic hydrogen (HI) in the universe will be comprehensively determined within the next few years by extremely sensitive surveys with the next generation of radio telescope instrumentation \citep[e.g.,][]{vdH:04,Raw:04,Joh:08}, and it is timely to consider mechanisms associated with this evolution."
+ The space density of HI in galaxies appears to evolve surprisingly little from 2.ο5 to 50.2 (Lahetal.2007). a span of roughly 10GGvr. the latter half of which sees a decline 1n the space density of star formation rate (SER) in galaxies by almost an order of magnitude (e.g..Hopkins&Beacom 2006).," The space density of HI in galaxies appears to evolve surprisingly little from $z\approx 5$ to $z\approx 0.2$ \citep{Lah:07}, a span of roughly Gyr, the latter half of which sees a decline in the space density of star formation rate (SFR) in galaxies by almost an order of magnitude \citep[e.g.,][]{HB:06}."
+. Given the SER density it is easy to show that the HI plus molecular gas at high redshift would be exhausted on timescales of a few Gyr if it were not continually replenished., Given the SFR density it is easy to show that the HI plus molecular gas at high redshift would be exhausted on timescales of a few Gyr if it were not continually replenished.
+ Erb(2008) presents a model incorporating gas infall. outflows and consumption by star formation. to explain both replenishment and the mass-metallicity relation in high-redshift (.2 2) galaxies.," \citet{Erb:08} presents a model incorporating gas infall, outflows and consumption by star formation, to explain both replenishment and the mass-metallicity relation in high-redshift $z\approx 2$ ) galaxies."
+ Hydrodynamic simulations advocating hot and cold modes of accretion indicate that the infall rate closely tracks the star formation rate (e.g.Keresetal.2005;Birnboimal. 2007). with star formation moderated by the rate of infall.," Hydrodynamic simulations advocating hot and cold modes of accretion indicate that the infall rate closely tracks the star formation rate \citep[e.g.][]{Ker:05,Bir:07}, with star formation moderated by the rate of infall."
+ The simulations. however. neglect gas outflows from galaxies. which are a significant component of gas depletion.," The simulations, however, neglect gas outflows from galaxies, which are a significant component of gas depletion."
+ The quantitative infall rates predicted are thus insufficient to maintain a constant HI density in galaxies., The quantitative infall rates predicted are thus insufficient to maintain a constant HI density in galaxies.
+ Observed rates of gas infall in local galaxies. also. are only about of the star formation rate (Sancisietal.2008)..," Observed rates of gas infall in local galaxies, also, are only about of the star formation rate \citep{San:08}."
+ The difficulties in explaining replenishment through infall leave the physical mechanism of this replenishment as a eritical open question in galaxy evolution., The difficulties in explaining replenishment through infall leave the physical mechanism of this replenishment as a critical open question in galaxy evolution.
+ In this Letter we suggest a mechanism directly associated with the SPR in galaxies that can provide the necessary replenishment of neutral gas to maintain an essentially unevolving. or slowly evolving. HI mass density.," In this Letter we suggest a mechanism directly associated with the SFR in galaxies that can provide the necessary replenishment of neutral gas to maintain an essentially unevolving, or slowly evolving, HI mass density."
+ We infer the density of gas required to reproduce the observed SFH in refdata.., We infer the density of gas required to reproduce the observed SFH in \\ref{data}.
+ In refdeltarho— we present a number of models for the replenishment of this gas. and show that a replenishment proportional to the SER density can reproduce the necessary gas mass density.," In \\ref{deltarho} we present a number of models for the replenishment of this gas, and show that a replenishment proportional to the SFR density can reproduce the necessary gas mass density."
+ A replenishment mechanism associated with galactic supershells is detailed in refdisc.. and the results are summarised in refsumm..," A replenishment mechanism associated with galactic supershells is detailed in \\ref{disc}, and the results are summarised in \\ref{summ}."
+" Throughout this analysis we adopt the cosmology with Πρ=T0kmss !MMpe |. Qa,=0.3. Oy=0.1 (e.g..Spergeletal.2003)."," Throughout this analysis we adopt the cosmology with $H_0=70\,$ $^{-1}$ $^{-1}$, $\Omega_M=0.3$, $\Omega_{\Lambda}=0.7$ \citep[e.g.,][]{Spe:03}."
+ While our motivation ts to understand the observed lack of significant evolution in the HI mass density. we approach this by considering the total mass density of gas available to form stars. which includes molecular as well as atomic σας.," While our motivation is to understand the observed lack of significant evolution in the HI mass density, we approach this by considering the total mass density of gas available to form stars, which includes molecular as well as atomic gas."
+ We neglect the intricacies in the conversion of HI to molecular gas associated with the star formation process. as this occurs on timescales very short compared to those involved in this analysis.," We neglect the intricacies in the conversion of HI to molecular gas associated with the star formation process, as this occurs on timescales very short compared to those involved in this analysis."
+ What is important is the total reservoir of gas available for star formation. “star-forming gas.” papgc;. ata given redshift. comprised of both atomic and molecular gas.," What is important is the total reservoir of gas available for star formation, “star-forming gas,"" $\rho_{\rm SFG}$, at a given redshift, comprised of both atomic and molecular gas."
+ Star formation is an inefficient process and page: will likely be somewhat less than the total of the atomic and molecular gas mass densities., Star formation is an inefficient process and $\rho_{\rm SFG}$ will likely be somewhat less than the total of the atomic and molecular gas mass densities.
+ The cosmic evolution of the HI mass density has been challenging to measure., The cosmic evolution of the HI mass density has been challenging to measure.
+ There is an implicit assumption that the damped Lya absorbers used to measure the HI mass density, There is an implicit assumption that the damped $\alpha$ absorbers used to measure the HI mass density
+measured 0; and (see ⊺≀↧↴∣↽≻↥≼↲−≻∣⋟∣⋝⋅∖∖⊽≼↲∐∐≺⇂≀↧↪∖⊽↕↖⊂↽↔↴∐∐↓≺∢≀↧↴∐⊔⋡∖⇁∐≀↧↴↕⋅↕⋅⋯∖⇁≼↲↕⋅≺∐⋟∖⊽⊔⋅↕∣↽≻⋯↕∪∐⋅⊔∣⋖⊥⇀∖∣⋟∶∩⋅≡↽⊰−≻ ∙↜↜ . ⋅⋅∙ ⋅⋅⋅ ⊾⋅⋅∣,"measured $\theta_j$ and (see Table \ref{tab:xray2}) ), we find a significantly narrower distribution, $\sigma_l(L_X)=0.32^{+0.10}_{-0.06}$."
+"∣⋡∣∣ipi The reduced. variance of Ly compared to that of Lyin requires a strong correlation between Lyix, and /, ‘such that bursts with a brighter isotropic X-ray luminosity are also more strongly collimated."," The reduced variance of $L_X$ compared to that of $L_{X,\rm iso}$ requires a strong correlation between $L_{X,{\rm iso}}$ and $f_b^{-1}$, such that bursts with a brighter isotropic X-ray luminosity are also more strongly collimated."
+ Lucleed. as can be seen from Figure 2. the data exhibit such a correlation.," Indeed, as can be seen from Figure \ref{fig:theta} the data exhibit such a correlation."
+" Ignoring the two bursts which are obvious outliers (980326 and 990705). as well as GRBs 980329 and 980519. which do not have a measured redshift. we find Lyiu,xfi."," Ignoring the two bursts which are obvious outliers (980326 and 990705), as well as GRBs 980329 and 980519, which do not have a measured redshift, we find $L_{X,{\rm iso}}\propto f_b^{0.88}$."
+" The linear correlation coefficient between. £yi4, and f, indicates a probability (hat the two cuantities are not correlated of only 4.610|."," The linear correlation coefficient between $L_{X,{\rm iso}}$ and $f_b$ indicates a probability that the two quantities are not correlated of only $4.6\times 10^{-4}$."
+" For Ey4, and. fj we lind a similar probability of 4.2x10. that the (vo quantities are not correlated."," For $E_{\gamma,{\rm iso}}$ and $f_b$ we find a similar probability of $4.2\times 10^{-4}$ that the two quantities are not correlated."
+ Thus. as with the 5-rav. emission. (he afterglow emission also exhibits strong luminosity cliversily due (ο strong variations in /;.," Thus, as with the $\gamma$ -ray emission, the afterglow emission also exhibits strong luminosity diversity due to strong variations in $f_b$."
+ Therefore. the mystery of GRBs is nolonger the enerev release but understanding what aspect of the central engine drives the wide diversity ol fy.," Therefore, the mystery of GRBs is nolonger the energy release but understanding what aspect of the central engine drives the wide diversity of $f_b$."
+" We note that there are [our possible outliers in the correlation between Lyjx, and /,L"," We note that there are four possible outliers in the correlation between $L_{X,{\rm iso}}$ and $f_b^{-1}$."
+ The afterelows of GhDs 980326 and 980519 exhibit rapid [acing etal... 2000).. which has been interpreted as (he signature of an early jet break.," The afterglows of GRBs 980326 and 980519 exhibit rapid fading \citep{ggv+98,vhc+00}, which has been interpreted as the signature of an early jet break."
+ However. il is possible that the rapid fading is instead due (o a pxr? density profile. and in fact for 9930519 such a model indicates 0;zz0.12. 3 times wider than in the constant density moclel.," However, it is possible that the rapid fading is instead due to a $\rho\propto
+r^{-2}$ density profile, and in fact for 980519 such a model indicates $\theta_j\approx 0.12$, $3$ times wider than in the constant density model."
+ This is sufficient (ο bring GRBO9OSO519 into agreement with the observed correlation., This is sufficient to bring 980519 into agreement with the observed correlation.
+ The redshift of 9980329 is not known. but with 2= il easily agrees with the correlation.," The redshift of 980329 is not known, but with $z=2$ it easily agrees with the correlation."
+ Finally. (he X-ray. [lax ancl jet opening angle for 9990705 are poorly characterized due to contamination from a nearby source (DePasqualeefaf2002) and a poor optical lightcurve (Masettefαἱ.2000).," Finally, the X-ray flux and jet opening angle for 990705 are poorly characterized due to contamination from a nearby source \citep{dpp+02}
+ and a poor optical lightcurve \citep{mpp+00}."
+ We have presented a comprehensive compilation of early X-ray observations of 41 GRBs. from which we inler Ενα. the flux in the LOkkeV band at hhr.," We have presented a comprehensive compilation of early X-ray observations of 41 GRBs, from which we infer $F_{X,10}$, the flux in the keV band at hr."
+ As first pointed by ήπια(2000) and Freedinan&Waxman (2001).. the alterglow luminosity above the cooling frequency is La;X6Lying Where Lyju is (ie isotropic-equivalent explosion kinetic energy.," As first pointed by \citet{kum00} and \citet{fw01}, , the afterglow luminosity above the cooling frequency is $L_{X,iso}\propto\epsilon_e E_{b,\rm iso}$ where $E_{b,\rm iso}$ is the isotropic-equivalent explosion kinetic energy."
+This orbit has a finite eccent‘icity ey with tle pericenter anti-aliened with the Suu. so that tle apOapse o ‘the orbit. points towards te Sun.,"This orbit has a finite eccentricity $e_f$ with the pericenter anti-aligned with the Sun, so that the apoapse of the orbit points towards the Sun."
+ This is grossv consistent. with the observed heliotropi: behavior of t1ie Chliarming Hiiglet shown in Figs., This is grossly consistent with the observed heliotropic behavior of the Charming Ringlet shown in Figs.
+ 3> and £L. , \ref{longscans} and \ref{elscan}. .
+"Furthermore. if B. is LOU-zero. hen this orbi also has a finite inclination. aud he «πόθοαπο uode is locatec +90"" from he sub-solar longitude. depecling on whether the Sun is north or south of the rineplane."," Furthermore, if $B_\Sun$ is non-zero, then this orbit also has a finite inclination, and the ascending node is located $\pm90^\circ$ from the sub-solar longitude, depending on whether the Sun is north or south of the ringplane."
+" The orbit will tlerefore be iucli1ος so that it is on tle opposite side of tte equator plane as tle Sun at longitucles near loc:"" 10011.", The orbit will therefore be inclined so that it is on the opposite side of the equator plane as the Sun at longitudes near local noon.
+ However. tliis steady-state solution is a sDEC‘ial case.," However, this steady-state solution is a special case."
+ More gejeral solutious to tl equation of motion can be most clearly described ine the variables (Horáunyi aud Burt 1991. see also Murray aud Dermott 1999. equations 7.18-7.19): Iu terms of these variables. the above equations ofmotion reduce to:," More general solutions to the equation of motion can be most clearly described using the variables (Horánnyi and Burns 1991, see also Murray and Dermott 1999, equations 7.18-7.19): In terms of these variables, the above equations ofmotion reduce to:"
+With the enormous increase in the amount of high-quality observational data of circumstellar disks in the last few years. a clear picture 1s emerging of how these objects evolve in time (222?2?)..,"With the enormous increase in the amount of high-quality observational data of circumstellar disks in the last few years, a clear picture is emerging of how these objects evolve in time \citep{jorgensen07a,jorgensen09a,looney07a,lommen08a,sicilia09a}."
+ They form during the collapse of a pre-stellar cloud core. undergo a number of accretion events (FU Orionis and EX Lupi outbursts). live for 3 to 10 Myr. and. shortly before they are destroyed. open up huge gaps visible in the dust continuum and sometimes also in gas lines (??????)..," They form during the collapse of a pre-stellar cloud core, undergo a number of accretion events (FU Orionis and EX Lupi outbursts), live for 3 to 10 Myr, and, shortly before they are destroyed, open up huge gaps visible in the dust continuum and sometimes also in gas lines \citep{dalessio05a,goto06a,brittain07a,ratzka07a,brown08a,pontoppidan08b}."
+ These physical changes are echoed in the evolution of their chemical composition and dust properties., These physical changes are echoed in the evolution of their chemical composition and dust properties.
+ Pre-stellar cores contain mostly simple hydrides. radicals and other small molecules. largely frozen out onto the cold dust grains (??)..," Pre-stellar cores contain mostly simple hydrides, radicals and other small molecules, largely frozen out onto the cold dust grains \citep{bergin97b,lee04a}."
+ A fully formed disk is predicted to contain a much richer chemical mixture with a wide variety of complex organic molecules (??).. although only simple organics have been observed so far (222)..," A fully formed disk is predicted to contain a much richer chemical mixture with a wide variety of complex organic molecules \citep{rodgers03a,aikawa08a}, although only simple organics have been observed so far \citep{lahuis06a,carr08a,salyk08a}."
+ The dust by this time has grown from less than a micron to millimetres and centimetres. and part of it has evolved from an amorphous to a erystalline structure (2?222?2??)," The dust by this time has grown from less than a micron to millimetres and centimetres, and part of it has evolved from an amorphous to a crystalline structure \citep{bouwman01a,bouwman08a,vanboekel05a,natta07a,lommen07a,lommen09a,watson09a,olofsson09a}."
+ Crystalline silicate dust is observed down to temperatures of 100 K. well below the threshold of 800 K required to convert amorphous silicates into crystalline form.," Crystalline silicate dust is observed down to temperatures of 100 K, well below the threshold of 800 K required to convert amorphous silicates into crystalline form."
+ One of the central questions of this paper is how much silicate material comes close enough to the star to be erystallised., One of the central questions of this paper is how much silicate material comes close enough to the star to be crystallised.
+ We also investigate how the erystalline silicates end up so far outside of the hot inner disk where they appear to be formed., We also investigate how the crystalline silicates end up so far outside of the hot inner disk where they appear to be formed.
+ One way to answer these questions is to construct detailed models of the evolution of circumstellar disks based on our current understanding of the physics of these objects. and then compare to the available observational data.," One way to answer these questions is to construct detailed models of the evolution of circumstellar disks based on our current understanding of the physics of these objects, and then compare to the available observational data."
+ However. it would require extraordinarily heavy computations to run a model that does justice to all physical processes known to be involved.," However, it would require extraordinarily heavy computations to run a model that does justice to all physical processes known to be involved."
+ A circumstellar disk ranges from a few stellar radii to hundreds of AU. and lasts for several million years.," A circumstellar disk ranges from a few stellar radii to hundreds of AU, and lasts for several million years."
+ A full model would therefore have to resolve hundreds of millions of inner orbits. and span some five orders of magnitude on a spatial scale.," A full model would therefore have to resolve hundreds of millions of inner orbits, and span some five orders of magnitude on a spatial scale."
+ Moreover. an accurate radiative transfer method is required to properly compute the temperatures.," Moreover, an accurate radiative transfer method is required to properly compute the temperatures."
+ All this ts clearly too demanding., All this is clearly too demanding.
+ Most multidimensional hydrodynamical simulations therefore solve sub-problems that only capture part of the disk. or only evolve over a limited time.," Most multidimensional hydrodynamical simulations therefore solve sub-problems that only capture part of the disk, or only evolve over a limited time."
+ Even these models. though. require days or weeks of CPU time for a single set of parameters.," Even these models, though, require days or weeks of CPU time for a single set of parameters."
+ An alternative approach is to parameterise most of the physics in some form. and treat the disk evolution as a simpler one-dimensional (1D) time-dependent problem.," An alternative approach is to parameterise most of the physics in some form, and treat the disk evolution as a simpler one-dimensional (1D) time-dependent problem."
+ One assumes axisymmetry and integrates the density vertically to obtain the surface density X. which is now only a function of the radial coordinate R and the time r.," One assumes axisymmetry and integrates the density vertically to obtain the surface density $\Sigma$, which is now only a function of the radial coordinate $R$ and the time $t$."
+ These kinds of models go back to the pioneering work by ? and ?.., These kinds of models go back to the pioneering work by \citet{shakura73a} and \citet{lyndenbell74a}.
+ In order to use these models throughout the disk’s lifetime. some way must be found to also include the birth phase of the disk in a reasonably realistic way.," In order to use these models throughout the disk's lifetime, some way must be found to also include the birth phase of the disk in a reasonably realistic way."
+ Two-dimensional axisymmetric hydrodynamical models of disk formation show the presence of a stand-off shock that decelerates the supersonically infalling matter as it approaches the disk from above and below (e.g..?222)..," Two-dimensional axisymmetric hydrodynamical models of disk formation show the presence of a stand-off shock that decelerates the supersonically infalling matter as it approaches the disk from above and below \citep[e.g.,][]{tscharnuter87a,yorke93a,neufeld94a}."
+ The structure of this stand-off shock is clearly multidimensional in the outer regions. but may be approximated in a simpler manner in the inner regions (2)..," The structure of this stand-off shock is clearly multidimensional in the outer regions, but may be approximated in a simpler manner in the inner regions \citep{nakamoto94a}."
+ ?. constructed a 1D disk evolution model with such an approximation and used it to analyse two T Tauri stars., \citet{hueso05a} constructed a 1D disk evolution model with such an approximation and used it to analyse two T Tauri stars.
+ This showed that simple models of disk formation and evolution can be very powerful and yield valuable insight into the evolutionary stage of young stellar objects., This showed that simple models of disk formation and evolution can be very powerful and yield valuable insight into the evolutionary stage of young stellar objects.
+" Similar models have also been used to analyse the statistics of the accretion rates measured in pre-main-sequence stars (??).,"," Similar models have also been used to analyse the statistics of the accretion rates measured in pre–main-sequence stars \citep{dullemond06c,vorobyov08a}."
+ Another problem addressed with these 1D parameterised models is the origin. evolution and transport of gas and dust in circumstellar disks.," Another problem addressed with these 1D parameterised models is the origin, evolution and transport of gas and dust in circumstellar disks."
+ For instance. ?.hereafterDAWO6 suggested that the initial outward expansion of the disk during the disk formation phase (observationally the Class 0/I phase) may be very effective in transporting thermally processed dust to the outer parts of the disk.," For instance, \citet[hereafter DAW06]{dullemond06a} suggested that the initial outward expansion of the disk during the disk formation phase (observationally the Class 0/I phase) may be very effective in transporting thermally processed dust to the outer parts of the disk."
+ Based on that work. one would expect to find a number of disks with nearly crystalline dust.," Based on that work, one would expect to find a number of disks with nearly crystalline dust."
+ However. no such extremely crystalline disks are observed (??)..," However, no such extremely crystalline disks are observed \citep{bouwman08a,watson09a}."
+ This is one of the issues addressed in this paper., This is one of the issues addressed in this paper.
+ Yet another application of parameterised disk evolution models was shown in ?.hereafterVO9.., Yet another application of parameterised disk evolution models was shown in \citet[hereafter V09]{visser09a}.
+ We followed the envelope material from thousands of AU inwards. through the accretion shock and into the disk. to analyse when ices evaporate from and recondense onto the grains.," We followed the envelope material from thousands of AU inwards, through the accretion shock and into the disk, to analyse when ices evaporate from and recondense onto the grains."
+ Since much of the interesting physics happens in the outer regions of the disk, Since much of the interesting physics happens in the outer regions of the disk
+38 percent [ον the two data sets in fie.,38 percent for the two data sets in fig.
+ 11. of being drawn from the same distribution. aud 87 percent when the data is restricted to the range C;€I.," \ref{fig11} of being drawn from the same distribution, and 87 percent when the data is restricted to the range $C_{j} \leq 1$."
+ In terms of the median values. the median value of C; for the C160 cores in simulation Bl for the epoch displayed in Fig.," In terms of the median values, the median value of $C_{j}$ for the C160 cores in simulation B1 for the epoch displayed in Fig."
+ 11 is 0.28£0.13 and the median value of the C160 cores in simulation D2 is 0.22+0.11. Whether the correction [actor C; Ivom joy to Jap is considered in ternis ofits characteristic value (~ 0.1) or in terms of ils median value (~0.25). the aim of Fig.," \ref{fig11} is $0.28 \pm 0.13$ and the median value of the C160 cores in simulation B2 is $0.22 \pm 0.11$ Whether the correction factor $C_{j}$ from $j_{2D}$ to $j_{3D}$ is considered in terms of its characteristic value $\sim 0.1$ ) or in terms of its median value $\sim 0.25$ ), the aim of Fig."
+ 11 is to show that the observed shift between the observed and munerically derived distributions of (he specific angular momentum as seen in Fig., \ref{fig11} is to show that the observed shift between the observed and numerically derived distributions of the specific angular momentum as seen in Fig.
+ 5 is most likely caused by the caleulation method of the specific angular momentum using the global gradient method under the assumption of uniform rotation of the cores., \ref{fig5} is most likely caused by the calculation method of the specific angular momentum using the global gradient method under the assumption of uniform rotation of the cores.
+ We thus conclude. based on Fig.," We thus conclude, based on Fig."
+ 5. and Fig., \ref{fig5} and Fig.
+ 11 that the observational determinations ol the specific angular momentum tend to overestimate the lane value of the specific angular momentum by a factor of at least 4—5 but most likely produces an overestimate of j by a factor of 8—10., \ref{fig11} that the observational determinations of the specific angular momentum tend to overestimate the true value of the specific angular momentum by a factor of at least $4-5$ but most likely produces an overestimate of $j$ by a factor of $8-10$.
+ The origin of the 2D-3D discrepancy stenis from the fact that the observational method is based on the global gradient method assuming uniform rotation. whereas the measurement of (he angular momentum in the intrinsic space is a summation running over all parcels of gas in the cores with their more complex dynamical behavior.," The origin of the 2D-3D discrepancy stems from the fact that the observational method is based on the global gradient method assuming uniform rotation, whereas the measurement of the angular momentum in the intrinsic space is a summation running over all parcels of gas in the cores with their more complex dynamical behavior."
+ A simplified method in theoretical works of assessing the specilic angular momentum of cores is through the use of a size-specilic angular momentum relation (japx 2)., A simplified method in theoretical works of assessing the specific angular momentum of cores is through the use of a size-specific angular momentum relation $j_{3D} \propto R_{c}^{\lambda}$ ).
+" If molions in the cores (hal are assimilated to rotational motions ave purely cue to turbulent motions following a Larson-like velocity dispersion-size relation of the [orm a,x27. then. the angular velocity O=σιHR. will be given by QxRR?! and the specific angular momentum by JapxBl. 7."," If motions in the cores that are assimilated to rotational motions are purely due to turbulent motions following a Larson-like velocity dispersion-size relation of the form $\sigma_{c} \propto R_{c}^{\beta}$, then, the angular velocity $\Omega=\sigma_{c}/R_{c}$ will be given by $\Omega \propto R_{c}^{\beta-1}$ and the specific angular momentum by $j_{3D} \propto R_{c}^{1+\beta}$ ."
+" For d=0.38 as observed initially by Larson (1981). the expected dependence of Jap is xRE""."," For $\beta =0.38$ as observed initially by Larson (1981), the expected dependence of $j_{3D}$ is $\propto R_{c}^{1.38}$."
+ On the other extreme hand. a rigid-body rotation (i.e.. O is constant) implies (hat DBDxXR2.," On the other extreme hand, a rigid-body rotation (i.e., $\Omega$ is constant) implies that $j_{3D} \propto R_{c}^{2}$."
+ such relations have been derived observationally by several groups (e.g.. Goldsmith Arquilla 1985: Goodman et al.," Such relations have been derived observationally by several groups (e.g., Goldsmith Arquilla 1985; Goodman et al."
+ 1993: Phillips 1999)., 1993; Phillips 1999).
+ Boclenheimer (1995) combined the data ol Goldsmith Arquilla (1935) and Goodman et al. (, Bodenheimer (1995) combined the data of Goldsmith Arquilla (1985) and Goodman et al. (
+1993) and found that the exponent ol the size-specilic angular momentum relation is of the order of A~ 1.6.,1993) and found that the exponent of the size-specific angular momentum relation is of the order of $\lambda \sim 1.6$ .
+ Phillips (1999) compiled a large number of published molecular cloud data ancl their substructure of clumps and cores and found A to be of the order ~1.43 ancl close to 0.96 [or flattenecl svstemis., Phillips (1999) compiled a large number of published molecular cloud data and their substructure of clumps and cores and found $\lambda$ to be of the order $\sim 1.43$ and close to $0.96$ for flattened systems.
+ Fig., Fig.
+ 12 and Fig., \ref{fig12} and Fig.
+13. display. al a few selected epochs. the intrinsic specific angular momenta dsp Ol thecores as a function oftheir characteristic size A2. lor C20 cores (top) and C160,"\ref{fig13} display, at a few selected epochs, the intrinsic specific angular momenta $j_{3D}$ of thecores as a function oftheir characteristic size $R_{c}$ for C20 cores (top) and C160"
+time to be T>>1/N. so that steady state is reached (tvpically T~104L/N).,"time to be $T\gg 1/\dot{N}$, so that steady state is reached (typically $T\sim 10^4 1/\dot{N}$ )."
+ The number of piusars generated during this lime is Nou=Z7/(1/N). with ages randomly drawn from a [Ia distribution between 0 and 2.," The number of pulsars generated during this time is $N_{\rm puls}=T/(1/\dot{N})$, with ages randomly drawn from a flat distribution between 0 and $T$ ."
+ The birth parameters 1). D are drawn from the distribution by ACC cleseribecl in 822; the periods of the pulsars are evolved. for the pulsar ages. according to Eq.(3)). and the luminosity as a function of time of each pulsar is estimated. according to Eq.(2)).," The birth parameters $P_0$, $B$ are drawn from the distribution by ACC described in 2; the periods of the pulsars are evolved, for the pulsar ages, according to \ref{eq:spin}) ), and the luminosity as a function of time of each pulsar is estimated according to \ref{eq:Lx}) )."
+ For every choice of IN. the results are the average over 2000 clilferent montecarlo realizations.," For every choice of $\dot{N}$, the results are the average over 2000 different montecarlo realizations."
+ The four curves in Figure 2 show the resulting. X-ray luminosity distribution in a galaxy with a pulsar birth rate of 1/10.1/50.1/200.1/760 !.," The four curves in Figure 2 show the resulting X-ray luminosity distribution in a galaxy with a pulsar birth rate of $1/10\,,1/50\,,1/200\,,1/760$ $^{-1}$."
+ The luminosity function is described by a roughly “universal” function. ie. a power law with index a&—0.4. whose normalization is proportional to the pulsar birth rate (or equivalentlv the SER).," The luminosity function is described by a roughly “universal” function, i.e. a power law with index $\alpha \approx -0.4$, whose normalization is proportional to the pulsar birth rate (or equivalently the SFR)."
+ An interesting comparison is (he one between the X-ray luminosity Funetion of the pulsars and that of the WAINBs., An interesting comparison is the one between the X-ray luminosity function of the pulsars and that of the HMXBs.
+ The latter. as shown bv Grimm et al. (," The latter, as shown by Grimm et al. ("
+2003). also has an almost “universal shape. which. in cumulative form. can be described by the Bunction N(2La) SERGM.vr.ILLU.—210.1],"2003), also has an almost “universal' shape, which, in cumulative form, can be described by the function $N(>L_{38})\approx 5.4$ $(M_\odot {\rm
+yr}^{-1})[L_{38}^{-0.61} -210^{-0.61}]$."
+ The normalization depends on the SFR and for the Galaxy they quote a value of ~0.2542. | as found from a combination of different SFR indicators., The normalization depends on the SFR and for the Galaxy they quote a value of $\sim 0.25 M_\odot$ $^{-1}$ as found from a combination of different SFR indicators.
+ Figure 3 shows a comparison between the integrated IININD. and pulsar counts for a ealaxv with a SFR~ LV./vr., Figure 3 shows a comparison between the integrated HMXB and pulsar counts for a galaxy with a $\sim 1 M_\odot$ /yr.
+ The relative normalization between the (wo populations is calibrated to be the same as that for the Galaxy. Le. so that a pulsar rate of 1/760 ! corresponds (to à SFR rate of 0.25 AL. /vr.," The relative normalization between the two populations is calibrated to be the same as that for the Galaxy, i.e. so that a pulsar rate of 1/760 $^{-1}$ corresponds to a SFR rate of 0.25 $M_\odot$ /yr."
+ The IIMXD population generally dominates the X- Iuminositv at sub-Ecdcdiugton huminosities: however at higher luminosities. where IAINBs drop out. the luminosity function of pulsars takes over.," The HMXB population generally dominates the X-ray luminosity at sub-Eddington luminosities; however at higher luminosities, where HMXBs drop out, the luminosity function of pulsars takes over."
+" Our results show (hat. for a pulsar birth rate tvpical of our Galaxy. e7% of galaxies are expected to have at least one source wilh huninosity Z10 erg/s. and e0.3%οί with luminosity >10710 ere/s. Starburst galaxies. wilh SFR ~10—20AL. /vr. are expected to each have at least one source with L,z10!"" erg/s. Note that our simulation for the ACC pulsar rate (about 1/4 of the value shown in Fig.3). predicts that there should be ~1 Crab-like pulsars (Ly~1075—10* erg/s)/ in our Galaxy. consistently with observations."," Our results show that, for a pulsar birth rate typical of our Galaxy, $\sim 7\%$ of galaxies are expected to have at least one source with luminosity $\ga 10^{39}$ erg/s, and $\sim 0.3\%$ with luminosity $\ga 10^{40}$ erg/s. Starburst galaxies, with SFR $\sim 10-20 M_\odot/$ yr, are expected to each have at least one source with $L_x\ga 10^{40}$ erg/s. Note that our simulation for the ACC pulsar rate (about 1/4 of the value shown in Fig.3), predicts that there should be $\sim 1$ Crab-like pulsars $L_X\sim 10^{36}-10^{37}$ erg/s) in our Galaxy, consistently with observations."
+ Another question of interest is the fraction of galaxies in which thefo/al X-ray Iuminosity is dominated by (hat of a single voung pulsar source., Another question of interest is the fraction of galaxies in which the X-ray luminosity is dominated by that of a single young pulsar source.
+ To address this issue. we ran 5000 random realizations of the steady-state pulsar population in a galaxy with a SFR similar to that of the Galaxy.," To address this issue, we ran 5000 random realizations of the steady-state pulsar population in a galaxy with a SFR similar to that of the Galaxy."
+ We kept (track of all the cases where the Iuminosity of a single source was >90% of the total X-ray luminosity of the galaxy due to all the pulsar sources together., We kept track of all the cases where the luminosity of a single source was $\ge 90\%$ of the total X-ray luminosity of the galaxy due to all the pulsar sources together.
+ The fraction of galaxies whose Iuminosity. is dominated by athat of a single source according to the criterion above is shown in Figure 4 as a function of the luminosity of the source., The fraction of galaxies whose luminosity is dominated by athat of a single source according to the criterion above is shown in Figure 4 as a function of the luminosity of the source.
+ If all, If all
+the jet is ~LOW (Ledlow&Owen1996).,"the jet is $\sim 10^{37}\,\rm W$ \citep{lo96}."
+. The plots are obtained using three differcut input powers that are below this characteristic power., The plots are obtained using three different input powers that are below this characteristic power.
+ The dots represeut the observations (cf., The dots represent the observations (cf.
+ Sec., Sec.
+ 5.2)., 5.2).
+ The plots are terminated at t=10!Myr.," The plots are terminated at $t=10^4\,\rm Myr$."
+ The lmminosities remain constant after reaching their maxima., The luminosities remain constant after reaching their maxima.
+ The buuinosities may eventually drop below detection., The luminosities may eventually drop below detection.
+ For example. oue may invoke a model in which the lobes are assumed to expand into a imuuch lower density region. which can result in a rapid decrease in the huninosity (Gopalsvishua&Wi-ita L988).," For example, one may invoke a model in which the lobes are assumed to expand into a much lower density region, which can result in a rapid decrease in the luminosity \citep{gw88}."
+. ITowever. as shown in figure L. the coustaut- model wuderpredicts the large-size sources while predicts excess number of the siiall-size sources.," However, as shown in figure \ref{fig:PD2}, the constant-pressure model underpredicts the large-size sources while predicts excess number of the small-size sources."
+" When the lobe expausion is pressure limited with 94 0. the three characteristic times cliscussed in Sec 3.2 are now eiven by where 3=3/2 aud àp=9/(39},"," When the lobe expansion is pressure limited with $\beta\neq0$ , the three characteristic times discussed in Sec 3.2 are now given by where $\beta=3/2$ and $\alpha_B=\beta/(3-\beta)$."
+ Hore the estimate for ap is obtained assuming cuerey cquipartition between the magnetic field and particles (cf., Here the estimate for $\alpha_B$ is obtained assuming energy equipartition between the magnetic field and particles (cf.
+ Table 1))., Table \ref{tab:alpha}) ).
+" Plots of (f,.f5.f.) ave shown in figure 5.."," Plots of $(t_a, t_b, t_c)$ are shown in figure \ref{fig:ct}."
+" Like the lieh-DIuuinositv sources. both f, and f,X are stronely dependent on the initial magnetic field whichBe is assumed to be the maeguetic field in the fare region."," Like the high-luminosity sources, both $t_a$ and $t_b\propto B^2_0$ are strongly dependent on the initial magnetic field which is assumed to be the magnetic field in the flare region."
+ At By> 26nT. the cnerev loss processes domunate along the evolutionary track in the following order: adiabatic. svuchrotrou. ICS: in the low field case Byx26uT. the ICS dominance occurs before the svuchrorou loss.," At $B_0>26\,\rm nT$ , the energy loss processes dominate along the evolutionary track in the following order: adiabatic, synchrotron, ICS; in the low field case $B_0\leq
+26\,\rm nT$, the ICS dominance occurs before the synchroron loss."
+ It is interesting to note that fj is very scusitive to + compared o ligh-hiuminosity sources., It is interesting to note that $t_b$ is very sensitive to $z$ compared to high-luminosity sources.
+" For local sources (2 lf, is over LOOMy."," For local sources $z\ll1$ ), $t_b$ is over $100\,\rm Myr$."
+ Thus. for local sources. the ICS losses ax a role only in the very late stage of the evolution.," Thus, for local sources, the ICS losses play a role only in the very late stage of the evolution."
+" The D, D tracks can be obtained analytically.", The $P_\nu$ $D$ tracks can be obtained analytically.
+ There are threerelevant phases: the initial rapid rise. followed * themore eradual increase m Μπορ]τν aud thendecline iu huninosity.," There are threerelevant phases: the initial rapid rise, followed by themore gradual increase in luminosity, and thendecline in luminosity."
+" Iu the gradual increasing phase. the article spectrum is jN(5.f)xtP""."," In the gradual increasing phase, the particle spectrum is $N(\gamma,t)\propto t\gamma^{-p}$."
+" The P, D track cau o approximated by a power-law. D,~D?."," The $P_\nu$ $D$ track can be approximated by a power-law, $P_\nu\sim D^{-\delta}$."
+ Frou (8)) using (1)}. one findsd=(3Αιap(l101p)/123/5 or p=2 and 3=3/2.," From \ref{eq:Pnu}) ) using \ref{eq:Dt3}) ), one finds $\delta=-(3-\beta)
+[4-\alpha_B(1+p)]/4=-3/8$ for $p=2$ and $\beta=3/2$."
+ When the selt-absorptiou effect is neelected. the corresponding radio spectruni is a—(p.1/2.," When the self-absorption effect is neglected, the corresponding radio spectrum is $\alpha=(p-1)/2$."
+" When f£.~f,. the source euters the declining phase in which the magnetic fields in the lobe ecole too low and eiven a fixed observation frequency. he Lorentz factor of the ciitting particles shifts to a uuch higher value."," When $t\sim t_a$, the source enters the declining phase in which the magnetic fields in the lobe become too low and given a fixed observation frequency, the Lorentz factor of the emitting particles shifts to a much higher value."
+" The tine £, when the track starts to Uh over is scusitive to the initial time ty and magnetic field By.", The time $t_a$ when the track starts to turn over is sensitive to the initial time $t_0$ and magnetic field $B_0$.
+ For fy=105 and By= 50uT. one estimates fa~20Ma.," For $t_0=10^4\,\rm yr$ and $B_0=50\,\rm nT$ , one estimates $t_a\approx 20\,\rm Myr$."
+" For fof.vr the svuchrotrou losses become dominant and the particle spectrum is stationary with he spectral slope steepening to p|A with A a function of 3,"," For $t>t_a$, the synchrotron losses become dominant and the particle spectrum is stationary with the spectral slope steepening to $p+\Delta$ with $\Delta$ a function of $\beta$."
+ This leads to 6=(p|A) 3/2., This leads to $\delta=(p+\Delta)\beta/2$ .
+ The radio spectimm steepens toa=(p|A1)/2., The radio spectrum steepens to $\alpha=(p+\Delta-1)/2$.
+ For ο)=3/2. oue has Awl.," For $\beta=3/2$, one has $\Delta\sim 1$."
+" Figure 6 shows the P, D tracks in the pressure-limiting case with the parameters given in Table 2..", Figure \ref{fig:PD3} shows the $P_\nu$ $D$ tracks in the pressure-limiting case with the parameters given in Table \ref{tab:parameters}.
+ Although there is a spread in 3. here we take the typical value 9=3/2.," Although there is a spread in $\beta$, here we take the typical value $\beta=3/2$."
+" The pressure at the core is assumed to be p.=3«10HPacorresponding the. density ay—21011"" aud the teiiperature Ty101 K."," The pressure at the core is assumed to be $p_c=3\times 10^{-11}\,\rm Pa$corresponding the density $n_0=2\times10^5\,{\rm m}^{-3}$ and the temperature $T_0=10^7\,\rm K$ ."
+ As iu figure L. the plots are overlaid ou the observational data of local Iuninositv sources represeuted by dots.," As in figure \ref{fig:PD2}, , the plots are overlaid on the observational data of local luminosity sources represented by dots."
+ Figure 7 shows how the turu-overdepends on the input power Qj., Figure \ref{fig:PD4} shows how the turn-overdepends on the input power $Q_j$ .
+ For low the track turus over at a uch sialler size.," For low $Q_j$ ,the track turns over at a much smaller size."
+ The evolutionQj. pace is characterized bv, The evolution pace is characterized by
+The Lyiman-a forest clouds may not be directly relaec o LLS. but we can explore t consequences of two assumption. llalrely that eq. (17)),"The $\alpha$ forest clouds may not be directly related to LLS, but we can explore the consequences of two assumption, namely that eq. \ref{gnorm}) )"
+ exteuds into the Lymau-a forest regiou with a compression [actor 5p in eq. (9 ), extends into the $\alpha$ forest region with a compression factor $\eta_0$ in eq. \ref{sigma}) )
+ that hias (hie same coIsleu value as for LLS and DLS., that has the same constant value as for LLS and DLS.
+ T filled triangles in Figure 6 are the obseved data for the l-a orest [rom and Huetal.(1995)., The filled triangles in Figure 6 are the observed data for the $\alpha$ forest from \citet{pet93} and \citet{hu95}.
+. The casled curves 5low the extra[yolations of the clistribition [unctio keeping a and yy coustant., The dashed curves show the extrapolations of the distribution functions keeping $\alpha$ and $\eta_0$ constant.
+ Note that these extrapolations. withieiw any additional parameters. give strprisinely good fits. especially tle best fit uodel eiven by eq. (15))," Note that these extrapolations, without any additional parameters, give surprisingly good fits, especially the best fit model given by eq. \ref{bestfit1}) )"
+ and tle 2g- ip model (the 25 —]ow model aud the best fit mo06¢el given by eq. (16)), and the $2\sigma$ -up model (the $2\sigma-$ low model and the best fit model given by eq. \ref{bestfit2}) )
+ lavouτα clifferent mechausin of coufinement in place for the very low columa «ensity clotds. like extenal pressure. whic1 would steepen te distribution by keeping the fractioal ionizaticix ol Η iudepeident from the cloid column density).," favour a different mechanism of confinement in place for the very low column density clouds, like external pressure, which would steepen the distribution by keeping the fractional ionization of H independent from the cloud column density)."
+ If Lyinau-a forest clouds were johysically ¢ilerent from LLS aud DLS. one might have expected a change in a or jj aud hence a uuch worse fit of the dashed curves in Figue 6.," If $\alpha$ forest clouds were physically different from LLS and DLS, one might have expected a change in $\alpha$ or $\eta_0$ and hence a much worse fit of the dashed curves in Figure 6."
+ The good fit iuakes it even more likely that a and jo are constant from LLS to DLS. whicl represents a much siualler rauge In Nyy.," The good fit makes it even more likely that $\alpha$ and $\eta_0$ are constant from LLS to DLS, which represents a much smaller range in $N_H$."
+" The results of the moclel fi to LLS aud DLS presented in this paper uuderline new aspects iu the coluii deusity distriution of nan-a absorbers: eTe excess of systeis in the daniped region. suggested by the Nyy, data. is naturally explaiued in terius ola sharp trausiion from alighly ionized to a highly neutral gas distribution and it does Dot redires any break ii the distribuion of the total gas column density."," The results of the model fit to LLS and DLS presented in this paper underline new aspects in the column density distribution of $\alpha$ absorbers: $\bullet$ The excess of systems in the damped region, suggested by the $N_{HI}$ data, is naturally explained in terms of a sharp transition from a highly ionized to a highly neutral gas distribution and it does not requires any break in the distribution of the total gas column density."
+ eThe total gas coluii deusity distributions. gVy). which best fits the data for iu re LLS aud DLS regio 1€ali ye described by a power law of index —a with 2«€McUREDEzcn ," $\bullet$ The total gas column density distributions, $g(N_{H\perp})$, which best fits the data for $1.75\le z <3.25$ in the LLS and DLS region can be described by a power law of index $-\alpha$ with $2\le \alpha \le 3.7$."
+This has the important consequence that low column density svsteius contalus more mass tla high coltuu deusity systems., This has the important consequence that low column density systems contains more mass than high column density systems.
+ e We have tested that our 'esults. which are relative to the redshift bin 1.75€2.<3.25. depeud weakly on the cata selection and on the number redshift evolutiou.," $\bullet$ We have tested that our results, which are relative to the redshift bin $1.75\le z \le 3.25$, depend weakly on the data selection and on the number redshift evolution."
+ They also do not slow a strong depeudeuce ou the assutried thickuess to diameter ratio of the slab or [roii its metallicity i Zx0.05Z.., They also do not show a strong dependence on the assumed thickness to diameter ratio of the slab or from its metallicity if $Z\le 0.05 Z_\odot$.
+ e The eas fractional ionizatiois Increase with decreasing column deusity aud data are best fitted when hydrogen fractional ionizations are of order 0.002 at τι=1 Le. X~2.8., $\bullet$ The gas fractional ionizations increase with decreasing column density and data are best fitted when hydrogen fractional ionizations are of order $\sim 0.002$ at $\tau_{LL}=1$ i.e. $X\sim 2.8$.
+ Gas [fractional ionizations for absorbers iui a backgrouud radiation field depends on the gas volume deusities aud temperature., Gas fractional ionizations for absorbers in a background radiation field depends on the gas volume densities and temperature.
+ The model presented iu detail in this paper cousiclers the gas sell gravity aud a dark matter potential in which the dark matter surface deusity inside one gas scale height is proportional, The model presented in detail in this paper considers the gas self gravity and a dark matter potential in which the dark matter surface density inside one gas scale height is proportional
+would displace the position of the break. thus mimicking a higher redshift.,"would displace the position of the break, thus mimicking a higher redshift."
+ A fourth parameter. the apparent magnitude normalization in the observed K band (at the epoch of our observations) wx. will be left as a non-interesting parameter and directly fitted to the data during the process.," A fourth parameter, the apparent magnitude normalization in the observed $K$ band (at the epoch of our observations) $m_K$, will be left as a non-interesting parameter and directly fitted to the data during the process."
+ The effect of the Intergalactic Medium (IGM) at the redshifts of interest (5> 6) Is very simple to include., The effect of the Intergalactic Medium (IGM) at the redshifts of interest $z \gtrsim 6$ ) is very simple to include.
+ At such a high redshift the HI absorption is complete—within our observational capabilities—below the Lyman-a line. and as such we include it in the models (Yoshii Peterson 1994).," At such a high redshift the HI absorption is complete—within our observational capabilities—below the $\alpha$ line, and as such we include it in the models (Yoshii Peterson 1994)."
+ The putative effects of a significatively different neutral fraction in the IGM were deliberately neglected for two reasons: on one side. the literature on GRBO90423 points to a normal environment (1.e. neutral. see Tanvir et al.," The putative effects of a significatively different neutral fraction in the IGM were deliberately neglected for two reasons: on one side, the literature on GRB090423 points to a normal environment (i.e. neutral, see Tanvir et al."
+ 20096); on the other side some authors have shown that those effects are difficult to model and challenging to observe even with better quality data (e.g. Patel et al., 2009c); on the other side some authors have shown that those effects are difficult to model and challenging to observe even with better quality data (e.g. Patel et al.
+ 2010)., 2010).
+ In. other cases one would of course need different parameters., In other cases one would of course need different parameters.
+ It could be necessary to add dust extinction either at the host or by the Milky Way (or both). with the amount of extinction and even its grain type left as free parameters.," It could be necessary to add dust extinction either at the host or by the Milky Way (or both), with the amount of extinction and even its grain type left as free parameters."
+ We do not consider it here. because the available afterglow photometry indicates a blue object. with an almost complete lack of intrinsic extinction. (Fernandez-Soto et al 2009 and Tanvir et al 2009c. in particular their Figure 2 where it is shown how the spectral slope is well represented by a pure power-law).," We do not consider it here, because the available afterglow photometry indicates a blue object, with an almost complete lack of intrinsic extinction (Fernandez-Soto et al 2009 and Tanvir et al 2009c, in particular their Figure 2 where it is shown how the spectral slope is well represented by a pure power-law)."
+ Moreover. given the narrow rest-frame wavelength range that we are observing Cl=1200—2200A). the resolution and signal-to-noise ratio of our data. there is an almost perfect degeneracy between the amount of dust extinction and a change in spectral Figure 2 shows a selectior of spectral templates. sampling part of the parameter space.," Moreover, given the narrow rest-frame wavelength range that we are observing $\lambda \approx 1200-2200 \AA$ ), the resolution and signal-to-noise ratio of our data, there is an almost perfect degeneracy between the amount of dust extinction and a change in spectral Figure 2 shows a selection of spectral templates, sampling part of the parameter space."
+ The full range covered by our templates is a€[-1.3]. z€[5.10]. and N(HD€[1077.107 Jem.," The full range covered by our templates is $\alpha
+\in [-1,3]$, $z \in [5,10]$, and $\in
+[10^{20},10^{24}]\rm{cm}^{-2}$ ."
+ All three ranges safely include the expected values of each variable., All three ranges safely include the expected values of each variable.
+ All models are normalised to have ABy=21.3. a value measured by GROND (Tanvir et al 2009c) at almost exactly the same time our observations were performed.," All models are normalised to have $AB_K=21.3$, a value measured by GROND (Tanvir et al 2009c) at almost exactly the same time our observations were performed."
+ It must be remarked. however. that because of the possibility of slit losses affecting the detected flux. we leave the normalisation factor for the flux as a free parameter. as explained in the next subsection.," It must be remarked, however, that because of the possibility of slit losses affecting the detected flux, we leave the normalisation factor for the flux as a free parameter, as explained in the next subsection."
+ Once satisfied with the set of spectral templates. we need to characterise the observations in terms of spectral resolution. efficiency of the instrument at different wavelengths. noise characterics of the detector. and position of the spectrum along both the spectral and spatial directions.," Once satisfied with the set of spectral templates, we need to characterise the observations in terms of spectral resolution, efficiency of the instrument at different wavelengths, noise characterics of the detector, and position of the spectrum along both the spectral and spatial directions."
+ We have used an archival solution to calibrate the Amici spectrum in wavelength., We have used an archival solution to calibrate the Amici spectrum in wavelength.
+ As was described in Fernandez-Soto et al (2009) we needed to add an offset of 5 pixels. determined via comparison with the observed sky absorption features.," As was described in Fernandez-Soto et al (2009) we needed to add an offset of 5 pixels, determined via comparison with the observed sky absorption features."
+To investigate RM in the LSS of the universe. we used structure formation simulations for a concordance AC DM universe with the following values of cosmological parameters: Op= 0.043. Op= 0.227. O4=0.73. h=Ly/(100kins|Mpe4)0.7. 0=1. and ay=0.8 (sameasinRyuetal.2008).,"To investigate RM in the LSS of the universe, we used structure formation simulations for a concordance $\Lambda$ CDM universe with the following values of cosmological parameters: $\Omega_{\rm BM}=0.043$ , $\Omega_{\rm DM}=0.227$ , $\Omega_{\rm \Lambda}=0.73$ , $h\equiv H_0/(100\ {\rm km\ s^{-1}\ Mpc^{-1}})=0.7$, $n=1$, and $\sigma_8=0.8$ \cite[same as in][]{rkcd08}."
+. They. were performed using a parlicle-mesh/Eulerian. cosmological hydrodynamic eode (Ryuetal.1993).," They were performed using a particle-mesh/Eulerian, cosmological hydrodynamic code \citep{rokc93}."
+. A cubic region of comoving volume (1005.tMpe)? was reproduced with 512° uniform grid zones for gas and gravity ancl 256° particles [or dark matter. so the spatial resolution is 195/.! kpc.," A cubic region of comoving volume $(100\ h^{-1}{\rm Mpc})^3$ was reproduced with $512^3$ uniform grid zones for gas and gravity and $256^3$ particles for dark matter, so the spatial resolution is $195\ h^{-1}$ kpc."
+ Sixteen simulations with different realizations of initial condition wereused to compensate cosmic variance., Sixteen simulations with different realizations of initial condition wereused to compensate cosmic variance.
+ For the IGME. we emploved the model of Ryuetal.(2003): il proposes that motions are induced. via the cascade of the vorticity generated at cosmological shocks during the formation of the LSS of the universe. and the IGME is produced as a consequence of the amplification of weak seed fields of anv origin bv (the turbulence.," For the IGMF, we employed the model of \citet{rkcd08}; it proposes that turbulent-flow motions are induced via the cascade of the vorticity generated at cosmological shocks during the formation of the LSS of the universe, and the IGMF is produced as a consequence of the amplification of weak seed fields of any origin by the turbulence."
+" Then. the energy density (or the strength) of the IGME ean be estimated with the eddy turnover number and the turbulent energv density as follow: Tere. the eddy turnover (me is defined as (he reciprocal of the vorticity at driving scales. leddy=Lfeuriving (=Vvx D). and © is the conversion [actor from turbulent to magnetic energv (hat depends on the eddy turnover number ///44,."," Then, the energy density (or the strength) of the IGMF can be estimated with the eddy turnover number and the turbulent energy density as follow: Here, the eddy turnover time is defined as the reciprocal of the vorticity at driving scales, $t_{\rm eddy} \equiv 1/\omega_{\rm driving}$ ${\vec \omega} \equiv {\vec \nabla}\times{\vec v}$ ), and $\phi$ is the conversion factor from turbulent to magnetic energy that depends on the eddy turnover number $t/t_{\rm eddy}$."
+ The eddy turnover number was estimated as the age of universe times the magnitude of the local vorticity. that is. μωρο«c.," The eddy turnover number was estimated as the age of universe times the magnitude of the local vorticity, that is, $t_{\rm age}\ \omega$."
+ The local vorticity and turbulent energy density were calculated from simulations for cosmological structure formation described above., The local vorticity and turbulent energy density were calculated from simulations for cosmological structure formation described above.
+ A functional form for the conversion factor was derived from a separate. incompressible. magnetohvdrodvnamie (MIID) simulation of turbulence denamo.," A functional form for the conversion factor was derived from a separate, incompressible, magnetohydrodynamic (MHD) simulation of turbulence dynamo."
+ For the direction of (he IGAIF. we used (hat of the passive fields from simulations for cosmological structure formation. in which weak seed fields were evolved passively. ignoring the back-reaction. along with flow motions (Ixulsrudetal.1997:Rawοἱ1993).," For the direction of the IGMF, we used that of the passive fields from simulations for cosmological structure formation, in which weak seed fields were evolved passively, ignoring the back-reaction, along with flow motions \citep{kcor97,rkb98}."
+. 1n our model. as seed magnetic fields. we took the ones generated through the Biermann battery mechanism (Biermann1950). at cosmological shocks.," In our model, as seed magnetic fields, we took the ones generated through the Biermann battery mechanism \citep{biermann50} at cosmological shocks."
+ There are. on the other haud. a number of mechanisms that have been suggested to create seed fields in the early universe.," There are, on the other hand, a number of mechanisms that have been suggested to create seed fields in the early universe."
+ Besicles various inflationary and string theory mechanisms. (the followings include a partial list of astrophysical mechanisms.," Besides various inflationary and string theory mechanisms, the followings include a partial list of astrophysical mechanisms."
+ At cosmological shocks. in addition. Weibel instability can operate and produce magnetic fields (Aledveclevοἱal.2006:Schlickeiser&Shukla2003).. and sireauuning cosmic ravs acceleratedby theshocks can amplilv weak upstream magnetic fields via non-resonant growing mode(Bell 2004)..," At cosmological shocks, in addition, Weibel instability can operate and produce magnetic fields \citep{msk06, ss03}, and streaming cosmic rays acceleratedby theshocks can amplify weak upstream magnetic fields via non-resonant growing mode\citep{bell04}. ."
+ In addition. for instance. galactic outflows," In addition, for instance, galactic outflows"
+All of the images in the NICMOS UDF observations were taken in this mode.,All of the images in the NICMOS UDF observations were taken in this mode.
+ The steps described in this section are done automatically in batch processing with no interaction., The steps described in this section are done automatically in batch processing with no interaction.
+ This is roughly equivalent to the STScl pipeline processing., This is roughly equivalent to the STScI pipeline processing.
+ The first step in the data reduction is the subtraction of the image obtained in the first read from all subsequent reads., The first step in the data reduction is the subtraction of the image obtained in the first read from all subsequent reads.
+ This step eliminates the NTC noise that is present in each of (he individual photodiodes at the beginning of an integration., This step eliminates the KTC noise that is present in each of the individual photodiodes at the beginning of an integration.
+ The number of reads carried (hroueh in the final processing is (hen 23 reads rather (han 24 alter (his step., The number of reads carried through in the final processing is then 23 reads rather than 24 after this step.
+ Alter the first τους subtraction the dark eurrent image is subtracted from each of the reads., After the first read subtraction the dark current image is subtracted from each of the reads.
+ This is a verv important step as the NICMOS detectors have dark current images wilh very significant structure., This is a very important step as the NICMOS detectors have dark current images with very significant structure.
+ This structure is larger in magnitude than the signal [rom most ol the galaxies in the image., This structure is larger in magnitude than the signal from most of the galaxies in the image.
+ The dark images are constructed [rom integrations in exactly (he same mode as the observations but with the cold blank filter in place., The dark images are constructed from integrations in exactly the same mode as the observations but with the cold blank filter in place.
+" This step cillers from the STscl pipeline that uses ""svnthetüe darks” caleulated [rom parameters developed during the operation of NICMOS (Mobasheretal.2004a).", This step differs from the STScI pipeline that uses “synthetic darks” calculated from parameters developed during the operation of NICMOS \citep{mob04a}.
+. The NICMOS UDF dark is a median dark image obtained [rom dark integrations taken during (he earth occultation period in each of the orbits assigned to the NICMOS UDF program., The NICMOS UDF dark is a median dark image obtained from dark integrations taken during the earth occultation period in each of the orbits assigned to the NICMOS UDF program.
+ Operational constraints prevented dark integrations on 2 orbits but the remaining 142 dark integrations were used to construct the median images., Operational constraints prevented dark integrations on 2 orbits but the remaining 142 dark integrations were used to construct the median images.
+ There is à median dark image lor each read constructed from (he medians of all of the dark images for that particular read., There is a median dark image for each read constructed from the medians of all of the dark images for that particular read.
+ Belween visit 24 ancl visit 35 of the 48 visits in the NICMOS UDF program. the temperature sel point on the NCS was reduced bv 0.1 Ix to compensate for the warmer conditions encountered during the period when the earth's orbit is closest to the sun.," Between visit 34 and visit 35 of the 48 visits in the NICMOS UDF program, the temperature set point on the NCS was reduced by 0.1 K to compensate for the warmer conditions encountered during the period when the earth's orbit is closest to the sun."
+ There was concern (hat this set point change would alter the nature of the NICMOS cdarks since ibis known that the darks are temperature sensitive., There was concern that this set point change would alter the nature of the NICMOS darks since it is known that the darks are temperature sensitive.
+ Comparison of a median of the darks taken before the set point change with the median clarks (taken alter (he set. point. change, Comparison of a median of the darks taken before the set point change with the median darks taken after the set point change
+lighteurve.,lightcurve.
+" Phe datapoints for nights 3-8 agree. well with a linear fit with AyjcfA,=O41+0.02.", The datapoints for nights 3-8 agree well with a linear fit with $\Delta_{J-K} / \Delta_J = 0.41 \pm 0.02$.
+ A similar slope is obtained by fitting the averages., A similar slope is obtained by fitting the averages.
+ This value. is. clearly inconsistent with variable extinction. but can roughly be reproduced by hot spots. which are likely the dominant source of variability for this object.," This value is clearly inconsistent with variable extinction, but can roughly be reproduced by hot spots, which are likely the dominant source of variability for this object."
+ In Fig., In Fig.
+ G6 we show the slopes for spot temperatures of WK (dashed) and WL (ash-dotted line). for comparison.," \ref{f4} we show the slopes for spot temperatures of K (dashed) and K (dash-dotted line), for comparison."
+ In the first two nights. however. the object is too faint and blue for the hot spot model.," In the first two nights, however, the object is too faint and blue for the hot spot model."
+ As can be seen in Fig. 2..," As can be seen in Fig. \ref{f2},"
+ the source becomes σαςπαν brighter and redder over the first three nights. a tvpical sign for variable clisk emission.," the source becomes gradually brighter and redder over the first three nights, a typical sign for variable disk emission."
+ In our lightceurves. we might see the effects. of an increase in the accretion rate. leacling a) to more heating in the inner disk and thus enhanced disk emission (nights 1-3) and b) to the formation of a hot spot close to the surface of the star. co-rotating with the object and thus modulating the [ux (nights 3-N).," In our lightcurves, we might see the effects of an increase in the accretion rate, leading a) to more heating in the inner disk and thus enhanced disk emission (nights 1-3) and b) to the formation of a hot spot close to the surface of the star, co-rotating with the object and thus modulating the flux (nights 3-8)."
+ The J vs. JAN data are well-approximat by a linear fit with a slope of AyjfAy=0.36+0.02., The J vs. $J-K$ data are well-approximated by a linear fit with a slope of $\Delta_{J-K} / \Delta_J = 0.36 \pm 0.02$.
+ ed.The scatter seen around this fit can be fully explained by a combination of photometric errors and the epoch dillerence oetween J- and WK-bancl data., The scatter seen around this fit can be fully explained by a combination of photometric errors and the epoch difference between J- and K-band data.
+ Fitting the nightly averages vields a very. similar. value., Fitting the nightly averages yields a very similar value.
+ The slope is clearly too small o be consistent with variable extinction. as seen in Lig. 6..," The slope is clearly too small to be consistent with variable extinction, as seen in Fig. \ref{f4}."
+ Llot spots provide the most. plausible explanation for he variability seen for this object., Hot spots provide the most plausible explanation for the variability seen for this object.
+ The measured. value or Ayκεδ ds best reproduced by a spot temperature of IxIx. Our J-band amplitude then constrains the filling actor to Z204., The measured value for $\Delta_{J-K} / \Delta_J$ is best reproduced by a spot temperature of K. Our J-band amplitude then constrains the filling factor to $\ga 20$.
+. This should be treated as a lower limit. rccause we cannot be certain that our observing window covers the total variability amplitude.," This should be treated as a lower limit, because we cannot be certain that our observing window covers the total variability amplitude."
+ The datapoints from wo nights (nights 2 and 5) seem to be separated. from all others. clustered around J=0.1 and JA—0.15.," The datapoints from two nights (nights 2 and 5) seem to be separated from all others, clustered around $J=0.1$ and $J-K=-0.15$."
+ In hese nights. the object reaches its maximum in brightness and the bluest. colour. indicating that we may be seeing a 10t region projected against the cool surface of the star.," In these nights, the object reaches its maximum in brightness and the bluest colour, indicating that we may be seeing a hot region projected against the cool surface of the star."
+ Finally. we note that the J vs. Jdy datapoints for object #2117. found to have a period of hh in the J-band data. mostly scatter within £0.05 mmae of the mean.," Finally, we note that the J vs. $J-K$ datapoints for object 17, found to have a period of h in the J-band data, mostly scatter within $\pm 0.05$ mag of the mean."
+ The colours tend to become redder as the object becomes fainter. i.c. Cool spots are the most likely agent of the variability.," The colours tend to become redder as the object becomes fainter, i.e. cool spots are the most likely agent of the variability."
+ As the origin of the high-level variability is assumed to be either hot spots or clumpy circumstellar material. and thus associated with the accretion disks. we aim to improve the variability analysis by investigating the near/mid-infrared spectral energy. distributions (SEED) for the highly. variable sources in the e OOri cluster.," As the origin of the high-level variability is assumed to be either hot spots or clumpy circumstellar material, and thus associated with the accretion disks, we aim to improve the variability analysis by investigating the near/mid-infrared spectral energy distributions (SED) for the highly variable sources in the $\sigma$ Ori cluster."
+ Spitzer URAC and ALPS photometry was carried out for the objects #22. lo. )33. 3é443 discussed here ancl in SEOL sce Appendix A for information on the photometry.," Spitzer IRAC and MIPS photometry was carried out for the objects 2, 19, 33, 43 discussed here and in SE04, see Appendix \ref{spitzerall} for information on the photometry."
+ For the variable source SOrLiJO53825.4-024241 identified by ὃν we obtained the Spitzer data from the survey by 2.. which classifies the source as Class LL object.," For the variable source SOriJ053825.4-024241 identified by \citet{2006A&A...445..143C}, we obtained the Spitzer data from the survey by \citet{2007ApJ...662.1067H}, which classifies the source as Class II object."
+The SEDs are complemented by near-infrared data from. PALASS and I-band data from either SEO4 or ?..,The SEDs are complemented by near-infrared data from 2MASS and I-band data from either SE04 or \citet{2006A&A...445..143C}.
+ Ht should be noted that the optical. near-infrared. and mid-infrared data are taken at dilferent epochs.," It should be noted that the optical, near-infrared, and mid-infrared data are taken at different epochs."
+ Phe SEDs are thus expected to be alfected. by. variability., The SEDs are thus expected to be affected by variability.
+ This particularly applies to the optical ancl near-infrared bands where the variations are strongest (at least [or 333. and 024241: not necessarilv for #443).," This particularly applies to the optical and near-infrared bands where the variations are strongest (at least for 2, 19, 33, and SOriJ053825.4-024241; not necessarily for 43)."
+ The Ηχος for the five highly variable objects are given in Table 2.., The fluxes for the five highly variable objects are given in Table \ref{sedfluxes}.
+ We show their SEDs. scaled to the J-band Dux. in Fig. 7..," We show their SEDs, scaled to the J-band flux, in Fig. \ref{f12}."
+ For comparison. we overplot the SEDs of the total disk sample in SOL (see Appencix A)).," For comparison, we overplot the SEDs of the total disk sample in SE04 (see Appendix \ref{spitzerall}) )."
+ AIL five highly variable objects have SEDs typical for. classical T Tauri stars., All five highly variable objects have SEDs typical for classical T Tauri stars.
+ None of them shows an extreme or highly unusual SED in comparison with the total disk sample. C, None of them shows an extreme or highly unusual SED in comparison with the total disk sample. (
+Ehis is also apparent from the colour plots given in Appendix A..),This is also apparent from the colour plots given in Appendix \ref{spitzerall}. .)
+ Thus. the presence of variability is not necessarily correlated. with unusual features in the SED.," Thus, the presence of variability is not necessarily correlated with unusual features in the SED."
+ The four objects from SIZ04 are relatively similar in the IRAC wavelength regime prm).," The four objects from SE04 are relatively similar in the IRAC wavelength regime $\,\mu m$ )."
+ At 0n. however. two of them. 2 and #448. have datapoints arouncl -1.0. while the other two are about 0.6 dex below that.," At $\,\mu m$, however, two of them, 2 and 43, have datapoints around -1.0, while the other two are about 0.6 dex below that."
+ To further explore the data. we use model SEDs generated. from a Monte Carlo radiation transfer code. the same set of models as applied in ?..," To further explore the data, we use model SEDs generated from a Monte Carlo radiation transfer code, the same set of models as applied in \citet{2006ApJ...645.1498S}."
+ In the following. we give a briefdescription of the main features of the code. for further information see the aforementioned. paper.," In the following, we give a briefdescription of the main features of the code, for further information see the aforementioned paper."
+ The models use NextGen model atmospheres (e.g.7) for the photospheric spectra. with logg=4.0.," The models use NextGen model atmospheres \citep[e.g.][]{1999ApJ...512..377H} for the photospheric spectra, with $\log g = 4.0$."
+ We apply a distribution of grain sizes following a power law with an exponential decay. for particles with sizes above 505 and a formal maximum grain size of mmm. see ?. for à more detailed. cliscussion of the dust. erain model.," We apply a distribution of grain sizes following a power law with an exponential decay for particles with sizes above $50\mu$ m and a formal maximum grain size of mm, see \citet{2002ApJ...564..887W} for a more detailed discussion of the dust grain model."
+ For all models we assume that dust in regions close to the star is destroved if temperatures rise above the value for dust. sublimation. which sets à minimum inner dust radius of 72..," For all models we assume that dust in regions close to the star is destroyed if temperatures rise above the value for dust sublimation, which sets a minimum inner dust radius of $\sim 7\,R_\star$."
+ Within that racius. the disks are assumed to be optically thin.," Within that radius, the disks are assumed to be optically thin."
+ In the models. the scaleheight of the disk increases with radius. h(r)2ho(rfB.) .sothat the degree of Haring can be varied by adjusting 23 and fro.," In the models, the scaleheight of the disk increases with radius, $h(r)=h_0\left ( {r /{R_\star}} \right )^\beta$, so that the degree of flaring can be varied by adjusting $\beta$ and $h_0$ ."
+ Fitting SED cata is subject to a number of degeneracies. see the discussion in 2..," Fitting SED data is subject to a number of degeneracies, see the discussion in \citet{2001ApJ...547.1077C}."
+ Evpicallv. à range of models is able," Typically, a range of models is able"
+Nevertheless.Neverthel the(he propagation of the emitted photons in eurvedcurvedspacetir spacetime cann alsoal produce some intrinsic peaks in the Fourier spectrum of the light curves (Schnitiiman&2004).,"Nevertheless, the propagation of the emitted photons in curved spacetime can also produce some intrinsic peaks in the Fourier spectrum of the light curves \citep{Schnittman2004}."
+. In combination with a vertically oscillating torus. the gravitational lensing effect can also reproduce the 3:2 ratio (Bursaetal... 2005).," In combination with a vertically oscillating torus, the gravitational lensing effect can also reproduce the 3:2 ratio \citep{Bursa2004,Schnittman2005}."
+. Resonances in the geodesic motion of a single particle have been investigated by Abramowiezοἱal.|(2003)., Resonances in the geodesic motion of a single particle have been investigated by \cite{Abramowicz2003}.
+. The specilie coupling force between radial and vertical oscillation was left unspecified., The specific coupling force between radial and vertical oscillation was left unspecified.
+ Their results for non-linear resonance were applied to accreting neutron stars., Their results for non-linear resonance were applied to accreting neutron stars.
+ In this paper. we describe a coupling between spiral density waves in (he accretion disk aud epievelic motions of test particles.," In this paper, we describe a coupling between spiral density waves in the accretion disk and epicyclic motions of test particles."
+ It is divided in (wo parts., It is divided in two parts.
+ li Sec., In Sec.
+ 2 we specily the perturbation pattern used in our model., \ref{sec:Model} we specify the perturbation pattern used in our model.
+ Then the equation of motions due to the perturbation are derived leading to some resonance conditions., Then the equation of motions due to the perturbation are derived leading to some resonance conditions.
+ In Sec. 3..," In Sec. \ref{sec:Discussion},"
+ the results are applied to GRS 19154-105 for which several components in the Fourier (ime analvsis are predicted in agreement with the IF-QPOs detected for this object., the results are applied to GRS 1915+105 for which several components in the Fourier time analysis are predicted in agreement with the HF-QPOs detected for this object.
+ We also put some constrain on the mass-spin relation for several DIICs., We also put some constrain on the mass-spin relation for several BHCs.
+ In this section. we describe (he main features of the model. starting with a simple treatment of the accretion disk. assumed {ο be made of non interacting single particles orbiüng in the equatorial plane of the black hole as was already done in (the previous studies (see paper I and 11).," In this section, we describe the main features of the model, starting with a simple treatment of the accretion disk, assumed to be made of non interacting single particles orbiting in the equatorial plane of the black hole as was already done in the previous studies (see paper I and II)."
+ We again neglect the hydrodyvnamical aspects of the disk such as pressure., We again neglect the hydrodynamical aspects of the disk such as pressure.
+ However. a detailed (magneto-)hvdrodsnoamical treatment of the response of the disk to gravitational or magnetic perturbations has been given in," However, a detailed (magneto-)hydrodynamical treatment of the response of the disk to gravitational or magnetic perturbations has been given in"
+et al.,et al.
+ 1997 lor example)., 1997 for example).
+ In the model two dillerent. shells ive cilferent Lorentz factors., In the model two different shells have different Lorentz factors.
+ The inner shell overtakes a gaower outer shell and form a shock., The inner shell overtakes a slower outer shell and form a shock.
+ The Lorentz factor of 10 shock as measured in the frame at rest with respect to re outer shell is assumed to be ~2., The Lorentz factor of the shock as measured in the frame at rest with respect to the outer shell is assumed to be $\sim 2$.
+ With only a part of kinetic energy converted into the internal energy the particle enerey distribution downstream of the shock will be non-rermal with. possibly. a substantial fraction of relativistic xurticles.," With only a part of kinetic energy converted into the internal energy the particle energy distribution downstream of the shock will be non-thermal with, possibly, a substantial fraction of relativistic particles."
+ As à result an amount of relativistic particles will » present in the shock., As a result an amount of relativistic particles will be present in the shock.
+ The particles can be accelerated across the mechanism presented in the paper and could be observed in the afterglow (cl, The particles can be accelerated across the mechanism presented in the paper and could be observed in the afterglow (cf.
+ Waxman 1997. Galama οἱ al.," Waxman 1997, Galama et al."
+ 1998)., 1998).
+ We derived some parameters of the process that could be used in GRBs models., We derived some parameters of the process that could be used in GRBs models.
+" The acceleration. time fou=1.0r, fe. measured in the downstream plasma rest frame in the unit of particle evroracdius in the homogeneous magnetic 101 component divided by the speed of light is the seconc important parameter besides the spectral index a= "," The acceleration time $t_{acc} = 1.0\, r_{g}/c$ , measured in the downstream plasma rest frame in the unit of particle gyroradius in the homogeneous magnetic field component divided by the speed of light is the second important parameter besides the spectral index $\sigma = 2.2$."
+The values of d? and 15 celine the dimensions of the shock wt allow the process to be effective. and the values of sin?8) shows how the svnchrotron radiation can influence 16 PLOocess.," The values of $d^{M}_{D}$ and $t^{D}_{D}$ define the dimensions of the shock that allow the process to be effective, and the values of $\langle\sin^{2}\theta \rangle$ shows how the synchrotron radiation can influence the process."
+ In the ejecta of the relativistic matter in the CRB moce 10 outer shells can be faster than the following ones., In the ejecta of the relativistic matter in the GRB model the outer shells can be faster than the following ones.
+In us case separated shocks with Lorentz factors reaching ~~10? will be generated.,In this case separated shocks with Lorentz factors reaching $\gamma \sim10^{3}$ will be generated.
+" The leading shock could produce seed. protons with: energies' ofzou 10107 eV. ""Phese protons ownstream of the first shock can interact with the following one to be rellected with energy. gains ~57 (ef.", The leading shock could produce seed protons with energies of $10^{14}-10^{16}$ eV. These protons downstream of the first shock can interact with the following one to be reflected with energy gains $\sim \gamma^{2}$ (cf.
+ Gallant Achterbere 1999. Beclnarz Ostrowski 1999).," Gallant Achterberg 1999, Bednarz Ostrowski 1999)."
+ For a constant rclleetion probability. the spectrum of these relleeted highest energv. particles. above 1072 eV. will be only the shifted. in energy. spectrum: of seed. particles with the universal spectral index 2.2.," For a constant reflection probability the spectrum of these reflected highest energy particles, above $10^{20}$ eV, will be only the shifted in energy spectrum of seed particles with the universal spectral index $\sim2.2$."
+ The author is grateful to Ostrowski for valuable discussions and the referee for comments that was helpful in clarifving the contents of this paper., The author is grateful to Ostrowski for valuable discussions and the referee for comments that was helpful in clarifying the contents of this paper.
+" The presented computations were partly cone on the HIP Exemplar 52000 in ACK ""CYERONIZE"" in Ixrakówsw.", The presented computations were partly done on the HP Exemplar S2000 in ACK `CYFRONET' in Krakóww.
+ The present work was supported by through the erant PD 179/DP03/96/11 and PB 258/P03/99/17., The present work was supported by through the grant PB 179/P03/96/11 and PB 258/P03/99/17.
+sampling implies a minimum event time-scale that can be detected.,sampling implies a minimum event time-scale that can be detected.
+ Lower mass lenses of course produce shorter events. thus more of the low-mass events are missed.," Lower mass lenses of course produce shorter events, thus more of the low-mass events are missed."
+ The finite total observing time would also subtract very. long events. but for our purposes. this is not a concern. as we are interested in the short events clue to O.O1-Q.1 AZ. stars.," The finite total observing time would also subtract very long events, but for our purposes, this is not a concern, as we are interested in the short events due to 0.01-0.1 $M_\odot$ stars."
+ We now illustrate the full Ny clistribution. integrated. over he simple mass function cliscussecl in Sec.," We now illustrate the full $N_F$ distribution, integrated over the simple mass function discussed in Sec."
+ 2., 2.
+ As discussed oeviouslv. Ny for a single mass acts as à smoothing filter or the mass function.," As discussed previously, $N_F$ for a single mass acts as a smoothing filter for the mass function."
+ We show the results for the HIST ACS in Fig., We show the results for the HST ACS in Fig.
+" 6 and the NGST in Fig. τι,", \ref{acsmf} and the NGST in Fig. \ref{ngstmf}.
+ The pure Salpeter mass function has a peak at the shortest. time-scale. the lattened mocels (Miller-Scalo and Salpeter with cutoff) has a longer peak. and the GDBE-tvpe model has the longest »ealkk time-scale.," The pure Salpeter mass function has a peak at the shortest time-scale, the flattened models (Miller-Scalo and Salpeter with cutoff) has a longer peak, and the GBF-type model has the longest peak time-scale."
+ With these surveys. the statisties should x: sullicient. to distinguish these models.," With these surveys, the statistics should be sufficient to distinguish these models."
+ We should. state hat the normalisation. alone is probably insullicient to distinguish models. but the position in time-scale of the peas of the rate distribution is quite robust.," We should state that the normalisation alone is probably insufficient to distinguish models, but the position in time-scale of the peak of the rate distribution is quite robust."
+ In fact. we have adjusted the normalisation of the D=0.3 and B=0.75 models so that the peak rates agree. in order to compare the time-scales.," In fact, we have adjusted the normalisation of the $B=0.3$ and $B=0.75$ models so that the peak rates agree, in order to compare the time-scales."
+ For the surveys we consider. the peak time-scale cillers by a factor of 2-3 between a mass function that is Hat for substellar masses (Miller-Scealo). and one that that is sharply declining at those masses (GB).," For the surveys we consider, the peak time-scale differs by a factor of 2-3 between a mass function that is flat for substellar masses (Miller-Scalo), and one that that is sharply declining at those masses (GBF)."
+ We note that mass functions that cüller only below 0.1 AZ. will be quite difficult to distinguish. but for mass functions which begin o differ at around a solar mass. the microlensing technique is quite powerful.," We note that mass functions that differ only below 0.1 $M_\odot$ will be quite difficult to distinguish, but for mass functions which begin to differ at around a solar mass, the microlensing technique is quite powerful."
+ We have shown that pixel microlensing can be a xowerful tool for measuring the mass function of low mass ancl brown dwarf stars. less massive than the sun.," We have shown that pixel microlensing can be a powerful tool for measuring the mass function of low mass and brown dwarf stars, less massive than the sun."
+ Since his technique is effective to very large distances. we have a chance to learn something about the universal properties of xown dwarf mass functions.," Since this technique is effective to very large distances, we have a chance to learn something about the universal properties of brown dwarf mass functions."
+clark lenses ancl virialized lenses are equally allectecd by noise.,dark lenses and virialized lenses are equally affected by noise.
+ Similarly. the ratio does not vary. significantly. over a wicle range in cosmological parameters so that uncertainties due o the Oyw degeneracy are minimized.," Similarly, the ratio does not vary significantly over a wide range in cosmological parameters so that uncertainties due to the $\Omega_0-w$ degeneracy are minimized."
+ We found tha or aperture sizes of ~15! the ratio varies by about2054. dropping from 0.5 to OA. between the ACDAL model anc w=0.6.," We found that for aperture sizes of $\sim 15'$ the ratio varies by about, dropping from $0.5$ to $0.4$, between the $\Lambda$ CDM model and $w = -0.6$."
+ We also showed that the ratio of dark to virialize enses increases with aperture size. in effect. because larger apertures enable the detection of the more extended radii of he non-virialized lenses.," We also showed that the ratio of dark to virialized lenses increases with aperture size, in effect because larger apertures enable the detection of the more extended radii of the non-virialized lenses."
+ Weak lensing has already. been shown to be a powerfu obe of the matter distribution in the universe (see e.g. Bartchnann Schneider 2001).," Weak lensing has already been shown to be a powerful probe of the matter distribution in the universe (see e.g., Bartelmann Schneider 2001)."
+ It also has the potentia o help constrain the amount and. nature of the. dark energy., It also has the potential to help constrain the amount and nature of the dark energy.
+ Lluterer (2002) showed that given. reasonable prior information on other cosmological parameters. the weak-ensing convergence power spectrum can impose constraints on the dark energy comparable to those of upcoming tvpoe la supernova and number-count surveys of galaxies. and ealaxy clusters.," Huterer (2002) showed that given reasonable prior information on other cosmological parameters, the weak-lensing convergence power spectrum can impose constraints on the dark energy comparable to those of upcoming type Ia supernova and number-count surveys of galaxies and galaxy clusters."
+ Constraining the dark energy from absolute measurements of weak-lens abundances will likely prove clillicult. however.," Constraining the dark energy from absolute measurements of weak-lens abundances will likely prove difficult, however."
+ The variation in the weak lens sky density with wis sullicientlv. small that modest: uncertainties in Oy (ancl observational noise) can mask the clleet of the dark energy., The variation in the weak lens sky density with $w$ is sufficiently small that modest uncertainties in $\Omega_0$ (and observational noise) can mask the effect of the dark energy.
+ More auspicious is the possibility of utilizing the relative abundance of dark lenses to virialized lenses to constrain w., More auspicious is the possibility of utilizing the relative abundance of dark lenses to virialized lenses to constrain $w$.
+ Future weak-lensing projects such as the the VISTA survey. the SNAP mission. and LSST (see Tyson οἱ al.," Future weak-lensing projects such as the the VISTA survey, the SNAP mission, and LSST (see Tyson et al."
+ 2002 for a discussion of its ereat promise as a probe of dark energy) are expected to provide the wide-Beld surveys needed for this technique to be viable., 2002 for a discussion of its great promise as a probe of dark energy) are expected to provide the wide-field surveys needed for this technique to be viable.
+ We thank Rk. Caldwell for helpful suggestions., We thank R. Caldwell for helpful suggestions.
+ NNW acknowledges the support of an NSP Graduate Fellowship., NNW acknowledges the support of an NSF Graduate Fellowship.
+ This work was supported by NSE AST-0096023.. NASA NAC5-9821. ancl Dol DIEE-ECGO3-92-121140701.," This work was supported by NSF AST-0096023, NASA NAG5-9821, and DoE DE-FG03-92-ER40701."
+The concept of magnetic helicity was introduced to solar physics in the 1980s (Heyvaerts Priest 1984: Berger Field 1984) and has attracted great attentions since that.,The concept of magnetic helicity was introduced to solar physics in the 1980s (Heyvaerts Priest 1984; Berger Field 1984) and has attracted great attentions since that.
+ It is a physical quantity that measures the topological complexity of magnetic field such as the degree of linkage, It is a physical quantity that measures the topological complexity of magnetic field such as the degree of linkage
+"For most extrasolar planets detected with the radial-velocity (RV) method, only their minimum masses are known because of their unknown orbit inclinations.","For most extrasolar planets detected with the radial-velocity (RV) method, only their minimum masses are known because of their unknown orbit inclinations."
+" Although the large number of planets allows us to draw statistically sound conclusions about their mass distribution (??),, it is highly desirable to derive this distribution without the inclination incertitude."," Although the large number of planets allows us to draw statistically sound conclusions about their mass distribution \citep{Udry:2007sf, Howard:2010lr}, it is highly desirable to derive this distribution without the inclination incertitude."
+ Astrometric measurements can resolve this ambiguity., Astrometric measurements can resolve this ambiguity.
+" For instance, ? used Hipparcos data to analyse the astrometric motion of stars with potential brown-dwarf companions and found that about half of the candidates are low-mass stars."," For instance, \cite{Sahlmann:2011fk} used Hipparcos data to analyse the astrometric motion of stars with potential brown-dwarf companions and found that about half of the candidates are low-mass stars."
+" Here, we extend this work to stars with planet candidates and non-standard Hipparcos solution, and discover the astrometric orbit of HD 5388, which hosts a recently announced planet candidate."," Here, we extend this work to stars with planet candidates and non-standard Hipparcos solution, and discover the astrometric orbit of HD 5388, which hosts a recently announced planet candidate."
+" In September 2010, the list of RV-planets at contained 461 entries around 389 stars."," In September 2010, the list of RV-planets at contained 461 entries around 389 stars."
+ Only 286 host stars are included in the new Hipparcos reduction (?).., Only 286 host stars are included in the new Hipparcos reduction \citep{:2007kx}.
+" Many host stars of transiting exoplanets discovered in transit surveys (e.g., Kepler, CoRoT, HAT, WASP) and confirmed by RV are fainter than the completeness limit of Hipparcos."," Many host stars of transiting exoplanets discovered in transit surveys (e.g., Kepler, CoRoT, HAT, WASP) and confirmed by RV are fainter than the completeness limit of Hipparcos."
+" We selected the stars for which the new Hipparcos reduction found a non-standard solution and that were not flagged as member of a multiple system, thus having solution types 1”. ’7’, or '9'."," We selected the stars for which the new Hipparcos reduction found a non-standard solution and that were not flagged as member of a multiple system, thus having solution types '1', '7', or '9'."
+" Type ""I solutions are termed stochastic and adopted when the standard five-parameter solution (type '5"") is not satisfactory and neither orbital nor acceleration models improve the solution in terms of y?.", Type '1' solutions are termed stochastic and adopted when the standard five-parameter solution (type '5') is not satisfactory and neither orbital nor acceleration models improve the solution in terms of $\chi^2$.
+" The types ’7’ and '9' are given, when the model has to include proper-motion derivatives of first and second order to obtain a reasonable fit."," The types '7' and '9' are given, when the model has to include proper-motion derivatives of first and second order to obtain a reasonable fit."
+ Six stars satisfied these criteria and are listed in Table 4.., Six stars satisfied these criteria and are listed in Table \ref{tab:4}.
+" The astrometric analysis was performed as described in ?,, where a detailed description of the method can be found."," The astrometric analysis was performed as described in \cite{Sahlmann:2011fk}, where a detailed description of the method can be found."
+ We briefly recall the main elements of the analysis., We briefly recall the main elements of the analysis.
+" Using the orbital parameters known from RV measurements, the intermediate astrometric data of the new Hipparcos reduction was fitted with a seven-parameter model depending on the inclination i, the longitude of the ascending node €, the parallax cv, and offsets to the coordinates (Aa*, Ad) and proper motions (Άμα»-. Aus) given in the published catalogue of ?.."," Using the orbital parameters known from RV measurements, the intermediate astrometric data of the new Hipparcos reduction was fitted with a seven-parameter model depending on the inclination $i$ , the longitude of the ascending node $\Omega$, the parallax $\varpi$, and offsets to the coordinates $\Delta \alpha^{\star}$, $\Delta \delta$ ) and proper motions $\Delta \mu_{\alpha^\star}$, $\Delta \mu_{\delta}$ ) given in the published catalogue of \cite{:2007kx}. ."
+ A two-dimensional search grid in i and © defined starting values for a standard nonlinear y7-minimisation procedure identifying the global minimum., A two-dimensional search grid in $i$ and $\Omega$ defined starting values for a standard nonlinear $\chi^2$ -minimisation procedure identifying the global minimum.
+ The uncertainties in the RV parameters are propagated to the astrometric solution by means of Monte Carlo simulations., The uncertainties in the RV parameters are propagated to the astrometric solution by means of Monte Carlo simulations.
+ The statistical significance of each astrometric orbit was determined by the distribution-free permutation test employing 1000 pseudo orbits., The statistical significance of each astrometric orbit was determined by the distribution-free permutation test employing 1000 pseudo orbits.
+ Uncertainties in the solution parameters were derived by Monte Carlo simulations., Uncertainties in the solution parameters were derived by Monte Carlo simulations.
+ This approach has proven to be reliable in detecting orbital signatures in the Hipparcos astrometric data and efficiently distinguishing a significant orbit in the present low signal-to-noise ratio regime (?).. (, This approach has proven to be reliable in detecting orbital signatures in the Hipparcos astrometric data and efficiently distinguishing a significant orbit in the present low signal-to-noise ratio regime \citep{Sahlmann:2011fk}. (
+HIP 4311) is listed with a stochastic solution in the catalogue of the new Hipparcos reduction.,HIP 4311) is listed with a stochastic solution in the catalogue of the new Hipparcos reduction.
+ ? used the HARPS spectrograph to discover a massive planet candidate around this F6V-star., \cite{Santos:2010fk2} used the HARPS spectrograph to discover a massive planet candidate around this F6V-star.
+ Figure 1. shows the radial velocities from thediscovery paper., Figure \ref{fig:rv} shows the radial velocities from thediscovery paper.
+ The companion has a minimum massof Ms»sini=1.96Μι and orbits its host in an eccentric orbit," The companion has a minimum massof $M_2 \sin i = 1.96\,M_\mathrm{J}$ and orbits its host in an eccentric orbit"
+Note however that for a given IR. [lux density. a steeper electron spectrum implies greater optical,"Note however that for a given IR flux density, a steeper electron spectrum implies greater optical"
+illumination. and observing geometries. accepts irregular shape models and arbitrary spin-vector solutions. works with roughness controlled by the oof the surface slopes. considers heat-conduction into the surface as well as multiple scattering of both the solar and the thermally emitted radiation.,"illumination and observing geometries, accepts irregular shape models and arbitrary spin-vector solutions, works with roughness controlled by the of the surface slopes, considers heat-conduction into the surface as well as multiple scattering of both the solar and the thermally emitted radiation."
+ The model has been tested and validated thoroughly for NEAs (e.g.. Mülller et citemueller05)) and MBAs (e.g.. Mülller Lagerros 2002)).," The model has been tested and validated thoroughly for NEAs (e.g., Mülller et \\cite{mueller05}) ) and MBAs (e.g., Mülller Lagerros \cite{mueller02}) )."
+ The TPM input parameters and applied variations are listed in Table. 3.., The TPM input parameters and applied variations are listed in Table. \ref{tbl:tpm_params}.
+ Campins et ((2009)) and Mueller (2007)) used à y or reduced y-test to find solutions for the thermal inertia T., Campins et \cite{campins09}) ) and Mueller\cite{mueller07}) ) used a $\chi^2$ or reduced $\chi^2$ -test to find solutions for the thermal inertia $\Gamma$.
+ Here we follow a modified approach to find the most robust solutions with respect to thermal inertia and allowing for the full range in effective diameter and geometric albedo at the same time., Here we follow a modified approach to find the most robust solutions with respect to thermal inertia and allowing for the full range in effective diameter and geometric albedo at the same time.
+ The following procedure was executed for all 84 possible shape and spin-vector solutions (1) For each value of El in a wide range (see Table 3)) we calculate the radiometric diameter and albedo solution via the TPM for each individually observed thermal flux (37 individual diameter and albedo solutions)., The following procedure was executed for all 84 possible shape and spin-vector solutions (1) For each value of $\Gamma$ in a wide range (see Table \ref{tbl:tpm_params}) ) we calculate the radiometric diameter and albedo solution via the TPM for each individually observed thermal flux (37 individual diameter and albedo solutions).
+ Diameter and albedo are linked by the absolute magnitude Hy which was kept constant (the rotational amplitude is only about (2) We calculate the weighted mean radiometric diameter and albedo solution for each given D (¥=Noc∖∣ with diameter/albedo errors o; connected to the observational (3) For each individual observation we predict TPM fluxes based on the given [and the corresponding weighted mean radiometric diameter and albedo from step (4) The most robust solutions occur when the observations and the TPM predictions agree best (taking the uncertainties of the measurements into account in a weighted mean sense. see step 2).," Diameter and albedo are linked by the absolute magnitude $H_{\rm{V}}$ which was kept constant (the rotational amplitude is only about (2) We calculate the weighted mean radiometric diameter and albedo solution for each given $\Gamma$ $\bar{x} = \frac{\Sigma x_i / \sigma_i^2}{\Sigma 1 / \sigma_i^2}$, with diameter/albedo errors $\sigma_i$ connected to the observational (3) For each individual observation we predict TPM fluxes based on the given $\Gamma$ and the corresponding weighted mean radiometric diameter and albedo from step (4) The most robust solutions occur when the observations and the TPM predictions agree best (taking the uncertainties of the measurements into account in a weighted mean sense, see step 2)."
+ This can be expressed as XXobs;-mod)oz. a modified reduced y method.," This can be expressed as $\frac{1}{N} \Sigma_{i=1}^{N} ((obs_i-mod_i)/\sigma_i)^2$, a modified reduced $\chi^2$ method."
+ The most likely thermal inertia is found at the smallest y. values: the connected effective diameter and geometric albedo values are the ones calculated at step (2)., The most likely thermal inertia is found at the smallest $\chi^2$ values; the connected effective diameter and geometric albedo values are the ones calculated at step (2).
+ In a first round of executing this procedure we kept the surface roughness constant at values which were specified as “default values” for large. regolith-covered asteroids (Miilller et citemueller99)).," In a first round of executing this procedure we kept the surface roughness constant at values which were specified as ""default values"" for large, regolith-covered asteroids (Mülller et \\cite{mueller99}) )."
+ The corresponding roughness parameter values are pz0.7. the oof the surface slopes. and f=0.6. the fraction of surface covered by craters.," The corresponding roughness parameter values are $\rho$ =0.7, the of the surface slopes, and $f$ =0.6, the fraction of surface covered by craters."
+ The results are show in Fig. 2.., The results are shown in Fig. \ref{fig:chi2a}.
+ The best shape and spin-vector solutions (with lowest values for the reduced y and clear minima in Fig. 2)), The best shape and spin-vector solutions (with lowest values for the reduced $\chi^2$ and clear minima in Fig. \ref{fig:chi2a}) )
+ were the the starting point for further tests: (1) Are these solutions robus= against sub-sets of the thermal data? G, were then the starting point for further tests: (i) Are these solutions robust against sub-sets of the thermal data? (
+i) How does the surface roughness influence the solutions? (,ii) How does the surface roughness influence the solutions? (
+111) Do the solutions explat the thermal behaviour over the observed phase angle range (from ~20° to ~55°)? (,iii) Do the solutions explain the thermal behaviour over the observed phase angle range (from $\sim$ $^{\circ}$ to $\sim$ $^{\circ}$ )? (
+iv) Is the TPM match of equal quality at all observed wavelengths? (,iv) Is the TPM match of equal quality at all observed wavelengths? (
+v) Are there large discrepancies at certain rotational phases?,v) Are there large discrepancies at certain rotational phases?
+ The shape and spin-vector solutions which produce the lowest y--values in Fig., The shape and spin-vector solutions which produce the lowest $\chi^{2}$ -values in Fig.
+ 2. are listed in Table 4.., \ref{fig:chi2a} are listed in Table \ref{tbl:sv_chi2}. .
+ The model IDs represent a full shape-model. each with more than 2000 surface elements and more than 1000 vertices.," The model IDs represent a full shape-model, each with more than 2000 surface elements and more than 1000 vertices."
+ The Julian date at zero rotational phase yo is in all cases 7522454289.0., The Julian date at zero rotational phase $\gamma_0$ is in all cases $T_0$ =2454289.0.
+"TheIn contoursummary,levels arethe 0.01,change0.02, of 0.03,the 0.05,PMF and0.09 theA m2.corresponding. change of the CMF observed in this study are not caused by the long-term development of the active region but occurred as rapid as the flare.","In summary, the change of the PMF and the corresponding change of the CMF observed in this study are not caused by the long-term development of the active region but occurred as rapid as the flare."
+ The magnetic field change may involve two closely related physical processes: the tether-cut reconnection producing the flare and the ensuing collapse of the CMF resulting from the energy release., The magnetic field change may involve two closely related physical processes: the tether-cut reconnection producing the flare and the ensuing collapse of the CMF resulting from the energy release.
+" lis a mission and launched by ISAS/JAXA, Japanesewith NAOJ as domestic developedpartner and NASA and STFC (UK) as international partners."," is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners."
+ It is operated by these agencies in co-operation with ESA and NSC (Norway)., It is operated by these agencies in co-operation with ESA and NSC (Norway).
+ lis a mission for NASA's Living With a Star program., is a mission for NASA's Living With a Star program.
+ iis a NASA Small Explorer., is a NASA Small Explorer.
+" We thank the SDO//HMI team for the free access to the newly released HMI vector magnetograms, which were used in revising the paper."," We thank the /HMI team for the free access to the newly released HMI vector magnetograms, which were used in revising the paper."
+ We thank the referee for helpful comments., We thank the referee for helpful comments.
+ This work uses the DAVEAVM code written and developed by the Naval Research Laboratory., This work uses the DAVE4VM code written and developed by the Naval Research Laboratory.
+" C.L., R.L., J.J., Y.X., S.W. and H.W. were supported by NSF grants AGS 08-19662, AGS 08-49453, AGS 09-36665, and AGS 08-39216, and NASA grants NNX 08AQ90G, NNX 08AJ23G, NNX 11ACO05G, and NNX 11AQ55G. N.D. was supported by NASA grant NNX 08AQ32G. J.L. was supported by NSF grant AST 09-08344."," C.L., R.L., J.J., Y.X., S.W. and H.W. were supported by NSF grants AGS 08-19662, AGS 08-49453, AGS 09-36665, and AGS 08-39216, and NASA grants NNX 08AQ90G, NNX 08AJ23G, NNX 11AC05G, and NNX 11AQ55G. N.D. was supported by NASA grant NNX 08AQ32G. J.L. was supported by NSF grant AST 09-08344."
+ T.W. was supported by DLR-grant 500C0501., T.W. was supported by DLR-grant 50OC0501.
+become a cataclysmic variable (CV) if mass is transferred stably from the main sequence star to the white dwarf.,become a cataclysmic variable (CV) if mass is transferred stably from the main sequence star to the white dwarf.
+ If on the other hand. the binary is too wide to become a CV. the main sequence star will evolve into a giant and the system will undergo another Cl phase.," If, on the other hand, the binary is too wide to become a CV, the main sequence star will evolve into a giant and the system will undergo another CE phase."
+ When the envelope is ejected. the resulting binary will be composed of two white chwarts a few solar radii apart - called a double degenerate (DD).," When the envelope is ejected, the resulting binary will be composed of two white dwarfs a few solar radii apart - called a double degenerate (DD)."
+ For details on the evolution ancl formation of DDs sec Nelemans et al, For details on the evolution and formation of DDs see Nelemans et al.
+s. (2001) recent population svnthesis studies and references therein.,'s \shortcite{nypv01} recent population synthesis studies and references therein.
+ The study of white-cdwarl close-binary stars can help us understand. the elusive. CIE phase that they must have gone through. at least once. during their evolution.," The study of white-dwarf close-binary stars can help us understand the elusive CE phase that they must have gone through, at least once, during their evolution."
+ This phase is very dillicult to stuck: in any other manner as it lasts only of the order of 1 to 100 vears., This phase is very difficult to study in any other manner as it lasts only of the order of 1 to 100 years.
+ For recent calculations on CE ejection elficiencies see Soker IIHIarpaz (2003) and references therein., For recent calculations on CE ejection efficiencies see Soker Harpaz \shortcite{sh03} and references therein.
+ The subjects of this paper. white dwarf - AL dwarl binaries ancl DDs. are. as mentioned above. the progenitors of CVs. and. potential progenitors of Type la supernova respectively.," The subjects of this paper, white dwarf - M dwarf binaries and DDs, are, as mentioned above, the progenitors of CVs, and potential progenitors of Type Ia supernova respectively."
+ A short period. DD where the combined mass of the white cwarls exceeds the Chandrasekhar mass might rccome a Tvpe la supernova (Iben&Tutukoy1984).. but no candidates have vet been found.," A short period DD where the combined mass of the white dwarfs exceeds the Chandrasekhar mass might become a Type Ia supernova \cite{it84}, but no candidates have yet been found."
+ We should mention that this idea is still quite controversial with some theorists claiming hat à DD does not become a Type Ia supernova (Saio&Someta1998) and others claiming that this can be the case if one includes rotation in the caleulations (Picrsantietal. 2003)., We should mention that this idea is still quite controversial with some theorists claiming that a DD does not become a Type Ia supernova \cite{sn98} and others claiming that this can be the case if one includes rotation in the calculations \cite{p03}.
+. The ESO Supernova la Progenitor Survey (SPY) las às its main goal to search. systematically for massive. short period. DDs in the galaxy to establish their. clirect ink with Pype la supernova ancl it is the source of more han 100 recently discovered. DD systems (Napiwotzkietal. 2003).," The ESO Supernova Ia Progenitor Survey (SPY) has as its main goal to search systematically for massive, short period DDs in the galaxy to establish their direct link with Type Ia supernova and it is the source of more than 100 recently discovered DD systems \cite{n04}."
+. Efforts are also been carried out to svstematically ind white - M dwarf binaries by using the Sloan Digital Sky Survey (SDSS) resulting in more than 400. possible candidates (Silvestri.Lawley&Szkocly2003).., Efforts are also been carried out to systematically find white - M dwarf binaries by using the Sloan Digital Sky Survey (SDSS) resulting in more than 400 possible candidates \cite{shs03}.
+ Schreiber CCannsicke (2003) review the evolution. of the. known sample of white-dwarl close binaries with main sequence companions. the PCEDs. anc conclude that. due to selection ellects. the (until then) known population of PCTDs is dominated by voung systems with hot white charts that will evolve into short period CVs (DP « 3 h).," Schreiber Gännsicke \shortcite{sg03} review the evolution of the known sample of white-dwarf close binaries with main sequence companions, the PCEBs, and conclude that, due to selection effects, the (until then) known population of PCEBs is dominated by young systems with hot white dwarfs that will evolve into short period CVs (P $<$ 3 h)."
+ The PCB sample is biased. Coward low mass companions as well which is the reason why they evolve into short period. CVs., The PCEB sample is biased toward low mass companions as well which is the reason why they evolve into short period CVs.
+ In contrast. the PCEDs found. in the SDSS (Raymondctal.2003).. published later on. show an average white dwarf temperatuic significantly. lower. demonstrating that to sample the fu= parameter space better selection criteria have to be devised.," In contrast, the PCEBs found in the SDSS \cite{r03}, published later on, show an average white dwarf temperature significantly lower, demonstrating that to sample the full parameter space better selection criteria have to be devised."
+ In this paper we study ο white dwarf close-binary stars., In this paper we study 6 white dwarf close-binary stars.
+ Four oΓ them are found. to x DDs. the other two are conipose of a white cdwarl anc an M dwarf star.," Four of them are found to be DDs, the other two are composed of a white dwarf and an M dwarf star."
+ The separation of both components in these binaries is of the order of a few solar radii. as determined from their short orbital perios. so they are detachec syslenms where no mass transfer between them takes place.," The separation of both components in these binaries is of the order of a few solar radii, as determined from their short orbital periods, so they are detached systems where no mass transfer between them takes place."
+ We obtain their orbital solutions and compare the results obtained with predictions drawn from population svnthesis studies., We obtain their orbital solutions and compare the results obtained with predictions drawn from population synthesis studies.
+ The cata used in this study were taken over many vears (since 1993) using five different telescopes and seven different setups., The data used in this study were taken over many years (since 1993) using five different telescopes and seven different setups.
+ Fable 1 gives a list of the number of spectra taken for cach target at cach observing campaign indicating also which telescope was used in cach case., Table \ref{obs} gives a list of the number of spectra taken for each target at each observing campaign indicating also which telescope was used in each case.
+ AAT: denotes data taken with the Roval Greenwich Observatory (ROO) spectrograph at the tmm Anelo-Australian ‘Telescope (AAT)., AAT: denotes data taken with the Royal Greenwich Observatory (RGO) spectrograph at the m Anglo-Australian Telescope (AAT).
+ The setup consisted of the S2cem camera with the RIZOOR. grating centred inLla., The setup consisted of the cm camera with the R1200R grating centred in.
+. Phe CCD used was an MET-LL (3kx1k) in fast readout mocle., The CCD used was an MIT-LL (3kx1k) in fast readout mode.
+ ‘This combination gives a dispersion of 0.23*., This combination gives a dispersion of 0.23.
+. 1ΝΤα: denotes data taken with the Intermediate Dispersion Spectrograph (LDS) at the 2.5m Isaac Newton ‘Telescope (INTE). on the island. of La Palma., INTa: denotes data taken with the Intermediate Dispersion Spectrograph (IDS) at the 2.5m Isaac Newton Telescope (INT) on the island of La Palma.
+ For these, For these
+and G is the gravitational constant.,and $G$ is the gravitational constant.
+ The relation between Mr) and the mass clensily per unit volume p is: We adopt the equation of state for a hydrogen aud helium mixture given by Chabrier et al. (, The relation between $M(r)$ and the mass density per unit volume $\rho$ is: We adopt the equation of state for a hydrogen and helium mixture given by Chabrier et al. (
+1992) for mass fractions of hydrogen aud. helium of 0.7 and 0.28. respectively.,"1992) for mass fractions of hydrogen and helium of 0.7 and 0.28, respectively."
+ The standard equation of radiative transport gives the DIuminositv μμ that is Gausported bv raciation through the atmosphere as a functionof the temperature gradient. dTdi: where # is the opacity. which in general depends on both p and 7. and 6 is the constant.," The standard equation of radiative transport gives the luminosity $L_{\rm rad}$ that is transported by radiation through the atmosphere as a functionof the temperature gradient $dT/dr$: where $\kappa$ is the opacity, which in general depends on both $\rho$ and $T$, and $\sigma$ is the Stefan--Boltzmann constant."
+ Asa laree part of the atmosphere interior is unstable to convection. only a [raction of the total luminosity is transported by radiation.," As a large part of the atmosphere interior is unstable to convection, only a fraction of the total luminosity is transported by radiation."
+ La the moclels presented here. we assume {hat the only energv source comes from the planetesimals (hat are accreted by the protoplanet and release their gravitational energy as thev collide with the surface of the core.," In the models presented here, we assume that the only energy source comes from the planetesimals that are accreted by the protoplanet and release their gravitational energy as they collide with the surface of the core."
+" They generate a total core luminosity Lo given bv: where A. and 7, are. respectively. (he mass and (he radius of the core. and M, is the planetesimal accretion rate."," They generate a total core luminosity $L_{\rm core}$ given by: where $M_{c}$ and $r_{c}$ are, respectively, the mass and the radius of the core, and $\dot{M}_{c}$ is the planetesimal accretion rate."
+" The radiative and aciabatic temperature —gradients. V,44rad and. ad Vag. are Sgiven by: and with the subscript s denoting evaluation at constant entropy."," The radiative and adiabatic temperature gradients, $\nabla_{\rm rad}$ and $\nabla_{\rm ad}$ , are given by: and with the subscript ${s}$ denoting evaluation at constant entropy."
+ In the regions where Venda<Wag. there is stability to convection and therefore all the energy is transported by radiation. ie. £44=L4 ," In the regions where $\nabla_{\rm rad} < \nabla_{\rm ad}$, there is stability to convection and therefore all the energy is transported by radiation, i.e. $L_{\rm rad}=L_{\rm core}$."
+In the regions where V44>Waa. there is instability to convection and (therefore part of the energy is transported by convection. Le. Loue=Lead Loa Where Logs is the luminosity associated. with convection.," In the regions where $\nabla_{\rm rad} > \nabla_{\rm ad}$, there is instability to convection and therefore part of the energy is transported by convection, i.e. $L_{\rm core}= L_{\rm rad}+L_{\rm conv}$ , where $L_{\rm conv}$ is the luminosity associated with convection."
+ Using the mixing lengththeory (Cox Giuli 1963). we obtain:," Using the mixing lengththeory (Cox Giuli 1968), we obtain:"
+planet are the only bodies in the svstem. then the transits will be strictly periodic. ie.. |;=lgxXxP6. where /; is the timeof the vith transit. 2. is (he transiting planet's sidereal orbital period. ancl anv (ransit timing variations (6/;) are due to measurement error.,"planet are the only bodies in the system, then the transits will be strictly periodic, i.e., $t_i = t_0
++ i\times P_s + \delta t_i$, where $t_i$ is the timeof the $i$ th transit, $P_s$ is the transiting planet's sidereal orbital period, and any transit timing variations $\delta t_i$ ) are due to measurement error."
+ llowever. if an additional planet orbits the star. (hen the times of the giant planets transits will be affected. (Miralda-Escude 2002: Holman Murray 2005: Agol et 22006: lev] Glachnan 2006).," However, if an additional planet orbits the star, then the times of the giant planet's transits will be affected (Miralda-Escude 2002; Holman Murray 2005; Agol et 2006; Heyl Gladman 2006)."
+ By analvzing the deviations of the observed TTVs from a strictly. periodic model (911). astronomers can search [ον additional planets orbiting the star.," By analyzing the deviations of the observed TTVs from a strictly periodic model $\delta t_i$ ), astronomers can search for additional planets orbiting the star."
+ Here. we show that a sub-Earth mass Trojan planet could induce a (ransit Ging signal (hat is easily measurable using existing ground-based observatories.," Here, we show that a sub-Earth mass Trojan planet could induce a transit timing signal that is easily measurable using existing ground-based observatories."
+ We consider a three body system. and denote the stellar mass (Gy). the planet mass (ny). and the Trojan mass (17).," We consider a three body system and denote the stellar mass $m_{\star}$ ), the planet mass $m_p$ ), and the Trojan mass $m_T$ )."
+ We reler to all bodies librating about the L4 or L5 fixed point of a planet as “Trojans”., We refer to all bodies librating about the L4 or L5 fixed point of a planet as “Trojans”.
+" If there are no other massive bodies in the svstem. then the L4/L5 fixed points are stable for circular orbits if the ratio. ji=(mpmg)/Gm,d mmy). is less than a critical threshold ji. where 0.02312.<yr.0.08852 ancl ji. depends on the ralio. επΠρΕΠΗ) (Langhlin Chambers 2002)."," If there are no other massive bodies in the system, then the L4/L5 fixed points are stable for circular orbits if the ratio, $\mu=(m_p+m_T)/(m_\star+m_p+m_T)$ , is less than a critical threshold $\mu_c$, where $0.03812\le\mu_{c}\le0.03852$ and $\mu_c$ depends on the ratio, $\epsilon\equiv m_T/(m_p+m_T)$ (Laughlin Chambers 2002)."
+ IF the planet and Trojan have equal eccentricities and the Trojan resides exactly at the L4/L5 fixed point. then the (transit timing signature for (he primary planet would be indistinguishable [rom a similar svstem without a Trojan.," If the planet and Trojan have equal eccentricities and the Trojan resides exactly at the L4/L5 fixed point, then the transit timing signature for the primary planet would be indistinguishable from a similar system without a Trojan."
+ More generally. lor a Trojan on an orbit that is librating about the L4/L5 fixed point. the times of the primary planets transits will deviate from being strictly periodic.," More generally, for a Trojan on an orbit that is librating about the L4/L5 fixed point, the times of the primary planet's transits will deviate from being strictly periodic."
+ llere. we focus our attention on Trojans that undergo small librations about the L4/L5 fixed points and are significantly less massive than (hie currently known planet.," Here, we focus our attention on Trojans that undergo small librations about the L4/L5 fixed points and are significantly less massive than the currently known planet."
+ The libration can be approximated as a linear superposition of (wo epicyclie motions., The libration can be approximated as a linear superposition of two epicyclic motions.
+" The star-Trojan separation can oscillate about. the semi-major axis of the planet (a5) with the amplitude. da«ja, on a limescale 7g47DP.. and the guiding center of the Trojan can oscillate on a longer (ünmescale. Tyo&£P4/27/(40) (Murray Dermott 2000)."," The star-Trojan separation can oscillate about the semi-major axis of the planet $a_p$ ) with the amplitude, $\delta a \ll \mu^{1/2} a_p$ on a timescale $\tau_{\rm fast}\simeq
+P_s$, and the guiding center of the Trojan can oscillate on a longer timescale, $\tau_{\rm slow}\simeq P_s\sqrt{27/(4\mu)}$ (Murray Dermott 2000)."
+ The timescale of the libration of the guiding center makes this motion most reaclily detectible bv transit timing observations., The timescale of the libration of the guiding center makes this motion most readily detectible by transit timing observations.
+ For a transiting planet. both P; aud each /; can be measured precisely using photometry alone.," For a transiting planet, both $P_s$ and each $t_i$ can be measured precisely using photometry alone."
+" Considering a series of continuous photometric observations wilh uncorrelated Gaussian uncertainties of magnitude 6,,. taken αἱ a rate P around a single transit. the mid-transit lime can be measured with an accuracy of a,©le/2Loyp ? where /, is the duration of ingress/egress and p isthe ratio of the planet radius to stellar radius (Ford Gaudi2006)."," Considering a series of continuous photometric observations with uncorrelated Gaussian uncertainties of magnitude $\sigma_{ph}$ , taken at a rate $\Gamma$ around a single transit, the mid-transit time can be measured with an accuracy of $\sigma_{t_i}\simeq~\sqrt{t_e/2\Gamma}\sigma_{ph}\rho^{-2}$ , where $t_e$ is the duration of ingress/egress and $\rho$ isthe ratio of the planet radius to stellar radius (Ford Gaudi2006)."
+this aim we performed extensive Moutecarlo tests using the detection procedures on the simulate data for 12 observations with different exposure times (ic. 1.680 s. 2.656 s. L976 s. 10.000 s. 16.080 s. 20.661 s. 27.158 s. 12.672 s. 52.88U s. SU.28S s. 107.712 s and 200.272 «).,"this aim we performed extensive Montecarlo tests using the detection procedures on the simulated data for 12 observations with different exposure times (i.e. 1,680 s, 2,656 s, 4,976 s, 10,000 s, 16,080 s, 20,664 s, 27,488 s, 42,672 s, 52,880 s, 80,288 s, 107,712 s and 200,272 s)."
+ For cach field of the survey we derived a couipleteuess function that Ooeives the detection probability as a fiction of flux and position of poiut-like sources., For each field of the survey we derived a completeness function that gives the detection probability as a function of flux and position of point-like sources.
+ Because of the worsening of the PSF. within the same field. the detection xobabilitv of a given fiux decreases for Increasing offaxis anele.," Because of the worsening of the PSF, within the same field, the detection probability of a given flux decreases for increasing off–axis angle."
+ Therefore. for cach observation the skv coverage is the integral of the completeness fuuction over the ποια of view.," Therefore, for each observation the sky coverage is the integral of the completeness function over the field of view."
+ Moreover. each observation has dierent conipleteness function depending on the exposure finie and ou the coluum density values.," Moreover, each observation has different completeness function depending on the exposure time and on the column density values."
+ The sky coverage of he whole survey is the stun of the coutributious of cach sinele field., The sky coverage of the whole survey is the sum of the contributions of each single field.
+ Some of the felds used to build the DNAIW-IIRI catalogue cover the same area ofthe ska: in this case iu the calculation of the total sky coverage we considered onlv the contribution from the longest observation performed over that area., Some of the fields used to build the BMW-HRI catalogue cover the same area of the sky: in this case in the calculation of the total sky coverage we considered only the contribution from the longest observation performed over that area.
+ All he procedures of data simulations aud the features of the Montecarlo tests are fully described in Moretti et al., All the procedures of data simulations and the features of the Montecarlo tests are fully described in Moretti et al.
+ (2002. in preparation)., \cite{moretti02} in preparation).
+ The complete skv coverage for poiut-like sources is slow in Fie., The complete sky coverage for point-like sources is shown in Fig.
+ 7 (for extended sources see Moretti et al., 7 (for extended sources see Moretti et al.
+ 2002 in preparation)., \cite{moretti02} in preparation).
+ The maxiumuu area of the survey is ~732 deg? and corresponds to fluxes above ~10!?eyesiemn7.," The maximum area of the survey is $\sim 732$ $^{2}$ and corresponds to fluxes above $\sim\,10^{-12} \ergs \cmdue$."
+ At 10ores+onn7 the surveved area is ~311 dee? aud 10 dee? at 10thorestem7., At $10^{-13} \ergs \cmdue$ the surveyed area is $\sim 314$ $^{2}$ and $\sim 10$ $^{2}$ at $10^{-14} \ergs \cmdue$.
+ Iu order to compute the iuteeral flux distribution (logCN)-log(8)) of cosinological sources we used a subsample of the catalogue., In order to compute the integral flux distribution (log(N)-log(S)) of cosmological sources we used a subsample of the catalogue.
+ Firstly. we selected all ligh galactic latitude fields b|>30 ) observed for more than 5 ks.," Firstly, we selected all high galactic latitude fields $|b| > 30^{\degr}$ ) observed for more than 5 ks."
+ Then. we filtered out those coutaidus extended sources (like," Then, we filtered out those containing extended sources (like"
+is confined to a region less than 200 pc im exteut.,is confined to a region less than 200 pc in extent.
+ The total measured CO flux for Mrk 163E is 6.80.9 Jv kau κἘν which agrees with the IRAM 30m measurement of T2408 Jy dans | for Myk 163 obtained by Alloin et al. (," The total measured CO flux for Mrk 463E is $\pm0.9$ Jy km $^{-1}$, which agrees with the IRAM 30m measurement of $\pm0.8$ Jy km $^{-1}$ for Mrk 463 obtained by Alloin et al. ("
+1992) to within6%.,1992) to within.
+". The difference between the single-dish and OVRO observations can be used to coustraiu the CO flux of the W uucleus: the difference of 0,141.7 Jv lan | oresults iu an upper limit of 2.1 Jv Jan s+.", The difference between the single-dish and OVRO observations can be used to constrain the CO flux of the W nucleus; the difference of $0.4\pm1.7$ Jy km $^{-1}$ results in an upper limit of 2.1 Jy km $^{-1}$.
+ This is cousisteut with the 36 upper limit of 2.7 Jv kins |! calculated using the riis noise iu the OVRO data and assuniue a velocity width equal to that of the E uucleus., This is consistent with the $3\sigma$ upper limit of 2.7 Jy km $^{-1}$ calculated using the rms noise in the OVRO data and assuming a velocity width equal to that of the E nucleus.
+ The higher flux is adopted as the upper CO flux limit of Mrk 163W (Table D)., The higher flux is adopted as the upper CO flux limit of Mrk 463W (Table 4).
+ The CO(1/» 0) spectruii of E uucleus is also shown in Figure 3h., The $1\to0$ ) spectrum of E nucleus is also shown in Figure 3b.
+ The CO data for IRAS 11318-1117. are discussed in detail bv Evans. Surace. Mazzarella. (2000). and thus the discussion will be onütted here.," The CO data for IRAS 14348-1447 are discussed in detail by Evans, Surace, Mazzarella (2000), and thus the discussion will be omitted here."
+ Table [ Μπαμπάσος the emüssiou-liue properties of the five ULICs., Table 4 summarizes the emission-line properties of the five ULIGs.
+" For a A=0 Universe. the lhuninosity distance for a source at a eiven redshift is Civeu the measured CO fux. SeoAe [Jy kin 1]. the CO luminosity of a source at redshift + is (Solomon. Downes. Badford 1992) where € [in m is the speed of light. & |] +] is the Boltzmann constant. and v1, [Hz] is the observed frequency."," For a $\Lambda = 0$ Universe, the luminosity distance for a source at a given redshift is Given the measured CO flux, $S_{\rm CO} \Delta v$ [Jy km $^{-1}$ ], the CO luminosity of a source at redshift $z$ is (Solomon, Downes, Radford 1992) where $c$ [km $^{-1}$ ] is the speed of light, $k$ [J $^{-1}$ ] is the Boltzmann constant, and $\nu_{\rm obs}$ [Hz] is the observed frequency."
+ In terms of useful its. Louyy Can be written as To calculate the mass of molecular gas in these galaxies. the reasonable assmuption is commonly made that the CO ciuission is optically thick and thermalized. audthat it originates in gravitationally bound molecular clouds.," In terms of useful units, $L'_{\rm
+CO(1\to0)}$ can be written as To calculate the mass of molecular gas in these galaxies, the reasonable assumption is commonly made that the CO emission is optically thick and thermalized, andthat it originates in gravitationally bound molecular clouds."
+" Thus. the ratio of the II5 mass aud the CO huuinosity 1s given by where (Io) aud Tj, ave the density of IT aud brielituess temperature for the 50) transitiou (Scoville Sauders 1987: Solomon. Downes. Radford 1992)."," Thus, the ratio of the $_2$ mass and the CO luminosity is given by where $n($ $_2)$ and $T_{\rm b}$ are the density of $_2$ and brightness temperature for the $\to$ 0) transition (Scoville Sanders 1987; Solomon, Downes, Radford 1992)."
+ Afultitrausition CO survers of molecular clouds in the ADlkv Way (c.g. Saucers et al., Multitransition CO surveys of molecular clouds in the Milky Way (e.g. Sanders et al.
+ 1993). aud iu nearby starburst galaxies (e.g. Cuüssteu et al.," 1993), and in nearby starburst galaxies (e.g. Güssten et al."
+ 1993) have shown that hotter clouds teud to be deuser such that the ceusity and temperature dependencies cancel each other., 1993) have shown that hotter clouds tend to be denser such that the density and temperature dependencies cancel each other.
+ The variatiou in the value of à is approximately a factor of 2 for a wide range of kinetic teiiperatures. eas densities. aud CO abundance (eg. à=25A. [dias 3 pe?)15: Radford. Solomon. Downes 1991).," The variation in the value of $\alpha$ is approximately a factor of 2 for a wide range of kinetic temperatures, gas densities, and CO abundance (e.g. $\alpha = 2-5 M_{\odot}$ [K km $^{-1}$ $^2]^{-1}$: Radford, Solomon, Downes 1991)."
+ Solomon et al. (, Solomon et al. (
+1997) aud Downes Solomon (1998) have made use of dynamical lnass estimates of a low-redshiftt infrared galaxy sample observed in CO with the Plateau de Bure Tuterferometer to argue that à may in some cases. be as low as 1 AL. (IN kins i per)il,"1997) and Downes Solomon (1998) have made use of dynamical mass estimates of a low-redshift infrared galaxy sample observed in CO with the Plateau de Bure Interferometer to argue that $\alpha$ may, in some cases, be as low as 1 $M_{\odot}$ (K km $^{-1}$ $^2)^{-1}$."
+ Iu order to determine an appropriate value of à for the present sample of galaxies. the assumption will be made that the mass of the immer region of cach galaxy is primarily comprised of molecular gas.," In order to determine an appropriate value of $\alpha$ for the present sample of galaxies, the assumption will be made that the mass of the inner region of each galaxy is primarily comprised of molecular gas."
+ Thus. the molecular gas mass will be asstuned to be equal to the dyaanical mass. where Aeg is the full CO velocity width at half the imaxiunun flux deusitv (Table 1) aud Rew is the radius of the CO distribution.," Thus, the molecular gas mass will be assumed to be equal to the dynamical mass, where $\Delta v_{\rm FWHM}$ is the full CO velocity width at half the maximum flux density (Table 4) and $R_{\rm CO}$ is the radius of the CO distribution."
+ Civen that the CO emission associated with each nucleus was not resolved with the OVRO observatious (Figure 13). Reg is estimated in two wavs.," Given that the CO emission associated with each nucleus was not resolved with the OVRO observations (Figure 1–3), $R_{\rm CO}$ is estimated in two ways."
+ First. the assmuption is made that the molecular eas is simular in extent to the radio cunission (Condon ot al.," First, the assumption is made that the molecular gas is similar in extent to the radio emission (Condon et al."
+ 1991: Table 5): this is plausible eiven that the radio enission nav. with the exception of IRAS 13151|1232 and Myk 163 (see 86.2). be due to superuovae frou star formation that has been fueled by the molecular gas (hereafter. size estimate 1).," 1991: Table 5); this is plausible given that the radio emission may, with the exception of IRAS 13451+1232 and Mrk 463 (see 6.2), be due to supernovae from star formation that has been fueled by the molecular gas (hereafter, size estimate 1)."
+ Secoud. the CO extent is estimated by asstuuine optically thick. thernmialized gas with a unity filline factor aud a blackbody temperature. Tij. equal to that of the (hereafter. size estimate 2).," Second, the CO extent is estimated by assuming optically thick, thermalized gas with a unity filling factor and a blackbody temperature, $T_{\rm bb}$, equal to that of the (hereafter, size estimate 2)."
+" Given the latter assumption. Tjj, can be determined using the 60:22 aud 100722 flux deusities (sce discussion in Solomon et al."," Given the latter assumption, $T_{\rm bb}$ can be determined using the $\micron$ and $\micron$ flux densities (see discussion in Solomon et al."
+ 1997)., 1997).
+ Thus. the radius of the CO distribution is caleulated via (see Table 5).," Thus, the radius of the CO distribution is calculated via (see Table 5)."
+ The sizes estimated via these two methods ave with a factor of 2[| of each other. with the size estimate I vielding smaller CO exteuts.," The sizes estimated via these two methods are with a factor of 2–4 of each other, with the size estimate 1 yielding smaller CO extents."
+ Adopting the more conservative CO extent determined from size estimate 2 vields ALinn/Log=L0.2.5 M. Us kins 3! pe?)! with a niea value of 1.6 M. US kan | pe?) 1., Adopting the more conservative CO extent determined from size estimate 2 yields $M_{\rm dyn} / L'_{\rm CO} = 1.0-2.5$ $_\odot$ (K km $^{-1}$ $^2)^{-1}$ with a mean value of 1.6 $_\odot$ (K km $^{-1}$ $^2)^{-1}$ .
+" These values are similar to Mag/Lt4,=0.8.2.5 M. (IN kins ο... derived by Solomon et al. ("," These values are similar to $M_{\rm dyn} /
+L'_{\rm CO} = 0.8-2.5$ $_\odot$ (K km $^{-1}$ $^2)^{-1}$ derived by Solomon et al. ("
+1997) for a sample of 37 ULIC: the average of their sample is 1:3 M. (IS lans 3 pet) |.,1997) for a sample of 37 ULIGs; the average of their sample is 1.3 $_\odot$ (K km $^{-1}$ $^2)^{-1}$ .
+appear softer than the nearer Tvpe 2 AGN because their unobscured hard X-ray emission is substantially redshifted into the soft band.,appear softer than the nearer Type 2 AGN because their unobscured hard X-ray emission is substantially redshifted into the soft band.
+ We predict that at still fainter ταν [lux limits. we will find substantially more of the faint optical counterparts. but few additional members of the resolved brighter population.," We predict that at still fainter X-ray flux limits, we will find substantially more of the faint optical counterparts, but few additional members of the resolved brighter population."
+ In conclusion. we note that theseLEST observations cover only some 7.5% of the 300 ksec CDES area (Tozzi et al.," In conclusion, we note that these observations cover only some $7.5\%$ of the full-depth 300 ksec CDFS area (Tozzi et al."
+ 2001)., 2001).
+ More and deeper observations should be undertaken., More and deeper observations should be undertaken.
+ Our current results suggest that HST/WEPC?2 or ACS exposures of the CDFS ab qrc24—25 mag 7 can easily resolve the optical counterparts of many more of the Chandra sources in our fainter population., Our current results suggest that /WFPC2 or ACS exposures of the CDFS at $\mu_I\sim24-25$ mag $^{-2}$ can easily resolve the optical counterparts of many more of the Chandra sources in our fainter population.
+ This should represent a complete sample of X-ray selected AGN host galaxies ont to 2e2. at or bevond the expected peak in AGN density evolution.," This should represent a complete sample of X-ray selected AGN host galaxies out to $z\sim 2$, at or beyond the expected peak in AGN density evolution."
+ T/NICMOS K-band observations and the eventualSIRTF Great Observatories Origins Deep Survey (GOODS) of this field will provide valuable infrared diagnostics of the AGN vs. starburst contributions. in conjunetion with additional eround-based optical and near-IR spectroscopy.," /NICMOS $K$ -band observations and the eventual Great Observatories Origins Deep Survey (GOODS) of this field will provide valuable infrared diagnostics of the AGN vs. starburst contributions, in conjunction with additional ground-based optical and near-IR spectroscopy."
+ These initial results already demonstrate the ability of(ST. in a relatively modest amount of observing time. to readily detect the host galaxies of distant. low-Iuminositv AGN and to reveal their morphology.," These initial results already demonstrate the ability of, in a relatively modest amount of observing time, to readily detect the host galaxies of distant, low-luminosity AGN and to reveal their morphology."
+ We will present more quantitative morphology results. detecting color gradients and distinguishing unresolved AGN emission [rom the host galaxy enussion. in a lortheoming paper that will include the optical counterparts from the full 940 ksec CDES exposure.," We will present more quantitative morphology results, detecting color gradients and distinguishing unresolved AGN emission from the host galaxy emission, in a forthcoming paper that will include the optical counterparts from the full 940 ksec CDFS exposure."
+ We gratefully acknowledge the award ofLST Directors Discretionary (ime in support ol this project., We gratefully acknowledge the award of Director's Discretionary time in support of this project.
+ We also acknowledge support for this work which was provided by NASA through GO erants GO-08809.01-À and GO-07267.01-A [rom the Space Telescope Science Institute. which is operated bv AURA. Inc.. under NASA Contract5-26555.," We also acknowledge support for this work which was provided by NASA through GO grants GO-08809.01-A and GO-07267.01-A from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA Contract."
+. We thank the referee [or very useful suggestions., We thank the referee for very useful suggestions.
+"The bottom panels of Figure 1. show the change in the average SFR over 3 Gyr lor ve 10/7AZ, and 1072. galaxies with different numbers of particles and. force resolutions.",The bottom panels of Figure \ref{fig:sf} show the change in the average SFR over 3 Gyr for the $10^{10} M_{\odot}$ and $10^{12} M_{\odot}$ galaxies with different numbers of particles and force resolutions.
+" For the simulations. withn the highestn mass resolution.n values ofB e<10cay7/2,5, result inn very V.imilar SFRs."," For the simulations with the highest mass resolution, values of $\epsilon \leq 10^{-2} R_{vir}$ result in very similar SFRs."
+ For simulations with 1000 DM particles or fewer. however. the softening length »egins to alfeet the SFR.," For simulations with 1000 DM particles or fewer, however, the softening length begins to affect the SFR."
+ For these simulations. softening lengths at both extremes result in V.naller SFRs.," For these simulations, softening lengths at both extremes result in smaller SFRs."
+ Large values of e reduce the SF by spreading local density enhancements over -arger volumes., Large values of $\epsilon$ reduce the SF by spreading local density enhancements over larger volumes.
+ While at late times this is not sufficient to limit the amount of SF. during je initial collapse it prevents the formation of a high densitv region in the center of the galaxv.," While at late times this is not sufficient to limit the amount of SF, during the initial collapse it prevents the formation of a high density region in the center of the galaxy."
+" Because of this. about fewer gas particles ave able to reach SF densities in the e—2x107R,;. than in the e22.5x10HR, simulation for both masses of galaxies."," Because of this, about fewer gas particles are able to reach SF densities in the $\epsilon = 2 \times 10^{-2} R_{vir}$ than in the $\epsilon = 2.5 \times 10^{-3} R_{vir}$ simulation for both masses of galaxies."
+ Small values of e. in contrast. are known to result in greater two-body heating (?)..," Small values of $\epsilon$, in contrast, are known to result in greater two-body heating \citep{Steinmetz97}."
+ In our low mass resolution simulations (1000 DM particle or less) this has the effect of heating the gas ancl lowering the density such that fewer particles are capable of forming stars., In our low mass resolution simulations (1000 DM particle or less) this has the effect of heating the gas and lowering the density such that fewer particles are capable of forming stars.
+" As the softening leneths decrease from 107 to 2.5xLO12,4. the fraction of gas that has sufficiently low temperature and high density to form stars alter 3 Gvrs decreases from to in the 107M. galaxy and from to in the 10A. galaxy."," As the softening lengths decrease from $10^{-2}$ to $2.5\times 10^{-4} R_{vir}$, the fraction of gas that has sufficiently low temperature and high density to form stars after 3 Gyrs decreases from to in the $10^{12} M_{\odot}$ galaxy and from to in the $10^{10} M_{\odot}$ galaxy."
+ The global SFR of our simulated galaxies begins to converge for simulations with more than 10 DM particles and for softening lengths smaller than 2.5x10πι., The global SFR of our simulated galaxies begins to converge for simulations with more than $10^4$ DM particles and for softening lengths smaller than $2.5 \times 10^{-3} R_{vir}$.
+ Star Formation histories (SEIIs) show the changes in the global SEI as the galaxy evolves and examining them gives us an idea of the global SFR on small time seales., Star formation histories (SFHs) show the changes in the global SFR as the galaxy evolves and examining them gives us an idea of the global SFR on small time scales.
+ These may be observationally determined through stellar populations svnthesis modeling (?) and are important for establishing the history of a galaxy. and relating the SF to other process such as mergers. gas infall. disk instabilities. ancl stellar feedback.," These may be observationally determined through stellar populations synthesis modeling \citep{Bruzal03} and are important for establishing the history of a galaxy and relating the SF to other process such as mergers, gas infall, disk instabilities, and stellar feedback."
+" In our analvsis. we calculate the global SER for every 5xLO"" vears and normalize bv the initial barvonic mass."," In our analysis, we calculate the global SFR for every $5 \times 10^7$ years and normalize by the initial baryonic mass."
+ Figure 2 shows both the effect of mass and Iorce resolution on ΘΕΣ for the 107M. and the LOMAM. galaxies., Figure \ref{fig:sfrhist} shows both the effect of mass and force resolution on SFHs for the $10^{12} M_{\odot}$ and the $10^{10} M_{\odot}$ galaxies.
+ For the LOMAL. galaxy. the SFIL converges for simulations with 10! DM particles or more.," For the $10^{12} M_{\odot}$ galaxy, the SFH converges for simulations with $10^4$ DM particles or more."
+ As seen in the cosmological simulations of ?.. in lower mass resolution simulations the initial burst of SF is delaved.," As seen in the cosmological simulations of \citet{Naab07}, in lower mass resolution simulations the initial burst of SF is delayed."
+" SEFIIs of both galaxies converge at a softening length of approximately ε--107,5 ", SFHs of both galaxies converge at a softening length of approximately $\epsilon = 10^{-3} R_{vir}$.
+As was seen with the global SF. larger values of € reduce the SFR. particularly affecting the initial burst of SF because the sudden increase in clensily al the core of the collapsing cloud is ellectively spread over a larger volume and shallower potential.," As was seen with the global SF, larger values of $\epsilon$ reduce the SFR, particularly affecting the initial burst of SF because the sudden increase in density at the core of the collapsing cloud is effectively spread over a larger volume and shallower potential."
+" The 10!M, galaxy is extremely sensitive to changes in mass resolution.", The $10^{10} M_{\odot}$ galaxy is extremely sensitive to changes in mass resolution.
+ The SFL of the 10* DM particle simulation is dramatically different. [vom all of the others and consists of a series of small bursts of SF., The SFH of the $10^3$ DM particle simulation is dramatically different from all of the others and consists of a series of small bursts of SF.
+ The 10 and 10? DM particle simulations both show a sustained burst of SF of approximately (he same strength but offset in (ime by approximately 1.5 ο, The $10^4$ and $10^5$ DM particle simulations both show a sustained burst of SF of approximately the same strength but offset in time by approximately 1.5 Gyrs.
+ Increasing the resolution [rom 10? to LO® DAL particles decreases the strength of the, Increasing the resolution from $10^5$ to $10^6$ DM particles decreases the strength of the
+In the present very. brief letter we present lwo simple lor observations and analyses that. while not easv. could be used to identify (he dominant (in terms of its contribution to the Ha rate) class of progenitors.,"In the present very brief letter we present two simple for observations and analyses that, while not easy, could be used to identify the dominant (in terms of its contribution to the Ia rate) class of progenitors."
+ There is little doubt that most Ha represent thermonuclear disruptions of mass- Carbon-Oxvgen (CO) white dwarls (WDs). when these white chwarls reach the Chandrasekhar limit ancl ignite carbon at their centers (see. e.g.. Livio 2000. for a detailed discussion).," There is little doubt that most Ia represent thermonuclear disruptions of mass-accreting Carbon-Oxygen (CO) white dwarfs (WDs), when these white dwarfs reach the Chandrasekhar limit and ignite carbon at their centers (see, e.g., Livio 2000, for a detailed discussion)."
+ This model is generally accepted even though many of the details of (he process are not fully understood. with one major uncertainty concerning the flame propagation itsell. and in particular the transition Irom subsonic dellagration to supersonic detonation (see. e.g.. IHóofflich et 22010 for a recent discussion).," This model is generally accepted even though many of the details of the process are not fully understood, with one major uncertainty concerning the flame propagation itself, and in particular the transition from subsonic deflagration to supersonic detonation (see, e.g., Höfflich et 2010 for a recent discussion)."
+ There are (wo scenarios (hat have been traditionally identified for the progenitor svstenis (and cliscussed for almost four decades)., There are two scenarios that have been traditionally identified for the progenitor systems (and discussed for almost four decades).
+ In (he single-degenerate (SD) scenario. a CO WD accretes hvdrogen-rieh or helium-rich malerial [rom a main-sequence. subgiant. or eiut companion al a steady rate (hat. allows for the WD to grow in mass (e.g.. Whelen Iben 1973: Nomoto 1982).," In the single-degenerate (SD) scenario, a CO WD accretes hydrogen-rich or helium-rich material from a main-sequence, subgiant, or giant companion at a steady rate that allows for the WD to grow in mass (e.g., Whelen Iben 1973; Nomoto 1982)."
+ The explosion occurs when carbon ignites. as (he mass of the accreting white dwarf approaches the Chnandrasekhar limit.," The explosion occurs when carbon ignites, as the mass of the accreting white dwarf approaches the Chandrasekhar limit."
+ Potential progenitor svstems of (his (wpe include. for instance. the supersoft x-ray sources and recurrent novae. assuming (hat the WDs in these svstems are not of O-Ne composition.," Potential progenitor systems of this type include, for instance, the supersoft x-ray sources and recurrent novae, assuming that the WDs in these systems are not of O-Ne composition."
+ One of (he main strengths of the SD scenario is the fact that. in principle al least. one could get two populations in terms of time delays (as appears to be observed. e.g. Ilowel et 22007): relatively. prompt explosions (aaa:z200 Myr) could result. from the WDs accreting Lom voung main-sequence companions. while late ones (/quq2 3 Gyr) from the WDs accreting from low-mass red giants.," One of the main strengths of the SD scenario is the fact that, in principle at least, one could get two populations in terms of time delays (as appears to be observed, e.g., Howel et 2007): relatively prompt explosions $t_\mathrm{delay} \lea 200$ Myr) could result from the WDs accreting from young main-sequence companions, while late ones $t_\mathrm{delay}\sim2$ –3 Gyr) from the WDs accreting from low-mass red giants."
+ The fact that itis apparently very difficult to detect (he hydrogen [rom the non-degenerate component remains a major stumbling block for a definitive confirmation of the SD scenario., The fact that it is apparently very difficult to detect the hydrogen from the non-degenerate component remains a major stumbling block for a definitive confirmation of the SD scenario.
+ In the double-degenerate (DD) scenario. (wo CO WDs in a binary svstem are brought," In the double-degenerate (DD) scenario, two CO WDs in a binary system are brought"
+C-configuration observations were presented in Paper I. The observatious were obtained at LO frequencies of 228.1 Cz (A=1.3 nuu) ane 106.2 CIIz (A=2.85 nuu),C-configuration observations were presented in Paper I. The observations were obtained at LO frequencies of 228.1 GHz $\lambda=1.3$ mm) and 106.2 GHz $\lambda=2.8$ mm).
+ The CARMA ««urelator at the time of the observations contained three bands. cach of which was configured to 168 AIIz bandwidth to provide maxima contiuuun sensitivity.," The CARMA correlator at the time of the observations contained three bands, each of which was configured to 468 MHz bandwidth to provide maximum continuum sensitivity."
+ The baud pass shape was calibrated by observing 3C'273: fux calibration was set by observing Uranus and 3C81., The band pass shape was calibrated by observing 3C273; flux calibration was set by observing Uranus and 3C84.
+ The radio galaxy 3CLLL was observed every 9 minutes f) correct for atinospheric aud iustimuental effects., The radio galaxy 3C111 was observed every 9 minutes to correct for atmospheric and instrumental effects.
+ Variations of the atmospheric conditious on time scales shorter than 9 utes are nof οςerected. ii effect resulting iu seenig.," Variations of the atmospheric conditions on time scales shorter than 9 minutes are not corrected, in effect resulting in seeing."
+ We quauti&ed the atinosphieric seeing by imeasuring the size of the phase calibrator tuage: if tlic|o ΝΟΜΟ 19 neeheible the phase calibrator appears as a poiut source., We quantified the atmospheric seeing by measuring the size of the phase calibrator image; if the seeing is negligible the phase calibrator appears as a point source.
+ Otherwise. the secing produces a Cassia πλουΠιο that can becuautified through the full width half mmaxinnun (FWIIMD) of the resulting Huage.," Otherwise, the seeing produces a Gaussian smoothing that can be quantified through the full width half maximum (FWHM) of the resulting image."
+ We find that at 15 un the effect of sccing is neeligible for RY Tau but produce sa FWIIM of ffor DG Tau., We find that at 1.3 mm the effect of seeing is negligible for RY Tau but produces a FWHM of for DG Tau.
+" Atmospheric couditious were slightly worse duriug the 2.8 nun observations. resulting in seeing of 0.07"" for both objects."," Atmospheric conditions were slightly worse during the 2.8 mm observations, resulting in seeing of $\arcsec$ for both objects."
+ These secing estimates do not account for variatlous in the atinospheric conditions on augular scales of corresponding to the separation between the source and the calibrator.," These seeing estimates do not account for variations in the atmospheric conditions on angular scales of, corresponding to the separation between the source and the calibrator."
+ Values forthe atiiosplieric seeing are sununnuarized in Table 1 anc are adopted in the model fitting described in Section. 1., Values for the atmospheric seeing are summarized in Table \ref{tab:obs} and are adopted in the model fitting described in Section \ref{sec:mod}.
+ The raw data were reduced using he MIRIAD software package., The raw data were reduced using the MIRIAD software package.
+ The maps of the cout cnussion shown in Figure 1 were αςYived use CULDAS software., The maps of the continuum emission shown in Figure \ref{fig:cont} were derived using GILDAS software.
+ Corresponding complex visibilities are shown iu Fieure 2.., Corresponding complex visibilities are shown in Figure \ref{fig:uvamp}.
+" At 1.3 lulu. natural weighting of the A. D and € οnfiguration observations produced a FWIIM svuthesized boeunun size of ~0.15""."," At 1.3 mm, natural weighting of the A, B and C configuration observations produced a FWHM synthesized beam size of $\sim$."
+ The nolse levels are 0.96 niJv/beam and 0.90 1Jv/beam respectively for DC Tau aud RY Tau., The noise levels are 0.96 mJy/beam and 0.90 mJy/beam respectively for DG Tau and RY Tau.
+ Dust cussion at 2.5 nua was observed in the A and D configurations at aueular resolution of  aand nolse levels of 0.15 ινρου aud 0.28 uyfbeam for DO Tau aud RY Taurespectively., Dust emission at 2.8 mm was observed in the A and B configurations at angular resolution of $\sim$ and noise levels of 0.45 mJy/beam and 0.28 mJy/beam for DG Tau and RY Tau respectively.
+ Iu Figue 1.. he dust emission in both disks is clearly resolved aud characterized by a smooth and ceutrally svuumetric radial profile.," In Figure \ref{fig:cont}, the dust emission in both disks is clearly resolved and characterized by a smooth and centrally symmetric radial profile."
+ DC Tau intensity contours are almost circular sugeesting a disk inclination smaller than307., DG Tau intensity contours are almost circular suggesting a disk inclination smaller than.
+. For RY Tau. the intensity contours are elongated in the North-East direction suggesting a disk position augle of about nuueasured East from North aud a disk inclination of at least657.," For RY Tau, the intensity contours are elongated in the North-East direction suggesting a disk position angle of about measured East from North and a disk inclination of at least."
+. For both sources the disk orientations aeree with those found in Paper I. The 1.3 nuu dust continua emission from the RY Tau disk shows two spatially resolved peaks separated by about 0.27(28 AU). and oriented along the ap]arent major axis of the disk.," For both sources the disk orientations agree with those found in Paper I. The 1.3 mm dust continuum emission from the RY Tau disk shows two spatially resolved peaks separated by about (28 AU), and oriented along the apparent major axis of the disk."
+ Details of the ceutra «0. rreelon are «lisplaved iu the imset iu the upper oft panel of Figure l.. aud the radial profile of he surface ¢eusitv along the disk major axis is shown in Figure 3..," Details of the central $\times$ region are displayed in the inset in the upper left panel of Figure \ref{fig:cont}, and the radial profile of the surface density along the disk major axis is shown in Figure \ref{fig:radialprofile}."
+ The intensity at both peaks is 29 uJv/beiuu. which is 2 11Jv/beii (1.0. 2.20) üegher than the intensity at the center of the disk.," The intensity at both peaks is 29 mJy/beam, which is 2 mJy/beam (i.e. $\sigma$ ) higher than the intensity at the center of the disk."
+ We also estimated the expected central surface xiehtuess by fitting a gaussian to the surface xiehtuess distribution at augular distances larger han5, We also estimated the expected central surface brightness by fitting a gaussian to the surface brightness distribution at angular distances larger than.
+"”, The fitted oeaussian is shown as the solid curve iu Figure }3..", The fitted gaussian is shown as the solid curve in Figure \ref{fig:radialprofile}.
+ A eaussian function was chosen since it provides a reasonable parametric represcutation of the dust emission., A gaussian function was chosen since it provides a reasonable parametric representation of the dust emission.
+ Iuterpolatiug this gaussiau fit to the center of the disk suggests an expected central surface brghtuess of 31 wJv/beam. which is lo ligher than the measured value.," Interpolating this gaussian fit to the center of the disk suggests an expected central surface brightness of 31 mJy/beam, which is $\sigma$ higher than the measured value."
+ The significance level of the two iuteusity peaks. the fact that they appear in the map before cleaning. their orientation along the disk major axis. aud the svuunetry with respect to the ceutral star. sugeest that they are real and. therefore. that the dust emission decreases inside an orbital radius of about 11 AU.," The significance level of the two intensity peaks, the fact that they appear in the map before cleaning, their orientation along the disk major axis, and the symmetry with respect to the central star, suggest that they are real and, therefore, that the dust emission decreases inside an orbital radius of about 14 AU."
+" This is analogous to the situation in ""transitional, disks. where the iuuer eaps observed in the dust emission are attributed to dusty depleted inner regions (sec.c.g..Hughesetal.2009:Brownct2008. 2009)."," This is analogous to the situation in ""transitional” disks, where the inner gaps observed in the dust emission are attributed to dusty depleted inner regions \citep[see, e.g.,][]{hu09,b08,b09}."
+. At a first sieht. this interpretation is compatible with RY Taus large near- and nmiddufrared excesses. Which sugeestOO the preseuce of wari dust," At a first sight, this interpretation is incompatible with RY Tau's large near- and mid-infrared excesses, which suggest the presence of warm dust"
+some hvpothetical magnetic field acceleration processes.,some hypothetical magnetic field acceleration processes.
+ The difference in the distribution of the excess of low aud üieher eunergv particles in our scenario arises from higher efficieucies of scattering for low energy particles., The difference in the distribution of the excess of low and higher energy particles in our scenario arises from higher efficiencies of scattering for low energy particles.
+ Our relation of the observed. cosiidc ray auisotropies o the heliotail is also supported by the sideral daily varlatious of galactic cosmic rays observed with the Tsouneb neutron monitors hourlv count during 1977-2000 reported iu Ikarapetvau (2010)., Our relation of the observed cosmic ray anisotropies to the heliotail is also supported by the sideral daily variations of galactic cosmic rays observed with the Tsumeb neutron monitor's hourly count during 1977-2000 reported in Karapetyan (2010).
+ There it was argued hat the observed cosmic ταν excess has holiotail rather han ealactic origin., There it was argued that the observed cosmic ray excess has heliotail rather than galactic origin.
+ No plwsical explanation of the excess was provided there. however.," No physical explanation of the excess was provided there, however."
+ On the contrary. we relate the excess of the cosuic ravs with the acceleration Xxocess induced by magnetic reconnection.," On the contrary, we relate the excess of the cosmic rays with the acceleration process induced by magnetic reconnection."
+ The paper has au exploratory character. as the quantitative description of mechanisms of cosnüc rav acceleration in the reconnection regions are at its παν," The paper has an exploratory character, as the quantitative description of mechanisms of cosmic ray acceleration in the reconnection regions are at its infancy."
+ Uulike shock acceleration. which is the subject of long history (Axford ct al.," Unlike shock acceleration, which is the subject of long history (Axford et al."
+ 1977. Kevinsky 1977. Bell 1975. Dlaudford Ostriker 10978) aud extensive literature (sec CGaisser 1990. Malkov Diamond 2009).," 1977, Krymsky 1977, Bell 1978, Blandford Ostriker 1978) and extensive literature (see Gaisser 1990, Malkov Diamond 2009)."
+ The existing analytical models (de Gouveia dal Pino Lazari 2003. Drake et al.," The existing analytical models (de Gouveia dal Pino Lazarian 2003, Drake et al."
+ 2006. Drake et al.," 2006, Drake et al."
+ 2010) are insutiiciceutly elaborated. while the ummuerical simulations (see Drake et al.," 2010) are insufficiently elaborated, while the numerical simulations (see Drake et al."
+ 2000. Lazgarian et al.," 2010, Lazarian et al."
+ 2010) are rather idealized., 2010) are rather idealized.
+ Nevertherless. the accumulated evidence is suggestive hat the process of the acceleration can be cficicut.," Nevertherless, the accumulated evidence is suggestive that the process of the acceleration can be efficient."
+ We note that dealing with the acceleration of xotons we do not distinguish between the collisiouless reconnection and the LV99 model of recounection., We note that dealing with the acceleration of protons we do not distinguish between the collisionless reconnection and the LV99 model of reconnection.
+ We ecl that. provided that the reconnection regions are hick aud filled with the reconnecting shrinkius loops. he acceleration happens the same way for the two cases.," We feel that, provided that the reconnection regions are thick and filled with the reconnecting shrinking loops, the acceleration happens the same way for the two cases."
+ We. however. claim that the formation of such regious nay be somewhat problematic within the paracligin of collisiouless reconnection.," We, however, claim that the formation of such regions may be somewhat problematic within the paradigm of collisionless reconnection."
+ At the same time. this situation is a clear consequence of the LV99 model. which appeals to the ubiquitous astrophysical turbulence to enpower it.," At the same time, this situation is a clear consequence of the LV99 model, which appeals to the ubiquitous astrophysical turbulence to enpower it."
+ While we accept that the model of acceleration iu the reconnection regions require more study; we would like to stress that the proposed scenario has several attractive catures.," While we accept that the model of acceleration in the reconnection regions require more study, we would like to stress that the proposed scenario has several attractive features."
+ First of all. it allows us to address the issues of coste ray excess over the entire rauge of energies that jese particles were observed.," First of all, it allows us to address the issues of cosmic ray excess over the entire range of energies that these particles were observed."
+ Moreover. the fact that re excess of the particles is observed iu the direction of the magnetotail i suggestive that the processes m uaenetotail are involved.," Moreover, the fact that the excess of the particles is observed in the direction of the magnetotail is suggestive that the processes in magnetotail are involved."
+ In addition. the alternative uechauisuis of producing the excess apparently have sclevident problems. as we discussed in the paper.," In addition, the alternative mechanisms of producing the excess apparently have self-evident problems, as we discussed in the paper."
+ We would ike to stress. that none of the alternative mechanisms xovides a mnifving explanation for the existence of the excess over a range of cucreies reported by differcut eroups (see 82).," We would like to stress, that none of the alternative mechanisms provides a unifying explanation for the existence of the excess over a range of energies reported by different groups (see 2)."
+ In this situation we think that the xoposed mechanisin should be cousidered seriously., In this situation we think that the proposed mechanism should be considered seriously.
+ We argue that the localized excesses: of Cosinic rays in the multi-TeV range and the tail-in excess below he TeV range are related by the same plenomcuoloey., We argue that the localized excesses of cosmic rays in the multi-TeV range and the tail-in excess below the TeV range are related by the same phenomenology.
+ Within our approach the localized regions of the TeV cosmic ravs are related to the sites of acceleration via reconnection., Within our approach the localized regions of the TeV cosmic rays are related to the sites of acceleration via reconnection.
+ The lower euerev particles can be accelerated over extended regions of the maguetotail: they are also expected to experience more scattering prior to reaching the observer at the Earth., The lower energy particles can be accelerated over extended regions of the magnetotail; they are also expected to experience more scattering prior to reaching the observer at the Earth.
+ More elaborate modeling of both cosmic rav acceleration im reconnection regions aud the propagation of cosmic rays in inagnetotail should provide detailed predictions to be compared with observations., More elaborate modeling of both cosmic ray acceleration in reconnection regions and the propagation of cosmic rays in magnetotail should provide detailed predictions to be compared with observations.
+ Our recent approaches to this problem combine the advances in understanding of the statistical structure of MIID turbuleuce. iu particular. tensorial structure of Alfvenic. slow and fast modes (see Cho. Lazarian Vishuiac 2002. Cho Lazarian 2002. 2003. Iowal Lazariau 2010). analytical description of the propagation of cosmic ravs (see Yan Lazarian 2002. 2001. 2008). and testing of analytical predictions nunericallv using uaenetic fields obtained through παΊσα. simulatious (see Beresuvak. Yan Lazari 2010).," Our recent approaches to this problem combine the advances in understanding of the statistical structure of MHD turbulence, in particular, tensorial structure of Alfvenic, slow and fast modes (see Cho, Lazarian Vishniac 2002, Cho Lazarian 2002, 2003, Kowal Lazarian 2010), analytical description of the propagation of cosmic rays (see Yan Lazarian 2002, 2004, 2008), and testing of analytical predictions numerically using magnetic fields obtained through numerical simulations (see Beresnyak, Yan Lazarian 2010)."
+ As we describe above. sumulatious of particle acceleration in turbulent reconnection is under wav.," As we described above, simulations of particle acceleration in turbulent reconnection is under way."
+ Thus we hope to have in uture a selfconsistent umuerically-tested picture of he acceleration and propagation., Thus we hope to have in future a self-consistent numerically-tested picture of the acceleration and propagation.
+ Combined with the advances in snmulations of magnuetotail maguctic fields (see Pogorelov ct al., Combined with the advances in simulations of magnetotail magnetic fields (see Pogorelov et al.
+ 2010) this eives hope that we wil lave a set of quantitative detailed predictions for the cose rav excess arising from the mechanisi describes in the paper., 2010) this gives hope that we will have a set of quantitative detailed predictions for the cosmic ray excess arising from the mechanism described in the paper.
+ Muevical modeling will also clarify the role of he second order Fermi acceleration which arise from. urbuleuce induced both by magnetic reconmection an existing within the iuagnetotail, Numerical modeling will also clarify the role of the second order Fermi acceleration which arise from turbulence induced both by magnetic reconnection and existing within the magnetotail.
+ The corresponding xocesses have been discussed at leugth iu the literature (see La Rosa et al., The corresponding processes have been discussed at length in the literature (see La Rosa et al.
+ 2006. Petrosian et al.," 2006, Petrosian et al."
+ 2006. Yan et al.," 2006, Yan et al."
+ 2008). but we expect the second order Fermi process o be less efficient than the first order Feri acceleration and therefore to be subdominant.," 2008), but we expect the second order Fermi process to be less efficient than the first order Fermi acceleration and therefore to be subdominant."
+ Tn situ measurement of the excess of the cuereectic article acceleration within reconnection regions could ο beneficial as well., In situ measurement of the excess of the energetic particle acceleration within reconnection regions could be beneficial as well.
+ So far. the attempts of 1icasuriug of such an excess were not successful (Cosling et al.," So far, the attempts of measuring of such an excess were not successful (Gosling et al."
+ 2005ab. 2007. Phan et al.," 2005ab, 2007, Phan et al."
+ 2007)., 2007).
+ We believe that this is due to the N-point. Petscheck-type recounnection Is iucfficient in the acceleration of cose (sec ο," We believe that this is due to the X-point, Petscheck-type reconnection is inefficient in the acceleration of cosmic (see LO09)."
+ This type of reconnection was sought iu the studies above., This type of reconnection was sought in the studies above.
+ The mechanisin we discussed above (GGEOS. DNOG) appeals to the thick exteuded recounuectiou regions.," The mechanism we discussed above (GL03, DX06) appeals to the thick extended reconnection regions."
+ Sucli reeions naturally ασ in the maeuetotail as turbuleut magnetic ficlds of oppositeος polarity are being pressed together (see Figure L)., Such regions naturally emerge in the magnetotail as turbulent magnetic fields of opposite polarity are being pressed together (see Figure 4).
+ The QGLO3 acceleration process has been already eniploved in Lazarian Opher (2009. henceforth LO09) to explain the origin of anomalous cosuiüc ravs. whose casurements by Vovagers secu to coutradict to their origin within qmost of the accepted models of shock acceleration.," The GL03 acceleration process has been already employed in Lazarian Opher (2009, henceforth LO09) to explain the origin of anomalous cosmic rays, whose measurements by Voyagers seem to contradict to their origin within most of the accepted models of shock acceleration."
+ A similar conclusion was also obtained iu Drake et al. (, A similar conclusion was also obtained in Drake et al. (
+2010) where the process of collisionless. but reconnection was discussed.,"2010) where the process of collisionless, but reconnection was discussed."
+ Whether snall-scale reconnection is collisionless or collisional docs rot plav a role for LV99 model., Whether small-scale reconnection is collisionless or collisional does not play a role for LV99 model.
+ The testing of this, The testing of this
+with currently used period-Inminosityv relations. it will be necessary to observe several more Cepheids with this technique before worthwhile quantitative comparisons can be made.,"with currently used period-luminosity relations, it will be necessary to observe several more Cepheids with this technique before worthwhile quantitative comparisons can be made."
+ In the near future long-baseline interferometers will provide a great deal of useful data in this area: in addition to further observations of the brightest galactic Cepheids. the very long baselines currently. being commissioned at the Navy Prototype Optical Interferometer (Armstrongetal.200110) and the Center for Ligh Angular Resolution Astronomy array (tenDrumnmelaaretal.2001) will allow direct measurements of the limb darkening effects through observations of Iringe visibilities past (he first visibility null.," In the near future long-baseline interferometers will provide a great deal of useful data in this area: in addition to further observations of the brightest galactic Cepheids, the very long baselines currently being commissioned at the Navy Prototype Optical Interferometer \citep{arm01b} and the Center for High Angular Resolution Astronomy array \citep{theo01} will allow direct measurements of the limb darkening effects through observations of fringe visibilities past the first visibility null."
+ Given the close relation between limb cdarkenine ancl projection factors we expect that. improvements in understanding one will improve our understanding of the other., Given the close relation between limb darkening and projection factors we expect that improvements in understanding one will improve our understanding of the other.
+ It is also clear that additional photometry and radial velocity measurements would be very. useful., It is also clear that additional photometry and radial velocity measurements would be very useful.
+ In particular ¢ Gem suffers [rom a lack ol good infrared photometry. while concerns about level effects make infrared radial velocity nmeasurenientis like those of Sasselov&Lester(1990) very desirable.," In particular $\zeta$ Gem suffers from a lack of good infrared photometry, while concerns about level effects make infrared radial velocity measurements like those of \citet{sasselov90} very desirable."
+ We thank D. Sasselov. A. F. Boden. M. M. Colavita. S. R. Ixulkarni. and ROR. Thompson for valuable comments.," We thank D. Sasselov, A. F. Boden, M. M. Colavita, S. R. Kulkarni, and R.R. Thompson for valuable comments."
+ We also wish to thank Ix. Rvkoski for his excellent observational work., We also wish to thank K. Rykoski for his excellent observational work.
+ Observations with PTI are only made possible through the efforts of the PTI collaboration. for which we are erateful.," Observations with PTI are only made possible through the efforts of the PTI collaboration, for which we are grateful."
+ Funding for the development of PTI was provided by NASA under its TOPS (Toward Other Planetary Systems) ancl ASEPS (Astronomical Studies of Extrasolar Planetary Systems) programs. and from the JPL Directors Discretionary Fund.," Funding for the development of PTI was provided by NASA under its TOPS (Toward Other Planetary Systems) and ASEPS (Astronomical Studies of Extrasolar Planetary Systems) programs, and from the JPL Director's Discretionary Fund."
+ Ongoing funding has been provided bv NASA through its Origins Program and [rom the JPL Directors Research aud Development Fund., Ongoing funding has been provided by NASA through its Origins Program and from the JPL Directors Research and Development Fund.
+ This work has made use of software produced by the Interferometry Science Center al the California Institute of Technology., This work has made use of software produced by the Interferometry Science Center at the California Institute of Technology.
+ This research has made use of the SIAIBAD database. operated al CDS. Strasbourg. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France."
+ D.F.L gratefully acknowledges the support of NASA through the Michelson fellowship program., B.F.L gratefully acknowledges the support of NASA through the Michelson fellowship program.
+"In the low-optical depth simulations, several MMRs stand out as having particularly strong peaks.","In the low-optical depth simulations, several MMRs stand out as having particularly strong peaks."
+" On the left side of Figure 4,, the small grains show a strong peak near the 3:2 MMRs with Saturn (12 AU) and a secondary peak near the 2:1 (16 AU)."," On the left side of Figure \ref{fig:semimajoraxis1}, the small grains show a strong peak near the 3:2 MMRs with Saturn $\sim 12$ AU) and a secondary peak near the 2:1 $16$ AU)."
+ Very few grains of any size make it interior to 10 AU; they are scattered out of the Solar System by Saturn., Very few grains of any size make it interior to 10 AU; they are scattered out of the Solar System by Saturn.
+at slightly later phases for increasing energies. and also the following CR increase ts delayed: moreover. at the ninimum egress the CR increases more suddenly at high energies than at the low ones.,"at slightly later phases for increasing energies, and also the following CR increase is delayed; moreover, at the minimum egress the CR increases more suddenly at high energies than at the low ones."
+ As a consequence. the HR between the hard and soft curves is highly variable in this phase interval: 1t first shows à sharp minimum just after the CR minimum. suddenly followed by a large peak.," As a consequence, the HR between the hard and soft curves is highly variable in this phase interval: it first shows a sharp minimum just after the CR minimum, suddenly followed by a large peak."
+ For the ssource and background spectra. we adopted the same extraction parameters used for the light curves: we generated the applicable response matrices and ancillary files using the tasks andazZgen.," For the source and background spectra, we adopted the same extraction parameters used for the light curves; we generated the applicable response matrices and ancillary files using the tasks and."
+. We considered also the ddata. using the source and background spectra and the response matrices obtained with the standard reduction pipeline.," We considered also the data, using the source and background spectra and the response matrices obtained with the standard reduction pipeline."
+ In order to ensure the applicability of the X? statistics. the aand sspectra were rebinned with a minimum of 100 and 30 counts per bin. respectively: then they were fitted in the energy range 0.3-12 keV using 12.4.0.," In order to ensure the applicability of the $\chi^{2}$ statistics, the and spectra were rebinned with a minimum of 100 and 30 counts per bin, respectively; then they were fitted in the energy range 0.3–12 keV using 12.4.0."
+ In the following. all spectral uncertainties and upper limits are given at 90 confidence level for one interesting parameter. and we assume a source distance of 3.3 kpe.," In the following, all spectral uncertainties and upper limits are given at 90 confidence level for one interesting parameter, and we assume a source distance of 3.3 kpc."
+ After checking that separate fits of the three ccameras gave consistent results. we fitted them simultaneously to increase the statistics: then we checked that both sspectra were consistent with the oones. therefore we included also them in the spectral analysis: to this aim. we introduced relative normalization factors among the spectra of the five cameras.," After checking that separate fits of the three cameras gave consistent results, we fitted them simultaneously to increase the statistics; then we checked that both spectra were consistent with the ones, therefore we included also them in the spectral analysis; to this aim, we introduced relative normalization factors among the spectra of the five cameras."
+ Using an absorbed power-law (PL)) model. we obtained a hydrogen column density ;/Vjj=(1.1920.02)«1022 ? and a photon-index P = 1.164-0.01. with 4Z/d.o.f.," Using an absorbed power–law ) model, we obtained a hydrogen column density $N_{\rm H} = (1.19\pm0.02)\times 10^{22}$ $^{-2}$ and a photon–index $\Gamma$ = $\pm$ 0.01, with $\chi^{2}_{\nu}$ /d.o.f."
+ = 2.097/1083., = 2.097/1083.
+ Using an absorbed blackbody (BB)) model. we obtained Njj=(3.3340.0.9)«10?! ? a temperature ADpp=1.58+0.01 keV. and a radius Rey=30643 m. with \2/d.o.f.," Using an absorbed blackbody ) model, we obtained $N_{\rm H} = (3.33\pm0.0.9)\times 10^{21}$ $^{-2}$ , a temperature $kT_{\rm BB} = 1.58 \pm 0.01$ keV, and a radius $R_{\rm BB} = 306 \pm 3$ m, with $\chi^{2}_{\nu}$ /d.o.f."
+ = 2.604/1083., = 2.604/1083.
+ In both cases the fits of the spectrum were unacceptable. with large residuals. so we repeated the fit with a model.," In both cases the fits of the spectrum were unacceptable, with large residuals, so we repeated the fit with a model."
+ In this way we obtained a significant improvement (Fig. 4)).," In this way we obtained a significant improvement (Fig. \ref{all_spetrum_powbb}) ),"
+ with \2/d.o.f = 1.105/1081., with $\chi^{2}_{\nu}$ /d.o.f = 1.105/1081.
+" The corresponding best- parameters are Nj=(7.330.1)x1074 2, DP = 0.85 + 0.07. and &Tpp = 1.34 + 0.04 keV. The normalization is Ipj,=(840.2)«10? phem ?! Lat 1 keV and the radius Rpp = 273 x 16 m. The absorbed flux in"," The corresponding best--fit parameters are $N_{\rm H} = (7.3\pm0.4) \times 10^{21}$ $^{-2}$, $\Gamma$ = 0.85 $\pm$ 0.07, and $kT_{\rm BB}$ = 1.34 $\pm$ 0.04 keV. The normalization is $I_{\rm PL} = (1.8 \pm 0.2)\times10^{-3}$ ph $^{-2}$$^{-1}$ $^{-1}$ at 1 keV and the radius $R_{\rm BB}$ = 273 $\pm$ 16 m. The absorbed flux in"
+The Cassini spacecraft gives us the unique opportunity to have accurate set of geodetic data for icy satellites of Saturn as for example. the shape. the gravitational field. the rotational data (Thomas.2010).,"The Cassini spacecraft gives us the unique opportunity to have accurate set of geodetic data for icy satellites of Saturn as for example, the shape, the gravitational field, the rotational data \citep{t10}."
+. The flybys of Mimas have provided high resolution images of the surface in the finest detail yet seen (Roatschetal..2009)., The flybys of Mimas have provided high resolution images of the surface in the finest detail yet seen \citep{rwhkmswdnhp09}.
+. Cassini spacecraft has detected temperature inhomogeneities (Howettetal..2011). usually attributed to exogenic process.," Cassini spacecraft has detected temperature inhomogeneities \citep{hssjphvs11}, usually attributed to exogenic process."
+ The theoretical model of Mimas rotational state can be used to interpret the Cassini data and to better understand its interior and evolution., The theoretical model of Mimas rotational state can be used to interpret the Cassini data and to better understand its interior and evolution.
+ Like for our Moon. Mimas is in synchronous rotation and shows almost the same face towards Saturn.," Like for our Moon, Mimas is in synchronous rotation and shows almost the same face towards Saturn."
+ Moreover. it is considered to have a large librational amplitude (Comstock&Bills. 2003).," Moreover, it is considered to have a large librational amplitude \citep{cb03}."
+. The rotational state of à synchronous body depends on the distribution of mass of the body. and therefore it is à signature of its internal structure.," The rotational state of a synchronous body depends on the distribution of mass of the body, and therefore it is a signature of its internal structure."
+ Here. we propose to model the rotation of Mimas considering it as a rigid body.," Here, we propose to model the rotation of Mimas considering it as a rigid body."
+ A highly rigid interior of Mimas for most of its history ts consistent with its un-relaxed shape (Thomasetal..Thomas. 2010).," A highly rigid interior of Mimas for most of its history is consistent with its un-relaxed shape \citep{tbhsvptmdgrjj07,t10}."
+. Since the distant spacecraft flybys of Mimas do not allow the determination of the GM nor the gravity harmonies. the mass of Mimas is determined from an analysis of its orbital resonances with Tethys and Methone (Jacobsonetal.. 2006).," Since the distant spacecraft flybys of Mimas do not allow the determination of the GM nor the gravity harmonics, the mass of Mimas is determined from an analysis of its orbital resonances with Tethys and Methone \citep{jabcijmpors06}."
+. Moreover. its internal structure remains uncertain.," Moreover, its internal structure remains uncertain."
+ The mean density of 1.15 & Cnr suggests that Mimas is made of homogenous mixture of ice and rocks., The mean density of $1.15$ $g$ $cm^{-3}$ suggests that Mimas is made of homogenous mixture of ice and rocks.
+ The observed shape of Mimas by Voyager has been interpreted. as an indication of interior mass concentration which can be either due to internal differentiation (Dermott&Thomas.1988) or radially variable porosity (Eluszkiewiez.1990)., The observed shape of Mimas by Voyager has been interpreted as an indication of interior mass concentration which can be either due to internal differentiation \citep{dt88} or radially variable porosity \citep{e90}.
+. However. Cassini observations showed that Mimas? shape. although a triaxial ellipsoid. is departed slightly from hydrostatic shape and therefore interpreting the interior configuration from the shape is limited (ThomasetaL.2007:Thomas.2010).," However, Cassini observations showed that Mimas' shape, although a triaxial ellipsoid, is departed slightly from hydrostatic shape and therefore interpreting the interior configuration from the shape is limited \citep{tbhsvptmdgrjj07,t10}."
+.. In the present study. we consider Mimas to be composed of two rigid layers.," In the present study, we consider Mimas to be composed of two rigid layers."
+ We consider both hydrostatic and non-hydrostatic interior models., We consider both hydrostatic and non-hydrostatic interior models.
+ The interior models considering compaction of ice-silica particle mixtures (Yasui&Arakawa.2009). are expected to yield realistic principal moment of inertia A«B<C (Eluszkiewiez.1990)., The interior models considering compaction of ice-silica particle mixtures \citep{ya09} are expected to yield realistic principal moment of inertia $A<B<C$ \citep{e90}.
+. Since Mimas orbits close to its parent planet. the present-day diurnal tidal stresses can be important. and we took the tidal effects into account as well.," Since Mimas orbits close to its parent planet, the present-day diurnal tidal stresses can be important, and we took the tidal effects into account as well."
+ The paper is structured as follows: we first model the internal. structure of Mimas. in considering two different assumptions: that Mimas ts in hydrostatic equilibrium. and that its ellipsoid of gravity 1s proportional to its ellipsoid of shape.," The paper is structured as follows: we first model the internal structure of Mimas, in considering two different assumptions: that Mimas is in hydrostatic equilibrium, and that its ellipsoid of gravity is proportional to its ellipsoid of shape."
+ From these two assumptions we derive 23 models of Mimas., From these two assumptions we derive 23 models of Mimas.
+ Then we perform numerical integrations of the rotation of these “Mimasses” im a full 3-degree of freedom conservative models.," Then we perform numerical integrations of the rotation of these ""Mimasses"" in a full 3-degree of freedom conservative models."
+ Finally. we check the influence of the tides on the equilibrium orientation of Mimas? long axis.," Finally, we check the influence of the tides on the equilibrium orientation of Mimas' long axis."
+ Interior structure models of planets and natural satellites are in general non-unique due to the presence of fewer constraints than unknowns., Interior structure models of planets and natural satellites are in general non-unique due to the presence of fewer constraints than unknowns.
+ For Mimas we have only two constraints: the mean radius R and the mean densityp. or the Mass zi (Tab. 1)).," For Mimas we have only two constraints: the mean radius $R$ and the mean density $\rho$, or the Mass $m$ \ref{tab:propmim}) )."
+ In this study where we deal with the rotation. the moment of inertia differences are the main point of interest.," In this study where we deal with the rotation, the moment of inertia differences are the main point of interest."
+ Because we have only few constraints. we prefer to have as simple interior structure models as possible.," Because we have only few constraints, we prefer to have as simple interior structure models as possible."
+ We assume a two-layer interior structure model with a rocky. core and icy mantle., We assume a two-layer interior structure model with a rocky core and icy mantle.
+ The models with variable porosity supported by recent compaction experiments (Yasut&Arakawa.2009).. yleld realistic moments of inertia (Eluszkiewiez.1990).," The models with variable porosity supported by recent compaction experiments \citep{ya09}, yield realistic moments of inertia \citep{e90}."
+. The mean density of Mimas ts close to the density of water ice and the interior is consistent with an icy mantle and small rocky core. alternatively Mimas can be homogenous with a variable or constant porosity.," The mean density of Mimas is close to the density of water ice and the interior is consistent with an icy mantle and small rocky core, alternatively Mimas can be homogenous with a variable or constant porosity."
+ With Mimas* figure departed from hydrostatic shape (Thomasetal.2007:Thomas.2010) and without the knowledge of Ca.and ος. we do not know the moment of inertia differences.," With Mimas' figure departed from hydrostatic shape \citep{tbhsvptmdgrjj07,t10} and without the knowledge of $C_{22}$and $J_2$ , we do not know the moment of inertia differences."
+ As it is the case for the Moon (see e.g., As it is the case for the Moon (see e.g.
+incorrectly. with the correct values for the correlation length being upto 25 per cent higher in some places.,"incorrectly, with the correct values for the correlation length being up to 25 per cent higher in some places."
+ To summarize. there is clear evidence that the MW. formula significantly. overestimates the expected. bias of the rarest’ halos. while the SMT model gives extremely good agreement.," To summarize, there is clear evidence that the MW formula significantly overestimates the expected bias of the rarest halos, while the SMT model gives extremely good agreement."
+ ] now make use of the SAPP model το compare the predictions of a range of cosmologies with observational data., I now make use of the SMT model to compare the predictions of a range of cosmologies with observational data.
+ Fig., Fig.
+ 2. shows the ryd relation for the APM cluster survey. as analyzed by Croft et (1997 - hereafter C97) and Lee Park (1998 - hereafter LPO98).," \ref{fig-data} shows the $r_0-d$ relation for the APM cluster survey, as analyzed by Croft et \markcite{C97} (1997 - hereafter C97) and Lee \markcite{LP}
+ (1998 - hereafter LP98)."
+ Although this is only a small fraction of currently available cata on the cluster. correlation length. it sullices to illustrate the wide degree of systematic uncertainty which exists in present observations — even two analyses of the same dataset give. results that. ciller by considerable. factors. and the situation is even less clear when results [roni Abell (see. for instance Baheall Cen 1992) and X-ray (sce LP99 for a etailed: discussion) cluster samples. are included.," Although this is only a small fraction of currently available data on the cluster correlation length, it suffices to illustrate the wide degree of systematic uncertainty which exists in present observations – even two analyses of the same dataset give results that differ by considerable factors, and the situation is even less clear when results from Abell (see for instance Bahcall Cen 1992) and X-ray (see LP99 for a detailed discussion) cluster samples are included."
+ Although present clay uncertainties are large. errors in ro will be ereathy reduced. by future. surveys.," Although present day uncertainties are large, errors in $r_0$ will be greatly reduced by future surveys."
+ The Sloan Digital Sky Survey (SDSS. see project book at http:/www.astro.princeton.edu/PBOOIl/welcome.htm for detailed specifications) is expected to identify roughly 1000 nearby clusters in its spectroscopic galaxy redshift: survey. and even more in its photometric survey.," The Sloan Digital Sky Survey (SDSS, see project book at http://www.astro.princeton.edu/PBOOK/welcome.htm for detailed specifications) is expected to identify roughly 1000 nearby clusters in its spectroscopic galaxy redshift survey, and even more in its photometric survey."
+ Phe inclusion of redshift information in the cluster identification procedure will greatly reduce svstematic uncertainties in ry. and statistical uncertainties will be reduced by approximately 50 per cent by the increased. sample size.," The inclusion of redshift information in the cluster identification procedure will greatly reduce systematic uncertainties in $r_0$, and statistical uncertainties will be reduced by approximately 50 per cent by the increased sample size."
+ In order to illustrate the type of results we can hope for. E will carry out the bull of my analysis using just the COT data.," In order to illustrate the type of results we can hope for, I will carry out the bulk of my analysis using just the C97 data."
+ This data is at least self-consistent. and 26e confidence limits for the SDSS survey should be similar in size to Le confidence limits from the C97 analysis.," This data is at least self-consistent, and $\sigma$ confidence limits for the SDSS survey should be similar in size to $\sigma$ confidence limits from the C97 analysis."
+ ] compute confidence limits [or various models. as follows: Each model gives a specific prediction for the for the ryd relation. given which the of observing a particular dataset is (up toa constant of proportionality)," I compute confidence limits for various models as follows: Each model gives a specific prediction for the for the $r_0-d$ relation, given which the of observing a particular dataset is (up to a constant of proportionality)"
+of the beam on one haud. aud scoping it as low as possible to minimize the single pion background aud better match the CP odd terms ou the other haud.,"of the beam on one hand, and keeping it as low as possible to minimize the single pion background and better match the $\cal{CP}$ odd terms on the other hand."
+ The signal correspouds to the untons produced by 74 charged-current eveuts in water. mainly via quasi-clastic iteractions at these energies.," The signal corresponds to the muons produced by $\nu_{\mu}$ charged-current events in water, mainly via quasi-elastic interactions at these energies."
+ Such events are selected by requiring a sinele-ving event. with the same identification algoritlinρα used by the Super-ISiuuiokaude experiment. aud by the detection of the electron from the mmon decay;," Such events are selected by requiring a single-ring event, with the same identification algorithms used by the Super-Kamiokande experiment, and by the detection of the electron from the muon decay."
+ At such οjergies the energv resolution is very poor due to the Fermi motion aud ot ermclear effects., At such energies the energy resolution is very poor due to the Fermi motion and other nuclear effects.
+ For these reasons. a CP violation search with 4=609100 is based on a couuting experiment only.," For these reasons, a $\cal{CP}$ violation search with $\gamma=60-100$ is based on a counting experiment only."
+ The beta-beam has no iutrinsic backerounds.C» contrary to conventional sources.," The beta-beam has no intrinsic backgrounds, contrary to conventional sources."
+ Ilowever. inefficieicies in particle identification. such as sinele-pion productiou in neural-current τὰ. (02) iuteractions. electrons (positrons) muisidentified as ΗΠΙΟΙΙΣ. as well as external sources. like atinosplieric neutro mteractions. ca xoduce backerotuds.," However, inefficiencies in particle identification, such as single-pion production in neutral-current $\nu_e$ $\bar{\nu}_e$ ) interactions, electrons (positrons) misidentified as muons, as well as external sources, like atmospheric neutrino interactions, can produce backgrounds."
+ The backeround comine frou suele pion production las a tweshold at about 150 MeV. therefore giviue uo contribution for >«55.," The background coming from single pion production has a threshold at about 450 MeV, therefore giving no contribution for $\gamma < 55$."
+ Standard algorithus for particle identification iu watey Ceereukov detectors are quite efficient iu suppressing the fake signa COMME roni electrons (positroux) uilsidenutifed as nmons., Standard algorithms for particle identification in water Čeerenkov detectors are quite efficient in suppressing the fake signal coming from electrons (positrons) misidentified as muons.
+ Concerning the atmospheric ueutrino interactions. estimated oO heo about 507stou/vr. this iniportaut heickerou is reduced to 1 event/E10 ston/vr by requiring a time bunch length or the 1οi of LO ns.," Concerning the atmospheric neutrino interactions, estimated to be of about 50/kton/yr, this important background is reduced to 1 event/440 kton/yr by requiring a time bunch length for the ions of 10 ns."
+ The expected events from [26] ave shown in Table 1.. as an exaltale.," The expected events from \cite{maur05} are shown in Table \ref{t:events}, as an example."
+ The discovery potential is analvzed in [0.2530]..," The discovery potential is analyzed in \cite{zucchelli,maur03,maur05,bur05,gugl05,cam06,ber05}."
+ A detailed study of option is made for example in [29] based oji the GLOBES software [12].. inchiding correlations aud degeueracies aud 1sing atmospheric data im the analysis [33]..," A detailed study of $\gamma=100$ option is made for example in \cite{cam06}
+ based on the GLoBES software \cite{hub05}, including correlations and degeneracies and using atmospheric data in the analysis \cite{hub06}."
+ The fluxes are shown in Figure L.., The fluxes are shown in Figure \ref{fig:fluxst}.
+ Figure 2. shows the CP discovery reach as an example of the scusitivity that can be reached ruunuiug the ious around 5= 100., Figure \ref{fig:CP} shows the $\cal{CP}$ discovery reach as an example of the sensitivity that can be reached running the ions around $\gamma=100$ .
+"The initial mass of the core. M.. is 0.1Ma and the core density. py. is 3.2gem,","The initial mass of the core, $M_\mathrm{c}$, is $0.1 \; \mathrm{M_{\oplus}}$ and the core density, $\rho_\mathrm{c}$, is $3.2 \; \mathrm{g \; cm^{-3}}$."
+ The resulting core and envelope mass evolution of our run is depicted in Fig. 2..," The resulting core and envelope mass evolution of our run is depicted in Fig. \ref{j3m},"
+ which shoulc be compared with Fig., which should be compared with Fig.
+ 2b of Pollack et al. (19960)., 2b of Pollack et al. \cite{pollack}) ).
+ We use the same mass range in the Y axis to favour the comparison. although the run was completed successfully to the end. that is. until the total mass of the planet. M. is that of Jupiter (318 Ma).," We use the same mass range in the Y axis to favour the comparison, although the run was completed successfully to the end, that is, until the total mass of the planet, $M$, is that of Jupiter $318 \; \mathrm{M_{\oplus}}$ )."
+ From Fig., From Fig.
+ 2 it can. be seen that in our caleulation it takes 19 My for the mass of the envelope to equal the mass of the core. while in Pollack et al. (1996))," \ref{j3m} it can be seen that in our calculation it takes 19 My for the mass of the envelope to equal the mass of the core, while in Pollack et al. \cite{pollack}) )"
+ the cross-over point (M.= Ma) is reached in only 1.5] My., the cross–over point $M_\mathrm{c}=M_\mathrm{env}$ ) is reached in only 1.51 My.
+ As ts immediately obvious. the time difference between both calculations is of approximately one order of magnitude.," As is immediately obvious, the time difference between both calculations is of approximately one order of magnitude."
+ This 1s a significant difference if we keep in mind that the estimated lifetime of the solar nebula is less than 10 My., This is a significant difference if we keep in mind that the estimated lifetime of the solar nebula is less than 10 My.
+ However. it is worth pointing out that the cross-over mass in both simulations is almost the same (29 Μ..).," However, it is worth pointing out that the cross–over mass in both simulations is almost the same $\sim 29$ $\mathrm
+{M_{\oplus}}$ )."
+ For the sake of completeness. we mention that the whole formation time is 20.6 My and the final mass of the core is 42 Ma.," For the sake of completeness, we mention that the whole formation time is 20.6 My and the final mass of the core is $42$ $\mathrm{M_{\oplus}}$."
+ From the comparison of both figures. it can also be seen that we do not find three phases in the formation of the planet as Pollack et al. (1996))," From the comparison of both figures, it can also be seen that we do not find three phases in the formation of the planet as Pollack et al. \cite{pollack}) )"
+ found in their simulations., found in their simulations.
+" The slow growth of the core guarantees a smooth variation of the slope of the M, curve.", The slow growth of the core guarantees a smooth variation of the slope of the $M_\mathrm{c}$ curve.
+ No different growth regimes in the mass of the core or in the mass of the envelope can be distinguished before the runaway growth of the envelope., No different growth regimes in the mass of the core or in the mass of the envelope can be distinguished before the runaway growth of the envelope.
+ Moreover. in Fig.," Moreover, in Fig."
+ 3 we show in a logarithmic scale. the solids and the gas aceretion rate.," \ref{j3mdot} we show in a logarithmic scale, the solids and the gas accretion rate."
+ Pollack et al. (1996)), Pollack et al. \cite{pollack}) )
+" obtained a different behaviour of the accretion rates which allowed them to define a short phase | in the growth of the protoplanet which ends when dM,/dt=dM /dt. and a longer phase 2 which ends when M,=Mj."," obtained a different behaviour of the accretion rates which allowed them to define a short phase 1 in the growth of the protoplanet which ends when $dM_\mathrm{c}/dt = dM_\mathrm{env}/dt$ , and a longer phase 2 which ends when $M_\mathrm{c}=M_\mathrm{env}$."
+" Phase 2 is characterised by a constant proportionality between 4M,/dt and dM,/dt.", Phase 2 is characterised by a constant proportionality between $dM_\mathrm{c}/dt$ and $dM_\mathrm{env}/dt$.
+ Phase 3 corresponds to the usual runaway growth of the envelope., Phase 3 corresponds to the usual runaway growth of the envelope.
+ From Fig., From Fig.
+ 3. we can see that a distinction between phase | and a phase 2 cannot be inferred from our simulation., \ref{j3mdot} we can see that a distinction between phase 1 and a phase 2 cannot be inferred from our simulation.
+ The time derivative of the mass of the envelope is a monotonously increasing function. with no flat slope after it becomes larger than the core growth rate.," The time derivative of the mass of the envelope is a monotonously increasing function, with no flat slope after it becomes larger than the core growth rate."
+ Our physical model is in essence the same as that of Pollack et al. (1996)).," Our physical model is in essence the same as that of Pollack et al. \cite{pollack}) ),"
+ except for the selection of the core aceretion model and the treatment of the interaction between incoming planetesimals and the gaseous envelope of the protoplanet., except for the selection of the core accretion model and the treatment of the interaction between incoming planetesimals and the gaseous envelope of the protoplanet.
+ Regarding the latter. as explained in Sect. 2.3..," Regarding the latter, as explained in Sect. \ref{sec:interaction},"
+ we consider a simple model for the energy deposition. while Pollack et al. (1996))," we consider a simple model for the energy deposition, while Pollack et al. \cite{pollack}) )"
+ developed à more complex model wherethe complete trajectories to the core of accreted planetesimals are calculated, developed a more complex model wherethe complete trajectories to the core of accreted planetesimals are calculated
+indicating (hat the radiative core is a perfect conductor.,indicating that the radiative core is a perfect conductor.
+ At the top boundary (r=R). we sel D—0 and smoothly match A onto an exterior potential field solution AC ," At the top boundary $r=R$ ), we set $B=0$ and smoothly match $A$ onto an exterior potential field solution \citep{1994A&A...291..975D}. ."
+both poles (8=0 and x). we set B=4=0 for the reguliuritv.," At both poles $\theta=0$ and $\pi$ ), we set $B=A=0$ for the regularity."
+ The nunmerical convergence is checked by runs with different grid spacings., The numerical convergence is checked by runs with different grid spacings.
+ A new indicator of the magnetie parity is defined in this study., A new indicator of the magnetic parity is defined in this study.
+" The radial magnetic field at the surface can be decomposed as where /2,H is the Legendree polynomial.", The radial magnetic field at the surface can be decomposed as where $P_n$ is the Legendre polynomial.
+ Then we define the svnmmetric parameter as Each even (odd) order of the Legendre polynomial is svinmetric (antisvmnmetric) about the equator., Then we define the symmetric parameter as Each even (odd) order of the Legendre polynomial is symmetric (antisymmetric) about the equator.
+ Therelore. SP=1 corresponds (o the purely svinetrie mode about the equator and SP=—1 is the antisvnunetric mode.," Therefore, $\mathrm{SP}=1$ corresponds to the purely symmetric mode about the equator and $\mathrm{SP}=-1$ is the antisymmetric mode."
+" We first show a representative reference solution. computed with the amplitude of the meridional flow a)1000ems|. the amplitude of the a-effect sj=160emsJl. the amplitude of the turbulent diffusivity near the surface laver 7,=2x107engs! and the thickness of the strong diffusivitv laver d;=0.14."," We first show a representative reference solution, computed with the amplitude of the meridional flow $u_0=1000\ \mathrm{cm}\ \mathrm{s^{-1}}$, the amplitude of the $\alpha$ -effect $s_0=160\ \mathrm{cm\ s^{-1}}$, the amplitude of the turbulent diffusivity near the surface layer $\eta_{\mathrm{s}}=2\times10^{12}\ \mathrm{cm^2}\ \mathrm{s^{-1}}$ and the thickness of the strong diffusivity layer $d_\mathrm{s}=0.1R$."
+ The results are shown in the time-Iatitude plots in Fie. 2.., The results are shown in the time-latitude plots in Fig. \ref{butterfly}.
+ This simulation is started with a svimmetric initial condition., This simulation is started with a symmetric initial condition.
+ As timepasses. the global magnetic field becomes antisvinmetric.," As timepasses, the global magnetic field becomes antisymmetric."
+ In such a case. the," In such a case, the"
+mass (ransler rate. but change the BINSYN mass transfer rate for à new simulation. and still produce a valid svstem svnthetic spectrum.,"mass transfer rate, but change the BINSYN mass transfer rate for a new simulation, and still produce a valid system synthetic spectrum."
+ The accuracy of (he accretion disk svnthetie spectrum is sensitive to the Ziy spacing of the source synthetic spectra., The accuracy of the accretion disk synthetic spectrum is sensitive to the $T_{\rm eff}$ spacing of the source synthetic spectra.
+ Linear interpolation between source spectra differing in Zur values by several thousand Ixelvins can produce an inaccurate interpolated spectrin., Linear interpolation between source spectra differing in $T_{\rm eff}$ values by several thousand Kelvins can produce an inaccurate interpolated spectrum.
+ After exlensive experiment. we adopted a “universal” set of GO source spectra. of which 62 were TLUSTY models.," After extensive experiment, we adopted a ""universal"" set of 69 source spectra, of which 62 were TLUSTY models."
+ These latter models had Zi; values spaced at roughly 500Ix. intervals between 10.620Ix. and 31.5641. and a slightly larger step between 31.5641. and 63.735Ix. The remaining svulhelic spectra were for Ixurucz models covering the ζω range 0000.1000019. In the wavelength range of interest. contributions from 27000A. or cooler Tay values are very small or negligible.," These latter models had $T_{\rm eff}$ values spaced at roughly 500K intervals between 10,620K and 31,564K and a slightly larger step between 31,564K and 63,735K. The remaining synthetic spectra were for Kurucz models covering the $T_{\rm eff}$ range 5000K–10,000K. In the wavelength range of interest, contributions from ${\approx}7000K$ or cooler $T_{\rm eff}$ values are very small or negligible."
+ Our initial study of the intermediate state adopted a variety of assumed mass (ransler rales. together with a Standard. Model accretion disk.," Our initial study of the intermediate state adopted a variety of assumed mass transfer rates, together with a Standard Model accretion disk."
+ We used the svstem parameters of Table 1. and DINSYN in a diagnostic mode. (to attempt a fit to the intermediate stateIUE spectra.," We used the system parameters of Table 1, and BINSYN in a diagnostic mode, to attempt a fit to the intermediate state spectra."
+With theexception of the parameters D. 7. Tug. rg. rg. and Lf (see Table 1 commentis). the Table 1 parameters for the WD and. secondary star are (he same as in 112004.,"	With theexception of the parameters $D$, $i$, $T_{\rm eff,s}$, $r_a$, $r_b$, and $H$ (see Table 1 comments), the Table 1 parameters for the WD and secondary star are the same as in H2004."
+ Our model divides the accretion disk into 66 annuli. with each annulus divided into 90 azimuthal segmentis.," Our model divides the accretion disk into 66 annuli, with each annulus divided into 90 azimuthal segments."
+ The svstem synthetic spectrum is (he integrated sum of the contributions of the WD. secondary component. accretion disk. and accretion disk rim. (," The system synthetic spectrum is the integrated sum of the contributions of the WD, secondary component, accretion disk, and accretion disk rim. ("
+Note that. αἱ an inclination of 7°. the accretion disk rim contributes a negligible observable effect.),"Note that, at an inclination of $7{\arcdeg}$, the accretion disk rim contributes a negligible observable effect.)"
+ We [ind that it is not possible to fit the intermediate stateZUE spectra bv. adding a Standard. Model accretion disk to the low state model of II2004 and using our TLUSTY annulus svnthetic spectra., We find that it is not possible to fit the intermediate state spectra by adding a Standard Model accretion disk to the low state model of H2004 and using our TLUSTY annulus synthetic spectra.
+ The radial temperature gradient in (he Standard Model produces either too much flux at short wavelengths or too little flux at long wavelengths., The radial temperature gradient in the Standard Model produces either too much flux at short wavelengths or too little flux at long wavelengths.
+ In making (his (ancl all subsequent) comparisons with theJOE spectra we maintained (he same scaling divisors. for both theZUE spectra and the svuthelic spectrum. (hat were adopted Lor the low state comparison.," In making this (and all subsequent) comparisons with the spectra we maintained the same scaling divisors, for both the spectra and the synthetic spectrum, that were adopted for the low state comparison."
+ Dased on the measured E(DB—V)=0.0 (Szkody we applied no interstellar extinction. corrections to theZUE spectra extracted. [rom the archive., Based on the measured $E(B-V) = 0.0$ \citep{sd82} we applied no interstellar extinction corrections to the spectra extracted from the archive.
+ Fig., Fig.
+" 4 illustrates the discrepaney. produced by adding an accretion disk component with a mass transfer rate of 1.0x10.M,vr.t.", 4 illustrates the discrepancy produced by adding an accretion disk component with a mass transfer rate of $1.0{\times}10^{-9}{\cal M}_{\odot}{\rm yr}^{-1}$.
+ Note that this rate equals the value given by Tlameury οἱ al. (, Note that this rate equals the value given by Hameury et al. (
+1983) al the top of the period gap.,1988) at the top of the period gap.
+ This mass transfer rate. aud a Standarcl Moclel disk. produces disk Zig values ranging from 23.765lx. at (he inner disk edge to 42221. al the outer disk edge. wilh a temperature maximum of 34.9721lx alr=1.3611κι.," This mass transfer rate, and a Standard Model disk, produces disk $T_{\rm eff}$ values ranging from 23,765K at the inner disk edge to 4222K at the outer disk edge, with a temperature maximum of 34,972K at $r=1.3611{\times}r_{\rm wd}$."
+ The absolute flix [rom the accretion disk. at the Earth. is à strong function of the mass transler rate and the approximate fit in Fig.," The absolute flux from the accretion disk, at the Earth, is a strong function of the mass transfer rate and the approximate fit in Fig."
+ 4 indicates (hat the adopted mass transfer rate is nearly correct. Le.. the resilual over the wavelength interval plotted is small.," 4 indicates that the adopted mass transfer rate is nearly correct, i.e., the residual over the wavelength interval plotted is small."
+ The synthetic, The synthetic
+By. where 6n and no are the fluctuating and background electron densities. and 6B and By are the fluctuating and background magnetic fields.,", where $\delta n $ and $n_0$ are the fluctuating and background electron densities, and $\delta {\bf
+ B}$ and ${\bf B}_0$ are the fluctuating and background magnetic fields."
+" For D~I. 6n/ng~6B/By at À,~pj."," For $\beta \sim 1$, $\delta n/n_0 \sim \delta B/B_0$ at $\lambda_\perp \sim \rho_i$."
+ Ateven smaller scales. A4<p;. the ion and electron velocities decouple for all B. the waves become dispersive. and the fluctuations produce parallel electric and magnetic field perturbations that cause the waves to damp.," At even smaller scales, $\lambda_\perp
+\lesssim \rho_i$, the ion and electron velocities decouple for all $\beta$, the waves become dispersive, and the fluctuations produce parallel electric and magnetic field perturbations that cause the waves to damp."
+" At A,< p;. these solutions to the Alfvénn-wave branch of the linear dispersion relation are called kinetic Alfvénn waves (KAWS)."," At $\lambda_\perp \lesssim \rho_i$ , these solutions to the Alfvénn-wave branch of the linear dispersion relation are called kinetic Alfvénn waves (KAWs)."
+ Many of the measured properties of the magnetic and electric field fluctuations in the near-Earth solar wind are consistent with. KAW turbulence on small scales (e.g.. Howes et al.," Many of the measured properties of the magnetic and electric field fluctuations in the near-Earth solar wind are consistent with KAW turbulence on small scales (e.g., Howes et al."
+ 2008a. 20050: Sahraoui et al.," 2008a, 2008b; Sahraoui et al."
+" 2009, and references therein)."," 2009, and references therein)."
+ A very Important. but somewhat indirect. test of the low-frequency turbulence model is provided by measurements of ion and electron temperatures. both and in coronal holes (the open-field-line regions from which the fast solar wind is thought to emanate).," A very important, but somewhat indirect, test of the low-frequency turbulence model is provided by measurements of ion and electron temperatures, both and in coronal holes (the open-field-line regions from which the fast solar wind is thought to emanate)."
+" Observations with UVCS show that 7>» for minor ions such as O? in coronal holes. where 7, 7]and are the temperatures corresponding to thermal motions 7|perpendicular and parallel to the background magnetic field By (Kohl et al 1998. Antonucci et al 2000)."," Observations with UVCS show that $T_\perp \gg T_\parallel$ for minor ions such as ${\rm O}^{+5}$ in coronal holes, where $T_\perp
+$ and $T_\parallel$ are the temperatures corresponding to thermal motions perpendicular and parallel to the background magnetic field ${\bf B}_0$ (Kohl et al 1998, Antonucci et al 2000)."
+ It has not yet been possible to unequivocally determine whether protons have the same temperature anisotropy in the corona., It has not yet been possible to unequivocally determine whether protons have the same temperature anisotropy in the corona.
+" However. measurements of the fast solar wind show that 7,> for the core of the proton distribution function. although 7|the anisotropy ts less pronounced for larger P (Marsch. Ao. Tu 2004: Hellinger et al."," However, measurements of the fast solar wind show that $T_\perp > T_\parallel$ for the core of the proton distribution function, although the anisotropy is less pronounced for larger $\beta$ (Marsch, Ao, Tu 2004; Hellinger et al."
+ 2006)., 2006).
+ It is not yet clear whether low-frequency Alfvénnic turbulence can explain perpendicular ton heating and the preferential heating of minor tons., It is not yet clear whether low-frequency Alfvénnic turbulence can explain perpendicular ion heating and the preferential heating of minor ions.
+ Dissipation of Alfvénnic turbulence occurs at small scales. at which the amplitude of the fluctuations is very small.," Dissipation of Alfvénnic turbulence occurs at small scales, at which the amplitude of the fluctuations is very small."
+ The hot-plasma dispersion relation for small-amplitude waves thus provides a plausible first estimate for how KAW turbulence dissipates in. the collisionless corona and solar wind., The hot-plasma dispersion relation for small-amplitude waves thus provides a plausible first estimate for how KAW turbulence dissipates in the collisionless corona and solar wind.
+" This predicts negligible damping for oblique Alfvénn waves with &,p;< I. where Ay and Kj are the wavevector components perpendicular and parallel to By (Barnes 1966)."," This predicts negligible damping for oblique Alfvénn waves with $k_\perp \rho_i \ll 1$ , where $k_\perp$ and $k_\parallel$ are the wavevector components perpendicular and parallel to ${\bf B}_0$ (Barnes 1966)."
+ As a result. the energy cascades to scales =p;.," As a result, the energy cascades to scales $\lesssim \rho_i$."
+ The damping of the resulting KAWs with ky| and frequencies <€; arises from Landau and/or transit-timeIR damping and leads to parallel electron heating for PX1. not perpendicular ion heating (Quataert 1998: Quataert Gruzinov 1999; Leamon et al 1999; Cranmer van Ballegooijen 2003; Gary Nishimura 2004: Howes et al 2008a).," The damping of the resulting KAWs with $k_\perp \gg |k_\parallel|$ and frequencies $\ll
+\Omega_i$ arises from Landau and/or transit-time damping and leads to parallel electron heating for $\beta \lesssim 1$, not perpendicular ion heating (Quataert 1998; Quataert Gruzinov 1999; Leamon et al 1999; Cranmer van Ballegooijen 2003; Gary Nishimura 2004; Howes et al 2008a)."
+ Nevertheless. a number of mechanisms have been proposed that might produce perpendicular ion heating from low-frequency turbulence. including heating by reconnection electric fields (Dmitruk. Matthaeus. Seenu 2004; see. however. Lehe. Parrish. Quataert 2009). secondary plasma instabilities triggered by the KAW velocity shear (Markovski et al 2006). ion heating by electron phase-space holes generated by the heating of electrons (Matthaeus et al 2003; Cranmer van Ballegootjen 2003). and perpendicular ton heating through stochastic ton orbits (Johnson Cheng 2001).," Nevertheless, a number of mechanisms have been proposed that might produce perpendicular ion heating from low-frequency turbulence, including heating by reconnection electric fields (Dmitruk, Matthaeus, Seenu 2004; see, however, Lehe, Parrish, Quataert 2009), secondary plasma instabilities triggered by the KAW velocity shear (Markovskii et al 2006), ion heating by electron phase-space holes generated by the heating of electrons (Matthaeus et al 2003; Cranmer van Ballegooijen 2003), and perpendicular ion heating through stochastic ion orbits (Johnson Cheng 2001)."
+ An outstanding problem is whether any of these mechanisms (or others) can quantitatively account for the measured perpendicular ton heating in the context of low-frequency turbulence models — this is a particularly important question given the growing body of evidence that the magnetic and electric field fluctuations at ~| AU consistent with low-frequency anisotropic Alfvénn waves and KAWS (e.g.. Sahraoui et al.," An outstanding problem is whether any of these mechanisms (or others) can quantitatively account for the measured perpendicular ion heating in the context of low-frequency turbulence models – this is a particularly important question given the growing body of evidence that the magnetic and electric field fluctuations at $\sim 1$ AU consistent with low-frequency anisotropic Alfvénn waves and KAWs (e.g., Sahraoui et al."
+ 2009)., 2009).
+ The goal of this paper is to quantitatively assess a second test of the importance of low-frequency turbulence in the solar wind: the measured power spectrum of density fluctuations., The goal of this paper is to quantitatively assess a second test of the importance of low-frequency turbulence in the solar wind: the measured power spectrum of density fluctuations.
+ Coles Harmon (1989) measured the spectrum of electron density fluctuations in the corona at radii as small as 5R. using Venus as à background radio source., Coles Harmon (1989) measured the spectrum of electron density fluctuations in the corona at radii as small as $5 R_{\sun}$ using Venus as a background radio source.
+ In addition. measurements of density fluctuations in the solar wind at ~| AU have been carried out by a variety of methods (e.g.. Celnikier et al.," In addition, measurements of density fluctuations in the solar wind at $\sim 1$ AU have been carried out by a variety of methods (e.g., Celnikier et al."
+ 1983. 1987: Hnat et al.," 1983, 1987; Hnat et al."
+ 2005; Kellogg Horbury 2005)., 2005; Kellogg Horbury 2005).
+" Because oblique Alfvénn waves become increasingly compressive for &,d;~|. the observed density fluctuation spectrum constrains the spectrum. of. oblique Alfvénn waves and provides an upper limit on the heating rate ε from Alfvénnic turbulence."," Because oblique Alfvénn waves become increasingly compressive for $k_\perp d_i \sim 1$, the observed density fluctuation spectrum constrains the spectrum of oblique Alfvénn waves and provides an upper limit on the heating rate $\epsilon$ from Alfvénnic turbulence."
+ In 2.. we summarize the predicted density fluctuations induced by low-frequency Alfvénnie turbulence. and deseribe some of the remaining uncertainties in these predictions (see also Schekochihin et al.," In \ref{sec:pred}, we summarize the predicted density fluctuations induced by low-frequency Alfvénnic turbulence, and describe some of the remaining uncertainties in these predictions (see also Schekochihin et al."
+ 2009)., 2009).
+ We then show how the measured density fluctuations in coronal holes and at ~| AU constrain the heating rate € due to Alfvénnic turbulence (33)., We then show how the measured density fluctuations in coronal holes and at $\sim 1$ AU constrain the heating rate $\epsilon$ due to Alfvénnic turbulence \ref{sec:turb}) ).
+" In 4. we describe the ""sweeping"" model for coronal heating (e.g.. Schwartz et al 1981; Axford MeKenzie 1992; Marsch Tu 1997; Ruzmaikin Berger 1998). in which the corona is heated by cyclotron damping of kHz waves launched directly from the Sun: we present a simple explanation for why radio observations do not rule out turbulent heating models. even though they appear to rule out the sweeping model (as was shown by Hollweg 2000)."," In \ref{sec:sweeping} we describe the “sweeping” model for coronal heating (e.g., Schwartz et al 1981; Axford McKenzie 1992; Marsch Tu 1997; Ruzmaikin Berger 1998), in which the corona is heated by cyclotron damping of kHz waves launched directly from the Sun; we present a simple explanation for why radio observations do not rule out turbulent heating models, even though they appear to rule out the sweeping model (as was shown by Hollweg 2000)."
+ In 5 we summarize and discuss our results., In \ref{sec:conc} we summarize and discuss our results.
+ Our analysis and results are broadly similar to those of Harmon Coles (2005). but we consider a different model for the turbulent cascade of Alfvénn waves. and apply the density fluctuation constraint both to remote observations of turbulence in coronal holes and to measurements of turbulence in the near-Earth solar wind.," Our analysis and results are broadly similar to those of Harmon Coles (2005), but we consider a different model for the turbulent cascade of Alfvénn waves, and apply the density fluctuation constraint both to remote observations of turbulence in coronal holes and to measurements of turbulence in the near-Earth solar wind."
+ In this section we briefly summarize the density fluctuations produced by low-frequency Alfvénnic turbulence (see Lithwick Goldreich 2001 and Schekochihin et al., In this section we briefly summarize the density fluctuations produced by low-frequency Alfvénnic turbulence (see Lithwick Goldreich 2001 and Schekochihin et al.
+ 2009 fora more comprehensive discussion)., 2009 for a more comprehensive discussion).
+" We assume that the Alfvénn wave power spectrum follows the ""critical balance"" theory of Goldreich Sridhar (1995).", We assume that the Alfvénn wave power spectrum follows the “critical balance” theory of Goldreich Sridhar (1995).
+" Initially we also assume that the turbulence is ""balanced."" re.. that there are equal fluxes of Alfvénn waves propagating towards and away from the Sun in the plasma frame. or equivalently. that there is zero cross helicity; we discuss the effects of a non-zero cross helicity at the end of the section."," Initially we also assume that the turbulence is “balanced,” i.e., that there are equal fluxes of Alfvénn waves propagating towards and away from the Sun in the plasma frame, or equivalently, that there is zero cross helicity; we discuss the effects of a non-zero cross helicity at the end of the section."
+ Although Alfvénn waves themselves are not compressive when κια“>l. low-frequency Alfvénnic turbulence nonetheless produces significant density fluctuations. via two different physical processes.," Although Alfvénn waves themselves are not compressive when $k_\perp
+d_i \gg 1$, low-frequency Alfvénnic turbulence nonetheless produces significant density fluctuations, via two different physical processes."
+ First. as energy cascades to scales Xd;. Alfvénn waves transition to KAWs. which are compressive (see Fig.," First, as energy cascades to scales $\lesssim d_i$, Alfvénn waves transition to KAWs, which are compressive (see Fig."
+ 3 discussed below)., \ref{fig:beta} discussed below).
+ Second. both slow waves and entropy modes are passively mixed by the Alfvénnic cascade (Lithwick Goldreich 2001).," Second, both slow waves and entropy modes are passively mixed by the Alfvénnic cascade (Lithwick Goldreich 2001)."
+ Because the Alfvénnie fluctuations have an anisotropic Kolmogorov spectrum. the density fluctuations. associated with the entropy modes and/or slow waves also have ananisotropic Kolmogorov spectrum.," Because the Alfvénnic fluctuations have an anisotropic Kolmogorov spectrum, the density fluctuations associated with the entropy modes and/or slow waves also have ananisotropic Kolmogorov spectrum."
+ For the collisionless conditions appropriate to the solar corona and solar wind. the entropy modes and slow waves," For the collisionless conditions appropriate to the solar corona and solar wind, the entropy modes and slow waves"
+"In the pre-Fermi era, it is widely expected that significant GeV emission will be detected in a good fraction of bright GRBs if they are powered by un-magnetized internal shocks (e.g.,Pilla&&Piran 2008).","In the pre-Fermi era, it is widely expected that significant GeV emission will be detected in a good fraction of bright GRBs if they are powered by un-magnetized internal shocks \citep[e.g.,][]{Pilla98,pw04,gz07,fp08}."
+". The detection of a distinct excess at GeV-TeV energies, the SSC radiation component of such shocks, will be a crucial evidence for the standard fireball model."," The detection of a distinct excess at GeV-TeV energies, the SSC radiation component of such shocks, will be a crucial evidence for the standard fireball model."
+ The non-detection of the GeV spectrum excess in almost all Fermi bursts (Abdoal.2009) is a surprise but does not impose tight constraint on the models., The non-detection of the GeV spectrum excess in almost all Fermi bursts \citep{Abdo09} is a surprise but does not impose a tight constraint on the models.
+" For example, in the standard internala shock model, the non-detection can be attributed to a too large hmyssc~ TeV and a relative low hveur~ GeV. Some alternatives, such as the photosphere-internal shock model, the magnetized internal shock model and the photosphere-gradual magnetic dissipation model, can be in agreement with the data, too (see Tab.2 for a summary)."," For example, in the standard internal shock model, the non-detection can be attributed to a too large $h\nu_{\rm m,ssc} \sim $ TeV and a relative low $h\nu_{\rm cut}
+\sim$ GeV. Some alternatives, such as the photosphere-internal shock model, the magnetized internal shock model and the photosphere-gradual magnetic dissipation model, can be in agreement with the data, too (see \ref{tab:sum} for a summary)."
+ We attribute the delay in the onset of LAT detection in quite a few Fermi bursts to the unfavorable condition for GeV emission of the early outflow (see section ?? for details)., We attribute the delay in the onset of LAT detection in quite a few Fermi bursts to the unfavorable condition for GeV emission of the early outflow (see section \ref{sec:GeV-delay} for details).
+ With the polarimetry of GRBs people can potentially distinguish between some prompt emission models (see Tab.1 for a summary; see also Toma et al., With the polarimetry of GRBs people can potentially distinguish between some prompt emission models (see \ref{tab:stat} for a summary; see also Toma et al.
+ 2009)., 2009).
+ We show in section 3.1 that in the photosphere-internal shock model the linear polarization degree is roughly anti-correlated with the weight of the thermal component and will be highly frequency-dependent.," We show in section \ref{sec:Lin-thermal}
+ that in the photosphere-internal shock model the linear polarization degree is roughly anti-correlated with the weight of the thermal component and will be highly frequency-dependent."
+" Such a unique behavior, if detected, labels its physical origin."," Such a unique behavior, if detected, labels its physical origin."
+" However, a moderate/high linear polarization level is expected only when the line of sight is outside of the cone of the ejecta (i.e., 0,>6j)."," However, a moderate/high linear polarization level is expected only when the line of sight is outside of the cone of the ejecta (i.e., $\theta_{\rm v}>\theta_{\rm j}$ )."
+" In addition, 0,—0;S;1/T; is needed otherwise the burst will be too weak to perform the gamma-ray polarimetry."," In addition, $\theta_{\rm
+v}-\theta_{\rm j}\lesssim 1/\Gamma_{\rm i}$ is needed otherwise the burst will be too weak to perform the gamma-ray polarimetry."
+ Consequently the detection prospect is not very promising., Consequently the detection prospect is not very promising.
+ In this work we have also briefly discussed the detection prospect of prompt PeV neutrinos from GRBs., In this work we have also briefly discussed the detection prospect of prompt PeV neutrinos from GRBs.
+ The roles of the intrinsic spectrum of the protons and the cooling of pions (muons) have been outlined., The roles of the intrinsic spectrum of the protons and the cooling of pions (muons) have been outlined.
+" The latter always increases the neutrino numbers at the energies εν, or εν,ve Dy a factor of 3."," The latter always increases the neutrino numbers at the energies $\varepsilon_{\nu_{\mu}}^{\rm c}$ or $\varepsilon_{\bar{\nu}_{\mu},\nu_{\rm e}}^{\rm c}$ by a factor of 3."
+" The former, however, is uncertain."," The former, however, is uncertain."
+" If the protons have an intrinsic spectrum dN/dEcE~*? and have a total energy about tens times that emitted in gamma-rays, the detection prospect would be as good as, or even better than that presented in Guettaetal.(2004)."," If the protons have an intrinsic spectrum $dN/dE\propto E^{-2.22}$ and have a total energy about tens times that emitted in gamma-rays, the detection prospect would be as good as, or even better than that presented in \citet{Guetta04}."
+". If the proton spectrum traces that of the electrons, i.e., typically dN/dEοςE?, the detection prospect would be discouraging."," If the proton spectrum traces that of the electrons, i.e., typically $dN/dE\propto E^{-2.5}$, the detection prospect would be discouraging."
+ We thank the anonymous referee for very helpful suggestions/comments and Drs., We thank the anonymous referee for very helpful suggestions/comments and Drs.
+" X. Ε. Wu, K. Toma, and Y. C. Zou for communication."," X. F. Wu, K. Toma, and Y. C. Zou for communication."
+" This work was supported in part by the Danish National Science Foundation, Chinese Academy of Sciences, National basic research program of China (grant 2009CB824800), and the National Natural Science Foundation of China (grant 10673034)."," This work was supported in part by the Danish National Science Foundation, Chinese Academy of Sciences, National basic research program of China (grant 2009CB824800), and the National Natural Science Foundation of China (grant 10673034)."
+Let us consider the break [frequency of the large scale jet inverse-Compton eniission.,Let us consider the break frequency of the large scale jet inverse-Compton emission.
+" Accordingly to the formalism presented in Appencix D. in the jet comoving frame a seed photon with the characteristic (break) frequency 1, is upscattered by the ultrarelativistic electron with Lorentz factor > to the frequency 5?5,4/d(1—cos)."," Accordingly to the formalism presented in Appendix D, in the jet comoving frame a seed photon with the characteristic (break) frequency $\nu'_{seed}$ is upscattered by the ultrarelativistic electron with Lorentz factor $\gamma$ to the frequency $\gamma^2 \, \nu_{seed}' \, (1 - \cos \chi')$."
+" For the electron break Lorentz lactor αν, one obtains the observed break lvequency of (he inverse-Compton enission", For the electron break Lorentz factor $\gamma_{br}$ one obtains the observed break frequency of the inverse-Compton emission
+"30degx(d,/40AU)a(1/20vears). but becomes negligible−− lor⊳∙ distances to the companion⋅ d,Z100 AU. or if we primarily use more recently discovered MSPs.","$30\deg\times \left(d_p/40\mbox{ AU}\right)^{-3/2}\left(t/20\mbox{ years}\right)$, but becomes negligible for distances to the companion $d_p\ga 100$ AU, or if we primarily use more recently discovered MSPs."
+ Assuming one of these latter conditions holds. we neglect the change of the direction of the acceleration in all subsequent discussion.," Assuming one of these latter conditions holds, we neglect the change of the direction of the acceleration in all subsequent discussion."
+ For each direction on the skv (α.δ) we construct (wo datasets based on the observational data for the 48 MSPs described above (in practice we used a grid spaced by 10 degrees in right ascension and declination. as shown in Figure 1)).," For each direction on the sky $\alpha,\delta$ ) we construct two datasets based on the observational data for the 48 MSPs described above (in practice we used a grid spaced by 10 degrees in right ascension and declination, as shown in Figure \ref{pic_objects}) )."
+ The first dataset contains pip! for all MSPs and the second dataset consists of cos@;. where £; is the angle between (0.9) and the direction to the object (a;.0;).," The first dataset contains $\dot{P}_i'/P_i'$ for all MSPs and the second dataset consists of $\cos\theta_i$ , where $\theta_i$ is the angle between $\alpha,\delta$ ) and the direction to the object $\alpha_i,\delta_i$ )."
+" If the solar svstem accelerates with e. in the direction (0.8). from equation (2)) we know that for all objects there is a term —a.cos@/e which contributes to the observed 27/2?"" value."," If the solar system accelerates with $a_{\odot}$ in the direction $\alpha, \delta$ ), from equation \ref{pdotprime}) ) we know that for all objects there is a term $-a_{\odot} \cos\theta/c$ which contributes to the observed $\dot{P}'/P'$ value."
+ If there is no acceleration in this direction. there should be no correlation between (he observed (timing properties of MSP?s and their position on the sky (the null hypothesis).," If there is no acceleration in this direction, there should be no correlation between the observed timing properties of MSPs and their position on the sky (the null hypothesis)."
+ The presence of the correlation is assessed using the Spearman rank correlation coefficient which is calculated after replacing all values in a dataset by their ranks (e.g.. the minimum value is replaced by 1 and (he maxinum by N if the dataset consists of No values).," The presence of the correlation is assessed using the Spearman rank correlation coefficient which is calculated after replacing all values in a dataset by their ranks (e.g., the minimum value is replaced by 1 and the maximum by $N$ if the dataset consists of $N$ values)."
+ The advantage of using the rank setsis (hat the results do not depend on the distribution from which the datasets were drawn (Pressetal.1992)., The advantage of using the rank setsis that the results do not depend on the distribution from which the datasets were drawn \citep{pres92}.
+. The rank correlation coefficient is is a signed quantity (positive if one value on average increases as a [function of the other and negative if it decreases): values of r; around 0 imply there is no correlation. whereas values close to 1 or —1 indicate a strong correlation.," The rank correlation coefficient $r_s$ is a signed quantity (positive if one value on average increases as a function of the other and negative if it decreases); values of $r_s$ around 0 imply there is no correlation, whereas values close to 1 or $-1$ indicate a strong correlation."
+ The significance of the rank correlation coellicient can be assessed using the probability WG.) that a given. value of ry is obtained for two uncorrelated sets of data., The significance of the rank correlation coefficient can be assessed using the probability $\Pi(r_s)$ that a given value of $r_s$ is obtained for two uncorrelated sets of data.
+ For each direction we evaluate the rank correlation coefficient re(a.d) between the two datasets pup and cos?;.," For each direction we evaluate the rank correlation coefficient $r_s(\alpha,\delta)$ between the two datasets $\dot{P}_i'/P_i'$ and $\cos\theta_i$."
+ We then evaluate the probability of the null hypothesis H(a.9) (i.e.. Che probability that pip! and cos8; are uncorrelated) aud use these values to construct a “probability map”.," We then evaluate the probability of the null hypothesis $\Pi(\alpha,\delta)$ (i.e., the probability that $\dot{P}_i'/P_i'$ and $\cos\theta_i$ are uncorrelated) and use these values to construct a “probability map”."
+ An example of a probability map is given in Figure 2. for a simulated dataset., An example of a probability map is given in Figure \ref{pic_test_18} for a simulated dataset.
+ For this simulation we used (he real positions of AISPs. but assigned (hem all the same P and P values and added an artificial acceleration to the data producing slightly different. observed P values.," For this simulation we used the real positions of MSPs, but assigned them all the same $P$ and $\dot{P}$ values and added an artificial acceleration to the data producing slightly different observed $\dot{P}'$ values."
+ The probability map lor the negative declinationsis fullv determined by the probability map for positive declinations. since (he ealeulated probabilities by construction are invariant wilh respect (o reversing (he direction. Πία.δ)=IH(x4. --δ].," The probability map for the negative declinationsis fully determined by the probability map for positive declinations, since the calculated probabilities by construction are invariant with respect to reversing the direction, $\Pi(\alpha,\delta)=\Pi(\pi+\alpha,-\delta)$ ."
+the second. long part of the run. with VW Livi having Laced by 0.4 mag. the main DNO moclulation is at 27.45 s and the short period modulation has increased in period to 15.15 s. Η Ἡ ds still a svnodic first harmonic it would. produce an expected beat at 292 s; which presumably. is now the first harmonic of the (still unobservable) QPO.,"the second, long part of the run, with VW Hyi having faded by 0.4 mag, the main DNO modulation is at 27.45 s and the short period modulation has increased in period to 15.15 s. If it is still a synodic first harmonic it would produce an expected beat at 292 s, which presumably is now the first harmonic of the (still unobservable) QPO."
+ EPs of the sections of light curve shown in Fig., FTs of the sections of light curve shown in Fig.
+ 3 show only fundamentals of the DNO moculations although the departure from sinusoidality of some of the pulsations shows that there must be harmonics present they are. not detectable above the noise., \ref{SALT004lc1} show only fundamentals of the DNO modulations – although the departure from sinusoidality of some of the pulsations shows that there must be harmonics present they are not detectable above the noise.
+ These oscillations in VW Lyi are almost identical to those commonly observed in intermediate polars. for example see figure 1 of Warner Cropper (1984). where the light curve of V1223 Ser has some sharp spikes in it similar to those in Fig.," These oscillations in VW Hyi are almost identical to those commonly observed in intermediate polars, for example see figure 1 of Warner Cropper (1984), where the light curve of V1223 Sgr has some sharp spikes in it similar to those in Fig."
+ 3. but where it is also stated that no first harmonic is detectable in the E'Es of the whole light CUPVOS., \ref{SALT004lc1} but where it is also stated that no first harmonic is detectable in the FTs of the whole light curves.
+ As mentioned above. there are no prominent DNOs in the lichteurve.," As mentioned above, there are no prominent DNOs in the lightcurve."
+ The run is so short in length that we cannot certainly icentily the nature of the three large amplitude peaks. with separations  770 s. After prewhitening (i.e. subtraction from the light curve) with these mocdulations. the EP (Fig. 8))," The run is so short in length that we cannot certainly identify the nature of the three large amplitude peaks, with separations $\sim$ 770 s. After prewhitening (i.e. subtraction from the light curve) with these modulations, the FT (Fig. \ref{SALT017ft1}) )"
+ shows several low amplitude oscillations that have significant. relationships among their frequencies., shows several low amplitude oscillations that have significant relationships among their frequencies.
+ The 5.7 mmag peak at 122.80 + 0.27 s has a harmonic at 61.50 + 0.08 s (4.4 mmag)., The 5.7 mmag peak at 122.80 $\pm$ 0.27 s has a harmonic at 61.50 $\pm$ 0.08 s (4.4 mmag).
+ The other two peaks are ab 67.36 c 0.10 s (4.1 mmae) and 38.33 + 0.03 s (44 mmag)., The other two peaks are at 67.36 $\pm$ 0.10 s (4.1 mmag) and 38.33 $\pm$ 0.03 s (4.4 mmag).
+ Phe latter is not a harmonic of the former. but ifthe former is a sidereal period the latter could be a harmonic of a corresponding svnodic period with an implied (hut not observed) QPO period  550 s (see discussion of similar structure in Sect.," The latter is not a harmonic of the former, but if the former is a sidereal period the latter could be a harmonic of a corresponding synodic period with an implied (but not observed) QPO period $\sim$ 550 s (see discussion of similar structure in Sect."
+ 3.2)., 3.2).
+ FTPs show that there are DNOs present about hall of the ime in this light curve. near three principal periods. viz 29 s. 42 s and 45 s. From the 4© diagrams at these »eriods we selected for detailed. analysis the regions where he amplitudes are largest (twpically 5r mmag) or the phases are most coherent.," FTs show that there are DNOs present about half of the time in this light curve, near three principal periods, viz 29 s, 42 s and 45 s. From the $A - \phi$ diagrams at these periods we selected for detailed analysis the regions where the amplitudes are largest (typically 5 mmag) or the phases are most coherent."
+ The individual coherent lengths. range rom 400 s to 740 s. Phe results are summarized in Table 2.., The individual coherent lengths range from 400 s to 740 s. The results are summarized in Table \ref{dno7tab2}.
+ We interpret the three periods in the following wav: the 45 s and 29 s periodicities are an example of the 3:2 ratio irst discussed in Paper IV. (which here is a 3:2 ratio in the irst harmonic of the svnodic period). and this is supported w the brief appearance of a fundamental of the svnocdic," We interpret the three periods in the following way: the 45 s and 29 s periodicities are an example of the 3:2 ratio first discussed in Paper IV (which here is a 3:2 ratio in the first harmonic of the synodic period), and this is supported by the brief appearance of a fundamental of the synodic"
+σος converted into stars (as long as the dynamical rate is involved) and. depends primarily on the cloud. structure. whereas the flat part of the EME depends exclusively on the details of clump-to-star conversion and is independent of the nature of the cloucl’s structure.,"gets converted into stars (as long as the dynamical rate is involved) and depends primarily on the cloud structure, whereas the flat part of the IMF depends exclusively on the details of clump-to-star conversion and is independent of the nature of the cloud's structure."
+" To ceseribe this process mathematically. we suppose that cach self-gravitating clump of mass AZ, makes a range of star masses Af. such that the probability distribution funetion. ο). of the relative star mass. €=AL. fAL.. is independent of AZ."," To describe this process mathematically, we suppose that each self-gravitating clump of mass $M_c$ makes a range of star masses $M_s$ such that the probability distribution function, $P(\epsilon)$, of the relative star mass, $\epsilon=M_s/M_c$ , is independent of $M_c$."
+ This is consistent with the self-similarity ol star formation that is assumed for the rest of the IME model., This is consistent with the self-similarity of star formation that is assumed for the rest of the IMF model.
+ “Phe distribution function is written for logarithmic intervals as P(a)dloge., The distribution function is written for logarithmic intervals as $P(\epsilon)d\log\epsilon$.
+ Lhe basic point of this paper is that P(c) must be approximately constant for all clump masses to give the [lat part of the IAIP at low mass., The basic point of this paper is that $P(\epsilon)$ must be approximately constant for all clump masses to give the flat part of the IMF at low mass.
+ The final mass function for stars. in logarithmic intervals. n.(AMgdlogM. can now be written in terms of the mass function for sell-gravitating. randomlv-chosen clumps. n(ALdlogM. as The upper limit to the integral. Gace. is the largest relative mass for a star that is likely to form from a self- clump.," The final mass function for stars, in logarithmic intervals, $n_s(M_s)d\log M_s$, can now be written in terms of the mass function for self-gravitating, randomly-chosen clumps, $n_c(M_c)d\log M_c$, as The upper limit to the integral, $\epsilon_{max}$, is the largest relative mass for a star that is likely to form from a self-gravitating clump."
+" Lt is perhaps slightly less than unity when Al,>>Aly. although its precise value is not necessary here."," It is perhaps slightly less than unity when $M_s>>M_J$, although its precise value is not necessary here."
+" We denote it by the constant 6,49 and take euΞCyne when AZ,2τον."," We denote it by the constant $\epsilon_{max,0}$ and take $\epsilon_{max}=\epsilon_{max,0}$ when $M_s>M_J\epsilon_{max,0}$."
+" When M,<του. the ellicicncey can be at most ALΑΙ since the smallest clump that can form stars is Aly."," When $M_s<M_J\epsilon_{max,0}$, the efficiency can be at most $M_s/M_J$ since the smallest clump that can form stars is $M_J$."
+ TFhus The lower limit to the integral in equation (2)). Gna. is not known vet from observations.," Thus The lower limit to the integral in equation \ref{eq:int}) ), $\epsilon_{min}$, is not known yet from observations."
+" The ratio ol €, Το Goin will turn out to be the mass range for the flat part of the ΙΔΗΣ. which is denoted by AR."," The ratio of $\epsilon_{max,0}$ to $\epsilon_{min}$ will turn out to be the mass range for the flat part of the IMF, which is denoted by ${\cal R}$."
+ I may have à value of 10 or more according to recent observations (Sect., It may have a value of $\sim10$ or more according to recent observations (Sect.
+ D). but future observations of lower mass brown dwarfs could extend. the Hat part further and make R [arger.," I), but future observations of lower mass brown dwarfs could extend the flat part further and make ${\cal R}$ larger."
+" In any case. we take Guin does not depend on whether A, is greater than or less than Mises."," In any case, we take $\epsilon_{min}$ does not depend on whether $M_s$ is greater than or less than $M_J\epsilon_{max,0}$."
+" To solve the integral in equation (2)). we convert ο to AL/M,. and dlogediogAL,—αλ£M, lor constant A. from the left hand side."," To solve the integral in equation \ref{eq:int}) ), we convert $\epsilon$ to $M_s/M_c$ and $d\log\epsilon=-d\log M_c=-dM_c/M_c$ for constant $M_s $ from the left hand side."
+" Then. for logarithmic intervals in άν. where /4,=Pleo)1fdlogeIlfloeR lor all AZ. and roy comes from the constant in the clump function. n(Ad.)=nuM, eo1.35 from the random sampling mocel and is the same as the power law in the Salpeter function."," Then, for logarithmic intervals in $M_s$, where $P_0=P(\epsilon)=1/\int d\log\epsilon=
+1/\log{\cal R}$ for all $M_c$, and $n_0$ comes from the constant in the clump function, $n(M_c)=n_0M_c^{-x}$; $x=1.35$ from the random sampling model and is the same as the power law in the Salpeter function."
+ “Phe integral limits are Mifensas=ALANCAL.ALSον). ancl fora.," The integral limits are $M_{c,min}=M_s/\epsilon_{max}=MAX\left(M_J,
+M_s/\epsilon_{max,0}\right)$ and $M_{c,max}=M_s/\epsilon_{min}
+=M_s{\cal R}/\epsilon_{max,0}$ ."
+ The solution to equation. (5)) depends on whether Mouse is greater than or less than Al.," The solution to equation \ref{eq:int2}) ) depends on whether $M_J\epsilon_{max,0}$ is greater than or less than $M_s$."
+" For Marone Por ταΓΡ«€AL.Mats. and for Ad,<Adsenseτν. this latter result is zero."," For $M_s>M_J\epsilon_{max,0}$ , For $M_J\epsilon_{max,0}/{\cal R}<M_s<M_J\epsilon_{max,0}$, and for $M_s\le M_J\epsilon_{max,0}/{\cal R}$, this latter result is zero."
+ At Al.=Maeuo. the expressions in equations (6)) and (7)) ave the same.," At $M_s=M_J\epsilon_{max,0}$, the expressions in equations \ref{eq:sol1}) ) and \ref{eq:sol2}) ) are the same."
+ A graph of n.(M.) from these equations is shown in figure | for Ro=10. ου=1l. and M;=0.3 M.," A graph of $n_s(M_s)$ from these equations is shown in figure 1 for ${\cal R}=10$, $\epsilon_{max,0}=1$, and $M_J=0.3$ $_\odot$ ."
+ Figure 2 shows the result. better using the numerical model with random sampling described in Papers E and LH. but now with a stellar mass equal to a random fraction « of the chosen clump mass.," Figure 2 shows the result better using the numerical model with random sampling described in Papers I and II, but now with a stellar mass equal to a random fraction $\epsilon$ of the chosen clump mass."
+ This random fraction is equally distributed. over a logarithmic range. as specified in the above discussion. bv using the equation c=Ro! for random variable r that is distributed. uniformly over 0.1].," This random fraction is equally distributed over a logarithmic range, as specified in the above discussion, by using the equation $\epsilon= {\cal R}^{r-1}$ for random variable $r$ that is distributed uniformly over $\left[0,1\right]$."
+ Four dillerent. values of AR. are used in the figure to show row the length of the Hattened. part equals AR., Four different values of ${\cal R}$ are used in the figure to show how the length of the flattened part equals ${\cal R}$.
+" The R=1 case shows the pure clump selection spectrum. as in papers Land EH. but with a sharper lower mass cutoff than in he other papers. taken here from a failure probability Ppo—erpALALi"").We also took μωρο=1 for simplicity: the exact value is not important. (it occurs in he expression for ες"," The ${\cal R}=1$ case shows the pure clump selection spectrum, as in papers I and II, but with a sharper lower mass cutoff than in the other papers, taken here from a failure probability $P_f=exp\left(-\left[M_c/M_J\right]^{4}\right)$.We also took $\epsilon_{max,0}=1$ for simplicity; the exact value is not important (it occurs in the expression for $\epsilon(r)$)."
+ For all of the cases. there are 10 evels of hierarchical structure in the cloud model. with an average of 2 subpieces per piece. ancl an actual number of subpieces per piece distributed: as a Poisson variable over he interval from 1 to4.," For all of the cases, there are 10 levels of hierarchical structure in the cloud model, with an average of 2 subpieces per piece, and an actual number of subpieces per piece distributed as a Poisson variable over the interval from 1 to4."
+" The results. indicate that for A, Αμμος the model IME is a power law with the same power as the"," The results indicate that for $M_s>M_J\epsilon_{max,0}$ , the model IMF is a power law with the same power as the"
+induced clectric field for the particles is heating he plasiua or conductor.,induced electric field for the particles is heating the plasma or conductor.
+ Tn plana. the induced electric field. is always oerpendicular to magnetic field. so the current by he iuduced electric field will he turu around by he magnetic field auc forms small circles.," In plasma, the induced electric field is always perpendicular to magnetic field, so the current by the induced electric field will be turn around by the magnetic field and forms small circles."
+ The radius of the current is much small., The radius of the current is much small.
+ There will be 10 lmacroscopic current due to the overlap of the circled electric current., There will be no macroscopic current due to the overlap of the circled electric current.
+ Iowever. the induced electric field will coutribute euncrey to the thermal enerey of the plasma.," However, the induced electric field will contribute energy to the thermal energy of the plasma."
+ Since the iuduced electric field depends ou the variation of magnetic field. the increase of the thermal euerev ofthe plasina will come from the variation of the maguetic field.," Since the induced electric field depends on the variation of magnetic field, the increase of the thermal energy of the plasma will come from the variation of the magnetic field."
+ We can suppose the increase of the thermal cnerey as: Though the transfer of maguctic feld to hermal euergv nav depends on the collisions οποσα charecd particles. there is no macroscopic electric current inside the plasia.," We can suppose the increase of the thermal energy as: Though the transfer of magnetic field to thermal energy may depends on the collisions between charged particles, there is no macroscopic electric current inside the plasma."
+ From the above discussions. we can couclude hat the heating of the plasina im maguetic ficld nay comes from the motion of plasma across naegnetic field. aud the variation of magnetic field.," From the above discussions, we can conclude that the heating of the plasma in magnetic field may comes from the motion of plasma across magnetic field, and the variation of magnetic field."
+" Eventually. the processes of plasma heating nu varlation of Mag,vetic Geld is observed in the solar atmosphere."," Eventually, the processes of plasma heating by variation of magnetic field is observed in the solar atmosphere."
+ Zhaug.Zhiug&Zhang(2007) studied the relation of CME with magnetic field variation., \citet{b18} studied the relation of CME with magnetic field variation.
+ Then found that all of the CATE have the variation of magnetic fleld aud maybe the source of CME cruption., Then found that all of the CME have the variation of magnetic field and maybe the source of CME eruption.
+ In the present paper. we get the clectric: curent and the plasma velocity: in: the fully. ∙⋅ ↴ : ⋅↴∐⋅∪≼⊳↸∖↴∖∷∖↴↕↴∖↴∐∪↑≯↥⋅∪⋯≼≓∐∐⊔⋅↴∖↴≼∐∖↴↴∖↴∏≻⋜↧↕∪∐∙↴∏≼∐↥⋅↸∖↸⊳↑↕↖⇁ ↕∪⋯∑↸∖≼⊔≻↕⋜↧↴∖⋯⋜↧↴⋝⋅↖↴∖∪↕∏∐∶↴∙↑↕∐∖≼↧⋅↖∐⋜⊔∐↸⊳↸∖≺∣∏⋜↧⊓∪∐↴∖ chargednu particles.," In the present paper, we get the electric current and the plasma velocity in the fully ionized plasma by solving the dynamic equations of charged particles."
+"⋅⋅↴ The↴ macroscopic⋅↴ electric⋅, ron current is: decided: by the difference"" of: the averaged M ↴ ⋅ sl↸∖↕∐∖↥⋅∩⊾↖↽≼∐∖⋉∖∐≼↴∖↴∪∐↑∐↸∖↖↽⋪", The macroscopic electric current is decided by the difference of the averaged velocities of ions and electrons.
+∐⋅↕⋪↧↑↕∪∐∪↕⋟⋯⋪↧∩⊾∐∖↑↕↸⊳∐↸∖↕≼⇂ current aud plasina velocity ⋅⋅is completely decided⋅ by electromagnetic field aud external forces., The electric current and plasma velocity is completely decided by electromagnetic field and external forces.
+" When the external forces f; aud f, acting on ions and electrous respectively. including the pressure eradieut. the friction aud gravitation. are. considered.↴⋅⋅ the electric⋅⋅ current⋅⋅ in⋅ the plane perpendicular: to magnetic ⋅⋅field will: be the form,: of: equation (50) to (52). the electric Seld perpeudicular o maesnetie field does not contrbute to the uacroscopie clectric current."," When the external forces $f_{i}$ and $f_{e}$ acting on ions and electrons respectively, including the pressure gradient, the friction and gravitation, are considered, the electric current in the plane perpendicular to magnetic field will be the form of equation (50) to (52), the electric field perpendicular to magnetic field does not contribute to the macroscopic electric current."
+ The macroscopic electric crent depends only on the external ORCC., The macroscopic electric current depends only on the external forces.
+ The electric. current perpendicular to the naenetic field do not depeud ou the electric field., The electric current perpendicular to the magnetic field do not depend on the electric field.
+ The induced electrie feld in magnetic field do iot contribute to the electric current. since the induced clectric feld. is always perpendicular to he maguetic field.," The induced electric field in magnetic field do not contribute to the electric current, since the induced electric field is always perpendicular to the magnetic field."
+" In auy reference svstem with velocity v. the induced. electric feld. v!«B is )orpendieular to the maguetic field. aud will not contribute fo the macroscopic electric current, so cannot distort the magnetic field in space."," In any reference system with velocity $\bf{v}'$ , the induced electric field $\bf{v}'\times \bf{B}$ is perpendicular to the magnetic field, and will not contribute to the macroscopic electric current, so cannot distort the magnetic field in space."
+ The velocity of the plasma is not coupled with maenctic field., The velocity of the plasma is not coupled with magnetic field.
+ When the external forces are ignored. there is: no electric: current in: the plane perpendicular: to maenetic field.," When the external forces are ignored, there is no electric current in the plane perpendicular to magnetic field."
+ The Pedersen current aud Tall cirrent are zero., The Pedersen current and Hall current are zero.
+ The plasma has a velocity. Tt is the global daitt of the plasina in electromagnetic field.," The plasma has a velocity, It is the global drift of the plasma in electromagnetic field."
+ In plasma. the electric field is screcued. the dift velocity is zero.," In plasma, the electric field is screened, the drift velocity is zero."
+ When plasma with average velocity ο cuter naenetic field. the plasiia will be confined N le maguetic field.," When plasma with average velocity $v$ enter magnetic field, the plasma will be confined by the magnetic field."
+ The kinetic enerev of the dauua perpendieulus to imaguetie fold will be rausported into plasma thermal cnerey., The kinetic energy of the plasma perpendicular to magnetic field will be transported into plasma thermal energy.
+ The uacroscopic velocity perpendicular to magnetic ποια is zero., The macroscopic velocity perpendicular to magnetic field is zero.
+ It is oue process for plasiua. heatiue., It is one process for plasma heating.
+ When plana is m varied magnetic field. the induced clectric field will heating plasma.," When plasma is in varied magnetic field, the induced electric field will heating plasma."
+ The nacroscopic‘] electric current is nof. presented or the existence of magneticas field., The macroscopic electric current is not presented for the existence of magnetic field.
+ The heatingatis the action of induced electric fieldl ud of naeneticto field.," The heating process is not from Ohm's dissipation, but directly from the action of induced electric field and magnetic field."
+ The increase‘ of the pavplasma thermal' ini ↖↽↸∖↕⋯⊳↕↑↕↸∖↴∖↴∪↕↕∪∐↴∖↴⋜⋯≼↧↸∖↕↸∖↸⊳⊓⋅∪∐↴∖↴∙↽∕∏∐∖↸∖↕↸∖↸⊳⊓⋅∐⊳to with ]time., The increase of the plasma thermal energy depends on the variation of magnetic field with time.
+ Th this paper. we don't consider the boundary condition of the plasma and the inhomogceucous maenetic ∙∙field.," In this paper, we don't consider the boundary condition of the plasma and the inhomogeneous magnetic field."
+ The↴ effect⋅ of. the boundary and inhomogencous. field: will: have effect. on the electric: current iu the plasma., The effect of the boundary and inhomogeneous field will have effect on the electric current in the plasma.
+ The work will be doneiu fntuture research., The work will be donein future research.
+ The work will be doneiu fntuture research.‘, The work will be donein future research.
+ The work will be doneiu fntuture research.‘], The work will be donein future research.
+"the spectrum to be coming [rom opposite sides of the cone and the true velocity direction is along the sides of the cone. then the observed. velocities e; and. rs are defined by. Using our values for the observed. velocities of the Gaussian components in the spectrum. ey=225 θα land 04,2230 wave can solve equations (1) and. (2) to obtain @=48°. a=23 and a velocity along the cone of r=245 (sce Fig. 6)).","the spectrum to be coming from opposite sides of the cone and the true velocity direction is along the sides of the cone, then the observed velocities $v_{1}$ and $v_{2}$ are defined by, Using our values for the observed velocities of the Gaussian components in the spectrum $v_{1}$, $v_{2}$ and $\alpha_{obs}$ we can solve equations (1) and (2) to obtain $\theta=48\degr$, $\alpha=23\degr$ and a velocity along the cone of $v$ (see Fig. \ref{schmod.fig}) )."
+ We use the [line profiles as measured at more than (from the nucleus in order to minimize contamination from the core region., We use the line profiles as measured at more than from the nucleus in order to minimize contamination from the core region.
+ lor simplicity. we used a Gaussian emissivity distribution for the wall of the cone (ic. the emissivity drops smoothly away from the local racius of the wall).," For simplicity, we used a Gaussian emissivity distribution for the wall of the cone (i.e. the emissivity drops smoothly away from the local radius of the wall)."
+ We assume that the emitting gas moves racially outwarels from the vertex of the cone., We assume that the emitting gas moves radially outwards from the vertex of the cone.
+ We also assume that the emissivity along the jet axis drops with a Gaussian distribution (FWILIM = 127 pe)., We also assume that the emissivity along the jet axis drops with a Gaussian distribution (FWHM = 127 pc).
+ Using the parameters derived from the spectrum. and erouncl based image. this model vields a reasonably good approximation to the data (Pigs.," Using the parameters derived from the spectrum and ground based image, this model yields a reasonably good approximation to the data (Figs."
+ 7 and S))., \ref{modim} and \ref{modspec}) ).
+ However. the apparent opening angle in the simulated image ancl the exact shape of the spectrum both depend on the thickness of the wall of the cone.," However, the apparent opening angle in the simulated image and the exact shape of the spectrum both depend on the thickness of the wall of the cone."
+ Similarly. the width of the spectral lino coming from. each side of the cone is determined by the width of the wall.," Similarly, the width of the spectral line coming from each side of the cone is determined by the width of the wall."
+ Note that in this model the side of the cone which is best aligned. with the line of sight will have a smaller spectral width than the other., Note that in this model the side of the cone which is best aligned with the line of sight will have a smaller spectral width than the other.
+ Vhis ellect can be seen in Fig. S..," This effect can be seen in Fig. \ref{modspec},"
+ where spectra are drawn with dillerent wall thicknesses., where spectra are drawn with different wall thicknesses.
+ Here a slit of width wivas set to be aligned. with the cone axis. and a section between aand [from the core was used to produce this spectrum.," Here a slit of width was set to be aligned with the cone axis, and a section between and from the core was used to produce this spectrum."
+ The spectral resolution was aand the spatial resolution was0., The spectral resolution was and the spatial resolution was.
+"8""... A larger model slit width was used than in the observations to compensate for the image motion due to seeing. which was not taken into account explicitly."," A larger model slit width was used than in the observations to compensate for the image motion due to seeing, which was not taken into account explicitly."
+ Phe solid line in Fig., The solid line in Fig.
+ NS. is for a FWILM, \ref{modspec} is for a FWHM
+is not attributed to selection effect and sharply peaked around a 4/3 ratio.,is not attributed to selection effect and sharply peaked around a 4/3 ratio.
+ For this special binary. il seems (hat some lrequencies are disfavored.," For this special binary, it seems that some frequencies are disfavored."
+ In other words. within the orbital QPO interpretation. preferred radii exist within the disk. supporting the resonance mocel.," In other words, within the orbital QPO interpretation, preferred radii exist within the disk, supporting the resonance model."
+" When the star rotates slowly. its geometrized angular momentum à remains small aud a first order expansion for zji,(6) wilh respect to à is possible."," When the star rotates slowly, its geometrized angular momentum $\tilde{a}$ remains small and a first order expansion for $\nu_{\rm isco}(\tilde{a})$ with respect to $\tilde{a}$ is possible."
+ In (he next section. we will show how to use this linear approximation to find severe constrains on the stellar mass ancl moment of inertia.," In the next section, we will show how to use this linear approximation to find severe constrains on the stellar mass and moment of inertia."
+ Another wav to tackle the resonance condition Eq. (1)).," Another way to tackle the resonance condition Eq. \ref{eq:Resonance}) ),"
+ in the general case for arbitrary à.d8 {ο work directly with the full expressions given by Eq. (2))-(3)).," in the general case for arbitrary $\tilde{a}$, is to work directly with the full expressions given by Eq. \ref{eq:FreqOrbitale}) \ref{eq:FreqVerticale}) )."
+ This requires a numerical algorithm to search for the allowed frequencies aud is also done in the next section. Sec. 3..," This requires a numerical algorithm to search for the allowed frequencies and is also done in the next section, Sec. \ref{sec:Results}."
+ A dozen LAINBs have been inventoried to exhibit the above mentioned behavior., A dozen LMXBs have been inventoried to exhibit the above mentioned behavior.
+ The LAINBs sample used to fit our model for the kKIIz-QDPO difference as measured by some other authors are summarized im Table 1 with appropriate references., The LMXBs sample used to fit our model for the kHz-QPO difference as measured by some other authors are summarized in Table \ref{tab:Data} with appropriate references.
+ We want our model to adjust to this set as close as possible bv looking for appropriate mass and moment of inertia., We want our model to adjust to this set as close as possible by looking for appropriate mass and moment of inertia.
+" Let us take an index 7 (racing this set of LAINBs bv writing ic(LAINBs),", Let us take an index $i$ tracing this set of LMXBs by writing $i\in(LMXBs)$.
+ For each binary. the observed (win kIIz-QPO Irequeney difference is known as Av’.," For each binary, the observed twin kHz-QPO frequency difference is known as $\Delta\nu_i^{\rm obs}$."
+" Fixing M, and £.. we get a predicted Nol. from our parametric resonance model."," Fixing $M_*$ and $I_*$, we get a predicted $\Delta\nu_i^{\rm model}$ from our parametric resonance model."
+ To evaluate the goodness of our fit. we introduce a merit function F defined by summation over all the LAINBs ancl compare the cliscrepancy between. predicted. and measured QDPO cdillerences. such that with a statistical weight σι.," To evaluate the goodness of our fit, we introduce a merit function $\mathcal{F}$ defined by summation over all the LMXBs and compare the discrepancy between predicted and measured QPO differences, such that with a statistical weight $\sigma_i$."
+ The summation should be understood over the set οἱ observed systems., The summation should be understood over the set of observed systems.
+ Av?|7Jl are the observed/predicted. IIF-QPO lrequencyB difference," $\Delta\nu_i^{\rm
+ obs/model}$ are the observed/predicted HF-QPO frequency difference"
+ Av?|7Jl are the observed/predicted. IIF-QPO lrequencyB difference.," $\Delta\nu_i^{\rm
+ obs/model}$ are the observed/predicted HF-QPO frequency difference"
+Disk-utegrated spectra of Neptune between 1.5 aud 13 μισο» were recorded ou May. 13. 2007. using bot1 the prisin and the evista modes of the Infrared Camera ou board ISAS/JANA’s AIKARI infrared astroLOWLY satellite (?).. which lauuched ou Febrwav 21.2yn (UT).,"Disk-integrated spectra of Neptune between 1.8 and 13 microns were recorded on May 13, 2007, using both the prism and the grism modes of the Infrared Camera on board ISAS/JAXA's AKARI infrared astronomy satellite , which launched on February 21, 2006 (UT)."
+ The broad waveleneth-coverage provided by ΑΝΑΗΙ pernüts smiultauecous observation of rear-IR reflecance of sunlight and nik-IR thermal emission., The broad wavelength-coverage provided by AKARI permits simultaneous observation of near-IR reflectance of sunlight and mid-IR thermal emission.
+" Tjose data are used to constrai1 models of Nep""nues atnospleric structure. compositiom aud aerosols in the troposphere aud stratosphere."," These data are used to constrain models of Neptune's atmospheric structure, composition and aerosols in the troposphere and stratosphere."
+ Iuterior models iindicate that Nepnues atnospleric envelope o| IIo sux Ile represcuts oiv a thin shell compared to the racius of the planet7).. but the collision-iuneed continuum of IL-IIe is the dominaut source of opacity 1i the mid-IR προςΈαii (6-12. pau).," Interior models indicate that Neptune's atmospheric envelope of $_2$ and He represents only a thin shell compared to the radius of the planet, but the collision-induced continuum of $_2$ -He is the dominant source of opacity in the mid-IR spectrum (6-13 $\mu$ m)."
+ Iu addition to continu enuüssion. the 6-13 jun spectru exhibits substantial structure due to he chemistry of stratospheric methane (0). CID and higher-order lvdrocarhois (Fig. 1i.," In addition to continuum emission, the 6-13 $\mu$ m spectrum exhibits substantial structure due to the chemistry of stratospheric methane $_4$ ), $_3$ D and higher-order hydrocarbons (Fig. \ref{spectrum}) )."
+ Neptune's bulk C/II ratio is kuown to be enriched over the solar aliudance of by σι15?)., Neptune's bulk C/H ratio is known to be enriched over the solar abundance of by $54\pm15$.
+. This is coisistout wit1 formation modeIs??).. which predict that Nepune received a larger proportion o| heavy οclients (relative to the Πο Πο cuvelooes) conmnipared ο the other ela plancts.," This is consistent with formation models, which predict that Neptune received a larger proportion of heavy elements (relative to the $_2$ -He envelopes) compared to the other giant planets."
+" AKARI soectroscopy. of boti CT, aud the ieher-order hvdrocarbons will be usec to deerniue Nep""ues stratospheric telerature and ¢Omposition.", AKARI spectroscopy of both $_4$ and the higher-order hydrocarbons will be used to determine Neptune's stratospheric temperature and composition.
+ The cold atinospheric teuperatures vield an extiπο] low-»ower thermal cuaissicn Προςσι which requires high sensitivity to measure accurately and AIARI resits will be compared to previous cerivatious of Neptune's hermal structure from the Vovager radio science invesigation?). infrared spectrometer and the Iufrired Space Observatorv η.," The cold atmospheric temperatures yield an extremely low-power thermal emission spectrum which requires high sensitivity to measure accurately, and AKARI results will be compared to previous derivations of Neptune's thermal structure from the Voyager radio science investigation, infrared spectrometer and the Infrared Space Observatory ."
+" Previous studies have shown that the stratospheric abundance of CIT; is larger than the saturated abundance at the tropopause(?).. which should serve as au efficieut ""cold trap! or CII, restricting it to the troposphere."," Previous studies have shown that the stratospheric abundance of $_4$ is larger than the saturated abundance at the tropopause, which should serve as an efficient `cold trap' for $_4$ , restricting it to the troposphere."
+" Vigorous vertical advecjon of both gaseous CII, aud CII, ice ανHcl subseqtrently sublimiaes) was invoked to explain the stratosphere abundance.", Vigorous vertical advection of both gaseous $_4$ and $_4$ ice (which subsequently sublimates) was invoked to explain the stratospheric abundance.
+ Such rapid convection is consistent with observations of Neptuue's strong internal heat flux. the disequiBbriun of para-hydrogen (?). the high levels of tropospheric CO cleternuned from the sub-nunu and with the visible observations of thick. high clouds casine shadows on deeoer levels in Vovager 2 nuages.," Such rapid convection is consistent with observations of Neptune's strong internal heat flux, the disequilibrium of para-hydrogen , the high levels of tropospheric CO determined from the sub-mm and with the visible observations of thick, high clouds casting shadows on deeper levels in Voyager 2 images."
+ However. couvective clotd activity is vpically restricted to Neptunes iid-latiudes and is time-variable73. and it oroniaius Tuc‘lear whether the streneth of the upwelling is sufficieit to maiutaiu the svatospheric CTL). wch is continually CLOSroved by pjotolvsis.," However, convective cloud activity is typically restricted to Neptune's mid-latitudes and is time-variable, and it remains unclear whether the strength of the upwelling is sufficient to maintain the stratospheric $_4$, which is continually destroyed by photolysis."
+" As an alteruaive. gromd-haseel lait-IR imaging demonstrated the preseuce of a 1x SOITh polar regio1 warn enough to permit significa CII, escape iu| the stratosphere witrout the need for strong convection."," As an alternative, ground-based mid-IR imaging demonstrated the presence of a hot south polar region, warm enough to permit significant $_4$ escape into the stratosphere without the need for strong convection."
+" Ultimately. it ds likely that both mechanisms contribute. but AKARI «lerivations of the elobal CII, anmudauce will be used to reassess the requirement for stroug couvectiou of nethane-lacden air into the stratosphere."," Ultimately, it is likely that both mechanisms contribute, but AKARI derivations of the global $_4$ abundance will be used to reassess the requirement for strong convection of methane-laden air into the stratosphere."
+" Once in the stratosphere. CIT, is photolvsed. to form the higher hydrocarbous."," Once in the stratosphere, $_4$ is photolysed to form the higher hydrocarbons."
+ Acetylene (Πο at 13.7 01) and ethane (Coll; at 12.2 nu) were first detected iu eround-base spectroscopy ancl confined bv Vovager/IRIS spectra2j., Acetylene $_2$ $_2$ at 13.7 $\mu$ m) and ethane $_2$ $_6$ at 12.2 $\mu$ m) were first detected in ground-based spectroscopy and confirmed by Voyager/IRIS spectra.
+" Ethylene P (Coll, at 10.5 jau) was deteced in ISO spectra. by.?).. and both moethlvlacetvlene (οι at ]Ks unn) and diacetylene IT» at 15.9 gan) were recently cletected in Spitzer/IRS spectra(2)."," Ethylene $_2$ $_4$ at 10.5 $\mu$ m) was detected in ISO spectra by, and both methylacetylene $_3$ $_4$ at 15.8 $\mu$ m) and diacetylene $_4$ $_2$ at 15.9 $\mu$ m) were recently detected in Spitzer/IRS spectra."
+. These liverocarhous may diffuse downuwwuds aud freeze out as haze lavers. axd sunlight absorption on these lydrocarbou hazes maybe partiallyresponsible for the warn teniperatiyes of the lower stratosphere.," These hydrocarbons may diffuse downwards and freeze out as haze layers, and sunlight absorption on these hydrocarbon hazes maybe partiallyresponsible for the warm temperatures of the lower stratosphere."
+ The near-IR region o| the AKARI spectrum. (4δ- gan) is dominated by he reflection of suulight from, The near-IR region of the AKARI spectrum (1.8-5.0 $\mu$ m) is dominated by the reflection of sunlight from
+On Dee 27. 2004. the most energetic explosion witnessed by humans within our galaxy for over 400 years was detected from the soft gamma-ray repeater SGR 1806-20 (e.g. Borkowski et al.,"On Dec 27, 2004, the most energetic explosion witnessed by humans within our galaxy for over 400 years was detected from the soft gamma-ray repeater SGR 1806-20 (e.g. Borkowski et al."
+ 2004: Palmer et al., 2004; Palmer et al.
+ 2004: Hurley et al., 2004; Hurley et al.
+ 2005)., 2005).
+ Shortly after the outburst an expanding radio source was detected associated with SGR 1806-20 (Cameron et al., Shortly after the outburst an expanding radio source was detected associated with SGR 1806-20 (Cameron et al.
+ 2005: Gaensler et al., 2005; Gaensler et al.
+ 2005)., 2005).
+ This radio emission traces the ejection of mass from the surface of the neutron star. and its interaction with the ambient medium (Gelfand et al.," This radio emission traces the ejection of mass from the surface of the neutron star, and its interaction with the ambient medium (Gelfand et al."
+ 2005: Tavlor et al., 2005; Taylor et al.
+ 2005: Granot et al., 2005; Granot et al.
+ 2005) Measuring the geometry and temporal evolution of this ejected matter is of key importance for our understanding of the origins of this enormous outburst. and its impact upon its immediate environment.," 2005) Measuring the geometry and temporal evolution of this ejected matter is of key importance for our understanding of the origins of this enormous outburst, and its impact upon its immediate environment."
+ SGR 1806-20 is believed to be a magnetar an isolated non-accreting neutron star with a magnetic field >1011 G (Kouveliotou et al.," SGR 1806-20 is believed to be a magnetar, an isolated non-accreting neutron star with a magnetic field $\geq 10^{14}$ G (Kouveliotou et al."
+ 1998)., 1998).
+ While several scenarios discussed for the origin of he radio emission from SGR 1806-20 predict possibly edge-brightened emission (Gaensler et al., While several scenarios discussed for the origin of the radio emission from SGR 1806-20 predict possibly edge-brightened emission (Gaensler et al.
+ 2005: Gelfand et al., 2005; Gelfand et al.
+ 2005: Granot 2005) or other spatial structure. especially at early times. he relatively low resolution radio data published to date have not allowed a test of these models.," 2005; Granot 2005) or other spatial structure, especially at early times, the relatively low resolution radio data published to date have not allowed a test of these models."
+ As a result. Gaussian models iive been fit to the data sets in order to quantify the motion and expansion of the source. despite the link between the fit parameters and physieal conditions in the radio source remaining uncertain.," As a result, Gaussian models have been fit to the data sets in order to quantify the motion and expansion of the source, despite the link between the fit parameters and physical conditions in the radio source remaining uncertain."
+ In this paper we present the highest-resolution radio images of the ejecta between nine and fifty-six days after the outburst. obtained with the US Very Long Baseline Array (VLBA) and the Multi-Element Radio-Linked Interferometer Network (MERLIN) in the UK.," In this paper we present the highest-resolution radio images of the ejecta between nine and fifty-six days after the outburst, obtained with the US Very Long Baseline Array (VLBA) and the Multi-Element Radio-Linked Interferometer Network (MERLIN) in the UK."
+ These are the first. and possibly only. data sets which are able to probe on angular scales. =100 mas and test for substructure in the evolving radio source.," These are the first, and possibly only, data sets which are able to probe on angular scales $\la 100$ mas and test for substructure in the evolving radio source."
+enough mass before the impulsive phase.,enough mass before the impulsive phase.
+ A high coronal density can prevent the electron beam [rom penetrating deeper., A high coronal density can prevent the electron beam from penetrating deeper.
+ Here we do not detect blueshifts at temperatures higher (han 15 MEN due to the limitation of the EIS dvnamie range. but we find that the Fe XXIII and Fe XXIV line intensities at this point are still strong aud. (heir profiles ave well in this event.," Here we do not detect blueshifts at temperatures higher than 15 MK due to the limitation of the EIS dynamic range, but we find that the Fe XXIII and Fe XXIV line intensities at this point are still strong and their profiles are well Gaussian-shaped in this event."
+ This seems (to support the hypothesis of a high coronal density., This seems to support the hypothesis of a high coronal density.
+" In addition. Brosius(2003) detected redshifted emission that persisted al least 20 min alter the cessation of blueshilts and suggested that flare plasma. heated and accelerated ipw during the impulsive phase. subsequently cooled aud fell back down in what may be thought of as ""warm rain’."," In addition, \cite{bros03} detected redshifted emission that persisted at least 20 min after the cessation of blueshifts and suggested that flare plasma, heated and accelerated upward during the impulsive phase, subsequently cooled and fell back down in what may be thought of as “warm rain”."
+ For the present event. scanning (he active region by EIS lasted about 26 min: therefore. we do not have an enough high temporal resolution here.," For the present event, scanning the active region by EIS lasted about 26 min; therefore, we do not have an enough high temporal resolution here."
+ However. from Figure 7.. we can find that the downflows still exist in the post-impulsive phase at point 2. contrary to the blueshifts at point 1. which are diminished to nearly zero in the phase.," However, from Figure \ref{velp1p2}, we can find that the downflows still exist in the post-impulsive phase at point 2, contrary to the blueshifts at point 1, which are diminished to nearly zero in the post-impulsive phase."
+ From the SOT Ca II IL movie. we find that the flare ribbons are nol brightened simultaneously.," From the SOT Ca II H movie, we find that the flare ribbons are not brightened simultaneously."
+ Therefore. we cannot exclude (he warm rain as a possible cause of the downflows.," Therefore, we cannot exclude the warm rain as a possible cause of the downflows."
+ The three points discussed here are located in different magnetic polarity regions., The three points discussed here are located in different magnetic polarity regions.
+ Thev show different patterus of mass flows., They show different patterns of mass flows.
+ Point 1 lies in the positive polarity region while points 2 and 3 in the negative polarity region., Point 1 lies in the positive polarity region while points 2 and 3 in the negative polarity region.
+ We check further (he magnetic connectivities between the positive and negative magnetic polarities., We check further the magnetic connectivities between the positive and negative magnetic polarities.
+ The available data cannot provide a definite conclusion regarding whether point 1 is magneticallv connected (to point 2 or 3., The available data cannot provide a definite conclusion regarding whether point 1 is magnetically connected to point 2 or 3.
+ However. even if (μον belong to different magnetic loops. the different evaporation patterns shown al (hem suggest (hat in one [Lung region. the heating mechanisms and atmospheric conditions may varv [rom point (to point.," However, even if they belong to different magnetic loops, the different evaporation patterns shown at them suggest that in one flaring region, the heating mechanisms and atmospheric conditions may vary from point to point."
+ The authors would like to thank the referee for valuable commentis on the paper and Feng Chen. Nin Chene. aud Zongjun Nine for helpful discussions.," The authors would like to thank the referee for valuable comments on the paper and Feng Chen, Xin Cheng, and Zongjun Ning for helpful discussions."
+ This work was supported by NSFC under grants 10828306 and 10933003 and by NIXDRSE under grant 2011CD311402., This work was supported by NSFC under grants 10828306 and 10933003 and by NKBRSF under grant 2011CB811402.
+ inode is à Japanese mission developed and launched by ISAS/JANA. collaborating with NAOJ as a domestic partner. and NASA (USA) and STFC (UK) as international partners.," Hinode is a Japanese mission developed and launched by ISAS/JAXA, collaborating with NAOJ as a domestic partner, and NASA (USA) and STFC (UK) as international partners."
+ scientific operation of the Hinode mission is conducted by the Linode science team organized a ISAS/JAXA., Scientific operation of the Hinode mission is conducted by the Hinode science team organized at ISAS/JAXA.
+ Support for the post-launch operation is provided by JANA and NAOJ (Japan). STFC (U.IX.). NASA. ESA. and NSC! (Norway).," Support for the post-launch operation is provided by JAXA and NAOJ (Japan), STFC (U.K.), NASA, ESA, and NSC (Norway)."
+"where the appropriate o can be determined from simulations, and is dependent on a tradeoff between the desired level of accuracy of the reconstructed data and the time taken to complete the reconstruction.","where the appropriate $\alpha$ can be determined from simulations, and is dependent on a tradeoff between the desired level of accuracy of the reconstructed data and the time taken to complete the reconstruction."
+" Choosing a to be large will result in an estimate of the solution that may be some distance away from the solution that would be obtained if absolute convergence were reached, but which is obtained in a small number of iterations."," Choosing $\alpha$ to be large will result in an estimate of the solution that may be some distance away from the solution that would be obtained if absolute convergence were reached, but which is obtained in a small number of iterations."
+ Figure B1 shows a characteristic example of the function as a function of iteration number N for the simulations describedAGN in 5.., Figure \ref{fg:conv} shows a characteristic example of the function $\Delta\mathfrak{G}_{pd}^N$ as a function of iteration number $N$ for the simulations described in \ref{sec:results}.
+" This function is clearly a smooth, largely steadily decreasing function of iteration number, and thus an appropriate choice for defining convergence."," This function is clearly a smooth, largely steadily decreasing function of iteration number, and thus an appropriate choice for defining convergence."
+ Note that the curve shows some oscillations with iteration number., Note that the curve shows some oscillations with iteration number.
+ Such oscillations arise on lines of sight where the noise results in the algorithm having difficulty fitting the data within the constraints., Such oscillations arise on lines of sight where the noise results in the algorithm having difficulty fitting the data within the constraints.
+" With appropriate choice of parameters, these oscillations are relatively small and the curve eventually becomes smooth."," With appropriate choice of parameters, these oscillations are relatively small and the curve eventually becomes smooth."
+" We find from experimentation that a=10$ yields a solution that is sufficiently accurate for our purposes, and is sufficient to largely remove the oscillations, thus we set this to be our threshold for all reconstructions presented above."," We find from experimentation that $\alpha = 10^{-6}$ yields a solution that is sufficiently accurate for our purposes, and is sufficient to largely remove the oscillations, thus we set this to be our threshold for all reconstructions presented above."
+" In addition, we require that each line of sight undergoes at least 1500 iterations, to avoid misidentification of convergence due to early oscillations of AGN, specifically a strong dip seen in this curve at the start of iteration."," In addition, we require that each line of sight undergoes at least 1500 iterations, to avoid misidentification of convergence due to early oscillations of $\Delta\mathfrak{G}_{pd}^N$, specifically a strong dip seen in this curve at the start of iteration."
+" It is possible, along certain lines of sight, for the estimate of the solution to remain constant at zero due to the soft thresholding while still varies."," It is possible, along certain lines of sight, for the estimate of the solution to remain constant at zero due to the soft thresholding while $\Delta\mathfrak{G}_{pd}^N$ still varies."
+" To account for this, if the current cumulative AGNestimate z"" does not vary for 200 iterations, we assume that convergence has been reached for that line of sight."," To account for this, if the current cumulative estimate $x^N$ does not vary for 200 iterations, we assume that convergence has been reached for that line of sight."
+ We now consider several practical issues involved in the implementation of this algorithm., We now consider several practical issues involved in the implementation of this algorithm.
+" w and 7 control the step size in the evolution of the algorithm, and are required to be positive and to satisfy the inequality where9=|X29+||®*||, is the sum of the {2 norms of the operators used in the algorithm."," $\omega$ and $\tau$ control the step size in the evolution of the algorithm, and are required to be positive and to satisfy the inequality where $\Theta \equiv \norm{\boldsymbol{\Sigma}^{-\tfrac{1}{2}}\mathbf{Q}}_2+\norm{\boldsymbol{\Phi}^*}_2$ is the sum of the $\ell_2$ norms of the operators used in the algorithm."
+" This sum is dominated by the second term, as the elements of the Q lensing efficiency matrix are small."," This sum is dominated by the second term, as the elements of the $\mathbf{Q}$ lensing efficiency matrix are small."
+" We have chosen a ó-function dictionary, therefore the application of the transformation ®* represents a multiplication by the identity matrix."," We have chosen a $\delta$ -function dictionary, therefore the application of the transformation $\boldsymbol{\Phi}^*$ represents a multiplication by the identity matrix."
+" Thus we have Θ~||®*||,1, which implies that wr~1 is appropriate."," Thus we have $\Theta \sim \norm{\boldsymbol{\Phi}^*}_2\sim 1$, which implies that $\omega\tau \sim 1$ is appropriate."
+" For all the results that follow, we choose w—T 1."," For all the results that follow, we choose $\omega = \tau = 1$ ."
+ Smaller values of these parameters may be used with little effect on the resulting solution., Smaller values of these parameters may be used with little effect on the resulting solution.
+" However, the smaller the values chosen, the smaller the steps taken in each iteration of the algorithm."," However, the smaller the values chosen, the smaller the steps taken in each iteration of the algorithm."
+ This results in a slower convergence than seen with larger values of w , This results in a slower convergence than seen with larger values of $\omega$ 
+coorbitals has already been pointed out by Cresswell Nelson (2006).,coorbitals has already been pointed out by Cresswell Nelson (2006).
+ The final outcome of this system consists of an inner coorbital system. a single Earth-mass planet trapped in an exterior mean-motion resonance and an additional coorbital pair in another resonance.," The final outcome of this system consists of an inner coorbital system, a single Earth-mass planet trapped in an exterior mean-motion resonance and an additional coorbital pair in another resonance."
+ Although this appears a very complex multiple resonant configuration. we found no indication of long-term instability.," Although this appears a very complex multiple resonant configuration, we found no indication of long-term instability."
+ Figure 16. shows the dvnamies of both pairs of coorbitals: planets | and 2 are displayed on the left-hand plots. while the coorbital system composed of planets 4 and 8 are shown on the right.," Figure \ref{fig5_p} shows the dynamics of both pairs of coorbitals: planets 1 and 2 are displayed on the left-hand plots, while the coorbital system composed of planets 4 and 8 are shown on the right."
+" Top graphs present the temporal evolution of the resonant angle στAX=AvA, while the middle plots show xe» wr.", Top graphs present the temporal evolution of the resonant angle $\sigma = \Delta \lambda = \lambda_2 - \lambda_1$ while the middle plots show $\Delta \varpi = \varpi_2 - \varpi_1$ .
+ Once planet 4 is scattered into the cavity. the resonance relation between planets | and 2 is temporarily disrupted. resulting in a short-lived circulation of both angles.," Once planet 4 is scattered into the cavity, the resonance relation between planets 1 and 2 is temporarily disrupted, resulting in a short-lived circulation of both angles."
+ However. once the Earth-mass planet is sent back outside the cavity. the coorbital configuration of the inner planets is reestablished. although around {ντ instead of £1.," However, once the Earth-mass planet is sent back outside the cavity, the coorbital configuration of the inner planets is reestablished, although around $L_5$ instead of $L_4$."
+ We did some follow-up integrations without hydrodynamical interaction choosing two intermediate stages as initial conditions., We did some follow-up integrations without hydrodynamical interaction choosing two intermediate stages as initial conditions.
+ The bottom left-hand plot shows the results choosing as initial conditions the system configuration at /=450 and /=11450. respectively.," The bottom left-hand plot shows the results choosing as initial conditions the system configuration at $t=450$ and $t=11450$, respectively."
+ The behavior of both critical angles show a small amplitude libration around the equilibrium solutions., The behavior of both critical angles show a small amplitude libration around the equilibrium solutions.
+" Between these two solutions the system experiments temporarily L4, and LL; configurations.", Between these two solutions the system experiments temporarily $AL_4$ and $AL_5$ configurations.
+ The dynamical evolution of the small-mass pair is more complex. and a stable configuration is only reached near the end of the simulation. and corresponds to an «Εις type orbit with large amplitude of oscillation of zc or about 150°.," The dynamical evolution of the small-mass pair is more complex, and a stable configuration is only reached near the end of the simulation, and corresponds to an $AL_5$ type orbit with large amplitude of oscillation of $\Delta \varpi$ or about $150^\circ$."
+ In this paper we have analyzed the detectability and possible formation mechanism of hypothetical massive planets in stable coorbital configurations., In this paper we have analyzed the detectability and possible formation mechanism of hypothetical massive planets in stable coorbital configurations.
+ So far there are no known extrasolar planetary systems containing coorbital bodies. whieh may imply that either these configurations are extremely difficult to form or to detect from RV surveys.," So far there are no known extrasolar planetary systems containing coorbital bodies, which may imply that either these configurations are extremely difficult to form or to detect from RV surveys."
+" We have studied the detectabilitv of three different types of coorbital motion (QS. L,/Ls and Εν ο. trying to evaluate possible bias in detections and identify what kind of compatible configuration. could be detected."," We have studied the detectability of three different types of coorbital motion (QS, $L_4/L_5$ and $AL_4/AL_5$ ), trying to evaluate possible bias in detections and identify what kind of compatible configuration could be detected."
+ The analysis of Keplerian contributions to radial velocities allowed us to predict the value for the signal of one single planet that could be confused with coorbital configurations., The analysis of Keplerian contributions to radial velocities allowed us to predict the value for the signal of one single planet that could be confused with coorbital configurations.
+ For even low values of errors in radial velocities measurements (¢ = 3 m/s) and observation time-spans covering four orbital periods (which include most of the presently detected exoplanets). coorbital configurations appear hard to identify: the results of the fitting process could easily confuse the RV data with that stemming from other configurations/systems (single planet or 2/| MMR system).," For even low values of errors in radial velocities measurements $\epsilon$ = 3 m/s) and observation time-spans covering four orbital periods (which include most of the presently detected exoplanets), coorbital configurations appear hard to identify: the results of the fitting process could easily confuse the RV data with that stemming from other configurations/systems (single planet or 2/1 MMR system)."
+ For large mass ratios. a correct identification of coorbital configuration is even more complicated and more easy to confuse with the other configurations.," For large mass ratios, a correct identification of coorbital configuration is even more complicated and more easy to confuse with the other configurations."
+ In all cases. the residuals of the different systems are comparable. even more so for large mass ratios (see Fig 4».," In all cases, the residuals of the different systems are comparable, even more so for large mass ratios (see Fig \ref{rms-stat}) )."
+ Observation data sets covering longer time-spans allow to detect mutual perturbations. but once again the best fits are not always associated to coorbital motion.," Observation data sets covering longer time-spans allow to detect mutual perturbations, but once again the best fits are not always associated to coorbital motion."
+ We have found several cases where other resonant configurations (.e. 3l commensurability) actually give smaller residuals and better results., We have found several cases where other resonant configurations (i.e. 3/1 commensurability) actually give smaller residuals and better results.
+ Coorbital motion is not only sensitive to the data set. but also to the fitting procedure.," Coorbital motion is not only sensitive to the data set, but also to the fitting procedure."
+ Nested two-planet strategies may also confuse the real dynamics and vield results widely different from he nominal orbits: in this sense simultaneous two-planet fits seem more robust., Nested two-planet strategies may also confuse the real dynamics and yield results widely different from the nominal orbits; in this sense simultaneous two-planet fits seem more robust.
+ Transit observations should help distinguish coorbitals planets Tom other solutions., Transit observations should help distinguish coorbitals planets from other solutions.
+ Finally. we have found that stable coorbital systems with two massive planets may be formed from originally non-resonant orbits hrough their interaction with a inner cavity in the protoplanetary disk. as long as the surface density of the disk is sufficiently arge.," Finally, we have found that stable coorbital systems with two massive planets may be formed from originally non-resonant orbits through their interaction with a inner cavity in the protoplanetary disk, as long as the surface density of the disk is sufficiently large."
+" Both our N-body and hydro-simulations indicate a preference owards coorbitals with similar masses (ie. my,mo ", Both our N-body and hydro-simulations indicate a preference towards coorbitals with similar masses (i.e. $m_1 \sim m_2$ ).
+In all our simulations with large mass ratios. the smaller planet was either pushed inside the cavity or trapped in a mean-motion commensurability outside the density jump.," In all our simulations with large mass ratios, the smaller planet was either pushed inside the cavity or trapped in a mean-motion commensurability outside the density jump."
+ This work has been supported by the Argentinian Research Council -CONICET- and the Fundac para a Ciénncia e a Tecnologia (FCT) of Portugal., This work has been supported by the Argentinian Research Council -CONICET- and the Funda\c{c}\\tikzmark{mainBodyEnd7408}\~\tikzmark{mainBodyStart7409}{a}oo para a Ciênncia e a Tecnologia (FCT) of Portugal.
+ol the templates produced a cousistent velocity with an internal dispersiou amoung the incividual measurements that was less than 250 kms |.,of the templates produced a consistent velocity with an internal dispersion among the individual measurements that was less than 250 km $^{-1}$.
+ In general. the proximity of the targets resulted in R> (see Toury Davis).," In general, the proximity of the targets resulted in $R\gtrsim8$ (see Tonry Davis)."
+ Velocity errors were assigned using the formula 280014-22)! Oegerle&Hill 1998).. again with a minimum of 20 kins !.," Velocity errors were assigned using the formula $280(1 + R)^{-1}$ \citep[Tonry \& Davis and][]{oege1998}, again with a minimum of 20 km $^{-1}$."
+ Finally. each galaxy. velocity was confined via visual inspection through identification of major features such as the Ι000Α break and. prominent absorption features such as the C baud. Mell aud Nab. The relative proximity of the sample meant that velocities for some galaxies in the fields of the radio galaxies bac already Όσοι measured.," Finally, each galaxy velocity was confirmed via visual inspection through identification of major features such as the $\mbox{\AA}$ break and prominent absorption features such as the G band, MgII, and NaD. The relative proximity of the sample meant that velocities for some galaxies in the fields of the radio galaxies had already been measured."
+ Consequently. we obtainecl velocities from the NASA/IPAC Extragalactic Database (NED) for galaxies within 1 Mpe of the radio galaxy positions.," Consequently, we obtained velocities from the NASA/IPAC Extragalactic Database (NED) for galaxies within 1 Mpc of the radio galaxy positions."
+ For galaxies in the field of 3C31 we have adopted the velocities of Ledlowetal.(1996).. since these observations were made using tle same telescope and detector.," For galaxies in the field of 3C31 we have adopted the velocities of \citet{ledl1996}, since these observations were made using the same telescope and detector."
+ Table 2. presents the results for all galaxies deemed to be associated with the radio galaxies (see Section ??))., Table \ref{tbl:memvel} presents the results for all galaxies deemed to be associated with the radio galaxies (see Section \ref{sec:anal}) ).
+ The same information lor foreground aud background galaxies nay be found iu Table 3.., The same information for foreground and background galaxies may be found in Table \ref{tbl:bkg_clus}.
+ Lf emission lines were present iu the spectrum. they are noted iu the final column.," If emission lines were present in the spectrum, they are noted in the final column."
+ When such lines were not used in the velocity calculation. they are offset by parentheses.," When such lines were not used in the velocity calculation, they are offset by parentheses."
+ The primary goals of this study are to confirm the preseuce of poor clusters around the radio ealaxies aud better understand the conuection of these galaxies to their local euvirouments., The primary goals of this study are to confirm the presence of poor clusters around the radio galaxies and better understand the connection of these galaxies to their local environments.
+ For hese purposes. the biases inherent iu our sampling of galaxy velocities should not be too iniportant.," For these purposes, the biases inherent in our sampling of galaxy velocities should not be too important."
+ However. it is instructive to examine the completeness of our velocity data.," However, it is instructive to examine the completeness of our velocity data."
+ Hence. we evaluate the raction of galaxies with mieasured velocities as a funetion of optical maeuitude aud radial separation rou the racio galaxies.," Hence, we evaluate the fraction of galaxies with measured velocities as a function of optical magnitude and radial separation from the radio galaxies."
+ aulaxy1 identiflieatious amd magnitudes are available [or 21 of the 25 radio galaxy. fields iu he Automated Plate Scanner (APS) catalogs (LoradescriptionofthescannerPenuiustonuetal. 1993).," Galaxy identifications and magnitudes are available for 21 of the 25 radio galaxy fields in the Automated Plate Scanner (APS) catalogs \citep[for a description of the scanner and procedure, see][]{penn1993}."
+. The other fields are generally too close to the Cralactic plane. causing difficulty in star/galaxy segregation.," The other fields are generally too close to the Galactic plane, causing difficulty in star/galaxy segregation."
+ We have obtained identifications aud rmaguitudes for all ealaxies located within a projected separation of 1 Mpc of the radio galaxies aud. used them to evaluate the completeuess of our velocity data., We have obtained identifications and magnitudes for all galaxies located within a projected separation of 1 Mpc of the radio galaxies and used them to evaluate the completeness of our velocity data.
+" Table Ll presents the results. includiug the linitiug magnitude (41. derived from the Palomar ""E plates) below which we have velocity data lor all £ealaxies (including those not associated. with the radio galaxies)."," Table \ref{tbl:complete} presents the results, including the limiting magnitude $R_c$, derived from the Palomar “E” plates) below which we have velocity data for all galaxies (including those not associated with the radio galaxies)."
+ Luformation is provided for all ealaxies within 1 Mpc of the radio galaxies. in addition to those within 500 kpe aud 250 kpe.," Information is provided for all galaxies within 1 Mpc of the radio galaxies, in addition to those within 500 kpc and 250 kpc."
+ Our, Our
+"folowing Efoiusky's torque where the positively defined [forcing frequency hela. the so-called G-finetions of απία C59; are related to power series in eccentricity via llansen's coefficients (e.g..Dobrovolskis1995):: 706). and the all-important“quality functions"" are remaining terms in this equation are a- —Y The Ry) and SO)) funetions are the real and imagery parts of the complex compliance. respectively,","following Efroimsky's torque where the positively defined forcing frequency |, the so-called G-functions of Kaula $G_{20j}$ are related to power series in eccentricity via Hansen's coefficients \citep[e.g.,][]{dobr}: (e), and the all-important“quality functions"" are Finally, the remaining terms in this equation areand The $\Re(\chi)$ and $\Im(\chi)$ functions are the real and imagery parts of the complex compliance, respectively."
+ Eq., Eq.
+ 7 includes oscillating terms of the tidal torque. ¢4 j.," \ref{qual.eq} includes oscillating terms of the tidal torque, $q\ne j$ ."
+ For a planet similar, For a planet similar
+smaller catastrophic failure rate is presumably largely. due to our removal of colour-space outliers prior to analvsis.,smaller catastrophic failure rate is presumably largely due to our removal of colour-space outliers prior to analysis.
+ We note that ρουetal. perform. a similar analysis with CELUELS z-band cata removed. with the result that a marked knee appears at Zzz 0.8 that is similar to what we observe in analyzing our intrinsically bluer DELP? sample.," We note that \citeauthor{Ilbert06} perform a similar analysis with CFHTLS $z$ -band data removed, with the result that a marked knee appears at $Z \approx$ 0.8 that is similar to what we observe in analyzing our intrinsically bluer DEEP2 sample."
+ This supports the hypothesis that adding data from other bandpasses to our DEEP? sample will lead to a marked iniprovement in fit at redshifts Z2 1., This supports the hypothesis that adding data from other bandpasses to our DEEP2 sample will lead to a marked improvement in fit at redshifts $Z \ga$ 1.
+" In this paper we apply an cigenmode-bascd framework utilizing the dilfusion map and linear regression. to the problem of estimating redshifts given SDSS and DEEP2/CELIVELS. ""gqriz photometry.", In this paper we apply an eigenmode-based framework utilizing the diffusion map and linear regression to the problem of estimating redshifts given SDSS and DEEP2/CFHTLS $ugriz$ photometry.
+ Because estimating diffusion map coordinates vie cigen-decomposition limits the size of training sets to ~ LO! objects. we implement the Nvstronun extension. which allows for computationally ollicicnt estimation of diffusion coordinates with a relatively small degradation of accuracy.," Because estimating diffusion map coordinates via eigen-decomposition limits the size of training sets to $\sim$ $^4$ objects, we implement the Nyströmm extension, which allows for computationally efficient estimation of diffusion coordinates with a relatively small degradation of accuracy."
+ For our SDSS AISC sample. we train our linear regression. model on 9.749 randomly selected. objects and via the Nvstrómm extension estimate redshifts for another 340.089 ealaxies.," For our SDSS MSG sample, we train our linear regression model on 9,749 randomly selected objects and via the Nyströmm extension estimate redshifts for another 340,989 galaxies."
+ Since the Nwstrómnm extension is not robust to extreme outliers. we use a nearest-neighbor algorithm to eliminate 5o. outliers in. colour space: this eliminates z of the AISG sample.," Since the Nyströmm extension is not robust to extreme outliers, we use a nearest-neighbor algorithm to eliminate $\sigma$ outliers in colour space; this eliminates $\approx$ of the MSG sample."
+ The loss in accuracy resulting from use of the NwstrGmim extension is z (as compared with directly fitting the data of the training set)., The loss in accuracy resulting from use of the Nyströmm extension is $\approx$ (as compared with directly fitting the data of the training set).
+ For our SDSS LRG sample. we train our regression moclel on 9.734 objects and via the Nystrómm extension estimate redshifts for another 20.082. with an outlier rate z and a degradation of accuracy zz3%..," For our SDSS LRG sample, we train our regression model on 9,734 objects and via the Nyströmm extension estimate redshifts for another 20,082, with an outlier rate $\approx$ and a degradation of accuracy $\approx$."
+ As the DEEP2/CELUELS sample has only z 6.000 objects (with an outlier rate of z 5.8'4)). we do not celine a validation set to check the accuracy of predictions generated: via the Nvstrómam extension.," As the DEEP2/CFHTLS sample has only $\approx$ 6,000 objects (with an outlier rate of $\approx$ ), we do not define a validation set to check the accuracy of predictions generated via the Nyströmm extension."
+ However. we will apply our regression model to a test set. comprised of all galaxies ας ΕΕΤὸ fields D1-D4 and make that catalog publicly available.," However, we will apply our regression model to a test set comprised of all galaxies in CFHTLS fields D1-D4 and make that catalog publicly available."
+ The observed bivariate distributions (2.Z) for our SDSS datasets are similar to those computed by. e.g. Collister&Lahav(2004) using (specilically. for the SDSS AISG dataset) and by Balletal.(2008) using a numerically intensive nearest-neighbor algorithm (for both the SDSS AISG and LRG datasets). with dispersion on parwith those techniques (Rey~ 0.02: see Balletal.2008. and references therein).," The observed bivariate distributions $(\zhat,Z)$ for our SDSS datasets are similar to those computed by, e.g., \cite{Collister04} using (specifically, for the SDSS MSG dataset) and by \cite{Ball08} using a numerically intensive nearest-neighbor algorithm (for both the SDSS MSG and LRG datasets), with dispersion on parwith those techniques $\Rhat \sim 0.02$ ; see \citealt{Ball08}
+ and references therein)."
+ These distributions indicate that. redshifts are eencrally overestimated at low Z and underestimated at hicsh Z., These distributions indicate that redshifts are generally overestimated at low $Z$ and underestimated at high $Z$.
+ We demonstrate that this is a manifestation. of attenuation bias. wherein measurement error. (uncertainty in the cliffusion coordinates resulting from uncertainty in the SDSS lux estimates) reduces the measured slope of the regression line.," We demonstrate that this is a manifestation of attenuation bias, wherein measurement error (uncertainty in the diffusion coordinates resulting from uncertainty in the SDSS flux estimates) reduces the measured slope of the regression line."
+ In. statistical parlance. the measured slope is not à consistent. estimator of the true slope.," In statistical parlance, the measured slope is not a consistent estimator of the true slope."
+ In order to use photometric redshift estimates in. precision. cosmology. it is vital that methods for producing consistent estimates (Le. mitigating the bias) be developed and implemented.," In order to use photometric redshift estimates in precision cosmology, it is vital that methods for producing consistent estimates (i.e., mitigating the bias) be developed and implemented."
+ We are exploring using theSIMEX. or simulation-extrapolation. algorithm (e.g... Carrolletal. 2006)) to produce consistent estimates in a computationally ellicient manner. and we will present our results in a future publication.," We are exploring using the, or simulation-extrapolation, algorithm (e.g., \citealt{Carroll06}) ) to produce consistent estimates in a computationally efficient manner, and we will present our results in a future publication."
+ For the DIZEDP2 cata. the dominant feature. in the observed bivariate distribution. bevond attenuation bias. is a marked reduction in prediction accuracy at redshifts Z= 0.75.," For the DEEP2 data, the dominant feature in the observed bivariate distribution, beyond attenuation bias, is a marked reduction in prediction accuracy at redshifts $Z \ga$ 0.75."
+ We demonstrate that this is due to a degeneracy. in 16 colour-space manifold that would be mitigated with the introduction of more data from other bandpasses., We demonstrate that this is due to a degeneracy in the colour-space manifold that would be mitigated with the introduction of more data from other bandpasses.
+ We note mt we also can mitigate the elfects of the cegencracy by μαrlitting the training set into low- and high-Z samples. but we do not prefer this approach because of the complexity -- adds to the precietion algorithm (through the addition ofa tuning parameter Zou and the necessity of providing a uantitative measure for robustly choosing between the two sreclictions we would generate for each test object).," We note that we also can mitigate the effects of the degeneracy by splitting the training set into low- and $Z$ samples, but we do not prefer this approach because of the complexity it adds to the prediction algorithm (through the addition of a tuning parameter $Z_{\rm cut}$ and the necessity of providing a quantitative measure for robustly choosing between the two predictions we would generate for each test object)."
+ At lower redshifts. we find that the observed. bivariate distribution (5.Z) compares favorably with that derived by (2006) (Roac 0.035 versus a = 0.032).," At lower redshifts, we find that the observed bivariate distribution $(\zhat,Z)$ compares favorably with that derived by \cite{Ilbert06} $\Rhat \approx$ 0.035 versus $\sigma$ = 0.032)."
+ Our current. statistical framework vields a single ohotometric redshift estimate for each object. in. the validation set. as opposed to a probability distribution unction. (PDE) for cach estimate (ef Balletal.2008)).," Our current statistical framework yields a single photometric redshift estimate for each object in the validation set, as opposed to a probability distribution function (PDF) for each estimate (cf. \citealt{Ball08}) )."
+ This is a valid approach for analyzing. at the very least. the galaxies of the SDSS sample that we consider in this work. as Balletal. demonstrate that the PDESs in the low-redshift reeime are approximately normal: we expect our single estimates to match the PDE means.," This is a valid approach for analyzing, at the very least, the galaxies of the SDSS sample that we consider in this work, as \citeauthor{Ball08} demonstrate that the PDFs in the low-redshift regime are approximately normal; we expect our single estimates to match the PDF means."
+ However. we would have to alter our framework if we were to analyze quasars. for which the PDFs are often bimodal (e.g. fig.," However, we would have to alter our framework if we were to analyze quasars, for which the PDFs are often bimodal (e.g., fig."
+ 5 of Ball al)., 5 of \citeauthor{Ball08}) ).
+ Bimodality is an indication of (near-)degeneracy in the colour-space manifold: when its colours are perturbed. a quasars nearest neighbor sometimes belongs to one range of redshifts. and sometimes to a completely dillerent. range.," Bimodality is an indication of (near-)degeneracy in the colour-space manifold; when its colours are perturbed, a quasar's nearest neighbor sometimes belongs to one range of redshifts, and sometimes to a completely different range."
+ Within our current framework. such a degeneracy would not alfect the computation of the dilfusion map. but the subsequent application of linear regression would. vield inaccurate recshift estimates for those quasars in the vicinity of the degeneracy.," Within our current framework, such a degeneracy would not affect the computation of the diffusion map, but the subsequent application of linear regression would yield inaccurate redshift estimates for those quasars in the vicinity of the degeneracy."
+ For quasar analysis. we would explore a variety of options. which include (a) utilizing a cilferent form of regression. (b) incorporating the response variables into the construction of the diffusion map (Costa&Llero 2005)). anclfor (ο) incorporating eracient information into cilfusion map construction. such that nearby objects that lic along 1e manifold have higher similarity measures.," For quasar analysis, we would explore a variety of options, which include (a) utilizing a different form of regression, (b) incorporating the response variables into the construction of the diffusion map \citealt{Costa05}) ), and/or (c) incorporating gradient information into diffusion map construction, such that nearby objects that lie along the manifold have higher similarity measures."
+ Such schemes =vould mitigate but not entirely lift the degeneracy and thus we would also have to quantify the relative probabilities of ual estimates., Such schemes would mitigate but not entirely lift the degeneracy and thus we would also have to quantify the relative probabilities of dual estimates.
+ In us work. we demonstrate the ellicacv of SCA. in parti‘ular our dilfusion. map framework. for analyzing atasets for which the spectroscopic redshifts are. known.," In this work, we demonstrate the efficacy of SCA, in particular our diffusion map framework, for analyzing datasets for which the spectroscopic redshifts are known."
+ The next step is to extend. our. framework such that. it vields accurate photometric redshift estimates for objects in alasets where the spectroscopic coverage will be minimal. such as deep sky surveys (c.g. LSST) or pointed: surveys bevond Zz1.," The next step is to extend our framework such that it yields accurate photometric redshift estimates for objects in datasets where the spectroscopic coverage will be minimal, such as deep sky surveys (e.g., LSST) or pointed surveys beyond $Z \approx 1$."
+ Even with long exposure times. the DEEP? Galaxy Redshift Survey is only able to determine secure redshifts for ~ of its objects. with about half the missed targets being star-forming galaxies at Z2»1.4 that have no features in DEEP? spectral window: cf. Cooperet (2006)..," Even with long exposure times, the DEEP2 Galaxy Redshift Survey is only able to determine secure redshifts for $\sim$ of its objects, with about half the missed targets being star-forming galaxies at $Z > 1.4$ that have no features in DEEP2 spectral window; cf. \cite{Cooper06}. ."
+ Evenwhen spectroscopic redshifts are available [or a significant subset of these objects. it is likely that they will be eleaned. from. intrinsically Luminous objects," Evenwhen spectroscopic redshifts are available for a significant subset of these objects, it is likely that they will be gleaned from intrinsically luminous objects"
+"The average HI deficiency of galaxies in the Coma I cloud is HI—def = 0.06 + 0.44, thus slightly higher than the average value for unperturbed field objects (HI—def = 0.00 + 0.30; Haynes Giovanelli 1984).","The average HI deficiency of galaxies in the Coma I cloud is $HI-def$ = 0.06 $\pm$ 0.44, thus slightly higher than the average value for unperturbed field objects $HI-def$ = 0.00 $\pm$ 0.30; Haynes Giovanelli 1984)."
+" This result is robust against the adopted calibration of the HI-deficiency parameter since it does not change significantly using the c — 7.00 and d = 0.94 coefficients for Scd-Im-BCD galaxies of Haynes Giovanelli (1984): HI—def = 0.03 + 0.44, thus consistent with our estimate."," This result is robust against the adopted calibration of the HI-deficiency parameter since it does not change significantly using the $c$ = 7.00 and $d$ = 0.94 coefficients for Scd-Im-BCD galaxies of Haynes Giovanelli (1984): $HI-def$ = 0.03 $\pm$ 0.44, thus consistent with our estimate."
+" Out of the 55 late-type Coma I cloud members with available HI data, only 13 (24 %)) can be considered as deficient in HI gas since having HI deficiencies greater than 0.3."," Out of the 55 late-type Coma I cloud members with available HI data, only 13 (24 ) can be considered as deficient in HI gas since having HI deficiencies greater than 0.3."
+ These most deficient objects (filled squares in Fig. 3)), These most deficient objects (filled squares in Fig. \ref{def}) )
+" do not seem to be located in priviledged zones of the sky or of the velocity space, nor are objects at the average distance of the Coma I cloud but with high velocity with respect to the cloud (Fig. 4))."," do not seem to be located in priviledged zones of the sky or of the velocity space, nor are objects at the average distance of the Coma I cloud but with high velocity with respect to the cloud (Fig. \ref{distvel}) )."
+" By studying the HI properties of 32 galaxies in the Coma I cloud with data taken at Effelsberg, Garcia-Barreto et al. ("," By studying the HI properties of 32 galaxies in the Coma I cloud with data taken at Effelsberg, Garcia-Barreto et al. ("
+1994) concluded that these objects are generally devoid of gas.,1994) concluded that these objects are generally devoid of gas.
+" In their sample of 23 late-type galaxies the average HI-deficiency is 0.40 x 0.59, significantly higher than the value found in this work (HI— def=0.06 + 0.44) on a more than doubled sample (55 objects)."," In their sample of 23 late-type galaxies the average HI-deficiency is 0.40 $\pm$ 0.59, significantly higher than the value found in this work $HI-def$ =0.06 $\pm$ 0.44) on a more than doubled sample (55 objects)."
+ The difference with Garcia-Barreto et al. (, The difference with Garcia-Barreto et al. (
+1994) might result from several reasons.,1994) might result from several reasons.
+" The HI fluxes used in this work, mostly (64%)) taken from the compilation of Springob et al. ("," The HI fluxes used in this work, mostly ) taken from the compilation of Springob et al. ("
+2005) are systematically higher (22%)) than those of Garcia-Barreto et al. (,2005) are systematically higher ) than those of Garcia-Barreto et al. (
+1994) (see Fig. 5)).,1994) (see Fig. \ref{comp}) ).
+ The resulting HI-deficiency parameter is thus lower by a factor of 0.09 on average than the previous estimate., The resulting HI-deficiency parameter is thus lower by a factor of 0.09 on average than the previous estimate.
+ This difference can be due to the fact that Springob et al. (, This difference can be due to the fact that Springob et al. (
+2005) correct the data,2005) correct the data
+prescription.,prescription.
+ Mass segregation may be characterized quantitatively through the Cini coellicient (Couverse&Staller2008.Sect101L2)., Mass segregation may be characterized quantitatively through the Gini coefficient \citep[][Section~4.2]{cs08}.
+. This quantity measures how ast the cumulative mass increases outward relative to the €uuulative number of systems., This quantity measures how fast the cumulative mass increases outward relative to the cumulative number of systems.
+ The iuitial state of the Pleiacles hadO., The initial state of the Pleiades had.
+LL. The initial nuuτο stellar systems. both binary aud siugle. was19219.," The initial number of stellar systems, both binary and single, was."
+. Figure 6 shows the evolutio - uass- and uunuber-shell radii., Figure 6 shows the evolution of mass- and number-shell radii.
+ Note tiat the current age of the Pleiades co‘responds to about 0. initial relaxation times., Note that the current age of the Pleiades corresponds to about 0.5 initial relaxation times.
+ Thus. these slots span a siguificautly briefer interval thau those in Fi‘es ] and 3.," Thus, these plots span a significantly briefer interval than those in Figures 1 and 3."
+ Bearing this fact in mincl we see that the οιIves are generaly slinilar to those iu Figure D+)3.," Bearing this fact in mind, we see that the curves are generally similar to those in Figure 3."
+ After a )‘ief initial plunge. the radii of mass shells witli expand. while t1e shiell contracts. at least over this time.," After a brief initial plunge, the radii of mass shells with expand, while the shell contracts, at least over this time."
+ Nuaber shells uude'£o ab analogous. early contraction. a then either remain staic ) or expaud.," Number shells undergo an analogous, early contraction, and then either remain static ) or expand."
+ If. binaries are energetically significant. wiv ds the cluster evoluti uot radically. altered?," If binaries are energetically significant, why is the cluster evolution not radically altered?"
+ This is au impo‘taut question. to which we shall 'eurn presentyf see Section 3.2).," This is an important question, to which we shall return presently (see Section 3.2)."
+ The early «ips seen in all the curves of Figure 6 signify that the cluster as a whole initjallv racts., The early dips seen in all the curves of Figure 6 signify that the cluster as a whole initially contracts.
+ This |)ehavior is an artifact of our specilic method for imple11011iο nass segregation., This behavior is an artifact of our specific method for implementing mass segregation.
+ As alnec iu Section 3 of Pape |]. tlie configuration starts out iu prec‘Ise vlr€ equilibrium.," As explained in Section 3 of Paper I, the configuration starts out in precise virial equilibrium."
+ However. redistribution of higher stelar masses toward tlie center alters slightly te gravitational potential 1 tha ASSOClated with au polytrope.," However, the redistribution of higher stellar masses toward the center alters slightly the gravitational potential from that associated with an polytrope."
+ Over a. perio lasing aOU two Crossing times frolas})- the cluster “botuces. and then settles into a coulieratio itlat evolves smoothly 'eafter.," Over a period lasting about two crossing times ), the cluster “bounces,” and then settles into a configuration that evolves smoothly thereafter."
+ The bounce does not occur if we impose Ho nass seeregalion |[unΠαν., The bounce does not occur if we impose no mass segregation initially.
+ In that case. both the nass deisity of stars and the gravitational potential correspond exactly to zuon polytrope.," In that case, both the mass density of stars and the gravitational potential correspond exactly to an polytrope."
+ Figure 7 shows results [rom suc hasiulation., Figure 7 shows results from such a simulation.
+" La this ""Pleiacdes-like"" cluster. the initial state is identical to that in Figure 6. but witho nass segregation."," In this “Pleiades-like” cluster, the initial state is identical to that in Figure 6, but without mass segregation."
+ Over the time spar1 covered (0.5/444). junber shells either remain static or expand (Figure Tb).," Over the time span covered $0.5\,\,t_{\rm relax}$ ), number shells either remain static or expand (Figure 7b)."
+ Tle eary contractiou of the iunermost shells seen .in Figure 3 never occurs. cie to the heating by p'iuoreial binaries.," The early contraction of the innermost shells seen in Figure 3 never occurs, due to the heating by primordial binaries."
+ Lua stummary. there is no evicerce of classical dynamical reaxation: the chister evolves purely through expausion.," In summary, there is no evidence of classical dynamical relaxation; the cluster evolves purely through expansion."
+ The adii of intejor mass shells do contract (Figure Ta) as a restt ofiicreaslug Wass segregation: the Cini coellicieut grows Ποια θ to 0.15 over this time (see Fiet eNO. Paper I)., The radii of interior mass shells do contract (Figure 7a) as a result of increasing mass segregation; the Gini coefficient grows from 0 to 0.15 over this time (see Figure 8 of Paper I).
+ Retting to the more reaistic Pleiades simulatlon. it ls agevin instructive to visualize the internal tr:sport of energy.," Returning to the more realistic Pleiades simulation, it is again instructive to visualize the internal transport of energy."
+ Frou our description thus far. there slould be no core-halo botudary. identified by the peaks of the euerey trausler profiles 1 Fieον 2 and d.," From our description thus far, there should be no core-halo boundary, identified by the peaks of the energy transfer profiles in Figures 2 and 4."
+" Figure 5. which plots Jy, as n function of AZ. bears out his expectation."," Figure 8, which plots $\dot K_r$ as a function of $M_r$, bears out this expectation."
+" Here. we have couputed Jy, by a linear fit over he [ull time span of the sunulation."," Here, we have computed $\dot K_r$ by a linear fit over the full time span of the simulation."
+" We see that A, 1101otouicalls: Falls [roin zero to increasiugly legative values. (", We see that $\dot K_r$ monotonically falls from zero to increasingly negative values. (
+Compare Figu'e 5 aud the accompawile «iscussion.),Compare Figure 5 and the accompanying discussion.)
+ The cluster as a whole is cooling dow1. and is therefore gaining in total energy.," The cluster as a whole is cooling down, and is therefore gaining in total energy."
+ The Pleiades evolved to its present state hrough global expansion. uot dynamical relaxation.," The Pleiades evolved to its present state through global expansion, not dynamical relaxation."
+"We discuss how the coutrast factor. Coy. depends on the spectral type of the star.μι, and on the optical depth. τ. of the disk.","We discuss how the contrast factor, $C_{60}$, depends on the spectral type of the star, and on the optical depth, $\tau$, of the disk."
+ The dust erains iu the remnant disk are relatively larec. at least iu cases where a determination of the erain size has been possible (Blicketal.1001:Aytviuowiezctal.1989) and the absorption efficiency for stellar radiation will be high for stars of all spectral types.," The dust grains in the remnant disk are relatively large, at least in cases where a determination of the grain size has been possible \citep{bliek:94, arty:89} and the absorption efficiency for stellar radiation will be high for stars of all spectral types."
+ The efficiency for emission is low: the dust particles ent bevoud aand these wavelengths are larger than that of the particles., The efficiency for emission is low: the dust particles emit beyond and these wavelengths are larger than that of the particles.
+ We assume that the dust erains are all of a sinele size. e. aud located at a single distance. p. from the star.," We assume that the dust grains are all of a single size, $a$, and located at a single distance, $r$, from the star."
+ We will introduce various coustants that we will call A;. κοοὐ," We will introduce various constants that we will call $A_i$, $i=0-6$."
+" First we determine L,4. the buuinositv of the disk at the frequeney v. aud Ly. the total Iuniuositv of the disk: aud We consider dust cussion atαπ D,(T) can be approximated by the Wien-cquation."," First we determine $L_{\nu,{\mathrm{d}}}$ , the luminosity of the disk at the frequency $\nu$, and $L_{\mathrm{d}}$, the total luminosity of the disk: and We consider dust emission at; $B_\nu(T)$ can be approximated by the Wien-equation."
+" We thus write: Define the average absorption efficiency: For low dust-teiiperatures Qaa. can be approximated by Qa=Ef with ax2 (Natta&Panagia1976) and thus Second. we determine the stellar luuinesitv. L,.. at frequency v and the total stellar luninosity. L both bv ienorime the effects of dust. that is the hwunuinositv at thephotospheric level."," We thus write: Define the average absorption efficiency: For low dust-temperatures $Q_{\mathrm{ave}}$ can be approximated by $Q_{\mathrm{ave}}=A_1 \Tdust^{\alpha}$ with $\alpha\approx 2$ \citep{natt:76}
+ and thus Second, we determine the stellar luminosity, $L_{\nu,*}$, at frequency $\nu$ and the total stellar luminosity, $L_*$, both by ignoring the effects of dust, that is the luminosity at thephotospheric level."
+ The photospheric cuission is approximated by the Ravleigh-Jeaus equation: C1 D2:: D1 arefeq:c6}). avefeqieL.., The photospheric emission is approximated by the Rayleigh-Jeans equation: \ref{eq:c1} \ref{eq:c7}: \ref{fig:contrast-analytically} \\ref{eq:c6}) \\ref{eq:c4}.
+Now we vetry the fit. forcing the abundauce of 9Li to zero. but keeping the 1 other parameters free.,"Now we retry the fit, forcing the abundance of $^6$ Li to zero, but keeping the 4 other parameters free."
+ We ect a differcut solution. with log(* Li/II) = 2.233. FWIIM- 15s. a differeutial redshift with Ca I 6717.677 of 0.005 aand a neeligible chanec in the coutimuiun position.," We get a different solution, with $^7$ Li/H) = 2.233, FWHM= 0.158, a differential redshift with Ca I 6717.677 of 0.005 and a negligible change in the continuum position."
+ The residuals of this new fit are shown iu fig., The residuals of this new fit are shown in fig.
+ 5., 5.
+ The iis of the otis 0.00119 (ith the coutim£n at 1.0). corresponding oa value o CX? of 39.8. rejecting this no-? Li model with a confidence level of 95.3 per ceut.," The rms of the fit is 0.00119 (with the continuum at 1.0), corresponding to a value of $X^2$ of 39.8, rejecting this $^6$ Li model with a confidence level of 95.3 per cent."
+ Would we have used the unfiltered spectrum. the rus of the fit svould have heen 100155. correspouding. to a 472 of qaot27.3 for an expectation. value of 27-—23. which is excluded ouly at the 76 per ceut evel.," Would we have used the unfiltered spectrum, the rms of the fit would have been 0.00155, corresponding to a $\chi^2$ of 27.3 for an expectation value of 27-4=23, which is excluded only at the 76 per cent level."
+ However. many authors use a reduced relative. X7Ug /r. iot botheriug for estimating the noise iudependoeutlv.," However, many authors use a reduced relative $\chi^2$ $\nu $, not bothering for estimating the noise independently."
+ Tn hat case the unfiltered 47 being 16.1 for the best fit with 5.2 per cent of SLi. oue cau claim that the 47 has con degraded in the ratio 27.53/16.l when the expected deeradation is 21/23.," In that case the unfiltered $\chi^2$ being 16.4 for the best fit with 5.2 per cent of $^6$ Li, one can claim that the $\chi^2$ has been degraded in the ratio 27.3/16.4 when the expected degradation is 24/23."
+ The probability of such a difference is only about 3 per cent., The probability of such a difference is only about 3 per cent.
+ Of course the same approach can be also applied. to the filtered data. leacinge to an exclusion of the zero °Li Lyphotlesis at the 99.5 per cont level.," Of course the same approach can be also applied to the filtered data, leading to an exclusion of the zero $^6$ Li hyphothesis at the 99.5 per cent level."
+ We do not support these nunbers. too optinistic. and we sugeest to bring instead. now more attention to the run of the residuals with waveleneth.," We do not support these numbers, too optimistic, and we suggest to bring instead, now more attention to the run of the residuals with wavelength."
+ The shape of the residuals with wavelength is very suggestive of beiug not due to a random noise., The shape of the residuals with wavelength is very suggestive of being not due to a random noise.
+ Iu order to check if this is the case we lave compared two svuthetic spectra here). one corresponding to the absolute vest ft. the other oue corresponding to the best fit. with i0 OLA. involving a 0.005 shift iu wavelength.," In order to check if this is the case we have compared two synthetic spectra ), one corresponding to the absolute best fit, the other one corresponding to the best fit, with no $^6$ Li, involving a 0.005 shift in wavelength."
+ The residuals of the second. versus the first oue are slow in Be., The residuals of the second versus the first one are shown in fig.
+ 6., 6.
+ The similarity between fig., The similarity between fig.
+ 5 aud 6 is striking., 5 and 6 is striking.
+ Fie., Fig.
+ 6 also shows how tuportaut it is to reach a S/N of 1000. ο discriminate between these two cases.," 6 also shows how important it is to reach a S/N of 1000, to discriminate between these two cases."
+" We cousider that he rejection of a zero-abunudanee of 9Li at the 95 per cout level.case, represents a serious advance with respect to former works. done with a lesser S/N ratio."," We consider that the rejection of a zero-abundance of $^6$ Li at the 95 per cent level, represents a serious advance with respect to former works, done with a lesser S/N ratio."
+" A Davesian approach of the problem. that we have not attempted. is likely to imerease our value of ""Li because of the positive plivsical nature of the abuudauce of ""Li."," A Bayesian approach of the problem, that we have not attempted, is likely to increase our value of $^6$ Li, because of the positive physical nature of the abundance of $^6$ Li."
+ For shifts larger than 0.005 tthe solution would need 9Li in eiissiou. not acceptable.," For shifts larger than 0.005 the solution would need$^6$ Li in emission, not acceptable."
+" The 05 per cent srobability around the optimal fit (Li /""Li = 0.052) can © computed when the coutimmun level. aud the two abundances are free parameters. because they occur Lnearily."," The 68 per cent probability around the optimal fit $^6$ Li $^7$ Li = 0.052) can be computed when the continuum level, and the two abundances are free parameters, because they occur linearily."
+ We fud that this amounts to + .012, We find that this amounts to $\pm$ .012.
+ An extra-allowauce must be made for the impact of the uncertainties ou the other two paruneters., An extra-allowance must be made for the impact of the uncertainties on the other two parameters.
+ For he FWIIM of the broadening. if we accept the ful ranec of fig.," For the FWHM of the broadening, if we accept the full range of fig."
+ 2. with equal probability of the FWHAL in the range. we obtain au extra contribution of + .007.," 2, with equal probability of the FWHM in the range, we obtain an extra contribution of $\pm$ .007."
+ The contribution of a zero-point shift in waveleneth is more difficult to estimate., The contribution of a zero-point shift in wavelength is more difficult to estimate.
+ A shift as larec as the one needed for the no °Li Bivpbothesis is larecly rejected., A shift as large as the one needed for the no $^6$ Li hyphothesis is largely rejected.
+ We consider that a shift of + .002 is allowed., We consider that a shift of $\pm$ .002 is allowed.
+ This adds an extra-excursion of τις 0.013., This adds an extra-excursion of rms 0.013.
+ The combined effect is 0.019. adding quadratically.," The combined effect is 0.019, adding quadratically."
+ AMoute Carlo simulation would be more correct to evaluate this uncertainty. but what is more nuportant is to have exeluded a zero abuudauce of Li at the 95 per cout level.," AMonte Carlo simulation would be more correct to evaluate this uncertainty, but what is more important is to have excluded a zero abundance of $^6$ Li at the 95 per cent level."
+ Iu one of their papers on proper motion stars (paper NIT). Carney ct al. (1991))," In one of their papers on proper motion stars (paper XII), Carney et al. \cite{Car94}) )"
+ cousicder ITD 8L937 as a suspected spectroscopic binary., consider HD 84937 as a suspected spectroscopic binary.
+ We have two recent nieasureimmenuts of this star with the OIIP instrmucut ELODIE., We have two recent measurements of this star with the OHP instrument ELODIE.
+ We compare in table 3 these measurements with those of Carney aud earlier., We compare in table 3 these measurements with those of Carney and earlier.
+" A rather arbitrary weight (20) has been attributed to the two values obtained with ELODIE which have a PAandard error of 0.25 kin |,", A rather arbitrary weight (20) has been attributed to the two values obtained with ELODIE which have a standard error of 0.25 km $^{-1}$.
+ There is no indication of a svsteniatie variation over 30 vears., There is no indication of a systematic variation over 30 years.
+ Moreover. Mawvor (private communication 1998) indicates that the star. observed repeatedly with CORAVEL caving more thaw six thousand cdavs. has no variation of radial velocity at the level of 1 sigiia = 1.19 kin !," Moreover, Mayor (private communication 1998) indicates that the star, observed repeatedly with CORAVEL during more than six thousand days, has no variation of radial velocity at the level of 1 sigma = 1.19 km $^{-1}$."
+ Tf we imagine that the ?Li component is actually he ‘Li component of a conipauion. the radial velocity difference is 7 kin 1," If we imagine that the $^6$ Li component is actually the $^7$ Li component of a companion, the radial velocity difference is 7 km $^{-1}$."
+ Iu order to produce the 5 per ceut streneth iu the bleud. the companion must be a dwarf of absolute magnitude about 6.5 having au effective temperature of 5100 I& aud a nass of 0.6 AL... whereas the primary has a mass of about 0.5 AL:.," In order to produce the 5 per cent strength in the blend, the companion must be a dwarf of absolute magnitude about 6.8 having an effective temperature of 5400 K and a mass of 0.6 $_{\sun}$ , whereas the primary has a mass of about 0.8 $_{\sun }$."
+" Because, A4 aud Ao are the amplitudes of the radial velocity variation of the two comuponcuts. we have the two coustraiuts : A4|Aoc7 λα 1 aud : and using the well known relation Allen (1985)): the followingcondition is obtained :"," Because, $K_1$ and $K_2$ are the amplitudes of the radial velocity variation of the two components, we have the two constraints : $K_1+K_2 \geq 7$ km $^{-1}$ and : and using the well known relation Allen \cite{AQ}) ): the followingcondition is obtained :"
+Qur purpose is to obtain inlormation about the IGC population from the study of the unresolved point sources by means of SBF analvsis.,Our purpose is to obtain information about the IGC population from the study of the unresolved point sources by means of SBF analysis.
+ The measured SBF signal is produced mainlv by faint galaxies and the IGC population Gl such a thing exists)., The measured SBF signal is produced mainly by faint galaxies and the IGC population (if such a thing exists).
+ For (his reason. during SBF measurements. a good characterization of the faint end. of the background differential galaxv number counts.n(m). is fundamental.," For this reason, during SBF measurements, a good characterization of the faint end of the background differential galaxy number counts,$n(m)$, is fundamental."
+ A number of authors have measured the slope of the faint end of i602) in the £ filter., A number of authors have measured the slope of the faint end of $n(m)$ in the $R$ filter.
+ Results range [from >=0.39 (Tyson1055) los — 0.3134 (Steidel&Hamilton1993)., Results range from $\gamma=0.39$ \citep{T88} to $\gamma$ = 0.31–34 \citep{SH93}.
+. This slope has also been measured in the IIubble Deep Field (Williamsοἱal. 1996).. with 5=0.36 for the W filter and 5=0.31 for the { filter down to magnitude 26.," This slope has also been measured in the Hubble Deep Field \citep{W96}, , with $\gamma=0.36$ for the $V$ filter and $\gamma=0.31$ for the $I$ filter down to magnitude 26."
+ For the intermediate f filler. the slope must be between =0.31 and 0.36.," For the intermediate $R$ filter, the slope must be between $\gamma=0.31$ and 0.36."
+ From the SBF analvsis presented in (his paper. we provide not only information about the existence or not of an IGC population. but also an estimate of the slope of the faint end of (77).," From the SBF analysis presented in this paper, we provide not only information about the existence or not of an IGC population, but also an estimate of the slope of the faint end of $n(m)$."
+ Observations of the 16 giant elliptical galaxies ancl the 4 “blank” regions studied in this paper were done on 2000 April 25 and 27. with (the 2.5 m Isaac Newton Telescope (INT) al (he Roque de los Muchachos Observatory (La Palma). using the Wide Field Camera and ihe Sloan £2 Filter.," Observations of the 16 giant elliptical galaxies and the 4 “blank"" regions studied in this paper were done on 2000 April 25 and 27, with the 2.5 m Isaac Newton Telescope (INT) at the Roque de los Muchachos Observatory (La Palma), using the Wide Field Camera and the Sloan $R$ Filter."
+ This work is based on the results obtained by Marin-Franch&Apari- (2002).. where the observations. photometric calibration and data reduction procedures are described in detail. as well as the SBF analvsis.," This work is based on the results obtained by \citet{MA02}, where the observations, photometric calibration and data reduction procedures are described in detail, as well as the SBF analysis."
+ We provide here only a short outline of ihe latter., We provide here only a short outline of the latter.
+ The concept of SBF was introduced by Tonry&Schneider(1988).. who noted that. in (he surface photometry of a galaxy. (oo [ar (ο be resolved. a pixel-to-pixel fluctuation is observed due to the Poisson statistics of the spatial distribution of stars. GCs. background ealaxies. etc.," The concept of SBF was introduced by \citet{TS88}, who noted that, in the surface photometry of a galaxy too far to be resolved, a pixel-to-pixel fluctuation is observed due to the Poisson statistics of the spatial distribution of stars, GCs, background galaxies, etc."
+ The variance of the fluctuation depends on (he stellar population. the GCS. background galaxies. foreground stars. aud. of course. the distance.," The variance of the fluctuation depends on the stellar population, the GCS, background galaxies, foreground stars, and, of course, the distance."
+ H can be assumed that the total pixel-to-pixel variance of an image is (he sum of all the independent contributions., It can be assumed that the total pixel-to-pixel variance of an image is the sum of all the independent contributions.
+" The SBF technique involves spectral analvsis of the signal and provides as a result the total PSE-convolved variance (£5). produced by all objects whose spatial flux distribution is convolved with the PSF: sp"" ∖∖↽↥∐↲↕⋅≼↲⊔⋝−⋟⊔⋮≺−⋟∶≺↴⋅⊔⋮∟−⋟⋉∶⋅≀↧↴∐≺⇂⊔⋮∖≀↧↴↕⋅≼↲⊔∐↲∖↽≀↧↴↕⋅↕≀↧↴∐≺∢≼↲⊳∖⊽↕↽≻↕⋅⋯⇂∏≺∢≼↲≼⇂∣↽≻⋡∖↽⊔∐↲⊳∖⊽∩↲∐≀∐⋅↕↽≻∪↕↽⊓∐≀↧↴∐∪∐⋝∖⊽⋅ GCs, background galaxies. and foreground. stars. respectivelv."," The SBF technique involves spectral analysis of the signal and provides as a result the total PSF-convolved variance $P_0$ ), produced by all objects whose spatial flux distribution is convolved with the PSF: where $\sigma^{2}_{\rm sp}$, $\sigma^{2}_{\rm GC}$, $\sigma^{2}_{\rm BG}$ and $\sigma^{2}_{\rm fs}$ are the variances produced by thestellar populations, GCs, background galaxies, and foreground stars, respectively."
+ If à population of IGCs is, If a population of IGCs is
+does not appear to readily explain why the UV. surface brightness profile would not exhibit a truncation. unless the ealaxy was observed shortly after such a burst. so that the UW outer disk would. still be clominatecl by stars formed during the recent star formation episode. while Lla emission. which traces star formation only over very short timescales. has already abatect.,"does not appear to readily explain why the UV surface brightness profile would not exhibit a truncation, unless the galaxy was observed shortly after such a burst, so that the UV outer disk would still be dominated by stars formed during the recent star formation episode, while $\alpha$ emission, which traces star formation only over very short timescales, has already abated."
+ Bakos.γι]ο&Pohlen(2008) find that the stellar surface mass density also exhibits a much less pronounced break than the optical light of the. stellar continuum., \citet{bakos} find that the stellar surface mass density also exhibits a much less pronounced break than the optical light of the stellar continuum.
+ They suggest that a change in the composition of the stellar population. rather than an actual break in the mass distribution. is responsible for the observed. break in the optical continuum surface brightness.," They suggest that a change in the composition of the stellar population, rather than an actual break in the mass distribution, is responsible for the observed break in the optical continuum surface brightness."
+ In this context. it is surprising that both the stellar surface mass density and the integrated. recent star formation rate (as measured by UV emission) supposedly show no or only weak breaks. but both stellar continuum and Loa clo.," In this context, it is surprising that both the stellar surface mass density and the integrated, recent star formation rate (as measured by UV emission) supposedly show no or only weak breaks, but both stellar continuum and $\alpha$ do."
+ As exceptions to the rule. those galaxies where we find no evidence for a truncation or break in the Lla emission deserve particular attention. as any theory attempting to explain the presence of a break in the Lla profile [or example. by invoking a critical gas surface density threshold below which star formation is inellicient must also be able to provide an explanation for objects that apparently violate the rule.," As exceptions to the rule, those galaxies where we find no evidence for a truncation or break in the $\alpha$ emission deserve particular attention, as any theory attempting to explain the presence of a break in the $\alpha$ profile — for example, by invoking a critical gas surface density threshold below which star formation is inefficient — must also be able to provide an explanation for objects that apparently violate the rule."
+ Of the objects that are formally consistent with an unbroken exponential profile. NGC 259 and ESO 478-CGO11 may be interesting cases for follow-up studies.," Of the objects that are formally consistent with an unbroken exponential profile, NGC 259 and ESO 478-G011 may be interesting cases for follow-up studies."
+ A final consideration must be given to the cllect of dust on the Ha surface brightness profiles. and. in particular. to the question whether cust absorption could. influence our measurement of the characteristic break radius and possibly even our classification of the composite Lla profile as a (sub-exponential) Twpe LH. rather than a (single exponential) Type LU dust. extinction sets in around this radius and increases continuously towards the galaxy. center. absorbing an increasing fraction of Hao Dux. it may artificially [atten the profile slope and possibly even create the false impression of a broken exponential shape.," A final consideration must be given to the effect of dust on the $\alpha$ surface brightness profiles, and, in particular, to the question whether dust absorption could influence our measurement of the characteristic break radius and possibly even our classification of the composite $\alpha$ profile as a (sub-exponential) Type II, rather than a (single exponential) Type I. If dust extinction sets in around this radius and increases continuously towards the galaxy center, absorbing an increasing fraction of $\alpha$ flux, it may artificially flatten the profile slope and possibly even create the false impression of a broken exponential shape."
+ This scenario. however would imply that the unabsorbed Lla profile could be recreated by extrapolating the outer-disk Lla profile back towards the center. implving that the real Lla surface brightness in the inner regions would be more than an order of magnitude ueher than observed here.," This scenario, however would imply that the unabsorbed $\alpha$ profile could be recreated by extrapolating the outer-disk $\alpha$ profile back towards the center, implying that the real $\alpha$ surface brightness in the inner regions would be more than an order of magnitude higher than observed here."
+ Xs dust shielding is unlikely to be uniform (even in cases of nearly perfect edge-on alignment. he slit intercepts regions both on and olf the central dust ane). ab least some sight lines should. permit elimpses of hese substantially higher surface brightness levels. leading o a larger dvnamic range in the IEuctuations of the inner-disk surface brightness profile.," As dust shielding is unlikely to be uniform (even in cases of nearly perfect edge-on alignment, the slit intercepts regions both on and off the central dust lane), at least some sight lines should permit glimpses of these substantially higher surface brightness levels, leading to a larger dynamic range in the fluctuations of the inner-disk surface brightness profile."
+ This is not the case: even he highest Hio. peaks remain far below the levels expected rom interpolating the outer-clisk profile. confirming that the oreak is indeed real.," This is not the case; even the highest $\alpha$ peaks remain far below the levels expected from interpolating the outer-disk profile, confirming that the break is indeed real."
+ Dust shielding may. however. plausibly modify the measured. value of the inner-disk profile slope by smaller amounts.," Dust shielding may, however, plausibly modify the measured value of the inner-disk profile slope by smaller amounts."
+ An additional argument against dust obscuring a Large fraction of the La Dux comes from the rotation curves., An additional argument against dust obscuring a large fraction of the $\alpha$ flux comes from the rotation curves.
+ If dust. plaved a significant role up to the break radius of 0.7 Hos. contributions to the observed. Hao. [lux would. be weighted: towards gas on the outskirts of the galaxy along the edge closer to the observer.," If dust played a significant role up to the break radius of 0.7 $R_{25}$, contributions to the observed $\alpha$ flux would be weighted towards gas on the outskirts of the galaxy along the edge closer to the observer."
+ We would therefore expect the rotation curve to rise very slowly in the inner disk and not [atten before it reaches this point., We would therefore expect the rotation curve to rise very slowly in the inner disk and not flatten before it reaches this point.
+ However. most rotation curves in this sample are already fat or close to Lat well before reaching 0.7. eo: (Christlein&Zaritsky2008:Christlein&Blanc-Llawthorn2008).. indicating that the llo. emission at this point alreacky samples the kineniatics of the gas along the entire sight linc. and that the observed kinematics and [lux cannot be strongly biased. by internal dust extinction.," However, most rotation curves in this sample are already flat or close to flat well before reaching 0.7 $R_{25}$ \citep{christleinzaritsky,christleinbh}, indicating that the $\alpha$ emission at this point already samples the kinematics of the gas along the entire sight line, and that the observed kinematics and flux cannot be strongly biased by internal dust extinction."
+ We have presented à study of Ho emission. and. stellar continuum in 15 low-redshift. late-tvpe. ecdec-on galaxies.," We have presented a study of $\alpha$ emission and stellar continuum in 15 low-redshift, late-type, edge-on galaxies."
+ The use of deep long-slit spectroscopy. rather than narrow-band imaging. allows us to probe Hla emission {ο very faint levels. ~10 15 org + 72 7.," The use of deep long-slit spectroscopy, rather than narrow-band imaging, allows us to probe $\alpha$ emission to very faint levels, $\sim$ $^{-18}$ erg $^{-1}$ $^{-2}$ $^{-2}$."
+ Ho. emission is traced out to bevond the Ro: radius. roughly twice as lar as typical Lla rotation curves in the literature.," $\alpha$ emission is traced out to beyond the $_{25}$ radius, roughly twice as far as typical $\alpha$ rotation curves in the literature."
+ lt is thus possible to probe the outer galactic disks. which have hitherto primarily been a domain of radio astronomy. in Ho. emission. and thus simultaneously eain. information about kinematics. star formation. metallicity. ancl stellar continuum with areseconc-scale spatial resolution.," It is thus possible to probe the outer galactic disks, which have hitherto primarily been a domain of radio astronomy, in $\alpha$ emission, and thus simultaneously gain information about kinematics, star formation, metallicity, and stellar continuum with arcsecond-scale spatial resolution."
+ In the present. paper. we have focused on the properties of the surface brightness profile of Πα. emission. and compared them to those of the stellar continuum.," In the present paper, we have focused on the properties of the surface brightness profile of $\alpha$ emission and compared them to those of the stellar continuum."
+ Our conclusions are:, Our conclusions are:
+"considered subsonic), the threshold level for kurtosis (Gr, above which the gas is considered supersonic and below it is considered subsonic), and the kernel box size chosen.","considered subsonic), the threshold level for kurtosis $\beta_T$, above which the gas is considered supersonic and below it is considered subsonic), and the kernel box size chosen."
+ The values for yr and £7 represent the threshold value between supersonic and subsonic regimes., The values for $\gamma_T$ and $\beta_T$ represent the threshold value between supersonic and subsonic regimes.
+ Any pixels below either yr and fp is deemed subsonic and any pixel above both is deemed supersonic., Any pixels below either $\gamma_T$ and $\beta_T$ is deemed subsonic and any pixel above both is deemed supersonic.
+" Of course, an intermediate threshold value could also be chosen to probe the transsonic regime, but we omit this here."," Of course, an intermediate threshold value could also be chosen to probe the transsonic regime, but we omit this here."
+ Again we should stress that we are not employing this method to get an exact Mach number; we simply view it as a way of determining whether our |VP| image shows supersonic or subsonic characteristics., Again we should stress that we are not employing this method to get an exact Mach number; we simply view it as a way of determining whether our $|\nabla \textbf{P}|$ image shows supersonic or subsonic characteristics.
+" The best fitting parameter values of box size, yr and Br are those that provide accurate translation between the moments and the LOS Mach number."," The best fitting parameter values of box size, $\gamma_T$ and $\beta_T$ are those that provide accurate translation between the moments and the LOS Mach number."
+ In order to determine these values we use a genetic algorithm which searches possible combinations of these three parameters in order to determine the best fit., In order to determine these values we use a genetic algorithm which searches possible combinations of these three parameters in order to determine the best fit.
+ T'he genetic algorithm can provide more computationally efficient way of testing for fitness rather then iterating over every possible combination of parameter space., The genetic algorithm can provide more computationally efficient way of testing for fitness rather then iterating over every possible combination of parameter space.
+ See the appendix for a detailed description of our algorithm., See the appendix for a detailed description of our algorithm.
+" Although multiple combinations of parameters showed high confidence levels, we chose yr=1.1 and 87p—1.58 and box size=64 pixels."," Although multiple combinations of parameters showed high confidence levels, we chose $\gamma_T$ =1.1 and $\beta_T$ =1.58 and box size=64 pixels."
+" With these values, the supersonic models were able to determine the Mach number regime with accuracy, while the subsonic cases had an accuracy of (see Figure 11))."," With these values, the supersonic models were able to determine the Mach number regime with accuracy, while the subsonic cases had an accuracy of (see Figure \ref{fig:corprct}) )."
+" This is not surprising however, since the moments are known to be a more robust measure of highly supersonic turbulence (Kowal, Lazarian Beresnyak 2007)."," This is not surprising however, since the moments are known to be a more robust measure of highly supersonic turbulence (Kowal, Lazarian Beresnyak 2007)."
+ We plot the LOS Mach number map for model number 1 in the top panel of Figure 12 with contours from the kurtosis moment map., We plot the LOS Mach number map for model number 1 in the top panel of Figure \ref{fig:mommap_obs} with contours from the kurtosis moment map.
+ The moments trace areas where the sonic Mach number is changing., The moments trace areas where the sonic Mach number is changing.
+" We apply the moving box method to the SGPS data cuts using the same parameters for yr, Sr and box size as were used for the simulations."," We apply the moving box method to the SGPS data cuts using the same parameters for $\gamma_T$, $\beta_T$ and box size as were used for the simulations."
+ For the SGPS data we obtained average skewness and kurtosis values for this moment map of 0.3 and 0.9 for skewness and kurtosis respectively., For the SGPS data we obtained average skewness and kurtosis values for this moment map of 0.3 and 0.9 for skewness and kurtosis respectively.
+ We over-plot the SGPS data with the kurtosis moment map contours in the bottom panel of Figure 12.., We over-plot the SGPS data with the kurtosis moment map contours in the bottom panel of Figure \ref{fig:mommap_obs}.
+" While these values seem to point in the direction that the SGPS data is subsonic or transonic, we note that this method is less accurate for subsonic type turbulence."," While these values seem to point in the direction that the SGPS data is subsonic or transonic, we note that this method is less accurate for subsonic type turbulence."
+" However, it does confirm that the gas in this patch of the sky is not statistically similar to what is expected for supersonic flows."," However, it does confirm that the gas in this patch of the sky is not statistically similar to what is expected for supersonic flows."
+" The filaments seen in |VP| show substantially different morphology when comparing maps of subsonic and supersonic turbulence, as was discussed in Section 3."," The filaments seen in $|\nabla \textbf{P}|$ show substantially different morphology when comparing maps of subsonic and supersonic turbulence, as was discussed in Section 3."
+" Thus, a natural avenue of characterization would be to use topological measures in order to pick out different structures."," Thus, a natural avenue of characterization would be to use topological measures in order to pick out different structures."
+ In this section we will investigate the utility of the genus statistics in order to characterize the topology of |VP| filaments., In this section we will investigate the utility of the genus statistics in order to characterize the topology of $|\nabla \textbf{P}|$ filaments.
+ The genus statistics was developed to study the topology and deviations from Gaussianity of the universe and the distribution of galaxies in three dimensions (Gott et al., The genus statistics was developed to study the topology and deviations from Gaussianity of the universe and the distribution of galaxies in three dimensions (Gott et al.
+ 1986; 1987)., 1986; 1987).
+" The use of genus statistics for the study of HI was first discussed in Lazarian (1999), and subsequent studies presented the genus curves for the SMC (Lazarian et al."," The use of genus statistics for the study of HI was first discussed in Lazarian (1999), and subsequent studies presented the genus curves for the SMC (Lazarian et al."
+" 2002; Lazarian 2004, Chepurnov et al."," 2002; Lazarian 2004, Chepurnov et al."
+" 2008) and for MHD simulations (Kowal, Lazarian Beresnyak 2007)."," 2008) and for MHD simulations (Kowal, Lazarian Beresnyak 2007)."
+ Genus is a quantitative measure of topology., Genus is a quantitative measure of topology.
+ It can characterize both 2D and 3D distributions., It can characterize both 2D and 3D distributions.
+" Generally speaking, the genus is used to detect departures for Gaussianity."," Generally speaking, the genus is used to detect departures for Gaussianity."
+" When dealing with the ISM one cannot expect deviations from symmetry to be small, especially in the presence of supersonic flows."," When dealing with the ISM one cannot expect deviations from symmetry to be small, especially in the presence of supersonic flows."
+" In this case, genus can be used to characterize flows that are supersonic since these show large deviations from Gaussianity."," In this case, genus can be used to characterize flows that are supersonic since these show large deviations from Gaussianity."
+ The 2D genus can be represented as (Coles 1988; Melott et al., The 2D genus can be represented as (Coles 1988; Melott et al.
+ 1989): where low- and high-density regions are selected with respect to a given contour threshold., 1989): where low- and high-density regions are selected with respect to a given contour threshold.
+" For instance, a uniform circle would have a genus of 0 (one connected region of high density, ie., an “island,” and one connected region of low density, while a ring (a donut, for example) would have a genus of -1 (one connected region of high density and two connected regions of low density)."," For instance, a uniform circle would have a genus of 0 (one connected region of high density, i.e., an “island,” and one connected region of low density, while a ring (a donut, for example) would have a genus of -1 (one connected region of high density and two connected regions of low density)."
+ 'Thus the genus can distinguish between *meatball and “swiss cheese” topologies (Gott 1990).," Thus the genus can distinguish between “meatball"" and “swiss cheese"" topologies (Gott 1990)."
+" For a 2D image, the genus is simply a number which corresponds to a given threshold value."," For a 2D image, the genus is simply a number which corresponds to a given threshold value."
+" What is considered to be high or low is dependent on the threshold value, which acts as a free parameter."," What is considered to be high or low is dependent on the threshold value, which acts as a free parameter."
+ As a, As a
+spectral index iu B2 varies frou 0.5 in the east to 0.1 at the base of jet to the northwest: further out along the jet it steepens again reaching 1.0.,spectral index in B2 varies from $-0.5$ in the east to 0.4 at the base of jet to the northwest; further out along the jet it steepens again reaching $-1.0$.
+ There is also a eradation of spectral index iu component Bl from cast to west. changing from 1.0 to 0.," There is also a gradation of spectral index in component B1 from east to west, changing from $-1.0$ to 0."
+ As remarked earlier. the ridge iu componcut € has a spectral index of about —0.5 iu the centre. which falls off to 1.0 towards he edges.," As remarked earlier, the ridge in component C has a spectral index of about $-0.5$ in the centre, which falls off to $-1.0$ towards the edges."
+" A the location of the transverse feature in component C. the spectral index appears to flatten from 0.9) to 0.5,"," At the location of the transverse feature in component C, the spectral index appears to flatten from $-0.9$ to $-0.5$."
+ A the eastern eud of C. the spectral iudex of the peak seen iu the tota intensity maps has a flat spectral iudex of about zero.," At the eastern end of C, the spectral index of the peak seen in the total intensity maps has a flat spectral index of about zero."
+ Frou this poiut to the leadiug edge of the je is the region in which Conway Schilizzi (2000)) detec masximaun IIT opacity., From this point to the leading edge of the jet is the region in which Conway Schilizzi \cite{conway}) ) detect maximum HI opacity.
+ The UST snapshot of 3C236 made with the WEPC-2 using a red broad-band filter ceutred near £000.A.. shows clear evidence of a substantial dust rine (de off ct al. 20003).," The HST snapshot of 3C236 made with the WFPC-2 using a red broad-band filter centred near 7000, shows clear evidence of a substantial dust ring (de Koff et al. \cite{dekoff}) )."
+ Fi, Fig.
+e. 9. (1niddle) reproduces the absorption model for the galaxy derive by de I&off et al..," \ref{Fig. 9} (middle) reproduces the absorption model for the galaxy derived by de Koff et al.,"
+ in which the nn colmponent of dust is iu the form of a riug|of radius ~ 5 kpc whose apparent sviunuetry axis differs iu position romrthie-overzidi-die-axisστοa 1Πλ Ἔπ129 2και 1defied. n IE o : [iun by the outer edees of the large scale structure (Fie. 9..," in which the main component of dust is in the form of a ring of radius $\sim$ 5 kpc whose apparent symmetry axis differs in position angle by 15 - 20 $\degr$ from the overall radio axis defined by the outer edges of the large scale structure (Fig. \ref{Fig. 9},"
+ bottom)., bottom).
+ The svunuetry axis of the ring is aligned with the apparent minor axis of the galaxy itself. within the errors.," The symmetry axis of the ring is aligned with the apparent minor axis of the galaxy itself, within the errors."
+ A dust feature —1.5 spe long lies iuterual to the rime and approximately parallel to it: this may be the remnant of another ring., A dust feature $\sim$ 1.5 kpc long lies internal to the ring and approximately parallel to it; this may be the remnant of another ring.
+ A further faint dus feature cau also be secu cluanating from the clear region towards the SE., A further faint dust feature can also be seen emanating from the nuclear region towards the SE.
+" From the ellipticity ofthe disk. we derive an apparent inclination angle ofthe radio source to the lune of sight of 60"" considering that the radio jets are approximately perpendicular to he dust rine."," From the ellipticity of the disk, we derive an apparent inclination angle of the radio source to the line of sight of $\sim 60\degr$ considering that the radio jets are approximately perpendicular to the dust ring."
+ Ikotzusi Ekers (1979)) firs pointed out that laree scale radio jets are roughly perpendicular to dust disks aud lanes. aud this has Όσοι amply confirmed auc extended to the nuclear regious by de I&off et al. (2000)).," Kotanyi Ekers \cite{kotanyi}) ) first pointed out that large scale radio jets are roughly perpendicular to dust disks and lanes, and this has been amply confirmed and extended to the nuclear regions by de Koff et al. \cite{dekoff}) ),"
+ in particular for well defined disks and lanes., in particular for well defined disks and lanes.
+ It is interesting to note that in NGC 1261. Jatfe et al. (1996))," It is interesting to note that in NGC 4261, Jaffe et al. \cite{jaffe}) )"
+ found a very simular offset in PLA. between he radio jet aud the svaunietry axis of the dust disk iu that ealaxv., found a very similar offset in P.A. between the radio jet and the symmetry axis of the dust disk in that galaxy.
+ These authors refer to Rees (1981)) in. pointing out that Leusce-Thirig precession will force the part of he aceretion disk nearest to the black hole to be axi-sviuuetre about the rotation axis of the hole. whatever its spin axis at laree radius.," These authors refer to Rees \cite{rees}) ) in pointing out that Lense-Thirring precession will force the part of the accretion disk nearest to the black hole to be axi-symmetric about the rotation axis of the hole, whatever its spin axis at large radius."
+ At small distances fro tle lack role the jet aud disk axes should coincide., At small distances from the black hole the jet and disk axes should coincide.
+" In the case of 30236 the linearity of the large scale radio jet to he south-east implies that the black hole axis has beeu oriented at 122 "" for the lifetime of the source. aud that he dust ring axis is offset frou this on kpe scales."," In the case of 3C236 the linearity of the large scale radio jet to the south-east implies that the black hole axis has been oriented at 122 $\degr$ for the lifetime of the source, and that the dust ring axis is offset from this on kpc scales."
+ This offset could arise if the dust has been captured from a s3inaller galaxy which has been canuibalised by 3€C236., This offset could arise if the dust has been captured from a smaller galaxy which has been cannibalised by 3C236.
+ The oscillation in direction of the compact and large scale jets (sec next section). if due to oscillation in the black. hole axis. niv well be related to a merger event.," The oscillation in direction of the compact and large scale jets (see next section), if due to oscillation in the black hole axis, may well be related to a merger event."
+ The mass of dus in the rine estimated by de off et al. (2000)), The mass of dust in the ring estimated by de Koff et al. \cite{dekoff}) )
+ of, of
+enussion by relativistic electrons through the IC: process.,emission by relativistic electrons through the IC process.
+ The hadronic component dominates the GeV 5-rav emission., The hadronic component dominates the GeV $\gamma$ -ray emission.
+ Note that since E?=EL. the 5-rav spectrum of the hadronic component cuts off at a lower energv (han the leptonic component.," Note that since $E_c^p=E_c^e$ , the $\gamma$ -ray spectrum of the hadronic component cuts off at a lower energy than the leptonic component."
+ Neutral pion decavs into two 5-rav photos., Neutral pion decays into two $\gamma$ -ray photos.
+ The eutolf energy of the 5-ray spectrum is at least a factor of 2 lower than the cutoff energv of the corresponding proton distribution., The cutoff energy of the $\gamma$ -ray spectrum is at least a factor of 2 lower than the cutoff energy of the corresponding proton distribution.
+ For the IC emission. (he cutoll enerev of the 5-rav spectrum can be the same as the corresponding electron distribution.," For the IC emission, the cutoff energy of the $\gamma$ -ray spectrum can be the same as the corresponding electron distribution."
+ The fit to TeV data shows improvement compared with the leptonic model. with average residual changing from ~2.30 to about 2.00.," The fit to TeV data shows improvement compared with the leptonic model, with average residual changing from $\sim 2.3\sigma$ to about $2.0\sigma$."
+ However. the hadronic component seems {ο overproduce the GeV thus. resulting in an even larger ve (han the leptonic scenario.," However, the hadronic component seems to overproduce the GeV flux, resulting in an even larger $\chi^2_{\rm GeV}$ than the leptonic scenario."
+ The 4? value for X-ray. data does not change significantly., The $\chi^2$ value for X-ray data does not change significantly.
+ The correlation of the model parameters are also similar to the leptonic model., The correlation of the model parameters are also similar to the leptonic model.
+" And the strong anti-correlation between nj, and I, is still due to the [act that the observed emission is determined by (he product of the two.", And the strong anti-correlation between $n_{\rm ISM}$ and $W_p$ is still due to the fact that the observed emission is determined by the product of the two.
+ Although the model has a weak magnetic field and relatively soft distributions of accelerated particles. the 26 lower limit of the proton energv of 1.0x100” eres is comparable to those of the hadronie models. which still challenges the energetics of the SNR.," Although the model has a weak magnetic field and relatively soft distributions of accelerated particles, the $2\sigma$ lower limit of the proton energy of $1.0\times 10^{52}$ ergs is comparable to those of the hadronic models, which still challenges the energetics of the SNR."
+ The energy content of relativistic protons is poorly determined due to the hish uncertainty in mig., The energy content of relativistic protons is poorly determined due to the high uncertainty in $n_{\rm ISM}$.
+ Perhaps the only observation one can use (to constrain ys is the lack of thermal X-ray emission Irom (he remnant (Cassam-Chenatetal.2004).., Perhaps the only observation one can use to constrain $n_{\rm ISM}$ is the lack of thermal X-ray emission from the remnant \citep{2004A&A...427..199C}.
+. To derive a robust constraint Oh yyy. One however needs (o consider the heating of electrons and the ionization of ions in the background plasma. bothof which are not well understood though a preliminary altempt has been taken (o model these processes quantitatively (Ellisonetal.2010)..," To derive a robust constraint on $n_{\rm ISM}$, one however needs to consider the heating of electrons and the ionization of ions in the background plasma, bothof which are not well understood though a preliminary attempt has been taken to model these processes quantitatively \citep{2010ApJ...712..287E}."
+ Here we assume that electrons have reached ionization equilibrium with the ions and so that the Ravyvmoud-Simith code can be used (o caleulate the thermal emission., Here we assume that electrons have reached ionization equilibrium with the ions and so that the Raymond-Smith code can be used to calculate the thermal emission.
+ The resultsabove do not differ significantlv for different values of 7;except Lor the constraint on nis and accordingly WW., The resultsabove do not differ significantly for different values of $T_e$except for the constraint on $n_{\rm ISM}$ and accordingly $W_p$.
+ In Fig., In Fig.
+" 5 we show the results for the hybrid scenario wilh 7,=10"" and 10 K. For 7;=10 I most of the line emission has energies lower than 0.5 keV. which is below the lower limit of the Suzealu data."," \ref{fig:hybrid-tem} we show the results for the hybrid scenario with $T_e=10^6$ and $10^8$ K. For $T_e=10^6$ K most of the line emission has energies lower than 0.5 keV, which is below the lower limit of the $Suzaku$ data."
+" IIowever. the emission in the X-ray band is sullicient to lead to well-constrained nj,~0.2 ! and Wy10?! eres."," However, the emission in the X-ray band is sufficient to lead to well-constrained $n_{\rm ISM}\sim 0.2$ $^{-3}$ and $W_p\sim 
+10^{51}$ ergs."
+ The model also predicts strong emission below the X-ray range., The model also predicts strong emission below the X-ray range.
+ A significant thermal component also helps to slightly improve the fit to the A-ray data., A significant thermal component also helps to slightly improve the fit to the X-ray data.
+"The 20 upper limit ofmis, for T,=105 Wis 0.2 7 which is muchlooser than that for 7,=101 Ix. For 7,=108 Ix the 2e upper limit of πιω is 0.02 7. which is also higher than 0.009 * for T;=10* Ix. The 2o lower limits of 15, are 3.5x LO"". 1.0x 107. and 4.4xLO"" eres for T,=10. LO"",","The $2\sigma$ upper limit of$n_{\rm ISM}$ for $T_e=10^6$ K is $0.2$ $^{-3}$ , which is muchlooser than that for $T_e=10^7$ K. For $T_e=10^8$ K the $2\sigma$ upper limit of $n_{\rm ISM}$ is $0.02$ $^{-3}$ , which is also higher than $0.009$ $^{-3}$ for $T_e=10^7$ K. The $2\sigma$ lower limits of $W_p$ are $3.5\times 10^{50}$ , $1.0\times 10^{52}$ , and $4.4\times 10^{51}$ ergs for $T_e=10^6$, $10^7$ ,"
+"intrinsic in the assumptions we made: for instance the adoption of a power law spectrum of accelerated particles with slope 4, which clearly fails when a precursor 15 formed.","intrinsic in the assumptions we made: for instance the adoption of a power law spectrum of accelerated particles with slope $4$, which clearly fails when a precursor is formed."
+ There are then complications coming trom deeper unknown pieces of Physics or from a not totally satisfactory mathematical approach., There are then complications coming from deeper unknown pieces of Physics or from a not totally satisfactory mathematical approach.
+" For instance, the standard perturbative approach adopted here is based on the assumption of a spatially uniform background."," For instance, the standard perturbative approach adopted here is based on the assumption of a spatially uniform background."
+" The presence of a precursor invalidates this assumption, although probably not in a dramatic way."," The presence of a precursor invalidates this assumption, although probably not in a dramatic way."
+" Since the non-resonant mode appears for large values of &, the relevant quantities can be assumed to be spatially constant in the precursor on scales ~1/k, so that in this respect our calculations are still expected to hold, and probably to a better accuracy for the non-resonant modes (k>> Πτι) than for the resonant ones (&~Πεμ)."," Since the non-resonant mode appears for large values of $k$, the relevant quantities can be assumed to be spatially constant in the precursor on scales $\sim 1/k$, so that in this respect our calculations are still expected to hold, and probably to a better accuracy for the non-resonant modes $k \gg 1/r_{L,0}$ ) than for the resonant ones $k \sim 1/r_{L,0}$ )."
+" Moreover, as stressed above, the dynamical reaction of the magnetic field leads to weaker modification of the shock, and therefore to spectra with less prominent concavity (closer to p)."," Moreover, as stressed above, the dynamical reaction of the magnetic field leads to weaker modification of the shock, and therefore to spectra with less prominent concavity (closer to $p^{-4}$ )."
+" Also in this respect, the calculations presented here should serve as a good description of all relevant physical effects related to the growth of the cosmic ray induced instabilities."," Also in this respect, the calculations presented here should serve as a good description of all relevant physical effects related to the growth of the cosmic ray induced instabilities."
+" More important, the acceleration process is directly affected by the physics of particles’ diffusion in the shock region, which in turn is determined by the excited waves."," More important, the acceleration process is directly affected by the physics of particles' diffusion in the shock region, which in turn is determined by the excited waves."
+" This intrinsic non-linearity cannot be taken into account in perturbative approaches like ours or like Bells, and one should always be aware of this limitation."," This intrinsic non-linearity cannot be taken into account in perturbative approaches like ours or like Bell's, and one should always be aware of this limitation."
+" Even more, while the diffusion coefficient for resonant modes can at least be derived in quasi-linear theory, at present there is no derivation of the diffusion coefficient associated with scattering on non-resonant modes (see ? for a first attempt at discussing this effect)."," Even more, while the diffusion coefficient for resonant modes can at least be derived in quasi-linear theory, at present there is no derivation of the diffusion coefficient associated with scattering on non-resonant modes (see \cite{zira08b} for a first attempt at discussing this effect)."
+ Another issue that deserves further investigation is that of determining the level of field amplification at which the instability saturates., Another issue that deserves further investigation is that of determining the level of field amplification at which the instability saturates.
+ This cannot be worked out within a linear theory calculation and only numerical simulations can address this issue., This cannot be worked out within a linear theory calculation and only numerical simulations can address this issue.
+ Recent efforts in this direction have been made by ? and ? through MHD simulations and by ? by using PIC simulations., Recent efforts in this direction have been made by \cite{bell04} and \cite{zira08a} through MHD simulations and by \cite{niem08} by using PIC simulations.
+" While the first two papers find a saturation level 6B/(4z)—(v,/c)P.. in the third paper a much lower level of field amplification is found."," While the first two papers find a saturation level $\delta B^2/(4 \pi) \sim (v_s/c) P_c$, in the third paper a much lower level of field amplification is found."
+ The authors conclude that the existence of large magnetic field amplification through the excitation of non-resonant modes is yet to be established., The authors conclude that the existence of large magnetic field amplification through the excitation of non-resonant modes is yet to be established.
+" Although we agree with this conclusion, we also think that the setup of the PIC simulation by ? is hardly applicable to investigate the excitation of the Bell instability at shocks, or at least several aspects of it should be studied more carefully."," Although we agree with this conclusion, we also think that the setup of the PIC simulation by \cite{niem08} is hardly applicable to investigate the excitation of the Bell instability at shocks, or at least several aspects of it should be studied more carefully."
+" First. they carried out the calculations in à regime in which the condition of strong magnetization, ω«Ωμ. was violated."," First, they carried out the calculations in a regime in which the condition of strong magnetization, $\omega\ll\Omega_0$, was violated."
+" Second, in order to carry out the calculations, ? are forced to assume unrealistically large values for the ratio Ner; "," Second, in order to carry out the calculations, \cite{niem08} are forced to assume unrealistically large values for the ratio $N_{CR}/n_i$ "
+"(thus. the anisotropy of the expansion) iucreases as f Mcreascs,","(thus, the anisotropy of the expansion) increases as $t$ increases."
+ Iu the following. we examine the cosmiological models that exhibit de Sitter volumetric expansion within the LRS Bianchi tvpe-I framework aud preseut two exact models.," In the following, we examine the cosmological models that exhibit de Sitter volumetric expansion within the LRS Bianchi type-I framework and present two exact models."
+" The LRS Bianchi tvpe-I metric reads Thus. ff,=IL. aud in the following they arerepresented by 11."," The LRS Bianchi type-I metric reads Thus, $H_{y}=H_{z}$, and in the following they arerepresented by $H_{y,z}$."
+ The energvauoinentuiu tensor eiven in (17) can be customized for the LRS Diauchi-I metric by choosing à=7. Considering (26) aud (27). the Eiusteiu field equation (I)-C7). can be reduced to the following system of equations: Then we have initially five variables (CA. D. p. uw. 7) and three linearly iudepeudoeut equations. niunclv the three Eiunsteiu fold equatious (28)-(00).," The energy-momentum tensor given in (17) can be customized for the LRS Bianchi-I metric by choosing $\delta=\gamma$, Considering (26) and (27), the Einstein field equations (4)-(7) can be reduced to the following system of equations: Then we have initially five variables $A$, $B$, $\rho$, $w$, $\gamma$ ) and three linearly independent equations, namely the three Einstein field equations (28)-(30)."
+ Thus we will need two additional constraints to close the system of equations., Thus we will need two additional constraints to close the system of equations.
+" However. before introducing the constraints to close the svsteni of equations. we can eive p. « aud 5 in terms of the mean Iubble parameter and the directional Hubble paraiueter ou the μη axis. manipulating the feld equatious (28)-(30). The anisotropy energy density can also be given iu teris of {41 and Jf, by using (13). (11) and (28). One may cheek that the sunnuation of (31) aud (31) leads to pop=p|paMP,"," However, before introducing the constraints to close the system of equations, we can give $\rho$, $w$ and $\gamma$ in terms of the mean Hubble parameter and the directional Hubble parameter on the $x$ axis, manipulating the field equations (28)-(30), The anisotropy energy density can also be given in terms of $H$ and $H_{x}$ by using (13), (14) and (28), One may check that the summation of (31) and (34) leads to $\rho_{\textnormal{ef}}=\rho+\rho_{\beta}=3H^{2}$."
+ As the first constraint to close the system of equatious.§f the effective euergy density is assumed to be constaut throughout the history of the universe: where ÀÁds a positive constant aud thus from (22) which corresponds to the wellknown de Sitter volunetric expansion. 1.6.. The solution of (33) by considering (31) and (36) eives the following equation for the evolution of the directional scale factor ou the we axis: where &>0 and A are real coustauts aud P(t)=5p is the skewness of the pressure.," As the first constraint to close the system of equations, the effective energy density is assumed to be constant throughout the history of the universe: where $k$ is a positive constant and thus from (22) which corresponds to the well-known de Sitter volumetric expansion, i.e., The solution of (33) by considering (31) and (36) gives the following equation for the evolution of the directional scale factor on the $x$ axis: where $\kappa>0$ and $\lambda$ are real constants and $\Gamma(t)=\gamma\rho$ is the skewness of the pressure."
+ Using (38) in (37) the cirectional scale factor on the y and z axes is obtained as follows: Usine the scale factors (38) aud (39). the directional IIubble paraicters are obtained as follows: Using (36). (10) and (£1) in (10) the anisotropy of the expansion. A. aud thus the anisotropy energy density. pa. are obtained as It can be secu that the skewness of the pressure P(t) also contributes to the evolution of the cosinological parameters.," Using (38) in (37) the directional scale factor on the $y$ and $z$ axes is obtained as follows: Using the scale factors (38) and (39), the directional Hubble parameters are obtained as follows: Using (36), (40) and (41) in (10) the anisotropy of the expansion, $\Delta$, and thus the anisotropy energy density, $\rho_{\beta}$ , are obtained as It can be seen that the skewness of the pressure $\Gamma(t)$ also contributes to the evolution of the cosmological parameters."
+"set of gas particles processed in this way to those particles which have at least a density of 0.01 times the threshold density for star formation. Le. pi,=8.61095?M.kpeο (seeSpringel&Llernaquist2003a.fordetailsonhowthispa-rameterisdetermined)...","set of gas particles processed in this way to those particles which have at least a density of $0.01$ times the threshold density for star formation, i.e. $\rho_{\rm th}=8.6\times 10^6 h^2\Msun\kpc^{-3}$ \citep[see][for details 
+on how this parameter is determined]{SH03a}."
+ Note that we are not interested in he gaseous components of galaxies we only include gas xwticles because they make the method more robust., Note that we are not interested in the gaseous components of galaxies – we only include gas particles because they make the method more robust.
+ Since most galaxies contain very dense star-formüng gas. such a method make it particularly easy. to select. galaxies when he eas is included.," Since most galaxies contain very dense star-forming gas, such a method make it particularly easy to select galaxies when the gas is included."
+ We found that the above method robustly links up star xuwticles that belong to the same isolated galaxy., We found that the above method robustly links up star particles that belong to the same isolated galaxy.
+ A simpler Folk algorithm: with a small linking length. can achieve a arecly similar result. but. the particular choice for. the inking length one needs to make in this method represents a oblematie compromise. either leading to artificial merging of galaxies if ib is selected: too large. or to loss of star xuwlicles that went astray from the dense galactic core. if selected too small.," A simpler FoF algorithm with a small linking length can achieve a largely similar result, but the particular choice for the linking length one needs to make in this method represents a problematic compromise, either leading to artificial merging of galaxies if it is selected too large, or to loss of star particles that went astray from the dense galactic core, if selected too small."
+ Note that. unlike in the detection of dark matter substructures. no gravitational unbinding algorithm is needed. to define the groups of stars that make up the galaxies formed in the simulations.," Note that, unlike in the detection of dark matter substructures, no gravitational unbinding algorithm is needed to define the groups of stars that make up the galaxies formed in the simulations."
+ We only consider galaxies with at least 32 particles (star and gas combined) in our subsequent analysis., We only consider galaxies with at least 32 particles (star and gas combined) in our subsequent analysis.
+ Each stellar particle contained in them is tagged by the simulation cocle with its mass. formation time. and metallicity of the gas particle that it formed out of.," Each stellar particle contained in them is tagged by the simulation code with its mass, formation time, and metallicity of the gas particle that it formed out of."
+ Based on these three tags. we compute the emission from each stellar particle. and co-acdd the Dux from all particles for a given galaxy to obtain the spectrum. of the simulated. galaxy.," Based on these three tags, we compute the emission from each stellar particle, and co-add the flux from all particles for a given galaxy to obtain the spectrum of the simulated galaxy."
+ We use the population svnthesis model GISSEL99 (Bruzual&Charlot1993). that assumes the Salpeter(1995). initial mass function with a mass range of 0.1.125]M...," We use the population synthesis model GISSEL99 \citep{BClib} that assumes the \citet{Salpeter} initial mass function with a mass range of $[0.1, 125]\,\Msun$."
+ Once the intrinsic spectrum is computed. we apply the Calzetti extinction law (Calzettietal.2000) with three cilferent values o£ (D.Y)=0.0.0.15.0.3 to investigate the ellects of extinction.," Once the intrinsic spectrum is computed, we apply the Calzetti extinction law \citep{Calzetti} with three different values of $E(B-V)=0.0, 0.15, 
+0.3$ to investigate the effects of extinction."
+ These values span the range of (D.V) estimated from observations of Εκ at z=3 CXdelberger&Steidel2000:Shapleyetal. 2001).," These values span the range of $E(B-V)$ estimated from observations of LBGs at $z=3$ \citep{Ade00, Sha01}."
+.. Rest-frame colours and Luminosity [functions of the simulated galaxies are then derived using the spectra computed in this manner., Rest-frame colours and luminosity functions of the simulated galaxies are then derived using the spectra computed in this manner.
+ To obtain the spectra in the observed frame. we redshift the spectra and apply absorption by the IGM following the prescription by Macau(1995).," To obtain the spectra in the observed frame, we redshift the spectra and apply absorption by the IGM following the prescription by \citet{Madau95}."
+". Once the redshifted spectra in the observed [rame are obtained. we convolve them with various filter functions. including C,.€.2 (Steidel&Llamil- and standard Johnson bands. and compute the magnitudes in both AD and Vega systems."," Once the redshifted spectra in the observed frame are obtained, we convolve them with various filter functions, including $\U, G, R$ \citep{Steidel93} and standard Johnson bands, and compute the magnitudes in both AB and Vega systems."
+" Apparent C,. C. I magnitudes are computed in the AD system to compare our results with Steideletal. (2003)... while the rest-frame V-band magnitude is computed in the Vega svstem to compare our results with those of Shapleyetal.(2001)."," Apparent $\U$ $G$ , $R$ magnitudes are computed in the AB system to compare our results with \citet{Ste03}, , while the rest-frame V-band magnitude is computed in the Vega system to compare our results with those of \citet{Sha01}."
+". In Figure Ἐν we show the colour-colour magnitude diagrams of simulated. galaxies at 2=3 in the (C,C vs. GOR plane. for galaxies brighter than /!=25.5 (themagnitudecutusedbySteideletal. 2003)."," In Figure \ref{colcol_Rcut_all.eps}, we show the colour-colour magnitude diagrams of simulated galaxies at $z=3$ in the $\U-G$ vs. $G-R$ plane, for galaxies brighter than $R=25.5$ \citep[the
+magnitude cut used by][]{Ste03}."
+. Phe three cüllerent symbols represent three different values ofC'alzetti extinction: (D13)=00 (blue dots). 0.15 (green. crosses). and. 0.3. (red open squares).," The three different symbols represent three different values of Calzetti extinction: $E(B-V)=0.0$ (blue dots), 0.15 (green crosses), and 0.3 (red open squares)."
+ The long-dashed lines mark the colour-colour selection criteria applied by Steideletal.(2003). to identify LBG candidates at z~3., The long-dashed lines mark the colour-colour selection criteria applied by \citet{Ste03} to identify LBG candidates at $z\sim 3$.
+ lt is encouraging to see that in all the panels most of the simulated: galaxies actually satisfv the observational colour selection criteria., It is encouraging to see that in all the panels most of the simulated galaxies actually satisfy the observational colour selection criteria.
+ This suggests that the simulated ealaxies have realistic colours. compared. to the observed ας at z=3., This suggests that the simulated galaxies have realistic colours compared to the observed LBGs at $z=3$.
+" In runs with larger box size (D- and the distribution is wider than the one in the Li,=NMpe runs (Qe-series). and the distribution actually extends bevond the colour selection boundaries of Steideletal.(2003)."," In runs with larger box size (D- and G-series), the distribution is wider than the one in the $\Lbox=10\,\himpc$ runs (Q-series), and the distribution actually extends beyond the colour selection boundaries of \citet{Ste03}."
+. The box size of the Q-series (Lins=101Alpe) is too small to contain a significant sample of LBGs. and no LBGs with 2«25.5 can be found in the Q-series for the cases OF E(BV)=0.15 and 0.3.," The box size of the Q-series $\Lbox=10\,\himpc$ ) is too small to contain a significant sample of LBGs, and no LBGs with $R<25.5$ can be found in the Q-series for the cases of $E(B-V)=0.15$ and 0.3."
+ Η we had not applied the Madau (1995). absorption to the spectra. the distribution would not have fallen into the colour selection region.," If we had not applied the Madau (1995) absorption to the spectra, the distribution would not have fallen into the colour selection region."
+" This is because the simulate galaxies would then appear too bright in the UV. such tha the distribution would fall below €,Go«2"," This is because the simulated galaxies would then appear too bright in the UV, such that the distribution would fall below $\U-G <
+1.0$."
+ As the leve of extinction. by dust. is increased. from {013200 to 0.3. the measured. points move towards the upper righ corner of cach panel.," As the level of extinction by dust is increased from $E(B-V)=0.0$ to 0.3, the measured points move towards the upper right corner of each panel."
+ This behaviour is expected. for a μαandard star-forming galaxy spectrum. as demonstrate in Figure 2 of Steidelctal.(2003).," This behaviour is expected for a standard star-forming galaxy spectrum, as demonstrated in Figure 2 of \citet{Ste03}."
+.. At the same time. the number of galaxies that satisfy the magnitude cut of R=25.5 decreases with increasing extinction. because stronger extinction results in a redder galaxy spectrum.," At the same time, the number of galaxies that satisfy the magnitude cut of $R= 25.5$ decreases with increasing extinction, because stronger extinction results in a redder galaxy spectrum."
+ Note that increasing the resolution from (Q3 to QA. ane then to Q5. also reduces the number of galaxies. brighter wan /?—25.5 slightly.," Note that increasing the resolution from Q3 to Q4, and then to Q5, also reduces the number of galaxies brighter than $R=25.5$ slightly."
+ Phe same is true for D4 and D5 runs., The same is true for D4 and D5 runs.
+ As the resolution is increased. not only are the mos massive halos in the simulation better resolved. but also all of their progenitors.," As the resolution is increased, not only are the most massive halos in the simulation better resolved, but also all of their progenitors."
+ The better resolution then allows a more accurate treatment of the wincd-feedback in these progenitor generations of galaxies: the net result of this is a decrease in the final luminosity of the brightest. galaxies., The better resolution then allows a more accurate treatment of the wind-feedback in these progenitor generations of galaxies; the net result of this is a decrease in the final luminosity of the brightest galaxies.
+ For the Q5-run. there are actually no galaxies brighter than R=25.5.," For the `Q5'-run, there are actually no galaxies brighter than $R=25.5$."
+ ‘This is not the case for the lower resolution. larger box size simulations where the trend appears to reverse.," This is not the case for the lower resolution, larger box size simulations where the trend appears to reverse."
+ In the case of the CG-series. the number of galaxies brighter than R=25.5 actually increases as the resolution increases.," In the case of the G-series, the number of galaxies brighter than $R=25.5$ actually increases as the resolution increases."
+ As we will show in Section 6.2.. this is because the peak of the simulated band luminosity function is still on the brighter side of /?=25.5. and the increase in the number of galaxies near the peak of the luminosity function wins over the slight decrease of the number at the brightest end.," As we will show in Section \ref{section:lf_R}, this is because the peak of the simulated $R$ -band luminosity function is still on the brighter side of $R=25.5$, and the increase in the number of galaxies near the peak of the luminosity function wins over the slight decrease of the number at the brightest end."
+ We now investigate the number density of LDBGs in the simulation., We now investigate the number density of LBGs in the simulation.
+ In Figure 2.. we plot the number density of galaxies that satisfy the colour-colour selection criteria of Steidelctal.(2003).. lor all the runs shown in Figure ," In Figure \ref{nden.eps}, we plot the number density of galaxies that satisfy the colour-colour selection criteria of \citet{Ste03}, for all the runs shown in Figure \ref{colcol_Rcut_all.eps}."
+Theee different svmbols represent the three different values of extinction we used: οV)=0.0 (black open squares). 0.15 (blue filled squares). ancl 0.3. (red filled triangles).," Three different symbols represent the three different values of extinction we used: $E(B-V)=0.0$ (black open squares), 0.15 (blue filled squares), and 0.3 (red filled triangles)."
+ The points for the same value of (D.V) are connected to guide the eve., The points for the same value of $E(B-V)$ are connected to guide the eye.
+ All the cases with zero LDGs are indicated as No= dex for plotting purposes., All the cases with zero LBGs are indicated as $N=-3.8$ dex for plotting purposes.
+ A conservativerange for the observed: number densities of LBCs is shown as a shaded region.with a median value o£4.10.!5Mpe.? (Adelbergor 2003)..," A conservativerange for the observed number densities of LBGs is shown as a shaded region,with a median value of $4\times 10^{-3}
+{h}^3\mpc^{-3}$ \citep{Ade03}. ."
+ We note that CGiavalisco&Dickinson.(2001) reported a slightly smaller value of 203:510.75?Mpe. 7., We note that \citet{Gia01} reported a slightly smaller value of $2-3\times 10^{-3}{ h}^3\mpc^{-3}$ .
+counts at and above ος is LON ον)=l1] in the absence of any background. field.,counts at and above $E_\gamma$ is 1 $N_x(>E_{high})=1$ ] in the absence of any background field.
+(> Phe spectrum of the source is set. here to -2.25. near the mean of the sources in “Table 1. and the p-lEBL is ignored.," The spectrum of the source is set here to -2.25, near the mean of the sources in Table \ref{tab:latsources}, and the p-EBL is ignored."
+" Civen these parameters. the contours on the plots show the source redshift and £ that svould be required to place a given SERD limit on pop-LHI star-formation at redshifts 2,—6 and 9. with 2e significance."," Given these parameters, the contours on the plots show the source redshift and $E_{\gamma}$ that would be required to place a given SFRD limit on pop-III star-formation at redshifts $z_r =6$ and 9, with $\sigma$ significance."
+ These contours are or limits derived: based. on a single source: combined imits for multiple sources like those in section 3.2.2.. if available. would. be somewhat stronger.," These contours are for limits derived based on a single source; combined limits for multiple sources like those in section \ref{sec:comb}, if available, would be somewhat stronger."
+ In Fig. 7..," In Fig. \ref{fig:sfrd_lar_higher},"
+ imits based on two hypothetical high-redshift) eanima- bursts are combined with the other sources of Table l., limits based on two hypothetical high-redshift gamma-ray bursts are combined with the other sources of Table \ref{tab:latsources}.
+ This plot shows that new GeW sources. either at ügher redshift than GRB 080016C.. or at a similar redshift with higher energv emission. could. strongly imit a pop-LL contribution to star-formation in the late rejionization. period.," This plot shows that new GeV sources, either at higher redshift than GRB 080916C, or at a similar redshift with higher energy emission, could strongly limit a pop-III contribution to star-formation in the late reionization period."
+ If the satellite remains in operation for its stated lifetime goal of ten vears from its launch date. then its mission is currently less than one-third complete. and we can reasonably hope to see new CRB events or high- AGN photons that will strengthen our results.," If the satellite remains in operation for its stated lifetime goal of ten years from its launch date, then its mission is currently less than one-third complete, and we can reasonably hope to see new GRB events or high-energy AGN photons that will strengthen our results."
+ The Cherenkov Telescope Array (CLA: TheCPACon-sortium 2010)) is another possible source of constraining events., The Cherenkov Telescope Array (CTA; \citealp{ctaconcept10}) ) is another possible source of constraining events.
+ CPA will have a lower threshold energy. than current-eeneration. eround-based. instruments. ancl may be able to detect. sources at much higher redshift than currently achieved. from. the ground.," CTA will have a lower threshold energy than current-generation ground-based instruments, and may be able to detect sources at much higher redshift than currently achieved from the ground."
+ Deteetions with either of these instruments could. potentially shed: new light on star-formation in the reionization cra., Detections with either of these instruments could potentially shed new light on star-formation in the reionization era.
+ Μο was supported. during this work by a ολ postdoctoralο fellowship. and thanks W. D. Atwood. J. Primack and A. Bouvier for helpful discussions related to this project. and J. Colucei and. the anonymous referee for reading the manuscript and. providing useful comments.," RCG was supported during this work by a SISSA postdoctoral fellowship, and thanks W. B. Atwood, J. Primack and A. Bouvier for helpful discussions related to this project, and J. Colucci and the anonymous referee for reading the manuscript and providing useful comments."
+| Some calculations in the paper were performed on the SISSA LHigh-Performance Computing Cluster., Some calculations in the paper were performed on the SISSA High-Performance Computing Cluster.
+"smallest radii, so from this we get an uncertainty range on the quadrupole from the unknown mass and radius of between  0.5-20 times the value in Eqn. B],","smallest radii, so from this we get an uncertainty range on the quadrupole from the unknown mass and radius of between $\sim0.5$ –20 times the value in Eqn. \ref{eq:quadmom2},"
+" with the most massive, but smallest stars at the lower end and vice versa."," with the most massive, but smallest stars at the lower end and vice versa."
+ Here we will assume the breaking strain is at the maximum value of Omax*0.1 calculated by (much previous work has assumed a maximum breaking strain of 107?€omax< 107?).," Here we will assume the breaking strain is at the maximum value of $\sigma_{\rm
+max} \approx 0.1$ calculated by \citet{Horowitz:2009} (much previous work has assumed a maximum breaking strain of $10^{-5} \le \sigma_{\rm max} \le
+10^{-2}$ )."
+" This value of the breaking strain was calculated for normal neutron star matter, but for other situations it may well not be a valid assumption."," This value of the breaking strain was calculated for normal neutron star matter, but for other situations it may well not be a valid assumption."
+" Using the higher value from the mass/radius uncertainty as an upper limit, and inserting in the maximum breaking strain, wecould get normal neutron stars with quadrupoles of Qua.74.5x1038kgm?."," Using the higher value from the mass/radius uncertainty as an upper limit, and inserting in the maximum breaking strain, we get normal neutron stars with quadrupoles of $Q_{\rm max} \approx 4.5\ee{33}\,{\rm kg}\,{\rm m}^2$."
+" Converting this to an approximate (order of magnitude) estimate of the ellipticity, assuming the canonical moment of inertia, would give €zz6x10?."," Converting this to an approximate (order of magnitude) estimate of the ellipticity, assuming the canonical moment of inertia, would give $\varepsilon
+\approx 6\ee{-5}$."
+" Although the reasoning behind it is quite different jjust coming from plugging in masses and radii at the extent of their ranges, with the majority of the increase over the fiducial value in coming from using a maximum radius of kkm) this value is very similar to that produced by the perturbative approach to the problem performed by [Haskelletal](2006)."," Although the reasoning behind it is quite different just coming from plugging in masses and radii at the extent of their ranges, with the majority of the increase over the fiducial value in \citet{Owen:2005}
+ coming from using a maximum radius of km) this value is very similar to that produced by the perturbative approach to the problem performed by \citet{Haskell:2006}."
+". Assuming the maximum breaking strain of 0.1 they would produce a maximum quadrupole (see Table 4 of ) of Qmax=3.1x1035kgm? for astar with a mass of lall[2006)Mc, radius kkm and crust thickness kkm."," Assuming the maximum breaking strain of 0.1 they would produce a maximum quadrupole (see Table 4 of \citealp{Haskell:2006}) ) of $Q_{\rm
+max} = 3.1\ee{33}\,{\rm kg}\,{\rm m}^2$ for astar with a mass of $M_{\odot}$, radius km and crust thickness km."
+" In and |Lin|(2007) the quadrupole is (2009),calculated for crystalline colour-superconducting (CSS) hybrid stars."," In \citet{Knippel:2009}, \citet{Haskell:2007} and \citet{Lin:2007} the quadrupole is calculated for crystalline colour-superconducting (CSS) hybrid stars."
+ In these stars the emission mainly comes from a deformed interior core of quark matter., In these stars the emission mainly comes from a deformed interior core of quark matter.
+" The quadrupole can again be approximated by Eqn. [f],"," The quadrupole can again be approximated by Eqn. \ref{eq:quadmom},"
+" but with a shear modulus given by (Mannarelliet_all|2007) where Ajo is the gap parameter in units of MMeV, and 44400 is the quark chemical potential in units of MMeV (which in is estimated to be in the range 350MeV<µᾳx 500MeV), and the stellar mass and radius are replaced by those of the quark core."," but with a shear modulus given by \citep{Mannarelli:2007}
+ where $\Delta_{10}$ is the gap parameter in units of MeV, and $\mu_{q~400}$ is the quark chemical potential in units of MeV (which in \citealp{Mannarelli:2007} is estimated to be in the range $350\,{\rm MeV} \le
+\mu_q \le 500\,{\rm MeV}$ ), and the stellar mass and radius are replaced by those of the quark core."
+" EUROAEsit assume a range of gap 10€A« 50MMeV, and find a maximum core mass of Mo and a maximum core radius of kkm."," \citet{Knippel:2009} assume a range of gap $10\le \Delta \le 50$ MeV, and find a maximum core mass of $M_{\odot}$ and a maximum core radius of km."
+ For the reasons stated in we will assume a slightly more conservative maximum breaking strain than that for normal neutron stars of Omax=10?., For the reasons stated in \\ref{sec:normalns} we will assume a slightly more conservative maximum breaking strain than that for normal neutron stars of $\sigma_{\rm max}=10^{-2}$.
+" This gives a maximum quadrupole (for A= 50MMeV, pq=500, ju=97 MMeVffm?z1.5x10°4Jm 3) of Qmax©1.4x10°°kgm?, or almost three orders of magnitude larger than anormal neutron star, which is not necessarily surprising since deformations are in the high density core rather than the crust."," This gives a maximum quadrupole (for $\Delta = 50$ MeV, $\mu_q = 500$, $\mu = 97$ $^{-3} \approx
+1.5\ee{34}\,{\rm J}\,{\rm m}^{-3}$ ) of $Q_{\rm max} \approx 1.4\ee{36}\,{\rm
+kg}\,{\rm m}^2$, or almost three orders of magnitude larger than a neutron star, which is not necessarily surprising since deformations are in the high density core rather than the crust."
+" note that for a star with a fluid envelope around the core the quadrupole will be suppressed, particularly if there is not a substantial change in density when transitioning between the core and envelope."," \citet{Haskell:2007} note that for a star with a fluid envelope around the core the quadrupole will be suppressed, particularly if there is not a substantial change in density when transitioning between the core and envelope."
+" Converting this to an approximateestimate of the ellipticity, by assuming the canonical moment of inertia, would give an equivalently large ε+0.02!"," Converting this to an approximateestimate of the ellipticity, by assuming the canonical moment of inertia, would give an equivalently large $\varepsilon \approx 0.02$!"
+ (2005) also looks at hybrid stars with charged meson condensates and quark-baryon cores., \citet{Owen:2005} also looks at hybrid stars with charged meson condensates and quark-baryon cores.
+" For these the shear modulus is given by where qo.4 is the charge density of quark droplets in units of -0.4e, Dis is their diameter in units of 15ffm, and αρ is their spacing in units of 30ffm."," For these the shear modulus is given by where $q_{0.4}$ is the charge density of quark droplets in units of $e$, $D_{15}$ is their diameter in units of fm, and $S_{30}$ is their spacing in units of fm."
+ Following the correction for charge screening in an upper limit on shear modulus is given as i©1.3x10~°MeVfm?.," Following the correction for charge screening in \citet{Owen:2005} an upper limit on shear modulus is given as $\mu \approx
+1.3\ee{-2}\,{\rm MeV}\,{\rm fm}^{-3}$."
+ If we evaluate Eqn., If we evaluate Eqn.
+"[] with this, again substituting for the core radius (which as in refsec:css we will set as 8kkm) and using a fiducial stellar mass of Mo and a maximum breaking strain of omax= 107?, we get an upper limit on the quadrupole moment of Qmax£3.5x107?kgm?."," \ref{eq:quadmom}
+ with this, again substituting for the core radius (which as in \\ref{sec:css}
+ we will set as km) and using a fiducial stellar mass of $M_{\odot}$ and a maximum breaking strain of $\sigma_{\rm max} = 10^{-2}$ , we get an upper limit on the quadrupole moment of $Q_{\rm max} \approx 3.5\ee{32}\,{\rm kg}\,{\rm
+m}^2$."
+ This is less than the extremal value for anormal neutron star., This is less than the extremal value for a neutron star.
+ The work by (2010ajb) into cold quark matter suggest that hybrid stars (with pure phases of hadronic and quark matter) could have masses up to ~2.1Mo and radii of ~13 kkm although these are likely to have only a tiny quark core tthey will mainly look like a normal hadronic neutron star.," The work by \citet{Kurkela:2010a, Kurkela:2010b} into cold quark matter suggest that hybrid stars (with pure phases of hadronic and quark matter) could have masses up to $\sim 2.1\,M_{\odot}$ and radii of $\sim 13$ km although these are likely to have only a tiny quark core they will mainly look like a normal hadronic neutron star."
+" However, they show that stars with mixed phases of quarks and hadrons can have masses of up to ~1.9Mc and radii of ~11kkm, which with the above assumptions allows larger quadrupole moments of Qmaxm1.8x1035kgm?, comparable to the maximum obtainable for anormal neutron star (although requiring a smaller breaking strain)."," However, they show that stars with mixed phases of quarks and hadrons can have masses of up to $\sim 1.9\,M_{\odot}$ and radii of $\sim 11$km, which with the above assumptions allows larger quadrupole moments of $Q_{\rm max} \approx 1.8\ee{33}\,{\rm kg}\,{\rm m}^2$, comparable to the maximum obtainable for a neutron star (although requiring a smaller breaking strain)."
+" Converting this to an approximate ellipticity, assuming the canonical moment of inertia, would give €zz2x105."," Converting this to an approximate ellipticity, assuming the canonical moment of inertia, would give $\varepsilon \approx
+2\ee{-5}$."
+ In[Xu] the possibility is presented that neutron stars could be made of solid strange quark matter., In \citet{Xu:2003} the possibility is presented that neutron stars could be made of solid strange quark matter.
+" uses the observation of kHz quasi-periodic oscillations (QPOs) in X-ray bursts from neutron stars in X-ray binaries, and their potential association with torsional modes in the star, to give a shear modulus for solid strange stars of µzz4x10?!Jm?."," \citet{Xu:2003} uses the observation of kHz quasi-periodic oscillations (QPOs) in X-ray bursts from neutron stars in X-ray binaries, and their potential association with torsional modes in the star, to give a shear modulus for solid strange stars of $\mu \approx 4\ee{31}\,{\rm
+J}\,{\rm m}^{-3}$."
+" As pointed out by the identification of the QPO frequencies with torsional modes is somewhat problematic, but similarly we will take this shear modulus to be an upper limit for strange stars."," As pointed out by \citet{Owen:2005} the identification of the QPO frequencies with torsional modes is somewhat problematic, but similarly we will take this shear modulus to be an upper limit for strange stars."
+ [Lin] notes that the theoretical arguments for solid Alsostrange stars are less robust that those for the crystalline colour superconducting stars discussed in §??., Also \citet{Lin:2007} notes that the theoretical arguments for solid strange stars are less robust that those for the crystalline colour superconducting stars discussed in .
+" The masses and radii for models of strange quark stars can be seen, for example, in Fig."," The masses and radii for models of strange quark stars can be seen, for example, in Fig."
+ 2 of , 2 of .
+Although these may not necessarily hold for solid strange (2001).stars we will use the range of masses from Mo and radii from 8-11km given by this figure to, Although these may not necessarily hold for strange stars we will use the range of masses from $M_{\odot}$ and radii from 8–11 km given by this figure to
+aabuudauce. whereas more metal-rich halo stars aud disk. stars are of mterest for the study of the formation aud astration of the light elements.,"abundance, whereas more metal-rich halo stars and disk stars are of interest for the study of the formation and astration of the light elements."
+ Receut studies of aabuudances have concentrated on halo stars., Recent studies of abundances have concentrated on halo stars.
+ Following the first detection of iu by Suüth et al (1993)), Following the first detection of in by Smith et al. \cite{smith93}) )
+ at a level corresponding to an isotopic ratio of ?Li/'Li~(0.05. Ilobbs Thorburn (1991. 1997)) have confirmed the detection. and found upper limits of ffor LO stars.," at a level corresponding to an isotopic ratio of $\sixseven \simeq 0.05$, Hobbs Thorburn \cite{hobbs94}, \cite{hobbs97}) ) have confirmed the detection, and found upper limits of for 10 stars."
+ More recently. Sunith et al (19983) ," More recently, Smith et al. \cite{smith98}) )"
+report the probable detection of lin another halo star with about the sale metal abundance. mass and evolutionary stage as81937.. and give tight upper limits of ffor 7 additional stars.," report the probable detection of in another halo star with about the same metal abundance, mass and evolutionary stage as, and give tight upper limits of for 7 additional stars."
+ Finally. Cavrel et al. (1999a))," Finally, Cayrel et al. \cite{cayrel99a}) )"
+ have observed the lime in with very Hel S/N aud confirmed the presence of wwith a ligh deeree of confidence., have observed the line in with very high S/N and confirmed the presence of with a high degree of confidence.
+ Iu the case of disk stars there has not been auv systematic search for ssinee the studies of Auderseu et al. (198 D) , In the case of disk stars there has not been any systematic search for since the studies of Andersen et al. \cite{and84}) )
+and Maurice et al. (198 1))., and Maurice et al. \cite{mau84}) ).
+ In these papers an upper limit of oof about 0.10 is set for about 10 disk stars ranesius in metallicity from 1.0 to 10.3., In these papers an upper limit of of about 0.10 is set for about 10 disk stars ranging in metallicity from $-1.0$ to +0.3.
+ The meteoritic rratio is close to 0.08 (Απο Crevesse 1989)) and the interstellar ratio is similar possibly with siguificaut varlatious (Lemoime et al. 1995))., The meteoritic ratio is close to 0.08 (Anders Grevesse \cite{anders89}) ) and the interstellar ratio is similar – possibly with significant variations (Lemoine et al. \cite{lemoine95}) ).
+ For metalpoor disk. stars the ratio may be considerably higher than iu the solar svstem., For metal-poor disk stars the ratio may be considerably higher than in the solar system.
+ According to recent models for the ealactic evolution of the light clemeuts (Vanegioni-Flami et al. 1999..," According to recent models for the galactic evolution of the light elements (Vangioni-Flam et al. \cite{flam99},"
+ Fields Olive 1999a.b)) the rratio reaches a Πακ of about 0.3 at a inetallicitv of Fe/H|z0.5., Fields Olive \cite{fields99}) ) the ratio reaches a maximum of about 0.3 at a metallicity of $\feh \simeq -0.5$.
+ At higher metallicities the ratio decreases due to the xoduction of iin ACD stars. novae and supernovae of tvpe II by the 1 (Matteucci et al. 1995.," At higher metallicities the ratio decreases due to the production of in AGB stars, novae and supernovae of type II by the $\nu$ -process (Matteucci et al. \cite{matte95},"
+ Woosley Weaver 1995.. Vaneioni-Flau oe al. 1996)3.," Woosley Weaver \cite{woosley95}, Vangioni-Flam et al. \cite{flam96}) )."
+ IIeuce. it seeunis well justified o look for in the metal-poor isk stars.," Hence, it seems well justified to look for in the metal-poor disk stars."
+ Any detection will provide nuportaunt constraints of the chemical evolutionary nodels. aud with a large set of data it may also be )ossible o constrain the degree of dadepletion as a function of stellar mass aud metallicity.," Any detection will provide important constraints of the chemical evolutionary models, and with a large set of data it may also be possible to constrain the degree of depletion as a function of stellar mass and metallicity."
+ Iu the present paper we present results for the iratio for five metal-poor disk stars ranging m metallicity TOM L8 to. 0.6., In the present paper we present results for the ratio for five metal-poor disk stars ranging in metallicity from $-0.8$ to $-0.6$.
+ Very ligh S/N spectra of the rresonance line are presented m Sect., Very high S/N spectra of the resonance line are presented in Sect.
+ 3 aud analyzed with nodel atmosphere echuiques in Lt., 3 and analyzed with model atmosphere techniques in 4.
+ This has led to avather clear detection of in the two stars with the lighest masses and tight upper iuüts for iin the other stars., This has led to a rather clear detection of in the two stars with the highest masses and tight upper limits for in the other stars.
+ The consequences of these results are discussed in 55., The consequences of these results are discussed in 5.
+ The programC» stars were sclected from the lareeOo survey of ∐↸∖⋜∐⋅↴⋝∙↖⇁≺∐∖↴↘↽≼↧↖↖⇁⋜∐⋅↕↸∖↴↴⋝∙↖↽⊏≼↧↖↽⋜∐⋅≼⇂↴∖∷∖↴∪↕⊔∖↑⋜↧," The program stars were selected from the large survey of nearby disk dwarfs by Edvardsson et al. \cite{edv93}) ),"
+↕∙∐∩∩∶≩⊔∙↖↖↽↕∏↸⊳∐ ↕↸⊳↕∏≼∐∖↴∖↴⋜↧↸⊳∏∐⋅⋜↧↑↸∖↖↽⋜↧↕⋯∖↴∖↴∪↕⋟⋜↧↑↕⊔∪↴∖↴↻∐↸∖↥⋅↕↸⊳↻⋜∐⋅⋜∐⊔↸∖↑↸∖↥⋅↴∖↴∙ ∏∏⋯≺↧⋜⋯↸⊳↸∖↴∖↴∙↨↘↽↕∐↸∖∐↓⋜↧↑↕↸⊳↴∖↴⋜⋯≼↧⋜↧∶↴∙⊾↸∖↴∖↴∪↕⋟↕≺∖∖∩⋯⋜↧↕∐↴∖↴↸∖≺∣⋯∖↕∐⊳↸∖ stars distributed in metallicity from [Fe/U]=1.0 to 0.3.," which includes accurate values of atmospheric parameters, abundances, kinematics and ages of 189 main sequence stars distributed in metallicity from $\feh = -1.0$ to +0.3."
+ As we wanted to avoid stars forie from interstellar 5eas ereatlv euriched iu ffrom ACB stars or novae. the first condition for including a star was |Fe/II|<0.5.," As we wanted to avoid stars formed from interstellar gas greatly enriched in from AGB stars or novae, the first condition for including a star was $\feh \la -0.5$."
+ Next. only stars with Jag2SOOO EK were included iu order to maximize the chance of survival of someSLi.," Next, only stars with $\teff \ga 5900$ K were included in order to maximize the chance of survival of some."
+ Finally. the program bad » be lunited to a few of the brightest stars in order to be ο to reach the high S/N that is needed to determine 1ο lithium isotope ratio from the profile of the 6707.58 ine.," Finally, the program had to be limited to a few of the brightest stars in order to be able to reach the high S/N that is needed to determine the lithium isotope ratio from the profile of the 6707.8 line."
+ The five stars observed are listed iu Table 1l., The five stars observed are listed in Table 1.
+ The ffective temperature (derived from the b4 color iudex). 16 logarithunie surface gravity. the iron abundance. aud 1ο nicroturbuleunce velocity. are taken from Edvardssou al. (1993)).," The effective temperature (derived from the $b-y$ color index), the logarithmic surface gravity, the iron abundance, and the microturbulence velocity, are taken from Edvardsson et al. \cite{edv93}) )."
+ Note. that noue ofthe stars are significantly affected by. interstellar reddening according to he color excesses derived from the Z£; index and)y.," Note, that none of the stars are significantly affected by interstellar reddening according to the color excesses derived from the $H_{\beta}$ index and $b-y$."
+ According to the kinematical paraiueters of the stars as elven lu Edvardsson et al. (1993)), According to the kinematical parameters of the stars as given in Edvardsson et al. \cite{edv93}) )
+ they belong to either he thick disk or the old hin disk., they belong to either the thick disk or the old thin disk.
+ The a-clements. c.g. O aud Mg. are somewhat enhanced in the stars. ranging from [a /Fe| ~0.15 inS181.. and to la /Fe| ~0.25 in and2575.," The $\alpha$ -elements, e.g. O and Mg, are somewhat enhanced in the stars, ranging from $\alpha$ /Fe] $\simeq 0.15$ in, and to $\alpha$ /Fe] $\simeq 0.25$ in and."
+. The observations were carricd out with the ESO Coudé Echelle Spectrometer (CES) in three different periods: October 2227. 1992. June 68S. 1993. aud February Ὁ9. 1995.," The observations were carried out with the ESO Coudé Echelle Spectrometer (CES) in three different periods: October 22–27, 1992, June 6–8, 1993, and February 5–9, 1995."
+ Iu Oct. 92 and Feb. 95 the CAT 1.Bu telescope was applied. whereas in June 93 the 3.6130 telescope was feeding the CES through a 351 loug fiber aud an image slicer (D'Odorico et al. 1989)).," In Oct. 92 and Feb. 95 the CAT 1.4m telescope was applied, whereas in June 93 the 3.6m telescope was feeding the CES through a 35m long fiber and an image slicer (D'Odorico et al. \cite{dodo89}) )."
+ Ou all occasions the detector was a οί ihuuinated Ford Aerospace 20185015 CCD with 15 gan pixels., On all occasions the detector was a front illuminated Ford Aerospace $2048 \times 2048$ CCD with 15 $\mu$ m pixels.
+ The CES camera has a dispersion of, The CES camera has a dispersion of
+ol the svstems are close {ο the border line. indicating that the orbits of these svstems were detected with significance close to99%.,"of the systems are close to the border line, indicating that the orbits of these systems were detected with significance close to."
+. The svstems with significance higher than are listed in Table 3., The systems with significance higher than are listed in Table 3.
+ Here we list the IHipparcos number and the stellar name. the confidence level of the derived astrometric orbit. (he derived semi-major axis. its uncertainty and the derived inclination: the derived secondary. mass. together with itslo range.," Here we list the Hipparcos number and the stellar name, the confidence level of the derived astrometric orbit, the derived semi-major axis, its uncertainty and the derived inclination; the derived secondary mass, together with its$\sigma$ range."
+ The values in square brackets are (he corresponding values calculated by Pourbaix (2001). listed here for conparison.," The values in square brackets are the corresponding values calculated by Pourbaix (2001), listed here for comparison."
+ In Table 4 aud Table 5 we repeat the above analvsis for the sub-stellar candidates with minimum masses between 15 and το ((1.e.. brown-dwarl candidates).," In Table 4 and Table 5 we repeat the above analysis for the sub-stellar candidates with minimum masses between 15 and 70 (i.e., brown-dwarf candidates)."
+ Table 4 summarizes the Hipparcos aud radial-velocity data ofthe brown-dwarf candidates., Table 4 summarizes the Hipparcos and radial-velocity data of the brown-dwarf candidates.
+ The structure of the table is identical to that of Table 1., The structure of the table is identical to that of Table 1.
+" The table includes IID 168442 which we ""expelled"" from Table 1.", The table includes HD 168443 which we “expelled” from Table 1.
+ HD 98230 is a quadruple svstem aud therefore its astrometric motion must be quite complicated and thus was not analyzed., HD 98230 is a quadruple system and therefore its astrometric motion must be quite complicated and thus was not analyzed.
+ Nine of the remaining 14 stars were analvzed by. Halbwachs et ((2000) and are marked accordingly in the table., Nine of the remaining 14 stars were analyzed by Halbwachs et (2000) and are marked accordingly in the table.
+ Table |5 presentis the results of our analvsis., Table 5 presents the results of our analysis.
+ Figuree 3 depicts (epeeπμ... versus eoo., Figure 3 depicts $a_{derived}$ versus $a_{99}$.
+" Contrary to Figuree 2. here a few svstems are above the line e,rivec=go. IndicatingS significantSIS detections."," Contrary to Figure 2, here a few systems are above the line $a_{derived} = a_{99}$, indicating significant detections."
+ As in the previous section. we list in Table 6 the svstems for which our analvsis indicated an astrometric orbit with a significance higher than90%.," As in the previous section, we list in Table 6 the systems for which our analysis indicated an astrometric orbit with a significance higher than."
+.. We indicate by an asterisk svstems that were analvzed by Halbwachs et ((2000)., We indicate by an asterisk systems that were analyzed by Halbwachs et (2000).
+ The structure of the table is similar to that of Table 3. except that the values in square brackets are the values obtained by Halbwachs et al..," The structure of the table is similar to that of Table 3, except that the values in square brackets are the values obtained by Halbwachs et al.,"
+ listed for comparison., listed for comparison.
+ Table 6 includes one star Η 164427 that did not appear in the Halbwachs οἱ ((2000) paper because its radial-velocity modulation had not vel been detected., Table 6 includes one star — HD 164427 — that did not appear in the Halbwachs et (2000) paper because its radial-velocity modulation had not yet been detected.
+ We find that its derived. astrometric orbit. which renders its companion stellar. is significant on a confidence level.," We find that its derived astrometric orbit, which renders its companion stellar, is significant on a confidence level."
+ For HD 164427 we present in Figure 1b the histogram of the falselv detected semi-major axes., For HD 164427 we present in Figure 1b the histogram of the falsely detected semi-major axes.
+ Out of 1000 simulations only 11 vielded semi-major axis larger than 3.11 mas., Out of 1000 simulations only 11 yielded semi-major axis larger than 3.11 $mas$.
+ It indicates that the significance of this detection is 99%... at about the 2.36 level.," It indicates that the significance of this detection is , at about the $\sigma$ level."
+Equation (13)) for the l-bodsy propagators is Fourier transformed with respect to wy using equation (27)). which gives: The coetficients 21 (eq. (29))),"Equation \ref{VlasovlinpourG1Lapl}) ) for the 1-body propagators is Fourier transformed with respect to ${\mathbf{w}}_1$ using equation \ref{expression14quasifinale}) ), which gives: The coefficients $A$ (eq. \ref{defA}) ))"
+ can be expressed in terms of the Fourier transform of the propagators by. using equation (28) Operating on equation (30)) as on the function G in equation (31)). a linear svstem is obtained for the species-cumulative cocllicients 2h.," can be expressed in terms of the Fourier transform of the propagators by using equation \ref{adeFtransformG}) ): Operating on equation \ref{eqGdekJnumero1}) ) as on the function $G$ in equation \ref{AetpropagateurG}) ), a linear system is obtained for the species-cumulative coefficients $A$."
+" It can be written: The solution of equation (32)). obtained by inverting the matrix e""(o). is then introduced in equation (30)). giving the Fourier and. Laplace transform of the propagator."," It can be written: The solution of equation \ref{eqpourAavecepsilon}) ), obtained by inverting the matrix $\varepsilon^{\alpha \beta}(\omega)$, is then introduced in equation \ref{eqGdekJnumero1}) ), giving the Fourier and Laplace transform of the propagator."
+ So doing. a function appears in the solution. which is defined by: Performing the inverse Fourier and Laplace transforms of equation (30)). the I-body propagator itself is eventually found: The correlation function is obtained from the solution (36)) for the I-bodxs propagator by using equations (10)) and (7)).," So doing, a function ${\cal{D}}$ appears in the solution, which is defined by: Performing the inverse Fourier and Laplace transforms of equation \ref{eqGdekJnumero1}) ), the 1-body propagator itself is eventually found: The correlation function is obtained from the solution \ref{propagateur1body}) ) for the 1-body propagator by using equations \ref{factorpropagateur}) ) and \ref{Green2}) )."
+ “Phe kinetic equation and its collision operator are then given by equations (4)) ancl (8))., The kinetic equation and its collision operator are then given by equations \ref{BBGKY1}) ) and \ref{poseCa}) ).
+ Thanks to the Bogoliubov synchronisation hypothesis. this equation is local in time. because the source term θα27.4T) in equation (7)) can be regarded: as independent of 7 and equal to its value at 7=0.," Thanks to the Bogoliubov synchronisation hypothesis, this equation is local in time, because the source term $S^{pq}(1',2', t-\tau)$ in equation \ref{Green2}) ) can be regarded as independent of $\tau$ and equal to its value at $\tau = 0$."
+ The collision operator for the evolution of the distribution function of species e. CCf). ds defined by equation (8)) and can be written as: The somewhat lengthy transformations that must be performed to express this equation in terms of the angle and action variables. of the densitv-potential basis and of its angle Fourier transforms are described in appendix A..," The collision operator for the evolution of the distribution function of species $a$, ${\cal{C}}^a(f)$, is defined by equation \ref{poseCa}) ) and can be written as: The somewhat lengthy transformations that must be performed to express this equation in terms of the angle and action variables, of the density-potential basis and of its angle Fourier transforms are described in appendix \ref{grossesmagouilles}."
+" They eventually vield the following final form of the kinetic equations: where D is defined by equation (35)) and the response matrix elements 2°"" needed to determine D are expressed in terms of the I-body. distribution functions by equation. (34)).", They eventually yield the following final form of the kinetic equations: where $\cal{D}$ is defined by equation \ref{definitionD}) ) and the response matrix elements $\varepsilon^{\alpha \beta}$ needed to determine $\cal{D}$ are expressed in terms of the 1-body distribution functions by equation \ref{epsilonalphabeta}) ).
+" No convective term διVy,/""(1) appears on the left hand. side of eq.(38)) because in a slowly relaxing svstem the distribution functions f""(1) are meant to depend only on the actions.", No convective term ${\mathbf{\Omega}}_1 \!\cdot\! {\mathbf{\nabla}}_{{\mathbf{w}}_1} f^a (1)$ appears on the left hand side of \ref{LAequation}) ) because in a slowly relaxing system the distribution functions $f^a(1)$ are meant to depend only on the actions.
+ Equation (38)) describes the relaxation of the distribution functions caused. by the. supposedly weak. noise created by the discreteness of the particles accompanied by their associated. gravitational polarization cloud," Equation \ref{LAequation}) ) describes the relaxation of the distribution functions caused by the, supposedly weak, noise created by the discreteness of the particles accompanied by their associated gravitational polarization cloud"
+do not attempt to calculate disk irradiation in cases where this is not true.,do not attempt to calculate disk irradiation in cases where this is not true.
+ Solving equation (10)). we can find the equilibrium temperature of the outer reaches of an optically thick disk for which irradiation dominates over viscous heating.," Solving equation \ref{tmid}) ), we can find the equilibrium temperature of the outer reaches of an optically thick disk for which irradiation dominates over viscous heating."
+ While low-mass protostellar disks can be stabilized in this regime (AILO5). massive-star disks are not.," While low-mass protostellar disks can be stabilized in this regime (ML05), massive-star disks are not."
+ We therefore account self-consistentIyfor ZC). in two steps.," We therefore account self-consistentlyfor $T_d(R_d)$, in two steps."
+ The dis cllective (surface) temperature (Z5. sav) is determined. by the requirement that it emit the viscous Ilux in addition to re-emitting the incident (ux: The midplane temperature Z; is derived. from 7; from radiation cillusion of the viscous Hux across optical depth TR. We account for the temperature dependence of the opacity when solving this equation numerically.," The disk's effective (surface) temperature $T_s$, say) is determined by the requirement that it emit the viscous flux in addition to re-emitting the incident flux: The midplane temperature $T_d$ is derived from $T_s$ from radiation diffusion of the viscous flux across optical depth $\tau_R$, We account for the temperature dependence of the opacity when solving this equation numerically."
+" As before. we identify, the critical disk ractius 444 al which Zu;(4;)= iua."," As before, we identify the critical disk radius $R_{\rm crit}$ at which $T_d(R_d) = T_{\rm crit}$ ."
+ Fragmentation occurs if the clisk extends beyond. A44., Fragmentation occurs if the disk extends beyond $R_{\rm crit}$.
+ We pause to address two minor concerns: Infalline matter is decelerated in an accretion shock upon reaching the disk. and heat racdiated by this shock warms the clisk surface.," We pause to address two minor concerns: – Infalling matter is decelerated in an accretion shock upon reaching the disk, and heat radiated by this shock warms the disk surface."
+ However the gravitational potential at 2; is very small compared to that at. the stellar surface. as 2yο," However the gravitational potential at $R_d$ is very small compared to that at the stellar surface, as $R_d\gg
+R_\star$."
+ Moreover. the stars emission is dominated by hydrogen burning rather than accretion. and a fair fraction of the starlight is reradiated onto the disk surface in our mocel (eq. 13)).," Moreover, the star's emission is dominated by hydrogen burning rather than accretion, and a fair fraction of the starlight is reradiated onto the disk surface in our model (eq. \ref{f}) )."
+ Shock heating is thus wholly negligible (by about four orders of magnitude. for a 30M. star). ," Shock heating is thus wholly negligible (by about four orders of magnitude, for a $30\,\Msun$ star). –"
+When Q=1 the ratio of gas to radiation pressure at a characteristic fragmentation radius is where face is the duration of accretion (see 2.4. and 3.1))., When $Q=1$ the ratio of gas to radiation pressure at a characteristic fragmentation radius is where $t_{\rm acc}$ is the duration of accretion (see \ref{nomodel} and \ref{core-collapse}) ).
+ Radiation pressure remains negligible out to periods of 3300 vears(scaling as (152)BSL in the core model of §??7))., Radiation pressure remains negligible out to periods of 3300 years(scaling as $(M_\star\Sigma)^{-3/4}$ in the core model of \ref{coremod}) ).
+ Moreover the photon cillusion time across the scale height. ££. faur2Bride. is a lew hundred times shorter than the orbital period.," Moreover the photon diffusion time across the scale height $H$, $t_{\rm diff} \simeq 3 \tau_R H/c$, is a few hundred times shorter than the orbital period."
+ Consequently photon pressure is irrelevant for disk fragmentation during massive star formation., Consequently photon pressure is irrelevant for disk fragmentation during massive star formation.
+ Aofore treating the core accretion model in detail in 77.. we wish to craw a few conclusions that are reasonably independent of a scenario for massive star formation.," Before treating the core accretion model in detail in \ref{coremod}, we wish to draw a few conclusions that are reasonably independent of a scenario for massive star formation."
+ We adopt in our irradiation model a fiducia cllicicney parameter ¢=0.5. but we consider other values in 277. ," We adopt in our irradiation model a fiducial efficiency parameter $\varepsilon= 0.5$, but we consider other values in \ref{CoreEffic}. ."
+"We begin by mapping the maximum clisk radius ane maximum cisk angular momentum as functions of the stellar mass AJ, and the accretion time. face=2M,/M,4. ("," We begin by mapping the maximum disk radius and maximum disk angular momentum as functions of the stellar mass $M_\star$ and the accretion time, $t_{\rm acc} = 2M_\star/{\dot{M}_{\star d}}$ . ("
+Vhe factor of two derives from the core accretion scenario of2003: aceretion time is simply. a convenien parametrization for accretion rate.),The factor of two derives from the core accretion scenario of; accretion time is simply a convenient parametrization for accretion rate.)
+ The results for Revi and jou are shown as the solid curves in figures 1 ane 2.. respectively.," The results for $R_{\rm crit}$ and $j_{\rm crit}$ are shown as the solid curves in figures \ref{riso} and \ref{critang}, respectively."
+ Not all of this parameter space is relevant. however.," Not all of this parameter space is relevant, however."
+ Observations of protostellar outllows. emerging from sites of massive star formation imply dynamical ages of order 10° vears., Observations of protostellar outflows emerging from sites of massive star formation imply dynamical ages of order $10^5$ years.
+" On both of these figures. we highlight. within the dotted. lines a plausible range of face as the range of values predicted by. for core column densities (XZ,) of 0.3. 3 & em7."," On both of these figures, we highlight within the dotted lines a plausible range of $t_{\rm acc}$ as the range of values predicted by for core column densities $\Sigma_c$ ) of 0.3 – 3 g $^{-2}$."
+ One may further restrict one's attention to masses between LO and. 120 AZ. . as more massive stars are not knownto exist.," One may further restrict one's attention to masses between 10 and 120 $\Msun$ , as more massive stars are not knownto exist."
+ From this we infer: ‘Table (1)) listsourestimates for the angular momentuni of several observed. disks. most. of which appear likely to fragment.," From this we infer: Table \ref{obsj}) ) listsourestimates for the angular momentum of several observed disks, most of which appear likely to fragment."
+contrast to field stars. the metallicity. age. aud distance o cluster stars are relatively easv to determine.,"contrast to field stars, the metallicity, age, and distance to cluster stars are relatively easy to determine."
+ As such. open clusters represent a poteutial testbed for lancet formation theories.," As such, open clusters represent a potential testbed for planet formation theories."
+ The frequency of slort-periocd anuets provides information about how often gas elauts orl. nderate. and survive in a sinele. uniformi. coeval »»pulatiou of stars.," The frequency of short-period planets provides information about how often gas giants form, migrate, and survive in a single, uniform, coeval population of stars."
+ Furthermore. observations of several clusters of different ietallicitics allow us to probe the dlanet-etallicity correlation (Fischer&Valeuti2005).. in which higher metallicity field stars are more likely to jost a planet.," Furthermore, observations of several clusters of different metallicities allow us to probe the planet-metallicity correlation \citep{fischer2005}, in which higher metallicity field stars are more likely to host a planet."
+" Planet search surveys du clusters also allow us to characterize the deeree to which the cluster euvirouimeut itself pacts the formation aud survival of plauctary «ποια»,", Planet search surveys in clusters also allow us to characterize the degree to which the cluster environment itself impacts the formation and survival of planetary systems.
+ The cluster properties at birth aud throughout its evolution are critical to determining whether the cluster environment is capable of affecting the formation and survival of planetary systems., The cluster properties at birth and throughout its evolution are critical to determining whether the cluster environment is capable of affecting the formation and survival of planetary systems.
+ The degree to which the effects of close cucounters and photIOVAPOLeEtinge radiation present iu deuse stellar environments iuflueuces the formation. evolution. aud survival of planets are not swell understood.," The degree to which the effects of close encounters and photoevaporating radiation present in dense stellar environments influences the formation, evolution, and survival of planets are not well understood."
+ There is evidence that the observed stellar densities of old open clusters tdav are sienificautly less than they were at birth. aud hat the στο! euvironnieuts iu old open clusters are not what hey were during the first 5-10 My when eiaut planets were prestunably forming.," There is evidence that the observed stellar densities of old open clusters today are significantly less than they were at birth, and that the current environments in old open clusters are not what they were during the first 5-10 Myr when giant planets were presumably forming."
+ In particular. a given cluster nay lose of its stars in the process of emocreiug youn its cimbedded stage. aud thus only the initiallv wost nassive clusters survive and are observed as old opeu clusters today (seeLada&2003:Exil1995).," In particular, a given cluster may lose of its stars in the process of emerging from its embedded stage, and thus only the initially most massive clusters survive and are observed as old open clusters today \citep[see][]{lada2003, friel1995}."
+. The degree to which plauctary systems are affected wv the cluster cuviromucut is still poorly understood voth observationallv and theoretically., The degree to which planetary systems are affected by the cluster environment is still poorly understood both observationally and theoretically.
+ Theoretical investigatious of the inportance of environment (I&obavashi&Ida2001:Adamsctal.2006:Boinellet2001:Armitage2000) suggest that open clusters are not dense enough to significantly affect the formation aud survival rates of planets. especially within the ~ 5-30 AU in which eas giants that later Ποτάτο arο thougit to form.," Theoretical investigations of the importance of environment \citep{kobayashi2001, adams2006, bonnell2001,armitage2000} suggest that open clusters are not dense enough to significantly affect the formation and survival rates of planets, especially within the $\sim$ 5-30 AU in which gas giants that later migrate are thought to form."
+ However. observatious of the Orion Nebula Cluster (ONC) (Eisneretal.2008) found that less than 1054 of the stars harbor disks of mass comparable to that o| the wun nass solar nebula. aud that the frequency of disks decreased with proximity to the massive ceital Trapeziuni stars.," However, observations of the Orion Nebula Cluster (ONC) \citep{eisner2008} found that less than $10\%$ of the stars harbor disks of mass comparable to that of the minimum mass solar nebula, and that the frequency of disks decreased with proximity to the massive central Trapezium stars."
+ They also claim that the frequency of disks in the dense ONC is statistically cüffereut TOM that of the lower deusitv Taurus cluster., They also claim that the frequency of disks in the dense ONC is statistically different from that of the lower density Taurus cluster.
+ A simular sπαν of the Arches also detected a disk fraction that varies with proximity to the massive. ceutral stars (Stolteetal.Ww 10).," A similar study of the Arches also detected a disk fraction that varies with proximity to the massive, central stars \citep{stolte2010}."
+ Of the umunerous planet detection methods avaiable o astronomers. photometric transit searches are among 1e most logical choices for an open cluster survey (JaunesWw 105)...," Of the numerous planet detection methods available to astronomers, photometric transit searches are among the most logical choices for an open cluster survey \citep{janes1996, pepper2005,pepper2006, vonbraun2005}."
+ Transit survevs have the ability to monitor a arec nuniber of stars simultaneously. aud νομοί TOM je fact that cluster stars are concentrated over a small xxtioun of the sky.," Transit surveys have the ability to monitor a large number of stars simultaneously, and benefit from the fact that cluster stars are concentrated over a small portion of the sky."
+ Photometric surveys can also be erformed on smaller. nore easilv accessile telescOpes ian conipetiue methods of planet detectio1 (PopperCandi2005. 20063.," Photometric surveys can also be performed on smaller, more easily accessible telescopes than competing methods of planet detection \citep{pepper2005, pepper2006}."
+.. The photometric data are simple to calibrate. aud in the case of clusters the netallicities. distance. ages. and radii for all stars cau beotained with relative ease.," The photometric data are simple to calibrate, and in the case of clusters the metallicities, distance, ages, and radii for all stars can be obtained with relative ease."
+ Because the technological requircineuts for a successful photometric survey are fulfilled Jy modest ancl readily available iustruments. transit searches are a simple and direct iiethod of detecting planets in these svsteiis. with the caveat that the radial velocity follow-up needed to coufiria planet candidates is not always as easily obtained (seeAierain&Pout2007).," Because the technological requirements for a successful photometric survey are fulfilled by modest and readily available instruments, transit searches are a simple and direct method of detecting planets in these systems, with the caveat that the radial velocity follow-up needed to confirm planet candidates is not always as easily obtained \citep[see][]{aigrain2007}."
+. However. despite a number of transit searches tarectineg open clusters (Παπαetal.2009:Burke2006:03:Rosvick&Robb2006:E:Montaltoetal. 2009).. uo convincing planctary transits have been found.," However, despite a number of transit searches targeting open clusters \citep{hartman2009, burke2006, mochejska2008, mochejska2005, mochejska2006, miller2008, bramich2005,bramich2006, hood2005, bruntt2003, rosvick2006, vonbraun2005, hidas2005, montalto2007, howell2005, pepper2008, vonbraun2004, vonbraun2005, lee2004, hidas2005, street2003, rosvick2006, montalto2009}, , no convincing planetary transits have been found."
+ There are two possible explanations for this paucity of plaucts (Janes&Iia2009): cither there is something differcut about the planet populatious of open clusters. or there are siuplv too few observed cluster stars to detect a ylanct from an otherwise “typical” planet population.," There are two possible explanations for this paucity of planets \citep{janes2009}: either there is something different about the planet populations of open clusters, or there are simply too few observed cluster stars to detect a planet from an otherwise “typical” planet population."
+ The frequency of short-period planets is ~LY (οπιαΊοetal.2008).. aud the geometric probability that such a oauet transits ix only ~1056. iieauiug that one naively expects to observe ~1000 stars before detecting even one rausiting planet.," The frequency of short-period planets is $\sim1\%$ \citep{cumming2008}, and the geometric probability that such a planet transits is only $\sim10\%$, meaning that one naively expects to observe $\sim1000$ stars before detecting even one transiting planet."
+ Because the transit depths are small (o 1%) and have a low duty cevcle. both precise (to a ew mulimaenitudes) plotometiy aud excellent temporal coverage are required in any transit search.," Because the transit depths are small $\sim1\%$ ) and have a low duty cycle, both precise (to a few milimagnitudes) photometry and excellent temporal coverage are required in any transit search."
+ When one considers the need for sufficicut a signal-to-noise ratio and multiple observed transits for robust detection. it is generally the case that may more than 1000 stars must be monitored to detect anv transiting planets (Burkeetal.2006:vouBraun 2005).," When one considers the need for sufficient a signal-to-noise ratio and multiple observed transits for robust detection, it is generally the case that many more than 1000 stars must be monitored to detect any transiting planets \citep{burke2006, vonbraun2005}."
+. Since the richest open clusters coutain a few thousand stars at best. the lack of detected trausiting planets iu amy imdividual survey may simply be due to au insufficient number of target stars.," Since the richest open clusters contain a few thousand stars at best, the lack of detected transiting planets in any individual survey may simply be due to an insufficient number of target stars."
+ While cach survey alone may not observe a sufficicut iuuber of stars to have expected a planct detection. we estimate the total umber of cluster stars observed in al rausit surveys to be roughly 10.000. aud that combines he sample of stars is rich οποιο to derive interesting upper lamits on the frequency of short-period plaucts.," While each survey alone may not observe a sufficient number of stars to have expected a planet detection, we estimate the total number of cluster stars observed in all transit surveys to be roughly 10,000, and that combined the sample of stars is rich enough to derive interesting upper limits on the frequency of short-period planets."
+ Dv carefully statistically combining the uull results of several photometric surveys. we provide a more strinecut upper limit than is possible with individual studies. ar hen compare this hit to the frequencies of planets amone field stars derived from both photometric are radial velocity surveys.," By carefully statistically combining the null results of several photometric surveys, we provide a more stringent upper limit than is possible with individual studies, and then compare this limit to the frequencies of planets among field stars derived from both photometric and radial velocity surveys."
+ As we will show. the tvpica detection efficiencies of these photometric surveys are iusufficieut. even with 10.000 total stars. to place tighter constraints ou the frequency of short-period plaucts thu surveys of field stars. and thus we conclude that these conibined upper limits are cousistent with the observed frequency of short-period giant planets iu the field.," As we will show, the typical detection efficiencies of these photometric surveys are insufficient, even with 10,000 total stars, to place tighter constraints on the frequency of short-period planets than surveys of field stars, and thus we conclude that these combined upper limits are consistent with the observed frequency of short-period giant planets in the field."
+ Caven the available data. we have no reason to suspect that the population of short-period planets in open clusters is auvthiug other than “ordinary.," Given the available data, we have no reason to suspect that the population of short-period planets in open clusters is anything other than “ordinary”."
+ The paper is organized as follows: in we discuss the imanner duo which upperHits on planet frequencies are derived frou transit surveys and how their individual results can be combined. in," The paper is organized as follows: in \\ref{sec:methods} we discuss the manner in which upperlimits on planet frequencies are derived from transit surveys and how their individual results can be combined, in"
+ExpandXpand coso(£)(ft) and sin©(f) usingsing trigonometric relations analogous to eqs. (17)),Expand $\cos \phi(t)$ and $\sin \phi(t)$ using trigonometric relations analogous to eqs. \ref{trigcos}) )
+ and (18)) and parameterizeparari the orbit of the encounter as in the polar form of eq. (43))., and \ref{trigsin}) ) and parameterize the orbit of the encounter as in the polar form of eq. \ref{polorb}) ).
+ Finally. in the resulting integrals. make a change of time coordinate from £>Iw€ according to eq. (47)).," Finally, in the resulting integrals, make a change of time coordinate from $t \rightarrow \xi$ according to eq. \ref{timeorb}) )."
+ Eliminating the integrals that are odd in © we find. after algebra: Inthese expressions. © depends implicitly on time through eq. (47))," Eliminating the integrals that are odd in $\xi$ we find, after algebra: Inthese expressions, $\Phi$ depends implicitly on time through eq. \ref{timeorb}) )"
+ according to and the upper and lower signs in the = and d- terms refer to prograde and retrograde coplanar encounters. respectively.," according to and the upper and lower signs in the $\mp$ and $\pm$ terms refer to prograde and retrograde coplanar encounters, respectively."
+" These can be put into a form amenable to further analysis by repeated application of trigonometric relations of the form giving Finally. these results can be written in terms of the ""generalized"" Airy functions of Press&Teukolsky(1977).. who defined giving where. as usual. the upper and lower signs in the Jr factors refer to prograde and retrograde coplanar encounters. respectively."," These can be put into a form amenable to further analysis by repeated application of trigonometric relations of the form giving Finally, these results can be written in terms of the “generalized” Airy functions of \citet{PT77}, who defined giving where, as usual, the upper and lower signs in the $\mp$ factors refer to prograde and retrograde coplanar encounters, respectively."
+ Computation of these expressions is facilitated using the recursion relations which are proven in Press&Teukolsky(1977)., Computation of these expressions is facilitated using the recursion relations which are proven in \citet{PT77}.
+". Equation (61)) makes it possible to obtain all the 7;,,""s from the {ως while equation (62)) allows the Z;jys for/= 1to be computed from Jou.fry.Lou.Dao"," Equation \ref{Rec1}) ) makes it possible to obtain all the $I_{lm}$ 's from the $I_{l0}$ 's while equation \ref{Rec2}) ) allows the $I_{l0}$ 's for $l \geq 4$ to be computed from $I_{00},I_{10},I_{20},I_{30}$."
+ In particular: and. so where the upper and lower signs in the + terms refer to prograde and retrograde co-planar encounters. respectively. and Av.=0.," In particular: and, so where the upper and lower signs in the $\pm$ terms refer to prograde and retrograde co-planar encounters, respectively, and $\Delta$ $_{z} = 0$."
+ For moderate arguments. the functions Z5o.19.Loy.{ου can be computed by numerical integration of eq. (58))," For moderate arguments, the functions $I_{00},I_{10},I_{20},I_{30}$ can be computed by numerical integration of eq. \ref{Ilmpt77}) )"
+ or from the rational function approximations providec by Press&Teukolsky (1977).. which are reproduced in the Appendix.," or from the rational function approximations provided by \citet{PT77}, , which are reproduced in the Appendix."
+Second. it is reasonable to asstune that the Quuueasurect) eccentricity is actually vanishiuslv small?,"Second, it is reasonable to assume that the (unmeasured) eccentricity is actually vanishingly small?"
+ In this paper we have attempted to provide partial answers to both of these questions., In this paper we have attempted to provide partial answers to both of these questions.
+ Our main result is that theη damping of a thin scl-eravitating disk at sub-pe distances from a black hole is relatively rapid., Our main result is that the damping of a thin self-gravitating disk at sub-pc distances from a black hole is relatively rapid.
+ The timescale at 0.1 pc is around LO Myr. and even this may be au overestimate since anv nonlinear effects (such as the formation of shocks as elliptical orbits precess) will hasten the decay further.," The timescale at 0.1 pc is around 10 Myr, and even this may be an overestimate since any nonlinear effects (such as the formation of shocks as elliptical orbits precess) will hasten the decay further."
+ Rapid damping is driven by differeutial precession. which occurs on a much shorter timescale than the viscous evolution of the disk.," Rapid damping is driven by differential precession, which occurs on a much shorter timescale than the viscous evolution of the disk."
+ The lack of gross ecceutricity iu NGC [258 is therefore uot surprising. and does nof constrain the disk formation mechanism.," The lack of gross eccentricity in NGC 4258 is therefore not surprising, and does not constrain the disk formation mechanism."
+ Once damping is underway. however. it cau take a surprisingly loug period for the eccentricity to decay to negligible levels.," Once damping is underway, however, it can take a surprisingly long period for the eccentricity to decay to negligible levels."
+" If the viscous cocficicnt governing eccentricity damping is relatively small (a,=0.1 in our description) the presence of waves in the disk allows significant ecceutricitv to survive for up to 50 Myr.", If the viscous coefficient governing eccentricity damping is relatively small $\alpha_e = 0.1$ in our description) the presence of waves in the disk allows significant eccentricity to survive for up to 50 Myr.
+ Evidently it would be useful todetermine the efficiency of eccentricity damping uuder the conditions likely to prevail at sub-pe radii. perhaps via improved simulations of sclberavitating eccentric disks. which to date have focused on simpler questions such as whether the disk fragments or uot (Alexaudcretal2008).," Evidently it would be useful to the efficiency of eccentricity damping under the conditions likely to prevail at sub-pc radii, perhaps via improved simulations of self-gravitating eccentric disks, which to date have focused on simpler questions such as whether the disk fragments or not \citep{alexander08}."
+ Cinrenth. thoueh. it sees muwise to conclude that a good upper liit on the eccentricity tuples strictly circular orbits.," Currently, though, it seems unwise to conclude that a good upper limit on the eccentricity implies strictly circular orbits."
+ Finally. we addressed the question. of the predicted orbital structure of an eccentric disk during the civeularization process.," Finally, we addressed the question of the predicted orbital structure of an eccentric disk during the circularization process."
+ Existing constraints on the eccentricity of the NGC [258 disk (huuplrevsctal.2008) have been derived assumnius a model. developed by Statler(2001). for different purposes. in which the eccentric orbits are aligned and nested.," Existing constraints on the eccentricity of the NGC 4258 disk \citep{humphreys08} have been derived assuming a model, developed by \cite{statler01} for different purposes, in which the eccentric orbits are aligned and nested."
+ Iu the case of very thin masing disks this model is not a good approximation to the likely structure. which imustead involves a 1noderatolv tightly wound spiral in the angle of periapse.," In the case of very thin masing disks this model is not a good approximation to the likely structure, which instead involves a moderately tightly wound spiral in the angle of periapse."
+ A reasonable fit. over a modest range of radii. is possible using the next order approximation in which the periapse angle is a linear function of orbital radius.," A reasonable fit, over a modest range of radii, is possible using the next order approximation in which the periapse angle is a linear function of orbital radius."
+ This work was stimulated by discussions with Fred Lo. and completed at the weime of Dick MeCrax. to whom I am indebted.," This work was stimulated by discussions with Fred Lo, and completed at the urging of Dick McCray, to whom I am indebted."
+ My research was supported bv NASA under erants NNCOLGLOLC and NNXOTAIIOSC: from the Astrophysics Theory Programs. aud bv the NSF under eraut. AST 0107010.," My research was supported by NASA under grants NNG04GL01G and NNX07AH08G from the Astrophysics Theory Programs, and by the NSF under grant AST 0407040."
+and relatively wider double-peaked lines characteristic of small dises.,and relatively wider double-peaked lines characteristic of small discs.
+" Our initial choice of parameters. described above. roughly matches the observed '""CO J26-5 and J =3- line fluxes. confirming the outer of 400 AU seen i scattered light observations."," Our initial choice of parameters, described above, roughly matches the observed $^{12}$ CO $J=$ 6–5 and $J=$ 3--2 line fluxes, confirming the outer of 400 AU seen in scattered light observations."
+ We performed test calculations for a lower value of the disc mass of 107 Mos. ie. tei times lower densities.," We performed test calculations for a lower value of the disc mass of $^{-3}$ $_{\odot}$, i.e., ten times lower densities."
+ The modelled line fluxes are founc not to vary significantly with respect to the noise levels of our observations., The modelled line fluxes are found not to vary significantly with respect to the noise levels of our observations.
+ Thus. in the disc mass range of 1077- 107 M. values found typically towards circumstellar dises. and temperatures similar to those assumed here. the observed CO J26-5 and J=3-2 lines are insensitive to dise mass.," Thus, in the disc mass range of $^{-3}$ $^{-2}$ $_{\odot}$, values found typically towards circumstellar discs, and temperatures similar to those assumed here, the observed $^{12}$ CO $J=$ 6–5 and $J=$ 3–2 lines are insensitive to disc mass."
+" If we decrease the dise mass to allow the '*CO line emission in our models to be sensitive to the density variations in the midplane (1.8. emission dominated by the midplane). the disc midplane temperatures (x20 K in the outer disc) would be the only physically appropriate assumption for the temperature in the ""Iow-mass' model."," If we decrease the disc mass to allow the $^{12}$ CO line emission in our models to be sensitive to the density variations in the midplane (i.e., emission dominated by the midplane), the disc midplane temperatures $\leq$ 20 K in the outer disc) would be the only physically appropriate assumption for the temperature in the `low-mass' model."
+ While the asymmetry in the line profile could be reproduced in this way. the resulting lines would be much weaker than observed.," While the asymmetry in the line profile could be reproduced in this way, the resulting lines would be much weaker than observed."
+ Given these considerations. we assume the two lines to be optically thick in the dise around HD 100546 and fix the disc mass to the initial value of 1077 M...??.," Given these considerations, we assume the two lines to be optically thick in the disc around HD 100546 and fix the disc mass to the initial value of $^{-2}$ $_{\odot}$."
+ In the further analysis we fit the exact line shapes and intensities. with a particular focus on the line asymmetry seen in both J26-5 and / 23-2 spectra.," In the further analysis we fit the exact line shapes and intensities, with a particular focus on the line asymmetry seen in both $J=$ 6–5 and $J=$ 3–2 spectra."
+ The characteristic temperatures and masses derived in Sect., The characteristic temperatures and masses derived in Sect.
+ 1: for the dise around HD 100546 are similar to the models used in?., \ref{ss:emission} for the disc around HD 100546 are similar to the models used in.
+. The modelling of the '*CO 3-2 line of HD 100546 in?) yielded very rough estimates of the outer radius of 300 AU and inclination of 357. consistent with the 400 AU and 50° from the scattered light.," The modelling of the $^{12}$ CO 3–2 line of HD 100546 in yielded very rough estimates of the outer radius of 300 AU and inclination of $\degr$, consistent with the 400 AU and $\degr$ from the scattered light."
+ We use their models to fit the 'CO spectra. with Τι as free parameter and varying q from its initial. value of 0.5 where necessary.," We use their models to fit the $^{12}$ CO spectra, with $T_{100}$ as free parameter and varying $q$ from its initial value of 0.5 where necessary."
+ We fix the outer radius and inclination to the observationally constrained values 400 AU and 50°??mamBodyCitationEnd3628Jaugereau., We fix the outer radius and inclination to the observationally constrained values 400 AU and $\degr$.
+ We use the Keplerian velocity field around a 2.5 M. star., We use the Keplerian velocity field around a 2.5 $_{\odot}$ star.
+ The dependence of the spectral profile on the stellar mass in the range M. does not affect our fit significantly., The dependence of the spectral profile on the stellar mass in the range 2.0-3.0 $_{\odot}$ does not affect our fit significantly.
+ The inner radius is assumed to be 0.6 AU. close to the dust sublimation radius.," The inner radius is assumed to be 0.6 AU, close to the dust sublimation radius."
+ Although an inner hole of 13 AU is found in HD 100546. its presence would not affect our results because the molecular lines observed are dominated by dise regions far beyond the inner tens of AU.," Although an inner hole of 13 AU is found in HD 100546, its presence would not affect our results because the molecular lines observed are dominated by disc regions far beyond the inner tens of AU."
+ Because the observed 'CO lines, Because the observed $^{12}$ CO lines
+Classical P. Tauri stars (ePTSs) are voung solar analogs which are accreting material from circumstellar clises.,Classical T Tauri stars (cTTSs) are young solar analogs which are accreting material from circumstellar discs.
+ Manv observations are consistent. with the scenario of the stellar field truncating the inner disc and channelling eas onto discrete regions of the stellar surface., Many observations are consistent with the scenario of the stellar field truncating the inner disc and channelling gas onto discrete regions of the stellar surface.
+ The shapes of near-Lht spectral energy distributions (e.g. 2)). and the kinematics of CO lines formed in the disc (?).. are consistent with the disc having been truncated at a distance of a few stellar racii," The shapes of near-IR spectral energy distributions (e.g.\citealt{rob07}) ), and the kinematics of CO lines formed in the disc \citep*{naj03}, are consistent with the disc having been truncated at a distance of a few stellar radii."
+ Average surface fields of order a kG have been detected on a numberof cT'TSs (2).. whieh models sugges will he strong cnough to disrupt the inner disc (?)..," Average surface fields of order a kG have been detected on a numberof cTTSs \citep{joh07}, which models suggest will be strong enough to disrupt the inner disc \citep{kon91}."
+ The detection of inverse P-Cveni profiles. with widths of several hundred kms|. can also be explained by material essentially [roc-fallinge alonge the field lines of the stellar magnetosphereὃν1from the location of the inner disc (2)..," The detection of inverse P-Cygni profiles, with widths of several hundred $^{-1}$, can also be explained by material essentially free-falling along the field lines of the stellar magnetospherefrom the location of the inner disc \citep{edw94}."
+ Furthermore. the excess continuum emission (veiling) in the optical and UV is likely to arise from shocks at the base of accretion funnels. with emission lines with high excitation potentials. e.g. HelSSTGA. forming mainly in such regions (?)..," Furthermore, the excess continuum emission (veiling) in the optical and UV is likely to arise from shocks at the base of accretion funnels, with emission lines with high excitation potentials, e.g. HeI, forming mainly in such regions \citep{ber01}."
+ The magnetic interaction between the stellar field and the disc may also haveimportant consequences for. the formation ofplanets., The magnetic interaction between the stellar field and the disc may also haveimportant consequences for the formation ofplanets.
+" Simulations by 2.. and analvtic work be? and οι, suggest that the inner disc hole. cleared by the star-disc interaction. may provide a natural barrier that decreases the rate of inward. migration of forming planets."," Simulations by \citet{rom06}, and analytic work by \citet*{lin96} and \citet{fle08}, suggest that the inner disc hole, cleared by the star-disc interaction, may provide a natural barrier that decreases the rate of inward migration of forming planets."
+ There is also evidence that the large scale magnetosphere maw directly disrupt the inner disc. producing warps which in some svstenis cross the observer's line-of-sight to the star (e.g. AA Tau. 2)).," There is also evidence that the large scale magnetosphere may directly disrupt the inner disc, producing warps which in some systems cross the observer's line-of-sight to the star (e.g. AA Tau, \citealt{bou07}) )."
+ Indeed 3D. AID simulations have demonstrated that complicated: warpingellects in the disc truncation region may be common for T ‘Tauri stars (??)..," Indeed 3D MHD simulations have demonstrated that complicated warpingeffects in the disc truncation region may be common for T Tauri stars \citep{rom03,rom04}."
+ The star-disc interaction may. also explain the slower rotation of ο)ος compared to the typically older weak-line T Tauri stars. whose cises have largely dispersed. (see e.g. the review by 2)).," The star-disc interaction may also explain the slower rotation of cTTSs compared to the typically older weak-line T Tauri stars, whose discs have largely dispersed (see e.g. the review by \citealt{bou07IAU}) )."
+ Accretion of material from the inner disc would act to spin-up the central star in the absence of some physical mechanism to remove angular momentum [rom the svstem., Accretion of material from the inner disc would act to spin-up the central star in the absence of some physical mechanism to remove angular momentum from the system.
+ Various magnetospheric accretion models have been developed to explain this mechanism. which diller in their assumed. location of the inner disc. the details of how angular momentum is removed. and how the magnetic Ποιά topoloev controls both accretion and outllows (?:: 2: Tu Pa ⋅⋅⋅⋅ τν TTTTu Tun 7)).," Various magnetospheric accretion models have been developed to explain this mechanism, which differ in their assumed location of the inner disc, the details of how angular momentum is removed, and how the magnetic field topology controls both accretion and outflows \citealt{kon91}; \citealt{col93}; \citealt{shu94}; ; \citealt*{fer00}; ; \citealt*{fer06}; ; \citealt*{kuk03}; ; \citealt{mat05a,mat05b,mat08a,mat08b}; ; \citealt*{lon05}; ; \citealt{bes08}) )."
+ Although observations indicate that the magnetic field topologies of οESs are complex, Although observations indicate that the magnetic field topologies of cTTSs are complex
+We stress. once again. that equation (58)) is valid to leading order in the deviation from spherical svnunetry.,"We stress, once again, that equation \ref{energies}) ) is valid to leading order in the deviation from spherical symmetry."
+ Ες does not mean that the total energy in the sphere is approximated by its spherical counterpart. (, This does not mean that the total energy in the sphere is approximated by its spherical counterpart. (
+By doing this we would lose all the information on the shape of the system.),By doing this we would lose all the information on the shape of the system.)
+ I is the whole ratio between the total energies in the final and initial spheres which is approximated by the ratio between their spherical counterparts., It is the whole ratio between the total energies in the final and initial spheres which is approximated by the ratio between their spherical counterparts.
+ hus. taking into account the relation (42)=£(I)|o8(H). equation (58)) implies to leading order in the deviation from spherical svmmetry.," Thus, taking into account the relation $E(R)={\cal E}(R)+\delta{\cal E}(R)$ , equation \ref{energies}) ) implies, to leading order in the deviation from spherical symmetry."
+" Substituting the expressions for ὃς and 38, in the virialised object and its seed(eq. 57]])"," Substituting the expressions for $\delta{\cal E}$ and $\delta{\cal
+ E}\p$ in the virialised object and its seed(eq. \ref{de}] ])"
+ into the relation (59)) and cilferentiating it. we are led to," into the relation \ref{cale}) ) and differentiating it, we are led to."
+" where POR)=£UD/S,GO. the so-called “spherical” energy. dissipation factor. is given by (eqs... 53]]"," where ${\cal D}(R)\equiv {\cal E}(R)/{\cal E}\p(R)$, the so-called “spherical” energy dissipation factor, is given by (eqs. \ref{vir0}] ]"
+ and 0) /Pa. Then. taking into account equations (10)) and (14)). both for the virialised object and its seed. equation (60)) establishing the link betweenthe respective mean crossed density.potential Ductuation profiles leads to where oit). being Vir)=1.g(ryn(r){1ld25]z(9<a| and 56r) the logarithmic derivative of the mean crossed [uctuation profile.," and \ref{diff}] ]) _0^R. Then, taking into account equations \ref{4th}) ) and \ref{D1}) ), both for the virialised object and its seed, equation \ref{1st}) ) establishing the link betweenthe respective mean crossed density–potential fluctuation profiles leads to where , being $V(r)=1-\xi(r)\gamma(r)\left\{1-[1+2\kappa]\gamma(r)-\frac{\der\ln
+ \gamma}{\der\ln r}\right\}$ and $\gamma(r)$ the logarithmic derivative of the mean crossed density--potential fluctuation profile."
+ Equations (49)) and (72)) determine the eecentricities of the virialisecl object grown by PA from those of its seed. as wanted.," Equations \ref{6th}) ) and \ref{7th}) ) determine the eccentricities of the virialised object grown by PA from those of its seed, as wanted."
+ From equations (72)) and (73)). we see that this relation involves the profile 2στὴν which depends on the shape of the final system and. hence. on that of its seed.," From equations \ref{7th}) ) and \ref{S}) ), we see that this relation involves the profile $\sigma^2(r)$, which depends on the shape of the final system and, hence, on that of its seed."
+ But such a dependence cannot be determined without previously determining the anisotropy profile., But such a dependence cannot be determined without previously determining the anisotropy profile.
+ This will be done in Section ??.., This will be done in Section \ref{anisotropy}.
+ Only at small kr. the term SC) in equation (72)) becomes neelieible?.," Only at small $r$, the term $S(r)$ in equation \ref{7th}) ) becomes ."
+. This means that. except for the factor C(r). equation. (72)) takes there theform of an identity relation. just as equation," This means that, except for the factor$U(r)$ , equation \ref{7th}) ) takes there theform of an identity relation, just as equation"
+ :~1 Uufortunatelv. little is known about the evolutionary history of SO ealaxies. especially in the field.," $z\sim1$ Unfortunately, little is known about the evolutionary history of S0 galaxies, especially in the field."
+ Although typical SO ealaxics appear to differ siguificauthy frou I galaxies. it is uot vot clear where SO ealaxics fit iuto the IIubble tuning fork or what amount of star formation they typically coutain2008).," Although typical S0 galaxies appear to differ significantly from E galaxies, it is not yet clear where S0 galaxies fit into the Hubble tuning fork or what amount of star formation they typically contain."
+. While uou-iuteracting S0. ealaxics end to have disks simular in thickuess to those of late-ype galaxies2009).. other xoperties of SO disks differ signuificautlv frou: those of ate-tvpe galaxies.," While non-interacting S0 galaxies tend to have disks similar in thickness to those of late-type galaxies, other properties of S0 disks differ significantly from those of late-type galaxies."
+ For example. their color eradicuts are ess pronounced than those of late-type disks2001).. and SO galaxies are typically fainter than ater type disks2009).," For example, their color gradients are less pronounced than those of late-type disks, and S0 galaxies are typically fainter than later type disks."
+.. SO ealaxies are xedonmüuautlv found in galaxw clusters and are mostly stripped of2009).. whereas field SO ealaxics like NGC LOL are less cohbunon and could be a type of post-starburst chwart2008).," S0 galaxies are predominantly found in galaxy clusters and are mostly stripped of, whereas field S0 galaxies like NGC 404 are less common and could be a type of post-starburst dwarf."
+". As the nearest face-on example of an SO ealaxy V,=190 kan +2000. NGC 101 has been previously studied in some detail."," As the nearest face-on example of an S0 galaxy; $V_{c}=190$ km $^{-1}$, NGC 404 has been previously studied in some detail."
+" Although its optica morphology suggests that NCC 1013s a classic ""red iux dead” early-type galaxy. the ceuter appears to have a sienificant voung component."," Although its optical morphology suggests that NGC 404 is a classic “red and dead” early-type galaxy, the center appears to have a significant young component."
+ With long-slit spectroscopy, With long-slit spectroscopy
+scale has also been used by Tokovinin (1992) to study the secondary mass distribution in spectroscopic binaries. ancl was suggested by Black (1998) to study the mass distribution of (he planetarv-nass companions (see also Mazel 1999a.b: Mazeh Zucker 2001: Mavor οἱ al.,"scale has also been used by Tokovinin (1992) to study the secondary mass distribution in spectroscopic binaries, and was suggested by Black (1998) to study the mass distribution of the planetary-mass companions (see also Mazeh 1999a,b; Mazeh Zucker 2001; Mayor et al."
+ 2001)., 2001).
+ The eap or the “brown-cwarl desert” are consistent also with the finding of Halbwachs et ((2000). who used Ilipparcos data and found that many of (he known brown-cdwat candidates are actuallv stellar companions.," The gap or the “brown-dwarf desert” are consistent also with the finding of Halbwachs et (2000), who used Hipparcos data and found that many of the known brown-dwarf candidates are actually stellar companions."
+ We will assume that the two populations are the planets. at the low-mass side of Figure 3. and the stellar companions at the high-mass end of the figure.," We will assume that the two populations are the planets, at the low-mass side of Figure 3, and the stellar companions at the high-mass end of the figure."
+ Interestingly. the mass distribution of stars extends [ar below LOO ((e.g.. Zapatero Osorio et 22000: Lucas Roche 2000). indicating that the gap separating the two populations of apparently does not exist in the population of single stars/brown dwarls.," Interestingly, the mass distribution of stars extends far below 100 (e.g., Zapatero Osorio et 2000; Lucas Roche 2000), indicating that the gap separating the two populations of apparently does not exist in the population of single stars/brown dwarfs."
+ This dillerence probably indicates different formation processes lor single and secondary objects., This difference probably indicates different formation processes for single and secondary objects.
+ The distribution we derived in Figure 3 suggestsoO (hat the planet mass distribution is almost flat in logAf over five bins from 0.3 to LO41., The distribution we derived in Figure 3 suggests that the planet mass distribution is almost flat in $\log M$ over five bins — from 0.3 to 10.
+ Actually. the figure suggests a slight rise of the distribution towards smaller masses.," Actually, the figure suggests a slight rise of the distribution towards smaller masses."
+ The distinction between these two distributions is not possible at this point. when our knowledge about planets with sub-Jupiter masses is very limited.," The distinction between these two distributions is not possible at this point, when our knowledge about planets with sub-Jupiter masses is very limited."
+ At the high-mass end of the planet distribution (he mass distribution dramatically drops olf at LOAZ... with a small high-end tail in the next bin.," At the high-mass end of the planet distribution the mass distribution dramatically drops off at 10, with a small high-end tail in the next bin."
+ Although the results are still consistent with zero. we feel that the small value bevond 160 mnmight be real.," Although the results are still consistent with zero, we feel that the small value beyond 10 might be real."
+ The dramatic drop at 10 aand (he small high-mass tail agree with the findings of Jorissen et ((2001)., The dramatic drop at 10 and the small high-mass tail agree with the findings of Jorissen et (2001).
+ Examination of the (wo panels of Figure 3 suggests that per equal dex range of masses the lvequeney. of stellar secondaries is higher than (that of the planets by a factor of about 2., Examination of the two panels of Figure 3 suggests that per equal dex range of masses the frequency of stellar secondaries is higher than that of the planets by a factor of about 2.
+ As we emphasized in the previous section. this is à very preliminary result that should be checked by future observations.," As we emphasized in the previous section, this is a very preliminary result that should be checked by future observations."
+ Nevertheless. the frequency. of planets is impressive by itself.," Nevertheless, the frequency of planets is impressive by itself."
+" Our results indicate that about of the stars have planets with masses between 1 and 103,.", Our results indicate that about of the stars have planets with masses between 1 and 10.
+. This is so because the number of multiple planets in this sample is small. so ihe number of planets considered in (he ligure is about the mumnber of stars found to have one or more planets.," This is so because the number of multiple planets in this sample is small, so the number of planets considered in the figure is about the number of stars found to have one or more planets."
+ If (his frequency extends further down the mass axis to Earth masses. we mieht find that more than of the stars have planets with periods shorter than 1500 clavs.," If this frequency extends further down the mass axis to Earth masses, we might find that more than of the stars have planets with periods shorter than 1500 days."
+ The analvsis presented here raises (he question what mechanism can produce flat or approximately [lat mass distribution of planets up to LO;., The analysis presented here raises the question what mechanism can produce flat or approximately flat mass distribution of planets up to 10.
+. What determines the mass of the lorming planet?, What determines the mass of the forming planet?
+ The present paracligm assumes (hat planets were formed ont of a protoplanetary disk., The present paradigm assumes that planets were formed out of a protoplanetary disk.
+ Is it (he mass. densitv. angular momentum or the viscosity of the disk," Is it the mass, density, angular momentum or the viscosity of the disk"
+core and the likely infalling structure. (,core and the likely infalling structure. (
+4) we detect 2 globular cluster candidates which may be part of the outer structure of NGC 1399. or may be intracluster svstems (lormerly part of this. or another galaxy).,"4) we detect 2 globular cluster candidates which may be part of the outer structure of NGC 1399, or may be intracluster systems (formerly part of this, or another galaxy)."
+ Their X-ray luminosity suggests either a population of low-mass X-ray binaries or possibly an intermecliate mass black hole., Their X-ray luminosity suggests either a population of low-mass X-ray binaries or possibly an intermediate mass black hole.
+ The morphology of the Fornax ICM emission bears some resemblance to the phenomena of cold-lronts seen in other. massive. clusters on scales of some 0.5 Mpe (e.g. (2001))).," The morphology of the Fornax ICM emission bears some resemblance to the phenomena of cold-fronts seen in other, massive, clusters on scales of some 0.5 Mpc (e.g. \citet{vik01}) )."
+ However. in these situations the clensity of the gas environment is significantly higher than that seen in Fornax. and much more easily attributable to cool. dense. substructure passing through a warmer. dense ICM.," However, in these situations the density of the gas environment is significantly higher than that seen in Fornax, and much more easily attributable to cool, dense, substructure passing through a warmer, dense ICM."
+ Furthermore. the proto-tvpical cold fronts of Abell 2142. (Markevitehetal.2000) and Abell 3667. (Vikhlinin.vitch.&Murray2001) are not physically close to the central ¢D galaxy. of those clusters. whereas in Fornax NGC 1399 appears to be close to the “head” of the cometary (wpe enussion pattern.," Furthermore, the proto-typical cold fronts of Abell 2142 \citep{mar00} and Abell 3667 \citep{vik01}
+ are not physically close to the central cD galaxy of those clusters, whereas in Fornax NGC 1399 appears to be close to the “head” of the cometary type emission pattern."
+ The striking temperature structure of Fornax also shows evidence for a much more extended cool component than is perhaps present in these richer svstenis., The striking temperature structure of Fornax also shows evidence for a much more extended cool component than is perhaps present in these richer systems.
+ There is in addition an apparent offset between the location of NGC 1399 and the central core of ICAL emission. where NGC! 1399 is shifted some 2 aremin to the North-East relative to the apparent geometric center of the core plateau.," There is in addition an apparent offset between the location of NGC 1399 and the central core of ICM emission, where NGC 1399 is shifted some 2 arcmin to the North-East relative to the apparent geometric center of the core plateau."
+ More detailed investigation of the eas density and temperature distribution is required in (his region. but it seems plausible that there is relative motion between NGC 1399 and this region of emission.," More detailed investigation of the gas density and temperature distribution is required in this region, but it seems plausible that there is relative motion between NGC 1399 and this region of emission."
+ As discussed in 844.1 it appears likely that the X-rav morphology of Fornax as seen in the CFS may be attributed to the ongoing coalescence of structure., As discussed in 4.1 it appears likely that the X-ray morphology of Fornax as seen in the CFS may be attributed to the ongoing coalescence of structure.
+" In particular. the infall of the group identifiel by Drinkwater.Gregg.&Colless(2001) suggests that the Fornax core may be experiencing an intergalactic ""wind due to its relative motion wilh respect to structure along this infall axis."," In particular, the infall of the group identified by \citet{dri01} suggests that the Fornax core may be experiencing an intergalactic “wind” due to its relative motion with respect to structure along this infall axis."
+ Unlike the case of strong cold fronts in the denser environment of massive clusters. (his may represent a gentler phenomenon. associated directly with the intergalactic medium in the surrounding large scale structure.," Unlike the case of strong cold fronts in the denser environment of massive clusters, this may represent a gentler phenomenon, associated directly with the intergalactic medium in the surrounding large scale structure."
+ Finally. as part of the CES project. processed maps and source catalogs will be made available and continously updated via (he Data Collections of the Department of Astrophysics αἱ the American Museum of Natural History.," Finally, as part of the CFS project, processed maps and source catalogs will be made available and continously updated via the Data Collections of the Department of Astrophysics at the American Museum of Natural History."
+ We thank D. Ilelfand and F. Paerels for useful discussions. E. Gotthelf for invaluable help in constructing the image maps. D. Neill for providing deep optical images. and M. Markevitch of the CLA/CXC. lor his expert assistance in (he observational preparation.," We thank D. Helfand and F. Paerels for useful discussions, E. Gotthelf for invaluable help in constructing the image maps, D. Neill for providing deep optical images, and M. Markevitch of the CfA/CXC for his expert assistance in the observational preparation."
+ CLAS. acknowledges the support of. grant SAO. GO03-4158A and. the Columbia, C.A.S. acknowledges the support of grant SAO G03-4158A and the Columbia
+"The second step is realized by introducing a population of thermal particles either far upstream, or at a location x, (defined below), and propagating them in time steps small compared to the collision time, until they escape.","The second step is realized by introducing a population of thermal particles either far upstream, or at a location $x_\mathrm{A}$ (defined below), and propagating them in time steps small compared to the collision time, until they escape."
+" A particle is considered to have escaped if a) it is found many diffusion lengths downstream, or b) it crosses the upstream free escape boundary."," A particle is considered to have escaped if a) it is found many diffusion lengths downstream, or b) it crosses the upstream free escape boundary."
+" As the particles are propagated, their momentum are randomly perturbed as described in the next paragraph."," As the particles are propagated, their momentum are randomly perturbed as described in the next paragraph."
+" When particles cross selected coordinates z;, their momenta and statistical weights are summed to calculate the particle distribution function in a momentum bin: Here, the summation takes place over the events of a particle crossing the coordinate z;: Δι is a bin in momentum space, Ay; is a bin in angles (4=p,/p) and o; is the properly normalized statistical weight of the particle."," When particles cross selected coordinates $x_j$, their momenta and statistical weights are summed to calculate the particle distribution function in a momentum bin: Here, the summation takes place over the events of a particle crossing the coordinate $x_j$: $\Delta p_k$ is a bin in momentum space, $\Delta \mu_l$ is a bin in angles $\mu = p_x / p$ ) and $\sigma_i$ is the properly normalized statistical weight of the particle."
+" In a similar fashion, the code calculates the moments of the distribution function, including the momentum and energy fluxes defined in Eq."," In a similar fashion, the code calculates the moments of the distribution function, including the momentum and energy fluxes defined in Eq."
+ §| and Bl., \ref{pflux} and \ref{eflux}.
+" When particles are propagated, they move in straight lines for a time At equal to a fraction of the collision time t,."," When particles are propagated, they move in straight lines for a time $\Delta t$ equal to a fraction of the collision time $t_c$."
+" After that, the momentum in the local plasma frame is rotated by a random angle chosen so that the averaged particle motion represents diffusion with the appropriate diffusion coefficient."," After that, the momentum in the local plasma frame is rotated by a random angle chosen so that the averaged particle motion represents diffusion with the appropriate diffusion coefficient."
+" The local plasma frame for CR ""n is assumed to be moving at a speed u(x)—vA(x) with respect to the subshock, where va(x)=Bo//Amp(x) is the local Alfvénn speed."," The local plasma frame for CR particles is assumed to be moving at a speed $u(x)-v_A(x)$ with respect to the subshock, where $v_A(x)=B_0/\sqrt{4\pi \rho(x)}$ is the local Alfvénn speed."
+" For thermal particles, the frame in which momentum rotation is performed is moving at a speed u(x) with respect to the subshock."," For thermal particles, the frame in which momentum rotation is performed is moving at a speed $u(x)$ with respect to the subshock."
+ The details of this procedure are described in ∙∙, The details of this procedure are described in \cite{andrey}.
+" In regions where the particle distribution is isotropic (e.g., far downstream), the code may set At=t., which simulates a random walk process and corresponds to the diffusion approximation."," In regions where the particle distribution is isotropic (e.g., far downstream), the code may set $\Delta t = t_c$, which simulates a random walk process and corresponds to the diffusion approximation."
+ A gradient of the local plasma speed in the above procedure leads to the first order Fermi acceleration of particles., A gradient of the local plasma speed in the above procedure leads to the first order Fermi acceleration of particles.
+ This applies to the thermal particles as well as to the superthermal ones., This applies to the thermal particles as well as to the superthermal ones.
+ Injection of thermal particles into the acceleration process occurs in this model only due to their Fermi-I acceleration at the subshock., Injection of thermal particles into the acceleration process occurs in this model only due to their Fermi-I acceleration at the subshock.
+" Elastic scatterings of thermal particles in the shock precursor will, in the presence of a small flow speed gradient, lead to adiabatic heating: Pjcp? (this heating is, in a sense, due to the same Fermi-I acceleration process, but on a smooth variation of the flow speed instead of a discontinuity)."," Elastic scatterings of thermal particles in the shock precursor will, in the presence of a small flow speed gradient, lead to adiabatic heating: $\Pth \propto \rho^{\gamma}$ (this heating is, in a sense, due to the same Fermi-I acceleration process, but on a smooth variation of the flow speed instead of a discontinuity)."
+ If additional heating operates in the precursor due to some wave, If additional heating operates in the precursor due to some wave
+Going through the lists of objects as published. taking only Chose larger than one minute along at least one axis ancl appearing on both the blue aud red films. the situation again appears rather distressing.,"Going through the lists of objects as published, taking only those larger than one minute along at least one axis and appearing on both the blue and red films, the situation again appears rather distressing."
+ There is an overlap of 46 objects: set against our candidate list of 194. this gives the Local Volume group a chance of less than one-quarter of recording an object meeting our criteria.," There is an overlap of 46 objects; set against our candidate list of 194, this gives the Local Volume group a chance of less than one-quarter of recording an object meeting our criteria."
+ Even if we confine ourselves to objects identified as extragalactic the Local Volume probability of detection. only reaches about., Even if we confine ourselves to objects identified as extragalactic the Local Volume probability of detection only reaches about.
+36%... There are similarly something like 200 objects in their list which appear from the tables to match our criteria. but do not appear in ours. giving us a chance of less (han one in five.," There are similarly something like 200 objects in their list which appear from the tables to match our criteria, but do not appear in ours, giving us a chance of less than one in five."
+ It seems barely likely that even a cursory visual survey would miss of the objects it was looking for., It seems hardly likely that even a cursory visual survey would miss of the objects it was looking for.
+ Again we turned our attention to the non-overlap region., Again we turned our attention to the non-overlap region.
+ Visually examining the objects in the Local Volume list which nominally match our criteria. almost all are too small and/or too bright to look like Local Group dwarls to us.," Visually examining the objects in the Local Volume list which nominally match our criteria, almost all are too small and/or too bright to look like Local Group dwarfs to us."
+ When laced with an object close to a minute of arc in size on the survey field. we would tend (ο sav it is smaller (han the Local Volume group would report it: ancl there are enough objects near the borderline (to make a big difference in the numbers.," When faced with an object close to a minute of arc in size on the survey field, we would tend to say it is smaller than the Local Volume group would report it; and there are enough objects near the borderline to make a big difference in the numbers."
+" The fact that all of these are very diffuse objects. whose size is difficult to estimate αναλ, only complicates matters."," The fact that all of these are very diffuse objects, whose size is difficult to estimate anyway, only complicates matters."
+ If. we count up those objects which we did judge to meet our criteria. and include some borderline cases. we find 14 which we missed.," If we count up those objects which we did judge to meet our criteria, and include some borderline cases, we find 14 which we missed."
+ This gives our group an estimated reliability (conservatively) of about56... (, This gives our group an estimated reliability (conservatively) of about. (
+A similarly corrected nummer for the Local Volume survey is not available without asking (hem to review our candidate objects. clearly an unreasonable request.),"A similarly corrected number for the Local Volume survey is not available without asking them to review our candidate objects, clearly an unreasonable request.)"
+ We wish to make clear what is happening in this process: the human eve and judgement. when applving a set of morphological criteria corresponding to known Local Group dwarl ealaxies to images. generates a fairly reliable or maybe better) list of those that fit.," We wish to make clear what is happening in this process: the human eye and judgement, when applying a set of morphological criteria corresponding to known Local Group dwarf galaxies to images, generates a fairly reliable or maybe better) list of those that fit."
+ It will also (probably to avoid missing anything important) throw up a laree number of doubtful cases., It will also (probably to avoid missing anything important) throw up a large number of doubtful cases.
+ These can be rejected. fairly easily by a second. independent examination.," These can be rejected fairly easily by a second, independent examination."
+ We may make an analogy with the classification of galaxies by eve. based on morphology: (he majority will be assigned (he same. or very similar. (wpes by different workers: but (here is a population whose assignment will vary. widely between survevs.," We may make an analogy with the classification of galaxies by eye, based on morphology: the majority will be assigned the same, or very similar, types by different workers; but there is a population whose assigment will vary widely between surveys."
+ seeking a wav (o check our completeness without dealing with the diffuse edges of morphology space. we turn to asample which is very definitely made up of objects morphologically like Local Group dwarl galaxies: known Local Group dwarls.," Seeking a way to check our completeness without dealing with the diffuse edges of morphology space, we turn to a sample which is very definitely made up of objects morphologically like Local Group dwarf galaxies: known Local Group dwarfs."
+ We compared our Local Group detections in Tables 1. through 4. with known ancl suspected Local Group galaxies (defining ihem observationallv. leaving aside such questions as whether the Sextans A/D/NGC 3109," We compared our Local Group detections in Tables \ref{northcand} through \ref{southnon} with known and suspected Local Group galaxies (defining them observationally, leaving aside such questions as whether the Sextans A/B/NGC 3109"
+"The ""minimal model” is in excellent agreement wilh the observational data points from EGRET (Sreekumaretal.1993).. both in amplitude and in spectral shape. for energies up to 15 GeV. For higher energies. absorption effects due to pair production. which have not been treated here. becomeimportant!.","The “minimal model” is in excellent agreement with the observational data points from EGRET \citep{sreek_obs}, both in amplitude and in spectral shape, for energies up to 15 GeV. For higher energies, absorption effects due to pair production, which have not been treated here, become."
+. For the first 10 points with energies <15 GeV. the minimal model has a 4? per degree of freedom v of 42=0.78. indicating an excellent fit.," For the first 10 points with energies $\la 15$ GeV, the minimal model has a $\chi^2$ per degree of freedom $\nu$ of $\chi^2_\nu = 0.78$, indicating an excellent fit."
+ For comparison. the blazar contribution alone has 47=4.63.," For comparison, the blazar contribution alone has $\chi^2_\nu =4.68$."
+ Had we made use of the free parameter in (he Stecker-Salanion blazar model which allows for the variation of the total amplitude of the blazar contribution. the blazar-only model has a minimum 7=0.95. «till somewhat larger (han (hat of the summed normal galaxy - blazar spectrum.," Had we made use of the free parameter in the Stecker-Salamon blazar model which allows for the variation of the total amplitude of the blazar contribution, the blazar-only model has a minimum $\chi^2_\nu = 0.95$, still somewhat larger than that of the summed normal galaxy - blazar spectrum."
+ Moreover. such an increase of the blazar contribution would be ignoring the guaranteed contribution from normal galaxies which. if added to the boosted blazar signal. would overpredict the EGRB.," Moreover, such an increase of the blazar contribution would be ignoring the guaranteed contribution from normal galaxies which, if added to the boosted blazar signal, would overpredict the EGRB."
+" Therefore. we conclude that no modification is needed in the Stecker Salamon (1996) calculation for energies S15 GeV. Uncertainties in our normal galaxy spectrum calculation are introduced due to uncertainties in the determination of f,(2). Masw fora and gv."," Therefore, we conclude that no modification is needed in the Stecker Salamon (1996) calculation for energies $\la 15$ GeV. Uncertainties in our normal galaxy spectrum calculation are introduced due to uncertainties in the determination of $\dot{\rho}_\star(z)$ , $M_{\rm gas, MW}$, $\mu_{\rm 0,MW}$ and $q_{\gamma,_{\rm MW}} $."
+ ΟΙ ο input parameters. egy and dyyy enter our caleulation as multiplicative factors and therefore uncertainties in their values do not affect the shape of the spectrum. but only the overall normalization (Gntroducing an overall uncertaintv of a [actor ~ 4).," Of our input parameters, $\psi_{\rm MW}$ and $q_{\gamma,_{\rm MW}} $ enter our calculation as multiplicative factors and therefore uncertainties in their values do not affect the shape of the spectrum, but only the overall normalization (introducing an overall uncertainty of a factor $\sim$ 4)."
+" Our results are relatively insensitive to the value of M,Bus.any since a change m its value affects the calculation through. L.ayy and αν in opposite directions."," Our results are relatively insensitive to the value of $M_{\rm gas, MW}$ since a change in its value affects the calculation through $L_{\gamma, {\rm MW}}$ and $\mu_{0, {\rm MW}}$ in opposite directions."
+ In addition. our ealeulation shows that most of the background intensity in the normal galaxy component originates from 2«1.," In addition, our calculation shows that most of the background intensity in the normal galaxy component originates from $z<1$."
+ Therefore. our results are not affected significantly by the CSER evolution al z>1where the CSETR. uncertainties can reach an order of magnitude.," Therefore, our results are not affected significantly by the CSFR evolution at $z>1$where the CSFR uncertainties can reach an order of magnitude."
+ This fact is demonstrated in the lower panel of Fig. 1..," This fact is demonstrated in the lower panel of Fig. \ref{fig1},"
+ where we have plotted the normal galaxy spectrum for both the dust-corrected CSETR. and the uncorrected CSER. together with the spectrum derived for a clust-corrected CSETR. in (hie extreme case where star lormation is assumed to have taken place at z>1.," where we have plotted the normal galaxy spectrum for both the dust-corrected CSFR and the uncorrected CSFR, together with the spectrum derived for a dust-corrected CSFR in the extreme case where star formation is assumed to have taken place at $z>1$."
+ The difference from the full integration up lo z=5 is less (han a factor of 2., The difference from the full integration up to $z=5$ is less than a factor of 2.
+ We note that in the latter case. the peak of the spectrum is displaced towards higher energies.," We note that in the latter case, the peak of the spectrum is displaced towards higher energies."
+ On (he other hand. if the CSETR. was much higherat high redshifts. as suggested recently by Lanzettaefaf (2002).. this would," On the other hand, if the CSFR was much higherat high redshifts, as suggested recently by \citet{lanzetta}, , this would"
+of My€n I8. the Etched Hourglass Nebula. 2)). it is believed hat the CSPN would have to form a common envelope (Cl) with its binary companion (?)..,"of MyCn 18, the Etched Hourglass Nebula, \citealp{bryce97}) ), it is believed that the CSPN would have to form a common envelope (CE) with its binary companion \citep{bond90}."
+ For a CI to form. one component of the binary must. accrete mass [rom its toche Iobe-filling partner more rapidly than it can thermally adjust to the additional material. thus also filling its Itoche obe.," For a CE to form, one component of the binary must accrete mass from its Roche lobe-filling partner more rapidly than it can thermally adjust to the additional material, thus also filling its Roche lobe."
+ After this point. any further mass lost by the donor will σο on to form a CI surrounding both stars. and it is his CLE which &oes on to form the high equatorial density required by the CISW. model (2)..," After this point, any further mass lost by the donor will go on to form a CE surrounding both stars, and it is this CE which goes on to form the high equatorial density required by the GISW model \citep{nordhaus06}."
+ This mechanism is seen as the most likely method by which very close binaries (for example. cataclysmic variables) are formed. (2)... because as the common envelope is ejected. by transfer of angular momentum. the binary spirals in. dramatically. shortening the period of the system.," This mechanism is seen as the most likely method by which very close binaries (for example, cataclysmic variables) are formed \citep{grauer83}, because as the common envelope is ejected by transfer of angular momentum, the binary spirals in, dramatically shortening the period of the system."
+ Abell 41. (PN 009.6]10.5... 02.037. 2000). discovered. by. 2... was classified bv 2? as elliptical under the classification scheme of ?..," Abell 41 (PN G009.6+10.5, , J2000), discovered by \cite{abell66}, was classified by \citet{bond90} as elliptical under the classification scheme of \citet{balick87}."
+ Llowever. deeper | iimageryreccalsthalthenchularmorphologyerhibitsan H' shape Fibuller {ΕΝide AORAMAW Meiid forafodacim Uedental edp (7).," However, deeper $+$ imagery reveals “that the nebular morphology exhibits an `H' shape with the addition of fainter material forming a continuous loop” \citep{pollacco97}."
+". hotometric analvsis of the CSPN. MT Ser. revealed it to be a close binary. showing minima at regular intervals of 2""43"" (?)."," Photometric analysis of the CSPN, MT Ser, revealed it to be a close binary, showing minima at regular intervals of $2^h43^m$ \citep{grauer83}."
+ ? confirmed the binary nature of MT Ser but were unable to accurately determine its orbital parameters because they found. two different models which fit the observed data. (, \citet{bruch01} confirmed the binary nature of MT Ser but were unable to accurately determine its orbital parameters because they found two different models which fit the observed data. (
+"a) The binary consists of a hot sub-clwarl ancl a less evolved secondary. in which case the period is 243'"" and the variations are due to a rellection cllect (inclination. /=42.52+ 1.737) t... (","a) The binary consists of a hot sub-dwarf and a less evolved secondary, in which case the period is $2^h43^m$ and the variations are due to a reflection effect (inclination, $i = 42.52\degr \pm 1.73 \degr$ ) . ("
+"b) The binary consists of two evolved. hot. sub-dwarls with a period. of 5726"" where the variability results from partial eclipses anc cllipsoidal variations (/=65.77dE 0.973.","b) The binary consists of two evolved, hot sub-dwarfs with a period of $5^h26^m$ where the variability results from partial eclipses and ellipsoidal variations $i = 65.7\degr \pm 0.9\degr$ )."
+ They. determine the optimum parameters for cach model. but conclude that only racial velocity observations would be able to distinguish between the two.," They determined the optimum parameters for each model, but concluded that only radial velocity observations would be able to distinguish between the two."
+ Subsequent observation. anc modelling by 2? confirmed. the presence of two sub-chwarl components. but gave no independent confirmation of the orbital inclination.," Subsequent observation and modelling by \citet{shimanskii08} confirmed the presence of two sub-dwarf components, but gave no independent confirmation of the orbital inclination."
+ ?— presented. photometric ancl raclia velocity. observations alone with modelling of AIT Ser. independently. determining an orbital inclination of 72 15. which is consistent with the second. model of 2. (?.. jo65.77 £0.97).," \citet{ogloza02} presented photometric and radial velocity observations along with modelling of MT Ser, independently determining an orbital inclination of $72\degr \pm 15\degr$ , which is consistent with the second model of \citeauthor{bruch01} \citeyear{bruch01}, $i = 65.7\degr \pm 0.9\degr$ )."
+ Hlowever. the values determined for the rest of the system parameters dilfer vastly. indicating that any agreement should be treated with caution.," However, the values determined for the rest of the system parameters differ vastly, indicating that any agreement should be treated with caution."
+ Additionally. the stellar temperatures derived by 2? are inconsistent. with the observational detection. of two hot. sub-cwarl binary components (?)..," Additionally, the stellar temperatures derived by \citet{ogloza02} are inconsistent with the observational detection of two hot sub-dwarf binary components \citep{shimanskii08}."
+ Of the two models of 7. and the mocel of ?.. only the second model of ?. (2... ;=65.77£ 0.97) is consistent with photometric observations and the detection of two hot sub-dwarl central stars. indicating that this is the most reliable modelling of the binary CSPN system.," Of the two models of \citet{bruch01} and the model of \citet{ogloza02}, only the second model of \citeauthor{bruch01} \citeyear{bruch01}, $i = 65.7\degr \pm 0.9\degr$ ) is consistent with photometric observations and the detection of two hot sub-dwarf central stars, indicating that this is the most reliable modelling of the binary CSPN system."
+ In this paper we present longslit spectroscopy of A 41. from which. combined with narrowband images. we clerive a spatio-kinematical model of the nebula. with the aim of uncerstanding the relationship between the nebula and MT SerSer.," In this paper we present longslit spectroscopy of A 41, from which, combined with narrowband images, we derive a spatio-kinematical model of the nebula, with the aim of understanding the relationship between the nebula and MT Ser."
+ Narrowbancl images of A 41. were acquired: using ACΛΑ combined with the 4.2-m William Lersehel Telescope on 2009 August 4 aancd A) and 2009 August 20 X))., Narrowband images of A 41 were acquired using ACAM combined with the 4.2-m William Herschel Telescope on 2009 August 4 and ) and 2009 August 29 ).
+ The sccing for both sets of observations did not exceed0., The seeing for both sets of observations did not exceed.
+97... ACAM was emploved. in standard imaging mode without binning resulting in a pixel scale of and using the NIIJ6584/21.. Taurus 5009/15 anc SIIJ6727/48 filters (ING filters #6885. ΠΙΟΣ ancl #6886).," ACAM was employed in standard imaging mode without binning resulting in a pixel scale of, and using the [NII]6584/21, Taurus 5009/15 and [SII]6727/48 filters (ING filters 85, 108 and 86)."
+" ""Three 15 minute exposures were taken in each filter. the data were bias-corrected. Hat-fielded: and cleaned. of cosmic ravs using software."," Three 15 minute exposures were taken in each filter, the data were bias-corrected, flat-fielded and cleaned of cosmic rays using software."
+ software was also used to remove the background: lunar contamination. arising due to the close proximity of A 41 to the Moon. from the images.," software was also used to remove the background lunar contamination, arising due to the close proximity of A 41 to the Moon, from the images."
+ The resulting images were then co-adedecl ancl are shown in Figure 1.., The resulting images were then co-added and are shown in Figure \ref{fig:images}.
+ Spatially resolved. longslit emission. line. spectra. of A 41 were obtained with the second. Manchester. Echelle Spectrometer combined with the 2.1-m San Pedro Márrtir Telescope. (MISS-SPM.. 2)).," Spatially resolved, longslit emission line spectra of A 41 were obtained with the second Manchester Echelle Spectrometer combined with the 2.1-m San Pedro Márrtir Telescope (MES-SPM, \citealt{meaburn03}) )."
+. MIES-SPM. was used. in its primary spectral mode with a narrow-band filter to isolate the aand Ν Η] 6548 and 6584 comission lines of the STth echelle order., MES-SPM was used in its primary spectral mode with a narrow-band filter to isolate the and [N ] 6548 and 6584 emission lines of the 87th echelle order.
+" Observations took place on two separate runs in 2004 June and 2007 June. both with the same instrument anc set-up. using a SITe3 CCD with 1024 1024 24 pm square pixels (=0.31"". +)."," Observations took place on two separate runs in 2004 June and 2007 June, both with the same instrument and set-up, using a SITe3 CCD with 1024 $\times$ 1024 24 $\mu$ m square pixels $\equiv 0.31\arcsec$ $^{-1}$ )."
+ ALL integrations were of 1500 seconds., All integrations were of 1800 seconds.
+" lnning of 2 2 was adopted. lor all the spectral observations. resulting in 512 pixels in the spatial direction (=0.62"" pixel 4) and 512 pixels in the spectral direction (=479kms! 4)."," Binning of 2 $\times$ 2 was adopted for all the spectral observations, resulting in 512 pixels in the spatial direction $\equiv 0.62 \arcsec$ $^{-1}$ ) and 512 pixels in the spectral direction $\equiv 4.79 \kms$ $^{-1}$ )."
+ The slit used. was 30-muin. long (— 5') and 150 pm wide (=2.07 and 15kms ly, The slit used was 30-mm long $\equiv 5 \arcmin$ ) and 150 $\mu$m wide $\equiv 2.0 \arcsec$ and $15\kms$ ).
+ Data reduction was performed using software., Data reduction was performed using software.
+ The spectra were bias-corrected and cleaned of cosmic ravs., The spectra were bias-corrected and cleaned of cosmic rays.
+The spectra were then wavelength calibrated against a Thr emission-lamp.,The spectra were then wavelength calibrated against a ThAr emission-lamp.
+ Finally. the data were rescaled to a linear," Finally, the data were rescaled to a linear"
+he ionisation of the ISM (characterised using Nel] and Sili]) than 12Ποσο].,the ionisation of the ISM (characterised using ] and ]) than 12+log(O/H).
+ The (PALL S (m)/160. yam ratio appears to. be. closely correlated with the 160 jam surface brightness measured on 45 aresee scales in most galaxies. even in nearby galaxies where this angular scale corresponds to. <1 kpe.," The (PAH 8 $\mu$ m)/160 $\mu$ m ratio appears to be closely correlated with the 160 $\mu$ m surface brightness measured on 45 arcsec scales in most galaxies, even in nearby galaxies where this angular scale corresponds to $\ltsim 1$ kpc."
+ Moreover. the (PAIL S jum)/160. pm. ratio sometimes traces high surface brightness large scale structures in the disces of these galaxies. such as the spiral arms in NGC 3031 or NGC 69046.," Moreover, the (PAH 8 $\mu$ m)/160 $\mu$ m ratio sometimes traces high surface brightness large scale structures in the discs of these galaxies, such as the spiral arms in NGC 3031 or NGC 6946."
+ This indicates that the variations in the ratio may no be primarily dependent. on radius as inferred. by Bencloeal.(2006) butinstead may be primarily dependent. on the 160 jana surface brightness., This indicates that the variations in the ratio may not be primarily dependent on radius as inferred by \citet{betal06} butinstead may be primarily dependent on the 160 $\mu$ m surface brightness.
+ However. the large. scale structures within these galaxies are only mareinally resolve in the 160 gm data.," However, the large scale structures within these galaxies are only marginally resolved in the 160 $\mu$ m data."
+ Higher. resolution observations a wavelengths longer than 100 yam are needed to confirm tha this interpretation is valid., Higher resolution observations at wavelengths longer than 100 $\mu$ m are needed to confirm that this interpretation is valid.
+ Nonetheless. i£ the above interpretation is) correct. then it also suggests that the variations in. the (PAL SN pm)/160 yam ratio may be more dependent on 160. fan surface brightness than metallicity within the regions studied in these galaxies.," Nonetheless, if the above interpretation is correct, then it also suggests that the variations in the (PAH 8 $\mu$ m)/160 $\mu$ m ratio may be more dependent on 160 $\mu$ m surface brightness than metallicity within the regions studied in these galaxies."
+ Since variations in metallicity have been linked. to decreased PALL emission. relative to longer-wavelength dust. emission in the integrated: spectra of galaxies (e.g.Engelbrachtetal.2005:Dale 2008).. it was not unreasonable to expect that the observed variations in the (PALL 8S pm)/160 jim ratio within these galaxies might be linked to metallicity variations.," Since variations in metallicity have been linked to decreased PAH emission relative to longer-wavelength dust emission in the integrated spectra of galaxies \citep[e.g.][]{eetal05, detal05, ddbetal07, eetal08}, , it was not unreasonable to expect that the observed variations in the (PAH 8 $\mu$ m)/160 $\mu$ m ratio within these galaxies might be linked to metallicity variations."
+ However. the 12|log(O/1) values measured in these galaxies by J. Moustalkas ct al. (," However, the 12+log(O/H) values measured in these galaxies by J. Moustakas et al. ("
+2008. in. preparation) generally. do not drop below 8- S.I]. which is where Draineetal.(2007) and Engelbracht showed that metallicity stronely alfects PALL S yan emission.,"2008, in preparation) generally do not drop below $\sim8$ -8.1, which is where \citet{ddbetal07} and \citet{eetal08} showed that metallicity strongly affects PAH 8 $\mu$ m emission."
+ Moreover. metallicity is expected to decrease monotonically with radius. while the (PALL S saa) /160 jun ratio and the 160 pm surface brightness do not. and the metallicity should not. peak within substructures such as spiral arms. whereas the (PALL S sam) /160 sem ratio ancl the 160 jam surface brightness both peak within such substructures.," Moreover, metallicity is expected to decrease monotonically with radius, while the (PAH 8 $\mu$ m)/160 $\mu$ m ratio and the 160 $\mu$ m surface brightness do not, and the metallicity should not peak within substructures such as spiral arms, whereas the (PAH 8 $\mu$ m)/160 $\mu$ m ratio and the 160 $\mu$ m surface brightness both peak within such substructures."
+ As an additional test. we compared the eradients in the (PALL S μαι) /160 jim ratio versus radius with the metallicity gradients [rom J. Moustakas et al. (," As an additional test, we compared the gradients in the (PAH 8 $\mu$ m)/160 $\mu$ m ratio versus radius with the metallicity gradients from J. Moustakas et al. ("
+2008. in preparation) calculated with the Pilvugin&Thuan(2005) calibration.,"2008, in preparation) calculated with the \citet{pt05} calibration."
+ For this comparison. we excluded NGC 4725 because the gradients in the (PALL δ μαι) 100 jm. ratio changes significantly between the nucleus and the outer disc. and we excluded NGC 3988 and NGC 4579 because abundance gradients are not given by J. Aloustakas et al.," For this comparison, we excluded NGC 4725 because the gradients in the (PAH 8 $\mu$ m)/160 $\mu$ m ratio changes significantly between the nucleus and the outer disc, and we excluded NGC 3938 and NGC 4579 because abundance gradients are not given by J. Moustakas et al."
+ The gradients for the other galaxies are plotted in Figure TL., The gradients for the other galaxies are plotted in Figure \ref{f_gradcomp_pah160_12logoh}.
+ I£ the (PALL S fam) /160 pam ratio was alfected by metallicity in the regions studied in these galaxies. then these data would be positively correlated.," If the (PAH 8 $\mu$ m)/160 $\mu$ m ratio was affected by metallicity in the regions studied in these galaxies, then these data would be positively correlated."
+ Since the data in Figure 11. do not exhibit such a correlation. the two eracicnts may be unrelated.," Since the data in Figure \ref{f_gradcomp_pah160_12logoh}
+ do not exhibit such a correlation, the two gradients may be unrelated."
+ We therefore conclude that. in the regions of the galaxies studied bere. metallicity variations are not as important as 160 am surface brightness variations in determining the (PALL &S μα) 100 p/m ratio. although metallicity may. be a factor outside the optical discs.," We therefore conclude that, in the regions of the galaxies studied here, metallicity variations are not as important as 160 $\mu$ m surface brightness variations in determining the (PAH 8 $\mu$ m)/160 $\mu$ m ratio, although metallicity may be a factor outside the optical discs."
+ Again. this is consistent. with the conclusions reached by Gordonetal.(2008)... who found that PALL equivalent widths in ALLOL were more dependent on the ionisation of the ESAL than abuncdances.," Again, this is consistent with the conclusions reached by \citet{getal08}, who found that PAH equivalent widths in M101 were more dependent on the ionisation of the ISM than abundances."
+ While the (PALL S μαι) 100 jm. ratio traces. large scale structure. we have demonstrated. that the ratio. is not enhanced within individual star-forming regions. aud we explained earlier. in this section that PALL S&S jun emission must be inhibited in regions with strong radiation iclds.," While the (PAH 8 $\mu$ m)/160 $\mu$ m ratio traces large scale structure, we have demonstrated that the ratio is not enhanced within individual star-forming regions, and we explained earlier in this section that PAH 8 $\mu$ m emission must be inhibited in regions with strong radiation fields."
+ Based on these conclusions anc the strong relation οοσα the (PALL S yam)/160 pam ratio and. 160 sim surface rightness. we infer that the PAILIs in these galaxies are eencrally associated with the cold. (~20 IX) dust. that dominates the 160 yam emission. at least on scales of ~2 kpe.," Based on these conclusions and the strong relation between the (PAH 8 $\mu$ m)/160 $\mu$ m ratio and 160 $\mu$ m surface brightness, we infer that the PAHs in these galaxies are generally associated with the cold $\sim20$ K) dust that dominates the 160 $\mu$ m emission, at least on scales of $\sim2$ kpc."
+ Because most of this cold. dust may be expected. το be ound in the dilluse ISAL the PALIs may also be found »wimarilv in the cdilfuse ISAL as well. although some of he cold dust and. PALS may also be found within clouds associated with star-forming regions.," Because most of this cold dust may be expected to be found in the diffuse ISM, the PAHs may also be found primarily in the diffuse ISM as well, although some of the cold dust and PAHs may also be found within clouds associated with star-forming regions."
+ Moreover. since the (PALL S sam)/160 pim ratio increases as the 160 jum surface xiehtness increases. the (PALL S j//m)/160 jim ratio may be an indicator of variations in the intensity of the radiation icld heating the dilfuse ISM.," Moreover, since the (PAH 8 $\mu$ m)/160 $\mu$ m ratio increases as the 160 $\mu$ m surface brightness increases, the (PAH 8 $\mu$ m)/160 $\mu$ m ratio may be an indicator of variations in the intensity of the radiation field heating the diffuse ISM."
+ This is further supported. by he tight correlation between the (PATI S j/ma)/160 jun ratio and the 24 pam/160 p/m ratio found for many regions with weak 24 jm emission in Figure 7.. which are presumably regions that primarily samplecust emission from the dilTuse ISM.," This is further supported by the tight correlation between the (PAH 8 $\mu$ m)/160 $\mu$ m ratio and the 24 $\mu$ m/160 $\mu$ m ratio found for many regions with weak 24 $\mu$ m emission in Figure \ref{f_pah160vs24160}, , which are presumably regions that primarily sampledust emission from the diffuse ISM."
+ Nonetheless. this interpretation is only valid if the PALL mass fraction does not vary appreciably between infrared- ancl infrared-bright regions in the cdilfuse. ISAL and far-infrared observations with higher angular resolution will be needed to determine whether this association is still applicable on smaller spatial scales.," Nonetheless, this interpretation is only valid if the PAH mass fraction does not vary appreciably between infrared-faint and infrared-bright regions in the diffuse ISM, and far-infrared observations with higher angular resolution will be needed to determine whether this association is still applicable on smaller spatial scales."
+We lave presented observations and imodcling of polarized 6 cni radio contimmuun enüssou toward 0.5 square deerces of the GC region.,We have presented observations and modeling of polarized 6 cm radio continuum emission toward 0.5 square degrees of the GC region.
+ The radio continu survey detects polarized emission thoughout the region iu the form of diffuse polarized enission. Colmpact sources. and flamentary sources.," The radio continuum survey detects polarized emission thoughout the region in the form of diffuse polarized emission, compact sources, and filamentary sources."
+ The two bauds iu the continua observations allow us to measure RM to this polarize cnussion., The two bands in the continuum observations allow us to measure RM to this polarized emission.
+ We develop a statistical technique to mcasure the RAL comparing our results to more robust RA measurements slows that our technique is reliable., We develop a statistical technique to measure the RM; comparing our results to more robust RM measurements shows that our technique is reliable.
+ There is a striking large-scale pattern in RAL tow the diffuse polarized cinission., There is a striking large-scale pattern in RM toward the diffuse polarized emission.
+ Values in the easteru par of. the survey are ecuerally about |330κ rad 57. bu change to —SSO rrad PEELonn the western part of the survey.," Values in the eastern part of the survey are generally about +330 rad $^{-2}$, but change to $-880$ rad $^{-2}$ in the western part of the survey."
+ There is a sharp transition around /—0235 aa all latitudes in the survey., There is a sharp transition around $l=-0\ddeg35$ at all latitudes in the survey.
+ Modeliug of the propagation of the polarized signa shows that this pattern is induced within ~1 kpc of the GC region., Modeling of the propagation of the polarized signal shows that this pattern is induced within $\sim$ 1 kpc of the GC region.
+ The BM measure oward radio filames known to be iu the GC region are eencrallv consistent with that of the diffuse polarize Cluission., The RM measured toward radio filaments known to be in the GC region are generally consistent with that of the diffuse polarized emission.
+ This coedence is consistent with inodels or the flameuts as kycalized chhaucemenuts to a eloba naenetic field., This coincidence is consistent with models for the filaments as localized enhancements to a global magnetic field.
+ The modeling of tre GC inaenetized plasima slows hat the RM structure constrains the orientation of the GC iaenetic Seld., The modeling of the GC magnetized plasma shows that the RM structure constrains the orientation of the GC magnetic field.
+" This RAL pattern shows that the GC uagnetie field is orgaized ou size scales of roughly 150 xusecs,", This RM pattern shows that the GC magnetic field is organized on size scales of roughly 150 parsecs.
+ Combining tljese and. other RM measurenients iu the GC region. we streugthen earlier sugecstious for a checkerboard patter nin RM covering the ceutral 300 ursecs but only if fje structure is shifted roughly 50 ος west of the dyaiianical center of the Galaxy.," Combining these and other RM measurements in the GC region, we strengthen earlier suggestions for a checkerboard pattern in RM covering the central 300 parsecs, but only if the structure is shifted roughly 50 pc west of the dynamical center of the Galaxy."
+ We show hat the RM measuresL along different lines of sight and oward differcut tracers are consistent with this shift., We show that the RM measured along different lines of sight and toward different tracers are consistent with this shift.
+ The observed polarization aud RM in the GC is consistent with the GC having a poloidal magnetic field that is perturbed by the motion of gas iu the Calactic disk (Uchidaetal.1985:Novak2003).," The observed polarization and RM in the GC is consistent with the GC having a poloidal magnetic field that is perturbed by the motion of gas in the Galactic disk \citep{u85, n03}."
+. This model is being supported by a growing body of evidence (Chussetal.2003:Nishivama2010).," This model is being supported by a growing body of evidence \citep{c03,n10}."
+.. Under this model. our RM observations constrain the GC maguetic field to be directed from south to north.," Under this model, our RM observations constrain the GC magnetic field to be directed from south to north."
+ Our observations also suggest that a second-order perturbation. a small outflow from the GC. has shifted the magnetic sviunuetry axis of the GC about 50 pc west of the dynamical center of the Calaxy.," Our observations also suggest that a second-order perturbation, a small outflow from the GC, has shifted the magnetic symmetry axis of the GC about 50 pc west of the dynamical center of the Galaxy."
+ New observations can test this model in several wavs., New observations can test this model in several ways.
+ First. observing the diffuse polarized emissioni betwee- 6 and 20 c0 (5Γ aud 1.1 GIIz). where it becomes Faraday thick. would constrain models of its plivsical distribution.," First, observing the diffuse polarized emission between 6 and 20 cm (5 and 1.4 GHz), where it becomes Faraday thick, would constrain models of its physical distribution."
+ Expanded VLA observations with thousands of chamucls at these frequencies will track the Faraday rotation aud depolarization well enough to create a 3D reconstruction of the magnetic field topology iu the Galactic Center., Expanded VLA observations with thousands of channels at these frequencies will track the Faraday rotation and depolarization well enough to create a 3D reconstruction of the magnetic field topology in the Galactic Center.
+ Second. measure the RAL of other radio filaments would test the idea that they are prefereutiallv algued with the RAL of the extended poluized emission.," Second, measuring the RM of other radio filaments would test the idea that they are preferentially aligned with the RM of the extended polarized emission."
+ Third. the detection of diffuse polarized cuuission aud its RM bevoud the region studied here (particularly south of the plane) would confirm that it traces a general property of the GC reeion.," Third, the detection of diffuse polarized emission and its RM beyond the region studied here (particularly south of the plane) would confirm that it traces a general property of the GC region."
+could be put on to slits.,could be put on to slits.
+ For the field of 4427. we did observe all but three candidates using five masks.," For the field of $-$ 4427, we did observe all but three candidates using five masks."
+ In the following. we will refer to these 8 masks as mask1346A to C and mask2138A to E. The observing conditions were generally mediocre due to very strong wind coming from the North.," In the following, we will refer to these 8 masks as mask1346A to C and mask2138A to E. The observing conditions were generally mediocre due to very strong wind coming from the North."
+" As a result. the seeing was always above 1""."," As a result, the seeing was always above $1\arcsec$."
+ The seeing deteriorated during the nights so that the spectra in the field of 0322 were obtained under better conditions than the ones in the other field., The seeing deteriorated during the nights so that the spectra in the field of $-$ 0322 were obtained under better conditions than the ones in the other field.
+" We used MOS slitlets having a width of 1.1"" on the sky.", We used MOS slitlets having a width of $1.4\arcsec$ on the sky.
+ All spectra were obtained with the 06008 erism covering the wavelength range from 3600 tto 6000 aat a resolution of about 800., All spectra were obtained with the G600B grism covering the wavelength range from 3600 to 6000 at a resolution of about 800.
+ The detector pixels were binned 242 for all observations through all masks., The detector pixels were binned $\times$ 2 for all observations through all masks.
+ The journal of spectroscopic observations Is given in Table 2.., The journal of spectroscopic observations is given in Table \ref{spec-journal}.
+ The MOS data were reduced and combined as described in Fynbo et al. (, The MOS data were reduced and combined as described in Fynbo et al. (
+2001).,2001).
+ The accuracy in the wavelength calibration is about -EO.1 pixel for a spectral resolution Ro=900. which translates to Az=0.0002.," The accuracy in the wavelength calibration is about $\pm 0.1$ pixel for a spectral resolution $R=900$, which translates to $\Delta$ z=0.0002."
+ Average object extraction was performed within a variable window size matching the spatial extension of the emission line(s)., Average object extraction was performed within a variable window size matching the spatial extension of the emission line(s).
+ Therefore. the flux shoulc be conserved.," Therefore, the flux should be conserved."
+ When two or more individual exposures οἱ the same target have been obtained through different masks. the spectra were appropriately combined with rescaling anc weights. and using a mask for rejecting cosmic ray impacts.," When two or more individual exposures on the same target have been obtained through different masks, the spectra were appropriately combined with rescaling and weights, and using a mask for rejecting cosmic ray impacts."
+ We first analysed the slitlets containing the spectra of the LEGO candidates., We first analysed the slitlets containing the spectra of the LEGO candidates.
+ The combined spectra are displayec in Figs., The combined spectra are displayed in Figs.
+ 5 and 7.," \ref{candfigs1346}
+ and \ref{candfigs2138}."
+ Out of the 27 candidates in the 0322 field. we confirm 20 as being emission- objects.," Out of the 27 candidates in the $-$ 0322 field, we confirm 20 as being emission-line objects."
+" We consider a candidate confirmed if there is an emission line detected with at least 30 significance at the correct position in the slitlet within the wavelength r""ange corresponding to the filter transmission.", We consider a candidate confirmed if there is an emission line detected with at least $\sigma$ significance at the correct position in the slitlet within the wavelength range corresponding to the filter transmission.
+ Five candidates were not observed and for the remaining two an emission hine Is not detected., Five candidates were not observed and for the remaining two an emission line is not detected.
+ Two of the confirmed emission-line sources are foreground galaxies with the [OI] line located in the narrow-band filter., Two of the confirmed emission-line sources are foreground galaxies with the ] line located in the narrow-band filter.
+ The overall efficiency for detection and confirmation of LEGOs is therefore Z((confirmed )/#((observed LEGOs) = 18/22 = so far., The overall efficiency for detection and confirmation of LEGOs is therefore (confirmed (observed LEGOs) = 18/22 = so far.
+ For the 4427 field. the overall efficiency is smaller.," For the $-$ 4427 field, the overall efficiency is smaller."
+ Three candidates were not observed and 9 observed candidates were not confirmed., Three candidates were not observed and 9 observed candidates were not confirmed.
+ For the remaining 25. we confirm the presence of an emission line.," For the remaining 25, we confirm the presence of an emission line."
+ Two of the confirmed emission-line sources are foreground objects., Two of the confirmed emission-line sources are foreground objects.
+ One is an I1] emitter and the other is az=2.0366414 AGN with located in the narrow-band filter., One is an ] emitter and the other is a z=2.03664i4 AGN with located in the narrow-band filter.
+ Hence. the fraction of confirmed LEGOs is23/34=68%.," Hence, the fraction of confirmed LEGOs is."
+. For the confirmed LEGOs. we derived Ίνα fluxes. equivalent widths (EWs) and star-formation rates (SFRs) as described in detail in Fynbo et al. (," For the confirmed LEGOs, we derived $\alpha$ fluxes, equivalent widths (EWs) and star-formation rates (SFRs) as described in detail in Fynbo et al. ("
+2002).,2002).
+ The confirmed LEGOs are in general very faint., The confirmed LEGOs are in general very faint.
+ In Fig. 8..," In Fig. \ref{lumfunc},"
+ we show an histogram with the RCAB) magnitudes measured for confirmed emission-line sources., we show an histogram with the R(AB) magnitudes measured for confirmed emission-line sources.
+" At the bright end (R<24). we find that 4 out of 6 sources are foreground emission-line galaxies (three 11] emitters and a z=?.0364 AGN with located in the narrow-band filter),"," At the bright end $<$ 24), we find that 4 out of 6 sources are foreground emission-line galaxies (three ] emitters and a z=2.0364 AGN with located in the narrow-band filter)."
+ of the confirmed LEGOs are fainter than the RCAB)225.5 spectroscopic limit for LBGs in current ground-based surveys (see e.g. Fig., of the confirmed LEGOs are fainter than the R(AB)=25.5 spectroscopic limit for LBGs in current ground-based surveys (see e.g. Fig.
+ 6 of Shapley et al., 6 of Shapley et al.
+ 2003)., 2003).
+ The few LEGOs in our sample that are so bright that they would have made it into the LBG samples are quite remarkable objects., The few LEGOs in our sample that are so bright that they would have made it into the LBG samples are quite remarkable objects.
+ LEGO2138.229 (see Fig. 7)), 29 (see Fig. \ref{candfigs2138}) )
+ has Lyo emission that is much more extended than its continuum emission., has $\alpha$ emission that is much more extended than its continuum emission.
+ This has already been seen for other LEGOs (e.g. Moller Warren 1998; Fynbo et al., This has already been seen for other LEGOs (e.g. ller Warren 1998; Fynbo et al.
+ 2001) but not as clearly as in this case., 2001) but not as clearly as in this case.
+ LEGOI346.117 (see Fig. 5) , 17 (see Fig. \ref{candfigs1346}) )
+seems to be part of à complex system with several components. although we cannot exclude chance alignment.," seems to be part of a complex system with several components, although we cannot exclude chance alignment."
+ Based on observed Ενα fluxes. the range of SERs for the confirmed LEGOs is 0.20-15 M- ! if the extinction is negligible.," Based on observed $\alpha$ fluxes, the range of SFRs for the confirmed LEGOs is 0.20–15 $\odot$ $^{-1}$ if the extinction is negligible."
+ The observed EWs range from less than 100 tto more than 1000A., The observed EWs range from less than 100 to more than 1000.
+ This corresponds to about 20 tto 250 lin the rest-frame and is consistent with the theoretically expected Ένα EWs formetal-poor starburst galaxies (Charlot Fall 1993; Valls-Gabaud 1993; Schaerer 2003)., This corresponds to about 20 to 250 in the rest-frame and is consistent with the theoretically expected $\alpha$ EWs formetal-poor starburst galaxies (Charlot Fall 1993; Valls-Gabaud 1993; Schaerer 2003).
+ The surface density of confirmed sources is of the order of 10 ? per unit redshift down to a Lya flux limit of —7«10 15 ere ! ! and the EW limit shown in Fig. 4.., The surface density of confirmed sources is of the order of 10 $^{-2}$ per unit redshift down to a $\alpha$ flux limit of $\sim$ $\times$ $^{-18}$ erg $^{-1}$ $^{-1}$ and the EW limit shown in Fig. \ref{select}.
+ This is about a factor of five higher than the surface density of LBGs down to R=25.5. ~2 « 1.2 (Steidel et al.," This is about a factor of five higher than the surface density of LBGs down to R=25.5, $\sim$ $\times$ 1.2 (Steidel et al."
+ 1999) even if most LBGs are not themselves Lyn emitters., 1999) even if most LBGs are not themselves $\alpha$ emitters.
+ In other words. the LBGs are the tip of an iceberg consistent with the conclusion of Fynbo et al. (," In other words, the LBGs are the tip of an iceberg consistent with the conclusion of Fynbo et al. ("
+1999).,1999).
+ This reflects the steepness of the luminosity function for z=3 galaxies., This reflects the steepness of the luminosity function for z=3 galaxies.
+ In. future papers. we will address the morphology. clustering properties and luminosity function of the LEGOs from this and complementary VLT surveys.," In future papers, we will address the morphology, clustering properties and luminosity function of the LEGOs from this and complementary VLT surveys."
+ In Fig. 9..," In Fig. \ref{zdist}, ,"
+ we show the redshift distributions of LEGOs in the two fields relative to the filter response curves., we show the redshift distributions of LEGOs in the two fields relative to the filter response curves.
+ The redshifts of, The redshifts of
+"Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England.","Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."
+ The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions., The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.
+" The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."
+" GALEX (Galaxy Evolution Explorer) is a NASA Small Explorer, launched in April 2003, developed in cooperation with the Centre National d’Etudes Spatiales of France and the Korean Ministry of Science and "," GALEX (Galaxy Evolution Explorer) is a NASA Small Explorer, launched in April 2003, developed in cooperation with the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and \nocite{Sha11}
+ "
+Sellwood(2010) adopted ay=0 for a star at its apocentre and consequently wy=Ἔπ for a star at its pericentre.,\citet{Sell10} adopted $w_R=0$ for a star at its apocentre and consequently $w_R=\pm\pi$ for a star at its pericentre.
+ Note that action-angle variables. unlike Lindblads epieveles. can also be used for more eccentric orbits. for which the guiding centres generally orbit more slowly than the circular speed and the racial oscillation is anharmonic.," Note that action-angle variables, unlike Lindblad's epicycles, can also be used for more eccentric orbits, for which the guiding centres generally orbit more slowly than the circular speed and the radial oscillation is anharmonic."
+ Fig., Fig.
+ 4 of Paper I showed the separate clistributions of wy and us. For stars in the ssample having Jg<0.05L.0.," 4 of Paper I showed the separate distributions of $w_R$ and $w_\phi$ for stars in the sample having $J_R < 0.05L_{z,0}$."
+ Here. Fig.," Here, Fig."
+ X2. shows the joint distribution of the same stars in the space of both angles., \ref{angdist} shows the joint distribution of the same stars in the space of both angles.
+ The azimuthal phase distribution is confined to [s]EO4 rellecting the limited spread in Galactic azimuths of the guiding centres for stars that pass through the survey volume., The azimuthal phase distribution is confined to $|w_\phi|\la 0.4$ reflecting the limited spread in Galactic azimuths of the guiding centres for stars that pass through the survey volume.
+" The distribution of ο, values for stars having wy=0. such as orbit 3 in Fig. Al."," The distribution of $w_\phi$ values for stars having $w_R=0$, such as orbit 3 in Fig. \ref{draw},"
+" or wy,=cx (orbit 1) is very narrow because their guiding centres lie along the radius vector from the Galactic centre to the Sun for all values of Jp ", or $w_R=\pm\pi$ (orbit 1) is very narrow because their guiding centres lie along the radius vector from the Galactic centre to the Sun for all values of $J_R$ .
+Stars in the first quadrant of Fig., Stars in the first quadrant of Fig.
+" A2 are inward moving stars (because wg 0) with &uiding centres ahead. of the Sun (us,> 0). such as orbit 4."," \ref{angdist} are inward moving stars (because $w_R > 0$ ) with guiding centres ahead of the Sun $w_\phi > 0$ ), such as orbit 4."
+" Conversely. stars in the third quacrant (us,« 0) are outward moving stars having wp<0 oorbit 2)."," Conversely, stars in the third quadrant $w_\phi < 0$ ) are outward moving stars having $w_R < 0$ orbit 2)."
+ Thus the selection criteria preclude stars [rom ving in the second and fourth equadrants., Thus the selection criteria preclude stars from lying in the second and fourth quadrants.
+" The spread of t, values for wy~cx/2 rellects the spread in the sizes of he epieveles of the stars in the sample. from which more eccentric orbits were eliminated."," The spread of $w_\phi$ values for $w_R \sim \pm \pi/2$ reflects the spread in the sizes of the epicycles of the stars in the sample, from which more eccentric orbits were eliminated."
+" Sellwood(2010) argued that a concentration of stars laving a nearly constant value of mus,|fey would be an indicator of trapping in a resonance for the selected: values of / and m.", \citet{Sell10} argued that a concentration of stars having a nearly constant value of $mw_\phi + lw_R$ would be an indicator of trapping in a resonance for the selected values of $l$ and $m$.
+ Thus he searched. for an excess of stars lving along lines of fixed slope with all possible intercepts in this lot. and reported the results in his Fig.," Thus he searched for an excess of stars lying along lines of fixed slope with all possible intercepts in this plot, and reported the results in his Fig."
+ 7 of Paper E for the ssample., 7 of Paper I for the sample.
+ The lines for inner Lindblad resonances (f= 1) lave à positive slope in Fig. A2.., The lines for inner Lindblad resonances $l=-1$ ) have a positive slope in Fig. \ref{angdist}.
+" Pheir slopes decrease as m increases. causing them to become more closely. parallel to he distribution near (ey.us)=(0.0). giving rise to a peak Dear muy,tp= 02s m increases."," Their slopes decrease as $m$ increases, causing them to become more closely parallel to the distribution near $(w_R,w_\phi)=(0,0)$, giving rise to a peak near $mw_\phi - w_R = 0$ as $m$ increases."
+ The distributions shown in Fig., The distributions shown in Fig.
+ 7 of paper E for m=2 and m=3. and in Fig.," 7 of paper I for $m=2$ and $m=3$, and in Fig."
+ X3 of his paper. show the increasing prominence of this feature. which is purely an artefact of the sample selection.," \ref{restest4} of this paper, show the increasing prominence of this feature, which is purely an artefact of the sample selection."
+" A similar eature appears near mus,|wg=cxx when /=1. since the ines have negative slope in these cases."," A similar feature appears near $mw_\phi + w_R = \pm \pi$ when $l=1$, since the lines have negative slope in these cases."
+" Sellwood(2010). drew attention to the peaks that lav away from mies,tp0 for the cases of inner Lindblad resonances.", \citet{Sell10} drew attention to the peaks that lay away from $mw_\phi-w_R=0$ for the cases of inner Lindblad resonances.
+ These peaks arise in part from the concentration of ssbars near up~LS. aes~0.15 in Fig A2.. but the clump is visibly extended. which MeMillan(2011) described as having a triangular shape.," These peaks arise in part from the concentration of stars near $w_R
+\sim -1.5$, $w_\phi \sim -0.15$ in Fig \ref{angdist}, but the clump is visibly extended, which \citet{McM11} described as having a triangular shape."
+" Since the excess lies in the third cquacirant. it gives rise to peaks in the clistributions of mrs,wp that shift closer to zero as m is increased."," Since the excess lies in the third quadrant, it gives rise to peaks in the distributions of $mw_\phi-w_R$ that shift closer to zero as $m$ is increased."
+" Obviously the sanie excess gives rise tO peaks near mue,|wgzo2 for lines of negative slope in the cases of an bbut. at least for the sseunple. they are not as striking as those for the CCASCS."," Obviously the same excess gives rise to peaks near $mw_\phi+w_R \ga -2$ for lines of negative slope in the cases of an but, at least for the sample, they are not as striking as those for the cases."
+ The case for an mmacde by Sellwood(2010) cid not rest solely on this slight difference. however.," The case for an made by \citet{Sell10} did not rest solely on this slight difference, however."
+ He attached far greater significance to the fact that stars Line along a line of positive slope extending through the clump were exactly those that. [ay along the resonant scattering tongue in action Space. as shown in Fig.," He attached far greater significance to the fact that stars lying along a line of positive slope extending through the clump were exactly those that lay along the resonant scattering tongue in action space, as shown in Fig."
+ S of Paper Ll. As this was not the case for stars lving on lines of negative slope. Sellwood concluded jit an wasresponsible.," 8 of Paper I. As this was not the case for stars lying on lines of negative slope, Sellwood concluded that an wasresponsible."
+ Unfortunately. MeMillan.(2011). found that his conclusion was compromised. by selection. ellects: if stars are not only in the vicinity of the Sun but are also rapped in a resonance. AleMillan was able to show that A2))," Unfortunately, \citet{McM11} found that his conclusion was compromised by selection effects: if stars are not only in the vicinity of the Sun but are also trapped in a resonance, McMillan was able to show that \ref{angdist})"
+Alodel E has a low value of df. a high value of ¢ and a low value of £ (See Table 5)).,"Model E has a low value of $H$, a high value of $\zeta$ and a low value of $I$ (See Table \ref{tab:mod}) )."
+" Each model explored thermal and chemical properties at two values of ele. re. 41, —3 and 8 mag."," Each model explored thermal and chemical properties at two values of $A_{v}$, i.e. $A_{v}=$ 3 and 8 mag."
+ Fhese values are intended to represent conditions near the edge and in the dark interior of a molecular region., These values are intended to represent conditions near the edge and in the dark interior of a molecular region.
+ o comparing clirectly the observed. fractional abundances values presented. in. Table 4. with those modelled. listed. in. Table 5.. for the same temperature range (i.e. here. we compare only observed: and modelled fractional abundances at ρω Li). we may be able to identify which heating process may be present anc consistent with the observed. emissions of both NGC 1275 and the filamentary region.," By comparing directly the observed fractional abundances values presented in Table \ref{tab:abun} with those modelled listed in Table \ref{tab:mod}, for the same temperature range (i.e. here, we compare only observed and modelled fractional abundances at $T_{rot} \sim T_{K}$ ), we may be able to identify which heating process may be present and consistent with the observed emissions of both NGC 1275 and the filamentary region."
+ A summary of our conclusions is presented in Table 6..., A summary of our conclusions is presented in Table \ref{tab:sum}.
+ As one can see. there are actually a relatively limited. number of models which can reproduce the observations well.," As one can see, there are actually a relatively limited number of models which can reproduce the observations well."
+ ους we arbitrarily considered that a moclel reproduces well an observation when there is a factor of 5 or less between the modelled and. observed. fractional abundances., Here we arbitrarily considered that a model reproduces well an observation when there is a factor of 5 or less between the modelled and observed fractional abundances.
+ This [actor has been selected such as taking into account possible uncertainties on the cletections (c.g. pointing. calibration. etc) as well as uncertainties in the eas:dust ratio that allect the column densities and fractional abundances: also. the model results for abunclances scale with the unknown metallicitv.," This factor has been selected such as taking into account possible uncertainties on the detections (e.g. pointing, calibration, etc) as well as uncertainties in the gas:dust ratio that affect the column densities and fractional abundances; also, the model results for abundances scale with the unknown metallicity."
+ Inspection of Table 6 suggests that the radiation field has little effect on the resulting chemistry. whatever values are attained by Jf and ¢.," Inspection of Table \ref{tab:sum} suggests that the radiation field has little effect on the resulting chemistry, whatever values are attained by $H$ and $\zeta$."
+ We shall ignore the FUV radiation field. parameter in the following cliscussion. and focus on the ellects of varving ff and ¢.," We shall ignore the FUV radiation field parameter in the following discussion, and focus on the effects of varying $H$ and $\zeta$."
+ Note that where the observations supply only upper limits. we have assumed that the actual value is close to the upper limit.," Note that where the observations supply only upper limits, we have assumed that the actual value is close to the upper limit."
+ Further. we note that the success or failure of the models to match observations appears to be the same for both the centre. Le. towards NCC 1275. and the eastern filamentary. position.," Further, we note that the success or failure of the models to match observations appears to be the same for both the centre, i.e. towards NGC 1275, and the eastern filamentary position."
+ Table ο shows that. individual species may have a match with observation for several models., Table \ref{tab:sum} shows that individual species may have a match with observation for several models.
+ For example. CN eives a match to observations lor Alodels DB. E fat 1.= 3 mag). Model D and Model €. while Coll could match the observations for Models I5 and A. However. if all the molecules are assumed to share the same space and physical conditions. then we require a single model to account for all the species considered.," For example, CN gives a match to observations for Models B, E (at $A_{v}=$ 3 mag), Model D and Model C, while $_{2}$ H could match the observations for Models E and A. However, if all the molecules are assumed to share the same space and physical conditions, then we require a single model to account for all the species considered."
+" Table 6 shows that there is such a model. Model I. Ht can account for CN and at id.= 3 mag (though not at S mag). and for Coll. The values of 1555 associated with all three molecules is 50 Ex. IH is encouraging that the same value of 7;,; applies to all three species."," Table \ref{tab:sum} shows that there is such a model, Model E. It can account for CN and $^{+}$ at $A_{v}=$ 3 mag (though not at 8 mag), and for $_{2}$ H. The values of $T_{rot}$ associated with all three molecules is 50 K. It is encouraging that the same value of $T_{rot}$ applies to all three species."
+ We discuss the implication of this finding in Section ??.., We discuss the implication of this finding in Section \ref{sec:con}.
+ The comparison in Section 77. between the molecular abundances obtained. [rom the observations and from the models of ?. suggests that we can ientity one model. Alocel I5. that. produces. results. consisten with the observations.," The comparison in Section \ref{sec:comp} between the molecular abundances obtained from the observations and from the models of \citet{Baye10c} suggests that we can identify one model, Model E, that produces results consistent with the observations."
+ This model has a low FUY radiaion field. a low rate of heating by dissipation. but a high οἱsme rav ionization rate.," This model has a low FUV radiation field, a low rate of heating by dissipation, but a high cosmic ray ionization rate."
+ Unpublished data from the ? calculations show that cosmic rav heating accounts for of all heating at either vt.= 32 or 5 mag., Unpublished data from the \citet{Baye10c} calculations show that cosmic ray heating accounts for of all heating at either $A_{v}=$ 3 or 8 mag.
+ The enhanced cosmic rav Dux may arise in a dyvnamica interaction. as suggested by 2..," The enhanced cosmic ray flux may arise in a dynamical interaction, as suggested by \citet{Ferl09}."
+ Those authors also. [oun hat an enhanced cosmic rav ionization rate was require o account. for the observations of the optical and. infrarec emitting. components of the filaments., Those authors also found that an enhanced cosmic ray ionization rate was required to account for the observations of the optical and infrared emitting components of the filaments.
+ It is interesting. herefore. that the results from the present work also sugecs hat the regions of cluster gas probed by millimetre anc sub-millimetre emissions also require a similarly. enhancec Cosmic rav ionization rate.," It is interesting, therefore, that the results from the present work also suggest that the regions of cluster gas probed by millimetre and sub-millimetre emissions also require a similarly enhanced cosmic ray ionization rate."
+ A second inference is that a high wating rate from energy dissipation is not required: in fact. as Table 6 indicates. a high heating rate from sources other han cosmic ravs appears to inhibit a match between models and observations.," A second inference is that a high heating rate from energy dissipation is not required; in fact, as Table \ref{tab:sum} indicates, a high heating rate from sources other than cosmic rays appears to inhibit a match between models and observations."
+ 1n the observations. we have detected only one [ine in each of three molecular species. so a reliable analysis of the observational data cannot be made.," In the observations, we have detected only one line in each of three molecular species, so a reliable analysis of the observational data cannot be made."
+ Lt would be useful for the further study of galaxy. cluster gas to make confirmed detections of several lines of each of the three molecular, It would be useful for the further study of galaxy cluster gas to make confirmed detections of several lines of each of the three molecular
+measured for 29055-10.,measured for G339.88-1.26.
+ The entire NGC 6334 region was imaged with the VLA by Rodrigeuez. Cantó Moran (1982).. but they were able to set only an upper limit of 20 mJy for other compact sources in the region.," The entire NGC 6334 region was imaged with the VLA by Rodrígguez, Cantó Moran \shortcite{Ro1982}, but they were able to set only an upper limit of 20 mJy for other compact sources in the region."
+ Gaume Alutel (1987). also imaged NGC 6334E. with the VLA and report no additional compact emission with a 5-e limit of 6.5 mv for their 15-Cillz image., Gaume Mutel \shortcite{Ga1987} also imaged NGC 6334F with the VLA and report no additional compact emission with a $\sigma$ limit of 6.5 mJy for their 15-GHz image.
+ We are able to set a 5-7 upper limit of 0.82 for any radio continuum emission from Ci318.95-0.20., We are able to set a $\sigma$ upper limit of 0.82 for any radio continuum emission from G318.95-0.20.
+ regions with peak Ilux densities less than our upper Limit have been detected., regions with peak flux densities less than our upper limit have been detected.
+ Llowever. the large-scale. high-resolution studies of regions which have been macle so far (Wood&Church-1994:Aliralles.Itodríguez&Scalise 1994).. typically have sensitivity comparable to. or worse than. our observation of C6318.95-0.20.," However, the large-scale, high-resolution studies of regions which have been made so far \cite{Wo1989,Ga1993,Ku1994,Mi1994}, typically have sensitivity comparable to, or worse than, our observation of G318.95-0.20."
+ Thus there is little information on whether regions with peak Iluxes less than 1 mJy are common., Thus there is little information on whether regions with peak fluxes less than 1 mJy are common.
+ The depth to which we could CLEAN the image toward C:318.95-0.20 was limited. by the presence of a confusing source with a peak flux density of 29.5  160 arcsec west and 34.5 arcsec north of the reference niaser postion., The depth to which we could CLEAN the image toward G318.95-0.20 was limited by the presence of a confusing source with a peak flux density of 29.5 $\sim$ 160 arcsec west and 34.5 arcsec north of the reference maser position.
+ The confusing source we detected is approximately coincident with theAS source 14567-5846. which has been identified as an region.," The confusing source we detected is approximately coincident with the source 14567-5846, which has been identified as an region."
+ The radio continuum emission appears to be a cometary region with a major axis of  LO aresec., The radio continuum emission appears to be a cometary region with a major axis of $\sim$ 10 arcsec.
+ Pwo groups have reported. maser emission toward 14567-5846 (Cohen.Baart&JonasLOSS:Ixemball.CavlardNicolson 1988).," Two groups have reported maser emission toward 14567-5846 \cite{Co1988,Ke1988}."
+. In both cases they report the position to be consistent with the OLLI maser position measured by Caswell 1avnes (LOST). which. in turn. is coincident with the 6.7-Gllz mascrs.," In both cases they report the position to be consistent with the OH maser position measured by Caswell Haynes \shortcite{Ca1987}, which, in turn, is coincident with the 6.7-GHz masers."
+ Therefore. it appears that all the maser emission reported in this region to date is [rom the same site. which is more than 2 arcmin away from the1115 source 14567-5846.," Therefore, it appears that all the maser emission reported in this region to date is from the same site, which is more than 2 arcmin away from the source 14567-5846."
+ Our 8.5-Cillz image of €:339.88-1.26 is shown in bie. 1.., Our 8.5-GHz image of G339.88-1.26 is shown in Fig. \ref{fig:g339}.
+ This is the first image to be produced of this region., This is the first image to be produced of this region.
+ We measured it to have a peak brightness of 6.1ab 5.5 Cillz. but it was too weak to image from our 6.7- spectral-Iine observations.," We measured it to have a peak brightness of 6.1at 8.5 GHz, but it was too weak to image from our 6.7-GHz spectral-line observations."
+ The bulk of the continuum emission is unresolved in our 1.2-arcsec svnthesised. beam. but shows sone low-level extension to. the north-cast. sugeesting à possible cometary morphology.," The bulk of the continuum emission is unresolved in our 1.2-arcsec synthesised beam, but shows some low-level extension to the north-east, suggesting a possible cometary morphology."
+ The reference maser (-38.7 )) is the most south-castern of the spots and is olfset from the continuum peak by 0.60.2 aresec., The reference maser (-38.7 ) is the most south-eastern of the spots and is offset from the continuum peak by $\pm$ 0.2 arcsec.
+ The methanol masers lic in a line approximately across the centre of the continuum emission. perpendicular to the direction of the extended emission.," The methanol masers lie in a line approximately across the centre of the continuum emission, perpendicular to the direction of the extended emission."
+ The positions of two of the OLL maser spots have been observed by Caswell (1095).. and they stracddle the line of 6.7-CGLIz methanol masers.," The positions of two of the OH maser spots have been observed by Caswell \shortcite{Ca1995e}, and they straddle the line of 6.7-GHz methanol masers."
+ The position of one of the niasers spots was measured with the VLA by Forster Caswell (1989)., The position of one of the masers spots was measured with the VLA by Forster Caswell \shortcite{Fo1989}.
+. μον quote an absolute positional accuracy of 0.5 aresec. but as C339.SS-.126 was the most southerly source in their sample. the maser position is probably less well determined than for the majority of sources.," They quote an absolute positional accuracy of 0.5 arcsec, but as G339.88-.126 was the most southerly source in their sample, the maser position is probably less well determined than for the majority of sources."
+ Ehe mascr positions they quote is approximately 1 aresee south of the 6.7-Gllz methanol masers., The maser positions they quote is approximately 1 arcsec south of the 6.7-GHz methanol masers.
+ This source was previously imaged at 4.9 and 15 Cllz using the VLA (Itodríguezetal.1982:Gaume&Mutel1987).," This source was previously imaged at 4.9 and 15 GHz using the VLA \cite{Ro1982,Ga1987}."
+. Our S.5-Cillz image. shown in Fig. 2..," Our 8.5-GHz image, shown in Fig. \ref{fig:ngc6334f},"
+ agrees with theirs., agrees with theirs.
+ Making sensitive high-resolution images of the NGC 6334F region is dillieult. because of the presence of the sources NGC 6334D and I. two nearby strong. cilfuse regions.," Making sensitive high-resolution images of the NGC 6334F region is difficult because of the presence of the sources NGC 6334D and E, two nearby strong, diffuse regions."
+ We measure a peak brightness of 585 for NGC 6334E at 8.5 Cllz ac 606 at 6.7 CGllz., We measure a peak brightness of 585 for NGC 6334F at 8.5 GHz and 606 at 6.7 GHz.
+" We also produced an s.5-Cillz image using a restoring beam with the same dimensions as the 6.7-Cillz beam and measured the spectral incex (a) of the peak to be 0.95 (S, xv"") between 6.7 and 8.5 Cllz.", We also produced an 8.5-GHz image using a restoring beam with the same dimensions as the 6.7-GHz beam and measured the spectral index $\alpha$ ) of the peak to be 0.95 $S_{\nu} \propto \nu^{\alpha}$ ) between 6.7 and 8.5 GHz.
+ This implies that the centre of the region is still optically thick at 8.5 Cillz., This implies that the centre of the region is still optically thick at 8.5 GHz.
+ ‘Toward NGC 63341. three centres of 6.7-Cllz methanol maser emission are within the primary bean of the APCA antennas.," Toward NGC 6334F, three centres of 6.7-GHz methanol maser emission are within the primary beam of the ATCA antennas."
+ We have labelled the three sites NGC 6334E (C) (all those masers which lic in projection against the region). NGC 6334b (NW) (the masers to the north- of NGC 63341 (€) and G351.54|0.66.," We have labelled the three sites NGC 6334F (C) (all those masers which lie in projection against the region), NGC 6334F (NW) (the masers to the north-west of NGC 6334F (C)) and G351.54+0.66."
+ G351.54|0.66 is not shown in Lig. 2. ," G351.54+0.66 is not shown in Fig. \ref{fig:ngc6334f}, ,"
+as it is olfset 14.0 arcsec east, as it is offset 14.0 arcsec east
+where we have normalized all the parameters to our fiducial values for the case we are discussie: the BIT mass was estimated by ? as 5.5«107AZ... Nyc107 ? is the difference observed between NAIAIOF and Sl. f£z20 hours is the time clapsed between hese two observations.,"where we have normalized all the parameters to our fiducial values for the case we are discussing: the BH mass was estimated by \citet{wold06} as $5.5\times10^7\,M_\odot$, $N_\mathrm{H}\simeq10^{23}$ $^{-2}$ is the difference observed between XMM07 and S1, $t\simeq20$ hours is the time elapsed between these two observations."
+ A crucial value is the electron deusitv: the value n=LO cm? corresponds to a cloud dimension D-14101 cu. ie. roughly 10 ry tor the DIL inass estimate reported above.," A crucial value is the electron density: the value $n=10^{9}$ $^{-3}$ corresponds to a cloud dimension $D=1\times10^{14}$ cm, i.e. roughly 10 $r_g$ for the BH mass estimate reported above."
+ A larecr density would shift the material to larger distances. but iuplvius dimensions of the clouds zinaller than LO ry aud. therefore. likely suaaller than tlhe N-rav source they should obscure.," A larger density would shift the material to larger distances, but implying dimensions of the clouds smaller than 10 $r_g$ and, therefore, likely smaller than the X-ray source they should obscure."
+ Ou the other haud. lower densities would result in a still smaller distance. which is already: an upper hut. given that the actual crossing time mast be lower than the separation vetween the two observations.," On the other hand, lower densities would result in a still smaller distance, which is already an upper limit, given that the actual crossing time must be lower than the separation between the two observations."
+ There is a plivsical nuit at this distance. which cannot be smaller han the dimension of the clouds D.," There is a physical limit at this distance, which cannot be smaller than the dimension of the clouds $D$ ."
+ This gives a ower lait for the deusitv. which is 923«107 Cll5m," This gives a lower limit for the density, which is $n>3\times10^8$ $^{-3}$."
+" Ou the basis of the average unabsorbed N-rav uniuositv of NGC 7582. as derived in this work (Eo«LoymaeymmDcqeDO2.3.10,D creyc D28 soo),1) we Cican estimate the radius of the DER in this source to be around Rapp=0.51«10% cin (see?.fortheative uncertainties).."," On the basis of the average unabsorbed X-ray luminosity of NGC 7582, as derived in this work $<L_{2-10\,keV}>\simeq2.3\times10^{42}$ erg $^{-2}$ $^{-1}$ ), we can estimate the radius of the BLR in this source to be around $R_{BLR}=0.5-1\times10^{15}$ cm \citep[see][for the relation between the two parameters and the relative uncertainties]{kaspi05}. ."
+ Moreover. a typical density or the BLR is believed to be 10°? cur?. or arecr for the imuer regions (e.g.?)..," Moreover, a typical density for the BLR is believed to be $10^{9.5}$ $^{-3}$, or larger for the inner regions \citep[e.g.][]{peterson97}."
+ Therefore. the ocation and plivsical properties of the absorbing clouds in NGC 7582 are consistent with being within or nuuediatelv outside the BLR.," Therefore, the location and physical properties of the absorbing clouds in NGC 7582 are consistent with being within or immediately outside the BLR."
+ Note that je sublimation radius iun this source is bevond 101 σ (seeeg.T). thus the BLR and the N-rav absorbing clouds must be cdust-free.," Note that the sublimation radius in this source is beyond $10^{17}$ cm \citep[see e.g.][]{barv87}, thus the BLR and the X-ray absorbing clouds must be dust-free."
+ This neans that these clouds are not responsible for 1 absorption of the BLR and the consequent Classification of NCC 7582 as a Seyfert 2., This means that these clouds are not responsible for the absorption of the BLR and the consequent classification of NGC 7582 as a Seyfert 2.
+ This is due to the large-scale absorber with column deusity of a few 107 ?., This is due to the large-scale absorber with column density of a few $10^{22}$ $^{-2}$.
+ Ou the other hand. we stress again that the torus is not along the line of sight iu this source.," On the other hand, we stress again that the torus is not along the line of sight in this source."
+ This scenario will be eeneralized in the next Section., This scenario will be generalized in the next Section.
+ N-rav observations have collected imcli evidence iu favor of the presence of the pe-scale envisaged iu Uuitication Models., X-ray observations have collected much evidence in favor of the presence of the pc-scale envisaged in Unification Models.
+ In particular. the ubiquitous presence of a Compton reflection conrponeut. invariably accompanied bv a jeutral iron narrow Ίνα enmüssion Luc. is a clear signature of the presence of Conmpton-thick uaterial also in Type 1 objects. even if it docs rot intercept the line of sight (seec.g.TYTL.," In particular, the ubiquitous presence of a Compton reflection component, invariably accompanied by a neutral iron narrow $\alpha$ emission line, is a clear signature of the presence of Compton-thick material also in Type 1 objects, even if it does not intercept the line of sight \citep[see e.g.][]{per02,bianchi04,bianchi07}."
+ The distance of the is generally inferred from the lack of variability of these components between observations separated vears one from the other., The distance of the is generally inferred from the lack of variability of these components between observations separated years one from the other.
+ Therefore. a pe-seale must be an fundamental ingredieu of any Unification. Model.," Therefore, a pc-scale must be an fundamental ingredient of any Unification Model."
+ However. there is now a erowing nuuber of sources which show dramatic absorptionvariability in timescales as short as hours (e.g.277).," However, there is now a growing number of sources which show dramatic absorption variability in timescales as short as hours \citep[e.g.][]{elvis04,ris05,puc07}."
+. These objects cannot be described iu the framework of classic Unification Mocls and they are generally considered exceptions of an otherwise successfu scenario., These objects cannot be described in the framework of classic Unification Models and they are generally considered exceptions of an otherwise successful scenario.
+ Iowever. it is likely that much more sources would present the same characteristics. if oulv they were observed with aimed mnonitornmg calupaigus. as we did for NGC 7582.," However, it is likely that much more sources would present the same characteristics, if only they were observed with aimed monitoring campaigns, as we did for NGC 7582."
+ We propose that the simplest scenario that fits the N-orav. observations should consider the preseuce of three neutral absorbers/enitters. eveu if not necessarily coexisting or observable in all the sources.," We propose that the simplest scenario that fits the X-ray observations should consider the presence of three neutral absorbers/emitters, even if not necessarily coexisting or observable in all the sources."
+ À Comptou-thick torus ids likely present in the vast majority of the sources at a distance from the DIT roughly around a pe., A Compton-thick torus is likely present in the vast majority of the sources at a distance from the BH roughly around a pc.
+ It is responsible for the production of the Compton reflection compoucut aud the ueutral iron narrow Ίνα line. both invariably present im all N-ray Spectra oC AGN iux eecnerallv found not to vary on timescales shorter than vears.," It is responsible for the production of the Compton reflection component and the neutral iron narrow $\alpha$ line, both invariably present in all X-ray spectra of AGN and generally found not to vary on timescales shorter than years."
+ Tf the torus intercepts the line of sight. he observer classifies the object as a Comptou-thick Sevfert 2.," If the torus intercepts the line of sight, the observer classifies the object as a Compton-thick Seyfert 2."
+ Ou a much Lueer scale. a Comiptou-thiu absorber with coluun deusitv around 1077 ? nay intercept the ineof sight. completely or partially obscurus the DER iu the optical aud absorbing he X-rayspectirin.," On a much larger scale, a Compton-thin absorber with column density around $10^{22}$ $^{-2}$ may intercept the lineof sight, completely or partially obscuring the BLR in the optical and absorbing the X-rayspectrum."
+ The effect of this, The effect of this
+We combine the criteria 1-1 iuto one single step.,We combine the criteria 1-4 into one single step.
+ The detections filtered out by cach steps are shown in Table. D., The detections filtered out by each steps are shown in Table. \ref{tab.detect}.
+ Anious the nova candidates; 21 are discovered by WeCAPP project for the first time. while 5 of them are shown but were not officially published aud can be found on the or Extragalactic webpages.," Among the nova candidates, 24 are discovered by WeCAPP project for the first time, while 5 of them are known but were not officially published and can be found on the or Extragalactic webpages."
+ The rest of the nova candidates are published and can be ound in the literature. see e.g. 2?ΕΠ. ," The rest of the nova candidates are published and can be found in the literature, see e.g. \cite{2007A+A...465..375P, 2010AN....331..187P}."
+The positions aud light curves of these 91 novae are oxeseuted in Table [and in the Appendix., The positions and light curves of these 91 novae are presented in Table \ref{tab.cat} and in the Appendix.
+ Although all novae slightly differ. it is possible to group uovae by their eht-curve or spectroscopic properties.," Although all novae slightly differ, it is possible to group novae by their light-curve or spectroscopic properties."
+ One of the commonly used methods to characterize novae is the “speed class’ proposed by ?.. who categorized. novae according to their lieght-curve evolution aud described the decline time-scale bv the time uceded to drop by 2 magnitudes below the maxima (fo).," One of the commonly used methods to characterize novae is the `speed class' proposed by \cite{1964gano.book.....P}, who categorized novae according to their light-curve evolution and described the decline time-scale by the time needed to drop by 2 magnitudes below the maximum $t_2$ )."
+ ?. did a thorough study of the spectroscopic propertics of the novae. and categorized novae into Fe (ealactic thick disk novae) or Ile (ealactic disk novae) group according to the most prominent features in their spectra.," \cite{1992AJ....104..725W}
+ did a thorough study of the spectroscopic properties of the novae, and categorized novae into Fe (galactic thick disk novae) or He (galactic disk novae) group according to the most prominent features in their spectra."
+ Dela Valle Livio (1998) further established. the connection. between the speed class aud. spectroscopic classification., Della Valle Livio (1998) further established the connection between the speed class and spectroscopic classification.
+ They found that fast rovac are mainly related to the He novae. while he slow novae tend to show Fe II features iu their spectra.," They found that fast novae are mainly related to the He novae, while the slow novae tend to show Fe II features in their spectra."
+ The xospoed explanation behind is that THe novae are Yolu the galactic disk aud prone to have massive white dwarfs. thus having fast and steep decline.," The prospoed explanation behind is that He novae are from the galactic disk and prone to have massive white dwarfs, thus having fast and steep decline."
+ On the other mand. the Fe II novae originate from the less massive yopulation II stars in the galactie thick disk. aud heuce ve a slow decline.," On the other hand, the Fe II novae originate from the less massive population II stars in the galactic thick disk, and hence have a slow decline."
+ The speed class is not chough to fully account for the differences between novae., The speed class is not enough to fully account for the differences between novae.
+ 2 gathered 93 ealactic novae youn the American Association of Variable Star Observers (AAVSO) and made a thorough study using the complete coverage of their light. curves., \cite{2010AJ....140...34S} gathered 93 galactic novae from the American Association of Variable Star Observers (AAVSO) and made a thorough study using the complete coverage of their light curves.
+ They suggested to classify the novae according to their distinct features ding their decline. such as he patem. he cusp by the secondary brightening aud the dip by the dust.," They suggested to classify the novae according to their distinct features during their decline, such as the plateau, the cusp by the secondary brightening and the dip by the dust."
+ Tn this section we classify our nova caxdidates (if xossible) following the taxonomy proposed by ?.., In this section we classify our nova candidates (if possible) following the taxonomy proposed by \cite{2010AJ....140...34S}.
+ Readers are referred to Table 3 aud Figure 2 in? for the definition id exemplary light curves for different nova classes;, Readers are referred to Table 3 and Figure 2 in \cite{2010AJ....140...34S} for the definition and exemplary light curves for different nova classes.
+ Note hat the classification scheme of ? is based on the V- magnitude. while we are using A-baud aud wight be affected by the stroug Πα cmission.," Note that the classification scheme of \cite{2010AJ....140...34S} is based on the $V$ -band magnitude, while we are using $R$ -band and might be affected by the strong $\alpha$ emission."
+ We thus check ou 7- lieht curve. which docs not affected by the strone Ta mission. aud identify the apparent features iu tle nova‘lassification scheme of ? iu both R aud f-haud.," We thus check our $I$ -band light curve, which does not affected by the strong $\alpha$ emission, and identify the apparent features in the novaclassification scheme of \cite{2010AJ....140...34S} in both $R$ and $I$ -band."
+ The S-class novae have sinooth light curves following the universal power-law decline (Fxt 1) due to frec-free enission expanding shell as proposed by 2.., The S-class novae have smooth light curves following the universal power-law decline $F \propto t^{-1.75}$ ) due to free-free emission expanding shell as proposed by \cite{2006ApJS..167...59H}.
+ In principle. the classification scheme of 2 is based on the fac tha all the Πο curves originate from the S-class.," In principle, the classification scheme of \cite{2010AJ....140...34S} is based on the fact that all the light curves originate from the S-class."
+ The S-class is indeed cousisteut to the vast majority of our nova cauclidates., The S-class is indeed consistent to the vast majority of our nova candidates.
+" To verity the universal decline law. we thus & our candidate light curves with a [parameter formula: where=fi fj, is the laselire level aud will be differen Yoni zero in cases where the nova candidate flux is xeseut in the reference frame used in difference inaeiug or there is a variable close to it (sec e.g. the light curve of WeCAPDP-NIO iu 1e appendix)."," To verify the universal decline law, we thus fit our candidate light curves with a 4-parameter formula: where $f_b$ is the baseline level and will be different from zero in cases where the nova candidate flux is present in the reference frame used in difference imaging or there is a variable close to it (see e.g. the light curve of WeCAPP-N10 in the appendix)."
+ fy gives the proportiona Actor between the flux ancl time. fy is the onset of nova outburst and à is the index of the power-law decline.," $f_0$ gives the proportional factor between the flux and time, $t_0$ is the onset of nova outburst and $\alpha$ is the index of the power-law decline."
+" After he first iteration. we found that some candidates have ""reasonable fy long before the nova eruption."," After the first iteration, we found that some candidates have unreasonable $t_0$ long before the nova eruption."
+" For such events, we use a 5-ouwnneter formula with?| fixeda the last data poiut in the baseline just before the eruption to avoid unreasonable ty."," For such events, we use a 5-parameter formula with $t_{_{-1}}$ fixed at the last data point in the baseline just before the eruption to avoid unreasonable $t_0$."
+ The best-fit parameters for equations (3)) aud (1)) are given in Table b. , The best-fit parameters for equations \ref{eq.free_t0}) ) and \ref{eq.fixed_t0}) ) are given in Table \ref{tab.free_t0}. .
+For the S-class nova. we first tried to fit the power- decline for all the nova. candidates.," For the S-class nova, we first tried to fit the power-law decline for all the nova candidates."
+ A candidate is classified as S-class nova ouly when the fitting routine, A candidate is classified as S-class nova only when the fitting routine
+"In addition to SNe Ia and GRBs, we have also used the constraints below following previous analyses (??) The corresponding x? for these constraints are directly calculated using Eq. (6)).","In addition to SNe Ia and GRBs, we have also used the constraints below following previous analyses \citep{Riess:2006fw,Sullivan:2007pd}
+ The corresponding $\chi^2$ for these constraints are directly calculated using Eq. \ref{eq:chi2_xi}) )."
+" We have also studied the dark energy EOS evolution with the above BAO constraints replaced by the latest BAO measurements presented in ?,, for which the Y. value is (?) where with r, the D4(035)comoving sound horizon at recombination and This constraint itself favors} a dark energy EOS of Q).."," We have also studied the dark energy EOS evolution with the above BAO constraints replaced by the latest BAO measurements presented in \citet{Percival:2007yw}, , for which the $\chi^2$ value is \citep{Percival:2007yw}
+ where with $r_s$ the comoving sound horizon at recombination and This constraint itself favors a dark energy EOS of $w<-1$ \citep{Percival:2007yw}."
+ Figures 3 and 4 show our results for the weak prior and strong prior respectively.," Figures \ref{fig:weak_prior_result} and \ref{fig:strong_prior_result}
+ show our results for the weak prior and strong prior respectively."
+" For these two figures, we have included subsets of data from section 3.3 same as that are used in ? besides SNe Ia. For the results presented in Figure 5,, the BAO constraints are updated with the latest measurements (?),, see Eq. (23)),"," For these two figures, we have included subsets of data from section \ref{sec:other_data} same as that are used in \citet{Sullivan:2007pd} besides SNe Ia. For the results presented in Figure \ref{fig:new_BAO_result}, , the BAO constraints are updated with the latest measurements \citep{Percival:2007yw}, see Eq. \ref{eq:chi2_BAO}) ),"
+" Eq. (24)),"," Eq. \ref{eq:X_BAO}) ),"
+ and Eq. (25))., and Eq. \ref{eq:inv_cov_BAO}) ).
+" A comparison between Figures 3 and 4 shows that the results are insensitive to the priors, i.e. insensitive to whether w(z>7)=—1 is assumed or not for dark energy."," A comparison between Figures \ref{fig:weak_prior_result}
+ and \ref{fig:strong_prior_result} shows that the results are insensitive to the priors, i.e. insensitive to whether $w(z>7)=-1$ is assumed or not for dark energy."
+" Since Figures 3 and 4only differ from results derived by ? in thatwe include GRB luminosity data, comparisons of Figures 3 and 4 with figures in ? demonstrate the"," Since Figures \ref{fig:weak_prior_result}
+ and \ref{fig:strong_prior_result} only differ from results derived by \citet{Sullivan:2007pd} in thatwe include GRB luminosity data, comparisons of Figures \ref{fig:weak_prior_result}
+ and \ref{fig:strong_prior_result} with figures in \citet{Sullivan:2007pd} demonstrate the"
+10 doubt that most of the NRB originates at redshift :>1.,no doubt that most of the XRB originates at redshift $z>1$.
+ Bovle et al (1991) and Page et al (1996) who fiud their samples of X-ray selected ACN consistent with pure unuinositv evolution models. predict a peak in the N-vay volune cuiussivity around τοναν2.," Boyle et al (1994) and Page et al (1996) who find their samples of X-ray selected AGN consistent with pure luminosity evolution models, predict a peak in the X-ray volume emissivity around $z\sim 1.5-2$."
+ Mivaji et al (1998) iustead. find better consistenev with luninosity dependent density evolution. in which case the N-vay volume cuissivity in ACN nore luminous than 10TIEeres+ (which for the broken power-law shape of the unminositv fiction account for most of the NX-ravs emitted by ACN) rises steeply your.=Oto2.=1 2 with no evidence for a decline at higher redshifts.," Miyaji et al (1998) instead find better consistency with luminosity dependent density evolution, in which case the X-ray volume emissivity in AGN more luminous than $10^{44.5}\, {\rm erg}\, {\rm s}^{-1}$ (which for the broken power-law shape of the luminosity function account for most of the X-rays emitted by AGN) rises steeply from $z=0$ to $z=1-2$ with no evidence for a decline at higher redshifts."
+ Iu both cases it is clear that soft N-rav ciuission frou the extragalactic «kv. comes mostly roni redshifts 7=1.2 or larger. in a situation very similar to the star formation in the Universe (Madau et al 1996. Bovle Terlevich 1998).," In both cases it is clear that soft X-ray emission from the extragalactic sky comes mostly from redshifts $z=1-2$ or larger, in a situation very similar to the star formation in the Universe (Madau et al 1996, Boyle Terlevich 1998)."
+ Studvine the N-rav Universe is then likely to provide a major handle to uuderstaud the evolution of the Universe at intermediate redshifts aud therefore it is an issue of prime cosmological relevance., Studying the X-ray Universe is then likely to provide a major handle to understand the evolution of the Universe at intermediate redshifts and therefore it is an issue of prime cosmological relevance.
+ There ave other reasons to prefer X-rays to carry out cosmological studies., There are other reasons to prefer X-rays to carry out cosmological studies.
+ Ou the one hand the hieh-latitude N-vay sky is clean. at least at photon energies above 2 keV. ealactic absorption has ucelieible effects aud the contribution of the Galaxy to the NRB is less than a few (Iwan ct al 1982).," On the one hand the high-latitude X-ray sky is `clean', at least at photon energies above 2 keV, galactic absorption has negligible effects and the contribution of the Galaxy to the XRB is less than a few (Iwan et al 1982)."
+ A further reason is the iuall content in stars of hieh ealactic latitude surveys. ranging from at bright fluxes down to probably less than at the faiutest fluxes.," A further reason is the small content in stars of high galactic latitude surveys, ranging from at bright fluxes down to probably less than at the faintest fluxes."
+ Iu this paper we review the current status of studies of the large-scale structure of the Universe. which up to now las produced relevant but certainly not spectacular results.," In this paper we review the current status of studies of the large-scale structure of the Universe, which up to now has produced relevant but certainly not spectacular results."
+ The two main questions that we address are: Except when otherwise stated we use Hy=LOOans|Alpe qy=0.5 aud A=0.," The two main questions that we address are: Except when otherwise stated we use $H_0=100\, h\, {\rm km}\, {\rm
+s}^{-1}\, {\rm Mpc}^{-1}$, $q_0=0.5$ and $\Lambda=0$."
+ The distribution of the NRB fluctuations on the largest scales aud their link to inhomogeneities in the distribution of matter has beeu an active field of research for many vears., The distribution of the XRB fluctuations on the largest scales and their link to inhomogeneities in the distribution of matter has been an active field of research for many years.
+" The observational resources have been mostly Μος to the A? experiment which scanned the sky with a resolution of 3°«1.5"" at photon energies 2-60 keV. Since the Galaxy is moving with respect to the frame where the CMDB would be isotropic towards /=2617.5Ls"". there must be an overdensity of sources which are pulling us towards that direction."," The observational resources have been mostly limited to the HEAO-1 A2 experiment which scanned the sky with a resolution of $3^{\circ}\times 1.5^{\circ}$ at photon energies 2-60 keV. Since the Galaxy is moving with respect to the frame where the CMB would be isotropic towards $l=264^{\circ},
+b=48^{\circ}$, there must be an overdensity of sources which are pulling us towards that direction."
+ The distribution of X-ray sources in the sky should therefore exhibit an approximate large-scale dipolar distribution pointing towards the same direction., The distribution of X-ray sources in the sky should therefore exhibit an approximate large-scale dipolar distribution pointing towards the same direction.
+where AY and AS are the changes in gas temperature and entropy.,where $\Delta{T}$ and $\Delta{S}$ are the changes in gas temperature and entropy.
+ Using the values obtained. above for these quantities. we derive an electron. density at the time of injection of 310 thsyZem?.," Using the values obtained above for these quantities, we derive an electron density at the time of injection of $3\times 10^{-4}{h_{50}}^{\frac{1}{2}}$ $^{-3}$."
+ This is about an order of magnitude lower than the mean gas density in cores of systems without cooling Hows. suggesting that the energy must have been injected. before. these systems. were fully lormecd.," This is about an order of magnitude lower than the mean gas density in cores of systems without cooling flows, suggesting that the energy must have been injected before these systems were fully formed."
+ Llowever. ifthe entropy injection took place before the systems collapsed it may. have allected the shock heating elliciency in the low mass systems. reducing the amount of entropy the shocks produced.," However, if the entropy injection took place before the systems collapsed it may have affected the shock heating efficiency in the low mass systems, reducing the amount of entropy the shocks produced."
+ In the extreme case. shock heating could have been totally suppressed in the Lowest mass systems. in which case they would have collapsed aciabatically and their present entropy would essentially be the total injected. entropy.," In the extreme case, shock heating could have been totally suppressed in the lowest mass systems, in which case they would have collapsed adiabatically and their present entropy would essentially be the total injected entropy."
+ The degree to which shocks have increased the entropy in the lowest mass svsteni is not at all clear., The degree to which shocks have increased the entropy in the lowest mass system is not at all clear.
+ However it should be noted that even in the lowest mass svstems in Fie. 5..," However it should be noted that even in the lowest mass systems in Fig. \ref{fig:plot2},"
+ the gas entropy is rising with radius outside the cooling region. suggesting that some shock heating has taken place.," the gas entropy is rising with radius outside the cooling region, suggesting that some shock heating has taken place."
+ Phe resolution of this problem will require detailed. hverodsnamic simulations of the formation of galaxy groups. which is not available at present., The resolution of this problem will require detailed hydrodynamic simulations of the formation of galaxy groups which is not available at present.
+ We therefore consider our previous result to be a lower bound on the excess entropy in these systems and the measured entropy. Hloor (~ 140 keV cm?) in Fig., We therefore consider our previous result to be a lower bound on the excess entropy in these systems and the measured entropy floor $\sim$ 140 keV $^{2}$ ) in Fig.
+ 3. to be an upper bound. applving in the case where shock heating is totally suppressed.," \ref{fig:plot2a} to be an upper bound, applying in the case where shock heating is totally suppressed."
+ For this second. case. Equation 10 results in an even lower value of 110. IbsuSem? for the density at which the entropy is injected.," For this second case, Equation \ref{eq:ne} results in an even lower value of $1\times
+10^{-4}{h_{50}}^{\frac{1}{2}}$ $^{-3}$ for the density at which the entropy is injected."
+ Even if the injection took place outside a collapsed svstem. it must have occurred. after the mean density. of the Universe dropped to 10 tem? as before this. even uniformly distributed gas would be too dense to produce the measured entropy. change from the available energy.," Even if the injection took place outside a collapsed system, it must have occurred after the mean density of the Universe dropped to $\times
+10^{-4}$ $^{-3}$, as before this, even uniformly distributed gas would be too dense to produce the measured entropy change from the available energy."
+" Using the value for the barvon censitv of the Universe derived from 3e Dang nucleosvnthesis. Q,h2,=0.07620.0096. (2).. and the fact that the density of the Universe scales as (1|z)*. it follows that the mean electron density of the Universe would be less than 3.10.tem ? when z<10 and less than 1.10tem ""when 2<7."," Using the value for the baryon density of the Universe derived from Big Bang nucleosynthesis, $\Omega_{b}h_{50}^{2}=0.076\pm0.0096$ \cite{burles99a}, and the fact that the density of the Universe scales as $(1+z)^3$ , it follows that the mean electron density of the Universe would be less than $3\times 10^{-4}$ $^{-3}$ when $z<10$ and less than $1\times
+10^{-4}$ $^{-3}$ when $z<7$."
+ Llenee we conclude that the entropy injection must have aken place alter z~7—10. depending on the assumed amount of shock heating in low mass systems. but. before he galaxy systems have fully formed.," Hence we conclude that the entropy injection must have taken place after $z
+\sim 7-10$, depending on the assumed amount of shock heating in low mass systems, but before the galaxy systems have fully formed."
+ In fact it is likely that he barvons in these svstems have abwavs been in overdense regions of the Universe. and therefore the entropy. injection obably took place at a considerably. lower redshift than his conservative upper limit.," In fact it is likely that the baryons in these systems have always been in overdense regions of the Universe, and therefore the entropy injection probably took place at a considerably lower redshift than this conservative upper limit."
+ If our value of 0.44 keV. per xvwticle for the excess energy is an overestimate. as clüiscussec in Section 5.2. this would have the clleet of lowering the inferred gas density at injection. anc reducing our redshil imit.," If our value of 0.44 keV per particle for the excess energy is an overestimate, as discussed in Section 5.2, this would have the effect of lowering the inferred gas density at injection, and reducing our redshift limit."
+ This all assumes that the gas cannot. expand. as the energy is injected. ie an isocensity assumption.," This all assumes that the gas cannot expand as the energy is injected, i.e an isodensity assumption."
+ This wil » true if the energy injection takes place at high redshift when the density field of the Universe is still fairly smooth and there is effectively. nowhere for the gas to expand. to., This will be true if the energy injection takes place at high redshift when the density field of the Universe is still fairly smooth and there is effectively nowhere for the gas to expand to.
+ Llowever if the energy injection takes place at lower redshif in partially formed: systems. the gas may expand in the potential of the svstem.," However if the energy injection takes place at lower redshift in partially formed systems, the gas may expand in the potential of the system."
+ A more realistic scenario in this case is that the energy is injected. under constant pressure. i.c. it is isobaric.," A more realistic scenario in this case is that the energy is injected under constant pressure, i.e. it is isobaric."
+ In the isobaric case the resulting entropy 'hange will be higher than the isodensity case. since density τους as the injection proceeds.," In the isobaric case the resulting entropy change will be higher than the isodensity case, since density drops as the injection proceeds."
+ To quantify the possible. error. involved. in. assuming mt (he gas does not expand as the energy is injected. we investigate the difference in entropy change between the ‘ase of isodensity and isobaric energy injection.," To quantify the possible error involved in assuming that the gas does not expand as the energy is injected, we investigate the difference in entropy change between the case of isodensity and isobaric energy injection."
+ Theentropy anges for the two cases will be:, Theentropy changes for the two cases will be:
+Damped Lvuiure systems (DLAS). are the rare. high III cohunn density. (Nyy-ZMAN1079 5 7) absorbers seen in spectra taken against distant quasars.,"Damped $\alpha$ systems (DLAS), are the rare, high HI column density $N_{\rm HI} \ga 10^{20}$ $^{-2}$ ) absorbers seen in spectra taken against distant quasars."
+ These svstcuis are the major observed repository of neutral gas at high redshift (2—3) and are thus logical candidates for the precursors of moderu-dav spiral galaxies (Wolfe1988)., These systems are the major observed repository of neutral gas at high redshift $z \sim 3$ ) and are thus logical candidates for the precursors of modern-day spiral galaxies \cite{wolfe88}) ).
+ However. despite more than a decade of svstemiatie study. the structure aud evolution of the absorbers remiadus acf issue of mach coutroversy.," However, despite more than a decade of systematic study, the structure and evolution of the absorbers remains an issue of much controversy."
+ The original optical surveys τς detect DLAS were carried out with the prime motivation of detecting disk galaxies at high redshift (e.g. Wolfe ot al., The original optical surveys to detect DLAS were carried out with the prime motivation of detecting disk galaxies at high redshift (e.g. Wolfe et al.
+ 1986)., 1986).
+ Follow-up observations of the kincmaticy. of the absorbers (as revealed bv their uusaturated. low ionization inetal liue profiles) showed that thes profiles are asvinmmetric iu most DLAS.," Follow-up observations of the kinematics of the absorbers (as revealed by their unsaturated, low ionization metal line profiles) showed that these profiles are asymmetric in most DLAS."
+ The asvunuetricy. can be simply interpreted if the absorption arises in a thick. rapidly rotating disk (Prochaska&Wolfe1997.Prochaska&Wolfe 1998)). consistent with the idea that the absorbers are the progenitors of inassive spiral galaxies.," The asymmetries can be simply interpreted if the absorption arises in a thick, rapidly rotating disk \cite{pw1,pw2}) ), consistent with the idea that the absorbers are the progenitors of massive spiral galaxies."
+ dILowever. it has been shown that the observed line profiles can also be explained bx mereers of sub-ealactic chumps in- hierarchical chistcring scenarios (Tachneltetal. 1998)). by dwarf galaxy. ejecta (Nulsenetal. 1998)) and even by randomly moving clouds in a spherica halo (McDonald&Miralda-Escude 1999)).," However, it has been shown that the observed line profiles can also be explained by mergers of sub-galactic clumps in hierarchical clustering scenarios \cite{haehnelt98}) ), by dwarf galaxy ejecta \cite{nulsen98}) ) and even by randomly moving clouds in a spherical halo \cite{mcdonald99}) )."
+ Further. Ledoux e al. (," Further, Ledoux et al. ("
+1998) fou that the asvuunuetry of the metal line oofiles Is pronoticed. ouly for svstenis with AV.«150 lau 5: this is coutrary o what would be expected if DLAS were indecd massive rotating disks (see. however. Wolfe Prochaska 1998).,"1998) found that the asymmetry of the metal line profiles is pronounced only for systems with $\Delta V < 150$ km $^{-1}$; this is contrary to what would be expected if DLAS were indeed massive rotating disks (see, however, Wolfe Prochaska 1998)."
+ DLAS are known to contain some dust (Pei. Fall AlcMahou 1989) aud the problems of quantitatively accounting for dust depletion make the study of their metallicities and chemical evolution difficult.," DLAS are known to contain some dust (Pei, Fall McMahon 1989) and the problems of quantitatively accounting for dust depletion make the study of their metallicities and chemical evolution difficult."
+ Studies using the abundances of metals like S or Zu. which are oulv slehtly depleted outo dust erains (Pettinietal.1997.Pettiniefal. 1999)). as well as attempts at modelling dust depletion (Vladilo 1998)). iudicate that the absorbers have low metallicities CZτςO.1Z ..) aud do not show mich inetallicitv evolution with redshift.," Studies using the abundances of metals like S or Zn, which are only slightly depleted onto dust grains \cite{pettini97,pettini99}) ), as well as attempts at modelling dust depletion \cite{vladilo98}) ), indicate that the absorbers have low metallicities $Z \la 0.1 Z_\odot$ ) and do not show much metallicity evolution with redshift."
+ Further. DLAS do not show the [o /Fo] οποιο! pattern that characterizes low metallicity halo stars in the Milkv Wavy (Pettini et al.," Further, DLAS do not show the $\alpha$ /Fe] enrichment pattern that characterizes low metallicity halo stars in the Milky Way (Pettini et al."
+ 1999. Molaro et al.," 1999, Molaro et al."
+ 1998. C'enturióun et al.," 1998, Centuriónn et al."
+ 2000)., 2000).
+ This difference in the [|o /Fe|] euricluneut pattern suggests that DLAS have star ormation histories different fro spirals and inore like those of def galaxies., This difference in the $\alpha$ /Fe] enrichment pattern suggests that DLAS have star formation histories different from spirals and more like those of dwarf galaxies.
+"disturbance of the flux tube, we consider a Gaussian function as the initial condition of v, at t=0, namely where Z and c are arbitrary parameters.","disturbance of the flux tube, we consider a Gaussian function as the initial condition of $v_r$ at $t=0$, namely where $\zeta$ and $\sigma$ are arbitrary parameters."
+" Whereas ὅ correspond to the position of the maximum of the excitation, o determines its width."," Whereas $\zeta$ correspond to the position of the maximum of the excitation, $\sigma$ determines its width."
+" In the following simulations, we consider the same model parameters as in Figures 5((c)-(d), i.e., Lp/L=0.2, vo/Vap= 0.1,and zo/L=-—0.25, but use the initial condition given by Equation (27))."," In the following simulations, we consider the same model parameters as in Figures \ref{fig:flow1}( (c)–(d), i.e., $\lp / L = 0.2$, $v_0 / \vap = 0.1$ ,and $z_0 / L = -0.25$, but use the initial condition given by Equation \ref{eq:excitat}) )."
+" To begin with, we take o/L=0.2 and consider different values of Z."," To begin with, we take $\sigma/L = 0.2$ and consider different values of $\zeta$."
+" First we use Z/L=—0.25, so the excitation is mainly confined to the dense prominence region of the flux tube."," First we use $\zeta / L = -0.25$, so the excitation is mainly confined to the dense prominence region of the flux tube."
+" The result of this simulation is displayed in Figure 6((a), which shows the evolution in time of v, at z= 0, whereas Figure 6((b) shows the corresponding wavelet power spectrum."," The result of this simulation is displayed in Figure \ref{fig:arb}( (a), which shows the evolution in time of $v_r$ at $z=0$ , whereas Figure \ref{fig:arb}( (b) shows the corresponding wavelet power spectrum."
+" It is interesting to compare Figures 5((d) and 6((b) to see that, in the present case, the oscillation dynamics is still governed by the fundamental normal mode."," It is interesting to compare Figures \ref{fig:flow1}( (d) and \ref{fig:arb}( (b) to see that, in the present case, the oscillation dynamics is still governed by the fundamental normal mode."
+" We see in Figure 6((a) that there is some contribution of higher harmonics to the behavior of v, in time, although their contribution to the overall oscillation is of very minor importance."," We see in Figure \ref{fig:arb}( (a) that there is some contribution of higher harmonics to the behavior of $v_r$ in time, although their contribution to the overall oscillation is of very minor importance."
+" In addition, the evolution of the amplitude of v, remains qualitatively described by Equation (26)) with n=1."," In addition, the evolution of the amplitude of $v_r$ remains qualitatively described by Equation \ref{eq:fit}) ) with $n=1$."
+" Next, we perform another simulation by taking the same parameters as before but assuming Z/L= 0."," Next, we perform another simulation by taking the same parameters as before but assuming $\zeta / L = 0$ ."
+" In this case, the maximum of the initial excitation is located in the evacuated part of the magnetic tube."," In this case, the maximum of the initial excitation is located in the evacuated part of the magnetic tube."
+" Again, we plot in Figure 6((c) v, at z=O versus time, and in Figure 6((d) the wavelet power spectrum."," Again, we plot in Figure \ref{fig:arb}( (c) $v_r$ at $z=0$ versus time, and in Figure \ref{fig:arb}( (d) the wavelet power spectrum."
+" The behavior of v, in time is substantially different in the present situation compared to the case of Figures 6((α)-- (b).", The behavior of $v_r$ in time is substantially different in the present situation compared to the case of Figures \ref{fig:arb}( (a)--(b).
+" First of all, we see that v, is not governed by the fundamental mode exclusively."," First of all, we see that $v_r$ is not governed by the fundamental mode exclusively."
+" The wavelet power spectrum indicates that the energy from the initial disturbance is mainly deposited to the fundamental mode, but also the first harmonic is excited."," The wavelet power spectrum indicates that the energy from the initial disturbance is mainly deposited to the fundamental mode, but also the first harmonic is excited."
+ The dependence in time of the fundamental mode period is again well described by Equation (23))., The dependence in time of the fundamental mode period is again well described by Equation \ref{eq:period}) ).
+" However, the contribution of the first harmonic to the overall oscillation seems to have disappeared when the thread is located at the center of the magnetic tube."," However, the contribution of the first harmonic to the overall oscillation seems to have disappeared when the thread is located at the center of the magnetic tube."
+" The reason for this result is that the first harmonic eigenfunction has a node at z=0 when the thread is centered, and so the first harmonic does not contribute to the signal displayed in Figure 6((c) in such a case."," The reason for this result is that the first harmonic eigenfunction has a node at $z=0$ when the thread is centered, and so the first harmonic does not contribute to the signal displayed in Figure \ref{fig:arb}( (c) in such a case."
+" On the other hand, it is now difficult to determine the effect of the flow on the amplitude of the oscillation."," On the other hand, it is now difficult to determine the effect of the flow on the amplitude of the oscillation."
+" Finally, we have performed several simulations for different values of c."," Finally, we have performed several simulations for different values of $\sigma$."
+" If the maximum of the excitation is located within the dense part of the flow tube, the results are rather insensitive to σ unless values much smaller than Ly are used."," If the maximum of the excitation is located within the dense part of the flow tube, the results are rather insensitive to $\sigma$ unless values much smaller than $\lp$ are used."
+" In all the cases, the fundamental mode is predominantly excited."," In all the cases, the fundamental mode is predominantly excited."
+" However, the results are more affected by the value of o if the maximum of the excitation is located in the evacuated partof the tube."," However, the results are more affected by the value of $\sigma$ if the maximum of the excitation is located in the evacuated partof the tube."
+" In such a case, the larger c, the more energy isdeposited in the fundamental mode."," In such a case, the larger $\sigma$ the more energy isdeposited in the fundamental mode."
+" On the contrary, as o gets"," On the contrary, as $\sigma$ gets"
+FOAL A. Notably. the regions contained by the FOAL D boundaries at low aud ligh redshift are similar whereas the FOAL A boundaries are significantly different.,"FOM A. Notably, the regions contained by the FOM B boundaries at low and high redshift are similar whereas the FOM A boundaries are significantly different."
+ We do not over-interpret this. uoting that FOX A is less reliable due to spectrophotometric uucertaimties.," We do not over-interpret this, noting that FOM A is less reliable due to spectrophotometric uncertainties."
+" The best-fit model (FOAL DB) has f,~1000 MAÀIVY with ;Ez 200\DIr (note degeneracy for low fij.", The best-fit model (FOM B) has $\tsf \sim 4000$ Myr with $\tin \la 200$ Myr (note degeneracy for low $\tin$ ).
+" Both redshift ranges have sXoft within the 26 levels even though the SER is simular on interchanee of ff; aud f, (sec approximation. Equ. 1)."," Both redshift ranges have $\tin \la \tsf$ within the $\sigma$ levels even though the SFR is similar on interchange of $f\tin$ and $\tsf$ (see approximation, Eqn. \ref{eqn:sfr-model}) )."
+ However. the metallicity evolution is different depending ou whether iufall of new eax or the starformation timescale determines theSER at late times.," However, the metallicity evolution is different depending on whether infall of new gas or the star-formation timescale determines theSFR at late times."
+ The fleure-ofinerit values become degenerate for fi< (galaxies formi quickly incomparison with the star-formation timescale) while maintaining a good ft., The figure-of-merit values become degenerate for $\tin \ll \tsf$ (galaxies form quickly incomparison with the star-formation timescale) while maintaining a good fit.
+" In Figure 5.. f; is set at MOMS and the best-fit regions of logf, versus logτρ are identified for cosmologics CI and C2."," In Figure \ref{fig:zform-versus-ts}, , $\tin$ is set at Myr and the best-fit regions of $\log\tsf$ versus $\log\zform$ are identified for cosmologies $\cal C$ 1 and $\cal C$ 2."
+ At the 3o limits (FOAL A and D). the redshift of formation is ereater than or about 0.65.," At the $\sigma$ limits (FOM A and B), the redshift of formation is greater than or about 0.65."
+ To aid understaudiug of the meaning of our results. Figure 6 shows a variety of star-formation histories that are the within3o limits.," To aid understanding of the meaning of our results, Figure \ref{fig:best-fit-scenarios} shows a variety of star-formation histories that are within the $\sigma$ limits."
+ The first plot shows scenarios with fx de. identified fromFigure 5 (C1).," The first plot shows scenarios with $\tin \ll \tsf$ , i.e., identified fromFigure \ref{fig:zform-versus-ts} $\cal C$ 1)."
+ The second plot (Fig. 6)), The second plot (Fig. \ref{fig:best-fit-scenarios}) )
+" shows ""smoother. scenarios with f; f.. identified"," shows `smoother' scenarios with $\tin \sim \tsf$ , identified"
+classes.,classes.
+ For some classes. low frequency oscillations are observed and the light curves resemble those from numerical simulations of unstable radiation pressure dominated disks based on the standard accretion disk theory.," For some classes, low frequency oscillations are observed and the light curves resemble those from numerical simulations of unstable radiation pressure dominated disks based on the standard accretion disk theory."
+ However. the viscosity prescription in the standard disk theory is ad hoe. and while it may represent approximately the time averages viscosity. 1t is not expected to reproduce the complex time-varying turbulent induced viscosity expected in an aceretion disk.," However, the viscosity prescription in the standard disk theory is ad hoc, and while it may represent approximately the time averages viscosity, it is not expected to reproduce the complex time-varying turbulent induced viscosity expected in an accretion disk."
+ Moreover. there could be different types of instabilities in the disk which could give rise to strong. variability.," Moreover, there could be different types of instabilities in the disk which could give rise to strong variability."
+ Nevertheless. the qualitative similarities between the results of the simulation and observations (Taamerαἱ.1997). suggests that the long term variability of this source is due to deterministic non-linear evolution of an unstable disk. rather than a manifestation of an underlying stochastic process.," Nevertheless, the qualitative similarities between the results of the simulation and observations \citep{Taa97}, suggests that the long term variability of this source is due to deterministic non-linear evolution of an unstable disk, rather than a manifestation of an underlying stochastic process."
+ It is important to determine in a more quantitative and general method. whether the long term variability is indeed due to deterministic non-linear behavior rather than having a stochastic. origin.," It is important to determine in a more quantitative and general method, whether the long term variability is indeed due to deterministic non-linear behavior rather than having a stochastic origin."
+ That would imply that the temporal behavior of the system can be described by à small number of non-linear ordinary differential equations., That would imply that the temporal behavior of the system can be described by a small number of non-linear ordinary differential equations.
+ In other words. the complex non-linear partial differential equations that are known to govern the hydrodynamical flow. can be approximated by a set of ordinary differential equations and hence can be more easily studied and understood.," In other words, the complex non-linear partial differential equations that are known to govern the hydrodynamical flow, can be approximated by a set of ordinary differential equations and hence can be more easily studied and understood."
+ Such an approximation can be obtained. for example. by studying the non-linear time evolution of a dominant linear mode.," Such an approximation can be obtained, for example, by studying the non-linear time evolution of a dominant linear mode."
+ This technique which is briefly described in the next section. was used to derive the equations forthe well known non-linear Lorenz system.," This technique which is briefly described in the next section, was used to derive the equations forthe well known non-linear Lorenz system."
+ A more physical method is to study the time evolution of spatially averaged quantities as in the one zone approximation by Paezynski(1983) for thermo-nuclear flashes on compact objects., A more physical method is to study the time evolution of spatially averaged quantities as in the one zone approximation by \citet{Pac83} for thermo-nuclear flashes on compact objects.
+ While the rewards of obtainingT such approximated equations are far-reaching. these methods are in general not straight forward and require good physical intuition. especially since it is not necessary that they can be obtained for all systems.," While the rewards of obtaining such approximated equations are far-reaching, these methods are in general not straight forward and require good physical intuition, especially since it is not necessary that they can be obtained for all systems."
+ Hence. evidence for the existence of such an approximation. would give the necessary impetus and direction to the study of these complex systems.," Hence, evidence for the existence of such an approximation, would give the necessary impetus and direction to the study of these complex systems."
+ Non-linear time series analysis have been used earlier to analyze X-ray light curves of astrophysical sources., Non-linear time series analysis have been used earlier to analyze X-ray light curves of astrophysical sources.
+ Lehtoetal.(1993) used the correlation dimension technique to analyze EXOSAT light curves of several AGN. and found that one. NGC 4051. showed signs of low dimensional chaos.," \cite{Leh93}
+ used the correlation dimension technique to analyze EXOSAT light curves of several AGN, and found that one, NGC 4051, showed signs of low dimensional chaos."
+ Such analysis have been undertaken on noise filtered satellite data of Cyg X-1 (Unnoetal.1990) and on EXOSAT data of Her X-1 (Vogesefαἱ.1987;Norris&Matilsky1989) and ASCA data of AGN ARK 567 (Gliozzietaf.2002).," Such analysis have been undertaken on noise filtered satellite data of Cyg X-1 \citep{Unn90} and on EXOSAT data of Her X-1 \citep{Vog87,Nor89} and ASCA data of AGN ARK 567 \citep{Gli02}."
+. In an earlier work. we used a modification of this technique to study RXTE observations of GRS 1915-105 and found evidence that for four of the twelve temporal classes. the system was consistent with harboring a low-dimensional attractor (Misraetal. 2004).," In an earlier work, we used a modification of this technique to study RXTE observations of GRS 1915+105 and found evidence that for four of the twelve temporal classes, the system was consistent with harboring a low-dimensional attractor \citep{Mis04}."
+ However. a positive. result for the correlation dimension analysis. although highly suggestive. is not conclusive evidence that the light curve of these systems ts due to a low dimensional chaotic system.," However, a positive result for the correlation dimension analysis, although highly suggestive, is not conclusive evidence that the light curve of these systems is due to a low dimensional chaotic system."
+ The results need to be counter checked using other non-linear techniques and compared with surrogate data analysis., The results need to be counter checked using other non-linear techniques and compared with surrogate data analysis.
+ Thus. in this work. we analyze the different temporal patterns exhibited by GRS 19154105 using correlation dimension analysis and the singular value decomposition technique.," Thus, in this work, we analyze the different temporal patterns exhibited by GRS 1915+105 using correlation dimension analysis and the singular value decomposition technique."
+ For each analysis. we undertake surrogate data analysis as a counter check.," For each analysis, we undertake surrogate data analysis as a counter check."
+ To facilitate better physical understanding. we draw analogies between the results obtained for GRS 19154105 and those for a well known deterministic non-linear system.," To facilitate better physical understanding, we draw analogies between the results obtained for GRS 1915+105 and those for a well known deterministic non-linear system."
+ It should be emphasized that proving the presence of non-linear dynamics using a finite time series with mathematical certainty is in the very least difficult and perhaps even not a well defined problem., It should be emphasized that proving the presence of non-linear dynamics using a finite time series with mathematical certainty is in the very least difficult and perhaps even not a well defined problem.
+ Our motivation here. is not to make model independent and quantitative non-linear diagnosis of the light curve. which as mentioned above is difficult and ambiguous.," Our motivation here, is not to make model independent and quantitative non-linear diagnosis of the light curve, which as mentioned above is difficult and ambiguous."
+ The goal here is to find out if there are features in the light curve which indicate (but may not necessarily rigorously prove) that the temporal behavior of the black hole anystem GRS 1915+105. can be described as a set of ordinary on-linear differential equations.," The goal here is to find out if there are features in the light curve which indicate (but may not necessarily rigorously prove) that the temporal behavior of the black hole system GRS 1915+105, can be described as a set of ordinary non-linear differential equations."
+ Obtaining such equations from first principles would be a major break through in our understanding of accretion disks around black holes and thus any indication that such equations may exist would be useful in formulating them., Obtaining such equations from first principles would be a major break through in our understanding of accretion disks around black holes and thus any indication that such equations may exist would be useful in formulating them.
+" In the next section. the well known non-linear system. ""Lorenz"". is introduced and some of the different types of non-linear behavior that the system can exhibit are described."," In the next section, the well known non-linear system, “Lorenz”, is introduced and some of the different types of non-linear behavior that the system can exhibit are described."
+ In 33. some standard non-linear time series analysis is described and as an example applied to the Lorenz system.," In 3, some standard non-linear time series analysis is described and as an example applied to the Lorenz system."
+ In S44. these techniques are applied to the observed light curves of GRS 1915-105 and in 355 the results are summarized and discussed.," In 4, these techniques are applied to the observed light curves of GRS 1915+105 and in 5 the results are summarized and discussed."
+ The Lorenz model (Lorenz1963) was developed from the Navier-Stokes hydrodynamic equations for the Rayleigh-Bénnard flow. which deseribes the two-dimensional convection of an incompressible fluid in a cell which has a higher temperature at bottom and a lower temperature at top.," The Lorenz model \citep{Lor63} was developed from the Navier-Stokes hydrodynamic equations for the Rayleigh-Bénnard flow, which describes the two-dimensional convection of an incompressible fluid in a cell which has a higher temperature at bottom and a lower temperature at top."
+ The essential idea is to choose a dominant linear mode that satisfies the boundary condition. and substitute this mode back into the hydrodynamic equations to obtain the temporal evolution of the mode as a set of ordinary non-linear differential equations.," The essential idea is to choose a dominant linear mode that satisfies the boundary condition, and substitute this mode back into the hydrodynamic equations to obtain the temporal evolution of the mode as a set of ordinary non-linear differential equations."
+ The choice of the dominant mode is rather arbitrary and hence makes this procedure possible only by physical intuition and/or prior knowledge of the solution from experiments or numerical simulations., The choice of the dominant mode is rather arbitrary and hence makes this procedure possible only by physical intuition and/or prior knowledge of the solution from experiments or numerical simulations.
+ In spite of the physical (and in particular) hydrodynamical origin of the Lorenz model. it is prudent to be careful about drawing analogies between it and other complex hydrodynamical flows like accretion.," In spite of the physical (and in particular) hydrodynamical origin of the Lorenz model, it is prudent to be careful about drawing analogies between it and other complex hydrodynamical flows like accretion."
+ For this work. it is sufficient to state that the Lorenz model is a mathematical set of non-linear equations which have been derived from non-linear partial differential equations. using approximations which may or may not be valid.," For this work, it is sufficient to state that the Lorenz model is a mathematical set of non-linear equations which have been derived from non-linear partial differential equations, using approximations which may or may not be valid."
+" These equations turn out to be There are three fixed points. or steady state values. of the system: (X,.¥,.Z,)=(0.0.0)— and (£y/|[8/3)[R-1].E|8/3||R-1)."," These equations turn out to be There are three fixed points, or steady state values, of the system: $ (X_o,Y_o,Z_o) = (0,0,0)$ and $( \pm \sqrt{[8/3][R-1]}, \pm \sqrt{[8/3][R-1]}, [R-1])$."
+ R is a control parameter whose value governsD]. Rthe system's behavior which is obtained by solving numerically these differential equations., $R$ is a control parameter whose value governs the system's behavior which is obtained by solving numerically these differential equations.
+ For |<R«14. the fixed point at the origin ts unstable. while the other two are stable.," For $1 < R < 14$, the fixed point at the origin is unstable, while the other two are stable."
+ The system evolves towards one of the stable fixed points depending on the initial conditions., The system evolves towards one of the stable fixed points depending on the initial conditions.
+ The temporal behavior is transitory in nature., The temporal behavior is transitory in nature.
+ For Α> 14. all three fixed points are unstable.," For $R > 14$ , all three fixed points are unstable."
+ For large values, For large values
+no quantitative predictions have so far been made for colour changes. it is plausible that in a disc with a strong temperature and hence colour gradient these avalanches will produce chromatic ellects as the flux varies.,"no quantitative predictions have so far been made for colour changes, it is plausible that in a disc with a strong temperature and hence colour gradient these avalanches will produce chromatic effects as the flux varies."
+ The problem here is that any variability would. be on a very. short timescale. and inconsistent with the observations of optical variations.," The problem here is that any variability would be on a very short timescale, and inconsistent with the observations of optical variations."
+ Definitive answers to these points must await model predictions for colour changes in the dilferent types of accretion disc., Definitive answers to these points must await model predictions for colour changes in the different types of accretion disc.
+ An alternative explanation for the elfects shown in Fig., An alternative explanation for the effects shown in Fig.
+ 5 comes [from microlensing.," \ref{fig:fig5}
+ comes from microlensing."
+ In this picture. the observed variation is produced by the gravitational microlensing cllect of a population of planctary or sub-stellar mass. bodies along the line of sight to the quasar (Llawkins1996).," In this picture, the observed variation is produced by the gravitational microlensing effect of a population of planetary or sub-stellar mass bodies along the line of sight to the quasar \cite{h96}."
+. Although the microlensing of a point source produces a strictly achromatic light curve. for an accretion disc with a racial temperature eracicnt this is not necessarily so.," Although the microlensing of a point source produces a strictly achromatic light curve, for an accretion disc with a radial temperature gradient this is not necessarily so."
+ For example. if the nucleus is a compact blue source unresolved bv the characteristic mass of the microlenses. but. in the red the source is less compact and. partially resolved: by the lensing objects. colour changes may be observed as the source is microlensed.," For example, if the nucleus is a compact blue source unresolved by the characteristic mass of the microlenses, but in the red the source is less compact and partially resolved by the lensing objects, colour changes may be observed as the source is microlensed."
+ “Phe cllect of this can be seen in the results of numerical simulation of microlensing of unresolved and partially resolved sources (Lewisctal..1993:Schneider&WeissLOST) where the smaller power for the resolved sources is well illustrated.," The effect of this can be seen in the results of numerical simulation of microlensing of unresolved and partially resolved sources \cite{l93,s87} where the smaller power for the resolved sources is well illustrated."
+ The application of this model to the microlensing of an accretion disc with a compact blue nucleus and a strong radial colour gradient. would be to produce less power in the red than the blue fluctuations. providing that the emitting region of the disc is comparable with the Einstein radius of the lenses.," The application of this model to the microlensing of an accretion disc with a compact blue nucleus and a strong radial colour gradient would be to produce less power in the red than the blue fluctuations, providing that the emitting region of the disc is comparable with the Einstein radius of the lenses."
+ These ideas have been put on a firmer and more quantitative footing in a recent paper by Yonehara et al. (, These ideas have been put on a firmer and more quantitative footing in a recent paper by Yonehara et al. (
+1999).,1999).
+ They. carry out. numerical simulations of the microlensing of acerction disks bv à compact body. and show that for a standard optically thick aceretion disc with a racial temperature eracient colour changes will be seen. whereas for an optically thin (advection dominated) disc where most of the emission takes place at the inner edge. the variation will be achromatic.," They carry out numerical simulations of the microlensing of accretion disks by a compact body, and show that for a standard optically thick accretion disc with a radial temperature gradient colour changes will be seen, whereas for an optically thin (advection dominated) disc where most of the emission takes place at the inner edge, the variation will be achromatic."
+ Yonehara οἱ al. (, Yonehara et al. (
+"1999) base their modelling on the multiply lensed quasar system, Q2237|0805.",1999) base their modelling on the multiply lensed quasar system Q2237+0305.
+ The individual images in this system have been shown to vary achromatically when microlensed (Corriganetal.1991:Houde&Racine1994). which would imply an optically thin disc.," The individual images in this system have been shown to vary achromatically when microlensed \cite{co91,hr94}
+ which would imply an optically thin disc."
+ Llowever. to account for the colour changes implied in Fig.," However, to account for the colour changes implied in Fig."
+ 5 and illustrated in the light curves. an aceretion clise of greater optical depth would be required.," \ref{fig:fig5} and illustrated in the light curves, an accretion disc of greater optical depth would be required."
+ There is one other aspect of microlensing which has relevance to the quasar light curves. especially those in Fig. 2..," There is one other aspect of microlensing which has relevance to the quasar light curves, especially those in Fig. \ref{fig:fig2}."
+ In a situation where the accretion disc has a blue compact core embedded. in receler outerparts. then lensing can produce cusp-like features from the unresolved. central region which are smoothed. out in the resolved. red. light source.," In a situation where the accretion disc has a blue compact core embedded in redder outerparts, then lensing can produce cusp-like features from the unresolved central region which are smoothed out in the resolved red light source."
+ The idea can be seen from the synthetic light curves for more and less resolved. sources in Schneider \Weiss (1987)., The idea can be seen from the synthetic light curves for more and less resolved sources in Schneider Weiss (1987).
+ This provides an explaination for the way sharp blue features become smoother in the red in Fig. 5.., This provides an explaination for the way sharp blue features become smoother in the red in Fig. \ref{fig:fig5}.
+ Lt is clear from examination of Figs., It is clear from examination of Figs.
+ 1-4 that colour changes can occur in quasar light curves., 1-4 that colour changes can occur in quasar light curves.
+ This result. is consistent with earlier work for Sevlert galaxies (Claveletal.1991) and quasars (Cristianictal.LOO7).. but also shows that there are apparently cilferent modes of colour change.," This result is consistent with earlier work for Seyfert galaxies \cite{c91} and quasars \cite{c97}, but also shows that there are apparently different modes of colour change."
+ We tentatively identify the following patterns: Lt is quite possible that no single model will be found that can account for such a civerse range of features in the light curves., We tentatively identify the following patterns: It is quite possible that no single model will be found that can account for such a diverse range of features in the light curves.
+ On the other hand. theories of quasar variability should make predictions about colour changes. which may well be similar ancl require detailed comparison with goocl data to distinguish them.," On the other hand, theories of quasar variability should make predictions about colour changes, which may well be similar and require detailed comparison with good data to distinguish them."
+ Fig., Fig.
+ 5 implies that even with a verv simple mocel for the underlying galaxy. the mean power spectra for του and. blue light can be brought into coincidence.," \ref{fig:fig5} implies that even with a very simple model for the underlying galaxy, the mean power spectra for red and blue light can be brought into coincidence."
+ Although it is clear that the presence of an undoerlving red galaxy plavs a significant role in AGN colour changes. it cannot account for all the features seen in the tsvo-colour light. curves.," Although it is clear that the presence of an underlying red galaxy plays a significant role in AGN colour changes, it cannot account for all the features seen in the two-colour light curves."
+ Examination of Fig., Examination of Fig.
+ 2. shows that there are features in the light curves which cannot be reconciled in this wav., \ref{fig:fig2} shows that there are features in the light curves which cannot be reconciled in this way.
+ To be more specific. certain cusp-like features in the blue light curves appear as if smoothed out in the red. although there is twpically little overall change in. colour between maximum and minimum light.," To be more specific, certain cusp-like features in the blue light curves appear as if smoothed out in the red, although there is typically little overall change in colour between maximum and minimum light."
+ At present. theoretical understanding of aceretion disc instabilities is not sullicienth well developed: that such detailed features can be modelled.," At present, theoretical understanding of accretion disc instabilities is not sufficiently well developed that such detailed features can be modelled."
+ It is certainly. possible that an event in the blue centre ofa nucleus could propagate into the redder outerparts and become. blurred in. the process. but the apparent symmetry of the colour changes imposes constraints on such a mechanism.," It is certainly possible that an event in the blue centre of a nucleus could propagate into the redder outerparts and become blurred in the process, but the apparent symmetry of the colour changes imposes constraints on such a mechanism."
+ Ln disc instability models where the emission is localised to a particular region of the disc. there may. well be colour changes associated with the outburst. but there is no reason to believe that the structure of the event will be dillerent in red ancl blue passbancds.," In disc instability models where the emission is localised to a particular region of the disc, there may well be colour changes associated with the outburst, but there is no reason to believe that the structure of the event will be different in red and blue passbands."
+ Microlensing does provide a possible explanation both for overall changes in colour. ancl for the smearing out in the rec of rapid brightness changes in the blue.," Microlensing does provide a possible explanation both for overall changes in colour, and for the smearing out in the red of rapid brightness changes in the blue."
+ This effect relies on an aecretion dise of comparable size to the Einstein radii of the lenses. but given this it is a prediction of microlensing," This effect relies on an accretion disc of comparable size to the Einstein radii of the lenses, but given this it is a prediction of microlensing"
+"conditions, we set α=1 to make the satellite smaller and hence to minimise satellite mass loss owing to initial adjustments when it is first placed in the external potential.","conditions, we set $\alpha=1$ to make the satellite smaller and hence to minimise satellite mass loss owing to initial adjustments when it is first placed in the external potential."
+ The tidal is the radius where r;=27/3., The tidal is the radius where $r_{t}=2x_{e}/3$.
+ This is the radius of the critical potential surface perpendicular to the direction toward the host halo centre so it is the maximum radius that a spherical satellite halo can have and not extend beyond the critical potential surface in any direction., This is the radius of the critical potential surface perpendicular to the direction toward the host halo centre so it is the maximum radius that a spherical satellite halo can have and not extend beyond the critical potential surface in any direction.
+ We plot the density profiles of the truncated satellite halo models in Fig. 2.., We plot the density profiles of the truncated satellite halo models in Fig. \ref{fig:models}.
+ To obtain the final density profiles for the satellite halo models truncated at Φε and Τε we apply the Eddington inversion procedure., To obtain the final density profiles for the satellite halo models truncated at $x_{e}$ and $r_{t}$ we apply the Eddington inversion procedure.
+" However, we do not apply this procedure when we truncate at the Roche limit since it would change the outer density, making it differ from that of the host halo, and it would no longer be the Roche limit."," However, we do not apply this procedure when we truncate at the Roche limit since it would change the outer density, making it differ from that of the host halo, and it would no longer be the Roche limit."
+ Fig., Fig.
+" 2 shows that at the given tidal distance of 0.4, the satellite truncated at the Roche limit is the largest and the satellite truncated at Τε is the smallest."," \ref{fig:models} shows that at the given tidal distance of $0.4$, the satellite truncated at the Roche limit is the largest and the satellite truncated at $r_{t}$ is the smallest."
+ Fig., Fig.
+ 3 shows the evolution of mass from circular orbit simulations for the three satellites shown in Fig., \ref{fig:massloss.Circ} shows the evolution of mass from circular orbit simulations for the three satellites shown in Fig.
+ 2 (see refsec:circ for a detailed discussion).," \ref{fig:models}
+ (see \\ref{sec:circ} for a detailed discussion)."
+ All three satellites show continuous mass loss., All three satellites show continuous mass loss.
+ The amount of mass loss correlates with the satellite size: the satellite truncated at the Roche limit loses the largest mass fraction and the satellite truncated at Τι loses the least mass., The amount of mass loss correlates with the satellite size: the satellite truncated at the Roche limit loses the largest mass fraction and the satellite truncated at $r_{t}$ loses the least mass.
+ We choose ze for our fiducial truncation radius on physical grounds., We choose $x_e$ for our fiducial truncation radius on physical grounds.
+ Ze is the transition point beyond which satellite particles on a circular orbit become unbound., $x_e$ is the transition point beyond which satellite particles on a circular orbit become unbound.
+" At the Roche limit radius for an NFW halo, the host halo potential dominates the gravitational potential of the satellite."," At the Roche limit radius for an NFW halo, the host halo potential dominates the gravitational potential of the satellite."
+" In contrast, using the tidal cut-off radius, r;, is a sensible choice for globular clusters, which have already orbited many times around a galaxy and have already been severely truncated, but using τε could underestimate a satellite halo's size since it has made only a few complete orbits."," In contrast, using the tidal cut-off radius, $r_{t}$, is a sensible choice for globular clusters, which have already orbited many times around a galaxy and have already been severely truncated, but using $r_t$ could underestimate a satellite halo's size since it has made only a few complete orbits."
+" Hence, we restrict our study to initial satellite haloes that are truncated at xe."," Hence, we restrict our study to initial satellite haloes that are truncated at $x_{e}$."
+" As mentioned in refsec:intro,, resonant interactions are expected to dominate the tidal heating."," As mentioned in \\ref{sec:intro}, resonant interactions are expected to dominate the tidal heating."
+" To accurately reproduce these resonant interactions, N-body simulations need to satisfy several numerical criteria."," To accurately reproduce these resonant interactions, N-body simulations need to satisfy several numerical criteria."
+ Weinberg&Katz(2007a) proposed explicit requirements for these criteria., \citet{WK07a} proposed explicit requirements for these criteria.
+" First, a sufficient number of particles are required to cover the phase space near resonance (hereafter, the criterion)."," First, a sufficient number of particles are required to cover the phase space near resonance (hereafter, the criterion)."
+" Second, a sufficient number of particles are required to reduce artificial diffusion."," Second, a sufficient number of particles are required to reduce artificial diffusion."
+" Artificial diffusion can come from both the gravitational forces of individual particles (hereafter, the criterion) and the potential fluctuations caused by Poisson noise (hereafter, the criterion)."," Artificial diffusion can come from both the gravitational forces of individual particles (hereafter, the criterion) and the potential fluctuations caused by Poisson noise (hereafter, the criterion)."
+" Besides these particle number criteria, the potential solver must also be able to resolve the scale of the resonant potential and the realised phase space distribution must cover this region."," Besides these particle number criteria, the potential solver must also be able to resolve the scale of the resonant potential and the realised phase space distribution must cover this region."
+" In our study, we will verify that our simulations satisfy all of these criteria."," In our study, we will verify that our simulations satisfy all of these criteria."
+" Although a simulation can correctly reproduce resonant interactions, it is hard to provide a detailed accounting of the individual resonances."," Although a simulation can correctly reproduce resonant interactions, it is hard to provide a detailed accounting of the individual resonances."
+" For intuitive guidance, the resonant interaction effects can be investigated using perturbation theory."," For intuitive guidance, the resonant interaction effects can be investigated using perturbation theory."
+ We use a numerical perturbation theory calculation as in Weinberg&Katz(2007a) to investigate resonant interaction effects., We use a numerical perturbation theory calculation as in \citet{WK07a} to investigate resonant interaction effects.
+" In this approach, one begins with the numerical integration of the perturbed orbit-averaged Hamilton equations in a fixed potential for the entire phase space."," In this approach, one begins with the numerical integration of the perturbed orbit-averaged Hamilton equations in a fixed potential for the entire phase space."
+ This step may be followed by an update of the gravitational potential., This step may be followed by an update of the gravitational potential.
+" Since this perturbation calculation uses the same satellite halo realisation, comparison with the N-body simulation result is straightforward."," Since this perturbation calculation uses the same satellite halo realisation, comparison with the N-body simulation result is straightforward."
+ A comparison between the results of the N-body simulation and those of, A comparison between the results of the N-body simulation and those of
+higher latitudes (see the discussion in. 2)). which gives rise to two separate lines in the length vs width plots.,"higher latitudes (see the discussion in \citealt{wil87}) ), which gives rise to two separate lines in the length vs width plots."
+ For a small source surface (see Fie. 2)), For a small source surface (see Fig. \ref{lw_small}) )
+ the longer Leld lines on BP Tau are typically wider than those on V2129 Oph., the longer field lines on BP Tau are typically wider than those on V2129 Oph.
+ This rellects the strength of the dipole components in the two stars. which is about J4-times stronger on BP ‘Tau than V2129 Oph (stars with a strong cdipolar field component would typically have wider field lines. connecting the dilferent. polarity poles in opposite hemispheres). and also the dominantly octupolar nature of V2129 Oph's field.," This reflects the strength of the dipole components in the two stars, which is about 4-times stronger on BP Tau than V2129 Oph (stars with a strong dipolar field component would typically have wider field lines, connecting the different polarity poles in opposite hemispheres), and also the dominantly octupolar nature of V2129 Oph's field."
+ In both cases. however. the fields are more complex than a dipole.," In both cases, however, the fields are more complex than a dipole."
+ For the case of a large source surface (see Fig. 3)), For the case of a large source surface (see Fig. \ref{lw_big}) )
+ the Ποια structure of BP Tau follows a similar trend to the dipole field. as do the longest field lines on V2129 Oph.," the field structure of BP Tau follows a similar trend to the dipole field, as do the longest field lines on V2129 Oph."
+ However. many of the smaller scale field lines on V2129 Oph are not as wide as the dipolar field lines.," However, many of the smaller scale field lines on V2129 Oph are not as wide as the dipolar field lines."
+ Fhis suggests that the smaller scale field on V2129 Oph is complex ancl multi-polar with the field strength decaying more rapidly with height than on BP Tau: we return to this point in £55., This suggests that the smaller scale field on V2129 Oph is complex and multi-polar with the field strength decaying more rapidly with height than on BP Tau; we return to this point in 5.
+ l'or V2129 Oph the smaller scale field (sce Fig. 2)), For V2129 Oph the smaller scale field (see Fig. \ref{lw_small}) )
+ is more closely matched to an, is more closely matched to an
+From the wave-structure of ΤΗ11) solver (Fig.D2)). it is clear that contact. Alfvénn and fast magnetosonic waves are resolved.,"From the wave-structure of HLLD solver \ref{fig:HLLD}) ), it is clear that contact, Alfvénn and fast magnetosonic waves are resolved."
+ The Uuxes at the interface for this solver are given with the following formulae The wave speeds are Sp=ΠΠονε.Οι)ὃς and Sy=max(esg.tea)|e. where ὃς=max(ecpesi) is the maximal signal speed in left or right state.," The fluxes at the interface for this solver are given with the following formulae The wave speeds are $S_L = \min(v_{xL}, v_{xR}) - c_{\rm s}$ and $S_R = \max(v_{xL},
+v_{xR}) + c_{\rm s}$, where $c_{\rm s} = \max(c_{{\rm s} L}, c_{{\rm s} R})$ is the maximal signal speed in left or right state."
+ Ehe speed of the middle wave is defined by ?..," The speed of the middle wave is defined by \cite{2005JCoPh.208..315M},"
+ , 
+"parameters, such as n, or 7, which couple across large multipole ranges.","parameters, such as $n_s$ or $\tau$, which couple across large multipole ranges."
+ Some caution is appropriate regarding bias in the recovery of the function., Some caution is appropriate regarding bias in the recovery of the function.
+ The function is a quadratic function of the beam., The function is a quadratic function of the beam.
+ Therefore a procedure which reconstructs an unbiased estimate of the beam can produce a biased estimate of the function., Therefore a procedure which reconstructs an unbiased estimate of the beam can produce a biased estimate of the function.
+" For our beam recovery techniques, we in practice detect little bias in the ensemble of functions for channels at 100 GHz and below."," For our beam recovery techniques, we in practice detect little bias in the ensemble of functions for channels at 100 GHz and below."
+" In higher bands, with smaller beams and higher signal-to-noise, the mean of the Monte Carlo ensemble (per /) slowly oscillates near, but slightly above or below the true function."," In higher bands, with smaller beams and higher signal-to-noise, the mean of the Monte Carlo ensemble (per $l$ ) slowly oscillates near, but slightly above or below the true function."
+" In principle a correction to this bias can be folded into the power spectrum analysis, but here we allow the bias to persist, to see if it has any effect in the cosmological analysis."," In principle a correction to this bias can be folded into the power spectrum analysis, but here we allow the bias to persist, to see if it has any effect in the cosmological analysis."
+ Here we compile results for beam fitting and the subsequent errors imposed onto the CMB power spectrum., Here we compile results for beam fitting and the subsequent errors imposed onto the CMB power spectrum.
+" We take a single Jupiter crossing as our baseline case for beam fitting, and consider a case with destriped 1/f noise, with no contribution from large-scale (|< 250) CMB. ("," We take a single Jupiter crossing as our baseline case for beam fitting, and consider a case with destriped $1/f$ noise, with no contribution from large-scale $l<250$ ) CMB. ("
+Confusion from signals on the sky can be removed because every region of the sky is re-observed at 7-month intervals).,Confusion from signals on the sky can be removed because every region of the sky is re-observed at 7-month intervals).
+" For each frequency band, we use one model LFI or HFI beam."," For each frequency band, we use one model LFI or HFI beam."
+" Unless noted, we assume nonlinearities in the detector response have been corrected before processing."," Unless noted, we assume nonlinearities in the detector response have been corrected before processing."
+ The errors on the recovered model parameters are shown in Table 3GHz)., The errors on the recovered model parameters are shown in Table \ref{tab:vanillaparameters} .
+" The quality of the parameter recovery is exceptionally good, due to the very high signal-to-noise on Jupiter."," The quality of the parameter recovery is exceptionally good, due to the very high signal-to-noise on Jupiter."
+" Comparing channels, the relative quality of the fits is a complicated interaction between Jupiter’s signal, the detector’s noise, and the beam size (small beams concentrate the signal but yield fewer useful data points)."," Comparing channels, the relative quality of the fits is a complicated interaction between Jupiter's signal, the detector's noise, and the beam size (small beams concentrate the signal but yield fewer useful data points)."
+" Except for 353 GHz, the quality of the fits tend to improve with increasing frequency band, largely due to the increase in Jupiter’s signal at high frequencies."," Except for 353 GHz, the quality of the fits tend to improve with increasing frequency band, largely due to the increase in Jupiter's signal at high frequencies."
+ Repeated observations of the planets during subsequent surveys reduce the errors roughly as expected for independent observations., Repeated observations of the planets during subsequent surveys reduce the errors roughly as expected for independent observations.
+" The errors at 353 GHz, although quite small, are puzzlingly larger than the errors at 217 GHz and 545 GHz, especially when fitting for a time constant."," The errors at 353 GHz, although quite small, are puzzlingly larger than the errors at 217 GHz and 545 GHz, especially when fitting for a time constant."
+" This seems to be due to the x? minimization getting caught in local minima away from the global minimum, which creates a population of outliers in the Monte Carlo ensemble of fitted parameters, driving up the errors."," This seems to be due to the $\chi^2$ minimization getting caught in local minima away from the global minimum, which creates a population of outliers in the Monte Carlo ensemble of fitted parameters, driving up the errors."
+ These outliers represent ~5% of samples and are seen only in the simulated 353 GHz beams., These outliers represent $\sim 5\%$ of samples and are seen only in the simulated 353 GHz beams.
+" Although the other beams span a large range of beam sizes, signal-to-noise, and time constant duration, none show any obvious population of outliers."," Although the other beams span a large range of beam sizes, signal-to-noise, and time constant duration, none show any obvious population of outliers."
+" As noted in Fig. 5,,"," As noted in Fig. \ref{fig:whats_with_353},"
+ several 353 GHz beams show this behavior., several 353 GHz beams show this behavior.
+" The outliers do not fall into any well-separated population which make them easy to cut, and we have not found a way to eliminate them robustly."," The outliers do not fall into any well-separated population which make them easy to cut, and we have not found a way to eliminate them robustly."
+" The 353 GHz case (signal, noise, and time constant) run with the similarly-sized 217 GHz beam show a large population of outliers."," The 353 GHz case (signal, noise, and time constant) run with the similarly-sized 217 GHz beam show a large population of outliers."
+" Visual inspection yields nothing obviously wrong with the 353 GHz beams, which are formatted the same way as the other HFI beams, and the timelines the 353 GHz beams produce in our pipeline are also unremarkable, so it remains unclear why these outliers occur."," Visual inspection yields nothing obviously wrong with the 353 GHz beams, which are formatted the same way as the other HFI beams, and the timelines the 353 GHz beams produce in our pipeline are also unremarkable, so it remains unclear why these outliers occur."
+" Even with the outliers, the beam fits for 353 are still quite good, only suffering by comparison to the spectacular results from the neighboring channels."," Even with the outliers, the beam fits for 353 are still quite good, only suffering by comparison to the spectacular results from the neighboring channels."
+" For all channels, the corresponding errors on the power spectrum due to the function uncertainty are depicted in Fig. 6.."," For all channels, the corresponding errors on the power spectrum due to the function uncertainty are depicted in Fig. \ref{fig:tf-par}."
+" Our ensemble of functions presents a slightly biased estimate of the truewindow function (section 2.8)), so instead of a standard deviation, we plot a contour which bounds the error for of the functions in our ensemble, including both bias and dispersion."," Our ensemble of functions presents a slightly biased estimate of the true function (section \ref{sec:tf}) ), so instead of a standard deviation, we plot a contour which bounds the error for of the functions in our ensemble, including both bias and dispersion."
+ Errors are strongly correlated between multipoles., Errors are strongly correlated between multipoles.
+" Depending on multipole, prior knowledge of the detector time constant improves the errors on HFI channels 100—353 GHz by a factor up to 2-3."," Depending on multipole, prior knowledge of the detector time constant improves the errors on HFI channels 100–353 GHz by a factor up to 2–3."
+ The errors on the higher frequency channels are less affected., The errors on the higher frequency channels are less affected.
+" In general, the recovery of the function for the higher frequency bands is exquisite, but this is a result of the rigidity of the model, due to thesmall number of parameters."," In general, the recovery of the function for the higher frequency bands is exquisite, but this is a result of the rigidity of the model, due to thesmall number of parameters."
+"poloidal diameters in arcseconds, and 04,=33"" at v=230 GHz.","poloidal diameters in arcseconds, and $\theta_\mathrm{mb}=33\arcsec$ at $\nu=230$ GHz."
+" We adopted an average Venus brightness temperatureT; from of 2872:20 K. For all other planets’ Tj, we used the JCMT online databasq!]."," We adopted an average Venus brightness temperature$T_b$ from of $287\pm20$ K. For all other planets' $T_b$, we used the JCMT online ."
+ We derived a ratio Ίνροι/ηΗροι of the two IF’s mean main beam efficiencies for both nights of 1.24+0.04., We derived a ratio $\eta_\mathrm{Vpol}/\eta_\mathrm{Hpol}$ of the two IF's mean main beam efficiencies for both nights of $1.24\pm0.04$.
+ We used this ratio to scale the Hpol polarization's antenna temperature up to match the level of the Vpol polarization's antenna temperature., We used this ratio to scale the Hpol polarization's antenna temperature up to match the level of the Vpol polarization's antenna temperature.
+" After fitting a baseline to each spectrum, we averaged the sum of the scaled Hpol brightness temperatures and the Vpol brightness temperatures: 1(TA(Hpol,scaled)+TA(Vpol))=74(sum)."," After fitting a baseline to each spectrum, we averaged the sum of the scaled Hpol brightness temperatures and the Vpol brightness temperatures: $\frac{1}{2}\langle T_A^\star(\mathrm{Hpol, scaled})+T_A^\star(\mathrm{Vpol})\rangle=T_A^\star(\mathrm{sum})$."
+ Thus we computed the corrected main beam temperature as The average beam efficiencies were (7Hpo1)=0.68+0.01 and (7ypo1)=0.88+0.01 for both nights., Thus we computed the corrected main beam temperature as The average beam efficiencies were $\langle\eta_\mathrm{Hpol}\rangle=0.68\pm0.01$ and $\langle\eta_\mathrm{Vpol}\rangle=0.88\pm0.01$ for both nights.
+" Since we had null detections for our two sources, we must assume a line-width to calculate upper limits on the integrated intensity"," Since we had null detections for our two sources, we must assume a line-width to calculate upper limits on the integrated intensity."
+ We assumed typcial a line-width of Av—10 km s! (=7.69 MHz)., We assumed typcial a line-width of $\Delta\nu=10$ km $^{-1}$ $=7.69$ MHz).
+" If we assume the CO line is well described by a Gaussian line shape, then the uncertainty in the integrated intensity is given by where o; and Av are the CO line fluxes and the the full width at half maximum (FWHM) and Ava, is the channel spacing 0.33 km s!; see Appendix I ofprep."," If we assume the CO line is well described by a Gaussian line shape, then the uncertainty in the integrated intensity is given by where $\sigma_I$ and $\Delta v$ are the CO line fluxes and the the full width at half maximum (FWHM) and $\Delta v_\mathrm{ch}$ is the channel spacing 0.33 km $^{-1}$; see Appendix I of."
+].. The observations are summarized in Table Bl., The observations are summarized in Table \ref{obssummary}.
+ The main-beam corrected spectra of our observations are shown in Figure [I]., The main-beam corrected spectra of our observations are shown in Figure \ref{spec}.
+" While 9’ is a rough spatial scale for comparison to the 33” beam of the SMT, and since we did not detect a !?CO line in any of our sources, the on-cloud results from SMT are consistent with (1987])."," While $\arcmin$ is a rough spatial scale for comparison to the $\arcsec$ beam of the SMT, and since we did not detect a $^{12}$ CO line in any of our sources, the on-cloud results from SMT are consistent with ."
+". It isunlikely that high spatial frequency variations of 33"" scales over 9' regions have systemic velocity shifts of 2-3 km7! ", It isunlikely that high spatial frequency variations of $\arcsec$ scales over $\arcmin$ regions have systemic velocity shifts of 2-3 $^{-1}$ 
+space or velocity.,space or velocity.
+" To compute these dispersions, we use the 32 nearest phase-space neighbours of each particle."," To compute these dispersions, we use the 32 nearest phase-space neighbours of each particle."
+" We define the ‘optimum’ choice of scaling for progenitor galaxy as that which minimises the quantity This is the sum in quadrature of the mean smoothing lengths in configuration and velocity space, normalized respectively by €x,min, the ‘minimal’ mean smoothing length in configuration space (obtained from the 32 nearest configuration space neighbours) and ευ, the ‘minimal’ mean smoothing length in velocity space (obtained from the 32 nearest velocity space neighbours)."," We define the `optimum' choice of scaling for progenitor galaxy as that which minimises the quantity This is the sum in quadrature of the mean smoothing lengths in configuration and velocity space, normalized respectively by $\bar{\epsilon}_{x,\mathrm{min}}$, the `minimal' mean smoothing length in configuration space (obtained from the 32 nearest configuration space neighbours) and $\bar{\epsilon}_{v,\mathrm{min}}$, the `minimal' mean smoothing length in velocity space (obtained from the 32 nearest velocity space neighbours)."
+ We find that the scaling obtained by matching the median interparticle separations in position and velocity as described above is typically a good approximation to this optimal value — a similar result is discussed in more detail by Maciejewski (2009)., We find that the scaling obtained by matching the median interparticle separations in position and velocity as described above is typically a good approximation to this optimal value – a similar result is discussed in more detail by Maciejewski (2009).
+" In the Cooper model, when a given stellar population is formed, the most bound of DM particles in the corresponding dark halo at that time are chosen as dynamical tracers of that population."," In the Cooper model, when a given stellar population is formed, the most bound of DM particles in the corresponding dark halo at that time are chosen as dynamical tracers of that population."
+" Hence, each DM to which stars are assigned has an individual mass-to-light ratio, M/L, which can be as high as c1 (Le. Motenarv103 Mo) and as low as ~107°."," Hence, each DM to which stars are assigned has an individual mass-to-light ratio, M/L, which can be as high as $\sim1$ (i.e. $M_{\mathrm{stellar}}\sim10^{4}\,M_{\sun}$ ) and as low as $\sim10^{-6}$."
+ This will affect the density of stars seeded by a DM particle independently of the density of its neighbours in phase space (i.e. a low M/L particle will create a denser ‘cluster’ of tracers relative to a high MIL particle with the same neighbouring positions and velocities)., This will affect the density of stars seeded by a DM particle independently of the density of its neighbours in phase space (i.e. a low M/L particle will create a denser `cluster' of tracers relative to a high M/L particle with the same neighbouring positions and velocities).
+ We have tested an alternative approach in which the M/L of each particle in a given progenitor is resampled by distributing the total stellar mass of the progenitor evenly amongst its taggedparticles., We have tested an alternative approach in which the M/L of each particle in a given progenitor is resampled by distributing the total stellar mass of the progenitor evenly amongst its tagged.
+ We find that the extra clustering due to a few *hot' particles in our default approach makes no difference to our results., We find that the extra clustering due to a few `hot' particles in our default approach makes no difference to our results.
+than 1.,than 1.
+ The H» densities derived for a single pixel vary from 6x107 7 to 10! 7.Ei and the iudex 5 ranges from 1.6 to 3.3.," The $_2$ densities derived for a single pixel vary from $6\times 10^{2}$ $^{-2}$ to $10^{4}$ $^{-3}$, and the index $b$ ranges from 1.6 to 3.3."
+ Alter comparing the IRS H» spectroscopic maps with the parameter maps. we fouud that the naps of the temperature distribution iudex 5 look most similar to the clistributious of mid-Iyiug H» euissions including 5(3). SCL) aud $(5).," After comparing the IRS $_2$ spectroscopic maps with the parameter maps, we found that the maps of the temperature distribution index $b$ look most similar to the distributions of mid-lying $_2$ emissions including S(3), S(4) and S(5)."
+ To show this similarity. we superpose the H» 5(5) emissiou contours on these images.," To show this similarity, we superpose the $_2$ S(5) emission contours on these images."
+ This fact implies that tle emission in these mid-Iviug trausitious is more strongly depeudent on 6 than on the deusity., This fact implies that the emission in these mid-lying transitions is more strongly dependent on $b$ than on the density.
+ Iu other words. these transitious. Πο 5(3) - $(3). trace iainly the hottest components of the gas.," In other words, these transitions, $_2$ S(3) – S(5), trace mainly the hottest components of the gas."
+ Since the gas temperature distribution at each positiou is determiued largely by the shock velocity. these Πο emissions may also serve as a good tracer of the ocal effective shock velocity.," Since the gas temperature distribution at each position is determined largely by the shock velocity, these $_2$ emissions may also serve as a good tracer of the local effective shock velocity."
+ la HH7 for example. the 5(3) — ο) line intensities appear strongest ear the head of the bow. where Vi reaches its maximum.," In HH7 for example, the S(3) – S(5) line intensities appear strongest near the head of the bow, where $V_s$ reaches its maximum."
+ Ou the other haud. although the S(6) aud S(7) euissions are also strougly affected by the gas temperature. they show more dependeuce pon n(H») compared to other lower-Iyiug trausitious.," On the other hand, although the S(6) and S(7) emissions are also strongly affected by the gas temperature, they show more dependence upon $n$ $_2$ ) compared to other lower-lying transitions."
+ The critical densities for the excitation of S(6) and S(7) are hiehere than 10? ei? at the typical temperatures of relevance here., The critical densities for the excitation of S(6) and S(7) are higher than $10^{5}$ $^{-3}$ at the typical temperatures of relevance here.
+ Thus. regions[n] oL enhanced deusity show up as clumpy features within the S(7T) map lor HH7.," Thus, regions of enhanced density show up as clumpy features within the S(7) map for HH7."
+ Finally. we uote that the derived column deusity of Πο at FT> 100 1 is mostly determined by the inteusities of the low-lying trausitious. especially S(0).," Finally, we note that the derived column density of $_2$ at $T>$ 100 K is mostly determined by the intensities of the low-lying transitions, especially S(0)."
+ The S(0) emission arises mainly from lower temperature eas with 7« 500 kx. which contributes most to the total ΑΗ.) for the power-law temperature distribution that we assume.," The S(0) emission arises mainly from lower temperature gas with $T < $ 500 K, which contributes most to the total $N$ $_2$ ) for the power-law temperature distribution that we assume."
+ ]., 1.
+ We have studied the plivsical couditious within shock-excited molecular gas associated witli ICLIS3C. Was. WIL 3C391. HAT aud HHS!," We have studied the physical conditions within shock-excited molecular gas associated with IC443C, W28, W44, 3C391, HH7 and HH54."
+ We mainly used the H» S(0) to SCV) spectral line maps obtained by IRS ou Spilzer to coustrain the best-fit parameters., We mainly used the $_{2}$ S(0) to S(7) spectral line maps obtained by IRS on $Spitzer$ to constrain the best-fit parameters.
+ IRS observations of HD emissions. IRAC baud 2 (L5 pin) intensity maps. aud{50 measurements of the Ho $(9)/5(3) ratio aud the CO high-lvine rotatioual lines (rom. = 11— 13 to / = 20 — 19) are also used when available to provide additional coustraints.," IRS observations of HD emissions, IRAC band 2 (4.5 $\mu$ m) intensity maps, and measurements of the $_{2}$ S(9)/S(3) ratio and the CO high-lying rotational lines (from $J$ = 14 – 13 to $J$ = 20 – 19) are also used when available to provide additional constraints."
+ 2., 2.
+ A comparison between the IRS Ho emission distribution and the IRAC maps for ICLI3C shows the IRAC band 2. 3 and | intensities are attributable almost entirely to H» pure rotational emissions.," A comparison between the IRS $_2$ emission distribution and the IRAC maps for IC443C shows the IRAC band 2, 3 and 4 intensities are attributable almost entirely to $_{2}$ pure rotational emissions."
+ IRAC banc 2 gives us access to the high-lyiug H» transitions 9S(9) to $(12) which are not available from URS observations., IRAC band 2 gives us access to the high-lying $_{2}$ transitions S(9) to S(12) which are not available from IRS observations.
+ For HH51. the similarity between the IRS Ho aud [RAC maps implies these IRAC baud [fluxes may come mostly from H» emissions as well.," For HH54, the similarity between the IRS $_2$ and IRAC maps implies these IRAC band fluxes may come mostly from $_2$ emissions as well."
+ We assumed that the HH51 IRAC baud 2 intensity is dominated by Ho» emissions anc used it as ai extra diagnostic iu the mocel., We assumed that the HH54 IRAC band 2 intensity is dominated by $_2$ emissions and used it as an extra diagnostic in the model.
+ For the other four sources the HAC maps show either a strongcontinuum component from PAHs or dust or are heavily polluted by point sources., For the other four sources the IRAC maps show either a strongcontinuum component from PAHs or dust or are heavily polluted by point sources.
+ 3., 3.
+" We adopted a power-law temperature distribution for the shocked gas. with the column density of gas at temperature between FT and T 4 dT assumed to be proportional to Z/ "". where T "," We adopted a power-law temperature distribution for the shocked gas, with the column density of gas at temperature between $T$ and $T$ + $dT$ assumed to be proportional to $T^{-b}$ , where $T$ "
+"of the source is polarized at a level of3.7%,,2.2%,, and at 18, 21, and 25 cm, respectively.","of the source is polarized at a level of, and at 18, 21, and 25 cm, respectively."
+" This radio galaxy has an NAT morphology, with tail extent of ~206"" (300 kpc)."," This radio galaxy has an NAT morphology, with a tail extent of $\sim206{\arcsec}$ (300 kpc)."
+" Starting from the head, the atail is directed towards the cluster center, and it bends towards north after 109"" (160 kpc)."," Starting from the head, the tail is directed towards the cluster center, and it bends towards north after ${\arcsec}$ (160 kpc)."
+" The source is polarized at2.1%,,2.0%,, and at 18, 21, and 25 cm, respectively."," The source is polarized at, and at 18, 21, and 25 cm, respectively."
+ This radio galaxy lies at 3.5 Mpc from the center ofA2255., This radio galaxy lies at 3.5 Mpc from the center of.
+". Given its peripheral location, no detailed studies of this source exist in the literature."," Given its peripheral location, no detailed studies of this source exist in the literature."
+" The Bean shows a tailed morphology, but it is not clear whether it should be classified as an NAT or a WAT (wideangletail,?),, given its apparent inclination with respect to the line of sight."," The Bean shows a tailed morphology, but it is not clear whether it should be classified as an NAT or a WAT \citep[wide
+angle tail, ][]{1976ApJ...203L.107R}, given its apparent inclination with respect to the line of sight."
+" Its maximum angular extent is ~78"" (110 kpc), and it is polarized at at 21 cm and at 25 cm."," Its maximum angular extent is $\sim78{\arcsec}$ (110 kpc), and it is polarized at at 21 cm and at 25 cm."
+ These values are significantly higher than those of the other extended radio galaxies ofA2255.., These values are significantly higher than those of the other extended radio galaxies of.
+ Point sources (expected to be instrumentally polarized) lying at approximately the same projected distance from the cluster center show a much lower fractional polarization., Point sources (expected to be instrumentally polarized) lying at approximately the same projected distance from the cluster center show a much lower fractional polarization.
+" Therefore, we conclude that the computed fractional polarization of the Bean should be mostly intrinsic and not instrumental."," Therefore, we conclude that the computed fractional polarization of the Bean should be mostly intrinsic and not instrumental."
+" Since this source lies outside the field of view at 18 cm, it is not possible to give an estimate of its fractional polarization at this wavelength."," Since this source lies outside the field of view at 18 cm, it is not possible to give an estimate of its fractional polarization at this wavelength."
+ The Embryo lies at ~1.6 Mpc from the cluster center and has a WAT morphology., The Embryo lies at $\sim1.6$ Mpc from the cluster center and has a WAT morphology.
+ Its angular extent is ~4’ (360 kpc) at 25 cm., Its angular extent is $\sim4^{\prime}$ (360 kpc) at 25 cm.
+ Twin jets originate from the core and extend to the northeast and southwest., Twin jets originate from the core and extend to the northeast and southwest.
+" The former bends towards the cluster center at a distance of ~40"" from the head, while the latter remains straight."," The former bends towards the cluster center at a distance of $\sim40{\arcsec}$ from the head, while the latter remains straight."
+" This source is polarized at a17%,,19.5%,, and at 18, 21, and 25 cm, respectively."," This source is polarized at a, and at 18, 21, and 25 cm, respectively."
+ The Beaver radio galaxy lies at ~1.6 Mpc from the cluster center and has a NAT morphology., The Beaver radio galaxy lies at $\sim1.6$ Mpc from the cluster center and has a NAT morphology.
+ Its size dramatically changes between high and low frequency., Its size dramatically changes between high and low frequency.
+ A recentstudy of this radio galaxy in total intensity (?) shows that the tail increases its length to almost 1 Mpc between 25 cm and 85 cm., A recentstudy of this radio galaxy in total intensity \citep{pizzospectrum} shows that the tail increases its length to almost 1 Mpc between 25 cm and 85 cm.
+" This suggests very steep spectral index values for the ending part of the tail (azn<—2.2+0.2 and amin« -3.34+02,"," This suggests very steep spectral index values for the ending part of the tail $\alpha_{25 \rm cm} ^{85 \rm cm} < -2.2\pm0.2$ and $\alpha_{85 \rm
+cm} ^{2 \rm m} < -3.3\pm0.2$ ,"
+The maximum-entropy brightness images for HD 141943 for the 4 observing epochs are shown in Fig.,The maximum-entropy brightness images for HD 141943 for the 4 observing epochs are shown in Fig.
+" 2 (2006 observations), the top-left image of Fig."," \ref{Fig_map2006} (2006 observations), the top-left image of Fig."
+" 3 (2007 observations), the top-left image of Fig."," \ref{Fig_allmap2007} (2007 observations), the top-left image of Fig."
+ 4 (2009 observations) and the top-left image of Fig 5 (2010 observations)., \ref{Fig_allmap2009} (2009 observations) and the top-left image of Fig \ref{Fig_allmap2010} (2010 observations).
+" These images were created fitting the data down to reduced x? values of 0.2, 0.3, 0.4 and 0.3 for the 2006, 2007, 2009 and 2010 datasets respectively."," These images were created fitting the data down to reduced $\chi^{2}$ values of 0.2, 0.3, 0.4 and 0.3 for the 2006, 2007, 2009 and 2010 datasets respectively."
+" As explained in Petitetal.(2004b) a reduced x? value smaller than unity can be achieved because, as mentioned in Section 2,, the S/N calculated for the Stokes I LSD profiles are underestimated."," As explained in \citet{PetitP:2004b} a reduced $\chi^{2}$ value smaller than unity can be achieved because, as mentioned in Section \ref{Sec_obs}, the S/N calculated for the Stokes I LSD profiles are underestimated."
+ This has no effect on the maps produced., This has no effect on the maps produced.
+ Fits of the modelled profiles to the observed LSD profiles are given in Fig., Fits of the modelled profiles to the observed LSD profiles are given in Fig.
+" 6 (2006 observations), Fig."," \ref{Fig_brifit2006} (2006 observations), Fig."
+" 7 (2007 observations), Fig."," \ref{Fig_brifit2007} (2007 observations), Fig."
+ 8 (2009 observations) and Fig 9 (2010 observations)., \ref{Fig_brifit2009} (2009 observations) and Fig \ref{Fig_brifit2010} (2010 observations).
+" The epochs of the observations, as calculated from the midpoint of each dataset, are: 2006.352, 2007.257, 2009.273 and 2010.244 in decimal years."," The epochs of the observations, as calculated from the midpoint of each dataset, are: 2006.352, 2007.257, 2009.273 and 2010.244 in decimal years."
+ The brightness images of HD 141943 show that at all 4 epochs HD 141943 had a smallish polar spot and numerous low-latitude features situated mostly between the equator and ~+30° latitude., The brightness images of HD 141943 show that at all 4 epochs HD 141943 had a smallish polar spot and numerous low-latitude features situated mostly between the equator and $\sim$ latitude.
+ In the May 2006 image (Fig. 2)), In the May 2006 image (Fig. \ref{Fig_map2006}) )
+ there appears to be some features below the equator and above+30°., there appears to be some features below the equator and above.
+". However, as there are no observations around these phases it could well be that the code has had trouble determining the latitude of spot features that are only seen in the wings of the profiles."," However, as there are no observations around these phases it could well be that the code has had trouble determining the latitude of spot features that are only seen in the wings of the profiles."
+ The spot filling factor (the level of spot coverage over the entire stellar surface) is also very similar over the 4 epochs., The spot filling factor (the level of spot coverage over the entire stellar surface) is also very similar over the 4 epochs.
+" In 2006 the spot coverage was 2.1 per cent, in 2007 it was 3.1 per cent, in 2009 2.7 per cent and in 2010 it was 2.9 per cent."," In 2006 the spot coverage was 2.1 per cent, in 2007 it was 3.1 per cent, in 2009 2.7 per cent and in 2010 it was 2.9 per cent."
+" The reason for the slightly lower value of spot coverage for the 2006 dataset may well be due to the limited phase coverage of the observations, see Fig. 2.."," The reason for the slightly lower value of spot coverage for the 2006 dataset may well be due to the limited phase coverage of the observations, see Fig. \ref{Fig_map2006}."
+ Thus some spots in these observing gaps may not have been recovered., Thus some spots in these observing gaps may not have been recovered.
+" The variation in spot occupancy with stellar latitude is given in Fig. 10,,"," The variation in spot occupancy with stellar latitude is given in Fig. \ref{Fig_frac_spot_lat},"
+ which plots fractional spottedness versus stellar latitude., which plots fractional spottedness versus stellar latitude.
+" Fractional spottedness is defined as: F(0)) where, S(0) is the average spot occupancy at latitude 0 and dé is the latitude width of each latitude ring."," Fractional spottedness is defined as: ) = where, $S(\theta)$ is the average spot occupancy at latitude $\theta$ and $d\theta$ is the latitude width of each latitude ring."
+" It has been reported that active solar-type stars show evidence of active longitudes, where certain longitudes (usually two longitudes around apart) are more active than others on the stellar surface (i.e.Berdyugina&Tuomi-nen1998;Járvinenetal. 2005)."," It has been reported that active solar-type stars show evidence of active longitudes, where certain longitudes (usually two longitudes around apart) are more active than others on the stellar surface \citep[i.e.][]{BerdyuginaSV:1998, JarvinenSP:2005}."
+. In order to testthis we have plotted the average spottedness versus stellar rotational phase for all 4 epochs of HD 141943 observations., In order to testthis we have plotted the average spottedness versus stellar rotational phase for all 4 epochs of HD 141943 observations.
+ This is displayed in Fig. 11.., This is displayed in Fig. \ref{Fig_frac_spot_lng}.
+ In case the polar spot is affecting the results we have plotted the average spottedness for both (a) to and (b) to in latitude., In case the polar spot is affecting the results we have plotted the average spottedness for both (a) to and (b) to in latitude.
+ For the 2006 and 2009 datasets there is very little evidence for active longitudes on the stellar surface and the limited phases observed in these datasets may well be influencing this result., For the 2006 and 2009 datasets there is very little evidence for active longitudes on the stellar surface and the limited phases observed in these datasets may well be influencing this result.
+" For the well sampled 2007 dataset, and looking at the top-left image in Fig. 3,,"," For the well sampled 2007 dataset, and looking at the top-left image in Fig. \ref{Fig_allmap2007},"
+ there appears to be a slight enhancement of the lower-latitude spots around phases ~0.25 and ~0.55., there appears to be a slight enhancement of the lower-latitude spots around phases $\sim$ 0.25 and $\sim$ 0.55.
+ However as shown in Fig. 11((, However as shown in Fig. \ref{Fig_frac_spot_lng}( (
+b) these enhancements are rather broad.,b) these enhancements are rather broad.
+ For the 2010 dataset there appears to be an increase in the spot coverage at phase ~0.00., For the 2010 dataset there appears to be an increase in the spot coverage at phase $\sim$ 0.00.
+" However, this is reduced when only considering latitude features (Fig. 11(("," However, this is reduced when only considering low-latitude features (Fig. \ref{Fig_frac_spot_lng}( ("
+b)) and when looking at the top-left image in Fig.,b)) and when looking at the top-left image in Fig.
+ 5 the enhancement could be caused by the extension of the polar spot to slightly lower-latitudes around phase ~0.00 in the 2010 epoch., \ref{Fig_allmap2010} the enhancement could be caused by the extension of the polar spot to slightly lower-latitudes around phase $\sim$ 0.00 in the 2010 epoch.
+ There would not appear to be any evidence of another active longitude on the star in 2010., There would not appear to be any evidence of another active longitude on the star in 2010.
+ We do not feel that these represent strong evidence for active longitudes on HD 141943., We do not feel that these represent strong evidence for active longitudes on HD 141943.
+ The magnetic field topology for HD 141943 has been reconstructed for three epochs using the modelling of Donati and including the spherical harmonic expansion of the surface magnetic field by Donatietal. (2006)., The magnetic field topology for HD 141943 has been reconstructed for three epochs using the modelling of \citet{DonatiJF:1997b} and including the spherical harmonic expansion of the surface magnetic field by \citet{DonatiJF:2006}.
+. The magnetic reconstruction is done assuming a generalised potential field plus a toroidal field using a high order (1 < 30) spherical harmonic expansion., The magnetic reconstruction is done assuming a generalised potential field plus a toroidal field using a high order $l$ $\le$ 30) spherical harmonic expansion.
+" A limit of Imax — 30 was chosen for the spherical harmonic expansion, as beyond this limit the magnetic topologies remain essentially unchanged."," A limit of $l$ $=$ 30 was chosen for the spherical harmonic expansion, as beyond this limit the magnetic topologies remain essentially unchanged."
+ Various weighting schemes can be applied to the spherical harmonic expansion so that the reconstruction favours different magnetic field topologies., Various weighting schemes can be applied to the spherical harmonic expansion so that the reconstruction favours different magnetic field topologies.
+" Following the principle of Occam's razor, we have used a weighting scheme that favours ""simpler"" magnetic fields tthose with lower I values) while still reconstructing a similar overall magnetic topology to an unweighted reconstruction."," Following the principle of Occam's razor, we have used a weighting scheme that favours “simpler” magnetic fields those with lower $l$ values) while still reconstructing a similar overall magnetic topology to an unweighted reconstruction."
+ Details of the spherical harmonic technique can be found in Donati (2006).., Details of the spherical harmonic technique can be found in \citet{DonatiJF:2006}. .
+ It should be noted that the April 2009 dataset can be modelled using a purely potential field without the need to, It should be noted that the April 2009 dataset can be modelled using a purely potential field without the need to
+"a few orders of magnitude fainter than the irradiated disc component, we may expect the CMD to follow the blackbody model (red solid line); similarly if the disc is several orders of magnitude fainter than the jet, the jet emission will dominate, which we assume to be optically thin, with a=—0.7 (magenta dotted line).","a few orders of magnitude fainter than the irradiated disc component, we may expect the CMD to follow the blackbody model (red solid line); similarly if the disc is several orders of magnitude fainter than the jet, the jet emission will dominate, which we assume to be optically thin, with $\alpha = -0.7$ (magenta dotted line)."
+ The blue dashed lines in panel (i) represent intermediate cases in which the jet begins to dominate the OIR emission at the different fluxes., The blue dashed lines in panel (i) represent intermediate cases in which the jet begins to dominate the OIR emission at the different fluxes.
+" These models are able to reproduce the deviation from the blackbody relation in the CMD at high flux levels, but the relative contribution of the jet compared to the disc is different on the rise and decline, because the rise jet and decline jet do not follow the same track in the CMD."," These models are able to reproduce the deviation from the blackbody relation in the CMD at high flux levels, but the relative contribution of the jet compared to the disc is different on the rise and decline, because the rise jet and decline jet do not follow the same track in the CMD."
+" For a given V magnitude, the jet normalization is higher on the decline than on the rise."," For a given V magnitude, the jet normalization is higher on the decline than on the rise."
+" This implies that at a given outer accretion disc temperature, the jet is brighter on the decline, or similarly, at a given jet flux, the temperature of the outer disc is higher on the rise."," This implies that at a given outer accretion disc temperature, the jet is brighter on the decline, or similarly, at a given jet flux, the temperature of the outer disc is higher on the rise."
+ This empirical hysteresis was seen in the NIR-X-ray correlation from the same outburst2007b)., This empirical hysteresis was seen in the NIR–X-ray correlation from the same outburst.
+". The combined result is that the NIR jet is brighter on the decline (a) at a given X-ray luminosity, and (b) at a given outer disc temperature."," The combined result is that the NIR jet is brighter on the decline (a) at a given X-ray luminosity, and (b) at a given outer disc temperature."
+" The jet is either more powerful or more radiatively efficient on the outburst decline, or the viscosity parameter of the disc is changed — any of those three possibilities could account for the hysteresis2007b)."," The jet is either more powerful or more radiatively efficient on the outburst decline, or the viscosity parameter of the disc is changed – any of those three possibilities could account for the hysteresis."
+". One clue is that the peak flux of the NIR jet is very similar on the outburst rise and decline, implying that the jet recovers to the same flux level as before the state transitions, whereas the disc and X-ray flux have faded during the soft state."," One clue is that the peak flux of the NIR jet is very similar on the outburst rise and decline, implying that the jet recovers to the same flux level as before the state transitions, whereas the disc and X-ray flux have faded during the soft state."
+ This would suggest that the hysteresis may originate in the changing disc component., This would suggest that the hysteresis may originate in the changing disc component.
+ It is interesting to note that the NIR jet does not return to the same pre-soft state flux level in the hard state decline in GX 339-4 during three outbursts2009)., It is interesting to note that the NIR jet does not return to the same pre-soft state flux level in the hard state decline in GX 339–4 during three outbursts.
+. A NIR-X-ray hysteresis effect was also not seen in this source., A NIR–X-ray hysteresis effect was also not seen in this source.
+" It appears that, as the source fades in the soft state and returns to the hard state, the jet of XTE J1550—-564 somehow retains its previous pre-soft state level of flux, but for GX 339-4 the jet does not."," It appears that, as the source fades in the soft state and returns to the hard state, the jet of XTE J1550–564 somehow retains its previous pre-soft state level of flux, but for GX 339–4 the jet does not."
+ 'The above models do not however reproduce the shape of the, The above models do not however reproduce the shape of the
+We will refer to this third iugredieut as as it is found to be a strong function of stellar mass.,We will refer to this third ingredient as as it is found to be a strong function of stellar mass.
+ Roughly speaking. this results iu the welbobserved phenomenon that more massive galaxies are more likely to be quenched.," Roughly speaking, this results in the well-observed phenomenon that more massive galaxies are more likely to be quenched."
+ We caleulate the mass quenching from the fraction of quenched objects which are uot explained by cuviromucutal quenching over the redshift rauge 0.5ρω«L., We calculate the mass quenching from the fraction of quenched objects which are not explained by environmental quenching over the redshift range $0.5<z_{phot}<1$.
+ The enviromental aud ass quenching efficiencies are shown in the two panels of Fieure ALL. and in both cases we fit a function of the form We perform Monte Carlo simulations in which we take the observed masses and deusitics for galaxies at Laud vaudomly queuch them according to the cuviromueutal and mass quenching efficiencies.," The environmental and mass quenching efficiencies are shown in the two panels of Figure \ref{fig:fit_qeff}, and in both cases we fit a function of the form We perform Monte Carlo simulations in which we take the observed masses and densities for galaxies at $0.5<z_{phot}<1$ and randomly quench them according to the environmental and mass quenching efficiencies."
+ Tle mai result of photthese simulations is shown in the top left panel of Figure. Al2.., The main result of these simulations is shown in the top left panel of Figure \ref{fig:model_mass_v_density}.
+ Tt is perhaps not surprising that the simulations more or less reproduce the measurements shown if Figure 3.. as the sinulationus make use of the deusities. mass quenching efficiency. aud ονολοτα] quenching efficiency that we infer roni the data.," It is perhaps not surprising that the simulations more or less reproduce the measurements shown if Figure \ref{fig:mass_v_density}, as the simulations make use of the densities, mass quenching efficiency, and environmental quenching efficiency that we infer from the data."
+ The key poiut is that the three ineredicuts described above are required to produce the characteristic shapes of the mass-density rolatious for both the star-forming aud quiescent populations., The key point is that the three ingredients described above are required to produce the characteristic shapes of the mass-density relations for both the star-forming and quiescent populations.
+ In the remainime paucls of Figure Al2 we remove cach of the three ineredicuts in turn iu order to provide some insight iuto how they interact o produce these characteristic shapes., In the remaining panels of Figure \ref{fig:model_mass_v_density} we remove each of the three ingredients in turn in order to provide some insight into how they interact to produce these characteristic shapes.
+ In the top right panel. we remove the enviromental quenching: this has the obvious effect of elininatius the cdiffercuce in deusities between quenched aud star-fornune galaxies.," In the top right panel, we remove the environmental quenching; this has the obvious effect of eliminating the difference in densities between quenched and star-forming galaxies."
+ In the bottoms left 21Ο] we remove the mass quenching., In the bottom left panel we remove the mass quenching.
+ Iu this case it is pramarily the galaxies in the densest regions that are queuchlied. since mass quenching is not available to quench galaxies at less extreme deusities.," In this case it is primarily the galaxies in the densest regions that are quenched, since mass quenching is not available to quench galaxies at less extreme densities."
+ Finally. iu the bottom right panel we remove the mass-density relation by randomizing the relationship between stellar mass aud deusities in our catalogs.," Finally, in the bottom right panel we remove the mass-density relation by randomizing the relationship between stellar mass and densities in our catalogs."
+ Tu this case there is no relationship between mass and density for the star-forming ealaxics. aud there is no upturn at Heh masses for the quiesceut galaxies.," In this case there is no relationship between mass and density for the star-forming galaxies, and there is no upturn at high masses for the quiescent galaxies."
+ But there is a promunent upturn in the densities for low-mass quiescent objects., But there is a prominent upturn in the densities for low-mass quiescent objects.
+ This is because mass quenching is very inefficient for those objects (Fig. A11)), This is because mass quenching is very inefficient for those objects (Fig. \ref{fig:fit_qeff}) )
+ and so it is primarily the few low mass ealaxies that are in very dense regious that are quenched., and so it is primarily the few low mass galaxies that are in very dense regions that are quenched.
+ A consideration ofthe top right aud bottom panels of Figure A12 shows how each of the three ingredieuts of the model interact to produce the shapes that are shown in the top eft panel: the cuvironmental quenching introduces a large offset between the star-forming aud quiescent tracks. the nass quenching reduces the offset (doing so more cffectively at intermediate and high masses than at low masses). aud he mass-deusity relation causes the rise iu deusitics at high massesfor both the star-forming and quiesccut galaxies.," A consideration of the top right and bottom panels of Figure \ref{fig:model_mass_v_density} shows how each of the three ingredients of the model interact to produce the shapes that are shown in the top left panel: the environmental quenching introduces a large offset between the star-forming and quiescent tracks, the mass quenching reduces the offset (doing so more effectively at intermediate and high masses than at low masses), and the mass-density relation causes the rise in densities at high massesfor both the star-forming and quiescent galaxies."
+ Tn $1.2. and 86 it was argued that the U-shaped curve followed by the quicsceut galaxies in the the plot of mass versus deusitv sugeests that the cuviromment plavs a more niportant role in building up the red sequence at lower nasses., In \ref{sec:mass} and \ref{sec:summary} it was argued that the U-shaped curve followed by the quiescent galaxies in the the plot of mass versus density suggests that the environment plays a more important role in building up the red sequence at lower masses.
+ This is shown explicitly iu Figure AL3.. which compares the mass and enviromental quenching efficiencies as a function of stellar mass.," This is shown explicitly in Figure \ref{fig:model_qeff}, which compares the mass and environmental quenching efficiencies as a function of stellar mass."
+ The euviromuoeutal quenching efficiency. in this figure is calculated as the mean value for ealaxies iu bius of stellar mass., The environmental quenching efficiency in this figure is calculated as the mean value for galaxies in bins of stellar mass.
+ It is apparent that the mass quenching dominates siguificantly over the environmental quenching at all but the lowest stellar masses., It is apparent that the mass quenching dominates significantly over the environmental quenching at all but the lowest stellar masses.
+ It is oulv at these relatively low masses that cuviroumental processes play a large role in building up the red sequence (seealsovaudenBoschetal.2008).," It is only at these relatively low masses that environmental processes play a large role in building up the red sequence \citep[see
+ also][]{vandenbosch08}."
+. The fact that the cuvirommental quenching efficiency is lower than the mass queuchius efficiency. does uot mean that cuviroument docs not exert a strong influence: it merely reflects the fact that most galaxies are not iu deuse chough regious for ονποιοιτα] processes to have a large effect., The fact that the environmental quenching efficiency is lower than the mass quenching efficiency does not mean that environment does not exert a strong influence; it merely reflects the fact that most galaxies are not in dense enough regions for environmental processes to have a large effect.
+ In this appeudix we lave focused ou the redshift range 0.5<2< 1. and it is expected," In this appendix we have focused on the redshift range $0.5<z<1$ , and it is expected"
+and density p. is abways resolved with a user-defined uunuber of cella.,"and density $\rho$, is always resolved with a user-defined number of cells."
+ We use the new IILL3R scheme for ideal MIID (Waaganuetal.2011).. which eiiplovs a 3-wave approxinate MIID Ricimann solver (Bouchutetal.2007:Waagan2009:Douchutetal. 2010).," We use the new HLL3R scheme for ideal MHD \citep{WaaganFederrathKlingenberg2011}, which employs a 3-wave approximate MHD Riemann solver \citep{BouchutKlingenbergWaagan2007,Waagan2009,BouchutKlingenbergWaagan2010}."
+. This MIID scheme is an extension of the hwdrodvuuuical version (Xliugeubergetal.2007).. developed for FLASII that preserves plivsical states (6.8.. positivity of πας density and pressure) bv construction. and is hiehlv efücieut and accurate im modeling astrophysical ΑΠΟ problems involving turbulence aud shocks (Waaeganetal.2011).," This MHD scheme is an extension of the hydrodynamical version \citep{KlingenbergSchmidtWaagan2007}, developed for FLASH that preserves physical states (e.g., positivity of mass density and pressure) by construction, and is highly efficient and accurate in modeling astrophysical MHD problems involving turbulence and shocks \citep{WaaganFederrathKlingenberg2011}."
+. The ionization degree is expected to be sufficicutly high in primordial clouds to eusure a strong coupling between ions and neutrals to maintain flus-freezing (Mali&Susa 2001)., The ionization degree is expected to be sufficiently high in primordial clouds to ensure a strong coupling between ions and neutrals to maintain flux-freezing \citep{MakiSusa2004}.
+.. ILowever. nou-ideal MIID effects may eveutuallv beconie iniportant at very high deusities. as suggested by simulations of contenrporary star formation (e.g..IHeu-uebelle&Tevssier2008:DiuthinPuduitz 2009).," However, non-ideal MHD effects may eventually become important at very high densities, as suggested by simulations of contemporary star formation \citep[e.g.,][]{HennebelleTeyssier2008,DuffinPudritz2009}."
+. These effects are not included im the preseut calculations. but should be subject of future studies.," These effects are not included in the present calculations, but should be subject of future studies."
+" The initial couditious for our numerical simulations were motivated from larec-scale cosmological models ίοιο,Abelctal.2002:Yoshidaet2008)."," The initial conditions for our numerical simulations were motivated from large-scale cosmological models \citep[e.g.,][]{AbelBryanNorman2002,YoshidaOmukaiHernquist2008}."
+. However. for simplicity we use a spherically svuuuetric initial density distribution. following a super-critical Bounor-Ebert profile (Ebert1955:Dounor1956) with a core density of pyg=L6S«10οσα? at a temperature of F= 30018.," However, for simplicity we use a spherically symmetric initial density distribution, following a super-critical Bonnor-Ebert profile \citep{Ebert1955,Bonnor1956} with a core density of $\rho_{\mathrm BE}=4.68\times10^{-20}\,\g\,\cm^{-3}$ at a temperature of $T=300\,\K$ ."
+ We did not include auv initial rotation of the core., We did not include any initial rotation of the core.
+ The Donunor-Ebert sphere has a radius of l.5pe and a total mass of AS=150037..," The Bonnor-Ebert sphere has a radius of $1.5\,\pc$ and a total mass of $M=1500\,\Msol$."
+ The three-dinieusional Cartesian computational domain has a vohuue of (3.9pe)?.," The three-dimensional Cartesian computational domain has a volume of $(3.9\,\pc)^3$."
+ For a similar approach sce Clarketal.(2008.2011) Although the existence of magnuetie fields on a wide range of astrophysical scales ds clear. thei origin is still poorly understood.," For a similar approach see \citet{ClarkGloverKlessen2008,ClarkGloverKlessenBromm2011}
+ Although the existence of magnetic fields on a wide range of astrophysical scales is clear, their origin is still poorly understood."
+ Some mechauisus iuchude the Biermann(1950) battery. the Weibel instability (c.e..Lazaretal. 2009).. the ejection of magnetic fields from active ealactic nuclei (e.e..Xuetal.2009.erences therein). production by cosmic ravs (Miniati&Bell 2011).. aud amplification by galaxy cluster mergers.," Some mechanisms include the \citet{Biermann1950} battery, the Weibel instability \citep[e.g.,][]{LazarEtAl2009}, the ejection of magnetic fields from active galactic nuclei \citep[e.g.,][and references therein]{XuEtAl2009}, production by cosmic rays \citep[][]{MiniatiBell2011}, and amplification by galaxy cluster mergers."
+ Receut lower limits of magnetic fields in the intergalactic medimn sugeest Ban210.1G (Taveechioetal.2010:Dolag 2011).," Recent lower limits of magnetic fields in the intergalactic medium suggest $B_\mathrm{rms}\gtrsim10^{-15}\,\mathrm{G}$ \citep{TavecchioEtAl2010,DolagEtAl2011}."
+. To keep our setup as simple aud general as possible. we add a small initial seed of the maguetie feld and study its selfconsistent wuplification during the collapse of a gravitatiouallv uustable gas cloud in detail.," To keep our setup as simple and general as possible, we add a small initial seed of the magnetic field and study its self-consistent amplification during the collapse of a gravitationally unstable gas cloud in detail."
+" In order to initialize seeds of turbulence and magnetic field. we impose a random initial velocity field with transonic velocity dispersion of amplitude l.lknis+ (equal to the initial sound speed) aud a weak random magnetic field with DB,= Luc. without a mean field component."," In order to initialize seeds of turbulence and magnetic field, we impose a random initial velocity field with transonic velocity dispersion of amplitude $1.1\,\km\,\mathrm{s}^{-1}$ (equal to the initial sound speed) and a weak random magnetic field with $B_\mathrm{rms}=1\,\mathrm{nG}$ , without a mean field component."
+ This initial field streugth corresponds to a plasma beta (ratio of thermal to magnetic pressure) of )j~A10!9., This initial field strength corresponds to a plasma beta (ratio of thermal to magnetic pressure) of $\beta\approx10^{10}$.
+" Both. the turbulent velocity and magnetic feld were set up with the same power-law depeudeuce m wavenunber space, Pik)X&7. peaking on scales of about 0.8pe. which roughly corresponds to the initial Jeaus leneth of the core."," Both, the turbulent velocity and magnetic field were set up with the same power-law dependence in wavenumber space, $P(k)\propto k^{-2}$, peaking on scales of about $0.8\,\pc$, which roughly corresponds to the initial Jeans length of the core."
+ The choice of the initial power spectrin is motivated by the finding that turbulence develops ak77 and k7 velocity spectrum for incompressible Iohuogorov(1911) aud for shock-dominated turbulence. respectively.," The choice of the initial power spectrum is motivated by the finding that turbulence develops a $k^{-5/3}$ and $k^{-2}$ velocity spectrum for incompressible \citet{Kolmogorov1941c} and for shock-dominated turbulence, respectively."
+ Astrophysical svstenis typically exhibit spectra of the turbulence iu between these wo extremes., Astrophysical systems typically exhibit spectra of the turbulence in between these two extremes.
+ Since both. Ikolinogorov aud Burecrs turbulent spectra are dominated by large-scale modes. Le. stuall waveuuubers A. our results are not expected. to depend strouglv on the partictiar choice of the imitial Spectruni.," Since both, Kolmogorov and Burgers turbulent spectra are dominated by large-scale modes, i.e., small wavenumbers $k$, our results are not expected to depend strongly on the particular choice of the initial spectrum."
+" However, varving parameters of the initial conditions will be subject of a follow-up study."," However, varying parameters of the initial conditions will be subject of a follow-up study."
+ After an initial transicut plase. the turbulence develops its own self-cousisteut spectrmu driven by the eravitational collapse.," After an initial transient phase, the turbulence develops its own self-consistent spectrum, driven by the gravitational collapse."
+ We consider iui isolated svstem for solvineC» the Poisson equation. and use Neuuauu bouudary conditions (zero-eracicut) for the MIID.," We consider an isolated system for solving the Poisson equation, and use Neumann boundary conditions (zero-gradient) for the MHD."
+ Since the initial couditious for the magnetic field were generate iu Fourier space to obtain a divergeuce-free field. the initial magnetic feld is naturally periodic.," Since the initial conditions for the magnetic field were generated in Fourier space to obtain a divergence-free field, the initial magnetic field is naturally periodic."
+ This introduces an inconsistency af the six boundaries of the simuliion domain aud may cause some uou-vanishing divergence there., This introduces an inconsistency at the six boundaries of the simulation domain and may cause some non-vanishing divergence there.
+ ILlowever. even the fastes AMID waves (the fast nüagneto-sonic waves) have a box-crossiug time of about 3«109yr. an order of uaenitude longer than the initial free-fall time scale of he svstem.," However, even the fastest MHD waves (the fast magneto-sonic waves) have a box-crossing time of about $3\times10^6\,\yr$, an order of magnitude longer than the initial free-fall time scale of the system."
+ Thus. auv poteutia perturbations produce at the boundaries can be ignored im the dense COLC.," Thus, any potential perturbations produced at the boundaries can be ignored in the dense core."
+ Consistent with previous works of Οικαὶetal.(2005) and Clover&Savin(20090). we adopt au effective equation of state with P—1.1 for number deusities in the range n—10? 10!em?.," Consistent with previous works of \citet{OmukaiEtAl2005} and \citet{GloverSavin2009}, we adopt an effective equation of state with $\Gamma=1.1$ for number densities in the range $n=10^5$ $10^{10}\,\cm^{-3}$."
+ However. this kind of setup is sutfiicicutly general to allow usto investigate basic properties of turbulence aud magnetic field amplification in the context of collapsing primordial as well as day eas clouds.," However, this kind of setup is sufficiently general to allow usto investigate basic properties of turbulence and magnetic field amplification in the context of collapsing primordial as well as present-day gas clouds."
+" We note that the efficiency. of the turbulent dyuaiuo depends on the kinematic Reynolds number. Re=fart, fv. with the driving scale (με. turbulent velocity dispersion o, on that length scale. aud pliysical viscosity D."," We note that the efficiency of the turbulent dynamo depends on the kinematic Reynolds number, $\mathrm{Re}=\ell_\mathrm{int}\sigma_v/\nu$ , with the driving scale $\ell_\mathrm{int}$, turbulent velocity dispersion $\sigma_v$ on that length scale, and physical viscosity $\nu$."
+ Also note that previous studies found a critical value of the magnetic Revuolds nuuber. Bii=se]. below which the sunall-scale dynamo is no excite (Braudenbure&Subramanian2005).," Also note that previous studies found a critical value of the magnetic Reynolds number, $\mathrm{Rm}=\ell_\mathrm{int}\sigma_v/\eta$, below which the small-scale dynamo is not excited \citep{BrandenburgSubramanian2005}."
+. Iu παπαΊσα sinulations. however. the viscosity. 7 aud the maguetic diffusivity. jj ave typically determined by the junnerica cutoff scale. as a result of the discretization of the flux variables on a computational eric| with finite resolution.," In numerical simulations, however, the viscosity, $\nu$ and the magnetic diffusivity, $\eta$ are typically determined by the numerical cutoff scale, as a result of the discretization of the fluid variables on a computational grid with finite resolution."
+ The ummerical values of Re ancL Raw are thus relate to the exid resolution and to how well the turbulent motions are resolved (e.g...Tangeenetal.2001:Balsaraetal.2001:Schekochihin 2001).," The numerical values of $\mathrm{Re}$ and $\mathrm{Rm}$ are thus related to the grid resolution and to how well the turbulent motions are resolved \citep[e.g.,][]{HaugenBrandenburgDobler2004,BalsaraEtAl2004,SchekochihinEtAl2004}."
+. Even if plivsica viscosity(diffusivity is added as an extra erm in the equations. it must be euaranteed hat it is at cast as high as the nunerical viscosity/dittusivity.," Even if physical viscosity/diffusivity is added as an extra term in the equations, it must be guaranteed that it is at least as high as the numerical viscosity/diffusivity."
+ Typical Revuolds numbersreached da wuuerical siulations of turbulence ire of the order of a few πιάd (dependingonwhat 20093.. which is usually orders οf magnitude below the plivsical Revuolds uuubers iu tlic svstenis that one alnus to study. but just large. cnough o excite the turbuleut sinall-scale dynamo.," Typical Reynolds numbersreached in numerical simulations of turbulence are of the order of a few hundred \citep[depending on what scales are estimated to be affected by numerical viscosity, which varies among different codes, see][]{KitsionasEtAl2009}, , which is usually orders of magnitude below the physical Reynolds numbers in the systems that one aims to study, but just large enough to excite the turbulent small-scale dynamo."
+ A strong resolutiou depeudeuce of turbulent and maguetic properies ds thus expected. with higher resolution resulting iu simaller uunucerical," A strong resolution dependence of turbulent and magnetic properties is thus expected, with higher resolution resulting in smaller numerical"
+ Ly-w ~0.5 ," $\alpha$ $\sim \, 0.5$ "
+" L-—-1/4 EF | fh. Ql rucemwhere (being , a universal constant. and D, a critical nonzero limiting value for the magnetic field strength) equation (15)) can be rewritten as (see Novello et al. (","L = - 1/4 F + /F, 0.5 truecm = - (B_1 c)^4, (being $\gamma$ a universal constant, and $B_1$ a critical nonzero limiting value for the magnetic field strength) equation \ref{eq.5}) ) can be rewritten as (see Novello et al. ("
+2004). I5es.(12))BUT. = 0.,"2004), Eqs.(12)) = 0."
+ As in previous works (Novello et al., As in previous works (Novello et al.
+ 2004: Albelek et al., 2004; Mbelek et al.
+ 2006). we consider hereafter the case with an average magnetic field and with a null mean electric field.," 2006), we consider hereafter the case with an average magnetic field and with a null mean electric field."
+ Therefore. equation (14)) vields ," Therefore, equation \ref{eq.4}) ) yields =."
+"Once again. were the NLED elfect null. the D, field would. be zero."," Once again, were the NLED effect null, the $B_1$ field would be zero."
+ Clearly. since Ly«0 (positive energy condition) and hence DBy. equation (17)) leads to a positive departure of axpep from the unperturbed fine structure constant a.," Clearly, since $L_F < 0$ (positive energy condition) and hence $B > B_1
+$, equation \ref{eq.7}) ) leads to a positive departure of $\alpha_{\rm
+NLED}$ from the unperturbed fine structure constant $\alpha$."
+ Unification theories which are generalization. of general relativity (GGIU like superstring theory. scalar-tensor or multidimensional gravitational theories predict the variation of the effective fine structure constant accp with respect to the redshift z (or the cosmic time) in the cosmological context. (Ciarctaa-Derro. Isern and Ixubvshin. 2007: Mboelek and Lachieze-ltey 2003: Gardner 2003: Sandvik. Barrow and Alagueijo 2002).," Unification theories which are generalization of general relativity (GGR) like superstring theory, scalar-tensor or multidimensional gravitational theories predict the variation of the effective fine structure constant $\alpha_{\rm 
+GGR}$ with respect to the redshift $z$ (or the cosmic time) in the cosmological context a-Berro, Isern and Kubyshin 2007; Mbelek and Lachieze-Rey 2003; Gardner 2003; Sandvik, Barrow and Magueijo 2002)."
+ Hence. the observed fine structure Constant. Aone. might be understood as resulting from a combination of both local NLED and cosmological GCL ellects. so that ," Hence, the observed fine structure constant, $\alpha_{\rm obs}$, might be understood as resulting from a combination of both local NLED and cosmological GGR effects, so that =."
+We show below that this approach can help to reconcile the negative variation claimed. by Webb et al. (, We show below that this approach can help to reconcile the negative variation claimed by Webb et al. (
+2001) and Alurphy et al. (,2001) and Murphy et al. (
+200142001020010). with the recent. positive variation found by Levshakoy et al. (,"2001a,2001b,2001c), with the recent positive variation found by Levshakov et al. ("
+"2007) which amounts = (0.543 0.252)19) between the redshifts2: 2,=1.15 and so=Ladd (Levshakov οἱ al.",2007) which amounts = (0.543 0.252) between the redshifts $z_1 = 1.15$ and $z_2 = 1.84$ (Levshakov et al.
+ 20062)., 2006a).
+ Indeed. on Earth. at present (2=0). in the best. laboratory conditions the residual magnetic Ποιος (including the gcomagnetic field) are such that By. O.5trucemsay O5brucem Lp so that = 0," Indeed, on Earth, at present $z = 0 $ ), in the best laboratory conditions the residual magnetic fields (including the geomagnetic field) are such that B_1, 0.5truecm , 0.5truecm 1 so that = ."
+2820) ‘Thus. by setting alpha(2)= a. 0.2truecm 0.2truecm 2 a.(22) one obtains ," Thus, by setting = -, 0.2truecm 0.2truecm = -, one obtains = ."
+"Averaging over the redshift range of a given sample of absorbers. relation (23)) above vields We will use the relation B=Ομ) οιο ""e proposed by J. P. Valléce for the magnetic field strength within intergalactic gas clouds (Valléce 2004)."," Averaging over the redshift range of a given sample of absorbers, relation \ref{eq.9}) ) above yields = We will use the relation $B = 6 (n(HI)/$ $^{-3})^{0.2}~\mu$ G proposed by J. P. Valléee for the magnetic field strength within intergalactic gas clouds (Valléee 2004)."
+ Vhis wav one linds, This way one finds 0.4 B < 1.5
+scattering parameter vanishes.,scattering parameter vanishes.
+ The perturbation by an elliptic mass galaxy is approximated bv the perturbation by a point mass (monopole) because the dipole moment of the elliptic mass cistributionis zero., The perturbation by an elliptic mass galaxy is approximated by the perturbation by a point mass (monopole) because the dipole moment of the elliptic mass distribution is zero.
+ The main lens galaxy. assumed to have an elliptic mass distribution. has a finite size caustic. and the effect of the perturber is to change ils shape. size. and position.," The main lens galaxy, assumed to have an elliptic mass distribution, has a finite size caustic, and the effect of the perturber is to change its shape, size, and position."
+ Even in the simpler case of the main ealaxv as the monopole-quadrupole lens requires numerical calculations., Even in the simpler case of the main galaxy as the monopole-quadrupole lens requires numerical calculations.
+ We leave the perturbations of the finite size caustics [or [future work., We leave the perturbations of the finite size caustics for future work.
+ It should be necessary to point out that I[xeeton(2003) uses Tavlor expansion and concludes that the effects of à perturbing mass on (he galaxy lens is to add. constant convergence and constant shear irrelevantly of whether the perturber is (he first scatterer or the last., It should be necessary to point out that \citet{keeton} uses Taylor expansion and concludes that the effects of a perturbing mass on the galaxy lens is to add constant convergence and constant shear irrelevantly of whether the perturber is the first scatterer or the last.
+ There may be a problem in the expansion cutoff., There may be a problem in the expansion cutoff.
+ In the region of interest. around the critical eurve of the galaxy lens. the first term in (he Tavlor expansion is small because the Jacobian determinant is zero or small and is likely to be smaller than the second order term.," In the region of interest around the critical curve of the galaxy lens, the first term in the Taylor expansion is small because the Jacobian determinant is zero or small and is likely to be smaller than the second order term."
+ The second order term is well known for the square root behavior of the lensing near the critical curve or caustic crossing., The second order term is well known for the square root behavior of the lensing near the critical curve or caustic crossing.
+ Η 15 not clear whether the Tavlor expansion can be used at all., It is not clear whether the Taylor expansion can be used at all.
+ We use power expansion around (he critical curve of (he main lens which is the region of interest., We use power expansion around the critical curve of the main lens which is the region of interest.
+ The DSTD lens equation is an obvious extension of the DSTP lens equation in which the delta function integral for the 2-d gravitational field of a point mass is generalized to the density [unction integral for the 2-d gravitational field of the distributed mass., The DSTD lens equation is an obvious extension of the DSTP lens equation in which the delta function integral for the 2-d gravitational field of a point mass is generalized to the density function integral for the 2-d gravitational field of the distributed mass.
+ The DSTP lens equation is known since 1936 (DBlandford anc Naravan) and have been studied. (INochanekandApostolakis1936:IExrdlSchneider1993:Werneretal2008).," The DSTP lens equation is known since 1986 (Blandford and Narayan) and have been studied \citep{KA86, ES93, werner}."
+. llere the derivation of the DSTP lens equation studied in RD10 is briefed lor clarity. and convenience., Here the derivation of the DSTP lens equation studied in RB10 is briefed for clarity and convenience.
+ Instead. of using the formula [or the (me delay and Fermat principle. the well-known derivation of the single lens equation from an exact solution of the general relativity. (he Schwarzschild metric. with (he assumption of the linear gravity and small angle approximation is used.," Instead of using the formula for the time delay and Fermat principle, the well-known derivation of the single lens equation from an exact solution of the general relativity, the Schwarzschild metric, with the assumption of the linear gravity and small angle approximation is used."
+ The Schwarzschild metric is asvimptoticallv flat. ancl (he scattering planes can be joined easily in (he asviaptotic regions., The Schwarzschild metric is asymptotically flat and the scattering planes can be joined easily in the asymptotic regions.
+ The DSTP lens equation is obtained bv joininge two scatteringe planes with the freedom to rotate., The DSTP lens equation is obtained by joining two scattering planes with the freedom to rotate.
+ The double scattering (wo point lens equation can be obtained [rom a diagram shown infigure 2. where (he linear gravity and small angle approximation are assumed., The double scattering two point lens equation can be obtained from a diagram shown in figure \ref{fig_double_ray} where the linear gravity and small angle approximation are assumed.
+ Since the irue photon path is three dimensional because of (he rotation of the scattering planes with, Since the true photon path is three dimensional because of the rotation of the scattering planes with
+elliplicilies based on the model proposed by Ilevinans et al. (,ellipticities based on the model proposed by Heymans et al. (
+2004: Hevinans et al.,2004; Heymans et al.
+ 2006)., 2006).
+ In 833. we study the dependence of the number of false peaks on the intrinsic alignment of background galaxies.," In 3, we study the dependence of the number of false peaks on the intrinsic alignment of background galaxies."
+ In 844. we analvze the constraints on the intrinsic alignment [rom the results of CFIFETLS Deep on the number of false peaks given by Gavazzi and Soucail (2007).," In 4, we analyze the constraints on the intrinsic alignment from the results of CFHTLS Deep on the number of false peaks given by Gavazzi and Soucail (2007)."
+ Discussions are presented in 55, Discussions are presented in 5.
+Hr Galaxies do not form in isolated. wavs., Galaxies do not form in isolated ways.
+ Environmental effects play important roles in shaping galaxies., Environmental effects play important roles in shaping galaxies.
+ Therefore correlations of ellipticities of galaxies are expected if (hev are close enough., Therefore correlations of ellipticities of galaxies are expected if they are close enough.
+ The ellipticity ofa galaxy is defined through the second moments of its surface brightness profile 5(r.y).," The ellipticity of a galaxy is defined through the second moments of its surface brightness profile $S(x,y)$."
+" Specifically. we adopt the following definitions where (7,4 and Z,, have similar forms) llere Cr.9) ave the coordinates of the center of the galaxy image."," Specifically, we adopt the following definitions where $I_{yy}$ and $I_{xy}$ have similar forms) Here $(\bar x, \bar y)$ are the coordinates of the center of the galaxy image."
+ Concerning (Gvo-point correlations e;;(r)=<οαλα)>.il is convenient to choose .r-axis and y-axis to be parallel aud. perpendicular to the line joining the two considered galaxies in (he projected plane.," Concerning two-point correlations $c_{ij}(\vec r)=<e_i(\vec x)e_j(\vec x+\vec r)>$,it is convenient to choose $x$ -axis and $y$ -axis to be parallel and perpendicular to the line joining the two considered galaxies in the projected plane."
+ Numerical simulations show thal cy=<eq(Cr)easGr++r)280 (e.g.. Jing 2002: ILevmans et al.," Numerical simulations show that $c_{12}=<e_1(\vec x)e_2(\vec x+\vec r)>\approx 0$ (e.g., Jing 2002; Heymans et al."
+ 2004: Hevimans et al., 2004; Heymans et al.
+ 2006)., 2006).
+" For ο,=<e;Cr)e;Cr+r)2 ξ1. 2). we use the fitting formula provided by Heyxanaus et al. ("," For $c_{ii}=<e_i(\vec x)e_i(\vec x+\vec r)>$ $i=1,\hbox{ 2}$ ), we use the fitting formula provided by Heymans et al. ("
+2004). which is Our following analvses primarily concern eo. which can also be written as,"2004), which is Our following analyses primarily concern $\eta(r)=<e_1(\vec x)e_1(\vec x+\vec r)>
++<e_2(\vec x)e_2(\vec x+\vec r)>=c_{11}+c_{22}$ which can also be written as"
+To oricut the reader. iu Figure 1. we show results obtained from the 1D code ouly.,"To orient the reader, in Figure \ref{fig:1Dcode} we show results obtained from the 1D code only."
+ The dust is initially well mixed with gas at solar uctallicity (μην=0.015)., The dust is initially well mixed with gas at solar metallicity $\mu_{\rm init} = 0.015$ ).
+" As dust settles and the midplane dust-to-gas ratio jy Increases, sharp cusps appear at the edges of the dust laver where particles pile wp vertically."," As dust settles and the midplane dust-to-gas ratio $\mu_0$ increases, sharp cusps appear at the edges of the dust layer where particles pile up vertically."
+ Pileups occur because particle fluxes palea]Ww increase with increasing height |:|., Pileups occur because particle fluxes $\rhod |v_{\rm rel}| \propto \mu |z|$ increase with increasing height $|z|$.
+ This follows from our assumption that fins Is constant. which as noted at the beginning of rofsecinethod. may not be realistic.," This follows from our assumption that $\mu_{\rm init}$ is constant, which as noted at the beginning of \\ref{sec:method}
+ may not be realistic."
+ Unlike us. Garaud&Lin(2001). cid not fud. vertical pileups at the edges of their laver because they chose their -initial dust profile to have a scale height equal to 0.177...," Unlike us, \citet{garaudlin04} did not find vertical pileups at the edges of their layer because they chose their initial dust profile to have a scale height equal to $0.1 H_{\rm g}$."
+ Their initial j/ profile decreased. with iore quickly than 1 aud thus did not satisfy the conditiou for pileups.," Their initial $\mu$ profile decreased with $|z|$ more quickly than $1/|z|$, and thus did not satisfy the condition for pileups."
+ We verified this bv inserting their initial profile oeito our LD code., We verified this by inserting their initial profile into our 1D code.
+ The shapes of the settled cust profiles pz) aud their relative spacing im time are independent of the dust internal deusity pi. dust particle size s. and the scaling paralucter PF for disk mass.," The shapes of the settled dust profiles $\mu(z)$ and their relative spacing in time are independent of the dust internal density $\rho_{\rm s}$, dust particle size $s$, and the scaling parameter $F$ for disk mass."
+ Clhiugiug these paramcters oulv alters the absolute plivsical time elapsed. (equation 3))., Changing these parameters only alters the absolute physical time elapsed (equation \ref{eq_tz}) ).
+ Relative time is tracked by the cümenusiouless paralcter fo=ως. labeled on this and many subsequent figures.," Relative time is tracked by the dimensionless parameter $f \equiv t/t_{\rm settle}$, labeled on this and many subsequent figures."
+ Below we compare these 1D-only. results to those that include the full 3D dynamics., Below we compare these 1D-only results to those that include the full 3D dynamics.
+ The solar inetallicitv case is described in rofssecisolar.., The solar metallicity case is described in \\ref{ssec:solar}.
+ The mctalrvich case (μμ=o 0.06) is presented iu rofssecuu.., The metal-rich case $\mu_{\rm init} = 0.06$ ) is presented in \\ref{ssec:mr}.
+ Figure 2 traces the evolution of dust that starts well nüxed with eas at solar mctallicitv., Figure \ref{fig:solarmoney} traces the evolution of dust that starts well mixed with gas at solar metallicity.
+ Plotted are several KII-stable curves frou the 3D code resulting from step (5) of our procedure., Plotted are several KH-stable curves from the 3D code resulting from step (5) of our procedure.
+ For ease of comparison with the purely 1D results. the relative timestamps in Figure 2.. measured by f. coicide with those in Figure 1..," For ease of comparison with the purely 1D results, the relative timestamps in Figure \ref{fig:solarmoney}, measured by $f$, coincide with those in Figure \ref{fig:1Dcode}."
+ The leftimost curve at f=1.0 represents the mareinally stable state identified using our staudaxrd procedure., The leftmost curve at $f = 1.0$ represents the marginally stable state identified using our standard procedure.
+ This state achieves a midplane dust-to-gas ratio of jn=2.15. about an order of maguitude below the value required for eravitational instability (equation 10)).," This state achieves a midplane dust-to-gas ratio of $\mu_0 = 2.45$, about an order of magnitude below the value required for gravitational instability (equation \ref{eqn:muToomre}) )."
+ Iu refsecioxt owe extend our procedure to see if we nüeht achieve still higher dust-to-gas ratios., In \\ref{sec:ext} we extend our procedure to see if we might achieve still higher dust-to-gas ratios.
+ Comparing Figures 1 and 2.. we see that the (possibly 1irealistic) pileups at the edges of the dust laver do not survive in he dvuzunuical 3D code.," Comparing Figures \ref{fig:1Dcode} and \ref{fig:solarmoney}, we see that the (possibly unrealistic) pileups at the edges of the dust layer do not survive in the dynamical 3D code."
+ By f50.11. the pileups are nearly gone.," By $f \approx 0.44$, the pileups are nearly gone."
+ At this point. the vertical exteut of the dust laver μιας has shrunk to —0.1/7.. aud the ouly pileup present is the one at the midplane.," At this point, the vertical extent of the dust layer $z_{\rm max}$ has shrunk to $\sim$$0.1 \Hg$, and the only pileup present is the one at the midplane."
+ The instability tiat eliminates the pileups at the edees of the laver is likely related to the Ravleigh-Tavlor instability (RTT). triggered bv heavy fluid Ivine ou top of lighter fluid. and we will refer to it henceforth as such.," The instability that eliminates the pileups at the edges of the layer is likely related to the Rayleigh-Taylor instability (RTI), triggered by heavy fluid lying on top of lighter fluid, and we will refer to it henceforth as such."
+ The RTI originateslocally at the edges of the dust laver., The RTI originateslocally at the edges of the dust layer.
+ By contrast. the midplane is relatively stable (at least uutil the mareinally stable state is reached).," By contrast, the midplane is relatively stable (at least until the marginally stable state is reached)."
+ Another wav of sccing this is to note that midplane dust-to-gas ratios jj in Figures 1 and 2 agree to within, Another way of seeing this is to note that midplane dust-to-gas ratios $\mu_0$ in Figures \ref{fig:1Dcode} and \ref{fig:solarmoney} agree to within.
+ Closer cxaminuation reveals that those iu Fieure 2. are consistently hieher.," Closer examination reveals that those in Figure \ref{fig:solarmoney}
+ are consistently higher."
+ This sugeests that the RTI trausters sole of the dust in the pileups to the midplane., This suggests that the RTI transfers some of the dust in the pileups to the midplane.
+ Figure 9. coufirius this transfer mechanism., Figure \ref{fig:solar67} confirms this transfer mechanism.
+ The top muddle panel shows that over the course of a 20-0rbit-long 3D simulation (iteration 4666. occurring at a finie f=O31. out of a total of 19 iterations). dust is redistributed frou the livers edges to the midplane. raising fig by about," The top middle panel shows that over the course of a 20-orbit-long 3D simulation (iteration 6, occurring at a time $f=0.31$, out of a total of 19 iterations), dust is redistributed from the layer's edges to the midplane, raising $\mu_0$ by about."
+ Note that the effect of the RTI has been to transport dust toward the midplane. not to higher altitudes.," Note that the effect of the RTI has been to transport dust toward the midplane, not to higher altitudes."
+ The RTI is coufined to where dust is uustably stratified Gucreasing total density iu the direction opposite to gravity)., The RTI is confined to where dust is unstably stratified (increasing total density in the direction opposite to gravity).
+ Compare this behavior with that in the top row of Figure L. which documents a later iteration. #116.," Compare this behavior with that in the top row of Figure \ref{fig:solar1617}, which documents a later iteration, 16."
+ The top middle panel shows that au instability has occurred near the edges of the dust laver., The top middle panel shows that an instability has occurred near the edges of the dust layer.
+ Dust is redistributed to higher. not lower. altitudes.," Dust is redistributed to higher, not lower, altitudes."
+ The midplane is not affected., The midplane is not affected.
+ The instability at this relatively late stage of settliug is probably driven by the vertical shear associated witli strong density eraclicuts at the edges of the laver. aud we will refer to it henceforth as the I&elviu-IHehuholtz instability (IKIID).," The instability at this relatively late stage of settling is probably driven by the vertical shear associated with strong density gradients at the edges of the layer, and we will refer to it henceforth as the Kelvin-Helmholtz instability (KHI)."
+ As a result of the KUT. eradicuts in density and velocity are reduced.," As a result of the KHI, gradients in density and velocity are reduced."
+ The marginally stable state ideutified using our standard procedure is displaved in Figure 5.., The marginally stable state identified using our standard procedure is displayed in Figure \ref{fig:solar19101930}.
+ The bottom panels show that during the last iteration #119. the usual increase in the midplane jy (left bottom) results iu a IkILuustable profile (1iiddle bottom).," The bottom panels show that during the last iteration 19, the usual increase in the midplane $\mu_0$ (left bottom) results in a KH-unstable profile (middle bottom)."
+ Iu the top panels. we redo iteration #119. this time incrementing py by only (left top).," In the top panels, we redo iteration 19, this time incrementing $\mu_0$ by only (left top)."
+ The resultant profile is KII stable (uuidedle aud right top paucls). aud has (49?=2.15.," The resultant profile is KH stable (middle and right top panels), and has $\langle \mu_0 \rangle = 2.45$."
+ In refssecaveielt.. we modifv our standard procedure aud extend it to later times to achieve still higher dust-to-gas ratios m stable flows.," In \\ref{ssec:weight}, we modify our standard procedure and extend it to later times to achieve still higher dust-to-gas ratios in stable flows."
+ The p-profiles iu Figures 2- 5. betray oscillatious just iuside the edges of the dust laver., The $\mu$ -profiles in Figures \ref{fig:solarmoney}- \ref{fig:solar19101930} betray oscillations just inside the edges of the dust layer.
+ We believe these ripples are artificial because when cach first appears. if spans oulv a few eril points of the 3D code: see the f=0.051 profile of Figure 2.. which shows two nascent ripples.," We believe these ripples are artificial because when each first appears, it spans only a few grid points of the 3D code: see the $f = 0.054$ profile of Figure \ref{fig:solarmoney}, which shows two nascent ripples."
+ The features probably arise because the truncated Chebyshev series used to model the flow in 2 has too few terms to adequately capture the steep vertical density eracicut (Cibbs1898)., The features probably arise because the truncated Chebyshev series used to model the flow in $z$ has too few terms to adequately capture the steep vertical density gradient \citep{gibbs1898}.
+. Originating in the 3D code. the ripples are then amplified as nüni-pileups iu the 1D code.," Originating in the 3D code, the ripples are then amplified as mini-pileups in the 1D code."
+ We could have tried to smooth away these oscillatious by reducing the order of our polvuomial fit (step T of our procedure). but chose mstead to retain all features of the dust profie generated by both codes to minimize bias.," We could have tried to smooth away these oscillations by reducing the order of our polynomial fit (step 7 of our procedure), but chose instead to retain all features of the dust profile generated by both codes to minimize bias."
+ Ta any c:we the oscillations are eventually erased by instabilitics caving the later stages of settling (Figure 2))., In any case the oscillations are eventually erased by instabilities during the later stages of settling (Figure \ref{fig:solarmoney}) ).
+ In and of heiselves the oscillations do uot appear to introduce instabilities. which as discussed above aro triggered instead by snooth deusity eradieutsrealistically couputedat the boundaries of the laver (top rows of Figures 3 and 1).," In and of themselves the oscillations do not appear to introduce instabilities, which as discussed above are triggered instead by smooth density gradients---realistically computed—at the boundaries of the layer (top rows of Figures \ref{fig:solar67} and \ref{fig:solar1617}) )."
+ Figure 6 follows the evolution of dust that is initially well mixed with eas at Lx solu metallicitv., Figure \ref{fig:mrmoney} follows the evolution of dust that is initially well mixed with gas at $4\times$ solar metallicity.
+ It shares the same timeline as Figures 1 aud 2.., It shares the same timeline as Figures \ref{fig:1Dcode} and \ref{fig:solarmoney}. .
+ Thus the last profile marked f=1.1 in Figure 6 is attained at a time later than that marked f=LO in the other figures., Thus the last profile marked $f=1.1$ in Figure \ref{fig:mrmoney} is attained at a time later than that marked $f=1.0$ in the other figures.
+ This last profile is the mareiually stable state, This last profile is the marginally stable state
+The COMPTEL 0.75-10 MeV lighteurve on the other hand reaches its maximum near 0.38 which coincides in phase with the shoulder clearly visible in the RXTE lghtcurve.,The COMPTEL 0.75-10 MeV lightcurve on the other hand reaches its maximum near 0.38 which coincides in phase with the shoulder clearly visible in the RXTE lightcurve.
+ Whether this apparent offset has a statistical origin (cf., Whether this apparent offset has a statistical origin (cf.
+ the typical error bar in the COMPTEL 0.75-10 MeV lighteurve which has a mean level of ~93000 counts in this 15 bin lighteurve) or is due to an intrinsic property of the pulsar’s high-energy emission is difficult to decide., the typical error bar in the COMPTEL 0.75-10 MeV lightcurve which has a mean level of $\sim 93000$ counts in this 15 bin lightcurve) or is due to an intrinsic property of the pulsar's high-energy emission is difficult to decide.
+ The intrinsic timing-resolution of 0.125 ms of CGRO/COMPTEL is sufficiently accurate to allow the lightcurve to be binned in several hundreds of bins and can be responsible for the offset., The intrinsic timing-resolution of 0.125 ms of CGRO/COMPTEL is sufficiently accurate to allow the lightcurve to be binned in several hundreds of bins and can be responsible for the offset.
+ Also. BATSE and COMPTEL use the same CGRO clock.," Also, BATSE and COMPTEL use the same CGRO clock."
+ In order to study the difference in morphology between the COMPTEL 0.75-10 MeV and RXTE 2-16 keV lightcurves we have fitted the RXTE 2-16 keV profile in terms of abackground and two Gaussians (7 free parameters)., In order to study the difference in morphology between the COMPTEL 0.75-10 MeV and RXTE 2-16 keV lightcurves we have fitted the RXTE 2-16 keV profile in terms of a background and two Gaussians (7 free parameters).
+ This resulted in a narrow component peaking at phase 0.250+0.008 with width 0.056+0.008 and a broader component at 0.286+0.012 and width 0.129+0.006., This resulted in a narrow component peaking at phase $0.250\pm 0.008$ with width $0.056\pm0.008$ and a broader component at $0.386\pm 0.012$ and width $0.129\pm0.006$.
+ The first narrow pulse accounts for 25.731.3% of the total pulsed emission., The first narrow pulse accounts for $25.7\pm4.3\%$ of the total pulsed emission.
+ A similar fit has been performed on COMPTEL 0.75-10 MeV data. but now with positions and widths fixed to the values found in the RXTE keV fit (3 free parameters).," A similar fit has been performed on COMPTEL 0.75-10 MeV data, but now with positions and widths fixed to the values found in the RXTE 2-16 keV fit (3 free parameters)."
+ In this case the first narrow pulse can account for only 13+18% of the total pulsed emission. consistent with being absent. and the profile can satisfactorily be described by just the broad second pulse near 0.39.," In this case the first narrow pulse can account for only $13\pm18\%$ of the total pulsed emission, consistent with being absent, and the profile can satisfactorily be described by just the broad second pulse near 0.39."
+ This strongly suggests that the pulse shape changes from soft X-rays to medium energy >-rays., This strongly suggests that the pulse shape changes from soft X-rays to medium energy $\gamma$ -rays.
+" Based on the RXTE 2-16 keV lightcurve we have defined a ""pulsed"" and an ""unpulsed"" phase interval in the pulse phase distribution: the pulsed interval extends from phase 0.15 to 0.65 and the unpulsed (background) interval from 0.65 to 1.15.", Based on the RXTE 2-16 keV lightcurve we have defined a “pulsed” and an “unpulsed” phase interval in the pulse phase distribution: the pulsed interval extends from phase 0.15 to 0.65 and the unpulsed (background) interval from 0.65 to 1.15.
+" This break-down ts such that for a pulse shape as measured by RXTE 90.[4 of the pulse is located in the ""pulsed"" interval.", This break-down is such that for a pulse shape as measured by RXTE $90.4\%$ of the pulse is located in the “pulsed” interval.
+ Applying this definition to the COMPTEL data we can determine the pulsed excess counts in various energy slices by estimating the underlying background as the averaged level in the unpulsed part of the lightcurve., Applying this definition to the COMPTEL data we can determine the pulsed excess counts in various energy slices by estimating the underlying background as the averaged level in the unpulsed part of the lightcurve.
+ We derived these pulsed excess counts for the 0.75-3. 3-10 and 10-30 MeV energy windows and converted these to pulsed flux values taking into account efficiency correction factors due to the applied ARM cuts in the timing-analysis (see Table 3)).," We derived these pulsed excess counts for the 0.75-3, 3-10 and 10-30 MeV energy windows and converted these to pulsed flux values taking into account efficiency correction factors due to the applied ARM cuts in the timing-analysis (see Table \ref{tab_pulsed_fluxes}) )."
+ The weak 10-30 MeV flux value should be treated with care because we do not detect significant modulation (2.10)., The weak 10-30 MeV flux value should be treated with care because we do not detect significant modulation $2.1\sigma$ ).
+" Moreover. the lightcurve shows indications for à second pulse in the ""unpulsed(background) phase interval."," Moreover, the lightcurve shows indications for a second pulse in the “unpulsed”(background) phase interval."
+ If this pulse is genuine. then the true flux is underestimated (see next section).," If this pulse is genuine, then the true flux is underestimated (see next section)."
+radio galaxy that contaius a large reservoir of cold molecular eas that has not (vet) been depleted by star formation or radio source feedback.,radio galaxy that contains a large reservoir of cold molecular gas that has not (yet) been depleted by star formation or radio source feedback.
+ CO(1-0) is the most robust tracer of molecular eas (including the wide-spread. low-density and sub-therually excited componcut) in hieh-: galaxies.," CO(1-0) is the most robust tracer of molecular gas (including the wide-spread, low-density and sub-thermally excited component) in $z$ galaxies."
+ The search for CO(1-0) in UzRCs at observiug frequencies below 50 GIIz with the ATCA and EVLA will be a crucial complement to survers of the higher CO transitious with ALALA., The search for CO(1-0) in HzRGs at observing frequencies below 50 GHz with the ATCA and EVLA will be a crucial complement to surveys of the higher CO transitions with ALMA.
+ We thank Laura Pentericci for the use of her USTΝΤΟΟΡ and VLA radio continu images., We thank Laura Pentericci for the use of her HST/NICMOS and VLA radio continuum images.
+ Reproduced by permission of the AAS., Reproduced by permission of the AAS.
+ The Australia Telescope is fuuded by the Couunonwealth of Australia for operation as a National Facility managed bv CSIRO., The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.
+ This research has made use of the NASA/TPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Tustitute of Techuoloey. uuder contract with the National Aeronautics and Space Adininistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
+relationship is predicted if the CER has been constant. this approach shows the approximate validity of this assumption once again.,"relationship is predicted if the CFR has been constant, this approach shows the approximate validity of this assumption once again."
+ Lf we assume that the CER in the cluster age eap has also been constant. although at à (much) lower level (cL.," If we assume that the CFR in the cluster age gap has also been constant, although at a (much) lower level (cf."
+ H03). then we derive that the ratio of the CLR. before and after the cluster age gap to that in the period between ~5 and 13 Gyr. is about (541):1.," H03), then we derive that the ratio of the CFR before and after the cluster age gap to that in the period between $\sim 3$ and 13 Gyr, is about $(5\pm1) : 1$."
+ 1109. considering the upper cluster masses. ancl assuming that the mass of the most massive cluster is determined by size-of-sample effects (which is approximately valid: 103). derived an equivalent ratio of ~10. although with large uncertainties.," H03, considering the upper cluster masses, and assuming that the mass of the most massive cluster is determined by size-of-sample effects (which is approximately valid; H03), derived an equivalent ratio of $\sim 10$, although with large uncertainties."
+ In. view of the independent methods used by 1109 and. us. based on entirely cülferent cliagnostics. these results are in reasonable agreement.," In view of the independent methods used by H03 and us, based on entirely different diagnostics, these results are in reasonable agreement."
+ Finally. LIOS suggested that the oldest sample clusters represent a separate population from the vounger LMC clusters.," Finally, H03 suggested that the oldest sample clusters represent a separate population from the younger LMC clusters."
+ They state that lower-mass old clusters could have »en observed. but are not in practice., They state that lower-mass old clusters could have been observed but are not in practice.
+ However. our new age and mass determinations do not concur with this result: Fig.," However, our new age and mass determinations do not concur with this result; Fig."
+ 6 shows that our 50 per cent completeness limit describes he lower mass limit of the entire cluster sample up to the oldest ages very well., \ref{agemasshist.fig} shows that our 50 per cent completeness limit describes the lower mass limit of the entire cluster sample up to the oldest ages very well.
+ Similarlv. the upper mass limit of he oldest clusters is commensurate with the upper mass imit expected from size-of-sample ellects (ef.," Similarly, the upper mass limit of the oldest clusters is commensurate with the upper mass limit expected from size-of-sample effects (cf."
+ 1103). and does not require that the oldest clusters represent a separate »opulation.," H03), and does not require that the oldest clusters represent a separate population."
+ However. because of the small number of old clusters. we cannot draw anv firmer conclusions on this issue xwsed on the information at hand.," However, because of the small number of old clusters, we cannot draw any firmer conclusions on this issue based on the information at hand."
+ ln Fig., In Fig.
+ 6bb we show the LAIC cluster mass distribution in away that allows us to assess the importance of disruption processes for the sample. in the presence of an age-dependent detection (completeness) limit. (see Boutloukos Lamers 2003).," \ref{agemasshist.fig}b b we show the LMC cluster mass distribution in a way that allows us to assess the importance of disruption processes for the sample, in the presence of an age-dependent detection (completeness) limit (see Boutloukos Lamers 2003)."
+ As we showed in de Crijs et al. (, As we showed in de Grijs et al. (
+200241. the slope of the distribution for the highest masses is in essence a ojection of theμίας CALL. provided that we can prove hat (semi-instantaneous) disruption will not vet have had he time to act on these masses.,"2003d), the slope of the distribution for the highest masses is in essence a projection of the CMF, provided that we can prove that (semi-instantaneous) disruption will not yet have had the time to act on these masses."
+ In ‘Table 2. we list the derived slopes for mass ranges rom the minimum masses indicated to the highest masses esent in our sample., In Table \ref{massslopes.tab} we list the derived slopes for mass ranges from the minimum masses indicated to the highest masses present in our sample.
+ We note that. for log(A4/M.)=3.0 he CALF slopes. derived. are very. stable (except for the ughest mass ranges. where the small number of clusters alfects the results). resulting in an intial CME slope of a=1.85+£0.05 as our best determination.," We note that, for $\log(M_{\rm cl}/{\rm M}_\odot)
+\gtrsim 3.0$ the CMF slopes derived are very stable (except for the highest mass ranges, where the small number of clusters affects the results), resulting in an intial CMF slope of $\alpha = -1.85 \pm
+0.05$ as our best determination."
+" This is significantly (at the 30 level) smaller than the ""universal"" initial CALE slopes of a=2 often found in interacting anc starburs ealaxies. and used as the basis for theoretical models of the evolution of voung cluster populations (seo. e.g.. de rijs e al."," This is significantly (at the $3\sigma$ level) smaller than the “universal” initial CMF slopes of $\alpha = -2$ often found in interacting and starburst galaxies, and used as the basis for theoretical models of the evolution of young cluster populations (see, e.g., de Grijs et al."
+ 2003d for a review)., 2003d for a review).
+ We will discuss the implications of this result in the context of our discussion of Fig., We will discuss the implications of this result in the context of our discussion of Fig.
+ SN. below., \ref{clfs2.fig} below.
+ We note that for logCAZ4/M.)c3.0. log(fai/vr)29.3: in this age range. the clusters that would have been allectec bv ongoing (semi-instantaneous) disruption have already faced to below the adopted: completeness. limit. so tha we conclude that here we are indeed. observing theniflial CALF slope.," We note that for $\log(M_{\rm cl}/{\rm M}_\odot)\ge 3.0$, $\log(t_{\rm dis}/{\rm
+yr}) \ge 9.3$; in this age range, the clusters that would have been affected by ongoing (semi-instantaneous) disruption have already faded to below the adopted completeness limit, so that we conclude that here we are indeed observing the CMF slope."
+ We note that the low density of the LALC field. while to some small extent effective in tidal stripping anc evaporation. does not lead to a significant breakdown of our assumption of (almost) instantaneous disruption: most of the evaporated and stripped stars will be of low mass. which hence contribute negligiblv to the integrated luminosities we use for our analysis.," We note that the low density of the LMC field, while to some small extent effective in tidal stripping and evaporation, does not lead to a significant breakdown of our assumption of (almost) instantaneous disruption: most of the evaporated and stripped stars will be of low mass, which hence contribute negligibly to the integrated luminosities we use for our analysis."
+ Using the value ofa =1.85. and the fading parameter C=0.648 (where fading of a clusters Hux. £A. is defined as PN d) from stellar population synthesis (Boutloukos Lamers 2003).the predicted: power-law slope for the mass range is (1/6)—|o].," Using the value of $\alpha = -1.85$ , and the fading parameter $\zeta =
+0.648$ (where fading of a cluster's flux, $F_\lambda$, is defined as $F_\lambda \sim t^{-\zeta}$ ) from stellar population synthesis (Boutloukos Lamers 2003),the predicted power-law slope for the low-mass range is $(1/\zeta)-|\alpha|$."
+ This slope is shown as the dash-dotted line in Fig., This slope is shown as the dash-dotted line in Fig.
+ 6bb. and matches the observed: mass distribution remarkably well (we have only applied a vertical shift to the slope in order to match the cluster numbers in he distributions).," \ref{agemasshist.fig}b b, and matches the observed mass distribution remarkably well (we have only applied a vertical shift to the slope in order to match the cluster numbers in the distributions)."
+" Alternatively, we can assess the CAI and its xossible evolution by examining the CALS of well-defined ancl well-uncerstood subsamples covering restricted: mass ranges."," Alternatively, we can assess the CMF and its possible evolution by examining the CMFs of well-defined and well-understood subsamples covering restricted mass ranges."
+ Following Fall et al. (, Following Fall et al. (
+2005). in Lig.,"2005), in Fig."
+ 8 we oesent mass-limited. LALC cluster subsamples. which are »»entiallv physically more informative than maegnituce-imited subsamples.," \ref{clfs2.fig} we present mass-limited LMC cluster subsamples, which are potentially physically more informative than magnitude-limited subsamples."
+ Alass-limited sample are less biased oward voung clusters than magnitude-Iimited samples., Mass-limited sample are less biased toward young clusters than magnitude-limited samples.
+ This is a novel approach for the LMC star cluster svstem., This is a novel approach for the LMC star cluster system.
+ 1n essence. a mass-limited: statistically complete. sample of clusters implies an imposed age limitation as well. so that for increasing masses. the upper age limit increases. and so does the median age of the subsample.," In essence, a mass-limited statistically complete sample of clusters implies an imposed age limitation as well, so that for increasing masses, the upper age limit increases, and so does the median age of the subsample."
+ The mass ancl age ranges used Lor the construction of the CMES in Fig., The mass and age ranges used for the construction of the CMFs in Fig.
+ S. are listed in Table 3.. as well as in the individual panels in the ligure.," \ref{clfs2.fig} are listed in Table \ref{mfslopes.tab}, as well as in the individual panels in the figure."
+ The error bars indicate the simple Poissonian uncertainties. and the vertical dotted lines indicate the münimum mass limits adopted for a particular cluster subsample: in all cases the corresponding age limits are well below the expected disruption time-scales for even the least massive clusters in a given sample.," The error bars indicate the simple Poissonian uncertainties, and the vertical dotted lines indicate the minimum mass limits adopted for a particular cluster subsample; in all cases the corresponding age limits are well below the expected disruption time-scales for even the least massive clusters in a given sample."
+ In. Table 3. we also include the CALF slopes we derive [rom cach eluster subsample.," In Table \ref{mfslopes.tab}
+ we also include the CMF slopes we derive from each cluster subsample."
+ For samples up to log(Age/vr)<S.Y. we use a mass fitting range of log(Aly/M.)23.0: for the remaining subsamples we use the full mass range available for the fits.," For samples up to $\log({\rm Age/yr}) \le 8.7$, we use a mass fitting range of $\log(M_{\rm cl}/{\rm M}_\odot) \ge 3.0$; for the remaining subsamples we use the full mass range available for the fits."
+ We note explicitly. that using a lower age limit of los.Xee/vr)=GS or 72. in order to avoid the artifact caused by the limited age resolutionof the isochrones used for the analysis does alter these results significantly (or may even strengthen these results. albeit mareinally).," We note explicitly that using a lower age limit of $\log({\rm Age/yr}) = 6.8$ or 7.2, in order to avoid the artifact caused by the limited age resolutionof the isochrones used for the analysis does alter these results significantly (or may even strengthen these results, albeit marginally)."
+"that this result has already been discussed in several previous studies using simulations (see for example Mihos Hernquist 1994, 1996).","that this result has already been discussed in several previous studies using simulations (see for example Mihos Hernquist 1994, 1996)."
+" This mechanism does not require any stellar feedback to work, that is, the gas inflows are a natural consequence of the dynamics of the interaction and the redistribution of the angular momentum that is induced during the progression of the merger (DiMatteoetal.2008;Rupke 2010)."," This mechanism does not require any stellar feedback to work, that is, the gas inflows are a natural consequence of the dynamics of the interaction and the redistribution of the angular momentum that is induced during the progression of the merger \citep{dimatteo08, rupke10}."
+". This intense inflows can deposit infewl05ys into the central (r<2 kpc) regions ~2—3x10?Me of gas, originally located before the interaction at an average distance of 6—7kpc from the galaxy centre."," This intense inflows can deposit $in few
+10^8 ys$ into the central $r\le 2\;\mathrm{kpc}$ ) regions $\sim 2-3
+\times 10^9 \;\mathrm{M_{\sun}}$ of gas, originally located before the interaction at an average distance of $6-7\;\mathrm{kpc}$ from the galaxy centre."
+ The amount and origin of the inflowing gas obviously depends on characteristics of the merger like orbital parameters of the interaction and gas fractiondiscussion)., The amount and origin of the inflowing gas obviously depends on characteristics of the merger like orbital parameters of the interaction and gas fraction.
+". In all cases, this inflow of gas fuels the first increase in the star formation rate during the merging process."," In all cases, this inflow of gas fuels the first increase in the star formation rate during the merging process."
+" A second, sometimes even stronger peak of SF takes place in the final phases of the interaction when the two galaxies are close to coalescence."," A second, sometimes even stronger peak of SF takes place in the final phases of the interaction when the two galaxies are close to coalescence."
+ The time of strong enhancement in the SFR also coincides with the time of high-dilution., The time of strong enhancement in the SFR also coincides with the time of high-dilution.
+" Typically, we find that the dilution lasts for 2x10? years, with half of the sample substaining a z/ziso<0.8 for less than 5x105 (Fig.3))."," Typically, we find that the dilution lasts for $2\times10^9$ years, with half of the sample substaining a $z/z_{iso}\le
+0.8$ for less than $5\times10^8$ \ref{fig:timehistograms}) )."
+" In the case of fly-bys, this dilution is still visible far after the pericentre passage, when the separation between the two galaxies is several hundreds of kpc."," In the case of fly-bys, this dilution is still visible far after the pericentre passage, when the separation between the two galaxies is several hundreds of kpc."
+ We emphasise that the gas redistribution and, We emphasise that the gas redistribution and
+eravitational potential,gravitational potential.
+ Although not constituting a formal rool of uniqueness. the numerical solutions to Alerritt’s equations do seem to indicate that accurate dynamical models. can be inferred. from the observable kinematic o»operties.," Although not constituting a formal proof of uniqueness, the numerical solutions to Merritt's equations do seem to indicate that accurate dynamical models can be inferred from the observable kinematic properties."
+ In theoretical studies of galaxy dynamics. manipulation of he moments of the velocity clistribution is mathematically attractive because these quantities obey the Jeans equations and their higher-order analogues (Moerrifield kent 1990. Dejonghe Merritt 1992).," In theoretical studies of galaxy dynamics, manipulation of the moments of the velocity distribution is mathematically attractive because these quantities obey the Jeans equations and their higher-order analogues (Merrifield Kent 1990, Dejonghe Merritt 1992)."
+ Llowever. the application of such analvses to observations is. in. practice. fraught with dillieulties.," However, the application of such analyses to observations is, in practice, fraught with difficulties."
+ The higher-order moments on which Dejonghe Alerritt’s (1992) proof depend are extremely sensitive to noise. so cannot be calculated from real cata.," The higher-order moments on which Dejonghe Merritt's (1992) proof depend are extremely sensitive to noise, so cannot be calculated from real data."
+ Even the velocity dispersion. calculated from the second moment ol the LOSVD. is difficult Oo estimate from noisy data. particularly if the velocity distribution has long tails out to high. velocities.," Even the velocity dispersion, calculated from the second moment of the LOSVD, is difficult to estimate from noisy data, particularly if the velocity distribution has long tails out to high velocities."
+ In. poorer-quality data. the velocity dispersion is often estimated. by fitting a Gaussian to the velocity distribution: there is in reality little justification for such a procedure. and svstematically-biassed estimates for the dispersion are almost certain to be the result.," In poorer-quality data, the velocity dispersion is often estimated by fitting a Gaussian to the velocity distribution; there is in reality little justification for such a procedure, and systematically-biassed estimates for the dispersion are almost certain to be the result."
+ In this paper. we therefore adopt à somewhat cillerent approach.," In this paper, we therefore adopt a somewhat different approach."
+ The prevalence of techniques for measuring full LOSVDs suggests that it might be worth moving away [roni analysis of moments to using the complete shape of the velocity distribution directly in the analysis., The prevalence of techniques for measuring full LOSVDs suggests that it might be worth moving away from analysis of moments to using the complete shape of the velocity distribution directly in the analysis.
+ To this end. we have been investigating the properties of a thin Utric disk model.," To this end, we have been investigating the properties of a thin tric disk model."
+ In Section 2. we discuss how the cvnanmies of an inclined thin disk galaxy can be inferred directly from. its observable kinematics.," In Section 2, we discuss how the dynamics of an inclined thin disk galaxy can be inferred directly from its observable kinematics."
+ Such a simplified model is clearly a rather special case. since cach line of sight passes through the disk at only a single. point.," Such a simplified model is clearly a rather special case, since each line of sight passes through the disk at only a single point."
+ Fherefore. in Section 32 we consider the extra complexity that is introduced when such a disk is viewed edge-on. so that cach line of sight passes through many points in the galaxy.," Therefore, in Section 3 we consider the extra complexity that is introduced when such a disk is viewed edge-on, so that each line of sight passes through many points in the galaxy."
+ We have used the anallvssis of the inclined. case to provide the basis for an iterative scheme for recovering the DE of such an on disk., We have used the sis of the inclined case to provide the basis for an iterative scheme for recovering the DF of such an edge-on disk.
+ In Section 4. we test this algorithm: on a realistic disk model. and show how the DE can. indeed. be recovered from the observable kinematies.," In Section 4, we test this algorithm on a realistic disk model, and show how the DF can, indeed, be recovered from the observable kinematics."
+ We further show that even small errors in the assumed. gravitational potential Lead to inconsistencies in the inferred. kinematic properties. and hence that the potential is very tightly. constrained by the observable properties of such a galaxy.," We further show that even small errors in the assumed gravitational potential lead to inconsistencies in the inferred kinematic properties, and hence that the potential is very tightly constrained by the observable properties of such a galaxy."
+ Section 5 discusses the possible practical application of this analysis to studies of disk galaxies., Section 5 discusses the possible practical application of this analysis to studies of disk galaxies.
+ The simplest. plausible model for a disk galaxy is one in which the system is axisvmimetric. with all the motion confined to a single plane.," The simplest plausible model for a disk galaxy is one in which the system is axisymmetric, with all the motion confined to a single plane."
+ For such a system. Jeans! theorem states that. in equilibrium. the DE can depend only on two isolating integrals of motion. the energy of stars in the disk plane. and the angular momentum of stars about the centre of the galaxy (Binney “Tremaine LOST).," For such a system, Jeans' theorem states that, in equilibrium, the DF can depend only on two isolating integrals of motion, the energy of stars in the disk plane, and the angular momentum of stars about the centre of the galaxy (Binney Tremaine 1987)."
+ Defining the usual polar coordinates about the centre of the system ancl (ling the gravitational potential in the plane of the galaxy as Wer). these integrals can be written as E=οο)|Wor). and L—re. and the DE can be expressed as a function GE.L).," Defining the usual polar coordinates about the centre of the system and ting the gravitational potential in the plane of the galaxy as $\Psi(r)$, these integrals can be written as $E = \frac{1}{2}(v^2_r + v^2_\phi) +
+\Psi(r)$, and $L = r\, v_\phi$, and the DF can be expressed as a function $f(E,L)$."
+" Ato any radius in the galaxy. the tangential velocity distribution can be obtained by integrating the DE over the whole range of racial velocity: ead) Lyde, =2 where Wu- V((r) | If we transform. variables ancl write LL). then equation (1)) is an Abel integral equation relating ποL) and fo.£)."," At any radius in the galaxy, the tangential velocity distribution can be obtained by integrating the DF over the whole range of radial velocity: ) = dv_r = 2 where = (r) + If we transform variables and write ) ,L), then equation \ref{abeleq}) ) is an Abel integral equation relating $f(E,L)$ and $f_\phi(W_\phi, L)$."
+" Thus. if fi. is known. one can use a standard Abel inversion to solvefor the full DE. =-l""f.SOE For a thin disk at inclination 7 to the line of sight. a quantity related to f£, that one can observe is the Line-of-sight velocity distribution as a function of projected radius along the galaxys apparent major axis. Pag(yp.Cros)."," Thus, if $f_\phi$ is known, one can use a standard Abel inversion to solvefor the full DF, f(E,L) = For a thin disk at inclination $i$ to the line of sight, a quantity related to $f_\phi$ that one can observe is the line-of-sight velocity distribution as a function of projected radius along the galaxy's apparent major axis, $F_{maj}(r_p, v_{los})$."
+" Via some simple geometry. one can show that Qype Cros) nm Sipe = i)/sini. ‘Thus. as first pointed out by. Merrifield Ixuijken (1994). if one observes the LOSVD alone the major axis of such a disk. then one can readily derive. f£, and hence solve for the DE. by inverting equation (1))."," Via some simple geometry, one can show that (r_p, ) (r = r_p, = i. Thus, as first pointed out by Merrifield Kuijken (1994), if one observes the LOSVD along the major axis of such a disk, then one can readily derive $f_\phi$ and hence solve for the DF by inverting equation \ref{abeleq}) )."
+ More. recently. a sophisticated investigation of this inversion has been made bv Pichon Thiébbaut (1998). who showed that it is possible to regularize à non-parametric algorithm to carry out the requisite Abel inversion without excessive noise amplification.," More recently, a sophisticated investigation of this inversion has been made by Pichon Thiébbaut (1998), who showed that it is possible to regularize a non-parametric algorithm to carry out the requisite Abel inversion without excessive noise amplification."
+ There is à degree of redundancy in the inversion. which means that its implementation can be simplified somewhat further.," There is a degree of redundancy in the inversion, which means that its implementation can be simplified somewhat further."
+ Every pair of [ML]values corresponds to. two pairs of {roe} values. and hence two points in the vvable (rp.eros} parameter space.," Every pair of $\{W_\phi, L\}$values corresponds to two pairs of $\{r, v_\phi\}$ values, and hence two points in the vable $\{r_p, v_{los}\}$ parameter space."
+ TFhus. fl(Wi.L) is sspecciffied by the observed fiwOy.eros).," Thus, $f_\phi (W_\phi, L)$ is fied by the observed $F_{maj}(r_p, v_{los})$."
+" ME we deline the ealaxys circular speed. e (ir). by the usual relation. er) =r, then it is straightforward to show that the DE is completely"," If we define the galaxy's circular speed, $v_c(r)$ , by the usual relation, v_c^2(r) = r , then it is straightforward to show that the DF is completely"
+reflected in the chain. are properly incorporated into our estimate of the stellar parameters.,"reflected in the chain, are properly incorporated into our estimate of the stellar parameters."
+ We then assign a weight to the likelihood of cach stellar model in the chain. applying a prior for the mitial mass function (IME) which assumes a Salpeter iudex.," We then assign a weight to the likelihood of each stellar model in the chain, applying a prior for the initial mass function (IMF) which assumes a Salpeter index."
+ The uunnuber of stars of cach mass and age. per 1000 stars. is eencrated by the interpolation software provided bv Yietal.(2001) for several IAIF assumptions. includiue the Salpeter IME.," The number of stars of each mass and age, per 1000 stars, is generated by the interpolation software provided by \cite{yi01} for several IMF assumptions, including the Salpeter IMF."
+ We designate the weight assigned to cach stellar 110del in the chain by normalizing to the highest IME value within the sample: iji practice. the weights vary from 0.3 to 1 (from the least to most likely).," We designate the weight assigned to each stellar model in the chain by normalizing to the highest IMF value within the sample; in practice, the weights vary from 0.3 to 1 (from the least to most likely)."
+ The IME prior changes the final answer bv less than half a σ for all parainecters., The IMF prior changes the final answer by less than half a $\sigma$ for all parameters.
+ We then incorporate this likelihood by discarding members of the clwun according to their weight. where the weight is equal to the likelihood. of remainingi samplue: about of the original chain roniins intact after this stage.," We then incorporate this likelihood by discarding members of the chain according to their weight, where the weight is equal to the likelihood of remaining sampling; about of the original chain remains intact after this stage."
+ The value for cach stellar paralucter is then assigned froimi the median of this weeated distribution. with the eor bars assigned from the nearest 234© of values.," The value for each stellar parameter is then assigned from the median of this weighted distribution, with the error bars assigned from the nearest $\pm34\%$ of values."
+ Iu this wav. we find M.— 1.0615015 AL. Re= L019 + 0. OLLR.. and an age = 2.9!17 Gyr.," In this way, we find $M_{\star}$ = $1.061^{+0.045}_{-0.040}$ $M_{\odot}$, $R_{\star}$ = 1.019 $\pm$ 0.014 $R_{\odot}$, and an age = $2.9^{+1.5}_{-1.6}$ Gyr."
+ These uncertainties are statistical as they exclude possible svstemiatie mucertaitics in the stellar uodels., These uncertainties are statistical as they exclude possible systematic uncertainties in the stellar models.
+ The best-fit solution is preseuted in Figure Γ5.., The best-fit solution is presented in Figure \ref{fig:isochrone}.
+ We caution that stellar isoclyrones are onlv poorly constrained for this faint star., We caution that stellar isochrones are only poorly constrained for this faint star.
+ The estimated error xus on the stellar parameters are smaller than what is expected for such a star of fjs maenitude., The estimated error bars on the stellar parameters are smaller than what is expected for such a star of this magnitude.
+ This is jocause we set the stellar gravity as a fixed value in our analysis. since the stellar spectnii has a low sienal-to-roise.," This is because we set the stellar gravity as a fixed value in our analysis, since the stellar spectrum has a low signal-to-noise."
+ We set the stellar eravity to the value we derive youn the stellar deusity 1ieasurec using the yphotometry (see Section 3.1))., We set the stellar gravity to the value we derive from the stellar density measured using the photometry (see Section \ref{sec:recon}) ).
+" The quality of the colmbined transit icehteurve allows us to measure the stellar density with a hieh mecision that tightly constrains the isochrone fits (soe. Figure r, 53).", The quality of the combined transit lightcurve allows us to measure the stellar density with a high precision that tightly constrains the isochrone fits (see Figure \ref{fig:isochrone}) ).
+ However. a recent study of the ρασα properties of the stellar conrponeuts of the trausitiug exoplauets by Soutlavorth(20021) shows that the curreut stella models are not deteruuued at better than in terms of radius aud iu mass (auecdian values): more conservatives values are 3 and for the stellar radius and mass respectively.," However, a recent study of the physical properties of the stellar components of the transiting exoplanets by \citet{southworth11} shows that the current stellar models are not determined at better than in terms of radius and in mass (median values); more conservatives values are 3 and for the stellar radius and mass respectively."
+ We adopt these conservatives values aud. propagate the svstemiatic errors arising from the dependence on stellar theory to the final errors., We adopt these conservatives values and propagate the systematic errors arising from the dependence on stellar theory to the final errors.
+" Adding the statistical auc svsteniatical error quadratically, we find A/,= 0.07 ALL. R,— 1.019 + 0.03 Rk..."," Adding the statistical and systematical error quadratically, we find $M_{\star}$ = $1.061\pm0.07$ $M_{\odot}$, $R_{\star}$ = 1.019 $\pm$ 0.03 $R_{\odot}$."
+ This study shows that jis consistent with a miaimsequence G dwarf star. its radius and aare incdistinewishable from Solar.," This study shows that is consistent with a main-sequence $\koicurYYspec$ dwarf star, its radius and are indistinguishable from Solar."
+ The first method we use to measure the occultatious from the oobservatious is described by Désertetal.(20115)., The first method we use to measure the occultations from the observations is described by \citet{desert11b}.
+.. We search for the occultation eveuts iu the short cadence helt curves., We search for the occultation events in the short cadence light curves.
+ We normalize aud combine 172 occultatious events., We normalize and combine 173 occultations events.
+ The best-fit aud the mnaxuuuni depth as a function of the orbital phase are found very close to the orbital phase of 0.5 as expected for a circular orbit., The best-fit and the maximum depth as a function of the orbital phase are found very close to the orbital phase of $0.5$ as expected for a circular orbit.
+ We estimate the significance of this detection by iieasuriug he occultation depth. ephemeris aud associated errors using a bootstrap Monte-Carlo analysis.," We estimate the significance of this detection by measuring the occultation depth, ephemeris and associated errors using a bootstrap Monte-Carlo analysis."
+ We find that he planet has au occultation depth of 58+10 ppin., We find that the planet has an occultation depth of $58\pm10$ ppm.
+ Iu a second mcthod. we include the occultatious iu a Markov Chain Monte Carlo global analysis as described (low in the Section 6..," In a second method, we include the occultations in a Markov Chain Monte Carlo global analysis as described below in the Section \ref{sec:mcmc}."
+" We preseut the normalized. olded. combined aud binned per 15 min Πο curve obtained at long cadence in Figure 6 frou which we neasure the occultatio1 depth with the AICAIC,"," We present the normalized, folded, combined and binned per 15 min light curve obtained at long cadence in Figure \ref{fig:keplerecllc} from which we measure the occultation depth with the MCMC."
+ The method we use to measure the occultatious from the oobservations is described in Désertetal.(2009)., The method we use to measure the occultations from the observations is described in \citet{desert09}.
+. κας observed during four occultations between August 2010 aud Jaunary 2011 with TRAC (Werneretal.2001:Fazio2001) at 3.6 and 1.5 (Cprograun ID 60028).," was observed during four occultations between August 2010 and January 2011 with /IRAC \citep{werner04,fazio04} at 3.6 and 4.5 (program ID 60028)."
+ Two occultatious were gathered per bandpass and cach visit lasted approximately 8.6 hi. The data were obtained in full-frame mode (256206 pixels) with an exposure time of 30.0 s per nuage ancl vielded 2161 images per visit., Two occultations were gathered per bandpass and each visit lasted approximately 8.6 h. The data were obtained in full-frame mode $256\times256$ pixels) with an exposure time of 30.0 s per image and yielded 2461 images per visit.
+ The method we use to produce photometric time serics from the images is described in Désertetal.(2011a)., The method we use to produce photometric time series from the images is described in \cite{desert11a}.
+. It consists of finding the centroid position of the stellar poiut spread function (PSF) aud perforuiug aperture photometry using a circular aperture on individual Basic Calibrated Data (BCD) images delivered. by the archive., It consists of finding the centroid position of the stellar point spread function (PSF) and performing aperture photometry using a circular aperture on individual Basic Calibrated Data (BCD) images delivered by the archive.
+ The optimal apertures were found to be 2.5 pixels iu radius., The optimal apertures were found to be $2.5$ pixels in radius.
+ The final photometric measurements used are presented in Table 2.., The final photometric measurements used are presented in Table \ref{tab:spitzer}.
+ The raw time series are presented in the top panels of Figure 7.., The raw time series are presented in the top panels of Figure \ref{fig:spitzerlc}.
+ Telescope pointing drift results in fluctuations of the stellar centroid position. which. in combination with iutra-pixel scusitivity variations. produces systematic noise iu the raw light curves (upper panel Figure 7)).," Telescope pointing drift results in fluctuations of the stellar centroid position, which, in combination with intra-pixel sensitivity variations, produces systematic noise in the raw light curves (upper panel Figure \ref{fig:spitzerlc}) )."
+ A description of this effect. known as the pixebphase effect. is given in the Spifzer//IRAC data haudbook (Reachetal.2006). and is well known in exoplanetarv studies (ce. Charbonneauetal.2005:Iuutsouetal. 2008)).," A description of this effect, known as the pixel-phase effect, is given in the /IRAC data handbook \citep{reach06} and is well known in exoplanetary studies (e.g. \citealt{charbonneau05,knutson08}) )."
+ To correct the light curve. we define a baseline function that is the stun of a linear function of time aud a quadratic function (with four paralcters) of the N and Y centroid positions.," To correct the light curve, we define a baseline function that is the sum of a linear function of time and a quadratic function (with four parameters) of the X and Y centroid positions."
+ We fiud that the point-to-point scatter in the photometry gives a typical signal-to-noise ratio (ΑΔ) 90 aud 110 per image at 3.6 and 1.5 rrespectivelv., We find that the point-to-point scatter in the photometry gives a typical signal-to-noise ratio $S/N$ ) $90$ and $110$ per image at 3.6 and 4.5 respectively.
+ These correspond to of the theoretical sienal-to-noise., These correspond to of the theoretical signal-to-noise.
+ We simultancously fit the iustruuenutal fictions with all the paraineters. measured the occultation depths for cach individual visit. aud report report the values in Table 2..," We simultaneously fit the instrumental functions with all the parameters, measured the occultation depths for each individual visit, and report report the values in Table \ref{tab:spitzer}."
+ The measureimieuts per bandpass agree at the l-o level., The measurements per bandpass agree at the $\sigma$ level.
+" The weighted mean of the transit depths are 0.250+0.030% aud 0.310dc0.035% at 3.6 and 15 rrespectively,", The weighted mean of the transit depths are $0.250\pm0.030$ and $0.310\pm0.035$ at 3.6 and 4.5 respectively.
+ We also included the oobservatious in the elobal MCAIC analysis described below., We also included the observations in the global MCMC analysis described below.
+ The analvsis of the pphotonmetrv and the determination of the stellar aud, The analysis of the photometry and the determination of the stellar and
+(his population is not related to the RGB-a. The SGD-a observed morphology could be indeed reproduced by old. Ilow-metallicitv isochrones. but (his would require the use of a clilferent distance and reddening with respect to main cluster population.,"this population is not related to the RGB-a. The SGB-a observed morphology could be indeed reproduced by old, low-metallicity isochrones, but this would require the use of a different distance and reddening with respect to main cluster population."
+ Such an hypothesis would implv that the anomalous SGB (race a metal-poor stellar svstem. in the background of the main body of w Cen.," Such an hypothesis would imply that the anomalous SGB trace a metal-poor stellar system, in the background of the main body of $\omega$ Cen."
+ Presently we have no possibility to discriminate between the various scenarios., Presently we have no possibility to discriminate between the various scenarios.
+ Onlv direct measurements of radial velocities and metal abundances of a significant sample of SGB-a stars will allow us to answer the enigma posed bv the discovery of this new [eature., Only direct measurements of radial velocities and metal abundances of a significant sample of SGB-a stars will allow us to answer the enigma posed by the discovery of this new feature.
+ We warily (hank Guido De Marchi for providing the photometric zero-points for the ACS fillers and Bob Rood and Flavio Fusi Pecci for helpful comments ancl suggestions., We warmly thank Guido De Marchi for providing the photometric zero-points for the ACS filters and Bob Rood and Flavio Fusi Pecci for helpful comments and suggestions.
+ We also thank the Releree. Russell Cannon. for his comments and suggestions.," We also thank the Referee, Russell Cannon, for his comments and suggestions."
+ This research was supported bv the Agenzia Spaziale Italiana. (ASI) and the Ministero dellIstruzione. dellUniversistà e della Ricerca.," This research was supported by the Agenzia Spaziale Italiana (ASI) and the Ministero dell'Istruzione, dell'Universistà e della Ricerca."
+ This research has made use of the ESO/ST-ECF Science Archive facility which is a joint collaboration of the European Southern Observatory and the Space Telescope - European Coordinating Facility., This research has made use of the ESO/ST-ECF Science Archive facility which is a joint collaboration of the European Southern Observatory and the Space Telescope - European Coordinating Facility.
+constant iniüial value of Ajj. Ado; for Ady. Ad in Eq. (,"constant initial value of $M_{\rm 1,i}$ , $M_{\rm 2,i}$ for $M_1$, $M_2$ in Eq. ("
+12) and Eq.(14)-(15). while in the iue case Vy. Ma should echange with time.,"12) and Eq.(14)-(15), while in the true case $M_1$, $M_2$ should change with time."
+" This will cause a big problem lor a=1 when Mo,>LM... which has been pointed out in 83.3."," This will cause a big problem for $\alpha=1$ when $M_{\rm 2,i} > 1M_\sun$, which has been pointed out in 3.3."
+ Filth reason is the use of wai. in Eq. (," Fifth reason is the use of $\omega_{\rm crit,\sun}$ in Eq. ("
+"14) as the value of wy, for all the donors ranging from 0.5.M. to L.3AL..",14) as the value of $\omega_{\rm crit}$ for all the donors ranging from $0.5M_\sun$ to $1.3M_\sun$.
+ At last we conclude that (1112 is a fair definition of bifurcation period. and (2)the period evolution during (he mass transfer phase is in first approximation sufficientlv well described bv the balance of mass transfer and angular momentum loss caused by MD.," At last we conclude that $\dot{P}$ is a fair definition of bifurcation period, and (2)the period evolution during the mass transfer phase is in first approximation sufficiently well described by the balance of mass transfer and angular momentum loss caused by MB."
+ For these rough assumptions mace in {his semi-analvtical method. its results agree with the numerical results only in the leading order.," For these rough assumptions made in this semi-analytical method, its results agree with the numerical results only in the leading order."
+ Our munerical caleulations show that there is an upper limit lor the donor massbevond which no converging svstems will form., Our numerical calculations show that there is an upper limit for the donor massbeyond which no converging systems will form.
+ Pylvser&Savonije(1983). found that. in the case ol M4;=40M... there is no converging svstem existing if οι>1.7.M.. ancl concluded that for any given initial aceretor mass there exists a maximum initial secondary. mass [or the formation of converging svstems.," \citet{pylyser88} found that, in the case of $M_{1, \rm i} =
+4.0M_\sun$, there is no converging system existing if $M_{2,\rm i}>
+1.7 M_\sun $, and concluded that for any given initial accretor mass there exists a maximum initial secondary mass for the formation of converging systems."
+ From our caleulations with M;—L4AL.. we find an upper limit lor the initial secondary mass M»; between 1.2 and 1.4M.. under saturated MD.," From our calculations with $M_{1,\rm
+i}=1.4M_\sun$, we find an upper limit for the initial secondary mass $M_{2,\rm i}$ between $1.2$ and $1.4 M_\sun$ under saturated MB."
+ The reason is (hat for binaries with a MS donor of initial mass >1.4V.. the bifurcation period is shorter than the minimum ZAMS period. so that thesesvstems will diverge.," The reason is that for binaries with a MS donor of initial mass $> 1.4M_\sun$, the bifurcation period is shorter than the minimum ZAMS period, so that thesesystems will diverge."
+ For tracitional MD. this upper limit is > 2... bevond the range of donor masses we adopt.," For traditional MB, this upper limit is $> 2M_\sun$ , beyond the range of donor masses we adopt."
+the plane.,the plane.
+ The Galactic bar has usually been regarded as either a triaxial boxy bulge (or “peamut’). principally on the basis of Cosmic Background Explorer (COBE) infrared observations. or as a long thin bar.," The Galactic bar has usually been regarded as either a triaxial boxy bulge (or `peanut'), principally on the basis of Cosmic Background Explorer (COBE) infrared observations, or as a long thin bar."
+ ?— speculated that the Galaxy might. contain two bar components aud recent consensus Is that both these types of bars exist (2??)..," \citet{blitz91} speculated that the Galaxy might contain two bar components and recent consensus is that both these types of bars exist \citep{hammersley00, benjamin05,cabrera08}."
+ The orientation of the bar with respect to the Suu-Galaetic centre line-ol-sight is thought to lie between 11 and. 15°. but mauy of the lower inclination angles are lor boxy bulge bar models. whilst the larger augles are for long thin bars (and confusion bas been adde with the interchangeable and sometimes ambiguous use of the bulge aud bar terms. see discussions of ? aud ?)).," The orientation of the bar with respect to the Sun-Galactic centre line-of-sight is thought to lie between $^{\circ}$ and $^{\circ}$, but many of the lower inclination angles are for boxy bulge bar models, whilst the larger angles are for long thin bars (and confusion has been added with the interchangeable and sometimes ambiguous use of the bulge and bar terms, see discussions of \citet{ng98} and \citet{lopez99}) )."
+ This has led to a likely picture of a triaxial bulge bar inclined at 20—307 and a loug thin bar at ~ 15°., This has led to a likely picture of a triaxial bulge bar inclined at $-$ $^{\circ}$ and a long thin bar at $\sim$ $^{\circ}$.
+ This combination is sliown relative to the 3-kpce arms in Figure 5.., This combination is shown relative to the 3-kpc arms in Figure \ref{barschematic}.
+ Primarily ou the basis of iuodels based ou infrared (IR) data. the radius ol corotation resonance of the bar (of the order of 1.2 times the semi-major axis of the bar (???))) is estimated to be LE0.5 kkpe (?.referencesthereiu)..," Primarily on the basis of models based on infrared (IR) data, the radius of corotation resonance of the bar (of the order of 1.2 times the semi-major axis of the bar \citep{elmegreen96, englmaier06, buta09}) ) is estimated to be $\pm$ kpc \citep[][references therein]{gerhard02}."
+ In galaxies this radius marks the trausitiou from elliptical orbits following the bar to circular orbits beyond (?).., In galaxies this radius marks the transition from elliptical orbits following the bar to circular orbits beyond \citep{contopoulos80}.
+ As noted in the introduction. several 6.7-Hz methanol masers Lave been associated with the Galactic bar.," As noted in the introduction, several 6.7–GHz methanol masers have been associated with the Galactic bar."
+ Where the Galactic bar aud the 3-kpc arms meet (discussed iu section ??)). a region of enhanced star formation is expected (e.g.22??)..," Where the Galactic bar and the 3–kpc arms meet (discussed in section \ref{3kpcdiscussion}) ), a region of enhanced star formation is expected \citep[e.g.][]{fux99, englmaier99, lopez01, binney08}."
+ This means that a deusity enhaucement in either the near or far 3-kpe ari 6.7-GHz methanol maser population could iudicate the interaction with the eud of the bar., This means that a density enhancement in either the near or far 3–kpc arm 6.7–GHz methanol maser population could indicate the interaction with the end of the bar.
+ Such au enhancement has beeu suggested iu the far 3-kpe arm population (2). aud we now address both this aud possible near-sicle interactious., Such an enhancement has been suggested in the far 3–kpc arm population \citep{green10mmb2} and we now address both this and possible near-side interactions.
+ The 6.7-GHz methanol maser population tracing the 3-kpce arms exhibits a high density ol sources within the far 3-kpe arm between lougitudes —9° to —15° (see Figure 3. and. Table 1)), The 6.7–GHz methanol maser population tracing the 3–kpc arms exhibits a high density of sources within the far 3–kpc arm between longitudes $-$ $^{\circ}$ to $-$ $^{\circ}$ (see Figure \ref{lvdensity} and Table \ref{resotable}) ).
+ Within this dense region. & sources with velocities >Okkuass ! partially overlap with the extrapolated outer Galaxy components of the Carina-Sagittarius aud Crusx-Seutuni aris (at distauces ml5kkpc). aud 6 sources with velocities between 0 aud. —30 ! overlap with the ari (which passes between the Galactic centre aud the Suu at a cistance of «1.1 kpe ?)).," Within this dense region, 8 sources with velocities $>$ $^{-1}$ partially overlap with the extrapolated outer Galaxy components of the Carina-Sagittarius and Crux-Scutum arms (at distances $>$ kpc), and 6 sources with velocities between 0 and $-$ $^{-1}$ overlap with the Carina-Sagittarius arm (which passes between the Galactic centre and the Sun at a distance of $<$ 1.1 kpc \cite{sato10}) )."
+ The distances of these arms will have au impact ou the flux density distribution of the sources. au ellect that can be estimated if we assume a simple power law luminosity. distribution above the seusitivity limit of the MMB (0.7JJsy. 2)): at Lokkpe heliocentric distance ouly the brightest sources would be detected. whilst at 1 kpc heliocentric cistauce very faint sources would," The distances of these arms will have an impact on the flux density distribution of the sources, an effect that can be estimated if we assume a simple power law luminosity distribution \citep[e.g.][]{pestalozzi07} above the sensitivity limit of the MMB Jy, \citealt{green09a}) ): at kpc heliocentric distance only the brightest sources would be detected, whilst at 1 kpc heliocentric distance very faint sources would"
+"In this experiment, the collapse of the wave function (seen in the pattern of the signal photons) is induced by an event (the detection of the idler photon, if it occurs at D3 or D4 at least) which happens at a moment in time.","In this experiment, the collapse of the wave function (seen in the pattern of the signal photons) is induced by an event (the detection of the idler photon, if it occurs at $D_3$ or $D_4$ at least) which happens at a moment in time."
+ This is a very striking result., This is a very striking result.
+ How can a measurement cause an entangled particle to collapsepast?, How can a measurement cause an entangled particle to collapse?
+"? It seems like the picture of an instantaneous wave function collapse, as sketched in the first sections, has to be wrong."," It seems like the picture of an instantaneous wave function collapse, as sketched in the first sections, has to be wrong."
+" One might be drastic and postulate a form of ‘backwards time influence’, where a measurement may influence the ‘behavior’ of particles (or here, photons) in the pasttikzmarkmainBodyCitationStart786|9]."," One might be drastic and postulate a form of `backwards time influence', where a measurement may influence the `behavior' of particles (or here, photons) in the past."
+". First of all, note that a quantitative computation (using standard quantum optical techniques) reproduces precisely the experimental outcome[5]."," First of all, note that a quantitative computation (using standard quantum optical techniques) reproduces precisely the experimental outcome."
+" This result follows without invoking any backwards causality, and clearly indicates that the experiment can be understood within the standard quantum mechanical framework."," This result follows without invoking any backwards causality, and clearly indicates that the experiment can be understood within the standard quantum mechanical framework."
+ But what is going on then?, But what is going on then?
+ How can we understand this experiment in a more way and what are the conceptual conclusions?, How can we understand this experiment in a more way and what are the conceptual conclusions?
+ We will resolve these issues in the next sections., We will resolve these issues in the next sections.
+Each coordinate wry. 4=Le... is giveu the weight 1. while the time coordinate / is given the weight 2.,"Each coordinate $x_{i}$ , $i=1, ..., n$ is given the weight $1$, while the time coordinate $t$ is given the weight $2$."
+" The vector a=(ay.....(yy.1)(OL...1.9)eg""1 is called the (η+L)-dineusioual parabolic anisotropy."," The vector $a=(a_{1},\ldots, a_{n}, a_{n+1}) = (1,\ldots, 1, 2)\in \R^{n+1}$ is called the $(n+1)$ -dimensional parabolic anisotropy."
+ For this given a. the action of j(/'€[0.x) ons =bref) is given by ps=(pri...pongqct).," For this given $a$ , the action of $\mu\in [0,\infty)$ on $z=(x,t)$ is given by $\mu^{a}z = (\mu x_{1},\ldots, \mu x_{n}, \mu^{2} t)$."
+ Forp>Q0 and s€E we set jpz=(Gr)2., For$\mu>0$ and $s\in \R$ we set $\mu^{s a} z = (\mu^{s})^{a} z$.
+" Iu particular. jpz=(jp1)!z and 27*2=(24)*z, jEZ."," In particular, $\mu^{-a} z = (\mu^{-1})^{a} z$ and $2^{-j a} z =
+(2^{-j})^{a} z$ , $j\in \Z$."
+" For eR”!, 240. let |z|, be the unique positive nunber ji such that: and let |z],=0 for z=0."," For $z\in \R^{n+1}$, $z\neq 0$, let $|z|_{a}$ be the unique positive number $\mu$ such that: and let $|z|_{a} = 0$ for $z=0$."
+" The map |-|, is called the parabolic distance function which is C'* (see for instance [22])).", The map $|\cdot|_{a}$ is called the parabolic distance function which is $C^{\infty}$ (see for instance \cite{Y86}) ).
+" Iu the case where a=(1.....1)e€RLl we get the usual Euclidean distance JGcvFPP,"," In the case where $a=(1,\ldots, 1)\in \R^{n+1}$, we get the usual Euclidean distance $\|z\|=(x^{2}_{1}+\cdots+x^{2}_{n}+t^{2})^{1/2}$."
+" Denoting OCE"". Fl any open subset of IE"".1. we are ready to give the definition of the first two parabolic spaces used in our aualysis."," Denoting $\mathcal{O}\subseteq \R^{n+1}$ , any open subset of $\R^{n+1}$, we are ready to give the definition of the first two parabolic spaces used in our analysis."
+" Along with the above parabolic distance |-|,. the Litthewood-Paley decomposition is now recalled (formore details. we refer to [11]))."," Along with the above parabolic distance $|\cdot|_{a}$, the Littlewood-Paley decomposition is now recalled (formore details, we refer to \cite{Grafakos}) )."
+ Let 0€CSUR”1)be any cut-oll function satisfvine: Let w(2)—0(z) 0f2%2)., Let $\theta\in C_{0}^{\infty}(\R^{n+1})$be any cut-off function satisfying: Let $\psi(z) = \theta(z) - \theta(2^{a} z)$ .
+ We now construct asmooth (compactly supported) parabolic dyaclic partition ofunity (6j);cz by letting satisfying, We now construct asmooth (compactly supported) parabolic dyadic partition ofunity $(\psi_{j})_{j\in \Z}$ by letting satisfying
+Close et al. (,Close et al. (
+2003) ancl Cizis et al. (,2003) and Gizis et al. (
+2003) provide the most complete set of observations to date of field very Iow-mass and brown dwarf binaries.,2003) provide the most complete set of observations to date of field very low-mass and brown dwarf binaries.
+ Alternatively. Martian et al. (," Alternatively, n et al. ("
+2003) have survevecl voung stellar clusters. such as a Persei and the Pleiades. to pin down the binary fraction among the brown dwarf population.,"2003) have surveyed young stellar clusters, such as $\alpha$ Persei and the Pleiades, to pin down the binary fraction among the brown dwarf population."
+ All these studies suggest that the binary [raction among very low-mass stars and brown chwarts is much lower than for C-tvpe stars. a trend. that Yve also find in our simulations (see Figure 3).," All these studies suggest that the binary fraction among very low-mass stars and brown dwarfs is much lower than for G-type stars, a trend that we also find in our simulations (see Figure 3)."
+ Specifically. Close et al. (," Specifically, Close et al. ("
+2003) find a binary [raction in the range for MS.0-L0.5 stars with separations greater than : AU. and a semi-major axis distribution peak at  4 AU.,"2003) find a binary fraction in the range $\pm$ for M8.0-L0.5 stars with separations greater than 2.6 AU, and a semi-major axis distribution peak at $\sim$ 4 AU."
+ In their sample. no verv-Iow mass binary has a separation e&reater than 15 AU.," In their sample, no very-low mass binary has a separation greater than 15 AU."
+ These results are in agreement with those of Gizis et al. (, These results are in agreement with those of Gizis et al. (
+2003) ane Bou et al. (,2003) and Bouy et al. (
+2003).,2003).
+" Martínn et al (2003) also concludes that a binary [frequeney. in the range IO,15%. a bias to separations smaller than about 15 AU. and a tendency towards high mass ratios (¢< 0.7) are the fundamental properties of brown cwarl binaries."," n et al (2003) also concludes that a binary frequency in the range $10\%-15\%$, a bias to separations smaller than about 15 AU, and a tendency towards high mass ratios $q
+\gsim$ 0.7) are the fundamental properties of brown dwarf binaries."
+ It must be noted. however. that the LO%15% observed binary frequeney is most likely a lower limit and that. in general. there is considerable uncertainty about the properties of brown cwarf binaries.," It must be noted, however, that the $10\%-15\%$ observed binary frequency is most likely a lower limit and that, in general, there is considerable uncertainty about the properties of brown dwarf binaries."
+ In our simulations. most. binary systems are tight (see Figure 1. right panel). with a median semi-major axis of 10 AU. but few. of these systems have primary masses below 0.3 M. (for a discussion of this issue. see section 3.2).," In our simulations, most binary systems are tight (see Figure 1, right panel), with a median semi-major axis of 10 AU, but few of these systems have primary masses below 0.3 $_\odot$ (for a discussion of this issue, see section 3.2)."
+ Adaptive optics imagine surveys of common associations. such as PucanaHorologium (Chauvin et al.," Adaptive optics imaging surveys of common associations, such as Tucana–Horologium (Chauvin et al."
+ 2003). TW Lvclrac (Zuckerman et al.," 2003), TW Hydrae (Zuckerman et al."
+ 2001). ALBAL 12 (Llearty ct al.," 2001b), MBM 12 (Hearty et al."
+ 2000) or the 37 Pictoris moving group (Zuckerman et al., 2000) or the $\beta$ Pictoris moving group (Zuckerman et al.
+ 2001a) are ideal to study the multiplicity ooperties of voung stars. due to their proximity to Earth (κ: TO pc) and their inferred vouth (e.g. ~ 20 Myr for the j Pictoris group).," 2001a) are ideal to study the multiplicity properties of young stars, due to their proximity to Earth $<$ 70 pc) and their inferred youth (e.g. $\sim$ 20 Myr for the $\beta$ Pictoris group)."
+ These associations clearly demonstrate 10 formation of stars in à clustered. mode and. therefore. represent an invaluable laboratory against which to compare vw results obtained by models of clustered star formation.," These associations clearly demonstrate the formation of stars in a clustered mode and, therefore, represent an invaluable laboratory against which to compare the results obtained by models of clustered star formation."
+ dynamical interactions among embedded stars are indeed as important as shown by our models. this should be reflected most. clearly on re multiplicity properties. of the stars populating these groups: Le. the binary. fraction gaiould be higher than in the field or in clusters. (since many singles should have sscaped the group). low-mass objects should be found to be effectively bound. to. more massive binaries/multiples. but at. large separations. and conversely. single unbound brown dwarfs should. be rare.," If dynamical interactions among embedded stars are indeed as important as shown by our models, this should be reflected most clearly on the multiplicity properties of the stars populating these groups: i.e. the binary fraction should be higher than in the field or in clusters (since many singles should have escaped the group), low-mass objects should be found to be effectively bound to more massive binaries/multiples, but at large separations, and conversely, single unbound brown dwarfs should be rare."
+ Companion frequencies should. also be high (in the range 0.5 1)., Companion frequencies should also be high (in the range $0.5-1$ ).
+ Recent results by Branceker. Javzwardhana Najita (2003) point to this direction: they find that the multiplicity frequencies in the TN Livclrac ancl MDBM 12 eroups are high (0.58+0.12 and 0.640.10. respectively) in comparison with other voung regions such as Taurus or p Ophiuchus (Duchenne 1999).," Recent results by Brandeker, Jayawardhana Najita (2003) point to this direction: they find that the multiplicity frequencies in the TW Hydrae and MBM 12 groups are high $0.58 \pm 0.12$ and $0.64 \pm 0.16$, respectively) in comparison with other young regions such as Taurus or $\rho$ Ophiuchus (Duchênne 1999)."
+ The companion frequencies (or average number of companions per star system) for hese two moving groups are even higher: 0.84+0.22 and 9]d0.30. suggesting that many of the multiples have NC2.," The companion frequencies (or average number of companions per star system) for these two moving groups are even higher: $0.84 \pm 0.22$ and $0.91 \pm 0.30$, suggesting that many of the multiples have $N > 2$."
+" These results may be compared with the value of. f, hat our models predict if ee. of the singles have left he group at /210.5 Myr. ie... fo=0.7."," These results may be compared with the value of $f_{\rm c}$ that our models predict if e.g. of the singles have left the group at $t= 10.5$ Myr, i.e., $f_{\rm c} = 0.7$."
+ High-resolution imaging has recently provided the first wo brown dwarf candidates orbiting solar-twpe. stars at small separations (1515 et al., High-resolution imaging has recently provided the first two brown dwarf candidates orbiting solar-type stars at small separations (Els et al.
+ 2001: Liu et al., 2001; Liu et al.
+ 2002)., 2002).
+ These xown cwarfs are at distance of z 15-20 AU of the xwimaryv., These brown dwarfs are at distance of $\approx$ 15-20 AU of the primary.
+ Although these. observations imply that brown dwarf companions do exist at separations Comparable to hose of giant. planets in our solar svstem. the frequency of this type of systems remains unclear: half of the stars wubouring planets have long term. trends in their racial velocities due to unseen companions (Fischer et al.," Although these observations imply that brown dwarf companions do exist at separations comparable to those of giant planets in our solar system, the frequency of this type of systems remains unclear: half of the stars harbouring planets have long term trends in their radial velocities due to unseen companions (Fischer et al."
+ 2001). rut so. fu no other. brown dwarf companion at close separations has been found.," 2001), but so far no other brown dwarf companion at close separations has been found."
+ In our simulations we find one ανν (Lable 1. πο," In our simulations we find one binary (Table 1, ref."
+ (ὁ7) in ας) out of 24 (at 10.5 Myr) to jwe a close brown ονα companion: this gives a frequency of ~4%..., $(6-7)$ in $\alpha3$ C) out of 24 (at 10.5 Myr) to have a close brown dwarf companion: this gives a frequency of $\sim$.
+ This binary is composed of a 0.21 AL. star and a 1.05 M. brown dwarf (q=0.24). has a semi-major axis of 10 AU and an eccentricity of 0.7.," This binary is composed of a 0.21 $_\odot$ star and a 0.05 $_\odot$ brown dwarf $q = 0.24$ ), has a semi-major axis of 10 AU and an eccentricity of 0.7."
+ Raclial velocity surveys find that the incidence of brown chvarls within 4 AU of solar-tvpe Εν stars is <τα., Radial velocity surveys find that the incidence of brown dwarfs within 4 AU of solar-type FGK stars is $<$.
+ The evidence for this at very small separations first emerged [rom radial velocity surveys in the late SOs and early 90s (e.g Walker et al., The evidence for this at very small separations first emerged from radial velocity surveys in the late 80's and early 90's (e.g Walker et al.
+ 1905). and has been confirmed by current high-precision radial velocity programs (Marcy Butler 2000: Llalbwachs et al.," 1995), and has been confirmed by current high-precision radial velocity programs (Marcy Butler 2000; Halbwachs et al."
+ 2000)., 2000).
+ Our results are consistent with this observed.descr no binary has a sub-stellar companion closer than LO AU., Our results are consistent with this observed: no binary has a sub-stellar companion closer than 10 AU.
+ The explanation of this result is very simple: most brown cwarls companions to stars are formed via the fragmentation of circtunstcllar disces. but this same clise drives quickly. the mass ratio of the binary towards unity. due to the accretion of material with higher specifie angular momentum than that of the binary orbit (Bate Bonnell 1997: Date 2000).," The explanation of this result is very simple: most brown dwarfs companions to stars are formed via the fragmentation of circumstellar discs, but this same disc drives quickly the mass ratio of the binary towards unity, due to the accretion of material with higher specific angular momentum than that of the binary orbit (Bate Bonnell 1997; Bate 2000)."
+ In some other cases. the brown cwarl companion is also likely to be exchanged by à more massive object after a three-bocdy encounter.," In some other cases, the brown dwarf companion is also likely to be exchanged by a more massive object after a three-body encounter."
+ Racial velocity measurements of the components. of visual double ancl multiple stars (Fekel. 1951: Fokovinin 1907: Mazeh et al., Radial velocity measurements of the components of visual double and multiple stars (Fekel 1981; Tokovinin 1997; Mazeh et al.
+ 2001: Tokovinin Smekhoy 2002) iwe resulted in the detection. of a substantial fraction of spectroscopic sub-systems., 2001; Tokovinin Smekhov 2002) have resulted in the detection of a substantial fraction of spectroscopic sub-systems.
+ Tokovinin. (1997). points out hat the frequency of sub-systems among spectroscopic jnaries with periods shorter than 10 days is at least of4., Tokovinin (1997) points out that the frequency of sub-systems among spectroscopic binaries with periods shorter than 10 days is at least of.
+". More recently. Tokovinin Smekhoy (2002) jwe found a frequency of spectroscopic sub-systems of z per component among 26 resolved. visual binaries (ic. of these binaries turned out. to. be triples. or alternatively, may be binary quacruples)."," More recently, Tokovinin Smekhov (2002) have found a frequency of spectroscopic sub-systems of $\approx$ per component among 26 resolved visual binaries (i.e. of these binaries turned out to be triples or alternatively, may be binary quadruples)."
+ In addition. 15 out of 59 apparently single tertiary components turned out to be spectroscopic binaries (Lo. of the svstenis are quadruples instead of triples).," In addition, 18 out of 59 apparently single tertiary components turned out to be spectroscopic binaries (i.e. of the systems are quadruples instead of triples)."
+ These results. seem o be in :erecment with the high abundance of high-order multiple svstems found in our simulations., These results seem to be in agreement with the high abundance of high-order multiple systems found in our simulations.
+ Note hat although no binaries with semi-major axis smaller han 1 AU can be produced by our simulations (due to softening of the gravitational acceleration between: point masses at short distances) there is no reason to believe hat such spectroscopic binaries would. not. have formed iwl the resolution limit been much lower: therefore. a direct. comparison of Tokovinin Smekhov findings with our results is indeed meaningful.," Note that although no binaries with semi-major axis smaller than 1 AU can be produced by our simulations (due to softening of the gravitational acceleration between point masses at short distances) there is no reason to believe that such spectroscopic binaries would not have formed had the resolution limit been much lower; therefore, a direct comparison of Tokovinin Smekhov findings with our results is indeed meaningful."
+ Further racial velocity observations of the components of multiple systems would, Further radial velocity observations of the components of multiple systems would
+(G09. Table L1 for exhaustive listing of known GC qLMXDz). and with the best-fit values obtained with (C009).,"(G09, Table 4 for exhaustive listing of known GC qLMXBs), and with the best-fit values obtained with (G09)."
+ The unabsorbed flux LOkeW)) ids also consistent with the flix of the thermal component of the oobservation (as will be demonstrated statistically below). estimated to be of the total flux (G09). the other being the coutribution of the power-law colmpoucut.," The unabsorbed flux ) is also consistent with the flux of the thermal component of the observation (as will be demonstrated statistically below), estimated to be of the total flux (G09), the other being the contribution of the power-law component."
+ The second sonrce n he Core. (015 counts including about two background counts). appears spectrally harder. as it has onlv seven counts below2keV.. two couuts in the eenerev range. and the rest (nime events) aboveΚ," The second source in the core, (18 counts including about two background counts), appears spectrally harder, as it has only seven counts below, two counts in the energy range, and the rest (nine events) above."
+"ον, The spectrum is fitted with au absorbed power law. to compare it to the power-law component fitted iu the spectrum of17."," The spectrum is fitted with an absorbed power law, to compare it to the power-law component fitted in the spectrum of."
+. The best-fit photon iudex is consistent with the hard power-law component for the source292717., The best-fit photon index is consistent with the hard power-law component for the source.
+ For completeness. the spectrum is fitted with a NS atmosphere imodel. for which the best-fit projected radius is Inconsistent with the typical radii of NSs.," For completeness, the spectrum is fitted with a NS atmosphere model, for which the best-fit projected radius is inconsistent with the typical radii of NSs."
+" The eooduess of this fit of Monte Carlo simulations frou, the NS atmosphere model give better statistics than the best fit) sueeests that the spectrum is not that of a NS T-atimosphere model.", The goodness of this fit of Monte Carlo simulations from the NS atmosphere model give better statistics than the best fit) suggests that the spectrum is not that of a NS H-atmosphere model.
+ These results provide further support that this source is not the candidate qLMXD. but another source of unknown classification.," These results provide further support that this source is not the candidate qLMXB, but another source of unknown classification."
+ As α- last) check. of statistical consistencv. a siuultaneous fit is performed using the XA/Af/pu. XAIM/MOSI. NALAL/AIOS2 for aac /ACIS spectra for both ando292715.," As a last check of statistical consistency, a simultaneous fit is performed using the /pn, /MOS1, /MOS2 for and /ACIS spectra for both and."
+"5.. While απο, the temperature. the radius and the photon iudex paranieters of each individual data set are kept tied together aud lis kept fixed at the value cited above."," While fitting, the temperature, the radius and the photon index parameters of each individual data set are kept tied together and is kept fixed at the value cited above."
+ The results are also shown in Table 3.. as a simultancous fif for292717.," The results are also shown in Table \ref{tab:res}, as a simultaneous fit for."
+.. Again. the fit is statistically acceptable.(0.86). and the obtained best-fit parauncters are in agrecment with typical values for accreting quiesceut. NS.," Again, the fit is statistically acceptable, and the obtained best-fit parameters are in agreement with typical values for accreting quiescent NS."
+ To characterize the variation in flux for the qLAINB. we performed a smimltaueous spectral fitting using the EPIC/pu data alone for aud with the ACTIS-S data for aand292715.5: a inultiplicative factor for the spectral normalization is used. fixed at lL for the XAZAM-Newton/f/pu spectra aud left as a free pariaueter for the Chendra//ACTS spectrum.," To characterize the variation in flux for the qLMXB, we performed a simultaneous spectral fitting using the EPIC/pn data alone for and with the ACIS-S data for and; a multiplicative factor for the spectral normalization is used, fixed at 1 for the /pn spectrum and left as a free parameter for the /ACIS spectrum."
+ The best-fit factor is πο confidence). which is ijareinallv consistent with the fixes beime the same.," The best-fit factor is $0.80\ud{0.19}{0.16}$ confidence), which is marginally consistent with the fluxes being the same."
+ We therefore conclude that17.. observed previously iu the core of NGC 6301 (609). is a composite of aand/292715.5.. which were not distinguishable at the resolution of but which are spatially resolved at the resolutionNewton... ofChandra.," We therefore conclude that, observed previously in the core of NGC 6304 (G09), is a composite of and, which were not distinguishable at the resolution of, but which are spatially resolved at the resolution of."
+ The low signalto-noise candidate qLMXD reported iu the aanalysis (C09) is also detected on the /ACTS observation as292916., The low signal-to-noise candidate qLMXB reported in the analysis (G09) is also detected on the /ACIS observation as.
+1.. Au offset of jis iueasured between the Chaendre//ACIS. and the oobservations. consistent within lo.," An offset of is measured between the /ACIS and the observations, consistent within $1\sigma$."
+ The ssource position Is located ffrom the possible Two-Micron All Sky Survey. (2MASS) counterpart reported ((CG09)., The source position is located from the possible Two-Micron All Sky Survey (2MASS) counterpart reported (G09).
+. This offset is cousisteunt (1.10) with the two sources aand 2920163). being associated where the uncertainty is due to μάναss svstematic and statistical uncertainties: the eror on the 2MASS position is assed to be negligible., This offset is consistent $1.4\sigma$ ) with the two sources and ) being associated where the uncertainty is due to s systematic and statistical uncertainties; the error on the 2MASS position is assumed to be negligible.
+ Also. the probability that another source as bright or brighter lies as close or closer to the ppositious is0.31%... providing further support to the association. with confidence.," Also, the probability that another source as bright or brighter lies as close or closer to the positions is, providing further support to the association, with confidence."
+ This ssource.292916.1.. is located ~1.5' off-axis aud requires a 3”-racdins extraction region.," This source, is located $\sim1.5\arcmin$ off-axis and requires a -radius extraction region."
+ The source has 19 counts Gucliding about three background counts) and is also fitted. using Casl-statistic. with a NS atinosphere model. keeping μου=0.266 fixed.," The source has 19 counts (including about three background counts) and is also fitted, using Cash-statistic, with a NS atmosphere model, keeping $\nhtt=0.266$ fixed."
+ The best-fit parameters are consistent with the previously published values (Table 3))., The best-fit parameters are consistent with the previously published values (Table \ref{tab:res}) ).
+ A simultancous fitting is also performed for this candidate qELMXD. using the aud," A simultaneous fitting is also performed for this candidate qLMXB, using the and"
+ A simultancous fitting is also performed for this candidate qELMXD. using the aud:," A simultaneous fitting is also performed for this candidate qLMXB, using the and"
+Panaiteseu.A. Numar.P. 2002. ApJ. 571. Pandey οἱ al.,"Panaitescu,A. Kumar,P. 2002, ApJ, 571, Pandey et al."
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+for distant clouds. because of the particular mechanism of acceleration in combination with projection elfects induces by galactic rotation.,"for distant clouds, because of the particular mechanism of acceleration in combination with projection effects induced by galactic rotation."
+ Thus. the model can explain the existence of gas with velocities up to 200 kni !. bat not if it is generally. nearby.," Thus, the model can explain the existence of gas with velocities up to 200 km $^{-1}$, but not if it is generally nearby."
+ The importance of detecting LIVCs in more than one emission line cannot be overstated., The importance of detecting HVCs in more than one emission line cannot be overstated.
+ A fountain is expecte to produce strong low ionisation linesON! ete.)," A fountain is expected to produce strong low ionisation lines, etc.)"
+ due to shocks and perhaps metal-enriched material from the central disk (Shapiro enjamin 1991)., due to shocks and perhaps metal-enriched material from the central disk (Shapiro Benjamin 1991).
+ The few LVCs with constrained metallicities have abundances no more than one third of solar abundance (de Boer Savage 1984: 11988)., The few HVCs with constrained metallicities have abundances no more than one third of solar abundance (de Boer Savage 1984; 1988).
+ While metal abundances are uncertain. the emission lines provide an important diagnostic. particularly in constraining the ionisation parameter.," While metal abundances are uncertain, the emission lines provide an important diagnostic, particularly in constraining the ionisation parameter."
+ Detailed line ratios have been computed for a range of ionising sources. including shocks. non-thermal power laws. and hot voung stars observed through an opaque medium. (Mathis. 1986: Veilleux Osterbrock 1987: Sokolowski 1992: Sutherland Dopita 1993: Shapiro Benjamin 1991).," Detailed line ratios have been computed for a range of ionising sources, including shocks, non-thermal power laws, and hot young stars observed through an opaque medium (Mathis 1986; Veilleux Osterbrock 1987; Sokolowski 1992; Sutherland Dopita 1993; Shapiro Benjamin 1991)."
+ H£ the surfaces of ΗΝος are collisionally ionised. it is unlikely that can give à useful constraint on clistance.," If the surfaces of HVCs are collisionally ionised, it is unlikely that can give a useful constraint on distance."
+ However. as noted in 54.2. the rratio peaks within of the vvelocitv.," However, as noted in $\S$ 4.2, the ratio peaks within of the velocity."
+ This is a major problem for shock ionisation models where the emitting regions arise [rom downstream σας and are therefore kinematically separated from the shock material Sutherland Dopita 1993). (, This is a major problem for shock ionisation models where the emitting regions arise from downstream gas and are therefore kinematically separated from the pre-shock material Sutherland Dopita 1993). (
+(1995) discuss alternative sources of LIVC ionisation and heating. but these are not expected to produce significant optical line emission.,"1995) discuss alternative sources of HVC ionisation and heating, but these are not expected to produce significant optical line emission."
+ The Galaxy is encircled by satellite galaxies which appear confined to one or two great ‘streams’ across the sky (q.v., The Galaxy is encircled by satellite galaxies which appear confined to one or two great `streams' across the sky (q.v.
+ Lynden-Dell Lynden-Dell 1995)., Lynden-Bell Lynden-Bell 1995).
+ Phe most renowned of these are the AMagellanic Clouds and the associated sstream., The most renowned of these are the Magellanic Clouds and the associated stream.
+ ALL of these are expected to merge with the Galaxy in the distant future. largely due to dynamical friction [rom the extended dark. halo. (Yremaine 1976).," All of these are expected to merge with the Galaxy in the distant future, largely due to dynamical friction from the extended dark halo (Tremaine 1976)."
+ But the most spectacular accreting satellite. the Ser ebwarf. was discovered only Four vears ago by Ibata. Gilmore Irwin (1994).," But the most spectacular accreting satellite, the Sgr dwarf, was discovered only four years ago by Ibata, Gilmore Irwin (1994)."
+ Ser is approximately 25 kpe from the Sun. and. 162 kpe from the Galactic Centre.," Sgr is approximately 25 kpc from the Sun, and $\pm$ 2 kpc from the Galactic Centre."
+ The long axis of the prolate body (axis ratios  3:1:1) is roughly 19 kpc. oriented perpendicular to the Galactic plane along /=6. centred ab b=—15.," The long axis of the prolate body (axis ratios $\sim$ 3:1:1) is roughly 10 kpc, oriented perpendicular to the Galactic plane along $l=6^\circ$, centred at $b=-15^\circ$."
+" Ser contains a mix of stellar. populations. an extended dark halo (mass 710"" M.) and at least. four elobular clusters 11997)."," Sgr contains a mix of stellar populations, an extended dark halo (mass $\geq 10^9$ ) and at least four globular clusters 1997)."
+ In Fig. 10.," In Fig. \ref{smith_view},"
+ we illustrate the relative positions of the Smith Cloud. the Ser dwarf and the Magellanie Clouds.," we illustrate the relative positions of the Smith Cloud, the Sgr dwarf and the Magellanic Clouds."
+ The Alagellanie Stream runs parallel to Q=90°/270° through the Lagrangian point of the LMC/SMC system., The Magellanic Stream runs parallel to $\Theta=90^\circ/270^\circ$ through the Lagrangian point of the LMC/SMC system.
+ The positions of the other dwarf spheroidals are given by Alajewski (19094)., The positions of the other dwarf spheroidals are given by Majewski (1994).
+ The Smith Clouc and Ser are at an identical galactic Latitude. and aapart in longitude.," The Smith Cloud and Sgr are at an identical galactic latitude, and apart in longitude."
+ Recent work (Ibata. personal communication) reveals hat the angular size of Ser is close to ((12 kpe) extending almost perpencicular to the Galactic xane.," Recent work (Ibata, personal communication) reveals that the angular size of Sgr is close to (12 kpc) extending almost perpendicular to the Galactic plane."
+ The Smith Cloud is about half this size if the distance rom the Sun is comparable: its orientation is to the plane., The Smith Cloud is about half this size if the distance from the Sun is comparable; its orientation is to the plane.
+ The projected separation is slightly more han the projected extent of Ser., The projected separation is slightly more than the projected extent of Sgr.
+ Ehe difference in velocity (~6Okms 1)) is three times higher than expected. for gas in cvnanical equilibrium at 15 kpe around a LO? solar mass object., The difference in velocity $\sim$ ) is three times higher than expected for gas in dynamical equilibrium at 15 kpc around a $^9$ solar mass object.
+" “Phe total numass of the cloud is about of the visible matter in Ser,", The total mass of the cloud is about of the visible matter in Sgr.
+ 1t our distance range for the Smith Cloucl is reliable. it sugeests a possible association with the Ser cwarf.," If our distance range for the Smith Cloud is reliable, it suggests a possible association with the Sgr dwarf."
+ In the rest [rame of the Galaxy. for Ser. sx ((Ihata. Cilmore Irwin 1995) compared with —236 [for the Smith Cloud. (assuming a rotation speed. of aat the Solar Circle).," In the rest frame of the Galaxy, for Sgr, $\approx$ (Ibata, Gilmore Irwin 1995) compared with $=$ for the Smith Cloud (assuming a rotation speed of at the Solar Circle)."
+ The stretched appearance of the lis suggestive of a tidal feature in strong interactions., The stretched appearance of the is suggestive of a tidal feature in strong interactions.
+ Lf the cloud constitutes a gaseous tidal arm. we predict a counterpart on the same ealactic latitude (b=15°) at longitude £3307. and GSR velocity +..," If the cloud constitutes a gaseous tidal arm, we predict a counterpart on the same galactic latitude $b=-15^\circ$ ) at longitude $\ell\sim 330^\circ$, and GSR velocity $\sim$."
+ This putative cloud has an LSR velocity greater than aancl would therefore be labelled a “high velocity cloud’., This putative cloud has an LSR velocity greater than and would therefore be labelled a `high velocity cloud'.
+ A direct association of the wwith Ser poses problems for our current understanding of the precursor since the dominant. stellar population is old 11996) with Fe/H] z -1 (Whitelock. Catehpole Irwin 1996).," A direct association of the with Sgr poses problems for our current understanding of the precursor since the dominant stellar population is old 1996) with [Fe/H] $\approx$ -1 (Whitelock, Catchpole Irwin 1996)."
+ Since the Smith Cloud. σας falls well bevonc the expected: tidal radius of Ser (5 kpc) an alternative interpretation is that the Smith Cloud has been cdislodged from the outer deisk hy the impact of the Ser dwarf.," Since the Smith Cloud gas falls well beyond the expected tidal radius of Sgr $\sim 5$ kpc), an alternative interpretation is that the Smith Cloud has been dislodged from the outer disk by the impact of the Sgr dwarf."
+ Such a model may be consistent with ((1997. Fie.," Such a model may be consistent with (1997, Fig."
+ L1) who use numerical simulations to show that Galactic tides can force a dwarf spheroidal into a prolate shape., 11) who use numerical simulations to show that Galactic tides can force a dwarf spheroidal into a prolate shape.
+ Most. models favour a short. period. orbit (<1 Civr: Oh. Lin Aarseth 1995) implying that Ser has undergone at least à dozen perigalacticon passages. consistent with the minimum age of the dominant stellar population.," Most models favour a short period orbit $\leq$ 1 Gyr; Oh, Lin Aarseth 1995) implying that Sgr has undergone at least a dozen perigalacticon passages, consistent with the minimum age of the dominant stellar population."
+ If future x-ray surveys detect either. emission. Bone. Hartquist Sandford 1983) or absorption Wane Taisheng 1996) towards the Smith Cloud. this would have important ramifications.," If future x-ray surveys detect either emission Bone, Hartquist Sandford 1983) or absorption Wang Taisheng 1996) towards the Smith Cloud, this would have important ramifications."
+ Nearby, Nearby
+sienificautly differentiate between models.,significantly differentiate between models.
+ At veryτο low inclinations (7<10°). this experiment is not able to exclude even very bright compauious due to both the lack of a significant Doppler-shitt between the primary and the secondary. aud the lack of a phase variation iu the light from the secondary.," At very low inclinations $i \lesssim 10^{\circ}$ ), this experiment is not able to exclude even very bright companions due to both the lack of a significant Doppler-shift between the primary and the secondary, and the lack of a phase variation in the light from the secondary."
+ However. these low inclination orbits may be excluded uuder a further Csideration: If the axis defined by the stellar rotation Is he same as fii of the orbit of the uauet. then the observed esuiz15lans3 for the star would inplv a tiie rotational velocity of ercater than 550 ks for |o1T ," However, these low inclination orbits may be excluded under a further consideration: If the axis defined by the stellar rotation is the same as that of the orbit of the planet, then the observed $v \, \sin {i} \simeq 15 \ {\rm 
+km \, s^{-1}}$ for the star would imply a true rotational velocity of greater than 50 $\rm{km \, s^{-1}}$ for $i \lesssim 17^{\circ}$ ."
+Such high roational velocities are no observed (€:ray 1982) for main-sequence FF stars., Such high rotational velocities are not observed (Gray 1982) for main-sequence F7 stars.
+ Wiel iiclination orldts C1 be excluded x the lack of eclipses frou plooietric monitoring., High inclination orbits can be excluded by the lack of eclipses from photometric monitoring.
+ Daliunas et al. (, Baliunas et al. (
+1997) exclude #>83°.,1997) exclude $i \gtrsim 83^{\circ}$.
+ ThiEE Csistent with our experiment as we fine no evideuce for a conrpandon at tjese hieh inclinations., This is consistent with our experiment as we find no evidence for a companion at these high inclinations.
+" We reiterate that the derivalon of au upper luit for he ecotric albedo requires he asstuuption of a value or the panetary radius (1.2 [8,) auc a factional form, or the phase variation (a Laubert law sphere).", We reiterate that the derivation of an upper limit for the geometric albedo requires the assumption of a value for the planetary radius (1.2 $R_{p}$ ) and a functional form for the phase variation (a Lambert law sphere).
+ If the actual vaues are significantly different than these. then he upper Iit on the geomoetrk albedo is modified as wο].," If the actual values are significantly different than these, then the upper limit on the geometric albedo is modified as well."
+ For exie. assuniug a smalcr planetary radius would )orndta arecr albedo (see eqiation 1)).," For example, assuming a smaller planetary radius would permit a larger albedo (see equation \ref{eps}) )."
+ Published predictions of the albedo of CEGPs vary Lauv orecrs of magnitude. aid are highly sensitive he presence of condcusates in the planetary atinospliere.," Published predictions of the albedo of CEGPs vary by many orders of magnitude, and are highly sensitive to the presence of condensates in the planetary atmosphere."
+ Birroews Sharp (1999) consider cloud formation axd depletion by rainout. and demonstrate that MeSiO; will )o an abundant condeusate at the effective teniperare of r Boo b (— 150014).," Burrows Sharp (1999) consider cloud formation and depletion by rainout, and demonstrate that $\rm{MgSiO_{3}}$ will be an abundant condensate at the effective temperature of $\tau$ Boo b $\sim 1500 \, \rm{K}$ )."
+ Alarley et al. (, Marley et al. (
+1999) calculate oth cloud-free aud silicate cloud atmospheres aud predict 135<pClsOum)x;0.55 for au EGP with a temperare of 1000 Ik. which is greater than our upper limit of ptISOuii)0.3.,"1999) calculate both cloud-free and silicate cloud atmospheres and predict $0.35 \lesssim p(480 \, {\rm nm}) \lesssim 0.55$ for an EGP with a temperature of 1000 K, which is greater than our upper limit of $p(480 \, {\rm nm}) = 0.3$."
+ They neglect the effects of stellar insolation ou the model atmosphere., They neglect the effects of stellar insolation on the model atmosphere.
+ Seager Sassclov (1998) explicitly include the stellar flux. solve the equation of radiative transfer through :vinodel atinosphere of 7 Doo b. and predict pClIstQuni)0.0002.," Seager Sasselov (1998) explicitly include the stellar flux, solve the equation of radiative transfer through a model atmosphere of $\tau$ Boo b, and predict $p(480 \, {\rm nm}) \simeq 0.0002$."
+ The low albedo is due in part to the absorption of photous by TiO in the atmosphere., The low albedo is due in part to the absorption of photons by TiO in the atmosphere.
+ However. it may be that the TiO forms and ralus out. and thus is not an nuportaut factor.," However, it may be that the TiO forms and rains out, and thus is not an important factor."
+" Iucludiug the presence of MeSiOs clotds. Seager Sasselov predict a lareer (but still ταν darV) albedo of ptISOuii)0.003, "," Including the presence of $\rm{MgSiO_{3}}$ clouds, Seager Sasselov predict a larger (but still very dark) albedo of $p(480 \, {\rm nm}) \simeq 
+0.003$ ."
+"The reflectivity of thie| MeSiO; exais af a eiven wavelength is hiehlysue dependent on the oerai1 size relative to the wavecheth of ποτ,", The reflectivity of the $\rm{MgSiO_{3}}$ grains at a given wavelength is highly dependent on the grain size relative to the wavelength of light.
+ Burrows Sharp (1999) also predict that other coideusates (such as Fe) may be present at these temperatures., Burrows Sharp (1999) also predict that other condensates (such as Fe) may be present at these temperatures.
+ If ou droplets are a sjenificaut coidensate. the resulting albedo would be very dark due to the high absorption at optical waveleneths.," If iron droplets are a significant condensate, the resulting albedo would be very dark due to the high absorption at optical wavelengths."
+ Given the current uncertaiiv in the models. there are many reasonable model plaxtary atmospheres which are consistent with our upper liuit.," Given the current uncertainty in the models, there are many reasonable model planetary atmospheres which are consistent with our upper limit."
+ We have achieved the. cirent upper limit usine only a lanited spectral range. and data obtained when the planet was far from opposition.," We have achieved the current upper limit using only a limited spectral range, and data obtained when the planet was far from opposition."
+ It is restricted bw the photon noise of the «ata set. uot bv systematic errors.," It is restricted by the photon noise of the data set, not by systematic errors."
+ By expanding the spectral ra1ος and observing on several welts when the plauet is uear opposition. it would be possible to significantly redice this upper luit.," By expanding the spectral range and observing on several nights when the planet is near opposition, it would be possible to significantly reduce this upper limit."
+ It inav be advantageous to conduct this experiueut at shorter wavelengths. since Seager Sassclov (19098) predict a dramatic rise m the albedo srortwards of 120 uo.," It may be advantageous to conduct this experiment at shorter wavelengths, since Seager Sasselov (1998) predict a dramatic rise in the albedo shortwards of 420 nm."
+ Wo eratefully acknowledge the NASA/Keck. Tine Assignment Conuuittee for t16 observing time allocation., We gratefully acknowledge the NASA/Keck Time Assignment Committee for the observing time allocation.
+ This work was supported iu xwt bv NASA Craut NACH-, This work was supported in part by NASA Grant NAG5-75005.
+üinages of 10 s duratiou were taken while it was faint. during the ime period October 2005 hrougl Feb. 2006.,"images of 10 s duration were taken while it was faint, during the time period October 2005 through Feb. 2006."
+ ATer that. the duration of the exposures wheu the star was [alu was LUCreasec to 150 s iu both V aid E aud normally | consecutive images were obtalrect and sui1ned.," After that, the duration of the exposures when the star was faint was increased to 150 s in both V and I and normally 4 consecutive images were obtained and summed."
+ Observatious at MMO were obtained in the E baud using tle 0.6 m aix| 1.5 m telescopes ancl aà512x 512axl 1096 x. 10906 CCD camera. respectively.," Observations at MMO were obtained in the I band using the 0.6 m and 1.5 m telescopes and a 512 x 512 and 4096 x 4096 CCD camera, respectively."
+ A range of 5 to 20 LLlages was taken each clear uight de;»enudiug on the pliase of the system., A range of 5 to 20 images was taken each clear night depending on the phase of the system.
+ Exposures we'e normally 3)QU s in leneth., Exposures were normally 300 s in length.
+ Photomery of the VVO aud CTIO images was done at Weslevau. wlie photometry of the MMO images was done at the Uzbek Academy of Sciences.," Photometry of the VVO and CTIO images was done at Wesleyan, while photometry of the MMO images was done at the Uzbek Academy of Sciences."
+ Iu eac1 Case. standard IRAP tasks for aperture photometry were employed.," In each case, standard IRAF tasks for aperture photometry were employed."
+ INH 15D aud several comALISON sars were measurecl., KH 15D and several comparison stars were measured.
+ The precise sizes of he aperture aud annulus chosen or the photonretry varied accord o the instrument employer., The precise sizes of the aperture and annulus chosen for the photometry varied according to the instrument employed.
+ Details are eeiven in Table 1.., Details are given in Table \ref{PhotParm}.
+ Comparison stars were choseu {ror le sel labeled A-G by Hailtonοἱal.(2005) as well as 16D. |LTD and 31D f‘oun Ixearis&HerbsOOS).," Comparison stars were chosen from the set labeled A-G by \citet{Ham05} as well as 16D, 17D and 31D from \citet{KH98}."
+. Iu each season. potertial comparison stars were evaluated for variabiliy and the most stable oyjects chosen.," In each season, potential comparison stars were evaluated for variability and the most stable objects chosen."
+ The priucipa comparisou star for most of the «ata reported Iere was sar F of and its coistancy was checked by reference O slar C: vari:ions were —0.01 mag or less., The principal comparison star for most of the data reported here was star F of \citet{Ham05} and its constancy was checked by reference to star C; variations were $\sim$ 0.01 mag or less.
+ Table 2. gives the adopted. V au ] magnitudes for hec ΟΕο objects based ou the pliotoneiry of Hamiltonetal.(2005)., Table \ref{CompMags} gives the adopted V and I magnitudes for the comparison objects based on the photometry of \citet{Ham05}.
+. The accuracy of the plolometry varies substantially depeudiug ou tle observatory. observil[n]ο couditious. exposure leneth. etc.," The accuracy of the photometry varies substantially depending on the observatory, observing conditions, exposure length, etc."
+ Generally speaking. however. the daa are accurate to 0.02 mag or less when the star is at or 1ear its bright phase (l= 11.5 mag) and accura to 0.05 mag or better when faint.," Generally speaking, however, the data are accurate to 0.02 mag or less when the star is at or near its bright phase (I = 14.5 mag) and accurate to 0.05 mag or better when faint."
+ Table 3. gives tle photometric resilts Grom the five observing seasons 2005-2010 reported lier combined with previously published CCD data from the period 1995-2005 (Hamiltonetal.2005)., Table \ref{Data} gives the photometric results from the five observing seasons 2005-2010 reported here combined with previously published CCD data from the period 1995-2005 \citep{Ham05}.
+. The full table is available in the elect‘onic version of the journal article., The full table is available in the electronic version of the journal article.
+ This represents the fhll set of CCD data obtained by οWo grou yon the Cousins system., This represents the full set of CCD data obtained by our group on the Cousins system.
+ It does uot include SMARTS cda€a transformed to hat system tha were (iscussecl and analyzed by Hamiltonetal.(2005).. nor does it iuclude the phooglapuc photometry that lias been reported by Joluson&Winn(2001).. (2005)... aid Mafei.Cipriui&Tosti(2005).," It does not include SMARTS data transformed to that system that were discussed and analyzed by \citet{Ham05}, nor does it include the photographic photometry that has been reported by \citet{J04}, \citet{J05}, and \citet{M05}."
+ In κοτοι to the shotometry. we inclide in the table the parameter ASN [rom Moxlel κ)+) of Winnetal.(206)6) th'ough tlthe 2008-9 seasou.," In addition to the photometry, we include in the table the parameter $\Delta$ X from Model 3 of \citet{w06} through the 2008-9 season."
+" This is a prediction. based ou he orbital aud other parameters of trat moclel. «""i he elevation o “the center of star A above (-) ο: below (+) tlie edge ol the occulting disk in uiis of the radius of star A (Ry = 13 BR.—9x10 m) from (2006)."," This is a prediction, based on the orbital and other parameters of that model, of the elevation of the center of star A above (-) or below (+) the edge of the occulting disk in units of the radius of star A $_A$ = 1.3 $_\odot = 9 \times 10^8$ m) from \citet{w06}."
+. We show iu what Kk|ows that this uodel is no longer au adequate 'epreseutation of the data. aud we caution tl€al the quantity AN is progressively. less successful iu accounting for the photometry as one moves fi|o1 2005 tlirougl 2009.," We show in what follows that this model is no longer an adequate representation of the data, and we caution that the quantity $\Delta$ X is progressively less successful in accounting for the photometry as one moves from 2005 through 2009."
+ It is included in Table κ)+) yecause we needed it to assess the validity of he extant models aud in other aspects of the analysis., It is included in Table \ref{Data} because we needed it to assess the validity of the extant models and in other aspects of the analysis.
+"Since the flux maps were constructed with a uultiplicative factor of hj,,;54/7, the correction actor of «E»/E,,,/44 for each measurement is required to recover the actual flux within the ρα.","Since the flux maps were constructed with a multiplicative factor of $\nu_{nominal}$, the correction factor of $<E>/E_{nominal}$ for each measurement is required to recover the actual flux within the band."
+ Iu Table 5 we give the counts aud fiux for cach jet component of interest., In Table \ref{tab:xflux} we give the counts and flux for each jet component of interest.
+ Conversion of flux to flux density was doue ‘Or o: rasstumed power law with a-1., Conversion of flux to flux density was done for an assumed power law with $\alpha$ =1.
+ Although lis procedure is not strictly correct. the error introduced by using an imcorrect value of a should ο of second order since the bands were only a ew keV wide.," Although this procedure is not strictly correct, the error introduced by using an incorrect value of $\alpha$ should be of second order since the bands were only a few keV wide."
+" In general. we did not have cnough counts to obtain an accurate value of à. acd for he brighter features such as KL a, is not far from l."," In general, we did not have enough counts to obtain an accurate value of $\alpha_x$, and for the brighter features such as k4, $\alpha_x$ is not far from 1."
+ Quoted imcertaiuties in fluxes and flux deusities are purely statistical., Quoted uncertainties in fluxes and flux densities are purely statistical.
+ They were derived by using the source and backeround regions on cout maps (i.c. before dividing by the exposure maps)., They were derived by using the source and background regions on count maps (i.e. before dividing by the exposure maps).
+ The fractional error in each flux was then carried forward to the flix densities., The fractional error in each flux was then carried forward to the flux densities.
+ Since ost features do not have suffücieut counts to provide an accurate estimate of tlic spectral paramcters using the normal fitting procedures in the X-ray band. we use our micasurements of flux densities (Table 20) to coustruct spectra (see sec.," Since most features do not have sufficient counts to provide an accurate estimate of the spectral parameters using the normal fitting procedures in the X-ray band, we use our measurements of flux densities (Table \ref{tab:fluxden} ) to construct spectra (see sec."
+ 77— for examples)., \ref{sec:eval} for examples).
+ Except for the uncertaintv in the absorption correction for the softest band. we believe that our techuique of deriving spectral parameters from the flux maps is reliable.," Except for the uncertainty in the absorption correction for the softest band, we believe that our technique of deriving spectral parameters from the flux maps is reliable."
+ For the case of kl there are sufficient counts to allow the usual N-rav unetlod of spectral fitting., For the case of k4 there are sufficient counts to allow the usual X-ray method of spectral fitting.
+ We did that with Ciao/Sherpa aud find aerecluent between the two methods. both iu values of the amplituce aud o.," We did that with Ciao/Sherpa and find agreement between the two methods, both in values of the amplitude and $\alpha_x$."
+ We planned aud obtained our new VLA radio data ou the basis of the ROSAT obscrvations of SC 120., We planned and obtained our new VLA radio data on the basis of the ROSAT observations of 3C 120.
+ At that time a persistent question was “Why are a few knots aud hotspots in radio jets detected with current N-rav seusitivities while the vast majority are not?”, At that time a persistent question was “Why are a few knots and hotspots in radio jets detected with current X-ray sensitivities while the vast majority are not?”
+ We now know that this question has been mostly answered because of the large muuber of jet detections withChandrat:: with sufücieut scusitivity aud augular resolution. N-rav detections of radio jets are quite colon and uo longer drive us to search for “special conditions.," We now know that this question has been mostly answered because of the large number of jet detections with: with sufficient sensitivity and angular resolution, X-ray detections of radio jets are quite common and no longer drive us to search for 'special conditions'."
+ Towever. it would still be useful to identify auv peculiaritics im shock regions containing electrons which produce significant X-rav chussion.," However, it would still be useful to identify any peculiarities in shock regions containing electrons which produce significant X-ray emission."
+" For k25 in particular. the difficulty of finding a reasonable enüssiou mechanism for the N-ravs led IHIISSV. to sugeest the possibility of a flatter spectrum (than deduced from the radio data) population ofrelativistic clectrous extcuding up to Lorentz energies of 5=10""."," For k25 in particular, the difficulty of finding a reasonable emission mechanism for the X-rays led HHSSV to suggest the possibility of a flatter spectrum (than deduced from the radio data) population of relativistic electrons extending up to Lorentz energies of $\gamma \approx 10^7$."
+ For these reasons. we undertook high frequency VLA observations to better determine the radio spectrin and to evaluate the behavior of the sharp eradieuts in radio surface brightuess at two locations in k25.," For these reasons, we undertook high frequency VLA observations to better determine the radio spectrum and to evaluate the behavior of the sharp gradients in radio surface brightness at two locations in k25."
+ Both of these parameters may be observational signatures of physical attributes of shocks., Both of these parameters may be observational signatures of physical attributes of shocks.
+ We used the AIPS tool NINER to measure the first derivative of the radio brightuess., We used the AIPS tool NINER to measure the first derivative of the radio brightness.
+ Iu order O lLüueasure conrerativo eracdicuts at different requencies. maps were convolved to the largest vcaunsize.," In order to measure comparative gradients at different frequencies, maps were convolved to the largest beamsize."
+ Tlowever. when comparing differcut catures on the same map. this convolution was rot necessary.," However, when comparing different features on the same map, this convolution was not necessary."
+ For all comparisons we computed the normalized eracieut by dividing the actual value of Jv/beam/pix w the intensity of the peak brightuess of the cature beiug measured., For all comparisons we computed the normalized gradient by dividing the actual value of Jy/beam/pix by the intensity of the peak brightness of the feature being measured.
+ When comparing maps with different pixel size. we also divided by the actor arcsec/pixcl.," When comparing maps with different pixel size, we also divided by the factor arcsec/pixel."
+ In addition to measuring the eeradieut for the outer edge of k25. we measured eradieuts for the core (which serves to define he value for au unresolved source). kl. aud the eadiug edge of k25 (vhich was undetected iu our ROSAT data but is clearly preseut in the Cliuidra iniages).," In addition to measuring the gradient for the outer edge of k25, we measured gradients for the core (which serves to define the value for an unresolved source), k4, and the leading edge of k25 (which was undetected in our ROSAT data but is clearly present in the Chandra images)."
+ To compare the spectra of the inner aud outer shocks of k25. we measured flux deusities ou the Walker et al. (," To compare the spectra of the inner and outer shocks of k25, we measured flux densities on the Walker et al. ("
+"1987) maps constructed to have the same beamsize of 1.257 FWITIM (1.1. 5. and 15 CGIIz) aud then repeated the measurements ou maps s1100thed to match the resolution of the 13 GIIz map (2.2""4 1.6"") in order to include the 13 GIIz flux density.","1987) maps constructed to have the same beamsize of $""$ FWHM (1.4, 5, and 15 GHz) and then repeated the measurements on maps smoothed to match the resolution of the 43 GHz map $''\times1.6''$ ) in order to include the 43 GHz flux density."
+" We defined a rectangle of BY42.1"" DEC) for the internal (southeru)", We defined a rectangle of $''\times2.4''$ $\times$ DEC) for the internal (southern)
+either Thomson-thin (viclding only a narrow line as in the case above) or Thonson-thick (vielding fractions of both the observed line aud reflection).,either Thomson-thin (yielding only a narrow line as in the case above) or Thomson-thick (yielding fractions of both the observed line and reflection).
+ The Gaussian Fe Nev line shows evideuce for a broademing and redshitt (see Table 2))., The Gaussian Fe $\alpha$ line shows evidence for a broadening and redshift (see Table \ref{t:fits}) ).
+ Therefore. we also consider a model with the ne emission and Compton reflection [tied via ((1))| bot[um originating iu a relativistic disk (83.1)).," Therefore, we also consider a model with the line emission and Compton reflection [tied via \ref{eq:line}) )] both originating in a relativistic disk \ref{s:models}) )."
+ We have ound that this model provides as good a ft. with vo=151.3/112. as the one with a Gaussian ine and static reflection.," We have found that this model provides as good a fit, with $\cnu=151.3/142$, as the one with a Gaussian line and static reflection."
+" Its parameters are DT7—egοLsG'UHP, O/2sQuocn=aRUBL0.6510 E,po_=qon120111110 ↘↸∖∙∣↕⊔≓∩↖∣∡⋯≼↧∏↕∖⊓MMeom(RL LT, Ty.↽ ∩∩⊐⋃↸∖∙∖↖↕↑↓⊔∪∖⊽ ⇁⋅ ↕∐↴∖↴↻∐⋅↖⇁↴∖↴↕↸⊳⋜↧↕↕⊔∪≼∐∖↕↖∏∖↥⋅↸∖⊣∖↘⋜⋯∐∐↸∖↑∐↸∖↴∖↴↕∶↴∙⊾∐↕∐↸⊳⋜∐∐⊳↸∖ of the presence of the soft excess."," Its parameters are $\Gamma=1.86_{-0.05}^{+0.05}$, $\Omega/2\pi=0.65_{- 0.14}^{+0.31}$, $\ec=120_{-20}^{+110}$ keV, $r_{\rm
+in}=6^{+17}$, and $\wfe=100^{+40}_{-20}$ eV. With this physical model we re-examine the significance of the presence of the soft excess."
+ Without it. he above model viclds νο=162.5/111. which corresponds to the significance increased.," Without it, the above model yields $\cnu=162.8/144$, which corresponds to the significance increased."
+. This shows that the phivsical requircment that oth the line aud the reflection continu are xoadened im the same way leads to au inercase of he significance of the preseuce of a soft excess., This shows that the physical requirement that both the line and the reflection continuum are broadened in the same way leads to an increase of the significance of the presence of a soft excess.
+ Then. we considered models with the coutiuuua even by thermal Comptonization (ucludiug the soft plasima cussion as in Table 2)).," Then, we considered models with the continuum given by thermal Comptonization (including the soft plasma emission as in Table \ref{t:fits}) )."
+" We use a model of Poutanen Svensson (1996). imitiallv for spherical geometry with a homogeneous distribution of sources of seed. photons. which we assumed to be a blackbody at a temperature of μι=5 eV. We obtaina temperature of the scatteriug medi of KT.=361 keV. a Thomson optical depth of E‘rD—2,5!75. 0/2=(56!012. and ry—12/1ου at yp=151.0/112."," We use a model of Poutanen Svensson (1996), initially for spherical geometry with a homogeneous distribution of sources of seed photons, which we assumed to be a blackbody at a temperature of $kT_{\rm bb}=5$ eV. We obtain a temperature of the scattering medium of $kT=36^{+100}_{-6}$ keV, a Thomson optical depth of $\tau=2.5^{+0.9}_{-1.9}$, $\Omega/2\pi=0.56^{+0.24}_{-0.19}$, and $r_{\rm in}=
+12_{-6}^{+100}$ at $\cnu= 151.0/142$."
+" The fitted parameters weakly depend on the assumed eeomoetry: 6.8... a geometry with hot plasma regions in the form of cxliuders ou the surface of a disk yields kT=502 keV. τς921ae OQ/2x=0.61!aw and rg,=10!: at Vom151.3/112."," The fitted parameters weakly depend on the assumed geometry; e.g., a geometry with hot plasma regions in the form of cylinders on the surface of a disk yields $kT=50^{+80}_{-8}$ keV, $\tau=2.2^{+0.3}_{-1.4}$, $\Omega/2\pi=0.64^{+0.24}_{-0.08}$, and $r_{\rm in}= 10_{-4}^{+4}$ at $\cnu= 151.3/142$."
+" The latter geometry vields an anisotropy break appearing around the peak of the 2ud scattering order (Poutanen Svensson 1996). which could. possibly, account for the broken power-law spectral solution with the break at ~1 keV and no additional soft compoucut described above."," The latter geometry yields an anisotropy break appearing around the peak of the 2nd scattering order (Poutanen Svensson 1996), which could, possibly, account for the broken power-law spectral solution with the break at $\sim 1$ keV and no additional soft component described above."
+ However. we have found that a coronal ecolctry without an additional soft comonet vields a relatively poor fit. A=159.1/111 with AEc120 keV. r=0.9.," However, we have found that a coronal geometry without an additional soft component yields a relatively poor fit, $\cnu=159.1/144$ with $kT\simeq 120$ keV, $\tau\simeq
+0.9$."
+ Comparing to the thermal-Comptou above. the significance of the preseuce of a soft compouent is still.," Comparing to the thermal-Compton above, the significance of the presence of a soft component is still."
+ If the temperature of seed photons is allowed to be free. KT=20 eV. which coustraint follows from the anisotropy break cutcring the fitted energy range.," If the temperature of seed photons is allowed to be free, $kT_{\rm bb}\la 20$ eV, which constraint follows from the anisotropy break entering the fitted energy range."
+ We also consider a model with a broken poweraw primary contimuni with a break at high energies., We also consider a model with a broken power-law primary continuum with a break at high energies.
+" However. this model requires the break o be above our data. at «110 κο, with the index yellow the break of P—1.91 aud an unconstrained iudex above the break."," However, this model requires the break to be above our data, at $\ga 110$ keV, with the index below the break of $\Gamma = 1.91$ and an unconstrained index above the break."
+ This model also provides a relatively- poor fit.* withB v5D=E151.6/139.," This model also provides a relatively poor fit, with $\cnu= 154.6/139$."
+idque Thus.Y here is no evidence for a sharp spectral break at Hel enereies in the data.," Thus, there is no evidence for a sharp spectral break at high energies in the data."
+ The spectrum analyzed in δ0 has been integrated. over the observation spanning nore than 2 davs (see Table 13). duriug which the source varied.," The spectrum analyzed in \ref{s:results} has been integrated over the observation spanning more than 2 days (see Table \ref{t:log}) ), during which the source varied."
+ The LECS and MECS light curves are shown in Figure 2aa. In both instimuents. the (P probability that the source were constaut was <10° independeutly of the temporal bin used.," The LECS and MECS light curves are shown in Figure \ref{f:var}a a. In both instruments, the $\chi^2$ probability that the source were constant was $<10^{-3}$ independently of the temporal bin used."
+ This is in agreement with the observed earlier on various time scales byENOSAT.. und (Maraschni et 11991. hereafter M91: Grandi ot 11997).," This is in agreement with the observed earlier on various time scales by, and (Maraschi et 1991, hereafter M91; Grandi et 1997)."
+ We soe in Figure 2aa that the soft spectra is niore variable than the hard oue., We see in Figure \ref{f:var}a a that the soft spectrum is more variable than the hard one.
+ Namely. the amplitude of the variatious is ~15% im the 0.32 keV αιαον range and oulv ~5% iu the 210 τον band.," Namely, the amplitude of the variations is $\sim 15\%$ in the 0.3--2 keV energy range and only $\sim 5\%$ in the 2–10 keV band."
+" This variability patter is driven by he spectrmu becomine softer with increasing soft Hux. as shown in Figure 2bb. The linear correlation cocfiicicnt between the harducss ratio aud the soft count rate js kr=0.92. and the probability that he 2 quantities are correlated is 299%,"," This variability pattern is driven by the spectrum becoming softer with increasing soft flux, as shown in Figure \ref{f:var}b b. The linear correlation coefficient between the hardness ratio and the soft count rate is $r=0.92$, and the probability that the 2 quantities are correlated is $>99\%$."
+ A similar auticorrelation of the X-ray flux aud spectral iudex was found on louger time scales in data x Talpern (1985) and in data by ΔΙ and Candi et ((1992)., A similar anticorrelation of the X-ray flux and spectral index was found on longer time scales in data by Halpern (1985) and in data by M91 and Grandi et (1992).
+ Tn order to &ud the range of the spectral index. D. correspouding to the anticorrelation shown iu Figure 2bb. we have used the model of Table 2 in which we have varied (onlv) D aud then adjusted the normalization to match the 0.32 keV LECS rate of the extreme best-fit poiuts in Figure 2bb. We have found that the rauge of P matching the observed spectral variability is quite," In order to find the range of the spectral index, $\Gamma$, corresponding to the anticorrelation shown in Figure \ref{f:var}b b, we have used the model of Table \ref{t:fits} in which we have varied (only) $\Gamma$ and then adjusted the normalization to match the 0.3–2 keV LECS rate of the extreme best-fit points in Figure \ref{f:var}b b. We have found that the range of $\Gamma$ matching the observed spectral variability is quite"
+" 1 . ⊳∖↓⊔⊓⋅⋏∙≟↓⋅⋜⋯⋅∠⇂∐⊔⇀∖∠⇂≺⊾⊔⊳∖⊔∙∖⇁≼∙∪↓⋅↓⋅≺⋅⊳∖↓≻∪⊔∠⊳∖∪⋜⋯∐↥⊔⋯⊳∖⊳∖∪⇂ 2.10""M...",$^{-1}$ integrated flux density corresponds to an mass of $2 \times 10^9\ \msol$.
+ A reasonable match of the integrated. line Hux densities o£ GALR'T data and single dish observations imply that we have not lost any dilluse extended emission aud the disk is indeed similar in size as the optical clisk., A reasonable match of the integrated line flux densities of GMRT data and single dish observations imply that we have not lost any diffuse extended emission and the disk is indeed similar in size as the optical disk.
+" The parameter that indicates whether a galaxy has Lost gas compared to a field galaxy of similar size ancl similar morphological type is typically known as the deficiency? and is given by where μι is the total mass of a galaxy and Di is the optical major isophotal diameter (in kpe) measured al or reduced to a surface brightness level mp = 25.0 miag/aresec"".", The parameter that indicates whether a galaxy has lost gas compared to a field galaxy of similar size and similar morphological type is typically known as the deficiency' and is given by where $M_{H_{I}}$ is the total mass of a galaxy and $D_{l}$ is the optical major isophotal diameter (in kpc) measured at or reduced to a surface brightness level $_B$ = 25.0 $^{2}$.
+ The 7precieted? field galaxy value of surface density or morphological twpe Se has been taken from Haynes&Ciovanelli (1984)., The `predicted' field galaxy value of surface density for morphological type Sc has been taken from \cite{1984AJ.....89..758H}.
+. While Havnes&Ciovanelli(1984) used the UGC blue major diameters for Dj. in this work t3 major diameter have been used.," While \cite{1984AJ.....89..758H} used the UGC blue major diameters for $D_{l}$, in this work RC3 major diameter have been used."
+ To take care of the difference in the surface matter density that result from the use o£ RCS diameters. a value of 0.08 (cleVaucouleursetal.991) has been added to the predicted surface density given bv Havnes&Ciovanelli(1984)...," To take care of the difference in the surface matter density that result from the use of RC3 diameters, a value of 0.08 \citep{1991trcb.book.....D} has been added to the predicted surface density given by \cite{1984AJ.....89..758H}."
+ Assuming a distance of 00.7 Alpe. derived using the optical velocity of UGC 07049 and using its ROSdiameter value 0.91. the deficiency of the galaxy is found to be ~ 0.41.," Assuming a distance of 100.7 Mpc, derived using the optical velocity of UGC 07049 and using its RC3diameter value $^{\prime}$, the deficiency of the galaxy is found to be $\sim$ 0.41."
+ This implies that the ealaxy is  2.6 times deficient inLh., This implies that the galaxy is $\sim$ 2.6 times deficient in.
+ Possible causes for the deficiency include tidal interactions. ram. pressure stripping. or a combination of hese two processes.," Possible causes for the deficiency include tidal interactions, ram pressure stripping, or a combination of these two processes."
+ In the images we do not see αν tidal extensions. although the stellar disk appears to be warped on the north-cast end.," In the images we do not see any tidal extensions, although the stellar disk appears to be warped on the north-east end."
+ Recent studies have shown hat in groups with X-ray bright IM. ram pressure alone or tically aided rani pressure is capable of removing a considerable fraction of the gas from constituent galaxies (Senguptactal.2007:Sengupta&Balasubramanvan2006:fasmussenetal.2006:Davis 1997)...," Recent studies have shown that in groups with X-ray bright IGM ram pressure alone or tidally aided ram pressure is capable of removing a considerable fraction of the gas from constituent galaxies \citep{2007MNRAS.378..137S,2006MNRAS.369..360S,2006MNRAS.370..453R,1997AJ....114..613D}."
+ The data oesented here show the gaseous disk of UGC 07049 to be of similar size to the optical disk. whereas normal galaxies are known to have larger disks compared to their optical disks.," The data presented here show the gaseous disk of UGC 07049 to be of similar size to the optical disk, whereas normal galaxies are known to have larger disks compared to their optical disks."
+ Eruncated LIE disks are common in clusters of galaxies and in many cases are thought to result from: rani pressure stripping., Truncated HI disks are common in clusters of galaxies and in many cases are thought to result from ram pressure stripping.
+ The low column density gas from the outer edges of the disk is swept out by the ram pressure offered by the dense intracluster gas. leaving behind a reduced clisk.," The low column density gas from the outer edges of the disk is swept out by the ram pressure offered by the dense intracluster gas, leaving behind a reduced disk."
+ The NGC 4065 group has been detected to have a hot IGM and also a bent radio jet indicating resistance from the ΕΑΝ., The NGC 4065 group has been detected to have a hot IGM and also a bent radio jet indicating resistance from the IGM.
+ Phe spiral UGC 07049 is located within the projected X-ray emitting eas., The spiral UGC 07049 is located within the projected X-ray emitting gas.
+ Using some simple calculations we will explore whether ram pressure in this group is strong enough to strip gas from UGC 07049., Using some simple calculations we will explore whether ram pressure in this group is strong enough to strip gas from UGC 07049.
+ We have followed the method outlined in Senguptactal.(2007) for calculating the possible gas loss from UGC 07049 due to ram pressure., We have followed the method outlined in \citet{2007MNRAS.378..137S} for calculating the possible gas loss from UGC 07049 due to ram pressure.
+" Ram pressure stripping will be cllective for a galaxy when the surface density. 0,4. ds less than POMegal(2xCo.) where e, is the stellar surface clensity. fron is the local IM density and. e,,; is the velocity. with which the galaxy is moving through the medium."," Ram pressure stripping will be effective for a galaxy when the surface density, $\sigma_{\mu}$, is less than $\rho_{\mbox{\tiny IGM}}{v}_{gal}^{2}/(2\pi~G\sigma_{*})$, where $\sigma_{*}$ is the stellar surface density, $\rho_{\mbox{\tiny IGM}}$ is the local IGM density and $v_{gal}$ is the velocity with which the galaxy is moving through the medium."
+ We use the local projected IGM density o£ 4: οι from the X-ray eas profile. and for the velocity of UGC 07049 we consider both the 220kms. and 416kms velocity. dispersion.," We use the local projected IGM density of $\times$ $^{-4} \cmc$ from the X-ray gas profile, and for the velocity of UGC 07049 we consider both the $220 \kms$ and $416 \kms$ velocity dispersion."
+ The stellar surface density for UGC 07049 is estimated from its 2ALASS Ix-band magnitude and We color., The stellar surface density for UGC 07049 is estimated from its 2MASS K-band magnitude and K-J color.
+ Relating the mass to light ratio in the Ix band (M/ Lj) to the Ix-J colors (Bell&deJong2001) along with the relation of Ly to the absolute magnitude in Ix-band (My) (Worthey1994)... we estimate the stellar surface density to be 0.0194 em ," Relating the mass to light ratio in the K band $M/L_{K}$ ) to the K-J colors \citep{2001ApJ...550..212B} along with the relation of $L_{K}$ to the absolute magnitude in K-band $M_{K}$ ) \citep{1994ApJS...95..107W}, we estimate the stellar surface density to be 0.0194 gm $^{-2}$."
+"With this value for σε. the critical surface density 0, bevond whichram pressure can strip gas olf the galaxy. is estimated to be 3.817gem or 107 2."," With this value for $\sigma_{*}$, the critical surface density $\sigma_{\mu}$ beyond whichram pressure can strip gas off the galaxy, is estimated to be $3.8 \times 10^{-5}\ \mathrm{g cm}^{-2}$ or $\times$ $^{19}$ $^{-2}$ ."
+ We assume theLI surface density distribution inside UGC 07049 to be of constant thickness and with a Gaussian prolile (Chamarauxοἱal.1950). where rg is the radius within which half the mass is present.," We assume the surface density distribution inside UGC 07049 to be of constant thickness and with a Gaussian profile \citep{1980A&A....83...38C}, where $r_{H}$ is the radius within which half the mass is present."
+ For ay an average value of 20 M. 7. as seen in normal late tvpe spirals (Omar&Dwarakanath2005). in eroup environments was used.," For $\sigma_{0}$ an average value of 20 $_\odot$ $^{-2}$, as seen in normal late type spirals \citep{2005JApA...26...34O} in group environments was used."
+ The central column density of UGC 07049 also could have been used but the disk was too isturbed and there wasa central HE depletion in the high resolution map and thus the map was not used for estimating 10 oy value., The central column density of UGC 07049 also could have been used but the disk was too disturbed and there wasa central HI depletion in the high resolution map and thus the map was not used for estimating the $\sigma_{0}$ value.
+ Integrating the surface density distribution to qual the entire observed. mass allows us to solve for rg uxd find a value o£ 5 kpe., Integrating the surface density distribution to equal the entire observed mass allows us to solve for $r_{H}$ and find a value of $5$ kpc.
+" The radius corresponding to a, 1s ren 10 kpe (for the case where 044;=416kms 1y.", The radius corresponding to $\sigma_{\mu}$ is then $10$ kpc (for the case where $v_{gal}=416 \kms$ ).
+ Finally 1e mass outside this radius. which would be able to o Lan pressure stripped. was estimated to be 105 M...," Finally the mass outside this radius, which would be able to be ram pressure stripped, was estimated to be $\times$ $^{7}$ $_\odot$ ."
+ A similar estimateof the stripped mass was done with jf 220km velocity. dispersion. anc. uncderstancdably. xocduced a smallers mass loss.," A similar estimateof the stripped mass was done with the $220 \kms$ velocity dispersion and, understandably, produced a smaller mass loss."
+ These caleulations assume the, These calculations assume the
+?).,.
+" The orbital period [ουν attains a minimum, which is typically close to mmin and the system then evolves to longer Por."," The orbital period $P_{\rm orb}$ attains a minimum, which is typically close to min and the system then evolves to longer $P_{\rm
+ orb}$."
+ After several hundred million years the donors become homogeneous degenerate objects and the helium star and white dwarf families of ultra-compact binaries become indistinguishable(??)., After several hundred million years the donors become homogeneous degenerate objects and the helium star and white dwarf families of ultra-compact binaries become indistinguishable.
+". Because of the lifetimes of the various phases of evolution the overwhelming majority of ultra-compact binaries formed via the helium-star channel should be seen in the post-Porb,min. echannel.."," Because of the lifetimes of the various phases of evolution the overwhelming majority of ultra-compact binaries formed via the helium-star channel should be seen in the $P_{\rm orb, min}$. $\bullet~$."
+ The third channel starts with a main-sequence star transferring mass to a white dwarf or neutron star., The third channel starts with a main-sequence star transferring mass to a white dwarf or neutron star.
+ This is a cataclysmic variable (CV) or low-mass X-ray binary (LMXB)., This is a cataclysmic variable (CV) or low-mass X-ray binary (LMXB).
+" If the main-sequence star begins mass transfer sufficiently late on the main sequence and if sufficient angular momentum is lost, by for instance magnetic braking, the hydrogen deficient core of the donor can be exposed during mass transfer so that the star evolves to far below the usual period minimum for population-I CVs????)."," If the main-sequence star begins mass transfer sufficiently late on the main sequence and if sufficient angular momentum is lost, by for instance magnetic braking, the hydrogen deficient core of the donor can be exposed during mass transfer so that the star evolves to far below the usual period minimum for population-I CVs."
+. In the most extreme cases they can fall to a period minimum of around 10 min?2???).," In the most extreme cases they can fall to a period minimum of around $10\,$ min."
+". One of the problems to distinguish these different formation channels is that they more or less lead to the same donors, very low-mass degenerate dwarfs."," One of the problems to distinguish these different formation channels is that they more or less lead to the same donors, very low-mass degenerate dwarfs."
+ Studies of the population of objects in the phase they become ultra-compact binaries could give insight into the origin of ultra-compact binaries., Studies of the population of objects in the phase they become ultra-compact binaries could give insight into the origin of ultra-compact binaries.
+" However, currently the putative progenitors are not observed in large enough numbers for such a study."," However, currently the putative progenitors are not observed in large enough numbers for such a study."
+" An alternative is to study the details of the chemical composition of the donor-stars(?),, which show up in the optical or X-ray spectra of these systems as discussed above, or alternatively for UCXBs in the properties of the thermonuclear explosions (type I X-ray bursts) that occur on the surface of the accreting neutron stars2222)."," An alternative is to study the details of the chemical composition of the donor-stars, which show up in the optical or X-ray spectra of these systems as discussed above, or alternatively for UCXBs in the properties of the thermonuclear explosions (type I X-ray bursts) that occur on the surface of the accreting neutron stars."
+ In this paper we model the chemical composition of the donor stars in ultra-compact binaries in detail to find out whether this can distinguish between the different proposed formation channels., In this paper we model the chemical composition of the donor stars in ultra-compact binaries in detail to find out whether this can distinguish between the different proposed formation channels.
+ In Section ?? we present the detailed calculations of the donor abundances and in Section 3 we investigate the distribution of abundances that is expected for the different formation channels., In Section \ref{results} we present the detailed calculations of the donor abundances and in Section \ref{population} we investigate the distribution of abundances that is expected for the different formation channels.
+ In Section ?? we develop a set of diagnostics that can be used to distinguish the formation channels given observed abundances or abundance ratios or limits thereon and apply these results to observed systems in Section ??.., In Section \ref{diagnostics} we develop a set of diagnostics that can be used to distinguish the formation channels given observed abundances or abundance ratios or limits thereon and apply these results to observed systems in Section \ref{application}. .
+ We summarise and discuss our results in Section ??.., We summarise and discuss our results in Section \ref{sec:discon}.
+" For all calculations we used the Eggleton stellar evolution code TWINcommunication), with opacity tables taken from OPAL and?."," For all calculations we used the Eggleton stellar evolution code TWIN, with opacity tables taken from OPAL and."
+. Convection is modelled by mixing length theory with the ratio of mixing length to pressure scale height //Hp=2.0., Convection is modelled by mixing length theory with the ratio of mixing length to pressure scale height $l/H_P=2.0$.
+ Mixing is modelled by a diffusion equation for the abundances., Mixing is modelled by a diffusion equation for the abundances.
+" Zero-age main-sequence stars have solar metallicity (X=0.70, Z= 0.02)."," Zero-age main-sequence stars have solar metallicity $X=0.70$, $Z=0.02$ )."
+" The code explicitly follows the abundances of H, He, C, N, O, ?2Ne and Mg and uses the the pp-chain and CNO bi-cycle for hydrogen burning and 3a and '?C(a,s)5Ο reactions for helium burning."," The code explicitly follows the abundances of H, He, C, N, O, $^{22}$ Ne and Mg and uses the the pp-chain and CNO bi-cycle for hydrogen burning and $3\alpha$ and ${\rm
+^{12}C(\alpha,\gamma)^{16}O}$ reactions for helium burning."
+ We model angular-momentum loss by magnetic braking according to equation (34) of with y= 4., We model angular-momentum loss by magnetic braking according to equation (34) of with $\gamma=4$ .
+" Following?,, we reduce the strength of the magnetic braking by an ad-hoc factor exp(1—0.02/qconv), where qconv is the mass fraction of the convective envelope of the donor star and assume that magnetic braking abruptly shuts off when gconv=1."," Following, we reduce the strength of the magnetic braking by an ad-hoc factor $\exp\left(1-0.02/q_\mathrm{conv}\right)$, where $q_\mathrm{conv}$ is the mass fraction of the convective envelope of the donor star and assume that magnetic braking abruptly shuts off when $q_\mathrm{conv} = 1$."
+ Angular-momentum loss owing to gravitational-wave emission is taken into account with a standard prescription?)., Angular-momentum loss owing to gravitational-wave emission is taken into account with a standard prescription.
+". For the AM CVn stars the donors are expected to be helium white dwarfs, as heavier white dwarf donors would either lead to unstable mass transfer and a complete merger of the system or to mass-transfer rates far in excess of the Eddington limit for the accreting white dwarf(??)."," For the AM CVn stars the donors are expected to be helium white dwarfs, as heavier white dwarf donors would either lead to unstable mass transfer and a complete merger of the system or to mass-transfer rates far in excess of the Eddington limit for the accreting white dwarf."
+. The most massive donors are expected to be no more massive than about 0.3Mo.," The most massive donors are expected to be no more massive than about $0.3\,\msun$."
+ They are born with hydrogen-helium envelopes of about 0.01Mo.," They are born with hydrogen-helium envelopes of about $0.01\,\msun$."
+ For UCXBs similar mass-transfer stability arguments have led us to conclude that the donors must have masses less than about 0.45Mo allowing helium white dwarfs and hybrid white dwarfs as donors.," For UCXBs similar mass-transfer stability arguments have led us to conclude that the donors must have masses less than about $0.45\,\msun$ allowing helium white dwarfs and hybrid white dwarfs as donors."
+ Hybrid WDshave C/O cores and thick (about 0.1 Mo) He-C-O mantles," Hybrid WDshave C/O cores and thick (about $0.1\,\msun$ ) He-C-O mantles"
+method which complements the results of our supervised classification.,method which complements the results of our supervised classification.
+ The method is described in more detail in the following section., The method is described in more detail in the following section.
+ Our classifiers are able to identify eclipsing binaries in a reliable way. provided that several orbital periods are sampled by the light curve. or that a sufficient amount of measurements during eclipse is present.," Our classifiers are able to identify eclipsing binaries in a reliable way, provided that several orbital periods are sampled by the light curve, or that a sufficient amount of measurements during eclipse is present."
+ Otherwise. their signatures in the Fourier spectrum are very weak and difficult to identify with an automated method.," Otherwise, their signatures in the Fourier spectrum are very weak and difficult to identify with an automated method."
+ Those cases are likely to be missed by the classifier., Those cases are likely to be missed by the classifier.
+ The presence of additional variability in the light curve. either instrumental or intrinsic to the object. hampers the detection of eclipses even more.," The presence of additional variability in the light curve, either instrumental or intrinsic to the object, hampers the detection of eclipses even more."
+ Therefore. we have developed an extractor method for those cases. which effectively complements the other classifiers.," Therefore, we have developed an extractor method for those cases, which effectively complements the other classifiers."
+ This method also allows to detect eclipses when the orbital period of the binary is similar to or even equal to the period of the additional variability in the light curve., This method also allows to detect eclipses when the orbital period of the binary is similar to or even equal to the period of the additional variability in the light curve.
+ Basically. eclipses are detected as downward outliers in a high-pass filtered version of the light curve.," Basically, eclipses are detected as downward outliers in a high-pass filtered version of the light curve."
+ The high-pass filtering removes the low-frequency content of the light curves. including instrumental trends and long-timescale variability.," The high-pass filtering removes the low-frequency content of the light curves, including instrumental trends and long-timescale variability."
+ The resulting filtered version of the light curve only retains the high frequency content. including part of the highly non-sinusoidal eclipse signal (the higher harmonies of the orbital frequency).," The resulting filtered version of the light curve only retains the high frequency content, including part of the highly non-sinusoidal eclipse signal (the higher harmonics of the orbital frequency)."
+ As an additional advantage. several combination frequency peaks are removed as well (e.g. combinations of low frequencies which are filtered out. and higher frequencies).," As an additional advantage, several combination frequency peaks are removed as well (e.g. combinations of low frequencies which are filtered out, and higher frequencies)."
+ This effectively makes the high frequency region in the amplitude spectrum less contaminated., This effectively makes the high frequency region in the amplitude spectrum less contaminated.
+ The filter works by convolving the original light curve v(rj.1.N) with a sine-function A(7;). resulting in a new light curve Y(t): where &(r) is defined as: with f the cutoff frequency. to be defined by the user.," The filter works by convolving the original light curve $y(t_i,i=1,N)$ with a sinc-function $k(t_i)$, resulting in a new light curve $Y(t_i)$: where $k(t)$ is defined as: with $f$ the cutoff frequency, to be defined by the user."
+ In our application to the Kepler data. we used a cutoff frequency of 1.5 47!.," In our application to the Kepler data, we used a cutoff frequency of 1.5 $d^{-1}$."
+ All frequencies above this value will be removed from the light curve., All frequencies above this value will be removed from the light curve.
+ This technique is well known i electronic filtering systems., This technique is well known in electronic filtering systems.
+ It is based on the mathematical result that convolution with a sinc-function in the time domain corresponds to multiplication with a rectangular. bandpass function in the Fourier domain., It is based on the mathematical result that convolution with a sinc-function in the time domain corresponds to multiplication with a rectangular bandpass function in the Fourier domain.
+ The resulting light curve Υ(1) is a low-pass filtered version of the original light curve v(r;)., The resulting light curve $Y(t_i)$ is a low-pass filtered version of the original light curve $y(t_i)$.
+" The desired high-pass filtered version y5,(fj) is then obtained as: We now scan v5,(5) for groups of downward outliers using box-plot statistics.", The desired high-pass filtered version $y_{hf}(t_i)$ is then obtained as: We now scan $y_{hf}(t_i)$ for groups of downward outliers using box-plot statistics.
+ This method has the advantage of being less sensitive to the underlying statistical distribution of the data., This method has the advantage of being less sensitive to the underlying statistical distribution of the data.
+ In the application to the data. we flagged the light curve if more than 10 outliers were detected this way.," In the application to the data, we flagged the light curve if more than 10 outliers were detected this way."
+ This flag was then combined with the usual classification labels., This flag was then combined with the usual classification labels.
+ Figure | shows two examples of eclipsing binaries detected using this method. while Fig.," Figure \ref{ecl-detect} shows two examples of eclipsing binaries detected using this method, while Fig."
+ 2 illustrates the filtering process for one of the light curves., \ref{fil-example} illustrates the filtering process for one of the light curves.
+ The filter will remove any kind of variability with frequencies below the cutoff value. but the eclipse detection only works well. if the additional variability (not related to the eclipses). is confined to a frequency region below the cutoff frequency of the filter. and if the eclipse signal has sufficient power (in the form of higher harmonics) above the cutoff frequency.," The filter will remove any kind of variability with frequencies below the cutoff value, but the eclipse detection only works well, if the additional variability (not related to the eclipses), is confined to a frequency region below the cutoff frequency of the filter, and if the eclipse signal has sufficient power (in the form of higher harmonics) above the cutoff frequency."
+ The value of the cutoff frequency we chose proved to be a good compromise between removing sufficient low-frequency content of the light curves (hampering the eclipse detection) and not removing too much high frequency content. since the latter contains part of the eclipse signal.," The value of the cutoff frequency we chose proved to be a good compromise between removing sufficient low-frequency content of the light curves (hampering the eclipse detection) and not removing too much high frequency content, since the latter contains part of the eclipse signal."
+ Given that we are especially interested i1 detecting pulsators in eclipsing binary systems (see Sect., Given that we are especially interested in detecting pulsators in eclipsing binary systems (see Sect.
+ 4.3). in particular of y Dor and SPB type. this cutoff value will remove most of the pulsation signal for those targets. making the detection of eclipses possible in these cases.," 4.3), in particular of $\gamma$ Dor and SPB type, this cutoff value will remove most of the pulsation signal for those targets, making the detection of eclipses possible in these cases."
+ At the expense of computation time. different cutoff values can be tried and the eclipse detection can be done on different filtered versions of the light curves.," At the expense of computation time, different cutoff values can be tried and the eclipse detection can be done on different filtered versions of the light curves."
+" For example. a higher cutoff frequency can be chosen to be able to detect eclipses in the presence of higher frequency pulsations (otherwise. the filter will not remove any ""disturbing! variability)."," For example, a higher cutoff frequency can be chosen to be able to detect eclipses in the presence of higher frequency pulsations (otherwise, the filter will not remove any `disturbing' variability)."
+ However. higher cutoff values also remove more of the eclipse signal. and not enough power might remain to detect them.," However, higher cutoff values also remove more of the eclipse signal, and not enough power might remain to detect them."
+ To avoid this. and to limit the computation time. we performed an additional outher detection step at the end of the light curve analysis procedure.," To avoid this, and to limit the computation time, we performed an additional outlier detection step at the end of the light curve analysis procedure."
+ The automated procedure removes a maximum of 3 different frequencies from the light curve (with each a maximum of 4+ harmonics). in 3 consecutive prewhitening steps.," The automated procedure removes a maximum of 3 different frequencies from the light curve (with each a maximum of 4 harmonics), in 3 consecutive prewhitening steps."
+ This way. we filter out only the dominant signal. irrespective of its frequency.," This way, we filter out only the dominant signal, irrespective of its frequency."
+ The residuals are then again checked for downward outliers. indicative of eclipses.," The residuals are then again checked for downward outliers, indicative of eclipses."
+ It is clear that a combination of techniques is needed to detect all kinds of eclipse signals. even more so because additional variability on several timescales can be present as well.," It is clear that a combination of techniques is needed to detect all kinds of eclipse signals, even more so because additional variability on several timescales can be present as well."
+" Our regular classifier reliably detects ""pure! eclipsing binary light curves. irrespective of their orbital period. and the extractor methods can detect eclipses in the presence of additional variability. or when the eclipse signal is too faint to cause clear signatures in the Fourier spectrum."," Our regular classifier reliably detects `pure' eclipsing binary light curves, irrespective of their orbital period, and the extractor methods can detect eclipses in the presence of additional variability, or when the eclipse signal is too faint to cause clear signatures in the Fourier spectrum."
+ The fact that the extractor scans the (filtered) light curve for outliers implies that it is well suited to detect detached system. with highly non-sinusoidal light curves.," The fact that the extractor scans the (filtered) light curve for outliers implies that it is well suited to detect detached system, with highly non-sinusoidal light curves."
+ Close binaries. showing sinusoidal-like light curves. are better detected with the regular classifier.," Close binaries, showing sinusoidal-like light curves, are better detected with the regular classifier."
+ Following the application of our automated methods. we estimated the number of periodic variables in the dataset and constructed samples of good candidate members for the major stellar variability classes we included m our classifier.," Following the application of our automated methods, we estimated the number of periodic variables in the dataset and constructed samples of good candidate members for the major stellar variability classes we included in our classifier."
+Ποιος et al. (1990) discussed the possibility of V426 Oph being an LP ancl concluded it was not since there was no prominent X-ray modulation.,Hellier et al (1990) discussed the possibility of V426 Oph being an IP and concluded it was not since there was no prominent X-ray modulation.
+ In the case of LS Pee. the fact that there is some evidence that its optical Hux is circularly polarised (albeit only at a significance level of 36) on a period of 29 min hints at a magnetic nature (Itodriguez-Cil et al 2001).," In the case of LS Peg, the fact that there is some evidence that its optical flux is circularly polarised (albeit only at a significance level of $\sigma$ ) on a period of 29 min hints at a magnetic nature (Rodriguez-Gil et al 2001)."
+ EIncleec. a number of other IPs show a modulation in the optical circular polarisation at the spin period (see the ]xatajainen et al 2007 for a recent reference list).," Indeed, a number of other IPs show a modulation in the optical circular polarisation at the spin period (see the Katajainen et al 2007 for a recent reference list)."
+ Lt is clear that there is a great deal of uncertainty as to the sub-type 26 Oph and LS Peg., It is clear that there is a great deal of uncertainty as to the sub-type of V426 Oph and LS Peg.
+ For instance. in the catalogue of Rutter Ixolb (2003). LS Pee is classed as an nova-like. while VY Scl. SW Sex and IP!," For instance, in the catalogue of Ritter Kolb (2003), LS Peg is classed as an nova-like, while VY Scl, SW Sex and IP!"
+ In the case of EL UMa both Panelel et al (2005) and Reimer et al (2008) suggest it is an LP., In the case of EI UMa both Pandel et al (2005) and Reimer et al (2008) suggest it is an IP.
+" We believe that the fact that all three systems show high levels of complex absorption (ic an equivalent. column density >5«1075 Ἐν, Table 3)) point to these systenis being LPs."," We believe that the fact that all three systems show high levels of complex absorption (ie an equivalent column density $>5\times10^{21}$ , Table \ref{spec}) ) point to these systems being IPs."
+ We now address why they do not show evidence for a spin period in N-ravs., We now address why they do not show evidence for a spin period in X-rays.
+ A strong X-ray. modulation has always been taken as one of the main defining characteristics of an IP., A strong X-ray modulation has always been taken as one of the main defining characteristics of an IP.
+ X modulation at the spin period arises due to phase-varving photoelectric absorption in the accretion column and/or self occultation bv the body of the white dwarf., A modulation at the spin period arises due to phase-varying photoelectric absorption in the accretion column and/or self occultation by the body of the white dwarf.
+ A similar modulation at the beat period arises due to the accretion stream Lipping between the poles., A similar modulation at the beat period arises due to the accretion stream flipping between the poles.
+ However. these modulations will only arise if the magnetic axis of the white dwarl is mis-aligned with the white cwarl spin axis (eg Wing Shaviv ORA).," However, these modulations will only arise if the magnetic axis of the white dwarf is mis-aligned with the white dwarf spin axis (eg King Shaviv 1984)."
+ 'Pherefore. for all confirmed. LPs. it is most likely that the magnetic and spin axes are olfset from cach other. typically bv ~ 10's of degrees.," Therefore, for all confirmed IPs, it is most likely that the magnetic and spin axes are offset from each other, typically by $\sim 10$ 's of degrees."
+" Only in one IP (XY Ari) is there an observational measurement of this olfset: Lellier (1997) estimates that in NY Ari the magnetic dipole axis is ollset from the spin axis by 27"" and that the main accretion region is ollset from the magnetic axis by a further 19.", Only in one IP (XY Ari) is there an observational measurement of this offset: Hellier (1997) estimates that in XY Ari the magnetic dipole axis is offset from the spin axis by $^{\circ}$ and that the main accretion region is offset from the magnetic axis by a further $^{\circ}$.
+ If the magnetic and spin axes of à white dwarf in an accreting binary svstem are closely aligned. then a disc-fed system will eive rise to circular accretion curtains above cach magnetic pole (extending to all azimuths).," If the magnetic and spin axes of a white dwarf in an accreting binary system are closely aligned, then a disc-fed system will give rise to circular accretion curtains above each magnetic pole (extending to all azimuths)."
+ Phere will essentially be no phase varving photoclect absorption and no variation in self occultation. and consequentisrie the X-ray signal will show no variation with spin phase.," There will essentially be no phase varying photoelectric absorption and no variation in self occultation, and consequently the X-ray signal will show no variation with spin phase."
+ Similarly. in à streame-fed system. with co-aligned magnetic and spin axes. equal amounts of material are likely to feed onto cach pole at all times. and there will be no variation in X-ray Lux with beat phase.," Similarly, in a stream-fed system with co-aligned magnetic and spin axes, equal amounts of material are likely to feed onto each pole at all times, and there will be no variation in X-ray flux with beat phase."
+ Axes that are aligned to within a few degrees will likely give rise to an X-ray modulation of less than a few percent depth. which would be undetectable in most. cases due to intrinsic X-ray Liekerine.," Axes that are aligned to within a few degrees will likely give rise to an X-ray modulation of less than a few percent depth, which would be undetectable in most cases due to intrinsic X-ray flickering."
+ ln. contrast. simulations made using the polarisation. models. of Potter. Llakala Cropper (1998) show that à mis-alignmoent between the spin and magnetic axes of even 5 (and assuming accretion onto à small spot at the magnetic poles) gives rise to a mocdulation in the circular polarisation Lux as seen in LS Pee.," In contrast, simulations made using the polarisation models of Potter, Hakala Cropper (1998) show that a mis-alignment between the spin and magnetic axes of even $^{\circ}$ (and assuming accretion onto a small spot at the magnetic poles) gives rise to a modulation in the circular polarisation flux as seen in LS Peg."
+ We therefore sugeest that there should. exist. a population of IPs with closely aligned. spin ancl magnetic axes which do not show any detectable spin or beat moclulation in twir X-ray [lux., We therefore suggest that there should exist a population of IPs with closely aligned spin and magnetic axes which do not show any detectable spin or beat modulation in their X-ray flux.
+ Should such systems exhibit any other defining variation in their X-ray lux?, Should such systems exhibit any other defining variation in their X-ray flux?
+ Up to half of all confirmed. IPs also show an X-ray mocdulation at he system: orbital period (Parker. Norton Alukai 2005).," Up to half of all confirmed IPs also show an X-ray modulation at the system orbital period (Parker, Norton Mukai 2005)."
+ This is presumed to be due to absorption in material at 1e cdge of the accretion disc. thrown up by the impact oft10 aceretion stream.," This is presumed to be due to absorption in material at the edge of the accretion disc, thrown up by the impact of the accretion stream."
+ Since ~50% of all known systems show his effect. and assuming their orbital planes to be randomly orientated with respect to our line of sight. this indicates hat the absorbing material must extend. far enough out of the orbital plane to be seen at all inclination angles above 607.," Since $\sim$ of all known systems show this effect, and assuming their orbital planes to be randomly orientated with respect to our line of sight, this indicates that the absorbing material must extend far enough out of the orbital plane to be seen at all inclination angles above $60^{\circ}$."
+ The question arises therefore. should. not half of the IPs with aligned. spin and magnetic axes show such an orbital modulation and be detected that wav?," The question arises therefore, should not half of the IPs with aligned spin and magnetic axes show such an orbital modulation and be detected that way?"
+ Norton Alukai (2007) showed that the LP NY Avi exhibits a broad N-rav modulation at its orbital period which comes and goes on a timescale of ~months., Norton Mukai (2007) showed that the IP XY Ari exhibits a broad X-ray modulation at its orbital period which comes and goes on a timescale of $\sim$ months.
+ They interpreted this as evidence for a precessing. tilted or warped accretion disc in that system.," They interpreted this as evidence for a precessing, tilted or warped accretion disc in that system."
+ They. further suggested. that such clises may exist in all LPs and that the cause of the warp may be related to the spinning magnetic field anchored to the white dwarf at its centre., They further suggested that such discs may exist in all IPs and that the cause of the warp may be related to the spinning magnetic field anchored to the white dwarf at its centre.
+ A tilted magnetic dipole will stir up the inner edge of the accretion cise aud lift material away from the orbital plane. thus initiating the precessing warp or tilt.," A tilted magnetic dipole will stir up the inner edge of the accretion disc and lift material away from the orbital plane, thus initiating the precessing warp or tilt."
+ The lifting of material far enough out of the orbital plane to cause an X-ray orbital modulation in half the known LPs is therefore due to this warp or tilt in the disc. which in turn is due to the tilted dipole at its centre. caused by mis-aligned spin and magnetic axes.," The lifting of material far enough out of the orbital plane to cause an X-ray orbital modulation in half the known IPs is therefore due to this warp or tilt in the disc, which in turn is due to the tilted dipole at its centre, caused by mis-aligned spin and magnetic axes."
+ For IPs with closely aligned spin and magnetic axes. the situation is less clear.," For IPs with closely aligned spin and magnetic axes, the situation is less clear."
+ However. we suggest that for these systems. material is azimuthally concentrated: at the point where the accretion stream from the secondary star meets the accretion disc. thereby giving rise to a mocdulation at the orbital period.," However, we suggest that for these systems, material is azimuthally concentrated at the point where the accretion stream from the secondary star meets the accretion disc, thereby giving rise to a modulation at the orbital period."
+ Closer to the white dwarl the accretion," Closer to the white dwarf, the accretion"
+Q=7/2.,$\Omega = \pi /2$.
+ This leads to an eccentric disk structure that is inclined respect to the original orbital plane of the parent body of approximately 50°., This leads to an eccentric disk structure that is inclined respect to the original orbital plane of the parent body of approximately $50^o$.
+" Finally,the case irs.=90° (Fig.6 bottom plots) is the most symmetric case."," Finally,the case $i_{ISM} = 90^o$ \ref{f6} bottom plots) is the most symmetric case."
+ The circular overdense shape of the disk close to the star is where the inclined orbits cross the parent body plane., The circular overdense shape of the disk close to the star is where the inclined orbits cross the parent body plane.
+" The dust particles have a statistical uniform distribution of the nodes for any value of inclination and, as a consequence, a high density region is formed in correspondence to the intersection between the inclined orbits and the initial parent body plane."," The dust particles have a statistical uniform distribution of the nodes for any value of inclination and, as a consequence, a high density region is formed in correspondence to the intersection between the inclined orbits and the initial parent body plane."
+" For larger dust grains (10um) and low optical depth (r=109), the dynamical scenario is slightly different."," For larger dust grains $\mu$ m) and low optical depth $\tau = 10^{-6}$ ), the dynamical scenario is slightly different."
+" The Stark period is of the order of 23 Myr, 10 times longer than that of lum particles, but the drift rate has not decreased by the same amount."," The Stark period is of the order of 23 Myr, 10 times longer than that of $\mu$ m particles, but the drift rate has not decreased by the same amount."
+" As a consequence, the grains evolve less into the Stark cycle and migrate inside before reaching large values of inclination."," As a consequence, the grains evolve less into the Stark cycle and migrate inside before reaching large values of inclination."
+" This is shown in Fig.8 where the eccentricity and inclination of the dust, when the disk is in a steady state, are illustrated."," This is shown in \ref{f8} where the eccentricity and inclination of the dust, when the disk is in a steady state, are illustrated."
+ The initial eccentricity is close to 0 since 8 is small and this leads to a different Stark cycle compared to that in Fig.6 middle plots., The initial eccentricity is close to 0 since $\beta$ is small and this leads to a different Stark cycle compared to that in \ref{f6} middle plots.
+ The particles slowly evolve towards larger inclination values but they plunge into the inner regions of the disk and are lost before they can develop significant inclinations., The particles slowly evolve towards larger inclination values but they plunge into the inner regions of the disk and are lost before they can develop significant inclinations.
+ The disk is then expected to be less perturbed compared to the case for 1 um size particles., The disk is then expected to be less perturbed compared to the case for 1 $\mu$ m size particles.
+ This is confirmed by Fig.9 where the spatial density distribution is illustrated and can be compared to that shown in Fig.7 (middle plot) for 1 jum size particles., This is confirmed by \ref{f9} where the spatial density distribution is illustrated and can be compared to that shown in \ref{f7} (middle plot) for 1 $\mu$ m size particles.
+" We have shown in this paper, by numerical modeling the evolution of debris disks under the effects of solar radiation pressure, PR drag and ISM flux, that for typical values of optical depth 7~10? the signatures of the ISM wind on grains with radius in the range 1—10 um, just above the cut- size imposed by radiation pressure, are almost negligible."," We have shown in this paper, by numerical modeling the evolution of debris disks under the effects of solar radiation pressure, PR drag and ISM flux, that for typical values of optical depth $\tau \sim 10^{-3}$ the signatures of the ISM wind on grains with radius in the range $1-10$ $\mu$ m, just above the cut-off size imposed by radiation pressure, are almost negligible."
+ 'The amount of perturbations due to the interaction of dust particles with the local ISM neutral atom flow are strongly reduced when the grain lifetime is short as in disks with large values of 7r., The amount of perturbations due to the interaction of dust particles with the local ISM neutral atom flow are strongly reduced when the grain lifetime is short as in disks with large values of $\tau$.
+" In this scenario, the presence of asymmetries must be ascribed to different mechanisms like the presence of massive bodies within the disk."," In this scenario, the presence of asymmetries must be ascribed to different mechanisms like the presence of massive bodies within the disk."
+ The neutral ISM fails in producing either warping or clumping in such disks., The neutral ISM fails in producing either warping or clumping in such disks.
+ Different is the scenario when the optical depth is small., Different is the scenario when the optical depth is small.
+ We have shown that for τ~105 significant asymmetries appear on the density profile of the disk both in the parent bodies plane and out-of-plane., We have shown that for $\tau \sim 10^{-6}$ significant asymmetries appear on the density profile of the disk both in the parent bodies plane and out–of–plane.
+ Interesting is a double-elliptical pattern that develops in the parent bodies plane when the ISM flow is almost coplanar to it., Interesting is a double--elliptical pattern that develops in the parent bodies plane when the ISM flow is almost coplanar to it.
+ The disk structures are caused by the dynamical evolution of the orbital elements of the dust grains., The disk structures are caused by the dynamical evolution of the orbital elements of the dust grains.
+" The way in which these orbital parameters evolve can be in part predicted on the basis of the general Stark model that helps in understanding the periodic nature of eccentricity, inclination and the dynamically related angles perihelion argument and nodal longitude (Belyaev&Rafikov2010;Pastor 2011).."," The way in which these orbital parameters evolve can be in part predicted on the basis of the general Stark model that helps in understanding the periodic nature of eccentricity, inclination and the dynamically related angles perihelion argument and nodal longitude \citep{bera,pasto}. ."
+" In addition, the semimajor axis has a fast inward drift due to the combination of PR drag and interaction with the"," In addition, the semimajor axis has a fast inward drift due to the combination of PR drag and interaction with the"
+Studying the Schmidt-Kennicutt law. most regions in the system follow closely the relation found in. spiral. galaxies by ?.. with the exception of the nuclear starburst and the tip of one of the tidal tails which show a significantly larger efficiency.,"Studying the Schmidt–Kennicutt law, most regions in the system follow closely the relation found in spiral galaxies by \cite{bigiel2008a}, with the exception of the nuclear starburst and the tip of one of the tidal tails which show a significantly larger efficiency."
+ Comparisons with the relations derived by ? exhibit the presence of 2 star formation modes., Comparisons with the relations derived by \cite{daddi2010a} exhibit the presence of 2 star formation modes.
+ The detection of these 2 modes in a resolved way hints that their origin is linked to the physics of the interstellar medium at scales no larger than I kpe. the size of the largest gravitational instabilities and the injection scale of turbulence.," The detection of these 2 modes in a resolved way hints that their origin is linked to the physics of the interstellar medium at scales no larger than 1 kpc, the size of the largest gravitational instabilities and the injection scale of turbulence."
+using the data-set published by Ferraro et al. (,using the data-set published by Ferraro et al. (
+2003b) and the procedure deseribed in Ferraro et al. (,2003b) and the procedure described in Ferraro et al. (
+20036).,2003c).
+ Additional HST Archive data in the V band have been used to combine the HST and the ground based dataset., Additional HST Archive data in the $V$ band have been used to combine the HST and the ground based dataset.
+ All the stars brighter than the cluster Main Sequence Turn-Off (V.<18) have been used to compute the projected density profile., All the stars brighter than the cluster Main Sequence Turn-Off $V<18$ ) have been used to compute the projected density profile.
+ Fig., Fig.
+ 1 shows the comparison between observed and modeled projected density profile., 1 shows the comparison between observed and modeled projected density profile.
+" This model has a concentration ¢=1.95. and a core radius 7,221""."," This model has a concentration $c=1.95$, and a core radius $r_c=21\arcsec$."
+ A typical uncertainty of +2” can be assumed in the 7. determination., A typical uncertainty of $\pm 2\arcsec$ can be assumed in the $r_c$ determination.
+" Note that the value assumed for 47 Tuc is consistent with that (r,.=23""+2”) obtained by Howell. Guhathakurta Gilliland (2000)."," Note that the value assumed for 47 Tuc is consistent with that $r_c=23\arcsec \pm 2\arcsec$ ) obtained by Howell, Guhathakurta Gilliland (2000)."
+ Assuming a distance of 4.6 kpe (Ferraro et al., Assuming a distance of 4.6 kpc (Ferraro et al.
+" 1999b). the core is 5r,=0.42 pe."," 1999b), the core is $r_c=0.42$ pc."
+" The dimensionless central potential is Wo=12 (Wo=W(0)/ (o7. where (c; is the mean core dispersion velocity. YOO)=Gy) (0). with (7) the gravitational potential and +, the tidal radius (Sigurdsson Phinney 1995)."," The dimensionless central potential is $W_0=12$ $W_0\equiv{}\Psi{}(0)/\langle{}\sigma{}\rangle{}^2$ , where $\langle{}\sigma{}\rangle{}$ is the mean core dispersion velocity, $\Psi{}(0)\equiv{}\Phi{}(r_t)-\Phi{}(0)$ , with $\Phi{}(r)$ the gravitational potential and $r_t$ the tidal radius (Sigurdsson Phinney 1995)."
+ 0.2truecm On this background we evolve the dynamics of BSs., 0.2truecm On this background we evolve the dynamics of BSs.
+ We assume that collisional BSs are generated exclusively in the innermost region. at radii less than 7. with i<20.1.0.5 and 0.8. where the density is high to guarantee a high collision rate (Pooley et al.," We assume that collisional BSs are generated exclusively in the innermost region, at radii less than $n\,{}r_c$, with $n\leq{}=0.1,~0.5$ and $0.8,$ where the density is high to guarantee a high collision rate (Pooley et al."
+ 2003)., 2003).
+ Internal BSs generated in PBs have been explored as last case and may be considered as extreme since dynamical interactions in dense cluster cores tend to destroy binaries and to alter those that remain through exchanges (Sigurdsson Phinney 1993: Ivanova et al., Internal BSs generated in PBs have been explored as last case and may be considered as extreme since dynamical interactions in dense cluster cores tend to destroy binaries and to alter those that remain through exchanges (Sigurdsson Phinney 1993; Ivanova et al.
+ 2004)., 2004).
+ External BSs formed in PBs are generated outside the core with initial positions distributed in several radial intervals. between 15 and 80 r..," External BSs formed in PBs are generated outside the core with initial positions distributed in several radial intervals, between 15 and 80 $r_c$."
+ All initial positions are randomly generated following a flat probability distribution (see Table 1) according to the fact that the number of stars in a King model scales as dN=xcarder dr.," All initial positions are randomly generated following a flat probability distribution (see Table 1) according to the fact that the number of stars in a King model scales as $\ud{}N=n(r)\,{}\ud{}V\propto{}r^{-2}\,{}\pi{}r^{2}\ud{}r\propto{}\ud{}r$ ."
+ This is the key difference between our simulations and those of Sigurdsson et al. (, This is the key difference between our simulations and those of Sigurdsson et al. (
+1995). who generated BSs only in the central region (below 0.8 7).,"1995), who generated BSs only in the central region (below 0.8 $r_c$ )."
+ BS velocities are randomly generated following the distribution illustrated in section 3 of Sigurdsson Phinney 1995 (eq., BS velocities are randomly generated following the distribution illustrated in section 3 of Sigurdsson Phinney 1995 (eq.
+ 3.3)., 3.3).
+ In addition. we assign a natal kick to those BSs formed collisionally in the core: kick velocities fall in between 1 and 6 c. and their distribution is flat or single valued.," In addition, we assign a natal kick to those BSs formed collisionally in the core: kick velocities fall in between 1 and 6 $\sigma{}$, and their distribution is flat or single valued."
+ The masses of BSs are generated between 1.2 and 2 M... following indications from Ferraro et al. (," The masses of BSs are generated between 1.2 and 2 $M_{\odot{}}$, following indications from Ferraro et al. ("
+1997) and Gilliland et al. (,1997) and Gilliland et al. (
+1998).,1998).
+" Every single BS is evolved for a time f;=fay*rand. where rand is à random number uniformly generated in [0.1] and fj, is the lifetime assumed for a BS (we have performed sets of runs with various £j44. between | and 5 Gyr)."," Every single BS is evolved for a time $t_i=t_{\rm last}\,{}*\,{}rand$, where $rand$ is a random number uniformly generated in [0,1] and $t_{\rm last}$ is the lifetime assumed for a BS (we have performed sets of runs with various $t_{\rm last}$, between 1 and 5 Gyr)."
+ Once generated. the BS drifts 1n the cluster background under the action of the cluster potential. dynamical friction and distant encounters (eq. [," Once generated, the BS drifts in the cluster background under the action of the cluster potential, dynamical friction and distant encounters (eq. ["
+3.4] of Sigurdsson and Phinney 1995).,3.4] of Sigurdsson and Phinney 1995).
+ Near encounters are uninfluent., Near encounters are uninfluent.
+ We performed more than 70.000 runs testing various scenarios.," We performed more than 70,000 runs testing various scenarios."
+ We first traced the BS evolution in the collisional hypothesis (Sigurdsson et al., We first traced the BS evolution in the collisional hypothesis (Sigurdsson et al.
+ 1994)., 1994).
+ We generated BSs at radii less than 0.8 7. with recoil velocities m various ranges., We generated BSs at radii less than 0.8 $r_c$ with recoil velocities in various ranges.
+ We observed that for recoil velocities greater than 3.5 σ BSs are expelled from the cluster. while for recoil velocities lower than 3 σ dynamical friction drags all of the BSs into the core in ~108 years.," We observed that for recoil velocities greater than 3.5 $\sigma{}$ BSs are expelled from the cluster, while for recoil velocities lower than 3 $\sigma{}$ dynamical friction drags all of the BSs into the core in $\sim 10^8$ years."
+ The final simulated distribution. shown in Fig.," The final simulated distribution, shown in Fig."
+ 2a. is peaked in the center. but does not reproduce the observed rise in the outer region of the GC.," 2a, is peaked in the center, but does not reproduce the observed rise in the outer region of the GC."
+ Thus. no collisional BSs ejected from the core by recoil contribute to the external population.," Thus, no collisional BSs ejected from the core by recoil contribute to the external population."
+ The best representation of the data is obtained generating of the BSs from mass-transfer in PBs between 30 and 60 rx. with no kick. and from collisions inside 0.5 7. with a natal kick of | σ (see Fig.," The best representation of the data is obtained generating of the BSs from mass-transfer in PBs between 30 and 60 $r_c$ with no kick, and from collisions inside 0.5 $r_c$ with a natal kick of 1 $\sigma{}$ (see Fig."
+ 2b)., 2b).
+ Q.2truecm Another key parameter to understand BS evolution is their lifetime., 0.2truecm Another key parameter to understand BS evolution is their lifetime.
+ We performed simulations withvarious lifetimes fj (1. 2. 3. 4. 5 Gyr).," We performed simulations withvarious lifetimes $t_{\rm
+last}$ (1, 2, 3, 4, 5 Gyr)."
+ We integrated the evolution of every single BS for a time homogeneously distributed between 0, We integrated the evolution of every single BS for a time homogeneously distributed between 0
+The discovery of the first accreting millisecond pulsar (AMSP) in 1998. (?).. confirmed the predictions of the recycling scenario. according to which millisecond radio pulsars are the end product of a long phase of accretion of matter and angular momentum onto a neutron star (NS) hosted in à low mass X-ray binary ?).,"The discovery of the first accreting millisecond pulsar (AMSP) in 1998, , confirmed the predictions of the recycling scenario, according to which millisecond radio pulsars are the end product of a long phase of accretion of matter and angular momentum onto a neutron star (NS) hosted in a low mass X-ray binary ."
+. In the twelve years since the first discovery. the class of AMSPs has grown to thirteen members. all X-ray transients.," In the twelve years since the first discovery, the class of AMSPs has grown to thirteen members, all X-ray transients."
+ To perform a timing analysis of different outbursts of the same source allows the estimate of its evolution over a time range of a few years., To perform a timing analysis of different outbursts of the same source allows the estimate of its evolution over a time range of a few years.
+ In the case ofJ1808.4—3058. the observations of five outbursts over 10 yr has allowed a firm estimate of its spin and orbital evolution.," In the case of, the observations of five outbursts over 10 yr has allowed a firm estimate of its spin and orbital evolution."
+ The orbital perioc has been observed to increase at a rate of nearly two orders of magnitude larger than what is predicted by conservative mass transfer (??.. see also ?.. HOS hereafter).," The orbital period has been observed to increase at a rate of nearly two orders of magnitude larger than what is predicted by conservative mass transfer , see also , H08 hereafter)."
+ This has led the authors to argue that a large fraction of the nass transferred by the companion star is ejected by the system taking away the angular momentun2 needed to match the observed value., This has led the authors to argue that a large fraction of the mass transferred by the companion star is ejected by the system taking away the angular momentum needed to match the observed value.
+ A regular NS spin dowi0 has also been measured by HOS leading to stringen= upper limits on the various mechanisms that car brake dowsαυ] a pulsar during quiescence such as magneto-dipole emission. emission of gravitational waves and a propeller effect.," A regular NS spin down has also been measured by H08 leading to stringent upper limits on the various mechanisms that can brake down a pulsar during quiescence such as magneto-dipole emission, emission of gravitational waves and a propeller effect."
+ These effects. and η particular the spin down torque associated with the emission of gravitational waves. Mew. crucially depenc on the spin frequency of the NS (Λίοx νο).," These effects, and in particular the spin down torque associated with the emission of gravitational waves, $N_{GW}$, crucially depend on the spin frequency of the NS $N_{GW}\propto
+\nu^5$ )."
+ It is therefore very appealing to shed light on the long-term behaviour of the fastest AMSP discovered so far. the 598.89 Hz pulsar in the following).," It is therefore very appealing to shed light on the long-term behaviour of the fastest AMSP discovered so far, the 598.89 Hz pulsar in the following)."
+ In this paper. we present a timing analysis based on the two outbursts shown by the source in 2008. and observed by the Rossi X-ray Timing Explorer (RXTE).," In this paper, we present a timing analysis based on the two outbursts shown by the source in 2008, and observed by the Rossi X-ray Timing Explorer )."
+ The results thus obtained are compared with the rotational state of at the end of the outburst exhibited on 2004 December. that is the only other outburst of this source for which high temporal resolution data are available.," The results thus obtained are compared with the rotational state of at the end of the outburst exhibited on 2004 December, that is the only other outburst of this source for which high temporal resolution data are available."
+ The X-ray transient.1002091. was discovered by INTEGRAL on 2004 December 2(?).," The X-ray transient, was discovered by INTEGRAL on 2004 December 2."
+. The 598.89 Hz pulsations found in its light curve make it the fastest AMSP discovered so farhereimafter)., The 598.89 Hz pulsations found in its light curve make it the fastest AMSP discovered so far.
+. Renewed activity was detected byRXTE on 2008 August 13(?)., Renewed activity was detected by on 2008 August 13.
+. The 2.5-25 keV X-ray reaches a peak level of (6.30.2)x107! ere em7? s7!. which is =0.5 times the peak flux observed during the 2004 outburst (GOS).," The 2.5–25 keV X-ray reaches a peak level of $(6.3\pm0.2) \times 10^{-10}$ erg $^{-2}$ $^{-1}$, which is $\approx 0.5$ times the peak flux observed during the 2004 outburst (G05)."
+ The flux decreases on a timescale r=3 d and the source returns to quiescence ~5 d after the first detection., The flux decreases on a timescale $\tau\approx3$ d and the source returns to quiescence $\sim5$ d after the first detection.
+ The light curve recorded by the PCU? of the Proportional Counter Array (PCA) aboardRXTE is plotted in Fig.1.., The light curve recorded by the PCU2 of the Proportional Counter Array (PCA) aboard is plotted in \ref{fig:lc}.
+" As the nearby source V709 Cas (17 aremin away) contributes to the X-ray flux detected byRXTE in the direction of (?).. the observed count-rate stays at a level of ~6 es! PCUT! (corresponding to (7£2)x107""! erg em 8711 2,5225 keV) even when the outburst is presumably over."," As the nearby source V709 Cas (17 arcmin away) contributes to the X-ray flux detected by in the direction of , the observed count-rate stays at a level of $\sim
+6$ c $^{-1}$ $^{-1}$ (corresponding to $(7\pm2)\times 10^{-11}$ erg $^{-2}$ $^{-1}$; 2.5–25 keV) even when the outburst is presumably over."
+ is again detected in outburst on 2008 September. 2] and the fluence of this second episode is similar to that of the first one.," is again detected in outburst on 2008 September, 21 and the fluence of this second episode is similar to that of the first one."
+ To perform a timing analysis on the 598.89 Hz pulsar signal. we consider events recorded by the PCA (Obsid P93013) both in good xenon (lys temporal resolution). and event mode (1254s temporal resolution) configurations.," To perform a timing analysis on the 598.89 Hz pulsar signal, we consider events recorded by the PCA (Obsid P93013) both in good xenon $\mu$ s temporal resolution), and event mode $\mu$ s temporal resolution) configurations."
+" All the arrival times were first corrected with respect to the Solar System barycentre. considering the position of the optical counterpart determined byhereinafter.. RA=00"" 29? 037.05 + 0.01. DECZ59* 34° 187.93 + 07.05."," All the arrival times were first corrected with respect to the Solar System barycentre, considering the position of the optical counterpart determined by, $^h$ $^m$ $^s$ .05 $\pm$ $^s$ .01, $^{\circ}$ 34' 18”.93 $\pm$ 0”.05."
+ A re-analysis of the data taken by during the 2004 outburst (Obslc P90052 and P90425). Is also reported.," A re-analysis of the data taken by during the 2004 outburst (ObsId P90052 and P90425), is also reported."
+ Despite a temporal analysis of the 2004 outburst of having already beer performed by GOS. andBO7.. such a re-analysis 1s aimed at deriving the most accurate estimate of the spin frequency at the end of the outburst that canther becompared to the spin frequency of the source measured 1 2008. after =3.7 yr of quiescence.," Despite a temporal analysis of the 2004 outburst of having already been performed by G05, and, such a re-analysis is aimed at deriving the most accurate estimate of the spin frequency at the end of the outburst that canthen becompared to the spin frequency of the source measured in 2008, after $\approx 3.7$ yr of quiescence."
+area produces the asvnuuetric enhanced. emission which is observed (Llorne The SW Sex 5ars and SA's in outbursts have high accretion rates.,area produces the asymmetric enhanced emission which is observed (Horne The SW Sex stars and SXTs in outbursts have high accretion rates.
+ In contrast. our Doppler map was obtained in quiescence when the aceretion rate is very low.," In contrast, our Doppler map was obtained in quiescence when the accretion rate is very low."
+ If the outbursts are due to the thermal-viscous instability. the hin disk becomes neutral which casts doubts on its ability o anchor a magnetic field for this propeller mechanism to work.," If the outbursts are due to the thermal-viscous instability, the thin disk becomes neutral which casts doubts on its ability to anchor a magnetic field for this propeller mechanism to work."
+ On the other hand. the inner regions of the thin disk are most probably. replaced. by a hot thick ancl optically hin aceretion How: curingὃν quiescence.," On the other hand, the inner regions of the thin disk are most probably replaced by a hot thick and optically thin accretion flow during quiescence."
+ This is required. to explain e.g. the X-ray. luminosities of quiescen BIL SATs (Lasota. Naravan Yi 199( danced the review by Narayvan. Alahadevan Quataert. 1998). or the recurrence times of SXTIsS (Dubus. llameurv Lasota 2001).," This is required to explain e.g. the X-ray luminosities of quiescent BH SXTs (Lasota, Narayan Yi 1996 and the review by Narayan, Mahadevan Quataert 1998) or the recurrence times of SXTs (Dubus, Hameury Lasota 2001)."
+ These ionised lows have very short accretion timescales which makes it unlikely that they could sustain large-scale steady magnetic iclds reaching to the accretion The neutron star magnetosphere itself can become an cHicient propeller in quiescence (Menou et al., These ionised flows have very short accretion timescales which makes it unlikely that they could sustain large-scale steady magnetic fields reaching to the accretion The neutron star magnetosphere itself can become an efficient propeller in quiescence (Menou et al.
+ 1999)., 1999).
+ Strong winds in the thick accretion How could also prevent much of the matter from reaching the S (Blandford Begelman 9)., Strong winds in the thick accretion flow could also prevent much of the matter from reaching the NS (Blandford Begelman 1999).
+ Yet. it is hard to see in both cases how this would load to the observed. asymmetric lla emission since the matter comes from anearisimancelrie We are grateful to D. innez-Delgado ancl €. Israelian for helpful comments.," Yet, it is hard to see in both cases how this would lead to the observed asymmetric $\alpha$ emission since the matter comes from an We are grateful to D. nez-Delgado and G. Israelian for helpful comments."
+ This work is based on observations collected. at the European Southern Observatory in Chile., This work is based on observations collected at the European Southern Observatory in Chile.
+ This research has mace use of theSHAIBAD database. operated. at CDS. Strasbourg. France.," This research has made use of the database, operated at CDS, Strasbourg, France."
+ €i Dubus acknowledges support) from NASA under grants NACG5-TO07 and NACG5-T034., G. Dubus acknowledges support from NASA under grants NAG5-7007 and NAG5-7034.
+. T. Shahbaz acknowledges support by the fellowship 1990002971., T. Shahbaz acknowledges support by the fellowship HP-MF-CT 199900297.
+sstar in a binary system as considered above.,star in a binary system as considered above.
+" However. the cooling time estimate for iun this case is considerably uncertain (see REreftable:re;,0.55) yluetotheextrapolation."," However, the cooling time estimate for in this case is considerably uncertain (see \\ref{table:re_mass}) ) due to the extrapolation."
+Wirhintheselargeerrormd LD bro FO SYM Chandrasekharmass forthemergerproduct. butthisprocessisvery unl DAL HOUR BATH aS PEST reet)..," Within these large error margins, we would in principle be able to obtain a sub-Chandrasekhar mass for the merger product, but this process is very unlikely when we consider the time needed for the white dwarfs to merge."
+ Nevertheless. the possibility of a binary origin for an ONe core aat Tay250000 K cannot be entirely excluded.," Nevertheless, the possibility of a binary origin for an ONe core at $\Teff=50\,000\,$ K cannot be entirely excluded."
+ We note that the effect of magnetic field strength on the structure of the white dwarf. considered in refsec:smgle 1 also important to binary evolution.," We note that the effect of magnetic field strength on the structure of the white dwarf, considered in \\ref{sec:single} is also important to binary evolution."
+ The implementation of this effect leads to an inference of slower cooling for aas in the single-star scenario., The implementation of this effect leads to an inference of slower cooling for as in the single-star scenario.
+ This would yield. shorter progenitor timescales for a constant evolutionary time. leading to the lower limits on the total mass of the coalescing white dwarfs becoming even more massive.," This would yield shorter progenitor timescales for a constant evolutionary time, leading to the lower limits on the total mass of the coalescing white dwarfs becoming even more massive."
+" This diminishes again the probability of binary evolution for Τομ=30 000K. However. for Ts,=50000 K the uncertainties still permit the possibility of merging."," This diminishes again the probability of binary evolution for $\Teff=30\,000\,$ K. However, for $\Teff=50\,000\,$ K the uncertainties still permit the possibility of merging."
+ Furthermore. the effect of magnetism on the stellar structure ensure that this scenario remains favourable due to the higher Chandrasekhar mass limit(??).," Furthermore, the effect of magnetism on the stellar structure ensure that this scenario remains favourable due to the higher Chandrasekhar mass limit."
+. bbelongs to the very rare population of ultra-massive white dwarfs with masses exceedingMsolar., belongs to the very rare population of ultra-massive white dwarfs with masses exceeding.
+. The competing theoretical explanations of the origin of these white dwarfs are single-star evolution versus. the merging of two degenerate stars., The competing theoretical explanations of the origin of these white dwarfs are single-star evolution versus the merging of two degenerate stars.
+ Without considering mass-loss during stellar evolution. we have shown that an upper limit of ffor the final white dwarf mass would exist for the white dwarfs because of the ignition of carbon in the core of the progenitor star.," Without considering mass-loss during stellar evolution, we have shown that an upper limit of for the final white dwarf mass would exist for the white dwarfs because of the ignition of carbon in the core of the progenitor star."
+ However. taking into account the effect of mass loss. mass ONe-core white dwarfs can be producedreview).," However, taking into account the effect of mass loss, high-mass ONe-core white dwarfs can be produced."
+. Furthermore. it was proposed that even 9 to mmass stars evolve into ONe core white dwarfs of mass 1.26 and 1.15 respectively. because of the off-centred carbon ignition in the partial degenerate conditions of their cores(??).," Furthermore, it was proposed that even 9 to mass stars evolve into ONe core white dwarfs of mass 1.26 and 1.15 respectively, because of the off-centred carbon ignition in the partial degenerate conditions of their cores."
+. In the light of our current results. we have undertaken a more precise investigation of the possible evolutionary scenarios for0317-853.," In the light of our current results, we have undertaken a more precise investigation of the possible evolutionary scenarios for."
+. We have shown that the cooling ages are almost the same for the two components., We have shown that the cooling ages are almost the same for the two components.
+" The detailed analysis very much depends on a precise determination of the effective temperature: for 7a,=30000K. we can use the calculations by and and conclude that within the limits of the uncertainties iis at least as old as9802."," The detailed analysis very much depends on a precise determination of the effective temperature; for $\Teff=30\,000\,$ K, we can use the calculations by and and conclude that within the limits of the uncertainties is at least as old as."
+. For a consistent interpretation of the system. we also have to take into account the time scales of the pre-white-dwarf evolution.," For a consistent interpretation of the system, we also have to take into account the time scales of the pre-white-dwarf evolution."
+ The more massive progenitor of sshould evolve more rapidly than the progenitor of9802., The more massive progenitor of should evolve more rapidly than the progenitor of.
+. Taking this into account. the total age difference between aand Wwe TA Myers is considered.," Taking this into account, the total age difference between and amounts to $\sim100\,$ Myr if single-star evolution is considered."
+ RAPE AH proposed by and as a solution to this age dilemma has severe drawbacks.," On the other hand, the alternative binary merger scenario proposed by and as a solution to this age dilemma has severe drawbacks."
+ When the evolutionary timescales are considered. the progenitor age of aat Zr 30000K yields lower limits on the mass of the merger product that is considerably higher than its estimated mass for all cases.," When the evolutionary timescales are considered, the progenitor age of at $\Teff=30\,000\,$ K yields lower limits on the mass of the merger product that is considerably higher than its estimated mass for all cases."
+ For 0317-853... we have large uncertainties in the cooling age estimate only for an effective temperature of 50000K. so that we cannot fully exclude the binary scenario.," For , we have large uncertainties in the cooling age estimate only for an effective temperature of $50\,000\,$ K, so that we cannot fully exclude the binary scenario."
+ We have also considered the effects of the magnetic fields on both of the scenarios., We have also considered the effects of the magnetic fields on both of the scenarios.
+ Magnetic fields cause an increase in radius. hence an underestimate of the mass. which wouldimply longer cooling ages than estimated.," Magnetic fields cause an increase in radius, hence an underestimate of the mass, which wouldimply longer cooling ages than estimated."
+ For the case of Toy=30000K. ," For the case of $\Teff=30\,000\,$ "
+We thank J. Trümmper for his comments and P. Freire for making the radio profiles of PSR J0024—7204D. J0024—7204O and J0024—7204R available to us prior publication.,"We thank J. Trümmper for his comments and P. Freire for making the radio profiles of PSR J0024–7204D, J0024–7204O and J0024–7204R available to us prior publication."
+" H.H. Huang acknowledges support by the International Max-Planck Research School on Astrophysics, IMPRS."," H.H. Huang acknowledges support by the International Max-Planck Research School on Astrophysics, IMPRS."
+ We acknowledge the use of the Chandra data archive., We acknowledge the use of the Chandra data archive.
+/75A)) for continuum monitoring and Lo (6563/75A)) for activity monitoring.,) for continuum monitoring and $\alpha$ ) for activity monitoring.
+ Phe Stromeren-v. Ho. and. Ha-olf filters. were available at the CPIO-Im for use with the Y4lx-Cam.," The Stromgren-y, $\alpha$ , and $\alpha$ -off filters, were available at the CTIO-1m for use with the Y4K-Cam."
+" An image quality 3-cavity custom filter with central wavelength: A, and. Άννας ordered from. Custom Scientific.", An image quality 3-cavity custom filter with central wavelength $\lambda_c$ and was ordered from Custom Scientific.
+ Vhe filter is 40.3 inches and is coated with anti-rellection material., The filter is $4\times 4\times 0.3$ inches and is coated with anti-reflection material.
+ The narrow continuum filters allow us. to. isolate specific regions of the continuum. free. of highly variable chromospheric emission lines for optimal transit detection., The narrow continuum filters allow us to isolate specific regions of the continuum free of highly variable chromospheric emission lines for optimal transit detection.
+ The filters avoid the Hydrogen. Balmer lines and the Ca LL 1I Ix lines associated with chromospheric emission. as well as the strong Ile features at4026...43686... and 5875... and the Na E doublet aand SSOGA)) where emission. peaks have been observed in absorption line cores of active Αννας.," The filters avoid the Hydrogen Balmer lines and the Ca II H K lines associated with chromospheric emission, as well as the strong He features at, and , and the Na I doublet and ) where emission peaks have been observed in absorption line cores of active M-dwarfs."
+ In. practice. the wavelength region covered. by the Stromgren-y. filter is shared by neutral metal lines Fe lL Mg Li D. and active ανα stars are known to show very faint emission in these features during Lares citetPuli. Paulson)).," In practice, the wavelength region covered by the Stromgren-y filter is shared by neutral metal lines Fe I, Mg I, Ti I), and active M-dwarf stars are known to show very faint emission in these features during flares \\citet{Fuhr,Paulson}) )."
+ The filters provide a wide spectral coverage to aid in distinguishing non-grav starspot variability from grav transits., The filters provide a wide spectral coverage to aid in distinguishing non-gray starspot variability from gray transits.
+ In addition. the narrow filters allow us to take longer exposures that do not saturate the bright. target star and that are less sensitive to instrumental svstematics.," In addition, the narrow filters allow us to take longer exposures that do not saturate the bright target star and that are less sensitive to instrumental systematics."
+ Finally. we monitored in Ha to identify residual variability in our continuum lighteurves caused by chromospheric activity.," Finally, we monitored in $\alpha$ to identify residual variability in our continuum lightcurves caused by chromospheric activity."
+ VPhroughout cach oberving night. we monitored in all four filters alternating between Lla and one ofthe continuum fillers. systematically eveling through the continuum filters.," Throughout each oberving night, we monitored in all four filters alternating between $\alpha$ and one of the continuum filters, systematically cycling through the continuum filters."
+ We adopted: 2 binnine to obtain a faster reaclout time on the detector (hereafter.pired refers to the binned 2.2 CCD pixel).," We adopted $2\times 2$ binning to obtain a faster readout time on the detector (hereafter, refers to the binned $2 \times 2$ CCD pixel)."
+ Our observing program was cesigned to place the target. on exactly. the same detector pixels in order to minimize inaccuracies due to [lat-fielding., Our observing program was designed to place the target on exactly the same detector pixels in order to minimize inaccuracies due to flat-fielding.
+ In reality. the position of AW Mic varied. within 5 pixels [rom the chosen position.," In reality, the position of AU Mic varied within $\sim 5$ pixels from the chosen position."
+ Exposure times were chosen to maximize the llux in the target star and nearby reference stars while keeping the peak pixel value in AU Mic. below (60.000 counts.," Exposure times were chosen to maximize the flux in the target star and nearby reference stars while keeping the peak pixel value in AU Mic below $\sim 60,000$ counts."
+ We defocused. the telescope to. avoid saturating XU Mic while taking longer exposures to build up signal in the fainter reference stars., We defocused the telescope to avoid saturating AU Mic while taking longer exposures to build up signal in the fainter reference stars.
+ We monitored during non-photometric weather ancl changed the exposure time continuously based on the photometric transpareney., We monitored during non-photometric weather and changed the exposure time continuously based on the photometric transparency.
+ Thus. exposure times were varied between 3λ40 seconds in all bands.," Thus, exposure times were varied between $3-40$ seconds in all bands."
+ In this wav. a median sampling rate of 0.8 minutes was obtained for La and ~2.5 minutes for all of the continuum filters.," In this way, a median sampling rate of 0.8 minutes was obtained for $\alpha$ and $\sim 2.5$ minutes for all of the continuum filters."
+ We observed AU. Mic for 6-10 hours per nieht on 19 nights during that time., We observed AU Mic for 6-10 hours per night on 19 nights during that time.
+ Due to poor weather. we obtained only 1-2 hours of data on 5 nights and completely lost an additional 5 nights.," Due to poor weather, we obtained only 1-2 hours of data on 5 nights and completely lost an additional 5 nights."
+ Flat feld ancl bias calibration frames necessary for processing the images were obtained during cach observing night., Flat field and bias calibration frames necessary for processing the images were obtained during each observing night.
+ We took 2-D bias frames approximately every. few hours in addition to sets of biases at the beginning and end of each. night., We took 2-D bias frames approximately every few hours in addition to sets of biases at the beginning and end of each night.
+ At least 10 dome Lats were observed per night in all four filters. and twilight [ats (3-4 per filter) were obtained when the weather was clear.," At least 10 dome flats were observed per night in all four filters, and twilight flats (3-4 per filter) were obtained when the weather was clear."
+ The images were processed in a standard way using routines written. by HlIebb in the LOL programming anguage., The images were processed in a standard way using routines written by Hebb in the IDL programming language.
+ Before performing any processing tasks. we checked for bad frames.," Before performing any processing tasks, we checked for bad frames."
+ Images in which the peak pixel value in AU Mic is equal to 65536 are saturated and those where he peak pixel value is less than 2000 counts have too low ranspareney to obtain useful magnitude measurements of he reference stars., Images in which the peak pixel value in AU Mic is equal to 65536 are saturated and those where the peak pixel value is less than 2000 counts have too low transparency to obtain useful magnitude measurements of the reference stars.
+ There were typically 10 out of ~1200 such images on a Lull night of observing which were removed roni our processing List., There were typically $\sim$ 10 out of $\sim$ 1200 such images on a full night of observing which were removed from our processing list.
+ Each of the four amplifiers was processed independently., Each of the four amplifiers was processed independently.
+ All object. and calibration frames were first overscan corrected. (by subtracting a line-by-line. median. overscan value) and then trimmed., All object and calibration frames were first overscan corrected (by subtracting a line-by-line median overscan value) and then trimmed.
+ We created nightly stacked bias images by average combining all bias frames observed. cach night., We created nightly stacked bias images by average combining all bias frames observed each night.
+" However. we noticed a smallscale ""herringbone pattern. in. the bias frames which varied over the course of an observing night."," However, we noticed a smallscale 'herringbone' pattern in the bias frames which varied over the course of an observing night."
+ This has subsequently been observed by other groups (see httpz//wsvw.dlowell.edu/users/massey/obins/bias.html)., This has subsequently been observed by other groups (see http://www.lowell.edu/users/massey/obins/bias.html).
+ The amplitude of the variability is at the. level of +10 counts/pixel. and it persists in our data.," The amplitude of the variability is at the level of $\pm 10$ counts/pixel, and it persists in our data."
+ This corresponcls to a maximum of of the typical AU. Mic Hux and of the combined Iux of all the reference stars., This corresponds to a maximum of of the typical AU Mic flux and of the combined flux of all the reference stars.
+ Therefore. it contributes to the noise in the resulting lightcurves at the milli-mag level.," Therefore, it contributes to the noise in the resulting lightcurves at the milli-mag level."
+ The stacked bias frames were subtracted from all object and Uat field images., The stacked bias frames were subtracted from all object and flat field images.
+ Average combined. nightly dome Lats were ereated in each filter. and each night. the object frames and any twilight [ats that were obtained were divided by the stacked. dome Hat.," Average combined nightly dome flats were created in each filter, and each night, the object frames and any twilight flats that were obtained were divided by the stacked dome flat."
+ After applying the dome flat correction. there is still residual large scale [Dat-Beld: structure in the images which is stable over the course of the observing run.," After applying the dome flat correction, there is still residual large scale flat-field structure in the images which is stable over the course of the observing run."
+ We tested the application of anaclelitional illumination correction creating a stacked: domoe-Iat corrected: twilight Hat. and divided this image by the object images.," We tested the application of anadditional illumination correction creating a stacked dome-flat corrected twilight flat, and divided this image by the object images."
+ We, We
+post-AGB stars.,post-AGB stars.
+ However. the argument strongly relies on the adopted (uncertain) value for the typical luminosity of AGB stars.," However, the argument strongly relies on the adopted (uncertain) value for the typical luminosity of post-AGB stars."
+ We now compare M giants in binaries with Te-rich S stars., We now compare M giants in binaries with Tc-rich S stars.
+ As expected. M giants are always less evolved than Te-rich S stars.," As expected, M giants are always less evolved than Tc-rich S stars."
+ As already discussed by ?.. Te-rich S stars are indeed found beyond the onset of the TP-AGB (re.. to the right of the early AGB evolutionary tracks in Fig. 5)).," As already discussed by \citet{VanEck-98}, Tc-rich S stars are indeed found beyond the onset of the TP-AGB (i.e., to the right of the early AGB evolutionary tracks in Fig. \ref{Fig:HR}) )."
+ There is one exception. though [HIP 38502 = ΝΟ Pup. a Te-rich S star with log(L/L...)= 2.9]. which illustrates the possible impact of biases when considering the individual locations of stars with non-negligible relative errors on their parallaxes (see?.andreferences therein)..," There is one exception, though [HIP 38502 = NQ Pup, a Tc-rich S star with $\log(L/L_\odot) = 2.9$ ], which illustrates the possible impact of biases when considering the individual locations of stars with non-negligible relative errors on their parallaxes \citep[see][ and references therein]{VanEck-98}."
+ Nevertheless. overall. the segregation between Te-rich S stars and M giants ts very clear.," Nevertheless, overall, the segregation between Tc-rich S stars and M giants is very clear."
+ When M giants evolve further on the AGB. they will indeed turn into Te-rich S stars. but at the same time are likely to become long-period variables (LPVs:?)..," When M giants evolve further on the AGB, they will indeed turn into Tc-rich S stars, but at the same time are likely to become long-period variables \citep[LPVs;][]{Little-87}."
+ As discussed in Papers I and IL. binary systems among LPVs are very difficult to detect for two reasons.," As discussed in Papers I and II, binary systems among LPVs are very difficult to detect for two reasons."
+ First. given their large radit. only long-period systems may host them (see Fig. 4)).," First, given their large radii, only long-period systems may host them (see Fig. \ref{Fig:radius}) ),"
+ but these systems necessarily have small values for the radial-velocity semi-amplitude A (smallerthanaboutI0kms.!:seeFig.5inPaperIIandthediscussionaboutFig.9.4in ?)..," but these systems necessarily have small values for the radial-velocity semi-amplitude $K$ \citep[smaller than
+ about 10~\kms; see Fig.~5 in Paper~II and the
+discussion about Fig.~9.4 in][]{Jorissen-03}."
+ Secondly. since they are LPVs. shock waves move across their atmospheres. and induce radial-velocity variations with amplitudes of 10 to 20kms citepHinkle- 1997.Alvarez-2001..," Secondly, since they are LPVs, shock waves move across their atmospheres, and induce radial-velocity variations with amplitudes of 10 to 20 \\citep{Hinkle-1997,Alvarez-2001}."
+ Hence they are very difficult to detect., Hence they are very difficult to detect.
+ Spectroscopic binaries involving LPVs are not included in the present discussion since very few cases are known. and usually their orbital elements are not known (the supposed post-AGB + Mira system HD 172481 discussed in Sect.," Spectroscopic binaries involving LPVs are not included in the present discussion since very few cases are known, and usually their orbital elements are not known (the supposed post-AGB + Mira system HD 172481 discussed in Sect."
+ 2.2 is no exception)., \ref{Sect:pAGB} is no exception).
+ The list of AGB stars with composite spectra compiled by ? includes for instance the Te-rich S stars W Aql. WY Cas and T Sgr. and the carbon stars SZ Ser. TU Tau and BD -2672983. but orbital periods are not known for them yet.," The list of AGB stars with composite spectra compiled by \citet{Jorissen-03} includes for instance the Tc-rich S stars W Aql, WY Cas and T Sgr, and the carbon stars SZ Sgr, TU Tau and BD $^\circ$ 2983, but orbital periods are not known for them yet."
+ Symbiotic stars hosting a Mira variable (theso-calledd-typesymbiotics:??) are perfect examples of binaries involving a very evolved AGB star.," Symbiotic stars hosting a Mira variable \citep[the so-called d-type symbiotics;][]{Allen-82,Whitelock87} are perfect examples of binaries involving a very evolved AGB star."
+ ? have succeeded in detecting the orbital motion of these systems using Raman polarimetry. and concluded that the orbital periods in these systems are of the order of 150 yr or 550000 d. Intringuingly. ? find a very short period of 141 d (from a fit to the Hipparcos Intermediate Astrometric Data) for the MSIL semiregular variable. star HIP 34922 (=HD 56096 = L? Pup). possibly a TP-AGB star since ? find Το to be possibly present.," \citet{Schmid-Schild-2002} have succeeded in detecting the orbital motion of these systems using Raman polarimetry, and concluded that the orbital periods in these systems are of the order of 150 yr or 000 d. Intringuingly, \citet{Goldin-Makarov-2007} find a very short period of 141 d (from a fit to the Hipparcos Intermediate Astrometric Data) for the M5III semiregular variable star HIP 34922 (=HD 56096 = $^2$ Pup), possibly a TP-AGB star since \citet{Little-87} find Tc to be possibly present."
+ The period — eccentricity pur obtained by ? (P=lll δα.0.52+rae Is. however. totally inconsistent with the values found for the other M giants in Fig. 2..," The period – eccentricity pair obtained by \citet{Goldin-Makarov-2007} $(P = 141\pm2$ d, $e =
+0.52\pm{0.30\atop0.21})$ is, however, totally inconsistent with the values found for the other M giants in Fig. \ref{Fig:elogP_panels}, ,"
+ so that its validity must be questioned. as discussed in the Appendix.," so that its validity must be questioned, as discussed in the Appendix."
+ It must be emphasised at this point thatTe-poor S (star symbols in Fig. 5)) arepost-mass-t, It must be emphasised at this point that S (star symbols in Fig. \ref{Fig:HR}) )
+ransfer systems. and as such. may not be directly compared to M giants and Te-rich S stars.," are systems, and as such, may not be directly compared to M giants and Tc-rich S stars."
+ Nevertheless. the above discussion. stating that binaries involving Te-rich S stars and LPVs should have long orbital periods. leads to a very surprising conclusion: extrinsic. Te-poor S stars occupy the region of the (+logP) diagram where binary S stars are expected (Fig. 1)).," Nevertheless, the above discussion, stating that binaries involving Tc-rich S stars and LPVs should have long orbital periods, leads to a very surprising conclusion: extrinsic, Tc-poor S stars occupy the region of the $(e - \log P)$ diagram where binary S stars are expected (Fig. \ref{Fig:elogP_M}) )."
+ This implies that This is quite surprising at first sight. since either the orbital period. must have shorter dramatically (for the so-called ‘case C RLOF) or it must have increased considerably (for wind accretion). according to standard evolutionary prescriptions (e.g..?)..," This implies that This is quite surprising at first sight, since either the orbital period must have shorten dramatically (for the so-called 'case C' RLOF) or it must have increased considerably (for wind accretion), according to standard evolutionary prescriptions \citep[e.g.,][]{Boffin-Jorissen-88}."
+ This conclusiot is clearly not compatible with the present data. and calls for alternative mass-transfer prescriptions. as it was already know for quite some time. ," This conclusion is clearly not compatible with the present data, and calls for alternative mass-transfer prescriptions, as it was already known for quite some time. \citet{Jorissen-03},"
+2.. ? and ? have proposed new avenues to explore., \citet{Frankowski-2007a} and \citet{Podsia-2007} have proposed new avenues to explore.
+ For instance. in the context of the ‘transient torus’ scenario proposed by ?.. a near constaney of the orbital period is not unexpected.," For instance, in the context of the 'transient torus' scenario proposed by \citet{Frankowski-2007a}, a near constancy of the orbital period is not unexpected."
+ If it is correct that the mass transfer process does not alter much the orbital period. then the existence of mild barium stars with rather short orbital periods (1.e.. the open triangles to the left of the solid line in Fig. 2))," If it is correct that the mass transfer process does not alter much the orbital period, then the existence of mild barium stars with rather short orbital periods (i.e., the open triangles to the left of the solid line in Fig. \ref{Fig:elogP_panels}) )"
+ may be explained by the fact that their polluting companion did not evolve far up the TP-AGB. hence the AGB envelope was not much enriched in s-process elements.," may be explained by the fact that their polluting companion did not evolve far up the TP-AGB, hence the AGB envelope was not much enriched in s-process elements."
+ This hypothesis is especially appealing since the other possibility. suggested by ? and ?. — namely. that mild barium stars belong to a more metal-rich population thar strong barium stars. because the s-process is more efficient i low-metallicity stars (2). — has been dismissed by the detailed abundance analysis of mild barium stars by ?.. who conclude that there is no obvious metallicity difference between mild anc strong barium stars.," This hypothesis is especially appealing since the other possibility, suggested by \citet{Jorissen-Boffin-92} and \citet{Jorissen-VE-98} – namely, that mild barium stars belong to a more metal-rich population than strong barium stars, because the s-process is more efficient in low-metallicity stars \citep{Goriely-00} – has been dismissed by the detailed abundance analysis of mild barium stars by \citet{Smiljanic-2007}, who conclude that there is no obvious metallicity difference between mild and strong barium stars."
+ The intriguing absence of s-process enrichment in rec symbiotics (e.g.2?). despite the fact that they are likely post-mass-transfer systems like barium stars. may perhaps be understood by invoking the same argument: as they fall in the same region as the (non-s-process-enriched) post-AGB stars in the (¢logP) diagram (Fig. 2)).," The intriguing absence of s-process enrichment in red symbiotics \citep[e.g., ][]{Jorissen-03a,Frankowski-2007a}, despite the fact that they are likely post-mass-transfer systems like barium stars, may perhaps be understood by invoking the same argument: as they fall in the same region as the (non-s-process-enriched) post-AGB stars in the $(e - \log P)$ diagram (Fig. \ref{Fig:elogP_panels}) ),"
+ it is possible that their companion did not evolve far up enough on the AGB to activate dredge-ups and s-process., it is possible that their companion did not evolve far up enough on the AGB to activate dredge-ups and s-process.
+" Interestingly enough. our data may be used to shed light on the much debated nature of the so-called ""sequence D found by ? and ? in theperiod — luminosity diagram of LPVs in the Large Magellanic Cloud (LMC)."," Interestingly enough, our data may be used to shed light on the much debated nature of the so-called 'sequence D' found by \citet{Wood-1999} and \citet{Wood-2000} in theperiod – luminosity diagram of LPVs in the Large Magellanic Cloud (LMC)."
+" This sequence (also called ""long secondary periods’) is located to the of the period — lummosity relationship for Miras pulsating in the fundamental", This sequence (also called 'long secondary periods') is located to the of the period – luminosity relationship for Miras pulsating in the fundamental
+Ad. distance. and the survey (lux limit.,"$M$, distance, and the survey flux limit."
+ We consider each of the 15 CVs that may have distance estimates sullering from Malmequist bias in turn. using the appropriate b. CA. and c. together with the X-ray lux limit of the survey it was detected in. and an exponential vertical density prolile for the," We consider each of the 15 CVs that may have distance estimates suffering from Malmquist bias in turn, using the appropriate $b$, $\left <M \right >$, and $\sigma_M$, together with the X-ray flux limit of the survey it was detected in, and an exponential vertical density profile for the."
+ Using à Monte Carlo simulation for cach system. we iteratively fined the distance at which a population with appropriate Gaussian AZ distribution. subject to an X-ray tux limit. would result in an estimate distance distribution with median equal to our distance estimate.," Using a Monte Carlo simulation for each system, we iteratively find the distance at which a population with appropriate Gaussian $M$ distribution, subject to an X-ray flux limit, would result in an estimated distance distribution with median equal to our distance estimate."
+ As expected. the bias is not present for sulliciently smal distance or ayy. or sulliciently deep X-ray. [lux limit.," As expected, the bias is not present for sufficiently small distance or $\sigma_{M}$, or sufficiently deep X-ray flux limit."
+" With the assumed correlation between £.,, and Lx. we woulc estimate biased. distances for only 5 of the €Vs in our sample (listed in Table 2))."," With the assumed correlation between $L_{opt}$ and $L_X$, we would estimate biased distances for only 5 of the CVs in our sample (listed in Table \ref{tab:bias}) )."
+ Although a few of the distance estimates may be seriously biased. these are svstems tha make only very small contributions to the space density and luminosity function. (see the 6th ane 7th columns of ‘Table 1.. and the explanation in Section 3.2)).," Although a few of the distance estimates may be seriously biased, these are systems that make only very small contributions to the space density and luminosity function (see the 6th and 7th columns of Table \ref{tab:distances}, and the explanation in Section \ref{sec:calc}) )."
+ Correcting these 5 distances for the possible bias does not significantly change the results that will be presented in Section + and 5.., Correcting these 5 distances for the possible bias does not significantly change the results that will be presented in Section \ref{sec:results} and \ref{sec:fluxl}.
+" '""Pherefore. although we do not know the relation between £x and Lo. and thus whether in principle we should. correct the distances. this possible bias can be safely. neglected."," Therefore, although we do not know the relation between $L_X$ and $L_{opt}$, and thus whether in principle we should correct the distances, this possible bias can be safely neglected."
+ However. even if unbiased distance estimates are used. the resulting luminosity function still contains Malniquist-tvpe bias (Stobieetal.1989).," However, even if unbiased distance estimates are used, the resulting luminosity function still contains Malmquist-type bias \citep{StobieIshidaPeacock89}."
+ We will return to this in Section 5.2.., We will return to this in Section \ref{sec:simphi}.
+ Alost non-magnetic CVs have X-ray emission that can be described. as thermal bremsstrahlung from the boundary aver (the inner part of the disc where the flow is no longer keplerian. but is slowing down to match the rotation of the white cwarl: Patterson&Ravmond1985a.. but see also e.g. Pernaetal. 2003).," Most non-magnetic CVs have X-ray emission that can be described as thermal bremsstrahlung from the boundary layer (the inner part of the disc where the flow is no longer keplerian, but is slowing down to match the rotation of the white dwarf; \citealt{PattersonRaymond85a}, but see also e.g. \citealt{Perna03}) )."
+ The X-ray spectrum should then be the sum of emission from material with temperatures ranging rom the temperature of the shock at the outer edge of he boundary [laver to the temperature of the white dwarf whotosphere (e.g. Mukaietal. 2003))., The X-ray spectrum should then be the sum of emission from material with temperatures ranging from the temperature of the shock at the outer edge of the boundary layer to the temperature of the white dwarf photosphere (e.g. \citealt{Mukai03}) ).
+ X-ray observations of manysystems can be fit by a single temperature thermal xenmsstrahlung spectrum. with A7 between roughly 5 and 20 keV (e.g. Patterson&Raymondδρα Vrtilek Mukaietal.1997: Szkody.etal.2000: Baskilletal.2005:: Pandeletal.2005: Alukaietal.2009))., X-ray observations of manysystems can be fit by a single temperature thermal bremsstrahlung spectrum with $kT$ between roughly 5 and 20 keV (e.g. \citealt{PattersonRaymond85a}; ;\citealt{VrtilekSilberRaymond94}; ; \citealt{Mukai97}; ; \citealt{SzkodyNishikidaLiller00}; \citealt{BaskillWheatleyOsborne05}; \citealt{Pandel05}; \citealt{MukaiZietsmanStill09}) ).
+ In other cases. multi-temperature (or cooling How) mocels are needed to provide satisfactory fits to observations citealtMulkai03:: Pandel.Córdova&Lowell2003: al.2005: Pandeletal.2005. Hiltonetal.2007:: Lloarcletal.2010: Byeklineetal.2010)).," In other cases, multi-temperature (or cooling flow) models are needed to provide satisfactory fits to observations \\citealt{Mukai03}; \citealt{PandelCordovaHowell03}; \citealt{BaskillWheatleyOsborne05}; \citealt{Pandel05} \citealt{Hilton07}; \citealt{Hoard10}; \citealt{Byckling10}) )."
+ Lligh-37 systems (nova-like CVs in a high state and DNe in outburst) are expected to have optically thick boundary. lavers. and. therefore much softer spectra: however. part of the boundary. laver remains optically thin so that the soft component does not dominate the spectrum above ~0.5 keV. (ee. Pattersonmoncl1985a:: Patterson&Itavmond1985b:: Jones&Wat-son1992: Wheatleyetal.2003)).," $\dot{M}$ systems (nova-like CVs in a high state and DNe in outburst) are expected to have optically thick boundary layers, and therefore much softer spectra; however, part of the boundary layer remains optically thin so that the soft component does not dominate the spectrum above $\sim 0.5$ keV (e.g. \citealt{PattersonRaymond85a}; \citealt{PattersonRaymond85b}; \citealt{JonesWatson92}; \citealt{WheatleyMaucheMattei03}) )."
+ We assume a Ad=10keV thermal bremsstrahlung μα»ectrum for all CVs in our sample. and quote X-ray Huxes ux luminosities in the 0.52.0 keV. band.," We assume a $kT=10\,\mathrm{keV}$ thermal bremsstrahlung spectrum for all CVs in our sample, and quote X-ray fluxes and luminosities in the 0.5–2.0 keV band."
+ Although there is no good physical justification for this simple approac— — isacceptable for our purposes. because the energy. band we are using is narrow (decreasing the sensitivity of £x to 10 assumed spectrum). and because our distances are for le most part quite imprecise (implving that error arising from the assumed spectral shape is unlikely to contribute gaignificantly to the total error in Lx: see below).," Although there is no good physical justification for this simple approach, it isacceptable for our purposes, because the energy band we are using is narrow (decreasing the sensitivity of $L_X$ to the assumed spectrum), and because our distances are for the most part quite imprecise (implying that error arising from the assumed spectral shape is unlikely to contribute significantly to the total error in $L_X$; see below)."
+ We use re dust to gas ratio of Predehl&Schmitt(1995) O convert the ely estimates to Na for each svstem., We use the dust to gas ratio of \cite{PredehlSchmitt95} to convert the $A_V$ estimates to $N_H$ for each system.
+" The Vy estimates are low (the highest being 54.107""em7. for SDSS J1730: Patterson 2011))."," The $N_H$ estimates are low (the highest being $5.4 \times 10^{20}\,\mathrm{cm^{-2}}$, for SDSS J1730; \citealt{Patterson11}) )."
+ We list unabsorbed fy and Lx in Table 1.., We list unabsorbed $F_X$ and $L_X$ in Table \ref{tab:distances}.
+" In order to provide further justification for our assumptions regarding the X-ray spectrum. we can consider the error in Ly using standard error propagation: Where o, is the error in distance (in the best. cases about1554.. but. larger for most systems). er.ele is the observational error (tvpically 21054)). and apy. ds the error caused by uncertainty in Ny. and by an incorrect assumption of X-rav spectrum."," In order to provided further justification for our assumptions regarding the X-ray spectrum, we can consider the error in $L_X$ using standard error propagation: Where $\sigma_d$ is the error in distance (in the best cases about, but larger for most systems), $\sigma_{F_{X,obs}}$ is the observational error (typically $\simeq$ ), and $\sigma_{F_{X,spec}}$ is the error caused by uncertainty in $N_H$, and by an incorrect assumption of X-ray spectrum."
+ In order for apy... to dominate σεν. we must have opP0.3.," In order for $\sigma_{F_{X,spec}}$ to dominate $\sigma_{L_X}$ , we must have $\sigma_{F_{X,spec}}/F_X \ga 0.3$."
+" ""his seenis unlikely. because in the narrow energy band (0.5.2.0 keV). [or moderate Ny and allowing for a error in Ny. the dilference in £x between single-temperature bremsstrahlung spectra with AY=2keV and 20keV is only 2:20%."," This seems unlikely, because in the narrow energy band (0.5–2.0 keV), for moderate $N_H$ and allowing for a error in $N_H$ the difference in $F_X$ between single-temperature bremsstrahlung spectra with $kT=2\,\mathrm{keV}$ and $20\,\mathrm{keV}$ is only $\simeq 20\%$."
+" Lligh-Al CVs are naturallyexpected. to have brighter Lx: therefore. Ly should. increase. with 2,54."," $\dot{M}$ CVs are naturallyexpected to have brighter $L_X$; therefore, $L_X$ should increase with $P_{orb}$."
+" This is certainly not apparent in the luminosities we find (see the Poy, and Ly values in Table. 1)).", This is certainly not apparent in the luminosities we find (see the $P_{orb}$ and $L_X$ values in Table \ref{tab:distances}) ).
+ Patterson&Raymonel show that. for low-A/ systems. Lx indeedincreases with AZ. but that at roughly 107es the relation between Lx and Al Uattens ο.," \cite{PattersonRaymond85a} show that, for $\dot{M}$ systems, $L_X$ indeedincreases with $\dot{M}$ , but that at roughly $10^{16}\,\mathrm{g/s}$ the relation between $L_X$ and $\dot{M}$ flattens off."
+ Binary inclination may also be expected to add noise to this relation., Binary inclination may also be expected to add noise to this relation.
+ Baskilletal.(2005) [inc onlya weak correlation between Ly and {νο while van lind none.," \cite{BaskillWheatleyOsborne05} find onlya weak correlation between $L_X$ and $P_{orb}$ , while \cite{vanTeeselingBeuermannVerbunt96} find none."
+" Given the large scatter or weakness of any correlation between Ly and 2,4. Lx is nota good indicator of period (or. by implication.age): in the calculations described in Section 5.2.. Ly istherefore the only physical parameter of the simulated CV's."," Given the large scatter or weakness of any correlation between $L_X$ and $P_{orb}$ , $L_X$ is nota good indicator of period (or, by implication,age); in the calculations described in Section \ref{sec:simphi}, , $L_X$ istherefore the only physical parameter of the simulated CVs."
+Some systems will contain an acereting WD which succeeds in reaching the Chandrasekhar mass but fails to produce a supernova as the WD is predominantly composed of oxygen. eon magnesium (ONeMg) rather than carbon and oxygen (CO).,"Some systems will contain an accreting WD which succeeds in reaching the Chandrasekhar mass but fails to produce a supernova as the WD is predominantly composed of oxygen, neon magnesium (ONeMg) rather than carbon and oxygen (CO)."
+ This can occur either because the WD began acereting as an ONeMg WD or because the accretion rate onto the WD did not allow the WD to remain a CO WD (e.g. Nomoto [ben 1985; Nomoto Kondo 1991; Martin et 22006)., This can occur either because the WD began accreting as an ONeMg WD or because the accretion rate onto the WD did not allow the WD to remain a CO WD (e.g. Nomoto Iben 1985; Nomoto Kondo 1991; Martin et 2006).
+ Such WDs will produce a neutron star (NS) via AIC., Such WDs will produce a neutron star (NS) via AIC.
+ Currently it does ot appear likely that AIC produces sufficiently large kicks to disrupt such close binaries (see. e.g.. Podsiadlowski et 22004).," Currently it does not appear likely that AIC produces sufficiently large kicks to disrupt such close binaries (see, e.g., Podsiadlowski et 2004)."
+ Single LMWDs may be the product of the merger of two low- He WDs. with formation rates comparable to or greater than the SN la rate (see. e.g.. Han etM.," Single LMWDs may be the product of the merger of two low-mass He WDs, with formation rates comparable to or greater than the SN Ia rate (see, e.g., Han et."
+.. We do not present an exhaustive description of the full evolutionary histories for single-denegerate SN Ia progenitors (see. e.g. Whelan Iben 1973; Nomoto 1982; van den Heuvel et 11992: Rappaport. Di Stefano Smith 1994; Hachisu. Kato Nomoto 1996. 1999; Li van den Heuvel 1997; Langer et 22000; Hachisu Kato 2001: Han Podsiadlowskt 2004).," We do not present an exhaustive description of the full evolutionary histories for single-denegerate SN Ia progenitors (see, e.g. Whelan Iben 1973; Nomoto 1982; van den Heuvel et 1992; Rappaport, Di Stefano Smith 1994; Hachisu, Kato Nomoto 1996, 1999; Li van den Heuvel 1997; Langer et 2000; Hachisu Kato 2001; Han Podsiadlowski 2004)."
+ There is no clear consensus on which donor stars are likely to produce a type la supernova., There is no clear consensus on which donor stars are likely to produce a type Ia supernova.
+ The favoured options involve either donors on the main sequence (MS) or the subgiant branch (known as the supersoft channel). or red-giant (RG) donors.," The favoured options involve either donors on the main sequence (MS) or the subgiant branch (known as the supersoft channel), or red-giant (RG) donors."
+" While the supersoft channel (e.g. Han Podsiadlowski 2004) is arguably the favoured channel for the majority of SNe Ia. Hachisu. Kato Nomoto (1996. 1999) and Hachisu Kato (2001) suggest situations in which à low-mass giant star may take a WD to the Chandrasekhar mass Mey, at long orbital Sokoloski et ((2006) used the 2006 outburst of RS Ophiuchi to confirm the conclusions of Hachisu Kato by inferring that RS Oph contains a very massive WD 1.4 MJ."," While the supersoft channel (e.g. Han Podsiadlowski 2004) is arguably the favoured channel for the majority of SNe Ia, Hachisu, Kato Nomoto (1996, 1999) and Hachisu Kato (2001) suggest situations in which a low-mass giant star may take a WD to the Chandrasekhar mass $M_{\rm Ch}$ at long orbital Sokoloski et (2006) used the 2006 outburst of RS Ophiuchi to confirm the conclusions of Hachisu Kato by inferring that RS Oph contains a very massive WD $M_{\rm WD} \approx 1.4 ~{\rm
+M_{\odot}}$ )."
+ [tis worth noting that we cannot be sure that RS Oph contains aCO WD rather than an ONeMg one and so we cannot be sure that it will explode rather than collapse., It is worth noting that we cannot be sure that RS Oph contains a CO WD rather than an ONeMg one and so we cannot be sure that it will explode rather than collapse.
+ Observational support for a giant donor in a system which produced a SN la has been provided via the observations by Patat et ((2007) of SN 2006X. King. Rolfe Schenker (2003) have also suggested that an acereting WD may not reach Mey via the supersoft channel alone. but that a later phase of WD growth could occur in long-period dwarf novae.," Observational support for a giant donor in a system which produced a SN Ia has been provided via the observations by Patat et (2007) of SN 2006X. King, Rolfe Schenker (2003) have also suggested that an accreting WD may not reach $M_{\rm Ch}$ via the supersoft channel alone, but that a later phase of WD growth could occur in long-period dwarf novae."
+ They argue that. even though the average mass-transfer rate does not reach the steady-burning band (Paczyfísski Zyytkow 1978: Nomoto Kondo 1991). the aceretion rate may be high enough for the WD to grow during dwarf nova outbursts driven by the thermal-viscous dise instability (Cannizzo. Ghosh Wheeler 1982).," They argue that, even though the average mass-transfer rate does not reach the steady-burning band (Paczyńsski Żyytkow 1978; Nomoto Kondo 1991), the accretion rate may be high enough for the WD to grow during dwarf nova outbursts driven by the thermal-viscous disc instability (Cannizzo, Ghosh Wheeler 1982)."
+ Providing the correct mass-aecretion rate for the CO WD to grow to Mey is a significant uncertainty in all these models., Providing the correct mass-accretion rate for the CO WD to grow to $M_{\rm Ch}$ is a significant uncertainty in all these models.
+ In order to understand the formation of LMWDs in systems which produce SN Ia explosions. we must consider the mass and evolutionary. stage of the donor star at the point of the explosion and also the extent to which the donor loses mass because of the explosion.," In order to understand the formation of LMWDs in systems which produce SN Ia explosions, we must consider the mass and evolutionary stage of the donor star at the point of the explosion and also the extent to which the donor loses mass because of the explosion."
+ There is a clear division between pre-giant and giant donor stars. with giant donors apparently able to leave LMWD remnants.," There is a clear division between pre-giant and giant donor stars, with giant donors apparently able to leave LMWD remnants."
+ Marietta. Burrows Fryxell (2000) performed numerical simulations of the effect of a SN [a explosion on the companion star.," Marietta, Burrows Fryxell (2000) performed numerical simulations of the effect of a SN Ia explosion on the companion star."
+ They found that 0.15 to 0.17M. is stripped away from à |Mi main-sequence or subgiant companion by the high-velocity ejecta.," They found that $\rm 0.15$ to $\rm 0.17 ~{\rm M_{\odot}}$ is stripped away from a $\rm
+1 ~{\rm M_{\odot}}$ main-sequence or subgiant companion by the high-velocity ejecta."
+ Han Podstadlowski (2004) found in their population synthesis simulations of the supersoft channel that. at the time of the explosion. the companion has a mass between >0.5Ma and 2.2M... with a typical mass of |M.. (for more details see also Han 2008).," Han Podsiadlowski (2004) found in their population synthesis simulations of the supersoft channel that, at the time of the explosion, the companion has a mass between $\rm \gtrsim
+0.5 ~{\rm M_{\odot}}$ and $\rm 2.2 ~{\rm M_{\odot}}$, with a typical mass of $\rm 1 ~{\rm M_{\odot}}$ (for more details see also Han 2008)."
+ Applying the results of Marietta et aas a percentage — of the donor mass — leads to a lowest estimated remnant mass of «0.42M..., Applying the results of Marietta et as a percentage – of the donor mass – leads to a lowest estimated remnant mass of $\rm \approx 0.42~{\rm M_{\odot}}$.
+ If the WD explodes as it reaches Mj. then this remant mass 1s a lower limit for the MS channel. assuming negligible subsequent mass loss in à wind.," If the WD explodes as it reaches $M_{\rm{Ch}}$, then this remant mass is a lower limit for the MS channel, assuming negligible subsequent mass loss in a wind."
+ Hachisu Kato (2001) found a lower limit on the mass of the donor from the supersoft channel (at the time of the SN) of >1.3M. (assuming an initial white dwarf mass of |Μι).," Hachisu Kato (2001) found a lower limit on the mass of the donor from the supersoft channel (at the time of the SN) of $\rm > 1.3 ~{\rm
+M_{\odot}}$ (assuming an initial white dwarf mass of $\rm 1 ~{\rm
+M_{\odot}}$ )."
+ Despite these differences. both studies suggest that it is difficult to produce LMWDs via main-sequence or subgiant donors.," Despite these differences, both studies suggest that it is difficult to produce LMWDs via main-sequence or subgiant donors."
+ Marietta et aalso found that a red-giant donor will lose almost its entire envelope — 98%)) due to the impact of the SN Ia explosion and leave only the core of the star. providing a possible pathway for the formation of a subset of single. low-mass He WDs.," Marietta et also found that a red-giant donor will lose almost its entire envelope – ) due to the impact of the SN Ia explosion and leave only the core of the star, providing a possible pathway for the formation of a subset of single, low-mass He WDs."
+ For the RG channel. Hachisv Kato (2001) found a lower limit on the total donor mass of >0.4M..," For the RG channel, Hachisu Kato (2001) found a lower limit on the total donor mass of $\rm \gtrsim 0.4 ~{\rm M_{\odot}}$."
+ If the RG channel produces SNe Ia. then ram-pressure stripping of the donor's envelope would be expected to lead to the formation of LMWDs.," If the RG channel produces SNe Ia, then ram-pressure stripping of the donor's envelope would be expected to lead to the formation of LMWDs."
+ The remnant WD mass is dependent on the core mass of the donor at explosion and ts therefore strongly correlated with the orbital period (see sectior 34., The remnant WD mass is dependent on the core mass of the donor at explosion and is therefore strongly correlated with the orbital period (see section \ref{sec:OrbitalVelocities}) ).
+ One formation channel that is rarely discussed in the literature 15 one where the donor star 1s a hot subdwarf star (see. e.g.. Geier et 22007).," One formation channel that is rarely discussed in the literature is one where the donor star is a hot subdwarf star (see, e.g., Geier et 2007)."
+ We do not expect significant stripping of the donor by the supernova ejecta in this case. as the donor star will be tightly bound. but the mass of the donor star could," We do not expect significant stripping of the donor by the supernova ejecta in this case, as the donor star will be tightly bound, but the mass of the donor star could"
+of maximum temperature versus maximum density during the calculation and the barotropic equation ofstate.,of maximum temperature versus maximum density during the calculation and the barotropic equation of state.
+ The red dot-dashed lines are for cuts perpendicular to the rotation axis along the .- (Le. in the plane of the disc). while the blue long-dashed lines display the temperature along the rotation axis.," The red dot-dashed lines are for cuts perpendicular to the rotation axis along the $x$ -axis (i.e. in the plane of the disc), while the blue long-dashed lines display the temperature along the rotation axis."
+ Not only is the run of maximum temperature versus maximum density always greater than or equal to the temperature from the barotropic equation of state. but the gas both in the midplane of the dise and along the rotation axis at the same density is even hotter.," Not only is the run of maximum temperature versus maximum density always greater than or equal to the temperature from the barotropic equation of state, but the gas both in the midplane of the disc and along the rotation axis at the same density is even hotter."
+ This is particularly true of the gas along the rotation axis. which is heated by the accretion shock at the surface of the first core.," This is particularly true of the gas along the rotation axis, which is heated by the accretion shock at the surface of the first core."
+ ? give a very similar plot for a snapshot from one of their simulations and find very similar behaviour.," \cite{Tomidaetal2010a}
+ give a very similar plot for a snapshot from one of their simulations and find very similar behaviour."
+" These hotter temperatures in the radiation hydrodynamical calculations mean that while the transition from rotationally stable to dynamically unstable first core occurs in the range 9=5105 ""using the barotropic equation of state. the transition oceurs at ;20.001 with radiation hydrodynamics (this ease undergoes an extremely weak instability. just visible in the fourth panel of the second row of Fig. 35)."," These hotter temperatures in the radiation hydrodynamical calculations mean that while the transition from rotationally stable to dynamically unstable first core occurs in the range $\beta=5\times 10^{-4}-10^{-3}$ using the barotropic equation of state, the transition occurs at $\beta\approx 0.001$ with radiation hydrodynamics (this case undergoes an extremely weak instability, just visible in the fourth panel of the second row of Fig. \ref{images_xyD}) )."
+ Similarly. while the barotropic calculation with =0.01 manages to produce a torus-shaped first core. the radiation hydrodynamical calculation with ;7.=0.01 is still detinitely dise shaped rather than torus shaped.," Similarly, while the barotropic calculation with $\beta=0.01$ manages to produce a torus-shaped first core, the radiation hydrodynamical calculation with $\beta=0.01$ is still definitely disc shaped rather than torus shaped."
+ As mentioned above. for the highest initial rotation rates 0.04) the first core is actually a torus or ring-like structure (e.g. 2223..," As mentioned above, for the highest initial rotation rates $\beta=0.04$) the first core is actually a torus or ring-like structure \citep[e.g.][]{NorWil1978,ChaWhi2003,Machidaetal2005}."
+ Such a contiguration is highly unstable to non-axisymmetric perturbations and. indeed. as is clearly visible in Figs.," Such a configuration is highly unstable to non-axisymmetric perturbations and, indeed, as is clearly visible in Figs."
+ 2. and 3 the rings rapidly fragment into four objects., \ref{images_D_barotropic} and \ref{images_xyD} the rings rapidly fragment into four objects.
+ Such a configuration is highly chaotic. and symmetry is broken quickly (due to truncation error and the use of a tree-structure to calculate gravity in the calculations).," Such a configuration is highly chaotic, and symmetry is broken quickly (due to truncation error and the use of a tree-structure to calculate gravity in the calculations)."
+ In the radiation hydrodynamical calculation. two of the fragments merge to produce a triple system. while in the barotropic calculation all four fragments survive (at least until the calculation was stopped).," In the radiation hydrodynamical calculation, two of the fragments merge to produce a triple system, while in the barotropic calculation all four fragments survive (at least until the calculation was stopped)."
+ Each of the fragments follows its own evolution toward the second collapse phase and stellar core formation., Each of the fragments follows its own evolution toward the second collapse phase and stellar core formation.
+ The calculations were stopped soon after the first fragment in each calculation produced a stellar core., The calculations were stopped soon after the first fragment in each calculation produced a stellar core.
+ Finally. as mentioned above. first cores may evolve into pre-stellar dises with radii ranging from z5 to 2100 AU before a stellar core forms (Fig. 3)).," Finally, as mentioned above, first cores may evolve into pre-stellar discs with radii ranging from $\approx 5$ to $\gsim 100$ AU before a stellar core forms (Fig. \ref{images_xyD}) )."
+ Those with radii greater than z10 AU are produced due to the angular momentum transport that occurs during the dynamical rotational instability., Those with radii greater than $\approx 10$ AU are produced due to the angular momentum transport that occurs during the dynamical rotational instability.
+ A further consequence is that all star formation should go through at least a brief phase when the dise mass is greater than the stellar mass., A further consequence is that all star formation should go through at least a brief phase when the disc mass is greater than the stellar mass.
+ Such disces are gravitationally unstable and may evolve through spiral density waves (e.g. the third row of Figs., Such discs are gravitationally unstable and may evolve through spiral density waves (e.g. the third row of Figs.
+ 3 and. 8)) and/or fragmentation (e.g. the fourth rows of Fig., \ref{images_xyD} and \ref{images_xyT}) ) and/or fragmentation (e.g. the fourth rows of Fig.
+ 3 and 89., \ref{images_xyD} and \ref{images_xyT}) ).
+ This is discussed further in Section 4.., This is discussed further in Section \ref{discussion}.
+ In conclusion. in switching from the simple barotropic equation of state to a realistic equation of state with radiation hydrodynamics. the qualitative evolution of the first core and its dependence on the initial rotation rate of the molecular cloud core is identical.," In conclusion, in switching from the simple barotropic equation of state to a realistic equation of state with radiation hydrodynamics, the qualitative evolution of the first core and its dependence on the initial rotation rate of the molecular cloud core is identical."
+ However. the gas temperature in the more realistic calculations tends to be hotter and is not only a function of density: for example. the gas is significantly hotter in the accretion shock at the surface of the first cores.," However, the gas temperature in the more realistic calculations tends to be hotter and is not only a function of density: for example, the gas is significantly hotter in the accretion shock at the surface of the first cores."
+ Quantitatively. the higher temperatures mean that the critical values of the initial molecular cloud core rotation rates required for bar instability of the first core. or the transition to a torus geometry is somewhat higher.," Quantitatively, the higher temperatures mean that the critical values of the initial molecular cloud core rotation rates required for bar instability of the first core, or the transition to a torus geometry is somewhat higher."
+ The value of > must be =50% greater with radiation hydrodynamics. which translates into a rotation rate which is z25% greater (since O7. where © is the angular frequency of the molecular cloud core).," The value of $\beta$ must be $\approx 50$ greater with radiation hydrodynamics, which translates into a rotation rate which is $\approx 25$ greater (since $\beta \propto \Omega^2$ , where $\Omega$ is the angular frequency of the molecular cloud core)."
+ Although the evolution of the first core or pre-stellar dise is qualitatively the same when computed with a barotropic equation of state or radiation hydrodynamics. as ?. showed the evolution subsequent to the formation of the stellar core isdifferent.," Although the evolution of the first core or pre-stellar disc is qualitatively the same when computed with a barotropic equation of state or radiation hydrodynamics, as \cite{Bate2010} showed the evolution subsequent to the formation of the stellar core is."
+ When using a barotropic equation of state. the formation of the stellar core deep within the optically-thick dise has no effect on the temperature of the gas further out in the dise because its temperature is set purely according to its density.," When using a barotropic equation of state, the formation of the stellar core deep within the optically-thick disc has no effect on the temperature of the gas further out in the disc because its temperature is set purely according to its density."
+ However. with radiation hydrodynamics. the situation is completely different.," However, with radiation hydrodynamics, the situation is completely different."
+ When the second collapse occurs and produces the stellar core. the gravitational potential energy that is released is ~GASRR=4.107 erg.," When the second collapse occurs and produces the stellar core, the gravitational potential energy that is released is $\sim GM_{\rm sc}^2/R_{\rm sc} = 4 \times 10^{42}$ erg."
+ Since the stellar core is in virial equilibrium. approximately half of this energy is radiated away.," Since the stellar core is in virial equilibrium, approximately half of this energy is radiated away."
+" Moreover. the stellar core rapidly begins to accrete from the first core. reaching a mass of e6 M, in only a few years (1.9. more quickly than the dynamical timescale of the large-scale disc: see below)."," Moreover, the stellar core rapidly begins to accrete from the first core, reaching a mass of $\approx 6$ $_{\rm J}$ in only a few years (i.e. more quickly than the dynamical timescale of the large-scale disc; see below)."
+ This increases the total energy released to =2.1077 erg., This increases the total energy released to $\approx 3 \times 10^{43}$ erg.
+ ? compared this energy with the binding energy of the dise in the 7=0.005 calculation., \cite{Bate2010} compared this energy with the binding energy of the disc in the $\beta=0.005$ calculation.
+ Just before the onset of the second collapse. the binding energy of the pre-stellar disc is only 4.1077 erg (estimated as ~GALTIa with Ady20.18M. and taking a mean ‘spherical’ radius of Aye15 AU).," Just before the onset of the second collapse, the binding energy of the pre-stellar disc is only $4 \times 10^{43}$ erg (estimated as $\sim GM_{\rm d}^2/R_{\rm d}$ with $M_{\rm d} \approx 0.18~{\rm M}_\odot$ and taking a mean `spherical' radius of $R_{\rm d} \approx 15$ AU)."
+ Thus. when the second collapse occurs. the dise suddenly finds itself irradiated from the inside by an energy source emitting a substantial fraction of the binding energy of the dise itself.," Thus, when the second collapse occurs, the disc suddenly finds itself irradiated from the inside by an energy source emitting a substantial fraction of the binding energy of the disc itself."
+ Because the dise is extremely optically hick. this energy is temporarily trapped in the centre of the disc and heats the gas dramatically. sending a weak shock wave out along the midplane of the disc at a speed of afew km +.," Because the disc is extremely optically thick, this energy is temporarily trapped in the centre of the disc and heats the gas dramatically, sending a weak shock wave out along the midplane of the disc at a speed of a few km $^{-1}$."
+ However. yerpendicular to the disc. the effect is even more dramatic.," However, perpendicular to the disc, the effect is even more dramatic."
+ Because qere is less material along the rotation axis. the hot gas finds it easiest to break out in this direction and a bipolar outflow is aunched.," Because there is less material along the rotation axis, the hot gas finds it easiest to break out in this direction and a bipolar outflow is launched."
+ Whereas the wave within the dise decays as it travels eaving the bulk of the dise gravitationally bound. the gas forming 1e bipolar outflow has velocities up to 10 km s.+ and travels out into the infalling envelope to distances in excess of 50 AU in less ain SO years.," Whereas the wave within the disc decays as it travels leaving the bulk of the disc gravitationally bound, the gas forming the bipolar outflow has velocities up to 10 km $^{-1}$ and travels out into the infalling envelope to distances in excess of 50 AU in less than 50 years."
+ Using two-dimensional radiation hydrodynamical calculations. 2?) have recently reported similar behaviour. although ye outflow in their simulations is less bipolar.," Using two-dimensional radiation hydrodynamical calculations, \cite{SchTsc2011} have recently reported similar behaviour, although the outflow in their simulations is less bipolar."
+ By disguarding the central regions of one of their calculations. they were able to follow 1ο outflow for a few tens of thousands of years and found that after reaching =500 AU. the material fell back in to reform a disc.," By disguarding the central regions of one of their calculations, they were able to follow the outflow for a few tens of thousands of years and found that after reaching $\approx 500$ AU, the material fell back in to reform a disc."
+ ? muinly discussed the 7=0.005 calculation as typical example., \cite{Bate2010} mainly discussed the $\beta=0.005$ calculation as typical example.
+ Here we examine how the effect of stellar core formation on the surrounding dise depends on the initial rotation rate of the molecular cloud core and. thus. on the degree of rotation that the first core/pre-stellar dise has.," Here we examine how the effect of stellar core formation on the surrounding disc depends on the initial rotation rate of the molecular cloud core and, thus, on the degree of rotation that the first core/pre-stellar disc has."
+ Figs., Figs.
+ 9 to 14. illustrate the evolution of calculations with 97=45to+0.01 following stellar core formation., \ref{images_xyD_OUTFLOW} to \ref{convergence} illustrate the evolution of calculations with $\beta=5\times 10^{-4} - 0.01$ following stellar core formation.
+ The 97=() case is not discussed further since the situation is as 2. described it., The $\beta=0$ case is not discussed further since the situation is as \cite{Larson1969} described it.
+ This ease remains spherically-symmetric. and although the stellar core irradiates the first core from within. the radiation liberated is not sufficient to stop the spherically-symmetric accretion flow onto the stellar core.," This case remains spherically-symmetric, and although the stellar core irradiates the first core from within, the radiation liberated is not sufficient to stop the spherically-symmetric accretion flow onto the stellar core."
+ We do not discuss the 7=0.04 case following stellar core formation since each of the three fragments is qualitatively similar to the tirst core obtained in the 97=0.001 case and. therefore. we assume that each of these cores would evolve in a similar manner.," We do not discuss the $\beta=0.04$ case following stellar core formation since each of the three fragments is qualitatively similar to the first core obtained in the $\beta=0.001$ case and, therefore, we assume that each of these cores would evolve in a similar manner."
+ Figs., Figs.
+ 9 and IO. provide snapshots of the column density in the directions parallel to the rotation axis and perpendicular to the rotation axis. respectively.," \ref{images_xyD_OUTFLOW} and \ref{images_xzD_OUTFLOW} provide snapshots of the column density in the directions parallel to the rotation axis and perpendicular to the rotation axis, respectively."
+ The shockwave propagating outwards through each of the first cores/dises is clearly visible in Fig. 9.., The shockwave propagating outwards through each of the first cores/discs is clearly visible in Fig. \ref{images_xyD_OUTFLOW}. .
+ For, For
+In this subsection we will trv to use a semi-analytical method to understand our numerical results.,In this subsection we will try to use a semi-analytical method to understand our numerical results.
+ First from Eq. (, First from Eq. (
+"2). we have the following equation If we assume a fractiona of the mass lost bv the donor is accreted by the NS. ie.. ML,=-aAds. we can write the period derivative as Our analvsis is limited to binary evolution with Ms<Aq.","2), we have the following equation If we assume a fraction$\alpha$ of the mass lost by the donor is accreted by the NS, i.e., $\dot{M_1}=-\alpha\dot{M_2}$, we can write the period derivative as where Our analysis is limited to binary evolution with $M_2 < M_1$."
+ In this case it is clearly seen (hat mass transfer increases (he orbital period and angular momentum loss decreases (he orbital period., In this case it is clearly seen that mass transfer increases the orbital period and angular momentum loss decreases the orbital period.
+ The bifurcation period is decided by the balance of these (wo factors., The bifurcation period is decided by the balance of these two factors.
+ Keeping the orbital period unchanged (i.e. DP~ 0). we ealeulate the maximum mass transfer rates lor orbital periods [rom 0.35 dav to 0.95 day.," Keeping the orbital period unchanged (i.e. $\dot{P}\simeq 0$ ), we calculate the maximum mass transfer rates for orbital periods from $0.35$ day to $0.95$ day."
+ This period interval covers the whole range of the bifurcation periods obtained in (his work and in (2002)., This period interval covers the whole range of the bifurcation periods obtained in this work and in \citet{pod02}.
+. We show the calculated mass (ransfer rates in Fie. 7..," We show the calculated mass transfer rates in Fig. \ref{mdot2},"
+ and find that they can be fitted by an approximate expression as Then we calculate the mean mass transfer rates with constant /? ancl find that they lie between Ma(?)/2 and Ms(P)., and find that they can be fitted by an approximate expression as Then we calculate the mean mass transfer rates with constant $P$ and find that they lie between $\dot{M}_2(P)/2$ and $\dot{M}_2(P)$.
+ This means that if we use Eq. (13)), This means that if we use Eq. \ref{mdot}) )
+ to calculate. P4. it will deviate no more than ~LOY. [rom the true value.," to calculate $P_{\rm rlof}$, it will deviate no more than $\sim 10\%$ from the true value."
+ The mean mass transfer rates here are calculated as follows., The mean mass transfer rates here are calculated as follows.
+ We fix the binary period P? in a constant value in our code. ancl then evolve the donor [rom its initial mass A»; to the time when it loses half of its initial mass 0.5.»;.," We fix the binary period $P$ in a constant value in our code, and then evolve the donor from its initial mass $M_{\rm 2,i}$ to the time when it loses half of its initial mass $0.5M_{2,i}$."
+" This mass (rausfer process takes a time of 71,5.", This mass transfer process takes a time of $T_{\rm 1/2}$.
+ Then we use 0.5.\/5;/T)9 as the mean A> for this period P.," Then we use $0.5M_{\rm2,i}/T_{1/2}$ as the mean $\dot{M}_2$ for this period $P$ ."
+ If we assume that angular momentum loss is dominated by saturated MD when 2<10 d. from Eqs. (," If we assume that angular momentum loss is dominated by saturated MB when $P<10$ d, from Eqs. ("
+2) and (7)) we have,2) and \ref{newmb}) ) we have
+p=1-5 is rather small for &105AIpe and we will consider only p=1.5 for the calculation of the redshift-space power spectrum. below.,"$p=1.5$ is rather small for $k \le 10 \impc$, and we will consider only $p=1.5$ for the calculation of the redshift-space power spectrum below."
+ We also found that the real-space power spectrum in the halo model is quite robust against a reasonable change of the mass function OfAL) and the linear bias factor b(A4)., We also found that the real-space power spectrum in the halo model is quite robust against a reasonable change of the mass function $\phi(M)$ and the linear bias factor $b(M)$.
+ In contrast we will see that the red-shift power spectrum is quite sensitive to the changes of these functions., In contrast we will see that the red-shift power spectrum is quite sensitive to the changes of these functions.
+ Vhe dark matter halo is nearly virialized inside Pog., The dark matter halo is nearly virialized inside $R_{200}$.
+ Phe velocity. distribution of the dark matter within the halo should be approximately \laxwellian distributed with a one-dimensional velocity. dispersion at? (Sheth 1996)., The velocity distribution of the dark matter within the halo should be approximately Maxwellian distributed with a one-dimensional velocity dispersion $\sigma_{v}^{1D}$ (Sheth 1996).
+ We have tested this assumption with the N-body simulations of Jing Suto (1998). and confirmed that the assumption 1s valid (sce Figure 3).," We have tested this assumption with the N-body simulations of Jing Suto (1998), and confirmed that the assumption is valid (see Figure 3)."
+λ Furthermore. we found that slightly smaller than 1/Y2.5 where νου=VOCALRou is the circular velocity at the viral radius. Poo. ane AL is the mass of the halo within Aoog.," Furthermore, we found that slightly smaller than $1/\sqrt{2}$ , where $V_{200} =
+\sqrt{GM/R_{200}}$ is the circular velocity at the viral radius $R_{200}$, and $M$ is the mass of the halo within $R_{200}$."
+ Phe virial motion in the halo clongates the density distribution of the halo alone the line-of-sight in redshilt space., The virial motion in the halo elongates the density distribution of the halo along the line-of-sight in redshift space.
+" ""Phe density distribution of a halo in redshift space po(rg.is) is a convolution of the real-space density profile with the velocity distribution along the linc-of-sight. where rz and or, are the distances parallel and perpendicular to the line-of-sight to the halo center. Lf is the Llubble constant. and fe.) is the velocity. distribution along the line-of-sight."," The density distribution of a halo in redshift space $\rho_{\alpha}^{S}(r_{\pi},r_{\sigma})$ is a convolution of the real-space density profile with the velocity distribution along the line-of-sight, where $r_{\pi}$ and $r_{\sigma}$ are the distances parallel and perpendicular to the line-of-sight to the halo center, $H$ is the Hubble constant, and $f(v_{z})$ is the velocity distribution along the line-of-sight."
+" The redshift space power spectrum DP(k.u) can then be written as. Where 2),(kegeAdy.Ads) is the redshift power spectrum for two dark matter halos with mass AJ; ancl Ado."," The redshift space power spectrum $P^{S}(k,u)$ can then be written as, Where $P^{S}_{hh}(k,\mu,M_{1},M_{2})$ is the redshift power spectrum for two dark matter halos with mass $M_{1}$ and $M_{2}$."
+ Under the asstunption that every halo is moving as a whole according to linear theory (Ixaiser. LOST)2 we can cerive the recshilt power spectrum for halos. We will show that the formula is a good description on large scales. but on small scales it gives too much power at large po," Under the assumption that every halo is moving as a whole according to linear theory (Kaiser 1987), we can derive the redshift power spectrum for halos, We will show that the formula is a good description on large scales, but on small scales it gives too much power at large $\mu$."
+ A mocified formula will be given in the next section., A modified formula will be given in the next section.
+ In Figure 4 we plot the redshift power spectrum Lor dark matter based on this halo model. ancl compare it to the simulation results of JB2001 for the two cosmological models.," In Figure 4 we plot the redshift power spectrum for dark matter based on this halo model, and compare it to the simulation results of JB2001 for the two cosmological models."
+ From the dot line in the top panels. we see that the dilference in the redshift power spectrum between the halo model ancl the simulations is small on large scales (1.0 small A).," From the dot line in the top panels, we see that the difference in the redshift power spectrum between the halo model and the simulations is small on large scales (i.e small $k$ )."
+ But on small scales the halo model gives significantA more power at larger j£ than the simulation data. especialA in the SCDAL model.," But on small scales the halo model gives significantly more power at larger $\mu$ than the simulation data, especially in the SCDM model."
+ It is also noted that the finite box size ellect should be taken into account., It is also noted that the finite box size effect should be taken into account.
+ In Figure 4 we also plot Po (A.C the dashed lines in the upper two panels) calculated: using a cut-olf of the power spectrum for a scale smaller than the box-size (1007 ‘Alpe in our simulation)," In Figure 4 we also plot $P^{S}(k,\mu)$ ( the dashed lines in the upper two panels) calculated using a cut-off of the power spectrum for a scale smaller than the box-size $h^{-1}$ Mpc in our simulation)."
+ Vhe value of P7(E.p) at larger p ave lower in the case. but the changes are quite small.," The value of $P^{S}(k,\mu)$ at larger $\mu$ are lower in the case, but the changes are quite small."
+ The difference is so significant that we have to check all the assumptions used in our moclel: the halo mass function: the density. profile of halos: and the halo-halo redshift power spectrum., The difference is so significant that we have to check all the assumptions used in our model: the halo mass function; the density profile of halos; and the halo-halo redshift power spectrum.
+ Before doing that. it would be helpful first to cheek which term. the one-haloterm or two halo term. is the main contribution to the cliscrepaney.," Before doing that, it would be helpful first to check which term, the one-haloterm or two halo term, is the main contribution to the discrepancy."
+ From the lower panels of Figure 4. it can be," From the lower panels of Figure 4, it can be"
+Iu the coming wears. gravitational lensiug is likely to become au effective tool for mapping larec-scale structure in the universe.,"In the coming years, gravitational lensing is likely to become an effective tool for mapping large-scale structure in the universe."
+ Over the past decade several measurements of weak lensing by ealaxy clusters lave been made., Over the past decade several measurements of weak lensing by galaxy clusters have been made.
+" Mass reconstruction techniques are now beime applied to wide feld leusiug survevs m blauk fields that will probe the dark matter distribution over angular scales of order 1’1"".", Mass reconstruction techniques are now being applied to wide field lensing surveys in blank fields that will probe the dark matter distribution over angular scales of order $1' - 1^\circ$.
+ Wide feld lensing observations have already detected filaments aud dark halos that were not visible bv their light distribution (vaiscr at al 1998: Exben et al 1999: Tyson et al., Wide field lensing observations have already detected filaments and dark halos that were not visible by their light distribution (Kaiser at al 1998; Erben et al 1999; Tyson et al.
+ 1999)., 1999).
+κ. Statistical properties of the clusteriug of dark matter can be probed from lensine data bw computing shear correlations over blank fields with area of order LO square degrees (Blandford ct al 1991: Alivalda-Excudé 1991: Isaiscr 1992: Bernardean ct al 1997: Jain Seljak 1997: Ikaiscr 1998: Stebbins 1996: Schueider et 11998)., Statistical properties of the clustering of dark matter can be probed from lensing data by computing shear correlations over blank fields with area of order 10 square degrees (Blandford et al 1991; Miralda-Escudé 1991; Kaiser 1992; Bernardeau et al 1997; Jain Seljak 1997; Kaiser 1998; Stebbins 1996; Schneider et 1998).
+ Aun alternative approach is to focus on the statistics of dark matter halos. identified through their lensing streneth. using ieasures such as the aperture mass (Schneider 1996: Ixruse Schneider 1999a: Iruse Schucider 1999a: Reblinsky ot al.," An alternative approach is to focus on the statistics of dark matter halos, identified through their lensing strength, using measures such as the aperture mass (Schneider 1996; Kruse Schneider 1999a; Kruse Schneider 1999a; Reblinsky et al."
+ 1999)., 1999).
+" The halo statistics approach has oen shown by the above authors to be a useful probe of the mass function for massive. cluster sized halos: the nain practical limitation is that only ~10 halos per square degree are expected to be detected with adequate signalO-1OISC,"," The halo statistics approach has been shown by the above authors to be a useful probe of the mass function for massive, cluster sized halos; the main practical limitation is that only $\sim 10$ halos per square degree are expected to be detected with adequate signal-to-noise."
+ This paper advocates a new approach to the ucasureimeut of the statistics of dark matter halos through chasing., This paper advocates a new approach to the measurement of the statistics of dark matter halos through lensing.
+ By modeling the distribution of peaks iu lensing data induced by the noise due to the intrinsic ellipticities of source galaxies. we show that it is possible to statistically detect the signal due to dark matter halos. even for mass scales below the signal-to-noise lait for the detection of individual halos.," By modeling the distribution of peaks in lensing data induced by the noise due to the intrinsic ellipticities of source galaxies, we show that it is possible to statistically detect the signal due to dark matter halos, even for mass scales below the signal-to-noise limit for the detection of individual halos."
+" Section 2 describes the construction of peak statistics from simulated data and frou, pure noise.", Section 2 describes the construction of peak statistics from simulated data and from pure noise.
+ Results for the peak statistics for a set of cosmological models are shown in Section 3., Results for the peak statistics for a set of cosmological models are shown in Section 3.
+ We discuss tle prospects for measuring the halo mass functiou and discriminating models from realistic data in Section , We discuss the prospects for measuring the halo mass function and discriminating models from realistic data in Section 4.
+We use shear aud convergence fields from rav tracing siuulatious through the dark matter distribution of N-body simulations (Jain. Seljak White 1999).," We use shear and convergence fields from ray tracing simulations through the dark matter distribution of N-body simulations (Jain, Seljak White 1999)."
+ The fields we use are about 3 degrees ou a side. sampled with a erid spacing of 0.17. with source ealaxies taken to be at 2=1.," The fields we use are about 3 degrees on a side, sampled with a grid spacing of $0.1'$, with source galaxies taken to be at $z=1$."
+ We use two cosmiological models. au Eiisteiu-«de Sitter model and an open model with Quatre=0.3.," We use two cosmological models, an Einstein-de Sitter model and an open model with $\Omega_{\rm matter}=0.3$."
+ The power spectrum corresponds to a cold dark matter shape parameter D—0.21 model., The power spectrum corresponds to a cold dark matter shape parameter $\Gamma=0.21$ model.
+ Further details of the models and the simulations are given in Jain et al (1999)., Further details of the models and the simulations are given in Jain et al (1999).
+" A simulated inoisv map of the convergence. {0}. is built by first smoothing the « field over scale 0c; with a Gaussian window Π(7)=exp(UEολz02,."," A simulated noisy map of the convergence, $\kappa({\vec \theta})$, is built by first smoothing the $\kappa$ field over scale $\theta_G$ with a Gaussian window $W(\theta)=\exp(-{|\thetag|^2/\theta_G^2})/\pi \theta_G^2$."
+" The noise due to the raudondy oricuted intrinsic cllipticities of source galaxies is 1nodeled as a Caussian random feld with variance. where o, is the xius amplitude of the intrinsic ellipticity distribution aud 5,4 is the umuber density of source ealaxies."," The noise due to the randomly oriented intrinsic ellipticities of source galaxies is modeled as a Gaussian random field with variance, where $\sigma_\epsilon$ is the rms amplitude of the intrinsic ellipticity distribution and $n_g$ is the number density of source galaxies."
+ This Gaussian noise is added to the simoothed κ. field: the accuracy of this noise model i8 discussed below., This Gaussian noise is added to the smoothed $\kappa$ field; the accuracy of this noise model is discussed below.
+ From the simoothed uoisy data. peaks are found bv ideutifving pixels that have a ligher/lower value of & than all neighboring pixels.," From the smoothed noisy data, peaks are found by identifying pixels that have a higher/lower value of $\kappa$ than all neighboring pixels."
+ This correspouds to the condition that the eradicut of the feld vanishes and thus includes peaks as well as troughs., This corresponds to the condition that the gradient of the field vanishes and thus includes peaks as well as troughs.
+ The height of the peak νΞW/Onoise IS Its value in units of the nolse ruis in the sanoothed field., The height of the peak $\nu=\kappa/\sigma_{\rm noise}$ is its value in units of the noise rms in the smoothed field.
+The O-Na abundance anti-correlation observed in. Galactic globular clusters (GCs) is thought to be an intrinsic property of the clusters (seereviewbyGrattonetal.2004.andreferences therein)...,The O-Na abundance anti-correlation observed in Galactic globular clusters (GCs) is thought to be an intrinsic property of the clusters \citep[see review by][and references therein]{gratton04}.
+ It is considered a global feature of GCs. because the anti-correlation has been observed in all GCs subject to high-resolution studies (Carrettaetal.2006) and is present among the cluster giants. as well as unevolved stars (Carrettaetal.2004:Ramírez&Cohen2002:Gratton 2001).," It is considered a global feature of GCs, because the anti-correlation has been observed in all GCs subject to high-resolution studies \citep{carretta06} and is present among the cluster giants, as well as unevolved stars \citep{carretta04, ramirezcohen,
+ gratton01}."
+. Iron and the heavier elements show little star-to-star abundance variations within a cluster (Suntzeff.1993)., Iron and the heavier elements show little star-to-star abundance variations within a cluster \citep{suntzeff93}.
+. The currently supported theory for the origin of the O-Na anti-correlation is that of primordial pollution from previous stars (Cottrell&DaCosta 1981).. although the mechanism responsible for the pollution is still unclear.," The currently supported theory for the origin of the O-Na anti-correlation is that of primordial pollution from previous stars \citep{cottrelldacosta}, although the mechanism responsible for the pollution is still unclear."
+ Several hypotheses are presently being debated. including pollution by the ejecta of massive stars (Decressinetal.2007a.b) or by AGB stars undergoing hot bottom burning (Venturaetal.2001;Fenner2004:Karakasetal. 20006).," Several hypotheses are presently being debated, including pollution by the ejecta of massive stars \citep{decressin07a, decressin07b} or by AGB stars undergoing hot bottom burning \citep{ventura01, fenner04, karakas06}."
+. In general. the halo stars have a chemical composition similar to that of the GCs with the exception of the lighter element abundance trends (Grattonetal.2000).," In general, the halo stars have a chemical composition similar to that of the GCs with the exception of the lighter element abundance trends \citep{gratton2000}."
+. That the O-Na anti-correlation is not seen in the halo stars presumably reflects the different chemical evolution of the high-density cluster environment., That the O-Na anti-correlation is not seen in the halo stars presumably reflects the different chemical evolution of the high-density cluster environment.
+ Therefore stellar populations showing GC-like chemical evolution can be isolated. from other populations by examining the O-Na abundance pattern (Geisleretal. 2007)., Therefore stellar populations showing GC-like chemical evolution can be isolated from other populations by examining the O-Na abundance pattern \citep{geisler07}.
+. The abundance mismatch with the halo has important implications for the formation of the Galactic halo., The abundance mismatch with the halo has important implications for the formation of the Galactic halo.
+ It i5 possible the halo was built up either from. clusters. that have long since dissolved. which had a different chemical enrichment history to the surviving GCs. or from the stars lost from the present-day GCs before taking on the effects of the polluting stars.," It is possible the halo was built up either from clusters that have long since dissolved, which had a different chemical enrichment history to the surviving GCs, or from the stars lost from the present-day GCs before taking on the effects of the polluting stars."
+ A similar investigation can be applied to the progenitors of the Galactic disk., A similar investigation can be applied to the progenitors of the Galactic disk.
+ It is often stated that open clusters (OCs) are the objects of choice for tracing the star-formation history in the disk (e.g.Friel1995)., It is often stated that open clusters (OCs) are the objects of choice for tracing the star-formation history in the disk \citep[e.g.][]{friel95}.
+. Present-day OCs cover a wide range in age. metallicity. and position.," Present-day OCs cover a wide range in age, metallicity, and position."
+ They are used to examine the disk chemical evolution. from the solar neighborhood to the outer Galactic disk.," They are used to examine the disk chemical evolution, from the solar neighborhood to the outer Galactic disk."
+ Older OCs are considered particularly useful because they provide a time line for change., Older OCs are considered particularly useful because they provide a time line for change.
+ In general the OC abundances match that of the field. albeit with a larger scatter (Frieletal.2002:DeSilva2007;Bragaglia2008).," In general the OC abundances match that of the field, albeit with a larger scatter \citep{friel02,desilva07,bragaglia08}."
+. It is interesting that some OCs are Na-enhanced (Frieletal.2005:Jacobsonetal.2007:Bragaglia 2008).," It is interesting that some OCs are Na-enhanced \citep{friel05, jacobson07, bragaglia08}."
+. Whether this ts truly an intrinsic property of the clusters or an artifact of the abundance measurements remains unclear in the literature., Whether this is truly an intrinsic property of the clusters or an artifact of the abundance measurements remains unclear in the literature.
+ A discrepancy in abundance patterns between the OCs and the disk has important implications for our understanding of disk formation., A discrepancy in abundance patterns between the OCs and the disk has important implications for our understanding of disk formation.
+ Recall that the O and Na abundance anomaly is the characteristic difference between the GCs and the halo., Recall that the O and Na abundance anomaly is the characteristic difference between the GCs and the halo.
+ To our knowledge no such characteristic abundance patterns have been reported for OCs., To our knowledge no such characteristic abundance patterns have been reported for OCs.
+ In this Letter we explore the abundance patterns of O and Na among the OC population and compare them against the GC abundance anti-correlation and the disk field abundances., In this Letter we explore the abundance patterns of O and Na among the OC population and compare them against the GC abundance anti-correlation and the disk field abundances.
+ We combine high-resolution studies that derive both O and Na abundances in open clusters., We combine high-resolution studies that derive both O and Na abundances in open clusters.
+ The homogenized open cluster abundances. associated rms scatter. the number of stars per cluster. and references are given in Table |..," The homogenized open cluster abundances, associated rms scatter, the number of stars per cluster, and references are given in Table \ref{tab1}."
+ To represent the GC O-Na anti-correlation. we use abundances of red giants in NGC 2808 as a template of the global GC O-Na anti- (Carrettaetal.2006.seeFig.5)..," To represent the GC O-Na anti-correlation, we use abundances of red giants in NGC 2808 as a template of the global GC O-Na anti-correlation \citep[][see Fig. 5]{carretta06}."
+ For comparisons with the disk field. we use the compilation by Soubiran&Girard(2005) mainly based on field dwarfs. the abundances published by Misheninaetal.(2006) based on field red clump stars. and the disk giants studied by Fulbrightetal.(2007).," For comparisons with the disk field, we use the compilation by \citet{soubirangirard} mainly based on field dwarfs, the abundances published by \citet{mishenina06} based on field red clump stars, and the disk giants studied by \citet{fulbright07}."
+. As always when comparing different literature sources. the presence of systematic effects must be highlighted.," As always when comparing different literature sources, the presence of systematic effects must be highlighted."
+ As the systematics arise at various stages. it is very cumbersome to accurately correct for all possible effects.," As the systematics arise at various stages, it is very cumbersome to accurately correct for all possible effects."
+" For example. the stellar effective temperatures (7,45) could be subject to large systematic differences."," For example, the stellar effective temperatures $T_\mathrm{eff}$ ) could be subject to large systematic differences."
+ Carrettaetal.(2007b) and Brownetal. derive Το based on photometry. while other studies are," \citet{carretta07} and \citet{brown} derive $T_\mathrm{eff}$ based on photometry, while other studies are"
+ Ho. Ha 0.013. A- £-bands. 10j0n , $\alpha$ $\alpha$ $\sim 0.01\Msun$ $K$ $L$ $\micron$ 
+the properties of the observed galaxies.,the properties of the observed galaxies.
+ Based ou the observation by Jerjen et (01905) that the scatter in the distance — velocity relationship lor the Sculptor Group members is “remarkably stnall’. we have derived new clistauces for these galaxies using the recessional velocities listed in Cótté et ((1997) aud the formula given tn Jerjen et (1905): For the uine galaxies (6 spirals and 3 dwarfs) used to clefine the relationship. the average difference between the measured distance and the estimated distauce is105«.," Based on the observation by Jerjen et (1998) that the scatter in the distance – velocity relationship for the Sculptor Group members is “remarkably small”, we have derived new distances for these galaxies using the recessional velocities listed in Côtté et (1997) and the formula given in Jerjen et (1998): For the nine galaxies (6 spirals and 3 dwarfs) used to define the relationship, the average difference between the measured distance and the estimated distance is."
+. Eight of the nine ealaxies show dillerences of less than (the exception being NGC 15. with a difference of 21%)).," Eight of the nine galaxies show differences of less than (the exception being NGC 45, with a difference of )."
+ Dolphin (private communication) has caleulatecdl distances from Hubble Space Telescope observatious of the red elaut brauch tip for five (1 spiral and. E cbwarls) Sculptor group galaxies with known recession velocities (DDO 6. DDO 226. NGC 253. ESO 215-C0025 aud ESO 201-010). auc these five galaxies show good agreement with the relatiouship derived by Jerjen et (01905): all five galaxy distances are within of that predicted w the relationship.," Dolphin (private communication) has calculated distances from Hubble Space Telescope observations of the red giant branch tip for five (1 spiral and 4 dwarfs) Sculptor group galaxies with known recession velocities (DDO 6, DDO 226, NGC 253, ESO 245-G005 and ESO 294-G010), and these five galaxies show good agreement with the relationship derived by Jerjen et (1998); all five galaxy distances are within of that predicted by the relationship."
+ The relationship should be updated with inclusion of these new data. but. based on the above. the anticipated revision will be small (of order the uucertainty in the relationship). and we will use the relationship as published.," The relationship should be updated with inclusion of these new data, but, based on the above, the anticipated revision will be small (of order the uncertainty in the relationship), and we will use the relationship as published."
+ The estimatecl errors in cdistauces are sminall enough that we cau begin to examine positional relationships between galaxies., The estimated errors in distances are small enough that we can begin to examine positional relationships between galaxies.
+ Note that the fiudiug by Jerjen Rejkuba (2001) that the distauces estimated for some of the dEs via the methocl of surface brightuess Iuctuatious could be siguilicautly in error does not directly imply that the formula relating distance and recessional velocity ueeds to be revised siuce most of the «Es do not have measured recession velocities and were uot used iu calibrating the relationship., Note that the finding by Jerjen Rejkuba (2001) that the distances estimated for some of the dEs via the method of surface brightness fluctuations could be significantly in error does not directly imply that the formula relating distance and recessional velocity needs to be revised since most of the dEs do not have measured recession velocities and were not used in calibrating the relationship.
+ This equation was derived for galaxies coveriug the range in corrected recessioual velocity from  TO to  190 kms toa thus may uot be strictly valid for the three galaxies observed here with corrected recessioual velocities in excess of 500 kin .," This equation was derived for galaxies covering the range in corrected recessional velocity from $\sim$ 70 to $\sim$ 490 km $^{-1}$, and thus may not be strictly valid for the three galaxies observed here with corrected recessional velocities in excess of 500 km $^{-1}$."
+ The fact that several of the dls have recessional velocities in excess of 500 kim + implies that a significant number of dL galaxies lie ou the far side of the Sculptor group. (, The fact that several of the dIs have recessional velocities in excess of 500 km $^{-1}$ implies that a significant number of dI galaxies lie on the far side of the Sculptor group. (
+Note that the spiral galaxy NCC 21. with a recession velocity ob 555 kurs is also iu this region.),"Note that the spiral galaxy NGC 24, with a recession velocity of 555 km $^{-1}$ is also in this region.)"
+ In comparison with the Local Group. tliis is not unexpectec. as several of the Local Group cs lie iu the low density periphery of the Local Group at. distance:J. in excess of 1 Mpc from the Milky Way aud M31 (Mateo 1998).," In comparison with the Local Group, this is not unexpected, as several of the Local Group dIs lie in the low density periphery of the Local Group at distances in excess of 1 Mpc from the Milky Way and M31 (Mateo 1998)."
+ The absolute B imaguitudes i[un Table 1 were calculated from the total B maeguituces aud extinctious listed in Cotté (1995)., The absolute B magnitudes in Table 1 were calculated from the total B magnitudes and extinctions listed in Côtté (1995).
+ From a comparison of the values in Cótté (1995) and other values in the literature. the uncertainty in NB) from the photometry is probably a little less than 0.2 iuaguitudes. aud. when cousicering the error in the distance estimates. the total error is probably a little larger than 0.2 maeuituces for the typical Sculptor Croup member.," From a comparison of the values in Côtté (1995) and other values in the literature, the uncertainty in M(B) from the photometry is probably a little less than 0.2 magnitudes, and, when considering the error in the distance estimates, the total error is probably a little larger than 0.2 magnitudes for the typical Sculptor Group member."
+ The error could be larger for those galaxies with velocities in excess of 500 kins +., The error could be larger for those galaxies with velocities in excess of 500 km $^{-1}$.
+ Nonetheless. these errors are sinall relative to the dynamic rauge of the luminosities of the galaxies aud allow us to investigate relationships between intrinsic properties of galaxies.," Nonetheless, these errors are small relative to the dynamic range of the luminosities of the galaxies and allow us to investigate relationships between intrinsic properties of galaxies."
+We assume below that the physical parameters do not deviale significantly from that chosen in previous sections.,We assume below that the physical parameters do not deviate significantly from that chosen in previous sections.
+ The contamination of the IC component in the high Irequency alterglow (e.g. the soft N-rav. afterglow) is not considered [ον simplicitv., The contamination of the IC component in the high frequency afterglow (e.g. the soft X-ray afterglow) is not considered for simplicity.
+ Llowever. the IC enissions can be inferred from equations (38)) and (66)).," However, the IC emissions can be inferred from equations \ref{eqn:fc:SSC-spectrum}) ) and \ref{eqn:sc:SSC-spectrum}) )."
+" Under these assumptions. the lieht curve al an observing frequency 7 can be determined by comparing the frequency. with the critical Irequencies v,,,, and 7, where 5, is the SSA/cooling frequency al /,, and can be calculated [rom equations (22)). (27)) and (23))."," Under these assumptions, the light curve at an observing frequency $\nu$ can be determined by comparing the frequency with the critical frequencies $\nu_{cm}$ and $\nu_{ac}$, where $\nu_{ac}$ is the SSA/cooling frequency at $t_{ac}$ and can be calculated from equations \ref{eqn:fc:spectrum}) ), \ref{eqn:fc:ISM:t_ac}) ) and \ref{eqn:fc:wind:t_ac}) )."
+ Roughlly. there are three tvpes of afterelow light eurves in various frequeney ranges separated by (these (wo critical frequencies.," Roughly, there are three types of afterglow light curves in various frequency ranges separated by these two critical frequencies."
+"A careful inspection of the order of the (transition (me /,,,, ancl the crossing times /4. /,. /,, gives Iour types of light curvesfor both the ISM case ancl the stellar wind case.","A careful inspection of the order of the transition time $t_{cm}$ and the crossing times $t_{a}$, $t_{c}$, $t_{m}$ gives four types of light curvesfor both the ISM case and the stellar wind case."
+" The crossing times /,. [adl /,, correspond to the times when the lrequencies 7. 1. and vy, equals the observing frequency. respectively. I"," The crossing times $t_{a}$, $t_{c}$ and $t_{m}$ correspond to the times when the frequencies $\nu_{a}$ , $\nu_{c}$ and $\nu_{m}$ equals the observing frequency, respectively. ,"
+"SM. the orders of these times are (A) /.<taluymdus lor vimVeet (D)f,«&be<dinmduy Tor uympomvue (C) baomduymuydy dor Mayem)MEMa (D)fu«&fymluydl lor v<vs)", the orders of these times are (A) $t_{c}<t_{a}<t_{m}<t_{cm}$ for $\nu>\nu_{ac}$; (B) $t_{a}<t_{c}<t_{m}<t_{cm}$ for $\nu_{cm}<\nu<\nu_{ac}$; (C) $t_{a}<t_{cm}<t_{m}<t_{c}$ for $\nu_{a}(t_{cm})<\nu<\nu_{cm}$; (D) $t_{cm}<t_{a}<t_{m}<t_{c}$ for $\nu<\nu_{a}(t_{cm})$.
+" Iere (ey) is the SSA frequeney at /,4,.", Here $\nu_{a}(t_{cm})$ is the SSA frequency at $t_{cm}$ .
+" Using the equations (29)). (30)). and (61)) in thecase of &= 0. the light curves in each case can beconstructed as (A) E,x£2 (bh <td. Fyx0004972> η, du. Ly). F,x|(3p2AX)(lOppí23 (m Las). Ε,xd(8p2Balla)(2ορ511ο)1Pypí23 doma (B) FxPP cg BexHOOOS (uq, FE,xpUNIoy12 um Ly). F,xd(Sp2BaletlOypí3 du. Las). F,,x|(8p2Balla)(2ορ511ο)1Pypí3 (| das) (C ESxty (l< oe Fyxl?tlagscOp (uud lay). Foxit?soledam3 TN LbxpPLdOpUp142 (QU qu, Ενκιο2:20/002(pAVOAgy,pi In)[m d (0D) FoxPan (0m dus). FuxPOEOO? (Qus Hu). Fux10BOEP (uL). EeαιταlotονUo1)/2 (liye d). E,xUD2XO0)(2«p2)/(1ο11mpi23 T— l.)."," Using the equations \ref{eqn:fc:syn-spectrum-1}) ), \ref{eqn:fc:syn-spectrum-2}) ), and \ref{eqn:sc:syn-spectrum}) ) in thecase of $k=0$ , the light curves in each case can beconstructed as (A) $F_{\nu}\propto t^{1}\nu^{2}$ $t<t_{c}$ ), $F_{\nu}\propto t^{(5-2\epsilon)/(4-\epsilon)}\nu^{5/2}$ $t_{c}$, $t_{a}$ ), $F_{\nu}\propto
+t^{-(1+2\epsilon)/(4-\epsilon)}\nu^{-1/2}$ $t_{a}$, $t_{m}$ ), $F_{\nu}\propto t^{-(3p-2+2\epsilon)/(4-\epsilon)}\nu^{-p/2}$ $t_{m}$, $t_{cm}$ ), $F_{\nu}\propto
+t^{-(3p-2+2\epsilon)/(4-\epsilon)+(2+\epsilon)(p-2)/(4+\epsilon)/(4-p)}\nu^{-p/2}$ $t>t_{cm}$ ); (B) $F_{\nu}\propto t^{1}\nu^{2}$ $t<t_{a}$ ), $F_{\nu}\propto t^{(2-11\epsilon)/3(4-\epsilon)}\nu^{1/3}$ $t_{a}$, $t_{c}$ ), $F_{\nu}\propto
+t^{-(1+2\epsilon)/(4-\epsilon)}\nu^{-1/2}$ $t_{c}$ , $t_{m}$ ), $F_{\nu}\propto t^{-(3p-2+2\epsilon)/(4-\epsilon)}\nu^{-p/2}$ $t_{m}$ , $t_{cm}$ ), $F_{\nu}\propto
+t^{-(3p-2+2\epsilon)/(4-\epsilon)+(2+\epsilon)(p-2)/(4+\epsilon)/(4-p)}\nu^{-p/2}$ $t>t_{cm}$ ); (C) $F_{\nu}\propto t^{1}\nu^{2}$ $t<t_{a}$ ), $F_{\nu}\propto t^{(2-11\epsilon)/3(4-\epsilon)}\nu^{1/3}$ $t_{a}$, $t_{cm}$ ), $F_{\nu}\propto
+t^{(2-3\epsilon)/(4-\epsilon)}\nu^{1/3}$ $t_{cm}$, $t_{m}$ ), $F_{\nu}\propto t^{-3(p-1+\epsilon)/(4-\epsilon)}\nu^{-(p-1)/2}$ $t_{m}$, $t_{c}$ ), $F_{\nu}\propto
+t^{-(3p-2+2\epsilon)/(4-\epsilon)+(2+\epsilon)(p-2)/(4+\epsilon)/(4-p)}\nu^{-p/2}$ $t>t_{c}$ ); (D) $F_{\nu}\propto t^{1}\nu^{2}$ $t<t_{cm}$ ), $F_{\nu}\propto t^{2(1-\epsilon)/(4-\epsilon)}\nu^{2}$ $t_{cm}$, $t_{a}$ ), $F_{\nu}\propto t^{(2-3\epsilon)/(4-\epsilon)}\nu^{1/3}$ $t_{a}$, $t_{m}$ ), $F_{\nu}\propto
+t^{-3(p-1+\epsilon)/(4-\epsilon)}\nu^{-(p-1)/2}$ $t_{m}$ , $t_{c}$ ), $F_{\nu}\propto
+t^{-(3p-2+2\epsilon)/(4-\epsilon)+(2+\epsilon)(p-2)/(4+\epsilon)/(4-p)}\nu^{-p/2}$ $t>t_{c}$ )."
+ The light curves in the ISM case are illustrated in Figure 1.., The light curves in the ISM case are illustrated in Figure \ref{fig:ISM:lightcurves}.
+" The crossing times /. and /, in case A and /, in case D occur very. early in high observing frequencies. while /. in case C and fy. £,, and /, in case D occur very late in low observing Irequencies."," The crossing times $t_{c}$ and $t_{a}$ in case A and $t_{a}$ in case B occur very early in high observing frequencies, while $t_{c}$ in case C and $t_{a}$, $t_{m}$ and $t_{c}$ in case D occur very late in low observing frequencies."
+ We thus neglect these crossing times in the figure., We thus neglect these crossing times in the figure.
+ As indicated in Figure L.. the radiation efficiency. e. has a marked effect on the afterglowlight curves.," As indicated in Figure \ref{fig:ISM:lightcurves}, , the radiation efficiency, $\epsilon$ , has a marked effect on the afterglowlight curves."
+" It changes the temporaldecaving index a (defined as Fyx!/ "") of the light curve significantly.", It changes the temporaldecaying index $\alpha$ (defined as $F_{\nu}\propto t^{-\alpha}$ ) of the light curve significantly.
+" Forillustration. we adopt e=e,1/3 and p=2.2 in the following."," Forillustration, we adopt $\epsilon=\epsilon_{e}=1/3$ and $p=2.2$ in the following."
+" The initial slowly increasing light curve segment. E,x 1°, predicted in the standard adiabaticblast wave model will changes to be a slowly decreasing one. E,xIο.οἱed0.15 Pas shown in the early segment of case C;This makesthe sub-millimeter altereglowless competitive to disünguish between (he ISAT and the stellar wind. as proposed by Panaitescu"," The initial slowly increasing light curve segment, $F_{\nu}\propto t^{1/6}$ , predicted in the standard adiabaticblast wave model will changes to be a slowly decreasing one, $F_{\nu}\propto t^{(2-11\epsilon)/3(4-\epsilon)}\sim
+t^{-0.15}$ , as shown in the early segment of case C.This makesthe sub-millimeter afterglowless competitive to distinguish between the ISM and the stellar wind, as proposed by Panaitescu"
+"Our two target LAEs were selected to have 2>6.5, to ensure that their redshifted Ilines could be observed with the sensitive GBT Ku-band receiver.","Our two target LAEs were selected to have $z > 6.5$, to ensure that their redshifted lines could be observed with the sensitive GBT Ku-band receiver."
+" The first system, HCM 6A at ο~6.56 (Huetal.2002).. is perhaps the best candidate LAE for a search for molecular emission as It is strongly lensed by a foreground cluster (Abell 370, at >~0.375; Kneibetal.1993)), with a magnification factor of ~4.5; this significantly improves the sensitivity to CO emission."," The first system, HCM 6A at $z \sim 6.56$ \citep{hu02}, is perhaps the best candidate LAE for a search for molecular emission as it is strongly lensed by a foreground cluster (Abell 370, at $z \sim 0.375$; \citealp{kneib93}) ), with a magnification factor of $\sim 4.5$; this significantly improves the sensitivity to CO emission."
+" It also has the highest estimated SER of all known LAEs: Charyetal.(2005) found excess broad-band emission in a IRAC 4.5;:m image, compared to the continuum at other wavelengths, and argue that this is due to strong Ha emission, with an implied SFR of 140A. yr+."," It also has the highest estimated SFR of all known LAEs; \citet{chary05} found excess broad-band emission in a IRAC $\mu$ m image, compared to the continuum at other wavelengths, and argue that this is due to strong $\alpha$ emission, with an implied SFR of $140 \: M_\odot$ $^{-1}$."
+" The SFR inferred from the UV continuum (uncorrected for dust effects) is significantly lower than this, 9M. yr! (Huetal.2002).. similar to values obtained in other LAEs at z~6.5 (c.%G Taniguchietal. 2005))."," The SFR inferred from the UV continuum (uncorrected for dust effects) is significantly lower than this, $\sim 9 \: M_\odot$ $^{-1}$ \citep{hu02}, similar to values obtained in other LAEs at $z \sim 6.5$ (e.g. \citealp{taniguchi05}) )."
+" If the SER derived trom the Spitzer image is correct, the discrepancy between the two SFR values implies a high dust extinction, sly~2.6 mag, consistent with the value independently derived from a fit to the broad-band photometric data (Charyetal.2005:; see also Schaerer&Pelló 2005))."," If the SFR derived from the image is correct, the discrepancy between the two SFR values implies a high dust extinction, $A_{\rm UV} \sim 2.6$ mag, consistent with the value independently derived from a fit to the broad-band photometric data \citealp{chary05}; see also \citealp{schaerer05}) )."
+ Such a high SFR would be similar to that of nearby ultra-Iuminous infrared galaxies (ULIRGs). which have typical molecular gas masses of 10°1017. (c.g. 1998)).," Such a high SFR would be similar to that of nearby ultra-luminous infrared galaxies (ULIRGs), which have typical molecular gas masses of $10^{9-10} \: M_{\odot}$ (e.g. \citealp{downes98}) )."
+" Conversely, Booneetal.(2007) argue that the limits on the 850 j/m and 1.2 mm continuum flux densities of HCM 6A imply upper limits to the SFR in the range 10—90 Μ. +. for assumed dust temperatures in the range 18—54 K: these SFR estimates are somewhat lower than the values obtained by Charyetal.(2005) and Schaerer&Pelló(2005)."," Conversely, \citet{boone07} argue that the limits on the 850 $\mu$ m and 1.2 mm continuum flux densities of HCM 6A imply upper limits to the SFR in the range $10 - 90$ $_\odot$ $^{-1}$, for assumed dust temperatures in the range $18-54$ K; these SFR estimates are somewhat lower than the values obtained by \citet{chary05} and \citet{schaerer05}."
+. Charyetal.(2005) argue that the properties of HCM 6A are similar to those of other :=6 LAEs: the molecular gas properties derived for this object are thus likely to be representative of the entire population., \citet{chary05} argue that the properties of HCM 6A are similar to those of other $z \gtrsim 6$ LAEs; the molecular gas properties derived for this object are thus likely to be representative of the entire population.
+" Our secondtarget, IOK-1. was discovered in a Subaru survey for 2~7 LAEs (lye and has the highest spectroscopically-confirmed redshift of all known galaxies."," Our secondtarget, IOK-1, was discovered in a Subaru survey for $z \sim 7$ LAEs \citep{iye06} and has the highest spectroscopically-confirmed redshift of all known galaxies."
+ 7T.. 2... 2.2? and references therein).,"\citealt{Lawrence2007}, , \citealt{Deacon2009a}, \citealt{Goldman2010}, \citealt{Burningham2010} and references therein)."
+ The Durgasser 2\LASS searches used. two. different Il—ky. euis and made photometric selections from 2MAÁSS data products before the final calibration., The Burgasser 2MASS searches used two different $H-K_s$ cuts and made photometric selections from 2MASS data products before the final calibration.
+ For comparison we use the final bluer eut. Jf—A.«0.0 and photometry from the final 2\LASS catalog.J201.03204-19.1072:, For comparison we use the final bluer cut $H-K_s<0.0$ and photometry from the final 2MASS catalog.:
+: The UIIDSS observation for this object is from Data Release 7 while the most recent publications (7.. ?)) onlv include data up to Data Release 4.," The UKIDSS observation for this object is from Data Release 7 while the most recent publications \citealt{Goldman2010}, \citealt{Burningham2010}) ) only include data up to Data Release 4."
+" It is too red in //-N, (0.06) for the 2MÀSS T. chwarls survevs.", It is too red in $H$ $K_s$ (0.06) for the 2MASS T dwarfs surveys.
+ However. it should appear in due to its red SDSS colors.," However, it should appear in \cite{Chiu2006} due to its red SDSS colors."
+ We are unsure as to why it does not appear in this study as ils observation date of May. 2005 is later than most objects in Chiu et αἱ5 catalog. but one object appears from June 2005.J226.2599-28.8959:," We are unsure as to why it does not appear in this study as its observation date of May 2005 is later than most objects in Chiu et al's catalog, but one object appears from June 2005.:"
+": This object falls outside the UIXIDSS and SDSS survey. areas and is too red (£-4,—0.30) to be detected by 2\LASS searches for T. dwarts.J246.42224-15.4698:", This object falls outside the UKIDSS and SDSS survey areas and is too red $H$ $K_s$ =0.30) to be detected by 2MASS searches for T dwarfs.:
+: This is similarly not in UINIDSS and is too faint in J (16.77) to fall into the 2MASS studies! selection sample., This is similarly not in UKIDSS and is too faint in $J$ (16.77) to fall into the 2MASS studies' selection sample.
+ It appears in the SDSS database that would have been searched by 2.. but has a high error on the z magnitude. which could have lead to it falling outside their sample.J247.3273+03.5932:," It appears in the SDSS database that would have been searched by \cite{Chiu2006}, but has a high error on the $z$ magnitude, which could have lead to it falling outside their sample.:"
+": This object is not in UKIDSS or SDSS and is too red in //- A, (0.39) to appear in the 241ASS T dwarf samples.", This object is not in UKIDSS or SDSS and is too red in $H$ $K_s$ (0.39) to appear in the 2MASS T dwarf samples.
+ Three of our objects appear redder than (he final color cuts of the Burgasser searches for T dwarfs., Three of our objects appear redder than the final color cuts of the Burgasser searches for T dwarfs.
+ Figure 7 shows how our objects compare to the discovered in these earlier slucdies., Figure \ref{burgasserplot} shows how our objects compare to the discovered in these earlier studies.
+ To characterize the parameter space covered bv the 332 survey and to compare with other leading wide-field survevs for ultracool dwarls we calculated. the expected volume each survey would cover lor different spectral types., To characterize the parameter space covered by the $\pi$ survey and to compare with other leading wide-field surveys for ultracool dwarfs we calculated the expected volume each survey would cover for different spectral types.
+ For the UNIDS5 survey we averaged (he brieht and faint spectral (wpe - absolute magnitude relations of ?7.— and assumed a J band completeness limit of 18.8 (?))., For the UKIDSS survey we averaged the bright and faint spectral type - absolute magnitude relations of \cite{Liu2006} and assumed a $J$ band completeness limit of 18.8 \citealt{Burningham2010}) ).
+" In the case of 221ASS most searches to date have only gone to the nominal completeness limit of J=15.8. so (his was used alongh"" with the absolute magnitude relations of ? transformed into the 2ALASS filler svstem usingh the relations from ?.."," In the case of 2MASS most searches to date have only gone to the nominal completeness limit of $J=15.8$, so this was used along with the absolute magnitude relations of \cite{Liu2006} transformed into the 2MASS filter system using the relations from \cite{Stephens2004}."
+" Searches [οι T. dwarls based on 2MASS are less complete than this estimate as these objects are blue and the 2\LASS / and A, bands are shallower than the J band.", Searches for T dwarfs based on 2MASS are less complete than this estimate as these objects are blue and the 2MASS $H$ and $K_s$ bands are shallower than the $J$ band.
+" Conversely 2MASS will be deeperin J and A, for the reddest L chwarls.", Conversely 2MASS will be deeperin $H$ and $K_s$ for the reddest L dwarfs.
+ For PS1, For PS1
+DPluuuucrs nurodel. and a spherical Pluinuers halo.,"Plummer's model, and a spherical Plummer's halo."
+ The mass of dark matter was set equal to the visible nass within the sohere containing 95 of the stellar iiass., The mass of dark matter was set equal to the visible mass within the sphere containing 95 of the stellar mass.
+ The combined potential of both comporents was used to solve the Jeaas equations aud to derive the initial velocity dispersion (IIeruquist 1993)., The combined potential of both components was used to solve the Jeans equations and to derive the initial velocity dispersion (Hernquist 1993).
+" Each sphere consisted of Nus10X0 particles (δε=20000 per stellar conmnponent aid INS,=20000 per halo)."," Each sphere consisted of $N_{tot} = 40\,000$ particles $N_{tot} = 20\,000$ per stellar component and $N_{tot} = 20\,000$ per halo)."
+ The addijon of an extended dark halo surrounudius cach galaxy uakes the effect of parameter changes less pronounced hau for the experiments without a dark halo., The addition of an extended dark halo surrounding each galaxy makes the effect of parameter changes less pronounced than for the experiments without a dark halo.
+" Aaplitides of relative chanecs of the parameters Phinuuer™ sphere ὅμως ~-- GOA, day Pluuunuerss sphere with halo O14 S0. 0709 zx Our muuceric:d experiments and observational data have shown that the elobal parameters of earbv-tvpe galaxies are rather stable to gravitational perturbation."," Amplitudes of relative changes of the parameters Plummer's sphere – $\delta r_{1/2}$ $\approx$ $\%$, $\delta \sigma_0$ $\approx$ $\%$, Plummers's sphere with halo – $\delta r_{1/2}$ $\approx$ $\%$, $\delta \sigma_0$ $\approx$ $\%$ Our numerical experiments and observational data have shown that the global parameters of early-type galaxies are rather stable to gravitational perturbation."
+ The FP parameters do change during close encounters but within a very short fiue iuterval (10 1075 years) just before the final mereer., The FP parameters do change during close encounters but within a very short time interval $\sim$ $^7$ $^8$ years) just before the final merger.
+ Furhermore. the amplitudes of these changes are comnparabο to the scatter of the observed EP of ellipticals.," Furthermore, the amplitudes of these changes are comparable to the scatter of the observed FP of ellipticals."
+ There is a very simal prohahiitv that we observe the system at these imteraction stages., There is a very small probability that we observe the system at these interaction stages.
+ Therefore. the FP is still a goo method to «erive disaliCes. even to the clusters that iucIude a large iunbero: juteracting ealaxies (e.g. van Dokstun et al.," Therefore, the FP is still a good method to derive distances, even to the clusters that include a large number of interacting galaxies (e.g. van Dokkum et al."
+ Loe10)., 1999).
+our ESO observations.,our ESO observations.
+ The majority of those sources however. are expected to lie at redshift >0.5.," The majority of those sources however, are expected to lie at redshift $z>0.5$."
+ Out of the 12+ unresolved X-ray sources with r.«20.5 mmag. a total of 28 have redshift available from the SDSS.," Out of the 124 unresolved X-ray sources with $r<20.5$ mag, a total of 28 have redshift available from the SDSS."
+ Of them only one lies in the redshift interval 0.].<z«0.5., Of them only one lies in the redshift interval $0.1<z<0.5$.
+ We therefore expect that the exclusion of optically unresolved X-ray sources is not going to have a strong effect on the results and conclusions., We therefore expect that the exclusion of optically unresolved X-ray sources is not going to have a strong effect on the results and conclusions.
+ This issue is further discussed in the results section., This issue is further discussed in the results section.
+ AGN at >zO.S are selected from the Chandra surveys of the AEGIS. GOODS-North MMs Chandra Deep Field North) and GOODS-South MMs Chandra Deep Field South).," AGN at $z\approx0.8$ are selected from the Chandra surveys of the AEGIS, GOODS-North Ms Chandra Deep Field North) and GOODS-South Ms Chandra Deep Field South)."
+ The Chandra observations in the those fields have been reduced and analysed in a homogeneous way using the methodology described by?., The Chandra observations in the those fields have been reduced and analysed in a homogeneous way using the methodology described by.
+. The optical counterparts of the X-ray sources have been identitied using the Likelihood Ratio method as described in?., The optical counterparts of the X-ray sources have been identified using the Likelihood Ratio method as described in.
+. For the AEGIS field we use the LAL ground based optical photometry obtained as part of the DEEP? spectroscopic survey(2)., For the AEGIS field we use the $BRI$ ground based optical photometry obtained as part of the DEEP2 spectroscopic survey.
+. For the GOODS North and South fields the optical identification of the X-ray sources uses the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging observations of those fieldsdetails)., For the GOODS North and South fields the optical identification of the X-ray sources uses the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging observations of those fields.
+ The spectroscopy for X-ray sources in the AEGIS is from a variety of sources: the DEEP? redshift survey(2).. follow-up observations of X-ray sources at the MMT using the Hectospec fiber spectrograph(2).. the SDSS and a number of spectroscopic programs that targeted galaxies in the original Groth Strip(2).," The spectroscopy for X-ray sources in the AEGIS is from a variety of sources: the DEEP2 redshift survey, follow-up observations of X-ray sources at the MMT using the Hectospec fiber spectrograph, the SDSS and a number of spectroscopic programs that targeted galaxies in the original Groth Strip."
+. Optical spectroscopy in the GOODS-North is available from either programmes that specifically targeted the X-ray population in these fields orthe Keck Treasury Redshift Survey?)., Optical spectroscopy in the GOODS-North is available from either programmes that specifically targeted the X-ray population in these fields or the Keck Treasury Redshift Survey.
+. There are many spectroscopic campaigns in the CDF-South., There are many spectroscopic campaigns in the CDF-South.
+ These include follow-up observations targeting specitie populations. such as X-ray sources(2).. A-band selected galaxies(2).. and high redshift candidates222).. as well as generic spectroscopic surveys of faint galaxies in the GOODS area using the FORS? and VIMOS spectrographs at the VLT.," These include follow-up observations targeting specific populations, such as X-ray sources, $K$ -band selected galaxies, and high redshift candidates, as well as generic spectroscopic surveys of faint galaxies in the GOODS area using the FORS2 and VIMOS spectrographs at the VLT."
+ We select X-ray sources detected in the kkeV band with optical magnitudes /?1g<24.1 mmag for the AEGIS and /ye<253.5 mmag (F775W HST/ACS band) for the GOODS-North and South fields., We select X-ray sources detected in the keV band with optical magnitudes $R_{AB}<24.1$ mag for the AEGIS and $i_{AB}<23.5$ mag (F775W HST/ACS band) for the GOODS-North and South fields.
+ At this magnitude cut the spectroscopic identification rate of the AEGIS. GOODS-North and GOODS-South X-ray sources is 67 (375/557). 85 (118/139) and 87 CIOS/121) per cent. respectively.," At this magnitude cut the spectroscopic identification rate of the AEGIS, GOODS-North and GOODS-South X-ray sources is 67 (375/557), 85 (118/139) and 87 (105/121) per cent, respectively."
+ From the spectroscopically identified sources we select those with redshifts in the interval 0.6<2«1.2., From the spectroscopically identified sources we select those with redshifts in the interval $0.6<z<1.2$.
+ This results in 149 sources in the AEGIS. 66 in the GOODS-North and 54 in the GOODS-South.," This results in 149 sources in the AEGIS, 66 in the GOODS-North and 54 in the GOODS-South."
+ The median redshift of the sample is 0.8., The median redshift of the sample is 0.8.
+ The choice of the X-ray band for the detection of sources is to ensure that our 2zO.S sample is selected at similar rest-frame energies kkeV) as the >=0.1 kkeV) and zz0.3 samples (3-lOkkeV)., The choice of the X-ray band for the detection of sources is to ensure that our $z\approx0.8$ sample is selected at similar rest-frame energies keV) as the $z\approx0.1$ keV) and $z\approx0.3$ samples keV).
+ Differential selection effects are therefore small. thereby facilitating the comparison of the AGN properties among the three samples.," Differential selection effects are therefore small, thereby facilitating the comparison of the AGN properties among the three samples."
+ The combined X-ray sensitivity curve for the 3 fields is shown in Figure l.., The combined X-ray sensitivity curve for the 3 fields is shown in Figure \ref{fig_curve}.
+ In the next sections the space density of X-ray AGN will be compared with that of the overall galaxy population., In the next sections the space density of X-ray AGN will be compared with that of the overall galaxy population.
+ We therefore compile three spectroscopic galaxy samples at 2(Q.l. 5m0.3 and zO.S. which probe similar redshift intervals as the low redshift subset of the XMM/SDSS survey. the NHS and the AEGIS+GOODS X-ray AGN samples respectively.," We therefore compile three spectroscopic galaxy samples at $z\approx0.1$, $z\approx0.3$ and $z\approx0.8$, which probe similar redshift intervals as the low redshift subset of the XMM/SDSS survey, the NHS and the AEGIS+GOODS X-ray AGN samples respectively."
+ The number of galaxies in each sample is listed in Table |.., The number of galaxies in each sample is listed in Table \ref{tab_sample}.
+ At zcO.L. we select a total of 9541 NYU-VAGC sources with r.«17.77 mmag that overlap with the XMM/SDSS survey fields (after excluding galaxy cluster pointings) and have spectroscopic redshifts in the interval 0.03«z0.2.," At $z\approx0.1$, we select a total of 9541 NYU-VAGC sources with $r<17.77$ mag that overlap with the XMM/SDSS survey fields (after excluding galaxy cluster pointings) and have spectroscopic redshifts in the interval $0.03<z<0.2$."
+ The data release 3 of the DEEP? spectroscopic survey in he AEGIS field is used toselect galaxies at 2.70.5., The data release 3 of the DEEP2 spectroscopic survey in the AEGIS field is used toselect galaxies at $z\approx0.8$.
+ This spectroscopic program uses the DEIMOS spectrograph on he 10mm Keck-IT telescope to obtain redshifts for galaxies to Hip= 24.lmmag.," This spectroscopic program uses the DEIMOS spectrograph on the m Keck-II telescope to obtain redshifts for galaxies to $R_{AB} =
+24.1$ mag."
+ The observational setup uses a moderately vigh resolution grating (2= 5000). which provides a velocity accuracy of 30knis1 and a wavelength coverage of AA.," The observational setup uses a moderately high resolution grating $R\approx5000$ ), which provides a velocity accuracy of $\rm
+30\,km\,s^{-1}$ and a wavelength coverage of ."
+. This spectral window allows the identification of the strong OTII] doublet emission line to z« 1.4., This spectral window allows the identification of the strong II] doublet emission line to $z<1.4$ .
+ We use DEEP? galaxies with redshift determinations secure at the >904. confidence level (quality flag (Q>3: Davis et al., We use DEEP2 galaxies with redshift determinations secure at the $>90\%$ confidence level (quality flag $Q \ge 3$; Davis et al.
+ 2007)., 2007).
+ A total of 6797 galaxies with redshifts L6«21.2 are selected to determine the space density of the galaxy population at a median redshift of 2z0.5 and to compare against that of X-ray AGN., A total of 6797 galaxies with redshifts $0.6<z<1.2$ are selected to determine the space density of the galaxy population at a median redshift of $z\approx0.8$ and to compare against that of X-ray AGN.
+ Although the AEGIS DEEP? spectroscopic survey is geared toward high redshift sources. it also includes a large number of galaxies at 2<0.6 (4601).," Although the AEGIS DEEP2 spectroscopic survey is geared toward high redshift sources, it also includes a large number of galaxies at $z<0.6$ (4601)."
+ We select a total of 1960 galaxies in the interval 0.2<2«0.4 to estimate their luminosity function at 270.3 and compare it with that of X-ray AGN identified in the NHS., We select a total of 1960 galaxies in the interval $0.2<z<0.4$ to estimate their luminosity function at $z\approx0.3$ and compare it with that of X-ray AGN identified in the NHS.
+ This section describes how the rest-frame colour. stellar mass. X- luminosity and intrinsic column density of galaxies and X-ray AGN are determined.," This section describes how the rest-frame colour, stellar mass, X-ray luminosity and intrinsic column density of galaxies and X-ray AGN are determined."
+ The version 4.2 routines developedby areused to fit spectral models to the optical photometry of X-ray sources, The version 4.2 routines developedby areused to fit spectral models to the optical photometry of X-ray sources
+(Press&Schechter1974).,\citep{pre74}.
+. In relsect we present our results., In \\ref{sec4} we present our results.
+ In relsec5 we sunmiarize and discuss our results., In \\ref{sec5} we summarize and discuss our results.
+ Issues related to image separation are presented in LOQ2 in detail. so here we focus on the time delay between multiple images produced by gravitational lensing.," Issues related to image separation are presented in LO02 in detail, so here we focus on the time delay between multiple images produced by gravitational lensing."
+ The densitv profile for an SIS is (Gott&Gunn1974:Turner.Ostriker.Gott1984) where σι is the constant velocity dispersion.," The density profile for an SIS is \citep{got74,tur84}
+ where $\sigma_v$ is the constant velocity dispersion."
+ Assuming that the angular-diameter distances from the observer to the lens and the source are respectively Dj) and Di. from the lens to the source is Djs.," Assuming that the angular-diameter distances from the observer to the lens and the source are respectively $D_L^A$ and $D_S^A$, from the lens to the source is $D_{LS}^A$."
+ Then. the time delay between the (wo images of the remote source lensed by an SIS halo is where σε ds the redshilt of the lens (dark halo). y is the distance from the source to the point where the line of sight through the lens center intersects the source plane. in units of 1—&DdDjie," Then, the time delay between the two images of the remote source lensed by an SIS halo is \citep{sch92}
+ where $z_L$ is the redshift of the lens (dark halo), $y$ is the distance from the source to the point where the line of sight through the lens center intersects the source plane, in units of $\eta_0 \equiv \xi_0 D_S^A / D_L^A$."
+ The cross-section for producing (wo images with a time delav >.M is ∖∖⊽∐≼↲↕⋅≼↲≀↗≼⋝∆∕↓−∆∕↕⋟↕⋝∖⊽⊔∐↲⋝∖⊽∩↲↕↽≻↓⋟∏∐≺∢∐∪∐⋅, The cross-section for producing two images with a time delay $> \Delta t$ is where $\vartheta(\Delta t_1 - \Delta t)$ is the step function.
+enable us to locate X-ray sources associated with the galaxy ISM.,enable us to locate X-ray sources associated with the galaxy ISM.
+ Enhancements of the emission due to ICM trapped in the potentials of the galaxies due to the cluster overpressure should show up in the gas pressure map. but hot in the entropy map. as gas compression occurs adiabatically.," Enhancements of the emission due to ICM trapped in the potentials of the galaxies due to the cluster overpressure should show up in the gas pressure map, but not in the entropy map, as gas compression occurs adiabatically."
+ Also. the fluctuations that are associated with shocks in the ICM. will (if at all) be seen as positive fluctuations in the eatropy map.," Also, the fluctuations that are associated with shocks in the ICM, will (if at all) be seen as positive fluctuations in the entropy map."
+ The issue of ISM/ICM separation m not unique to identifying Coma galaxies since Briel et al. (, The issue of ISM/ICM separation in not unique to identifying Coma galaxies since Briel et al. (
+2001). amorg others. report a quite inhomogeneous hardness ratio map of the Coma center. which is not understood.,"2001), among others, report a quite inhomogeneous hardness ratio map of the Coma center, which is not understood."
+ There additional uncertainties associated the low entropy ISM of galaxies in a cluster., There additional uncertainties associated the low entropy ISM of galaxies in a cluster.
+ First it is subject to a number of instabilities. such as cooling and a combination of stripping and Kelvin-Helmholtz instability and should be understood as result of dynamical equilibrium between the processes of gas removal and gas replenishment (e.g. Gaetz et al.," First it is subject to a number of instabilities, such as cooling and a combination of stripping and Kelvin-Helmholtz instability and should be understood as result of dynamical equilibrium between the processes of gas removal and gas replenishment (e.g. Gaetz et al."
+ 1987: Matsushita 2001)., 1987; Matsushita 2001).
+ However in Coma. an additional," However in Coma, an additional"
+In general. we find that the PPDES are not log-normal. even though the underlving gas column densities are.,"In general, we find that the PDFs are not log-normal, even though the underlying gas column densities are."
+ One reason for the dillerence is that he PPDES themselves are not log-normal., One reason for the difference is that the PDFs themselves are not log-normal.
+ Further. in most of he mocels. the PPDE itselfdoes not neatly follow that of/Nco.," Further, in most of the models, the PDF itself does not neatly follow that of."
+. Since CO races the dense gas. iis more intermittent than the underlying gas clistribution.," Since CO traces the dense gas, is more intermittent than the underlying gas distribution."
+ Due to the elfects of saturation. this intermittency is not captured byVW.," Due to the effects of saturation, this intermittency is not captured by."
+ In the two models with log-normal aand PDEs. the variances between the distributions are nevertheless dillerent.," In the two models with log-normal and PDFs, the variances between the distributions are nevertheless different."
+ Taken together. we conclude that the clistribution of observed CO intensities is not an accurate measure of the underlying distribution. of molecular gas.," Taken together, we conclude that the distribution of observed CO intensities is not an accurate measure of the underlying distribution of molecular gas."
+ ‘This conclusion is allirmed by the observational analysis of ?.. who found significant dillerences in the CO and based cistributions.," This conclusion is affirmed by the observational analysis of \citet{Goodmanetal09b}, who found significant differences in the $^{13}$ CO and dust-based distributions."
+ We have shown that. in general. the CO integrated intensity does not linearly traceNyo.. even within individual MC's. so that the [factor is not constant.," We have shown that, in general, the CO integrated intensity does not linearly trace, even within individual MCs, so that the factor is not constant."
+" Ehe intrinsic cloud properties. such as density. metallicity. and. background. UV radiation field. all inlluence how iis related to/Ng,."," The intrinsic cloud properties, such as density, metallicity, and background UV radiation field, all influence how is related to."
+". In the previous sections. our analysis has dealt with all positions in the 2D. ""observed? maps. which are idealized svnthetie maps with high spatial resolution of  0.1 pe (the size of the grid zone in the MILD simulations)."," In the previous sections, our analysis has dealt with all positions in the 2D “observed” maps, which are idealized synthetic maps with high spatial resolution of $\sim$ 0.1 pc (the size of the grid zone in the MHD simulations)."
+ Llowever. in practice the derived [factor is likely to be an average over a range in extinction values. especially in. observations of extragalactic clouds where the resolution may be comparable to the cloud size.," However, in practice the derived factor is likely to be an average over a range in extinction values, especially in observations of extragalactic clouds where the resolution may be comparable to the cloud size."
+ In order for a more direct. comparison with these types of integrated. observations. we now shift our focus to the discussion of average quantities in the synthetic maps.," In order for a more direct comparison with these types of integrated observations, we now shift our focus to the discussion of average quantities in the synthetic maps."
+ Figure 7 shows the mean [factor in cillerent bbins for the four models shown in Figures 5--6.. as well as Alodel n300-Z01.," Figure \ref{meanX} shows the mean factor in different bins for the four models shown in Figures \ref{Xfig}- \ref{XvsAv}, as well as Model n300-Z01."
+ The emission-weighted mean aand [for each model is also shown (bv the large symbols)., The emission-weighted mean and for each model is also shown (by the large symbols).
+ A number of features of the averaged [factor are similar to those already. cliscussecl: a decrease in wwith increasing extinction for models with low densities or metallicities. the opposite trend for Model n1000 (and to some extent Mocoel n300) cue to line saturation. and only a small variation in aat high densities for Model n300.," A number of features of the averaged factor are similar to those already discussed: a decrease in with increasing extinction for models with low densities or metallicities, the opposite trend for Model n1000 (and to some extent Model n300) due to line saturation, and only a small variation in at high densities for Model n300."
+ Qualitativelv. the mean values of the [factor binned with extinction. resemble the extinction averaged. quantities presented in Paper Lh (see their Fig.," Qualitatively, the mean values of the factor binned with extinction resemble the extinction averaged quantities presented in Paper II (see their Fig."
+ S)., 8).
+ One clear dilflerence is that values of the [factor averaged over a range in extinctions for a given model do not span as wide a range as whenall positions are considered. (compare. e.g. to Figs. 5--6)).," One clear difference is that values of the factor averaged over a range in extinctions for a given model do not span as wide a range as whenall positions are considered (compare, e.g. to Figs. \ref{Xfig}- \ref{XvsAv}) )."
+ Only when comparing all the mocels at the low extinction 55 does the large extent in the (factor (1077« i107 s)) become clear., Only when comparing all the models at the low extinction 5 does the large extent in the factor $10^{20} < $ $< 10^{24}$ ) become clear.
+ The striking feature of Figure 7. is the limited variation in the flactor at large extinctions. both for a given model as well as between models.," The striking feature of Figure \ref{meanX} is the limited variation in the factor at large extinctions, both for a given model as well as between models."
+ At extinctions r7. [falls in a narrow range 107. 107 [Lor all ‘This range is similar to the [factor values cerived for the Galaxy 227)...," At extinctions 7, falls in a narrow range $\sim 10^{20}$ $10^{21}$ for all This range is similar to the factor values derived for the Galaxy \citep{Solomonetal87,Young&Scoville91,Dameetal01}."
+ Phe emission weighted mean aand vyvalues (Iarge symbols) also portray a near constant value between the MCS. with the exception of the very. low metallicity MC.," The emission weighted mean and values (large symbols) also portray a near constant value between the MCs, with the exception of the very low metallicity MC."
+ Thus. only considering CO bright regions. corresponding to high extinctions. may not expose any real variation in the rratio. as discussed in Paper LL.," Thus, only considering CO bright regions, corresponding to high extinctions, may not expose any real variation in the ratio, as discussed in Paper II."
+ Observations of the Small Magellanic Clouc (SAIC). which has lower than Galactic metallicity. has resulted. in ugh factor estimates (77.andreferencestherein)...," Observations of the Small Magellanic Cloud (SMC), which has lower than Galactic metallicity, has resulted in high factor estimates \citep[][and references therein]{ Israel97, Leroyetal09}."
+ Averaged over à whole cloud in the SAIC. ?. found that the factor varies by 11 order of magnitude. whereas the factor computed at the CO peaks is similar to the Galactic value.," Averaged over a whole cloud in the SMC, \citet{Leroyetal09} found that the factor varies by 1 order of magnitude, whereas the factor computed at the CO peaks is similar to the Galactic value."
+ Our analysis of CO emission. from models. with ower metallicity. especially Alocel n300-Z03.. which has a metallicity similar to that of SAIC (2)... quantitatively reproduces the estimated factor. both the larger value due to cilfuse gas and the lower Galactic value found in the densest regions.," Our analysis of CO emission from models with lower metallicity, especially Model n300-Z03, which has a metallicity similar to that of SMC \citep{Vermeij&vanderHulst02}, quantitatively reproduces the estimated factor, both the larger value due to diffuse gas and the lower Galactic value found in the densest regions."
+o 1n our cliscussion of the Galactic factor.we have focused on observations of molecular clouds (e.g.?22)..," In our discussion of the Galactic factor,we have focused on observations of molecular clouds \citep[e.g.][]{Young&Scoville91,
+ Solomonetal87}."
+ However. CO has also been detected in the dilfuse ISM (ος. 22).. and the flactor for these dilluse lines of sight is found to be consistent with the standard galactic value of citepfew10760) ]Lisztetallo.," However, CO has also been detected in the diffuse ISM \citep[e.g.][]{Polketal88,Burghetal07}, , and the factor for these diffuse lines of sight is found to be consistent with the standard galactic value of \\citep[few $\times10^{20}$ ."
+ Though we consider models of individualIK. (or large volumes within) MCs. we investigate whether regions with dillerent. densities are comparable with the observations of dilferent. phases of the ISAL. focusing on the recent. discussion on the uniformity of the [factor in ?.. hereafter LPLIO.," Though we consider models of individual (or large volumes within) MCs, we investigate whether regions with different densities are comparable with the observations of different phases of the ISM, focusing on the recent discussion on the uniformity of the factor in \citet{Lisztetal10}, hereafter LPL10."
+ LPLIO find that diffuse gas. with molecular column densities ~ q407* 1075 and dense Galactic elouds. characterized σεν are always found tohave," LPL10 find that diffuse gas, with molecular column densities $\sim$ $^{20}$ $^{21}$ , and dense Galactic clouds, characterized by $\sim$ $^{23}$ are always found tohave"
+offers a natural means to sustain strong and broad lines at late times. as observed in AI. ,"offers a natural means to sustain strong and broad lines at late times, as observed in \ref{tab_term_comp} "
+"also explains why the 2D luminosity relations (3,3) and (4,4) have little correlation with each other despite their similarity at first sight (see discussion in Section 4.7 of Schaefer(2007); the correlation coefficient between the residual of fit of (3,3) and y(? and the correlation coefficient between the residual of fit of (4,4) and y(? also show their weak correlation).","also explains why the 2D luminosity relations $(3, \, 3)$ and $(4, \, 4)$ have little correlation with each other despite their similarity at first sight (see discussion in Section 4.7 of \citet{Schaefer:2006pa}; the correlation coefficient between the residual of fit of $(3, \, 3)$ and $y^{(4)}$ and the correlation coefficient between the residual of fit of $(4, \, 4)$ and $y^{(3)}$ also show their weak correlation)."
+" This is because of the difference between E, and L, where a new independent variable—the characteristic time scale—enters."," This is because of the difference between $E_{\gamma}$ and $L$, where a new independent variable—the characteristic time scale—enters."
+" In fact, we could check the guess partially with current data by examining the correlation between 2s. In Table 3,, one can find that ce), z(2, and «© are strongly correlated with each other, while all of them have only weak correlation with z(? (see also etal.(2001) and Section 4.5 of Schaefer(2007) for discussions on the correlations between the luminosity indicators)."," In fact, we could check the guess partially with current data by examining the correlation between $x^{(i)}$ s. In Table \ref{tab:cor_x}, one can find that $x^{(1)}$, $x^{(2)}$, and $x^{(5)}$ are strongly correlated with each other, while all of them have only weak correlation with $x^{(3)}$ (see also \citet{Schaefer:2001ap} and Section 4.5 of \citet{Schaefer:2006pa} for discussions on the correlations between the luminosity indicators)."
+ This is consistent with the guess that the luminosity indicators i44 and ΤΗΤ are correlated with a characteristic time scale and Epeak is correlated with a characteristic energy scale which is independent of the characteristic time scale., This is consistent with the guess that the luminosity indicators $\tau_{\mathrm{lag}}$ and $\tau_{\mathrm{RT}}$ are correlated with a characteristic time scale and $E_{\mathrm{peak}}$ is correlated with a characteristic energy scale which is independent of the characteristic time scale.
+" In addition, the correlations presented in Table 3 seems to imply that V is also correlated with the characteristic time scale."," In addition, the correlations presented in Table \ref{tab:cor_x} seems to imply that $V$ is also correlated with the characteristic time scale."
+" Accordingly, there is indeed some reduction in the intrinsic scatter for the 3D luminosity relation (2,3) compared with corresponding 2D luminosity relations, but such reduction is relatively smaller than that of (1,3) and (3,5)."," Accordingly, there is indeed some reduction in the intrinsic scatter for the 3D luminosity relation $(2, \, 3)$ compared with corresponding 2D luminosity relations, but such reduction is relatively smaller than that of $(1, \, 3)$ and $(3, \, 5)$."
+ Maybe the correlation of V with the characteristic time scale is not so strong as that of Tj4g or ΤΗΤ., Maybe the correlation of $V$ with the characteristic time scale is not so strong as that of $\tau_{\mathrm{lag}}$ or $\tau_{\mathrm{RT}}$.
+" If our guess about the GRB luminosity relations is correct, it would be very enlightening."," If our guess about the GRB luminosity relations is correct, it would be very enlightening."
+ It suggests us to include an energy scale and a corresponding time scale for seeking more precise luminosity relations for GRBs in the future., It suggests us to include an energy scale and a corresponding time scale for seeking more precise luminosity relations for GRBs in the future.
+" However, it should be emphasized that, even if it is true, only appropriate energy and time"," However, it should be emphasized that, even if it is true, only appropriate energy and time"
+(5) and redshift.,$(b)$ and redshift.
+ In the redshift range available to Si TV outside the Lyman forest of tle compoucnts defined: in C TV are also detected in Si IV., In the redshift range available to Si IV outside the Lyman forest of the components defined in C IV are also detected in Si IV.
+ Excellent siuultaucous fits are achieved (as is obvious in Figure 1) with coupoucuts cach having the same redshift over all species. aud the same b-value for all ious of a eiven atom. but different column deusities.," Excellent simultaneous fits are achieved (as is obvious in Figure 1) with components each having the same redshift over all species, and the same $b$ -value for all ions of a given atom, but different column densities."
+ Most of the components are narrow: have b(C TV) distributed from 10 ku 4 to below |lans while have b2 20 kins 1., Most of the components are narrow: have $b$ (C IV) distributed from 10 km $^{-1}$ to below $4\ {\rm km \ s}^{-1}$ while have $b > $ 20 km $^{-1}$.
+ The distribution here is wore peaked to lower P-values than that found by Rauchof (, The distribution here is more peaked to lower $b$ -values than that found by Rauch. (
+1996) for clouds donuünautlv at lugher redshifts.,1996) for clouds dominantly at higher redshifts.
+ Particularly for the stronger components the resultant ratios of b-values for ious of different atoms. c.e.. ο /b( €. IV). are plysically realistic. aud vield a teniperature structure within the complexes coutainiug values distributed up to a few 1011. typical of photoionization heating. as ound carlicr (Raucha," Particularly for the stronger components the resultant ratios of $b$ -values for ions of different atoms, e.g., $b$ (Si $b$ (C IV), are physically realistic, and yield a temperature structure within the complexes containing values distributed up to a few $10^4$ K, typical of photoionization heating, as found earlier (Rauch."
+f 1996)., 1996).
+ A frequent feature of the svstems is the presence of a few broad. high ionization compoucuts which co-exist iu velocity space with the much more iuuerous narrow components of lower ionization.," A frequent feature of the systems is the presence of a few broad, high ionization components which co-exist in velocity space with the much more numerous narrow components of lower ionization."
+ A strong example of this. indicated with C IV aud Si IV. is shown iu Figure 1.," A strong example of this, indicated with C IV and Si IV, is shown in Figure 1."
+ Iu one display the lower ionization componcuts have been suppressed in the fitted profile leaving a very xoad component of b= 32 kaun  with two narrower components. all of which are present strongly in C IV but weak or abseut in Si IV.," In one display the lower ionization components have been suppressed in the fitted profile leaving a very broad component of $b$ = 32 km $^{-1}$ with two narrower components, all of which are present strongly in C IV but weak or absent in Si IV."
+ The converse case shows oulv the lower ionization componcuts. which now demonstrate a striking similarity between the C IV and Si IV profiles.," The converse case shows only the lower ionization components, which now demonstrate a striking similarity between the C IV and Si IV profiles."
+ Such sets ofdifferent compoucut structures must therefore be signatures of plivsically distinct but spatially closely related regions which cau be isolated in the fitting procedure., Such sets of different component structures must therefore be signatures of physically distinct but spatially closely related regions which can be isolated in the fitting procedure.
+ While the nuplicit 1iiodel in such profile constructions has ouly teiiperature aud Cassia turbulence broadening mcluded in the specific b-parameter characterising cach assumed cloud i a couples. large velocity eradieuts from bulk motions must also coutribute to the true overall absorption profile.," While the implicit model in such profile constructions has only temperature and Gaussian turbulence broadening included in the specific $b$ -parameter characterising each assumed cloud in a complex, large velocity gradients from bulk motions must also contribute to the true overall absorption profile."
+ Nouctleless. amy spectrum can be described with clustered Voigt profile fits to the accuracy required with the available signal-to-noise ratio.," Nonetheless, any spectrum can be described with clustered Voigt profile fits to the accuracy required with the available signal-to-noise ratio."
+ The broad. high ionization compoucuts revealed here thus probably represeut regions of low volume deusity dominated by bulk motions.," The broad, high ionization components revealed here thus probably represent regions of low volume density dominated by bulk motions."
+ Comparison with the results of simulations (c.g. Rauch. Tachuelt Steumuuetz 1997) is nuportaut to derive proper physical nieauiug from such observed profiles.," Comparison with the results of simulations (e.g. Rauch, Haehnelt Steinmetz 1997) is important to derive proper physical meaning from such observed profiles."
+ Figure 2 shows values ofN(S1 IV)/N(CC IV) vs redshift for all svstei components found iu the spectrum of Q1626|613 having NCC IV) 26«101«n? aud Si IV hus redwd of the Lyiuau forest.," Figure 2 shows values of N(Si IV)/N(C IV) vs redshift for all system components found in the spectrum of Q1626+643 having N(C IV) $\geq 6
+\times 10^{11}\ {\rm cm}^{-2}$ and Si IV lying redward of the Lyman forest."
+ Inuucdiately noticeable is a remarkable coherence in these values among coniponenuts in cach svstem. typically extending over a factor ouly ~10. while there are bulk differeuces between systems.," Immediately noticeable is a remarkable coherence in these values among components in each system, typically extending over a factor only $\sim 10$, while there are bulk differences between systems."
+ Sucli an ionization pattern is not predicted im recent bydrodvuamical simulations of collapsing eas structures in the Universe plotoiouized by a metagalactic, Such an ionization pattern is not predicted in recent hydrodynamical simulations of collapsing gas structures in the Universe photoionized by a metagalactic
+that the magnetic field. ecneration. and thus the magnetic and rotational properties. change when objects become fully convective at masses <0.304M. (7).,"that the magnetic field generation, and thus the magnetic and rotational properties, change when objects become fully convective at masses $<0.3-0.4\,M_{\odot}$ \citep{1997A&A...327.1039C}."
+ However. no clear change of rotation ancl activity indicators has vet been detected. at or around. this mass limit (e.g...?)..," However, no clear change of rotation and activity indicators has yet been detected at or around this mass limit \citep[e.g., ][]{1998A&A...331..581D}."
+ In addition. it is unclear what tvpe of magnetic field. is harboured by fully convective objects. and if it depends on rotation.," In addition, it is unclear what type of magnetic field is harboured by fully convective objects, and if it depends on rotation."
+ Investigating the rotational evolution and angular momentum. loss of very low mass (VLM) objects on the nmiin-sequence can contribute to clarify these issues., Investigating the rotational evolution and angular momentum loss of very low mass (VLM) objects on the main-sequence can contribute to clarify these issues.
+ An ideal laboratory to analyse the rotation of VLM niün-sequence stars is Pracsepe: With an age probably between 0.6 and O.OCCivr (seo2?) the cluster is stenificanthy: older than zero age main sequence (ZAALS) clusters like the Pleiades or a PPer.," An ideal laboratory to analyse the rotation of VLM main-sequence stars is Praesepe: With an age probably between 0.6 and Gyr \citep[see][]{1981A&A....97..235M,2002AJ....124.1570A}, the cluster is significantly older than zero age main sequence (ZAMS) clusters like the Pleiades or $\alpha$ Per."
+ At these ages. all stars have safely arrived on the main-sequence and the rotational regulation is thus dominated by magnetic wind braking. ancl not anvmore alfected by initial conditions. disk-braking. and contraction — the objects have essentially forgotten their pre-main sequence history.," At these ages, all stars have safely arrived on the main-sequence and the rotational regulation is thus dominated by magnetic wind braking, and not anymore affected by initial conditions, disk-braking, and contraction – the objects have essentially 'forgotten' their pre-main sequence history."
+ Thus. it is possible to isolate the ellect of wind braking on the rotational properties.," Thus, it is possible to isolate the effect of wind braking on the rotational properties."
+ Compared with the similarly. old. clusters Hades and Coma. Praesepe is relatively compact. vet not. too. far away (180pe.2).. allowing us deep. ellicient. observations with wicde-field. Facilities.," Compared with the similarly old clusters Hyades and Coma, Praesepe is relatively compact, yet not too far away \cite[180\,pc, ][]{1999A&A...345..471R}, allowing us deep, efficient observations with wide-field facilities."
+ Here we report on photometric monitoring for 18 members of Praesepe. which provided the first five rotation periods for members of this cluster all for objects with estimated masses below M...," Here we report on photometric monitoring for 18 members of Praesepe, which provided the first five rotation periods for members of this cluster – all for objects with estimated masses below $\,M_{\odot}$."
+ Combined with previously published: periods for vounger objects (27?).. this allow us to probe the long-term evolution of rotation in the VLM The analysis in this paper is based on two photometric time series of VLM stars in Praesepe.," Combined with previously published periods for younger objects \citep{2004A&A...419..249S,2004A&A...421..259S,2005A&A...429.1007S}, this allow us to probe the long-term evolution of rotation in the VLM The analysis in this paper is based on two photometric time series of VLM stars in Praesepe."
+ The observing strategy in both runs was similar: To mimimize internal inconsistencies in the cata and thus svstematic uncertainties. we stared? at a particular field in Praesepe.," The observing strategy in both runs was similar: To mimimize internal inconsistencies in the data and thus systematic uncertainties, we 'stared' at a particular field in Praesepe."
+ We did not ‘dither’ around a central position and made an elfort to position the field of view at the same coordinates in each observing night., We did not 'dither' around a central position and made an effort to position the field of view at the same coordinates in each observing night.
+ Therefore each object was at roughly the same pixel position on the detector throughout the run., Therefore each object was at roughly the same pixel position on the detector throughout the run.
+ The exposure time for the single frames was ssec in both runs., The exposure time for the single frames was sec in both runs.
+ Since we were interested. in. very low mass objects. which have a spectral energy distribution peaking in the near-infrared. all observations were carried out in the I-band filter.," Since we were interested in very low mass objects, which have a spectral energy distribution peaking in the near-infrared, all observations were carried out in the I-band filter."
+ The target fields were selected to maximise the number of known Praesepe members in. the field of view., The target fields were selected to maximise the number of known Praesepe members in the field of view.
+ We compiled an initial catalogue of VLM. members [rom the surveys o£ οοτι at the time of the observations (2001. 2003) essentially the complete census of the VLAL population in this cluster.," We compiled an initial catalogue of VLM members from the surveys of \citet{1995MNRAS.273..505H,1995A&AS..109...29H,1997MNRAS.287..180P,1998ApJ...497L..47M}, at the time of the observations (2001, 2003) essentially the complete census of the VLM population in this cluster."
+ For all these objects. the main criterium for cluster membership is multi-colour photometry. confirmed in many cases by proper motions and/or spectroscopy.," For all these objects, the main criterium for cluster membership is multi-colour photometry, confirmed in many cases by proper motions and/or spectroscopy."
+ According to a follow-up study by ον the contamination rate is ~θέ in the Lambly et al.," According to a follow-up study by \citet{1999MNRAS.310...87H}, the contamination rate is $\sim 10$ in the Hambly et al."
+ sample and ~50% among the (fainter) Pinfield et αἱ., sample and $\sim 50$ among the (fainter) Pinfield et al.
+ objects., objects.
+ The first. time series was obtained using the 2-m Schmidt telescope at. the. “Phtrringer Landessternwarte ‘Tautenburg (PLS. Germany). equipped with a 2048 Site CCD camera.," The first time series was obtained using the 2-m Schmidt telescope at the Thürringer Landessternwarte Tautenburg (TLS, Germany), equipped with a $2048 \times 2048$ SiTe CCD camera."
+ The wide-field camera provides a spatial resolution of 1722/pixel. resulting in an unvignetted field of view of about 0.36ssqdes.," The wide-field camera provides a spatial resolution of 2/pixel, resulting in an unvignetted field of view of about sqdeg."
+ The observations at the PLS were Carried out in two sessions in January ancl February 2001. with a gap of almost four weeks.," The observations at the TLS were carried out in two sessions in January and February 2001, with a gap of almost four weeks."
+ Thus. although we cover more than a month in total. our sensitivity to lone periods (1-4 weeks) will be limited.," Thus, although we cover more than a month in total, our sensitivity to long periods (1-4 weeks) will be limited."
+ The observations were partly allectecd by cirrus and mediocre. seeing conclitions., The observations were partly affected by cirrus and mediocre seeing conditions.
+ In total. the run. provided a time series of 125 images of the same field.," In total, the run provided a time series of 125 images of the same field."
+" The target Geld for the ‘PLS run was centred at a=S'36""753. 6=ιο. (J2000.0)."," The target field for the TLS run was centred at $\alpha = 8^h36^m53^s$, $\delta = +19^\circ 48\arcmin 24\arcsec$ (J2000.0)."
+ This Geld contains nine members from the Llambly ct al., This field contains nine members from the Hambly et al.
+ catalogue (15ο. 91. 102. 106. 115. 126. 140. 158. 151 in their nomenclature) and. (wo from the Pinfield survey (P1 and P2 in their nomenclature). plus some more higher-mass members which are saturated in our images.," catalogue (H85, 91, 102, 106, 115, 126, 140, 158, 181 in their nomenclature) and two from the Pinfield survey (P1 and P2 in their nomenclature), plus some more higher-mass members which are saturated in our images."
+ A second campaign was carried out using the wicle- imager LALCA at the 3.5-m telescope at Calar Alto Observatory [rom 23-28 Jan 2003 (in service mode)., A second campaign was carried out using the wide-field imager LAICA at the 3.5-m telescope at Calar Alto Observatory from 23-28 Jan 2003 (in service mode).
+" LALCA is à 2.2 mosaic of 4. 4Ix CCDs. which we used to ""stare at our target field in Pracsepe."," LAICA is a $2 \times 2$ mosaic of $4\times 4$ K CCDs, which we used to 'stare' at our target field in Praesepe."
+" Thus. we did not observe a continuous field. but four ""patches! of 1515). separated by gaps of similar size. in total ssqdeg at a resolution of 2/pixel."," Thus, we did not observe a continuous field, but four 'patches' of $15'\times 15'$, separated by gaps of similar size, in total sqdeg at a resolution of 22/pixel."
+ The total length of the campaign was I0 nights (scheduled as 10 half nights). but most of the first half of the run was not useful due to excessively high seeing and cloud coverage.," The total length of the campaign was 10 nights (scheduled as 10 half nights), but most of the first half of the run was not useful due to excessively high seeing and cloud coverage."
+ In the last six nights. however. we were able to obtain in total LOS images with mostly &ood quality.," In the last six nights, however, we were able to obtain in total 108 images with mostly good quality."
+ Thus. this time series will be highhy sensitive to periods up to a few davs.," Thus, this time series will be highly sensitive to periods up to a few days."
+" The LAICA run was focused on a target field at a=S40""56.57, 8=|19*32/30"" 50000). not overlapping with the PLS field."," The LAICA run was focused on a target field at $\alpha = 8^h40^m56.5^s$, $\delta = +19^\circ 32\arcmin 30\arcsec$ (J2000.0), not overlapping with the TLS field."
+ Since the LICX images are considerably deeper than the TLS data. we aimed to cover some of the faintest member candidates in the cluster.," Since the LAICA images are considerably deeper than the TLS data, we aimed to cover some of the faintest member candidates in the cluster."
+ The field thus contains six objects from the Pinfield survey (P124. 15. 16.," The field thus contains six objects from the Pinfield survey (P14, 15, 16,"
+Slo83344 was observed.,$3.1\to3.3R_*$ was observed.
+ There is no reason to believe that the same mechanisms should not lead to similar cavities in 0535|26., There is no reason to believe that the same mechanisms should not lead to similar cavities in A0535+26.
+" Curves for different ol valuesrane, assume I2,=14.78. and Al,=26M. (Vaccaetal.1996). based. upon an O9.ΤΗΙΟ classification: note the star's volume produces a ""cavity of riusΞMIS.", Curves for different values of $r_{inner}$ assume $R_*=14.7R_\odot$ and $M_*=26M_{\odot}$ \cite{vacca1996} based upon an O9.7IIIe classification; note the star's volume produces a 'cavity' of $r_{inner}=1R_*$.
+" Note that resonances are with the orbital beat frequeney of 4,=103 days rather than the orbital period of δι2111 cays for reasons discussed in Section 7.. though this has a minimal elect."," Note that resonances are with the orbital beat frequency of $P_{beat}=103$ days rather than the orbital period of $P_{orb}\simeq111$ days for reasons discussed in Section \ref{section:periods}, though this has a minimal effect."
+ Of the three Ht photometric wavebands Ix has. the largest optical depth ancl most closely approximates the optically thick assumption., Of the three IR photometric wavebands K has the largest optical depth and most closely approximates the optically thick assumption.
+ Photospheric emission. is also minimized in this band. so the Αηdis data are used hereon. though all wavebands vield similar results.," Photospheric emission is also minimized in this band, so the $\Delta m_K^{disc}$ data are used hereon, though all wavebands yield similar results."
+ Table 2/— and Figure 2. vield a value for zin of 0.60: consulting Figure 32 this suggests a central cavity Pie£I&4.3 taking states A and D to be truncated at 6:1 and 5:1 respectively., Table \ref{tab:fluxquant} and Figure \ref{fig:a0535phothisto} yield a value for $\Delta m_K^{disc}$ of 0.60; consulting Figure \ref{fig:cavity} this suggests a central cavity $r_{inner}/R_*\simeq 4.3$ taking states A and B to be truncated at 6:1 and 5:1 respectively.
+" Whilst the various assumptions make this only an approximate result. M, and H. are sulliciently well determined.to vield maximum errors in. Minerff, Of ~30X requiring a central cavity to be present."," Whilst the various assumptions make this only an approximate result, $M_*$ and $R_*$ are sufficiently well determinedto yield maximum errors in $r_{inner}/R_*$ of $\sim30\%$ requiring a central cavity to be present."
+ Lack of isothermality will cause Minner tO be underestimated if as expected: Piss. decreases racially., Lack of isothermality will cause $r_{inner}$ to be underestimated if as expected $T_{disc}$ decreases radially.
+ Departures from. optical thickness will primarily alect the outer disc anc will have the same ellect., Departures from optical thickness will primarily affect the outer disc and will have the same effect.
+ This result is in encouraging agreement with the central cavities observed in 4Cen. whereas using radii for dwarves vields VinnerfDisc7.5.," This result is in encouraging agreement with the central cavities observed in $\eta~Cen$, whereas using radii for dwarves yields $r_{inner}/R_*\simeq 7.5$."
+ This result therefore supports the giant (LLL) classification., This result therefore supports the giant (III) classification.
+ IR. photometry (Persietal.1979).. and the my data presented hy Lyuty and Zaitseva (2000).. suggest that the disc was in an even brighter state (€) from the carly LOTOs until 1980. (see Table 2)).," IR photometry \cite{persi1979}, and the $m_V$ data presented by Lyuty and tseva \shortcite{lyuty2000}, suggest that the disc was in an even brighter state (C) from the early 1970s until 1980 (see Table \ref{tab:fluxquant}) )."
+ Optically thick emission. in the IR. bands requires this to have been a physically larger cise., Optically thick emission in the IR bands requires this to have been a physically larger disc.
+ As Okazaki and Neguerucela (2001) note. truncation at ΠKe places the outer edge of the «isc mareinally outside the 3e star Roche lobe at. periastron. and thus represents the largest stable disc state.," As Okazaki and Negueruela \shortcite{natural2001} note, truncation at 4:1 places the outer edge of the disc marginally outside the Be star Roche lobe at periastron, and thus represents the largest stable disc state."
+ The identity of state C with this 4:1 truncation. and thus states D and A with 5:1 and 6:1. is appealing as it explains the prodigious X-ray activity of the system during the 1970s. periastric Roche lobe overflow alone enabling accretion and. X-ray activity (Okazakianc 2001).," The identity of state C with this 4:1 truncation, and thus states B and A with 5:1 and 6:1, is appealing as it explains the prodigious X-ray activity of the system during the 1970s, periastric Roche lobe overflow alone enabling accretion and X-ray activity \cite{natural2001}."
+. leentifving state C with a 3:1 truncation places much of the disc outside the Be star Roche lobe a periastron. preventing sability. anc requires an unrealistic viscosity (Okazakietal.2002).," Identifying state C with a 3:1 truncation places much of the disc outside the Be star Roche lobe at periastron preventing stability, and requires an unrealistic viscosity \cite{okazaki2002}."
+. ligure 3 shows tha a change in truncation between 5: and 4:1 (state C) will produce a zmdiscg0.56 and thus ' ↓≻↓⋅∢⊾∠⇂⊔∼↿⊳∖⋯∆∣≥≼≻⋅↖∖≤⋗dis⋅ or state C. in excellen agreenien with. the isolated. measurement of mydis/=6.94X0.03 in the literature (Table 2)).," Figure \ref{fig:cavity} shows that a change in truncation between 5:1 and 4:1 (state $\to$ C) will produce a $\Delta m_K^{disc}\approx0.56$ and thus predicts $m_K^{disc}\simeq6.89$ for state C, in excellent agreement with the isolated measurement of $m_K^{disc}=6.94\pm0.03$ in the literature (Table \ref{tab:fluxquant}) )."
+ Lt should be noted here that the strongly shephoerdec structure of a truncated disc. leads to highly stable continuum fluxes - this is discussed in Section 7.., It should be noted here that the strongly shepherded structure of a truncated disc leads to highly stable continuum fluxes - this is discussed in Section \ref{section:periods}. .
+ Figure daa plots mi vs. between 1987 and 2001., Figure \ref{fig:a0535correlation1}a a plots $m_K$ vs. between 1987 and 2001.
+ For each measurement of the closest photometric my measurement - always within 30 davs and mostly within 10, For each measurement of the closest photometric $m_K$ measurement - always within 30 days and mostly within 10
+with the same random. seed of the non-Gaussian one. and use it to compute the theoretical expectation.,"with the same random seed of the non-Gaussian one, and use it to compute the theoretical expectation."
+ This is repeated for the entire set of non-Gaussian realizations., This is repeated for the entire set of non-Gaussian realizations.
+ The procedure is essentially the CALB analogous of what has been proposed by Seljak (2009) for the LSS., The procedure is essentially the CMB analogous of what has been proposed by Seljak (2009) for the LSS.
+ In fact. in this way the cosmic variance effect is completely. cancelled: even at πι=100. a clustering analysis would then provide ~5'4 dilference at the Doppler peak with respect to the Gaussian Case.," In fact, in this way the cosmic variance effect is completely cancelled; even at $f_{\rm NL}=100$, a clustering analysis would then provide $\sim 5\%$ difference at the Doppler peak with respect to the Gaussian case."
+ The situation described: here is clearly ideal. because only the first. procedure. (Left. panels in. Figure. 10)). can be performed. from a real dataset.," The situation described here is clearly ideal, because only the first procedure (left panels in Figure \ref{clustering_smart_smarter_test_fig}) ) can be performed from a real dataset."
+ However. it provides some important insights: cosmic variance is the real limit and. obstacle within this statistical framework.," However, it provides some important insights: cosmic variance is the real limit and obstacle within this statistical framework."
+ If we could somehow control the Ductuations in the m-mocdes. then the excursion set. analysis would. provide a powerful. tool to detect non-Gaussianity.," If we could somehow control the fluctuations in the $m$ -modes, then the excursion set analysis would provide a powerful tool to detect non-Gaussianity."
+ The problem is that the €MD alone does not allow one to compare ‘tracers’ at different epochs (as for the LSS case). and so to eliminate completely. the ellect of cosmic variance.," The problem is that the CMB alone does not allow one to compare `tracers' at different epochs (as for the LSS case), and so to eliminate completely the effect of cosmic variance."
+ We have extended and applied the statistics of the excursion sets to models with primordial non-Caussianity of the (νι ocal type., We have extended and applied the statistics of the excursion sets to models with primordial non-Gaussianity of the $f_{\rm NL}$ local type.
+ While in presence of Gaussian initial conditions many statistics based on geometrical. and topological woperties of the CAIB temperature have been developed and. well-stuclied. to date fewer analyses have been focused on geometrical properties of the CMD. radiation in the oesence of primordial non-Gaussianity.," While in presence of Gaussian initial conditions many statistics based on geometrical and topological properties of the CMB temperature have been developed and well-studied, to date fewer analyses have been focused on geometrical properties of the CMB radiation in the presence of primordial non-Gaussianity."
+ In. particular. our work is the first extension of the excursion set formalism to ocal fee tvpe non-Ciaussianity.," In particular, our work is the first extension of the excursion set formalism to local $f_{\rm NL}$ type non-Gaussianity."
+ From a large set of simulated full-sky non-CGiaussian maps. we computed the number density anc the spatial clustering of CAIB patches above/below a temperature hreshold (Section 3)).," From a large set of simulated full-sky non-Gaussian maps, we computed the number density and the spatial clustering of CMB patches above/below a temperature threshold (Section \ref{NG maps
+analysis}) )."
+ We found that a positive value of fice enhances the number density of the cold CMD excursion sets (Figures 3.. 4)) along with their clustering strength (Figures Te 8)) and reduces that of the hot ones.," We found that a positive value of $f_{\rm NL}$ enhances the number density of the cold CMB excursion sets (Figures \ref{nd_smart_scale_fig}, , \ref{nd_difference_ratio_fig}) ) along with their clustering strength (Figures \ref{clustering_fig}, \ref{clustering_difference_ratio_fig}) ) and reduces that of the hot ones."
+ We performed a thorough statistical analysis to evaluate he sensitivity of the two observables to the level of non-CGaussianity and to the smoothing resolution., We performed a thorough statistical analysis to evaluate the sensitivity of the two observables to the level of non-Gaussianity and to the smoothing resolution.
+ We also srovidleck the analytical formalism to interpret. our results (Section 2))., We also provided the analytical formalism to interpret our results (Section \ref{NG theory}) ).
+ Expressions for the one- ancl two-cimensional PDES (Equations 15 and 21)) were obtained from a »erturbative approach by the multidimensional Edgeworth expansion around a Gaussian distribution function. and used o characterize the abundance and. clustering statistics as a function of [κι (equations 13... 16... 24)).," Expressions for the one- and two-dimensional PDFs (Equations \ref{one_d_pdf_fnl}
+ and \ref{2d_edge_eq}) ) were obtained from a perturbative approach by the multidimensional Edgeworth expansion around a Gaussian distribution function, and used to characterize the abundance and clustering statistics as a function of $f_{\rm NL}$ (Equations \ref{nd_fnl_eq}, \ref{corr_smart}, , \ref{corr_smart_gauss}) )."
+ We showed hat there are optimal thresholds which maximize the local [xL non-Gaussianity Gv=0.25.0.50 and v=2.00.2.25). as well as others (v=1.00) which do not allow for a distinction between the Gaussian. and. the non-Gaussian signals (Figures 5. and 9)).," We showed that there are optimal thresholds which maximize the local $f_{\rm NL}$ non-Gaussianity $\nu
+= 0.25, 0.50$ and $\nu=2.00, 2.25$ ), as well as others $\nu=1.00$ ) which do not allow for a distinction between the Gaussian and the non-Gaussian signals (Figures \ref{nd_sigma_distances_fig} and \ref{clustering_sigma_units_fig}) )."
+ We devised a new statistical test based of the number density. (Section 3.2)). which combines two thresholds where departures from Caussianity are most significant (Figure 6 and Equation 27)).," We devised a new statistical test based of the number density (Section \ref{nd_stat_subsection}) ), which combines two thresholds where departures from Gaussianity are most significant (Figure \ref{nd_combined_fig} and Equation \ref{nd_composite_eq}) )."
+ We also proposed a new procedure aimed at minimizing the elect of cosmic variance (Section 3.4)). which involves the clustering information alone (Figure 10.. Equations 30. ancl 31)).," We also proposed a new procedure aimed at minimizing the effect of cosmic variance (Section \ref{clustering_stat_subsection}) ), which involves the clustering information alone (Figure \ref{clustering_smart_smarter_test_fig}, Equations \ref{cf_test_smart_hp_eq} and \ref{cf_test_smart_cp_eq}) )."
+ Alrough we focused here on. fxp models of the local vpe. the statistical tools developed are more general and can x applied to describe any other tvpe of non-Caussianity.," Although we focused here on $f_{\rm NL}$ models of the local type, the statistical tools developed are more general and can be applied to describe any other type of non-Gaussianity."
+" A typical example is represented. by the curvaton moclel. or which the cubic term indicated: as ονι can be larec. while {νι can be negligible,"," A typical example is represented by the curvaton model, for which the cubic term indicated as $g_{\rm NL}$ can be large, while $f_{\rm NL}$ can be negligible."
+ Our technique can be applied ο this case as well. and it is the subject of a forthcoming xublication.," Our technique can be applied to this case as well, and it is the subject of a forthcoming publication."
+ This work was primarily motivated. by our previous incline (Rossi et al., This work was primarily motivated by our previous finding (Rossi et al.
+ 2009). namely a remarkable cdillerence in the clustering of hot and cold. pixels at relatively small angular scales from the WALADP 5-vr data.," 2009), namely a remarkable difference in the clustering of hot and cold pixels at relatively small angular scales from the WMAP 5-yr data."
+ We analyzed the »ossibilitv that this discrepancy may. arise from. primordial non-Gaussianity of the local [νι type (Section 3.3)). and concluded that only a large value of fxn would: provide such a ilference (Figure 7)).," We analyzed the possibility that this discrepancy may arise from primordial non-Gaussianity of the local $f_{\rm NL}$ type (Section \ref{clustering_subsection}) ), and concluded that only a large value of $f_{\rm NL}$ would provide such a difference (Figure \ref{clustering_fig}) )."
+ Cosmic. variance plays a crucial role within this statistical framework. so that the Gaussian. correlation function of the excursion sets is not easily clistinguishable from the non-CGaussian one. contrary to what was previously thought.," Cosmic variance plays a crucial role within this statistical framework, so that the Gaussian correlation function of the excursion sets is not easily distinguishable from the non-Gaussian one, contrary to what was previously thought."
+ In fact. while a clistinet signature in the clustering of hot and. cold. pixels. clearly emerges for a large {κι non-CGaussianityv.. particularly. at angular scales of about 75 aremin (around. the Doppler peak). as expected this feature is reduced when {κι=100.," In fact, while a distinct signature in the clustering of hot and cold pixels clearly emerges for a large $f_{\rm NL}$ non-Gaussianity, particularly at angular scales of about 75 arcmin (around the Doppler peak), as expected this feature is reduced when $f_{\rm NL}=100$."
+ The clustering behavior is also stronely alleetec by the smoothing angle., The clustering behavior is also strongly affected by the smoothing angle.
+ These findings suggest that Caussianity itself cannot be accurately constrained [rom the exeursion set clustering statistics., These findings suggest that Gaussianity itself cannot be accurately constrained from the excursion set clustering statistics.
+ In fact. if in principle the use of pixel-pixel correlation functions as a test of Gaussianity is very powerful. because there are no free parameters once the uncerlving power spectrum has been measured. this may no be thecase if the non-Gaussian model is of the {νι loca type. ancl fixe is small.," In fact, if in principle the use of pixel-pixel correlation functions as a test of Gaussianity is very powerful, because there are no free parameters once the underlying power spectrum has been measured, this may not be thecase if the non-Gaussian model is of the $f_{\rm NL}$ local type, and $f_{\rm NL}$ is small."
+Our study was focused. on a few selected: values of thresholds and two different statistics. so that the predicte,"Our study was focused on a few selected values of thresholds and two different statistics, so that the predicted"
+survey are shown in Fie. L.,"survey are shown in Fig. \ref{fig:CMD},"
+ together with all available photometric data of surveved non-members., together with all available photometric data of surveyed non-members.
+ Photometry or the fainter stars is from) a new catalogue (Jeffries. Thurstou and IEuublv. in preparation). wlile for stars xieshter than V~€ dt is a collection of data comiue rol various sources (cf. Jeffriesetal. 19973).," Photometry for the fainter stars is from a new catalogue (Jeffries, Thurston and Hambly, in preparation), while for stars brighter than $V \sim 9$ it is a collection of data coming from various sources (cf. \cite{JTP97}) )."
+ Cluster uecnmbership has been assigned by selecting stars witlin xuids around fiducial main sequences in IIR. diagrams of Vows. (BV) and V vs. (VI). following a procedure described by Thurston (2000) aud reportec by Tarucden et al. (," Cluster membership has been assigned by selecting stars within bands around fiducial main sequences in HR diagrams of $V$ vs. $(B-V)$ and $V$ vs. $(V-I)$, following a procedure described by Thurston (2000) and reported by Harnden et al. ("
+20003.,2000).
+ Our final list comprises those stars fulfilling oue of the abovecriteria®.. schien all three colors are available. aud the V vs. (V.I) criterion aloue. for the reddest stars having no (5.V) neasureient.," Our final list comprises those stars fulfilling one of the above, when all three colors are available, and the $V$ vs. $(V-I)$ criterion alone, for the reddest stars having no $(B-V)$ measurement."
+" Iu suWary, woe have 510 likely xXiotonmietrie menibers out of 1117 objects with known photometry aud falling in the field-of-view (FOV)."," In summary, we have 540 likely photometric members out of 4117 objects with known photometry and falling in the field-of-view (FOV)."
+ Table 2 eives the ummber of 10e1ibers observed aud detected (Cu the detected faction) grouped according to spectral types (B. dA. dF. dC dix. and dAL) photometrically assigned on the basis of reddenuiug-corrected color ranges.," Table \ref{tab:stars} gives the number of members observed and detected (and the detected fraction) grouped according to spectral types (B, dA, dF, dG, dK, and dM) photometrically assigned on the basis of reddening-corrected color ranges."
+ One late-tvpe eiaut falls in the FOV and has not been detected., One late-type giant falls in the FOV and has not been detected.
+ In the same table we report also the same quantities. but for the restricted FOV iu conmunon with the survey (EHarudeuetal. 20003).," In the same table we report also the same quantities, but for the restricted FOV in common with the survey \cite{H++00}) )."
+ Identiicatious with N-rav sources lave been performed through positional matching with a match radius of LO”., Identifications with X-ray sources have been performed through positional matching with a match radius of $^{\prime\prime}$.
+ We have chosen this somewhat eenerous value to account for current limitation iu the absolute aspect reconstruction., We have chosen this somewhat generous value to account for current limitation in the absolute aspect reconstruction.
+ Indeed with a match radius smaller than 8 we would lave lost boua-fide ideutificatious., Indeed with a match radius smaller than $^{\prime\prime}$ we would have lost bona-fide identifications.
+ Over the eutiro FOV we have found 112 detections having a single cluster weber as counterpart. 16 detections having 2 mcmibers as counterparts aud 1 detection having 3 members as counterparts.," Over the entire FOV we have found 112 detections having a single cluster member as counterpart, 16 detections having 2 members as counterparts and 1 detection having 3 members as counterparts."
+ The percentage of chance coincidence between cluster members aud N-ray sources ls o making us confident on the reliability of our identification procedure.," The percentage of chance coincidence between cluster members and X-ray sources is $\sim$, making us confident on the reliability of our identification procedure."
+ The table shows also that in the cutire ΕΟΝ ~2 of surveved cluster members have been detected. while the detection fraction lnereascs to in the smaller region iu common withChandra.," The table shows also that in the entire FOV $\sim$ of surveyed cluster members have been detected, while the detection fraction increases to in the smaller region in common with."
+ We will see in the following that distinguishing between those two regions is muportaut im interpreting sole of our results., We will see in the following that distinguishing between those two regions is important in interpreting some of our results.
+ There ave 79 129) detections not associated with known cluster imeiibers., There are 79 $-$ 129) detections not associated with known cluster members.
+" We have found at least one counterpart (in the catalogue we have used) for other 39 sources, however we expect ~ 28 spurious ideutifications (bv chance coincidence) among the non-members."," We have found at least one counterpart (in the catalogue we have used) for other 39 sources, however we expect $\sim$ 28 spurious identifications (by chance coincidence) among the non-members."
+ Since we have found 81 counterparts among the non-members. about of them are likely to be spurious identifications.," Since we have found 81 counterparts among the non-members, about of them are likely to be spurious identifications."
+ AMauy of these objects. as well as the uou-icentified oues.," Many of these objects, as well as the non-identified ones,"
+The properties of the highest-density region of matter in the interior of relativistic stars have been studied to date by several different theoretical models. which yield very different macroscopic properties of compact stars.,"The properties of the highest-density region of matter in the interior of relativistic stars have been studied to date by several different theoretical models, which yield very different macroscopic properties of compact stars."
+ Many new interactions have been proposed to occur at the highest densities attained. ranging from the ocewrence of hyperons. to quark deconfinement. to the formation of kaon condensates and H-matter (see Weber. 2001: Heiselberg 2002. for recent reviews).," Many new interactions have been proposed to occur at the highest densities attained, ranging from the occurrence of hyperons, to quark deconfinement, to the formation of kaon condensates and H-matter (see Weber, 2001; Heiselberg 2002, for recent reviews)."
+ Observational constraints on pulsar properties are currently still too weak to allow to distinguish which (if any) of all the proposed theoretical descriptions of the interior of relativistic stars is the correct one., Observational constraints on pulsar properties are currently still too weak to allow to distinguish which (if any) of all the proposed theoretical descriptions of the interior of relativistic stars is the correct one.
+ A solution to the problem of determining the correct equation of state in the central region of a compact star must come from new. more accurate observations of their properties and any new observational method that will help in this direction is more than welcome.," A solution to the problem of determining the correct equation of state in the central region of a compact star must come from new, more accurate observations of their properties and any new observational method that will help in this direction is more than welcome."
+ One new observational method. that could be interesting in the case that the equation of state (EOS) features a deconfinement phase transition to quark matter. has been proposed by Glendenning. Pet and Weber (1997). (hereafter GPW).," One new observational method, that could be interesting in the case that the equation of state (EOS) features a deconfinement phase transition to quark matter, has been proposed by Glendenning, Pei and Weber (1997), (hereafter GPW)."
+ Specifically. when a rapidly rotating pulsar spins down. its central density increases with time.," Specifically, when a rapidly rotating pulsar spins down, its central density increases with time."
+ At a certain central density. a mixed quark-hadron phase can appear (or can already be present in the pulsar).," At a certain central density, a mixed quark-hadron phase can appear (or can already be present in the pulsar)."
+ For some chosen parameters of the equation of state and of the baryonic mass of the pulsar. a pure quark core appears when the pulsar reaches very high densities.," For some chosen parameters of the equation of state and of the baryonic mass of the pulsar, a pure quark core appears when the pulsar reaches very high densities."
+ In GPW., In GPW.
+ a particular spin-down sequence was studied. that in the nonrotating limit reached nearly at the maximum mass allowed by the chosen EOS.," a particular spin-down sequence was studied, that in the nonrotating limit reached nearly at the maximum mass allowed by the chosen EOS."
+ For this sequence. it was noticed that. when the pure quark core appears. the star undergoes an brief era of spin-up (brief. compared to the pulsar’s lifetime) and its braking index shows an anomalous behaviour (it becomes singular at a certain rotation rate).," For this sequence, it was noticed that, when the pure quark core appears, the star undergoes an brief era of spin-up (brief, compared to the pulsar's lifetime) and its braking index shows an anomalous behaviour (it becomes singular at a certain rotation rate)."
+ This change in the braking index has been proposed in GPW to be potentially observable., This change in the braking index has been proposed in GPW to be potentially observable.
+" The anomalous behaviour of the spin evolution is traced back to a ""backbending"" of the moment of inertia (as a function of angular velocity).", The anomalous behaviour of the spin evolution is traced back to a “backbending” of the moment of inertia (as a function of angular velocity).
+ Other authors (Hetselberge Hjorth-Jensen 1998. Chubarian et al.," Other authors (Heiselberg Hjorth-Jensen 1998, Chubarian et al."
+ 2000) have further investigated the observational consequences in the models proposed in GPW and in Glendenning and Weber (2000)., 2000) have further investigated the observational consequences in the models proposed in GPW and in Glendenning and Weber (2000).
+ In all these studies the relativistic slow-rotation approximation is In the present work. we re-investigate the deconfinement phase-transition," In all these studies the relativistic slow-rotation approximation is In the present work, we re-investigate the deconfinement phase-transition"
+(??7).,.
+. In a few possible scenarios have been put forward to explain these features. including suppressed convection due to magnetic activity. excess Hux from accretion. and. carly evolutionary stage.," In a few possible scenarios have been put forward to explain these features, including suppressed convection due to magnetic activity, excess flux from accretion, and early evolutionary stage."
+" Llere we set out to put. further constraints on the properties of EU ""au A by analysing its photometric and spectroscopic variability.", Here we set out to put further constraints on the properties of FU Tau A by analysing its photometric and spectroscopic variability.
+ This paper is mainly based on photometric time series obtained with the instruments CAPOS and BUSCA at the. 2.2mm telescopes of. the German-Spanish Astronomical Center at Calar Alto observatory., This paper is mainly based on photometric time series obtained with the instruments CAFOS and BUSCA at the m telescopes of the German-Spanish Astronomical Center at Calar Alto observatory.
+ ln Sect., In Sect.
+ 2 we discuss these observations ancl the reduction of the data., \ref{data} we discuss these observations and the reduction of the data.
+ Ehe analysis of the photometry and spectroscopy is presented in Sect., The analysis of the photometry and spectroscopy is presented in Sect.
+ 3. and 4.., \ref{phot} and \ref{spec}. .
+ In Sect., In Sect.
+ 5 we compile all available information on the variability of the system from our new observations. the literature. and archives and constrain the origin of the variations using spot mocels.," \ref{disc} we compile all available information on the variability of the system from our new observations, the literature, and archives and constrain the origin of the variations using spot models."
+ We discuss the results in the context of the two anomalies mentioned above in the final Sect. 6.., We discuss the results in the context of the two anomalies mentioned above in the final Sect. \ref{nature}.
+ Our primary photometric time series was obtained: with CAPOS at the mum telescope on Calar Alto over five nights in Nov/Dec 2010., Our primary photometric time series was obtained with CAFOS at the m telescope on Calar Alto over five nights in Nov/Dec 2010.
+ CAPOS is a2> 2k CCD camera mounted in the RC focus., CAFOS is a $2\times 2$ k CCD camera mounted in the RC focus.
+" With a pixel scale of 07553. it vives a field of view (FOV) of 16«16""."," With a pixel scale of 53, it gives a field of view (FOV) of $16'\times 16'$."
+ Phe filters. however. do not cover the full FOV: in ellect a circular FOV with diameter of ~14 can be used.," The filters, however, do not cover the full FOV; in effect a circular FOV with diameter of $\sim 14'$ can be used."
+ While the whole run was allected by dodgy. weather conditions. including bad secing. high humidity. and clouds. we obtained 62 useful images in the H-band and the same number in the I-band for our target.," While the whole run was affected by dodgy weather conditions, including bad seeing, high humidity, and clouds, we obtained 62 useful images in the R-band and the same number in the I-band for our target."
+ The final night of the run we observed. Landolt standard stars under photometric conditions for calibraton purposes (2x field. 8.92. 3x Ποιά Φιλ).," The final night of the run we observed Landolt standard stars under photometric conditions for calibraton purposes (2x field SA92, 3x field SA98)."
+ The observing log for the run is given in Table 1.., The observing log for the run is given in Table \ref{obs}.
+" FU ""Tau is located in the middle of a clark cloud devoid of stars.", FU Tau is located in the middle of a dark cloud devoid of stars.
+ Since we need non-variable field stars to calibrate the lightcurves. our FOV was not centered on FU Tau itselt.," Since we need non-variable field stars to calibrate the lightcurves, our FOV was not centered on FU Tau itself."
+" ]nsteacd. we positioned EU ""Tau in the south-west (SW) corner of the CCD. which allows us to cover a sullicient number of field. stars in the area immediately. north-east (NE) of the cloud."," Instead, we positioned FU Tau in the south-west (SW) corner of the CCD, which allows us to cover a sufficient number of field stars in the area immediately north-east (NE) of the cloud."
+ Lo minimize llatfield problems. we aimed to keep the position of the time series field as constant as possible: the olfsets between the images are <107.," To minimize flatfield problems, we aimed to keep the position of the time series field as constant as possible; the offsets between the images are $<10""$."
+" We also aimed to keep the lux level of FU ""Tau A roughly constant. i.c. we varied the exposure times to account [or changes in seeing ancl transparency."," We also aimed to keep the flux level of FU Tau A roughly constant, i.e. we varied the exposure times to account for changes in seeing and transparency."
+ For all images we carried out a standard: reduction: subtracting the average bias level and dividing by a scaled. averaged domellat.," For all images we carried out a standard reduction: subtracting the average bias level and dividing by a scaled, averaged domeflat."
+ We found that the [Iatfielding is not perfect: the resulting frames are allectecd by ai large-scale interference pattern. which might be due to water condensation on the detector window.," We found that the flatfielding is not perfect; the resulting frames are affected by a large-scale interference pattern, which might be due to water condensation on the detector window."
+ The cllect increases with the time olfset between science frames ancl domellats., The effect increases with the time offset between science frames and domeflats.
+ Therefore we obtained two sets of domellats per night and corrected the images using the Hatfield with the minimum time offset., Therefore we obtained two sets of domeflats per night and corrected the images using the flatfield with the minimum time offset.
+ Since the pattern has a spatial scale of 250° and the spatial olfsets in the time series are «LO” we clo not think that the pattern has an ellect on the lighteurves.," Since the pattern has a spatial scale of $>50""$ and the spatial offsets in the time series are $<10""$ we do not think that the pattern has an effect on the lightcurves."
+ In addition. the ρα frames show a faint. small-scale interference pattern due to nightsky emission lines. which contributes to the noise.," In addition, the I-band frames show a faint small-scale interference pattern due to nightsky emission lines, which contributes to the noise."
+" As part of the same run. we obtained 5 low-resolution spectra for FU ""Eau A. using erism R400 with a nominal resolution ofAX."," As part of the same run, we obtained 5 low-resolution spectra for FU Tau A, using grism R400 with a nominal resolution of."
+ The spectra. for EU. Tau. X were. debiasecl and backeround-subtracted by fitting a 2nd. order polynomial to cach line in the spatial direction., The spectra for FU Tau A were debiased and background-subtracted by fitting a 2nd order polynomial to each line in the spatial direction.
+ They. were extracted. dispersion-corrected and. Uux-calibrated using. stanclare routines in LAL.," They were extracted, dispersion-corrected and flux-calibrated using standard routines in IRAF."
+ Complementary time series photometry in. the I-band was obtained using BUSCA at the mim telescope on Calar Alto., Complementary time series photometry in the I-band was obtained using BUSCA at the m telescope on Calar Alto.
+ BUSCA allows to take images in four bands simultaneously. achieved through 3 dichroic beam splitters.," BUSCA allows to take images in four bands simultaneously, achieved through 3 dichroic beam splitters."
+ Our target. however. was not detected. in the three blue channels (Stromgren vhy filters): we only use the images in the reddest. channel. which corresponds to the Cousins ]-band.," Our target, however, was not detected in the three blue channels (Stromgren vby filters); we only use the images in the reddest channel, which corresponds to the Cousins I-band."
+ The observations started about a week after. the CAJFOS run and continued for another week., The observations started about a week after the CAFOS run and continued for another week.
+ Similar to the CAFOS run. parts of the observations were allected by clouds. strong winds. ancl high humidity.," Similar to the CAFOS run, parts of the observations were affected by clouds, strong winds, and high humidity."
+ No photometric calibration was carried out., No photometric calibration was carried out.
+ An Il’.11 POV centered on EU Tau was observed in 7 nights in Dec 2010. of which 5. provided usable data (see Table. 1)).," An $11'\times 11'$ FOV centered on FU Tau was observed in 7 nights in Dec 2010, of which 5 provided usable data (see Table \ref{obs}) )."
+ The FOV covers the bright. IX21ILI star 2ALASS 04232455|2500084 ancl 5-10 point sources 2mmag fainter than FU Tau A. For all images. we carried out a standard. reduction. including bias subtraction and Ilatfield correction.," The FOV covers the bright K2III star 2MASS J04232455+2500084 and 5-10 point sources mag fainter than FU Tau A. For all images, we carried out a standard reduction including bias subtraction and flatfield correction."
+ From the CAFOS time serieswe derived. R- and. I-band, From the CAFOS time serieswe derived R- and I-band
+"'The simulated galaxy has a total stellar mass of M5, an HI mass of 1.9x10? and total gas mass (within R;,) of 1.5x1019Mo.","The simulated galaxy has a total stellar mass of $1.4\times10^{10}M_{\odot}$ , an HI mass of $1.9\times10^{9}M_{\odot}$ and a total gas mass (within $_{vir}$ ) of $1.5\times10^{10}M_{\odot}$."
+ The Mcvalue log(M(HT)/Lg)a=—0.8 fits right in the middle of the relation for observed galaxies Verheijen et al (2010)., The value $log(M(HI)/L_R)=-0.8$ fits right in the middle of the relation for observed galaxies Verheijen et al (2010).
+" The disc has a metallicity which peaks at [Fe/H]=—0.5, while the cold gas has O/H+12=8.25."," The disc has a metallicity which peaks at $[Fe/H]=-0.5$, while the cold gas has $O/H+12=8.25$."
+ The simulated galaxy's merger history is referred to in the analysis which follows., The simulated galaxy's merger history is referred to in the analysis which follows.
+" The interaction of the last major merger (mass ratio 2:1) begins at z~2.7, with coalescence finished by z~2.2 and is followed rapidly by 2 other significant merger events (mass ratios of 10:1 and 20:1)."," The interaction of the last major merger (mass ratio 2:1) begins at $z\sim2.7$, with coalescence finished by $z\sim2.2$ and is followed rapidly by 2 other significant merger events (mass ratios of 10:1 and 20:1)."
+ We identify the period between z=2.7 and z=1.7 as the galaxy’s “merger epoch”.," We identify the period between $z=2.7$ and $z=1.7$ as the galaxy's “merger epoch""."
+" Since z~1.7, several dark matter merger events occur, but these are too low in mass to contain baryons."," Since $z\sim1.7$, several dark matter merger events occur, but these are too low in mass to contain baryons."
+" In Figure 1,, we plot the surface brightness profile at z=0 in the SDSS g-band, shown face-on and edge-on."," In Figure \ref{gband}, we plot the surface brightness profile at $z=0$ in the SDSS g-band, shown face-on and edge-on."
+ The loose spiral arms are indicative of a late type galaxy., The loose spiral arms are indicative of a late type galaxy.
+" The existence of a bar is also evident, and we contend that the simulated galaxy would be classified as SBc/d. These surface profile maps were created with Sunrise (?) which allows us to measure the dust reprocessed spectral energy distribution (SED) of every resolution element of our simulated galaxies from the far UV to the far IR with a full 3D treatment of radiative transfer."," The existence of a bar is also evident, and we contend that the simulated galaxy would be classified as SBc/d. These surface profile maps were created with Sunrise \citep{jonsson06} which allows us to measure the dust reprocessed spectral energy distribution (SED) of every resolution element of our simulated galaxies from the far UV to the far IR with a full 3D treatment of radiative transfer."
+" We assume a simple relationship between metallicity of gas, which is traced in the simulations, and dust by using a constant dust-to metals ratio of 0.4 ?.."," We assume a simple relationship between metallicity of gas, which is traced in the simulations, and dust by using a constant dust-to metals ratio of 0.4 \cite{dwek98}."
+ Filters mimicking those on major telescopes are used to create mock observations., Filters mimicking those on major telescopes are used to create mock observations.
+" Sunrise uses Monte Carlo techniques to calculate radiation transfer through astronomical dust, including such effects in the determination of SEDs."," Sunrise uses Monte Carlo techniques to calculate radiation transfer through astronomical dust, including such effects in the determination of SEDs."
+" The galaxy sits in the blue cloud in the Mg, u-g colour magnitude diagram of SDSS galaxies, reproduced from ? in Figure 2,, with the trend lines of the blue and red clouds indicated."," The galaxy sits in the blue cloud in the $_g$, $u$ $g$ colour magnitude diagram of SDSS galaxies, reproduced from \cite{blanton06} in Figure \ref{colmag}, with the trend lines of the blue and red clouds indicated."
+" The simulated galaxy is shown as star symbols; the light blue star shows the face-on values, while the dark blue stars show various angles of inclination (0°, 30°, 45°, 60° and 90°), with greater inclination resulting in redder colours and lower magnitudes."," The simulated galaxy is shown as star symbols; the light blue star shows the face-on values, while the dark blue stars show various angles of inclination $^{\circ}$, $^{\circ}$, $^{\circ}$, $^{\circ}$ and $^{\circ}$ ), with greater inclination resulting in redder colours and lower magnitudes."
+ The inclusion of the effects of dust reprocessing explains thesignificantly lower luminosity and redder colour of the simulation when seen edge-on., The inclusion of the effects of dust reprocessing explains thesignificantly lower luminosity and redder colour of the simulation when seen edge-on.
+ The rotation curve (V.=Mn) of the simulation is shown in Fig., The rotation curve $_c=\sqrt{\frac{M(<r)}{r}}$ ) of the simulation is shown in Fig.
+" 3 at z—0 (blue line), z—0.4 (green) and z=1 (red)."," \ref{RC} at $z=0$ (blue line), $z=0.4$ (green) and $z=1$ (red)."
+ Also shown are the contributions from stars (dotted lines) and dark matter (dashed) at those times., Also shown are the contributions from stars (dotted lines) and dark matter (dashed) at those times.
+ The flat curve at z=1 reflects the success of our simulation in preventing excessive star formation in the central regions during the merger epoch., The flat curve at $z=1$ reflects the success of our simulation in preventing excessive star formation in the central regions during the merger epoch.
+" The z=0 curve is not perfectly flat, and perhaps indicates that the secular processes which build the bulge may be too efficient, and also indicates that, despite significant improvements, our simulations do not yet exactly reproduce the mass distribution of real galaxies."," The $z=0$ curve is not perfectly flat, and perhaps indicates that the secular processes which build the bulge may be too efficient, and also indicates that, despite significant improvements, our simulations do not yet exactly reproduce the mass distribution of real galaxies."
+" We plot the observed Tully-Fisher relation using data from ? who plot the SDSS i-band magnitudes against Vago, the rotation velocity at the radius which encompass 80% of the i-band flux (open squares)."," We plot the observed Tully-Fisher relation using data from \cite{pizagno07} who plot the SDSS i-band magnitudes against $_{80}$, the rotation velocity at the radius which encompass $\%$ of the i-band flux (open squares)."
+" Our simulated galaxy is overplotted using star symbols, where we show Vgo (red star) to mimic the observations, as well as Vmaz (blue star), to show that the degree of the inner peak in our rotation curve is not “catasptrophic”."," Our simulated galaxy is overplotted using star symbols, where we show $_{80}$ (red star) to mimic the observations, as well as $_{max}$ (blue star), to show that the degree of the inner peak in our rotation curve is not “catasptrophic""."
+" Also overplotted as triangles is the recent “Eris” simulation (?),, with colours again indicating Vgo (red triangle) and Vmaz (blue triangle)."," Also overplotted as triangles is the recent “Eris"" simulation \citep{guedes11}, with colours again indicating $_{80}$ (red triangle) and $_{max}$ (blue triangle)."
+" Using similar inputs physics and resolution to our simulation, *Eris"" also has a good fit to the Tully-Fisher relation which does not depend on the radius at which the measurement is made."," Using similar inputs physics and resolution to our simulation, “Eris"" also has a good fit to the Tully-Fisher relation which does not depend on the radius at which the measurement is made."
+" The SDSS i-band surface brightness maps of the simulation at redshit z=1 (left), z=0.4 (middle) and z=0 (right) are shown in Fig 5,, with the surface brightness range indicated in the colour bar."," The SDSS i-band surface brightness maps of the simulation at redshit $z=1$ (left), $z=0.4$ (middle) and $z=0$ (right) are shown in Fig \ref{Iband}, with the surface brightness range indicated in the colour bar."
+ Note the inside out growth of the disc and the strong bar which has developed by z—0.4., Note the inside out growth of the disc and the strong bar which has developed by $z=0.4$.
+" 'The 2nd mode of the Fourier harmonics of the simulations is shown in Fig 6,, confirming that no bar exists at z—1, but a strong bar with h,/h,~1.2 has formed by z=0.4 (where hy is the bar length and h, is the disc scale length)."," The 2nd mode of the Fourier harmonics of the simulations is shown in Fig \ref{fourier}, confirming that no bar exists at $z=1$, but a strong bar with $h_b/h_l\sim1.2$ has formed by $z=0.4$ (where $h_b$ is the bar length and $h_l $ is the disc scale length)."
+ The bar weakens somewhat by z=0., The bar weakens somewhat by $z=0$.
+" In the three panels of Fig 7,, we show the decompositions of the SDSS i-band surface brightness maps from Fig 5.."," In the three panels of Fig \ref{profiles}, , we show the decompositions of the SDSS i-band surface brightness maps from Fig \ref{Iband}."
+" Note that all these one dimensional profile fits were cross-checked GALFIT (?),, producing similar results."," Note that all these one dimensional profile fits were cross-checked GALFIT \citep{peng10}, producing similar results."
+" At z—1 (left panel), the simulation has formed a pure disc galaxy, best fit by a single Sérrsic profile having Sérrsic index n— 1.1."," At $z=1$ (left panel), the simulation has formed a pure disc galaxy, best fit by a single Sérrsic profile having Sérrsic index $n=1.1$ ."
+ Recall that this is ~2 Gyrs since the last significant merger event., Recall that this is $\sim$ 2 Gyrs since the last significant merger event.
+ At z=0.4 (middle panel) and z=0 (right panel)we fit a bulge+bar+disc., At $z=0.4$ (middle panel) and $z=0$ (right panel)we fit a bulge+bar+disc.
+" Also shown in the panels are the fit parameters, i.e. disc scale-length (h) and central"," Also shown in the panels are the fit parameters, i.e. disc scale-length (h) and central"
+"per night for P'TF, it is clearly not feasible to present candidates to human scanners to determine the reality of every candidate.","per night for PTF, it is clearly not feasible to present candidates to human scanners to determine the reality of every candidate."
+" To keep data volumes small enough to be human-scanned, several options are available."," To keep data volumes small enough to be human-scanned, several options are available."
+" First, restrict the candidates to a certain domain-specific set."," First, restrict the candidates to a certain domain-specific set."
+" For example, scanning only those candidates that are near but offset from extended galaxies will generally succeed at finding some supernovae (and ignore most variable stars), but it will fail to find supernovae far from their host galaxy, supernova associated with low-luminosity hosts, and supernovae near the centers of galaxies (cf., Sullivanetal. 2011))."," For example, scanning only those candidates that are near but offset from extended galaxies will generally succeed at finding some supernovae (and ignore most variable stars), but it will fail to find supernovae far from their host galaxy, supernova associated with low-luminosity hosts, and supernovae near the centers of galaxies (cf., \citealt{2011ApJ...732..118S}) )."
+" There are active areas of research in all three of these cases (e.g., Milleretal. 2010))."," There are active areas of research in all three of these cases (e.g., \citealt{2010AJ....139.2218M}) )."
+" Second, require several candidates to appear at or near the same location on several epochs."," Second, require several candidates to appear at or near the same location on several epochs."
+" This is indeed good at mitigating against cosmic rays and other transient artifacts, but mis-subtractions tend to correlate at the same locations even at different epochs (that is, when a subtraction is bad at some position on the sky at some epoch, there is an increased tendency for it to be bad at other epochs)."," This is indeed good at mitigating against cosmic rays and other transient artifacts, but mis-subtractions tend to correlate at the same locations even at different epochs (that is, when a subtraction is bad at some position on the sky at some epoch, there is an increased tendency for it to be bad at other epochs)."
+ This approach also runs the risk of waiting until too late to identify a (short-lived) astrophysical transient., This approach also runs the risk of waiting until too late to identify a (short-lived) astrophysical transient.
+" Third, impose restrictive threshold cuts on the derived parameters of the candidate and the subtraction, such as requiring a 30-c detection with a shape that is well-fit by the inferred PSF of the image."," Third, impose restrictive threshold cuts on the derived parameters of the candidate and the subtraction, such as requiring a $\sigma$ detection with a shape that is well-fit by the inferred PSF of the image."
+" But, since most (real) candidates occur near the detection threshold and there is no guarantee that highly significant flux differences are all due to real astrophysical events, this approach will systematically exclude the lion's share of real events."," But, since most (real) candidates occur near the detection threshold and there is no guarantee that highly significant flux differences are all due to real astrophysical events, this approach will systematically exclude the lion's share of real events."
+ Our approach—to remove the human element in any real-time decision processes—is to use machine learning to provide a statistical statement about whether a given candidate should be considered astrophysically real or spuriously bogus., Our approach—to remove the human element in any real-time decision processes—is to use machine learning to provide a statistical statement about whether a given candidate should be considered astrophysically real or spuriously bogus.
+" Such statements can then be combined over several epochs, if required, to determine if that identified candidate should be considered adiscovery of an astrophysical source."," Such statements can then be combined over several epochs, if required, to determine if that identified candidate should be considered a of an astrophysical source."
+" To arrive at deterministic statements about each candidate, there are three broad classes of inputs that can be used to create a ""labelled"" set of candidates for use in the machine training: use trained/expert human scanners to opine on the real/bogus nature of a subset of the candidates, add a set of artificial sources to the raw data, or construct a ground-truth labelled set by using knowledge of which candidates turned out to real based on follow-up observations (e.g., using spectroscopically identified supernovae) of earlier incarnations of the survey."," To arrive at deterministic statements about each candidate, there are three broad classes of inputs that can be used to create a “labelled” set of candidates for use in the machine training: use trained/expert human scanners to opine on the real/bogus nature of a subset of the candidates, add a set of artificial sources to the raw data, or construct a ground-truth labelled set by using knowledge of which candidates turned out to real based on follow-up observations (e.g., using spectroscopically identified supernovae) of earlier incarnations of the survey."
+ Each labeling approach inheres advantages and drawbacks:, Each labeling approach inheres advantages and drawbacks:
+fluctuations iu the hieher resolution ruus. but these are eenerallv smaller iu amplitude and less miportant for deteriuuiug the overall mean.,"fluctuations in the higher resolution runs, but these are generally smaller in amplitude and less important for determining the overall mean."
+ Nevertheless. it is clear that one must average over relatively long baselimes to obtain a representative value. making higher resolutious prohibitively expensive.," Nevertheless, it is clear that one must average over relatively long baselines to obtain a representative value, making higher resolutions prohibitively expensive."
+ A power spectral analysis of the magnetic field also indicates couvergence. at least for the large scales where most of the power resides.," A power spectral analysis of the magnetic field also indicates convergence, at least for the large scales where most of the power resides."
+ Fievure 3. shows the averaged PSD for the S32R1Z SGIRIZI. and 91958121 sinuulations.," Figure \ref{f:pscomp} shows the averaged PSD for the S32R1Z4, S64R1Z4, and S128R1Z4 simulations."
+ We average over 1.spherical shells iu A-space (SEC refft)) and in fiue. excluding the first 50 orbits to avoid the initial trausicuts.," We average over spherical shells in $k$ -space (see \\ref{fft}) ) and in time, excluding the first 50 orbits to avoid the initial transients."
+ There is a significaut drop In power in eoine from the 32//I to GI/II resolution runs. combined with a shift in the peak of PSD to larger k.," There is a significant drop in power in going from the $32/H$ to $64/H$ resolution runs, combined with a shift in the peak of PSD to larger $k$."
+ Wowever. when going from 61/77 to 128/77. there is sienificautly simaller drop iu amplitude at most scales and a auch simaller shift in the peak wave number. also inclicating convergence.," However, when going from $64/H$ to $128/H$, there is significantly smaller drop in amplitude at most scales and a much smaller shift in the peak wave number, also indicating convergence."
+ Although we focus on the magnetic energv density. a simular convergence is observed iu the PSD of the kinetic energv deusitv.," Although we focus on the magnetic energy density, a similar convergence is observed in the PSD of the kinetic energy density."
+ We show a comparison of the kinetic and magnetic enorev deusity PSDs for rui 51258111 in Figure [L., We show a comparison of the kinetic and magnetic energy density PSDs for run S128R1Z4 in Figure \ref{f:psmeke}.
+ It is notable that power iu the magnetic Ποια fluctuations exceeds that of the kinetic euergy at all scales., It is notable that power in the magnetic field fluctuations exceeds that of the kinetic energy at all scales.
+ This is in coutrast to unstrati&ed runs which vpical show ereater power in the kinetic euergv at the owest &. with maeuetic energv dominating the power at higher À.," This is in contrast to unstratified runs which typical show greater power in the kinetic energy at the lowest $k$, with magnetic energy dominating the power at higher $k$."
+ It also differs from sinulatious of helically driven turbulence where the kinetic and magnetic energy lave comparable amplitude at all but the lowest & where naenetic energy dominates (Draudeuburg2001)., It also differs from simulations of helically driven turbulence where the kinetic and magnetic energy have comparable amplitude at all but the lowest $k$ where magnetic energy dominates \citep{bra01}.
+. The convergent behavior of the stratified rus should )o contrasted with that of the unstratified simulations shown in Figure 5.., The convergent behavior of the stratified runs should be contrasted with that of the unstratified simulations shown in Figure \ref{f:psun}. .
+ This plot shows the PSD for four uustratified ruus with resolutions of32/IT. 61/IT. 128/IT. and 256/77 in I7«UTII shearing boxes.," This plot shows the PSD for four unstratified runs with resolutions of $32/H$, $64/H$, $128/H$, and $256/H$ in $H \times 4H
+\times H$ shearing boxes."
+ Each factor of two merease in resolution results in a decrease by nearly a factor of two in the integrated power., Each factor of two increase in resolution results in a decrease by nearly a factor of two in the integrated power.
+ There is also a shift iu the peak wavemuuber to laveer & as resolution increases., There is also a shift in the peak wavenumber to larger $k$ as resolution increases.
+ This lack of convergence is ahnost identical to the that found by previous authors (Fromaug&Pa-paloizou2007:Chuanetal.2009:Simon 2009).," This lack of convergence is almost identical to the that found by previous authors \citep{fp07,gua09,shb09}."
+. It seems that both the power aud characteristic scale of the turbulence are set by the domain resolution., It seems that both the power and characteristic scale of the turbulence are set by the domain resolution.
+ Adding stratification appears to fundamentally change the cywnamics and provides a characteristic scale aud amplitude of the turbulence which is independent of the resolution., Adding stratification appears to fundamentally change the dynamics and provides a characteristic scale and amplitude of the turbulence which is independent of the resolution.
+ This could be related to the different mechanisnis that lead to the saturation of the MRI in the presence of stratification. perhaps associated with the development. aud subsequent buovant rise. of large scale magnetic fields (Pessalietal.2007).," This could be related to the different mechanisms that lead to the saturation of the MRI in the presence of stratification, perhaps associated with the development, and subsequent buoyant rise, of large scale magnetic fields \citep{pcp07}."
+. Tn Figure 6 we show spacetime diagrams for several variables associated with the magnetic field., In Figure \ref{f:st128} we show spacetime diagrams for several variables associated with the magnetic field.
+ For the sake of brevity. we focus on magnetic quantities. which appear to plav the dominant role. as suggested by the PSD analysis above.," For the sake of brevity, we focus on magnetic quantities, which appear to play the dominant role, as suggested by the PSD analysis above."
+ The spacetime plots are generated bv averaging over the νο and y coordinates at cach height iu the domain every quarter of an orbit., The spacetime plots are generated by averaging over the $x$ and $y$ coordinates at each height in the domain every quarter of an orbit.
+ The top paucl of Fienre 6 shows J= where theangle brackets denote horizoutal averages.," The top panel of Figure \ref{f:st128} shows $\beta = 2 \langle P\rangle/\langle
+B^2\rangle$, where theangle brackets denote horizontal averages."
+"2(P)/(B?). As noted previously, magnetic pressure remains relatively weak near the midplaue. but dominates in the surface regions 2 1.577)."," As noted previously, magnetic pressure remains relatively weak near the midplane, but dominates in the surface regions $|z| \gtrsim 1.5 H$ )."
+ The middle panucls show the normalized .« and y conrponeuts of the maguctic field., The middle panels show the normalized $x$ and $y$ components of the magnetic field.
+" The D, componcut is considerably larger than D, aud they are uceatively correlated.", The $B_y$ component is considerably larger than $B_x$ and they are negatively correlated.
+ The svuunuetrv of the boundary couditious and the initial conditions require the vertical average of these quantities to be zero., The symmetry of the boundary conditions and the initial conditions require the vertical average of these quantities to be zero.
+ Nevertheless. there are localized regious of uct field that. under the effects of buovancy. trace out curved trajectories in the spacetime plot.," Nevertheless, there are localized regions of net field that, under the effects of buoyancy, trace out curved trajectories in the spacetime plot."
+" This is similar to other ""butterfly diagrams’ seen iu previous shearingbox calculations of stratified domains (Brandenburgetal.1995:Stone1996:Turner 2009).."," This is similar to other `butterfly diagrams' seen in previous shearingbox calculations of stratified domains \citep{bra95,sto96,tur04,jyk09,si09}. ."
+ Consistent with previous simulations. the polnuitv is ustally even about the midplane aud. at fixed height.," Consistent with previous simulations, the polarity is usually even about the midplane and, at fixed height,"
+2002)). Although the PP mocel is not a necessary explanation for such behaviour. (which is a phenomenological outcome of the rms-Iux relation). it provides a natural physical framework for understanding it. in that the PP model appears to be the correct. physical explanation for the rms-IHux relation.,"), Although the PP model is not a necessary explanation for such behaviour (which is a phenomenological outcome of the rms-flux relation), it provides a natural physical framework for understanding it, in that the PP model appears to be the correct physical explanation for the rms-flux relation."
+ The PP model allows a simple understanding. of other aspects of the variability., The PP model allows a simple understanding of other aspects of the variability.
+ For example. the characteristic ime-seales observed in. the variability of NRBs and AGN can be understood. in terms of time-scales in the accretion [low (e.g. the broad Lorentzian [features can oe formed if perturbations are produced. over certain narrow ranges of radii). thus potentially unifving models or the aperiodic variability with models for quasi-perioclic oscillations that are sometimes observed in. SRBs (though not vet conclusively in AGN).," For example, the characteristic time-scales observed in the variability of XRBs and AGN can be understood in terms of time-scales in the accretion flow (e.g. the broad Lorentzian features can be formed if perturbations are produced over certain narrow ranges of radii), thus potentially unifying models for the aperiodic variability with models for quasi-periodic oscillations that are sometimes observed in XRBs (though not yet conclusively in AGN)."
+ What. physical time-scales hese characteristic features correspond to d8 πο vet clear., What physical time-scales these characteristic features correspond to is not yet clear.
+ “Phe PP model requires. that perturbations are oocduced: at dillerent. radii in the accretion low. that hese perturbations can propagate inwards without being Lguppressecl (e.g. camped by viscous dissipation). and that he perturbations produced at cillerent radii can couple ogether.," The PP model requires that perturbations are produced at different radii in the accretion flow, that these perturbations can propagate inwards without being suppressed (e.g. damped by viscous dissipation), and that the perturbations produced at different radii can couple together."
+ A possible configuration which could. fulfil these criteria is a geometrically thick accretion [low (such as a thick disk. or an advection dominated accretion How) where accretion time-scales are relatively short so that variations. e.g. on the thermal time-scale. can propagate to the inner regions of the accretion [low without being significantly damped (Manmotoctal.1996:Churazov.Gilfanov&Revnivtsey 20011).," A possible configuration which could fulfil these criteria is a geometrically thick accretion flow (such as a thick disk, or an advection dominated accretion flow), where accretion time-scales are relatively short so that variations, e.g. on the thermal time-scale, can propagate to the inner regions of the accretion flow without being significantly damped \citealt{man96,chu01}) )."
+ Alternatively. the fact that a linear rms-llux relation is observed in (νο X-1 in both the soft ancl hard. states has been used. by Cleissner.etal.(2003) to suggest that the variations originate in a coronal accretion How (rather than a disk). which should also show a short accretion time-scale ancl hence might satisfv the PP model requirements.," Alternatively, the fact that a linear rms-flux relation is observed in Cyg X-1 in both the soft and hard states has been used by \citet{gle03} to suggest that the variations originate in a coronal accretion flow (rather than a disk), which should also show a short accretion time-scale and hence might satisfy the PP model requirements."
+ Phe physical origin of the perturbations is unclear. although a variety. of well-known accretion instabilities could contribute (Frank.Wing&Raine. 1992).," The physical origin of the perturbations is unclear, although a variety of well-known accretion instabilities could contribute \citep{fra92}."
+. Furthermore. Wineetal.(2003) have recently shown that MIID turbulence can cause acerction perturbations on sulliciently long time-scales for a linear rms-ILux relation to be produced by the inward. propagation and. coupling of the perturbations.," Furthermore, \citet{kin03} have recently shown that MHD turbulence can cause accretion perturbations on sufficiently long time-scales for a linear rms-flux relation to be produced by the inward propagation and coupling of the perturbations."
+ Finally. we note that a PP. model origin. for. aperiocdi variability in ARBs and ACN implies that the variability can be used to probe the location ancl structure of the X- emitting regions close to the neutron star surface or black hole event horizon.," Finally, we note that a PP model origin for aperiodic variability in XRBs and AGN implies that the variability can be used to probe the location and structure of the X-ray emitting regions close to the neutron star surface or black hole event horizon."
+ For example. an extended emitting region acts as a low pass filler. suppressing variations which originate within the emitting region relative to slower variations which originate outside. for the simple reason that an imward-propagating perturbation can only modulate emission within the radius at whieh it is formed.," For example, an extended emitting region acts as a low pass filter, suppressing variations which originate within the emitting region relative to slower variations which originate outside, for the simple reason that an inward-propagating perturbation can only modulate emission within the radius at which it is formed."
+ This simple picture can help to explain why neutron star ARBs show stronger high-frequency noise (at. [recuencies 10 Lz) than black hole svstems (Sunvaey&Revnivi-sev. 2000).. Le. because their X-ray emission originates xedominantly on the neutron star surface. within the radius where the highest frequency accretion Dow perturbations are »oduced.," This simple picture can help to explain why neutron star XRBs show stronger high-frequency noise (at frequencies $>10$ Hz) than black hole systems \citep{sun00}, i.e. because their X-ray emission originates predominantly on the neutron star surface, within the radius where the highest frequency accretion flow perturbations are produced."
+ Similarly. in black hole svstems the suppression of variability within a coronal emitting region with a emperature gradient. will lead to energy dependent. power-spectral shapes. which can be used to constrain the racial emission structure of the corona (Ixotov.Churazov&Gibanov2001:Zvcki2003)).," Similarly, in black hole systems the suppression of variability within a coronal emitting region with a temperature gradient will lead to energy dependent power-spectral shapes, which can be used to constrain the radial emission structure of the corona \citealt{kot01,zyc03}) )."
+ We have demonstrated that the aperiodic variability which carries the linear rmis-IHux. relation in the accreting milliseconcl pulsar SAN JLSOS.4-3658. is. coupled. to. the 401 Lz pulsation in this source. ancl hence the component of X-ray emission which contains the rms-Iux relation is produced at the magnetic caps of the neutron. star.," We have demonstrated that the aperiodic variability which carries the linear rms-flux relation in the accreting millisecond pulsar SAX J1808.4-3658, is coupled to the 401 Hz pulsation in this source, and hence the component of X-ray emission which contains the rms-flux relation is produced at the magnetic caps of the neutron star."
+ We conclude that the aperiodic variability is produced. by inwarcd-propagating perturbations in the aceretion How on othe neutron star. with the rms-IHux relation produced hy a coupling of perturbations produced on dillerent time-scales.," We conclude that the aperiodic variability is produced by inward-propagating perturbations in the accretion flow on to the neutron star, with the rms-flux relation produced by a coupling of perturbations produced on different time-scales."
+ Dv extension. this result suggests that the same mechanism xocduces the rms-Hux relations observed in black hole NIUDs and AGN. so that the aperiocic X-ray variability in all these diverse systems is caused by perturbations in the accretion low. and not by Hares due to magnetic reconnection in the COLONa.," By extension, this result suggests that the same mechanism produces the rms-flux relations observed in black hole XRBs and AGN, so that the aperiodic X-ray variability in all these diverse systems is caused by perturbations in the accretion flow, and not by flares due to magnetic reconnection in the corona."
+ We wish to thank the anonymous referee. for helpful comments., We wish to thank the anonymous referee for helpful comments.
+The major result is that no statistically significant rapid variability was observed for auv of the sources listed Tables 1 and 2..,The major result is that no statistically significant rapid variability was observed for any of the sources listed Tables \ref{three-quasars} and \ref{twenty-quasars}.
+ The data also reveal no night to welt or longer term variabilitv for amy of the sources. with the sole exception of21121059.," The data also reveal no night to night or longer term variability for any of the sources, with the sole exception of."
+.. This source brightened by 0.18 magnitudes in the V-baud between September 1992 and June 1996 (Table 1/ and Fig. 2))., This source brightened by 0.18 magnitudes in the V-band between September 1992 and June 1996 (Table \ref{three-quasars} and Fig. \ref{PG2112+059}) ).
+ The source with the largest umber of observations is (Table 13) and some of the differential V-band results are presented iu Fie. 3.., The source with the largest number of observations is (Table \ref{three-quasars}) ) and some of the differential V-band results are presented in Fig. \ref{PG0117+213}.
+ No siguificaut short term variability was observed., No significant short term variability was observed.
+ Furthermore careful analysis of the remaincer of the V-baud data aud all of the B-baud revealed no significant short or long terii variability., Furthermore careful analysis of the remainder of the V-band data and all of the B-band revealed no significant short or long term variability.
+ The sources in this sample can be divided iuto three main redshift eroups: AC.« 2). D(2<2 <3). Cl.> 3).," The sources in this sample can be divided into three main redshift groups; $z<2$ ), $2<z<3$ ), $z>3$ ),"
+of the siuguluitv.,of the singularity.
+" Iu all three cases. the elapsed time between the initiation of collapse aud the formation of the density singularity is fine&lEEr. where τσ, is the sound crossing time of the region interior to ry."," In all three cases, the elapsed time between the initiation of collapse and the formation of the density singularity is $t_{\rm sing} \simeq 1.44 \tau$, where $\tau =
+r_{0}/\sigma_{c}$ is the sound crossing time of the region interior to $r_{0}$."
+ This is also just larecr than the mean free-fall time of the region interior to ry., This is also just larger than the mean free-fall time of the region interior to $r_{0}$.
+ Recall that the initial density profile in the outer regions (r> rg) of the nousimegular logatrope closely ollows the power law profile of the singular logatrope (see Fie. 1))., Recall that the initial density profile in the outer regions $r>r_{0}$ ) of the nonsingular logatrope closely follows the power law profile of the singular logatrope (see Fig. \ref{fig:logdp}) ).
+ Thus. it is reasonable that the time taken for he global readjustineut to power lav deusity behaviour should be of order the free-fall time of the initially flat-opped region. rzrg.," Thus, it is reasonable that the time taken for the global readjustment to power law density behaviour should be of order the free-fall time of the initially flat-topped region, $r < r_{0}$."
+ This information is sununiarized in Table 3.., This information is summarized in Table \ref{tab:mdotab}.
+ For all three masses studied. inimiediatelv following the ormation of the sineularitv. the central mass accretion rate increases abruptly.," 	For all three masses studied, immediately following the formation of the singularity, the central mass accretion rate increases abruptly."
+ The inflow then moves from the collapse phase into an SLS-like accretion pliase similar to hat secu in Figure 8.., The inflow then moves from the collapse phase into an SLS-like accretion phase similar to that seen in Figure \ref{fig:mdotvstsing}.
+ Simulations of the collapse of a critical Dounuor-Ebert sphere performed by FC93 showed that. at the moment he density profile becomes singular. of the mass is in supersonic infall with Mach uunuboers as high as ~3.25.," 	Simulations of the collapse of a critical Bonnor-Ebert sphere performed by FC93 showed that, at the moment the density profile becomes singular, of the mass is in supersonic infall with Mach numbers as high as $\sim 3.25$."
+ AIP96 predicted that. because the logatropic EOS is softer han the isothermal EOS. a nonsingular logatropic collapse uieht not eive rise to such hieh iufall velocities.," MP96 predicted that, because the logatropic EOS is softer than the isothermal EOS, a nonsingular logatropic collapse might not give rise to such high infall velocities."
+ Our results are consistent with this prediction., Our results are consistent with this prediction.
+ We have fouud that. while lighly subcritical logatropes are characterized bv Supersonic iufall at the moment of singularity formation. the trend is toward a gentler collapse as we approach criticality (i.e. as we increase the radius of the core).," We have found that, while highly subcritical logatropes are characterized by supersonic infall at the moment of singularity formation, the trend is toward a gentler collapse as we approach criticality (i.e. as we increase the radius of the core)."
+ Table tL lists the percentage of the mass of each simulated logatropic core which is iufalliug supersouicallv at f=0., 	Table \ref{tab:cftab} lists the percentage of the mass of each simulated logatropic core which is infalling supersonically at $t=0$.
+ The clear trend is that. as the radius of the core increases. both the fractional amount of mass which Is in supersomic iufall aud the Mach wmuber of that iufall decrease.," The clear trend is that, as the radius of the core increases, both the fractional amount of mass which is in supersonic infall and the Mach number of that infall decrease."
+ Extrapolating the treud. it ποσα» likely that little or none of the mass of a critical Ré/ry=21.37 logatrope would be in supersonic infall at £=0. in accord with the prediction of MP96.," Extrapolating the trend, it seems likely that little or none of the mass of a critical $R/r_{0} =24.37$ logatrope would be in supersonic infall at $t=0$, in accord with the prediction of MP96."
+ Simulations of the collapse ofa critical core will be needed to confirm this prediction., Simulations of the collapse of a critical core will be needed to confirm this prediction.
+" As star-forming cores evolve from Class 0 to Class IV. heir protostellar mass accretion rate may vary by ~2 orders of magnitude (see André,Ward-Thompson.&Bar-sony 2000.. and references therem)."," 	As star-forming cores evolve from Class 0 to Class IV, their protostellar mass accretion rate may vary by $\sim 2$ orders of magnitude (see \citeauthor{AndrePPIV} \citeyear{AndrePPIV}, and references therein)."
+ It should be noted hat estimates of the accretion rate im voung stellar objects are not mace by direct measure. but rather bv iufereuce roni a combination of models and other data. as will )o discussed shortly.," It should be noted that estimates of the accretion rate in young stellar objects are not made by direct measure, but rather by inference from a combination of models and other data, as will be discussed shortly."
+ Iu. coutrast to the observations. the standard SIS model predicts a time-invariant protostellar nass accretion rate.," In contrast to the observations, the standard SIS model predicts a time-invariant protostellar mass accretion rate."
+ Foster&Chevalier(1993) aud BossaudBlack(1982)0 have obtained variable mass accretion rates for isothermal collapse models which draw uass from finite reservoirs. but these imnodels show a eudeunev to evolve toward the constant mass accretion rate predicted by the SIS model.," \citet{FC93} and \citet{BB} have obtained variable mass accretion rates for isothermal collapse models which draw mass from finite reservoirs, but these models show a tendency to evolve toward the constant mass accretion rate predicted by the SIS model."
+ Heurikseu.Audré.&Bou-ens(1997) and CaselliaudMyers(1995). have proposed alternative models for protostellar collapse which predict variable accretion rates., \citet{Henriksen} and \citet{CM95} have proposed alternative models for protostellar collapse which predict variable accretion rates.
+ Like the logatrope. these models are. phenomenologically based. desigued to match the observed properties of star-forming cores (density profiles. vouthermal linewidths. ete.)," Like the logatrope, these models are phenomenologically based, designed to match the observed properties of star-forming cores (density profiles, nonthermal linewidths, etc.)"
+ These modols. however. have uanvy nore free parameters than the logatrope. which has only one: the coustaut in equation (3)).," These models, however, have many more free parameters than the logatrope, which has only one: the constant $A$ in equation \ref{eq:eqos1}) )."
+ As shown in he previous section. the logatrope also predicts a highly variable accretion rate.," As shown in the previous section, the logatrope also predicts a highly variable accretion rate."
+ We must ask. then. how closely he logatropic accretion profile corresponds to available observational data.," We must ask, then, how closely the logatropic accretion profile corresponds to available observational data."
+" Douteimipsetal.(1996) surveved 36 Class IT and 9 Class 0 xotostars in the p Oph. Taurus-Auriea. aud Perseus star- regions aud found that the outflow moment fux. Foo declines from ~101 M, kins tye | in the Class 0 sources to ~ος109 ML, Jan fxr | in the Class I sources."," \citet{Bontemps} surveyed 36 Class I and 9 Class 0 protostars in the $\rho$ Oph, Taurus-Auriga, and Perseus star-forming regions and found that the outflow momentum flux, $F_{\rm CO}$ declines from $\sim 10^{-4}$ $_{\odot}$ km $^{-1}$ $^{-1}$ in the Class 0 sources to $\sim 2 \times 10^{-6}$ $_{\odot}$ km $^{-1}$ $^{-1}$ in the Class I sources."
+" Their suggestion was that this decrease i Foo aud the accompanving decrease iu the mass ejection rate of the protostellay wind. AT... were attributable to a decrease in the protostellar nass accretion rate. AL. from ~10ο M. 3 to~ 2.107 M, xr.L|"," Their suggestion was that this decrease in $F_{\rm CO}$ and the accompanying decrease in the mass ejection rate of the protostellar wind, $\dot{M}_{w}$, were attributable to a decrease in the protostellar mass accretion rate, $\dot{M}_{\rm acc}$, from $\sim 10^{-5}$ $_{\odot}$ $^{-1}$ to $\sim 2 \times 10^{-7}$ $_{\odot}$ $^{-1}$."
+ Clearly the largest of these accretion rates is significantly higher than those shown in Figure ll.. but we note that there Is Significant room for movement in both the observations and the scaling of our siumulatious.," Clearly the largest of these accretion rates is significantly higher than those shown in Figure \ref{fig:mdot}, but we note that there is significant room for movement in both the observations and the scaling of our simulations."
+ We have scaled our accretion profiles to. central temperatures and truncation pressures which are characteristic of regions of isolated star formation., 	We have scaled our accretion profiles to central temperatures and truncation pressures which are characteristic of regions of isolated star formation.
+ If we instead choose Z5 aud P. iu keeping with observations of regious such as p Oph. we can make up the difference between our Maz values aud those suggested by Ward-Thompson.&Darsouv," If we instead choose $T_{c}$ and $P_{s}$ in keeping with observations of regions such as $\rho$ Oph, we can make up the difference between our $\dot{M}_{\rm acc}$ values and those suggested by \citet{AndrePPIV}."
+ (2000).. Johustoneetal.(2000) fitted 55 molecular cloud cores iu p Oph to Dounor- spheres aud thereby made estimates of the surface pressure ou each core., \citet{Johnstone} fitted 55 molecular cloud cores in $\rho$ Oph to Bonnor-Ebert spheres and thereby made estimates of the surface pressure on each core.
+" The typical truucation pressures found in that study lay in the range P,=10°—10*bg Ik. These are between L aud 2 orders of magnitude ercater than the fiducial tziucation pressure used hereim (P.=L3ςWkp cun? K)", The typical truncation pressures found in that study lay in the range $P_{s} = 10^{6}-10^{7} k_{B}$ $^{-3}$ K. These are between 1 and 2 orders of magnitude greater than the fiducial truncation pressure used herein $ P_{s} = 1.3 \times 10^{5} k_{B}$ $^{3}$ K).
+" The relationship between the total mass of a nonsimgular logatropic core and its truucation pressure takes the formu, MiXJA“πι "," The relationship between the total mass of a nonsingular logatropic core and its truncation pressure takes the form $M_{\rm tot}
+\propto P_{s}^{-1/2}$."
+Increasing the truucation pressure by a factor of 100 would. reduce the mass of a eiven core by a factor of 10.," Hence, increasing the truncation pressure by a factor of 100 would reduce the mass of a given core by a factor of 10."
+ This would also bring the mass of the critical A=0.2 logatrope down from 92 ΔΕ. typical of an cutive molecular cloud to 9.2 M. which is typical of a molecular cloud situated within a chump.," This would also bring the mass of the critical $A=0.2$ logatrope down from 92 $_{\odot}$ —typical of an entire molecular cloud —to 9.2 $_{\odot}$, which is typical of a molecular cloud situated within a clump."
+ Heuce. our models would theu represent cores of comparatively low mass.," Hence, our models would then represent cores of comparatively low mass."
+ We would then ive to look at logatropic spheres closer to the critical radius in order to find cores of mass ~1 M... iu which case the accretion rates ought to be considerably higher iu those listed in Table 2..," We would then have to look at logatropic spheres closer to the critical radius in order to find cores of mass $\sim 1$ $_{\odot}$ , in which case the accretion rates ought to be considerably higher than those listed in Table \ref{tab:nstable}."
+ The method used bv Johustoneetal.(2000) το xtract truncation pressures was. however. dependent ou 1c asstuuption that all of the cores could be well-fit by Dounor-Ebert spheres. and hence the truncation pressures xtracted cannot necessarily be cousidered reflective of rose that would be required to truucate loeatropic PApheres.," 	The method used by \citet{Johnstone} to extract truncation pressures was, however, dependent on the assumption that all of the cores could be well-fit by Bonnor-Ebert spheres, and hence the truncation pressures extracted cannot necessarily be considered reflective of those that would be required to truncate logatropic spheres."
+ The dimensionless results of Figures Llaa aud — lbb are meant to be rescalable. should future moeasures of Z2; become available.," The dimensionless results of Figures \ref{fig:mdot}a a and \ref{fig:mdot}b b are meant to be rescalable, should future EOS-independent measures of $P_{s}$ become available."
+ Disreemrdiug the absolute umubers for a monent which are. aswe have eimpliasized. subject to considerable uncertainty). we note that the in our logatropic Macca bears significante reseiiblauces to the data.," 	Disregarding the absolute numbers for a moment (which are, aswe have emphasized, subject to considerable uncertainty), we note that the in our logatropic $\dot{M}_{\rm acc}$ bears significant resemblances to the data."
+ Estimates, Estimates
+regions. about the depth and extent of thermal disturbances beneath sunspots aud other surface phenomena. and about the nature of the magnetic fields that rise to form active regions.,"regions, about the depth and extent of thermal disturbances beneath sunspots and other surface phenomena, and about the nature of the magnetic fields that rise to form active regions."
+ The frequencies of global oscillations change with the overall level of solar activity (Woodard&Noves1935:LibbrechtWoodard1990): this is bv now νουν well established (seereviewbyChristensen-Dalsgaard2002.anclreferences(herein)..," The frequencies of global oscillations change with the overall level of solar activity \citep{WN85,LW90}; this is by now very well established \citep[see review by][and references therein]{JCD02}."
+ The frequencies of both low degree modes (e.g.Chaplinetal.2007) and medium degree modes (e.g.Dziembowskielal.1993:Loweet1999:Dziembowski2000) increase with solar activity level. and this frequency increase is stronger al higher frequencies.," The frequencies of both low degree modes \citep[e.g.][]{Cetal07} and medium degree modes \citep[e.g.][]{Dzetal98,Howeetal99,Dzetal00} increase with solar activity level, and this frequency increase is stronger at higher frequencies."
+ Though high degree global mode measurements are not routinelv made. some sets of high degree mode lrequency measurements have been made. and these are found to increase wilh activity as well 2009)..," Though high degree global mode measurements are not routinely made, some sets of high degree mode frequency measurements have been made, and these are found to increase with activity as well \citep{RSandKorz}. ."
+ The use of so-called ‘ring diagrams (lil1988) to study solar structure is by now a well-established technique in helioseismology (seereviewbyGizon&Birch2005)., The use of so-called `ring diagrams' \citep{Hill88} to study solar structure is by now a well-established technique in helioseismology \citep[see review by][]{GB05}.
+. In (his paper. we will discuss the changes to mode parameters in ring diagrams between active regions and the surrounding «quiet Sun.," In this paper, we will discuss the changes to mode parameters in ring diagrams between active regions and the surrounding quiet Sun."
+ Bine diagrams prove useful for studyiug the effects of solar activity on helioseismie modes for (vo reasons., Ring diagrams prove useful for studying the effects of solar activity on helioseismic modes for two reasons.
+ First. rings are measured on a localized patch of the Sun. providing both temporal and spatial resolution.," First, rings are measured on a localized patch of the Sun, providing both temporal and spatial resolution."
+ This allows us (ο isolate phenomena associated wilh solar activity [rom the surrounding Sun., This allows us to isolate phenomena associated with solar activity from the surrounding Sun.
+ Second. measurements can be made to much higher degree much more easily than with global mode analvsis.," Second, measurements can be made to much higher degree much more easily than with global mode analysis."
+ Ring diagrams were first used by Till(1988) to measure flow rates near the solar surface., Ring diagrams were first used by \citet{Hill88} to measure flow rates near the solar surface.
+ Rings have been used subsequently bv a number of authors to study the near-surface dynamics of ihe Sun (e.g.Sehou&Bogart1993:Basuetal.1999:IIaber1999).," Rings have been used subsequently by a number of authors to study the near-surface dynamics of the Sun \citep[e.g.][]{SchouBogart98,BAT99,Haberetal99}."
+.. Ring diagrams have also been used to study the thermal structure beneath sunspots aud in (he near-surlace lavers (Dasuetal.2004.2007:Bogart2008).," Ring diagrams have also been used to study the thermal structure beneath sunspots and in the near-surface layers \citep{Basuetal2004,Basuetal07,Bogartetal08}."
+. The effects of active regions on ring diagram mode parameters have been studied in previous works., The effects of active regions on ring diagram mode parameters have been studied in previous works.
+ Hindaimanetal.(2000) Found (hat the high degree mode frequencies obtained from ring diagrams were enhanced in active regions., \citet{Hindetal2000} found that the high degree mode frequencies obtained from ring diagrams were enhanced in active regions.
+ Rajagurnetal.(2001) found that the mode widths were also enhanced in active regions. while the amplitudes were suppressed. ancl Rabello-Soaresetal.(2008) [ound that the relation between the change in width and mode amplitude was verv nearly linear.," \citet{Raj01} found that the mode widths were also enhanced in active regions, while the amplitudes were suppressed, and \citet{CRSetal08} found that the relation between the change in width and mode amplitude was very nearly linear."
+ Loweetal.(2004) assumed (hat the relation between aclivily and mode parameter variation was quadratic. ancl found a peak increase in mocle frequency at around 5mllIz. with a corresponding maxinum change in width and amplitude.," \citet{Howeetal04}
+ assumed that the relation between activity and mode parameter variation was quadratic, and found a peak increase in mode frequency at around 5mHz, with a corresponding maximum change in width and amplitude."
+ In this work. we study the properties of 264 active region ring diagrams from solar evcle 23.," In this work, we study the properties of 264 active region ring diagrams from solar cycle 23."
+ This sample gives us a statistically significant number of measurements over a substantial range of activity levelsfrom all phases of the solar cycle. when compared (o earlier works.," This sample gives us a statistically significant number of measurements over a substantial range of activity levelsfrom all phases of the solar cycle, when compared to earlier works."
+in slope.,in slope.
+" ""The difference inX7 for each of the dillerent constant couplings is shown in. Table 4.. and we see that lensing with Iuclid should be able to discriminate between jy2:0.05 and ACDAL at a confidence level of 5o. while DES should be able to discriminate between Ju :Ü.land ACDAL at a confidence level of 4o."," The difference in$\chi^2$ for each of the different constant couplings is shown in Table \ref{chi sq table}, and we see that lensing with Euclid should be able to discriminate between $\beta_0\geq0.05$ and $\Lambda$ CDM at a confidence level of $5\sigma$, while DES should be able to discriminate between $\beta_0\geq0.1$ and $\Lambda $ CDM at a confidence level of $4\sigma$."
+ Figure 3. shows that the best fit ACDAL models for each of the couplings occupy quite different parameter regions. especially for Euclid.," Figure \ref{fig:contours} shows that the best fit $\Lambda$ CDM models for each of the couplings occupy quite different parameter regions, especially for Euclid."
+ The discrepancies heοσο DIES and I5uclid. predictions in these plots are found o be due to the oll-diagonal covariance matrix terms: this can be seen by examining the best fit models for DIES and Euclid aong with the cDE model we are trving to fit., The discrepancies between DES and Euclid predictions in these plots are found to be due to the off-diagonal covariance matrix terms; this can be seen by examining the best fit models for DES and Euclid along with the cDE model we are trying to fit.
+ Phe bes fit for our DIES survey appears to be a worse fit at small @ and à betor fit at large 8 than the Euclid best fit., The best fit for our DES survey appears to be a worse fit at small $\theta$ and a better fit at large $\theta$ than the Euclid best fit.
+" Phis is due to the e""variance being largest for large angles ancl high recshifts.", This is due to the covariance being largest for large angles and high redshifts.
+ So while DES has a larger contribution from shape nolse a small ϐ allowing a worse fit on small scales. conversev Eucli dis more sensitive to the covariance on large scales.," So while DES has a larger contribution from shape noise at small $\theta$ allowing a worse fit on small scales, conversely Euclid is more sensitive to the covariance on large scales."
+ This descrepancy tween the DES and Euclid best fit AC DAL inereases as uj increases., This descrepancy between the DES and Euclid best fit $\Lambda$ CDM increases as $\beta_0$ increases.
+" ‘These results show that if dark energy and clark matter ruly do. interact in the way described. by our. class. of models. and we attempt to fit a ACDAL cosmology to the observations. then we will infer increased. values of Z4, and osx. ane a decrease in uw and Q,,, as dy increases."," These results show that if dark energy and dark matter truly do interact in the way described by our class of models, and we attempt to fit a $\Lambda$ CDM cosmology to the observations, then we will infer increased values of $H_0$ and $\sigma_8$, and a decrease in $w$ and $\Omega_m$ as $\beta_0$ increases."
+ 1t should be noted that Kirkοἱal.(2011) and Laszloal.(2011) have recently shown that the effects οἱ mocified gravity ancl alternative dark «nergyv models. can be degenerate witi svstematies due to intrinsic alignments., It should be noted that \cite{Kirk:2011sw} and \cite{Laszlo:2011sv} have recently shown that the effects of modified gravity and alternative dark energy models can be degenerate with systematics due to intrinsic alignments.
+ Barvonic physics has also been shown to jàve possibly large ellects on the matter power spectrum from scales as small as k=0.3 h/Mpe (vanDaalenctal.201>Semboloni 2011).," Baryonic physics has also been shown to have possibly large effects on the matter power spectrum from scales as small as $k$ =0.3 h/Mpc \citep[][]{vanDaalen:2011xb,Semboloni_etal_2011}."
+. In this paper we do not include hese cllects. as we are seeking to present the pure shear signal predictions.," In this paper we do not include these effects, as we are seeking to present the pure shear signal predictions."
+ Our results should therefore be considered best-case predictions which will be diluted. by the impact of. systematic. and barvonic elfects., Our results should therefore be considered best-case predictions which will be diluted by the impact of systematic and baryonic effects.
+ Although for the previous section we restricted ourselves to looking at constant coupling models with an exponential potential. the ¢DE model has the freedom: to. examine different potentials ancl an evolving coupling.," Although for the previous section we restricted ourselves to looking at constant coupling models with an exponential potential, the cDE model has the freedom to examine different potentials and an evolving coupling."
+ Two of the simulations explore this freedom: EEXPOQ0Se3. which has the same potential as the models in the previous section but with an evolving coupling. ancl SUCGILAQO03. which has," Two of the simulations explore this freedom: EXP008e3, which has the same potential as the models in the previous section but with an evolving coupling, and SUGRA003, which has"
+functions between channels zé£00. aud #600 are shown.,functions between channels $\# 400$ and $\#600$ are shown.
+ The scale of the vertical axe in Fig., The scale of the vertical axe in Fig.
+ το is significantly larger than that in Fig., 7c is significantly larger than that in Fig.
+ Td thus showing stroug excessive cross-correlation due to RFI., 7d thus showing strong excessive cross-correlation due to RFI.
+ It is necessary to add two further commucuts here for the purposes of discussion., It is necessary to add two further comments here for the purposes of discussion.
+ lL., 1.
+ The estimators of variance described iu Section 2 and those tested in Section 3 are essentially uoulinear procedures., The estimators of variance described in Section 2 and those tested in Section 3 are essentially nonlinear procedures.
+ For example. one can. at least theoretically. inagiue a huge outlier which reuders the conventional estimator (1) completely nou-functional whereas these estimators work pertecth.," For example, one can, at least theoretically, imagine a huge outlier which renders the conventional estimator (1) completely non-functional whereas these estimators work perfectly."
+ Radioastronomers often ask wha is the value of REI suppression. (μπα in dB) when an RFI uitigation algorithnià is applied?, Radioastronomers often ask what is the value of RFI suppression (usually in dB) when an RFI mitigation algorithm is applied?
+ Example in Fig., Example in Fig.
+ 3 demonstrates that it Is no always possible to auswer this question correctly., 3 demonstrates that it is not always possible to answer this question correctly.
+ The larger the outliers aimplituces the luore effectively they are deleted., The larger the outlier's amplitudes the more effectively they are deleted.
+ If the amplitudes of inpulses in Fig., If the amplitudes of impulses in Fig.
+ 2c are 10 times larger the result iu Fig., 3c are 10 times larger the result in Fig.
+ 3e will be the same or even slightly improved., 3e will be the same or even slightly improved.
+ This is also valid for the “thresholding anc απο algorithm which has been succesfully used in several articles on REI mitigation., This is also valid for the “thresholding and blanking” algorithm which has been succesfully used in several articles on RFI mitigation.
+" That is why it is better to judge an RFI uitigation oxocedure in each patieular case in a combined uauuer. that is looking at the ""sigual-of-iuterest? distortions by both the RFI residuals aud the xocedure itself."," That is why it is better to judge an RFI mitigation procedure in each paticular case in a combined manner, that is looking at the “signal-of-interest” distortions by both the RFI residuals and the procedure itself."
+ 2., 2.
+ The estimators of Section 2 are intended for applications when sporadic. inipulse-lTHike iiterference disturbs observations.," The estimators of Section 2 are intended for applications when sporadic, impulse-like interference disturbs observations."
+ Ποπονο interference is often continuous. persistent aud practically coustaut diving the averaging interval.," However interference is often continuous, persistent and practically constant during the averaging interval."
+ For cxamiple. for Af=100.N512.20MIT« this interval is equal to 1.28«10 see which is rather a short iuterval for several RFI to chauge their auplitudes.," For example, for $M=100, N=512, \Delta f=20MHz$ this interval is equal to $1.28 \times 10^{-3}$ sec which is rather a short interval for several RFI to change their amplitudes."
+" The estimators of Section 2 will not vield any benefits in this Case,", The estimators of Section 2 will not yield any benefits in this case.
+ But the Sue fact that RET is quasi-ccoustant at a reasonably chosen averaging interval can help to decouple the Gaussian component with a “quiescent” value of σ and REI with case., But the same fact that RFI is quasi-constant at a reasonably chosen averaging interval can help to decouple the Gaussian component with a “quiescent” value of $\sigma$ and RFI with ease.
+ A simple procedure cau do this., A simple procedure can do this.
+ The power spectu after FFT is usually calculated as The stuns of RFT aud “useful” Caussian noise in each spectral cliaunel are squared aud averaged., The power spectrum after FFT is usually calculated as The sums of RFI and “useful” Gaussian noise in each spectral channel are squared and averaged.
+ Strong REI dominates in this case over the noise., Strong RFI dominates in this case over the noise.
+ Another algoritlin is proposed here: to separately estimate the variances of real aud imaginary parts of the spectrmm and then add them to obtain he total variance m each spectral chamuel. i.6.. he power spectrum sought.," Another algorithm is proposed here: to separately estimate the variances of real and imaginary parts of the spectrum and then add them to obtain the total variance in each spectral channel, i.e., the power spectrum sought."
+ The variances of real and nuaegeunuuy parts of the complex spectra. uust be calculated taking mto consideration that he mean value now is uo longer equal to zero jecause of the presence of RET., The variances of real and imaginary parts of the complex spectrum must be calculated taking into consideration that the mean value now is no longer equal to zero because of the presence of RFI.
+" So the ecucral ornula for saluple variance must be applied: Or a random value vw. the sample variance is carte)—o27=↽1ASMLi) ⋅⋟ ↕∐∖↻∪↖↖⇁↸∖↥⋅↴∖↴↻↸∖↸⊳⊓⋅↿⋯⋜↧↑↕≯↥⋅↸∖≺⋯∖∐↸⊳⋅↖↽⋅↗⊔↕↴∖↴ this case REI is climunated due to its constant value for all A sauples of the instantaneous spectra s(Cf)],."," So the general formula for sample variance must be applied: for a random value $x$, the sample variance is $var(x)=$$\widehat{\sigma
+_{x}^{2}}=1/M\sum_{m=1}^{M}(x_{m}-\widehat{x})^{2}$ which for the power spectrum at frequency $f$ is In this case RFI is eliminated due to its constant value for all $M$ samples of the instantaneous spectra $s(f)]_{m}$."
+ Tt aay also be useful for the litigation of weak but persistent ΠΕΙ whose detrimental impact is revealed only after lengthy averaging., It may also be useful for the mitigation of weak but persistent RFI whose detrimental impact is revealed only after lengthy averaging.
+" This is a conjecture which has been proved iu computer simulations but which. of course, requires experimental coufirmation."," This is a conjecture which has been proved in computer simulations but which, of course, requires experimental confirmation."
+ Radio source LLis|762 was observed in coutinuuu, Radio source 1448+762 was observed in continuum
+ Radio source LLis|762 was observed in coutinuuuu, Radio source 1448+762 was observed in continuum
+"The wealth of cosmological data in the last few decades (???) has led to the establishment of a standard model of cosmology, which describes the Universe as composed today of approximately baryons, dark matter and dark energy.","The wealth of cosmological data in the last few decades \citep{wmap7,Schrabback:2010,Percival:2007} has led to the establishment of a standard model of cosmology, which describes the Universe as composed today of approximately baryons, dark matter and dark energy."
+" The main challenges in modern cosmology are to understand the nature of both dark energy and dark matter, as well as the initial conditions of the Universe (??).."," The main challenges in modern cosmology are to understand the nature of both dark energy and dark matter, as well as the initial conditions of the Universe \citep{DETF,WGFC}."
+ A thorough understanding of these three topics may lead to a revision of Einstein’s theory of General Relativity and our view of the early Universe., A thorough understanding of these three topics may lead to a revision of Einstein's theory of General Relativity and our view of the early Universe.
+" New surveys are planned who aim to answer these important questions e.g. Planck for the CMB (?),, DES (Dark ?),,BOSS (BaryonOscillationSpectroscopicSurvey, ?),, LSST (LargeSynopticSurveyTelescope,?) and Euclid (?) for weak lensing and the study of large scale structure with galaxy surveys."," New surveys are planned who aim to answer these important questions e.g. Planck for the CMB \citep{Planck}, DES \citep[Dark Energy Survey,][]{DES:2005}, BOSS \citep[Baryon Oscillation Spectroscopic Survey,][]{Schlegel:2007}, LSST \citep[Large Synoptic Survey Telescope,][]{LSST} and Euclid \citep{Euclid:2011} for weak lensing and the study of large scale structure with galaxy surveys."
+ The challenge with these upcoming large data-sets is to extract the cosmological information in the most suitable manner in order to test the cosmological paradigm., The challenge with these upcoming large data-sets is to extract the cosmological information in the most suitable manner in order to test the cosmological paradigm.
+" Depending on the signal one wishes to extract, and/or survey geometry, different bases may be more or less suitable (e.g., Fourier, Spherical Harmonic, Configuration or Wavelet Space)."," Depending on the signal one wishes to extract, and/or survey geometry, different bases may be more or less suitable (e.g., Fourier, Spherical Harmonic, Configuration or Wavelet Space)."
+" Moreover, future surveys may be in 2D (e.g. Planck) or in 3D (e.g. galaxy or weak lensing surveys)."," Moreover, future surveys may be in 2D (e.g. Planck) or in 3D (e.g. galaxy or weak lensing surveys)."
+" Where 3D data is available, a tomographic analysis is possible (also known as 2D 1/2), or a full 3D analysis can be done."," Where 3D data is available, a tomographic analysis is possible (also known as 2D 1/2), or a full 3D analysis can be done."
+" For data in spherical coordinates, this corresponds to a Spherical "," For data in spherical coordinates, this corresponds to a Spherical Fourier-Bessel (SFB) decomposition \citep{Heavens:1995,Fisher:1995,weak3d,Erdogdu:2005wi,Erdogdu:2006dv,Leistedt2011,Rassat:2011bao}. ."
+"Wavelets are particularly well suited to the analysis of cosmological data (??),, since cosmological data can often be sparsely represented in wavelet space."," Wavelets are particularly well suited to the analysis of cosmological data \citep{aw:martinez93,starck:sta05_2}, since cosmological data can often be sparsely represented in wavelet space."
+" 2D Wavelets have been used in many astrophysical studies (?) for a broad range of applications such as denoising, deconvolution, detection, etc."," 2D Wavelets have been used in many astrophysical studies \citep{starck:book06} for a broad range of applications such as denoising, deconvolution, detection, etc."
+ CMB studies havemotivated the development of 2D spherical wavelet decompositions., CMB studies havemotivated the development of 2D spherical wavelet decompositions.
+" Continuous wavelet transforms on the sphere (????) have been proposed, mainly for non Gaussianity studies."," Continuous wavelet transforms on the sphere \citep{wave:antoine99,wave:tenerio99,wave:cayon01,wave:holschneider96} have been proposed, mainly for non Gaussianity studies."
+" In ?,, an invertible isotropic undecimated wavelet transform (UWT) on the sphere based on spherical harmonics was described, that can be also used for other applications such as deconvolution, component separation (???),, inpainting (??),, or Poisson denoising (?).."," In \citet{starck:sta05_2}, an invertible isotropic undecimated wavelet transform (UWT) on the sphere based on spherical harmonics was described, that can be also used for other applications such as deconvolution, component separation \citep{starck:yassir05,bobin-gmca-cmb,delabrouille08}, inpainting \citep{inpainting:abrial06,starck:abrial08}, or Poisson denoising \citep{schmitt2010}."
+" A similar wavelet construction has been published in (???) using so-called “needlet filters"", and in ?,, an algorithm was proposed which allows us to reconstruct an image from its steerable wavelet transform."," A similar wavelet construction has been published in \citep{marinucci08,fay08a,fay08} using so-called “needlet filters"", and in \citet{wiaux08}, an algorithm was proposed which allows us to reconstruct an image from its steerable wavelet transform."
+" Other multiscale transforms on the sphere such as ridgelets and curvelets have been developed (?),, and are well adapted to detect anisotropic features."," Other multiscale transforms on the sphere such as ridgelets and curvelets have been developed \citep{starck:sta05_2}, and are well adapted to detect anisotropic features."
+" Other multiscale transforms on the sphere, such as ridgelets and curvelets, have been developed (?) and are well adapted to detect anisotropic features."," Other multiscale transforms on the sphere, such as ridgelets and curvelets, have been developed \citep{starck:sta05_2} and are well adapted to detect anisotropic features."
+ An extension of this UWT has also been developed for polarised CMB data in ?.., An extension of this UWT has also been developed for polarised CMB data in \citet{starck:pola09}.
+" In this paper, we describe a new 3D isotropic spherical wavelet decomposition, which is reversible, and could therefore be useful for many different applications."," In this paper, we describe a new 3D isotropic spherical wavelet decomposition, which is reversible, and could therefore be useful for many different applications."
+" It is based on the UWT proposed by ? and extended into 3D. The UWT proposed here can be used to analyse 3D data in spherical coordinates, such as a 3D galaxy or weak lensing survey with large (but not necessarily full) sky coverage."," It is based on the UWT proposed by \cite{starck:sta05_2} and extended into 3D. The 3D-UWT proposed here can be used to analyse 3D data in spherical coordinates, such as a 3D galaxy or weak lensing survey with large (but not necessarily full) sky coverage."
+" The SFB transform of a square integrable scalar field f(r,6,Φ) can be defined as: where Υ7 are spherical harmonics and j; are spherical Bessel functions and Y represents the complex conjugate of Y."," 	 	The SFB transform of a square integrable scalar field $f(r,\theta,\phi)$ can be defined as: where $Y_l^m$ are spherical harmonics and $j_{l}$ are spherical Bessel functions and $\overline{Y}$ represents the complex conjugate of $Y$."
+" Note Equation | uses the same convention as ? which differs slightly from that of ?,, ? and ?,, as explained below."," Note Equation \ref{SFBT} uses the same convention as \cite{Heavens:1995} which differs slightly from that of \cite{weak3d}, \cite{Leistedt2011} and\cite{Rassat:2011bao}, , as explained below."
+ This expression allows the expansion of a 3D field provided in spherical coordinates onto a set of orthogonal functions:, This expression allows the expansion of a 3D field provided in spherical coordinates onto a set of orthogonal functions:
+We stress that in order for this method (ο be successful. known strong-lensing clusters should be targeted specifically.,"We stress that in order for this method to be successful, known strong-lensing clusters should be targeted specifically."
+ The best constraints on the cluster potential would ideally be obtained by follow-up observations with instrumentis such as ACS of clusters for which SN lage pairs are actually observed., The best constraints on the cluster potential would ideally be obtained by follow-up observations with instruments such as ACS of clusters for which SN image pairs are actually observed.
+ Iowever. the co-added. images [rom a long-term monitor program would be of significant depth. and coukl also be searched [or strongly lensed background features.," However, the co-added images from a long-term monitor program would be of significant depth, and could also be searched for strongly lensed background features."
+ The authors wish to thank Paul Schechter for valuable discussion of these topics. Ian sinail for pointing out the work of Giraud(1992).. and the anonymous referee for comments that led (o a greatly improved manuscript.," The authors wish to thank Paul Schechter for valuable discussion of these topics, Ian Smail for pointing out the work of \citet{gir92}, and the anonymous referee for comments that led to a greatly improved manuscript."
+ itis clearly due to the transition from the relativistic phase o the non-relativistic phase.,it is clearly due to the transition from the relativistic phase to the non-relativistic phase.
+ The simulation by Moderski. Sikora Bulik (1999) does not show such breaks. because heir model is not appropriate for non-relativistic expansion (lluang et al.," The simulation by Moderski, Sikora Bulik (1999) does not show such breaks, because their model is not appropriate for non-relativistic expansion (Huang et al."
+ 1999c): (ui) When £. is large. the break disappears.," 1999c); (iii) When $\xi_{\rm e}$ is large, the break disappears."
+ This is not dillicult to understand. (Huang οἱ al., This is not difficult to understand (Huang et al.
+ 1999c)., 1999c).
+ According to the analysis in the ultra-relativistic imit. the time that the light curve peaks scales as (Wijers Galama 1999: Bottteher Dermer 1999: Chevalier Li 1999) ποια Figure 3 we can also see that with the increase of £.. ly becomes larger and larger. consistent with equation (14)).," According to the analysis in the ultra-relativistic limit, the time that the light curve peaks scales as (Wijers Galama 1999; Bötttcher Dermer 1999; Chevalier Li 1999) >From Figure 3 we can also see that with the increase of $\xi_{\rm e}$, $t_{\rm m}$ becomes larger and larger, consistent with equation \ref{tm14}) )."
+ In the case of ἐς=1.0. ἐμι is as large as 10 s. Note that the expansion has already. ceased. to be ultra-relativistic at that moment.," In the case of $\xi_{\rm e} = 1.0$ , $t_{\rm m}$ is as large as $\sim 10^5$ s. Note that the expansion has already ceased to be ultra-relativistic at that moment."
+ Phen we can not see the initial rower Law decay (Le. with a 1.1) in the relativistic phase. and so it is not strange that the break due to the relativistic-rewtonian transition does not appear (Huang et al.," Then we can not see the initial power law decay (i.e., with $\alpha \sim 1.1$ ) in the relativistic phase, and so it is not strange that the break due to the relativistic-Newtonian transition does not appear (Huang et al."
+ 19000): (iv) In all cases. the light curves during the non-relativistic hase are characterized by quick decavs. with az2.1.," 1999c); (iv) In all cases, the light curves during the non-relativistic phase are characterized by quick decays, with $\alpha \geq 2.1$."
+ This is quite dillerent from isotropic fireballs. whose light curves steepen only slightly after entering the non-relativistic phase (Wijers. Rees Mésszárros 1997: Huang. Dai Lu 1998a).," This is quite different from isotropic fireballs, whose light curves steepen only slightly after entering the non-relativistic phase (Wijers, Rees Mésszárros 1997; Huang, Dai Lu 1998a)."
+ We thus suggest that the most obvious characteristic of jet ellects is à sharp decay. of afterglows at late stages (with aze 2)., We thus suggest that the most obvious characteristic of jet effects is a sharp decay of afterglows at late stages (with $\alpha \geq 2$ ).
+ Εις will be further proved by other figures followed., This will be further proved by other figures followed.
+ Figure 4 illustrates the ellect of £5 on the optical light curves., Figure 4 illustrates the effect of $\xi_{\rm B}^2$ on the optical light curves.
+ Again no break appears duringWdsctf., Again no break appears during.
+ Interestingly but not surprisingly. we see that £5 has an ellect. similar to £: for small values of £5. there are obvious breaks at the transition from relativistic stage to non-relativistic stage (Le. at (|10° s): but for large & values. the break disappears. we could only observe a single steep line with àzc2.1.," Interestingly but not surprisingly, we see that $\xi_{\rm B}^2$ has an effect similar to $\xi_{\rm e}$: for small values of $\xi_{\rm B}^2$, there are obvious breaks at the transition from relativistic stage to non-relativistic stage (i.e., at $t \sim 10^{6.5}$ s); but for large $\xi_{\rm B}^2$ values, the break disappears, we could only observe a single steep line with $\alpha \geq 2.1$."
+ The reason is also similar to that of &., The reason is also similar to that of $\xi_{\rm e}$.
+ With the increase of £5. {μι becomes larger and larger. as can be clearly seen from equation (14)).," With the increase of $\xi_{\rm B}^2$, $t_{\rm m}$ becomes larger and larger, as can be clearly seen from equation \ref{tm14}) )."
+ When {μι is large enough (i.e. enters the mildly relativistic zone). the initial power law cdecaving segment (with à~ 1.1) in the relativistic phase will be hidden completely.," When $t_{\rm m}$ is large enough (i.e., enters the mildly relativistic zone), the initial power law decaying segment (with $\alpha \sim 1.1$ ) in the relativistic phase will be hidden completely."
+ Then we can only see the quick decay in the Newtonian phase., Then we can only see the quick decay in the Newtonian phase.
+ The figure also shows that with the decrease of £5. the us density decreases substantially.," The figure also shows that with the decrease of $\xi_{\rm B}^2$, the flux density decreases substantially."
+ Figure 5 illustrates the effect of 6 on the light curves., Figure 5 illustrates the effect of $\theta_0$ on the light curves.
+" Lorsmall 6, values. the breaks due to the relativistic- transition are very obvious. consistent. with a recent analytic treatment by Wei Lu (1999)."," Forsmall $\theta_0$ values, the breaks due to the relativistic-Newtonian transition are very obvious, consistent with a recent analytic treatment by Wei Lu (1999)."
+ For large 6) , For large $\theta_0$ 
+sky-subtraction residuals are the dominant source of uncertainty over a wavelength interval of some 2000À..,"sky-subtraction residuals are the dominant source of uncertainty over a wavelength interval of some $2000\,$."
+ The spectroscopic region involved is extensive and includes features of significant astrophysical interest: examples include the Calcium triplet (8300. 8545. 8665 AY). a powerful diagnostic of stellar populations in low- galaxies. and the H.? + [OIII] 4959. 5007 eemission region in quasars and active galactic nuclei (AGN) in the redshift interval 0.4<2«OLS.," The spectroscopic region involved is extensive and includes features of significant astrophysical interest; examples include the Calcium triplet (8500, 8545, $8665\,$ ), a powerful diagnostic of stellar populations in low-redshift galaxies, and the $\beta$ + [OIII] 4959, $5007\,$ emission region in quasars and active galactic nuclei (AGN) in the redshift interval $0.4 < z < 0.8$."
+ With sufficient care (e.g.Boltonetal.2004) it is possible to quantify the noise properties of the SDSS spectra in the red. allowing the statistical significance of features to be estimated reliably.," With sufficient care \citep[e.g.][]{2004AJ....127.1860B} it is possible to quantify the noise properties of the SDSS spectra in the red, allowing the statistical significance of features to be estimated reliably."
+ However. the decrease in the S/N relative to that expected from counting statistics can be factors of 2-3.," However, the decrease in the S/N relative to that expected from counting statistics can be factors of 2-3."
+ Coupled with the substantial fraction of the spectral range affected. many potential scientific investigations are compromised.," Coupled with the substantial fraction of the spectral range affected, many potential scientific investigations are compromised."
+ The sky-subtraction procedures incorporated in the SDSS spectroscopic pipeline are very effective. overcoming a number of the longstanding problems associated with wide-tield multi-fibre observations.," The sky-subtraction procedures incorporated in the SDSS spectroscopic pipeline are very effective, overcoming a number of the longstanding problems associated with wide-field multi-fibre observations."
+ Brief details can be found in the Early Data Release paper (Stoughtonetal.2002.Sections4.8.5and4.10.1) and information on calibration improvements for the Second Data Release (DR2) are given in Abazajian et al. (2004a)..," Brief details can be found in the Early Data Release paper \citep[][Sections 4.8.5 and
+4.10.1]{2002AJ....123..485S} and information on calibration improvements for the Second Data Release (DR2) are given in Abazajian et al. \nocite{2004AJ....128..502A}."
+ While he large area of sky. 7.1 square areseconds. observed through he fibre aperture exacerbates the problem of achieving accurate sky-subtraction. the origin of the dominant systematic residuals resent in the SDSS spectra is not a preserve of fibre spectroscopy alone.," While the large area of sky, $7.1\,$ square arcseconds, observed through the fibre aperture exacerbates the problem of achieving accurate sky-subtraction, the origin of the dominant systematic residuals present in the SDSS spectra is not a preserve of fibre spectroscopy alone."
+ Rather. the fundamental issue lies in the ability to remove OH emission features from spectra in which the line profiles are barely resolved.," Rather, the fundamental issue lies in the ability to remove OH emission features from spectra in which the line profiles are barely resolved."
+ Combined with sub-pixel changes in the pixel-o-wavelength calibration between spectra. sharp residuals often remain.," Combined with sub-pixel changes in the pixel-to-wavelength calibration between spectra, sharp residuals often remain."
+ Kelson(2003). provides a recent summary of the difficulties associated with accurate sky-subtraction in long-slit observations. presenting a highly effective procedure for removing the signature of even rapidly varying and poorly sampled emission line features.," \citet{2003PASP..115..688K} provides a recent summary of the difficulties associated with accurate sky-subtraction in long-slit observations, presenting a highly effective procedure for removing the signature of even rapidly varying and poorly sampled emission line features."
+ The technique described by Kelson is certainly not applicable to the extracted tibre spectra available as part of the ofticial SDSS Data Releases and any improvement must rely on an alternative procedure., The technique described by Kelson is certainly not applicable to the extracted fibre spectra available as part of the official SDSS Data Releases and any improvement must rely on an alternative procedure.
+ The sky-subtraction residuals arise from the subtraction of two essentially identical tooth-comb signatures that have been very slightly misaligned relative to one another leading to well-detined patterns (Fig. |)., The sky-subtraction residuals arise from the subtraction of two essentially identical tooth-comb signatures that have been very slightly misaligned relative to one another leading to well-defined patterns (Fig. \ref{fig_skyegs}) ).
+ This suggests a correction procedure that takes advantage of the correlations present in the wavelength direction. offering significant advantages over simply masking the affected pixels.," This suggests a correction procedure that takes advantage of the correlations present in the wavelength direction, offering significant advantages over simply masking the affected pixels."
+ More specifically. we develop an approach for the removal of the dominant OH sky-subtraction residuals in the. SDSS spectra based on principal component analysis (PCA).," More specifically, we develop an approach for the removal of the dominant OH sky-subtraction residuals in the SDSS spectra based on principal component analysis (PCA)."
+ PCA (also called. Karhunen—Loevve transformation) is a) well-established data reduction technique in astronomy. frequently applied. to classification and reconstruction problems associated with large numbers of spectra of various types of object (e.g. galaxies: Connolly et al.," PCA (also called Karhunen–Loèvve transformation) is a well-established data reduction technique in astronomy, frequently applied to classification and reconstruction problems associated with large numbers of spectra of various types of object (e.g. galaxies: \nocite{1995AJ....110.1071C,1996MNRAS.283..651F,2002MNRAS.333..133M,
+2003ApJ...599..997M,2004AJ....128..585Y,1992ApJ...398..476F,astro-ph/0408578,
+1983A&AS...51..443W} Connolly et al."
+ 1995: Folkes et al., 1995; Folkes et al.
+ 1996: Madgwick et al., 1996; Madgwick et al.
+ 2002. 2003: Yip et al.," 2002, 2003; Yip et al."
+ 2004a., 2004a.
+ Quasars: Francis et al., Quasars: Francis et al.
+ 1992: Yip et al., 1992; Yip et al.
+ 2004b., 2004b.
+ Stars: Whitney 1983)., Stars: Whitney 1983).
+ The idea of employing PCA for sky-subtraction has been suggested by Kurtz&Mink(2000).. who present a complex method to remove the sky signal without the need for concurrent sky observations.," The idea of employing PCA for sky-subtraction has been suggested by \citet{2000ApJ...533L.183K}, who present a complex method to remove the sky signal without the need for concurrent sky observations."
+ However. the scheme appears to have generated little interest. perhaps because of the ambitious goal of the technique and the targeting of observations in which sky spectra are unavailable.," However, the scheme appears to have generated little interest, perhaps because of the ambitious goal of the technique and the targeting of observations in which sky spectra are unavailable."
+ By contrast. we develop a much more specific application of the PCA technique to the SDSS DR2 spectra that results in an improvement by over a factor of 2 in the S/N of those pixels longward of G700A affected by OH sky lines. dramatically increasing the potential use of the red half of the SDSS spectra for a variety of scientific investigations.," By contrast, we develop a much more specific application of the PCA technique to the SDSS DR2 spectra that results in an improvement by over a factor of 2 in the S/N of those pixels longward of $6700\,$ affected by OH sky lines, dramatically increasing the potential use of the red half of the SDSS spectra for a variety of scientific investigations."
+ The technique is equally applicable to the spectra in the recent DR3 release., The technique is equally applicable to the spectra in the recent DR3 release.
+ We adopt the same convention as employed in the SDSS and use vacuum wavelengths throughout the paper., We adopt the same convention as employed in the SDSS and use vacuum wavelengths throughout the paper.
+ In Section 2. we present our method which is applied to SDSS galaxy and quasar spectra in Section ??.., In Section \ref{sec_method} we present our method which is applied to SDSS galaxy and quasar spectra in Section \ref{sec_recon}.
+ Section 2? uses subsets of the SDSS DR2 spectroscopic catalogue to demonstrate application of the method to various astronomical studies.," Section \ref{sec_tests}
+ uses subsets of the SDSS DR2 spectroscopic catalogue to demonstrate application of the method to various astronomical studies."
+ The code and documentation with which to carry out the method on public release SDSS spectra is available on the web at, The code and documentation with which to carry out the method on public release SDSS spectra is available on the web at.
+ Our overall approach is determined by the extent of the spectroscopic information provided in a SDSS public data release., Our overall approach is determined by the extent of the spectroscopic information provided in a SDSS public data release.
+ The raw CCD exposures. typically + or 5 per spectroscopic plate. that make up the total exposure in each spectroscopic field are not available. precluding any attempt to improve the sky-subtraction on an exposure by exposure basis.," The raw CCD exposures, typically 4 or 5 per spectroscopic plate, that make up the total exposure in each spectroscopic field are not available, precluding any attempt to improve the sky-subtraction on an exposure by exposure basis."
+" However. the SDSS data releases ""o provide the tinal reduced spectra for both target objects and for the fibres allocated to blank sky regions employed to detine 18 underlying spectrum of the night sky."," However, the SDSS data releases do provide the final reduced spectra for both target objects and for the fibres allocated to blank sky regions employed to define the underlying spectrum of the night sky."
+ These contain significant yooiagnostie information about the quality of sky subtraction for each »ectroscopie plate., These contain significant diagnostic information about the quality of sky subtraction for each spectroscopic plate.
+ For each observation of a SDSS spectroscopic plate. yproximately 32> fibres. 16 for each| of the 2 spectrographs. are assigned to blank sky regions. selected from areas containing no detected objects in the SDSS imaging survey.," For each observation of a SDSS spectroscopic plate, approximately 32 fibres, 16 for each of the 2 spectrographs, are assigned to blank sky regions, selected from areas containing no detected objects in the SDSS imaging survey."
+" The sky fibres are identified as ""SKY"" in the catalogue's “OBJTYPE” and ""SPECCLASS"" field.", The sky fibres are identified as ” in the catalogue's ” and ” field.
+" The sky spectra are combined to create a ""master-skv"" spectrum for each spectroscopic plate. which is then scaled and subtracted from each of the 640 spectra. producing 608 sky-subtracted object spectra and 32 sky-subtracted sky spectra. all of which are part of the standard SDSS data releases."," The sky spectra are combined to create a “master-sky” spectrum for each spectroscopic plate, which is then scaled and subtracted from each of the 640 spectra, producing 608 sky-subtracted object spectra and 32 sky-subtracted sky spectra, all of which are part of the standard SDSS data releases."
+ Throughout the remainder of the paper we will refer to the sky-subtracted sky spectra as “sky spectra’. and the sky-subtracted object spectra as “object spectra”.," Throughout the remainder of the paper we will refer to the sky-subtracted sky spectra as “sky spectra”, and the sky-subtracted object spectra as “object spectra”."
+ The availability of large numbers of sky spectra. over 18.500 in DR2. thus provides a direct empirical measure of the noise resulting from) counting statistics as well as any systematic residuals from the sky-subtraction procedure.," The availability of large numbers of sky spectra, over 18,500 in DR2, thus provides a direct empirical measure of the noise resulting from counting statistics as well as any systematic residuals from the sky-subtraction procedure."
+ The scale of the SDSS releases is such that the application of empirical self-calibration techniques. based on the statistical properties of the data set itself. can be a powerful tool.," The scale of the SDSS releases is such that the application of empirical self-calibration techniques, based on the statistical properties of the data set itself, can be a powerful tool."
+ Visual inspection of the spectra of faint objects. or sky spectra (Fig. D).," Visual inspection of the spectra of faint objects, or sky spectra (Fig. \ref{fig_skyegs}) ),"
+ immediately reveals the presence of “patterns” due to small imperfections in sky subtraction., immediately reveals the presence of “patterns” due to small imperfections in sky subtraction.
+ The presence of systematic deviations that are correlated over extended wavelength ranges suggests that a technique capable of quantifying the form and amplitude of the correlated deviations could allow the removal of a substantial fraction of the sky-subtraction noise., The presence of systematic deviations that are correlated over extended wavelength ranges suggests that a technique capable of quantifying the form and amplitude of the correlated deviations could allow the removal of a substantial fraction of the sky-subtraction noise.
+ PCA is a well-established technique with a number of desirable properties for such an application., PCA is a well-established technique with a number of desirable properties for such an application.
+ The principles behind our sky-subtraction method are simple to understand: a PCA of the sky spectra produces a set of orthogonal components that provides a compact representation of, The principles behind our sky-subtraction method are simple to understand: a PCA of the sky spectra produces a set of orthogonal components that provides a compact representation of
+\ dwarfs are the dominant stellar compoient of the Galaxy by both ininber and mass.,M dwarfs are the dominant stellar component of the Galaxy by both number and mass.
+ With ain sequence Lifetimes nmich lounger than the age of the universe. they a‘ea fair tracer of the overall properties of the Galactic disk.," With main sequence lifetimes much longer than the age of the universe, they are a fair tracer of the overall properties of the Galactic disk."
+ Their clromospheric activity decays ο1 timescales of billions oL vears. providing au age indicator that is relevan Inx studies of Calaectic evolution.," Their chromospheric activity decays on timescales of billions of years, providing an age indicator that is relevant for studies of Galactic evolution."
+ By relatiug he activity levels in M dwarls to age. we cau measwe the local star formatjon history.," By relating the activity levels in M dwarfs to age, we can measure the local star formation history."
+ The latter yaraimeter is one of the majOr requirements in mo«elli1g the local substellar nass [fuuctio1 1999).., The latter parameter is one of the major requirements in modelling the local substellar mass function \citep{ldwarfmf}.
+ Àoreover. M dwarf componeuts in mutipe systems provide coustralints ou tlie age of he system.," Moreover, M dwarf components in multiple systems provide constraints on the age of the system."
+ Fiially. au exteusive sample of young. low-Iuninosity stars 1ui the field cau furuish a 2ime huutiue DODeround for unagiug surveys designed o [iud young. luminous own dwarL aud giant R9]auet companions.," Finally, an extensive sample of young, low-luminosity stars in the field can furnish a prime hunting ground for imaging surveys designed to find young, luminous brown dwarf and giant planet companions."
+ As with other low luminosity objects. detailec observatious are onlv possible foOM dwarfs -— the iminediate Solar Neiglibourhood.," As with other low luminosity objects, detailed observations are only possible for M dwarfs in the immediate Solar Neighbourhood."
+ The most exteusive source for such objects remaius the ‘eliminary version of the third Nearby Star Catalogue (Cliese&JalreiB1991.hereafter pCNS3).., The most extensive source for such objects remains the preliminary version of the third Nearby Star Catalogue \citep[hereafter pCNS3]{gj91}. .
+" Papers I (Reid.Hawley&Cizis1995) aud II (Hawles.Cizis&Hei(L99¢)) in this series descril (w moderate€ resolution ( 3A)). red (6200—T3 JOA)) spect""'OSCODIC οervatious of candida Ν warts in the pCNS3."," Papers I \citep{rhg95} and II \citep{hgr96} in this series describe our moderate resolution $\sim 3 $ ), red $6200-7500$ ) spectroscopic observations of candidate M dwarfs in the pCNS3."
+ We have used those spectra. together with clata [rom the literature. estimate cIsistances aud spectral types.," We have used those spectra, together with data from the literature, to estimate distances and spectral types."
+ In Paper I we defined a volume-lHiited sample of norther (à2—230* ) stars. ancl investigated the luminosity Ποσο aud sineiaties of low-1nass stars int Galactic disk.," In Paper I we defined a volume-limited sample of northern $\delta > -30\arcdeg$ ) stars, and investigated the luminosity function and kinematics of low-mass stars in the Galactic disk."
+ Paper IE presented data for the southern stars and investieatecl various aspects of the chromosj»herie behaviour of the whole sample using tle Ha ine as a In thisH paper. we presenti echelle observations of M. cdwarfs from the volume-lIimitec saldle defined in Paper 1. Qur eclelle spectra are of hieh ( .2A)) resolution aud cover tle waveleneth rauge [for all stars. with data extending to [Lor a subset of the brighter stars.," Paper II presented data for the southern stars and investigated various aspects of the chromospheric behaviour of the whole sample using the $\alpha$ line as a In this paper, we present echelle observations of M dwarfs from the volume-limited sample defined in Paper I. Our echelle spectra are of high $\sim .2 $ ) resolution and cover the wavelength range $\lambda\lambda 4800-9400$ for all stars, with data extending to for a subset of the brighter stars."
+ These observations eucompass Chromospheric emission lines due to hydrogen. helium. aud ionised calcium.," These observations encompass chromospheric emission lines due to hydrogen, helium, and ionised calcium."
+ Previous surveys of activity in 1 dwarls liave generally conceutrated ou earlier spectral types (< ML). as in the Ha surveys of 202 stars by (1956).. or have been limited to relatively sijall samples. suc ras the 21 late-type M chwarls observed by Ciampapa&Liebert(1986).," Previous surveys of activity in M dwarfs have generally concentrated on earlier spectral types $\le$ M4), as in the $\alpha$ surveys of 202 stars by \citet{sh86}, or have been limited to relatively small samples, such as the 24 late-type M dwarfs observed by \citet{gl86}."
+. Tle OLly publishec allaysis based ou a sample is the receut work by Dellosseetal.(1995.1999a).. who present observatious of field AL cdwarfs within eight parsecs.," The only published analysis based on a volume-limited sample is the recent work by \citet{dfpm98,dfbump99}, who present observations of field M dwarfs within eight parsecs."
+ Their spectroscopy las higher resolution hau our data. but their sample includes ouly 118 stars.," Their spectroscopy has higher resolution than our data, but their sample includes only 118 stars."
+ Our survey therefore provides a more «etailed study than hereto‘ore possible of the distribution of chromospheric activity amouest late-type dwarts. and. combined with an age-activily relation calibrated by ΔΙ dwarls in open clusters. the irst opportunity touse tlOne stars to probe the Calactic disk star formation histey.," Our survey therefore provides a more detailed study than heretofore possible of the distribution of chromospheric activity amongst late-type dwarfs, and, combined with an age-activity relation calibrated by M dwarfs in open clusters, the first opportunity touse those stars to probe the Galactic disk star formation history."
+contamination. we niust use some other method to separate the vellow supergiants Irom the [oreground. vellow stars.,"contamination, we must use some other method to separate the yellow supergiants from the foreground yellow stars."
+ We expect to be able to do this based on radial velocities. as the SMC has a heliocentric radial velocity of 158 km + (Richter et 11987). while stars in the Milky Way should have radial velocities around 0 kins !.," We expect to be able to do this based on radial velocities, as the SMC has a heliocentric radial velocity of 158 km $^{-1}$ (Richter et 1987), while stars in the Milky Way should have radial velocities around 0 km $^{-1}$."
+ Once (he vellow supergiant content has been determined. (he SMC's massive star population will have been characterized [rom one side of the IRD to the other.," Once the yellow supergiant content has been determined, the SMC's massive star population will have been characterized from one side of the HRD to the other."
+ Previous studies tell us much about OD stars and (heir evolved descendants. (he red supergiants and Woll-Ravet stars. and thus their numbers are all relatively well known (Massey. 2002. Massey et 11995. Massey. et 22003. \lassev Dully 2001. Massey Olsen 2003. Mokiem et 22006).," Previous studies tell us much about OB stars and their evolved descendants, the red supergiants and Wolf-Rayet stars, and thus their numbers are all relatively well known (Massey 2002, Massey et 1995, Massey et 2003, Massey Duffy 2001, Massey Olsen 2003, Mokiem et 2006)."
+ The completion of this massive star survey will provide a testing ground for both current and future stellar models., The completion of this massive star survey will provide a testing ground for both current and future stellar models.
+ In the following sections we will explain how we established membership of vellow supereiants in the SAIC! and how well our observations matched (he evolutionary (racks., In the following sections we will explain how we established membership of yellow supergiants in the SMC and how well our observations matched the evolutionary tracks.
+ In Secon 2 we describe our observation and reduction procedures., In Section \ref{OS} we describe our observation and reduction procedures.
+ In Section 3. we discuss how we separated the foreground stars from the SAIC supereiants., In Section \ref{A} we discuss how we separated the foreground stars from the SMC supergiants.
+ In Section 4 we put the SAIC! members on the IRD and compare the results with current evolutionary tracks aud in Section 5 we summarize our findings and list future goals., In Section \ref{HRD} we put the SMC members on the HRD and compare the results with current evolutionary tracks and in Section \ref{C} we summarize our findings and list future goals.
+ To identify F and G supergiants in the SMC. we initially selected stars from the USNO CCD Astrograph Catalogue Part 3 (UCACS) to have negligible proper motions (less than 15 mas tin à and 9).," To identify F and G supergiants in the SMC, we initially selected stars from the USNO CCD Astrograph Catalogue Part 3 (UCAC3) to have negligible proper motions (less than 15 mas $^{-1}$ in $\alpha$ and $\delta$ )."
+" We chose a 1.75? radius circle around 055""11* —72°57'00"" (J2000) to include most of the SMC's optical body and the cataloged OD associations (Hodge 1935).", We chose a $^\circ$ radius circle around $0^{h}55^{m}11^{s}$ $-72^\circ57\arcmin00\arcsec$ (J2000) to include most of the SMC's optical body and the cataloged OB associations (Hodge 1985).
+" We additionally included a small region centered on NGC 602 (172640° —73721'00"" (J2000)) in the wing of the SAIC. a region rich in OD stars."," We additionally included a small region centered on NGC 602 $1^{h}26^{m}40^{s}$ $-73^\circ21\arcmin00\arcsec$ (J2000)) in the wing of the SMC, a region rich in OB stars."
+" For control fields. we selected (wo 1.75* radius regions at the SAIC’s ealactie latitude (—44.2°) but 7.5 degrees higher and lower in ealactic longitude (2247""41. —72704/50"" (J2000) and 207435 —71741/20"" (J2000))."," For control fields, we selected two $^\circ$ radius regions at the SMC's galactic latitude $-44.2^\circ$ ) but 7.5 degrees higher and lower in galactic longitude $23^{h}47^{m}41^{s}$ $-72^\circ04\arcmin50\arcsec$ (J2000) and $2^{h}07^{m}43^{s}$ $-71^\circ41\arcmin20\arcsec$ (J2000))."
+ We used the stars’ 24ÀSS photometry (Skrutskie et 22006) to then select a sample in (he necessary color and magnitude range in order to be complete for vellow supereiants down to I2A£.. (, We used the stars' 2MASS photometry (Skrutskie et 2006) to then select a sample in the necessary color and magnitude range in order to be complete for yellow supergiants down to $M_\odot$. (
+Although 2—V. would be more sensitive to Tig. reliable B—V. values were not reaclily available for all of the UCACS stars.),"Although $B-V$ would be more sensitive to $T_{\rm eff}$, reliable $B-V$ values were not readily available for all of the UCAC3 stars.)"
+ Following Drout et ((2009). we define the vellow supergiant Tir range as 4800 Ix to 7500 Ix. The Geneva evolutionary (racks (Maeder Alevnet 2001) and the J and A magnitudes of Ixuruez's (1992) ATLASO stellar atmosphere," Following Drout et (2009), we define the yellow supergiant $T_{\rm eff}$ range as 4800 K to 7500 K. The Geneva evolutionary tracks (Maeder Meynet 2001) and the $J$ and $K$ magnitudes of Kurucz's (1992) ATLAS9 stellar atmosphere"
+to survive (?)..,to survive \citep{2005Howk}.
+" This is consistent with the low o,.. that we derive for the disk-halo clouds iu both quadrants.", This is consistent with the low $\sigma_{cc}$ that we derive for the disk-halo clouds in both quadrants.
+ Based ou the results from our comparisons of the QT aud QIV tangent samples. we therefore propose tle following scenario for the origin aud evolution of halo cclouds: the clouds are related to areas of star formation. where stella winds and supernova activity sweep aud push eas from the disk into the lower halo.," Based on the results from our comparisons of the QI and QIV tangent samples, we therefore propose the following scenario for the origin and evolution of halo clouds: the clouds are related to areas of star formation, where stellar winds and supernova activity sweep and push gas from the disk into the lower halo."
+ Some neutral gas resides in the walls of superbubbles. whose shells eventually fragment into clouds.," Some neutral gas resides in the walls of superbubbles, whose shells eventually fragment into clouds."
+ As star formation is abundant i spiral aris. the clouds are naturally correlated with the spiral structure of the Calaxy.," As star formation is abundant in spiral arms, the clouds are naturally correlated with the spiral structure of the Galaxy."
+ ILowever. as the timescale for formation of a superbubble (~20 30 Awa: 7273) as lavee compared to the lifetime of a star-formune region (~0.1 Mx: 23). clouds that are xoduced in shells may no lonecr be at the same locations as the sites where hiel-mass stars are formine at the xeseut day.," However, as the timescale for formation of a superbubble $\sim 20$ $30$ Myr; \citealt{2004deAvillez, 2006McClure-Griffiths}) ) is large compared to the lifetime of a star-forming region $\sim
+0.1$ Myr; \citealt{2007Prescott}) ), clouds that are produced in shells may no longer be at the same locations as the sites where high-mass stars are forming at the present day."
+ The scale heights of the cloud population are reasonable if the gas is brought iuto the lower halo x superbubbles or feedback. as high vertical velocities are not required.," The scale heights of the cloud population are reasonable if the gas is brought into the lower halo by superbubbles or feedback, as high vertical velocities are not required."
+ The maeuetic field lines ii a supershell are compressed (e.e.. 2)). which increases the maguetic oessure and mv aid in cloud stability if the clouds are related to supershells.," The magnetic field lines in a supershell are compressed (e.g., \citealt{2001Ferriere}) ), which increases the magnetic pressure and may aid in cloud stability if the clouds are related to supershells."
+ It is portant to contrast this scenario with that of a standard galactic fountain. which proposes that clouds are formed by the cooling aud condcusing of hot eas that has been expelled from the disk. which then falls back. towards the plane (27)..," It is important to contrast this scenario with that of a standard galactic fountain, which proposes that clouds are formed by the cooling and condensing of hot gas that has been expelled from the disk, which then falls back towards the plane \citep{1976Shapiro,1980Bregman}."
+ While this model has similarities to our proposed scenario. an iurportaut difference is that the distribution of clouds would not be expected to have siuall-scale features. such as à peaked radial distribution. or a dramatic difference in the ΠΠο of clouds between different regions of the Galaxy at simular radii as the hot eas from which they condense is expected to be fairly uuiform in the halo (?)..," While this model has similarities to our proposed scenario, an important difference is that the distribution of clouds would not be expected to have small-scale features, such as a peaked radial distribution, or a dramatic difference in the number of clouds between different regions of the Galaxy at similar radii, as the hot gas from which they condense is expected to be fairly uniform in the halo \citep{1980Bregman}."
+ Such features are clearly present in the disk-halo ccloud distributions. which argues for a scenario where clouds are produced more directly bv events occuring within spiral arms.," Such features are clearly present in the disk-halo cloud distributions, which argues for a scenario where clouds are produced more directly by events occurring within spiral arms."
+ There is also uo reason to expect the clouds to be associated with loops and filaments if related to a galactic fountain. but these structures are often observed.," There is also no reason to expect the clouds to be associated with loops and filaments if related to a galactic fountain, but these structures are often observed."
+ Iu recent vears the definition of a galactic fountain has been expanded to include not just the classical fountain but any scenario where eas is expelled from the disk iuto the lower halo and later returus to the disk reeardless of gas phase aud temperature (e.g. see 7]).," In recent years the definition of a galactic fountain has been expanded to include not just the classical fountain but any scenario where gas is expelled from the disk into the lower halo and later returns to the disk regardless of gas phase and temperature (e.g., see \citealt{2008Spitoni}) )."
+ Our proposal falls under this broader categorization of a ealactic fountain., Our proposal falls under this broader categorization of a galactic fountain.
+" A total of 255 disk-halo cclouds. some 2 kpe from the plane. were detected at the tangent points in the first quadrant region of CLASS data. a region in longitude. latitude and velocity that is sviunietrie to the fourth quadrant region studied iu Paper LE. Individual cloud properties iu the QI sample are very similar to those in the QTV sample. having median values Tk0.5 IK. Ae=10.6 kins!l. r=28 pe and Mg,=TOOAL..."," A total of 255 disk-halo clouds, some $>2$ kpc from the plane, were detected at the tangent points in the first quadrant region of GASS data, a region in longitude, latitude and velocity that is symmetric to the fourth quadrant region studied in Paper I. Individual cloud properties in the QI sample are very similar to those in the QIV sample, having median values $T_{\mathrm{pk}}=0.5$ K, $\Delta
+v=10.6$ km $^{-1}$, $r=28$ pc and $M_{HI}=700 M_{\odot}$."
+ The clouds do not have euouch lass to be sel-eravitatiug., The clouds do not have enough mass to be self-gravitating.
+ They must either be pressure-confined or transitory., They must either be pressure-confined or transitory.
+ The observed increase in linevidthi with distance from the plane suggestsOO that the clouds are pressure-confined aud that the linewidths reflect pressure variations throughout the halo., The observed increase in linewidth with distance from the plane suggests that the clouds are pressure-confined and that the linewidths reflect pressure variations throughout the halo.
+" The cloud-cloud line of sight velocity dispersion is also similar in both regious. with a value σι,2l6 luus Ἡ,"," The cloud-cloud line of sight velocity dispersion is also similar in both regions, with a value $\sigma_{cc}
+\approx 16$ km $^{-1}$."
+ Towever. the QT clouds lave twice the expoucutial scale icielit as the QTV clouds (/2800 pe vs. /=LOO pc).," However, the QI clouds have twice the exponential scale height as the QIV clouds $h=800$ pc vs. $h=400$ pc)."
+ As with the QTV sample. this is wav times larecr than cau )e supported by vertical motions with the magnitude of 16 cloud-cloud line of sight velocity dispersion.," As with the QIV sample, this is many times larger than can be supported by vertical motions with the magnitude of the cloud-cloud line of sight velocity dispersion."
+ Thus the scale height in the two quadrants is neither derived from ror even related to the measured velocity dispersion of 16 cloud population., Thus the scale height in the two quadrants is neither derived from nor even related to the measured velocity dispersion of the cloud population.
+ Both the cloud uuubers aud their Galactic distribution are also markedly different between the two regions. witli wee times as many clouds being detected in OI than in QTV.," Both the cloud numbers and their Galactic distribution are also markedly different between the two regions, with three times as many clouds being detected in QI than in QIV."
+ As the clouds were selected from a wuitorm data set using identical criteria. this difference between ie reeions inust result frou a fundamental asviunetrv )etwoeen the two parts of the Galaxy.," As the clouds were selected from a uniform data set using identical criteria, this difference between the regions must result from a fundamental asymmetry between the two parts of the Galaxy."
+ We bolieve that ie differences arise frou the coincideutal location of the QT sample on a region where a major spiral ari nierges aith the tip of the Galactic bar. whereas the QTV sample enconipasses only a portion of a minor spiral arm.," We believe that the differences arise from the coincidental location of the QI sample on a region where a major spiral arm merges with the tip of the Galactic bar, whereas the QIV sample encompasses only a portion of a minor spiral arm."
+ While wre Is no aerecmeut iu detail between the Galactic distributions of disk-halo cclouds and iregious. methanol masers. or molecular clouds. we μονο that a link with large-scale star forming reeious is the only explanation for the extreme difference in iiubers. distribution and scale height of clouds in the WO roelolns.," While there is no agreement in detail between the Galactic distributions of disk-halo clouds and regions, methanol masers, or molecular clouds, we believe that a link with large-scale star forming regions is the only explanation for the extreme difference in numbers, distribution and scale height of clouds in the two regions."
+ The most likely scenario is that the disk-halo cclouds are related to areas of star formation aud result roni stellar feedback aud superbubbles that have swept eas into the halo forming (or releasing) the clouds iu situ., The most likely scenario is that the disk-halo clouds are related to areas of star formation and result from stellar feedback and superbubbles that have swept gas into the halo forming (or releasing) the clouds in situ.
+ These events occur frequently within spiral aris. mt take tens of Myr. to reach thei maxima extent. weowhich time the stellar clusters that produced them are no longer active in star formation.," These events occur frequently within spiral arms, but take tens of Myr to reach their maximum extent, by which time the stellar clusters that produced them are no longer active in star formation."
+ Simulations of superbubble expansion (e.g. ?: Ford et al.," Simulations of superbubble expansion (e.g., \citealt{2008Melioli}; Ford et al.,"
+ iu xeparation) aud semi-uialvtie models (e... 7)) show hat this is a viable mechanisin for producing cclouds in the lower halo.," in preparation) and semi-analytic models (e.g., \citealt{2008Spitoni}) ) show that this is a viable mechanism for producing clouds in the lower halo."
+ Disk-halo ceclouds are abuudaut in both QI and QTV. a volune of umnv kpe?.," Disk-halo clouds are abundant in both QI and QIV, a volume of many $^3$."
+ They are uot an isolated phenomenon. bu a inajor component of the Galaxy.," They are not an isolated phenomenon, but a major component of the Galaxy."
+ The properties of the disk-halo cloud population rule out the possibility that nost of the clouds are created through tidal stripping of satellite galaxies or infalling primordial gas he clouds are clearly a disk population. concentrated toward the aue. highly coupled to Galactic rotation. aud correlatec with the spiral structure of the Galaxy.," The properties of the disk-halo cloud population rule out the possibility that most of the clouds are created through tidal stripping of satellite galaxies or infalling primordial gas — the clouds are clearly a disk population, concentrated toward the plane, highly coupled to Galactic rotation, and correlated with the spiral structure of the Galaxy."
+ The disk-halo cclouds therefore play an important role in Calaxy evolution aud the circulation of gas between the disk ar iilo. and are likely couuion in nuuiv external galaxies. hough the augular resolution and scusitivity liuuts of current mstrinents would make their detection difficult.," The disk-halo clouds therefore play an important role in Galaxy evolution and the circulation of gas between the disk and halo, and are likely common in many external galaxies, though the angular resolution and sensitivity limits of current instruments would make their detection difficult."
+ We thank an anonviuous referee for conuuents that led to improvements in the presentation and clarity of this work. R. A. Benjamin for a discussion of the GLIAMIPSE model of the Galaxy. D. Saxton for his help," We thank an anonymous referee for comments that led to improvements in the presentation and clarity of this work, R. A. Benjamin for a discussion of the GLIMPSE model of the Galaxy, B. Saxton for his help"
+"how to efficiently model the full shock dynamics (Berezhko&Vélk2006;Caprioli,et.al.2010:Zank2000:Lietal.2003:Lee 2005).","how to efficiently model the full shock dynamics \citep{bv06,ckvj10,zank00,li03,Lee05}."
+". To efficiently model the shock dynamics and the particles’ acceleration, there are largely three basic approaches: stationary Monte Carlo simulations, tully numerical simulations, and semi-analytic solutions."," To efficiently model the shock dynamics and the particles' acceleration, there are largely three basic approaches: stationary Monte Carlo simulations, fully numerical simulations, and semi-analytic solutions."
+" In the stationary Monte Carlo simulations, the full particle population with a prescribed scattering law is calculated based on the particle-in-cell (PIC) techniques (Ellisonetal.1996;Vladimirov2006)."," In the stationary Monte Carlo simulations, the full particle population with a prescribed scattering law is calculated based on the particle-in-cell (PIC) techniques \citep{ebj96,veb06}."
+". In the fully numerical simulations, a time-dependent diffusion-convection equation for the CR transport is solved with coupled gas dynamics conservation laws (Kang&Jones2007;ZirakashviliAharonian2010)."," In the fully numerical simulations, a time-dependent diffusion-convection equation for the CR transport is solved with coupled gas dynamics conservation laws \citep{kj07,ZA10}."
+". In the semi-analytic approach, the stationary or quasi-stationary diffusion-convection equations coupled to the gas dynamical equations are solved (Blasi.et.al.2007:Malkov,2000)."," In the semi-analytic approach, the stationary or quasi-stationary diffusion-convection equations coupled to the gas dynamical equations are solved \citep{bac07,mdv00}."
+". Since the velocity distribution of suprathermal particles in the Maxwellian tail is not isotropic in the shock frame, the diffusion-convection equation cannot directly follow the injection from the non-ditfusive thermal pool into the diffusive CR population."," Since the velocity distribution of suprathermal particles in the Maxwellian tail is not isotropic in the shock frame, the diffusion-convection equation cannot directly follow the injection from the non-diffusive thermal pool into the diffusive CR population."
+" So considering both the quasi-stationary analytic models and the time-dependent numerical models. the injection of particles into the acceleration mechanism is based on an assumption of the transparency function for thermal leakage (Blasi,et.al.2005:Jones2007;Vainio&Laitinen 2007)..."," So considering both the quasi-stationary analytic models and the time-dependent numerical models, the injection of particles into the acceleration mechanism is based on an assumption of the transparency function for thermal leakage \citep{bgv05,kj07,vainio07}."
+" Thus, the dynamical Monte Carlo simulations based on the PIC techniques are expected to model the shock dynamics time-dependently and also can eliminate the suspicion arising from the assumption of the injection (Knerr,1996;Wang&Yan 2011)."," Thus, the dynamical Monte Carlo simulations based on the PIC techniques are expected to model the shock dynamics time-dependently and also can eliminate the suspicion arising from the assumption of the injection \citep{knerr96,wang11}."
+". In plasma simulation (PIC and hybrid), there is no distinction between thermal and non-thermal particles, hence particle injection is intrinsically defined by the prescribed scattering properties, and so it 15 not controlled with à free parameter (Caprioli,et.al.2010)."," In plasma simulation (PIC and hybrid), there is no distinction between thermal and non-thermal particles, hence particle injection is intrinsically defined by the prescribed scattering properties, and so it is not controlled with a free parameter \citep{ckvj10}."
+. Actually. Wang citewangl1l have extended the dynamical Monte Carlo models with an anisotropic scattering law.," Actually, Wang \\cite{wang11} have extended the dynamical Monte Carlo models with an anisotropic scattering law."
+ Unlike the previous isotropic prescribed scattering law. the Gaussian scattering angular distribution is used as the complete prescribed scattering law.," Unlike the previous isotropic prescribed scattering law, the Gaussian scattering angular distribution is used as the complete prescribed scattering law."
+" According to the extended prescribed scattering law, we obtained a series of similar energy spectrums with little difference in terms of the tail."," According to the extended prescribed scattering law, we obtained a series of similar energy spectrums with little difference in terms of the power-law tail."
+" However, it is not clear how such a prescribed scattering law can affect the particles’ diffusion and the shock dynamics evolution."," However, it is not clear how such a prescribed scattering law can affect the particles' diffusion and the shock dynamics evolution."
+" To probe these problems, we expect to diagnose the energy losses in the simulations by monitoring all of the behaviors of the simulated particles."," To probe these problems, we expect to diagnose the energy losses in the simulations by monitoring all of the behaviors of the simulated particles."
+" In the time-dependent Monte Carlo models coupled with a Gaussian angular scattering law, the results show that the total energy spectral index and the compression ratio are both effected by the preseribed scattering law."," In the time-dependent Monte Carlo models coupled with a Gaussian angular scattering law, the results show that the total energy spectral index and the compression ratio are both effected by the prescribed scattering law."
+" Specifically, the total energy spectral index is an increasing function of the dispersion of the scattering angular distribution, but the subshock's energy spectral index is a digressive function of the dispersion of the scattering angular distribution (Wang&Yan2011)."," Specifically, the total energy spectral index is an increasing function of the dispersion of the scattering angular distribution, but the subshock's energy spectral index is a digressive function of the dispersion of the scattering angular distribution \citep{wang11}."
+" In the dynamical Monte Carlo simulations, one find that it is the only way for the particles to escape upstream via free escaped boundary (FEB)."," In the dynamical Monte Carlo simulations, one find that it is the only way for the particles to escape upstream via free escaped boundary (FEB)."
+" With the same size of the FEB which limited the maximum energy of accelerated particles, we find that different Gaussian scattering angular"," With the same size of the FEB which limited the maximum energy of accelerated particles, we find that different Gaussian scattering angular"
+"high-flux phases, whereas the spectrum is much softer for low flux phases because of the lower energy cutoff.","high-flux phases, whereas the spectrum is much softer for low flux phases because of the lower energy cutoff."
+" Figure presents the SED averaged over the phase ranges of the three simultaneous observations during the first outburst (phases 0.62, 0.66 and 0.70), and shows that both the flux levels and the photon indices at X-ray and VHE are well reproduced."," Figure \ref{fig:sed}
+ presents the SED averaged over the phase ranges of the three simultaneous observations during the first outburst (phases 0.62, 0.66 and 0.70), and shows that both the flux levels and the photon indices at X-ray and VHE are well reproduced."
+" We found that the phase-averaged SED calculated using a power law with a,=2.1 and a high-energy cutoff produces flux too high in energies between 10 and GGeV when compareda to the phase-averaged spectrum measured by Fermi//LAT(?).", We found that the phase-averaged SED calculated using a power law with $\alpha_\mathrm{e}=2.1$ and a high-energy cutoff produces a flux too high in energies between 10 and GeV when compared to the phase-averaged spectrum measured by /LAT.
+. The GeV spectrum and fluxes along the orbit appear incompatible with one leptonic population., The GeV spectrum and fluxes along the orbit appear incompatible with one leptonic population.
+" A way to avoid this excess flux is to consider the electron injection spectrum described by a broken power law with a harder particle index below E,=4x10!! eeV. We found that the softest particle index for which the computed GeV spectrum is compatible with the Fermi//LAT measurement is o,S1.8.", A way to avoid this excess flux is to consider the electron injection spectrum described by a broken power law with a harder particle index below $E_\mathrm{e}=4\times10^{11}$ eV. We found that the softest particle index for which the computed GeV spectrum is compatible with the /LAT measurement is $\alpha_\mathrm{e}\la 1.8$.
+" It must be noted that this change in the particle index at low energies does not affect the spectrum of particles that emit in the X-ray and VHE bands through synchrotron and IC, respectively."," It must be noted that this change in the particle index at low energies does not affect the spectrum of particles that emit in the X-ray and VHE bands through synchrotron and IC, respectively."
+ The Fermi//LAT spectrum along with the computed phase averaged SED is shown in Fig. 5.., The /LAT spectrum along with the computed phase averaged SED is shown in Fig. \ref{fig:sedavg}.
+ The X-ray/VHE flux ratio is a very sensitive indicator of the magnetic field in the emitter., The X-ray/VHE flux ratio is a very sensitive indicator of the magnetic field in the emitter.
+ We found the magnetic field that best describes the observed light curves by performing a exploration of the parameter space of B and the normalization of the injected particle spectrum Qo., We found the magnetic field that best describes the observed light curves by performing a exploration of the parameter space of $B$ and the normalization of the injected particle spectrum $Q_0$.
+" For each (B,Qo) pair we calculated the X-ray and VHE light curves and estimated the goodness-of-fit to the observed flux points using a x? test."," For each $(B,Q_0)$ pair we calculated the X-ray and VHE light curves and estimated the goodness-of-fit to the observed flux points using a $\chi^2$ test."
+" The observed light curves are best described using an ambient magnetic field of B—0.22 G. It is not trivial to set a formal uncertainty range on this value because of the unknown number of constraints that should be considered (e.g., the shape used for the adiabatic cooling curve)."," The observed light curves are best described using an ambient magnetic field of $B=0.22$ G. It is not trivial to set a formal uncertainty range on this value because of the unknown number of constraints that should be considered (e.g., the shape used for the adiabatic cooling curve)."
+" However, we see that for variations of the order of 0.05 G around the best-fit value of B=0.22 G the observed X-ray and VHE light curves are no longer well described by the computed ones."," However, we see that for variations of the order of $0.05$ G around the best-fit value of $B=0.22$ G the observed X-ray and VHE light curves are no longer well described by the computed ones."
+ The adopted luminosity in injected accelerated particles is around 2x10? aalong the whole orbit., The adopted luminosity in injected accelerated particles is around $2\times10^{35}$ along the whole orbit.
+" The computed emission bolometric luminosity, on the other hand, varies between 10? and ~1.5x1055 ergs.."," The computed emission bolometric luminosity, on the other hand, varies between $\sim$$10^{34}$ and $\sim$$1.5\times10^{35}$ ."
+ Note that the adopted injected luminosity is only a lower limit because we arbitrarily chose the lowest ratio between the X-ray flux and the adiabatic cooling time scale., Note that the adopted injected luminosity is only a lower limit because we arbitrarily chose the lowest ratio between the X-ray flux and the adiabatic cooling time scale.
+" For higher adiabatic losses (while still proportional to X-ray emission), the"," For higher adiabatic losses (while still proportional to X-ray emission), the"
+"fy|OLLP:O26P,,5. and the second to fy|OOLP,τνL062,ων.","$t_0+0.11P_{orb} \div t_0+0.26P_{orb}$, and the second – to $t_0+0.91P_{orb} \div t_0+1.06P_{orb}$."
+ Figures la and tb show the ceusity distributions for the moments of time of these two sets., Figures 4a and 4b show the density distributions for the moments of time of these two sets.
+ Analysis of the data of Fig., Analysis of the data of Fig.
+ lao. shows that the blob retains by its interaction with the aris if spiral shocks.," 4a,b, shows that the blob retains by its interaction with the arms if spiral shocks."
+ Let us cousider this mechauisia im detail., Let us consider this mechanism in detail.
+ Tuitially appearing as the residue of the stream. the blob tends to distribute muitormiy along the disk under the action of dissipatio- but retards after passing trough spiral shock so the commpactuess of the blob retains.," Initially appearing as the residue of the stream, the blob tends to distribute uniformly along the disk under the action of dissipation but retards after passing trough spiral shock so the compactness of the blob retains."
+ Later tle Increasing deusitv contrast between the blob and the disk and growths of pressure eracdicut will force the sandstilled blob to move., Later the increasing density contrast between the blob and the disk and growths of pressure gradient will force the standstilled blob to move.
+ When reaching the second arm of spiral shock the process of formatiou/retainent of the blob is repeated., When reaching the second arm of spiral shock the process of formation/retainment of the blob is repeated.
+ This mechanisii is confirmed bv data of Fie., This mechanism is confirmed by data of Fig.
+ 5., 5.
+ Figure 5a preseuts the velocity of the blob (he velocity of the point with naxinal density} versus time (solid line)., Figure 5a presents the velocity of the blob (the velocity of the point with maximal density) versus time (solid line).
+ The seplerian velocity of his point Vj=ναr is also shown bv dashed. line., The keplerian velocity of this point $V_{K}=\sqrt{GM_1/r}$ is also shown by dashed line.
+" The velocity variations are shown for time iuterval ty|V91P,τν|1.)1DP,,5 including the time interval or Fie.", The velocity variations are shown for time interval $t_0+0.91P_{orb} \div t_0+1.11P_{orb}$ including the time interval for Fig.
+ tb aud covering the full seriod of blob's revolution., 4b and covering the full period of blob's revolution.
+ Figure 5b shows variation of maximal density in the equatorial aue for the same time interval., Figure 5b shows variation of maximal density in the equatorial plane for the same time interval.
+ I Is seen roni Fig., It is seen from Fig.
+" 5 tha uatter ds retarded after owssius the shock aux becomes more dense. he maximal deusitv Όρων being increased 1.5 ines,"," 5 that matter is retarded after passing the shock and becomes more dense, the maximal density $\rho_{max}$ being increased 1.5 times."
+ When accinimlatiue a sufficient amount of matter. the blob comes off the shock aud its velocity ducreascs while maximal deusitv decreases.," When accumulating a sufficient amount of matter, the blob comes off the shock and its velocity increases while maximal density decreases."
+ After passing the second arm of spiral shock the blob is retarded again., After passing the second arm of spiral shock the blob is retarded again.
+ Note hat the coutrast of density between the blob and the disk remains the same up to the noment when the blob disappears., Note that the contrast of density between the blob and the disk remains the same up to the moment when the blob disappears.
+ Iu this ποιοί of time the disk is contracted aud spiral shock disappears as well., In this moment of time the disk is contracted and spiral shock disappears as well.
+ Later the density. contrast blob/disk decreases under he action of dissipation but the blob exists up to the full vanishing of the disk., Later the density contrast blob/disk decreases under the action of dissipation but the blob exists up to the full vanishing of the disk.
+ This is illustrated in Fie., This is illustrated in Fig.
+ 6 where tine depeucdency of he density contrast blob/disk is shown., 6 where time dependency of the density contrast blob/disk is shown.
+ The aree value of density contrast as well as the variable velocity of the blob revolution (but with constant period ~ 0.182.) make this feature very interesting for observations., The large value of density contrast as well as the variable velocity of the blob revolution (but with constant period $\sim0.18P_{orb}$ ) make this feature very interesting for observations.
+ We have presented the results of 3D nmnuerical simulations of niass transfer m senüdoetacled Dinarics after the mass trauster termination., We have presented the results of 3D numerical simulations of mass transfer in semidetached binaries after the mass transfer termination.
+ Prior to simulation of flow structure with turned-off ass transfer the nemr-steadv-state solutions for the case of coustaut nou-zero rate of mass transfer was obtained aud used as the initial couditious., Prior to simulation of flow structure with `turned-off' mass transfer the near-steady-state solutions for the case of constant non-zero rate of mass transfer was obtained and used as the initial conditions.
+ At tle mouent of time f.=fy the rate of mass rausfer was decreased iu five order of magnitude. which corresponds o the cessation of mass trausfer.," At the moment of time $t=t_0$ the rate of mass transfer was decreased in five order of magnitude, which corresponds to the cessation of mass transfer."
+" To investigate the influence of the viscosity we conduct 3 ruus for various values of viscosity. corresponding to following values ofparameter o (Gn terms of a-disk)y: à~O08:OL LOL: 0.06. aud à50.01.:0,02."," To investigate the influence of the viscosity we conduct 3 runs for various values of viscosity, corresponding to following values of parameter $\alpha$ (in terms of $\alpha$ -disk): $\alpha\sim0.08\div0.1$, $\alpha\sim0.04\div0.06$ , and $\alpha\sim0.01\div0.02$."
+ The investigation of structure of he residual disk reveals an essential increasing of dts Ποιο when the viscosity deceases., The investigation of structure of the residual disk reveals an essential increasing of its lifetime when the viscosity deceases.
+" Eveu for (Q0v105 the lifetime of residual disk exceeds 12DP,4. and for a~0.01 (tha js fvpica Oroervable accretion disks) the lifetime of residual disk is as uuch as 507,4."," Even for $\alpha\sim0.05$ the lifetime of residual disk exceeds $12P_{orb}$, and for $\alpha\sim0.01$ (that is typical for observable accretion disks) the lifetime of residual disk is as much as $50P_{orb}$."
+" Our sinulatious show that near the momen of time f£=ty|0.22, the flow structure is chauged significautly.", Our simulations show that near the moment of time $t=t_0+0.2P_{orb}$ the flow structure is changed significantly.
+ The stream from E doesut dominate anvinore. and the shape of accretion disk changes from quasi-elliptical to circular.," The stream from $L_1$ doesn't dominate anymore, and the shape of accretion disk changes from quasi-elliptical to circular."
+ The second iu of tically induces spiral shock is formed while earlier (before the ternunmation of mass transfer) it was suppressed by the stream from Z4., The second arm of tidally induced spiral shock is formed while earlier (before the termination of mass transfer) it was suppressed by the stream from $L_1$.
+ The Lass of the disk is eracdually decreased but spiral shocks exist practically wp to the full vanishing of the disk., The mass of the disk is gradually decreased but spiral shocks exist practically up to the full vanishing of the disk.
+ Our simulations also show that a deuse blob is formed in the residual disk. the velocity of the blob motion through the disk Deine variable.," Our simulations also show that a dense blob is formed in the residual disk, the velocity of the blob motion through the disk being variable."
+ The blob doesut siuear out macer he action of dissipation but is sustained by interaction with axius of spiral shock up to the uonment of time when spiral shock disappears., The blob doesn't smear out under the action of dissipation but is sustained by interaction with arms of spiral shock up to the moment of time when spiral shock disappears.
+" The deusitv coutrast between the blob aud he disk is rather large 1.6 aud begins to decrease ouly when spiral shock disappears (it occurs at time ~fy| 107,4) but even for lis time aud up to the full vanishing of the", The density contrast between the blob and the disk is rather large $\sim1.6$ and begins to decrease only when spiral shock disappears (it occurs at time $\sim t_0+10P_{orb}$ ) but even for this time and up to the full vanishing of the
+ , 
+and submillimeter emissions (preferentially in the 850. pm band) for galaxies at z=(5.7. 6.6: FIR in the LAE rest-frame) are correlated and. therefore. a fraction of high-z LAEs (but significantly smaller than the predicted by Finkelstein et al. 2009c)),"and submillimeter emissions (preferentially in the 850 $\mu\textrm{m}$ band) for galaxies at z=(5.7, 6.6; FIR in the LAE rest-frame) are correlated and, therefore, a fraction of high-z LAEs (but significantly smaller than the predicted by Finkelstein et al. \cite{finkelstein09c}) )"
+ could be observed in the submillimeter regime., could be observed in the submillimeter regime.
+ This could be supported by the spatial correlation claimed between SMGs and LAEs. where both populations act as high density tracers (Tamura et al. 2009)).," This could be supported by the spatial correlation claimed between SMGs and LAEs, where both populations act as high density tracers (Tamura et al. \cite{tamura09}) )."
+ Thus. AGN fraction. dust contents. and correlation with FIR data would help to provide clues for the evolution of LAEs.," Thus, AGN fraction, dust contents, and correlation with FIR data would help to provide clues for the evolution of LAEs."
+ From this brief review. it is clear that the high-z LAE properties are poorly known and on other hand. finding possible counterparts of these objects i the FIR and submillimeter regimes -as we try to demonstrate in this paper- can help to constrain the nature of this apparent duality of LAEs.," From this brief review, it is clear that the high-z LAE properties are poorly known and on other hand, finding possible counterparts of these objects in the FIR and submillimeter regimes -as we try to demonstrate in this paper- can help to constrain the nature of this apparent duality of LAEs."
+ We present the first results of a multiwavelength analysis of LAE candidates with observations performed with the ESA Space Observatory (Pilbratt et al. 2010)), We present the first results of a multiwavelength analysis of LAE candidates with observations performed with the ESA Space Observatory (Pilbratt et al. \cite{pilbratt10}) )
+ anc the PACS instrument (Poglitsch et al. 2010)), and the PACS instrument (Poglitsch et al. \cite{poglitsch10}) )
+ in the framework of the PACS Evolutionary Probe (PEP. PI D. Lutz).," in the framework of the PACS Evolutionary Probe (PEP, PI D. Lutz)."
+ The PEP is the Guaranteed Time Key-Project designed to obtai the best profit from instrumentation to study the FIR galaxy population., The PEP is the Guaranteed Time Key-Project designed to obtain the best profit from instrumentation to study the FIR galaxy population.
+ In our case. only very strong and dusty LAEs could be detected with PACS.," In our case, only very strong and dusty LAEs could be detected with PACS."
+" Finally. a relative fractio of LAEs hosting AGNs with respect to the overall populatio is estimated,"," Finally, a relative fraction of LAEs hosting AGNs with respect to the overall population is estimated."
+ Throughout this paper a concordant cosmology with Ho=70kms!Mpe? is assumed., Throughout this paper a concordant cosmology with ${\rm H}_0=70\ {\rm km}\ {\rm s}^{-1}\ {\rm Mpc}^{-3}$ is assumed.
+ Unless otherwise specified. all magnitudes are given in the AB system.," Unless otherwise specified, all magnitudes are given in the AB system."
+ We searched for FIR counterparts of LAEs at z~2.2 in the northeastern half of the GOODS-North field (- 70 sq-aremin) by using selected filters of the ALHAMBRA system as a part of a more extended study., We searched for FIR counterparts of LAEs at ${\rm z} \sim 2.2$ in the northeastern half of the GOODS-North field $\sim$ 70 sq-arcmin) by using selected filters of the ALHAMBRA system as a part of a more extended study.
+ The Advanced Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) survey is aimed at providing a tomography of the evolution of the contents of the universe over most of their cosmic history (see Moles et al., The Advanced Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) survey is aimed at providing a tomography of the evolution of the contents of the universe over most of their cosmic history (see Moles et al.
+ 2008 for a more detailed description of the survey and its scientific goals).," \cite{moles08}
+ for a more detailed description of the survey and its scientific goals)."
+ This novel approach employs 20 contiguous. equal-width. ~ FWHM320 ttop-hat filters covering from 3500 to 9700 plus the Johnson-standard JHKs near-infrared (NIR) bands. to observe a total area of 3.5 deg? on the sky (a description of the ALHAMBRA photometric system is given in Aparicio Villegas et al. 2010)).," This novel approach employs 20 contiguous, equal-width, $\sim$ 320 top-hat filters covering from 3500 to 9700 plus the Johnson-standard JHKs near-infrared (NIR) bands, to observe a total area of 3.5 ${\rm deg}^2$ on the sky (a description of the ALHAMBRA photometric system is given in Aparicio Villegas et al. \cite{apariciov10}) )."
+ The observations were carried out with the Calar Alto 3.5 m telescope using the wide-field cameras in the optical. Large Area Imager for Calar Alto (LAICA). and in the NIR. Omega-2000.," The observations were carried out with the Calar Alto 3.5 m telescope using the wide-field cameras in the optical, Large Area Imager for Calar Alto (LAICA), and in the NIR, Omega-2000."
+ The magnitude limits achieved by ALHAMBRA are AB = 25.5 mag (for an unresolved object. the signal-to-noise ratio S/N=5) in the optical filters from the blue to 8300A.. and from AB = 24.7 to 23.4 for the redder ones.," The magnitude limits achieved by ALHAMBRA are AB = 25.5 mag (for an unresolved object, the signal-to-noise ratio S/N=5) in the optical filters from the blue to 8300, and from AB = 24.7 to 23.4 for the redder ones."
+ The limits in the NIR are in the Vega system J~22 mag. H~21] mag. and Ks~20 mag.," The limits in the NIR are in the Vega system $\sim$ 22 mag, $\sim$ 21 mag, and $\sim$ 20 mag."
+ The searching procedure adopted is similar to the well- narrow-band techniques used to find high-redshift galaxies (Cowie Hu 1998.. Gronwall et al. 2007..," The searching procedure adopted is similar to the well-known narrow-band techniques used to find high-redshift galaxies (Cowie Hu \cite{cowie98}, Gronwall et al. \cite{gronwall07},"
+ Ouchi et al. 2008..," Ouchi et al. \cite{ouchi08},"
+ Shioya et al. 2009..," Shioya et al. \cite{shioya09},"
+ Murayama et al. 2007)).," Murayama et al. \cite{murayama07}) ),"
+ but instead of a combination of narrow and broad filters to isolate the line and define the continuum. we used selected ALHAMBRA intermediate bandpass filters for both purposes.," but instead of a combination of narrow and broad filters to isolate the line and define the continuum, we used selected ALHAMBRA intermediate bandpass filters for both purposes."
+ Details of the methodology are given in the online Appendix ??.., Details of the methodology are given in the online Appendix \ref{sect:z2LyaCandidatesSelection}.
+ Figure 1. shows a detail of the medium-band color-magnitude distribution for our catalog of 2532 spurious-free sources. detected in the northeast fraction of the GOODS-North field.," Figure \ref{CMD} shows a detail of the medium-band color-magnitude distribution for our catalog of 2532 spurious-free sources, detected in the northeast fraction of the GOODS-North field."
+ After applying the color- and limiting magnitude selection criteria defined in Appendix ??.. with an additional o color-magnitude restriction (dashed line in Fig. 1)).," After applying the color- and limiting magnitude selection criteria defined in Appendix \ref{sect:z2LyaCandidatesSelection}, with an additional $\sigma$ color-magnitude restriction (dashed line in Fig. \ref{CMD}) ),"
+ we found 134 raw LAE candidates., we found 134 raw LAE candidates.
+ This gives a mean number density of ~2x10Mpe7., This gives a mean number density of $\sim2\times10 ^{-3}\ \textrm{Mpc}^{-3}$.
+ However. without spectroscopic information for a statistically significant sample of our raw LAE candidates. these sources were fitted with galaxy templates BCO3 (Bruzual Charlot 2003)). using the procedure described in Appendix ?? to discard the continuum-only objects that show a color excess.," However, without spectroscopic information for a statistically significant sample of our raw LAE candidates, these sources were fitted with galaxy templates BC03 (Bruzual Charlot \cite{bruzual03}) ), using the procedure described in Appendix \ref{sect:z2LyaCandidatesSelection} to discard the continuum-only objects that show a color excess."
+ Individual fittings also allow us to obtain reliable photometric redshifts and preliminary spectral classifications for the raw LAE candidates., Individual fittings also allow us to obtain reliable photometric redshifts and preliminary spectral classifications for the raw LAE candidates.
+ For this purpose. we adopted the photometry from Capak et al. (2004))," For this purpose, we adopted the photometry from Capak et al. \cite{capak04}) )"
+ in the optical (UBVRIZz’) instead of the ALHAMBRA one., in the optical (UBVRIz') instead of the ALHAMBRA one.
+ The former data are about 1.1 to 1.5 mag (AB) deeper in U. B. V. and R bands than the latter.," The former data are about 1.1 to 1.5 mag (AB) deeper in U, B, V, and R bands than the latter."
+ Not so for the NIR photometry. where ALHAMBRA data are given in the canonical bands.," Not so for the NIR photometry, where ALHAMBRA data are given in the canonical bands."
+ After applying this procedure. we combined the results with an analysis of detection reliability of the Lyc emission line and found 16 secure candidates to LAEs. which are represented in the color-magnitude diagram of Fig.," After applying this procedure, we combined the results with an analysis of detection reliability of the $\alpha$ emission line and found 16 secure candidates to LAEs, which are represented in the color-magnitude diagram of Fig."
+ | with their corresponding error bars., \ref{CMD} with their corresponding error bars.
+ Optical pseudo-spectra from ALHAMBRA survey and relevant data of these LAEs. including the estimated Lya luminosity. are given in online Fig.," Optical pseudo-spectra from ALHAMBRA survey and relevant data of these LAEs, including the estimated $\alpha$ luminosity, are given in online Fig."
+ C] and Table CI.. respectively.," \ref{z2LyaCandidatesSpectra} and Table \ref{z2LyaCandidatesTable}, respectively."
+ Additionally. each pseudo-spectrum is complemented with à 3x3 sq-aresee cutout in z-band from HST-ACS (1.9. close to the UV rest-frame of the source. avoiding possible clumpy features in the far-UV images). when available.," Additionally, each pseudo-spectrum is complemented with a $\times$ 3 sq-arcsec cutout in z-band from HST-ACS (i.e. close to the UV rest-frame of the source, avoiding possible clumpy features in the far-UV images), when available."
+ With these data we estimated sizes and morphologies of the sources from the isophotal radius (2-7 above background) and fitted one-component Sérrsic profiles using (Peng et al. 2002))., With these data we estimated sizes and morphologies of the sources from the isophotal radius $\sigma$ above background) and fitted one-component Sérrsic profiles using (Peng et al. \cite{peng02}) ).
+ In all cases. this approach converged succesfully.," In all cases, this approach converged succesfully."
+ The results of this analysis are also included in Table C1.., The results of this analysis are also included in Table \ref{z2LyaCandidatesTable}.
+ The LAEs at z~ 2.2 have a mean radius of 1.7+0.4 kpe. except for the objects ALH06146 and ALHO7181. which exhibit Sérrsic profiles and residuals that suggest the presence of bars and out-of-mean radit.," The LAEs at $\sim$ 2.2 have a mean radius of $1.7\pm0.4$ kpc, except for the objects ALH06146 and ALH07181, which exhibit Sérrsic profiles and residuals that suggest the presence of bars and out-of-mean radii."
+ Apart from these two objects. sources in the sample are essentially compact and their Sérrsic indexes are consistent with bulge-like galaxies.," Apart from these two objects, sources in the sample are essentially compact and their Sérrsic indexes are consistent with bulge-like galaxies."
+ We took advantage of the availability of PACS data on the GOODS-North field to search for the counterparts. of the final LAE sample in the FIR (100 and 160jm PACS, We took advantage of the availability of PACS data on the GOODS-North field to search for the counterparts of the final LAE sample in the FIR (100 and $\mu\textrm{m}$ PACS
+and 3 Mj. giving a density of ~ 3.54.0 οcm7. nearly three times that of Jupiter.,"and 3 $_{\rm Jup}$, giving a density of $\sim$ 3.5–4.0 $\rm \rm{g} \ \rm{cm}^{-3}$, nearly three times that of Jupiter."
+ More interesting however are the planet's orbital characteristics: (à) The 21.2 d orbital period is roughly a factor 7 times longer than other transiting planets: (3) While most hot Jupiter planets have low eccentricities (the majority consistent with zero). LID 17156b has a very high eccentricity of e—0.67.," More interesting however are the planet's orbital characteristics: (i) The 21.2 d orbital period is roughly a factor 7 times longer than other transiting planets; (ii) While most hot Jupiter planets have low eccentricities (the majority consistent with zero), HD 17156b has a very high eccentricity of e=0.67."
+ Although the high eccentricity coupled with the small semimajor axis (0.16 AU) does not necessarily require the presence of a third body perturbing the planets orbit (Gillon οἱ al., Although the high eccentricity coupled with the small semimajor axis (0.16 $\rm AU$ ) does not necessarily require the presence of a third body perturbing the planet's orbit (Gillon et al.
+ 2008). il suggests (hat such a body may be present.," 2008), it suggests that such a body may be present."
+ In (his work we examine the published radial velocities of Fischer et al. (, In this work we examine the published radial velocities of Fischer et al. (
+2007) and the (transit times as given in Irwin et al. (,2007) and the transit times as given in Irwin et al. (
+2008) using a Newtonian (not Ixeplerian) 3-bodx integrator aud conclude that à second planet is not only possible. but. probable.,"2008) using a Newtonian (not Keplerian) 3-body integrator and conclude that a second planet is not only possible, but probable."
+ Notably. while the (wo planets exhibit strong dynamical interaction leading to large eccentricides and periastron advances. (μον remain stable via an elegant exchange of orbital angular momentum.," Notably, while the two planets exhibit strong dynamical interaction leading to large eccentricities and periastron advances, they remain stable via an elegant exchange of orbital angular momentum."
+ Our initial investigation of the WD 17156 svstem began with a l-planet fit to the Neck and Subaru radial velocity data from Fischer et al. (, Our initial investigation of the HD 17156 system began with a 1-planet fit to the Keck and Subaru radial velocity data from Fischer et al. (
+2007).,2007).
+ We omitted the radial velocity data ol Narita et al. (, We omitted the radial velocity data of Narita et al. (
+2008) since these data are influenced by the Rossiter-MeLaughlin effect. but (heir inclusion has essentially no effect on the results.,"2008) since these data are influenced by the Rossiter-McLaughlin effect, but their inclusion has essentially no effect on the results."
+ We reproduced the parameters of the planet HD 17156b as reported in Fischer et al. (, We reproduced the parameters of the planet HD 17156b as reported in Fischer et al. (
+2007). though we found that an additional 0.14 ms+ offset added to the Subaru data set gave a slightly better fit.,"2007), though we found that an additional 0.14 $\rm 
+ms^{-1}$ offset added to the Subaru data set gave a slightly better fit."
+ We computed a power spectrum of the residuals of the radial velocities after removing the one-planet fit., We computed a power spectrum of the residuals of the radial velocities after removing the one-planet fit.
+ A Monte Carlo technique was used to allow us to assess the signilicance of any peaks., A Monte Carlo technique was used to allow us to assess the significance of any peaks.
+ The power spectrum indicated a possible peak with a period of approximately 115 clays., The power spectrum indicated a possible peak with a period of approximately 115 days.
+ This prompted us to undertake a much more thorough and realistic 3-bocy investigation described below., This prompted us to undertake a much more thorough and realistic 3-body investigation described below.
+ In addition to the power spectra. we computed Ixepleriai periodograms: for a eiven period the parameters of a Ixeplerian fit to the radial velocities were optimized (Ix. e. οὖν 15. 5). Le. the LehmannFilhéss equation (see Lilditeh 2001 for example).," In addition to the power spectra, we computed Keplerian periodograms: for a given period the parameters of a Keplerian fit to the radial velocities were optimized (K, e, $\omega$, $T_{0}$, $\gamma$ ), i.e. the Lehmann–Filhéss equation (see Hilditch 2001 for example)."
+ While a traditional Fourier power spectrum has no free parameters. il uses sines and cosines as basis functions.," While a traditional Fourier power spectrum has no free parameters, it uses sines and cosines as basis functions."
+ However. an eccentric orbit is far from being sinusoidal and as a consequence a Fourier power spectrum will require power al many periods to match (he radial velocities.," However, an eccentric orbit is far from being sinusoidal and as a consequence a Fourier power spectrum will require power at many periods to match the radial velocities."
+ In contrast. by using the LehmannFilliéss equation as the basis function we obtain an optimal periodogram.," In contrast, by using the Lehmann–Filhéss equation as the basis function we obtain an optimal periodogram."
+ Furthermore. unlike a power spectrum. fitting a Ixeplerian orbit al each (rial," Furthermore, unlike a power spectrum, fitting a Keplerian orbit at each trial"
+Stars with planets detected with the Doppler. method (SWPs) have been shown to be more metal-rich (Conzalez1997:Santosetal.2001:ValentiandFischer2005) and more massive (Lawsctal.2003:Johnsonet2010). as a group when compared to similar stars without. detected: planets (non-SWDPs).,"Stars with planets detected with the Doppler method (SWPs) have been shown to be more metal-rich \citep{gg97, san01, vf05} and more massive \citep{law03, jj10} as a group when compared to similar stars without detected planets (non-SWPs)."
+ Recently. SWP and non-SWI's have also been reported to differ in vsini (Gonzalez2008:Gonzalezctal. 2010a).. abundance-condensation temperature. (Lo) trends (Molendezctal.2009:Ramirez2009.2010:Gonza- 2010b).. Li abundance (Gonzalez2008:Ixraelianetal.2009:Gonzalez20102) and chromospheric activity (Gonzalez2008).. but each of these findings has been disputed.," Recently, SWP and non-SWPs have also been reported to differ in vsini \citep{gg08, gg10a}, , abundance-condensation temperature $_{\rm c}$ ) trends \citep{mel09, ram09, ram10, gg10b}, Li abundance \citep{gg08, israel09, gg10a}, and chromospheric activity \citep{gg08}, but each of these findings has been disputed."
+ Alvesetal.(2010). cid not find a significant. clillerence in vsini between their samples of SWDPs and. non-SWP's., \citet{alv10} did not find a significant difference in vsini between their samples of SWPs and non-SWPs.
+ Baumannetal.(2010). found the Li abundance distributions to be indistinguishable between their samples of solar analog SWHPs ancl non-SWP's., \citet{bau10} found the Li abundance distributions to be indistinguishable between their samples of solar analog SWPs and non-SWPs.
+ GonzalezHernandezctal.(2010) do not find a significant dillerence in abundance- trends between their samples of solar analog SWP's and non-SWI?s., \citet{gh10} do not find a significant difference in $_{\rm c}$ trends between their samples of solar analog SWPs and non-SWPs.
+T. Finally. CantoMartinsetal.(2011) clo not find a significant difference in chromospheric activity between their samples of SWI's and non-SWPs.," Finally, \citet{cm11} do not find a significant difference in chromospheric activity between their samples of SWPs and non-SWPs."
+ The purpose of the present studs is to revisit. these controversies using published cata anc the method. of analysis described in our recent series of papers (Gonzalez2008:Gonzalezctal. 2010a.b).," The purpose of the present study is to revisit these controversies using published data and the method of analysis described in our recent series of papers \citep{gg08, gg10a, gg10b}."
+. Phe paper is organized. as follows., The paper is organized as follows.
+ In Section 2 we compare the vsini distributions between SWI's and non-SWDPs., In Section 2 we compare the vsini distributions between SWPs and non-SWPs.
+ In Section 3 we examine abundance-T. trends., In Section 3 we examine $_{\rm c}$ trends.
+ We compare chromospheric activity in Section 4., We compare chromospheric activity in Section 4.
+ We summarize our results in Section 5., We summarize our results in Section 5.
+ Gonzalez(2008) and Gonzalezetal.(2010a)| compared vsini values of SWI's and non-SWI's using two samples., \citet{gg08} and \citet{gg10a} compared vsini values of SWPs and non-SWPs using two samples.
+ One of the samples was based on the extensive dataset of ValentiandFischer(2005).. which remains the best data for comparing SWP and non-SWP vsini values.," One of the samples was based on the extensive dataset of \citet{vf05}, which remains the best data for comparing SWP and non-SWP vsini values."
+ However. since we completed our most recent analysis using their data. many new exoplanets have been discovered.," However, since we completed our most recent analysis using their data, many new exoplanets have been discovered."
+ The presence of undiscovered. planets among the non-SWPs has been a source of unavoidable svstematie error. but it is one that is becoming less important as new planets are discovered.," The presence of undiscovered planets among the non-SWPs has been a source of unavoidable systematic error, but it is one that is becoming less important as new planets are discovered."
+ The full sample of stars from. ValentiandFischer(2005) contains 1040 «ναί»: at the time of the paper's publication S5 of these stars with Tr5500 Ix were known to host Doppler-detectecl planets., The full sample of stars from \citet{vf05} contains 1040 dwarfs; at the time of the paper's publication 85 of these stars with $_{\rm eff} > 5500$ K were known to host Doppler-detected planets.
+ To form our subsample. we first. calculated. the absolute visual magnitudes using the recalibratecl Hipparcos parallaxes and then excluclecl those stars with a parallax value less than 10 times the parallax error.," To form our subsample, we first calculated the absolute visual magnitudes using the recalibrated Hipparcos parallaxes and then excluded those stars with a parallax value less than 10 times the parallax error."
+ Next. we excluded stars with Tar< 5500 Ix and Tarc 6450 Ix: this is slightly broader than the range we had used in Gonzalezetal.(2010a).. 5550 to 6250 Ix. Our final sample contains 00 SWDPs and 627 non-SWEP's.," Next, we excluded stars with $_{\rm eff} <$ 5500 K and $_{\rm eff} >$ 6450 K; this is slightly broader than the range we had used in \citet{gg10a}, 5550 to 6250 K. Our final sample contains 99 SWPs and 627 non-SWPs."
+ This compares to 82 SWPs and 594 non-SWPs used in Gonzalezetal.(2010a)., This compares to 82 SWPs and 594 non-SWPs used in \citet{gg10a}.
+.4 We applied. our method. of analysis described. in Gonzalez(2008) and Gonzalezetal.(2010a) to the present data., We applied our method of analysis described in \citet{gg08} and \citet{gg10a} to the present data.
+ In. brief. we calculated a weighted average dillerence xtween the vsini value of an SWP and the vsini values of all he comparison stars using the inverse square of the Ay index as the weight.," In brief, we calculated a weighted average difference between the vsini value of an SWP and the vsini values of all the comparison stars using the inverse square of the $\Delta_{\rm 1}$ index as the weight."
+" The A, index is à measure of the distance tween two stars in Tar-log g- Fe/1]-My: parameter space.", The $\Delta_{\rm 1}$ index is a measure of the distance between two stars in $_{\rm eff}$ -log $g$ $_{\rm V}$ parameter space.
+ We have made one minor change to this procedure compared o our previous studies., We have made one minor change to this procedure compared to our previous studies.
+ Previously. we had. used Fe/1I] as one of the parameters needed: to caleulate the Ay index.," Previously, we had used [Fe/H] as one of the parameters needed to calculate the $\Delta_{\rm 1}$ index."
+ However. using Fe/L could lead to à systematic error when hick disk stars are in the sample. since they have a dilferent value of a Fe] comparedto thin disk stars.," However, using [Fe/H] could lead to a systematic error when thick disk stars are in the sample, since they have a different value of $\alpha$ /Fe] comparedto thin disk stars."
+ When we are, When we are
+"Damped Lyman-a absorbers. historically. defined. as quasar absorption systems with neutral hydrogen columndensity Ng>2510U76m""7 (Wolfeetal.1986). are one of the hest probes of structure formation in the early. universe.","Damped $\alpha$ absorbers, historically defined as quasar absorption systems with neutral hydrogen columndensity $\NHI>2\times
+10^{20} \cm^{-2}$ \citep{Wol86}, are one of the best probes of structure formation in the early universe."
+ Since DLAs are dense concentrations of gas often found at 3. it is natural to suppose that they are closely linked. to the formation of galaxies and stars at high redshift.," Since DLAs are dense concentrations of gas often found at $z\geq 3$ , it is natural to suppose that they are closely linked to the formation of galaxies and stars at high redshift."
+" It has become clear in recent vears from the study of Lyman-break ealaxies. at 273.""d (e.g.Adelbergerctal.1998:SteidelMNοἱal.1999:Shapleyet2001). that the assembly of galaxies is actively going on at 23. consistent with hierarchical structure formation⋅ sin a cold dark matter universe. (c.g.Mo 2002).."," It has become clear in recent years from the study of Lyman-break galaxies at $z\sim 3-4$ \citep[e.g.][]{Ade98, Ste99,
+Sha01} that the assembly of galaxies is actively going on at $z\sim
+3$, consistent with hierarchical structure formation in a cold dark matter universe \citep[e.g.][]{Mo96, Bau98, Jin98, KHW99, Kau99, Mo99, Nag02, Wei02}. ."
+ A picture of the history of cosmic star formation, A picture of the history of cosmic star formation
+"indicating large gas column densities. ofNy,=107!—101 7 and a range of ionization parameters. log£~1—5 eres em | (Sambrunaetal.2007.. Grandiοἱal.2007.. Piconcellietal. 2008.. Torresietal. 2009.. Torresietal.2009.. Reevesοἱal.2009.. Torresietal.2010.. Tombesiοἱal. 2010b)).","indicating large gas column densities, of$N_{\rm H} = 10^{21} - 10^{23}$ $^{-2}$ and a range of ionization parameters, $\log\xi \sim 1-5\;$ ergs cm $^{-1}$ \citealt {sambruna07}, , \citealt{grandi07}, , \citealt{piconcelli08}, \citealt{torresi09}, \citealt{torresi09}, \citealt{reeves09}, \citealt{torresi10}, \citealt{tombesi10b}) )."
+ Ionized soft. X-ray emission lines have so far been detected in the DLRG 3C 445 (Sambrunaetal.2007: Grandietal.2007)) and in the NLRGs 2234 (Piconcelletal.2008) and 3€ 33 (Torresietal.2009)., Ionized soft X-ray emission lines have so far been detected in the BLRG 3C 445 \citealt{sambruna07}; \citealt{grandi07}) ) and in the NLRGs 234 \citep{piconcelli08} and 3C 33 \citep{torresi09}.
+. Photoionized absorption lines. consistent wilh gas outflowing on parsec scales with velocities of hundreds of !. were detected for the fist tme with grating resolution X-ray spectra in the DLBG 3382. with Chandra/IIETG (Reevesetal.2009). and independently with NMM-Newton/RG5 (Torresietal. 2010).," Photoionized absorption lines, consistent with gas outflowing on parsec scales with velocities of hundreds of $^{-1}$ , were detected for the first time with grating resolution X-ray spectra in the BLRG 382, with Chandra/HETG \citep{reeves09} and independently with XMM-Newton/RGS \citep{torresi10}."
+. Interestingly. Suzaku observations of BLRGs has also uncovered evidence at higher energies. al 7— 9kkeV in the iron Ix band. for fast outflowing gas with velocities Pou~0.04—0.150. carrying; substantial masses and kinetic powers similar to the radio jets (Tombesietal.2010b).," Interestingly, Suzaku observations of BLRGs has also uncovered evidence at higher energies, at $7-9$ keV in the iron K band, for fast outflowing gas with velocities $v_{\rm out}\sim 0.04-0.15c$, carrying substantial masses and kinetic powers similar to the radio jets \citep{tombesi10b}."
+. Thus there appears to be substantial ionizecl gas in the nuclei of radio-loud AGN. and this gas may be an energetically important component that needs to be accounted for in models for accretion ancl jet formation.," Thus there appears to be substantial ionized gas in the nuclei of radio-loud AGN, and this gas may be an energetically important component that needs to be accounted for in models for accretion and jet formation."
+ Indeed. (here are reasons to expect the presence of such a medium in BLRGs and other radio-loud AGN.," Indeed, there are reasons to expect the presence of such a medium in BLRGs and other radio-loud AGN."
+ For example centrifugallv-driven winds. lifting matter off the clisk’s surface and channelling it down the magnetic field. are a proposed scenario for the origin of relativistic jets (Blandford&Pavne1982): at favorable orientations. these winds leadto observable discrete absorpüon/enmission features αἱ soft N-ravs (INónigl&Nartje1994).," For example centrifugally-driven winds, lifting matter off the disk's surface and channelling it down the magnetic field, are a proposed scenario for the origin of relativistic jets \citep{blandford82}; at favorable orientations, these winds leadto observable discrete absorption/emission features at soft X-rays \citep{konig94}."
+ Jet formation models predict that (he relativistically moving plasma should be enveloped ina sub-relativisie wind (Mcelxinney.2006).. with velocities <0.1e.," Jet formation models predict that the relativistically moving plasma should be enveloped ina sub-relativistic wind \citep{mckinney06}, with velocities $\ls 0.1c$ ."
+ Unilication models [orracio-loud sources also postulate the presence of a warm. scattering gas to explain (wpe-2 sources CAntonucci1993: Urry&Padovani 1995)).," Unification models forradio-loud sources also postulate the presence of a warm, scattering gas to explain type-2 sources \citealt{antonucci93}; \citealt{urry95}) )."
+ 4445 is a bright. nearby (2=0.0562. Hewitt&Burbidge1991:: Eracleous 2004)) and luminous (ρα~LOY |. Marchesinietal. 2004)) radio galaxy with an ERI norphology (Ixronberg1986).," 445 is a bright, nearby $z=0.0562$, \citealt{hewitt91}; \citealt{erac04}) ) and luminous $L_{\rm bol}\sim10^{45}$ $^{-1}$, \citealt{marchesini04}) ) radio galaxy with an FRII morphology \citep{kronberg86}."
+. 4445 appears lobe rather than core dominated etal.1993). and is likely to be highly inclined. with respect to the radio-jet axis. with an inclination angle of ~60—70* ((Evacleous&Halpern 1998: Sambrunaetal. 2007)).," 445 appears lobe rather than core dominated \citep{morganti93} and is likely to be highly inclined with respect to the radio-jet axis, with an inclination angle of $\sim60-70$ \citealt{erac98}; ; \citealt{sambruna07}) )."
+ Based on ils optical spectra it is Classed as a BLIBG. due to thepresence ofstrong broad permitted lines inunpolarized lieht (Osterbrocketal. 1976: Crenshawetal. 1938... Eracleous&Halpern 1994: 1993)).," Based on its optical spectra it is classed as a BLRG, due to thepresence ofstrong broad permitted lines inunpolarized light \citealt{osterbrock76}; ; \citealt{crenshaw88}, , \citealt{erac94}; ; \citealt{corbett98}) )."
+ From its rather large Balmer decrement. the lineof sight reddening towards 4445," From its rather large Balmer decrement, the lineof sight reddening towards 445"
+models presented in this paper can reproduce the molecular abundances observed towards the brightest prototvpes. 882 and 2253.,"models presented in this paper can reproduce the molecular abundances observed towards the brightest prototypes, 82 and 253."
+ Moreover. no significant changes in the abundances of and ΠΟ are found towards the nuclear AGN of 11063 where X-ray radiation is significantly more important than in SB nuclei. as shown in Sect. 4.1.2..," Moreover, no significant changes in the abundances of $^+$ and HCO are found towards the nuclear AGN of 1068 where X-ray radiation is significantly more important than in SB nuclei, as shown in Sect. \ref{sect.PDR_AGN}."
+ Unfortunately. no — observation has been reported towards (his Sevlert 2 nucleus.," Unfortunately, no $^+$ observation has been reported towards this Seyfert 2 nucleus."
+ The comparison of model predictions with the observations presented. show that the abundance of the species observed in this work towards 22523. namely. . and IICO. are most efficiently formed in the outer region of the molecular clouds where the gas is highly imnradiated bv the incident UV. photons [rom massive stars.," The comparison of model predictions with the observations presented show that the abundance of the species observed in this work towards 253, namely $^+$, $^+$, and HCO, are most efficiently formed in the outer region of the molecular clouds where the gas is highly irradiated by the incident UV photons from massive stars."
+ The high molecular abundances derived for these species in 2253 suggest that the PDR component in this galaxy is similar (o that found in 58382. claimed to be the prototvpe of extragalactic PDR.," The high molecular abundances derived for these species in 253 suggest that the PDR component in this galaxy is similar to that found in 82, claimed to be the prototype of extragalactic PDR."
+ The abundance ratios found for this limited sample of galaxies are of the same order as those observed (towards galactic PDRs. which stress the importance of photo-dominated chemistry in galaxy nuclei.," The abundance ratios found for this limited sample of galaxies are of the same order as those observed towards galactic PDRs, which stress the importance of photo-dominated chemistry in galaxy nuclei."
+ Large amounts of molecular material are allected by photodissociation not only in 2253. bul also towiuds the star forming regions around the Sevlert 2 nuclei in 44945 and 11068.," Large amounts of molecular material are affected by photodissociation not only in 253, but also towards the star forming regions around the Seyfert 2 nuclei in 4945 and 1068."
+ This is consistent. with the INCO/CS ratio in these galaxies which suggest that a fraction of IIENCO has been photodissociated in PDRs., This is consistent with the HNCO/CS ratio in these galaxies which suggest that a fraction of HNCO has been photodissociated in PDRs.
+ The combination of the observations of ICO. and with that of INCO seems to confirm that their abundances reflect the evolutionary stage of the starbursts in these galaxies.," The combination of the observations of HCO, $^+$ and $^+$ with that of HNCO seems to confirm that their abundances reflect the evolutionary stage of the starbursts in these galaxies."
+ Although photodissociation is the most likely scenario lor the enhancement of (he observed reactive ion in starburst environments. X-ray. dominated chemistry has been claimed (to be responsible for the high abuucdanuces observed around AGNs in cireunnuclear disk of 11068 (IOC)Useroetal.2004) and towards the ultra," Although photodissociation is the most likely scenario for the enhancement of the observed reactive ion in starburst environments, X-ray dominated chemistry has been claimed to be responsible for the high abundances observed around AGNs in circunnuclear disk of 1068 \citep[HOC$^+$][]{Usero04} and towards the ultra"
+by an angle of order J/my/Myj» in the Gime it takes to harden significantly.,by an angle of order $\sqrt{\mf/\m12}$ in the time it takes to harden significantly.
+ This result. will be assessed more quantitatively in 85., This result will be assessed more quantitatively in 5.
+sampling on 44051 revealed that its BLR size is actually a factor ~3 smaller than inferred from earlier undersampled data (Denney et al.,sampling on 4051 revealed that its BLR size is actually a factor $\sim$ 3 smaller than inferred from earlier undersampled data (Denney et al.
+ 2009b)., 2009b).
+" Therefore, we suggest that some more of the BLR sizes measured so far can be improved with well sampled reverberation data."," Therefore, we suggest that some more of the BLR sizes measured so far can be improved with well sampled reverberation data."
+" Applying the flux variation gradient (FVG) method to B and V band data and adopting a host colour range determined for other local AGN, we find that for both objects PG0003--199 and Ark120 the host-subtracted AGN luminosity L519, differs significantly from previous measurements."," Applying the flux variation gradient (FVG) method to $B$ and $V$ band data and adopting a host colour range determined for other local AGN, we find that for both objects PG0003+199 and Ark120 the host-subtracted AGN luminosity $L_{5100\AA~}$ differs significantly from previous measurements."
+" While for PG0003+199 we find a stronger host contribution leading to lower AGN luminosity, for Ark120 our host estimate is consistent with others but the AGN was in a brighter state during our campaign."," While for PG0003+199 we find a stronger host contribution leading to lower AGN luminosity, for Ark120 our host estimate is consistent with others but the AGN was in a brighter state during our campaign."
+" The AGN/host luminosity contrast of both objects is relatively low, Lagn/Lnos~1 for the 7""—8” apertures used."," The AGN/host luminosity contrast of both objects is relatively low, $L_{AGN}/L_{host} \sim 1$ for the $7\arcsec - 8\arcsec$ apertures used."
+" The uncertainties of L599, are and in Ark120 and PG0003+199.", The uncertainties of $L_{5100\AA~}$ are and in Ark120 and PG0003+199.
+" These uncertainties include the measurement errors, the AGN variations and the uncertainty of the host flux."," These uncertainties include the measurement errors, the AGN variations and the uncertainty of the host flux."
+" For Lagn/Lnos:~1, the errors are dominated by the uncertainty of the host flux."," For $L_{AGN}/L_{host} \sim 1$, the errors are dominated by the uncertainty of the host flux."
+ It depends on the error of the AGN slope and the range adopted for the host slope., It depends on the error of the AGN slope and the range adopted for the host slope.
+" If improved image quality allows us to use smaller photometric apertures containing less host flux, the uncertainty caused by the range of host slopes may be reduced."," If improved image quality allows us to use smaller photometric apertures containing less host flux, the uncertainty caused by the range of host slopes may be reduced."
+" Also, applying the FVG method to more than one filter pair, for instance from UBVRI monitoring data, allows one to construct several independent AGN slopes and thus to determine the host contribution in a consistent manner, largely independent of the adopted range of host slopes."," Also, applying the FVG method to more than one filter pair, for instance from $UBVRI$ monitoring data, allows one to construct several independent AGN slopes and thus to determine the host contribution in a consistent manner, largely independent of the adopted range of host slopes."
+ For powerful AGN with Lacn/Lnost>2 the uncertainty of the host contribution plays a minor role., For powerful AGN with $L_{AGN}/L_{host} > 2$ the uncertainty of the host contribution plays a minor role.
+ An important result from spectroscopic reverberation mapping is the relationship between the BLR size and the nuclear luminosity Ἆπικ«L with a predicted slope a = 0.5 (Netzer 1990; Netzer Marziani 2010)., An important result from spectroscopic reverberation mapping is the relationship between the BLR size and the nuclear luminosity $R_{\rm BLR} \propto L^{\alpha}$ with a predicted slope $\alpha$ = 0.5 (Netzer 1990; Netzer Marziani 2010).
+" This relationship allows one to derive the virial black hole mass for high redshift AGN from single epoch spectra by inferring Rgig from L (e.g. Vestergaard 2002; Netzer 2003, McLure Dunlop 2004)."," This relationship allows one to derive the virial black hole mass for high redshift AGN from single epoch spectra by inferring $R_{\rm BLR}$ from $L$ (e.g. Vestergaard 2002; Netzer 2003, McLure Dunlop 2004)."
+ While early observations indicated a=0.6+0.1 (Kaspi et al., While early observations indicated $\alpha = 0.6 \pm 0.1$ (Kaspi et al.
+" 2000, 2005), for Hf line and 5100 luminosity a recent analysis including host galaxy subtraction yields a=0.063 (Bentz et al."," 2000, 2005), for $\beta$ line and 5100 luminosity a recent analysis including host galaxy subtraction yields $\alpha = 0.519 \pm 0.063$ (Bentz et al."
+ 2009)., 2009).
+" Note that the slope of the current Rgir—L relationship depends on the adopted cosmology, because the more luminous sources are at higher redshift than the low-luminosity AGN."," Note that the slope of the current $R_{\rm BLR} - L$ relationship depends on the adopted cosmology, because the more luminous sources are at higher redshift than the low-luminosity AGN."
+" The current Rgijg—L relationship exhibits a large scatter over an order of magnitude in both Rg_r and L, and many objects have large error bars (Fig. 15))."," The current $R_{\rm BLR} - L$ relationship exhibits a large scatter over an order of magnitude in both $R_{\rm BLR}$ and $L$, and many objects have large error bars (Fig. \ref{fig_r_l}) )."
+ The new photometric reverberation measurements shift the position of PG0003--199 and Ark120 in this diagram outside the quoted error range of the previous positions., The new photometric reverberation measurements shift the position of PG0003+199 and Ark120 in this diagram outside the quoted error range of the previous positions.
+ Notably the shift is larger in L than in Agra., Notably the shift is larger in $L$ than in $R_{\rm BLR}$.
+ The new positions are about closer to the relationship fitted by Bentz et al. (, The new positions are about closer to the relationship fitted by Bentz et al. (
+dashed line in Fig. 15)).,dashed line in Fig. \ref{fig_r_l}) ).
+ This suggests that well sampled reverberation data and improved, This suggests that well sampled reverberation data and improved
+intensity profiles aud Stokes vectors.,intensity profiles and Stokes vectors.
+ To get images aligned within sub-pixels accuracy. we have used Fourier transform based registration method implemented in the Interactive Data Language (IDL).," To get images aligned within sub-pixels accuracy, we have used Fourier transform based registration method implemented in the Interactive Data Language (IDL)."
+ The Fourier modulated ΗΝ data curing the flare were obtained [rom the RIIESSI data archive (Linetal.2002)., The Fourier modulated HXR data during the flare were obtained from the RHESSI data archive \citep{Lin2002}.
+. RIIESSI observes the Sun in the energv range 3kkeV to MMeV. with a spatial resolution of ~2”..3 in the full Sun field-of-view.," RHESSI observes the Sun in the energy range keV to MeV, with a spatial resolution of $\sim$ .3 in the full Sun field-of-view."
+ We have used the “clean” algorithm implemented uncer the Solar SoftWare (SSW). to reconstruct the INR images.," We have used the “clean” algorithm implemented under the Solar SoftWare (SSW), to reconstruct the HXR images."
+ The basic method was first developed for radio astronomy by Hógbom(1974)., The basic method was first developed for radio astronomy by \citet{Hogbom1974}.
+. It is an iterative algorithm based on the assumption that the image can be well represented by a superposition of point sources., It is an iterative algorithm based on the assumption that the image can be well represented by a superposition of point sources.
+ Details of this method to reconstruct the images from the RUESSI data are described in IIurfordetal.(2002)., Details of this method to reconstruct the images from the RHESSI data are described in \citet{Hurford2002}.
+". For studying the association of the (transients driven by the X2.2 flare with ILXNR sources. we have constructed the RIIESSI WAR. images in the enereyv band kkeV with spatial and temporal resolutions of | and ss. respectively. keeping the image center fixed at the position(205"".. -222""))."," For studying the association of the transients driven by the X2.2 flare with HXR sources, we have constructed the RHESSI HXR images in the energy band keV with spatial and temporal resolutions of $^{-1}$ and s, respectively, keeping the image center fixed at the position, )."
+ Association of ΗΝ sources with the II flare ribbons and the transients are discussed in the Section 3.3.., Association of HXR sources with the H flare ribbons and the transients are discussed in the Section \ref{Sb-HXR}.
+ Figures 1 13 show the results obtained [rom the analvsis of the observational data for the AR NOAA 11158 during the X2.2 flare of 2011 February 15., Figures \ref{TimSeqImg} – \ref{StkProf} show the results obtained from the analysis of the observational data for the AR NOAA 11158 during the X2.2 flare of 2011 February 15.
+ In the following. we discuss these results in detail.," In the following, we discuss these results in detail."
+ AR NOAA 11158 appeared near the disk center at location 919W03 on 2011 February 12 in the rising phase of the current solar evcle 24., AR NOAA 11158 appeared near the disk center at location S19W03 on 2011 February 12 in the rising phase of the current solar cycle 24.
+ Subsequent to its birth on February 12. it evolved very rapidly and quickly developed from a simple o- to a very complex ;359- by 2011 February 15. C," Subsequent to its birth on February 12, it evolved very rapidly and quickly developed from a simple $\beta$ - to a very complex $\beta\gamma\delta$ -configuration by 2011 February 15. ("
+A detailed study of the surface and sub-surface evolution ol this AR has been undertaken and results therefrom will be communicated in a subsecuent paper.),A detailed study of the surface and sub-surface evolution of this AR has been undertaken and results therefrom will be communicated in a subsequent paper.)
+ During its disk transit. NOAA 11158 produced several C-class aud MAT-class flares.," During its disk transit, NOAA 11158 produced several C-class and M-class flares."
+ It also unleashed the first X-class flare of the current solar evcle observed on 2011 February 15., It also unleashed the first X-class flare of the current solar cycle observed on 2011 February 15.
+ This event was a wo ribbon WLE as seen in LAT white-light images., This event was a two ribbon WLF as seen in HMI white-light images.
+ The flare peaked αἱ, The flare peaked at
+that we have identified chemically.,that we have identified chemically.
+ Subsequently. in Figs 14 16 we examine the distributions in the Ca/Fe}.Fe/1]) plane of model stars that have been kinematically identifie as belonging to the thin or thick disc.," Subsequently, in Figs \ref{fig:Bensbysel}- \ref{fig:Benage} we examine the distributions in the $(\afe,\feh)$ plane of model stars that have been kinematically identified as belonging to the thin or thick disc."
+ shows the Toomre diagrams for the thin. thick and intermediate components. respectively.," shows the Toomre diagrams for the thin, thick and intermediate components, respectively."
+ In al densities are separately normalised to unity. while shows the density ratios of components in the Toomre diagram.," In all densities are separately normalised to unity, while shows the density ratios of components in the Toomre diagram."
+ The extensive overlap of the chemicallv-selectec populations in the Toomre diagram is striking. but a natura consequence of the approximately Gaussian. nature of the distribution functions of each component. which implies tha the density of thick-disc stars peaks at velocities close to the LS. which is where the thin cise is dominant.," The extensive overlap of the chemically-selected populations in the Toomre diagram is striking, but a natural consequence of the approximately Gaussian nature of the distribution functions of each component, which implies that the density of thick-disc stars peaks at velocities close to the LSR, which is where the thin disc is dominant."
+ Consequentby. no kinematic selection of stars from a particular. chemica component can be very clean.," Consequently, no kinematic selection of stars from a particular chemical component can be very clean."
+ This point is underlined. by the white curves in Figs., This point is underlined by the white curves in Figs.
+ 12. and 13.. which are such tha Bensbyetal.(2003) classified stars IW=0.550 as hick-disc ifthey lay outside the outermost white curve and hin-dise if they lay inside the innermost curve.," \ref{fig:toomreI} and \ref{fig:toomreIb}, which are such that \cite{Bensby03} classified stars $W=0.55U$ as thick-disc if they lay outside the outermost white curve and thin-disc if they lay inside the innermost curve."
+ The top xiuel in shows that this criterion does exclude most hin-clise stars [rom a thick-clise sample., The top panel in shows that this criterion does exclude most thin-disc stars from a thick-disc sample.
+ However. the upper wo panels of imply substantial contamination. of he thick clise: in these ;unels red indicates a region where most stars are not thick disc stars. vet at lower right. red extends significantly. bevond the outermost white curve in xh panels.," However, the upper two panels of imply substantial contamination of the thick disc: in these panels red indicates a region where most stars are not thick disc stars, yet at lower right red extends significantly beyond the outermost white curve in both panels."
+ From it is evident that a slightly cleaner kinematic separation could be obtained if a non-Caussian distribution Function were used in place of (2)). but the main xoblem with kinematic selection is the extensive overlap of he components in velocity space.," From it is evident that a slightly cleaner kinematic separation could be obtained if a non-Gaussian distribution function were used in place of \ref{equ:Bens}) ), but the main problem with kinematic selection is the extensive overlap of the components in velocity space."
+ From the centre panel of we see that a, From the centre panel of we see that a
+intracluster medium.,intracluster medium.
+" A simple model involving a IIattened j-mocdel gas distribution in hyelrostatic equilibrium within a NEW (Equation 4)) potential. suggests that our result derived. from the innermost O.004A/oq, of the gas. may the excess energy. integrated over the ICM. by a [actor of ~2."," A simple model involving a flattened $\beta$ -model gas distribution in hydrostatic equilibrium within a NFW (Equation \ref{eq:nfw}) ) potential, suggests that our result derived from the innermost $M_{200}$ of the gas, may the excess energy, integrated over the ICM, by a factor of $\sim$ 2."
+ Our analysis assumes that Equation δ holds even in the lowest mass systems., Our analysis assumes that Equation \ref{eq:mass} holds even in the lowest mass systems.
+ Semi-analvtical models of the ellects of preheating. by ? and 7. indicate that preheating has little effect on gas temperature except in systems with virial temperatures close to the preheating temperature.," Semi-analytical models of the effects of preheating, by \scite{balogh98a} and \scite{cavaliere98a} indicate that preheating has little effect on gas temperature except in systems with virial temperatures close to the preheating temperature."
+ The mass-temperature relations in both the ? and Ὁ studies deviate significantlv [rom the expected. ALx1772 only at T«0.8 keV. Only one member of our sample. 668. with a mean gas temperature of 0.54 keV. lies in this region.," The mass-temperature relations in both the \scite{balogh98a} and \scite{cavaliere98a} studies deviate significantly from the expected $M\propto T^{3/2}$ only at $T<0.8$ keV. Only one member of our sample, 68, with a mean gas temperature of 0.54 keV, lies in this region."
+ To investigate the possibility that this point in Fig., To investigate the possibility that this point in Fig.
+ 9 mav have been significantly allected. we derived. the mass of this svstem from our fitted. model.," \ref{fig:plot6} may have been significantly affected, we derived the mass of this system from our fitted model."
+ Due to fact that the data extend to only ~ 0.2 1t. this involves considerable extrapolation out to the virial radius. with an associated (and uncertain) systematic error.," Due to fact that the data extend to only $\sim$ 0.2 $_{v}$, this involves considerable extrapolation out to the virial radius, with an associated (and uncertain) systematic error."
+ The mass derived. [rom our fitted model was 2.41075 M... compared to a value of 3.45.101? M. from Equation 8 using the mean temperature of the system.," The mass derived from our fitted model was $2.4\times 10^{13}$ $_{\odot}$, compared to a value of $3.45\times 10^{13}$ $_{\odot}$ from Equation \ref{eq:mass} using the mean temperature of the system."
+ Lowe have overestimated Aou for this svstenm. then the gas mass we have considered. will be too Large. and its binding energy (which decreases with radius) will be too low.," If we have overestimated $M_{200}$ for this system, then the gas mass we have considered will be too large, and its binding energy (which decreases with radius) will be too low."
+" Using Mou,=2.36 1077M. instead. would result in the derived binding energv of the 0.004750 of gas being increased by1354."," Using $M_{200}=2.36 \times 10^{13}$ $_{\odot}$ instead, would result in the derived binding energy of the $M_{200}$ of gas being increased by."
+.. ‘Vhis svstematic error is much less than the statistical error on the point and so should have a minimal ellect on the fit., This systematic error is much less than the statistical error on the point and so should have a minimal effect on the fit.
+ Any elfect would be in the direction of reducing the injection energy., Any effect would be in the direction of reducing the injection energy.
+ The excess energy we have derived. can be compared o what might reasonably be available from. galaxy winds., The excess energy we have derived can be compared to what might reasonably be available from galaxy winds.
+ Assuming that the galaxy. wind ejecta have approximately solar metallicity. it appears that this gas has been diluted w a factor of ~3-5 with primordial gas. to arrive at the vpical metallicities of 0.2-0.3 solar. seen in galaxy groups and clusters (?:?)..," Assuming that the galaxy wind ejecta have approximately solar metallicity, it appears that this gas has been diluted by a factor of $\sim$ 3-5 with primordial gas, to arrive at the typical metallicities of 0.2-0.3 solar, seen in galaxy groups and clusters \cite{fukazawa98a,finoguenov99a}."
+ A final excess of —0.4 keV. per xwiicle after dilution. therefore implies an injected: wind . ⋅ ∖⇁⋖⋅∪≼⇍⊔∙∖⇁∪⇂∿↓∪∪∪↓∡⊔↓⊳∖⊳⋜↧⊳∖⊳∖⊔⊔∐⊔⋏∙≟↿↓⋯↿↓↕∢⋅⋖⊾⊔∢⊾↓⋅⋏∙≟∙∖⇁∪⊓∐⊾ 1 . ⋠↓⊔≯⊲⋖⋅≼∙↿∢⋅∠⇂⋏∙≟⋜↧⊳∖⊲↓⊳∖∠⇂∢≱↓↥↓↕↓↥⋜↧↿⋖⋅∠⇂∣⋡∙∖⇁⋠↓↿," A final excess of $\sim$ 0.4 keV per particle after dilution, therefore implies an injected wind velocity of $\sim 1000$ km $^{-1}$, assuming that the energy of the injected gas is dominated by its bulk flow energy."
+≱∖∣⋡⊔∐⊊∐∪∖∖⊽∢⋅⊔⋖⋅↓⋅⋏∙≟∙∖⇁⋡↔↿⋯∐∢⋅≱∖∪⇂∎ ∪≼⇍⋜↧↓⇂⇂↓⇂↓⋅⋜↧↓⇂⇂↓↕↓↕↓↕⋖≱⇂⇂≻≱∖↥⋜⊔⋅⋡⊔↓⋅⊳∖↿⋏∙≟⋜↧↓⋜∟∖⊀⊓⊾⊳∖⊳∖↓↕∪∖∖⊽⋯∐∐∪∖∖⊽≱∖∪⇂∎≼∙∪∪⇂ emission line gas with. velocities of a few hundred km and models suggest terminal velocities for the hot gas of a ow thousand kn (?:?:?)..," Studies of local ultraluminous starburst galaxies show outflows of cool emission line gas with velocities of a few hundred km $^{-1}$, and models suggest terminal velocities for the hot gas of a few thousand km $^{-1}$ \cite{heckman90a,suchkov94a,tenorio97a}."
+ Galactic winds therefore seem capable of providing the energy we observe., Galactic winds therefore seem capable of providing the energy we observe.
+" As both the excess entropy ancl preheating temperature of the LOCAL have been measured. it can be seen from the definition of entropy in Equation 5.. that it should be possible to derive the electron density 2, at which the energy was injected."," As both the excess entropy and preheating temperature of the ICM have been measured, it can be seen from the definition of entropy in Equation \ref{eq:entropy}, that it should be possible to derive the electron density $n_{e}$ at which the energy was injected."
+ The details of the energy injection process itself do not matter. provided that sullicient mixing of the gas has subsequently occurred to distribute the energy uniformly at the time of observation.," The details of the energy injection process itself do not matter, provided that sufficient mixing of the gas has subsequently occurred to distribute the energy uniformly at the time of observation."
+ The inferred injection density. is, The inferred injection density is
+Galaxy redshift surveys such as the Sloan Digital Sky Survey (York et al.,Galaxy redshift surveys such as the Sloan Digital Sky Survey (York et al.
+ 2000) and the 2dE€IS (Colless et al., 2000) and the 2dFGRS (Colless et al.
+ 2001) show that galaxies are spread out in a fairly complicated way. over the so.called. Cosmic Web.," 2001) show that galaxies are spread out in a fairly complicated way, over the so–called Cosmic Web."
+ This network consists of the largest nonlinear structures in the Universe. galaxy clusters. which are interconnected. through filaments. and sheets.," This network consists of the largest non–linear structures in the Universe, galaxy clusters, which are interconnected through filaments and sheets."
+ Embedded: in this network are vast regions that contain almost no galaxies. so.called: voids.," Embedded in this network are vast regions that contain almost no galaxies, so–called voids."
+ Νbody simulations of cosmic structure formation (for example Springel et al., N–body simulations of cosmic structure formation (for example Springel et al.
+ 2005) have been able to reproduce the of the matter distribution very well: and the interplay between theoretical simulations and observational results has contributed to a large extent to our knowledge of the properties of the ACDAL concordance model., 2005) have been able to reproduce the of the matter distribution very well; and the interplay between theoretical simulations and observational results has contributed to a large extent to our knowledge of the properties of the $\Lambda$ CDM concordance model.
+ Deseribing the network ancl comparing observations and simulations is no easy task., Describing the network and comparing observations and simulations is no easy task.
+ Phe twopoint and. to a much lesser degree. higherorder correlation functions (e.g. Peebles Groth 1975: Pechles 1980: Peacock 1999) have been used most. frequently.," The two–point and, to a much lesser degree, higher–order correlation functions (e.g. Peebles Groth 1975; Peebles 1980; Peacock 1999) have been used most frequently."
+" Other tools. include. Minimal Spanning ""Trees (see e.g. Barrow et al.", Other tools include Minimal Spanning Trees (see e.g. Barrow et al.
+ 1985: Bhavsar Splinter 1996: INrzewina Saslaw 1996). the genus statistics (Cott et 11986: Springel et al.," 1985; Bhavsar Splinter 1996; Krzewina Saslaw 1996), the genus statistics (Gott et 1986; Springel et al."
+ 1998). shape statistics (sec c.g. Babul Starkman 1992: Luo Vishniac 1995: Luo οἱ al.," 1998), shape statistics (see e.g. Babul Starkman 1992; Luo Vishniac 1995; Luo et al."
+ 1996). and. Minkowski funetionals (Alecke et αἱ.," 1996), and Minkowski functionals (Mecke et al."
+ 1994: for avery detailed review see Sheth Sahni 2005 and references therein)., 1994; for a very detailed review see Sheth Sahni 2005 and references therein).
+ Opinions about the nature anc elements. of LargeSeale Structure (LSS) diller to some extent., Opinions about the nature and elements of Large--Scale Structure (LSS) differ to some extent.
+ Are filaments or sheets the dominant. structural elements?, Are filaments or sheets the dominant structural elements?
+ In a recent study. Colberg et al. (," In a recent study, Colberg et al. ("
+2005) investigated the configurations of matter between neighbouring clusters in an. Nbody simulation.,2005) investigated the configurations of matter between neighbouring clusters in an N–body simulation.
+" ""Thev found. a very strong preference. for filaments over sheets for those pairs of clusters whose connection was not cutting through a void.", They found a very strong preference for filaments over sheets for those pairs of clusters whose connection was not cutting through a void.
+ The existence of both filunents and sheets is very encouraging., The existence of both filaments and sheets is very encouraging.
+ This is because the visual impression. from large redshift surveys indicates a filamentary network that includes very prominent sheets such as the “Sloan Great. Wall” (Vogeley et al., This is because the visual impression from large redshift surveys indicates a filamentary network that includes very prominent sheets such as the “Sloan Great Wall” (Vogeley et al.
+ 2004)., 2004).
+ Colbere ct al. (, Colberg et al. (
+2005) also reported: on. sizes of intercluster filaments. incl.,"2005) also reported on sizes of inter–cluster filaments, incl."
+ averaged density. profiles., averaged density profiles.
+ As it turns out. the averaged. densities agree very well with predictions of an analvtical model by Shen et al. (," As it turns out, the averaged densities agree very well with predictions of an analytical model by Shen et al. ("
+2005).,2005).
+ However. the method employed by Colberg et al. (," However, the method employed by Colberg et al. ("
+2005) has its problems.,2005) has its problems.
+ First. given that they investigated. intercluster matter configurations by eve. the method is simply not feasible for larger data sets than those used in. their," First, given that they investigated inter--cluster matter configurations by eye, the method is simply not feasible for larger data sets than those used in their"
+Japann A uuuber of observations provides evidence for super-lmassive black holes in galactic centers or black hole iu galaxies (c.g.Mivoshietal.1995:Ghez1998.2005:Ceuzel2000:Schódel2003:Benderetal.2005:Eiseuliauer 2005).,"n A number of observations provides evidence for super-massive black holes in galactic centers or stellar-mass black hole in galaxies \citep[e.g.][]{Miyoshi+95,Ghez+98,Ghez+05,Genzel+00,Schodel+03,
+Bender+05,Eisenhauer+05}."
+. Several observations show hielh-euergv phenomena around black hole caucidates where some amount of enerev m accretion flows is released., Several observations show high-energy phenomena around black hole candidates where some amount of energy in accretion flows is released.
+ In this paper. to uuderstand the high-eucrey phenomena ucar the black hole aud the nature of the curved. spacetime due to the holes stroug gravity. we consider Igoe maguetolivdrodvuamic (MITD) flows in the maeuetosphere of a," In this paper, to understand the high-energy phenomena near the black hole and the nature of the curved spacetime due to the hole's strong gravity, we consider ingoing magnetohydrodynamic (MHD) flows in the magnetosphere of a"
+TTauri (CTT).,TTauri (CTT).
+" On the other hand, he proposed a mean age of 1.4 Myr for the members inside the central 4 arcminutes, where the outer population would have a mean age of 2.8 Myr."," On the other hand, he proposed a mean age of 1.4 Myr for the members inside the central 4 arcminutes, where the outer population would have a mean age of 2.8 Myr."
+ He suggested in this case that a young cluster was being observed in projection onto an older background population of PMS stars., He suggested in this case that a young cluster was being observed in projection onto an older background population of PMS stars.
+ Baume et al. (, Baume et al. (
+"1999), regarding results on6231,, proposed the existence of primordial mass segregation, in the sense that lower mass stars would be located at outer locations.","1999), regarding results on, proposed the existence of primordial mass segregation, in the sense that lower mass stars would be located at outer locations."
+" In their study of1893,, Marco Negueruela (2002) found a distinct spatial distribution for MS and PMS members, not related to differences in concentration."," In their study of, Marco Negueruela (2002) found a distinct spatial distribution for MS and PMS members, not related to differences in concentration."
+ They found a relative lack of PMS members at places where the MS members are more numerous., They found a relative lack of PMS members at places where the MS members are more numerous.
+" On the other hand, in a study of the Carina OB association, Sartori et al. ("," On the other hand, in a study of the Carina OB association, Sartori et al. ("
+"2003) found no differences between Massive MS members and PMS members, neither in the spatial distribution, nor in kinematic properties or the age distribution.","2003) found no differences between Massive MS members and PMS members, neither in the spatial distribution, nor in kinematic properties or the age distribution."
+ The suggestions of sequential or induced star formation in star forming regions is a topic in itself., The suggestions of sequential or induced star formation in star forming regions is a topic in itself.
+ Here we mention the results of Prisinzano et al. (, Here we mention the results of Prisinzano et al. (
+"2005) on6530,, where they indeed found what was searched for and claimed as not present in the Carina region mentioned before: signs of spatially sequential formation, as a phenomenon different from primordial spatial segregation.","2005) on, where they indeed found what was searched for and claimed as not present in the Carina region mentioned before: signs of spatially sequential formation, as a phenomenon different from primordial spatial segregation."
+" The issue of spatially sequential formation is currently the subject of relatively intense study, as has been suggested in several studies of stars-forming regions (Puga et al."," The issue of spatially sequential formation is currently the subject of relatively intense study, as has been suggested in several studies of stars-forming regions (Puga et al."
+" 2009, Delgado et al."," 2009, Delgado et al."
+" 2010, and their references)."," 2010, and their references)."
+" So, how do our PMS samples reflect the properties of the spatial structure of the different clusters?"," So, how do our PMS samples reflect the properties of the spatial structure of the different clusters?"
+ The scale of spatial concentration defined in Sect., The scale of spatial concentration defined in Sect.
+" 3.2 above has been calculated for PMS stars in two separated mass ranges,1-2 Μο and 2-3.5 Μο."," 3.2 above has been calculated for PMS stars in two separated mass ranges,1-2 $M_\odot$ and 2-3.5 $M_\odot$."
+" These mass intervals were chosen to enhance the possible differences between spatial distributions, and were also limited to the mass range in which we are more confident, avoiding the completeness limit at the lower limit, and the merging at the upper mass limit with possible MS members."," These mass intervals were chosen to enhance the possible differences between spatial distributions, and were also limited to the mass range in which we are more confident, avoiding the completeness limit at the lower limit, and the merging at the upper mass limit with possible MS members."
+ In the upper panel of Fig., In the upper panel of Fig.
+ 8 we plot A versus age for all PMS members of mass above the approximate completeness limit., \ref{HmLm} we plot $\Delta$ versus age for all PMS members of mass above the approximate completeness limit.
+" Symbols for and are included for comparison, as in previous figures."," Symbols for and are included for comparison, as in previous figures."
+ shows a relatively higher concentration for its age., shows a relatively higher concentration for its age.
+" A clear decreasing trend of concentration with age is observed, which can however be affected by some bias due to the distances of the different clusters."," A clear decreasing trend of concentration with age is observed, which can however be affected by some bias due to the distances of the different clusters."
+ In the lower panel of Fig., In the lower panel of Fig.
+ 8 we plot the ratio between the concentrations of lower and higher mass PMS members (1-2 Μο and 2-3.5 Μο)., \ref{HmLm} we plot the ratio between the concentrations of lower and higher mass PMS members (1-2 $M_\odot$ and 2-3.5 $M_\odot$ ).
+" In spite of the large error bars, we conjecture a widening of the lower mass PMS members distribution relative to the one for PMS members of higher mass, which amounts to around in the age range covered."," In spite of the large error bars, we conjecture a widening of the lower mass PMS members distribution relative to the one for PMS members of higher mass, which amounts to around in the age range covered."
+" This suggests the presence of dynamical mass segregation, in the sense of a wider distribution for lower mass stars, as the cluster age increases."," This suggests the presence of dynamical mass segregation, in the sense of a wider distribution for lower mass stars, as the cluster age increases."
+" A formal relation is obtained through a linear least squares fit, also plotted in Fig. 8,,"," A formal relation is obtained through a linear least squares fit, also plotted in Fig. \ref{HmLm},"
+ with a correlation coefficient equal to 0.7., with a correlation coefficient equal to 0.7.
+" In this fit we exclude the two most deviating points, marked in the plot, which correspond to the clusters and18."," In this fit we exclude the two most deviating points, marked in the plot, which correspond to the clusters and."
+. The case of has been commented in connection with the plot in Fig. 7.., The case of has been commented in connection with the plot in Fig. \ref{AdvsC}.
+" The field of the cluster is probably containing two superimposed associations, a fact which might influence the measured properties."," The field of the cluster is probably containing two superimposed associations, a fact which might influence the measured properties."
+" As commented above, has a relatively larger number of massive MS members, as compared to the other clusters in the sample."," As commented above, has a relatively larger number of massive MS members, as compared to the other clusters in the sample."
+ Some particular features of the star formation process in the cluster could be showing up in its spatial structure., Some particular features of the star formation process in the cluster could be showing up in its spatial structure.
+ We have presented the results obtained from our procedure in establishing PMS membership in YOCs and simultaneously in measuring the physical parameters of the selected member stars., We have presented the results obtained from our procedure in establishing PMS membership in YOCs and simultaneously in measuring the physical parameters of the selected member stars.
+ The procedure is ultimately aimed at checking the, The procedure is ultimately aimed at checking the
+which is à svstematic hardening of the spectrum. which is a possible cause of the additional hard component the spectral fits appear to require.,"which is a systematic hardening of the spectrum, which is a possible cause of the additional hard component the spectral fits appear to require."
+ The count-rate calculator predicts ~8% of the total counts are piled-up given the observed count rate of this source., The count-rate calculator predicts $\sim 8$ of the total counts are piled-up given the observed count rate of this source.
+ This is close to the level at which the CAC warn that spectra are likely to be significantly allected. suggesting pile-up max be a problem.," This is close to the level at which the CXC warn that spectra are likely to be significantly affected, suggesting pile-up may be a problem."
+ To investigate whether there is appreciable pile-up in the NGC 3628 INO spectrum we compared the event grade branching ratios (the fraction of events with a given grade. see the Proposers Observatory. Guide) for photons with 2xE (keV) <8 from the INO (1646 events) with the summed emission from the 14 next brightest point sources seen in NGC 3628 which are individually too faint to suffer from anv pile-up (672 events in total).," To investigate whether there is appreciable pile-up in the NGC 3628 IXO spectrum we compared the event grade branching ratios (the fraction of events with a given grade, see the Proposers Observatory Guide) for photons with $2 \le E$ (keV) $\le 8$ from the IXO (1646 events) with the summed emission from the 14 next brightest point sources seen in NGC 3628 which are individually too faint to suffer from any pile-up (672 events in total)."
+ Pile-up leads to a svstematic increase in the fraction of events with high grades ASCA erades 5. 6 7).," Pile-up leads to a systematic increase in the fraction of events with high grades ASCA grades 5, 6 7)."
+ Ilowever. we find that the event grade branching ratios for the INO and (he summed fainter point source enmüssion are identical to. within 2e [or all grades. which sugeests (hat there is no appreciable pile-up in the NGC 3628 INO spectrum.," However, we find that the event grade branching ratios for the IXO and the summed fainter point source emission are identical to within $2\sigma$ for all grades, which suggests that there is no appreciable pile-up in the NGC 3628 IXO spectrum."
+ Applving this technique to the public 34 ks ACIS-I observation of M32 (ObsID 361) shows a very significant migration of the events [rom (he M82 INO to higher grades with respect to the fainter point sources in M82., Applying this technique to the public 34 ks ACIS-I observation of M82 (ObsID 361) shows a very significant migration of the events from the M82 IXO to higher grades with respect to the fainter point sources in M82.
+ Other evidence that the Πα excess seen in the NGC 3628 INO is not due to pile-up is (hat spectral fitting of a brighter point source seen in our two observations of NGC 253 (Weaveral... in preparation) shows no sign of a lard excess. even though the predicted pile-up fraction is 12. (higher than the NGC 3628 INO). and the total number of counts in the spectrum is similar to that in (he NGC 3628 INO spectrum.," Other evidence that the hard excess seen in the NGC 3628 IXO is not due to pile-up is that spectral fitting of a brighter point source seen in our two observations of NGC 253 (Weaver, in preparation) shows no sign of a hard excess, even though the predicted pile-up fraction is 12 – (higher than the NGC 3628 IXO), and the total number of counts in the spectrum is similar to that in the NGC 3628 IXO spectrum."
+ Slalistically acceptable multi-color disk spectral models. be obtained if we restrict ihe energy range used to 0.5. 5.0 keV deliberately exeluding data in the energy range where the multi-color disk model does worst)., Statistically acceptable multi-color disk spectral models be obtained if we restrict the energy range used to 0.3 – 5.0 keV deliberately excluding data in the energy range where the multi-color disk model does worst).
+ However. it should be noted that absorbed power law and absorbed bremsstrahlung models provide mareinally better fits to the data in (his restricted energy range.," However, it should be noted that absorbed power law and absorbed bremsstrahlung models provide marginally better fits to the data in this restricted energy range."
+ It therefore seems that a power law model provides the best description of the current. spectral state of (this source. and (hat a multi-color disk model does provide an adequate fit to the spectrum of the INO.," It therefore seems that a power law model provides the best description of the current spectral state of this source, and that a multi-color disk model does provide an adequate fit to the spectrum of the IXO."
+ source count rates and absorption-corrected fluxes and Iuminosities. assuming the power law spectral model (using the restricted 0.3. 5.0 keV energy range). are given in Table 4..," Source count rates and absorption-corrected fluxes and luminosities, assuming the power law spectral model (using the restricted 0.3 – 5.0 keV energy range), are given in Table \ref{tab:fluxes}."
+ All spectral fits give absorption columns in the range Nj—5. 8xI0?!em.7., All spectral fits give absorption columns in the range $\nH = 5$ – $8 \times 10^{21} \pcmsq$.
+ These columns are consistent wilh foreground absorption of the source by the edee-on disk of NGC 3625. and its location in or behind (he optical dust lane.," These columns are consistent with foreground absorption of the source by the edge-on disk of NGC 3628, and its location in or behind the optical dust lane."
+Figure 5 gives the CMB temperature maps extracted from the WMAP 5 yr maps by NN.,Figure \ref{hunn_wmap} gives the CMB temperature maps extracted from the WMAP 5 yr maps by NN.
+" For an estimate of the systematic errors in this map, a set of 30 maps were constructed from the NN-foreground model including Gaussian noise derived from the WMAP hitmaps."," For an estimate of the systematic errors in this map, a set of 30 maps were constructed from the NN-foreground model including Gaussian noise derived from the WMAP hitmaps."
+" For one of these sets of simulated maps, Fig."," For one of these sets of simulated maps, Fig."
+ 6 shows the residual (T(in)—T(out)) map as output from NN., \ref{09_720_0_model_128} shows the residual $(T(in) - T(out))$ map as output from NN.
+ The neural network has a problem covering the full dynamic range of the fluxes close to the Galactic plane., The neural network has a problem covering the full dynamic range of the fluxes close to the Galactic plane.
+ The inner part of the Milky Way has been masked out (WMAP KQ75 mask = 0)., The inner part of the Milky Way has been masked out (WMAP KQ75 mask = 0).
+" The errors are close to being Gaussianly distributed (skewness = 0.00, kurtosis = 0.09), with only very small systematic errors."," The errors are close to being Gaussianly distributed (skewness = 0.00, kurtosis = 0.09), with only very small systematic errors."
+ The data released by the WMAP team was extensively analysed., The data released by the WMAP team was extensively analysed.
+ Delabrouille et al. (, Delabrouille et al. (
+"2009, hereafter DCLBFG) discuss the different methods applied to extract the CMB signal in detail.","2009, hereafter DCLBFG) discuss the different methods applied to extract the CMB signal in detail."
+" The WMAP team has extracted ‘internal linear combination’ (ILC) maps, simply obtained by a summation of the 5 frequency maps (after reduction of the resolution of the maps to 1 deg)."," The WMAP team has extracted `internal linear combination' (ILC) maps, simply obtained by a summation of the 5 frequency maps (after reduction of the resolution of the maps to 1 deg)."
+ The weights for each map are determined by minimizing the total variance of the output map., The weights for each map are determined by minimizing the total variance of the output map.
+" The sky is divided into 12 areas, in which the weights are estimated independently."," The sky is divided into 12 areas, in which the weights are estimated independently."
+" The KQ75 mask, used in this investigation, is contained within Area 0."," The KQ75 mask, used in this investigation, is contained within Area 0."
+ A basic problem with the ILC method is that it does not take the known variations of the spectral shapes and the relative contributions of the different foreground components into account., A basic problem with the ILC method is that it does not take the known variations of the spectral shapes and the relative contributions of the different foreground components into account.
+" Due to the statistical properties of the ILC map, the WMAP team does not recommend using it for cosmological investigations."," Due to the statistical properties of the ILC map, the WMAP team does not recommend using it for cosmological investigations."
+" Only Tegmark et ((2003, hereafter TOH) and DCLBFG have produced CMB maps with an angular resolution close to resolution of the best, W, channel."," Only Tegmark et (2003, hereafter TOH) and DCLBFG have produced CMB maps with an angular resolution close to resolution of the best, W, channel."
+" TOH developed a variant of the ILC method in the spherical harmonic domain, in which the weights are allowed to vary as a function of the multipole 1. The weights are computed in 9 independent areas on the sky."," TOH developed a variant of the ILC method in the spherical harmonic domain, in which the weights are allowed to vary as a function of the multipole l. The weights are computed in 9 independent areas on the sky."
+ The method was developed by means of the WMAP 1 yr maps and the WMAP 5yr maps have been analysed with the same method and made available athttp://space., The method was developed by means of the WMAP 1 yr maps and the WMAP 5yr maps have been analysed with the same method and made available at.
+mit.edu/home/tegmark/cleaned5yr.map.fits.. The DCLBFG team developeda variant of the ILC method exploiting the properties of needlet functions (Narcowich et al., The DCLBFG team developed a variant of the ILC method exploiting the properties of needlet functions (Narcowich et al.
+ 2006)., 2006).
+ These functions are both localized in the spherical harmonic domain and in the spatial domain., These functions are both localized in the spherical harmonic domain and in the spatial domain.
+" They incorporated the IRAS IRIS 100 wm map in the analysis ( Miville-Deschénnes and Lagache, 2005)."," They incorporated the IRAS IRIS 100 $\mu$ m map in the analysis ( Miville-Deschênnes and Lagache, 2005)."
+" All WMAP maps are deconvolved to the resolution of the W channel, which, of course, has increased the noise in the maps with poorer angular resolution."," All WMAP maps are deconvolved to the resolution of the W channel, which, of course, has increased the noise in the maps with poorer angular resolution."
+ DCLBFG used maps produced with the PSM simulation package to check the level of systematic errors in their CMB map., DCLBFG used maps produced with the PSM simulation package to check the level of systematic errors in their CMB map.
+ In their Fig., In their Fig.
+ 4 they give the residual map: some structures are seen but are difficult to quantify since the colour scale of the map covers + 600 µε. The DCLBFG ILC map has been taken from The difference between the DCLBFG and the TOH CMB maps is given in Fig.7., 4 they give the residual map: some structures are seen but are difficult to quantify since the colour scale of the map covers $\pm$ 600 $\mu$ K. The DCLBFG ILC map has been taken from The difference between the DCLBFG and the TOH CMB maps is given in \ref{res_dela_tegm_128} .
+" Due to an apparent small difference in temperature scale, the TOH map has been multiplied by a factor of 1.04."," Due to an apparent small difference in temperature scale, the TOH map has been multiplied by a factor of 1.04."
+" The scale and the HEALPix nside is the same as in Fig.6 (1.8. 37.5 wK, 128)."," The scale and the HEALPix nside is the same as in \ref{09_720_0_model_128} $\pm$ 37.5 $\mu$ K, 128)."
+" The residuals in Fig.7 deviate from a Gaussian distribution (skewness = 0.00, kurtosis = 0.26), and the systematic errors seem to reach a level of + 20 LK inside the KQ75 mask."," The residuals in \ref{res_dela_tegm_128} deviate from a Gaussian distribution (skewness = 0.00, kurtosis = 0.26), and the systematic errors seem to reach a level of $\pm$ 20 $\mu$ K inside the KQ75 mask."
+ Both the NN map in Fig.5 and the DCLBFG and TOH maps have obvious problems estimating the CMB temperatures close to the Galactic plane., Both the NN map in \ref{hunn_wmap} and the DCLBFG and TOH maps have obvious problems estimating the CMB temperatures close to the Galactic plane.
+" Therefore, only the sky area covered by the WMAP KQ75 mask will be used in deriving the power spectra of the maps, see below."," Therefore, only the sky area covered by the WMAP KQ75 mask will be used in deriving the power spectra of the maps, see below."
+" As emphasized above, the WMAP team has not produced a CMB map where it is possible to derive their optimal power spectrum directly."," As emphasized above, the WMAP team has not produced a CMB map where it is possible to derive their optimal power spectrum directly."
+ The method for deriving the optimal power, The method for deriving the optimal power
+the measured expansion curve at the higher frequencies. but not at GGHz.,"the measured expansion curve at the higher frequencies, but not at GHz."
+ This interpretation of the expansion curve. taking also the early break at day ~400 into consideration. will be analyzed in Paper II.," This interpretation of the expansion curve, taking also the early break at day $\sim400$ into consideration, will be analyzed in Paper II."
+ We measured the supernova shell radius using a method unrelated to model fitting in Fourier space (1. e.. the CPM).," We measured the supernova shell radius using a method unrelated to model fitting in Fourier space (i. e., the CPM)."
+ Thus. we can use these measured sizes as fixed parameters in a model fitting. in which we can estimate the fractional shell width.," Thus, we can use these measured sizes as fixed parameters in a model fitting, in which we can estimate the fractional shell width."
+ Given that the CPM has a small bias. dependent on the emission structure of the supernova (see Marcaide et al. 2009).," Given that the CPM has a small bias, dependent on the emission structure of the supernova (see Marcaide et al. \cite{Marcaide2009}) ),"
+ we should correct the shell sizes with the right bias before estimating the shell width., we should correct the shell sizes with the right bias before estimating the shell width.
+ However. the bias of the CPM depends on the degree of absorption by the ejecta. and also on the fractional shell width. which is the quantity to be determined from model fitting.," However, the bias of the CPM depends on the degree of absorption by the ejecta, and also on the fractional shell width, which is the quantity to be determined from model fitting."
+ In short. we have a coupling between fitted shell widths and CPM biases.," In short, we have a coupling between fitted shell widths and CPM biases."
+ We can look for self-consistency in that coupling. finding a shell width for which the bias of the CPM. applied to the (fixed) shell sizes in the model fitting. translates into a fitted shell width corresponding to the CPM bias already applied.," We can look for self-consistency in that coupling, finding a shell width for which the bias of the CPM, applied to the (fixed) shell sizes in the model fitting, translates into a fitted shell width corresponding to the CPM bias already applied."
+ See Sects., See Sects.
+ 6.2 and 7.2 of Mareaide et al., 6.2 and 7.2 of Marcaide et al.
+ 2009 for a detailed description of the trial-error procedure to find this self-consisteney., \cite{Marcaide2009} for a detailed description of the trial-error procedure to find this self-consistency.
+ Such a self-consistent fractional shell width is ~0.35. for a model with maximum (1.e.. 100%)) ejecta opacity.," Such a self-consistent fractional shell width is $\sim$ 0.35, for a model with maximum (i.e., ) ejecta opacity."
+ The percentage of ejecta opacity could be somewhat lower than and/or could evolve in time., The percentage of ejecta opacity could be somewhat lower than and/or could evolve in time.
+ When we require self-consistency between (bias-corrected) CPM results and (model-fitted) shell widths. lower ejecta opacities translate into narrower shell widths.," When we require self-consistency between (bias-corrected) CPM results and (model-fitted) shell widths, lower ejecta opacities translate into narrower shell widths."
+ In that sense. a value of 0.35 can be considered as an observational upper bound of the fractional shell width of 11993]. An appropriate percentage of absorption to use in our fits 1s the average of the estimates obtained from fitting a shell model to the data of our best epochs (1.e.. with good in-coverages and large signal-to-noise ratios).," In that sense, a value of 0.35 can be considered as an observational upper bound of the fractional shell width of 1993J. An appropriate percentage of absorption to use in our fits is the average of the estimates obtained from fitting a shell model to the data of our best epochs (i.e., with good -coverages and large signal-to-noise ratios)."
+ The epochs selected for such fits were all at GGHz between days 1638 and 2369 after explosion., The epochs selected for such fits were all at GHz between days 1638 and 2369 after explosion.
+ We used data only at GGHz to avoid any possible frequency-dependent bias., We used data only at GHz to avoid any possible frequency-dependent bias.
+ For all 10 epochs. we fitted the fractional shell width.€=(Row—Rin)/Row. the supernova radius. Row. the location of the shell center. the percentage of absorption. and the total flux density. obtaining an average relative shell width of -- 00.02 and an average percentage of absorption of 488)%.," For all 10 epochs, we fitted the fractional shell width,$\xi = (R_{\mathrm{out}}-R_{\mathrm{in}})/R_{\mathrm{out}}$, the supernova radius, $R_{\mathrm{out}}$, the location of the shell center, the percentage of absorption, and the total flux density, obtaining an average relative shell width of $\pm$ 0.02 and an average percentage of absorption of $\pm$."
+. These results are compatible with those reported in Mareaide et al. (2009) ).," These results are compatible with those reported in Marcaide et al. \cite{Marcaide2009}) ),"
+ who used a subset of the observations presented here., who used a subset of the observations presented here.
+ For an ejecta opacity of80%.. the shell widths obtained from model fitting are shown in Fig. 5..," For an ejecta opacity of, the shell widths obtained from model fitting are shown in Fig. \ref{SHELLWIDTH}."
+ Only observations of epochs from year 1995 onwards were used in the fitting., Only observations of epochs from year 1995 onwards were used in the fitting.
+ Using these values. we obtain a weighted mean of the shell width of £x 00.011 for GGHz data. + 00.005 for GGHz data. + 00.02 for GGHz data. and + 00.008 for GGHz data.," Using these values, we obtain a weighted mean of the shell width of $\pm$ 0.011 for GHz data, $\pm$ 0.005 for GHz data, $\pm$ 0.02 for GHz data, and $\pm$ 0.008 for GHz data."
+ All these quantities are close to 0.3., All these quantities are close to 0.3.
+ Based on very few and noisy data. the shell widths estimated at GGHz are the smallest. within 2c from the value 0.3.," Based on very few and noisy data, the shell widths estimated at GHz are the smallest, within $\sigma$ from the value 0.3."
+ On the other hand. data at 8.4 and GGHz give wider shell width estimates than at GGHz.," On the other hand, data at 8.4 and GHz give wider shell width estimates than at GHz."
+ The shell width at GGHz is compatible with that at GGHz at a Lc level., The shell width at GHz is compatible with that at GHz at a $\sigma$ level.
+ The average shell width at GGHz is about 2c wider than at GGHz., The average shell width at GHz is about $\sigma$ wider than at GHz.
+ The difference between shell widths at these frequencies could be due to either a physically wider shell at GGHz. to instrumental effects related to the finite sensitivity of the interferometers. or to a lower ejecta opacity at GGHz (lower opacities translate into narrower fitted shell widths).," The difference between shell widths at these frequencies could be due to either a physically wider shell at GHz, to instrumental effects related to the finite sensitivity of the interferometers, or to a lower ejecta opacity at GHz (lower opacities translate into narrower fitted shell widths)."
+ Any of these explanations (or a combination of them) could help explain the different shell widths obtained for different frequencies (see Marcaide et al. 2009))., Any of these explanations (or a combination of them) could help explain the different shell widths obtained for different frequencies (see Marcaide et al. \cite{Marcaide2009}) ).
+ In Paper IL. we will analyze these possibilities and their relationship. with features in the radio light curves published by Weiler et al. (20075.," In Paper II, we will analyze these possibilities and their relationship with features in the radio light curves published by Weiler et al. \cite{Weiler2007}) )."
+ From Fig. 5 .," From Fig. \ref{SHELLWIDTH},"
+ we also notice that no time evolution of the relative shell width is discernible at any, we also notice that no time evolution of the relative shell width is discernible at any
+from the Πα ot (1991) back to the older Munakata et ((1985) neutrino eiuission rates (FRANEC codo).,from the Haft et (1994) back to the older Munakata et (1985) neutrino emission rates (FRANEC code).
+ This is the same result as Cassisi et ((1998: models 5 and 7 in them Table 1) obtained for an 0.5AL. model withj—0.23. Z=0.0001 aud also identical to what we find in the case of the Padua-code for the same meocel.," This is the same result as Cassisi et (1998; models 8 and 7 in their Table 1) obtained for an $0.8\,M_\odot$ model with$Y=0.23$, $Z=0.0001$ and also identical to what we find in the case of the Padua-code for the same model."
+ In the latter case. we also verified that usine the Munakata et ((1985) emission down to logZ'=7.1 increases the ο core mass by zz0.001A...," In the latter case, we also verified that using the Munakata et (1985) emission down to $\log T = 7.4$ increases the He core mass by $\approx 0.001\,M_\odot$."
+ Therefore. the total budget of core mass reduction due to the C98 treatment of neutiiuo Cluission plivsics amounts to 0.007AM...," Therefore, the total budget of core mass reduction due to the G98 treatment of neutrino emission physics amounts to $0.007\,M_\odot$."
+" Recall that for the 1.2Af. model. the GOs value for AZ, is 0.02LAL. smaller than that of C99."," Recall that for the $1.2\,M_\odot$ model, the G98 value for $M_c$ is $0.024\,M_\odot$ smaller than that of C99."
+ We checked the effect of electron. conduction opacity by switching in the FRANEC code from Παανα Lape (1969) to Itoh et (1983) electron conduction oacities., We checked the effect of electron conduction opacity by switching in the FRANEC code from Hubbard Lampe (1969) to Itoh et (1983) electron conduction opacities.
+ The radiative opacitics iu these test cases are of eeneration older than OPAL. but the differential effect changing condution opacities can safely be assumed to e largely independent of the radiative opacities.," The radiative opacities in these test cases are of a generation older than OPAL, but the differential effect of changing condution opacities can safely be assumed to be largely independent of the radiative opacities."
+ The test model was a 1.5AL. star of 320.27. Z=0.02.," The test model was a $1.5\,M_\odot$ star of $Y=0.27$, $Z=0.02$."
+ The use of the older couductive opacities tthose used by GOs) leads to a reduction of 0.008Af.. in AL.," The use of the older conductive opacities those used by G98) leads to a reduction of $0.008\,M_\odot$ in $M_c$."
+ The influence of switchine from the 92 to the “96 OPAL opacitics was uot tested. but according to our experience it should be nünor compared to that of the electron conduction.," The influence of switching from the '92 to the '96 OPAL opacities was not tested, but according to our experience it should be minor compared to that of the electron conduction."
+ The EOS being a complicated part of voth programs. we could not easily exchange one for the other.," The EOS being a complicated part of both programs, we could not easily exchange one for the other."
+ However. we could perform the following test: we ook the pressure and temperature stratification of a nodel on the RGB and applied the 699-EOS to it in order ο obtain the deusitv.," However, we could perform the following test: we took the pressure and temperature stratification of a C99-model on the RGB and applied the G99-EOS to it in order to obtain the density."
+ We compared with the orginal C99 density stratification., We compared with the original C99 density stratification.
+ The result is shown iu Fie., The result is shown in Fig.
+ 6 for a RGB model with Y20.238. Z=0.001: while the core woulel rave densities higher bv abot in the Padua code. he envelope would be less dense by.," \ref{f:eoscomp} for a RGB model with Y=0.238, Z=0.004: while the core would have densities higher by about in the Padua code, the envelope would be less dense by."
+. Both effects reflect the evolutionary changes along the RGB. such that a CGi9s8-1iodel would appear to o nore evolved than a C99 one.," Both effects reflect the evolutionary changes along the RGB, such that a G98-model would appear to be more evolved than a C99 one."
+ Therefore. also the difference oein the EOS is expected to lead to a lower core mass at helium ignition for the Gos calculatious.," Therefore, also the difference in the EOS is expected to lead to a lower core mass at helium ignition for the G98 calculations."
+ From these three investigations we conclude that with the differences in neutrino eniüssiou rates and conductive opacities we can explain almost of the discrepancy nu core mass., From these three investigations we conclude that with the differences in neutrino emission rates and conductive opacities we can explain almost of the discrepancy in core mass.
+ This moves the C9s8 core masses already within the general spread of results., This moves the G98 core masses already within the general spread of results.
+ At least part of the remaining difference can be ascribed to the EOS., At least part of the remaining difference can be ascribed to the EOS.
+" Finally. we have compared results with three further codes. Which use almost ideutical iuput plysics as C99, in particular with regard to radiative opacitics. neutrino cluission aud electron conduction."," Finally, we have compared results with three further codes, which use almost identical input physics as C99, in particular with regard to radiative opacities, neutrino emission and electron conduction."
+" With regard to the Garching stellar evolution code (see. c.g.. Schlatt] Weiss 1999) we find that AZ. is O.OOLAL. larecr in the C99 models for a 0.5AV, star of =0.23 and two uctallicitics. Z=0.0001.0.001."," With regard to the Garching stellar evolution code (see, e.g., Schlattl Weiss 1999) we find that $M_c$ is $0.004\,M_\odot$ larger in the C99 models for a $0.8\,M_\odot$ star of $Y=0.23$ and two metallicities, $Z=0.0001,\> 0.001$."
+ This small difference can be uuderstood as beiug a consequence of the fact that more (0.001) helium is dredged up in the C99 models., This small difference can be understood as being a consequence of the fact that more $0.004$ ) helium is dredged up in the C99 models.
+ Finally. evolutionary calculations by Pols et al. (," Finally, evolutionary calculations by Pols et al. ("
+1998) and Domineucz et al. (,1998) and Dominguez et al. (
+1999) with their respective codes (Pols et al.,1999) with their respective codes (Pols et al.
+ 1998: Stranicro et al., 1998; Straniero et al.
+ 1997) revea for various chemical compositions a very high degree of agreement with those of C99 as shown in Fie 7.. including AL. which differs by less than 0.01 AD. between Domiueuez and C99.," 1997) reveal for various chemical compositions a very high degree of agreement with those of C99 as shown in Fig \ref{f:spscomp}, including $M_c$, which differs by less than 0.01 $_\odot$ between Dominguez and C99."
+ We therefore can conclude that more than half of the difference in the core mass at helium ignition- between G9N and C99 can be removed by adopting the same neutrino chussion rates and electron conduction opacitics: πας identical EOS would lead to further convergence. although we cannot quantify this point.," We therefore can conclude that more than half of the difference in the core mass at helium ignition between G98 and C99 can be removed by adopting the same neutrino emission rates and electron conduction opacities; using identical EOS would lead to further convergence, although we cannot quantify this point."
+ At the same time. codes with identical physics do indeed result iu very sinülar core lasses which differ at a level of a few 10°AJ. ouly.," At the same time, codes with identical physics do indeed result in very similar core masses which differ at a level of a few $10^{-3}\,M_\odot$ only."
+ Therefore. the differences between the C98 aud C99 results concerning this quautitv are well uuderstood as a consequence of different plivsical iuputs.," Therefore, the differences between the G98 and C99 results concerning this quantity are well understood as a consequence of different physical inputs."
+ Note that taking from the literature (sec c.g. Sweigart Cross 1978) AlosL/L.. =3.1AALS. for stars with degenerate progenitors. As a conclusion. the different predicted bpuuinosities we are dealing with appear as the natural results of evolutionary codes with cdiffereut but in both cases reasonable," Note that taking from the literature (see e.g. Sweigart Gross 1978) $\Delta$ $_{\odot}$ $\approx 3.4~\Delta M_c$ for stars with degenerate progenitors, As a conclusion, the different predicted luminosities we are dealing with appear as the natural results of evolutionary codes with different – but in both cases reasonable"
+of groups is based on angular and velocity coincidences. there will be spurious groupings or separations.,"of groups is based on angular and velocity coincidences, there will be spurious groupings or separations."
+ We note corrections to the group definitions where appropriate in. the text. and otherwise use the information as a means to illustrate the overall environmental characteristics of the HALOGAS sample.," We note corrections to the group definitions where appropriate in the text, and otherwise use the information as a means to illustrate the overall environmental characteristics of the HALOGAS sample."
+ The survey galaxies sample a fairly broad range in environment., The survey galaxies sample a fairly broad range in environment.
+ One quarter (6/24) of the HALOGAS sample reside in the same large group (Coma I)., One quarter (6/24) of the HALOGAS sample reside in the same large group (Coma I).
+ Three targets are members of pairs., Three targets are members of pairs.
+ In only one case is there a galaxy with a strongly interacting neighbor: NGC 672. which was included in the pilot survey described in this paper.," In only one case is there a galaxy with a strongly interacting neighbor: NGC 672, which was included in the pilot survey described in this paper."
+ The range of galaxy properties with respect to the group to which they belong also exhibits a wide range of values., The range of galaxy properties with respect to the group to which they belong also exhibits a wide range of values.
+ The HALOGAS sample contains galaxies which dominate their group. as well as those which are minor group members and companions.," The HALOGAS sample contains galaxies which dominate their group, as well as those which are minor group members and companions."
+ If these smaller targets are gas rich. we may be probing gas aceretion às Well as recipients.," If these smaller targets are gas rich, we may be probing gas accretion as well as recipients."
+ Considering all of these properties. after observations of the full HALOGAS sample. we expect to be able to assess whether there is an environmental dependence on target galaxy halo properties.," Considering all of these properties, after observations of the full HALOGAS sample, we expect to be able to assess whether there is an environmental dependence on target galaxy halo properties."
+ Because the HALOGAS galaxies are all nearby. there 15 the added advantage that most have beer extensively observed at other wavelengths. for example as part of recent surveys such as the Spitzer Infrared Nearby Galaxies Survey (SINGS:?) and the 11 Mpe Ha and Ultraviolet Galaxy Survey (1IHUGS: ?)..," Because the HALOGAS galaxies are all nearby, there is the added advantage that most have been extensively observed at other wavelengths, for example as part of recent surveys such as the Spitzer Infrared Nearby Galaxies Survey \citep[SINGS;][]{kennicutt_etal_2003} and the 11 Mpc $\alpha$ and Ultraviolet Galaxy Survey \citep[11HUGS;][]{lee_etal_2007}."
+ The star formation process is clearly of interest. with relation to the extraplanar. halo. and accreting gas that we are tracing. and we will therefore benefit by having these data available for our investigation.," The star formation process is clearly of interest with relation to the extraplanar, halo, and accreting gas that we are tracing, and we will therefore benefit by having these data available for our investigation."
+ Although the available data will help to characterize disk star formation rates. we note that the coverage is not enough to cover the full WSRT primary beam.," Although the available data will help to characterize disk star formation rates, we note that the coverage is not enough to cover the full WSRT primary beam."
+ Furthermore. we are pursuing deep observations at other observational facilities to fill gaps where necessary (see refsection:multiwavelength)).," Furthermore, we are pursuing deep observations at other observational facilities to fill gaps where necessary (see \\ref{section:multiwavelength}) )."
+ The data are being obtained using the WSRT. which is an east-west interferometer consisting of 10 fixed (of which one is not used) and 4 movable 25-m antennas.," The data are being obtained using the WSRT, which is an east-west interferometer consisting of 10 fixed (of which one is not used) and 4 movable 25-m antennas."
+ Baselines range from 36 m to 2.7 km. and the fixed antennas are on a regular grid with à spacing of 144 m. We used the array in its Maxishort configuration. which ts designed to optimize the imaging performance for extended sources in individual tracks.," Baselines range from 36 m to 2.7 km, and the fixed antennas are on a regular grid with a spacing of 144 m. We used the array in its Maxishort configuration, which is designed to optimize the imaging performance for extended sources in individual tracks."
+ The correlator was set up to provide two linear polarizations in 1024 channels over a 10 MHz bandwidth centered at the systemic velocity of each target., The correlator was set up to provide two linear polarizations in 1024 channels over a 10 MHz bandwidth centered at the systemic velocity of each target.
+ Each galaxy was observed for 10 full 12-hour tracks. and each track was bracketed by standard flux calibrator sources.," Each galaxy was observed for 10 full 12-hour tracks, and each track was bracketed by standard flux calibrator sources."
+ Data reduction was performed using usual techniques i1 the Miriad software package (?).., Data reduction was performed using usual techniques in the Miriad software package \citep{sault_etal_1995}.
+ A standard data reductior path was used for most targets: exceptions were necessary due to individual circumstances and will be described where appropriate., A standard data reduction path was used for most targets; exceptions were necessary due to individual circumstances and will be described where appropriate.
+ First. the raw data were visually inspected. anc samples corrupted by radio frequency interference. (RFI) were flagged where necessary.," First, the raw data were visually inspected, and samples corrupted by radio frequency interference (RFI) were flagged where necessary."
+ System temperature variations. which are measured and recorded at each antenna during the observations. were corrected for in both the calibrator and target data sets.," System temperature variations, which are measured and recorded at each antenna during the observations, were corrected for in both the calibrator and target data sets."
+ Next. the standard calibrator sources were used to set the flux scale. as well as define and correct for the bandpass response.," Next, the standard calibrator sources were used to set the flux scale, as well as define and correct for the bandpass response."
+" The radio continuum emission in the field was subtracted in the visibility domain and saved as ""channel-Q0"" data.", The radio continuum emission in the field was subtracted in the visibility domain and saved as ``channel-0'' data.
+ An imaging and self-calibration loop was used on the continuum data to solve for time-variable antenna gain phases., An imaging and self-calibration loop was used on the continuum data to solve for time-variable antenna gain phases.
+ The resulting antenna gains were subsequently applied to the continuum-subtracted spectral line data., The resulting antenna gains were subsequently applied to the continuum-subtracted spectral line data.
+ The ddata were imaged with a variety of weighting schemes (described below). creating several different data cubes for each target (see Table 3)).," The data were imaged with a variety of weighting schemes (described below), creating several different data cubes for each target (see Table \ref{table:cubes}) )."
+ Offline Hanning smoothing led to a final velocity resolution of 4.12kms~! although we may choose to degrade this resolution in post-processing in order to maximize sensitivity to features with broad velocity width.," Offline Hanning smoothing led to a final velocity resolution of $4.12\,\mathrm{km\,s^{-1}}$, although we may choose to degrade this resolution in post-processing in order to maximize sensitivity to features with broad velocity width."
+ Finally. Clark CLEAN deconvolution was performed in two stages. the first within masked regions containing the brightest line emission. and the second within the entire imaged region.," Finally, Clark CLEAN deconvolution was performed in two stages, the first within masked regions containing the brightest line emission, and the second within the entire imaged region."
+ Different weighting schemes are used in inverting the data from the wv plane into the image domain.," Different weighting schemes are used in inverting the data from the $u,v$ plane into the image domain."
+ In practice. within miriad’s task. we use a robust parameter of O for intermediate resolution and sensitivity.," In practice, within miriad's task, we use a robust parameter of $0$ for intermediate resolution and sensitivity."
+" To maximize sensitivity to faint extended emission we additionally use a Gaussian d.v taper corresponding to 30"" in the image plane."," To maximize sensitivity to faint extended emission we additionally use a Gaussian $u,v$ taper corresponding to $30\arcsec$ in the image plane."
+" See Figures 1.. 3... ον, and 7.."," See Figures \ref{figure:u2082}, \ref{figure:n0672}, \ref{figure:n0925}, and \ref{figure:n4565}."
+ For the pilot survey galaxies presented in this paper. we list in Table 3 à summary of the data cubes which have been produced and analyzed for the purposes of the presentation in refsection:results..," For the pilot survey galaxies presented in this paper, we list in Table \ref{table:cubes} a summary of the data cubes which have been produced and analyzed for the purposes of the presentation in \\ref{section:results}."
+ The columns are (1) Galaxy ID: (2) cube description: (3.4) beam size in aresee and in kpe (note. the beam position angle is in all cases very close to 0° because WSRT is an east-west array): (5) rms noise level: (6) the 3c column density sensitivity to emission with a velocity width of I6kms ': and (7) the mmass for a 3c detection of a spatially unresolved source with the same I6kms! velocity width.," The columns are (1) Galaxy ID; (2) cube description; (3,4) beam size in arcsec and in kpc (note, the beam position angle is in all cases very close to $0^\circ$ because WSRT is an east-west array); (5) rms noise level; (6) the $3\sigma$ column density sensitivity to emission with a velocity width of $16\,\mathrm{km\,s^{-1}}$ ; and (7) the mass for a $3\sigma$ detection of a spatially unresolved source with the same $16\,\mathrm{km\,s^{-1}}$ velocity width."
+ The mmasses are calculated using dp. from Table 1.., The masses are calculated using $d_\mathrm{best}$ from Table \ref{table:sample}.
+ The data cubes were used to generate images of the total lline intensity (moment-O. images). and of the intensity-averaged line-of-sight velocity (first-moment images).," The data cubes were used to generate images of the total line intensity (moment-0 images), and of the intensity-averaged line-of-sight velocity (first-moment images)."
+ These were produced by smoothing the data cubes to a resolution of 90”. clipping the original cubes at the 3c level of the smoothed cubes. and performing the moment calculations mentioned above.," These were produced by smoothing the data cubes to a resolution of $90\arcsec$, clipping the original cubes at the $3\sigma$ level of the smoothed cubes, and performing the moment calculations mentioned above."
+ The miriad task was used for this process., The miriad task was used for this process.
+" In the case of the total intensity map. the primary beam correction was applied (for the WSRT 25-m antennas. the primary beam shape takes the mathematical form cosServ), where e is a constant with a value of 68 at L-band. v is the frequency inGHz. and r Is the field radius in radians)."," In the case of the total intensity map, the primary beam correction was applied (for the WSRT 25-m antennas, the primary beam shape takes the mathematical form $\cos^6(cr\nu)$, where $c$ is a constant with a value of 68 at L-band, $\nu$ is the frequency inGHz, and $r$ is the field radius in radians)."
+ Then.intensitieswere converted to column densities (Ng) assuming optically thin gas.," Then,intensitieswere converted to column densities $N_{\mathrm{HI}}$ ) assuming optically thin gas."
+ The, The
+bv Flower (1993).. Flower&Rouell(1993).. Flower&Rouell(1995b).. Flower.Rouell&Zeippen(1998) aud LeBourlot.PineaudeForets&Flower(1999).,"by \citet{F98}, , \citet{FR98}, , \citet{FR98b}, \citet{FRZ98} and \citet{LB99}."
+. For levels where quanti calculations are not available. (he extrapolation scheme for the Is rate collisions provided bv Le Dourlot and workers in their code for photou—cdominatec regions (DDhs) has been adopted (Le Dourlot private communication).," For levels where quantum calculations are not available, the extrapolation scheme for the $_2$ rate collisions provided by Le Bourlot and workers in their code for $-$ dominated regions (PDRs) has been adopted (Le Bourlot private communication)."
+ For all other collisional partners when «quantum caleulations are lacking. the collision scheme put forward bv Tineetal.(1997). has been emploved.," For all other collisional partners when quantum calculations are lacking, the collision scheme put forward by \citet{T97} has been employed."
+ For models with temperatures larger (han 30 Ix. we have incorporated three rate coefficients for para conversions provided bv Sun&Dalgarno(1994).," For models with temperatures larger than 30 K, we have incorporated three rate coefficients for para conversions provided by \citet{SD94}."
+. Energy levels. radiative decay rates and dissociation probabilities lor electronic (ransiüons have been published by Aberalletal.(1992).. Aberalletal. (1993).. Aberalletal.(1993b) and Aberall.Rouelf&Drira(2000).," Energy levels, radiative decay rates and dissociation probabilities for electronic transitions have been published by \citet{A92}, \citet{A93}, \citet{A93b} and \citet{A00}."
+. Extra data. covering levels up to J=25. were kindly provided by Aberall (private communication).," Extra data, covering levels up to $J = 25$, were kindly provided by Abgrall (private communication)."
+ Quacdrupole radiative decavs and energies of vibrational levels of the ground electronic state were taken from Dalgarno (1993)., Quadrupole radiative decays and energies of vibrational levels of the ground electronic state were taken from \citet{WSD98}.
+". The Ils formation rate is more fully described by moment equations 2009).. rather than by rate equations using (he expression 7n4,2740;."," The $_2$ formation rate is more fully described by moment equations \citep{LP09}, rather than by rate equations using the expression ${\cal R} n_{\rm H} n_1 \delta_i$."
+ Lhis is because small erain sizes and low atom [fluxes are subject to large fluctuations. and thus ealeulating the ll» formation rate requires stochastic methods.," This is because small grain sizes and low atom fluxes are subject to large fluctuations, and thus calculating the $_2$ formation rate requires stochastic methods."
+ However. LePetitetal.(2009). [ind that the moment equation results agree wilh (he rate equation results in a wide range of conditions. except for dust grains al temperatures larger than 18 Ix. in which case the rate equations overestimate the Ils formation rate.," However, \citet{LP09} find that the moment equation results agree with the rate equation results in a wide range of conditions, except for dust grains at temperatures larger than 18 K, in which case the rate equations overestimate the $_2$ formation rate."
+ For dark clouds. as investigated in this paper. where dust temperature are ~10 Ix throughout the cloud. the Hà formation rate can be adequately described using the standard rate equation term assumed in eq.(1)).," For dark clouds, as investigated in this paper, where dust temperature are $\sim 10$ K throughout the cloud, the $_2$ formation rate can be adequately described using the standard rate equation term assumed in \ref{SEE}) )."
+ Of course. if (he radiation environment differs substantially [rom the standard interstellar conditions. dust temperatures may be noticebly larger than 20 Ix (see Section 4).," Of course, if the radiation environment differs substantially from the standard interstellar conditions, dust temperatures may be noticebly larger than 20 K (see Section 4)."
+ In the present study. for all formation pumping models. except the one presented in section 2. the relative (normalized) populations of the vibrational states are given by where C is a normalization constant and AF.) is the energy in Ix of level (6.7) referred to the eround state.," In the present study, for all formation pumping models, except the one presented in Section 2, the relative (normalized) populations of the vibrational states are given by where ${\cal C}$ is a normalization constant and $\Delta E_{vJ}$ is the energy in K of level $(v,J)$ referred to the ground state."
+ fy ancl f» are shapeFunctions depending on (he specific formation mocel., $f_1$ and $f_2$ are shapefunctions depending on the specific formation model.
+ We consider thefollowinge IH» formation pumpinge models:, We consider thefollowing $_2$ formation pumping models:
+therefore identify with the orbital period.,therefore identify with the orbital period.
+ is a very bright LAINB in the elobular cluster NCC 6621., is a very bright LMXB in the globular cluster NGC 6624.
+ Stellaetal.(1987). analyzed data from) N-rayv observations withZXOSAT aud discovered the 1l nüuute orbital period., \citet{spw87} analyzed data from X-ray observations with and discovered the 11 minute orbital period.
+ The periodicity is oulv evident as a or less peak-to-peak modulation in the overall N-ray intensity., The periodicity is only evident as a or less peak-to-peak modulation in the overall X-ray intensity.
+ Chou&Caindlay(2001)/ used nieasurenients nade by a nuniber of N-rav satellites of, \citet{chougrn01} used measurements made by a number of X-ray satellites of
+A schemathic 2D map of the disk cussion flux is eiveu in Fig.,A schemathic 2D map of the disk emission flux is given in Fig.
+ 3., 3.
+ Profiles for different lines of sight are preseuted in Fig., Profiles for different lines of sight are presented in Fig.
+ L, 4.
+ Hoe the bolometric huninosity is LOtteres|. he black hole mass is 105ML... aud the itial inclination angle is 107.," Here the bolometric luminosity is $10^{44}\, \mathrm{erg\,s}^{-1}$, the black hole mass is $10^{8}\, \mathrm{M_{\mathrm{\odot}}}$, and the initial inclination angle is $10{{}^{\circ }}$."
+ The Ίνα piriuneter ¢=1 aud the viscosity xumneter a=0.)υπο Dz130.," The Kerr parameter $a=1$ and the viscosity parameter $\alpha=0.1$, so $\Gamma 
+\approx 130$."
+ The most miportau result of this work is that the xofiles of the disk emission (Fig., The most important result of this work is that the profiles of the disk emission (Fig.
+ £) are τοιςνοΊσα and red or blue frequeney shifted. as expected if only about a ια of the disk emuts in the direction towards he observer (Fig.," 4) are nonsymmetrical and red or blue frequency shifted, as expected if only about a half of the disk emits in the direction towards the observer (Fig."
+ 3)., 3).
+ Oulv for special viewing angles. hese profiles could be almost sviuuctric. double or single-)eaked and non yequency-shifted.," Only for special viewing angles, these profiles could be almost symmetric, double or single-peaked and non frequency-shifted."
+ In Fie., In Fig.
+ 5 the profile dependence of various quantities i presented., 5 the profile dependence of various quantities is presented.
+ D is an inportaut parameter. affecting siguificautlv the disk shape and respectively the line profiles.," $\Gamma$ is an important parameter, affecting significantly the disk shape and respectively the line profiles."
+ Iu. Fig., In Fig.
+ Sa the profiles or D=10 (for instance &=OL. a=0.1): 130 (o=1. a=0.1) and 100 (the upper nit ο=la =1) are shown.," 5a the profiles for $\Gamma=40$ (for instance $a=0.1$ , $\alpha=0.1$ ); 130 $a=1$, $\alpha=0.1$ ) and 400 (the upper limit – $a=1$, $\alpha=1$ ) are shown."
+ In Fig., In Fig.
+ 5b the profile dependence ou 10 ποτος wieght Ze is shown., 5b the profile dependence on the source height $Z_\mathrm{S}$ is shown.
+ Increasing Za. a larger part of the central disk region is irradiated and the profiles approach hose from the planar disks — the second. svuumetrically displaced peas increases its intensity.," Increasing $Z_\mathrm{S}$, a larger part of the central disk region is irradiated and the profiles approach those from the planar disks – the second, symmetrically displaced peak increases its intensity."
+ We do not see ay physical reason. however. to put the source far above the centia object.," We do not see any physical reason, however, to put the source far above the central object."
+" The depeudence of the profiles ou he iux ταν ""unuinuositv is also siguificaut. because of the effect of he saturation of the lines. which limits the emission liue flux a sanall distances (igh velocities). independent of an iucrease of £x."," The dependence of the profiles on the hard X-ray luminosity is also significant, because of the effect of the saturation of the lines, which limits the emission line flux at small distances (high velocities), independent of an increase of $L_{\mathrm{X}}$."
+ For higher £x. the lines should become warrower (Fie.," For higher $L_{\mathrm{X}}$, the lines should become narrower (Fig."
+ 5e)., 5c).
+ One should keep in mined. however. hat Lx should be 10%Pores| to match the observer ine intensities.," One should keep in mind, however, that $L_{\mathrm{X}}$ should be $10^{43-45}\, \mathrm{erg\,s}^{-1}$ to match the observed line intensities."
+ Profile shapes are almost indepeucent of he initial disk tilt (Fie., Profile shapes are almost independent of the initial disk tilt (Fig.
+ 5d)., 5d).
+ The EWIIM aud the shit slightly decrease with increasing tilt., The $\mathrm{FWHM}$ and the shift slightly decrease with increasing tilt.
+ Note that the profiles are also not depeucent directly on the black hole mass aux he accretion rate (of course. the mass aud the accretion rate may affect the incident flux at a given distance auc fusCR.ο) respectively).," Note that the profiles are also not dependent directly on the black hole mass and the accretion rate (of course, the mass and the accretion rate may affect the incident flux at a given distance and $f_{\mathrm{H\beta}}(R,\psi)$ respectively)."
+ Weaker cussion from the opposite side of the disk lay appear in case the disk is not filly opaque at visua wavelengths., Weaker emission from the opposite side of the disk may appear in case the disk is not fully opaque at visual wavelengths.
+ This might be the case or the outer regious. where the optical depth is probably not significant if no dust is present (Collin-Souttin Diunont 1990).," This might be the case for the outer regions, where the optical depth is probably not significant if no dust is present (Collin-Souffrin Dumont 1990)."
+ Profiles should then be double-peaked and more or less sviunetric., Profiles should then be double-peaked and more or less symmetric.
+ Although this case is not considered here. one cau easily reproduce such profiles.," Although this case is not considered here, one can easily reproduce such profiles."
+ A similar situation occurs when the disk is transparent to the hard radiation. which is then absorbed witlin the whole vertical structure of the disk.," A similar situation occurs when the disk is transparent to the hard radiation, which is then absorbed within the whole vertical structure of the disk."
+ The hard X-rav vacation. comine from the center. can iluumate the outer parts of the nonplanar disk. where optical cussion lines will be emütted as a result of reprocessing.," The hard X-ray radiation, coming from the center, can illuminate the outer parts of the nonplanar disk, where optical emission lines will be emitted as a result of reprocessing."
+ Profiles of such lines are modeledhere (Fig., Profiles of such lines are modeledhere (Fig.
+ 1)., 4).
+ Chaneing some basic parameters. such as the lard," Changing some basic parameters, such as the hard"
+feedback. SHO3 followed a phenomenological scheme to include the effect of galactic winds. whose velocity. 7... scales with the fraction 1 of the SN-II feedback energy that contributes to the winds. as ryox.4437 (see eq[28] in SHO3).,"feedback, SH03 followed a phenomenological scheme to include the effect of galactic winds, whose velocity, $v_w$, scales with the fraction $\eta$ of the SN-II feedback energy that contributes to the winds, as $v_w\propto \eta^{1/2}$ (see eq.[28] in SH03)."
+ The total energy provided by SN-II is computed by assuming that they originate from stars with mass 7SM. fora initial mass function IMF). with each SN releasing 1075 ergs.," The total energy provided by SN-II is computed by assuming that they originate from stars with mass $>8\,{\rm M}_\odot$ for a initial mass function (IMF), with each SN releasing $10^{51}$ ergs."
+" As discussed in the following. we will assume jj=0.5 and |. yielding ο,2340 and 480 km ‘respectively. while we will also explore the effect of switching off galactic winds altogether."," As discussed in the following, we will assume $\eta=0.5$ and 1, yielding $v_w\simeq 340$ and 480 km $^{-1}$, respectively, while we will also explore the effect of switching off galactic winds altogether."
+ We consider two sets of clusters. which have been selected from different parent cosmological boxes.," We consider two sets of clusters, which have been selected from different parent cosmological boxes."
+ Initial conditions for both sets have been generated using the Zoomed Initial Condition (ZIC) technique by?., Initial conditions for both sets have been generated using the Zoomed Initial Condition (ZIC) technique by.
+. This technique increases the mass resolution in a suitably chosen high-resolution Lagrangian region surrounding the structure to be re-simulated., This technique increases the mass resolution in a suitably chosen high–resolution Lagrangian region surrounding the structure to be re-simulated.
+ It. then adds additional initial displacements. assigned according to the Zeldovich approximation2).. from the newly sampled high—frequency modes which were not assigned in the low-resolution parent simulation.," It then adds additional initial displacements, assigned according to the Zeldovich approximation, from the newly sampled high--frequency modes which were not assigned in the low–resolution parent simulation."
+ Furthermore.the mass resolution is progressively degraded in more distant regions. so as to save computational resources while still correctly describing the large-scale tidal field of the cosmological environment.," Furthermore,the mass resolution is progressively degraded in more distant regions, so as to save computational resources while still correctly describing the large–scale tidal field of the cosmological environment."
+ Once initial positions and velocities are assigned. a DM- run is performed to check for any contamination of the surroundings of the cluster virial region by heavy particles that may have moved in from the low- to the high-resolution region.," Once initial positions and velocities are assigned, a DM--only run is performed to check for any contamination of the surroundings of the cluster virial region by heavy particles that may have moved in from the low– to the high–resolution region."
+ If required. the shape of the Lagrangian high-resolution region is optimized by trial and error until any such contamination around the halo of interest is prevented.," If required, the shape of the Lagrangian high–resolution region is optimized by trial and error until any such contamination around the halo of interest is prevented."
+ With a typical number of 3-5 trials. we end up with initial conditions which produce a cluster that. at. =O. is free of contaminants out to 4.," With a typical number of 3-5 trials, we end up with initial conditions which produce a cluster that, at $z=0$, is free of contaminants out to $\,R_{\rm vir}$."
+ Once initial conditions are created. we split particles in the high-resolution region into a DM and a gas component. whose mass ratio is set to reproduce the assumed cosmie baryon fraction.," Once initial conditions are created, we split particles in the high–resolution region into a DM and a gas component, whose mass ratio is set to reproduce the assumed cosmic baryon fraction."
+ Instead of placing them on top of each other. we displace gas and DM particles such that the centre of mass of each parent particle is preserved and the final gas and dark matter particle distributions are interleaved by one mean particle spacing.," Instead of placing them on top of each other, we displace gas and DM particles such that the centre of mass of each parent particle is preserved and the final gas and dark matter particle distributions are interleaved by one mean particle spacing."
+ This set includes four clusters. resimulated at different resolutions. with virial mass in the range My=(1.6—13) 10HΤΝ. (CLI to CL4 in Table 11).," This set includes four clusters, resimulated at different resolutions, with virial mass in the range $M_{\rm
+ vir}=(1.6$ $13)\times 10^{14}h^{-1}{\rm M}_\odot$ (CL1 to CL4 in Table \ref{tab:sets}) )."
+ These clusters have been extracted from the cosmological hydrodynamical simulation presented by?., These clusters have been extracted from the cosmological hydrodynamical simulation presented by.
+". The simulation followed 480° DM particles and an initially equal number of gas particles. within a box of 192. Mpe on a side. for a flat ACDM model with (2,=0.3. /QT. ms0.5 and 0.04."," The simulation followed $480^3$ DM particles and an initially equal number of gas particles, within a box of $192\,h^{-1}$ Mpc on a side, for a flat $\Lambda$CDM model with $\Omega_m=0.3$, $h=0.7$, $\sigma_8=0.8$ and $\Omega_{\rm
+b}=0.04$ ."
+ With these choices. the masses ofthe DM and gas particles are mpapc4.6LO’1M. and Mans&6.91030BI respectively.," With these choices, the masses ofthe DM and gas particles are $m_{\rm DM}\simeq 4.6\times 10^9\msun$ and $m_{\rm
+gas}\simeq 6.9\times 10^8\msun$, respectively."
+ The force accuracy is set by ej=7.5.!kpe for the Plummer-equivalent softening parameter. fixed in physical units from z= Oto 2=2. and kept fixed in comoving units at higher redshifts.," The force accuracy is set by $\epsilon_{\rm Pl}=7.5\hk$ for the Plummer–equivalent softening parameter, fixed in physical units from $z=0$ to $z=2$, and kept fixed in comoving units at higher redshifts."
+ Since initial conditions of the parent simulations have been generated on a grid. a grid is also used to assign initial displacements for these resimulations.," Since initial conditions of the parent simulations have been generated on a grid, a grid is also used to assign initial displacements for these resimulations."
+ Initial conditions for euch cluster are generated at four different mass resolutions. corresponding to the basic resolution of the parent box (low resolution. LR). and to 3 times (medium resolution. MR). 10 times (high resolution. HR) and 45 times (very high resolution. VR) smaller particle masses.," Initial conditions for each cluster are generated at four different mass resolutions, corresponding to the basic resolution of the parent box (low resolution, LR), and to 3 times (medium resolution, MR), 10 times (high resolution, HR) and 45 times (very high resolution, VR) smaller particle masses."
+ The VR run is not carried out for the CLI cluster. whose large mass would result in a too large computational cost.," The VR run is not carried out for the CL1 cluster, whose large mass would result in a too large computational cost."
+ The gravitational softening in the high-resolution regions is rescaled with the mass of the particles according to cjxmi where the LR runs were set to have the same softening as used in the parent simulation.," The gravitational softening in the high–resolution regions is rescaled with the mass of the particles according to $\epsilon_{\rm Pl}\propto m^{1/3}$, where the LR runs were set to have the same softening as used in the parent simulation."
+ In Table 2.. we list the masses of the DM and gas particles. as well as the force softening for the different resolutions.," In Table \ref{tab:res}, we list the masses of the DM and gas particles, as well as the force softening for the different resolutions."
+ At the highest achieved resolution. each cluster is resolved with at least 1.5 million DM particles within the virial radius. with CL2 reaching 2.2 million particles.," At the highest achieved resolution, each cluster is resolved with at least 1,5 million DM particles within the virial radius, with CL2 reaching 2,2 million particles."
+ The reference runs for the clusters of havebeen performed by assuming that 100 per cent of the energy provided by SNe is carried by winds., The reference runs for the clusters of havebeen performed by assuming that 100 per cent of the energy provided by SNe is carried by winds.
+" This gives a wind speed of ο,&480kms", This gives a wind speed of $v_w\simeq 480\vel$.
+ This set includes 2 clusters having mass c1007IM. and clothΤΝ. CLS and CL6 in Table Ι.. respectively).," This set includes 2 clusters having mass $\simeq 10^{15}\msun$ and $\simeq 10^{14}\msun$ (CL5 and CL6 in Table \ref{tab:sets}, respectively)."
+ They have been selected from a larger sample of20 clusters with masses in the range 5.10123107A1 NI... which have been identified in simulations of 9 Lagrangian regions (Dolag et al..," They have been selected from a larger sample of20 clusters with masses in the range $5\times 10^{13}-2.3\times
+10^{15}\msun$ , which have been identified in simulations of 9 Lagrangian regions (Dolag et al.,"
+ in preparation)., in preparation).
+" These systems were extracted from a DM-only simulation with a box size of 479ff Mpc of a flat XCDM model with ο= 0.3. hf= 0.7. os0.9 and Qj,=0.04 ο)."," These systems were extracted from a DM–only simulation with a box size of $479\,h^{-1}$ Mpc of a flat $\Lambda$ CDM model with $\Omega_m=0.3$ , $h=0.7$ , $\sigma_8=0.9$ and $\Omega_{\rm b}=0.04$ ."
+ Differently from £1.. the initial displacementswere generated using a ‘glass’ for the Lagrangian particle distribution.," Differently from , the initial displacementswere generated using a `glass' for the Lagrangian particle distribution."
+ Only, Only
+Eq. (13)),Eq. \ref{eq:selfcal-dpq}) )
+ add either constructively or destructively., add either constructively or destructively.
+" In these two cases, we get: For any non-trivial array configuration. each baseline has a different fringe rate. so at any point in time some baselines will be closer to constructive addition. and others will be close to destructive addition."," In these two cases, we get: For any non-trivial array configuration, each baseline has a different fringe rate, so at any point in time some baselines will be closer to constructive addition, and others will be close to destructive addition."
+" Therefore. no set of G, can achieve a perfect fit of D, to V,,."," Therefore, no set of $\jones{\tilde G}{p}$ can achieve a perfect fit of $\coh{D}{pq}$ to $\coh{V}{pq}$."
+" However. from the above we can infer an upper bound on the relative error of the fit: I shall call Zo, the factor [of source I into source 0]."," However, from the above we can infer an upper bound on the relative error of the fit: I shall call $\Xi_{0,1}$ the factor [of source 1 into source 0]."
+ I do not have a formal proof for a lower boundary on the error terms in Eq. (15))," I do not have a formal proof for a lower boundary on the error terms in Eq. \ref{eq:contamination}) ),"
+ but extesive simulations with MeqTrees suggest that it ts also proportional to Ey).," but extensive simulations with MeqTrees suggest that it is also proportional to $\Xi_{0,1}$."
+ We can therefore summarize these considerations as follows: in the presence of DDEs. traditional selfcal will tend to subsume the DDEs in the direction of the dominant source into its selfeal gain solutions: the fitted visibilities will be subject to from the unmodelled DDEs towards the source. with a relative error proportional to Zo.," We can therefore summarize these considerations as follows: in the presence of DDEs, traditional selfcal will tend to subsume the DDEs in the direction of the dominant source into its selfcal gain solutions; the fitted visibilities will be subject to from the unmodelled DDEs towards the next-brightest source, with a relative error proportional to $\Xi_{0,1}$."
+ Similar considerations apply to any discrepancies (1.8. missing sources. etc.)," Similar considerations apply to any discrepancies (i.e. missing sources, etc.)"
+ in the sky model., in the sky model.
+ Ultimately. selfcal contamination makes itself felt via artefacts in the resulting images. which can be extraordinarily complicated and counter-intuitive (foranexample.seeFig.17ofPaperIIL.?)..," Ultimately, selfcal contamination makes itself felt via artefacts in the resulting images, which can be extraordinarily complicated and counter-intuitive \citep[for an example, see Fig.~17 of Paper III,][]{RRIME3}."
+ The algorithm was originally proposed by ?. as a way of calibrating and removing DDEs from bright sources one by one. in order of decreasing brightness.," The algorithm was originally proposed by \citet{JEN:peeling} as a way of calibrating and removing DDEs from bright sources one by one, in order of decreasing brightness."
+ Since its introduction. the term “peeling” has been misunderstood and diluted to the point where it is occasionally used to describe technique incorporating direction-dependent solutions. but this 15 incorrect.," Since its introduction, the term “peeling” has been misunderstood and diluted to the point where it is occasionally used to describe technique incorporating direction-dependent solutions, but this is incorrect."
+ In its original formulation. peeling refers to a very specific calibration algorithm: Peeling has the considerable advantage that all existing 2GC calibration packages provide sufficient functionality to implement its steps. so it has been widely tested and accepted in the community.," In its original formulation, peeling refers to a very specific calibration algorithm: Peeling has the considerable advantage that all existing 2GC calibration packages provide sufficient functionality to implement its steps, so it has been widely tested and accepted in the community."
+ The major drawback of peeling is that it can be very expensive computationally., The major drawback of peeling is that it can be very expensive computationally.
+" Note that the solutions at step | are subject to selfcal contamination =,,.,."," Note that the solutions at step 1 are subject to selfcal contamination $\Xi_{s_0,s_1}$ ."
+" This error is ""frozen in at step 2. when the fitted visibilities (for source sq) are subtracted from the data."," This error is “frozen in” at step 2, when the fitted visibilities (for source $s_0$ ) are subtracted from the data."
+" It can then further contaminate the solutions for s, (in addition to the contamination E,.,."," It can then further contaminate the solutions for $s_1$ (in addition to the contamination $\Xi_{s_1,s_2}$."
+" If the source being peeled is truly dominant. then this contamination can be negligible. but if the brightness of so and s, is comparable. it can become pretty severe."," If the source being peeled is truly dominant, then this contamination can be negligible, but if the brightness of $s_0$ and $s_1$ is comparable, it can become pretty severe."
+ These errors can be driven down by repeated iterations through the peeling cycle (with clever subtraction of sources). at the cost of significant CPU and I/O overhead.," These errors can be driven down by repeated iterations through the peeling cycle (with clever subtraction of sources), at the cost of significant CPU and I/O overhead."
+ This makes peeling impractical when dealing with more than just a few sources., This makes peeling impractical when dealing with more than just a few sources.
+ The approach is closely related to peeling., The approach is closely related to peeling.
+ It may be thought of as a generalized. simultaneous form of peeling.," It may be thought of as a generalized, simultaneous form of peeling."
+" A detailed practical example will be discussed in Paper IH (2).. but the essence is to use a RIME of the form: and solve for G, on small time/frequency scales (as per normal selfeal). then solve for AE,, on larger time/frequency scales. for a subset of fainter sources."," A detailed practical example will be discussed in Paper III \citep{RRIME3}, but the essence is to use a RIME of the form: and solve for $\jones{G}{p}$ on small time/frequency scales (as per normal selfcal), then solve for $\Delta\jones{E}{ps}$ on larger time/frequency scales, for a subset of fainter sources."
+" The G, solutions then subsume all DDEs in the direction of the dominant source. while the AE,, terms account for the towards the fainter sources."," The $\jones{G}{p}$ solutions then subsume all DDEs in the direction of the dominant source, while the $\Delta\jones{E}{ps}$ terms account for the towards the fainter sources."
+" If some of the DDEs are knownpriori.. suitable terms for them can be inserted into the equation above in addition to AE,,."," If some of the DDEs are known, suitable terms for them can be inserted into the equation above in addition to $\Delta\jones{E}{ps}$."
+ The differential gain solution will then account only for the remaining unknown DDEs., The differential gain solution will then account only for the remaining unknown DDEs.
+ Note that solving for ΔΙ on a single off-axis source is equivalent to peeling the dominant source and solving for the off-axis source (with suitable solution intervals chosen for each selfcal step)., Note that solving for $\Delta\jones{E}{}$ on a single off-axis source is equivalent to peeling the dominant source and solving for the off-axis source (with suitable solution intervals chosen for each selfcal step).
+ The AZ approach overcomes a lot of the drawbacks of peeling (contamination of solutions and frozen-in errors. the need for repeated selfcal eycles) by doing a single simultaneous solution in one step.," The $\Delta\jones{E}{}$ approach overcomes a lot of the drawbacks of peeling (contamination of solutions and frozen-in errors, the need for repeated selfcal cycles) by doing a single simultaneous solution in one step."
+ Differential gains share a common weakness with peeling: that of proliferation of degrees of freedom (DoF's)., Differential gains share a common weakness with peeling: that of proliferation of degrees of freedom (DoF's).
+ This ts partially mitigated by using larger solution intervals. but it is obvious that we cannot simultaneously solve forAE. towards sources 1n a typical field. since that would be gross (," This is partially mitigated by using larger solution intervals, but it is obvious that we cannot simultaneously solve for$\Delta\jones{E}{ps}$ towards sources in a typical field, since that would be gross over-fitting. ("
+Not to mention the CPU cost of solving for that many,Not to mention the CPU cost of solving for that many
+for raw CCD images were applied (bias ancl clark-frame subtract and [at-feld correction) using the program.,for raw CCD images were applied (bias and dark-frame subtract and flat-field correction) using the program.
+ Reduced images of the same series were Co-added: to. improve the S/N ratio and then used. for photometry., Reduced images of the same series were co-added to improve the S/N ratio and then used for photometry.
+" We used to perform. “Optimal photometry” (based. on fitting of ""SE profiles). D.V.H."," We used to perform “Optimal photometry” (based on fitting of PSF profiles). $B, V, R$,"
+ and. £ magnitudes for comparison stars were taken from the Local Ciroup Survey (LOGS) catalog of stars in 333 (Massey.etCamal., and $I$ magnitudes for comparison stars were taken from the Local Group Galaxy Survey (LGGS) catalog of stars in 33 \citep{m3}.
+mp90060)... 1n the ease of SDSS M3μα images. we ni magnitudes for comparison stars from DVRL magnitudes aken from Masseyetal.(2006) using empirical color ransformations between the SDSS αν system and Johnson-Cousins CDVHI system published by Jordietal. (2006).," In the case of SDSS $r'$ band images, we computed $r'$ magnitudes for comparison stars from $BVRI$ magnitudes taken from \citet{m3} using empirical color transformations between the SDSS $u'g'r'i'z'$ system and Johnson-Cousins $UBVRI$ system published by \citet{j2}."
+. Nishivama=&lxabashima—(2009) continued their. unliltered observations at the Mivaki Argenteus Observatory. Japan. from 2009 August 18 to 2010 January 3 and kindly provided us with 16 new images taken in this period.," \citet{n1} continued their unfiltered observations at the Miyaki Argenteus Observatory, Japan, from 2009 August 18 to 2010 January 3 and kindly provided us with 16 new images taken in this period."
+ All the photometric measurements of 182006] 40671 (collected.inadditionto2006) are presented in Table 1, All the photometric measurements of [HBS2006] 40671 \citep[collected in addition to those of][]{h1} are presented in Table 1.
+ We created finding chart for the star [rom hieh-quality 2 band image taken with the Subaru telescope on 2002 November 4 (Lig., We created a finding chart for the star from high-quality $R$ band image taken with the Subaru telescope on 2002 November 4 (Fig.
+ , 1).
+A relatively bright. visual companion is located 2.1 aresec north-cast of the variable., A relatively bright visual companion is located 2.1 arcsec north-east of the variable.
+" Alasseyetal.(2006) the du M this star as RA=015349927719, Deccataloged=30758 οn and eive D. V. A and 4 band magnitudes of 21.40. 20.94. and 20.71. respectively."," \citet{m3}
+ cataloged the position of this star as $\rmn{RA} = 01^{\rmn{h}} 34^{\rm
+n{m}} 27\fs19$, $\rmn{Dec} = 30\degr 58\arcmin 44\farcs 4$ (J2000) and give $B$, $V$, $R$, and $I$ band magnitudes of 21.40, 21.11, 20.94, and 20.71, respectively."
+ The observations of the LOGS (Masseyetal.2006) were obtained from October 2000 to September 2001., The observations of the LGGS \citep{m3} were obtained from October 2000 to September 2001.
+ The variable star is not included in the catalog. as it is only detected on the £ band image taken during the survey on 2001 September IS(criterion for inclusion in catalog is detection in the three bands D.V. 2).," The variable star is not included in the catalog, as it is only detected on the $I$ band image taken during the survey on 2001 September 18 (criterion for inclusion in catalog is detection in the three bands $B,V,R$ )."
+from DO03.,from B03.
+ As an example we plot the median lines derived using the (ο r) and AlfL(n—q) relations for both EPCs and LPGs., As an example we plot the median lines derived using the $\ML-(g-r)$ and $\ML-(u-g)$ relations for both ETGs and LTGs.
+ The trends with aanel velocity clispersion are qualitatively unchanged. but some cdillerences emerge since the AZ/Ls from cach 09 relation are derived using different colours. which probe different wavelength spectral regions.," The trends with and velocity dispersion are qualitatively unchanged, but some differences emerge since the s from each B03 relation are derived using different colours, which probe different wavelength spectral regions."
+ The Ls obtained using the gor colours seems to resemble our trends. Lor L'TCGs. while the agreement is poorer when wg is used.," The s obtained using the $g-r$ colours seems to resemble our trends for LTGs, while the agreement is poorer when $u-g$ is used."
+ For ECGs our trend is between the two BOS results at low mass. while the from e—g is a little bit better at large mass.," For ETGs our trend is between the two B03 results at low mass, while the from $u-g$ is a little bit better at large mass."
+ We have also checked. the οσο of the wavebaand acopted for the rratios in the bottom panels of Fig. 3.., We have also checked the effect of the waveband adopted for the ratios in the bottom panels of Fig. \ref{fig:fig3}.
+ Here. the B-band eeradients are compared to the ones in. V- and. ;-band.," Here, the $B$ -band gradients are compared to the ones in $V$ - and $i$ -band."
+ Except for the most massive I7I€is. in general the eeracients tend to become shallower (closer to zero) when using redcder bands.," Except for the most massive ETGs, in general the gradients tend to become shallower (closer to zero) when using redder bands."
+ Also. the trends with mass and velocity dispersion. become weaker.," Also, the trends with mass and velocity dispersion become weaker."
+ Thus. redder bands. which are," Thus, redder bands, which are"
+"The source has a total Kp magnitude of 20.3 (20.6 if a single-component is fit) and, again assuming a formation redshift z—3 and solar metallicity, this implies that the rest-frame K-band magnitude is 21.0, the luminosity is Lk,sc=10195[L45, and the stellar mass is Myre=10199 Mo.","The source has a total Kp magnitude of 20.3 (20.6 if a single-component is fit) and, again assuming a formation redshift $z = 3$ and solar metallicity, this implies that the rest-frame K-band magnitude is 21.0, the luminosity is $_{\rm K,src} = 10^{10.8}~L_{\rm K,\odot}$, and the stellar mass is $_{\rm *,src} = 10^{10.9}~{\rm M}_\odot$ ."
+" The (1.ο., observed) source magnitude is 17.6, and we therefore find a factor of 12 magnification due to lensing."," The (i.e., observed) source magnitude is 17.6, and we therefore find a factor of 12 magnification due to lensing."
+ The background source size is 0.5 kpc if a single de Vaucouleurs profile is assumed or 1.1 kpc if a component de Vaucouleurs and Sersic profile is used., The background source size is 0.5 kpc if a single de Vaucouleurs profile is assumed or 1.1 kpc if a two-component de Vaucouleurs and Sersic profile is used.
+ The SDSS spectrum allows us to verify that our stellar masses from the Keck AO-LGS photometry are robust., The SDSS spectrum allows us to verify that our stellar masses from the Keck AO-LGS photometry are robust.
+ We fit Bruzual&Charlot(2003) templates to the foreground and background components of the spectrum to determine the appropriate normalisation of the templates and therefore the stellar mass of the flux observed by the SDSS spectroscopic fibre., We fit \citet{bc03} templates to the foreground and background components of the spectrum to determine the appropriate normalisation of the templates and therefore the stellar mass of the flux observed by the SDSS spectroscopic fibre.
+ The lens (foreground) stellar mass determined from the SDSS spectrum is 10111Mo which implies a 0.5 dex loss of flux due to the fibre aperture; this is consistent with what we find if we convolve our model with the SDSS point spread function (which has FWHM — 2722 for SDSSJ1347-0101) and integrate the flux within the SDSS fibre aperture., The lens (foreground) stellar mass determined from the SDSS spectrum is $10^{11.1}~M_\odot$ which implies a 0.5 dex loss of flux due to the fibre aperture; this is consistent with what we find if we convolve our model with the SDSS point spread function (which has FWHM = 2 for SDSSJ1347-0101) and integrate the flux within the SDSS fibre aperture.
+" We perform the same procedure for the lensed (background) source and find that, when accounting for magnification and fibre losses, the source stellar mass inferred from the Keck LGS-AO photometry and the SDSS spectrum agree to within 0.2 dex, consistent with our assumed errors on the stellar mass."," We perform the same procedure for the lensed (background) source and find that, when accounting for magnification and fibre losses, the source stellar mass inferred from the Keck LGS-AO photometry and the SDSS spectrum agree to within 0.2 dex, consistent with our assumed errors on the stellar mass."
+ The background source of SDSSJ1347-0101 is a clear outlier from the size-mass relationship of local ETGs and has properties that are similar to high-redshift ETGs (Figure 3))., The background source of SDSSJ1347-0101 is a clear outlier from the size-mass relationship of local ETGs and has properties that are similar to high-redshift ETGs (Figure \ref{F_sizeMass}) ).
+" However, the inferred size varies by a factor of two depending on whether a one- or two-component surface brightness model is fit to the galaxy; our imaging data clearly indicate that the two-component model is required to describe the light distribution of SDSSJ1347-0101."," However, the inferred size varies by a factor of two depending on whether a one- or two-component surface brightness model is fit to the galaxy; our imaging data clearly indicate that the two-component model is required to describe the light distribution of SDSSJ1347-0101."
+" Larger samples of intermediate-redshift objects are need to make any strong claims, but we note that the extended ‘wing’ of flux from the background source of SDSSJ1347-0101 may help alleviate the tension between the verycompact high-redshift galaxies and the apparent lack of local-universe counterparts (e.g.,Trujilloetal.2009;Taylor in two ways."," Larger samples of intermediate-redshift objects are need to make any strong claims, but we note that the extended `wing' of flux from the background source of SDSSJ1347-0101 may help alleviate the tension between the verycompact high-redshift galaxies and the apparent lack of local-universe counterparts \citep[e.g.,][]{trujillo09,taylor} in two ways."
+" First, single-component fits may be poor models for the true surface brightness distribution of compact ETGs (e.g.,Stocktonetal. 2010), and observations of high-redshift galaxies may lack the sensitivity required to characterise low-surface-brightness extended components of red nuggets."," First, single-component fits may be poor models for the true surface brightness distribution of compact ETGs \citep[e.g.,][]{stockton}, and observations of high-redshift galaxies may lack the sensitivity required to characterise low-surface-brightness extended components of red nuggets."
+" This is unlikely to fully resolve the issue, however, since a factor of two size difference is not enough to move all of the high-redshift objects to the local size-mass relation."," This is unlikely to fully resolve the issue, however, since a factor of two size difference is not enough to move all of the high-redshift objects to the local size-mass relation."
+" We also note that deep imaging of the high-redshift galaxies does not indicate the presence of a significant second component for most red nuggets (e.g.,Damjanovetal. 2009).."," We also note that deep imaging of the high-redshift galaxies does not indicate the presence of a significant second component for most red nuggets \citep[e.g.,][]{damjanov}. ."
+" Alternatively, the low-surface-brightness components of"," Alternatively, the low-surface-brightness components of"
+individual channels (figure 6)). we see that the amplitude of variation is highly energy. dependent.,"individual channels (figure \ref{fig:fold_channs}) ), we see that the amplitude of variation is highly energy dependent."
+ The variation at energies 1.3 - 3.0 keV. represented by ASAL channels 1 and 2. . 1 ↓↥⋜↧⊳∖⋜⋯↓↓≻↓∐⋯⇂∢⋅∿↓∠⋅⋅∺⊽⋜⋯∠⇂↿↓↕⋖⋅∖⇁⋜⊔⋅↓⋜⊔↓∪⊔↓⊳∖⊳∖⊔↓∪∪↿↓↕⊳∖∖⋎↓↥⋖⋅↓⋅∢⋅⋜↧≱∖ ⋠⋠⋠ at energies 5.0 - 12.1 keV the variation is about twice this amplitude.," The variation at energies 1.3 - 3.0 keV, represented by ASM channels 1 and 2, has amplitude $\sim$ 1 $cs^{-1}$ and the variation is smooth, whereas at energies 5.0 - 12.1 keV the variation is about twice this amplitude."
+" Our analysis of the RATE and CGRO archival datasets has not only confirmed the presence of the superorbital period in SAIC’ NX-1. it has clearly demonstratec that this itself is varving on an even longer timescale (conceivably a ""fourth"," Our analysis of the RXTE and CGRO archival datasets has not only confirmed the presence of the superorbital period in SMC X-1, it has clearly demonstrated that this itself is varying on an even longer timescale (conceivably a “fourth”"
+a choice of the wavelength regions is justified for magnetic field diagnostics as bandhead regions contain a mixture of lines with different /-numbers and accordingly different magnetic sensitivity and formation height.,a choice of the wavelength regions is justified for magnetic field diagnostics as bandhead regions contain a mixture of lines with different $J$ -numbers and accordingly different magnetic sensitivity and formation height.
+ Therefore. the differential Hanle effect technique can be applied.," Therefore, the differential Hanle effect technique can be applied."
+" Moreover the bandhead is formed higher in the atmosphere than the radiation at the nearest wavelengths (1—2 away from the bandhead) so the information about conditions at a broad range of heights can be inferred,", Moreover the bandhead is formed higher in the atmosphere than the radiation at the nearest wavelengths (1–2 away from the bandhead) so the information about conditions at a broad range of heights can be inferred.
+ The intensity and linear polarization in. the region containing the (1.1) bandhead (3868.9-3871.4 Á) was observed at five limb angle positions from pe=0.1 to pe=0.5 (here µ is the cosine of the angle between the propagation direction of radiation and the local solar radius).," The intensity and linear polarization in the region containing the (1,1) bandhead (3868.9–3871.4 ) was observed at five limb angle positions from $\mu=0.1$ to $\mu=0.5$ (here $\mu$ is the cosine of the angle between the propagation direction of radiation and the local solar radius)."
+ The intensity in the second region containing the (0.0) bandhead (3879.7—3883.6 A)) was observed at ten limb angle positions from pe=0.1 tojc=1.0 with the constant step Au=0.1.," The intensity in the second region containing the (0,0) bandhead (3879.7--3883.6 ) was observed at ten limb angle positions from $\mu=0.1$ to $\mu=1.0$ with the constant step $\Delta \mu=0.1$."
+ The polarization in the second region was observed at two positions: wp=0.1 and yt=0.2., The polarization in the second region was observed at two positions: $\mu=0.1$ and $\mu=0.2$.
+ The pointing of the telescope allows a precision of about | aresec. but due to seeing and the curvature of the solar limb relative to the straight spectrograph slit. we need to take into account an uncertainty of about £0.02 at jj=0.1.," The pointing of the telescope allows a precision of about 1 arcsec, but due to seeing and the curvature of the solar limb relative to the straight spectrograph slit, we need to take into account an uncertainty of about $\pm 0.02$ at $\mu = 0.1$."
+ The error for µ values quickly decreases toward the disk centre., The error for $\mu$ values quickly decreases toward the disk centre.
+ In the following we introduce our numerical method employed for solving the radiative transfer problem., In the following we introduce our numerical method employed for solving the radiative transfer problem.
+ We have performed calculations in à framework of plane-parallel model atmospheres., We have performed calculations in a framework of plane-parallel model atmospheres.
+ The modeling consists from two maim steps. as was previously suggested by Flurietal.(2003).," The modeling consists from two main steps, as was previously suggested by \citet{flurietal2003}."
+. We firstly calculate opacities and intensity without taking into account any polarization., We firstly calculate opacities and intensity without taking into account any polarization.
+ Then we iteratively calculate polarization assuming that opacities obtained in the first step remain unchanged., Then we iteratively calculate polarization assuming that opacities obtained in the first step remain unchanged.
+ In the weak-field regime the redistribution. matrix. can. be factorized into a scalar function depending only on frequencies of incoming and outgoing radiation and the phase matrix., In the weak-field regime the redistribution matrix can be factorized into a scalar function depending only on frequencies of incoming and outgoing radiation and the phase matrix.
+ The phase matrix does not directly depend on frequencies. but it has different appearance in different frequency domains (Bommier1997;Flurietal. 2003).," The phase matrix does not directly depend on frequencies, but it has different appearance in different frequency domains \citep{bommier1997b, flurietal2003}."
+". Under the assumption of complete frequency redistribution (CRD) and an isotropic single-value turbulent magnetic field the phase matrix for the line core domain (roughly speaking in this domain both absorption and emission of à photon occur close to the line core) is given by (Flurtetal.2003) and in the line wing domain by In these equations yz and pe’ indicate the outgoing and incoming directions of the scattered photon. W> is the effective scattering polarizability. Wy is the Hanle depolarization factor. and Ey, and P are 2x matrices (as we solve the radiative transfer problem for Stokes / and Q only) which are given by In agreement with the principle of spectroscopic stability. line wings are not affected by the Hanle effect. and the Hanle depolarization factor Wy does not enter Eq. (2))."," Under the assumption of complete frequency redistribution (CRD) and an isotropic single-value turbulent magnetic field the phase matrix for the line core domain (roughly speaking in this domain both absorption and emission of a photon occur close to the line core) is given by \citep{flurietal2003}
+ and in the line wing domain by In these equations $\mu$ and $\mu'$ indicate the outgoing and incoming directions of the scattered photon, $W_2$ is the effective scattering polarizability, $W_{\rm H}$ is the Hanle depolarization factor, and $\,{\vec E}_{11}$ and ${\vec P}^{(2)}$ are $2 \times 2$ matrices (as we solve the radiative transfer problem for Stokes $I$ and $Q$ only) which are given by and In agreement with the principle of spectroscopic stability, line wings are not affected by the Hanle effect, and the Hanle depolarization factor $W_{\rm H}$ does not enter Eq. \ref{eq:Pwings}) )."
+ Values of the dimensionless frequency for a core-wing boundary separation are calculated for certain values of the Voigt parameter 4 by Bommier(1997).., Values of the dimensionless frequency for a core-wing boundary separation are calculated for certain values of the Voigt parameter $a$ by \citet{bommier1997b}.
+ For a given damping parameter a. we interpolate between the known values.," For a given damping parameter $a$, we interpolate between the known values."
+" The matrix £j, represents isotropic. unpolarized scattering. while P describes linearly polarized coherent scattering (e.g..Stenflo 1994)."," The matrix $\vec{E}_{11}$ represents isotropic, unpolarized scattering, while ${\vec P}^{(2)}$ describes linearly polarized coherent scattering \citep[e.g.,][]{stenflo1994}."
+. Due to the latter even initially unpolarized radiation becomes polarized after scattering. and the degree of polarization scales with the effective polarizability W..," Due to the latter even initially unpolarized radiation becomes polarized after scattering, and the degree of polarization scales with the effective polarizability $W_2$."
+ The Hanle effect in the line core for the case of a turbulent single-value magnetic field is introduced by (Stenflo1982) where Here Γι.ΓΙ and Γι. are the radiative damping. inelastic and elastic collision rates. respectively. d is the efficiency of the depolarization by elastic collisions. B is the magnetic field strength. and σι is the effective Landé factor of the transition’s upper state.," The Hanle effect in the line core for the case of a turbulent single-value magnetic field is introduced by \citep{stenflo1982}
+ where Here $\Gamma_{\rm R}, \Gamma_{\rm I}$ and $\Gamma_{\rm E}$ are the radiative damping, inelastic and elastic collision rates, respectively, $d$ is the efficiency of the depolarization by elastic collisions, $B$ is the magnetic field strength, and $g_{\rm L}$ is the effective Landé factor of the transition's upper state."
+do not depend on a lack of rellectional svuumetiy in the flow.,do not depend on a lack of reflectional symmetry in the flow.
+ The dependence of (he eml on {he mean field and its gradient can be extremely. complicated. as shown by expression (37)). which considers the relatively simple case of an ideal MIID analysis with v = η=0.," The dependence of the emf on the mean field and its gradient can be extremely complicated, as shown by expression \ref{eq:emfx_Gilman}) ), which considers the relatively simple case of an ideal MHD analysis with $\nu$ = $\eta =0$."
+ For the more general treatment of the instability. discussed in relseczunidirectional.. relsecisheared.. the stability problem and the subsequent evaluation of the emt have to be performed numerically.," For the more general treatment of the instability, discussed in \\ref{sec:unidirectional}, \\ref{sec:sheared}, the stability problem and the subsequent evaluation of the emf have to be performed numerically."
+ In order to treat the competition between modes of equal growth rates. but different ems. it is necessary (o introduce some weighting procedure. such as that described by expression (26)).," In order to treat the competition between modes of equal growth rates, but different emfs, it is necessary to introduce some weighting procedure, such as that described by expression \ref{eq:weighted_emf}) )."
+ We can then obtain both the Iatitudinal ancl depth dependence of (he emls. as well as exploring the dependence on parameters such as rotation.," We can then obtain both the latitudinal and depth dependence of the emfs, as well as exploring the dependence on parameters such as rotation."
+ We have shown (hat a net emf arises naturally [rom the prelerred modes of magnetic buovancy instabilities in a rotating svstem., We have shown that a net emf arises naturally from the preferred modes of magnetic buoyancy instabilities in a rotating system.
+ Our results also make clear (hat (he relationship between the effectiveness of the emf and the vigour of the instability is not straightforward (his reinforces the important message (hat an instability cannot guarantee a mean, Our results also make clear that the relationship between the effectiveness of the emf and the vigour of the instability is not straightforward — this reinforces the important message that an instability cannot guarantee a mean
+"With this change of variables equation (1)) becomes The first term on the right hand side represents radiation pressure, and the second represents gas pressure.","With this change of variables equation \ref{momeqn}) ) becomes The first term on the right hand side represents radiation pressure, and the second represents gas pressure."
+" This equation is not exactly correct near xj;= 1, because in writing the gas pressure term we have implicitly assumed that the density inside the region is uniform and has the value given by ionization balance, equation (2))."," This equation is not exactly correct near $\xii=1$ , because in writing the gas pressure term we have implicitly assumed that the density inside the region is uniform and has the value given by ionization balance, equation \ref{rhoiieqn}) )."
+" This assumption cannot be precisely true when xjS1, because while radiation pressure is significant it will exert a force on material in the region interior that will make the density higher toward the shell wall than near the region center, while equation (2)) assumes uniform density."," This assumption cannot be precisely true when $\xii\ltsim 1$, because while radiation pressure is significant it will exert a force on material in the region interior that will make the density higher toward the shell wall than near the region center, while equation \ref{rhoiieqn}) ) assumes uniform density."
+" Nonetheless, equation (10)) represents a reasonable approximation that becomes exact everywhere except near xyz=1."," Nonetheless, equation \ref{momeqnnondim}) ) represents a reasonable approximation that becomes exact everywhere except near $\xii=1$."
+" At early times, when xy<1, we can drop the gas pressure term  on the right hand side, and the resulting equation aifadmits the similarity solution 'The dynamics of this solution can be understood by noting that since the momentum of the shell equals the radiant momentum modified by the trapping factor (Msn?= ftrapLt/c), the shell’s kinetic energy Mgn7‘7,/2 is a very small fraction, Γαμρήπ/(29), of the total radiated energy Lt."," At early times, when $\xii \ll 1$, we can drop the gas pressure term $\xii^{1/2}$ on the right hand side, and the resulting equation admits the similarity solution The dynamics of this solution can be understood by noting that since the momentum of the shell equals the radiant momentum modified by the trapping factor $\msh \riidot = f_{\rm trap} Lt/c$ ), the shell's kinetic energy $\msh \riidot^2/2$ is a very small fraction, $f_{\rm trap}^2 \riidot/(2c)$, of the total radiated energy $L t$."
+" In fact, if fiap1, then the energy of the shell’s motion approximately matches the energy of the photons currently crossing its interior: MayT4/2© (n/2)Lrir/c, where η=fyt/rm2/(4—"," In fact, if $f_{\rm trap}\sim 1$, then the energy of the shell's motion approximately matches the energy of the photons currently crossing its interior: $\msh\riidot^2/2 \approx (\eta/2) L \rii/c$ , where $\eta=\riidot t/\rii = 2/(4-\krho)$."
+ The inefficiency of direct radiation driving is related kp).to the low value of an issue we return to in 3..," The inefficiency of direct radiation driving is related to the low value of $f_{\rm trap}$, an issue we return to in \ref{trapping}."
+" If we were to ftrap,drop the radiation pressure term, we would have the usual similarity solution for gas pressure expansion Although the exact solution will approach this value when xy;>1, the existence of a characteristic scale Tech implies that there is no true similarity solution that includes both the radiation- and gas-driven phases."," If we were to drop the radiation pressure term, we would have the usual similarity solution for gas pressure expansion Although the exact solution will approach this value when $\xii\gg 1$, the existence of a characteristic scale $r_{\rm ch}$ implies that there is no true similarity solution that includes both the radiation- and gas-driven phases."
+" When radiation pressure is significant it provides an extra boost of momentum in the phase before gas pressure takes over, accelerating the expansion relative to the standard similarity solution."," When radiation pressure is significant it provides an extra boost of momentum in the phase before gas pressure takes over, accelerating the expansion relative to the standard similarity solution."
+" This breaks the self-similarity of the gas-driven expansion phase, although the expansion approaches self-similarity as T—oo and the extra momentum provided by the radiation becomes small compared to that input by the gas."," This breaks the self-similarity of the gas-driven expansion phase, although the expansion approaches self-similarity as $\tau\rightarrow \infty$ and the extra momentum provided by the radiation becomes small compared to that input by the gas."
+" In the absence of a similarity solution, however, it is trivial to integrate equation (10)) numerically."," In the absence of a similarity solution, however, it is trivial to integrate equation \ref{momeqnnondim}) ) numerically."
+" We do so subject to the boundary condition that xy and dxy/dr approach the values that correspond to the similarity solution (11)) as T—0, and plot the result in Figure 3 for some sample values of k,."," We do so subject to the boundary condition that $\xii$ and $d\xii/d\tau$ approach the values that correspond to the similarity solution \ref{radsolution}) ) as $\tau\rightarrow 0$, and plot the result in Figure \ref{xiisol} for some sample values of $\krho$."
+" For comparison, we also show the pure radiation and pure gas similarity solutions."," For comparison, we also show the pure radiation and pure gas similarity solutions."
+ 'The true solution may be reasonably approximated by an appropriately weighted sum between the two., The true solution may be reasonably approximated by an appropriately weighted sum between the two.
+" The expression is accurate to better than for k,20—1.", The expression is accurate to better than for $\krho=0-1$.
+" As discussed in 1, one of the reasons that radiation-driven expansion is of interest is that gas-driven expansion will fail in regions where the ambient velocity dispersion and escape velocity exceed the ionized gas sound speed (e.g. ??).."," As discussed in \ref{intro}, one of the reasons that radiation-driven expansion is of interest is that gas-driven expansion will fail in regions where the ambient velocity dispersion and escape velocity exceed the ionized gas sound speed \citep[e.g.][]{matzner02, krumholz06d}. ."
+" The expansion velocity is ΤΠ=vay(dag/dr), where 'The expansion rate therefore drops to the ionized gas sound speed when day/dr=8)."," The expansion velocity is $\riidot=v_{\rm ch} (d\xii/d\tau)$, where The expansion rate therefore drops to the ionized gas sound speed when $d\xii/d\tau = \zeta^{(3-2\krho)/4}/\sqrt{(3,8)}$."
+" Since we have solved for ἀππ/άτ numerically,¢8-?e)/4/,/(3, it is trivial to numerically invert this equation for a given ¢ to obtain the radius and time at which the expansion becomes subsonic."," Since we have solved for $d\xii/d\tau$ numerically, it is trivial to numerically invert this equation for a given $\zeta$ to obtain the radius and time at which the expansion becomes subsonic."
+" However, it is more illuminating to consider the radiation-dominated case ¢>>1, because in that case the similarity solution (11)) applies, and the resulting analytic form for allows us to solve for the radius at which the subsonic dxy;/drtransition occurs in closed form."," However, it is more illuminating to consider the radiation-dominated case $\zeta\gg 1$, because in that case the similarity solution \ref{radsolution}) ) applies, and the resulting analytic form for $d\xii/d\tau$ allows us to solve for the radius at which the subsonic transition occurs in closed form."
+" In this limit, expansion becomes subsonic at To give some idea of this in physical units, for k,=0 the radius at which the expansion becomes subsonic is Clearly the transition to subsonic expansionwill not happen until an region has swept up a significant fraction of the gas in the protocluster, and it is therefore"," In this limit, expansion becomes subsonic at To give some idea of this in physical units, for $\krho=0$ the radius at which the expansion becomes subsonic is Clearly the transition to subsonic expansionwill not happen until an region has swept up a significant fraction of the gas in the protocluster, and it is therefore"
+more (0.3596 in A2 — 0.68% in Al; 0.43% in A5 — 1.1296 in A4).,more $0.35\%$ in A2 $\rightarrow$ $0.68\%$ in A1; $0.43\%$ in A5 $\rightarrow$ $1.12\%$ in A4).
+ The difference between the before-arm areas and inter-arm areas are relatively small., The difference between the before-arm areas and inter-arm areas are relatively small.
+" On the other hand, the young and dusty population (P2) is most dominant in the before-arm areas (~10% in A2 and A5, but 4—8% in other areas)."," On the other hand, the young and dusty population (P2) is most dominant in the before-arm areas $\sim10\%$ in A2 and A5, but $4-8\%$ in other areas)."
+ The old population (P4) shows an increasing fraction along after-arm — before-arm — inter-arm areas., The old population (P4) shows an increasing fraction along after-arm $\rightarrow$ before-arm $\rightarrow$ inter-arm areas.
+ Fig., Fig.
+ 17 compares the outskirt populations between the two spiral arms., \ref{oring} compares the outskirt populations between the two spiral arms.
+" In the outskirt area of SA1 (Bl and B2), the fraction of the young population (P1) is almost constant (~ 4%), whereas that in B4 (9.3%)is significantly larger than that in B3 (5.996; by more than 1.5 factor)."," In the outskirt area of SA1 (B1 and B2), the fraction of the young population (P1) is almost constant $\sim4\%$ ), whereas that in B4 $9.3\%$ )is significantly larger than that in B3 $5.9\%$; by more than 1.5 factor)."
+" We also found that the fraction of the old population (P4) shows opposite trends between the outskirts of SA1 and SA2: the P4 fraction along B3 — B4 decreases almost by half (3896— 2196), while that along B1 — B2 increases by a 1.4 factor (3396— 4796)."," We also found that the fraction of the old population (P4) shows opposite trends between the outskirts of SA1 and SA2: the P4 fraction along B3 $\rightarrow$ B4 decreases almost by half $38\%\rightarrow21\%$ ), while that along B1 $\rightarrow$ B2 increases by a 1.4 factor $33\%\rightarrow47\%$ )."
+" The fraction of the young and dusty population (P2) decreases along the outward direction of spiral arms both in SAI and SA2, but the decrease along B3 — B4 (11.796— 10.9%) is smaller than that along B1 > B2 (9.996— 6.7%)."," The fraction of the young and dusty population (P2) decreases along the outward direction of spiral arms both in SA1 and SA2, but the decrease along B3 $\rightarrow$ B4 $11.7\%\rightarrow10.9\%$ ) is smaller than that along B1 $\rightarrow$ B2 $9.9\%\rightarrow6.7\%$ )."
+" Since the B4 area is connected to NGC 5195, the interaction with NGC 5195 seems to have affected the stellar populations in B4."," Since the B4 area is connected to NGC 5195, the interaction with NGC 5195 seems to have affected the stellar populations in B4."
+" In the NGC 5194 pCMD, one interesting feature is found at the bright-end of the red pixel sequence: the sequence turns into the opposite direction, resulting in bluer colors for brighter pixels."," In the NGC 5194 pCMD, one interesting feature is found at the bright-end of the red pixel sequence: the sequence turns into the opposite direction, resulting in bluer colors for brighter pixels."
+" To investigate the nature of those bright pixels, we first divided the bright-end (V«17.25 mag arcsec?) pixels using their colors."," To investigate the nature of those bright pixels, we first divided the bright-end $V<17.25$ mag $^{-2}$ ) pixels using their colors."
+ Fig., Fig.
+ 18 shows the pCMDs and pCCD of the NGC 5194 bright-end pixels., \ref{btpop} shows the pCMDs and pCCD of the NGC 5194 bright-end pixels.
+" There is a population forming a tight sequence in the pCMD (bright-end sequence population; BSP), which is defined as the pixels within a narrow cylinder in the 3-dimensional"," There is a population forming a tight sequence in the pCMD (bright-end sequence population; BSP), which is defined as the pixels within a narrow cylinder in the 3-dimensional"
+"This means that only particles having the boundary condition 8, and oO) at py can reach (he region where Equation (20)) is satisfied.",This means that only particles having the boundary condition $\theta_0$ and $\phi_0$ at $\rho_0$ can reach the region where Equation \ref{bdry}) ) is satisfied.
+ To examine the validitv of the transformation from Equation (5)) to Equation (7)). we compare (he analvtical solutions wilh a numerical simulation. in which a cosmic ταν particle is directly traced in the magnetic flux rope.," To examine the validity of the transformation from Equation \ref{eom}) ) to Equation \ref{eom_r}) ), we compare the analytical solutions with a numerical simulation, in which a cosmic ray particle is directly traced in the magnetic flux rope."
+ We integrate Equation (5)) and υ=dr/dl by using the Buneman-Boris Method., We integrate Equation \ref{eom}) ) and $\vec v=d\vec r/dt$ by using the Buneman-Boris Method.
+ Needless to say. the numerical simulation includes both evralion and geradient-curvature drift effects.," Needless to say, the numerical simulation includes both gyration and gradient-curvature drift effects."
+ Hereafter. we consider a paralleltvpe magnetic {lux rope model (i.e.. s= 1) without loss of generality.," Hereafter, we consider a parallel-type magnetic flux rope model (i.e., $s=1$ ) without loss of generality."
+ We use 2p=0.1 AU and By=20 nT as (vpical values near (he Earth (Marubashi 1997)., We use $R_0=0.1$ AU and $B_0=20$ nT as typical values near the Earth (Marubashi 1997).
+ Figure 2. shows the particle trajectories on the r—5 plane., Figure \ref{xy} shows the particle trajectories on the $r-\varphi$ plane.
+ A dashed circle with a radius of 1 in the ligure is the edge of flix rope., A dashed circle with a radius of 1 in the figure is the edge of flux rope.
+" The solid curves starting from the point (£r.y)=(1.0) aud (c.y)=(71.0) are the particle trajectories of GO GY cosmic rays. which correspond (o. fy=0.669. and those of 6 GV cosmic ravs. which correspond (o. fi,=0.0669. respectively. for various boundary. conditions 8, and Oy al py=1."," The solid curves starting from the point $(x,y)=(1,0)$ and $(x,y)=(-1,0)$ are the particle trajectories of 60 GV cosmic rays, which correspond to $f_0=0.669$, and those of 6 GV cosmic rays, which correspond to $f_0=0.0669$, respectively, for various boundary conditions $\theta_0$ and $\phi_0$ at $\rho_0=1$."
+ The starting points are not important for the results because the magnetic field in the flux rope is svmmetrical with regard (o the z axis., The starting points are not important for the results because the magnetic field in the flux rope is symmetrical with regard to the $z$ axis.
+ All these particles entering [rom the outside of the [Iux rope are escaping from the flix rope within one gvro motion., All these particles entering from the outside of the flux rope are escaping from the flux rope within one gyro motion.
+" A (hick spiral curve in (he ligure shows a (trajectory of α 6 GV trapped cosmic ray particle for randomly selected boundary condition 8, and oy at po=0.5.", A thick spiral curve in the figure shows a trajectory of a 6 GV trapped cosmic ray particle for randomly selected boundary condition $\theta_0$ and $\phi_0$ at $\rho_0=0.5$.
+ The trapped particle trajectory obviously shows a eracdient-curvature dift., The trapped particle trajectory obviously shows a gradient-curvature drift.
+ The dift velocity components are in the y and 2 directions as caleulated from the definition of the flux Figure 3 shows the three components of normalized velocity w against the normalized distance p [rom the [ας rope axis for 60. GV cosmic ravs., The drift velocity components are in the $\varphi$ and $z$ directions as calculated from the definition of the flux Figure \ref{rvrvpvz_60GV} shows the three components of normalized velocity $\vec u$ against the normalized distance $\rho$ from the flux rope axis for 60 GV cosmic rays.
+" Panels a). b). and €) show the r. 92. and z components. respectively,"," Panels a), b), and c) show the $r$, $\varphi$, and $z$ components, respectively."
+" Grav plus signs show results of numerical simulation for various penetration angles 6, and ó αἱ py=1. corresponding to those in Figure 2.."," Gray plus signs show results of numerical simulation for various penetration angles $\theta_0$ and $\phi_0$ at $\rho_0=1$, corresponding to those in Figure \ref{xy}. ."
+ Solid lines show the analvtical solutions for (he same parameters used in the numerical simulation., Solid lines show the analytical solutions for the same parameters used in the numerical simulation.
+ lt is evident that the analvtical solutions exactly (trace the simulation results., It is evident that the analytical solutions exactly trace the simulation results.
+" It is noticed that unphysical solutions. in which w, is an inagiary number. are also drawn bv dashed lines in Panels b) and ο) in the Figure 4 also shows the three components of normalized velocity against the normalized distance for a 6 GV. trapped cosmic ταν particle."," It is noticed that unphysical solutions, in which $u_r$ is an imaginary number, are also drawn by dashed lines in Panels b) and c) in the Figure \ref{rvrvpvz_trap} also shows the three components of normalized velocity against the normalized distance for a 6 GV trapped cosmic ray particle."
+ Gray plus signs show results of numerical simulation. represented by the spiral curve in Figure 2..," Gray plus signs show results of numerical simulation, represented by the spiral curve in Figure \ref{xy}."
+ Solid lines are the analytical solutions for the same parameters used in nunerical simulation., Solid lines are the analytical solutions for the same parameters used in numerical simulation.
+ Ht is also evident (hat the analvtical solutions exactly trace (he simulation results., It is also evident that the analytical solutions exactly trace the simulation results.
+" It is again noticed that unphysical solutions. in whieh u, is an imaginary number. are also drawn in Panels b) and ο) in the figure."," It is again noticed that unphysical solutions, in which $u_r$ is an imaginary number, are also drawn in Panels b) and c) in the figure."
+ The trapped cosmic ray. particle obviously evrates and drilis in the magnetic fields. as described above.," The trapped cosmic ray particle obviously gyrates and drifts in the magnetic fields, as described above."
+ The trajectories ofthese particles in velocity space show oscillatory motions on the, The trajectories ofthese particles in velocity space show oscillatory motions on the
+First. let us expauid the integral expressions in Eqs.(2)) and (2)) in the limit of small z.,"First, let us expand the integral expressions in \ref{eq:kapdef}) ) and \ref{eq:A,B,C,D}) ) in the limit of small $z$."
+" We find lor z«1. pi: and f=Q,/2—OX,"," We find for $z\ll 1$ , - $\overline{C_3}=\frac{1}{17920}$, $\overline{C_4}=\frac{3}{3942400}$ , and $q_0 \equiv \Omega_m/2 - \Omega_{\Lambda}$."
+" Citz) (= 1.2.3.4) can be rewritten as Cz} Cals) Cis)C 10). lem?=2.3.4) where C, (/=1.2.3. £) are nearly constant."," $C_i(z)$ $i=1,2,3,4$ ) can be rewritten as C_1(z) (z) |, C_i(z) (z) C_1(z) (z), 1cm (i=2,3,4) where $C_{i0}$ $i=1,2,3,4$ ) are nearly constant."
+ We find that Cig) 0.3. TemC ag(2) lemC(z) lemοὗ Guided by the small z limit. we are able to find simple analytical forms (ο approximate Fanin(-} and Ants).," We find that (z) 0.3, 1cm (z) 1cm (z) 1cm (z) Guided by the small $z$ limit, we are able to find simple analytical forms to approximate $\tilde{\kappa}_{min}(z)$ and $A_0(z)$."
+ For a flat universe. we found:," For a flat universe, we found: = +1 ) +1 ],"
+We wish. to compare theoretical ancl observed ACV/A ΡΟΗ].,We wish to compare theoretical and observed $\Delta (B-V)/\Delta [Fe/H]$ .
+ As reference loci we take isochrones xublished recently by our group., As reference loci we take isochrones published recently by our group.
+ For Population LE we adopt the results bv D'Antona et al. (, For Population II we adopt the results by D'Antona et al. (
+1997). especially computed: for dating elobular clusters: for Population Lowe use either he main sequence location for Z=0.01 aand 0.02 from DAntona Mazzitelli (1997). or the homogeneous ericl of results by Ventura et al. (,"1997), especially computed for dating globular clusters; for Population I we use either the main sequence location for $Z=0.01$ and 0.02 from D'Antona Mazzitelli (1997), or the homogeneous grid of results by Ventura et al. ("
+1998).,1998).
+ In all the mocels the helium abundance is scaled according to the law AY/AlogZ = 3., In all the models the helium abundance is scaled according to the law $\Delta Y/\Delta log Z$ = 3.
+ The theoretical tracks are transformed to the observational plane A. tthrough lxurucz. (1993) relations. except isochrones by Ventura οἱ al. (," The theoretical tracks are transformed to the observational plane $M_v$, through Kurucz (1993) relations, except isochrones by Ventura et al. ("
+1998). transformed through Castelli (1998) relations.,"1998), transformed through Castelli (1998) relations."
+ In Fig., In Fig.
+ Al main sequence objects from the metallicity sample are shown. for various Fe/1I] intervals.," A1 main sequence objects from the metallicity sample are shown, for various [Fe/H] intervals."
+ We estimated by eve the colours at == 6: the estimated error is about + 0.03 mag., We estimated by eye the colours at = 6; the estimated error is about $\pm$ 0.03 mag.
+ Around == (0. the ratio ALBV/AFef1] is about 0.20. decreasing to 0.16 for lower metallicities.," Around = 0, the ratio $\Delta (B-V)/\Delta [Fe/H]$ is about 0.20, decreasing to 0.16 for lower metallicities."
+ Towards very low ((< -1.2). the ratio seems to decrease further. but the objects are too few for a meaningful estimate.," Towards very low $\leq$ -1.2), the ratio seems to decrease further, but the objects are too few for a meaningful estimate."
+ The tracks by D'Xntona ct al. (, The tracks by D'Antona et al. (
+1997 and extensions to ügher Z)) give. at. == 6 and for very low (10710.75. AUBVONFefH] = 0.08: for higherZ.. up to (0.01. the ratio is about 0.16.,"1997 and extensions to higher ) give, at = 6 and for very low $10^{-4} -- 10^{-3}$ ), $\Delta (B -
+V)/\Delta [Fe/H]$ = 0.08; for higher, up to 0.01, the ratio is about 0.16."
+ )ovond. the solar metallicitiv. the ratio increases to about 0.25.," Beyond the solar metallicitiy, the ratio increases to about 0.25."
+ Phe theoretical relation is also shown in Fig., The theoretical relation is also shown in Fig.
+ Al., A1.
+ We see that changes in metal content are mürrored by shifts in the main sequence average colours. in reasonable agreement with theoretical predictions.," We see that changes in metal content are mirrored by shifts in the main sequence average colours, in reasonable agreement with theoretical predictions."
+ We conclude that. with some caution. it is possible to follow changes in populations (with dilfering metal contents) through changes in CM diagram main sequence loci.," We conclude that, with some caution, it is possible to follow changes in populations (with differing metal contents) through changes in CM diagram main sequence loci."
+ Another check on the behaviour with metallicity of Llipparcos objects has been performed considering the subclwarls in the catalogue studied. by Gratton et al. (, Another check on the behaviour with metallicity of Hipparcos objects has been performed considering the subdwarfs in the catalogue studied by Gratton et al. (
+1997. Table 1).,"1997, Table 1)."
+ Phese objects have LHipparcos parallaxes such that An/m<0.12. ancl abundances derived from analysis of high dispersion spectra.," These objects have Hipparcos parallaxes such that $\Delta\pi / \pi < 0.12$, and abundances derived from analysis of high dispersion spectra."
+ The location of these stars is shown in Fig., The location of these stars is shown in Fig.
+ A2. where we adopt as reference lines isochrones of 10 Gyr for metal poor stars. and of 105 vr for the metal rich population.," A2, where we adopt as reference lines isochrones of 10 Gyr for metal poor stars, and of $10^8$ yr for the metal rich population."
+ On the whole. the agreement between theory. and observations turns out satisfactory. but with some exceptions which caution to apply average conclusions to isolated. cases. without a specific analysis.," On the whole, the agreement between theory and observations turns out satisfactory, but with some exceptions which caution to apply average conclusions to isolated cases, without a specific analysis."
+ One of the cdillicultios is given bv. the not negligible dependence on the adopted transformation of the location in CM clagrams of theoretical tracks., One of the difficulties is given by the not negligible dependence on the adopted transformation of the location in CM diagrams of theoretical tracks.
+ In any case. we are interested in relative positions and the following considerations should remain substantially valid also after a shift of the zero point on the observationa plane.," In any case, we are interested in relative positions and the following considerations should remain substantially valid also after a shift of the zero point on the observational plane."
+ Within the errors. LS out of the 20 more metal poor stars (Fefl] € -1) lie on or at the left of the == 10 *isocrone == -1.26). therefore in good overall agreement with theoretical expectations.," Within the errors, 18 out of the 20 more metal poor stars ([Fe/H] $\leq$ -1) lie on or at the left of the = $10^{-3}$ isocrone = -1.26), therefore in good overall agreement with theoretical expectations."
+ Besides. if we consider only the subdwarfs which. within errors. fall on the main sequence of 10.7 (14 objects) and compute the average of their vvalues. we find -1.28. that is. almost exactly," Besides, if we consider only the subdwarfs which, within errors, fall on the main sequence of $10^{-3}$ (14 objects) and compute the average of their values, we find -1.28, that is, almost exactly"
+errors in lensing measurements.,errors in lensing measurements.
+" This method has been used by various authors in studies on real data (see,e.g. ?),, and is straightforward to implement in the algorithm presented here."," This method has been used by various authors in studies on real data \citep[see, e.g.][]{simonetal11}, and is straightforward to implement in the algorithm presented here."
+" A full treatment of photometric redshift errors, which is essential in order for the method to be useful on real data, will be presented in an upcoming work."," A full treatment of photometric redshift errors, which is essential in order for the method to be useful on real data, will be presented in an upcoming work."
+ This paper is structured as follows., This paper is structured as follows.
+" In 2,, we outline the weak lensing formalism in three dimensions, and outline several linear inversion methods to solve the 3D weak lensing problem."," In \ref{sec:theory}, we outline the weak lensing formalism in three dimensions, and outline several linear inversion methods to solve the 3D weak lensing problem."
+ We introduce our compressed sensing framework and describe our proposed algorithm in 3., We introduce our compressed sensing framework and describe our proposed algorithm in \ref{sec:nonlin}.
+".In 4,, we discuss practical considerations in implementing the method, and describe our simulated dataset."," In \ref{sec:impl}, we discuss practical considerations in implementing the method, and describe our simulated dataset."
+ In 5 we demonstrate the performance of our algorithm in reconstructing simulated cluster haloes at various redshifts., In \ref{sec:results} we demonstrate the performance of our algorithm in reconstructing simulated cluster haloes at various redshifts.
+ We conclude with a discussion of our results and future applications in 6.., We conclude with a discussion of our results and future applications in \ref{sec:discuss}.
+" Throughout the text, we assume ACDM cosmology, with O4=0.736,Oy0.264,h0.71,og0.801, consistent with the WMAP-7 results (?).."," Throughout the text, we assume $\Lambda$ CDM cosmology, with $\Omega_\Lambda = 0.736,\ \Omega_{\rm M} = 0.264,\ h=0.71,\ \sigma_8 = 0.801$, consistent with the WMAP-7 results \citep{larsonetal11}."
+" The distortion of galaxy images due to the weak lensing effect is described, on a given source plane, by the Jacobian matrix of the coordinate mapping between source and image planes: where & is the projected dimensionless surface density, and y=71+iflg is the complex shear."," The distortion of galaxy images due to the weak lensing effect is described, on a given source plane, by the Jacobian matrix of the coordinate mapping between source and image planes: where $\kappa$ is the projected dimensionless surface density, and $\gamma = \gamma_1+\rm{i}\gamma_2$ is the complex shear."
+" The shear is related to the convergence via a convolution in two dimensions: where 0=0,i05, and an asterisk * represents complex conjugation."," The shear is related to the convergence via a convolution in two dimensions: where $\bt = \theta_1+{\rm i}\theta_2$, and an asterisk $^\ast$ represents complex conjugation."
+" 'The convergence,in turn, can be related to the dimensional density contrast ó(r)=p(r)/p—1 where Ho is the hubble parameter, Qu is the matter density parameter, c is the speed of light, a(w) is the scale parameter evaluated at comoving distance w, and gives the comoving angular diameter distance as a function of the comoving distance and the curvature, K, of the Universe."," The convergence,in turn, can be related to the three-dimensional density contrast $\delta(\boldsymbol{r}) \equiv \rho(\boldsymbol{r})/\overline{\rho} - 1$ where $H_0$ is the hubble parameter, $\Omega_M$ is the matter density parameter, $c$ is the speed of light, $a(w)$ is the scale parameter evaluated at comoving distance $w$, and gives the comoving angular diameter distance as a function of the comoving distance and the curvature, $K$ , of the Universe."
+" If the shear (or convergence) data is divided into Ni, redshift bins, and the density contrast reconstruction is divided into Ληρ redshift bins (where Nsp is not necessarily equal to Mp); we can write the convergence &(? on each source plane as where and Thus, for each line of sight, equation describes a matrix multiplication, encoding a convolution along the line of sight."," If the shear (or convergence) data is divided into $N_{\rm sp}$ redshift bins, and the density contrast reconstruction is divided into $N_{\rm lp}$ redshift bins (where $N_{\rm sp}$ is not necessarily equal to $N_{\rm lp}$ ), we can write the convergence $\kappa^{(i)}$ on each source plane as where and Thus, for each line of sight, equation describes a matrix multiplication, encoding a convolution along the line of sight."
+ It is the inversion of this transformation: that is the focus of this paper., It is the inversion of this transformation: that is the focus of this paper.
+ We note that the inversion of equation can be straightforwardly performed on each source plane in Fourier space., We note that the inversion of equation can be straightforwardly performed on each source plane in Fourier space.
+ We focus here on the methods presented in ? and ?.., We focus here on the methods presented in \cite{sth09} and \cite{vanderplasetal11}.
+" For a review of other linear methods, the reader is referred to ?.."," For a review of other linear methods, the reader is referred to \cite{hk02}."
+" The three dimensional lensing problem is effectively one of observing the density contrast convolved with the linear operator R, and contaminated by noise, which is assumed to be Gaussian."," The three dimensional lensing problem is effectively one of observing the density contrast convolved with the linear operator $\mathbf{R}$, and contaminated by noise, which is assumed to be Gaussian."
+" Formally, we can write where d is the observation, s the real density and ε the Gaussian noise."," Formally, we can write where $\boldsymbol{d}$ is the observation, $\boldsymbol{s}$ the real density and $\varepsilon$ the Gaussian noise."
+" The general idea behind linear inversion methods is to find a linear operator H which acts on the data vector to yield a solution which minimises some functional, such as the variance of the residual between the estimated signal and the true signal, subject to some regularisation or prior-based constraints."," The general idea behind linear inversion methods is to find a linear operator $\mathbf{H}$ which acts on the data vector to yield a solution which minimises some functional, such as the variance of the residual between the estimated signal and the true signal, subject to some regularisation or prior-based constraints."
+" The simplest instance of such a linear operation is an inverse variance filter (?),, which weights the data only by the noise covariance, and places no priors on the signal itself: where ©= gives the covariance matrix of the noise."," The simplest instance of such a linear operation is an inverse variance filter \citep{aitken34}, which weights the data only by the noise covariance, and places no priors on the signal itself: where $\Sigma\equiv\left\langle\boldsymbol{n}\boldsymbol{n}^\dagger\right\rangle$ gives the covariance matrix of the noise."
+" This method (nn!)proves problematic when the matrices involved are non-invertible, such as when there are degeneracies inherent in the allowed solution."," This method proves problematic when the matrices involved are non-invertible, such as when there are degeneracies inherent in the allowed solution."
+" In order to make the problem invertible, some regularisation must be introduced."," In order to make the problem invertible, some regularisation must be introduced."
+" ? opt to use a Saskatoon filter (??),, which combines a Wiener filter andan inverse variance filter, with a tuning parameter α introduced that allows switching between the two."," \cite{sth09} opt to use a Saskatoon filter \citep{tegmark97, tegmarketal97}, which combines a Wiener filter andan inverse variance filter, with a tuning parameter $\alpha$ introduced that allows switching between the two."
+" This gives rise to a minimum variance filter, expressed as:"," This gives rise to a minimum variance filter, expressed as:"
+((2007) gives a poor fit to the optical (reduced x? of 15.1).,(2007) gives a poor fit to the optical (reduced $\chi^{2}$ of 15.1).
+" From this we conclude that during the internal plateau, the X-ray and optical emission have separate origins for the four GRBs for which we have multi-wavelength data."," From this we conclude that during the internal plateau, the X-ray and optical emission have separate origins for the four GRBs for which we have multi-wavelength data."
+ Henceforth we concentrate on the X-ray behaviour of our sample., Henceforth we concentrate on the X-ray behaviour of our sample.
+ As the time at which the internal plateau ends differs markedly GRB 070110 and GRB 070616) it is possible they have a different origin., As the time at which the internal plateau ends differs markedly GRB 070110 and GRB 070616) it is possible they have a different origin.
+" Thus we further sub-divide the sample into those GRBs in which the constant emission phase ends before or after 10,000 seconds."," Thus we further sub-divide the sample into those GRBs in which the constant emission phase ends before or after 10,000 seconds."
+" Those which end before 10,000 seconds are denoted as having early internal plateaus whereas those ending after this time have late internal plateaus."," Those which end before 10,000 seconds are denoted as having early internal plateaus whereas those ending after this time have late internal plateaus."
+ In the next section we compare the results for these two groups to determine if their properties are consistent with being caused by the same physical process and whether that process is consistent with being due to a magnetar., In the next section we compare the results for these two groups to determine if their properties are consistent with being caused by the same physical process and whether that process is consistent with being due to a magnetar.
+ Of the 8 GRBs in the early internal plateau group 5 have a redshift measurement as do both GRBs in the late plateau group., Of the 8 GRBs in the early internal plateau group 5 have a redshift measurement as do both GRBs in the late plateau group.
+" For the 3 GRBs with no redshift measurement we adopt a redshift of 2.22, the mean redshift of GRBs to determine the luminosity."," For the 3 GRBs with no redshift measurement we adopt a redshift of 2.22, the mean redshift of GRBs to determine the luminosity."
+ Our conclusions are not sensitive to this choice., Our conclusions are not sensitive to this choice.
+First we address the low opacity calculations that we have performed.,First we address the low opacity calculations that we have performed.
+ The resulting migration rates from these calculations appear scattered. showing no evident trend with changes in the dise temperature profile.," The resulting migration rates from these calculations appear scattered, showing no evident trend with changes in the disc temperature profile."
+ This can be seen in Fig., This can be seen in Fig.
+ 7. which gathers all the low opacity results shown in Fig., \ref{fig:lubow} which gathers all the low opacity results shown in Fig.
+ 3. into a single panel. as well as including the analytic rates for an isothermal disc calculated using ?. (dashed lines) and rates based upon the recent work of ? (solid lines) for a locally-isothermal disc.," \ref{fig:profiles} into a single panel, as well as including the analytic rates for an isothermal disc calculated using \cite{TanTakWar2002} (dashed lines) and rates based upon the recent work of \cite{DAnLub2010} (solid lines) for a locally-isothermal disc."
+ At these low opacities we expect the migration results from our models to be similar to those predicted with isothermal analytic expressions as we found in ?.., At these low opacities we expect the migration results from our models to be similar to those predicted with isothermal analytic expressions as we found in \cite{AylBat2010}.
+" Indeed. despite the scatter. these migration results do reveal a trend with increasing mass that is matched by ?""7s values."," Indeed, despite the scatter, these migration results do reveal a trend with increasing mass that is matched by \cite{TanTakWar2002}' 's values."
+ However. ?. have found that in the locally-isothermal (rather than globally isothermal) regime protoplanet migration rates depend upon the parent dise's temperature profile. with steeper negative temperature profiles (higher values of 6) leading to more rapid inward migration.," However, \citeauthor{DAnLub2010} have found that in the locally-isothermal (rather than globally isothermal) regime protoplanet migration rates depend upon the parent disc's temperature profile, with steeper negative temperature profiles (higher values of $\beta$ ) leading to more rapid inward migration."
+ This trend is not seen in our low opacity calculation results within which. as mentioned previously. it is not possible to establish a trend that is distinguishable from the numerical uncertainties: this is also the case in the locally-isothermal calculations shown in Fig. 4..," This trend is not seen in our low opacity calculation results within which, as mentioned previously, it is not possible to establish a trend that is distinguishable from the numerical uncertainties; this is also the case in the locally-isothermal calculations shown in Fig. \ref{fig:isothermal}."
+ However. the variation in migration rates obtained from ? across the range of 6 considered in this work is relatively small. less than a factor of 2 for each of the masses shown in Fig. 7..," However, the variation in migration rates obtained from \cite{DAnLub2010} across the range of $\beta$ considered in this work is relatively small, less than a factor of 2 for each of the masses shown in Fig. \ref{fig:lubow}."
+ Our rather large uncertainties prevent us from definitively ruling out the model., Our rather large uncertainties prevent us from definitively ruling out the model.
+" Returning to 2""s analytic form for an isothermal disc. it is interesting to note that the acceleration of inward migration with increasing f is in qualitative agreement with the description of ? dises with high thermal diffusivity."," Returning to \cite{DAnLub2010}' 's analytic form for an isothermal disc, it is interesting to note that the acceleration of inward migration with increasing $\beta$ is in qualitative agreement with the description of \cite{MasCas2010} discs with high thermal diffusivity."
+ As a brief aside we compare these two analytic models with which we draw comparisons., As a brief aside we compare these two analytic models with which we draw comparisons.
+ Fig., Fig.
+" 8 illustrates the migration rates calculated using ?""7s isothermal formula for a 33 pprotoplanet (dashed line). with the rates obtained using ?""s formula for a whole range of thermal ditfusivities also shown."," \ref{fig:lubmas} illustrates the migration rates calculated using \citeauthor{DAnLub2010}' 's isothermal formula for a 33 protoplanet (dashed line), with the rates obtained using \citeauthor{MasCas2010}' 's formula for a whole range of thermal diffusivities also shown."
+ It can be seen that at the highest ditfusivity (thick red line labelled C) the gradient of the change of migration rate with increasing £ for the two descriptions is extremely similar. and they are displaced in magnitude by a factor of =5/3. equivalent to y. as was found in 2..," It can be seen that at the highest diffusivity (thick red line labelled C) the gradient of the change of migration rate with increasing $\beta$ for the two descriptions is extremely similar, and they are displaced in magnitude by a factor of $\approx 5/3$, equivalent to $\gamma$, as was found in \cite{PaaPap2008}."
+ This similar behaviour is to be expected. with a high thermal ditfusivity leading to a dise that resembles a locally-isothermal model. and responds to ditferen temperature profiles in the same manner.," This similar behaviour is to be expected, with a high thermal diffusivity leading to a disc that resembles a locally-isothermal model, and responds to different temperature profiles in the same manner."
+ As seen earlier when considering our low opacity calculations. the manner in which the migration rate of a protoplanet changes with the dises therma ditfusivity is dependent upon the temperature profile of the dise.," As seen earlier when considering our low opacity calculations, the manner in which the migration rate of a protoplanet changes with the discs thermal diffusivity is dependent upon the temperature profile of the disc."
+ For dises with 8>0.5. as the thermal ditfusivity is increased from its lowest value (thick purple line labelled A) the migration rate of a protoplanet can be expected to initially increase in the outware direction. or slow down if the migration is inwards.," For discs with $\beta \gtrsim 0.5$, as the thermal diffusivity is increased from its lowest value (thick purple line labelled A) the migration rate of a protoplanet can be expected to initially increase in the outward direction, or slow down if the migration is inwards."
+ Beyond a certain ditfusivity. shown by the thick blue line labelled B in Fig. 8..," Beyond a certain diffusivity, shown by the thick blue line labelled B in Fig. \ref{fig:lubmas},"
+" the trend is reversed with increasing diffusivity slowing outward migration, and accelerating inward migration."," the trend is reversed with increasing diffusivity slowing outward migration, and accelerating inward migration."
+" This behaviour is a result of the edge term of the Horsehoe drag in ?""s model.", This behaviour is a result of the edge term of the Horsehoe drag in \citeauthor{MasCas2010}' 's model.
+ In future it would be desirable to explore a broader opacity space with greater refinement using our numerical models to determine whether we can capture the effects of the edge terms of the Horseshoe drag., In future it would be desirable to explore a broader opacity space with greater refinement using our numerical models to determine whether we can capture the effects of the edge terms of the Horseshoe drag.
+ In our high opacity (low thermal ditfusivity) models we find, In our high opacity (low thermal diffusivity) models we find
+valv as py>ὦM Or pl al various. stages of. the evolution. so (the actual grain. radiiae at which. (he regime transitions occur do vary.,vary as $\rho_d^{-2} \phi^3$ or $\rho_d^{-1}$ at various stages of the evolution so the actual grain radii at which the regime transitions occur do vary.
+ In the Stokes regime. density plays a non-trivial role in the effects of turbulence on the erain trajectory (15)) and therefore in determining the boundary between the two drag515 regimes as well as the details of the regimes5 of mve+.," In the Stokes regime, density plays a non-trivial role in the effects of turbulence on the grain trajectory \ref{tauS}) ) and therefore in determining the boundary between the two drag regimes as well as the details of the regimes of $\frac{v_c}{H_d}$."
+ In figure5 5 we plot the time scales for py=0.5gcmoE, In figure \ref{TimeVarious} we plot the time scales for $\rho_d=0.5 \rm{gcm}^{-3}$.
+ From (3)). we see (hat increasing the clust disc surface density X; will decrease the growth (ime scale.," From \ref{main}) ), we see that increasing the dust disc surface density $\Sigma_d$ will decrease the growth time scale."
+" However. in our equations XM, frequently appears in a ratio with YX,."," However, in our equations $\Sigma_d$ frequently appears in a ratio with $\Sigma_g$."
+" The elfect of changing X, while keeping X, constant 15 greater than that of changing both equally, as can be seen in Fig. (5))."," The effect of changing $\Sigma_d$ while keeping $\Sigma_g$ constant is greater than that of changing both equally, as can be seen in Fig. \ref{TimeVarious}) )."
+ The total surface density. primarily affects the condition for gravitational instability. which determines (he (ime spent in regime 3.3., The total surface density primarily affects the condition for gravitational instability which determines the time spent in regime $3.3$.
+ This dominates the erowth time scale at large 2., This dominates the growth time scale at large $R$.
+ Changing the dust surface density alone has a strong influence throughout the disc., Changing the dust surface density alone has a strong influence throughout the disc.
+ The MRI(Dalbus&Hawley1991) instability may be the primary source of turbulence in a protoplanetarv dise but the entire gas disc need not be sufficiently ionized [or the instability (o occur., The MRI \citep{Balbus91} instability may be the primary source of turbulence in a protoplanetary disc but the entire gas disc need not be sufficiently ionized for the instability to occur.
+ The MBI-stable region of the dise is labeled a dead zone (2005).. Sanoetal. (2000))) ancl will have à smaller value for a than the live zone.," The MRI-stable region of the disc is labeled a dead zone \citet{Matsumura05}, \citet{Sano00}) ) and will have a smaller value for $\alpha$ than the live zone."
+ If there is a dead zone for approximately (he gas scale height over some range of A. then we can simply (reat the live and dead zones as having seperate values of a and merging (hem in our racially depedencent caleulations. while noting that. dust unable to decouple [rom the (turbulence on a viscous time scale could be deposited at the outer edee of the dead zone.," If there is a dead zone for approximately the gas scale height over some range of $R$, then we can simply treat the live and dead zones as having seperate values of $\alpha$ and merging them in our radially depedendent calculations, while noting that dust unable to decouple from the turbulence on a viscous time scale could be deposited at the outer edge of the dead zone."
+" If instead we consider a turbulent disc with a dead zone near (he midplane of the dise (with a height //5) for some range of R (but live for a significant thickness above the midplane) we can approximate the growth (ime scales by caleulating the time scales for the live zone turbulence until the dust dise is contained within the dead zone fy,=I, at which point we proceed with the dead zone turbulence.", If instead we consider a turbulent disc with a dead zone near the midplane of the disc (with a height $H_D$ ) for some range of $R$ (but live for a significant thickness above the midplane) we can approximate the growth time scales by calculating the time scales for the live zone turbulence until the dust disc is contained within the dead zone $H_d=H_D$ at which point we proceed with the dead zone turbulence.
+ Noting that the Gime scales of regimes 2.2 and 3.2 depend on à only for their beginning and end conditions. respectively. and that the onset of regime 2.2 is precisely the same as (hat of settling it follows that the deacl zone a only ellects the time scale of regime 3.2 and so the effect is simply calculated.," Noting that the time scales of regimes $2.2$ and $3.2$ depend on $\alpha$ only for their beginning and end conditions, respectively, and that the onset of regime $2.2$ is precisely the same as that of settling it follows that the dead zone $\alpha$ only effects the time scale of regime $3.2$ and so the effect is simply calculated."
+" Note that halfway settling the dust. 77;=0.5/7, occurs for roughly within regime 2.2 (Table 2))."," Note that halfway settling the dust, $H_d=0.5 H_g$ occurs for roughly within regime $2.2$ (Table \ref{RegimeOrder}) )."
+ The time scale behaviour with a dead zone is important, The time scale behaviour with a dead zone is important
+performances of the evolutionary models used in this task. once the third ingredient of spectroscopic observations is added to photometry and models in order to provide an independent confirmation of the membership assignments.,"performances of the evolutionary models used in this task, once the third ingredient of spectroscopic observations is added to photometry and models in order to provide an independent confirmation of the membership assignments."
+ At present. the status of the procedure already appears to be not only promising but actually capable of providing valuable results.," At present, the status of the procedure already appears to be not only promising but actually capable of providing valuable results."
+ This discussion has lead us to suggest some relations between the parameters measured. which agree with previous findings.," This discussion has lead us to suggest some relations between the parameters measured, which agree with previous findings."
+ Independently of these relations. affected by differert sources of uncertainty. the main result consists in the presencee of regularities which could not plausibly be expected if the selections of members were not well founded.," Independently of these relations, affected by different sources of uncertainty, the main result consists in the presence of regularities which could not plausibly be expected if the selections of members were not well founded."
+ In the presert paper we refer to 11 clusters in an age range between 4 and 30 Myr. as determined from comparison of the upper main sequence to isochrones in the CM diagrams.," In the present paper we refer to 11 clusters in an age range between 4 and 30 Myr, as determined from comparison of the upper main sequence to isochrones in the CM diagrams."
+reveals a significantly smaller iuclination anele (127) than that sueeestedOO ]xw the ellipticitv of the 850424 continui inage (127).,reveals a significantly smaller inclination angle $\degr$ ) than that suggested by the ellipticity of the $\mu$ m continuum image $\degr$ ).
+" The submillimeter image also shows that «ust has been depleted within 50 AAU, while we find that molecular gas persists at LAAT. but not closer to the star."," The submillimeter image also shows that dust has been depleted within $\sim$ AU, while we find that molecular gas persists at AU, but not closer to the star."
+ Tn many wavs. this disk appears to be similar to εiat of another transition disk. SR 21. «escribed in?.," In many ways, this disk appears to be similar to that of another transition disk, SR 21, described in."
+. This star is probabv best shown for having a substelar conipauion. GQ Lup bJ. cHILOlLlv locaed (ue west of GO Lup.," This star is probably best known for having a substellar companion, GQ Lup b, currently located due west of GQ Lup."
+ The sooctro-asti«nuctry of the GQ Lup disk shows that it is oriented along tle N-5 axis and has a relativiolv high inclinajon of 65E107., The spectro-astrometry of the GQ Lup disk shows that it is oriented along the N-S axis and has a relatively high inclination of $65\pm 10\degr$.
+ It is uot known wheher CQ Lup b orbits iu the disk pane. but if it (oes. the plysical separation wi] be higicr than the projected separation of 0777 by a factor 2.1. brineie f16 physical separation to 210 AU.," It is not known whether GQ Lup b orbits in the disk plane, but if it does, the physical separation will be higher than the projected separation of 7 by a factor 2.4, bringing the physical separation to 240 AU."
+ Further. he preciction is that auv orbital motion of the companion will be aloug thο N-S axis.," Further, the prediction is that any orbital motion of the companion will be along the N-S axis."
+ Tt cau be noted that the stellar inclination of CC) Lup has ECL fouud to be 274-5n? very οποιοl tlau that of ιο disk. ταῖςΠιο the question of whether this difference is cuc to lnteractious dOween the companion axd the disk.," It can be noted that the stellar inclination of GQ Lup has been found to be $27\pm 5 \degr$ – very different than that of the disk, raising the question of whether this difference is due to interactions between the companion and the disk."
+ The disk around his borderline Herbie Ac/ite T Tauri star (8pectral Type = F6) has ος1 nuage iu 16 contiuuunui at near- to miceraved wavelengths., The disk around this borderline Herbig Ae/Be – T Tauri star (Spectral Type = F6) has been imaged in the continuum at near- to mid-infrared wavelengths.
+ At nik-infiared waveleughs yan). the outer Isse xlübisa ronglv asviunievic structire. with the castern side eine wach xiehter than tjo western(?2).," At mid-infrared wavelengths $\mu$ m), the outer disk exhibits a strongly asymmetric structure, with the eastern side being much brighter than the western."
+. These au1OYS SUESed iat the bright eastern are |iue an ihuuinated rin of a disk incined along a ixvethesoutl axis., These authors suggested that the bright eastern arc being an illuminated rim of a disk inclined along a north-south axis.
+ The specPO-asronietry. iowevor. deuLOWSrate that the actual axis of the (iuver) disk is :ifa e Near-infrared. scattere:-lieh Ποιο vw fud that he disk is elliptical along a major axis in the NW-SE direclon. more Cousistent wii the PLA. Further. a NIR wavelengths. the soutlavester1 part of the disk is brighter. indicatiug hatt his is the coscr part of the clisk. exhilting strong forward scatering.," The spectro-astrometry, however, demonstrate that the actual axis of the (inner) disk is at a. Near-infrared, scattered-light imaging by find that the disk is elliptical along a major axis in the NW-SE direction, more consistent with the spectro-astrometric P.A. Further, at NIR wavelengths, the south-western part of the disk is brighter, indicating that this is the closer part of the disk, exhibiting strong forward scattering."
+ The inclination angle of 25°5] matches both f10 nk-jnfrared ancl uear-ufr“ALOE nuaenie., The inclination angle of $25\degr$ matches both the mid-infrared and near-infrared imaging.
+ The polarizaion axis of the disk iotnud TD 11132 was found to be1117(2)., The polarization axis of the disk around HD 144432 was found to be.
+". deteriinued t1e size of ,1e H-baud source (tracing an inner rim of the disk) to AAT using closure-plase interferometry. or slightly smaller than the CO enüttiug region."," determined the size of the H-band source (tracing an inner rim of the disk) to AU using closure-phase interferometry, or slightly smaller than the CO emitting region."
+ While this C5 T Tauri star has featured xonmineutlv i studies o auid-iufrared spectroscopic disk properties?7j. little is known about the ecometry of the disk.," While this G5 T Tauri star has featured prominently in studies of mid-infrared spectroscopic disk properties, little is known about the geometry of the disk."
+ Using CC) spectroustrometry. it can be deternuned that the lucination is :MEN and that the major axis of the disk is oriened along the N-S axis with a D.À. = 17724:x.," Using CO spectro-astrometry, it can be determined that the inclination is $37\pm 5\degr$ and that the major axis of the disk is oriented along the N-S axis with a P.A. = $177\pm 3\degr$."
+ There is no apparent inner gap in the CO cinission. which cau be traced to witli10 LAAT.," There is no apparent inner gap in the CO emission, which can be traced to within AU."
+ This Herbie Ac/Be star is known to have a proimineit disk shadow(??)., This Herbig Ae/Be star is known to have a prominent disk shadow.
+. The disk oricutation. PLA. and i1οination was determined by using the disk shadow iu combination with near-infrared iterferometric visihilities.," The disk orientation, P.A. and inclination was determined by using the disk shadow in combination with near-infrared interferometric visibilities."
+" The P.A. of of 19-ΕὉ can be compared to the spectro-astromevic PLA. o0 nur5‘while the disk shadow inclination of FOE"" Cau be compared to he astrometric inclination of 65dE57,"," The P.A. of of $15\pm 5$ can be compared to the spectro-astrometric P.A. of $17\pm 5\degr$, while the disk shadow inclination of $70\pm 5\degr$ can be compared to the astrometric inclination of $65\pm 5\degr$."
+ It is iuportaut to note that the likely distance to he Serpeus star forming clotul. of which VV Ser is a member. las been significantly revised from ppc to ppeC2).," It is important to note that the likely distance to the Serpens star forming cloud, of which VV Ser is a member, has been significantly revised from pc to pc."
+.. The radius of the IK-baud οὐαι emission determined by is then revised to AAT. in comparison toa CO emitting radius of 3.150.1 AU.," The radius of the K-band continuum emission determined by is then revised to AU, in comparison to a CO emitting radius of $3.4\pm 0.4\,$ AU."
+ DR Tau is a wellSHOWi high activity T Tauri star with a high degree of ootical veiling ancl spectral variability7)., DR Tau is a well-known high activity T Tauri star with a high degree of optical veiling and spectral variability.
+ Near-intrared interferometry has provided an uncertain measure of the disk P.A.=160+55°(E). consisteut wih our spectro-astromoetry.," Near-infrared interferometry has provided an uncertain measure of the disk $160\pm 55\degr$, consistent with our spectro-astrometry."
+" finds a disk P.A.=170dEN"". while fus a D.À.—98 aud an inenation of using hieh resolutiou (sub)uiIuueter interferometry."," finds a disk $=170\pm 8\degr$, while finds a $98$ and an inclination of, using high resolution (sub)millimeter interferometry."
+ Based on stellay es/0/ measroinents coupled with periodic variability. finds a high stellar inclination ofV," Based on stellar $vsini$ measurements coupled with periodic variability, finds a high stellar inclination of."
+o dmnosunmunmerws the basic geometry of the DR Tau «isk is still uncertain. 11t the spectro-astromery dudicates an uncertain PLA. close to O2nd a low inclination.," In summary, the basic geometry of the DR Tau disk is still uncertain, but the spectro-astrometry indicates an uncertain P.A. close to and a low inclination."
+" KRU Lup is a woll-kuowi1 classical T Tauri star with strong accretion siguatiPOs,", RU Lup is a well-known classical T Tauri star with strong accretion signatures.
+ sugecsted that the star nav have a close sellar companion due to the Oresenceo o periodical radial velocity changes. although the presence of starspots cading to the observed radial velocitv signal is not ruled out (see discussion iu ?)).," suggested that the star may have a close stellar companion due to the presence of periodical radial velocity changes, although the presence of starspots leading to the observed radial velocity signal is not ruled out (see discussion in )."
+" I£ the variability is due to stars]2015, a lucasurement of esiu/=941kESloq inplies a nearly face-on orieitation of the star. and presumably the dis sas well.of;221°(?).."," If the variability is due to starspots, a measurement of $v\sin{i} = 9\pm 1\,\rm km\,s^{-1}$ implies a nearly face-on orientation of the star, and presumably the disk as well, of $i=24\degr$."
+ preseited s)ectro-astromoetrv of the Πα line aud found evideice for a jet with a P.À.—15, presented spectro-astrometry of the $H\alpha$ line and found evidence for a jet with a $\sim 45\degr$.
+" The CO P.A. of 80° is significatly cffe""ut.", The CO P.A. of $80\degr$ is significantly different.
+ This sar. also known as AS 205A. the wimary of the close binary (separatiou 1733) syste Kkiow for exhibiting biieht urolecular chussion from water an orgaues throughout the mid-infrared7).," This star, also known as AS 205A, the primary of the close binary (separation 3) system known for exhibiting bright molecular emission from water and organics throughout the mid-infrared."
+. Since the CRIRES PSF has awidth o 10/7112. there is no coutaiinatkn frou the secondary.," Since the CRIRES PSF has a width of $\sim$ 12, there is no contamination from the secondary."
+ The ceutral star js a late specral type (I5) relative to its huninosity (£L ..). resulting Ina verv voung apparent age of 5107vre À," The central star has a late spectral type (K5) relative to its luminosity $L_{\odot}$ ), resulting in a very young apparent age of $5~10^{5}\,\rm yr$."
+ compariscn το the disk ecometyv of ?.. derived with high spatial resohtion subimillimeter interferometric contimuni aud lue Huagine with tre SubMilineter Array (SALA). is instructive.," A comparison to the disk geometry of , derived with high spatial resolution submillimeter interferometric continuum and line imaging with the SubMillimeter Array (SMA), is instructive."
+ They fiud. using the dust continu contours. au incliation of ~25 ‘which is consistent with the wind model reeiring the disk to be nearly facc-ou.," They find, using the dust continuum contours, an inclination of $\sim 25\degr$, which is consistent with the wind model requiring the disk to be nearly face-on."
+ Their PLA. is different. from that derived frou the spectro-astromoetry., Their P.A. is different from that derived from the spectro-astrometry.
+ While coulun socontour fits can be uncertain for uearly face-ou disks. spatialv resolved SMIA CO (3-2) tunages clearly show rotation consistent with a disk at P.A.~165°.," While continuum isocontour fits can be uncertain for nearly face-on disks, spatially resolved SMA CO (3-2) images clearly show rotation consistent with a disk at $\sim$."
+. In contrast. tlie spectreastroluery requires a P.A.~2357 of the AS 205N disk major axis.," In contrast, the spectro-astrometry requires a $\sim 235\degr$ of the AS 205N disk major axis."
+ We suggest that the discrepancy could be explaiied if the rotation pattern seen in the rotational CO line is due to coutamination fromAS 2058: a scenario, We suggest that the discrepancy could be explained if the rotation pattern seen in the rotational CO line is due to contamination fromAS 205S; a scenario
+Space Experiment (AISN) 8.3 jan images (available frou the NASA/IPAC Infrared Science Archive).,Space Experiment (MSX) 8.3 $\mu$ m images (available from the NASA/IPAC Infrared Science Archive).
+ The ligh DM is somewhat surprising eiven the N-rax absorption quoted by RRK. uy=(5.040.25) ς1031 7. where the errors represent the confidence region.," The high DM is somewhat surprising given the X-ray absorption quoted by RRK, $_{\rm H}$ $\pm0.25)\times 10^{21}$ $^{-2}$, where the errors represent the confidence region."
+ The total Galactic II column density in this direction as estimated from the FTOOLwh. which uses the ITE map of Tod 1.2ο 2.," The total Galactic HI column density in this direction as estimated from the FTOOL, which uses the HI map of \citet{dl90}, is $1.2\times 10^{22}$ $^{-2}$."
+ This should be a good approximation if the source is truly at the far edee of the outer spiral arm., This should be a good approximation if the source is truly at the far edge of the outer spiral arm.
+ Noting that the nuage shows faint. softer Cluission iu the region (Fieure ?7)). aud eiven the likely possibility of either associated thermal X-ray flux from a Supernova reliant or a nearby massive star. we fit the spectimm of RRK. adding a thermal compoucut to the absorbed power-law model," Noting that the image shows faint, softer emission in the region (Figure \ref{fig:xray}) ), and given the likely possibility of either associated thermal X-ray flux from a supernova remnant or a nearby massive star, we fit the spectrum of RRK, adding a thermal component to the absorbed power-law model."
+ Accounting for ~1 : the photon flux with a MERAL thermal plasiina model of temperature AL~0.1 keV in NSPEC (7)| statistically nuproves the fit (Fittest chance probability of ))., Accounting for $\sim4$ of the photon flux with a MEKAL thermal plasma model of temperature $kT\sim 0.1$ keV in XSPEC \citep{arn96} statistically improves the fit -test chance probability of ).
+ The best-fit absorption for this three componucut mode is ng7.610?5 cm7 with a confidence region of (L400 41021 2. consistent with the total Galactic cohuun density.," The best-fit absorption for this three component model is $_{\rm H}$ $\times 10^{21}$ $^{-2}$ with a confidence region of (4.1 – $\times 10^{21}$ $^{-2}$, consistent with the total Galactic column density."
+ The best-fit photon iudex is P—1.86. stil consistent with the 1.17 2.01 range iu RRIN derived frou the simple absorbed power model.," The best-fit photon index is $\Gamma=1.86$, still consistent with the 1.47 – 2.01 range in RRK derived from the simple absorbed power-law model."
+ Hence the N-rav absorption does not force us to adopt a smaller distance than is suggested by the DM., Hence the X-ray absorption does not force us to adopt a smaller distance than is suggested by the DM.
+ For a distance d44=d/10 kpe. the interred isotropic X-rav huninosity Ly=L8«10?dia (2. 10 keV).," For a distance $d_{10}=d/10$ kpc, the inferred isotropic X-ray luminosity $L_X=4.8\times 10^{34} d_{10}^2$ (2 – 10 keV)."
+" The N-ray efficieuey yy=Lx Eds 0.0142, ", The X-ray efficiency $\eta_X=L_X/\dot E$ is $d^2_{10}$ .
+Compared to the total pulsar plus nebula X-ray huninositv of other spin-powered pulsus this is somewhat high. but within the observed scatter (C27).," Compared to the total pulsar plus nebula X-ray luminosity of other spin-powered pulsars this is somewhat high, but within the observed scatter \citep{pccm02,che00}."
+ The pulsars positional coincidence with the error box of the hard spectrmu. low variabilityEGRET ~-vav source GeV J2020|3658 coupled with the hieh iuferred spiu-dowu huninosity strouely sugeests this pulsar cuits pulsed +-raves.," The pulsar's positional coincidence with the error box of the hard spectrum, low variability $\gamma$ -ray source GeV J2020+3658 coupled with the high inferred spin-down luminosity strongly suggests this pulsar emits pulsed $\gamma$ -rays."
+" Unfortunately. confuiung this bv folding archivalEGRET data is problematic due to the likelihood of sjenificaut past timing noise and elitches., which make the back-extrapolation of the rotational ephemeris uncertain."," Unfortunately, confirming this by folding archival data is problematic due to the likelihood of significant past timing noise and glitches, which make the back-extrapolation of the rotational ephemeris uncertain."
+ RRB noted that the chance probability of an X-ray source as brieht as AN J2021.113651 in theECRET eor box was ~LO%.. but the nearby WolfRavet star WRIΕ was equally bright in N-ravs aud also a potential x-ray cinitter.," RRK noted that the chance probability of an X-ray source as bright as AX J2021.1+3651 in the error box was $\sim10$, but the nearby Wolf-Rayet star WR141 was equally bright in X-rays and also a potential $\gamma$ -ray emitter."
+ However. voung pulsars remain the oulv firmly established class of GalacticEGRET sources.," However, young pulsars remain the only firmly established class of Galactic sources."
+" The known 2-av pulsars cluster at the top of pulsar lists rauk-ordered bw spiu-down flux E/d. with 5-rav efficiencies ij,=L-E mostly between 0.001. and 0.03 (assuniug 1 sr beamine) with a tendency to iucrease with pulsar age (?2).."," The known $\gamma$ -ray pulsars cluster at the top of pulsar lists rank-ordered by spin-down flux $\dot E/d^2$, with $\gamma$ -ray efficiencies $\eta_\gamma=L_{\gamma}/\dot E$ mostly between 0.001 and 0.03 (assuming 1 sr beaming) with a tendency to increase with pulsar age \citep{tbb+99}."
+ The exception is PSR 52. with an apparent οταν efficiency yj.c0.2 eiven its nominal DM distance of 1.5 kpc.," The exception is PSR $-$ 52, with an apparent $\gamma$ -ray efficiency $\eta_\gamma \sim 0.2$ given its nominal DM distance of 1.5 kpc."
+" The interred +- efficiency. for PSR J2021|3651 is y,=0.1541, in the 100 MeV. to 10 GeV range.", The inferred $\gamma$ -ray efficiency for PSR J2021+3651 is $\eta_\gamma =0.15 d_{10}^2$ in the 100 MeV to 10 GeV range.
+ If the pulsar is located within he Perseus axir at a distance of 5 kpc. then the iuferred N-rav and y-ray hDwuninosities would be fairly typical of the other pulsars with Vela-like spiu-down luminosities.," If the pulsar is located within the Perseus arm at a distance of 5 kpc, then the inferred X-ray and $\gamma$ -ray luminosities would be fairly typical of the other pulsars with Vela-like spin-down luminosities."
+ While here is currently no observational evidence for a distance lis close. increased) DAL from an iutervening source iu lis relatively crowded direction would not be surprising.," While there is currently no observational evidence for a distance this close, increased DM from an intervening source in this relatively crowded direction would not be surprising."
+ We note that the DM derived distance for another voung misar receuthly discovered within an LORET error box. PSR J2229/6111. also leads to an anomalously high interred x-ray efficiency. (2)..," We note that the DM derived distance for another young pulsar recently discovered within an $EGRET$ error box, PSR J2229+6114, also leads to an anomalously high inferred $\gamma$ -ray efficiency \citep{hcg+01}."
+ Determining the fraction of radio-quiet versus radio-loud pulsars is iuportaut for our understanding of 5-rav pulsar endssiou mechnanisis., Determining the fraction of radio-quiet versus radio-loud pulsars is important for our understanding of $\gamma$ -ray pulsar emission mechanisms.
+ The two leading classes of enission models. the outer-gap (7)| aud polar-cap (7) models. make verv different estimates of the fraction of σαν pulsus that should be seen at radio energies.," The two leading classes of emission models, the outer-gap \citep{rom96a} and polar-cap \citep{dh96} models, make very different estimates of the fraction of $\gamma$ -ray pulsars that should be seen at radio energies."
+ Out of the 25 brightest sources above 1 CoV not associated with blazars. 10 are now kuown to either be energetic radio pulsars or coutai such pulsars within their error boxes.," Out of the 25 brightest sources above 1 GeV not associated with blazars, $\sim 10$ are now known to either be energetic radio pulsars or contain such pulsars within their error boxes."
+ Searching the brightest unidentified. X-ray sources in five GeV error boxes. we detected radio pulsations at the 0.1 imuJy level (similar to the liuitiug sensitivity of the Parkes observatious) from one of these with Arecibo.," Searching the brightest unidentified X-ray sources in five GeV error boxes, we detected radio pulsations at the $\sim 0.1$ mJy level (similar to the limiting sensitivity of the Parkes observations) from one of these with Arecibo."
+ This is well below the average flux level expected for typical radio huuinosities of voune pulsars (7)— and distances ο star forniüng regions statistically associated with οταν sources (?).., This is well below the average flux level expected for typical radio luminosities of young pulsars \citep{bj99} and distances to star forming regions statistically associated with $\gamma$ -ray sources \citep{yr97}.
+ Two of the sources observed with Parkes. AN 6058 (the Rabbit) and AN 2333. wave radio and X-rav properties that clearly iceutity hem as pulsar wind nebulae (??).. aud the third. AN 1900. is an extended hard N-rvav source that has cow other source class optious.," Two of the sources observed with Parkes, AX $-$ 6058 (the Rabbit) and AX $-$ 2333, have radio and X-ray properties that clearly identify them as pulsar wind nebulae \citep{rrjg99,brrk02}, and the third, AX $-$ 1300, is an extended hard X-ray source that has few other source class options."
+ Therefore. all three remain viable candidates for 2-av loud. radio-quiet pulsars.," Therefore, all three remain viable candidates for $\gamma$ -ray loud, radio-quiet pulsars."
+ Out of this sue sample of 25 bright GeW sources. the total πο of reasonable candidate neutron stars within the σαν error boxes which have now been searched deeply for radio-pulsatious without success is 7.," Out of this same sample of 25 bright GeV sources, the total number of reasonable candidate neutron stars within the $\gamma$ -ray error boxes which have now been searched deeply for radio-pulsations without success is $\sim 7$."
+" A current ""best euess fraction of radio-loud οταν pulsars of ~1/2 falls in between the predictious of the two main compcting models."," A current “best guess"" fraction of radio-loud $\gamma$ -ray pulsars of $\sim 1/2$ falls in between the predictions of the two main competing models."
+ We thank Jiu Cordes for useful discussions., We thank Jim Cordes for useful discussions.
+ We acknowledge support from NSERC. CFL an NSF CAREER Award. and a Sloan Fellowship.," We acknowledge support from NSERC, CFI, an NSF CAREER Award, and a Sloan Fellowship."
+ M.S.E.R. is a Quebec Merit. fellow., M.S.E.R. is a Quebec Merit fellow.
+ SALR. is a Tomlinson fellow., S.M.R. is a Tomlinson fellow.
+ JWTIL is an NSERC PGS Α fellow. V.NL. is a Canada Research Chair.," J.W.T.H. is an NSERC PGS A fellow, V.M.K. is a Canada Research Chair."
+ The Arecibo Observatory is part of the National Astronomy and Ionosphere Ceuter. which is operated by Cornell University under a cooperative agreement with the National Science Foundation.," The Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated by Cornell University under a cooperative agreement with the National Science Foundation."