diff --git "a/batch_s000050.csv" "b/batch_s000050.csv" new file mode 100644--- /dev/null +++ "b/batch_s000050.csv" @@ -0,0 +1,10350 @@ +source,target + Also clear is the large discrepancy relative to a regular écchelle spectrum around 1000Hz., Also clear is the large discrepancy relative to a regular écchelle spectrum around $1000\:{\rm{\mu Hz}}$. + The only mode present in the and not detected with the EACF is the mixed mode at 695.75uHz., The only mode present in the and not detected with the EACF is the mixed mode at $695.75\:{\rm{\mu Hz}}$. + This peak appears as supernumerary when compared to the regular agency of the modes., This peak appears as supernumerary when compared to the regular agency of the modes. + The EACF makes it possible to derive the large separation one radial order further than does peak-bagging., The EACF makes it possible to derive the large separation one radial order further than does peak-bagging. + Results for KIC 10920273 are given in Fig. [[3.., Results for KIC 10920273 are given in Fig. \ref{fig_autodeltanuridge_10920273}. + The lower SNR is counterbalanced by using a broader filter when computing the EACF., The lower SNR is counterbalanced by using a broader filter when computing the EACF. +" Again, the analysis is not conclusive for one mixed mode at low frequency, but it is able to recover the /21 ridge."," Again, the analysis is not conclusive for one mixed mode at low frequency, but it is able to recover the $l\!=\!1$ ridge." + We note that the even ridge is affected by the proximity of mixed modes., We note that the even ridge is affected by the proximity of mixed modes. +" As opposed to the case of KIC 10273246, the EACF does not provide any further modes."," As opposed to the case of KIC 10273246, the EACF does not provide any further modes." +" Stellar rotation removes the (2/+1)-fold degeneracy of the frequencies of non-radial modes, allowing for a direct measurement of the stellar angular velocity averaged over the regions probed by these modes, as conveyed by Eq. A]. "," Stellar rotation removes the $(2l + 1)$ -fold degeneracy of the frequencies of non-radial modes, allowing for a direct measurement of the stellar angular velocity averaged over the regions probed by these modes, as conveyed by Eq. \ref{ledoux}. ." +Using the radii and masses computed from model-grid-based methods by Creevey et al. (, Using the radii and masses computed from model-grid-based methods by Creevey et al. ( +"in preparation) together with the estimates of P,o, we have computed the ratio of the surface angular velocity to the Keplerian break-up velocity, i.e., Ω/~GM/R>, which returned a value of approximately for both stars, indicating that these are most likely slow rotators.","in preparation) together with the estimates of $P_{\rm{rot}}$, we have computed the ratio of the surface angular velocity to the Keplerian break-up velocity, i.e., $\Omega/\sqrt{GM/R^3}$, which returned a value of approximately for both stars, indicating that these are most likely slow rotators." +" In view of this and given the precision achievable from the spectra, we have thus decided not to include any second-order effects on the rotational splitting."," In view of this and given the precision achievable from the spectra, we have thus decided not to include any second-order effects on the rotational splitting." +" The overall profile of a non-radial multiplet thus consists of the sum of 2/+1 Lorentzian profiles regularly spaced in frequency, and scaled in height according to the 5j,(i) factors (222): where i is the inclination angle between the direction of the stellar rotation axis and the line of sight, and P/""(x) are the associated Legendre functions."," The overall profile of a non-radial multiplet thus consists of the sum of $2l + 1$ Lorentzian profiles regularly spaced in frequency, and scaled in height according to the $\mathscr{E}_{l m}(i)$ factors \citep[][]{Dz77,DzG85,GS03}: where $i$ is the inclination angle between the direction of the stellar rotation axis and the line of sight, and $P_l^m(x)$ are the associated Legendre functions." +" Note that 26imn(@)=1, meaning that the &;,,(i) factors represent the relative power contained in the modes within a multiplet."," Note that $\sum_m \mathscr{E}_{l m}(i) \! = \! 1$, meaning that the $\mathscr{E}_{l m}(i)$ factors represent the relative power contained in the modes within a multiplet." +" While we are not able to robustly constrain the rotational splitting and inclination for both stars, we are however in a position to impose loose constraints on these parameters."," While we are not able to robustly constrain the rotational splitting and inclination for both stars, we are however in a position to impose loose constraints on these parameters." +" Figures [[4] and [[5] map the two-dimensional posterior probability distributions of these parameters respectively for KIC 10273246 and KIC 10920273, based on the samples from a MCMC analysis of the ten-month-long time series by IAS.OOB."," Figures \ref{inc_splt_M} and \ref{inc_splt_S} map the two-dimensional posterior probability distributions of these parameters respectively for KIC 10273246 and KIC 10920273, based on the samples from a MCMC analysis of the ten-month-long time series by OB." +" We have overlaid each of these correlation maps withcurves representing the estimate of P,.¢ given in Sect.", We have overlaid each of these correlation maps withcurves representing the estimate of $P_{\rm{rot}}$ given in Sect. +" ?? and the P,(i) relation ofCreevey et al. (", \ref{rotmod} and the $P_{\rm{rot}}(i)$ relation ofCreevey et al. ( +"in preparation),","in preparation)," +"Explaining the IHubble acceleration. the ""dark energv. is one of the main challenges to cosinologists.","Explaining the Hubble acceleration, the “dark energy,” is one of the main challenges to cosmologists." + Weak gravitational lensing (WL) has perhaps the most potential to constrain dark enerev parameters of any observational window. but is a newly developed technique which could be badly degraded by systematic errors (Albrecht et al 2005).," Weak gravitational lensing (WL) has perhaps the most potential to constrain dark energy parameters of any observational window, but is a newly developed technique which could be badly degraded by systematic errors (Albrecht et al 2005)." + A WL survey requires an estimate of the shape and the redshift of cach source: dominant observational svsteniatie errors are expected to be errors in galaxy shape due to the uncorrected influcuce of the point spread function (PSF) aud errors iu estimation of redshift distributions if they are determined by photometric redshifts (photo-z«)., A WL survey requires an estimate of the shape and the redshift of each source; dominant observational systematic errors are expected to be errors in galaxy shape due to the uncorrected influence of the point spread function (PSF) and errors in estimation of redshift distributions if they are determined by photometric redshifts (photo-z's). + Interpretation of WL data could also be systematically incorrect due to errors in the theory of the non-linear matter power spectrum or intrinsic alieumoeuts of ealaxies., Interpretation of WL data could also be systematically incorrect due to errors in the theory of the non-linear matter power spectrum or intrinsic alignments of galaxies. + Iu this paper we present a new and more general analysis of the effect of photo-z calibration errors aud of the size of the spectroscopic survey required to reduce photo-z errors to a desired level., In this paper we present a new and more general analysis of the effect of photo-z calibration errors and of the size of the spectroscopic survey required to reduce photo-z errors to a desired level. + Recent work has addressed imauv of these potential systematic errors in WL data aud theory: from the conrputation of the nonlinear matter power spectrui (Vale&White2003:Vale2001:Ποιαoet 2007): from barvouic cooling aud pressure forces on the distribution of large-scale structures (White2001:Zhanueretal. 2008): approximations in iuferrius the shear from the maps2006): aud the presence of dust (Valeetal.2001).," Recent work has addressed many of these potential systematic errors in WL data and theory: from the computation of the nonlinear matter power spectrum \citep{Vale_White, White_Vale, LosAlamos, Huterer_Takada, Hagan_Ma_Kravtsov, +Linder05, Ma06, Francis07}; from baryonic cooling and pressure forces on the distribution of large-scale structures \citep{White_baryons, Zhan_Knox, Jing06, Rudd07, Zentner07}; approximations in inferring the shear from the maps; and the presence of dust \citep{Vale_Hoekstra}." +". The promise aud problems of WL have stimulated work on how to improve the PSF reconstruction (Jarvis&Jain200 Εν, estimate shear from noisv nuages (Berustein&Jarvis2002:ID-Nakajima&Derusteiu2007:Masseyetal. 2007).. aud protect against errors iu the theoretical power spectrum at siiall scales (ITuterer&White2005)."," The promise and problems of WL have stimulated work on how to improve the PSF reconstruction \citep{Jarvis_Jain}, , estimate shear from noisy images \citep{Bernstein_Jarvis,Hirata_Seljak,Hoekstra04,Heymans06, +Nakajima06,STEP2_07}, and protect against errors in the theoretical power spectrum at small scales \citep{nulling}." +. For visible-NIR WL galaxw surveys. the dounünaut systematic error is likely to be inaccuracies in the ploto-z calibration.," For visible-NIR WL galaxy surveys, the dominant systematic error is likely to be inaccuracies in the photo-z calibration." + The effect of photo-z calibration on weal: chsing is studied by Alaetal.(2006):IIuterer(2006):Jainetal.(2007):Abdalla (2007): and Dile&ing(2007).," The effect of photo-z calibration on weak lensing is studied by \cite{Ma05, Huterer05_wlsys, Jain06, Abdalla07}; and \cite{Bridle07}." +. The distributions of photo-z errors assuned for these studies are. however. much simpler hau will exist iu real surveys (Dahlenetal.2007:Ovaizuotal.2007:WittmanetStabenau2007 )..," The distributions of photo-z errors assumed for these studies are, however, much simpler than will exist in real surveys \citep{Dahlen07,Oyaizu07,Wittman07,Stabenau07}. ." + IIutereretal.(2006). assumed that photo-z errors take he form of simple shifts (a bias that varies with :). while Maetal.(2006) assume the photo-z error distribution is a Gaussian. with a biasend dispersion that are functions of +.," \citet{Huterer05_wlsys} assumed that photo-z errors take the form of simple shifts (a bias that varies with $z$ ), while \cite{Ma05} assume the photo-z error distribution is a Gaussian, with a bias dispersion that are functions of $z$." + These studies find that dark cucrey constraints are very scusitive to the uncertainties of photo-z parameters., These studies find that dark energy constraints are very sensitive to the uncertainties of photo-z parameters. + A spectroscopic calibration sample of galaxies on t order of 10? is required to liave less than 50% degradation ou dark euergv constramts., A spectroscopic calibration sample of galaxies on the order of $10^5$ is required to have less than $50\%$ degradation on dark energy constraints. + In this work we relax f Gaussian assuniptionu. presenting a method to evaluate the degradation of dark energv paranueter accuracy versus the size of the spectroscopic calibration survey. for the case of a photo-z eror distribution described by any paralucterized function.," In this work we relax the Gaussian assumption, presenting a method to evaluate the degradation of dark energy parameter accuracy versus the size of the spectroscopic calibration survey, for the case of a photo-z error distribution described by any parameterized function." + We then apply this to a modelin which the core of the photo-z error distribution is the stun of multiple Gaussians. igunoriugfor uow the effect of," We then apply this to a modelin which the core of the photo-z error distribution is the sum of multiple Gaussians, ignoringfor now the effect of" +Another interesting issue is whether the extra freedom in the dark energy fluid will affect the constraints on the other parameters in our cosmological model.,Another interesting issue is whether the extra freedom in the dark energy fluid will affect the constraints on the other parameters in our cosmological model. +" That is, are the parameter constraints in the ACDM model robust to changes in c2;, and c?,,,."," That is, are the parameter constraints in the $\Lambda$ CDM model robust to changes in $\cvis$ and $\clam$." +" This was also studied in (?),, where they found that a,:, did not change the constraints in the other cosmological parameters significantly, but that varying Gam Shifted the other parameter ranges slightly."," This was also studied in \citep{ichiki:2007}, where they found that $\avis$ did not change the constraints in the other cosmological parameters significantly, but that varying $\clam$ shifted the other parameter ranges slightly." +" In Figure 8 we have plotted the marginalized likelihoods for different cosmological parameters in the case of a 7 parameter model with free w but with avis=0 and cZ,,=1.", In Figure \ref{fig:1D} we have plotted the marginalized likelihoods for different cosmological parameters in the case of a 7 parameter model with free $w$ but with $\avis = 0$ and $\clam=1$. +" We compare this to a model where ayis is allowed to vary freely in the interval (—20,20) (the same model as shown in Figure 4))."," We compare this to a model where $\avis$ is allowed to vary freely in the interval $\{-20,20\}$ (the same model as shown in Figure \ref{fig:alpha_w}) )." +" Also shown is a model with Qvis=0 and c2,,,=0.", Also shown is a model with $\avis=0$ and $\clam = 0$. + We see that the extra freedom in the Qyis parameter does not change the other parameter distributions significantly., We see that the extra freedom in the $\avis$ parameter does not change the other parameter distributions significantly. +" We do however get a slight shift in the parameter distributions by changing c7,,, from 1 to 0.", We do however get a slight shift in the parameter distributions by changing $\clam$ from 1 to 0. + This is consistent with the results from (?).., This is consistent with the results from \citep{ichiki:2007}. +" The most notable effect of changing from a model with Gam=1 to a model with c2,,,=0, is that the probability distributionfor w becomes narrower in the latter case."," The most notable effect of changing from a model with $\clam=1$ to a model with $\clam=0$, is that the probability distributionfor $w$ becomes narrower in the latter case." +" For a model with c2,,,=1 we find w=(—1.47,—0.57} at CL, while this range changes to w={—1.26,—0.52} for a model with c2,,,= 0."," For a model with $\clam=1$ we find $w=\{-1.47,-0.57\}$ at CL, while this range changes to $w=\{-1.26,-0.52\}$ for a model with $\clam=0$ ." +" For the other parameters, the effect of changing c2,,, is not very notable."," For the other parameters, the effect of changing $\clam$ is not very notable." +" As we have seen, only weak constraints can be found on the c2,,, Qvis and c7,,, parameters using present data."," As we have seen, only weak constraints can be found on the $\cvis$, $\avis$ and $\clam$ parameters using present data." +" We have also argued that the effect of includingother types of data sets, like LSS and SNIa, would not be very helpful, as such kinds of data sets are not affected significantly by these parameters."," We have also argued that the effect of includingother types of data sets, like LSS and SNIa, would not be very helpful, as such kinds of data sets are not affected significantly by these parameters." +" Also, unless w is significantly below -1, they will not serve to break parameter degeneracies for the parameters studied here."," Also, unless $w$ is significantly below -1, they will not serve to break parameter degeneracies for the parameters studied here." + Will it then be possible to improve our constraints with future CMB data?, Will it then be possible to improve our constraints with future CMB data? +" To answer this question we have simulated a “perfect” CMB temperature data set, where the error bars are defined only from cosmic variance (CV) around a power spectrum generated from the best-fit ACDM model (with w=—1, Cà;,=0 and Cy,= 1) from WMAP data."," To answer this question we have simulated a “perfect” CMB temperature data set, where the error bars are defined only from cosmic variance (CV) around a power spectrum generated from the best-fit $\Lambda$ CDM model (with $w=-1$, $\cvis=0$ and $\clam=1$ ) from WMAP data." + The likelihood part of CosmoMC has been modified to use this perfect data instead of the WMAP measurements., The likelihood part of CosmoMC has been modified to use this perfect data instead of the WMAP measurements. +" The likelihood is calculated as in (?):: For this mock data set we have used multipoles from |=2 to l=2000 in our analysis, and also here we have added the same prior on Ho and age as earlier."," The likelihood is calculated as in \citep{verde:2003}: For this mock data set we have used multipoles from $l=2$ to $l=2000$ in our analysis, and also here we have added the same prior on $H_0$ and age as earlier." + A completely noise-free data set is of course not realistic., A completely noise-free data set is of course not realistic. +" However, it is an interesting case to study, sinceeffects that cannot be seen here, will never be possible to see using a real CMB temperature experiment."," However, it is an interesting case to study, sinceeffects that cannot be seen here, will never be possible to see using a real CMB temperature experiment." +" Note that, when using this mock data set, we do not include any polarization data in our analysis."," Note that, when using this mock data set, we do not include any polarization data in our analysis." +" In Figure 9 we show the constraints in the a,;s-w plane in a model with c7,,,=1 and avis<0.", In Figure \ref{fig:alpha_w_p} we show the constraints in the $\avis$ $w$ plane in a model with $\clam=1$ and $\avis<0$. +" This is compared with the results from using WMAP data alone, as also shown in Figure 4.."," This is compared with the results from using WMAP data alone, as also shown in Figure \ref{fig:alpha_w}." +" As we can see, even in this idealized case, we do not see any major improvement in our constraints on Qyis."," As we can see, even in this idealized case, we do not see any major improvement in our constraints on $\avis$ ." + In this case the lower limit increases from ayis>—0.23 (from WMAP data) to avis>—0.22., In this case the lower limit increases from $\avis>-0.23$ (from WMAP data) to $\avis>-0.22$. +" In Figure 10 we have used the CV limited mock data to redo one the most interesting case from the analysis with WMAP data, namely the constraints in the c2;,-w plane with w«—1 and c2;,« 0, as shown inFigure 3.."," In Figure \ref{fig:cvis_w_p} we have used the CV limited mock data to redo one the most interesting case from the analysis with WMAP data, namely the constraints in the $\cvis$ $w$ plane with $w<-1$ and $\cvis<0$ , as shown inFigure \ref{fig:cvis_w}. ." +" We see that the constraints in this area improve slightly, but not very significantly."," We see that the constraints in this area improve slightly, but not very significantly." +" Using the CV-limited mockdata we find c2;,> —17.5, compared to c2;,>19.5 using WMAP data."," Using the CV-limited mockdata we find $\cvis>-17.5$ , compared to $\cvis>19.5$ using WMAP data." +used to explain the rapid damping of kink oscillations (see. e.g. Ofman and Aschwanden 2002. Ruderman and Roberts 2002. Ruderman 2008. ete).,"used to explain the rapid damping of kink oscillations (see, e.g. Ofman and Aschwanden 2002, Ruderman and Roberts 2002, Ruderman 2008, etc)." + Equation (3)) implies that the eigenfunctions. v. are driven by particular forms of e&(z). through the particular profile of the quantities that make up the kink speed (density. magnetic field).," Equation \ref{eq:2.3}) ) implies that the eigenfunctions, $v_r$, are driven by particular forms of $c_K(z)$, through the particular profile of the quantities that make up the kink speed (density, magnetic field)." + Inspired from the eigenvalue problem of Rayleigh-Ritz procedure. McEwan et al. (," Inspired from the eigenvalue problem of Rayleigh-Ritz procedure, McEwan et al. (" +2008) used a variational principle that allows the calculation of eigenvalues. c. - a method that is employed by our analysis.,"2008) used a variational principle that allows the calculation of eigenvalues, $\omega$, - a method that is employed by our analysis." +" Let us multiply the above equation by v; and integrate from the apex to the footpoint of the loop as Using integration by parts in the first integral (taking into account that for the fundamental mode vL)=dv(0)/dz0 and for the first harmonic v,(0)=vl) 0). the above equation simplifies to which Cu)results into theV equation derived earlier by McEwan et al. ("," Let us multiply the above equation by $v_r$ and integrate from the apex to the footpoint of the loop as Using integration by parts in the first integral (taking into account that for the fundamental mode $v_r(L)=dv_r(0)/dz=0$ and for the first harmonic $v_r(0)=v_r(L)=0$ ), the above equation simplifies to which results into the equation derived earlier by McEwan et al. (" +"2008) where In order to express the eigenvalueCR) of such problem. we consider some trial functions for v, that satisfy the boundary conditions imposed at the footpoints and the apex of the loop.","2008) where In order to express the eigenvalue of such problem, we consider some trial functions for $v_r$ that satisfy the boundary conditions imposed at the footpoints and the apex of the loop." + Since we are interested only in the characteristics. of fundamental mode of kink oscillations and its first harmonic. we will assume that v(z) will be proportional to coscrz/2) for the fundamental mode and sinGzz/L) for the first harmonic.," Since we are interested only in the characteristics of fundamental mode of kink oscillations and its first harmonic, we will assume that $v_r(z)$ will be proportional to $\cos(\pi z/2L)$ for the fundamental mode and $\sin(\pi z/L)$ for the first harmonic." + It is obvious that these choices for eigenfunctions correspond to the homogeneous plasma. however - as we show in the Appendix - the corrections to the eigenfunction due to density stratification are rather small.," It is obvious that these choices for eigenfunctions correspond to the homogeneous plasma, however - as we show in the Appendix - the corrections to the eigenfunction due to density stratification are rather small." + The problem of how the kink speed depends on the longitudinal coordinate. z. is a rather delicate problem and only simplified cases can be solved analytically.," The problem of how the kink speed depends on the longitudinal coordinate, $z$, is a rather delicate problem and only simplified cases can be solved analytically." +" For simplicity. let us consider that the magnetic field inside and outside of the coronal loop are identical and homogeneous. while the density varies exponentially according to where o;(0) and p,(0) are the densities inside and outside the loop at z=0. re. at the the loop apex and H; and H, are the density scale-heights inside and outside the loop."," For simplicity, let us consider that the magnetic field inside and outside of the coronal loop are identical and homogeneous, while the density varies exponentially according to where $\rho_i(0)$ and $\rho_e(0)$ are the densities inside and outside the loop at $z=0$, i.e. at the the loop apex and $H_i$ and $H_e$ are the density scale-heights inside and outside the loop." + Obviously the choice of density reflects a simplified description of the coronal loop model where plasma ts tsothermal and other further effects are neglected. however. this density profile allows us to obtain analytical results.," Obviously the choice of density reflects a simplified description of the coronal loop model where plasma is isothermal and other further effects are neglected, however, this density profile allows us to obtain analytical results." + A realistic deseription would require taking into account that the plasma is not isothermal (inside and outside the loop). the loop is curved and the density can depend on other coordinates. as well.," A realistic description would require taking into account that the plasma is not isothermal (inside and outside the loop), the loop is curved and the density can depend on other coordinates, as well." + This form of density dependence on the coordinate was earlier used by. e.g. Verth et al.," This form of density dependence on the $z$ coordinate was earlier used by, e.g. Verth et al." + 2007. McEwan et al.," 2007, McEwan et al." + 2008. Morton and Erdéllyi 2009. Morton and Ruderman 2011. Morton et al.," 2008, Morton and Erdéllyi 2009, Morton and Ruderman 2011, Morton et al." + 2011., 2011. + With our chosen density profiles. the kink speed given by Eq. (2))," With our chosen density profiles, the kink speed given by Eq. \ref{eq:2.2}) )" +" becomes where Bo 1s the magnitude of the magnetic field. v4,(0) 18 the Alfvénn speed at the apex of the loop. and & is the density ratio. Le. o;(0)/p,(0)."," becomes where $B_0$ is the magnitude of the magnetic field, $v_{Ai}(0)$ is the Alfvénn speed at the apex of the loop, and $\xi$ is the density ratio, i.e. $\rho_i(0)/\rho_e(0)$." + Since the density outside the coronal loop is smaller than inside. we will consider that &>1.," Since the density outside the coronal loop is smaller than inside, we will consider that $\xi\geq 1$." +" The quantities H; and H, are the density scale-heights and they are proportional to the temperature of the plasma.", The quantities $H_i$ and $H_e$ are the density scale-heights and they are proportional to the temperature of the plasma. +" Here we denoted y=H,/H;.", Here we denoted $\chi=H_e/H_i$. + Since the temperature of the loop is higher than its environment. we will take y| ye a hostile e1virouruent for the formation and evolution of planetary s¥stelus.," In addition to observational complications, binary systems were traditionally assumed to be a hostile environment for the formation and evolution of planetary systems." + He»wvever. direc1 linagine of st:us kuown to harbor panets detected radial. velocities has revealed several bihary star systelis OT.," However, direct imaging of stars known to harbor planets detected by radial velocities has revealed several binary star systems \mycitep{Pat02, Egg09}." + Protoplanetary disks. which form the material basis for planet formaion. are observed in both circumstella circumbinary. configurations in binary systems (?? uid the growh and settling of dus Sl:o]ulls is COLL iu ary star systems (?)..," Protoplanetary disks, which form the material basis for planet formation, are observed in both circumstellar and circumbinary configurations in binary systems \mycitep{Rod96, Tri07}, and the growth and settling of dust grains is common in binary star systems \mycitep{Pas08}." + Theoreical uumerical simulatious successfully node the evoluu of protoplanets (?).. terrestrlal planets (?)..? giant jxlauets (/2) and bfowl dwars (0) in circumbinary disks.," Theoretical numerical simulations successfully model the evolution of protoplanets \mycitep{Pie07}, terrestrial planets \mycitep{Qui06}, giant planets \mycitep{Pie08} and brown dwarfs \mycitep{Jia04} in circumbinary disks." + Furthermore. theoretical models also permit planet [ortiallol through graviational instability iu binary systems.," Furthermore, theoretical models also permit planet formation through gravitational instability in binary systems." + Planes forued iu 11is way have large separaious from their sals aud are therefore particularly importa largets for direct imaele., Planets formed in this way have large separations from their stars and are therefore particularly important targets for direct imaging. + The intheeuce of a secondary star cau i some Cases prevel ita collapse th‘ough tical heating (?) Or 1Ἰσορ) he collapse for au otherwise stable clisk (?).. leaviug a calacteristic iiiprint ou t edemographics of planets in binary systems. the observation oL which weuld xovide au invaluable test for R9]planet formation theory.," The influence of a secondary star can in some cases prevent a collapse through tidal heating \mycitep{May05} or trigger the collapse for an otherwise stable disk \mycitep{Bos06}, leaving a characteristic imprint on the demographics of planets in binary systems, the observation of which would provide an invaluable test for planet formation theory." + A secondary star can alsO act as a sjurce of angular nometum for : 'cumbinary planet and either scatter or tidaly pus ithe planet ino wider orljts. ths enrichi ie expected population of wide-orbit stars (227?)..," A secondary star can also act as a source of angular momentum for a circumbinary planet and either scatter or tidally push the planet into wider orbits, thus enriching the expected population of wide-orbit stars \mycitep{Nel03, Ver04, Hol99, Kle00}." + Di‘ect cleection tecμιαles are critical for iivestigating extrasolar planets οi large (> 10 AU) orbital separations. and the first clirect detectious of extrasoar planets have confiriued that planets do exist iu these orbits (e.g.. ?2??)).," Direct detection techniques are critical for investigating extrasolar planets on large $>$ 10 AU) orbital separations, and the first direct detections of extrasolar planets have confirmed that planets do exist in these orbits (e.g., \mycitealt{Mar08,Kal08,Lag09}) )." + High contrast instrumeration aud didirect detection techniques are beiig develo»ed to probe planet fonaljon aud the evolitiou of planeary systens., High contrast instrumentation and direct detection techniques are being developed to probe planet formation and the evolution of planetary systems. +" In order to achieve high courast (> 10°) at smal alglar sep:uations (« 1""). one must controI the diffracted ight [rom the host star in the image dlane."," In order to achieve high contrast $>$ $^{-6}$ ) at small angular separations $<$ $\arcsec$ ), one must control the diffracted light from the host star in the image plane." +" Howe,rer. the uajoriiy of coonagrapls are designed o remove light roni siiele host stars."," However, the majority of coronagraphs are designed to remove light from single host stars." +" Ie secondary star lies close to ilthe taget star and it is 101 suppressed. the secxdary stars light. will ove""wlielia he sienal [roi1 ahy allI conmpatlOlis."," If the secondary star lies close to the target star and it is not suppressed, the secondary star's light will overwhelm the signal from any faint companions." + The peak of the G dwar. comipaniou cisribution is near 30 AU [y. and wlile also accountii& lor 'andoim orbital inclinatiius and phases ou tle sky. he vast ajo‘ity of nearyw biuary stars uw 100 0€) targetec by high conFast imaging stt'veys woul benelit from having a specialized corouag'apli.," The peak of the G dwarf companion distribution is near 30 AU \mycitep{Duq91}, and while also accounting for random orbital inclinations and phases on the sky, the vast majority of nearby binary stars $<$ 100 pc) targeted by high contrast imaging surveys would benefit from having a specialized coronagraph." + Coronaeraphis capadle of simultanecsusly blockug the light from binary stars can be grouped luto two caegorles: COromagraphs with inear mask:s. aud coronagraplis with dual circular masks.," Coronagraphs capable of simultaneously blocking the light from binary stars can be grouped into two categories: coronagraphs with linear masks, and coronagraphs with dual circular masks." + Each type las advantagees aud cdisadvaitages: in tie. following. we preseut examples of each aud discuss thei performance in the presence ola typical low-order wavelrout uoise following au adaptive Oplles systeur," Each type has advantages and disadvantages; in the following, we present examples of each and discuss their performance in the presence of a typical low-order wavefront noise following an adaptive optics system." + Iu particular. we present adwabinask design based on an APLC which allows [or a simall inier working :iuele aud a large «liSCOVeI “space even for au obstructed aperture. and which miniulzes cross-talk between the masks.," In particular, we present a dual-mask design based on an APLC which allows for a small inner working angle and a large discovery space even for an obstructed aperture, and which minimizes cross-talk between the masks." + We also address manulacturiug and implementation COLLCELLIS slch as obstrueed apertures. liekl rotation. manulacturing. and mask placement. and," We also address manufacturing and implementation concerns such as obstructed apertures, field rotation, manufacturing, and mask placement, and" + A* A* (~10* 101. , $^*$ $\sim $ $^*$ $\sim 10^3$ $10^4 M_{\odot}$ +of the Hubble radius at EoR and has an amplitude proportional to T.,of the Hubble radius at EoR and has an amplitude proportional to $\tau$. + Any model of reionization must reproduce the observed value of optical depth., Any model of reionization must reproduce the observed value of optical depth. + For a forecast on anticipated improvements of observational estimation of 7. please see (Colombo&Pierpaoli 2009)..," For a forecast on anticipated improvements of observational estimation of $\tau$, please see \citep{2009NewA...14..269C}." + The reionization history depends on the star formation history of he universe. which in the simplified models is closely related to he halo formation history.," The reionization history depends on the star formation history of the universe, which in the simplified models is closely related to the halo formation history." + The IMF of stars and the escape fraction or ionizing photons then give us the number of ionizing photons hat are available as a function of time., The IMF of stars and the escape fraction for ionizing photons then give us the number of ionizing photons that are available as a function of time. + These can then be used to compute the evolution of the neutral or ionized fraction of gas in he universe., These can then be used to compute the evolution of the neutral or ionized fraction of gas in the universe. + As mentioned above. we assume that star formation is triggered during formation of haloes.," As mentioned above, we assume that star formation is triggered during formation of haloes." + As most time scales of interest are longer than the dynamical time scale over which the bulk of star formation takes place. we assume star formation to be instantaneous in our model.," As most time scales of interest are longer than the dynamical time scale over which the bulk of star formation takes place, we assume star formation to be instantaneous in our model." + We consider a global averaged evolution of ionized fractio= instead of following evolution of HII regions around haloes. the approach used in most studies (Chiu&Ostriker2000:Sethi 2005).," We consider a global averaged evolution of ionized fraction instead of following evolution of HII regions around haloes, the approach used in most studies \citep{2000ApJ...534..507C, +2005MNRAS.363..818S}." + Further. we assume that during reionization. a region is either neutral or completely ionized.," Further, we assume that during reionization, a region is either neutral or completely ionized." + With these assumptions. the evolution of the ionized fraction evolves as: Here .r is the fractional volume that is ionized. and y is the number of ionizing photons per baryon.," With these assumptions, the evolution of the ionized fraction evolves as: Here $x$ is the fractional volume that is ionized, and $y$ is the number of ionizing photons per baryon." +" c, denotes the effective cross-section of photoionization. àg is the recombination coefficient. for all levels except the ground state of neutral hydrogen. and m, denotes the mass of a proton."," $\sigma_{p}$ denotes the effective cross-section of photoionization, $\alpha_{B}$ is the recombination coefficient for all levels except the ground state of neutral hydrogen, and $m_p$ denotes the mass of a proton." + The first term on the right hand side of equation (50) describes recombination., The first term on the right hand side of equation \ref{xtoy}) ) describes recombination. + C is the clumping factor defined as C=nuling ?.," ${\mathcal C}$ is the clumping factor defined as ${\mathcal C}^2 = +{\langle}n_{H}^2{\rangle}/{\langle}n_H{\rangle}^2$ ." + This term usually involves square of the ionized fraction but in our model we assume that the ionized fraction is either unity or zero., This term usually involves square of the ionized fraction but in our model we assume that the ionized fraction is either unity or zero. + This. when used in volume averaging over the universe with an additional assumption that the clumping is the same in ionized and neutral regions. leads to a linear dependence.," This, when used in volume averaging over the universe with an additional assumption that the clumping is the same in ionized and neutral regions, leads to a linear dependence." + In the process of averaging. the meaning of . changes from the ionized fraction to the volume filling fraction of the ionized regions.," In the process of averaging, the meaning of $x$ changes from the ionized fraction to the volume filling fraction of the ionized regions." +" We can express this in terms of equations: We have assumed that the clumping factor is the same in all parts of the universe. this allows us to take {73,) outside the integral."," We can express this in terms of equations: We have assumed that the clumping factor is the same in all parts of the universe, this allows us to take $\langle n_{H}^2\rangle$ outside the integral." + The third equality in equation (7) follows from the definition of .r as a filling fraction., The third equality in equation \ref{eqls}) ) follows from the definition of $x$ as a filling fraction. + We also expect C to change with the evolution of clustering., We also expect ${\mathcal C}$ to change with the evolution of clustering. + Wetake this dependence to be of the form (Tlievetal.2007) Sources of ionizing radiation are represented in the last term of equation (63). Pb being related to the formation rate of collapsed haloes.," Wetake this dependence to be of the form \citep{2007MNRAS.376..534I} + Sources of ionizing radiation are represented in the last term of equation \ref{ytoy}) ), $\dot{F}$ being related to the formation rate of collapsed haloes." + This is obtained from the Press-Schechter formalism as described above., This is obtained from the Press-Schechter formalism as described above. + ;V. denotes the number of photons produced per unit mass of star formation., $N_{\gamma}$ denotes the number of photons produced per unit mass of star formation. + Ionization of neutral hydrogen is described in the last term on the right hand side of equation (53)., Ionization of neutral hydrogen is described in the last term on the right hand side of equation \ref{xtoy}) ). + This term occurs in both equations., This term occurs in both equations. + We neglect the contribution of collisional ionization., We neglect the contribution of collisional ionization. + We solve these equations numerically for different cosmological models., We solve these equations numerically for different cosmological models. + The system of equations (59) and. (6)) is “stiff since (ως=O.y0) is a stable point and time scales for evolution of . and y are very different.," The system of equations \ref{xtoy}) ) and \ref{ytoy}) ) is “stiff,” since $(x=0,y=0)$ is a stable point and time scales for evolution of $x$ and $y$ are very different." + Further. ας is bounded from above (by unity) while y is not.," Further, $x$ is bounded from above (by unity) while $y$ is not." + Thus the usual forward differencing methods do not give accurate solutions easily., Thus the usual forward differencing methods do not give accurate solutions easily. + We bypass this problem by noting that during the process of reionization almost every ionizing photon will be immediately absorbed by themedium’., We bypass this problem by noting that during the process of reionization almost every ionizing photon will be immediately absorbed by the. +. This means that the two terms in the right hand side of the second equation are of the same order till a becomes nearly equal to 1. whereas the left hand side is much smaller and may be assumed to be zero.," This means that the two terms in the right hand side of the second equation are of the same order till $x$ becomes nearly equal to $1$, whereas the left hand side is much smaller and may be assumed to be zero." + This reduces the system of equations to a single equation. which ean now be solved using forward differencing methods.," This reduces the system of equations to a single equation, which can now be solved using forward differencing methods." + Note that this approximation is not valid when . approaches |. although in practice the approximate solution is fairly accurate up tour 0.9.," Note that this approximation is not valid when $x$ approaches 1, although in practice the approximate solution is fairly accurate up to $x \sim 0.9$." + Indeed. if we use the approximation up to.r —1.0 then we make an error in estimation of of less than 54.," Indeed, if we use the approximation up to $x=1.0$ then we make an error in estimation of $\tau$ of less than $5\%$." + We take ap=1.0104%envtsee+. ignoring its dependence on temperature.," We take $\alpha_{\mathrm B} = 1.0 \times 10^{-13} \; \mathrm{cm^3} \, +\mathrm{sec^{-1}}$, ignoring its dependence on temperature." + This dependence is fairly weak at temperatures of interest., This dependence is fairly weak at temperatures of interest. +" We use oa,=6.30.10.DPcm.", We use $\sigma_p = 6.30 \times 10^{-18}\;\mathrm{cm^2}$. +? We thus assume that most of the ionizing radiation is around the Lyman limit., We thus assume that most of the ionizing radiation is around the Lyman limit. + The number of ionizing photons released per baryon of stars formed. denoted by ;V.. depends on the initial mass function (IMF) of the stars.," The number of ionizing photons released per baryon of stars formed, denoted by $N_{\gamma}$, depends on the initial mass function (IMF) of the stars." + We obtain this number from the stellar population synthesis code (Leithereretal.therer 2005).," We obtain this number from the stellar population synthesis code \citep{1999ApJS..123....3L, 2005ApJ...621..695V}." + Our aim here is to study a variety of models with varying cosmological parameters as well as parameters related to star formation and enrichment., Our aim here is to study a variety of models with varying cosmological parameters as well as parameters related to star formation and enrichment. + We consider a random subset of fla ACDM models allowed by WMAPS (Komatsuetal.2008:Dunkleyetal. 2008)..," We consider a random subset of flat $\Lambda$ CDM models allowed by WMAP5 \citep{2008arXiv0803.0547K, 2008arXiv0803.0586D}." + We do not consider models with massive neutrinos or a non-vanishing tensor component. or models where the primordia yower spectrum deviates from a pure power law.," We do not consider models with massive neutrinos or a non-vanishing tensor component, or models where the primordial power spectrum deviates from a pure power law." + We use only WMAP constraints for limiting cosmological parameters., We use only WMAP constraints for limiting cosmological parameters. + We used he MCMC chains made available by the WMAP team /)., We used the MCMC chains made available by the WMAP team ). + We considered a random subse of all models allowed with a confidence level of GS% from the ICMC chains., We considered a random subset of all models allowed with a confidence level of $68\%$ from the MCMC chains. + We studied a handful of models for parameters related to star formation: details of these are given in Table (1)., We studied a handful of models for parameters related to star formation; details of these are given in Table \ref{sfmodels}) ). +" The table lists the IMFs used in our study"".", The table lists the IMFs used in our . +.. We have also listed he amount of ionizing photons produced per baryon in stars.and," We have also listed the amount of ionizing photons produced per baryon in stars,and" +" rg M, (V~ος). 26. rover. these Nrirag=0.9Vie/tsFl) [1IS-requioverr and [15]."," $r_p$ $M_\ast$ $V_w\sim\cs$ $2\cs$ $r_{\rm over}$ $\Delta r_{\rm over}/\Delta\rarm=0.5\,(V_w/\cs\mp1)$ r] and \ref{equ:del1}] ])." +" In cool AGB envelopes. the wind is usually much faster than the souud speed (Vi.29 σι). makiug Are, relatively large."," In cool AGB envelopes, the wind is usually much faster than the sound speed $V_w\gg\cs$ ), making $\Delta r_{\rm over}$ relatively large." +" For instauce. with Vi,=10e, which is easily found for ACB stars. the outer aud iuner arm boundaries can meet only alter five turis."," For instance, with $V_w=10\cs$, which is easily found for AGB stars, the outer and inner arm boundaries can meet only after five turns." + For the case of an observational detection of ouly parts of the spiral. especially when the partial spiral is expected over the distance of Arvey. a more careful analysis is required to avoid misideutifyiug the outer aud inner boundaries.," For the case of an observational detection of only parts of the spiral, especially when the partial spiral is expected over the distance of $\Delta r_{\rm over}$, a more careful analysis is required to avoid misidentifying the outer and inner boundaries." + We have also provided an empirical formula (eq. [12]]), We have also provided an empirical formula (eq. \ref{equ:jump}] ]) +" for the arm-interarm density contrast. α=6p/py. along a normalized distance r/ry as a function of Vip/e;. Vi/e; aud rgr,y=GMy/(2r,)."," for the arm-interarm density contrast, $\alpha=\delta\rho/\rho_w$, along a normalized distance $r/r_p$ as a function of $V_w/\cs$, $V_p/\cs$, and $r_B/r_p=GM_p/(\cs^2r_p)$." +" Usiug this empirical formula. we estimate the properties of a Jupiter wake in the stellar wind when ¢u Stun becomes a giant of size AAU (AL,=0.8sun. AL,=2*«107spy.. Z4=3000/0: according to Hurleyetal. 2000))."," Using this empirical formula, we estimate the properties of a Jupiter wake in the stellar wind when our Sun becomes a giant of size AU $M_\ast=0.8$, $\dot{M_\ast}=2\times10^{-7}$, $T_\ast=3000K$; according to \citealp{hur00}) )." +" The wind speed V, is set to be ~ Pbasecd on the trend. between the mass-Ioss rate aud the envelope expausion speed 2006).. and tlie sonic speed c; is assumed to beanps."," The wind speed $V_w$ is set to be $\sim$ based on the trend between the mass-loss rate and the envelope expansion speed \citep[see Fig.~16 in][]{fon06}, and the sonic speed $\cs$ is assumed to be." +". The estimated orbital speed V,=(GM,/rj)? of Jupiter in situ (rp—9 AAU) isaups.. corresponding to the aruriuterarimn deusity contrast of only. contrast does not significantly depend ou the orbital cistauce. ie.. detect the gravitational wake of a Jupiter mass object with the current observatioual linitatious of sensitivity aud augular resolution."," The estimated orbital speed $V_p=(GM_\ast/r_p)^{1/2}$ of Jupiter in situ $r_p=5$ AU) is, corresponding to the arm-interarm density contrast of only contrast does not significantly depend on the orbital distance, i.e., detect the gravitational wake of a Jupiter mass object with the current observational limitations of sensitivity and angular resolution." + In the same rauge of orbital distance. a 10 Jupiter mass object can create a gravitational wake with the deusity contrast of aud for a brown dwarf mass Msun)). the contrast increases to performauce of the Atacama Large Millimeter/submillimeter Array (ALALA).," In the same range of orbital distance, a 10 Jupiter mass object can create a gravitational wake with the density contrast of and for a brown dwarf mass ), the contrast increases to performance of the Atacama Large Millimeter/submillimeter Array (ALMA)." +" We note that these uunmerical values are lower limits since the peak deusity contrast at the arm boundary can be higher with a realistic size of the object much smaller than >0.1 AAU employed in this study: but the effect of the object size ry is uot significant uuless the size is comparable to the accretion raclius ry.Therequiredspatial resolution to distinguish the arm pattern separation is AAU depending on the orbital distance (rj,= 3-30AAU).", We note that these numerical values are lower limits since the peak density contrast at the arm boundary can be higher with a realistic size of the object much smaller than $\geq0.1$ AU employed in this study; but the effect of the object size $r_s$ is not significant unless the size is comparable to the accretion radius $r_B$.Therequiredspatial resolution to distinguish the arm pattern separation is AU depending on the orbital distance $r_p=3$ AU). + On a larger scale. a distancecorresponding to 5 times," On a larger scale, a distancecorresponding to 5 times" +Three binary svstems containing a massive star and a compact object 5039.. and have been clearly detected in TeV energy baud (see lor the updated information).,"Three binary systems containing a massive star and a compact object –, and – have been clearly detected in TeV energy band (see for the updated information)." + While the nature of the compact companion in and is not vet. establishecl 2005a.b:;Sartyetal. 2011).. the detection of the pulsed radio emission Irom indicates the presence of a 47.7 ms pulsar in (he svstem (Johnstonetal.1992).," While the nature of the compact companion in and is not yet established \citep{casares05a,casares05b,sarty11}, the detection of the pulsed radio emission from indicates the presence of a 47.7 ms pulsar in the system \citep{johnston92}." +". The pulsar orbits a luminous star in a very eccentric orbit with the following orbital parameters: eccentricity e=0.87. period 2,=1237 d. and semi-major axis e»=6.9AU (seeNegueru-elaetal.2011.andreferences therein).."," The pulsar orbits a luminous star in a very eccentric orbit with the following orbital parameters: eccentricity $e=0.87$, period $P_{{\rm orb}}= 1237$ d, and semi-major axis $a_{\rm 2}=6.9\rm \, AU$ \citep[see][and references +therein]{negueruela10}." + The svstem displavs variable broadband nonthermal radio. X-ray and TeV gama ray. emission close {ο periastron passage (Johnstonetal.2005: 2009).. which currently lacks successful multiwavelength interpretations.," The system displays variable broadband nonthermal radio, X-ray and TeV gamma ray emission close to periastron passage \citep{johnston05,uchiyama09,masha09,grove95,aharonian05,aharonian09}, which currently lacks successful multiwavelength interpretations." + Moreover. (heFermi LAT observations of periastron passage in December 2010 have shown that in general the GeV [lux level [rom the svstem is quite low. although a short intensive [lare was detected as well (seee.g.Tamοἱal.2011:Abdoet2011).," Moreover, the LAT observations of periastron passage in December 2010 have shown that in general the GeV flux level from the system is quite low, although a short intensive flare was detected as well \citep[see e.g.][]{tam11,abdo11}." +". Recently. optical observations with discovered that the optical star corresponds to a late O-star and has a significantly higher luminositv of L,=2.3x10""ergs.! than previously thought (Negueruelaetal.2011)."," Recently, optical observations with discovered that the optical star corresponds to a late O-star and has a significantly higher luminosity of $L_*=2.3\times10^{38}\rm +\, erg\,s^{-1}$ than previously thought \citep{negueruela10}." +. Because of [ast rotation thestar is significantly oblated with equatorial radius of Log=9.72. and the polar radius of Aj= 5.142..," Because of fast rotation thestar is significantly oblated with equatorial radius of $R_{\rm eq}=9.7 R_\sun$ and the polar radius of $R_{\rm + pole}=8.1 R_\sun$ ." +" This leads as well to a strong gradient of the star surface temperature with 7,=27500 lk and Έρως=34000 IX. The star rotation axis is inclined by 7,33° in respect to the Hne-ofsielt (Negueruelaetal.2011)."," This leads as well to a strong gradient of the star surface temperature with $T_{\rm eq}=27\,500$ K and $T_{\rm + pole}=34\,000$ K. The star rotation axis is inclined by $i_*\simeq33^\circ$ in respect to the line-of-sight \citep{negueruela10}." +. The distance to (he svstem is now estimated to be 2.3+40.4kpc.," The distance to the system is now estimated to be $2.3\pm0.4\,\rm +kpc$." + Moreover. the observations favored an orbital inclination value of /~25. which is remarkably smaller than the previously obtained value ol e35? (Johnstonetal. 1994)..," Moreover, the observations favored an orbital inclination value of $i\simeq25^\circ$, which is remarkably smaller than the previously obtained value of $\sim35^\circ$ \citep{johnston94}. ." + Allthese new parameters together should have an importaat impact on (the multiwavelength properties of (his svstem., Allthese new parameters together should have an important impact on the multiwavelength properties of this system. +ransit window. itis now larecly dominated by the transit duration. which is expected to be ~3.0 davs as shown in Table 2..,"transit window, it is now largely dominated by the transit duration, which is expected to be $\sim 3.0$ days as shown in Table \ref{probdepdur}." + Eveu so. attempts to obtain full coverage of je transit window from the eround will require a niulti-ongitudinal campaign during which oue can only hope ⋅cooperative weather.," Even so, attempts to obtain full coverage of the transit window from the ground will require a multi-longitudinal campaign during which one can only hope for cooperative weather." +: The complete. observation of. au $3 or ceress durius a single night is a substantially ; achievable goal under such circumstances., The complete observation of an ingress or egress during a single night is a substantially more achievable goal under such circumstances. + However. 200 still must contend with the challenge of mecting Date photometric precision requirenieuts for à successful fie. etection.," However, one still must contend with the challenge of meeting the photometric precision requirements for a successful detection." + SIMDAD refers to ( Dra as a variable star based ou its citation as NSV 7077 iu the (Ixulguwkiunetal.1982)., SIMBAD refers to $\iota$ Dra as a variable star based on its citation as NSV 7077 in the \citep{kuk82}. +. The NSV eutry is based on the photometric study of Jackisch(1963)... who reported a magnitude range of 0.09 mae.," The NSV entry is based on the photometric study of \citet{jac63}, who reported a magnitude range of 0.09 mag." + Later. Percy(1993) included. 7 Dra in his search for photometric variability in [KW giants chosen from the (loffeit&Jaschek1991) and found the star to be coustant to a limit of 0.01 mae.," Later, \citet{per93} included $\iota$ Dra in his search for photometric variability in K giants chosen from the \citep{hof91} and found the star to be constant to a limit of 0.01 mag." + We investigated the photometric stability of ; Dra musing newer observations., We investigated the photometric stability of $\iota$ Dra using newer observations. + The satellite observed the star diving its three-year mission ac acquired a photometric data set consisting of 10 lucasurements spanning a period of 1100 davs (Perrvinanetal. 1997)., The satellite observed the star during its three-year mission and acquired a photometric data set consisting of 104 measurements spanning a period of 1160 days \citep{per97}. +. The scatter of the 10147 Dra measurements 15is (0.005 mag. while the rauge of the observations. defined in terms of the 5th aud 95th perceutiles of their distribution. is 0.02 mae.," The scatter of the 104 $\iota$ Dra measurements is 0.005 mag, while the range of the observations, defined in terms of the 5th and 95th percentiles of their distribution, is 0.02 mag." + The scatter is roughly consistent with the expected unucertaintv of a single observation. but the rauge is roughly twice that expecος fromi a coustaut star.," The scatter is roughly consistent with the expected uncertainty of a single observation, but the range is roughly twice that expected from a constant star." +" Cousequenuth. the Catalogue (Permvinanetal.L997) lists the variability type for ; Dra as a blank. indicating that the star ""couk uot be classified as variable or constant.”"," Consequently, the Catalogue \citep{per97} lists the variability type for $\iota$ Dra as a blank, indicating that the star “could not be classified as variable or constant.”" + We performed a Fourier analysis of the data. plotted in Figure 5.. and confined the abseuce of any significant periodic variability.," We performed a Fourier analysis of the data, plotted in Figure \ref{phot_hip}, and confirmed the absence of any significant periodic variability." + We also acquired new Joliusou £2 aud V. observations with the Τὸ 0.1 mi Automatic Photoclectric Telescope (APT) located at Fairboru Observatory iu the Patagonia Mountains of southern Arizona., We also acquired new Johnson $B$ and $V$ observations with the T3 0.4 m Automatic Photoelectric Telescope (APT) located at Fairborn Observatory in the Patagonia Mountains of southern Arizona. + Between 2010 Jauuuv and May. T3 observed + Dra cifferentially with respect to a nearby comparison star iu the following sequence. termed a eroup observation:V.C.S. where Sis a sky reading. C ds the comparison star ID 110δι = 0 Dra (V Lol 8V0.53. Fs IV). and V ds the program (variable?)," Between 2010 January and May, T3 observed $\iota$ Dra differentially with respect to a nearby comparison star in the following sequence, termed a group observation:, where $S$ is a sky reading, $C$ is the comparison star HD 144284 = $\theta$ Dra $V=4.01$ , $B-V=0.53$, F8 IV), and $V$ is the program (variable?)" + star ; Dra (V 520. DBV— 1.17. A2 ΠΠ).," star $\iota$ Dra $V=3.29$ , $B-V=1.17$ , K2 III)." + A 2.5 mag neutral-density filter was used iu combination with the B aud V filters to attenuate the signal aud so minimize the deadtine correction for the two bright stars., A 2.3 mag neutral-density filter was used in combination with the $B$ and $V$ filters to attenuate the signal and so minimize the deadtime correction for the two bright stars. + Three C differcutial maenitudesOo in both B and V were computed frou cach sequence and averaged to creacB and V. eroup nieaus., Three $V-C$ differential magnitudes in both $B$ and $V$ were computed from each sequence and averaged to create $B$ and $V$ group means. + Croup mean differeutial maeuitudes with internal standard deviatious greater than 0.01 mae were rejected to eliminate observations taken uider nou-photometric conditions., Group mean differential magnitudes with internal standard deviations greater than 0.01 mag were rejected to eliminate observations taken under non-photometric conditions. + The surviving eroup leas were corrected for differential extinction with niehtlv extinction coefficieits. transformed to the Johnson system with vearly-ean transformation cocficicuts. ancl treated as single Oservations thereafter.," The surviving group means were corrected for differential extinction with nightly extinction coefficients, transformed to the Johnson system with yearly-mean transformation coefficients, and treated as single observations thereafter." + The tvvical precision of a single eroup-uean observation from T3. as micasured for pairs o: constant stars. ds ~0.00L0.005 mae (Πανetal.2000).," The typical precision of a single group-mean observation from T3, as measured for pairs of constant stars, is $\sim$ 0.004–0.005 mag \citep{hen00}." +. The APT acquired one or two group observations each clear nigit except for three full nights when the star was oserved at a much ueher cadence of LO eroup observations TOS 10r., The APT acquired one or two group observations each clear night except for three full nights when the star was observed at a much higher cadence of $\sim~10$ group observations per hour. + The APT collected a total of 221 B iux 220 V ex nposervations., The APT collected a total of 224 $B$ and 220 $V$ group observations. + Further details ou the automatic oweraloli ¢ft tus telescope. the observing procedures. aud he¢ata 1°cduetion process ean be found in Παινeal.(2000) alu references therein.," Further details on the automatic operation of this telescope, the observing procedures, and the data reduction process can be found in \citet{hen00} and references therein." + The complete. reduced Johnson 2B data set is plotted in the top panel of Figure 6: tie bottou panel prescuts just the high-cadewe B photometry roin one of the three monitoring welts.," The complete, reduced Johnson $B$ data set is plotted in the top panel of Figure \ref{phot_apt}; the bottom panel presents just the high-cadence $B$ photometry from one of the three monitoring nights." + The data in thi paucls scatter about their means with a standard deviajon of 0.0011 mag. after a half dozei outliers are removed im cach case.," The data in both panels scatter about their means with a standard deviation of 0.0041 mag, after a half dozen outliers are removed in each case." + Resultsfor theV. observatious are essentially ideutical (0.0013 mae)., Resultsfor the$V$ observations are essentially identical (0.0043 mag). +" This, our observatious sueecstOO that + Dra. as well as its comparison star theta Dra. are both constant to a Dini of approxinatelv 0.00£ mae."," Thus, our observations suggest that $\iota$ Dra, as well as its comparison star $theta$ Dra, are both constant to a limit of approximately 0.004 mag." +data. the power-law fitting vields a scaling of divine~510 UD. where the units are pe.,"data, the power-law fitting yields a scaling of $d_{\rm min,pc}\sim 5\times 10^{-5}D_{\rm pc}^{0.7}$ , where the units are pc." + This arguably reflects the uistory of how the filamentary turbulence evolves as the jet propagates. increasing the width.," This arguably reflects the history of how the filamentary turbulence evolves as the jet propagates, increasing the width." + The physical implication can be revealed by translating a quantity DAU.παν 48 he upper limit of the numberof outer-scale. filaments. CNNaimax:," The physical implication can be revealed by translating a quantity $\la D^{2}/d_{\rm min}^{2}$ as the upper limit of the numberof outer-scale filaments, $(N_{\lambda\sim d})_{\rm max}$." + Fig. 4((, Fig. \ref{fig:4}( ( +b) plots the values of (Nydias (=D>fd. or convenience) as a function of the deprojected. length of jets L.,"b) plots the values of $(N_{\lambda\sim d})_{\rm max}$ $=D^{2}/d_{\rm min}^{2}$, for convenience) as a function of the deprojected length of jets $L$." + Interpolating them. vields the scaling GN\y-dues Lee. indicating the trend that the capacity of outer- filaments increases as £ increases (shaded area).," Interpolating them yields the scaling $(N_{\lambda\sim d})_{\rm max}\sim 10^{9}L_{\rm kpc}^{0.6}$ , indicating the trend that the capacity of outer-scale filaments increases as $L$ increases (shaded area)." + In order to see the significance. we recall à promising scenario in which jets having large-scale magnetic fields are necessarily accompanied by huge currents in the bulk plasmas (Appl&Camenzinc 1992).. the kinetic energy of which is dissipated only a little during the transport from the cores to the lobes (Tashiro&Isobe2004).," In order to see the significance, we recall a promising scenario in which jets having large-scale magnetic fields are necessarily accompanied by huge currents in the bulk plasmas \citep{appl92}, the kinetic energy of which is dissipated only a little during the transport from the cores to the lobes \citep{tashiro04}." +.. As a whole. this is compatible with he superconductivity of plasmas.," As a whole, this is compatible with the superconductivity of plasmas." + For example. let us consider thewell-confirmed samples AIST and AA. the nuclei of which have the supermassive Mack holes with mass 10A4; (Alaechettoetal.1997) and (107LOYAL. (Marconietal.2006)... respectively.," For example, let us consider thewell-confirmed samples M87 and A, the nuclei of which have the supermassive black holes with mass $\sim 10^{9}M_{\sun}$ \citep{macchetto97} and $(10^{7}-10^{8})M_{\sun}$ \citep{marconi06}, respectively." + According to the arguments of Appl&Camoenzind(1992).. heir central engines. incorporated with their accretion disces. ought to have the potential to drive a current of the order of magnitude of £101A and ~1077AL respectively.," According to the arguments of \citet{appl92}, their central engines, incorporated with their accretion discs, ought to have the potential to drive a current of the order of magnitude of $I\sim 10^{19}~{\rm A}$ and $\sim 10^{18}~{\rm A}$, respectively." + Such a huge current could not be transported. by a single uniform column. on account of the current inhibition (Lloncla 2007).," Such a huge current could not be transported by a single uniform column, on account of the current inhibition \citep{honda07}." +. One possible solution is to allow for the presence of many filaments that each carry a current. [limited by ig~(me?fe)5E; (onda2000)., One possible solution is to allow for the presence of many filaments that each carry a current limited by $i_{0}\sim (mc^{3}/e)\beta_{j}\Gamma_{j}$ \citep{honda00}. +. It is noted that the value of fy is independent of A (Llondactal.2000).., It is noted that the value of $i_{0}$ is independent of $\lambda$ \citep{honda00b}. + Phe number of current filaments can then be estimated as NC4/74)~10477 and 107. respeetivelv.," The number of current filaments can then be estimated as $N(\sim I/i_{0})\sim 10^{15}$ and $\sim 10^{14}$, respectively." + Note that these values are just in the expected ranges of (Nyoadias for AIST and AA (cf., Note that these values are just in the expected ranges of $(N_{\lambda\sim d})_{\rm max}$ for M87 and A (cf. + Fig., Fig. + 4bb)., \ref{fig:4}b b). + The outcome suggests that. if the actual capacity of the outer-scale filaments reaches the level ~(Nymax: the filament cluster. which consists of the smaller filaments with size A«d. would not be closely. packed. in the jet.," The outcome suggests that, if the actual capacity of the outer-scale filaments reaches the level $\sim (N_{\lambda\sim d})_{\rm max}$, the filament cluster, which consists of the smaller filaments with size $\lambda=0.83., It is apparent that the progenitors of the lower redshift E+A's are very different from those at $z=0.83$. + As with their huninositv. the E|As with the ehest internal velocity dispersions are found in our nios distant cluster.," As with their luminosity, the E+A's with the highest internal velocity dispersions are found in our most distant cluster." + Another key result from our analvsis is that iu the owest redshift cluster. we fud no counterparts to the xieht. high σ late-tvpes found at 2=0.83.," Another key result from our analysis is that in the lowest redshift cluster, we find no counterparts to the bright, high $\sigma$ late-types found at $z=0.83$." + The a>200 galaxies iu MS105L include SO/a-Sa’s. E|A’s. spirals. aud mergers while the only galaxies in CLI358 with such high dispersions are E-SO’s (Fies. 2???)).," The $\sigma>200$ galaxies in MS1054 include S0/a-Sa's, E+A's, spirals, and mergers while the only galaxies in CL1358 with such high dispersions are E-S0's (Figs. \ref{nsigma_hist} +\ref{rh_lognsigma}) )." + If we assume that. eiven their similar cluster dispersions (Table ο). CL1358 (2= 0.33) is an evolved. version of MS1051 (2= 0.83). then the wide mis of hieh o svstenis in MS105£ iust be morphologically transformed iuto E-SOs within ~2.5 Gar.," If we assume that, given their similar cluster dispersions (Table \ref{clusters}) ), CL1358 $z=0.33$ ) is an evolved version of MS1054 $z=0.83$ ), then the wide mix of high $\sigma$ systems in MS1054 must be morphologically transformed into E-S0's within $\sim2.5$ Gyr." + The E|A phase may be an iuteeral step in this process., The E+A phase may be an integral step in this process. + The οΑν in our sample arc found at Πρες of ~1ου9005 kpe (Fie. ??3)., The E+A's in our sample are found at $R_{BCG}$ of $\sim100-900$ kpc (Fig. \ref{dzsigma_Rbcg}) ). + Like D99. we find that E|A’s tend to avoid the 3uner cluster core (Προς=1005 kpcj.," Like D99, we find that E+A's tend to avoid the inner cluster core $R_{BCG}\lesssim100$ kpc)." +" At.Ξ0:50, three of the eight E|A’s are associated with a large subcluster (220members:?).. while at =0.58 the E|Αν are found in both the main cluster and massive subcluster (Fig. ??.."," At $z=0.83$, three of the eight E+A's are associated with a large subcluster \citep[$>20$ members;][]{tran:02}, while at $z=0.58$ the E+A's are found in both the main cluster and massive subcluster (Fig. \ref{dzsigma_Rbcg}," + muddle right)., middle right). + This sueeests that ~30% of E|Als. if not more. are associated with the eroups that are being accreted by the clusters.," This suggests that $\sim30$ of E+A's, if not more, are associated with the groups that are being accreted by the clusters." + Iu the following section. we atteiipt to form a colerent picture of the cluster E|A population at intermediate redshifts.," In the following section, we attempt to form a coherent picture of the cluster E+A population at intermediate redshifts." + Usiug the plysical properties detailed in ll. we determine if E|A’s would be equally as nuuerous iu aidnass selected sample aud test if EÀs are drawn frou the same parent population as regular clustermembers’. and establish a connection between the progenitors and descendauts of these systeuis.," Using the physical properties detailed in 4, we determine if E+A's would be equally as numerous in a mass selected sample and test if E+A's are drawn from the same parent population as regular cluster, and establish a connection between the progenitors and descendants of these systems." + As in ΕΙ. we only consider cluster mienibers brighter than Mp.=19.1Slogh.. aud E|A’s that satisfy our strict selection criteria (833.2).," As in 4, we only consider cluster members brighter than $M_{Be}=-19.1$, and E+A's that satisfy our strict selection criteria 3.2)." + One possible concern is how the varving richness of the three clusters affects the couclusious drawn frou these data., One possible concern is how the varying richness of the three clusters affects the conclusions drawn from these data. + Wowever. we cluphasize it is the relative uunuber of spectra that is iurportaut.," However, we emphasize it is the relative number of spectra that is important." + Our large sample of confined cluster members (> 120/cluster) combined with the extensive spectroscopic and photometric properties we have gathered allows us to make a 1ieauimeful analysis of the cluster E|A population., Our large sample of confirmed cluster members $>120$ /cluster) combined with the extensive spectroscopic and photometric properties we have gathered allows us to make a meaningful analysis of the cluster E+A population. + We find the fraction of E|A galaxies in intermediate redshift clusters ranges from 7.13% (Table ??))., We find the fraction of E+A galaxies in intermediate redshift clusters ranges from $7-13$ (Table \ref{eafractions}) ). + However. we note our spectroscopic survey is magnitude lited.," However, we note our spectroscopic survey is magnitude limited." + From refbrieht.. we know E|As can be brightened by as uch as AATp.~1.25mae. aud so the E|A fraction in aselected cluster sample might be lower.," From \\ref{bright}, we know E+A's can be brightened by as much as $\Delta M_{Be}\sim1.25$mag, and so the E+A fraction in a cluster sample might be lower." + Tere we determine the influence of brighteniug on the ΕΙA fraction and estimate a mass selected fraction., Here we determine the influence of brightening on the E+A fraction and estimate a mass selected fraction. +" We first use the Schechter Iuuinositv fiction (7) to populate cluster menmbers as a function of magnitude: at DomO83. Mj,19.5 imag aud à=1 (7)."," We first use the Schechter luminosity function \citep{schechter:76} to populate cluster members as a function of magnitude; at $z=0.83$, $M_{Be}^{\ast}=-19.5$ mag and $\alpha=-1$ \citep{hoekstra:00}." +" Since E|As are brightened by _{med}=0.25$ mag (see \\ref{bright}) ), they follow a luminosity function with $M_{Be}^{\ast}=-19.75$ mag." + By combining the two luminosity fuuctious. we can estimate approximately how biased a luminosity selected sample is (Fig. 2?)).," By combining the two luminosity functions, we can estimate approximately how biased a luminosity selected sample is (Fig. \ref{lumfunc}) )." + Note this approach assumes 1) all E|A’s are brightened by 0.25 maes aud 2) E|Avs wave the same à as regular cluster menibers., Note this approach assumes 1) all E+A's are brightened by $0.25$ mags and 2) E+A's have the same $\alpha$ as regular cluster members. +" If of he members are E|Avs. ie. if the total chister Iuuinositv ""unction conprises reenlar and brightened. we estimate the E|A yaction in a luminosity selected sample (Mp,—zx19.1 5logh)) is ~1/3 larger than that of a ass selected suuple."," If of the members are E+A's, i.e. if the total cluster luminosity function comprises regular and brightened, we estimate the E+A fraction in a luminosity selected sample $M_{Be}\leq-19.1$ ) is $\sim1/3$ larger than that of a mass selected sample." + Depending ou the magnitude limit. the E|A Traction dn a mass selected siuuple can differ bv ~30% conrpared to a maguitude selected fraction.," Depending on the magnitude limit, the E+A fraction in a mass selected sample can differ by $\sim30$ compared to a magnitude selected fraction." +"Iu Coma. known E|Às are low luminosity (L«ο,LL""). low dispersion (a«150 iy svstenis that are uulikely to evolve into massive carly-type members (??7)..","In Coma, known E+A's are low luminosity $L<0.4L^{\ast}$ ), low dispersion $\sigma<150$ ) systems that are unlikely to evolve into massive early-type members \citep{caldwell:96,caldwell:99,poggianti:03}." + Towever. we find this is not the case at 2>0.3.," However, we find this is not the case at $z>0.3$." + From Fies., From Figs. + ?7 TUS we see that at 2=0.33. E-SQO's aud SO/a-Sa’s are the onlv logical descendauts of the high cispersion (o>1950 ')) BE]A’s at 2=O83.," \ref{nsigma_hist} \ref{rh_lognsigma}, we see that at $z=0.33$, E-S0's and S0/a-Sa's are the only logical descendants of the high dispersion $\sigma>150$ ) E+A's at $z=0.83$." +" The EJA phase lay signify the trausforiiationu of earlv-tvpoe spirals iuto Τομ, and stronely star-forming spirals iuto SO/a-Sas."," The E+A phase may signify the transformation of early-type spirals into E-S0's, and strongly star-forming spirals into S0/a-Sa's." +" The voune stellar ages implied by the E|A phase may seein to conflict with the old stellar ages (:,> 2) derived from studies usine the FP and absorption liue streneths (2773.."," The young stellar ages implied by the E+A phase may seem to conflict with the old stellar ages $z_f>2$ ) derived from studies using the FP and absorption line strengths \citep{kelson:97,vandokkum:98b,kelson:01}." + However. these ages represent the mean epoch of star formation aud do not preclude activity at Doc2.," However, these ages represent the mean epoch of star formation and do not preclude activity at $z<2$." + Furthermore. it is not clear whether alb salaxies uudergo the E|A phase.," Furthermore, it is not clear whether all galaxies undergo the E+A phase." + Also note that the total starburst population cau be as little as of the galaxy’s final stellar imuass (7). , Also note that the total starburst population can be as little as of the galaxy's final stellar mass \citep{barger:96}. . +Assuming the majority of their stars formed at zy> 2. even eaxbv-tyvpe members eau be E|As.," Assuming the majority of their stars formed at $z_f>2$ , even early-type members can be E+A's." + The connection between E|A progenitors and descendants aerees very well with the concept of “progenitor bias” introduced by ?.., The connection between E+A progenitors and descendants agrees very well with the concept of “progenitor bias” introduced by \citet{vandokkum:01}. + Du this scenario. as manyas of present dav early-type members are transformed from (later) galaxy types at :< 1l.," In this scenario, as manyas of present day early-type members are transformed from (later) galaxy types at $z<1$ ." + This morphological evolution is strouely supported by the likely transformation of the IE]À's at 2=0.83 to early-type members by i= 0:33., This morphological evolution is strongly supported by the likely transformation of the E+A's at $z=0.83$ to early-type members by $z=0.33$ . +Much corroborating evidence is presented for this conclusion is presented in the literature.,Much corroborating evidence is presented for this conclusion is presented in the literature. + A particularly distinctive feature of the YH GCs is their distribution of core radii 2004;; see also Mackey&vandenBergh 2005))., A particularly distinctive feature of the YH GCs is their distribution of core radii \citeauthor{Mackey04} \citeyear{Mackey04}; ; see also \citeauthor{MackeyvdB05} \citeyear{MackeyvdB05}) ). +" The core radii (r.) of the YH GCs shows a very long tail to very large radii (all but one GC with r,>9 pc resides in the Mackey&Gilmore grouping of GCs associated with the outer halo GCs).", The core radii $r_c$ ) of the YH GCs shows a very long tail to very large radii (all but one GC with $r_c > 9$ pc resides in the \citeauthor{Mackey04} grouping of GCs associated with the outer halo GCs). +" Furthermore, the Το distribution of these GCs shows no statistical difference to that observed from a compilation of GCs from the LMC, Fornax and Sagittarius dwarf galaxies (Mackey&Gilmore2003).."," Furthermore, the $r_c$ distribution of these GCs shows no statistical difference to that observed from a compilation of GCs from the LMC, Fornax and Sagittarius dwarf galaxies \citep{Mackey03b}." +" Together with the similarity in morphology of the horizontal branch between the external GCs and the YH GC grouping, this evidence leads Mackey&Gilmore(2004) to propose that all the YH GCs are accreted."," Together with the similarity in morphology of the horizontal branch between the external GCs and the YH GC grouping, this evidence leads \citet{Mackey04} to propose that all the YH GCs are accreted." + The implications of the size distribution for an accreted origin of the outer halo GCs are elucidated in the study of Hurley&Mackey(2010)., The implications of the size distribution for an accreted origin of the outer halo GCs are elucidated in the study of \citet{Hurley10}. +". In this study, the authors use simulations of star clusters in a tidal field to investigate the conditions required to produce and sustain a GC of large core radius."," In this study, the authors use N-body simulations of star clusters in a tidal field to investigate the conditions required to produce and sustain a GC of large core radius." +" Hurley&Mackey show that clusters may be born with a range of r, governed by how much the cluster fills its initial tidal radius.", \citeauthor{Hurley10} show that clusters may be born with a range of $r_c$ governed by how much the cluster fills its initial tidal radius. + When a cluster completely fills its natal tidal radius an extended GC can result (τε>10 pc)., When a cluster completely fills its natal tidal radius an extended GC can result $r_c > 10$ pc). + Conditions for a cluster to completely fill its tidal radius at birth are optimal in regions where background tidal forces are low: such conditions are best satisfied at large distances from MW-like galaxies and in dwarf systems (see discussion in Elmegreen 2008 and 2009))., Conditions for a cluster to completely fill its tidal radius at birth are optimal in regions where background tidal forces are low: such conditions are best satisfied at large distances from MW-like galaxies and in dwarf systems (see discussion in \citeauthor{Elmegreen08} \citeyear{Elmegreen08} and \citeauthor{DaCosta09} \citeyear{DaCosta09}) ). + This again argues for the accretion of the outer halo GCs to the MW., This again argues for the accretion of the outer halo GCs to the MW. + The timing of the delivery of the outer Young Halo GCs through accretion is not constrained by the physical parameters of the GCs., The timing of the delivery of the outer Young Halo GCs through accretion is not constrained by the physical parameters of the GCs. +" Gnedin(1997) describe the stability of the MW's GCs against two-body relaxation, tidal truncation, and tidal shocks due to passage through the disk and due to close proximity to the bulge."," \citet{Gnedin97} describe the stability of the MW's GCs against two-body relaxation, tidal truncation, and tidal shocks due to passage through the disk and due to close proximity to the bulge." +" With the exception of two clusters (Pal 1 and Pal 13), GCs of R >10 kpc are expected to be long-lived, with lifetimes of between 5 and 100 Hubble times."," With the exception of two clusters (Pal 1 and Pal 13), GCs of R $> 10$ kpc are expected to be long-lived, with lifetimes of between 5 and 100 Hubble times." +" Hence, by this criterion, these systems could have been accreted into the MW at any stage over the last Hubble time."," Hence, by this criterion, these systems could have been accreted into the MW at any stage over the last Hubble time." + We can ask the question: how many satellites of a given mass are required to contribute the observed (conservative) 22 Young Halo GCs at R >10 kpc., We can ask the question: how many satellites of a given mass are required to contribute the observed (conservative) 22 Young Halo GCs at R $>10$ kpc. +" Given the specific frequency of GCs (Sy)as a function of host galaxy luminosity (first introduced by Harris&vandenBergh 1981,, and ddiscussed recently by Georgievetal. 2010)), we find this would require for example, approximately 2 Magellanic-like (My~—18 with GC Sy~ 1) systems or 22 systems with Sculptor-like luminosities (My—11 with GC Sy~ 70)."," Given the specific frequency of GCs $S_{N}$ )as a function of host galaxy luminosity (first introduced by \citeauthor{Harris81} \citeyear{Harris81}, , and discussed recently by \citeauthor{Georgiev10} \citeyear{Georgiev10}) ), we find this would require for example, approximately 2 Magellanic-like $_{V} \sim -18$ with GC $S_{N} \sim 1$ ) systems or 22 systems with Sculptor-like luminosities $_{V} \sim -11$ with GC $S_{N} \sim 70$ )." + If we then consider that the number of accreted clusters islikely to besupplemented by 10-12 OH clusters (Mackey&Gilmore2004) we estimate that the MW may have experienced mergers with 3 Magellanic-like to 30, If we then consider that the number of accreted clusters islikely to besupplemented by 10-12 OH clusters \citep{Mackey04} we estimate that the MW may have experienced mergers with 3 Magellanic-like to 30 +There were two approaches we considered in estimating the metallicities of the NGC 524 GCs from our integrated spectra.,There were two approaches we considered in estimating the metallicities of the NGC 524 GCs from our integrated spectra. + The empirical calibration of Brodie&Lluchra (1990) was specifically designed to estimate metallicitics for extragalactic GCs from. low-resolution. ancl potentially low S/N spectra.," The empirical calibration of \citeANP{Brodie90} (1990) was specifically designed to estimate metallicities for extragalactic GCs from low-resolution, and potentially low S/N spectra." + Alternatively. stellar population models may be emploved to derive metallicities either by assuming an age for the GCs (necessary due to the agemetallicity degeneracy). or by allowing age cliscrimination to come from Balmer indices.," Alternatively, stellar population models may be employed to derive metallicities either by assuming an age for the GCs (necessary due to the age–metallicity degeneracy), or by allowing age discrimination to come from Balmer indices." + The former technique ids tied to Alilky Way and Andromeda GC calibrators with independently derived, The former technique is tied to Milky Way and Andromeda GC calibrators with independently derived +In Figure 3 we show a histogram of compact radio source monochromatic 18cm power [or M32. and for each of the two nuclei of Arp 220.,"In Figure 3 we show a histogram of compact radio source monochromatic 18cm power for M82, and for each of the two nuclei of Arp 220." + The detection threshold for Arp 220 is ~LOM OW |! while that for M82 is ~LON W |.," The detection threshold for Arp 220 is $\sim 10^{19.6}$ W $^{-1}$, while that for M82 is $\sim 10^{18.0}$ W $^{-1}$." + It is notable that only one of the AIS2 sources [alls above the Arp 220 luminosity detection threshold., It is notable that only one of the M82 sources falls above the Arp 220 luminosity detection threshold. + If the supernova rate in M32 is 50 times lower than in Arp 220. consistent with the ratio of FIR luminosities. we expect only one RSN in M32 of comparable vouth to the 50 that we have detected in Arp 220.," If the supernova rate in M82 is 50 times lower than in Arp 220, consistent with the ratio of FIR luminosities, we expect only one RSN in M82 of comparable youth to the 50 that we have detected in Arp 220." + In fact. the last RSN to appear in M82 was ~40 vears ago. so another is somewhat overdue.," In fact, the last RSN to appear in M82 was $\sim$ 40 years ago, so another is somewhat overdue." + The bright M32 source 41.95+57.5 is decaving al δις νε. and while it may be a plausible candidate for a voung RSN. there is strong evidence (hat this object is alwpical. may not be an RSN. and may be much older (Pedlar et al.," The bright M82 source 41.95+57.5 is decaying at $\sim$ /yr, and while it may be a plausible candidate for a young RSN, there is strong evidence that this object is atypical, may not be an RSN, and may be much older (Pedlar et al." + 1999. MeDonald et al.," 1999, McDonald et al." + 2001. Beswick et al.," 2001, Beswick et al." + 2006 submitted)., 2006 submitted). + The hypothesis that the starburst in M32 is a scaled-down version of the same phenomenon occurring in Arp 220 is thus attractive. and supported by the data.," The hypothesis that the starburst in M82 is a scaled-down version of the same phenomenon occurring in Arp 220 is thus attractive, and supported by the data." + Based on (his. we can make an estimate of the number and strength of supernova remnants. similar to those observed in M32. that lie below our detection threshold in Arp 220.," Based on this, we can make an estimate of the number and strength of supernova remnants, similar to those observed in M82, that lie below our detection threshold in Arp 220." + This number should scale with the FIR huminosity. and the resulting total flix density from 1500 SNRs is 11 mJy. comparable to the total [Iux density in (he 49 detected sources.," This number should scale with the FIR luminosity, and the resulting total flux density from 1500 SNRs is $\sim$ 11 mJy, comparable to the total flux density in the 49 detected sources." + Based on the observed sizes of (he M82 sources (e.g. Muxlow et al., Based on the observed sizes of the M82 sources (e.g. Muxlow et al. + 1994. \leDonald οἱ al.," 1994, McDonald et al." + 2001). the SNRs will have a volume filling factor of up to a few percent in the Arp 220 nuclei.," 2001), the SNRs will have a volume filling factor of up to a few percent in the Arp 220 nuclei." + The predicted Ll mJy will contribute to the apparently diffuse emission from the Arp 220 nuclei. but the Πας density will actually reside in angularly compact but undetectably weak supernova renimant(s.," The predicted 11 mJy will contribute to the apparently diffuse emission from the Arp 220 nuclei, but the flux density will actually reside in angularly compact but undetectably weak supernova remnants." + This is in addition to the 12 mJv of the nuclear flux density that resides in the detected sources., This is in addition to the $\sim$ 12 mJy of the nuclear flux density that resides in the detected sources. + Together. these total ~12% of the nuclear aud ~s% of the total LSem flux density in Arp 220.," Together, these total $\sim$ of the nuclear and $\sim$ of the total 18cm flux density in Arp 220." + This constitutes a measure of the number of relativistic electrons (hat remain trapped in hiel-emissivily regions of supernova renmantis. and that have not vet diffused into the lower emissivity environment of the general ISA.," This constitutes a measure of the number of relativistic electrons that remain trapped in high-emissivity regions of supernova remnants, and that have not yet diffused into the lower emissivity environment of the general ISM." + This conclusion must be tempered by (he realization (hat (he evolution of older supernova remnants in the dense Arp 220 environment may differ svstematically from Chat occurring in M82., This conclusion must be tempered by the realization that the evolution of older supernova remnants in the dense Arp 220 environment may differ systematically from that occurring in M82. + While the hypothesized weak SNRs may be undetectable in continuum emission. it is possible (hat they. will contribute compact spots of enhanced continuum brightness. which may exhibit OLI maser amplification to detectable levels.," While the hypothesized weak SNRs may be undetectable in continuum emission, it is possible that they will contribute compact spots of enhanced continuum brightness, which may exhibit OH maser amplification to detectable levels." + Interpretation of OII maser properties ol galaxies such as Arp 220 should take this possibility into account., Interpretation of OH maser properties of galaxies such as Arp 220 should take this possibility into account. +pure starbursts.,pure starbursts. + This result can be seen in Figure 1 of Desaietal.(2007) which compares the average starburst spectrum from Drandletal.(2006) (o the average spectrum of heavily absorbed ULIBRGs., This result can be seen in Figure 1 of \citet{des07} which compares the average starburst spectrum from \citet{bra06} to the average spectrum of heavily absorbed ULIRGs. + The to ratio is approximately 1.0 in both cases. even though the feature is within the silicate absorption so should be suppressed i£ it is obscured by (he same silicate absorption (hat obscures the buried source.," The to ratio is approximately 1.0 in both cases, even though the feature is within the silicate absorption so should be suppressed if it is obscured by the same silicate absorption that obscures the buried source." + The average absorbed ULIRG shown in Desaietal.(2007) has a silicate optical depth of 1.5., The average absorbed ULIRG shown in \citet{des07} has a silicate optical depth of 1.5. + For (his absorption. the feature is extincted by 1.1 mag compared to 0.48 mag of extinction for the feature. using the extinction curve of DraineandLi.(2001).," For this absorption, the feature is extincted by 1.1 mag compared to 0.48 mag of extinction for the feature, using the extinction curve of \citet{dra01}." +. This differential extinction would imply that the observed to ratio would be 0.56 for an intrinsic ratio of 1.0., This differential extinction would imply that the observed to ratio would be 0.56 for an intrinsic ratio of 1.0. + That such a lower ratio is not observed in the absorbed ULIRGs is evidence that their starbursts are not extincted by the same dust that produces the silicate absorption., That such a lower ratio is not observed in the absorbed ULIRGs is evidence that their starbursts are not extincted by the same dust that produces the silicate absorption. + This reasoning justifies treating ULIRG starbursts the same as other starbursts regarding exGinelion corrections., This reasoning justifies treating ULIRG starbursts the same as other starbursts regarding extinction corrections. +" Therefore. we do not apply exGuelion corrections to the ULIRGs and will apply the same transformation between PAI] luminosities and L;, to the ULIRG starbursts as to the other starbursts."," Therefore, we do not apply extinction corrections to the ULIRGs and will apply the same transformation between PAH luminosities and $L_{ir}$ to the ULIRG starbursts as to the other starbursts." + The plotted. values and [fitted envelope in Figure 3 derive strictly. [roii observed. data. with no assumptions regarding templates or spectral shapes for starburst galaxies.," The plotted values and fitted envelope in Figure 3 derive strictly from observed data, with no assumptions regarding templates or spectral shapes for starburst galaxies." +" The only assumption is that the values of pL, μη) arise purely [rom a starburst. with no contribution from an AGN."," The only assumption is that the values of $\nu$ $_{\nu}$ $\mu$ m) arise purely from a starburst, with no contribution from an AGN." + As discussed above. the sample was chosen in order to tse only pure starbursts with no evidence that the PAIL complex is diluted by an AGN. or to use sources with published Inminosities of individual PAIL features for the starburst component when there is evidence of an AGN.," As discussed above, the sample was chosen in order to use only pure starbursts with no evidence that the PAH complex is diluted by an AGN, or to use sources with published luminosities of individual PAH features for the starburst component when there is evidence of an AGN." +" The pL, μαι) in Figure 3 can be transformed to bolometric luminosities (L;.) and star formation rates (SFR) using empirically determined conversions.", The $\nu$ $_{\nu}$ $\mu$ m) in Figure 3 can be transformed to bolometric luminosities $L_{ir}$ ) and star formation rates (SFR) using empirically determined conversions. + Such conversions ancl their relevant uncertainties are subject to further refinement. but this would not affect the data shown in Figure 3.," Such conversions and their relevant uncertainties are subject to further refinement, but this would not affect the data shown in Figure 3." + For further discussion. the conversions which are adopted are those," For further discussion, the conversions which are adopted are those" +the intensity in the region below the Lyman edge.,the intensity in the region below the Lyman edge. + We will describe this in more detail in section 3 below., We will describe this in more detail in section 3 below. + This approach requires the observations to be obtained through an aperture that encloses the bulk of the starburst’s emission (so that a global constraint is obtained)., This approach requires the observations to be obtained through an aperture that encloses the bulk of the starburst's emission (so that a global constraint is obtained). + It also requires that the width of instrumental spectral line-spread function is significantly smaller than the characteristic velocity dispersion in the starburst (so that the interstellar absorption lines are well resolved)., It also requires that the width of instrumental spectral line-spread function is significantly smaller than the characteristic velocity dispersion in the starburst (so that the interstellar absorption lines are well resolved). +" Finally, the data need to have a high signal-to-noise ratio in the far- UV continuum so that useful constraints are derived."," Finally, the data need to have a high signal-to-noise ratio in the far- UV continuum so that useful constraints are derived." +" Based on these considerations, we will consider two data sets in this paper."," Based on these considerations, we will consider two data sets in this paper." + The first consists of the sample of eighteen galaxies studied by H01 and G09., The first consists of the sample of eighteen galaxies studied by H01 and G09. + These are local starburst or star-forming galaxies observed with the Far-Ultraviolet Spectroscopic Explorer (FUSE - Moos et al., These are local starburst or star-forming galaxies observed with the Far-Ultraviolet Spectroscopic Explorer (FUSE - Moos et al. +" 2000), each having signal-to-noise better than 4.6 per 0.078 25 km spectral element in the FUSE LiF1A channel(~ (see s!)"," 2000), each having signal-to-noise better than 4.6 per 0.078 $\sim$ 25 km $^{-1}$ ) spectral element in the FUSE LiF1A channel (see G09)." + The observations and properties of this sample are G09).described in Table 1., The observations and properties of this sample are described in Table 1. + Three of these galaxies are in fact LBAs without a DCO: Mrk 54 (Deharveng et al., Three of these galaxies are in fact LBAs without a DCO: Mrk 54 (Deharveng et al. + Haro 11 (Grimes et al.," 2001), Haro 11 (Grimes et al." +" 2007), and VV 114 et "," 2007), and VV 114 (Grimes et al." +"2001),al.", 2006). +" However, most of these galaxies have (Grimesconsiderably 2006).lower UV luminosities and star-formation rates than the LBAs."," However, most of these galaxies have considerably lower UV luminosities and star-formation rates than the LBAs." +" They also span a much broader range in galaxy mass and metallicity (see G09 and O09, and compare Table 1 and 2)."," They also span a much broader range in galaxy mass and metallicity (see G09 and O09, and compare Table 1 and 2)." + The second is a sample of eight LBAs observed with the Cosmic Origins Spectrograph Green 2009) on the Hubble Space Telescope (Froning 11727: PI T. Heckman)., The second is a sample of eight LBAs observed with the Cosmic Origins Spectrograph (Froning Green 2009) on the Hubble Space Telescope (Program 11727: PI T. Heckman). + These are members of a (Programsample of 31 LBAs with HST UV images discussed by O09 and were selected for spectroscopy based on a high UV flux through the COS aperture and a compact UV size (so that the COS line-spread function is not significantly degraded)., These are members of a sample of 31 LBAs with HST UV images discussed by O09 and were selected for spectroscopy based on a high UV flux through the COS aperture and a compact UV size (so that the COS line-spread function is not significantly degraded). + These observations and the properties of this sample are listed in Table 2 and HST images are shown in Figure 1., These observations and the properties of this sample are listed in Table 2 and HST images are shown in Figure 1. + In the discussion to follow we will refer to the eight LBAs with HST COS data and the three LBAs with FUSE data as the LBA sample., In the discussion to follow we will refer to the eight LBAs with HST COS data and the three LBAs with FUSE data as the LBA sample. + We will refer to the other fifteen galaxies with FUSE data as the local starburst sample., We will refer to the other fifteen galaxies with FUSE data as the local starburst sample. + The observations and data reduction of the FUSE sample have been described in detail in HO1 and G09., The observations and data reduction of the FUSE sample have been described in detail in H01 and G09. + We refer the reader to these papers., We refer the reader to these papers. +" All the data were obtained through the 30 x 30 arcsec LWRS aperture, except for the cases of NGC 5253 and NGC 7714 (which used the 4 x 20 arcsec MDRS aperture)."," All the data were obtained through the 30 x 30 arcsec LWRS aperture, except for the cases of NGC 5253 and NGC 7714 (which used the 4 x 20 arcsec MDRS aperture)." + As shown by G09 these apertures encompass most or all of the starburst in the far-UV., As shown by G09 these apertures encompass most or all of the starburst in the far-UV. + These spectra cover the observed wavelength range from 905 to 1187 Table 1 for the corresponding range in the rest-((see, These spectra cover the observed wavelength range from 905 to 1187 (see Table 1 for the corresponding range in the rest-frame). +" Depending on the angular size of the starburst in the frame).far-UV, the instrumental spectral resolution is R~ 5000 to 14,000, corresponding to a velocity dispersion of ac 9 to 25 km s-! "," Depending on the angular size of the starburst in the far-UV, the instrumental spectral resolution is $R \sim$ 5000 to 14,000, corresponding to a velocity dispersion of $\sigma \sim$ 9 to 25 km $^{-1}$ (G09)." +In all cases the interstellar absorption lines in the (G09).starbursts are well resolved., In all cases the interstellar absorption lines in the starbursts are well resolved. + For the HST-COS sample we have used the COS G130M and G160M gratings to obtain spectra of our eight targets., For the HST-COS sample we have used the COS G130M and G160M gratings to obtain spectra of our eight targets. +" As can be seen in Figure 1, the COS aperture encompasses most or all of the galaxy."," As can be seen in Figure 1, the COS aperture encompasses most or all of the galaxy." + We have retrieved these data from the HST MAST archive after they have been processed through the standard COS pipeline., We have retrieved these data from the HST MAST archive after they have been processed through the standard COS pipeline. + The merged spectra cover a range from about 1160 to 1780 with the corresponding range in the rest- frame, The merged spectra cover a range from about 1160 to 1780 with the corresponding range in the rest- frame +of <2 mCrab in bothdetections!.,of $<2$ mCrab in both. +. Analysing all ppublic data and using the data available on the public page of the GGalactic Bulge program!. ? discovered a likely period of ~185 days as the source was detected by aat a level of z5c for a few days during March and September each year between 2003-2007.," Analysing all public data and using the data available on the public page of the Galactic Bulge $^{1}$, \citet{Zuritaal07} discovered a likely period of $\sim185$ days as the source was detected by at a level of $\gtrsim 5 \sigma$ for a few days during March and September each year between 2003–2007." + Following this announcement. pperformed a target of opportunity (ToO) observation of 5 ks on March 30. 2007 (?)s7!..," Following this announcement, performed a target of opportunity (ToO) observation of 5 ks on March 30, 2007 \citep{Romanoal07a}." +". They detected a brightsource at the position R.A. (2000) =1749'""06.8 and Dec. =—27°3230.6” (6:93 at confidence). 51"" away from the pposition-."," They detected a brightsource at the position R.A. (2000) $=\ra{17}{49}{06.8}$ and Dec. $=\dec{-27}{32}{30.6}$ $\arcsec$ at confidence), $51\arcsec$ away from the ." +. Its spectrum could be fitted with an absorbed power-law (Ny=23x42-4107ο. FPΞ 2.577%) and the observed 2-10 keV flux is ~107!!ergsem77s7!.," Its spectrum could be fitted with an absorbed power-law $\nh=23_{-10}^{+14}\times10^{22}\ \unit{cm}{-2}$, $\Gamma=2.5_{-1.7}^{+2.0}$ ) and the observed 2–10 keV flux is $\sim10^{-11}\ \ecms$." + The Swift//UVOT telescope did not detect any optical counterpart with a 3c upper limit of V=20.67 mag., The /UVOT telescope did not detect any optical counterpart with a $3\sigma$ upper limit of $V=20.67$ mag. + Within the error circle. ? report three 2MASS candidate counterparts whose infrared (HR) magnitudes in the JHK bands suggest a strong optical extinction of 20 mag.," Within the error circle, \citet{Romanoal07a} report three 2MASS candidate counterparts whose infrared (IR) magnitudes in the JHK bands suggest a strong optical extinction of 20 mag." + Only one candidate is compatible with a supergiant., Only one candidate is compatible with a supergiant. + Thus. the nature of rremains a mystery.," Thus, the nature of remains a mystery." + aalso performed a ToO observation of the source during the expected outburst of 2007 March., also performed a ToO observation of the source during the expected outburst of 2007 March. + From this observation. reported the discovery of a pulsation of ~132 s. The pulse profile displays a double-peak structure with a pulse fraction of ~30% in the 2-10 keV energy range.," From this observation, \citet{Karaseval07,Karaseval08} reported the discovery of a pulsation of $\sim132$ s. The pulse profile displays a double-peak structure with a pulse fraction of $\sim30$ in the 2–10 keV energy range." + They also detected a pulsation during the outburst detected by oon Sept. 8-10. 2003 in the 20-60 keV energy range with a higher pulse fraction of50G.," They also detected a pulsation during the outburst detected by on Sept. 8–10, 2003 in the 20–60 keV energy range with a higher pulse fraction of." +. Here we report multiwavelength observations performed on wwithJNTEGRAL..XMM-Newton... and. the ESO/NTT telescope.," Here we report multiwavelength observations performed on with, and the ESO/NTT telescope." + In Sect. ??..," In Sect. \ref{secObs}," + we first describe the observations and the data analysis of each instrument., we first describe the observations and the data analysis of each instrument. + Then. we present the results in Sect. ??..," Then, we present the results in Sect. \ref{secRes}." + Finally. we finish with a discussion and the conclusion on the nature of the source in Sect. ??..," Finally, we finish with a discussion and the conclusion on the nature of the source in Sect. \ref{secDis}." + The present work is based on data of two high-energy space missions. citepWinkleral03 and citepJansenalO!.. of the European Space Agency (ESA).," The present work is based on data of two high-energy space missions, \\citep{Winkleral03} and \\citep{Jansenal01}, of the European Space Agency (ESA)." + Multi- follow-up observations were also performed with the 3.5 m New Technology Telescope (NTT) at La Silla Observatory. Chile.," Multi-wavelength follow-up observations were also performed with the 3.5 m New Technology Telescope (NTT) at La Silla Observatory, Chile." + The INTErnational Gamma-Ray Astrophysics Laboratory TEGRAL)) is a hard X-ray and sspacecraft (S/C) laboratory operating since Oct. 2002., The INTErnational Gamma-Ray Astrophysics Laboratory ) is a hard X-ray and spacecraft (S/C) laboratory operating since Oct. 2002. + The scientific payload is composed of four instruments., The scientific payload is composed of four instruments. + However. only data from the hard X-ray and soft ccoded-mask imager IBIS/ISGRI (15 keV-1 MeV) (??) are going to be considered in this work.," However, only data from the hard X-ray and soft coded-mask imager IBIS/ISGRI (15 keV–1 MeV) \citep{Ubertinial03,Lebrunal03} are going to be considered in this work." + The imager possesses a wide field of view (FOV) of 29° square with a spatial resolution of 12’., The imager possesses a wide field of view (FOV) of $\degr$ square with a spatial resolution of $\arcmin$. + The source is located near the galactic centre at a distance of 1.67., The source is located near the galactic centre at a distance of $\degr$. + As the galactic centre is one of the major scientific goals ofINTEGRAL.. the source's field has been extensively observed.," As the galactic centre is one of the major scientific goals of, the source's field has been extensively observed." + All public data available in March 2007 for hhave been considered in this work., All public data available in March 2007 for have been considered in this work. + Only pointings where the source is located less than 14 from the FOV centre and whose time exposure is longer than 600 s are kept., Only pointings where the source is located less than $\degr$ from the FOV centre and whose time exposure is longer than 600 s are kept. + In total. we collected 4759 pointings distributed in 129 revolutions of the S/C that goes from Feb. 2003 (revolution 46. MJD 52698.0) to Oct. 2005 (revolution 370. MJD 53670.1).," In total, we collected 4759 pointings distributed in 129 revolutions of the S/C that goes from Feb. 2003 (revolution 46, MJD 52698.0) to Oct. 2005 (revolution 370, MJD 53670.1)." + The total exposure time on the source is 10.8 Ms 125.4 days) spanning 2.5 years of observations., The total exposure time on the source is 10.8 Ms 125.4 days) spanning 2.5 years of observations. + They are not equally. distributed along this period for scheduling reasons., They are not equally distributed along this period for scheduling reasons. + The ISGRI data were reduced using the Offline Scientific Analysis (OSA)) version 6.0 software that is publicly released by the SScience Data Centre (ISDC) (?).., The ISGRI data were reduced using the Offline Scientific Analysis ) version 6.0 software that is publicly released by the Science Data Centre (ISDC) \citep{Courvoisieral03}. + Individual sky images for each pointing were produced in the energy band 22-50 keV. Sky mosaics with longer exposures were built combining pointings in which the source is not detected at a δ.σ level or higher in individual pointings., Individual sky images for each pointing were produced in the energy band 22–50 keV. Sky mosaics with longer exposures were built combining pointings in which the source is not detected at a $\sigma$ level or higher in individual pointings. + The light curves were built using the imaging products., The light curves were built using the imaging products. + The source count rate was extracted with help of the tool (version 1.4) that is part of the OSA package., The source count rate was extracted with help of the tool (version 1.4) that is part of the OSA package. + Detections of the source in mosaics are considered at a 6c level or higher., Detections of the source in mosaics are considered at a $\sigma$ level or higher. + We extracted à spectrum of the source during the first bright flare detected with ISGRI., We extracted a spectrum of the source during the first bright flare detected with ISGRI. + The spectral extraction was performed using the recently released OSA version 7.0., The spectral extraction was performed using the recently released OSA version 7.0. + The source spectrum was extracted with within OSA for each pointing., The source spectrum was extracted with within OSA for each pointing. + Then. each individual spectra was summed to build one single spectrum of the source using the OSA toolpick.," Then, each individual spectra was summed to build one single spectrum of the source using the OSA tool." + The redistribution matrix. file (RMF) was rebinned into 5channels spread between 15 and 80 keV. Light curves with a binning of 10 s of the first bright flare observed with ISGRI were also extracted with, The redistribution matrix file (RMF) was rebinned into 5channels spread between 15 and 80 keV. Light curves with a binning of 10 s of the first bright flare observed with ISGRI were also extracted with +excellent performance is independent of whether the Edclington approximation. diffusion approximation. or flux-Iimited dilfusion approximation is emploved for the cloud. as well as of the optical depth assumed.,"excellent performance is independent of whether the Eddington approximation, diffusion approximation, or flux-limited diffusion approximation is employed for the cloud, as well as of the optical depth assumed." + Considering that tvpical disk instability caleulations with the diffusion approximation last [or only ~10? vr. the fact that these models show that the radiative (ransler scheme is highly accurate over (ime scales of al least ~109 vr is reassuring for the mechanism of giant planet formation by disk instability.," Considering that typical disk instability calculations with the diffusion approximation last for only $\sim 10^3$ yr, the fact that these models show that the radiative transfer scheme is highly accurate over time scales of at least $\sim 10^6$ yr is reassuring for the mechanism of giant planet formation by disk instability." + These moclels presented here test only the raciative (ransfer routines and other (hermodvnamical aspects of the Boss codes. not the coupling between these processes and the hyedrodynanmies (hat occurs in full disk instability models.," These models presented here test only the radiative transfer routines and other thermodynamical aspects of the Boss codes, not the coupling between these processes and the hydrodynamics that occurs in full disk instability models." + Ideally. one would test the full radiative hydrodynamics codes against analytical solutions.," Ideally, one would test the full radiative hydrodynamics codes against analytical solutions." + In the absence of such solutions. one can test the codes with respect to their ability (ο represent convective motions. which do involve a coupling of hvedrodsnamies and thermodsyvnamies.," In the absence of such solutions, one can test the codes with respect to their ability to represent convective motions, which do involve a coupling of hydrodynamics and thermodynamics." + Boss (2004) analvzed in detail the convective stability oL his disk instability models. and founda good agreement between where transient. upwellings and downwellings occurred ancl where the Schwarzschild criterion for convection was met.," Boss (2004) analyzed in detail the convective stability of his disk instability models, and found a good agreement between where transient, convective-like upwellings and downwellings occurred and where the Schwarzschild criterion for convection was met." + Bolev et al. (, Boley et al. ( +2007b) presented the results of several tests for convection in (heir codes. finding that convection occurred when it should have ancl did not occur when it should nol have.,"2007b) presented the results of several tests for convection in their codes, finding that convection occurred when it should have and did not occur when it should not have." + Convection and convective-like motions thus appear to be appropriately modeled by both the Boss and Boley et al., Convection and convective-like motions thus appear to be appropriately modeled by both the Boss and Boley et al. + codes., codes. + Boss Avhill (1992) described a variety of other Cests to which the code has been subjected. including the standard nonisothermal test case for protostellar collapse (tested on two different codes by Myhill Boss 1993). whose results have since been confirmed by Whitehouse Bate (2006).," Boss Myhill (1992) described a variety of other tests to which the code has been subjected, including the standard nonisothermal test case for protostellar collapse (tested on two different codes by Myhill Boss 1993), whose results have since been confirmed by Whitehouse Bate (2006)." + Further tests of the Boss ΔΙΝΕΙ (1992) code have been presented as follows: spatial resolution (Boss 2000. 2005): gravitational potential solver (Boss 2000. 2001. 2005). artificial viscosity (Boss 2006a): and radiative transfer (Boss 2001. 2007. 2008).," Further tests of the Boss Myhill (1992) code have been presented as follows: spatial resolution (Boss 2000, 2005); gravitational potential solver (Boss 2000, 2001, 2005), artificial viscosity (Boss 2006a); and radiative transfer (Boss 2001, 2007, 2008)." + Given (he ongoing theoretical debate over the viability of disk instability for giant planet formation. it will continue to be important for other workers to conduct their own tests of these key numerical issues.," Given the ongoing theoretical debate over the viability of disk instability for giant planet formation, it will continue to be important for other workers to conduct their own tests of these key numerical issues." + The r analvtical solution was derived while I was a lecturer al the Winter School on Exoplanets at the Theoretical Institute for Advanced Research in Astrophysics (TIARA) of the National Tsing Hua. University. in [IIsinehu. Taiwan.," The $r$ analytical solution was derived while I was a lecturer at the Winter School on Exoplanets at the Theoretical Institute for Advanced Research in Astrophysics (TIARA) of the National Tsing Hua University, in Hsinchu, Taiwan." + | thank the Acting Director of TIARA. Ronald Taam. for making possible my visit to TIARA.," I thank the Acting Director of TIARA, Ronald Taam, for making possible my visit to TIARA." + The 9 analytical solution was derived in part while I was a visitor at the Roval Observatory. Edinburgh and at St Andrews University in Scotland.," The $\theta$ analytical solution was derived in part while I was a visitor at the Royal Observatory, Edinburgh and at St Andrews University in Scotland." + I thank [νου Rice and lan Bonnell for making those visits possible. and the referee for promplting me to imvestigate this second lest case as well as for other good advice.," I thank Ken Rice and Ian Bonnell for making those visits possible, and the referee for prompting me to investigate this second test case as well as for other good advice." + E also thank Saucy Weiser [or computer svstems support at DTM., I also thank Sandy Keiser for computer systems support at DTM. + This research was supported in part by NASA Planetary Geology ancl Geophysics grant, This research was supported in part by NASA Planetary Geology and Geophysics grant +more than three hundred cool Ap stars from which we also found. several stars with very strong magnetic fields.,more than three hundred cool Ap stars from which we also found several stars with very strong magnetic fields. + The strongest. Geld of ΚΚ was found in 775049., The strongest field of kG was found in 75049. + Most probably this value is close to a physical limit for the observed magnetic field in cool Ap stars., Most probably this value is close to a physical limit for the observed magnetic field in cool Ap stars. + DWI and. WOE acknowledge support for this work from the Science and Technology Facilities Council (ος)., DWK and VGE acknowledge support for this work from the Science and Technology Facilities Council (STFC). + This research has made use of SIMDBAD database. operated. at CDS. Strasbourg. France.," This research has made use of SIMBAD database, operated at CDS, Strasbourg, France." +"outermost zones (Αι=115""— 155""). containing 33890 measured stars.","outermost zones $R_{gc} = +115''-155''$ ), containing 33890 measured stars." + The RGB spans a broad color range. suggesting a large range in metallicity. or very large internal photometric scatter. or both.," The RGB spans a broad color range, suggesting a large range in metallicity, or very large internal photometric scatter, or both." + Our ability to see the true metallicity spread of the RGB tip is limited by the F606W exposures. which set the very distinet red-edge cutoff to the data at Vx30 (for similar cases. see the NGC 3379 or NGC 5128 studies of Harris et al. 2002..," Our ability to see the true metallicity spread of the RGB tip is limited by the $F606W$ exposures, which set the very distinct red-edge cutoff to the data at $V \lesssim 30$ (for similar cases, see the NGC 3379 or NGC 5128 studies of Harris et al. \cite{har02}," + 2007b where the most metal-rich part of the population is cut off)., \cite{har07} where the most metal-rich part of the population is cut off). + A more specific demonstration of this point is shown in Figure 4.. where the combined photometry for the two outermost annuli is plotted along with fiducial tracks for 12-Gyr-old RGB stars over the metallicity range [Fe/H] =—-2.3 to +0.4.," A more specific demonstration of this point is shown in Figure \ref{cmd_fiducials}, where the combined photometry for the two outermost annuli is plotted along with fiducial tracks for 12-Gyr-old RGB stars over the metallicity range [Fe/H] $= -2.3$ to $+0.4$." + These tracks are the same ones used in previous studies of NGC 3128 and NGC 3379 (Harris et al. 2002. 2007b))," These tracks are the same ones used in previous studies of NGC 5128 and NGC 3379 (Harris et al. \cite{har02,har07}) )" + and are drawn primarily from the model library of VandenBerg et al. (2000))., and are drawn primarily from the model library of VandenBerg et al. \cite{vdb00}) ). + At the right-hand edge of the CMD. the detection limits set by the V filter prevent us from measuring any stars more metal-rich than [m/H] =—0.2 (i.e. stars in the range of the three reddest tracks in the model grid).," At the right-hand edge of the CMD, the detection limits set by the $V$ filter prevent us from measuring any stars more metal-rich than [m/H] $\simeq -0.2$ (i.e. stars in the range of the three reddest tracks in the model grid)." + In addition. at levels I>27.6 the increasing photometric measurement uncertainties produce an scatter in the observed colors: objects measured too blue by random errors fall well to the blue side of the most," In addition, at levels $I \gtrsim 27.6$ the increasing photometric measurement uncertainties produce an scatter in the observed colors: objects measured too blue by random errors fall well to the blue side of the most" +Long Gamina Ray Bursts (CRBs) are intrinsically linked to core collapse supernovae.,Long Gamma Ray Bursts (GRBs) are intrinsically linked to core collapse supernovae. + This conclusion comes frou the detection of Type le supernovae nearly coincident with loug GRBs (??)..," This conclusion comes from the detection of Type Ic supernovae nearly coincident with long GRBs \citep{smg+03,Hjorth}." + [t is also confirmed by studies of the host galaxies of long GRBs. which turued out to be actively star-lormine (?)..," It is also confirmed by studies of the host galaxies of long GRBs, which turned out to be actively star-forming \citep{Djorgovski}." + The leadiug mocel of long GRBs is a collapsar model (??).. which postttlates that a comyact central source (a black bole or rapidly. rotating citelsov92 Oorms inside the collapsing core.," The leading model of long GRBs is a collapsar model \citep{1999ApJ...524..262M,2008MNRAS.385L..28B}, which postulates that a compact central source (a black hole or rapidly rotating \\cite{Usov92}) ) forms inside the collapsing core." + The ceural engine generates a collimated out!OW. which upo reaking out of tlie star reaches relativisic velocities and eventually produces 75-1:vs.," The central engine generates a collimated outflow, which upon breaking out of the star reaches relativistic velocities and eventually produces $\gamma$ -rays." + Moder uodels of neutrino-driven SN explosior are uot. OstableO. in a sense that cifeent eroups do 1 agree with each other aid the role of dierent ing‘eclieut is not settled (e.g.?)..," Modern models of neutrino-driven SN explosion are not ÒstableÓ, in a sense that different groups do not agree with each other and the role of different ingredient is not settled \citep[\eg][]{2009AIPC.1171..273B}." + The Mlapsar 110€el assumes that in αποτοι to the conveional ueutrino-cdriven SN explosion. tle'e Is 1 additio lxjirce of energy. the GRB ceutral eugiue.," The collapsar model assumes that in addition to the conventional neutrino-driven SN explosion, there is an addition source of energy, the GRB central engine." + ]t is possible that depencling on the dealled 'operties of he pre-collapse core (like angular momeuim. initialfielcl.. sinall differences COMPOSποu etc). the two euergy sources that tay potentially lead to the explosion. convection and the GRB central engine. may cotribute different amount of euergy. restilting," It is possible that depending on the detailed properties of the pre-collapse core (like angular momentum, initial, small differences in composition etc), the two energy sources that may potentially lead to the explosion, neutrino-driven convection and the GRB central engine, may contribute different amount of energy, resulting" +technique and compared the model to the data by eye.,technique and compared the model to the data by eye. +" This method yields (at best) a model that is consistent with the data, but it cannot provide errors of the parameters, and different models could fit as well."," This method yields (at best) a model that is consistent with the data, but it cannot provide errors of the parameters, and different models could fit as well." + The three-dimensional radiative-transfer code was used to compute the radiation that a model emits., The three-dimensional radiative-transfer code was used to compute the radiation that a model emits. +" It allows adaptive mesh refinement, following user-defined criteria."," It allows adaptive mesh refinement, following user-defined criteria." +" Dust properties and the dust density distribution as well as location, surface temperature and radius of stars are given as input."," Dust properties and the dust density distribution as well as location, surface temperature and radius of stars are given as input." + The program then computes the dust temperature by tracing photon packets which are randomly emitted by the stars., The program then computes the dust temperature by tracing photon packets which are randomly emitted by the stars. +" Additional inputs are density and temperature of ionized gas, the velocity field, fundamental molecular data, and the molecular abundance."," Additional inputs are density and temperature of ionized gas, the velocity field, fundamental molecular data, and the molecular abundance." +"Alultiple-component sources only alfect the first term in this expression. producing an olfset in the Cy spectrum jut Ju,= \Delta \Omega$ from equation \ref{eqjlm}, and this expression simplifies to an offset independent of $\ell$: Most multiple-component sources in the NVSS catalogue are double radio sources." + Let a fraction e<1 of the radio galaxies be doubles., Let a fraction $e \ll 1$ of the radio galaxies be doubles. + Phen e=1|¢ ance?=11356. thus the constant olfset may be written We can deduce ο=0.07x0.005. from the form of the NVSS angular correlation function w(8) at small angles 0«0.1. where double sources dominate the close pairs (seco Blake Wall 2002a ancl also Section. 4.2)).," Then $\overline{c} = 1 + e$ and $\overline{c^2} = 1 + 3e$, thus the constant offset may be written We can deduce $e = 0.07 \pm 0.005$ from the form of the NVSS angular correlation function $w(\theta)$ at small angles $\theta < 0.1^\circ$, where double sources dominate the close pairs (see Blake Wall 2002a and also Section \ref{secalm}) )." + This correction was applied to the measured NVSS C spectrum and successfully removed the small systematic olfset in 6 al high f£., This correction was applied to the measured NVSS $C_\ell$ spectrum and successfully removed the small systematic offset in $C_\ell$ at high $\ell$. + A sophisticated suite of analytical tools has been developed bv the CAIB community. for deriving the angular power spectra of the observed CMD temperature and. polarization maps., A sophisticated suite of analytical tools has been developed by the CMB community for deriving the angular power spectra of the observed CMB temperature and polarization maps. + These methods can also be exploited. to. analyze galaxy data (see for example Efstathiou Moody. 2001. lluterer. Ixnox Nichol 2001 and Tegmark et al.," These methods can also be exploited to analyze galaxy data (see for example Efstathiou Moody 2001, Huterer, Knox Nichol 2001 and Tegmark et al." + 2002)., 2002). + In this approach the power spectrum is determined. using an iterative maximum likelihood analysis. in contrast to the direct estimator ciscussed in Section 3.," In this approach the power spectrum is determined using an iterative maximum likelihood analysis, in contrast to the direct estimator discussed in Section \ref{secestharm}." + Phe likelihood is a fundamental statistical quantity. and this analysis method permits straightforward control of such issues as edge cllects. noise correlations and svstematic errors.," The likelihood is a fundamental statistical quantity, and this analysis method permits straightforward control of such issues as edge effects, noise correlations and systematic errors." + The starting point for maximum likelihood estimation (AILE) is Bayes’ theorem where à. are the parameters one is trying determine. D is the data ancl Z is the additional information describing the problem.," The starting point for maximum likelihood estimation (MLE) is Bayes' theorem where $\alpha$ are the parameters one is trying determine, $D$ is the data and $I$ is the additional information describing the problem." + The quantity ία) is the likelihood. i.c. the probability of the data given a specifie set of parameters. while the left-hand side is the posterior. i.e. the probability of the parameters given the data.," The quantity $P(\alpha|I)$ is the likelihood, i.e. the probability of the data given a specific set of parameters, while the left-hand side is the posterior, i.e. the probability of the parameters given the data." + We will assume that the sky is a realization of a stationary Gaussian process. with an angular power spectrumCy.," We will assume that the sky is a realization of a stationary Gaussian process, with an angular power spectrum $C_\ell$." + We assume no cosmological information abou the distribution of the €., We assume no cosmological information about the distribution of the $C_\ell$. + The rendition of the sky wil be a pixelized. map. created. by binning the galaxy. data in equal-area cells such that the count in the ;/th. eel is n;. cllectively constructing a “temperature map” of galaxy surface density.," The rendition of the sky will be a pixelized map, created by binning the galaxy data in equal-area cells such that the count in the $i$ th cell is $n_i$, effectively constructing a “temperature map” of galaxy surface density." + We performec this task using the IHIZALDPLIN. software. package (Gorksi. Hivon. Wanelel 1900: http://www.eso.org/science/healpix).," We performed this task using the HEALPIX software package (Gorksi, Hivon Wandelt 1999; )." + We chose the HISALPIN. pixelization scheme rig.=382. which corresponds to 12.288 pixels over a full sky.," We chose the HEALPIX pixelization scheme $n_{\rm side} = 32$, which corresponds to 12,288 pixels over a full sky." + Phe angular power spectrum may be safely extracted to multipole 20 page., The angular power spectrum may be safely extracted to multipole $\ell_{\rm max} \approx 2 \times n_{\rm side}$ . + We then defined a data vector: where 7 is the mean count per pixel., We then defined a data vector: where $\overline{n}$ is the mean count per pixel. + Figure 3 demonstrates that the data vector e; For the NVSS sample is well-approximated by a Gaussian distribution. as assumed in a maximum likelihood analvsis.," Figure \ref{fighist} demonstrates that the data vector $x_i$ for the NVSS sample is well-approximated by a Gaussian distribution, as assumed in a maximum likelihood analysis." + The covariance matrix CL due ο primordial Iluctuations is given by where 2 is the Legendre polvnomial anc 6 is the angle between pixel pair (7.7).," The covariance matrix $C^T_{ij}$ due to primordial fluctuations is given by where $P_\ell$ is the Legendre polynomial and $\theta_{ij}$ is the angle between pixel pair $(i,j)$." + In order to apply a likelihood analvsis we must also specify a noise covariance matrix CN., In order to apply a likelihood analysis we must also specify a noise covariance matrix $C^N_{ij}$. + We mocellecd the noise as a Gaussian random. process with variance l/m. uncorrelated between pixels. such that Ch=(1/7)δι.," We modelled the noise as a Gaussian random process with variance $1/\overline{n}$, uncorrelated between pixels, such that $C^N_{ij} = +(1/\overline{n}) \, \delta_{ij}$." + The likelihood of the map. with a particular power spectrum C'. is given by The goal of ALLE is to maximize this function. and the astest general method is to use Newton-Raphson iteration o find the zeroes of the derivatives in InP(C|]x) with respect to C.," The likelihood of the map, with a particular power spectrum $C_\ell$, is given by The goal of MLE is to maximize this function, and the fastest general method is to use Newton-Raphson iteration to find the zeroes of the derivatives in $\ln P(C_{\ell}|{\bf x})$ with respect to $C_\ell$." + We used the ALADCAP package (Borrill 1999: http://www.nersc.gov/--borrill/cmb/madcap) to «derive he maximum likelihood. handed angular power spectrum. rom the pixelized galaxy map and noise matrix., We used the MADCAP package (Borrill 1999; ) to derive the maximum likelihood banded angular power spectrum from the pixelized galaxy map and noise matrix. + NLADC'ATP is a parallel implementation of the Bond. Jalle Knox (JOOS) maximunm-likelihood algorithms for the analysis of CAMB datasets.," MADCAP is a parallel implementation of the Bond, Jaffe Knox (1998) maximum-likelihood algorithms for the analysis of CMB datasets." + We ran the analysis software on the supercomputer Seaborg. administered. by the National Enereyv Research Scientific Computing Centre (NERSC) at Lawrence Berkeley National Laboratory. California.," We ran the analysis software on the supercomputer Seaborg, administered by the National Energy Research Scientific Computing Centre (NERSC) at Lawrence Berkeley National Laboratory, California." + We again applied equation. 12 to the ALADCADP results to correct the measured. power spectrum for the inlluence of multiple-component sources., We again applied equation \ref{eqcldoub} to the MADCAP results to correct the measured power spectrum for the influence of multiple-component sources. + Boughn Crittenden (2002) also. performed. a HEALPIX analysis of the NVWSS as. part. of a. cross- analysis with the CAIB searching for evidence, Boughn Crittenden (2002) also performed a HEALPIX analysis of the NVSS as part of a cross-correlation analysis with the CMB searching for evidence +Thus our results Irom [mode frequencies which effectively measure (he solar radius in the subsurface lavers. are probably not inconsistent. with these measurements.,"Thus our results from f-mode frequencies which effectively measure the solar radius in the subsurface layers, are probably not inconsistent with these measurements." + This work utilizes data obtained by the Solar Oscillations Investigation / Michelson Doppler Luager on the Solar and IHeliospherie Observatory (SOIIO)., This work utilizes data obtained by the Solar Oscillations Investigation / Michelson Doppler Imager on the Solar and Heliospheric Observatory (SOHO). +" SOILO is a project of internalional cooperation between ESA and NASA,", SOHO is a project of international cooperation between ESA and NASA. +A search in the Geneva photometry database revealed that several Cepheids already had a substantial number of measurements.,A search in the Geneva photometry database revealed that several Cepheids already had a substantial number of measurements. + These data could constitute a basis for expanding Bersier et al., These data could constitute a basis for expanding Bersier et al. +'s (1997) efforts to determine Period-Raclius ancl Period-Liuninosityv. relations via the Baacle-Wesselink method.,'s (1997) efforts to determine Period-Radius and Period-Luminosity relations via the Baade-Wesselink method. + I present these old unpublished together with new data obtained in several runs curing 1996 and 1997., I present these old unpublished together with new data obtained in several runs during 1996 and 1997. + Like the data eiven in Bersier.Durki.&Burnet(1994).. the measurements are in the Geneva 7-color svstem (Golav 1980. Rutener 1988) and most have been obtained with the 70-cm Swiss telescope al La Sila Observatory.," Like the data given in \citet{ber94a}, the measurements are in the Geneva 7-color system (Golay 1980, Rufener 1988) and most have been obtained with the 70-cm Swiss telescope at La Silla Observatory." + The instrument used is a photometer (Burnet1976). that measures each filler several times per second: (he exposure is stopped alter a mininunm signal-to noise ratio has been reached in each filter: the integration time was at least three minutes., The instrument used is a photometer \citep{b76} that measures each filter several times per second; the exposure is stopped after a minimum signal-to noise ratio has been reached in each filter; the integration time was at least three minutes. + Given that most of our stars are brighter Chan my=10 the uncertainty is better than Q.01' for virtually all measurements., Given that most of our stars are brighter than $m_V = 10$ the uncertainty is better than $0.01^m$ for virtually all measurements. + Furthermore all measurements have been obtained in photometric conditions., Furthermore all measurements have been obtained in photometric conditions. + Table 1. lists all 62 Cepheids that have data.," Table \ref{tbl_nph} + lists all 62 Cepheids that have data." + The 1250 inclivicual measurements in seven colors are given in Table 2p.harvard.edu/pub/cdbersier/., The 1250 individual measurements in seven colors are given in Table \ref{tbl_ph}. +. Forty-three stars have more (han 20 measurements., Forty-three stars have more than 20 measurements. + Figure 1. presents examples of light aad color curves for well-observecl Cepheids., Figure \ref{fig_lc} presents examples of light and color curves for well-observed Cepheids. + Most observations were obtained in several runs on the 1.5 meter Danish telescope at ESO La Silla in 1996 and 1997. hence these data are contemporaneous with most of the photometry presented above.," Most observations were obtained in several runs on the 1.5 meter Danish telescope at ESO La Silla in 1996 and 1997, hence these data are contemporaneous with most of the photometry presented above." + I used the CORAVEL spectrograph. described in detail in Daranne.Mavor&DPoncet(1979).," I used the CORAVEL spectrograph, described in detail in \citet{bmp79}." +. The instrument. was optimized to vield accurate radial velocities through a cross-correlation method., The instrument was optimized to yield accurate radial velocities through a cross-correlation method. + The light is dispersed and (hen goes through a mask (based on the spectrum of Arcturus) before being detected by a photomultiplier., The light is dispersed and then goes through a mask (based on the spectrum of Arcturus) before being detected by a photomultiplier. + An are spectrum is obtained just before ancl just after each star exposure. to provide a eood wavelength solution.," An arc spectrum is obtained just before and just after each star exposure, to provide a good wavelength solution." + The observing setup is such (hat the cross-correlation function (CCF) is viewed in real-time., The observing setup is such that the cross-correlation function (CCF) is viewed in real-time. + This allows to stop the exposure when the CCF has a sufficient signal-to-noise., This allows to stop the exposure when the CCF has a sufficient signal-to-noise. + A Gaussian is fitted to the observed. eross-correlation function to vield the, A Gaussian is fitted to the observed cross-correlation function to yield the +cosmological gas. and the approximations that are mace in.,"cosmological gas, and the approximations that are made in." +. To facilitate comparison with other radiative transfer codes we review some of the other approximations which can be mace., To facilitate comparison with other radiative transfer codes we review some of the other approximations which can be made. + 1n what follows. we use Roman numerals to indicate the ionization state of an element (HLLIo) in the standard wav.," In what follows, we use Roman numerals to indicate the ionization state of an element (H,He) in the standard way." + Elements without Roman numerals refer to the nuclei of atoms (or all ionization states)., Elements without Roman numerals refer to the nuclei of atoms (or all ionization states). + A subscripted η refers to the number density of an clement (or a specific ionization state of an element)., A subscripted $n$ refers to the number density of an element (or a specific ionization state of an element). + A subscripted a refers to the ratio of the number density of a specific ionization state to the number density of all nuclei of that clement., A subscripted $x$ refers to the ratio of the number density of a specific ionization state to the number density of all nuclei of that element. +" A subsceripted y refers to the ratio of the number density of the subscripted species to the number density of LE nuclei. for example. The 3-D radiative transfer equation in a frame comoving with the expansion of the Universe can be written (c.g.?).. where ce, and 5, are the emission and extinction coefficients respectively. Lf=6/0 ds the Hubble parameter. a—afa; is the scale factor at time £ divided bv the scale [actor at time ἐν (when the photons in the ray were emitted). and J,=(κ.i.9.1) is the specific intensity."," A subscripted $y$ refers to the ratio of the number density of the subscripted species to the number density of H nuclei, for example, The 3-D radiative transfer equation in a frame comoving with the expansion of the Universe can be written \citep[e.g.][]{1998MmSAI..69..455N}, where $ \epsilon_{\nu} $ and $ \kappa_{\nu} $ are the emission and extinction coefficients respectively, $H = \dot{a}/a$ is the Hubble parameter, $\bar{a} = +a / a_e $ is the scale factor at time $t$ divided by the scale factor at time $t_e$ (when the photons in the ray were emitted), and $I_{\nu} = I +({\mathbf {\vec{x}}}, {\mathbf {\hat{n}}}, \nu, t) $ is the specific intensity." +" For photons with à mean free path Aj, much. less than the Horizon size c/44. the classical radiative transfer equation is a valid approximation."," For photons with a mean free path $\lambda_{\rm mfp}$ much less than the Horizon size $c/H$, the classical radiative transfer equation is a valid approximation." + This local approximation holds fairly well before the percolation stage of reionization when the growing ionization bubbles are still insulated. (rom each other by the optically thick ICM., This local approximation holds fairly well before the percolation stage of reionization when the growing ionization bubbles are still insulated from each other by the optically thick IGM. + Care must be taken once the majority of the ICM. is reionized and becomes optically thin allowing photons to travel distances greater than the simulation box length., Care must be taken once the majority of the IGM is reionized and becomes optically thin allowing photons to travel distances greater than the simulation box length. + The ellect of these background fluxes from outside the simulation volume must be taken into account. especially for. high enerev photons which have longer mean free paths and the potential to tonize and heat the IGM after being redshifted.," The effect of these background fluxes from outside the simulation volume must be taken into account, especially for high energy photons which have longer mean free paths and the potential to ionize and heat the IGM after being redshifted." + The treatment of these non-local Duxes should be tailored to the specific problem at hand and so were not hardewired into., The treatment of these non-local fluxes should be tailored to the specific problem at hand and so were not 'hard-wired' into. +. For the test cases presented in £4 they were not necessary., For the test cases presented in 4 they were not necessary. + Another caveat to using the classical equation. as explained in ?).. is that it is only valid when [gdfe]< and hence only for continuum radiation.," Another caveat to using the classical equation, as explained in \cite{1999ApJ...523...66A}, is that it is only valid when $ |\nu \partial +I_{\nu} / \partial \nu| \leq I_{\nu} $ and hence only for continuum radiation." + However. the classical equation can still be used for line radiation if the redshiltec absorption (photo-ionization) cross-sections are used when determining By.," However, the classical equation can still be used for line radiation if the redshifted absorption (photo-ionization) cross-sections are used when determining $\kappa_{\nu}$." +" Ife, and s, can be approximated as constant. a time independent RV equation can be used."," If $\epsilon_{\nu}$ and $\kappa_{\nu}$ can be approximated as constant, a time independent RT equation can be used." + This is à good approximation for individual SPL particles over a sulliciently. short time. however (asisalsodiscussedin2). ijt breaks down close to sources ancl allows the possibility of ionization. fronts that travel faster than the speed. of light.," This is a good approximation for individual SPH particles over a sufficiently short time, however \citep[as is also discussed in][]{1999ApJ...523...66A} it breaks down close to sources and allows the possibility of ionization fronts that travel faster than the speed of light." + his can be quantified by examining the ionization front jump conclition for a single point source ionizing a uniform density. constant temperature. Livclrogen eas. where. ry is the distance to the ionization front from the source. A is the number of photons per second emitted by the source. and ag is the recombination rate.," This can be quantified by examining the ionization front jump condition for a single point source ionizing a uniform density, constant temperature, Hydrogen gas, where, $r_{I}$ is the distance to the ionization front from the source, $\dot{N}$ is the number of photons per second emitted by the source, and $\alpha_{\rm H}$ is the recombination rate." + An upper limit on the radius. 7 within which the ionization front has a speed greater than c is. Within this region. use of the time independent equation breaks down.," An upper limit on the radius, $r_c$ within which the ionization front has a speed greater than c is, Within this region, use of the time independent equation breaks down." + In à ravtracing scheme. this can be avoided by stopping rays once they have reached a distance (d—clos where £o) is the amount of time the source has been on.," In a raytracing scheme, this can be avoided by stopping rays once they have reached a distance $d = ct_{on}$ where $t_{on}$ is the amount of time the source has been on." + The photons that were in the ray can be saved and traced from the stopping point once cnough time has elapsed., The photons that were in the ray can be saved and traced from the stopping point once enough time has elapsed. + Ln practice this is not always necessary., In practice this is not always necessary. +" For example. the first test presented in 8&4 has rr,=6.9.105 where the Strommeren radius. r,=5.4 kpe. In.. the diffuse component of the radiation field is modeled using the on-the-spot (OLS) approximation. Or às à set of many point sources and so for all calculations we can set ce,=0 along the rav. further simplifving the ICE equation. which has the analytic solution. where In principle. &, should include contributions [rom every process that removes. photons from. the rav. under consideration (photo absorption. Thomson scattering. dust. etc)."," For example, the first test presented in 4 has $r_c/r_s = 6.9 +\times 10^{-3}$ where the Strömmgren radius, $r_s = 5.4$ kpc, In, the diffuse component of the radiation field is modeled using the on-the-spot (OTS) approximation, or as a set of many point sources and so for all calculations we can set $\epsilon_{\nu}=0$ along the ray, further simplifying the RT equation, which has the analytic solution, where In principle, $\kappa_{\nu}$ should include contributions from every process that removes photons from the ray under consideration (photo absorption, Thomson scattering, dust, etc.)." + For the tests presented. here. we consider only photo absorption. however it would be straightforward. το add terms to account for other processes.," For the tests presented here, we consider only photo absorption, however it would be straightforward to add terms to account for other processes." + In this section we review the equations that determine the time cevelopment of the ionization fractions., In this section we review the equations that determine the time development of the ionization fractions. + They represent the contributions from photo-ionization. collisional ionization and recombination.," They represent the contributions from photo-ionization, collisional ionization and recombination." + Analytic and time averaged solutions in the case of constant rates are derived for use in an iterative solution scheme which relaxes the stringent constraints on the time step., Analytic and time averaged solutions in the case of constant rates are derived for use in an iterative solution scheme which relaxes the stringent constraints on the time step. +(121) right))-e, ) -. + As compared with Eq.(76)). the new exponcutial factor ef js que to the discontinuitv of As atq. associated with shell crossing within the ‘sticky model.," As compared with \ref{Psc-def1}) ), the new exponential factor $e^{-\ii k f q \mu}$ is due to the discontinuity of $\Delta\vs$ at, associated with shell crossing within the “sticky model”." + The factors (1|f£) that uniltiply the longitudinal wavenuuuber & could be expected from Eqs.(108))-(113))., The factors $(1+f)$ that multiply the longitudinal wavenumber $k$ could be expected from \ref{ks-sticky1}) \ref{ks-sticky2}) ). + As for the reabspace Fig. l..," As for the real-space Fig. \ref{fig_lDk}," + we show in Fig., we show in Fig. + b. our uuuerncal results for the redshift-space loganritlinie power. for longitudinal waveuunibers k. defined as Lah? PUO.," \ref{fig_lsDk} our numerical results for the redshift-space logarithmic power, for longitudinal wavenumbers $\vk$, defined as (k) = k^3 (k)." + We use the same defiuitiou (77)). even though Pith) ouly holds aloug the lougitucinal direction and Py(kh)}(=P(k)) holds along the two trausverse directions (so that using a factor Jl iustead of A? would be more uatural here). to make the comparison with Fig.," We use the same definition \ref{Delta2def}) ), even though $P^s_{\parallel}(k)$ only holds along the longitudinal direction and $P^s_{\perp}(k) (=P(k))$ holds along the two transverse directions (so that using a factor $k$ instead of $k^3$ would be more natural here), to make the comparison with Fig." + 1. easier., \ref{fig_lDk} easier. + In particular.," In particular," +Ou the other haud. the thermodynamics require the black hole eutropy has to be normalized. to the Bekenstein-Tawking- expression.- ic.. 9*=SpyA(77).,"On the other hand, the thermodynamics require the black hole entropy has to be normalized to the Bekenstein-Hawking expression, i.e., $S=S_{BH}=A/(4l_p^2)$." +2 Then.d we obtain the ummber NV as follows Tn the next section. we will show that the result of (75)) is not only valid for the Schwarzschild black hole. it is also right for all static spherical black holes.," Then, we obtain the number $N$ as follows In the next section, we will show that the result of \ref{NN}) ) is not only valid for the Schwarzschild black hole, it is also right for all static spherical black holes." + To reveal the physical ucaning of the brick wall thickness / introduced by t IHooft. we calculate the statistical average value of A(e) Comparing eq.(76)) with (27)). we find where a=N'z?2/(080003)) is a constant.," To reveal the physical meaning of the brick wall thickness $h$ introduced by 't Hooft, we calculate the statistical average value of $\Delta(\omega)$ Comparing \ref{ad}) ) with \ref{h}) ), we find where $\alpha= N'\pi^2/(1080\zeta(3))$ is a constant." + Therefore we conclude. the “brick wall thickness represcuts the statistical average effects of the quantum horizon spread rauge A(uw).," Therefore we conclude the ""brick wall"" thickness $h$ represents the statistical average effects of the quantum horizon spread range $\Delta(\omega)$." + Finally in this section. we argue that the effects of Q(£?) in eq.C607)) raise the effective temperature of the hole as it radiates;," Finally in this section, we argue that the effects of $\mathcal{O}(\xi^2)$ in \ref{xi}) ) raise the effective temperature of the hole as it radiates." + Namely. the £-depeudeucy in the eq.(67)}) should be thought as its thermal statistical average €dependeucy.," Namely, the $\xi$ -dependency in the \ref{xi}) ) should be thought as its thermal statistical average $\overline{\xi}$ -dependency." + like eq.(76)). (fray)/ Lothen the effective temperature] for the hole is where the Ley is Tawkine temperature aud the second terii in the rigbit-haud-side represents a correction to the temperature duc to the space-time non-conmmiutative property near the eveut horizon.," like \ref{ad}) ), $\overline{\xi^2}=l_p^4\overline{\omega^2}/(4r_H^2)=1/160\times(l_p/r_H)^4$ , then the effective temperature for the hole is where the $T_{BH}$ is Hawking temperature and the second term in the right-hand-side represents a correction to the temperature due to the space-time non-commutative property near the event horizon." + Obviously. this correction to the Το is tuy as ry2P. aud houce it can be ignored indeed.," Obviously, this correction to the $T_{BH}$ is tiny as $r_H\gg +l_p$, and hence it can be ignored indeed." + The corrections of O(£*) with No>2 can be analyzed likewise aud they are also ignorable as τμ2»1)., The corrections of $\mathcal{O}(\xi^N)$ with $N>2$ can be analyzed likewise and they are also ignorable as $r_H\gg l_p$. + Iu this section. we study our OFT inodel with quanti horizou for general static black holes.," In this section, we study our QFT model with quantum horizon for general static black holes." + The static spherical black holes metric ecnerically cau be written as the eq.(33)). and the Sclavarzschild black hole is a special case of this metric.," The static spherical black hole's metric generically can be written as the \ref{metric}) ), and the Schwarzschild black hole is a special case of this metric." + The calculation process is similar to the previous section. except the metric is different.," The calculation process is similar to the previous section, except the metric is different." + As discussed in above. the nonconmuutative rauee near the horizon is not bieeero0 than the Plauck leneth.," As discussed in above, the noncommutative range near the horizon is not bigger than the Planck length." + Heuce. to the metric near the horizon the function D(r) in 219 (33)) can be approximately written as follows," Hence, to the metric near the horizon the function $D(r)$ in \ref{metric}) ) can be approximately written as follows" +of our simulation.,of our simulation. +" Also, we are unable to count all of the most massive clusters due to our limited simulation volume."," Also, we are unable to count all of the most massive clusters due to our limited simulation volume." +" However, we can estimate the magnitude of these effects in a simple way."," However, we can estimate the magnitude of these effects in a simple way." +" By extrapolating our mass function, we estimate that we are missing ~40 clusters with M,>1.2x101?5-7!Mg in our simulation volume."," By extrapolating our mass function, we estimate that we are missing $\sim$ 40 clusters with $M_v > 1.2 \times 10^{15} \hmsol$ in our simulation volume." +" We can use the fits to the Pi.4anz—M, relation to find the radio power of these missing halos, which for all models leads to P414>3x10245WHz! for the missing clusters."," We can use the fits to the $\pmvir$ relation to find the radio power of these missing halos, which for all models leads to $P_{1.4} > 3 \times 10^{24} h_{70}^{-1} \whz$ for the missing clusters." +" We assign radio halosd to of these most massive clusters, which gives us an additional 12 halos."," We assign radio halos to of these most massive clusters, which gives us an additional 12 halos." +" If we assume that these clusters are evenly distributed within a 1 Gpc volume, then even the least luminous radio halo has flux = 100 mJy, so essentially all of these radio halos contribute to the number counts."," If we assume that these clusters are evenly distributed within a $\sim$ 1 Gpc volume, then even the least luminous radio halo has flux $\gtrsim$ 100 mJy, so essentially all of these radio halos contribute to the number counts." +" This increases our 1.4 GHz number counts to ~12 objects above the 10 mJy flux limit, roughly in line with known observations (???).."," This increases our 1.4 GHz number counts to $\sim$ 12 objects above the 10 mJy flux limit, roughly in line with known observations \citep{GIOVANNINI1999, Cassano2006, Cassano2010}." +" Since we expect these high-mass objects to host roughly the same proportion of 150 MHz radio halos, a similar number contributes to our 150 MHz number counts."," Since we expect these high-mass objects to host roughly the same proportion of 150 MHz radio halos, a similar number contributes to our 150 MHz number counts." +" While the model trends continue from the above analysis, we find that at high flux limits (>100 mJy) and high frequencies, we have too few radio halos to strongly distinguish several models, even those with large discrepancies in either assumed average magnetic field or scalings with virial mass or total turbulent pressure."," While the model trends continue from the above analysis, we find that at high flux limits $>100$ mJy) and high frequencies, we have too few radio halos to strongly distinguish several models, even those with large discrepancies in either assumed average magnetic field or scalings with virial mass or total turbulent pressure." +" This is due to the suppression of radio halos at high redshift, meaning that the integrated counts depend most strongly on high-luminosity objects, where the counts are nearly the same."," This is due to the suppression of radio halos at high redshift, meaning that the integrated counts depend most strongly on high-luminosity objects, where the counts are nearly the same." +" At 150 MHz and an assumed LOFAR sensitivity limit of 30 mJy, we find that although some models, such as Model Sets 2A and 2B, produce an almost factor of two difference in the total counts, the large uncertainties preclude any clean distinction."," At $150$ MHz and an assumed LOFAR sensitivity limit of $30$ mJy, we find that although some models, such as Model Sets 2A and 2B, produce an almost factor of two difference in the total counts, the large uncertainties preclude any clean distinction." + In we show the total counts of radio halos within redshift z«0.2 at 1.4GHz and 150MHz., In we show the total counts of radio halos within redshift $z<0.2$ at $1.4 \ghz$ and $150 \mhz$. + This redshift range fits largely within our computational volume without the need for periodic replication of the domain and is more easily accessible to observers., This redshift range fits largely within our computational volume without the need for periodic replication of the domain and is more easily accessible to observers. +" Although we find little degradation in the total number counts in the LOFAR-accessible regime (>30 mJy), the models remain indistinguishable."," Although we find little degradation in the total number counts in the LOFAR-accessible regime $>30$ mJy), the models remain indistinguishable." +" While we could in principle produce mock sky maps within any frequency range, we choose LOFAR-like parameters since low-frequency instruments are able to survey large portions of the sky and hence collect many halo images for use in statistical comparison."," While we could in principle produce mock sky maps within any frequency range, we choose LOFAR-like parameters since low-frequency instruments are able to survey large portions of the sky and hence collect many halo images for use in statistical comparison." + We generate raw mock sky maps in the 20—240 MHz LOFAR bandpass by following a similar strategy of interpolating and redshift-correcting clusters as used above.," We generate raw mock sky maps in the $20 +- 240$ MHz LOFAR bandpass by following a similar strategy of interpolating and redshift-correcting clusters as used above." + Appropriate cosmological dimming and redshift are then applied to determine the contribution of the slice to the sky observed at z=0., Appropriate cosmological dimming and redshift are then applied to determine the contribution of the slice to the sky observed at $z = 0$. +" We generate a radio image for each cluster by projecting its density and turbulent pressure onto the sky map and computing the relevant radio intensity using a given set of radio model parameters, ensuring that the integrated radio power across the projected cluster is equal to the value obtained using M, and Ἐν in the above sections."," We generate a radio image for each cluster by projecting its density and turbulent pressure onto the sky map and computing the relevant radio intensity using a given set of radio model parameters, ensuring that the integrated radio power across the projected cluster is equal to the value obtained using $M_v$ and $\Gamma_v$ in the above sections." +" We only project gas values within R,.", We only project gas values within $R_v$. +" For halos not within the high-resolution sample, we identify the nearest high-resolution cluster in mass and copy that high-resolution image to the location of the low-resolution halo."," For halos not within the high-resolution sample, we identify the nearest high-resolution cluster in mass and copy that high-resolution image to the location of the low-resolution halo." +" Also, since we do not have imaging information for missing high-mass halos due to our limited simulation volume, these are not included in the mock skies."," Also, since we do not have imaging information for missing high-mass halos due to our limited simulation volume, these are not included in the mock skies." +" While this procedure is admittedly somewhat crude, it does allow us to explore some of the observational consequences of these models and demonstrates a method of generating radio maps in the future using more sophisticated and realistic simulated data."," While this procedure is admittedly somewhat crude, it does allow us to explore some of the observational consequences of these models and demonstrates a method of generating radio maps in the future using more sophisticated and realistic simulated data." +" shows the entire radio sky containing our simulated clusters at 120 arcsec resolution assuming no background (i.e., a threshold sensitivity of 0 mJy)."," shows the entire radio sky containing our simulated clusters at $120$ arcsec resolution assuming no background (i.e., a threshold sensitivity of $0$ mJy)." + This resolution best approximates the LOFAR beam at an average frequency of ~120 MHz and a longest baseline of L~2 km., This resolution best approximates the LOFAR beam at an average frequency of $\sim 120$ MHz and a longest baseline of $L \sim 2$ km. + For this example we have chosen Model Set A1., For this example we have chosen Model Set A1. +" This map particularly highlights the paucity of radio halos in the universe, even at low sensitivity thresholds, but it is useful for providing a mock all-sky map for linking simulations to observations."," This map particularly highlights the paucity of radio halos in the universe, even at low sensitivity thresholds, but it is useful for providing a mock all-sky map for linking simulations to observations." +" highlights a region of the sky 6 degrees on a side at a resolution of 10 arcsec, representing the high-resolution capability between 20 and 240 MHz at the longest baseline configuration of LOFAR."," highlights a region of the sky $6$ degrees on a side at a resolution of $10$ arcsec, representing the high-resolution capability between $20$ and $240$ MHz at the longest baseline configuration of LOFAR." +" We also draw contour levels at varying sensitivities: 1, 10, and 30 mJy."," We also draw contour levels at varying sensitivities: $1$, $10$, and $30$ mJy." + These sensitivities represent different configurations of the LOFAR array., These sensitivities represent different configurations of the LOFAR array. +" At high resolution and peak sensitivity, we are able to clearly distinguish several substructures and features within the two radio halos, indicating that LOFAR may be able to cleanly distinguish various radio power models based on their dependence on local gas density or local turbulent pressure, which can have different characteristic structures in the cluster atmosphere (Figure 3))."," At high resolution and peak sensitivity, we are able to clearly distinguish several substructures and features within the two radio halos, indicating that LOFAR may be able to cleanly distinguish various radio power models based on their dependence on local gas density or local turbulent pressure, which can have different characteristic structures in the cluster atmosphere (Figure \ref{fig:rh_projgamma}) )." +" At lower sensitivities, we can still distinguish features in the cluster cores, and early LOFAR images of nearby and bright radio halos may also provide useful distinguishing results."," At lower sensitivities, we can still distinguish features in the cluster cores, and early LOFAR images of nearby and bright radio halos may also provide useful distinguishing results." +" We will present a detailed radio morphological study, which requires knowledge of the spatial dependence of the magnetic field, in a future paper."," We will present a detailed radio morphological study, which requires knowledge of the spatial dependence of the magnetic field, in a future paper." + shows the same region of the sky as above with a much lower resolution of 240 arcsec., shows the same region of the sky as above with a much lower resolution of $240$ arcsec. + The contours are the same as above., The contours are the same as above. +" While we lose significant information about distant and small clusters, some larger clusters, such as the one shown, still show significant structure even at lower resolutions."," While we lose significant information about distant and small clusters, some larger clusters, such as the one shown, still show significant structure even at lower resolutions." +" We see that we can still identify substructure within the large cluster, and the effects of higher sensitivity thresholds are limited to distant clusters and the outer regions of nearby objects."," We see that we can still identify substructure within the large cluster, and the effects of higher sensitivity thresholds are limited to distant clusters and the outer regions of nearby objects." +" 'These results are encouraging, since they indicate that LOFAR may be able to give detailed radio maps of many radio halos."," These results are encouraging, since they indicate that LOFAR may be able to give detailed radio maps of many radio halos." + We have introduced the first set of radio halo statistics derived entirely from large-scale cosmological simulation., We have introduced the first set of radio halo statistics derived entirely from large-scale cosmological simulation. + Our radio power model is sufficiently broad to encompass many viable and more realistic models of CR generation and synchrotron emission in clusters of galaxies., Our radio power model is sufficiently broad to encompass many viable and more realistic models of CR generation and synchrotron emission in clusters of galaxies. +" Our approach demonstrates the viability of using large-scale simulation to bridge simulations and observations, both by deriving radio halo statistics from the simulated"," Our approach demonstrates the viability of using large-scale simulation to bridge simulations and observations, both by deriving radio halo statistics from the simulated" +the star to star abundance at low metallicities is strongly needed.,the star to star abundance at low metallicities is strongly needed. + Gravitational waves seem interesting in this respec (seco Talon Charbonnel 2003). but we still wait for ful metallicity dependent computations.," Gravitational waves seem interesting in this respect (see Talon Charbonnel 2003), but we still wait for full metallicity dependent computations." + We should. recall at this. point that. our. stancare chemical evolution models refer to. large-scale. long-term phenomena and cannot account for small-scale. short-term variations.," We should recall at this point that our standard chemical evolution models refer to large-scale, long-term phenomena and cannot account for small-scale, short-term variations." + Lf we want to reproduce also the observed spreac in the abundances of the light elements. as observed. [or instance. by in the local ISM (6g... Moos et al.," If we want to reproduce also the observed spread in the abundances of the light elements, as observed, for instance, by in the local ISM (e.g., Moos et al." + 2002). or for Πο across the Galactic disce (Dania et al.," 2002), or for$^3$ He/H across the Galactic disc (Bania et al." + 2002). we should also take into account the possible inhomogencitics in the chemical enrichment of cach region and the cllects of possible orbital diffusion of the stars.," 2002), we should also take into account the possible inhomogeneities in the chemical enrichment of each region and the effects of possible orbital diffusion of the stars." + ALY. is) particularly grateful. to Corinne Charbonnel. Johannes Geiss. and Ceorge Gloeckler of the LOLA-CI team for the enlightening discussions at the International Space Science Institute in Berne (611).," M.T. is particularly grateful to Corinne Charbonnel, Johannes Geiss, and George Gloeckler of the LOLA-GE team for the enlightening discussions at the International Space Science Institute in Berne (CH)." + Dana Balser. Tom Dania. and Bob Rood are warmly thanked for always being ready to share updated: values of the ο abundances.," Dana Balser, Tom Bania, and Bob Rood are warmly thanked for always being ready to share updated values of the $^3$ He abundances." + We also thank Daniele Calli and Cary Steigman for their useful comments., We also thank Daniele Galli and Gary Steigman for their useful comments. + Exil Jenkins. Warren Moos and νο Viclal-Aladjar are gratefully acknowledged for elarifving what is the range o£ LISM D/L values which should be quoted according to the most reliable data.," Ed Jenkins, Warren Moos and Alfred Vidal-Madjar are gratefully acknowledged for clarifying what is the range of LISM D/H values which should be quoted according to the most reliable data." + This work has been partially supported by the through grant HULII301ZAM., This work has been partially supported by the through grant 11301ZAM. +ppc. and (i)m most of these sources show only modest variability at GGllIz on timescales of 13 vears.,"pc, and (ii) most of these sources show only modest variability at GHz on timescales of 1–3 years." + The opticalp counterpart' of this radio| source is |a member of PLSa compact group of galaxies (Figure 3))., The optical counterpart of this radio source is a member of a compact group of galaxies (Figure \ref{fig:J031010-573041_optical}) ). + No redshift has been measured for the host galaxy (object A in Figure 3)). so we adopt the measured 6dE665 redshift of z=0.082 for the companion galaxy as the redshift of the whole eroup.," No redshift has been measured for the host galaxy (object A in Figure \ref{fig:J031010-573041_optical}) ), so we adopt the measured 6dFGS redshift of $z=0.082$ for the companion galaxy as the redshift of the whole group." + None of the other galaxies in this group has a redshift measurement., None of the other galaxies in this group has a redshift measurement. +" ThiVhis source""Co wasOWE detectedποσο ini the PPAIN. surveyOON (Grillithvilli et Eal.", This source was detected in the PMN survey (Griffith et al. + 1994) with a [lux density of 534511 mmJv in the aarcmin Parkes beam at 1., 1994) with a flux density of $\pm$ mJy in the arcmin Parkes beam at 4.8GHz. + This is significantly lower than the Αθ value of 92x94 mnmiJy. (in a L5aaresee beam). suggesting that the source may be variable.," This is significantly lower than the AT20G value of $\pm$ mJy (in a arcsec beam), suggesting that the source may be variable." + Phe 041 spectrum shows absorption lines twpical of an carbtvpe galaxy but no obvious optical emission lines., The 6dFGS spectrum shows absorption lines typical of an early–type galaxy but no obvious optical emission lines. + The 6dEGS spectrum shows absorption lines together with possible weak ILLI] emission., The 6dFGS spectrum shows absorption lines together with possible weak III] emission. + There is a faint NVSS source associated with this object (see Table 2)). but it lies below the limit of the MMIIz SUAISS catalogue.," There is a faint NVSS source associated with this object (see Table \ref{table:sumss_nvss}) ), but it lies below the limit of the MHz SUMSS catalogue." +ratios of ~0.01 ./L. (neglecting dust).,ratios of $\sim$ $_{\odot}$ $_{\odot}$ (neglecting dust). + Thus the stellar mass of these structures is probably ~10*.—107M .. similar to globular clusters.," Thus the stellar mass of these structures is probably $\sim10^4-10^5$ $_\odot$, similar to globular clusters." + From their Ha fluxes. we estimate the star-formation rates to be AZ. vr.1. and hence their star-formation time-scales are « I.0GGyr.," From their $\alpha$ fluxes, we estimate the star-formation rates to be $\,{M_\odot}$ $^{-1}$, and hence their star-formation time-scales are $<$ Gyr." + The tireball masses are similar to those estimated for the TDGs in Arp 305 by Hancock et al. (, The fireball masses are similar to those estimated for the TDGs in Arp 305 by Hancock et al. ( +2009).,2009). + For TDGs in interacting field galaxies. it is a matter of dispute whether they will eventually become independent of the galaxies which originally hosted their gas.," For TDGs in interacting field galaxies, it is a matter of dispute whether they will eventually become independent of the galaxies which originally hosted their gas." + By contrast. in the case of ram-pressure stripped cluster galaxies. the ultimate detachment of the clumps from the host galaxy seems quite likely. and if they survive as bound systems they may evolve into stellar systems resembling intra-cluster globular clusters or compact dwarf galaxies.," By contrast, in the case of ram-pressure stripped cluster galaxies, the ultimate detachment of the clumps from the host galaxy seems quite likely, and if they survive as bound systems they may evolve into stellar systems resembling intra-cluster globular clusters or compact dwarf galaxies." + Similar objects have been noted in simulations of ram-pressure stripping by Kapferer et al. (, Similar objects have been noted in simulations of ram-pressure stripping by Kapferer et al. ( +2008). who term them “stripped baryonic dwarfs”.,"2008), who term them “stripped baryonic dwarfs”." + Finally. we consider the destiny of the galaxies themselves after stripping is completed.," Finally, we consider the destiny of the galaxies themselves after stripping is completed." + It has been known for a long time that cluster spirals are deficient in neutral gas. relative to their counterparts in the field (e.g. Haynes Giovanelli 1984).," It has been known for a long time that cluster spirals are deficient in neutral gas, relative to their counterparts in the field (e.g. Haynes Giovanelli 1984)." + In Coma. Gavazzi et al. (," In Coma, Gavazzi et al. (" +2006) tind that a significant average HI deficiency extends from the cluster core out to ~2 MMpc. the gas content becoming consistent with a field reference sample at ~3 MMpc. (,"2006) find that a significant average HI deficiency extends from the cluster core out to $\sim2$ Mpc, the gas content becoming consistent with a field reference sample at $\sim$ Mpc. (" +A similar trend is seen for Virgo. e.g. Cayatte et al.,"A similar trend is seen for Virgo, e.g. Cayatte et al." + 19943., 1994). + The HI detficieney data for Coma show an apparently sharp transition at a radius of ο MMpe. within which nearly all cluster members are gas-poor compared to field spirals.," The HI deficiency data for Coma show an apparently sharp transition at a radius of $\sim$ Mpc, within which nearly all cluster members are gas-poor compared to field spirals." + Figure 4. compares the Gavazzi et., Figure \ref{fig:stripfrac} compares the Gavazzi et. + al., al. + HI-deficient fraction to the incidence of ongoing stripping events identified in this paper., HI-deficient fraction to the incidence of ongoing stripping events identified in this paper. +" For this test. the galaxies are flagged as gas-deficient if they have Defy,>0.64. corresponding to the 95th percentile of Defi among galaxies beyond 3MMpe from the Coma core."," For this test, the galaxies are flagged as gas-deficient if they have $_{\rm HI}>0.64$, corresponding to the 95th percentile of $_{\rm HI}$ among galaxies beyond Mpc from the Coma core." + It is notable that a similar characteristic radius of 1 MMpe seems to apply to both phenomena., It is notable that a similar characteristic radius of $\sim$ Mpc seems to apply to both phenomena. + On the other hand we found no ongoing stripping events. with the uncertain exception of GMP 5422. beyond MMpe. where pper cent of spirals are HI-deficient.," On the other hand we found no ongoing stripping events, with the uncertain exception of GMP 5422, beyond Mpc, where per cent of spirals are HI-deficient." + This result can be understood in terms of a “backsplash” population (Sanchis et al., This result can be understood in terms of a “backsplash” population (Sanchis et al. + 2002: Gill. Knebe Gibson 2004): although stripping itself is only effective within -1 MMpe. HI-deficient galaxies can be observed at larger radit after the initial stripping event is complete and the galaxy has passed through the cluster core.," 2002; Gill, Knebe Gibson 2004): although stripping itself is only effective within $\sim$ Mpc, HI-deficient galaxies can be observed at larger radii after the initial stripping event is complete and the galaxy has passed through the cluster core." + This is contirmed by Figure 7.. which shows that our simple stripping model. tuned to reproduce the fraction of GSE galaxies. also produces a post-stripping population consistent with the observed HI-deficient galaxy fraction.," This is confirmed by Figure \ref{fig:millengse}, which shows that our simple stripping model, tuned to reproduce the fraction of GSE galaxies, also produces a post-stripping population consistent with the observed HI-deficient galaxy fraction." + We have used UV and optical imaging to identify a sample of candidate gaseous stripping events in the Coma cluster., We have used UV and optical imaging to identify a sample of candidate gaseous stripping events in the Coma cluster. + The stripped galaxies are characterised by tails or trails of UV-bright debris. which we interpret as young stars formed within gas stripped by ram pressure from the intra-cluster medium.," The stripped galaxies are characterised by tails or trails of UV-bright debris, which we interpret as young stars formed within gas stripped by ram pressure from the intra-cluster medium." + Some of these cases have been noted as peculiar in previous work. in a variety of wavebands (Vollmer et al.," Some of these cases have been noted as peculiar in previous work, in a variety of wavebands (Vollmer et al." + 2001: Finoguenov et al., 2001; Finoguenov et al. + 2004: Yagi et al., 2004; Yagi et al. + 2007: Yoshida et al., 2007; Yoshida et al. + 2008: Miller et al., 2008; Miller et al. + 2009). while others are newly identitied here as possible stripping events.," 2009), while others are newly identified here as possible stripping events." + The trails are predominantly oriented away from the cluster centre. indicating that he galaxies are falling into the cluster for the first time. along fairy radial orbits. and that the stripping events are completed rapidly compared to the orbital time-scale.," The trails are predominantly oriented away from the cluster centre, indicating that the galaxies are falling into the cluster for the first time, along fairly radial orbits, and that the stripping events are completed rapidly compared to the orbital time-scale." + All but one uncertain case lie :it projected radit of kkpe from the cluster centre., All but one uncertain case lie at projected radii of kpc from the cluster centre. + The racial distribution of these galaxies is much more centrally concentrated than the distribution of blue galaxies from which they were selected. and more similar to the distribution of passive galaxies.," The radial distribution of these galaxies is much more centrally concentrated than the distribution of blue galaxies from which they were selected, and more similar to the distribution of passive galaxies." + Wihin MMpe projected radius. some pper cent of blue galaxies are currently undergoing stripping. a fraction which is compatible with a -500 MMyr time-scale for the stripping events.," Within Mpc projected radius, some per cent of blue galaxies are currently undergoing stripping, a fraction which is compatible with a $\sim$ Myr time-scale for the stripping events." + The radius within which UV trails are observed corresponds to an. ICM density of ~107'ggeem . in agreement with simulations which show significant star formation in the stripped wake in this density regime for infall velocities ~ ((Kapferer et al.," The radius within which UV trails are observed corresponds to an ICM density of $\sim10^{-27}$ $^{-3}$, in agreement with simulations which show significant star formation in the stripped wake in this density regime for infall velocities $\sim$ (Kapferer et al." + 2009)., 2009). + There are hints that some stripping events are associated with local enhancements in the ICM density. e.g. the western structure and the NGC 4839 group. but a firm link can not be concluded from the present data.," There are hints that some stripping events are associated with local enhancements in the ICM density, e.g. the western structure and the NGC 4839 group, but a firm link can not be concluded from the present data." + We propose an interpretation of these objects as a stage in ram-pressure stripping that is subsequent to the HI gas-tail phase (Chung et al., We propose an interpretation of these objects as a stage in ram-pressure stripping that is subsequent to the HI gas-tail phase (Chung et al. + 2007). and occurring at higher ambient densities.," 2007), and occurring at higher ambient densities." + The star formation triggered in the stripping events may add mass to the galaxy bulge. if newly-formed stars fall back into the source galaxy.," The star formation triggered in the stripping events may add mass to the galaxy bulge, if newly-formed stars fall back into the source galaxy." + Alternatively they may escape. forming intra-cluster stellar systems that could evolve into objects resembling globular clusters or compact dwarf galaxies.," Alternatively they may escape, forming intra-cluster stellar systems that could evolve into objects resembling globular clusters or compact dwarf galaxies." + After the initial stripping. the infalling galaxies will remain as gas-deficient spirals before fading slowly into SOs as they exhaust their remaining gas.," After the initial stripping, the infalling galaxies will remain as gas-deficient spirals before fading slowly into S0s as they exhaust their remaining gas." + As stressed by Sun et al. (, As stressed by Sun et al. ( +2010). a fuller understanding of the relationship between different manifestations of gas stripping (HI deficiency. and tails in HI. UV. Ha and. X-ray) will be made possible by improving the overlap between observations in the various wavebands. for the same galaxy cluster.,"2010), a fuller understanding of the relationship between different manifestations of gas stripping (HI deficiency, and tails in HI, UV, $\alpha$ and X-ray) will be made possible by improving the overlap between observations in the various wavebands, for the same galaxy cluster." + Our work has assembled a comorehensive wide-tield optical. UV. Ha and spectroscopic dataset or Coma. complemented by archival XMM imaging and the radio continuum survey of Miller et al. (," Our work has assembled a comprehensive wide-field optical, UV, $\alpha$ and spectroscopic dataset for Coma, complemented by archival XMM imaging and the radio continuum survey of Miller et al. (" +2009).,2009). + A key missing element is high-sensitivity 21em HI mapping of a large sample of Coma member galaxies. which should be possible in the next few years using tye Expanded Very Large Array.," A key missing element is high-sensitivity 21cm HI mapping of a large sample of Coma member galaxies, which should be possible in the next few years using the Expanded Very Large Array." + We are grateful to Stephen Gwyn for generating a custom stack of the Adami deep v-band data for our use. to Masafumi Yagi for communicating the Subaru Πα results in advance of submission. and to Neal Miller for helpful comments on this paper.," We are grateful to Stephen Gwyn for generating a custom stack of the Adami deep $u$ -band data for our use, to Masafumi Yagi for communicating the Subaru $\alpha$ results in advance of submission, and to Neal Miller for helpful comments on this paper." + RJS was supported for this work by STFC Rolling Grant PP/C301568/1 “Extragalactic Astronomy and Cosmology at Durham 2008—20137., RJS was supported for this work by STFC Rolling Grant PP/C501568/1 “Extragalactic Astronomy and Cosmology at Durham 2008–2013”. + This work is based on observations made with the NASA(GALEX)., This work is based on observations made with the NASA. +GALEX is a NASA Small Explorer. developed in cooperation with the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and Technology.," is a NASA Small Explorer, developed in cooperation with the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and Technology." + This work is based on observations obtained with MegaPrime/MegaCam. a joint project of CFHT and CEA/DAPNIA. at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada. the Institute National des Sciences de l'Univers. of the Centre National de la Recherche Scientitique of France. and the University of Hawaii.," This work is based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada–France–Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institute National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii." + The work has made use of data, The work has made use of data +Lt is possible to model several dillerent twpes of galaxy and compare the isophotal magnitude and the total magnitude as calculated in $4 with the “true” magnitude.,It is possible to model several different types of galaxy and compare the isophotal magnitude and the total magnitude as calculated in 4 with the “true” magnitude. + Phe moclels are simple. assuming a face on circular galaxy. composed of a bulge . witha ce Vaucouleurs. 77n law (de .Vaucouleurs 1948) and a disk with an exponential profile (see Eqn. SN)).," The models are simple, assuming a face on circular galaxy, composed of a bulge with a de Vaucouleurs $r^{\frac{1}{4}}$ law (de Vaucouleurs 1948) and a disk with an exponential profile (see Eqn. \ref{eq:exp}) )." + where rs ds the hall-light radius of the bulge. (5. is the ellective surface brightness of the bulge.," where $r_e$ is the half-light radius of the bulge, $\mu_e$ is the effective surface brightness of the bulge." + Llere we define it as the mean surface brightness within r5., Here we define it as the mean surface brightness within $r_e$. + However. it is more useful to define galaxies in terms of their Iuminosities and bulge-to-disk ratios than their elective radii or disk scale-lengths.," However, it is more useful to define galaxies in terms of their luminosities and bulge-to-disk ratios than their effective radii or disk scale-lengths." + The magnitude of a galaxy and the bulge-disk ratio can be found in terms of the above parameters. by: where D is the magnitude of the bulge and. D is the magnitude of the disk.," The magnitude of a galaxy and the bulge-disk ratio can be found in terms of the above parameters, by: where $B$ is the magnitude of the bulge and $D$ is the magnitude of the disk." + 6/7 is the bulge-to-total ratio., $B/T$ is the bulge-to-total ratio. + Given the parameters AZ. DBZT. p and pi. a galaxy’s light profile is Cully defined.," Given the parameters $M$, $B/T$, $\mu_e$ and $\mu_o$, a galaxy's light profile is fully defined." + To caleulate the difference between the total ancl the isophotal magnitude it is necessary to find the fraction of light lost. below the isophote., To calculate the difference between the total and the isophotal magnitude it is necessary to find the fraction of light lost below the isophote. + Since the intrinsic detection isophote varies with the redshift. this dilference will he a Function of redshift.," Since the intrinsic detection isophote varies with the redshift, this difference will be a function of redshift." + Fora varietv of redshifts from z=0.001 to 2=0.201. the fraction of light under the isophote was calculated. by first converting the above magnitudes to apparent magnitudes. the intrinsic surface brightnesses to apparent surface brightnesses and then caleulating the scale- as above.," For a variety of redshifts from $z=0.001$ to $z=0.201$, the fraction of light under the isophote was calculated, by first converting the above magnitudes to apparent magnitudes, the intrinsic surface brightnesses to apparent surface brightnesses and then calculating the scale-lengths as above." + The conversions [rom absolute to apparent properties are given in Eqn., The conversions from absolute to apparent properties are given in Eqn. + 17. and Eqn. I8.., \ref{eq:absmag} and Eqn. \ref{eq:absmu}. +" Using jay,= 24.67mag aresec7. the isophotal radii of the disk and bulge are calculated."," Using $\mu_{lim}=24.67$ mag $^{-2}$, the isophotal radii of the disk and bulge are calculated." + The fraction of light) above the isophote is then calculated using the equation below., The fraction of light above the isophote is then calculated using the equation below. + where 7 is the de Vaucouleur's parameter. which is 1 fora disk and 4 for a bulge.," where $\beta$ is the de Vaucouleur's parameter, which is 1 for a disk and 4 for a bulge." + g=7.67(—y in bulges and g=— in disks., $g=7.67(\frac{r}{r_e})^{1/4}$ in bulges and $g=\frac{r}{\alpha}$ in disks. + The isophotal magnitude and isophotal radius of the galaxy can now be calculated., The isophotal magnitude and isophotal radius of the galaxy can now be calculated. +"the evolution of active regions (AR), which are structures with filling factors larger than 89.1 ppm (Class IV).","the evolution of active regions (AR), which are structures with filling factors larger than 89.1 ppm (Class IV)." +" The brown and black lines show the evolution of the sunspots penumbrae and umbrae, respectively."," The brown and black lines show the evolution of the sunspots penumbrae and umbrae, respectively." +" Note that for a better visualization, the filling factors of penumbrae and umbrae were multiplied by a factor of five (5)."," Note that for a better visualization, the filling factors of penumbrae and umbrae were multiplied by a factor of five (5)." + We find that the filling factors of Classes I and II structures do not present trends during the period considered., We find that the filling factors of Classes I and II structures do not present trends during the period considered. +" However, an increase of the filling factors of Class I structures in relation to the average value is observed from 29-Oct-2010 to 07-Mar-2011."," However, an increase of the filling factors of Class I structures in relation to the average value is observed from 29-Oct-2010 to 07-Mar-2011." + Changes of the filling factors of Class Π structures are observed near the boundaries of this interval., Changes of the filling factors of Class II structures are observed near the boundaries of this interval. + These changes appear as decreases of the filling factors of Class II structures from 29-Oct-2010 to 10-Nov-2010 and from 15-Feb-2011 to 07-Mar-2011., These changes appear as decreases of the filling factors of Class II structures from 29-Oct-2010 to 10-Nov-2010 and from 15-Feb-2011 to 07-Mar-2011. + We speculate that these variations are due to small changes in the calibration of the magnetograms or the mapping of the quicklook images., We speculate that these variations are due to small changes in the calibration of the magnetograms or the mapping of the quicklook images. +" In this interval, we did not observe any such discontinuity in the filling factors of Classes III and IV structures."," In this interval, we did not observe any such discontinuity in the filling factors of Classes III and IV structures." + We, We +of 107. which covers part of the disc and thus increasing the observed mass transfer rate necessary to match the [ux level of the system.,"of $10^{\circ}$, which covers part of the disc and thus increasing the observed mass transfer rate necessary to match the flux level of the system." + During the decline. we believe that a cooling front. as described in \lineshige&Osaki(1985).. moves inward reducing the disc temperature and at least for the duration of the eclipses the dise behaves in a steady state manner.," During the decline, we believe that a cooling front, as described in \scite{Mineshige85}, moves inward reducing the disc temperature and at least for the duration of the eclipses the disc behaves in a steady state manner." + Also. Mineshige(1901). showed that for the case of Z Cha. for the disc temperature to decrease with time it is necessary for the dise to behave like. or at least be very close to. steady state.," Also, \scite{Mineshige91} showed that for the case of Z Cha, for the disc temperature to decrease with time it is necessary for the disc to behave like, or at least be very close to, steady state." + Conversely. models by Cannizzo(1994). on the decline of the optical [Luxes during outbursts of dwarf novae require the accretion disc to be departing from steady state mocels.," Conversely, models by \scite{Cannizzo94} on the decline of the optical fluxes during outbursts of dwarf novae require the accretion disc to be departing from steady state models." + Clearly this is not the case that we observe. since our steacky state models for the eclipses during the late decline are in eood agreement with the observed data.," Clearly this is not the case that we observe, since our steady state models for the eclipses during the late decline are in good agreement with the observed data." + Comparing the results from the eruption of LET Cas with other outbursts of SU UMa systems we see many similarities., Comparing the results from the eruption of HT Cas with other outbursts of SU UMa systems we see many similarities. + In the case of OY Car. eclipse light curves observed by Vogt(1983) and later reexamined by Ruttenetal.(1992). show the same kind of behavior as the outburst eclipses of LEE Cas.," In the case of OY Car, eclipse light curves observed by \scite{Vogt83} and later re–examined by \scite{Rutten92} show the same kind of behavior as the outburst eclipses of HT Cas." + Both systems are slowly eparting [rom their quiescent eclipse shape. moving towards a more symmetric shape with a distinct flat eclipse bottom during the carly rise.," Both systems are slowly departing from their quiescent eclipse shape, moving towards a more symmetric shape with a distinct flat eclipse bottom during the early rise." +" οσο results are also in extreme contrast with the results of Webbetal.(1999). for the ""insideout” outburst of the U Gem. system IP Poe.", These results are also in extreme contrast with the results of \scite{Webb99} for the “inside–out” outburst of the U Gem system IP Peg. +" A hot transition front of material. which is moving towards the centre of the disc. is suggested by the preference of the modelling code to place a hole (or non-Iuminous material) with a radius of about 472, from the centre of the accretion disc during the rising phase of the outburst."," A hot transition front of material, which is moving towards the centre of the disc, is suggested by the preference of the modelling code to place a hole (or non-luminous material) with a radius of about $4R_{wd}$ from the centre of the accretion disc during the rising phase of the outburst." + Lt is unclear as to whether the dise is truncated or not when at the peak of the outburst. as the [are angle of the disc grows to 15 and so the innermost parts of the disc are hidden from. view.," It is unclear as to whether the disc is truncated or not when at the peak of the outburst, as the flare angle of the disc grows to $15^{\circ}$ and so the innermost parts of the disc are hidden from view." + During the decline from outburst the truncation radius is ZOLO., During the decline from outburst the truncation radius is zero. + Several theories have been put forward in. order. to explain the delay in the rise of the ultraviolet Hux as opposed o the optical., Several theories have been put forward in order to explain the delay in the rise of the ultraviolet flux as opposed to the optical. + For example. Wing(1997) proposed that he inner parts of the dise remain void of material during cuiescence due to irradiation from the white dwarf.," For example, \scite{King97} proposed that the inner parts of the disc remain void of material during quiescence due to irradiation from the white dwarf." + Similarly Livio&Pringle(1992) emploved a weak magnetic field to runeate the disc. in the same manner as in intermediate »olar svstenmis.," Similarly \scite{Livio92} employed a weak magnetic field to truncate the disc, in the same manner as in intermediate polar systems." + Also. Mever(1990) suggested that a “siphon” coronal mass [low was responsible for emptving the inner wis of the accretion disc.," Also, \scite{Meyer90} suggested that a “siphon” coronal mass flow was responsible for emptying the inner parts of the accretion disc." + Lrraciation of the inner parts of the accretion disc by à hot corona that lies above the cool quiescent disc. leads to the evaporation of material in those inner disc regions.," Irradiation of the inner parts of the accretion disc by a hot corona that lies above the cool quiescent disc, leads to the evaporation of material in those inner disc regions." + Material from the dise joins the hot corona above and then is accreted onto the white dwarf leaving the inner parts of the accretion dise relatively empty., Material from the disc joins the hot corona above and then is accreted onto the white dwarf leaving the inner parts of the accretion disc relatively empty. + Llowever. the fact that LP Cas shows X-ray eclipses (Wood 1995: Mukai 1997) does not support the wory of a hot X-ray. producing corona. but instead suggests jiu the X-ray emitting regions in LEE Cas are very close to 1ο white dwactl.," However, the fact that HT Cas shows X-ray eclipses (Wood 1995; Mukai 1997) does not support the theory of a hot X-ray producing corona, but instead suggests that the X-ray emitting regions in HT Cas are very close to the white dwarf." + There has been previous observational evidence for 1e truncation of accretion discs in non-magnetic dwarf nova svstems., There has been previous observational evidence for the truncation of accretion discs in non-magnetic dwarf nova systems. + LaDous.Mever&AleverHofmoeister(1996) ound evidence of truncated accretion dises for at least four iferent. svstenis., \scite{ladous96} found evidence of truncated accretion discs for at least four different systems. + They. compared. the ratio of UV. Duxes xoduced by white chwarts and accretion cdises as predicted w the evaporation theory of Mever ancl Meyer.Hofmoeister (1989) and Alever(1990).," They compared the ratio of UV fluxes produced by white dwarfs and accretion discs as predicted by the evaporation theory of Meyer and Meyer–Hofmeister \shortcite{Meyer89} + and \scite{Meyer90}." +. 1n all three scenarios outlined above. the delay of the UV [lux arises because of the time it takes for the inner vats of the dise to be filled by material in outburst that is moving inwards.," In all three scenarios outlined above, the delay of the UV flux arises because of the time it takes for the inner parts of the disc to be filled by material in outburst that is moving inwards." + Unfortunately we do not possess any UV data for this outburst in order to confirm that our model results are compatible with the above theories., Unfortunately we do not possess any UV data for this outburst in order to confirm that our model results are compatible with the above theories. + However. Wheatleyetal.(1996). and Navlor(1997). speculate that the delay in the UV Dux observed in the VW. Livi svsteni. which was observed simultaneously in the X-ray. UV. and optical parts of the spectrum during an eruption. could be explained by such a mechanism.," However, \scite{Wheatley96} and \scite{Naylor97} speculate that the delay in the UV flux observed in the VW Hyi system, which was observed simultaneously in the X-ray, UV and optical parts of the spectrum during an eruption, could be explained by such a mechanism." + Our data appear to show such a gap being filled., Our data appear to show such a gap being filled. + There is substantial evidence that the cise is highly. Dared hroughout the outburst. especially near the peak of the eruption.," There is substantial evidence that the disc is highly flared throughout the outburst, especially near the peak of the eruption." + The semi-opening angle of the disc is seen to expand rom LO” during the rise to 15 at the peak and then starts o decrease again during the decline., The semi-opening angle of the disc is seen to expand from $10^{\circ}$ during the rise to $15^{\circ}$ at the peak and then starts to decrease again during the decline. +" This could. possibly o» explained. by the ""avalanche"" ellect that Mineshige&Osaki(1985). see in their model caleulations.", This could possibly be explained by the “avalanche” effect that \scite{Mineshige85} see in their model calculations. + As the hot pont travels towards the inner parts ofthe cisc. it causes 10 viscosity of the material that has just. gone through 10 heating front to rise sharply.," As the hot front travels towards the inner parts of the disc, it causes the viscosity of the material that has just gone through the heating front to rise sharply." + Therefore as the front moves inwards. material that is now in outburst. is piled up behind the hot front. perhaps thickening the disc.," Therefore as the front moves inwards, material that is now in outburst, is piled up behind the hot front perhaps thickening the disc." + As 10 outburst. declines. a cooling front that moves inwarcs makes the material at the outer parts of the dise return to ein quiescent cold state.," As the outburst declines, a cooling front that moves inwards makes the material at the outer parts of the disc return to their quiescent cold state." + Again. as the cooling front travels inwards the disc is seen to decrease in size both racdiallv and vertically.," Again, as the cooling front travels inwards the disc is seen to decrease in size both radially and vertically." + Evidence that accretion disces thicken during outburst has been observed by others., Evidence that accretion discs thicken during outburst has been observed by others. + In. particular. in the case of another two SU UMa svstems. OY Car and Z Cha.," In particular, in the case of another two SU UMa systems, OY Car and Z Cha." + For the case of OY Car Navloretal.(1987). were confronted with a similar problem of not being able to fit the outburst eclipses with a steady state model and they speculate that this could be due to a rim wall shadowing the inner parts of the disc., For the case of OY Car \scite{Naylor87} were confronted with a similar problem of not being able to fit the outburst eclipses with a steady state model and they speculate that this could be due to a rim wall shadowing the inner parts of the disc. + Also. Navloretal.(1988) found evidence of a rim wall for OY Car by studying the UV. and Xray lux of the 1985 Alay superoutburst of OY Car.," Also, \scite{Naylor88} found evidence of a rim wall for OY Car by studying the UV and X–ray flux of the 1985 May superoutburst of OY Car." + They suggest that the lack ofan Xray eclipse during the superoutburst. the existence of an orbital modulation of the UV ux and the observation that the UV. spectra show emission. lines which become," They suggest that the lack of an X–ray eclipse during the superoutburst, the existence of an orbital modulation of the UV flux and the observation that the UV spectra show emission lines which become" +"where 7.; is the cooling Irequency. ej; and e; are the fractions of the shock energy given to magnetic field and electrons at the shock. y=(p-2)/(p—1). Ex=E/10? eres. nj=n/l proton em*. gas=veο Lz. and here /; is the observer's time in unit of day. Dox is the huninosity distance in unit of 1075 em. a, is a correction [actor to the extinction along the line of sight to the burst.","where $\nu_{c,f}$ is the cooling frequency, $\epsilon_B$ and $\epsilon_e$ are the fractions of the shock energy given to magnetic field and electrons at the shock, $g=(p-2)/(p-1)$ , $E_{52}=E/10^{52}$ ergs, $n_0=n/1$ proton $^{-3}$, $\nu_{R,15}=\nu_R/10^{15}$ Hz, and here $t_d$ is the observer's time in unit of day, $D_{28}$ is the luminosity distance in unit of $10^{28}$ cm, $a_\nu$ is a correction factor to the extinction along the line of sight to the burst." +" Assuming (hat the re-brightening with the peak liminosityv of ~1 mJy around ~0.1 day is caused by this peak. we get the following formulae for e, ancl iy as functions of eg and other known parameters."," Assuming that the re-brightening with the peak luminosity of $\sim 1$ mJy around $\sim 0.1$ day is caused by this peak, we get the following formulae for $\epsilon_e$ and $n_0$ as functions of $\epsilon_B$ and other known parameters." + Holland et al. (, Holland et al. ( +2002a) claim the extinction ;ly.=0.26mag. which implies a ~20% correction in (he hR-band.,"2002a) claim the extinction $A_V=0.26$mag, which implies a $\sim 20 \%$ correction in the R-band." + The slope ~—1.05 of the optical afterglow at late (nme implies p2.4., The slope $\sim -1.05$ of the optical afterglow at late time implies $p\sim2.4$. + However. there is still some debate about the value of p (Sako Harrison 2002: llollauxd et al.," However, there is still some debate about the value of $p$ (Sako Harrison 2002; Holland et al." + 2002a; Pandey et al., 2002a; Pandey et al. + 2002)., 2002). + We will discuss (wo cases p=2.2 and 2.4., We will discuss two cases $p=2.2$ and $2.4$. + The evolution of reverse shocks is classified into two cases (IXobavashi 2000)., The evolution of reverse shocks is classified into two cases (Kobayashi 2000). +" If the initial Lorentz factor of the shell 7 is larger than a critical value jj.=(3E/32znmjc.NT) where m,P is (he mass of proton. the reverse shock becomes relativistic in the frame of unshockecl shell material during crossing the shell. and drastically decelerates the shell (thick shell case)."," If the initial Lorentz factor of the shell $\eta$ is larger than a critical value $\eta_c= (3E/32\pi n m_p c^2 \Delta_0^3)^{1/8}$ where $m_p$ is the mass of proton, the reverse shock becomes relativistic in the frame of unshocked shell material during crossing the shell, and drastically decelerates the shell (thick shell case)." + Ifa 0.85$ for all simulated galaxies. + We note that although the bulk of disc stars are formedtesta. a non-neglieible fraction. of stars (<= 15%) can be contributed by disrupted satellites that come in on nearly coplanar orbits. as is the case for Ag-l-5. but. in general these bring relatively old stars to the final disc.," We note that although the bulk of disc stars are formed, a non-negligible fraction of stars $\le 15\%$ ) can be contributed by disrupted satellites that come in on nearly coplanar orbits, as is the case for Aq-E-5, but in general these bring relatively old stars to the final disc." + This latter result is very similar to that obtained by Abacdi et al. (, This latter result is very similar to that obtained by Abadi et al. ( +2003h). who also found that debris from disrupted satellites can be found in z—0 thin/thick disc components.,"2003b), who also found that debris from disrupted satellites can be found in $z=0$ thin/thick disc components." + We find very good. agreement. of the overallsiu fractions for disces in Aq-C-6 and Adq-I-6b compared to Aq-C-5 and Aq-E-5. with changes of 54 and 34. respectively (Table 43).," We find very good agreement of the overall fractions for discs in Aq-C-6 and Aq-E-6b compared to Aq-C-5 and Aq-E-5, with changes of $5\%$ and $3\%$, respectively (Table \ref{table_insitu}) )." + In the case of λαγό. the diseon-sihut fraction is 17% lower than in Aq-E-5. (," In the case of Aq-E-6, the disc fraction is $17\%$ lower than in Aq-E-5. (" +Note that the disc/spheroid decomposition can also introduce some cdillerences since. as explained in SOO. Aq-E has a rotating bulge and the decomposition is dillicult.),"Note that the disc/spheroid decomposition can also introduce some differences since, as explained in S09, Aq-E has a rotating bulge and the decomposition is difficult.)" + The fractions for stars of given age (in particular for the three stellar age bins used above) show small dillerences with varving resolution., The fractions for stars of given age (in particular for the three stellar age bins used above) show small differences with varying resolution. + The largest cilferences CS 10%) are found. for the oldest. stellar populations., The largest differences $\lesssim 10\%$ ) are found for the oldest stellar populations. + For stars vounger than 9 Civr. we recover the result. from the level 5 simulations: all such stars formedbn-siit.," For stars younger than $9$ Gyr, we recover the result from the level 5 simulations: all such stars formed." + The motion of stars in the simulated clises are dominated by the tangential velocity component., The motion of stars in the simulated discs are dominated by the tangential velocity component. + In Fig., In Fig. +" 7 we show the mean tangential velocity V7, as a function of pacdius (fillecl circles). as well as V,860,,/2. where o,, is the dispersion in V2, in the corresponding radial bin."," \ref{vtita_vs_r} we show the mean tangential velocity $V_\phi$ as a function of radius (filled circles), as well as $V_\phi\pm \sigma_\phi/2$, where $\sigma_\phi$ is the dispersion in $V_\phi$ in the corresponding radial bin." + For each simulation. we divided stars in the three age bins we used to analyse the disc structure.," For each simulation, we divided stars in the three age bins we used to analyse the disc structure." + Young stars (f<9 Cir) usually have higher tangential velocities than older stars. particularly at large radii. and lower tangential velocity," Young stars $t\le 9$ Gyr) usually have higher tangential velocities than older stars, particularly at large radii, and lower tangential velocity" +include both grain opacities aid an improved TiO line list. although incompleteness in the Πο) line list leads to inaccuracies a uear-iutrared waveleneths (Chabrier. priv.,"include both grain opacities and an improved TiO line list, although incompleteness in the $_2$ O line list leads to inaccuracies at near-infrared wavelengths (Chabrier, priv." + comm..," comm.," + 2001: see also Reid Cruz. 2002. for comparison agalust iufrared data for late-ty‘pe dwarts).," 2001; see also Reid Cruz, 2002, for comparison against infrared data for late-type dwarfs)." + The BCAH models are a closest to the empirical main seqence iu the (My. (1-J)) plane. albeit to some exter| smoothinD>oO over the break at Mj~10.5.," The BCAH models are a closest to the empirical main sequence in the $_I$, (I-J)) plane, albeit to some extent smoothing over the break at $_I \sim 10.5$." + TIe extremely red colours at low ltuninosities reflect the absence oL graiu opacities in those moclels: the DUSTY moclels are clearly a better match to t1ο data., The extremely red colours at low luminosities reflect the absence of grain opacities in those models; the DUSTY models are clearly a better match to the data. + A optical wavelengths. the BCAH 1iodels show poorer agreement. fallit& below the main sequence at My~10 and remaining 0.5 to ] magnitudes fainter than the obse'valions at lower Again. the DUSTY modes are better match the data. rellecine the more extensive TiO lineliss. but these modes still iniss the M3/M1 break iu (Aly. (V-I). while the mismatch at wavelengths refects tle HeO opacity deficietcles.," At optical wavelengths, the BCAH models show poorer agreement, falling below the main sequence at $_V \sim 10$ and remaining 0.5 to 1 magnitudes fainter than the observations at lower Again, the DUSTY models are better match the data, reflecting the more extensive TiO linelists, but these models still miss the M3/M4 break in $_V$, (V-I)), while the mismatch at near-infrared wavelengths reflects the $_2$ O opacity deficiencies." + Bedin (2001) point oi similar discrej»ancles between theory aud observation at Owera bundanuces., Bedin (2001) point out similar discrepancies between theory and observation at lower abundances. + As the latter authors emphasine. resolving those discrepatcies is important both iu interpreting colowr-maguituce diagrams. aud iu establishing reliable theoretical mass-Iuminositv translprimallous.," As the latter authors emphasise, resolving those discrepancies is important both in interpreting colour-magnitude diagrams, and in establishing reliable theoretical mass-luminosity transformations." + h teris of the present survey. structure i1 the main sectrence has two consequences: first. systematic uuiscalibration. if the colour-iagulttde relation we aclopt fails to follow the empirical distributio> second. higher Malimquist bias. au a consequent inc'eased contamination from more distant star*. at colours where the main-sequence is steepest.," In terms of the present survey, structure in the main sequence has two consequences: first, systematic miscalibration, if the colour-magnitude relation we adopt fails to follow the empirical distribution; second, higher Malmquist bias, and a consequent increased contamination from more distant stars, at colours where the main-sequence is steepest." + Bot1 of these biases are likely to be inost signiicant near the break at My— 12:10 1£( 52«(V—KKuw2.6. 1.15«(1—J) 1.65).," Both of these biases are likely to be most significant near the break at $_V =12$ to 14 ( $5 < (V-K) < 5.6$, $1.45 < (I-J) < 1.65$ )." + These effecs will be taken Cully into account in statistical aualvsis of the nearby star sauple., These effects will be taken fully into account in statistical analysis of the nearby star sample. + For present pu‘poses. we siniply uote the increased uncertainty in plooimetric parallax for stars of the appropriate colours.," For present purposes, we simply note the increased uncertainty in photometric parallax for stars of the appropriate colours." + We have used the SINIBAD database to cross-'elereuce the NLTT sample agaiust the published iterature. checking all potential uaued couuterpars within 1 areuinute of the 2MLASS position.," We have used the SIMBAD database to cross-reference the NLTT sample against the published literature, checking all potential named counterparts within 1 arcminute of the 2MASS position." + The alter step is essential since SINIBAD cloes not iuclude cross-refe'euces to all of the LP uaumes cited in the NLTT. while some stars apyear twice (or 1jore) with clilerent uames aud slightly different j»ositions.," The latter step is essential since SIMBAD does not include cross-references to all of the LP names cited in the NLTT, while some stars appear twice (or more) with different names and slightly different positions." + Moreover. a significant 1umber of stars in the NLTT «atalogue have no associated uaime - a deliberate choice ou Luyteu's part.," Moreover, a significant number of stars in the NLTT catalogue have no associated name - a deliberate choice on Luyten's part." + The overwlelinine majority oftlese stars are actually from he Lowell Observatory proper moion survey (Ci‘las. Burnham Thomas. 1971).," The overwhelming majority of these stars are actually from the Lowell Observatory proper motion survey (Giclas, Burnham Thomas, 1971)." + Over 100 stars in the sample as a whole prove to lave either ploOluetric Or asrometric observatious available in, Over 400 stars in the sample as a whole prove to have either photometric or astrometric observations available in +"Relevant invariants introduced in AppendixA have the following values in the primed frame. implied by A=(0.0.0.0). in=(0.0.0.0):(2p, Omegall’,gamma, μμ”. where we assume A?=0?—[KP>0 and write i!—55*.","Relevant invariants introduced in Appendix\ref{sect:covariant} have the following values in the primed frame, implied by $K^{\mu'}=(\Omega',0,0,0)$, $K_D^{\mu'}=(0,0,0,\Omega')$:, t', u', where we assume $K^2=\Omega^2-|{\bi K}|^2>0$ and write $u'=\gamma'\beta'$." + The electric field. E(x). is an invariant. and has the same form in all frames.," The electric field, $E(\chi)$, is an invariant, and has the same form in all frames." + The equation of motion max be written in (wo equivalent forms:," The equation of motion may be written in two equivalent forms: u', ." +eround-based telescopes find (hat (he configuration of the magnetic field plavs an important role in the solar eruptive events. lLe.. Coronal Mass Ejections (CME) and solar flares (?)..,"ground-based telescopes find that the configuration of the magnetic field plays an important role in the solar eruptive events, i.e., Coronal Mass Ejections (CME) and solar flares \citep[]{canfield1999}." + It is thus of great importance to study the building up of the magnetic field in the solar ab(mosphere. as il rises [rom (he convection zone.," It is thus of great importance to study the building up of the magnetic field in the solar atmosphere, as it rises from the convection zone." + ILowever. the study of the transport οἱ magnetic flux and energv has been hampered by the invisibility of subsurface structures.," However, the study of the transport of magnetic flux and energy has been hampered by the invisibility of subsurface structures." + With (the time-distance helioseismic analvsis. ? and ? provide a view on the horizontal and vertical flow velocities on the subsurface lavers under sunspots and identify shear flows and rotation of the sunspots underneath the surface. which may build up the enerev aud helicity in the atmosphere.," With the time-distance helioseismic analysis, \cite{sasha1996} and \cite{zhao2003} provide a view on the horizontal and vertical flow velocities on the subsurface layers under sunspots and identify shear flows and rotation of the sunspots underneath the surface, which may build up the energy and helicity in the atmosphere." + Over the past decades. the development of numerical models have also ereatly improved our understanding of the cvnamics ancl energetics of magnetic flux emergence.," Over the past decades, the development of numerical models have also greatly improved our understanding of the dynamics and energetics of magnetic flux emergence." + ? describes a two-dimensional magnetohvdrodvnamic (ATID) simulation on the emergence of a horizontal magnetic [lux rope from the photosphere into the chromosphere using a iwo-lavered atmosphere., \cite{shibata1989} describes a two-dimensional magnetohydrodynamic (MHD) simulation on the emergence of a horizontal magnetic flux rope from the photosphere into the chromosphere using a two-layered atmosphere. + ? and ?/— carry oul sets of anelastic MIID simulations on the buovant rise of the magnetic flux tube Irom the base of convection zone to near the top. respectively.," \cite{fan2008} and \cite{jouve2009} carry out sets of anelastic MHD simulations on the buoyant rise of the magnetic flux tube from the base of convection zone to near the top, respectively." + In particular. ? shows the rotation of the flux tube driven by the Lorentz force ab the two ends while the twisted tube is bent.," In particular, \cite{fan2008} shows the rotation of the flux tube driven by the Lorentz force at the two ends while the twisted tube is bent." + ? suggested Chat shearing motion driven bv the Lorentz force draws (he magnetic field parallel to the Polarity Inversion Line (PIL). which was demonstrated in simulations of emereiug flux ropes (???7?777)..," \cite{manchester2000} suggested that shearing motion driven by the Lorentz force draws the magnetic field parallel to the Polarity Inversion Line (PIL), which was demonstrated in simulations of emerging flux ropes \citep[]{fan2001,magara2003,abbett2003,manchester2004,archontis2008,mactaggart2009}." + ?. [ound that during emergence. energy flix through the photosphere is first dominated bv the vertical flows while horizontal flows dominate the later phase.," \cite{magara2003} found that during emergence, energy flux through the photosphere is first dominated by the vertical flows while horizontal flows dominate the later phase." + The energy. Wausport of shear flows naturally provides an energv source for CMESs (??)..," The energy transport of shear flows naturally provides an energy source for CMEs \citep[]{manchester2007,manchester2008}." + Simulations have also revealed (hat shear [lows driven by the Lorentz lorce can produce eruptions in both magnetic arcacles and emerging flux ropes (2???) providing further evidence of a mechanism for CMESs. flares and filament eruptions.," Simulations have also revealed that shear flows driven by the Lorentz force can produce eruptions in both magnetic arcades \citep[]{manchester2003} and emerging flux ropes \citep[]{manchester2004,archontis2008,mactaggart2009} providing further evidence of a mechanism for CMEs, flares and filament eruptions." +" +0d ot = 2,(foA0 2⋅ 242(2.1) 2⋅⊾ 4 Ilere ιν D, = spectrum . of Higgs.» of mass i » . particle > massconsis",The fluctuation operator is defined in general form as where $\psi_i$ denotes the fluctuating fields and $\psi_i^{cl}$ the “classical” background field configuration; here these will be the instanton and the vacuum configurations. +"tsmq> 72 -B bosonsHiggsvector andbosons gaugemj, dilute gas approximationand be describedas separateobjects wit"," If the fields are expanded around the background configuration as $\psi_i = \psi_i^{cl} + \phi_i$ and if the Lagrange density is expanded accordingly, then the fluctuation operator is related to the second order Lagrange density via In terms of the fluctuation operators $\calm$ on the instanton and $\calm^0$ on the vacuum backgrounds, the effective action is defined as For our specific model we expand as In order to eliminate the gauge degrees of freedom we introduce, as in Ref. \cite{Kripfganz:1989vm}," +"h topological chargebyq= +1. Αα).zen"" (y (2.3)", the background gauge function which leads in the Feynman background gauge to the gauge-fixing Lagrange density +Magnetic ‘fields may play au iuportant dynamical role iu the CRB outflows (e.g.??)..,"Magnetic fields may play an important dynamical role in the GRB outflows \cite[\eg][]{LyutikovJPh,Lyutikov:2009}." + They may power the rel:uivistic outflow through? process (e.g.2).. aud contribute to particle acceleration iu the emission reeious.," They may power the relativistic outflow through\cite{BlandfordZnajek} process \citep[\eg][]{Komissarov05}, and contribute to particle acceleration in the emission regions." + Iu this p:iper we discuss the dynamics of the relativistic. strongly magnetized ejecta.," In this paper we discuss the dynamics of the relativistic, strongly magnetized ejecta." + The ‘estults are based Oh an exact solution of a one-dimensional Riemann problem of expausion of a cold. strongly iuagnetized into vacuum aud into external inedium of clensity pos (Lyutikov. stbinitted): they are reviewed in 82..," The results are based on an exact solution of a one-dimensional Riemann problem of expansion of a cold, strongly magnetized into vacuum and into external medium of density $\rho_{\rm ex}$ (Lyutikov, submitted); they are reviewed in \ref{Riemann}." + In application to GRBs. àve assumes that the central engine produces jet with density po aud nagnelizatio 10 (c=BiJgpo: iis normalized by li). moving with Lorentz factor οZ91l.," In application to GRBs, we assumes that the central engine produces jet with density $\rho_{0}$ and magnetization $\sigma$ $\sigma=B_0^2/\rho_{0}$; is normalized by $\sqrt{4 \pi} $ ), moving with Lorentz factor $\gamma_w\gg 1$." + Du fact. parzaiueters ο aud σ are 100 always idependent quantities: at παπα radii. when the motion of the ejecta is subsonic. they should be deermined together with the motionof the boundary. see 83.3..," In fact, parameters $\gamma_w$ and $\sigma$ are not always independent quantities: at small radii, when the motion of the ejecta is subsonic, they should be determined together with the motionof the boundary, see \ref{subsonic}." + Ln a supersonic regime. ‘elation between ον and σ cdeyends ou the details of the flow acceleration iin conical flows we expect ri Vo).," In a supersonic regime, relation between $\gamma_w$ and $\sigma$ depends on the details of the flow acceleration in conical flows we expect $\gamma_w \sim \sqrt{\sigma}$ )." + For generality. we do uot assume any relatiouship between σ aud η.," For generality, we do not assume any relationship between $\sigma$ and $\gamma_w$ ." + The ejecta is moviο into external density. pos., The ejecta is moving into external density $\rho_{\rm ex}$ . +and Ac.=0.,and $\Delta v_z=0$. + In these expressions. for the terms with Xx or + symbols the upper and lower signs correspond to prograde and retrograde cases. respectively.," In these expressions, for the terms with $\mp$ or $\pm$ symbols the upper and lower signs correspond to prograde and retrograde cases, respectively." + These integrals can be evaluated in terms of the modified Bessel functions. Ay and A» (Abramowitz&Stegun1972)., These integrals can be evaluated in terms of the modified Bessel functions $K_1$ and $K_2$ \citep{AS72}. + Employing the recursion relation we arrive at where the upper and lower signs are for prograde and retrograde encounters. respectively. and Av.=0 for coplanar collisions.," Employing the recursion relation we arrive at where the upper and lower signs are for prograde and retrograde encounters, respectively, and $\Delta$ $_{z}$ =0 for coplanar collisions." +" The structure of the expressions in terms of the modified Bessel functions Ay and Jv, is reminiscent of the results describing the perturbations of orbits of stars within disks owing to passing molecular clouds (Julian&Toomre1966).", The structure of the expressions in terms of the modified Bessel functions $K_0$ and $K_1$ is reminiscent of the results describing the perturbations of orbits of stars within disks owing to passing molecular clouds \citep{JT66}. +. It is of interest to consider various limiting cases for these expressions., It is of interest to consider various limiting cases for these expressions. + When ©»0. corresponding to a slowly rotating system. the Bessel functions asymptote to Aya)~—Ino and Ay(a)~1/0 (Abramowitz&Stegun1972).. and we find which can be obtained from the usual result for the impulse approximation (eq.(7-54)inBinney&Tremaine1987).. as this limit describes the situation when the stars in the disk remain nearly stationary during the collision.," When $\alpha \rightarrow 0$ , corresponding to a slowly rotating system, the Bessel functions asymptote to $K_0 (\alpha) \sim- \ln \alpha$ and $K_1(\alpha) \sim 1/ \alpha \ $ \citep{AS72}, and we find which can be obtained from the usual result for the impulse approximation \citep[eq. (7-54) in][]{BT87}, as this limit describes the situation when the stars in the disk remain nearly stationary during the collision." + Note that this limit is insensitive to the sign of O and hence does not distinguish between prograde and retrograde encounters., Note that this limit is insensitive to the sign of $\Omega$ and hence does not distinguish between prograde and retrograde encounters. + The limita>x to an interaction where the response should be weak because. for example. the encounter is a distant one or the spin and correspondsorbital frequencies are highly mismatched.," The limit $\alpha \rightarrow \infty$ corresponds to an interaction where the response should be weak because, for example, the encounter is a distant one or the spin and orbital frequencies are highly mismatched." + Employing the asymptotic expansion for the Bessel functions (Abramowitz&Stegun1972).. where j/=I. we find for the prograde and retrograde cases separately We note that the response is exponentially suppressed in the limita5ox. which demonstrates explicitly that the perturbed system is protected by adiabatic invariance.," Employing the asymptotic expansion for the Bessel functions \citep{AS72}, where $\mu=4\nu^2$, we find for the prograde and retrograde cases separately: We note that the response is exponentially suppressed in the limit $\alpha \rightarrow \infty$, which demonstrates explicitly that the perturbed system is protected by adiabatic invariance." + It is also interesting that in this limit the prograde and retrograde cases are simply related: and for the y-component: Thus. the prograde response diverges relative to the retrograde one. by a factor of à. and. for a given à the magnitude in the velocity perturbation is exactly a factor of four larger.," It is also interesting that in this limit the prograde and retrograde cases are simply related: and for the y-component: Thus, the prograde response diverges relative to the retrograde one, by a factor of $\alpha$, and, for a given $\alpha$ the magnitude in the velocity perturbation is exactly a factor of four larger." + From the above expressions. thechange in the energy of the perturbed system can be determined from:," From the above expressions, thechange in the energy of the perturbed system can be determined from:" +"where D,,0( and Bo, ave the upstream and downstream magnetic field strengths in units of iG. In the second step. we assumed that Bo/By=(paf/py)""o"". where w=1 corresponds to Boxp implied by the diffusion model in Equation (4)). Figure 6 shows {σοι} ala. =107. and (Jo/J4)os)=Jo)/sy(v) ad v=280 AMIIz for By= μα and ic=1 for the cases considered in Figure 5.","where $B_{0,\mu{\rm G}}$ and $B_{2,\mu{\rm G}}$ are the upstream and downstream magnetic field strengths in units of $\mu$ G. In the second step, we assumed that $B_2/B_0 = (\rho_2/\rho_0)^w = \sigma^w$ , where $w=1$ corresponds to $B \propto \rho$ implied by the diffusion model in Equation \ref{diffcoef}) ), Figure 6 shows $f_{e,0}(\gamma_e)/f_{e,2}(\gamma_e)$ at $\gamma_e=10^4$, and $(J_2/J_1)_{280} \equiv J_2({\nu}) / J_0({\nu})$ at $\nu = 280$ MHz for $B_0 = 1 \mu$ G and $w = 1$ for the cases considered in Figure 5." + Ilere. we assume that Nesp is (he same for both the pre-existing aud injected populations.," Here, we assume that $K_{e/p}$ is the same for both the pre-existing and injected populations." +" Since the electron cutoff momentum is 44c10 for the shock parameters considered here. the choice of 4,=10! and v=280 MllIz (see Equation(18))) as the representative values should be safe."," Since the electron cutoff momentum is $\gamma_{\rm cut}\sim 10^8$ for the shock parameters considered here, the choice of $\gamma_e=10^4$ and $\nu = 280$ MHz (see \ref{peaknu}) )) as the representative values should be safe." + As shown in Figure 5. for MS3. the downstream CR proton pressure can absorb typically only a few to of the shock ram pressure even [or /2=0.05.," As shown in Figure 5, for $M \la 3$, the downstream CR proton pressure can absorb typically only a few to of the shock ram pressure even for $R=0.05$." + Yet. (he acceleration of CI. electrons can result in a substantial enhancement in svnchrotron radiation across the shock.," Yet, the acceleration of CR electrons can result in a substantial enhancement in synchrotron radiation across the shock." + Our estimation indicates that the enhancement factor. (Jo/4)oso9. can be up to several al shocks with M1.5. up to several 10s for M.~ 2. and up (o several 1008 for M.~3.," Our estimation indicates that the enhancement factor, $(J_2/J_1)_{280}$, can be up to several at shocks with $M \sim 1.5$, up to several 10s for $M \sim 2$ , and up to several 100s for $M \sim 3$." + This is partly due to the large enhancement of the electron population across the shock. {οfio. which is ἐνρισα]]ν an order of magnitude smaller than the ratio (Js/4)»s).," This is partly due to the large enhancement of the electron population across the shock, $f_{e,2}/f_{e,0}$ , which is typically an order of magnitude smaller than the ratio $(J_2/J_0)_{280}$." + Additionalenhancement comes from the amplification of magnetic fields across the shock. οD.," Additionalenhancement comes from the amplification of magnetic fields across the shock, $B_2/B_0$." + We note that for the compression ofa uniform magnetic field. Boxp?. that is. ie=2/3.," We note that for the compression of a uniform magnetic field, $B \propto \rho^{2/3}$, that is, $w=2/3$." +" With this scaling. (J5/Ju)os, should be a bit smaller (han that in Figure 6."," With this scaling, $(J_2/J_0)_{280}$ should be a bit smaller than that in Figure 6." + However. it is also «quite plausible that the downstream magnetic field is stronger Chan (that expected for simple compression.," However, it is also quite plausible that the downstream magnetic field is stronger than that expected for simple compression." + lt has been suggested (hat at shocks. especially at strong shocks. the downstream magnetic field is amplifiecl by plasma instabilities (see.e.g..Dell 2004).. although the existence of such instabilities has not been fully explored [or weak shocks.," It has been suggested that at shocks, especially at strong shocks, the downstream magnetic field is amplified by plasma instabilities \citep[see, e.g.,][]{lucek00,bell04}, although the existence of such instabilities has not been fully explored for weak shocks." + Moreover. (he magnetic field can be further amplified by the turbulence that is induced through cascade of the vorticity generated behind shocks (GiacaloneΊναetal. 2008).," Moreover, the magnetic field can be further amplified by the turbulence that is induced through cascade of the vorticity generated behind shocks \citep{giacal07,ryuetal08}." +. In such cases. the ratio (J5/.Jg)os; could be larger than that in Figure 6.," In such cases, the ratio $(J_2/ J_0)_{280}$ could be larger than that in Figure 6." + In that sense. our estimate for the svnchrotron enhancement factor may be considered. as conservalive one.," In that sense, our estimate for the synchrotron enhancement factor may be considered as conservative one." + We also note that wilh s>r in Equation (21)). Js(»)/Ju(i) is larger al hieher lrequencies. but smaller with larger Bp.," We also note that with $s \geq r$ in Equation \ref{emirat2}) ), $J_2({\nu}) / J_0({\nu})$ is larger at higher frequencies, but smaller with larger $B_0$." + The above enhancement in svnchrotron emissionacross (he shock can be compared (o ihe enhancement in Dremsstrahling X-ray., The above enhancement in synchrotron emissionacross the shock can be compared to the enhancement in Bremsstrahlung X-ray. + The Bremsstrahling X-ray emissivity isgiven asJyX(Pv> T. so the ratioB of. the downstream to upstream emissivity. can be written. as," The Bremsstrahlung X-ray emissivity isgiven as$J_X \propto \rho^2\sqrt{T}$ , so the ratio of the downstream to upstream emissivity can be written as" +starting with up to Nox32000 stars and. dillerent binary fractions. density distributions. ry and Z4; values.,"starting with up to $N \simeq 32\,000$ stars and different binary fractions, density distributions, $r_{\rm h}$ and $R_{\rm gc}$ values." + Our nmocels extend this work to include a distribution of stellar masses and stellar evolution for N=100000.," Our models extend this work to include a distribution of stellar masses and stellar evolution for $N = 100\,000$." + In doing so we confirm the findings of Ixüppper. Ixroupa Baumegardt (2008).," In doing so we confirm the findings of Küppper, Kroupa Baumgardt (2008)." + The common sequence shows a mfr ratio that starts in the range of 0.15.—0.2 and increases slightlv with decreasing mass., The common sequence shows a $r_{\rm h} / r_{\rm t}$ ratio that starts in the range of $0.15 - 0.2$ and increases slightly with decreasing mass. + Relatecl to this the same authors found that clusters in a tidal field show an equilibrium half-mass radius after core-collapse., Related to this the same authors found that clusters in a tidal field show an equilibrium half-mass radius after core-collapse. + This was 2 pe for their standard set of models. noting that the particular value will increase for higher initial mass and larger Aue.," This was $2\,$ pc for their standard set of models, noting that the particular value will increase for higher initial mass and larger $R_{\rm gc}$." + Our models MI and A2 have a similar tidal tidal field. but [arger initial mass., Our models M1 and M2 have a similar tidal tidal field but larger initial mass. + οσο moels also show an ecuilibrium half-mass racius and as expectecL it is larger. im 21xc. with the inclusion of stellar evolution ikely contributing to some of the increase.," These models also show an equilibrium half-mass radius and as expected it is larger, $\sim 5\,$ pc, with the inclusion of stellar evolution likely contributing to some of the increase." + This COLPLPCSPOHls to a projected wil-light radius of about 3 pc which fits with the tvpical value observed for compact CC's in the Milky Way (Daumgardt et al.," This corresponds to a projected half-light radius of about $3\,$ pc which fits with the typical value observed for compact GCs in the Milky Way (Baumgardt et al." + 2010) and. M31. and indeed almost all galaxies where we see GC's (Da Costa οἱ al.," 2010) and M31, and indeed almost all galaxies where we see GCs (Da Costa et al." + 2009. for example).," 2009, for example)." + Of our models in the weaker tidal field only NI gets close to core-collapse and. indeed has a larger half-miass radius at this point. 10 pc. but in this case appears to still be rising.," Of our models in the weaker tidal field only N1 gets close to core-collapse and indeed has a larger half-mass radius at this point, $\sim 10\,$ pc, but in this case appears to still be rising." + Using a direct N-body code we have Followed the evolution of star clusters with cilferent initial sizes in a tidal field appropriate for a ealaxy such as the cdwarl irregular 6822 or the Large Magellanic Cloud.," Using a direct $N$ -body code we have followed the evolution of star clusters with different initial sizes in a tidal field appropriate for a galaxy such as the dwarf irregular $\,6822$ or the Large Magellanic Cloud." + We also looked at the clleet of increasing the galaxy mass by a factor of ten. appropriate for larger galaxies such as M31 and the Milky Way. on the evolution of clusters which initially fill. their tidal racii.," We also looked at the effect of increasing the galaxy mass by a factor of ten, appropriate for larger galaxies such as M31 and the Milky Way, on the evolution of clusters which initially fill their tidal radii." + Our main findings can be summarised as: We are indebted to Sverre Aarseth ancl Weigo Nitadori for creating and maintaining the GPU library forNBODY6., Our main findings can be summarised as: We are indebted to Sverre Aarseth and Keigo Nitadori for creating and maintaining the GPU library for. + JRIL also wishes to thank Ben Darsdell anc David. Barnes [or assistance with GPU usage at Swinburne. as well as Annic llughes for informative discussions regarding molecular clouds.," JRH also wishes to thank Ben Barsdell and David Barnes for assistance with GPU usage at Swinburne, as well as Annie Hughes for informative discussions regarding molecular clouds." + We also thank the referee for a number of insightul comments., We also thank the referee for a number of insightful comments. +MOND requires dark. matter of some form.,MOND requires dark matter of some form. + As discussed in Angusetal.(2008) there appears to be a scale at which MOND begins to poorly describe the dynamics of astrophysical systems., As discussed in \cite{afb} there appears to be a scale at which MOND begins to poorly describe the dynamics of astrophysical systems. + Εις is highlighted by RomanowskyO'Sullivanetal.(2007) which show that no dark matter is necessary to explain the detailed: cdvnamies of relatively low mass groups of galaxies ancl svstems smaller.," This is highlighted by \cite{romanowsky03,milgrom03,aftcz,osullivan08} which show that no dark matter is necessary to explain the detailed dynamics of relatively low mass groups of galaxies and systems smaller." + This is expected for sterile neutrino dark matter because Ht would have a free streaming length greater significantly larger than a typical galaxy (~50kpe for the Milky: Way., This is expected for sterile neutrino dark matter because it would have a free streaming length greater significantly larger than a typical galaxy $\sim$ 50kpc for the Milky Way. + However. just as numerical simulations of clusters of cold dark matter were necessary to show that the CDAL halos are a poor match to observed galaxies (cleBlok&MeGaugh1998:Gilmorectal. 2007)). the equilibrium distribution of the sterile neutrino DM must be checked to be consistent. with eroups and clusters of galaxies (see Sanders 2007)).," However, just as numerical simulations of clusters of cold dark matter were necessary to show that the CDM halos are a poor match to observed galaxies \citealt{deblok98,mcgaughdeblok,gnedin02,gentile04,gilmore07}) ), the equilibrium distribution of the sterile neutrino DM must be checked to be consistent with groups and clusters of galaxies (see \citealt{sanders07}) )." +" On the other hand. the three active neutrinos should oobablve have masses well below 0.5eV. Otherwise it. will »come cillieult to match the CMDB power spectrum because he angular scale of the peaks prefers O57=0.117. while QO,xm»."," On the other hand, the three active neutrinos should probably have masses well below 0.5eV. Otherwise it will become difficult to match the CMB power spectrum because the angular scale of the peaks prefers $\Omega_{\nu}h^2=0.117$ while $\Omega_{\nu}\propto m_{\nu}$." + Increasing the mass of another neutrino reduces he mass of the sterile neutrino and. the amplitude of the hire peak of the CAIB diminishes due to the rapidly decreasing maximum clensity (p.Μεταx ml)., Increasing the mass of another neutrino reduces the mass of the sterile neutrino and the amplitude of the third peak of the CMB diminishes due to the rapidly decreasing maximum density $\rho_{\nu}^{max}\propto m_{\nu}^4$ ). + Certain analyses of neutrino mixing experiments seen ο require an additional. sterile neutrino with a mass in the range 4eV«η1l."," We use a model of the observed GRB rate suggested by Bloom (2003), who constructed a correction factor of $D_L^{-2}$ when $z>1$." + This factor leads to the observed GBD rate deeply decay when :>l1., This factor leads to the observed GRB rate deeply decay when $z>1$. + Thus. different models of the star formation rate may eive almost the sue observed GRD rate (Bloom 2003). aud then the model of the star formation rate does not significantly affect our results.," Thus, different models of the star formation rate may give almost the same observed GRB rate (Bloom 2003), and then the model of the star formation rate does not significantly affect our results." + In fact. we focus ou the comparison of both results ou theoretical bases aud on the observational bases.," In fact, we focus on the comparison of both results on theoretical bases and on the observational bases." + The results of the comparison should not be greatly affected by the model of star formation rate (Liang. Wu Dai 2001).," The results of the comparison should not be greatly affected by the model of star formation rate (Liang, Wu Dai 2004)." + Our empirical results are derived by the GCGL-relation., Our empirical results are derived by the GGL-relation. + This relationship depends on cosmological parameters., This relationship depends on cosmological parameters. +" Iu this work we adopt O3,=0.5 and O4=(0.7.", In this work we adopt $\Omega_M=0.3$ and $\Omega_{\Lambda}=0.7$. + We check if the cosimological parameters siguificautlv affect the results of the comparisous between our empirical results aud model predictions., We check if the cosmological parameters significantly affect the results of the comparisons between our empirical results and model predictions. +" We take Qa,=0.5 and Q4= 0.5.", We take $\Omega_M=0.5$ and $\Omega_{\Lambda}=0.5$ . + In this case. the CCL-relation becomes L.ου=(0.90+0.12)pLEton for a CRB sample presented by Au et al. (," In this case, the GGL-relation becomes $E_{\gamma,50}=(0.90\pm0.12) E_{\rm p}^{1.42\pm 0.10}$ for a GRB sample presented by Xu et al. (" +2005).,2005). +" We show the comparison between the PMO) based on this relationship and Phy predicted by the power-law jet model iu the cosmology model with Q5,=0.5 and O4=0.5 in Figure 6.", We show the comparison between the $P^{\rm em}(\theta)$ based on this relationship and $P^{\rm th}(\theta)$ predicted by the power-law jet model in the cosmology model with $\Omega_M=0.5$ and $\Omega_{\Lambda}=0.5$ in Figure 6. + The I&-S test for the two distributions shows Pys=0.123. confidently: sugecsting that they are consistent.," The K-S test for the two distributions shows $P_{K-S}=0.123$, confidently suggesting that they are consistent." + Comparing the results shown in Figure 6 to that shown in the left panel of Figure 3. one can find that cosmological parameters do uot significantly affect our results.," Comparing the results shown in Figure 6 to that shown in the left panel of Figure 3, one can find that cosmological parameters do not significantly affect our results." + We should clarity that our empirical approach aud theoretical model are independent without toutologv., We should clarify that our empirical approach and theoretical model are independent without toutology. + The model predictions are statistical distributions. while the clupirical results are based ou the relationships related to the spectral properties aud energy release of CRBs.," The model predictions are statistical distributions, while the empirical results are based on the relationships related to the spectral properties and energy release of GRBs." + The enipirical approach and theoretical model are intrinsically different., The empirical approach and theoretical model are intrinsically different. + Our enpirical results are roughly consistent with the results from currently 0-known CRB sample., Our empirical results are roughly consistent with the results from currently $\theta$ -known GRB sample. + This is a selt-consistent result because the GOGL-relation was discovered w this CRB sample., This is a self-consistent result because the GGL-relation was discovered by this GRB sample. + For the bursts in this sample their oeakk energies. teniporal breaks of optical afterglow light curves. and redshifts are well measured.," For the bursts in this sample their peak energies, temporal breaks of optical afterglow light curves, and redshifts are well measured." + Such a sample uust suffers ercatly observational biases and sample selection. effects. especially when the completeness at low Huxes and the bias of redshift micasurement are considered.," Such a sample must suffers greatly observational biases and sample selection effects, especially when the completeness at low fluxes and the bias of redshift measurement are considered." + Daud Preece (2005) argued that the GGL-velation may © an artifact of the selection effects. aud these selection effects may favor sub-populations of CRBs.," Band Preece (2005) argued that the GGL-relation may be an artifact of the selection effects, and these selection effects may favor sub-populations of GRBs." + If it is really he case. the selection effects should affect our empirical results.," If it is really the case, the selection effects should affect our empirical results." + We thauk the anonuvinious referee for his/her valuable sugecstions and conunents., We thank the anonymous referee for his/her valuable suggestions and comments. + We also thank Diug Zhaug. Zieno Dai. and Yiping Qiu for their helpful discussious.," We also thank Bing Zhang, Zigao Dai, and Yiping Qin for their helpful discussions." + This work was supported by the National Natural Scieuce Foundation of China (Cwauts10163001)., This work was supported by the National Natural Science Foundation of China (Grants10463001). +The presence of the solar atmosphere will result also in the de-Iocusing of the coherent raciation. (hus worsening the quality of (he solar gravitational lens.,"The presence of the solar atmosphere will result also in the de-focusing of the coherent radiation, thus worsening the quality of the solar gravitational lens." + To analvze this influence let us estimate (he optical distance for the (wo sources affecting the light propagation in the solar vicinity. namely gravitv and plasma.," To analyze this influence let us estimate the optical distance for the two sources affecting the light propagation in the solar vicinity, namely gravity and plasma." + One may expect that the beginning of the interference zone will be shifted further away from the Sun., One may expect that the beginning of the interference zone will be shifted further away from the Sun. + For estimation purposes we will consider here only the steadi-state part of the plasma model., For estimation purposes we will consider here only the steady-state part of the plasma model. + The beginning of the interference zone (e.q., The beginning of the interference zone (e.q. +" the effective optical distance) in this case may be determined from This expression ngives the effective optical distance for the svstem nleravilv+plasma. JF,grpl>0: One may note (hat. lor any given impact parameter b there is a critical frequency rogi such (hat the denominator in (he expression (15)) vanishes ancl (he effective optical distance Ferpi becomes infinitive.", the effective optical distance) in this case may be determined from This expression gives the effective optical distance for the system gravity+plasma ${\cal F}_{\tt gr+pl}\ge 0$: One may note that for any given impact parameter $b$ there is a critical frequency $\nu_{\tt crit}$ such that the denominator in the expression \ref{eqtot}) ) vanishes and the effective optical distance ${\cal F}_{\tt gr+pl}$ becomes infinitive. + This is the case when there is no lensing at all and the solar plasma enlively neutralizes influence of the solar gravity., This is the case when there is no lensing at all and the solar plasma entirely neutralizes influence of the solar gravity. + This critical frequency is given as follows: Dased on the estimates [or Fgx presented in the Table 1. and. [rom the practical considerations for the solar gravity lens mission. one will have to limit the range of possible impact parameters to those in the interval b/R...ε|1.05.1.35]. which correspond to the optical distance Ferpi€|601.1000|. AU.," This critical frequency is given as follows: Based on the estimates for ${\cal F}_{\tt gr}$ presented in the Table \ref{tab66} and from the practical considerations for the solar gravity lens mission, one will have to limit the range of possible impact parameters to those in the interval $ {b}/{{\cal R}_\odot } \in [1.05, 1.35]$, which correspond to the optical distance ${\cal F}_{\tt gr+pl} \in [601, 1000[$ AU." + For this range of impact parameter. (he main contribution comes from the term ~(R.pn»).," For this range of impact parameter, the main contribution comes from the term $\sim +\big({{\cal R}_\odot / b}\big)^{15}$." + Therefore. approximating to the sufficient order. we will have the critical frequency wilh Merit=ανν...)120Gllz or. equivalently. 2.5 mim.," Therefore, approximating to the sufficient order, we will have the critical frequency with $\nu_{0\,\tt crit}\equiv\nu_{\tt crit}({\cal R}_\odot )=120~{\rm GHz}$ or, equivalently, 2.5 mm." + As a result of this analvsis we find that the effective optical distance for the svstem gravitv-plasma will be determined from the following expression:, As a result of this analysis we find that the effective optical distance for the system gravity+plasma will be determined from the following expression: +"Optical imaging of the RA 02:30 hy field of the ΗΠΑΏου) Survey was obtained on 22 October 2001 UT using the prime focus dmager Suprime-Cam (Mivazakietal.1998) ou the Subaru 8.2-11. Telescope on Mama Wea. Πανάς,","Optical imaging of the RA 02:30 hr field of the IfA-Deep Survey was obtained on 22 October 2001 UT using the prime focus imager Suprime-Cam \citep{1998SPIE.3355..363M} on the Subaru 8.2-m Telescope on Mauna Kea, Hawaii." + The instrument is a mosaic of ten contiguous 1006 AITT/Liucolu Lab phase 2 and 3 CCDs with a total field of view of 31/«27'.., The instrument is a mosaic of ten contiguous $\times$ 4096 MIT/Lincoln Lab phase 2 and 3 CCDs with a total field of view of $\times$. + Conditions were photometric with O’s8 FWHAL seeing., Conditions were photometric with 8 FWHM seeing. + We tmaged two adjacent fields with a total area of 0.5 ddeerees., We imaged two adjacent fields with a total area of 0.5 degrees. + DitheredR..£.. z/—baud observations were obtained with iuteerations of 560 x. GI5 s. and 960 s per filter per pointing. respectively.," Dithered, -band observations were obtained with integrations of 560 s, 645 s, and 960 s per filter per pointing, respectively." + The aad F--lband filter are Cousins filters., The and -band filter are Cousins filters. + The falter has an effective wavelength of 9195 aad a FWOAL of 10A.. very similar to that used by the SDSS survey (Fukueitaetal.1996)..," The filter has an effective wavelength of 9195 and a FWHM of 1410, very similar to that used by the SDSS survey \citep{1996AJ....111.1748F}." + huages were flattened. defringed. warped onto a cohbunon sky coordinate svsteun. registered. aud cleaned of cosunic rays.," Images were flattened, defringed, warped onto a common sky coordinate system, registered, and cleaned of cosmic rays." + A preliminary photometric calibration of the πω ddata was done using optical Πασάς previously obtained from smaller telescopes. which was calibrated with standards from Landolt(1992)..," A preliminary photometric calibration of the and data was done using optical imaging previously obtained from smaller telescopes, which was calibrated with standards from \citet{1992AJ....104..340L}." + For the ddata. the preliminary calibration was done by comparing the ccolors of stars in the Suprime-Cam data with the stellar locus.," For the data, the preliminary calibration was done by comparing the colors of stars in the Suprime-Cam data with the stellar locus." + The latter was svuthesized from the spectral enerey distributions of Camu&Stryker(19835) and the instrumental (filter|detectoratumospliere) transmission profiles., The latter was synthesized from the spectral energy distributions of \citet{1983ApJS...52..121G} and the instrumental (filter+detector+atmosphere) transmission profiles. + The resulting maguitudes in Table 1 are Vega-based., The resulting magnitudes in Table 1 are Vega-based. + We identified an extremely red stellar object at RA(2000) = 02:26:37.6. DEC(2000) = 00:51:51.7 in the I aud 2/--baud imaging.," We identified an extremely red stellar object at RA(2000) = 02:26:37.6, DEC(2000) = 00:51:54.7 in the $I$ and -band imaging." + We refer to it as “IEA 0230-Z17 hereinafter., We refer to it as “IfA 0230-Z1” hereinafter. + We obtained J aud ZI-baud photometry ou 06 November 2001 UT using the facility spectrograph Spex (Πανetal.1998).., We obtained $J$ and $H$ -band photometry on 06 November 2001 UT using the facility spectrograph Spex \citep{1998SPIE.3354..468R}. + Spex has a slitiewing camera. which uses a 5124512 InSb array from Ravtheou-SBRC and has a pixel scale of 071118Ἐ," Spex has a slit-viewing camera, which uses a $\times$ 512 InSb array from Raytheon-SBRC and has a pixel scale of 118." +"ν, Conditious were photometric with QO/ss5 FWTIAL secing.", Conditions were photometric with 85 FWHM seeing. + We obtained a total of 18 nuu aud 10 min of iutegration at J and 1 - respectively., We obtained a total of 18 min and 10 min of integration at $J$ and $H$ -band respectively. + The Spex filters were purchased as part of the Mauna hea Filter Cousortimm (Simons&TokunagaWw01:Tokunagaetal. 2001).. and hence will be common to most of the current major infrared telescopes.," The Spex filters were purchased as part of the Mauna Kea Filter Consortium \citep{mkofilters1, mkofilters2}, and hence will be common to most of the current major infrared telescopes." + We obtained inages of the standard star $J 9105 frou Perssonctal.(1098) imuneciately after observing HA 0230-Z1., We obtained images of the standard star SJ 9105 from \citet{1998AJ....116.2475P} immediately after observing IfA 0230-Z1. + The resulting maeguitudes i Table 1 are Vega-based., The resulting magnitudes in Table 1 are Vega-based. + We obtained an Z-baud spectrmm of ΠΔ 0230-Z1 on LO November 2001 UT with the Neck Telescope aud. the facility spectrograplh NIRSPEC (MeLeanetal.1995)., We obtained an $H$ -band spectrum of IfA 0230-Z1 on 10 November 2001 UT with the Keck Telescope and the facility spectrograph NIRSPEC \citep{1998SPIE.3354..566M}. + NIRSPEC uses a 102141021 InSh ALADDIN: detector from: Ravtheou-SBRC., NIRSPEC uses a $\times$ 1024 InSb ALADDIN detector from Raytheon-SBRC. + A total of 30 min of integration was obtained in low resolution mode using the NIRSPEC-5 blocking filter and the 07776 «lit., A total of 30 min of integration was obtained in low resolution mode using the NIRSPEC-5 blocking filter and the 76 slit. + Conditious were very nou-plotometric due to high thick cirrus., Conditions were very non-photometric due to high thick cirrus. + The object was dithered on the slit between exposures., The object was dithered on the slit between exposures. +" The slit PA was set to T3766 cast of north. so that the bright object D/665 away (""object AT} was also on the slit for all the exposures."," The slit PA was set to 6 east of north, so that the bright object 65 away (“object A”) was also on the slit for all the exposures." + This provided a well-detected reference for registering the frames. and also a check on the resulting spectrophotometry (see below).," This provided a well-detected reference for registering the frames, and also a check on the resulting spectrophotometry (see below)." + A nearby AOV star was observed inmuediately afterward to calibrate the tellurc and iustrmucutal throughput., A nearby A0V star was observed immediately afterward to calibrate the telluric and instrumental throughput. + The spectra were reduced using custom IDL scripts., The spectra were reduced using custom IDL scripts. + The raw images on the NIRSPEC detector are curved iu both the spectral aud spatial directions., The raw images on the NIRSPEC detector are curved in both the spectral and spatial directions. +" After subtracting a dark frame and dividing bv a flat field. the individual Huages were cleaned of outlier pixels aud rectified using traces of the arc lamp lines and the object spectra,"," After subtracting a dark frame and dividing by a flat field, the individual images were cleaned of outlier pixels and rectified using traces of the arc lamp lines and the object spectra." + Pairs of images taken at successive nods were subtracted to remove the sky cussion., Pairs of images taken at successive nods were subtracted to remove the sky emission. + huages were then registered. shifted. and stacked to form a final 2-d mosaic of the spectrum.," Images were then registered, shifted, and stacked to form a final 2-d mosaic of the spectrum." +" Extractions of I-d spectra frou, the mosaic were done in a manner to produce reliable errors based ou photon counting (Poisson) statistics.", Extractions of 1-d spectra from the mosaic were done in a manner to produce reliable errors based on photon counting (Poisson) statistics. + Details will be presented in a future paper., Details will be presented in a future paper. + We divided the extracted spectra bv the spectra of the AOV. calibrator star and then multiplied bv a 9720 IK blackbody to restore the true shape ofthe coutimuun., We divided the extracted spectra by the spectra of the A0V calibrator star and then multiplied by a 9720 K blackbody to restore the true shape of the continuum. + Uvdrogen absorption features in thecalibrator were removed by linear interpolation., Hydrogen absorption features in thecalibrator were removed by linear interpolation. + Wavelength calibration was done with spectra of argou and ueon lamps., Wavelength calibration was done with spectra of argon and neon lamps. + The spectral resolution (A/AA) of the original extracted spectra was Ro=1610 (9.7 Aj): nuum of the telluric OI ciission lines are well-separated from each other., The spectral resolution $\lambda/\Delta{\lambda}$ ) of the original extracted spectra was $R=1640$ (9.7 ); many of the telluric OH emission lines are well-separated from each other. + The resulting S/N was only zL35. so we xin!oothed the spectra with a 32 pixel EWIINME Gaussian. with proper weighting accounting for the measurement errors. and rebiuued the data to 2 pixels per spectral resolution clement.," The resulting S/N was only $\approx1\!-\!3$, so we smoothed the spectra with a 32 pixel FWHM Gaussian, with proper weighting accounting for the measurement errors, and rebinned the data to 2 pixels per spectral resolution element." + The final spectra have a resolution of R=150 and are plotted in Figure L.., The final spectra have a resolution of $R=180$ and are plotted in Figure \ref{fig-spectra}. +" The zpJ bendeolorsoffA 0230. Zlarceatremelyrcd, whilethe]- IIeolorsarceclatieclgbluc."," The $J$ -band colors of IfA 0230-Z1 are extremely red, while the $J-H$ colors are relatively blue." +Sucheolorsaveuniquelgeharacteristicof., Such colors are uniquely characteristic of T dwarfs. + Zlhasi-J-2.r120.15 mae (Vega). comparable to the reddest known T dwarfs.," IfA 0230-Z1 has $\zp-J=2.74\pm0.15$ mag (Vega), comparable to the reddest known T dwarfs." + Its J)II color of 0.312:0.05 indicate a spectral type of ΤὸTl (Leeecttetal. 2002).., Its $J-H$ color of $\pm$ 0.05 indicate a spectral type of T3–T4 \citep{leg01}. . + Figure | shows the Ieck/NIRSPEC spectra of I£A 0230-Zl and object A. which were observed simultaneously aud reduced in an identical fashion.," Figure \ref{fig-spectra} shows the Keck/NIRSPEC spectra of IfA 0230-Z1 and object A, which were observed simultaneously and reduced in an identical fashion." + The spectrum of object A shows a featureless continumn fy~AP. cousisteut with the near-IR continu of a low redshift galaxy C(Manunuuccietal. 2001)..," The spectrum of object A shows a featureless continuum $f_\lambda\sim\lambda^{-0.7}$, consistent with the near-IR continuum of a low redshift galaxy \citep{2001MNRAS.326..745M}." + On the other hand. IA 0230-Z1 shows a peak iu its conutimmun around 1.58 ;42.," On the other hand, IfA 0230-Z1 shows a peak in its continuum around 1.58 ." +. The continu is depressed in the blue aud the red around the peak. indicating the presence of aud aabsorption. respectively.," The continuum is depressed in the blue and the red around the peak, indicating the presence of and absorption, respectively." + Since object A's spectrum docs not show anv such features. we conclude that thesefeatures," Since object A's spectrum does not show any such features, we conclude that thesefeatures" +up to 100 days.,up to 100 days. + Exposures were acquired in pairs to be later summed. except when bad weather conditions forced us to stop observations after the first frame.," Exposures were acquired in pairs to be later summed, except when bad weather conditions forced us to stop observations after the first frame." + We thus collected fourteen epochs of data over 2.5 months., We thus collected fourteen epochs of data over 2.5 months. + The log of the observations is given in Table |.. where each exposure is identified with a unique ID. and the epoch at the middle of the acquisition period is indicated. along with the exposure time and the observing mode (v=Vvisitor. s=service).," The log of the observations is given in Table \ref{t_obs}, where each exposure is identified with a unique ID, and the epoch at the middle of the acquisition period is indicated, along with the exposure time and the observing mode (v=visitor, s=service)." + Data were reduced with the dedicated CPL-based pipeline available at the ESO web site., Data were reduced with the dedicated CPL-based pipeline available at the ESO web site. + Because of the extremely low signal collected for the hottest targets. we performed many trial reductions to find the choices and parameter sets that maximized the output quality.," Because of the extremely low signal collected for the hottest targets, we performed many trial reductions to find the choices and parameter sets that maximized the output quality." + The frames were de-biased and flat-fielded with standard procedures based on the frames collected within the standard calibration plan., The frames were de-biased and flat-fielded with standard procedures based on the frames collected within the standard calibration plan. + The dark current was found to be non-negligible only along the top edge of the CCD. not used in our work. and no dark correction was applied to avoid the corresponding decrease in S/N by10-15%.," The dark current was found to be non-negligible only along the top edge of the CCD, not used in our work, and no dark correction was applied to avoid the corresponding decrease in S/N by." +. We gave particular attention to. the wavelength calibration (wle). whose defects can easily affect the radial velocity (RV) measurements.," We gave particular attention to the wavelength calibration (wlc), whose defects can easily affect the radial velocity (RV) measurements." + The goodness of the wle was checked by analyzing the spectra of the lamp fibers acquired simultaneously with target stars., The goodness of the wlc was checked by analyzing the spectra of the lamp fibers acquired simultaneously with target stars. + This reduction step was particularly problematic. because we found that running the complete wle routine resulted in an incorrect solution. with a deviation from the correct one that increased with wavelength and fiber number. up to 10-15 km s'.," This reduction step was particularly problematic, because we found that running the complete wlc routine resulted in an incorrect solution, with a deviation from the correct one that increased with wavelength and fiber number, up to 10-15 km $^{-1}$." + We therefore adopted the standard solution for the H7A setup. included in the instrumental package downloadable from the GIRAFFE web site. allowing the pipeline to use the lamp fibers to find rigid shifts and changes in the spectral geometry on the chip.," We therefore adopted the standard solution for the H7A setup, included in the instrumental package downloadable from the GIRAFFE web site, allowing the pipeline to use the lamp fibers to find rigid shifts and changes in the spectral geometry on the chip." + After the final extraction. the lamp fibers showed only small random deviations from laboratory wavelengths (0.3 km rms).," After the final extraction, the lamp fibers showed only small random deviations from laboratory wavelengths (0.3 km $^{-1}$ rms)." + RVThis wle error is small compared to uncertainties in the measurement. and can be safely neglected in the final error budget.," This wlc error is small compared to uncertainties in the RV measurement, and can be safely neglected in the final error budget." + Finally. science spectra were extracted using both an optimum algorithm and a simple sum.," Finally, science spectra were extracted using both an optimum algorithm and a simple sum." + We found that these two methods were in general equivalent and the choice did not alter the results. but in some noisy spectra one or the other returned more precise measurements.," We found that these two methods were in general equivalent and the choice did not alter the results, but in some noisy spectra one or the other returned more precise measurements." + This was probably due to small cosmetic. defects or noise spikes being treated differently by the two algorithms., This was probably due to small cosmetic defects or noise spikes being treated differently by the two algorithms. + We therefore preferred optimum-extracted spectra. but we opted for a simple sum in the few cases in which this clearly returned smaller RV errors.," We therefore preferred optimum-extracted spectra, but we opted for a simple sum in the few cases in which this clearly returned smaller RV errors." + The background flux was estimated by averaging nine fibers allocated to the sky and. after subtracting their mean spectrum from those of the targets. we checked that the weak interstellar emission in the core of the Πρ line had been effectively removed.," The background flux was estimated by averaging nine fibers allocated to the sky and, after subtracting their mean spectrum from those of the targets, we checked that the weak interstellar emission in the core of the $_\beta$ line had been effectively removed." + The spectra were then trimmed to retain only the central region (1780-4930 ). and we normalized them fitting a linear relation to the continuum on both sides of the Hy line.," The spectra were then trimmed to retain only the central region (4780-4930 ), and we normalized them fitting a linear relation to the continuum on both sides of the $_\beta$ line." + We verified that a higher order polynomial was not required in the normalization. as there was no appreciable change in either the fitted function and or the results.," We verified that a higher order polynomial was not required in the normalization, as there was no appreciable change in either the fitted function and or the results." + As a final step of the reduction. the spectra forming à pair of exposures (see Table 1)) were added.," As a final step of the reduction, the spectra forming a pair of exposures (see Table \ref{t_obs}) ) were added." + Some example spectra are shown in Figure 2.. for two stars at the edge of the temperature range 7700 and 2200 K) and one of intermediate temperature. plus the star #337345. discussed later.," Some example spectra are shown in Figure \ref{f_spectra}, for two stars at the edge of the temperature range 700 and 200 K) and one of intermediate temperature, plus the star 37345, discussed later." + The presented spectra are the sum of all the spectra collected for each star. after shifting them to laboratory wavelengths.," The presented spectra are the sum of all the spectra collected for each star, after shifting them to laboratory wavelengths." + The observed HB was fitted with the zero-age HB model (ZAHB) of with. metallicity [Fe/H]=-1.10 to derive a temperature scale along the HB., The observed HB was fitted with the zero-age HB model (ZAHB) of with metallicity $-$ 1.10 to derive a temperature scale along the HB. + The procedure was not straightforward using the (U— color. and uncertainties remained in the determination of the required distance modulus and reddening.," The procedure was not straightforward using the $U-V$ ) color, and uncertainties remained in the determination of the required distance modulus and reddening." + These problems could be due to the use of the, These problems could be due to the use of the +with zero slope. although it is fair to say that there is evidence for a slight positive correlation.,"with zero slope, although it is fair to say that there is evidence for a slight positive correlation." + On the other hand. his correlation is largely. driven by the rare clusters which ormed at very high redshifts: most of these objects formed ab αρ0.0 and are evenly distributed about the mean mass-emperature relationship.," On the other hand, this correlation is largely driven by the rare clusters which formed at very high redshifts; most of these objects formed at $z_f < 0.6$ and are evenly distributed about the mean mass-temperature relationship." + Correlation coellicients ancl best-fit line parameters for hese data are summarized in Table 1.., Correlation coefficients and best-fit line parameters for these data are summarized in Table \ref{tzcorrtable}. . + The correlations within reo) are significantly inlluenced by a cluster with a ormation redshift of OLS ancl very large error. bars on that value., The correlations within $r_{200}$ are significantly influenced by a cluster with a formation redshift of 0.8 and very large error bars on that value. + This cluster acquired most ofits mass very early in the simulation and grew through gradual accretion thereafter. so he reshift range during which it had a mass of 75% inal mass is very long.," This cluster acquired most of its mass very early in the simulation and grew through gradual accretion thereafter, so the reshift range during which it had a mass of $75\% \pm 7.5\%$ its final mass is very long." + Its temperature. while higher than he ensemble average. is well within the variations seen for more recently formed clusters.," It's temperature, while higher than the ensemble average, is well within the variations seen for more recently formed clusters." + LE this point is left out the analysis. then all the slopes become consistent with zero in their one-sigma uncertainty range. and the correlation coefficients. drop to 0.24 (25). 0.19. (75). and. 0.005 (77).," If this point is left out the analysis, then all the slopes become consistent with zero in their one-sigma uncertainty range, and the correlation coefficients drop to 0.24 $T_v$ ), 0.19 $T_s$ ), and 0.005 $T_f$ )." + These coellicients. correspond. respectively to324...θα. and probabilities of uncorrelated data.," These coefficients correspond respectively to, and probabilities of uncorrelated data." + The cliscrepaney between our intuition (clusters which first virialized at an carly cpoch should. be hotter) and these simulations can be resolved by acknowledging the essentially cvnamic. nature ol clusters in. a. [ow-density universe., The discrepancy between our intuition (clusters which first virialized at an early epoch should be hotter) and these simulations can be resolved by acknowledging the essentially dynamic nature of clusters in a low-density universe. +" Multiple lines of observational evidence point to an,~0.3 cosmology in which clusters are still forming at the present day. and the theoretical construct of a relaxed. virialized. cluster seems to have few counterparts in the observable population."," Multiple lines of observational evidence point to an $\Omega_m \sim 0.3$ cosmology in which clusters are still forming at the present day, and the theoretical construct of a relaxed, virialized cluster seems to have few counterparts in the observable population." + Itather than treating clusters as static fossils of the primordial density field. we should attempt to model them explicitly as evolving entities.," Rather than treating clusters as static fossils of the primordial density field, we should attempt to model them explicitly as evolving entities." + One example.of such a model has. been presented by, One exampleof such a model has been presented by +"Water is one of the most important molecules in star-forming regions: it is a dominant form of oxygen, is important in the energy balance, and is associated with the formation of planets and emergence of life.","Water is one of the most important molecules in star-forming regions: it is a dominant form of oxygen, is important in the energy balance, and is associated with the formation of planets and emergence of life." +" Thus, following the water ""trail"" from collapsing clouds to protoplanetary disks is a fundamental problem in astronomy and astrochemistry."," Thus, following the water “trail” from collapsing clouds to protoplanetary disks is a fundamental problem in astronomy and astrochemistry." +" In the cold and quiescent regions the gaseous water abundance is low, only 107?— (e.g.,Bergin&Snell2002),, but in regions with intense heating or active shocks, its abundance can reach 107 with respect to H5 — comparable to or higher than that of CO 1998)."," In the cold and quiescent regions the gaseous water abundance is low, only $10^{-9}-10^{-8}$ \citep[e.g.,][]{bergin02h2o}, but in regions with intense heating or active shocks, its abundance can reach $^{-4}$ with respect to $_2$ – comparable to or higher than that of CO \citep[e.g.,][]{harwit98}." +". Which mechanism is most important for regulating the H2O abundance in low-mass protostars is still heavily debated, however."," Which mechanism is most important for regulating the $_2$ O abundance in low-mass protostars is still heavily debated, however." +" Is it passive heating of the collapsing envelope by the accretion luminosity from forming stars (e.g.,Ceccarellietal.1998;Maret 2002),, or shocks caused either by protostellar outflows (e.g.,Nisinietal.1999) or related to ongoing accretion onto circumstellar disks 2007)?"," Is it passive heating of the collapsing envelope by the accretion luminosity from forming stars \citep[e.g.,][]{ceccarelli98h2o,maret02}, , or shocks caused either by protostellar outflows \citep[e.g.,][]{nisini99} or related to ongoing accretion onto circumstellar disks \citep{watson07}?" +"? Η20Ο is also a key molecule in the chemistry in regions of star formation: in large parts of the cold and dense envelopes around low-mass protostars, H2O is the dominant constituent of the icy mantles of dust grains (e.g.,Whittetetal.1988;Boogert2008)."," $_2$ O is also a key molecule in the chemistry in regions of star formation: in large parts of the cold and dense envelopes around low-mass protostars, $_2$ O is the dominant constituent of the icy mantles of dust grains \citep[e.g.,][]{whittet88,boogert08}." +". Its evaporation at temperatures higher than 90-100 K determines at what point water itself and any complex organic molecules, formed in these ice mantles, are injected into the gas-phase."," Its evaporation at temperatures higher than 90–100 K determines at what point water itself and any complex organic molecules, formed in these ice mantles, are injected into the gas-phase." +" This discussion has received new fuel with the detection of surprisingly strong highly excited H5O lines at mid-infrared wavelengths with the Telescope's infrared spectrograph, IRS, toward one deeply embedded Class 0 protostar, NGC 1333-IRAS4B, by Watsonetal.(2007)."," This discussion has received new fuel with the detection of surprisingly strong highly excited $_2$ O lines at mid-infrared wavelengths with the 's infrared spectrograph, IRS, toward one deeply embedded Class 0 protostar, NGC 1333-IRAS4B, by \cite{watson07}." +". Based on the high critical density of the observed lines and temperature (170 K), Watsonetal. argue that the water emission observed toward this source has its origin in an accretion shock in its circumstellar disk."," Based on the high critical density of the observed lines and temperature $\sim 170$ K), \citeauthor{watson07} argue that the water emission observed toward this source has its origin in an accretion shock in its circumstellar disk." +" Those data could not spatially or spectrally resolve the water emission, however."," Those data could not spatially or spectrally resolve the water emission, however." +" In this letter we present observations at 203 GHz of the Hj*0 isotopologue at high-angular resolution (0.5"") using the Institut de Radioastronomie Milliméttrique (IRAM) Plateau deBure Interferometer to determine the origin of water emission in low-mass protostars.", In this letter we present observations at 203 GHz of the $_2^{18}$ O isotopologue at high-angular resolution $''$ ) using the Institut de Radioastronomie Milliméttrique (IRAM) Plateau deBure Interferometer to determine the origin of water emission in low-mass protostars. +" This isotopic line is a useful tracer of HzO as it can be detected and imaged at high angular resolution from the ground under good weather conditions (e.g.,Jacqetal.1988;Gensheimer1996;vanderTak2006)."," This isotopic line is a useful tracer of $_2$ O as it can be detected and imaged at high angular resolution from the ground under good weather conditions \citep[e.g.,][]{jacq88,gensheimer96,vandertak06}." +. Its upper level energy of 203.6 K is well matched to the observed excitation temperature of water seen by Spitzer., Its upper level energy of 203.6 K is well matched to the observed excitation temperature of water seen by . +" We observed NGC 1333-IRAS4B (IRASAB in the following; a=03529™ 128000, 6—4-31?13/008""711 [J2000] Jorgensenetal.20072)"," We observed NGC 1333-IRAS4B (IRAS4B in the following;$\alpha$ $^{\mathrm h}$ $^{\mathrm m}$ 00, $\delta$ $^\circ$ 1 [J2000] \citealt{prosacpaper})" +We present the discovery of X-ray omission. [rom the symbiotic svstem 4+ Draconis.,We present the discovery of X-ray emission from the symbiotic system 4 Draconis. + The X-rav lux is hieA variable on timescales [rom minutes to vears., The X-ray flux is highly variable on timescales from minutes to years. + X-ray spectroscopy shows the spectrum is sometimes dominated yw strong absorption by partially ionised material. probaA he wind of the red. giant.," X-ray spectroscopy shows the spectrum is sometimes dominated by strong absorption by partially ionised material, probably the wind of the red giant." +" When free from absorption —z spectrum is consistent with bremsstrahlung emission at a empoerature around kkeV. We conclude that these cata are consistent with the presence of an accreting white dwarf, out. that the lack of periodic X-ray. modulation. rules out he previously proposed identification of the hot companion as an XM. Her svstem (2).."," When free from absorption the spectrum is consistent with bremsstrahlung emission at a temperature around keV. We conclude that these data are consistent with the presence of an accreting white dwarf, but that the lack of periodic X-ray modulation rules out the previously proposed identification of the hot companion as an AM Her system \cite{Reimers88}." + Instead. we conclude that the companion is most likely a single white chwarl accreting rom the wind of the giant., Instead we conclude that the companion is most likely a single white dwarf accreting from the wind of the giant. + Consequently the evolutionary constraints derived by 2? need. not apply.," Consequently the evolutionary constraints derived by \scite{Eggleton89} + need not apply." + Finally. we show hat wind accretion is a viable energy source in this svsten.," Finally, we show that wind accretion is a viable energy source in this system." + We thank Boris Gaensicke for providing information on his LIST observations in advance of publication., We thank Boris Gaensicke for providing information on his HST observations in advance of publication. + Astrophysics research at the. University of Leicester is. supported. by PPARC rolling grants., Astrophysics research at the University of Leicester is supported by PPARC rolling grants. + ROSAT data were extracted fron the Leicester Database and Archive Service (LEDAS) at the University of Leicester., ROSAT data were extracted from the Leicester Database and Archive Service (LEDAS) at the University of Leicester. +"8 um emission, except source C14, which corresponds tothe BCO clump col4, and the BCO clump col7 (see Table 3)).","8 $\mu$ m emission, except source C14, which corresponds tothe $^{13}$ CO clump co14, and the $^{13}$ CO clump co17 (see Table \ref{param_nubi}) )." +" Both clumps correspond to IRDCs seen against the 8 wm emission and identified by(2006a,b).", Both clumps correspond to IRDCs seen against the 8 $\mu$ m emission and identified by. +. The above information suggests to us that all the ATLASGAL clumps but C14 are at the “far” (around 12 kpc) distance rather than the near (around 4 kpc)., The above information suggests to us that all the ATLASGAL clumps but C14 are at the “far” (around 12 kpc) distance rather than the near (around 4 kpc). +" This is likely to be true for the clumps with velocity around 42 km s! (cloud 2 in the nomenclature of Table 2)), as shown by and confirmed by(2009)."," This is likely to be true for the clumps with velocity around 42 km $^{-1}$ (cloud 2 in the nomenclature of Table \ref{cloud_param}) ), as shown by and confirmed by." +". We therefore use the far distance as a working hypothesis in what follows for all clumps, with the exception of continuum emission clump C14 and clumps col4 and col7, seen in 3|CO(1-0) emission, for which we used the near distance."," We therefore use the far distance as a working hypothesis in what follows for all clumps, with the exception of continuum emission clump C14 and clumps co14 and co17, seen in $^{13}$ CO(1-0) emission, for which we used the near distance." + We demonstrate the association between ATLASGAL sources and 24 um MIPSGAL sources in Fig., We demonstrate the association between ATLASGAL sources and 24 $\mu$ m MIPSGAL sources in Fig. + 5 where we plot a histogram (upper panel) of the angular separations between the 870 uum peak and the nearest 24 um source., \ref{histo} where we plot a histogram (upper panel) of the angular separations between the 870 $\mu$ m peak and the nearest 24 $\mu$ m source. +" To estimate the reliability of the associations of the infrared sources with the millimeter continuum cores, we have simulated randomly located samples of 14 cores and associated them with the closest infrared source."," To estimate the reliability of the associations of the infrared sources with the millimeter continuum cores, we have simulated randomly located samples of 14 cores and associated them with the closest infrared source." + The bottom panel of Fig., The bottom panel of Fig. + 5 shows the distribution of the average separation between the infrared sources and the random sample of millimeter cores., \ref{histo} shows the distribution of the average separation between the infrared sources and the random sample of millimeter cores. +" One sees that the histogram for the real millimeter cores has a strong peak for separations of less than 10"" (roughly half the APEX beam) which is not present for the random samples.", One sees that the histogram for the real millimeter cores has a strong peak for separations of less than $^{\prime\prime}$ (roughly half the APEX beam) which is not present for the random samples. + A statistical test on the two histograms shows that there is only a ~0.1% pprobability that they are drawn from the same parent distribution., A statistical test on the two histograms shows that there is only a $\sim$ probability that they are drawn from the same parent distribution. +" Indeed, the simulation shows that one roughly expects 2 chance coincidence within 15"" whereas there are 11 APEX sources within 15"" of the nearest Spitzer 24 um source."," Indeed, the simulation shows that one roughly expects 2 chance coincidence within $^{\prime\prime}$ whereas there are 11 APEX sources within $^{\prime\prime}$ of the nearest Spitzer 24 $\mu$ m source." +" We thus conclude that, with the exception of the three sources with separations larger than 30”, the associations of the ATLASGAL 870 µπι cores with their neighboring Spitzer 24 um sources are real."," We thus conclude that, with the exception of the three sources with separations larger than $^{\prime\prime}$ , the associations of the ATLASGAL 870 $\mu$ m cores with their neighboring Spitzer 24 $\mu$ m sources are real." +core mass. and may be violated for cores more massive than those observed. with consequences for the core mass function.,"core mass, and may be violated for cores more massive than those observed, with consequences for the core mass function." + Here we consider these within the turbulent excitation picture., Here we consider these within the turbulent excitation picture. + The starless cores. or their progenitors. are constantly being buffeted by the turbulence within the parent molecular cloud.," The starless cores, or their progenitors, are constantly being buffeted by the turbulence within the parent molecular cloud." + The ability of a core to survive long enough to potentially form a star requires that the turbulence not excite pulsations with sufficient amplitudes to tear the core apart. either by a single catastrophic excitation or a sequence of smaller excitations.," The ability of a core to survive long enough to potentially form a star requires that the turbulence not excite pulsations with sufficient amplitudes to tear the core apart, either by a single catastrophic excitation or a sequence of smaller excitations." + We noting that in the absence of oscillations there ts a well definedbegin byM(R). shown in Figure |.. and at low masses roughly κανι ," We begin by noting that in the absence of oscillations there is a well defined $M(R)$, shown in Figure \ref{fig:PvR}, and at low masses roughly $\propto R^{-3/2}$." +When dynamically significant oscillations are present. the core mass is a function of radius Ej.," When dynamically significant oscillations are present, the core mass is a function of radius $\Eo$." + Nevertheless. that low mass cores are generally large and vice versa.," Nevertheless, that low mass cores are generally large and vice versa." + As a consequence. the binding energy of cores. comparable to EMG)ο/3R (within at all masses). is a strong function of core mass. and in particular considerably larger for massive. compact cores.," As a consequence, the binding energy of cores, comparable to $\Eb(R)\simeq GM^2/3R$ (within at all masses), is a strong function of core mass, and in particular considerably larger for massive, compact cores." +" In contrast. the energy in turbulent motions (for Kolmogorov turbulence) on the core scale is E,xR27. which decreases with size."," In contrast, the energy in turbulent motions (for Kolmogorov turbulence) on the core scale is $\Et\propto R^{2/3}$, which decreases with size." +" This implies that for some radius. Ro (or mass. Mo). which depends upon the strength of the turbulence. we have £,,(Ro)2£,\(RXo)."," This implies that for some radius, $R_0$ (or mass, $M_0$ ), which depends upon the strength of the turbulence, we have $\Eb(R_0)=\Et(R_0)$." + Since the turbulent motions fluctuate on timescales comparable to the circulation time of a single eddy (1e.. 27 times the sound crossing time of the core). which ts itself comparable to the core dynamical timescale. we expect to see at least one such excitation event for every core.," Since the turbulent motions fluctuate on timescales comparable to the circulation time of a single eddy (i.e., $2\pi$ times the sound crossing time of the core), which is itself comparable to the core dynamical timescale, we expect to see at least one such excitation event for every core." + For large. low-mass cores we have Ey<£j. and we expect the core to be torn apart when this occurs. placing a lower-limit upon the mass of long-lived cores.," For large, low-mass cores we have $\Eb<\Et$, and we expect the core to be torn apart when this occurs, placing a lower-limit upon the mass of long-lived cores." +" In contrast. for compact. massive cores we have Ey>E, and external turbulence is no longer able to excite large-amplitude motions within the core leading again to the inherited turbulence picture described in Section 4.2."," In contrast, for compact, massive cores we have $\Eb>\Et$, and external turbulence is no longer able to excite large-amplitude motions within the core leading again to the inherited turbulence picture described in Section \ref{sec:ESfRT}." +" The fact that E,/E,~(R/Ro)? is such a strong function of implies that the range in core radit about Ao. and thus mass aboutR Mo. in which large-amplitude pulsations can be excited is narrow."," The fact that $\Eb/\Et\simeq(R/R_0)^{-14/3}$ is such a strong function of $R$ implies that the range in core radii about $R_0$, and thus mass about $M_0$ in which large-amplitude pulsations can be excited is narrow." + In particular. Cores much less massive than Mo are torn apart. while those much more massive than M never develop the observed large-amplitude pulsations.," In particular, Cores much less massive than $M_0$ are torn apart, while those much more massive than $M_0$ never develop the observed large-amplitude pulsations." + The latter issue is moderated somewhat if an adiabatic contraction phase occurs during the formation Le. if the pulsation are representative of process.those generated when the core was amplitudeconsiderably larger.," The latter issue is moderated somewhat if an adiabatic contraction phase occurs during the formation process, i.e., if the pulsation amplitude are representative of those generated when the core was considerably larger." + Nevertheless. the former places a hard constraint upon the minimum mass of starless cores.," Nevertheless, the former places a hard constraint upon the minimum mass of starless cores." + The onset of instability in isothermal gas spheres depends upon the dynamical state of the object., The onset of instability in isothermal gas spheres depends upon the dynamical state of the object. + While this has long been known. usually within the context of effective turbulent how this occurs m practice upon the oscillation support.mode energy spectrum. and dependstherefore the mechanism which pulsations are excited.," While this has long been known, usually within the context of effective turbulent support, how this occurs in practice depends upon the oscillation mode energy spectrum, and therefore the mechanism by which pulsations are excited." + In large-amplitude breathingby modes can induce instability for principle.masses well below ¢>4 the static stability limit. a fact that ts reflective of the nature of the instability.," In principle, large-amplitude breathing modes can induce instability for masses well below $\zeta>4$ the static stability limit, a fact that is reflective of the nature of the instability." + However. 1n practice. doing so requires extraordinarily non-linear mode amplitudes. at which point the dynamical effect is unclear.," However, in practice, doing so requires extraordinarily non-linear mode amplitudes, at which point the dynamical effect is unclear." + In contrast. higher-order pulsations are generically supportive. increasing the maximum stable mass significantly.," In contrast, higher-order pulsations are generically supportive, increasing the maximum stable mass significantly." + For oscillation energies comparable to those required to explain the self-absorbed. asymmetric molecular line profiles typically observed in starless cores. the maximum stable mass is about 10-30% higher than the static case.," For oscillation energies comparable to those required to explain the self-absorbed, asymmetric molecular line profiles typically observed in starless cores, the maximum stable mass is about $10$ $30\%$ higher than the static case." + If the modes are excited during the core’s formation. presumably inherited from the turbulence of the parent molecular cloud. followed by an adiabatic contraction. it is natural to expect low-n oscillations to dominate the energy spectrum.," If the modes are excited during the core's formation, presumably inherited from the turbulence of the parent molecular cloud, followed by an adiabatic contraction, it is natural to expect $n$ oscillations to dominate the energy spectrum." + That is. even prior to mode decay via mode-mode or mode-environment coupling. energy from the collapse is preferentially shunted into the long-wavelength pulsations.," That is, even prior to mode decay via mode-mode or mode-environment coupling, energy from the collapse is preferentially shunted into the long-wavelength pulsations." + Thus. it is not unreasonable to expect starless cores to pulsate predominantly in low-order multipole modes. with />2.," Thus, it is not unreasonable to expect starless cores to pulsate predominantly in low-order multipole modes, with $l\ge2$." + The presence of large-amplitude oscillations can dramatically alter the morphology of the column density— maps of starless cores. mimicking the unstable configurations of static BE spheres.," The presence of large-amplitude oscillations can dramatically alter the morphology of the column density maps of starless cores, mimicking the unstable configurations of static BE spheres." + For turbulent energy spectra. dynamically significant pulsations dramatically bias the maximum column densities towards larger values. with the exceeding that associated with the critical configuration of static BE models by factors of order unity.," For turbulent energy spectra, dynamically significant pulsations dramatically bias the maximum column densities towards larger values, with the exceeding that associated with the critical configuration of static BE models by factors of order unity." + This ts born out by the azimuthally-averaged column density profiles. which are very similar to isothermal gas profiles associated with ¢ above the critical value.," This is born out by the azimuthally-averaged column density profiles, which are very similar to isothermal gas profiles associated with $\zeta$ above the critical value." + Despite this. the two-dimensional column density maps are strongly asymmetric. featuring in some cases multiple peaks. similar to those observed in practice.," Despite this, the two-dimensional column density maps are strongly asymmetric, featuring in some cases multiple peaks, similar to those observed in practice." + The ultimate decay of the oscillations. facilitated by non-linear mode coupling or by coupling to the surrounding molecular gas. results 1n the collapse of super-eritical cores.," The ultimate decay of the oscillations, facilitated by non-linear mode coupling or by coupling to the surrounding molecular gas, results in the collapse of super-critical cores." + For slow decay (lifetimes exceeding the mode periods) this results in à sequence of quasi-stable isothermal gas spheres. and the evolution may be determined ," For slow decay (lifetimes exceeding the mode periods) this results in a sequence of quasi-stable isothermal gas spheres, and the evolution may be determined explicitly." +This assumes that the oscillations are not continuallyexplicitly. re-excited by small scale processes within or near the starless cores themselves., This assumes that the oscillations are not continually re-excited by small scale processes within or near the starless cores themselves. + However. the very existence of a significant. number of pulsating cores. with mode energies being a considerable fraction of the cores’ binding energy. argues against this.," However, the very existence of a significant number of pulsating cores, with mode energies being a considerable fraction of the cores' binding energy, argues against this." + Taken together. these suggest a picture of star formation. framed entirely within a hydrodynamical paradigm.," Taken together, these suggest a picture of star formation, framed entirely within a hydrodynamical paradigm." + Self-gravitating cores condense out of the turbulent sea within molecular clouds. born with large-amplitude pulsations.," Self-gravitating cores condense out of the turbulent sea within molecular clouds, born with large-amplitude pulsations." + These pulsations drastically perturb the core shape. mimicking non-equilibrium structures as well as initially supporting the cores against collapse.," These pulsations drastically perturb the core shape, mimicking non-equilibrium structures as well as initially supporting the cores against collapse." + As the oscillations decay the core becomes unstable resulting in star formation., As the oscillations decay the core becomes unstable resulting in star formation. + In this scheme the rate of star formation is set not by ambipolar diffusion of a large scale magnetic field. but by the non-linear decay of the core pulsations.," In this scheme the rate of star formation is set not by ambipolar diffusion of a large scale magnetic field, but by the non-linear decay of the core pulsations." + We should emphasize that while we have framed this new picture entirely in terms of hydrodynamics. small scale tangled magnetic fields in equipartition with the turbulent energy are still allowed and might be required.," We should emphasize that while we have framed this new picture entirely in terms of hydrodynamics, small scale tangled magnetic fields in equipartition with the turbulent energy are still allowed and might be required." + The model of oscillations as perturbations does not allow amplitudes large enough to produce the supersonic motions occasionally seen in a few cores., The model of oscillations as perturbations does not allow amplitudes large enough to produce the supersonic motions occasionally seen in a few cores. + These are the exception rather than the rule and might not be pulsations at all. but rather inward motions as the core center transitions to free-fall collapse.," These are the exception rather than the rule and might not be pulsations at all, but rather inward motions as the core center transitions to free-fall collapse." + However. if these motions are sub-Alfvénnie pulsations. they may be subsumed into an equivalent magnetohydrodynamie formulation.in which we consider only small-scale magnetic fields.," However, if these motions are sub-Alfvénnic pulsations, they may be subsumed into an equivalent magnetohydrodynamic formulation,in which we consider only small-scale magnetic fields." + In this case. It would be the decay of the magnetohydrodynamic," In this case, it would be the decay of the magnetohydrodynamic" +"for w Cen and 18.9 km s! for NGC 6397) taken from the catalogue compiled by Harris(1996) and updated The velocities of V214. V240. and V254 may seem a bit lareish for their distances from the cluster center (17:0. 1479. and 1477. respectively). even though the published cluster tidal radius is 7=44/8 (Trageretal.1995).. or y,=57:03 according to the Harris(1996) catalog.","for $\omega$ Cen and 18.9 km $^{-1}$ for NGC 6397) taken from the catalogue compiled by \cite{har96} + and updated The velocities of V214, V240, and V254 may seem a bit largish for their distances from the cluster center $17\farcm0$, $14\farcm9$, and $14\farcm7$, respectively), even though the published cluster tidal radius is $r_t = 44\farcm8$ \citep{tea95}, or $r_t = 57\farcm03$ according to the \citet{har96} catalog." + That these stars are well within the limits for cluster membership is confirmed by Fig., That these stars are well within the limits for cluster membership is confirmed by Fig. + 6 in Sollimaetal.(2009).. which shows the variation in radial velocity of ω Cen stars as a function of distance from the cluster center.," 6 in \citet{sol09}, which shows the variation in radial velocity of $\omega$ Cen stars as a function of distance from the cluster center." + Still. V240 turned out to be à doubtful case (see Sect. 3.3.1)).," Still, V240 turned out to be a doubtful case (see Sect. \ref{sect: omegaCen}) )." + As for V214 and V254. we checked that the best fits described in Sect.," As for V214 and V254, we checked that the best fits described in Sect." + 3.3.1. were not affected when vo was lowered. respectively. to 10 and 6 km s.," \ref{sect: omegaCen} were not affected when $v_0$ was lowered, respectively, to 10 and 6 km $^{-1}$." + The velocity of NV360. although also rather large. is entirely consistent with the distance of this system from the center of ω Cen ," The velocity of NV360, although also rather large, is entirely consistent with the distance of this system from the center of $\omega$ Cen $3\farcm6$ ), at which the relative velocities of cluster members reach $\pm 35$ km $^{-1}$ \citep{sol09}." +"With 7 being fixed. the task is to find the orbital separation a. inclination of the orbit /, and masses of the components #77 and nin."," With $T$ being fixed, the task is to find the orbital separation $a$, inclination of the orbit $i$, and masses of the components $m_1$ and $m_2$." + Unless indicated otherwise. we assume that the system is semi-detached. with the visible component filling its Roche lobe.," Unless indicated otherwise, we assume that the system is semi-detached, with the visible component filling its Roche lobe." + It must be stressed here that this particular model of the binary (n fact. in some cases it might imply à mass transfer unstable on a dynamical scale).," It must be stressed here that this particular model of the binary (in fact, in some cases it might imply a mass transfer unstable on a dynamical scale)." +" A semi-detached system is simply the most compact one among those with M;,—My,", A semi-detached system is simply the most compact one among those with $M^c_{bol}=M^o_{bol}$. +" Focusing on it. we minimize the orbital separation. so that the corresponding ""semi-detached"" masses nrsd| and ni are the smallest allowable given P and q."," Focusing on it, we minimize the orbital separation, so that the corresponding “semi-detached” masses $m_1^{sd}$ and $m_2^{sd}$ are the smallest allowable given $P$ and $q$." +" The lower limits of the actual masses of the components are obtained by finding ""the best mass ratio gp. defined as the one for which AV./AV,s,=| (see Sect."," The lower limits of the actual masses of the components are obtained by finding “the best” mass ratio $q_b$, defined as the one for which $\Delta V_c/\Delta V_{obs}=1$ (see Sect." + 3.2. for further discussion)., \ref{sect:errors} for further discussion). + Our analysis involves the following steps: The calculations in steps (3)4 and (4) are performed using the PHOEBE interface (Pr&a&Zwitter2005). to the Devinney code (Wilson&Devinney1971)., Our analysis involves the following steps: The calculations in steps (3) and (4) are performed using the PHOEBE interface \citep{prs05} to the Wilson-Devinney code \citep{wil71}. +" In principle. using a relation between V. B—V and stellar angular diameter @ (Kervellaetal.2004) would be more straightforward and simpler than calculating M7, and T. and comparing My, to M; (note that 7 is needed for PHOEBE to derive Mj)."," In principle, using a relation between $V$, $B-V$ and stellar angular diameter $\theta$ \citep{ker04} + would be more straightforward and simpler than calculating $M^o_{bol}$ and $T$, and comparing $M^o_{bol}$ to $M^c_{bol}$ (note that $T$ is needed for PHOEBE to derive $M^c_{bol}$ )." +" Based on ,such a relation. we could directly fit the ""observed"" radius of the visible component R°=6D (where D is the distance to the cluster) to the calculated average radius of the Roche lobe."," Based on such a relation, we could directly fit the “observed” radius of the visible component $R^o\equiv\theta D$ (where $D$ is the distance to the cluster) to the calculated average radius of the Roche lobe." + Unfortunately. fits of Kervellaetal.(2004) proved to be unreliable when extrapolated to low metallicity and small 8.," Unfortunately, fits of \cite{ker04} proved to be unreliable when extrapolated to low metallicity and small $\theta$." + This is not surprising. as these authors explicitly warn about the nonlinearity of the relation involving V and B-Y.," This is not surprising, as these authors explicitly warn about the nonlinearity of the relation involving $V$ and $B-V$." + The values of our key input parameters. i.e. temperatures and bolometric luminosities. are not known accurately. and their errors are difficult to estimate without engaging in a lengthly (and likely ambiguous) discussion of involved factors.," The values of our key input parameters, i.e. temperatures and bolometric luminosities, are not known accurately, and their errors are difficult to estimate without engaging in a lengthly (and likely ambiguous) discussion of involved factors." +" In order to verify how these uncertainties influence the output we varied T and M7, by small amounts and observed the corresponding", In order to verify how these uncertainties influence the output we varied $T$ and $M^o_{bol}$ by small amounts and observed the corresponding +lt is combined. with the standard. model for cosmic X-ray ickeround.,It is combined with the standard model for cosmic X-ray background. + Appropriate response files for NIS nominal »ointing available from the calibration database CALDB (version NIS-20101108. LIND-20101202) are The NIS spectra are grouped such that the final spectra iàve ~250 energv channels so that there are about three channels per energy resolution of 150eV.," Appropriate response files for XIS nominal pointing available from the calibration database CALDB (version XIS-20101108, HXD-20101202) are The XIS spectra are grouped such that the final spectra have $\sim 250$ energy channels so that there are about three channels per energy resolution of $\sim 150 eV$." + Energy channels corresponding to the energv range of 1.75-1.95 keV are ignored since the response files do not. adequately. remove the absorption edge present in this energy range., Energy channels corresponding to the energy range of 1.75-1.95 keV are ignored since the response files do not adequately remove the absorption edge present in this energy range. + Ten consecutive energy channels arc grouped. into one energy channel of the final grouped. PLN spectrum., Ten consecutive energy channels are grouped into one energy channel of the final grouped PIN spectrum. + The net count rates for the NIS and PIN spectra are given in Table 1.., The net count rates for the XIS and PIN spectra are given in Table \ref{tab:table1}. + We use V12.5.1n to fit the spectral models to the observed X-ray spectrum., We use V12.5.1n to fit the spectral models to the observed X-ray spectrum. + We have used. two different phenomenological models to describe the observed spectra of the source in both the ELS and BS., We have used two different phenomenological models to describe the observed spectra of the source in both the EIS and BS. + In the first model (henceforth referred to as MI) we model the soft component using multi-temperature clisk blackbody (DBB) and the hard component as Comptonised emission [from the boundary laver., In the first model (henceforth referred to as M1) we model the soft component using multi-temperature disk blackbody (DBB) and the hard component as Comptonised emission from the boundary layer. + The hot boundary. laver is assumed. to completely cover the neutron star surface., The hot boundary layer is assumed to completely cover the neutron star surface. + This Eastern-like model has two variants., This Eastern-like model has two variants. + One. where the input photons to the boundary laver are from the accretion disk (Alla) and second. where the input. photons are from the underlving blackbody emission. of the neutron. star surface (Mb).," One, where the input photons to the boundary layer are from the accretion disk (M1a) and second where the input photons are from the underlying blackbody emission of the neutron star surface (M1b)." +" The presence of a standard. accretion disk allows for the possibility of a broad. Iron. line. emission in this model which we include. using the moclel ""diskline.", The presence of a standard accretion disk allows for the possibility of a broad Iron line emission in this model which we include using the model “diskline��. + In the second. Western-like model (M2) we mocel the soft component using a single-temperature. blackbody (BB) emitted from the boundary Iaver., In the second Western-like model (M2) we model the soft component using a single-temperature blackbody (BB) emitted from the boundary layer. + The hard component is modelled as Comptonised emission from an inner hot disk where the input photons are from the boundary layer., The hard component is modelled as Comptonised emission from an inner hot disk where the input photons are from the boundary layer. + The Comptonisecl spectra for. both. the models. is represented by the function. “ntheomp” (Zdziarski.Johnson&Alagelziarz1996:Zvcki.DoneSmith 1999).," The Comptonised spectra for both the models is represented by the function “nthcomp” \citep{Zdz96, Zyc99}." +. We apply this Comptonization model mainly because. it can have input seed. photon populations of different nature and distribution (pure blackbody. multicolour disk) thus allowing to test. different emission &eometries.," We apply this Comptonization model mainly because it can have input seed photon populations of different nature and distribution (pure blackbody, multicolour disk) thus allowing to test different emission geometries." + In the Alla model the input photon distribution is due to disk blackbocdvy ancl hence the input temperature is set equal to. the maximum temperature of the disk blackbody emission., In the M1a model the input photon distribution is due to disk blackbody and hence the input temperature is set equal to the maximum temperature of the disk blackbody emission. + In the Al2b model. input. photon distribution is due to the blackbody emission from the NS surface and hence the input temperature is a free parameter.," In the M2b model, input photon distribution is due to the blackbody emission from the NS surface and hence the input temperature is a free parameter." + On the other hand in the AR model. the photon distribution is due to neutron star boundary laver and hence of a blackbocly shape ancl the input tempertature is set equal to the temperature of this neutron star boundary laver.," On the other hand in the M2 model, the photon distribution is due to neutron star boundary layer and hence of a blackbody shape and the input tempertature is set equal to the temperature of this neutron star boundary layer." + A multiplicative component (wabs) is introduced in all spectral fitting to model the absorption of the source spectrum by intervening material along the line sight., A multiplicative component (“wabs”) is introduced in all spectral fitting to model the absorption of the source spectrum by intervening material along the line sight. + We note here that the average Dickey Lockman nll value in the clireetion of Aql X-1 is 0.331077 em?., We note here that the average Dickey Lockman nH value in the direction of Aql X-1 is $0.33 \times 10^{22}$ $^{-2}$. + The nll values obtained in our fits agree with this average value., The nH values obtained in our fits agree with this average value. + Another constant multiplicative term is used in both the models for the relative normalisation of the XLS and corresponding LIND) spectra., Another constant multiplicative term is used in both the models for the relative normalisation of the XIS and corresponding HXD spectra. + Phe cross-calibration constant for NLS nominal pointing as suggested by the Suzaku team is 1.16€0.014 74.," The cross-calibration constant for XIS nominal pointing as suggested by the Suzaku team is $1.16 \pm 0.014$ $^,$." +0 The value for the constant that we get from our fits agree with those suggested by the Suzaku team within errors., The value for the constant that we get from our fits agree with those suggested by the Suzaku team within errors. + Phe model components used for M2 and Ml are tabulated in Table 2.., The model components used for M2 and M1 are tabulated in Table \ref{tab:XSPEC_models}. + While fitting the near simultaneousTIE spectra. we fix the absorbing column density. nll to the corresponding nll value derived from the spectral fit sinceTE data alone cannot constrain the nll value.," While fitting the near simultaneous spectra, we fix the absorbing column density, nH to the corresponding nH value derived from the spectral fit since data alone cannot constrain the nH value." + The normalisation parameter of the component gives the blackhock luminosity Lee and the normalisation parameter of the componont eives the blackbody radius. Pee., The normalisation parameter of the component gives the blackbody luminosity $L_{BB}$ and the normalisation parameter of the component gives the blackbody radius $R_{BB}$. +" Similarly from the xwameter values of the component we can estimate the total Compton luminosity Leow, the required uminositv of the input. photons L;;,í. the amplification actor (A) and when A5, is a free parameter the radius of the blackbody Ree."," Similarly from the parameter values of the component we can estimate the total Compton luminosity $L_{comp}$, the required luminosity of the input photons $L_{inp}$, the amplification factor (A) and when $kT_{bb}$ is a free parameter the radius of the blackbody $R_{BB}$ ." + From the model we calculate the inner aceretion cisk radius (11) and the disk uminositv Loge., From the model we calculate the inner accretion disk radius $R_{in}$ ) and the disk luminosity $L_{DBB}$. + Phe caleulated values of these parameters allow us to constrain the two mocels considered here., The calculated values of these parameters allow us to constrain the two models considered here. + Note hat throughout this paper for calculating luminosities we use distance to the source as 2=5.2541.25 Ixpe (Rutledge et al., Note that throughout this paper for calculating luminosities we use distance to the source as $D = 5.25 \pm 1.25 $ Kpc (Rutledge et al. + 2001) and the error quoted for luminosities take into account this uncertainty in the clistance., 2001) and the error quoted for luminosities take into account this uncertainty in the distance. + The results from the observations Ell. EI2 and E13 when the source was in the ELS will be presented. together in the next sub-section and that of the BS in the subsequent one.," The results from the observations EI1, EI2 and EI3 when the source was in the EIS will be presented together in the next sub-section and that of the BS in the subsequent one." + We start with analvsing the spectra using Moclel Alla., We start with analysing the spectra using Model M1a. + ΙΓ the Lron line emission is omitted the best. fit fe obtained are 284.50/241. 205.74/237 and 305.31/241 for observations LLL. El2 and 1919 respectively.," If the Iron line emission is omitted the best fit $\chi^2/\nu$ obtained are 284.50/241, 295.74/237 and 305.31/241 for observations EI1, EI2 and EI3 respectively." + Adding a Gaussian line at6.4 keV improves the fit considerably., Adding a Gaussian line at$6.4$ keV improves the fit considerably. + “Phe, The +"where op is a suitable velocity dispersion and o,=200 kms |.","where $\sigma_0$ is a suitable velocity dispersion and $\sigma_\ast = +200$ km $^{-1}$." + The uncertainty in the power-law slope is the largest source of uncertainty in our estimated number of high-velocity stars., The uncertainty in the power-law slope is the largest source of uncertainty in our estimated number of high-velocity stars. + Recent estimates for. (the variation in à is small since all studies agree Lor ση~σι) range [rom 3=4.02£0.32 (a—8.13220.06) (Tremaineetal.2002). to 34=4.65dE0.48 (n!=817 +40.07) (Merritt&Ferrarese2001)., Recent estimates for $\beta$ (the variation in $\alpha$ is small since all studies agree for $\sigma_0 \sim \sigma_\ast$ ) range from $\beta^L=4.02\pm0.32$ $\alpha^L=8.13\pm 0.06$ ) \citep{tremaine} to $\beta^H=4.65\pm0.48$ $\alpha^H=8.17\pm0.07$ ) \citep{mf}. +. These agree within their quoted errors. but. on extrapolation to the globular cluster regime. the use of 3 predicts 20 times as many high-velocity stars as does the use of 34," These agree within their quoted errors, but, on extrapolation to the globular cluster regime, the use of $\beta^L$ predicts 20 times as many high-velocity stars as does the use of $\beta^H$." + We therefore give results for both these slopes below., We therefore give results for both these slopes below. + The original claim for globular clusters (Gebhardt.Rich.&Ho2002) used 3%., The original claim for globular clusters \citep{G1} used $\beta^L$. + substituting equations (1)) and (10)) into equation (7)) we arrive al (he Iollowing where gy is measured in km *1 and My is the number of stars per square parsec., Substituting equations \ref{E:rh}) ) and \ref{E:mbh}) ) into equation \ref{E:N2}) ) we arrive at the following where $\sigma_0$ is measured in km $^{-1}$ and $\Sigma_0$ is the number of stars per square parsec. +" What we can easily observe is not X, but the central surface density. jn. so we need to rewrite X, in terms of µῃ for a reasonable globular cluster stellar population."," What we can easily observe is not $\Sigma_0$ but the central surface density, $\mu_0$, so we need to rewrite $\Sigma_0$ in terms of $\mu_0$ for a reasonable globular cluster stellar population." +" For a delined population of stars. let L. be the cluster Iuminosity per star in that population in solar units. and let g, be the fraction of these stars that are usefully measurable."," For a defined population of stars, let $\bar L_*$ be the cluster luminosity per star in that population in solar units, and let $g_*$ be the fraction of these stars that are usefully measurable." + Then for po 11 V. magnitude per square arc second. and (taking AM...=4.79 In this case where a=2.37x107. 32=404. A”=36.0. and 34=5.30.," Then for $\mu_0$ in $V$ magnitude per square arc second, and taking $M_{V\sun}=4.79$ In this case where $\hat\alpha^L=2.37\times 10^4$, $\hat\beta^L=4.04$, $\hat\alpha^H=36.0$, and $\hat\beta^H=5.30$." +" For our problem. L, is determined by (he luminosity function in the core of the cluster in «question."," For our problem, $\bar L_*$ is determined by the luminosity function in the core of the cluster in question." + It needs to take into account mass segregation ellects and other possible population peculiarities as might be indicated by. for example. color gradients.," It needs to take into account mass segregation effects and other possible population peculiarities as might be indicated by, for example, color gradients." +" The measurable Iraction. 4,. Is an observational selection effect on the luminosity function."," The measurable fraction, $g_*$, is an observational selection effect on the luminosity function." + It will depend on the observational technique to be used. the distance of the cluster. crowding and so forth.," It will depend on the observational technique to be used, the distance of the cluster, crowding and so forth." +" since a complete stellar census is a difficult undertaking. we estimate L, as follows."," Since a complete stellar census is a difficult undertaking, we estimate $\bar L_*$ as follows." + Define our population to be all the stars brighter (han some magnitude. Vy (e.g. (he expected magnitude limit of the observations) in a cluster color-magnitude diagram (CMD).," Define our population to be all the stars brighter than some magnitude, $V_d$ (e.g. the expected magnitude limit of the observations) in a cluster color-magnitude diagram (CMD)." + Then. The quantities Lj and Ly are the mean huninosities Lor the bright and faint parts of the CMD (divided at V) and f is the ratio of the munber of stars brighter than V; to the number," Then, The quantities $\bar L_b$ and $\bar L_f$ are the mean luminosities for the bright and faint parts of the CMD (divided at $V_d$ ) and $f$ is the ratio of the number of stars brighter than $V_d$ to the number" +"an excess is due to a chance comeidence is ruled out with probability (1—δι300)=99.999466, which corresponds to a 4.50 significance of the source detection above 100 GeV. images of the sky region around source #22 are shown in Fig. l..","an excess is due to a chance coincidence is ruled out with probability $(1-P_{100-300})\simeq 99.9994\%$, which corresponds to a $4.5\sigma$ significance of the source detection above 100 GeV. images of the sky region around source 2 are shown in Fig. \ref{fig:1-10-100GeV}." + The new source is situated approximately 0.6* to the southwest from the bright source IFGL J0319.7--4130. which ts identified with the radio galaxy NGC 1275 1n the center of Perseus galaxy cluster.," The new source is situated approximately $0.6^\circ$ to the southwest from the bright source 1FGL J0319.7+4130, which is identified with the radio galaxy NGC 1275 in the center of Perseus galaxy cluster." + The spectrum of the new source 15 harder than the spectrum of NGC 1275. so that emission from NGC 1275 dominates in the 1-10 GeV energy band. while emission from the new source dominates the signal above 100 GeV. At energies above 30 GeV. of events from a point source are contained in a circle of the radius 0.37.," The spectrum of the new source is harder than the spectrum of NGC 1275, so that emission from NGC 1275 dominates in the 1-10 GeV energy band, while emission from the new source dominates the signal above 100 GeV. At energies above 30 GeV, of events from a point source are contained in a circle of the radius $0.3^\circ$." + This means that events from the bright source IFGL JO319.7+4130 do not affect the signal from the newly detected source 0.67 away., This means that events from the bright source 1FGL J0319.7+4130 do not affect the signal from the newly detected source $0.6^\circ$ away. + Taking this into account. we included events with energies above 30 GeV in the analysis.," Taking this into account, we included events with energies above 30 GeV in the analysis." + We found two more events from the source within the 0.1? search circle in the 30-100 GeV band., We found two more events from the source within the $0.1^\circ$ search circle in the 30-100 GeV band. +" To calculate the probability Όλο(ος of finding two additional events at the source position one can use modification of the expression for the 100-300 GeV band with a substitution Ko,-1—Και and Njo571— Njo.", To calculate the probability $P_{30-100}$ of finding two additional events at the source position one can use modification of the expression for the 100-300 GeV band with a substitution $K_{0.1}-1\rightarrow K_{0.1}$ and $N_{10}-1\rightarrow N_{10}$ . + Doing this we find Pao_joo=1.1x 107+., Doing this we find $P_{30-100}=1.1\times 10^{-4}$ . + The probability to find >2 additional photons in the 30-100 GeV to a cluster of >3 photons in the 100-300 GeV band is Γιοςο=6.6x107? (which corresponds to 6c for Gaussian statistics)., The probability to find $\ge 2$ additional photons in the 30-100 GeV to a cluster of $\ge 3$ photons in the 100-300 GeV band is $P_{100-300}P_{30-100}\simeq 6.6\times 10^{-10}$ (which corresponds to $6\sigma$ for Gaussian statistics). + Equivalently. the combined probability to find a 3.9 and 4.55 excess in the two bands is ~2x1075. which corresponds to the significance of source detection at the level of 5.60 (integrating the probability density outside constant likelihood contour for Gaussian statistics).," Equivalently, the combined probability to find a 3.9 and $\sigma$ excess in the two bands is $\simeq 2\times 10^{-8}$, which corresponds to the significance of source detection at the level of $5.6\sigma$ (integrating the probability density outside constant likelihood contour for Gaussian statistics)." + In order to verify the detection of the source withFermi. we performed a standard Fermi for the sky region containing310.," In order to verify the detection of the source with, we performed a standard Fermi for the sky region containing." +.. In this analysis we used photons with energies between 10 GeV and 300 GeV. collected from a circular area with a radius of 5 degrees around the position of310.," In this analysis we used photons with energies between 10 GeV and 300 GeV, collected from a circular area with a radius of 5 degrees around the position of." +. We included all sources mentioned in the Fermi first year catalog (Abdoetal..2009) for this region of the sky., We included all sources mentioned in the Fermi first year catalog \citep{fermi_catalog} for this region of the sky. + All the sources had freely varying normalizations and spectral indices., All the sources had freely varying normalizations and spectral indices. + We assumed that the spectra of all the sources included in the likelihood analysis had power-law shape., We assumed that the spectra of all the sources included in the likelihood analysis had power-law shape. + The likelihood analysis has resulted in the detection of wwith the Test Statistic (TS) (Mattoxetal..1996) value of 53. which corresponds to approximately Το source detection significance and is compatible with the 6c source detection significance found from the direct photon counting above 30 GeV. Figure 2. shows the map of TS values generated with tool by varying the position of the source on the grid of 12 by 12 positions with a 0.1 degree step.," The likelihood analysis has resulted in the detection of with the Test Statistic (TS) \citep{mattox} value of 53, which corresponds to approximately $7\sigma$ source detection significance and is compatible with the $6\sigma$ source detection significance found from the direct photon counting above 30 GeV. Figure \ref{fig:TSmap} shows the map of TS values generated with tool by varying the position of the source on the grid of 12 by 12 positions with a 0.1 degree step." + The uncertainty of the source position found from the TS map is also compatible with the one found from the direct photon counting., The uncertainty of the source position found from the TS map is also compatible with the one found from the direct photon counting. + Figure 3 shows a comparison of the Fermi image above 100 GeV with the images of the same region of the sky in X-ray(ROSAT all sky survey)) and radio (WENSS survey (Rengelinketal..1997))) bands obtained through the SkyViewinterface?., Figure \ref{fig:ROSAT+radio} shows a comparison of the Fermi image above 100 GeV with the images of the same region of the sky in X-ray all sky ) and radio (WENSS survey \citep{wenss}) ) bands obtained through the SkyView. +. The radio and X-ray source at the position of the new ssource Is the galaxy IC 310. which ts a part of Perseus cluster.," The radio and X-ray source at the position of the new source is the galaxy IC 310, which is a part of Perseus cluster." + There are no other bright radio or X-ray sources within the 0.17 degree circle around the position of the ssource., There are no other bright radio or X-ray sources within the $0.1^\circ$ degree circle around the position of the source. + This provides an unambiguous identification of the source with IC 310., This provides an unambiguous identification of the source with IC 310. + In order to estimate the flux from the source in. the 30-300 GeV energy range. we calculated the exposure ofFermi/LAT in the direction of the source in this energy band with the tool.," In order to estimate the flux from the source in the 30-300 GeV energy range, we calculated the exposure of in the direction of the source in this energy band with the tool." + Collecting the photons from the containment circles of the energy-dependent point spread function for the front and back-converted photons (Abdo2009a).. we find the estimates of the source flux in two energy bins. 30-100 GeV and 100-300 GeV are Fioi00=23333xlov! erg/cens) and Ετοςτου=...x10711 erg/(cms). respectively.," Collecting the photons from the containment circles of the energy-dependent point spread function for the front and back-converted photons \citep{lat-performance}, , we find the estimates of the source flux in two energy bins, 30-100 GeV and 100-300 GeV are $F_{30-100}= 2.3_{-1.2}^{+2.3}\times 10^{-11}$ $^2$ s) and $F_{100-300}= 1.4_{-0.6}^{+1.1}\times 10^{-11}$ $^2$ s), respectively." + These estimates are shown in Fig., These estimates are shown in Fig. + + together with the multiwavelength data on IC 310 collected from the NASA ExtragalacticDatabase?., \ref{fig:SED} together with the multiwavelength data on IC 310 collected from the NASA Extragalactic. +. At energies below 30 GeV. the signal from NGC 1275 could give a non-zero number of photons at the position of the new source.," At energies below 30 GeV, the signal from NGC 1275 could give a non-zero number of photons at the position of the new source." + In order to estimate the background at the source position we adopted the following procedure., In order to estimate the background at the source position we adopted the following procedure. +" We have chosen three ""background"" circular regions of the radius 0.37 situated at the same angular distance from NGC 1275 as the new source. but at the position angles 90°.180° and 270°. with respect to the direction from NGC 1275 toward the new source."," We have chosen three ""background"" circular regions of the radius $0.3^\circ$ situated at the same angular distance from NGC 1275 as the new source, but at the position angles $90^\circ,\ 180^\circ$ and $270^\circ$, with respect to the direction from NGC 1275 toward the new source." +" The signal of NGC 1275 should give approximately the same number of counts in the three ""background"" regions and in the ""source"" region. which we choose to be a circle of the radius 0.3* around the source position."," The signal of NGC 1275 should give approximately the same number of counts in the three ""background"" regions and in the ""source"" region, which we choose to be a circle of the radius $0.3^\circ$ around the source position." + We found that the signal in the source circle is compatible at €3c level with the signal in the background regions in the energy bins 1-3 GeV. 3-10 GeV and 10-30 GeV. see Fig. 4..," We found that the signal in the source circle is compatible at $\le 3\sigma$ level with the signal in the background regions in the energy bins 1-3 GeV, 3-10 GeV and 10-30 GeV, see Fig. \ref{fig:SED}." + Known VHE loud Active Galactic Nuclei (AGN) are divided into several classes., Known VHE loud Active Galactic Nuclei (AGN) are divided into several classes. + Most of the sources are BL Laes. which are relativistically beamed versions of Fanaroff-Riley type I radio galaxies.," Most of the sources are BL Lacs, which are relativistically beamed versions of Fanaroff-Riley type I radio galaxies." + Two of the detected sources are the nearest FR I radio galaxies themselves (M87 and Cen A)., Two of the detected sources are the nearest FR I radio galaxies themselves (M87 and Cen A). + One source. 3C 279. belongs to the Flat Spectrum Radio Quasar (FSRQ) class.," One source, 3C 279, belongs to the Flat Spectrum Radio Quasar (FSRQ) class." + Unless pproves to be a weak BL Laetype object. the detection of VHE eemission from a head-tail radio galaxy provides à new class of extragalactic VHE ssources.," Unless proves to be a weak BL Lactype object, the detection of VHE emission from a head-tail radio galaxy provides a new class of extragalactic VHE sources." + Ifthe interpretation of the source as a weak BL Lac, Ifthe interpretation of the source as a weak BL Lac +is unclear.,is unclear. + Similar problems also exist for the explanation of the solid-body rotation profile within the radiative layers of the Sun ∙∙, Similar problems also exist for the explanation of the solid-body rotation profile within the radiative layers of the Sun \citep{chaplin2001}. +" While there is a growing body of observational evidence that early type stars have measurable magnetic fields, no attempt has led to a comprehensive theory which explains both the origin of and the sustaining mechanism of the magnetic field."," While there is a growing body of observational evidence \citep{donati2006,mm2004} that early type stars have measurable magnetic fields, no attempt has led to a comprehensive theory which explains both the origin of and the sustaining mechanism of the magnetic field." + Two leading possibilities are the fossil field theory and the dynamo., Two leading possibilities are the fossil field theory \citep{cowling1945} and the dynamo. + Existing theories of dynamo generated fields focus on different assumptions but propose that dynamos operate either in the fully convective cores or in the differentially rotating radiative envelope., Existing theories of dynamo generated fields focus on different assumptions but propose that dynamos operate either in the fully convective cores or in the differentially rotating radiative envelope. + MacDonald&Mullan|(2004) report serious difficulties with the, \citet{mm2004} report serious difficulties with the +predicted by the external shock prior emission mocel.,predicted by the external shock prior emission model. + Once again. the predicted. prior emission optical light curves are ultimately constrained by the bottom of the green range. and we must conclude that CRB O50401 and GRB 051109 are not consistent with the external shock prior emission hypothesis.," Once again, the predicted prior emission optical light curves are ultimately constrained by the bottom of the green range, and we must conclude that GRB 050401 and GRB 051109A are not consistent with the external shock prior emission hypothesis." + GRB 0601191 is the only burst. in our sample for which the early optical data fall below the ercen range., GRB 061121 is the only burst in our sample for which the early optical data fall below the green range. + Consequently. the only way to explain this burst within the external shock prior emission model is to introduce the ad hoc assumption that there are two spectral breaks between the A-ray and. optical bands (ape n1. > ns. addHn> — which. are subject. to tlie constraint. wy>bey7=OTIíq-Cieσα) V). seven ofJ these eight. Parameters may be cousidered free.," includes eight model parameters — $\lambda_i$ $(i=1,\ldots,5)$, $m^2_1$ , $m^2_2$ , and$m_{ql}^2$ — which are subject to the constraint $v_{q}^2+v^2_\ell = (174\ {\rm GeV})^2$ , seven of these eight parameters may be considered free." + Iu what follows. it will be useful to work in a different. more physicallyineauiugful basis for these paraimeters:," In what follows, it will be useful to work in a different, more physicallymeaningful basis for these parameters:" +in the Introduction. we have developed a procedure to search for dust in galaxy. clusters that is sensitive to any ratio of general to selective extinction. ft.,"in the Introduction, we have developed a procedure to search for dust in galaxy clusters that is sensitive to any ratio of general to selective extinction, $R_{\lambda}$." + Galaxy clusters were selected from the APM Caalogue with redshifts of zx0.08 in order to eusure that the clusters subtended ai angle of the sky large enough to contain a siglificant number oL background. dus-allected galaxies. and a small uuuber of foreground galaxies. al 2«XSefer.," Galaxy clusters were selected from the APM Catalogue with redshifts of $z \leq 0.08 $ in order to ensure that the clusters subtended an angle of the sky large enough to contain a significant number of background dust-affected galaxies, and a small number of foreground galaxies, at $z acc«lingly."," To that end, we tried masking out the central regions of Cluster Groups (which typically have the highest density of galaxies), and adjusting the size of the Control Groups accordingly." + However. reduciug the fractional cdillerence between { iunuber of galaxies in the er and Control Groups ος1—3% (fΟι cAv10% had little e OLL Olr cleterminations of —ction aud redclenine.," However, reducing the fractional difference between the number of galaxies in the Cluster and Control Groups to $\lesssim 1 - 3 \%$ (from $\approx 10\%$ ) had little effect on our determinations of extinction and reddening." + ext. we divided the distribution of gaaxles in the color-1uaguiude (CA) plane of both the ClIser aud the Control Groups into pixels o size ADR. and Ap(By—H) (see (yp panels of Fig. 2)).," Next, we divided the distribution of galaxies in the color-magnitude (CM) plane of both the Cluster and the Control Groups into pixels of size $\Delta_p R$, and $\Delta_p (B_J-R)$ (see top panels of Fig. \ref{ndist}) )." +" We present results for A,=A,(—HR)09025.", We present results for $\Delta_p R=\Delta_p (B_J-R)=0\fm025$. + Given the nunyer deusity of ADMI galaxies. this is the smallest reasonable. pixel size.," Given the number density of APM galaxies, this is the smallest reasonable pixel size." + Tve CAM-plane pixel size «leterinines the sensitivity. or ‘resolution of our method.," The CM-plane pixel size determines the sensitivity, or `resolution' of our method." + Let rege(ej) aud ni(i.j) be the oπόνος. pixellated: CM-plane," Let $n_{clust}(i,j)$ and $n_{cont}(i,j)$ be the observed pixellated CM-plane" +Oue of the most exciting vet observationally challenging scicutifie objectives of the Laree Arca Telescope (LAT) on board theTelescope (Atwoodctal.2009).. is the indirect detection of particle darkmatter (Daltzetal.2008)..,"One of the most exciting yet observationally challenging scientific objectives of the Large Area Telescope (LAT) on board the \citep{Atwood:2009ez}, is the indirect detection of particle darkmatter \citep{2008JCAP...07..013B}." + ILowever. limited gamunarayv statistics make diffuse sienals arising frou the pai-aunililation of dark matter dificult to differentiate from astroplivsical processes.," However, limited gamma-ray statistics make diffuse signals arising from the pair-annihilation of dark matter difficult to differentiate from astrophysical processes." + The limitation of using a diffuse signal to search for non-standard cussion stenis from difüculties i controlling the instrumental background aud formulating a rigorous model for the astrophysical diffuse foregrounds., The limitation of using a diffuse signal to search for non-standard emission stems from difficulties in controlling the instrumental background and formulating a rigorous model for the astrophysical diffuse foregrounds. + Au intriguing excess of microwave radiation iu the WMAP data has been uncovered by Fiukbeiner(200 and Dobler&Fiukbeiner(2008).., An intriguing excess of microwave radiation in the WMAP data has been uncovered by \citet{Finkbeiner:2004us} and \citet{Dobler:2007wv}. + The morphology aud spectrma of the WALAP haze indicates a hard electrou-»»itron injection spectrum spherically distributed around the ealactic center., The morphology and spectrum of the WMAP haze indicates a hard electron-positron injection spectrum spherically distributed around the galactic center. + While the origin of this maze need not be related tonew particle plysics. he possibility that the WALAP haze corresponds to svuchrotron radiation of stable leptons produced by dark. uatter has been explored iu several studies (seee.g.llooperetal. 2007)..," While the origin of this haze need not be related to particle physics, the possibility that the WMAP haze corresponds to synchrotron radiation of stable leptons produced by dark matter has been explored in several studies \citep[see e.g.][]{Hooper:2007kb}." + A potentially couclusive wav to determine whether the WMLADP haze originates from a »pulatiou of energetic leptons is to observe eanunia-ravs produced by inverse Compton up-scattering (IC) of ολους in the interstellar ealactic radiation Ποια (ISRE)., A potentially conclusive way to determine whether the WMAP haze originates from a population of energetic leptons is to observe gamma-rays produced by inverse Compton up-scattering (IC) of photons in the interstellar galactic radiation field (ISRF). +" Recently, Dobleretal.(2009) (hereafter. DOO) exinnined the LAT eamuna-rav sky and reported an excess Cluission morphologically similar to the WALAP jiize."," Recently, \citet{Dobler:2009xz} (hereafter D09) examined the LAT gamma-ray sky and reported an excess emission morphologically similar to the WMAP haze." + DSs observations sugeest a confirmation of thehypothesis: that excess microwave enuüssion stenis roni relativistic electron svuchrotron with a spherical source distribution and a hard injection spectrum., D09's observations suggest a confirmation of the: that excess microwave emission stems from relativistic electron synchrotron with a spherical source distribution and a hard injection spectrum. +" Iu he ""Ivpe 2 and “Type 3° fits of DOO. the excess was claimed over a best-fit backerounc usime spatial cluplates which curploved the eas map of Schlegel (SED) to trace sanunia-raw clission roni x"" decay. and the los Mhz Iaskuu svuchrotron nap (Ilashuuetal.1982) to trace IC onuüssionu from ealactic cosmic rav electrons."," In the “Type 2"" and “Type 3"" fits of D09, the excess was claimed over a best-fit background using spatial templates which employed the gas map of \citet{1998ApJ...500..525S} (SFD) to trace gamma-ray emission from $\pi^0$ decay, and the 408 Mhz Haslam synchrotron map \citep{1982A&AS...47....1H} to trace IC emission from galactic cosmic ray electrons." + The spatial teiiplates (plus an isotropic component obtained bw meau-subtracting he residual xkwviuap) were used to fit the observed σαΑΝ sky iu enerev bius spanning 2-100 GeV. This analysis uncovered a residual eamuna-rayv euission above and below the ealactic center with a morphology aud spectrum similar to that found in the WALAP dataset (Fiukbeiuer2001).., The spatial templates (plus an isotropic component obtained by mean-subtracting the residual skymap) were used to fit the observed gamma-ray sky in energy bins spanning 2-100 GeV. This analysis uncovered a residual gamma-ray emission above and below the galactic center with a morphology and spectrum similar to that found in the WMAP dataset \citep{2004ApJ...614..186F}. +" Iu this Letter. we test the following assmuptions used in DOO for the removal of astrophysical foregrounds at σαΜατα energies: Asstuuption (1) cutails ucelecting the iiorpholosv of galactic cosmic-ray sources. since ἴμο observed zU cinission results from the line-of-sielt iuteeral of the eas density (""target) times the cosmic-ray density (""beam)."," In this $Letter$, we test the following assumptions used in D09 for the removal of astrophysical foregrounds at gamma-ray energies: Assumption (1) entails neglecting the morphology of galactic cosmic-ray sources, since the observed $\pi^0$ emission results from the line-of-sight integral of the gas density (“target”) times the cosmic-ray density (“beam”)." + Asstmption (2) neglects the difference between the morphology of the ISRF aud the galactic magnetic fields., Assumption (2) neglects the difference between the morphology of the ISRF and the galactic magnetic fields. + Ou theoretical grounds. we expect that any detailed ealactic cosmic-ray model would precict from the templates used in DOO.," On theoretical grounds, we expect that any detailed galactic cosmic-ray model would predict from the templates used in D09." + Utilizing the ealactic cosmic-ray propagation code Galprop. we find," Utilizing the galactic cosmic-ray propagation code , we find" +"For m1 we have a power-law cusp with logarithmic slope 1—i,"," At $m=1$ the model has a logarithmic cusp, at $m>1$ we have a power-law cusp with logarithmic slope $1-\frac{1}{m}$." +" In particular, the de Vaucouleurs model has a luminosity density profile that behaves as s?/ as small radii (Young1976;Mellier&Mathez1987).."," In particular, the de Vaucouleurs model has a luminosity density profile that behaves as $s^{-3/4}$ as small radii \citep{1976AJ.....81..807Y, 1987A&A...175....1M}." +" Surprisingly, the Sérrsic models with m«1 do not have a monotonically decreasing luminosity density profile with increasing radius."," Surprisingly, the Sérrsic models with $m<\frac12$ do not have a monotonically decreasing luminosity density profile with increasing radius." +" In the expansions (37a)) and (37b)), the first non-constant term has a positive coefficient and hence the luminosity density increases with increasing radius in the nuclear region."," In the expansions \ref{nuasymp0-13}) ) and \ref{nuasymp13}) ), the first non-constant term has a positive coefficient and hence the luminosity density increases with increasing radius in the nuclear region." + The same accounts 51«m i since the coefficient of the second term in the expansion (37c)) is positive for i10!°4Mo and sizes re~3—10."," At $1.610^{10.4}M_{\odot}$ and sizes $r_e\sim3\--10$." +" Finally, at 2«z2.5 we can detect of the galaxies with M>10195Mo and sizes re~3—10."," Finally, at $210^{10.8}M_{\odot}$ and sizes $r_e\sim3\--10$." +" The first interesting result is that at 1.2«z<1.6, 1.6«z2 and 2«z2.5 respectively about65%,, and of early-type galaxies are more than 1—o below the local relation, and that about25%,, and are ultracompact, according to our definition."," The first interesting result is that at $1.21019-5M, we should detect “normal” ETG with re2—4 kpc at z>1.6, if they were present, but we detect none."," In particular, at $M\gtrsim10^{10.6-8}M_{\odot}$, we should detect “normal” ETG with $r_e\sim2-4$ kpc at $z>1.6$, if they were present, but we detect none." +" However, since at z>1.6 we might progressively miss more and more large galaxies, it is possible that the compact and ultra-compact fractions at those redshifts are slightly over-estimated."," However, since at $z>1.6$ we might progressively miss more and more large galaxies, it is possible that the compact and ultra-compact fractions at those redshifts are slightly over-estimated." +" In the following sections and figures, in order to improve the statistics, we will combine the three redshift bins of Figure 4 in one."," In the following sections and figures, in order to improve the statistics, we will combine the three redshift bins of Figure \ref{fig4} in one." +" Note that the absence in our sample of very massive galaxies with large size is due to their rarity, as with a surface density of one every ~500 arcmin? (Mancini et al."," Note that the absence in our sample of very massive galaxies with large size is due to their rarity, as with a surface density of one every $\sim 500$ $^2$ (Mancini et al." + 2010) one does not expect to find any in the 40 arcmin? covered by the, 2010) one does not expect to find any in the 40 $^2$ covered by the +"binary composed of ΜΑΡΑ=1.15Mc; and MNBS2,=1.55Mo stars.","binary composed of $M_{\rm ADM}^{\rm NS1}=1.15 +M_{\odot}$ and $M_{\rm ADM}^{\rm NS2}=1.55 M_{\odot}$ stars." +" The thin (black) solid and thin (green) dotted curves are the results of the 3PN approximation for the equal-mass and unequal-mass binaries, respectively."," The thin (black) solid and thin (green) dotted curves are the results of the 3PN approximation for the equal-mass and unequal-mass binaries, respectively." +" When the mass ratio decreases to the value as small as 1.15Mo/1.55Mo~0.74, the fractional binding energy Ey/Mo and orbital angular velocity MoQ at the closest separation decrease by about10%."," When the mass ratio decreases to the value as small as $1.15 M_{\odot}/1.55 M_{\odot} \simeq 0.74$, the fractional binding energy $E_{\rm b}/M_0$ and orbital angular velocity $M_0 \Omega$ at the closest separation decrease by about." +. The reason why the orbital angular velocity at the closest separation decreases for the unequal-mass case is that the less massive star is tidally deformed by the companion more massive star and starts shedding mass at a larger separation than that for the equal-mass case., The reason why the orbital angular velocity at the closest separation decreases for the unequal-mass case is that the less massive star is tidally deformed by the companion more massive star and starts shedding mass at a larger separation than that for the equal-mass case. +" The binding energy decreases for the unequal-mass case because it is proportional to the reduced mass wp=ΜΑΡΙMN8*,/Mo according to the results of the 3PN approximation (the ratio of the unequal-mass case to the equal-mass one is //uneq/1teq 0.978) and the orbital angular velocity at the termination point of the sequence should be smaller."," The binding energy decreases for the unequal-mass case because it is proportional to the reduced mass $\mu \equiv M_{\rm ADM}^{\rm NS1} M_{\rm ADM}^{\rm +NS2}/M_0$ according to the results of the 3PN approximation (the ratio of the unequal-mass case to the equal-mass one is $\mu_{\rm +uneq}/\mu_{\rm eq} \simeq 0.978$ ) and the orbital angular velocity at the termination point of the sequence should be smaller." +" In Figure 17,, the total angular momentum for the same models as in Figure 16 is shown along both equal-mass and unequal-mass sequences."," In Figure \ref{fig17}, the total angular momentum for the same models as in Figure \ref{fig16} is shown along both equal-mass and unequal-mass sequences." + 'The sequence of the total angular momentum for the unequal-mass case is located below that of the equal-mass case at the same orbital angular velocity., The sequence of the total angular momentum for the unequal-mass case is located below that of the equal-mass case at the same orbital angular velocity. +" This is also because the total angular momentum is proportional to the reduced mass, according to the results of the 3PN approximation."," This is also because the total angular momentum is proportional to the reduced mass, according to the results of the 3PN approximation." +" However, because the orbital angular velocity at the termination point of the sequence is smaller for the unequal-mass case, its total angular momentum is approximately the same value as that for the equal-mass case coincidentally."," However, because the orbital angular velocity at the termination point of the sequence is smaller for the unequal-mass case, its total angular momentum is approximately the same value as that for the equal-mass case coincidentally." +" Finally, we show the effect of the total mass of binary neutron stars on the binding energy in Figure 18.."," Finally, we show the effect of the total mass of binary neutron stars on the binding energy in Figure \ref{fig18}." +" The EOS we choose for this figure is one of the tabulated realistic EOSs, the APR EOS."," The EOS we choose for this figure is one of the tabulated realistic EOSs, the APR EOS." +" Figure 18 shows the results for three total masses, 24Mo, 2.7Mo, and 3.0Mo."," Figure \ref{fig18} shows the results for three total masses, $2.4 M_{\odot}$, $2.7 M_{\odot}$, and $3.0 M_{\odot}$." +" As the neutron star mass increases, the star becomes more compact and less subject to tidal disruption."," As the neutron star mass increases, the star becomes more compact and less subject to tidal disruption." +" For a binary system composed of more massive neutron stars, the two stars are necessary to come closer each other to reach their mass-shedding limit."," For a binary system composed of more massive neutron stars, the two stars are necessary to come closer each other to reach their mass-shedding limit." + This, This +"for these galaxies, the maximum rotational velocity Vmax is an approximation for the virial mass of the system.","for these galaxies, the maximum rotational velocity $_{max}$ is an approximation for the virial mass of the system." +" For this investigation we use galaxy A in simulation 1 (see Table 1)), at a snapshot when the two galaxies are still well separated."," For this investigation we use galaxy A in simulation 1 (see Table \ref{sims}) ), at a snapshot when the two galaxies are still well separated." + The adopted inclination of the galaxy is 35? (90? is defined to be edge-on)., The adopted inclination of the galaxy is $^\circ$ $^\circ$ is defined to be edge-on). + The velocity field is very regular at all redshifts., The velocity field is very regular at all redshifts. +" The appearance of our VFs is dominated by seeing, as we adopted a constant value of 0.8"" for the FWHM, which is always larger than the angular resolution we use."," The appearance of our VFs is dominated by seeing, as we adopted a constant value of 0.8"" for the FWHM, which is always larger than the angular resolution we use." +" Both effects, the worse sampling at higher redshifts and the large seeing smear out the velocity field when shifted to higher z. In Fig."," Both effects, the worse sampling at higher redshifts and the large seeing smear out the velocity field when shifted to higher z. In Fig." + 1 we present the VFs of an undisturbed disc galaxy as seen at two different redshifts (z=0.1 and z=0.5)., \ref{regular0105} we present the VFs of an undisturbed disc galaxy as seen at two different redshifts (z=0.1 and z=0.5). + Overlayed on the VF are the best fitting ellipses from the kinemetry analysis., Overlayed on the VF are the best fitting ellipses from the kinemetry analysis. +" At a redshift of 0.1 there is some structure visible in the VF, e.g. a small twist of the position angle I' towards the centre."," At a redshift of 0.1 there is some structure visible in the VF, e.g. a small twist of the position angle $\Gamma$ towards the centre." + Also in the disc some fluctuations of the rotational velocity are present., Also in the disc some fluctuations of the rotational velocity are present. + These small structures in the VF are completely smeared out at redshift z—0.5., These small structures in the VF are completely smeared out at redshift $z=0.5$. + Quantitatively the differences can be seen in Fig., Quantitatively the differences can be seen in Fig. +" 2 in the radial profiles of the kinemetric properties, calculated using the kinemetry programme."," \ref{plotsreg} in the radial profiles of the kinemetric properties, calculated using the kinemetry programme." +" The program also calculates formal lo errors from the covariance matrix, which are shown as error bars in the plots."," The program also calculates formal $\sigma$ errors from the covariance matrix, which are shown as error bars in the plots." + 'These uncertainties are estimated from the measurement uncertainties in the kinematic data., These uncertainties are estimated from the measurement uncertainties in the kinematic data. + As we do not account for the spectral resolution of the instruments we use the scatter of the velocity field., As we do not account for the spectral resolution of the instruments we use the scatter of the velocity field. +" Note that this is just a formal uncertainty, which in reality is higher, also because systematical errors add up."," Note that this is just a formal uncertainty, which in reality is higher, also because systematical errors add up." +" While at z=0.1 both, I and q show variations with radius, they are almost constant at z—0.5."," While at $z=0.1$ both, $\Gamma$ and $q$ show variations with radius, they are almost constant at $z=0.5$." + The first order moment k corresponds to the rotation curve (RC) of a spiral galaxy or more generally spoken to the bulk motion in the velocity field., The first order moment $k_1$ corresponds to the rotation curve (RC) of a spiral galaxy or more generally spoken to the bulk motion in the velocity field. +" For the undisturbed velocity field presented here it shows the typical behaviour of a rotation curve, i.e. rising in the inner part and turning over to a flat regime."," For the undisturbed velocity field presented here it shows the typical behaviour of a rotation curve, i.e. rising in the inner part and turning over to a flat regime." + This undisturbed shape is present at redshift z=0.1 and at z=0.5., This undisturbed shape is present at redshift $z=0.1$ and at $z=0.5$. + In Fig., In Fig. +" 3 we show the rotation curves of the system at redshift z—0.5 obtained from the 2D velocity field (triangles) and from a simulated slit (asterisks), extracted as described in Kronberger et al. ("," \ref{RCs_regular} we show the rotation curves of the system at redshift $z=0.5$ obtained from the 2D velocity field (triangles) and from a simulated slit (asterisks), extracted as described in Kronberger et al. (" +2006).,2006). +" The modelled slit was placed over the major axis of the galaxy with a slit width of 1""."," The modelled slit was placed over the major axis of the galaxy with a slit width of 1""." +" The RCs extracted in these different ways agree very well, as expected for such a regular velocity field."," The RCs extracted in these different ways agree very well, as expected for such a regular velocity field." +" As à dashed line we plot in the same figure the RC extracted at redshift z=0.1, which agrees reasonably well with the higher redshift RCs."," As a dashed line we plot in the same figure the RC extracted at redshift $z=0.1$, which agrees reasonably well with the higher redshift RCs." +" 'This demonstrates the principle power of 2D velocity fields for distant Tully-Fisher studies regular, undisturbed velocity fields are considered."," This demonstrates the principle power of 2D velocity fields for distant Tully-Fisher studies regular, undisturbed velocity fields are considered." + 'The last row in Fig., The last row in Fig. + 2 shows a quantitative measure for distortions in the 2D velocity field., \ref{plotsreg} shows a quantitative measure for distortions in the 2D velocity field. +" The fifth order term of the harmonic expansion ks represents complex, kinematically separate components in the velocity field."," The fifth order term of the harmonic expansion $k_5$ represents complex, kinematically separate components in the velocity field." + In the plot the ratio ks/k; is shown., In the plot the ratio $k_5/k_1$ is shown. +" For the regular VF presented in this section, this ratio is small, generally below 0.1 for all redshifts."," For the regular VF presented in this section, this ratio is small, generally below 0.1 for all redshifts." +" However, this value is very"," However, this value is very" +be destroyed when crossing the binary system.,be destroyed when crossing the binary system. +" We notice that these dynamical arguments favor L;=10°” and 1095 erg/s in the HMMQ Cygnus X-1 and Cygnus X-3, respectively."," We notice that these dynamical arguments favor $L_{\rm j}\gtrsim 10^{37}$ and $10^{38}$ erg/s in the HMMQ Cygnus X-1 and Cygnus X-3, respectively." + The cocoon/clumpy wind case deserves few words., The cocoon/clumpy wind case deserves few words. +" This situation takes place when the forward shock is well within the binary system, and the cocoon pressure is high, preventing clumps from entering the cocoon."," This situation takes place when the forward shock is well within the binary system, and the cocoon pressure is high, preventing clumps from entering the cocoon." +" When the forward shock has reached the outskirts of the binary, the cocoon pressure drops quickly (PBK10), allowing wind clumps to penetrate into the cocoon and reach the jet, and eventually dissipate the cocoon away."," When the forward shock has reached the outskirts of the binary, the cocoon pressure drops quickly (PBK10), allowing wind clumps to penetrate into the cocoon and reach the jet, and eventually dissipate the cocoon away." +" In jets A and B, those clumps reaching the jet relatively close to its base are destroyed just by jet expansion or erosion."," In jets A and B, those clumps reaching the jet relatively close to its base are destroyed just by jet expansion or erosion." +" These interactions trigger a shock wave that propagates inside the jet, and when interactions are frequent such a wave forces the strongly disruptive asymmetric recolimation shock."," These interactions trigger a shock wave that propagates inside the jet, and when interactions are frequent such a wave forces the strongly disruptive asymmetric recollimation shock." +" This phenomenon is illustrated in Fig. 13)),"," This phenomenon is illustrated in Fig. \ref{fig:maps12}) )," +" in which the first clump is completely destroyed by jet expansion, whereas the second one, even when it does not fully penetrate into the jet, triggers a shock strong that propagates all through the latter lasting for the whole simulation (several ta; see Sect. ??))."," in which the first clump is completely destroyed by jet expansion, whereas the second one, even when it does not fully penetrate into the jet, triggers a shock strong that propagates all through the latter lasting for the whole simulation (several $t_{\rm d}$; see Sect. \ref{phys}) )." + The clump at the highest z in jet A’ (1.4x em) is shocked but still not significantly disrupted by instabilities after few t4., The clump at the highest $z$ in jet A' $1.4\times 10^{12}$ cm) is shocked but still not significantly disrupted by instabilities after few $t_{\rm d}$. +" Later, this clump could be destroyed or may eventually escape the jet, although jet bending in the down-wind direction makes the latter unlikely."," Later, this clump could be destroyed or may eventually escape the jet, although jet bending in the down-wind direction makes the latter unlikely." +" When clumps are disrupted inside the jet, all the clump mass is entrained by the flow."," When clumps are disrupted inside the jet, all the clump mass is entrained by the flow." + The level of mass loading can be easily estimated from the amount of clumps entering into the jet per time unit: Να~(n/47)(3M/A4xR3p.)©0.02 clump/s or zz5x1077 g/s. This is ~3 times more mass flux than in the jet., The level of mass loading can be easily estimated from the amount of clumps entering into the jet per time unit: $\dot{N}_{\rm cj}\sim (\eta/4\pi)(3\dot{M}/4\pi R_{\rm c}^3\rho_{\rm c})\approx 0.02$ clump/s or $\approx 5\times 10^{17}$ g/s. This is $\sim 3$ times more mass flux than in the jet. +" Therefore, jet deceleration due to mass loading can be very efficient, as is most clearly seen in the simulation results for jet B. The implications also apply to faster and lighter, but"," Therefore, jet deceleration due to mass loading can be very efficient, as is most clearly seen in the simulation results for jet B. The implications also apply to faster and lighter, but" +disruption is quite well defined. /?0.080.3. due to the strong dependence of the tidal density on A.,"disruption is quite well defined, $R\sim 0.03 - 0.2$, due to the strong dependence of the tidal density on $R$." + Therefore we predict a pile-up of smaller planets at those radiias the actual type E migration rate of the disruption remnants is far smaller than the theoretical tvpe E migration rate (cf.Ida&Lin 2008)., Therefore we predict a pile-up of smaller planets at those radii the actual type I migration rate of the disruption remnants is far smaller than the theoretical type I migration rate \citep[cf.][]{IdaLin08}. +. Such a pile-up may be testable with the current exoplanet data., Such a pile-up may be testable with the current exoplanet data. + Theoretical astrophysics research in Leicester is supported by an STEC Rolline Grant., Theoretical astrophysics research in Leicester is supported by an STFC Rolling Grant. + Andrew Wine ids thanked [or discussions., Andrew King is thanked for discussions. + Richard Alexander is thanked Lor useful comments on the draft of the manuscript., Richard Alexander is thanked for useful comments on the draft of the manuscript. +factor bv which the radiation pressure force is enlianced by trapping of eunergv within the expanding shell.,factor by which the radiation pressure force is enhanced by trapping of energy within the expanding shell. + If Fuap=0. then the shell is optically thin aud all stellar photous escape without depositing any moment.," If $f_{\rm trap} = 0$, then the shell is optically thin and all stellar photons escape without depositing any momentum." + Given the hieh color temperature of the cuiitting stars and the large opacity of the eas clouds where massive clusters form. this is not realistic.," Given the high color temperature of the emitting stars and the large opacity of the gas clouds where massive clusters form, this is not realistic." +" A value fray=1 corresponds to every photon emitted by the stars beiug absorbed once iu the shell aud depositing its ποιοται rere, then promptly escaping."," A value $f_{\rm trap} = 1$ corresponds to every photon emitted by the stars being absorbed once in the shell and depositing its momentum there, then promptly escaping." + If there is more than one oeiteractiou per photon then fray could potcutially be uuch larger than uuity., If there is more than one interaction per photon then $f_{\rm trap}$ could potentially be much larger than unity. + In this case the velocity to which je shell accelerates will be lamited by the rate at which je stars supply οποίον rather than momentum., In this case the velocity to which the shell accelerates will be limited by the rate at which the stars supply energy rather than momentum. + Trapping cau happen iu three wavs., Trapping can happen in three ways. + First. some raction of the stellar radiation will go iuto accelerating πιο driven winds off stellar surfaces (7). and the expanding wind will collide with the slower-moving shell.," First, some fraction of the stellar radiation will go into accelerating line driven winds off stellar surfaces \citep{castor75}, and the expanding wind will collide with the slower-moving shell." + This will produce some transfer of momentum. which could be large if the shocked gas becomes trapped iuside he shell (??)..," This will produce some transfer of momentum, which could be large if the shocked gas becomes trapped inside the shell \citep{castor75a, weaver77a}." + Second. if the shell is sufficiently optically hick to loug-waveleusth radiation. then ultraviolet aud visible photous that ire absorbed by dust eraius in the shell and ve-rachated at infrared waveleugths may remain rapped in the shell and interact more times before finally escaping.," Second, if the shell is sufficiently optically thick to long-wavelength radiation, then ultraviolet and visible photons that are absorbed by dust grains in the shell and re-radiated at infrared wavelengths may remain trapped in the shell and interact more times before finally escaping." + Third. Lxiuan à photons that are produced by reconibimatious in the shell or in the region interior nay undergo many resonant interactions before escapiug.," Third, Lyman $\alpha$ photons that are produced by recombinations in the shell or in the region interior may undergo many resonant interactions before escaping." + We defer a discussion of these trapping mechanisis uutil 3.. and for now we simply assert the result from that section: fray Is always likely to be of order a few.," We defer a discussion of these trapping mechanisms until \ref{trapping}, and for now we simply assert the result from that section: $f_{\rm trap}$ is always likely to be of order a few." + For this reason. we choose to leave it as a free parameter of constant value. for which we adopt a fiducial value frap=2 when we wish to ο ΕΠ evaluations.," For this reason, we choose to leave it as a free parameter of constant value, for which we adopt a fiducial value $f_{\rm trap}=2$ when we wish to perform numerical evaluations." + We can characterize when radiation pressure ds sienificant by examining the limiting cases of gas- and radiation-pressure dominated flows., We can characterize when radiation pressure is significant by examining the limiting cases of gas- and radiation-pressure dominated flows. + In the eas-pressure dominated case. we have the usual ?. reeion solution.," In the gas-pressure dominated case, we have the usual \citet{spitzer78} region solution." + Once expansion of the region becomes subsonic with respect to the ionized eas. the region iuterior approaches a uniform densitv. aud ionization balance requires that where rp. Dy. and ο are the radius. temperature. and sound speed of the ionized region. ap is the case-D recombination coefficieut. o 1s a dimenusiouless nunboer that accounts for absorption of ionizing photous by dust erains and for free electrons provided by clemeuts other than hydrogen. aud we have adopted the usual ou-the-spot approximation.," Once expansion of the region becomes subsonic with respect to the ionized gas, the region interior approaches a uniform density, and ionization balance requires that where $\rii$, $\tii$, and $\cii$ are the radius, temperature, and sound speed of the ionized region, $\alphab$ is the case-B recombination coefficient, $\phi$ is a dimensionless number that accounts for absorption of ionizing photons by dust grains and for free electrons provided by elements other than hydrogen, and we have adopted the usual on-the-spot approximation." + If Πο is siuelv-jonized aud of photons are absorbed by dust rather than eas. as expected for gas pressurc-douunmated reeious with Allkv Way dust-to-gas ratios (7).. then o= 0.73.," If He is singly-ionized and of photons are absorbed by dust rather than gas, as expected for gas pressure-dominated regions with Milky Way dust-to-gas ratios \citep{mckee97}, then $\phi=0.73$ ." + We discuss the value of o. and of dust absorption generally. in more detail in Appendix À..," We discuss the value of $\phi$, and of dust absorption generally, in more detail in Appendix \ref{dustabsorption}." + Note that equation (2)) holds approximately even in the case of a blister-type hemispherical region., Note that equation \ref{rhoiieqn}) ) holds approximately even in the case of a blister-type hemispherical region. + Following ?.. we consider iu that iu the case of an embedded. spherical region that ayαςο. while for a blister-tvpe one αμ726g.," Following \citet{matzner02}, we consider in that in the case of an embedded, spherical region that $\uii \ll \cii$, while for a blister-type one $\uii\approx 2\cii$." + Thus the ooOgas pressure term on the right-haucl side of equation (1)) becomes Iu the lamiting case of a radiatiou-pressire dominated flow. the radiation pressure terim is simply £L(large).," Thus the gas pressure term on the right-hand side of equation \ref{momeqn}) ) becomes In the limiting case of a radiation-pressure dominated flow, the radiation pressure term is simply $L/(4\pi \rii^2 c)$." + Since the raciation- aud eas-pressure terius have differcut radial dependences. we can calculate a characteristic radius for which they are equal: where the munerical evaluation is for our fiducial parameters Tip=TOOO WN. ο=0.73. fray=2.0 =1. aud ap=3.16«10Is cnm? sloaud Sip=S/10P «1.," Since the radiation- and gas-pressure terms have different radial dependences, we can calculate a characteristic radius for which they are equal: where the numerical evaluation is for our fiducial parameters $\tii=7000$ K, $\phi=0.73$, $f_{\rm trap}=2$, $\psi=1$, and $\alphab=3.46\times 10^{-13}$ $^3$ $^{-1}$, and $S_{49}=S/10^{49}$ $^{-1}$." + Since radiation forces vary with radius as n radiation dominates at smaller radii and eas pressure at larger radii.," Since radiation forces vary with radius as $\rii^{-2}$ , radiation dominates at smaller radii and gas pressure at larger radii." + Tt is useful to compare this to the Strouunercn radius at which eas pressure-driven expansion beeius iu the case of negligible radiation pressure force., It is useful to compare this to the Strömmgren radius at which gas pressure-driven expansion begins in the case of negligible radiation pressure force. +" Setting (3; in equation (2)) equal to the mean density p(raco) iuside μι we fiud and computing the ratio of ra, to this we fud where jap=0.61 is the mean molecular weight in the fully ionized gas (so eq=9.71 luu 3) aud Wye=Preo100g) is the mean density of II nuclei in units of 107 7. and p=1. Lis the atomic mass per II nucleus for gas of standard cosiie Composition."," Setting $\rhoii$ in equation \ref{rhoiieqn}) ) equal to the mean density $\overline{\rho}(r_{\rm St,0})$ inside $r_{\rm St,0}$, we find and computing the ratio of $r_{\rm ch}$ to this we find where $\muii=0.61$ is the mean molecular weight in the fully ionized gas (so $\cii=9.74$ km $^{-1}$ ) and $\overline{n}_{\rm H,2}=\overline{\rho}(r_{\rm St,0})/(100 \mu m_{\rm H})$ is the mean density of H nuclei in units of $10^2$ $^{-3}$, and $\mu=1.4$ is the atomic mass per H nucleus for gas of standard cosmic composition." +" Thus we see that for sinele OD stars. 949~1. expanding into Galactic molecular clouds. συ~1. radiation force is neeheible once the region reaches a tenth of a pe in size (ra,&OL pc). aud is often ueelieible as soon as the ionized region has fuished its initial rapid expansion to the Stromumeren radius (¢X 1)"," Thus we see that for single OB stars, $S_{49}\sim 1$, expanding into Galactic molecular clouds, $\overline{n}_{\rm H,2}\sim 1$, radiation force is negligible once the region reaches a tenth of a pc in size $r_{\rm ch}\la 0.1$ pc), and is often negligible as soon as the ionized region has finished its initial rapid expansion to the Strömmgren radius $\zeta \la 1$ )." + Thereafter the usual gas pressure-driven expansion solution applies., Thereafter the usual gas pressure-driven expansion solution applies. + Towever. we reach a very different conclusion if we cousider the formation of very massive clusters in dense environments," However, we reach a very different conclusion if we consider the formation of very massive clusters in dense environments." + Iu Table 1 woe lst xoperties for a sample of massive star clusters in the ADlkv Wav. M82. the Áuteuuae. and NOC 5253.," In Table \ref{clusterlist} we list properties for a sample of massive star clusters in the Milky Way, M82, the Antennae, and NGC 5253." + We ot ο versus Wye for these objects in Figme 2..," We plot $S_{49}$ versus $\overline{n}_{\rm H,2}$ for these objects in Figure \ref{clustersample}." + As the plot shows. these clusters have ¢ in the range ] 105 iudicatiug that they eo from the border vetween radiation- aud eas-domunatedto completely raciatiou-douunated.," As the plot shows, these clusters have $\zeta$ in the range $\sim 1 - 10^4$ , indicating that they go from the border between radiation- and gas-dominatedto completely radiation-dominated." + The characteristic radii where gas xessure becomes comparable to radiation pressure run rou ~1—100 pc. which is eenerally huger than the shysical size of the cluster iu question.," The characteristic radii where gas pressure becomes comparable to radiation pressure run from $\sim 1-100$ pc, which is generally larger than the physical size of the cluster in question." +" The exception is the Orion. Nebular Cluster (the inverted triangle). by ar the snallest cluster shown in Figure 2.. This has ro,=0.06pe (αππαςa blister-type region. which is observed). considerably aller than the 0.5 pe radius of the cluster."," The exception is the Orion Nebular Cluster (the inverted triangle), by far the smallest cluster shown in Figure \ref{clustersample}.. This has $r_{\rm ch}=0.06$pc (assuminga blister-type region, which is observed), considerably smaller than the $0.8$ pc radius of the cluster." +that show for a shell of the thickness of the solar convection zone as a fraction of the radius. the latitudinal Revnolds stress (hat (rausports angular momentum toward (he equator to maintain the differential rotation reaches only to about 607. latitucle.,"that show for a shell of the thickness of the solar convection zone as a fraction of the radius, the latitudinal Reynolds stress that transports angular momentum toward the equator to maintain the differential rotation reaches only to about $60^{\circ}$ latitude." + Bul even this evindrical problem must be solved ummerically: we can get a first idea of the nature of meridional flow in hieh latitucles by farther approximating (he evlinder with a cartesian analog., But even this cylindrical problem must be solved numerically; we can get a first idea of the nature of meridional flow in high latitudes by further approximating the cylinder with a cartesian analog. + In this analog the evlinder is replaced by a channel infinite in longitude. whose left side boundary is identified with the axis of the evlinder. ancl whose right side boundary is identified with the outer wall of the cvlinder.," In this analog the cylinder is replaced by a channel infinite in longitude, whose left side boundary is identified with the axis of the cylinder, and whose right side boundary is identified with the outer wall of the cylinder." + Thus through this sequence of transformations of the equations we can trace the side boundaries of the cartesian channel back to the polar axis and equatorwarc boundary of the spherical polar cap., Thus through this sequence of transformations of the equations we can trace the side boundaries of the cartesian channel back to the polar axis and equatorward boundary of the spherical polar cap. + This cartesian eeonmeltry allows solutions in latitude. in terms of simple periodic aud exponential hunctions., This cartesian geometry allows solutions in 'latitude' in terms of simple periodic and exponential functions. + We judge (hat such a simplification is justified for a first study of (he polarcell problem. but should be followed by much more realistic svstems. which we plan for future papers.," We judge that such a simplification is justified for a first study of the polarcell problem, but should be followed by much more realistic systems, which we plan for future papers." + To make (his connection back to the spherical problem as strong as possible. we apply the same boundary conditions in (he cartesian case as we would have in the cvlindrical and spherical cases.," To make this connection back to the spherical problem as strong as possible, we apply the same boundary conditions in the cartesian case as we would have in the cylindrical and spherical cases." + In words. in the spherical cap case these conditions are (hat all plivsieal variables remain bounded at the polar axis and axisvimetry is maintained.," In words, in the spherical cap case these conditions are that all physical variables remain bounded at the polar axis and axisymmetry is maintained." + These requirements imply that the azimuthal flow. (he latitudinal flow. the latituclinal pressure gradient aud the viscous stress all vanish on the axis.," These requirements imply that the azimuthal flow, the latitudinal flow, the latitudinal pressure gradient and the viscous stress all vanish on the axis." + To actually solve the exlindrical problem. we would apply the same conditions on the axis of the evlinder. but latitude is replaced by the evlindrical radius variable as a coordinate.," To actually solve the cylindrical problem, we would apply the same conditions on the axis of the cylinder, but latitude is replaced by the cylindrical radius variable as a coordinate." + In the cartesian analog. the evlindrical radius variable is replaced by the cross-channel coordinate of the infinite channel. and the azimuthal coordinate by (the coordinate along the channel.," In the cartesian analog, the cylindrical radius variable is replaced by the cross-channel coordinate of the infinite channel, and the azimuthal coordinate by the coordinate along the channel." +" In all three svstems. (he meridional and azimuthal flows are specified on the boundary Chat corresponds to the equatorward boundary of (he spherical polar cap. namely the outer boundary of the exlinder. and the right hand side boundary. of ihe channel,"," In all three systems, the meridional and azimuthal flows are specified on the boundary that corresponds to the equatorward boundary of the spherical polar cap, namely the outer boundary of the cylinder, and the right hand side boundary of the channel." + In the cartesian problem. the boundary conditions at the sides introduce the possibility (hat momentum associated with the flow parallel to the channel walls can enter the domain from the rieht side and exit from the left. which has no counterpart in the cvlindrical or spherical cases.," In the cartesian problem, the boundary conditions at the sides introduce the possibility that momentum associated with the flow parallel to the channel walls can enter the domain from the right side and exit from the left, which has no counterpart in the cylindrical or spherical cases." + But we can show (hat this transfer has no effect on the solutions for meridional flow. so it is not significant dvuamically.," But we can show that this transfer has no effect on the solutions for meridional flow, so it is not significant dynamically." + In determining meridional circulation quantitativelv. the large increase in [hud density with depth in the convection zone has to be important. but it also adds considerable mathematical complexity.," In determining meridional circulation quantitatively, the large increase in fluid density with depth in the convection zone has to be important, but it also adds considerable mathematical complexity." + It is possible (ο write (he equations of motion in terms of mass flux rather than velocities. in which case the effect of the density increase with depth is seen explicitly only in lower order terms in the turbulent diffusion expressions.," It is possible to write the equations of motion in terms of mass flux rather than velocities, in which case the effect of the density increase with depth is seen explicitly only in lower order terms in the turbulent diffusion expressions." + We will keep these, We will keep these + The soft gamma-ray repeater pplaved a kev role in our understanding of high energv transicuts.,] The soft gamma-ray repeater played a key role in our understanding of high energy transients. + It was from this source that au iuteuse burst was observed on 5 March. 1979 (Mazoetsetal.1979:Clineetal 1980j.," It was from this source that an intense burst was observed on 5 March, 1979 \citep{mgia+79,cdpt+80}." +". The burst was followed by an ""afterelow Cluission with anu apparent ds periodicity.", The burst was followed by an “afterglow” emission with an apparent 8-s periodicity. + The source of the burst was quickly localized to the supernova remnant N19 (also known as SNR 66.1) in the Largeay Maeellanic. DouCloud (Evansctal.ToS1980)., The source of the burst was quickly localized to the supernova remnant N49 (also known as SNR $-$ 66.1) in the Large Magellanic Cloud \citep{eklc+80}. +". Observations↽⋅ with üdeutified, xd:a quiesceut.""cent oiand briehtS CLNo107 oreTes 1j] counterpart.- RN ⋜⋯⊳↥⋅↸∖↑↕∪∐≺⋜∏∏≻⋜∐⋅↸∖∐↑↕⋯⊳↘↽∪↕≯↸⊳∪∐∏≻⋜∐∏∪↕∪∙∖⊽⋜∐⋅↕⋯↕↴∖↴⋜⋯↑∐∪↥∷∖↴ . ayocnlated ↴∖↴⋉∏∏⋞⋔↸↧⋞⋯↸↧↴∖∏∶↰≔⋮"," Observations with identified a quiescent and bright $L_X\sim 10^{36}\,$ erg $^{-1}$ ) X-ray counterpart, \\citep*{rkl94}." +↰≔↸↴∖↾∪∏↕⋯↾⋎⊸∖↕↴∖⋞⋯⋞↧↕↴∖∪⋯⋞↧⋮↰≔∐↸↾⋞⊔↴∖ ⋜↧↕⋟↸∖↥⋅∶↴∙⊾↕∪↖↖⇁↖↖↽↕↑∐≺∖∖≓↴∖↴↻↸∖↥⋅↕∪≼∐↸⊳↕↑⋅↖↽↻↥⋅∪↖↽↕≼∐∖≼↧↑↕∐∖∐↥⋅↴∖↴↑⋜⋯≼↧ strongest evideuce for super-strong maenoetie field streugtlis. B~4101?n G. Such] strong∙⋅ fields* are needed to both confine. radiatius plasnia⋅⋅ as well as allow the radiatiou toThe ⋅ escape (Duncan&Thompson1992:Paczvuski1992).," The intense burst of 5 March 1979 and the luminous afterglow with 8-s periodicity provided the first and strongest evidence for super-strong magnetic field strengths, $B\sim 10^{15}\,$ G. Such strong fields are needed to both confine the radiating plasma as well as allow the radiation to escape \citep{dt92,paczynski92}." +". However. such lighly iiagnetized neutron stars or “maguctars” were originally motivated by theoretical cousiderations namely strong convection would naturally lead to growth of maeuctic fields during the process of the collapse of the proto-neutrou star core (Duncan&Thompson1992:""Thompson&Duncan 1993)."," However, such highly magnetized neutron stars or “magnetars” were originally motivated by theoretical considerations — namely strong convection would naturally lead to growth of magnetic fields during the process of the collapse of the proto-neutron star core \citep{dt92,td93}." +". Separately, another eroup of neutron stars. the so-called Anomalous N-ray pulsars (AXPs). were recognized as a new class of neutron stars (vanParaclijs.Taam.&vandenΠαινο 1995: Moereghetti&Stella 1995))."," Separately, another group of neutron stars, the so-called Anomalous X-ray pulsars (AXPs), were recognized as a new class of neutron stars \citealt*{pth95}; \citealt{ms95}) )." +" The ANPs- were noted for. a narrow period: distribution.⋅⋅⋅ between 6⋅ and .20 s: huuuinous. X-rav- οσοι,⋅⋅ Ly~aquisLO’? ere aud apparent lack of. a donor star."," The AXPs were noted for a narrow period distribution, between 6 and 20 s; luminous X-ray emission, $L_X\sim +10^{35}\,$ erg and apparent lack of a donor star." + The: sources “anomalous” in ⋅⊀⋅that the source of the⋅ quiescenut N-rav- ↖⊳↕≼∖≻∶∶⋡∏∖↽↕≺⊔ ∎ U ; ↴⋉⋉∖↴∖ ; CPa, The sources were “anomalous” in that the source of the quiescent emission was neither rotational (from the known $\dot P$ ) nor accretion (apparent lack of companion). + avo ale ⊀⋉∖⊀⋅↴ ⊺∐↸∖↕∐↑↸∖∐↴∖↴↸∖↴∏∐∷∖↴↑∪↕⋅↱⊐⋀∖↕⋜⋯⊳∐↕∩⊤∩⋜⋯≼↧↑↕∐∖↕⋯⊔↕∐∪∏↴∖↴ the M oen MN from uMC of a eeemagnetar-d&ei Ποια strength (thompson 1993). ," Various authors speculated and suggested that AXPs are also magnetars — specifically, their X-ray emission to arise from the decay of a magnetar-like field strength \citep{td93}. ." +discoverv of peoriodictv ⋅in SGBs, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs , The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (I, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Io, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iou, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouv, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouve, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouvel, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouveli, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouvelio, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouveliot, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouvelioto, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouveliotou, The discovery of periodicity in SGRs +discoverv of peoriodictv ⋅in SGBs (Iouveliotou↴, The discovery of periodicity in SGRs +solutions presented in re ..,solutions presented in \\ref{RF}. + For ease of further caleulations. we will use @=1.5 in equation (49)).," For ease of further calculations, we will use $a=1.5$ in equation \ref{GR}) )." + Phe only uncertainty [left in the evolution of Py is that ol the ejecta shell comoving thickness A‘., The only uncertainty left in the evolution of $\Gamma_R$ is that of the ejecta shell comoving thickness $\Delta'$. + This uncertainty also allects the adiabatic cooling of the electrons ane the evolution of the magnetic field in the ejecta., This uncertainty also affects the adiabatic cooling of the electrons and the evolution of the magnetic field in the ejecta. +" The evolution of the electron Lorentz factors 5; and 5, at 4?27Rois where V is the comoving frame ejecta volume and an acliabatie index e,=4/3 for the relativistic electrons has »en used for the last term.", The evolution of the electron Lorentz factors $\gamma_i$ and $\gamma_c$ at $R > R_+$ is where $V'$ is the comoving frame ejecta volume and an adiabatic index $a_e = 4/3$ for the relativistic electrons has been used for the last term. +" Because the ejecta emission switches. olf. when the decreasing. cooling. Lrequency. 4,ph als below the observing frequency i. we will search. for afterglow⋅ parameters for⋅ which. disiο(5,44)c£. where bres is the latest time when the RS emission was (or thought o have been) observed."," Because the ejecta emission switches off when the decreasing cooling frequency $\nu_c^{(RS)}$ falls below the observing frequency $\nu$, we will search for afterglow parameters for which $\nu_c^{(RS)}(t_{max}) > \nu$, where $t_{max}$ is the latest time when the RS emission was (or thought to have been) observed." + Therefore the electrons. racliating at frequency ν΄ cool mostly adiabatically ancl the ejecta radiative cooling alter 2 can be ignored., Therefore the electrons radiating at frequency $\nu$ cool mostly adiabatically and the ejecta radiative cooling after $R_+$ can be ignored. + For the magnetic ield. the Dlux-freezing condition vields where ο) is the magnetic field. perpendicular (parallel) to the racial direction of the fireball motion.," For the magnetic field, the flux-freezing condition yields where $B_\perp$ $B_\parallel$ ) is the magnetic field perpendicular (parallel) to the radial direction of the fireball motion." + ‘To assess the elfect of the uncertainty of the behaviour ol A’ on the ejecta synchrotron emission. we consider (wo extreme cases: AY=const. as could. result from the compression ejecta against the decelerating contact discontinuity. and A’=R/V. corresponding to a comovine-frame expansion of the ejecta shell at a speed comparable to the speed. of light.," To assess the effect of the uncertainty of the behaviour of $\Delta'$ on the ejecta synchrotron emission, we consider two extreme cases: $\Delta' = const$, as could result from the compression ejecta against the decelerating contact discontinuity, and $\Delta' = R/\Gamma_R$, corresponding to a comoving-frame expansion of the ejecta shell at a speed comparable to the speed of light." + For the former case. relating the ejecta radius with the observer time through Rx VS leads to Rox£83 [for s20 and Rox(> for s=2 (just as for the ES).," For the former case, relating the ejecta radius with the observer time through $R \propto \Gamma_R^2 t$ , leads to $R \propto t^{1/4}$ for $s=0$ and $R \propto t^{1/2}$ for $s=2$ (just as for the FS)." + Substituting in equation (51)) shows that Broxd? decays slower than 2)., Substituting in equation \ref{B2}) ) shows that $B_\perp \propto R^{-1}$ decays slower than $B_\parallel$ . + Then. equations (28)). (32)). (36)).0 and (50)) vield For an ejecta shell spreading law AYΤμ. one obtains that Rox(£7 for s=0 and Rox£7 for s=2.," Then, equations \ref{Fp}) ), \ref{nuaic}) ), \ref{ga}) ), and \ref{gic}) ) yield For an ejecta shell spreading law $\Delta' = R/\Gamma_R$, one obtains that $R \propto t^{1/9}$ for $s=0$ and $R \propto t^{1/5}$ for $s=2$." + Equation (51)) shows that Byx4 decavs slower than By. leading to From the above scalings. it can be seen that the temporal index of the break frequencies changes by ~0.2 (0.05| 0.25) for s=0 (s= 2). while that of the peak Hux by 0.05 for either type of medium.," Equation \ref{B2}) ) shows that $B_\parallel \propto R^{-2}$ decays slower than $B_\perp$, leading to From the above scalings, it can be seen that the temporal index of the break frequencies changes by $\sim 0.2$ $0.05-0.25$ ) for $s=0$ $s=2$ ), while that of the peak flux by 0.05 for either type of medium." + The solutions presented in’ γαλ vary little between the above assumed behaviours of AN, The solutions presented in \\ref{RF} vary little between the above assumed behaviours of $\Delta'$. + Equations (54)) and (55)) are used to calculate the characteristies of the RS svncehrotron emission at />{ from those at /, Equations \ref{scale0}) ) and \ref{scale2}) ) are used to calculate the characteristics of the RS synchrotron emission at $t > t_+$ from those at $t_+$. + Vhe elfect of radiative losses on. the RS emission is estimated in a similar way as for the E (equation 43)). by adjusting the Iluxes obtained. in the acdiabatic case by a factor which accounts for the Laster deceleration of the ES due to the radiative losses.," The effect of radiative losses on the RS emission is estimated in a similar way as for the FS (equation \ref{rad}) ), by adjusting the fluxes obtained in the adiabatic case by a factor which accounts for the faster deceleration of the FS due to the radiative losses." + For the hiehly raciative regime. the evolution of the RS Lorentz [actor Py is calculated. as in the acliabatic case (equations 44 and 49)) but using the scaling of the FS Lorentz [actor Ep with radius corresponding to the radiative dynamics case (equation 42))!..," For the highly radiative regime, the evolution of the RS Lorentz factor $\Gamma_R$ is calculated as in the adiabatic case (equations \ref{pR} and \ref{GR}) ) but using the scaling of the FS Lorentz factor $\Gamma_F$ with radius corresponding to the radiative dynamics case (equation \ref{GFrad})." +" ""Phe absorption of the RS radio emission in the FS is also taken into account.", The absorption of the RS radio emission in the FS is also taken into account. + The formalism. presented in refdvnamies and &refradiation allows the calculation. of the RS and FS emission at a given observer time and observing frequency., The formalism presented in \\ref{dynamics} and \\ref{radiation} allows the calculation of the RS and FS emission at a given observer time and observing frequency. +" These emissions depend. on the dvnamics of the FS and @ecta shell. on the fireball kinetic energy £ and. the particle density of the CDM (2 for a homogeneous medium or ch, for a wind surrounding a massive star)."," These emissions depend on the dynamics of the FS and ejecta shell, on the fireball kinetic energy $E$ and the particle density of the CBM $n$ for a homogeneous medium or $A_*$ for a wind surrounding a massive star)." + The ejecta-shell shock-crossing time f also depends on the fireball initial. Lorentz factor Py. for thin ejecta. or on the duration T ol the fireball ejection. for thick ejecta.," The ejecta-shell shock-crossing time $t_+$ also depends on the fireball initial Lorentz factor $\Gamma_0$, for thin ejecta, or on the duration $\tau$ of the fireball ejection, for thick ejecta." + The initial Lorentz [actor also determines the number of electrons in the ejecta and. therefore. the RS emission.," The initial Lorentz factor also determines the number of electrons in the ejecta and, therefore, the RS emission." + Finallv. the RS and. ES emissions depend on the two microphysical parameters. 2; and zg which quantify the typical electron energy ancl the magnetic field.," Finally, the RS and FS emissions depend on the two microphysical parameters $\epsi$ and $\epsB$ which quantify the typical electron energy and the magnetic field." + Phus. the RS emission is determined by five parameters in the thin ejecta case. or six in the opposite case. while the FS emission depends on four. parameters.," Thus, the RS emission is determined by five parameters in the thin ejecta case, or six in the opposite case, while the FS emission depends on four parameters." + Note that £ and η (or cl.) determine the emission of both shocks., Note that $E$ and $n$ (or $A_*$ ) determine the emission of both shocks. + 1n this section we determine in the framework of the reverse-lorward shock scenario. the values of the above parameters allowed by the radio and optical emissions of the CRB afterelows 990123 and 021211. the only two afterglows [or which an optical emission has been detected. at early times. ~LOO seconds after the burst.," In this section we determine in the framework of the reverse-forward shock scenario the values of the above parameters allowed by the radio and optical emissions of the GRB afterglows 990123 and 021211, the only two afterglows for which an optical emission has been detected at early times, $\sim 100$ seconds after the burst." + ‘Table 1 lists the properties of the burst. optical. and radio emissions of the two afterglows.," Table 1 lists the properties of the burst, optical, and radio emissions of the two afterglows." +" For the afterglow 021211. the optical emission is decaving since the first measurement. at fy,=130 seconds after the burst. (Li 2003)."," For the afterglow 021211, the optical emission is decaying since the first measurement, at $t_1 = 130$ seconds after the burst (Li 2003)." + For the alterelow 090123. 1e emission begins to οσαν al ~45 seconds. CXkerlof 1999). after which the ourst exhibits some variability.," For the afterglow 990123, the emission begins to decay at $\sim 45$ seconds (Akerlof 1999), after which the burst exhibits some variability." + This raises the possibility of some energy. injection in the RS after 45 seconds., This raises the possibility of some energy injection in the RS after 45 seconds. +" For lis reason. we choose /,=τὸ seconds as the beginning of ye afterglow decay. as after this epoch the burst exhibits a weaker. decaving emission."," For this reason, we choose $t_1 = 73$ seconds as the beginning of the afterglow decay, as after this epoch the burst exhibits a weaker, decaying emission." + In both cases. the early optical emission fall-olfs steeper jan at later times.," In both cases, the early optical emission fall-offs steeper than at later times." +" For the afterglow 021211. the transition )tween these two regimes hasbeen observed: it occurs at f,=550750 seconds (Li 2003)."," For the afterglow 021211, the transition between these two regimes hasbeen observed: it occurs at $t_* = 550 - 750$ seconds (Li 2003)." + For GRB 990123. 10 transition is inferred to occur at ἐν=400TOO seconds (Li 2003). around. or after the last carly optical measurementat /»=GLO seconds GXkerlof 1999) but xior to the next available measurement at τω~4.0 hours after the burst (Ixulkarni 19995).," For GRB 990123, the transition is inferred to occur at $t_* = 400 - 700$ seconds (Li 2003), around or after the last early optical measurementat $t_2 = 610$ seconds (Akerlof 1999) but prior to the next available measurement at $t_3 \sim 4.0$ hours after the burst (Kulkarni 1999b)." +oscillations of the Tov Star ancl compare the results to simulations using SPIL,oscillations of the Toy Star and compare the results to simulations using SPH. + We then analyze the non linear motions for arbitrary ~ and show that the equations reduce to a small set of ordinary dilferential equations which can be integrated with high accuracy., We then analyze the non linear motions for arbitrary $\gamma$ and show that the equations reduce to a small set of ordinary differential equations which can be integrated with high accuracy. + We then compare the results of these integrations with SPILL simulations., We then compare the results of these integrations with SPH simulations. +" IP—Np the density of the static model is given by where the radius 7. is The mass AZ is given by If the Jv]ὃν, where ὃς is the unperturbed speed. of sound. the equations of motion can be linearized about the static structure."," If $P = K \rho^\gamma$ the density of the static model is given by where the radius $r_e$ is The mass $M$ is given by If the $|{\bf v}| \le c_s$, where $c_s$ is the unperturbed speed of sound, the equations of motion can be linearized about the static structure." + It is convenient to define and write /?=HR|og where His I? calculated: using the unperturbed. density. p., It is convenient to define and write $R = \bar{R} + \eta$ where $\bar{ R}$ is $R$ calculated using the unperturbed density $\bar{\rho}$. + The equations of motion then become We assume the time variation is οσος and write If these expressions are substituted into the linearized equations. V can be eliminated to get the following equation for D Assuming separable solutions. they must be of the form GG)sind or Cr)cos9 and the equation for ¢ is The solutions of this equation determine the values of e.," The equations of motion then become We assume the time variation is $e^{\imath \sigma t }$, and write If these expressions are substituted into the linearized equations, $V$ can be eliminated to get the following equation for $D$ Assuming separable solutions, they must be of the form $\zeta(r) \sin{\theta} $ or $\zeta(r) \cos{\theta} $ and the equation for $\zeta$ is The solutions of this equation determine the values of $\sigma$." + While this equation can be transformed to the equation for a Lypergeometrie function it is more convenient to determine the solutions directly using expansions in series following the method of Frobenius., While this equation can be transformed to the equation for a Hypergeometric function it is more convenient to determine the solutions directly using expansions in series following the method of Frobenius. + We thus take where .X—rfr., We thus take where $X=r/r_e$. + Le is convenient to replace σ by v according to using the definition of r.., It is convenient to replace $\sigma$ by $\nu$ according to using the definition of $r_e$. + Lf the series is substituted into the equation for ς we get the following recurrence relation for the cocLlicients The indicial equation gives ὁ=s and there is one solution with @y arbitrary and ej zero., If the series is substituted into the equation for $\zeta$ we get the following recurrence relation for the coefficients The indicial equation gives $c=s$ and there is one solution with $a_0$ arbitrary and $a_1$ zero. + Because the equation is second. order there must be (vo arbitrary constants but because the solutions of the inclicial equation diller by an integer (s is an integer) or are equal (s—0). the second arbitrary constant multiplies a solution containing Law. anc must be zero.," Because the equation is second order there must be two arbitrary constants but because the solutions of the indicial equation differ by an integer (s is an integer) or are equal (s=0), the second arbitrary constant multiplies a solution containing $\ln{x}$, and must be zero." + The remaining series only converges if where j is an integer and the associated value of ( is denoted by aj)., The remaining series only converges if where $j$ is an integer and the associated value of $\sigma$ is denoted by $\sigma_{j}$. +" The last term in the series for a given jj ds a,X.", The last term in the series for a given $j$ is $a_j X^j$. + Por numerical work we write the velocity in the form From (10)) Further details of the linear modes are given in Appendix A.., For numerical work we write the velocity in the form From \ref{eq:dvdtgradeta}) ) Further details of the linear modes are given in Appendix \ref{sec:linearmodeappendix}. + Smoothecl Particle Lvclrodvnamics is a Lagrangian particle method for solving the equations of Εις dynamics., Smoothed Particle Hydrodynamics is a Lagrangian particle method for solving the equations of fluid dynamics. + Since a primary application of SPILL is to self-gravitating gas in astrophysical svstems. in most cases involving free boundaries. Toy Stars represent an ideal test. of the algorithms capabilities on these systenis.," Since a primary application of SPH is to self-gravitating gas in astrophysical systems, in most cases involving free boundaries, Toy Stars represent an ideal test of the algorithm's capabilities on these systems." + Whilst the standard. SPIE algorithm has been well tested and benchmarked. we use the opportunity provided by the Tov Star solutions to benchmark more recent improvements to the algorithm.," Whilst the standard SPH algorithm has been well tested and benchmarked, we use the opportunity provided by the Toy Star solutions to benchmark more recent improvements to the algorithm." + In particular we formulate the SPLE equations fron a variational principle such that the spatial variation of the smoothing length according to the density variation is accounted for sell-consistently(2772)., In particular we formulate the SPH equations from a variational principle such that the spatial variation of the smoothing length according to the density variation is accounted for self-consistently. +.. We also use the Tov Stars to test a reversible time integration algorithm for SPI described. in?., We also use the Toy Stars to test a reversible time integration algorithm for SPH described in. +. The specific implementation of the SPILL algorithm used for the test problems presented in this paper is described below., The specific implementation of the SPH algorithm used for the test problems presented in this paper is described below. + The SPL equations are formulated. from a variational principle which accounts for the spatial variation of the smoothing length with density., The SPH equations are formulated from a variational principle which accounts for the spatial variation of the smoothing length with density. + Prior to the force evaluation. the density is caleulateck via a clirect summation over the particles which is iteratecl to self-consistent) determine," Prior to the force evaluation, the density is calculated via a direct summation over the particles which is iterated to self-consistently determine" +"Maguetic cataclysinic variables Guc'Vs). cosisting of the classes kuown as polars aud intermediae polar""S. are composed of a Roche-lobe-fillinge AL type mai sequence star m orbit about a maguetic wute chwart (see Warner(1995) for a review).","Magnetic cataclysmic variables (mCVs), consisting of the classes known as polars and intermediate polars, are composed of a Roche-lobe-filling M type main sequence star in orbit about a magnetic white dwarf (see \citet{warner95} for a review)." + Mass is los through the iuuer Lagrangian poiut. L4. aud flows owoard the magnetosphere of the white dwarf either predominatelv πι a stream (polars) or after orniug a truncated accretion disk circulati18o around the white dwarf Gutermediate polars).," Mass is lost through the inner Lagrangian point, $L_{1}$, and flows toward the magnetosphere of the white dwarf either predominately in a stream (polars) or after forming a truncated accretion disk circulating around the white dwarf (intermediate polars)." + Iu either case. the ionized gas ollows mmaeuctic field ines to the surface of he white dwarf after the eas reacjos the uagnetospiere where he magnetic pressure exceeds t10 Sus ται pressure.," In either case, the ionized gas follows magnetic field lines to the surface of the white dwarf after the gas reaches the magnetosphere where the magnetic pressure exceeds the gas ram pressure." + Upon reaching the wute dwut surface the gas will ο essentially at “free all. wih highlv supersonic velocities.," Upon reaching the white dwarf surface the gas will be essentially at “free fall”, with highly supersonic velocities." + The abrupt sop of tje radial inflow near he surface of the white dwarf leads to the formatio- of a shock. which heats t1¢ Inflowing material (Fabian.andMasters1979:Wu20 ).," The abrupt stop of the radial inflow near the surface of the white dwarf leads to the formation of a shock, which heats the inflowing material \citep{fabian76,king79,lamb79,wu00}." +. The hot subsonie post- flow settles eradualv outo the white clwart. and cooS via enmüttius biusstrahluug N-vavs aid optical/iifra-red cyclotron raclation.," The hot subsonic post-shock flow settles gradually onto the white dwarf, and cools via emitting bremsstrahlung X-rays and optical/infra-red cyclotron radiation." +" The hvadrodyvuiuaic strucure ofthe post-sliock settincl flow is etermuned bv raclaive and particle energv Xocesses, Which are esseutialv characterized by the wenisstrahluusg cooling time £fwe the evelotron cooling iue Τον. the electron-iou οverev-cxchange thue τω. he clectron-clectrou collisioid time fee. and the lon-ion collisional time f (IsingandLasota1979: 2005)."," The hydrodynamic structure of the post-shock settling flow is determined by radiative and particle energy processes, which are essentially characterized by the bremsstrahlung cooling time $t_{\mbox{\small br}}$, the cyclotron cooling time $t_{\mbox{\small cy}}$, the electron-ion energy-exchange time $t_{\mbox{\small ei}}$, the electron-electron collisional time $t_{\mbox{\small ee}}$, and the ion-ion collisional time $t_{\mbox{\small ii}}$ \citep{king79,lamb79,imamura96,saxton05}." +.For weakly maejetfic svstfeius (with, For weakly magnetic systems (with +"sienal-to-noise of the spectimin of the iwuermost fliuneut is rather low. we used both the iuner and middle Glament for the SES, spectrum.","signal-to-noise of the spectrum of the innermost filament is rather low, we used both the inner and middle filament for the $_{\rm in}$ spectrum." + A fit to the innermost fibuneut solely revealed a width of the broad line similar to the width found for the combined spectrum., A fit to the innermost filament solely revealed a width of the broad line similar to the width found for the combined spectrum. +" We determuned clectrou temperatures frou, N-rav spectra. taken with the NADLNewtou/EPIC MOS instruments (Turneretal.2001)."," We determined electron temperatures from X-ray spectra, taken with the XMM-Newton/EPIC MOS instruments \citep{Turner2001}." +. We chose for the MOS iunstruinents as they have a higher spectral resolution than the NADENewtou/EPIC pu CCDs (Strideretal. 20013., We chose for the MOS instruments as they have a higher spectral resolution than the XMM-Newton/EPIC pn CCDs \citep{Struder}. +". The observations for the E. SE;, aud SE; spectruni were taken on August 13 (ObsId 0501510501. Th ks). the NE on July 28 (ObsId 0501810101. 117 kx). the N and NW on August 25 2007 (ObsId 0501810301. TL ks ) and for the SW. spectruii on August 23 2007 (ObsId 0501510101. 73 ks)."," The observations for the E, $_{\rm in}$ and $_{\rm out}$ spectrum were taken on August 13 (ObsId 0504810201, 75 ks), the NE on July 28 (ObsId 0504810101, 117 ks), the N and NW on August 25 2007 (ObsId 0504810301, 74 ks ) and for the SW spectrum on August 23 2007 (ObsId 0504810401, 73 ks)." + The spectra (shown in Fie. ), The spectra (shown in Fig. ) +) were extracted at locations close to the regious for which we have Πα spectra. as indicated in Fig.3," were extracted at locations close to the regions for which we have $\alpha$ spectra, as indicated in Fig.," +.. using the NMM SAS data reduction software. version 1.52.8.," using the XMM SAS data reduction software, version 1.52.8." + Uufortunatelv. the position angle of he NAIAL telescope was choseji Such that only the EPIC* MOS?2 instriuncut observed the region of interest for tlie NE. NW aud SW thus.," Unfortunately, the position angle of the XMM telescope was chosen such that only the EPIC MOS2 instrument observed the region of interest for the NE, NW and SW rims." + For he other spectra. we used thi the MOS1 aud ΑΠΟΣΣ instiruuents.," For the other spectra, we used both the MOS1 and MOS2 instruments." + We fitted the extracted spectra with a equilibrium ionization (NED) model UsaastradJausen 1993).. combined with an absorption model. using the SPEX spectral fitting software version 10.0.0 (IXaastraetal. 1996).. using the maxima likelihood statistic for Poisson distributions (Costatistic.Cash1979).," We fitted the extracted spectra with a non-equilibrium ionization (NEI) model \citep{Kaastra1993}, combined with an absorption model, using the SPEX spectral fitting software version 10.0.0 \citep{spex}, using the maximum likelihood statistic for Poisson distributions \cite[C-statistic,][]{Cash1979}." +. This statistic is more appropriate than the classical anethod. for fitting spectra which coutain bins with few counts (AWWheatouetal.1995)., This statistic is more appropriate than the classical $\chi^2$ -method for fitting spectra which contain bins with few counts \citep{Wheaton}. +. For more counts. this statistic asvinptotically approaches the \?-statistic.," For more counts, this statistic asymptotically approaches the $\chi^2$ -statistic." + For most of the spectra. this method was relatively straightforward.," For most of the spectra, this method was relatively straightforward." + Some regious needed. some special, Some regions needed some special +svuchrotron electrons can interact with the CAIB photons to give inverse Compton (100) X-ray radiation (Perola Reinhardt 1972: Rephaeli 1979).,synchrotron electrons can interact with the CMB photons to give inverse Compton (IC) X-ray radiation (Perola Reinhardt 1972; Rephaeli 1979). + Several attempts to detect hare tails in the spectrum of a few clusters of galaxies were performed wilh various experiments (Dazzano 1934.90: Rephaeli. Gruber Rothschild 1987: Rephaeli Gruber 1988: Rephaeli. Ulmer Gruber 1994) that reported only upper limits to the flux.," Several attempts to detect hard tails in the spectrum of a few clusters of galaxies were performed with various experiments (Bazzano 1984,90; Rephaeli, Gruber Rothschild 1987; Rephaeli Gruber 1988; Rephaeli, Ulmer Gruber 1994) that reported only upper limits to the flux." + A significant breakthrough in the measurement of INR emission was obtained thanks to (he improved sensitivity ancl wide spectral capabilities of the and Rossi X-Ray. Timing Explorer )) satellities., A significant breakthrough in the measurement of HXR emission was obtained thanks to the improved sensitivity and wide spectral capabilities of the and Rossi X-Ray Timing Explorer ) satellities. + As pointed out by Petrosian (2003). the discovery. of INR radiation has led to a remarkable increase of the theoretical investigations regarding (hie possible acceleration mechanisms and origin of the relativistic electrons responsible for the emission. although the presence of phenomena in (he intracluster medium (ICM) of some clusters was established decades ago (Willson 1970).," As pointed out by Petrosian (2003), the discovery of HXR radiation has led to a remarkable increase of the theoretical investigations regarding the possible acceleration mechanisms and origin of the relativistic electrons responsible for the emission, although the presence of phenomena in the intracluster medium (ICM) of some clusters was established decades ago (Willson 1970)." + Nonthermal INR radiation was detected in excess of the thermal emission in the Coma cluster by a first. observation (Fusco-Femiano 1999) using the Phoswich Detection System (PDS) and confirmed by a second independent observation with a time interval of about 3 vr (Fusco-Femiano 2004: therealter FFO4)., Nonthermal HXR radiation was detected in excess of the thermal emission in the Coma cluster by a first observation (Fusco-Femiano 1999) using the Phoswich Detection System (PDS) and confirmed by a second independent observation with a time interval of about 3 yr (Fusco-Femiano 2004; thereafter FF04). + The presence of a second component in the X-ray spectrum of the cluster has been MM also by (wo observations (Rephaeli. Gruber Blanco 1999: Rephaeli Gruber 2002).," The presence of a second component in the X-ray spectrum of the cluster has been reported also by two observations (Rephaeli, Gruber Blanco 1999; Rephaeli Gruber 2002)." +n A2256 is (he second cluster where a excess has been measured by (yo observations (Fusco-Femiano 2000: Fuseo-Femiano 2005) and by (Rephaeli Gruberκ...2003)., A2256 is the second cluster where a excess has been measured by two observations (Fusco-Femiano 2000; Fusco-Femiano 2005) and by (Rephaeli Gruber 2003). + At à lower confidence level. with respect to Coma and A2256. IINR has been detected by in A754 (Fusco-Femiano 200," At a lower confidence level, with respect to Coma and A2256, HXR radiation has been detected by in A754 (Fusco-Femiano 2003)." +" An upper limit to the flux has been reportedin À3667 no-Feniano al.s2001). A119 (Fusco-Femiano usa£,2003) and 42163 (Feretti af2001)."," An upper limit to the flux has been reported in A3667 (Fusco-Femiano 2001), A119 (Fusco-Femiano 2003) and A2163 (Feretti 2001)." + For the last cluster a observation shows instead the presence of a IIXR. excess (Rephaeli. Gruber. Arieli 2006).," For the last cluster a observation shows instead the presence of a HXR excess (Rephaeli, Gruber, Arieli 2006)." + veporis also some evidence of emission by the Bullet Cluster (Petrosian. Madejski. Lali 2006).," reports also some evidence of emission by the Bullet Cluster (Petrosian, Madejski, Luli 2006)." + The PDS spectra of all the observations were extracted using the NAS version 2.1 package (Chiappelli Dal Fiume 1997) specifically created to handle the PDS peculiarities., The PDS spectra of all the observations were extracted using the XAS version 2.1 package (Chiappetti Dal Fiume 1997) specifically created to handle the PDS peculiarities. +" Llowever, a PDS data analvsis performed with a different software package"," However, a PDS data analysis performed with a different software package" +Tarc 6420 Wk: we also applied the same parallax quality cut used. above in our vsini analysis.,$_{\rm eff} >$ 6420 K; we also applied the same parallax quality cut used above in our vsini analysis. + These cuts resulted in samples of 63 SWI's ancl 364 non-SWPs., These cuts resulted in samples of 63 SWPs and 364 non-SWPs. + We calculated weighted differences in log μι using these two samples and corrected. for bias using the same method. used to produce ligure 1., We calculated weighted differences in $\log$ $^{\rm \prime}_{\rm HK}$ using these two samples and corrected for bias using the same method used to produce Figure 1. + We show the results in Figure 4., We show the results in Figure 4. + The dillerences between the SWPs ancl non-S\WDPs are readilv apparent in Figure da., The differences between the SWPs and non-SWPs are readily apparent in Figure 4a. + Llowever. we should be cautious in how we interpret this result.," However, we should be cautious in how we interpret this result." + The SWP log μις values range from -5.117 to -4.610. while it ranges from -5.206 to -3.879 for the non-SWDPs.," The SWP $\log$ $^{\rm \prime}_{\rm HK}$ values range from -5.117 to -4.610, while it ranges from -5.206 to -3.879 for the non-SWPs." + The apparent. negative differences in log It; for the majority of SWPs. then. could be due. in part. to the excess number of active stars in the non-SWP sample.," The apparent negative differences in $\log$ $^{\rm \prime}_{\rm HK}$ for the majority of SWPs, then, could be due, in part, to the excess number of active stars in the non-SWP sample." + In order to determine if this dillerence in the two samples can fully account for the pattern in Figure Ja. we have produced. a second. non-SWDP sample using a conservative upper cutoll of -4.60 for log Ray. resulting in a sample size of 307 stars.," In order to determine if this difference in the two samples can fully account for the pattern in Figure 4a, we have produced a second non-SWP sample using a conservative upper cutoff of -4.60 for $\log$ $^{\rm \prime}_{\rm HK}$, resulting in a sample size of 307 stars." + We repeated the above analysis using the same SWDP sample as for Figure ta and the new. more conservative non-SWDP sample: the results are shown in Figure th.," We repeated the above analysis using the same SWP sample as for Figure 4a and the new, more conservative non-SWP sample; the results are shown in Figure 4b." + There are. far fewer SWDPs with negative mean differences in log Rig in Figure 4b compared to Figure da., There are far fewer SWPs with negative mean differences in $\log$ $^{\rm \prime}_{\rm HK}$ in Figure 4b compared to Figure 4a. + Llowever. a trend. is still evident.," However, a trend is still evident." + A linear least-squares fit to the data yields a slope of (1.33£0.58).10DN te the mean weighted dillerence is zero at Fr=5925 Ix. The Pearson correlation coelficient for the data in Figure 4b is 0.283., A linear least-squares fit to the data yields a slope of $(1.33 \pm 0.58) \times 10^{\rm -4}$ $^{\rm -1}$; the mean weighted difference is zero at $_{\rm eff} = 5925 $ K. The Pearson correlation coefficient for the data in Figure 4b is 0.283. +" ""his translates into aS probability that the trend is due to chance alone.", This translates into a 5 probability that the trend is due to chance alone. + The truth should. lie somewhere between Figures da and 4b., The truth should lie somewhere between Figures 4a and 4b. + While the more conservative cut in log Ray values emploved. in preparing Figure 4th excludes stars that are much more active than any SWPs in our sample. it probably also excludes some stars whose log Ry values would. not prevent. Doppler detection. of planets.," While the more conservative cut in $\log$ $^{\rm \prime}_{\rm HK}$ values employed in preparing Figure 4b excludes stars that are much more active than any SWPs in our sample, it probably also excludes some stars whose $\log$ $^{\rm \prime}_{\rm HK}$ values would not prevent Doppler detection of planets." + For instance. HD 22049 has a log Ruy value near -4.5. 0.1 unit larger than our cutolf.," For instance, HD 22049 has a $\log$ $^{\rm \prime}_{\rm HK}$ value near -4.5, 0.1 unit larger than our cutoff." + We don't know why our conclusions are different [rom those of CantoMartinsetal.(2011).. but we do note some differences with their study.," We don't know why our conclusions are different from those of \citet{cm11}, but we do note some differences with their study." + First. our samples are very different: we emplov a much larger sample of non-SWDs.," First, our samples are very different; we employ a much larger sample of non-SWPs." + Second. our method of analysis compares SWDPs to non-SWPs with similar physical parameters. including age.," Second, our method of analysis compares SWPs to non-SWPs with similar physical parameters, including age." + The log Iggy index is known to be sensitive to age., The $\log$ $^{\rm \prime}_{\rm HK}$ index is known to be sensitive to age. + Perhaps the difference we uncovered. between οΑς ancl non-S\WDPs is too subtle to detect with other statistical approaches., Perhaps the difference we uncovered between SWPs and non-SWPs is too subtle to detect with other statistical approaches. + Using an updated. version of the method. of analysis described in (Gonzalez2008:Gonzalezetal.2010a.b).. we have verified that there are significant. dillerences in. vsini. abundancee-Ic. trends. ancl chromospheric activity between SWPs and non-SWPs.," Using an updated version of the method of analysis described in \citep{gg08, gg10a, gg10b}, we have verified that there are significant differences in vsini, $_{\rm C}$ trends, and chromospheric activity between SWPs and non-SWPs." + We emploved high-quality data from the literature. taking into account new planets that have been discovered since the data were originally. published.," We employed high-quality data from the literature, taking into account new planets that have been discovered since the data were originally published." + We have verified that SWIs have significantly smaller values of vsini. abundance-Fc slope. and Igi compared to otherwise similar non-SWPs.," We have verified that SWPs have significantly smaller values of vsini, $_{\rm C}$ slope, and $^{\rm \prime}_{\rm HK}$ compared to otherwise similar non-SWPs." + For the case of the Teo slope dilferences. we also verified that they are significant when comparing stars with ML] > 0.10. but not for more metal-poor stars.," For the case of the $_{\rm C}$ slope differences, we also verified that they are significant when comparing stars with [M/H] $>$ 0.10, but not for more metal-poor stars." + It is also notable that all three parameters display the largest dillerences between the SWPP ancl SWP samples for Er less than about 5900 Ix. We thank the anonymous reviewer for helpful suggestions., It is also notable that all three parameters display the largest differences between the SWP and non-SWP samples for $_{\rm eff}$ less than about 5900 K. We thank the anonymous reviewer for helpful suggestions. +We find that the morphology. spectral index. radio luminosity. and radio-to-X ray luminosity ratio of the AI-A5 complex are consistent with that of an LLAGN. and rules out the possibility that it consists of a chain of young RSNe and SNRs in a young SSC.,"We find that the morphology, spectral index, radio luminosity, and radio-to-X ray luminosity ratio of the A1-A5 complex are consistent with that of an LLAGN, and rules out the possibility that it consists of a chain of young RSNe and SNRs in a young SSC." + We therefore conclude that Al is the long-sought AGN in Arp 299-A. Since Arp 299-A had long been thought of as a pure starburst. our finding of a buried. low- AGN in its central region. coexisting with a recent burst of starformation. suggests that both a starburst and AGN are frequently associated phenomena in mergers.," We therefore conclude that A1 is the long-sought AGN in Arp 299-A. Since Arp 299-A had long been thought of as a pure starburst, our finding of a buried, low-luminosity AGN in its central region, coexisting with a recent burst of starformation, suggests that both a starburst and AGN are frequently associated phenomena in mergers." + In this case. our result is likely to have an impact on evolutionary scenarios proposed for AGN and the triggering mechanism of activity in general.," In this case, our result is likely to have an impact on evolutionary scenarios proposed for AGN and the triggering mechanism of activity in general." + Finally. we also note that component AQ. previously identified as a young RSN. is not seen at our low-frequency observations. which implies there is a foreground absorbing H I region.," Finally, we also note that component A0, previously identified as a young RSN, is not seen at our low-frequency observations, which implies there is a foreground absorbing H II region." + It is remarkable that this RSN exploded at the mere distance (projected) of two parsecs from the putative AGN in Arp 299-A. which makes this supernova one of the closest to a central supermassive black hole ever detected.," It is remarkable that this RSN exploded at the mere distance (projected) of two parsecs from the putative AGN in Arp 299-A, which makes this supernova one of the closest to a central supermassive black hole ever detected." + This result may also be relevant to accreting models in the central regions of galaxies. since it is not easy to explain the existence of very massive. supernova progenitor stars so close to an AGN.," This result may also be relevant to accreting models in the central regions of galaxies, since it is not easy to explain the existence of very massive, supernova progenitor stars so close to an AGN." + While seemingly contradictory. this could explain the low-luminosity of the AGN we see in Arp 299-A. In fact. since massive stars shed large amounts of mechanical energy into their surrounding medium. thereby significantly increasing its temperature. those massive stars would hinder the accretior of material to the central black hole. which could in turn result in a less powerful AGN than usual.," While seemingly contradictory, this could explain the low-luminosity of the AGN we see in Arp 299-A. In fact, since massive stars shed large amounts of mechanical energy into their surrounding medium, thereby significantly increasing its temperature, those massive stars would hinder the accretion of material to the central black hole, which could in turn result in a less powerful AGN than usual." +theje. radial wavelengthlength iis eventuallyn(uallv lost near the griderid scale.le. and due to aliasing Uthe codel picks up the evolution of the shwave again as a leading shwave.,"the radial wavelength is eventually lost near the grid scale, and due to aliasing the code picks up the evolution of the shwave again as a leading shwave." +" Repeating this test at higher resolutions indicates that successive swings from leadiug to trailing occur al an interval of To—N,/n,. where n,= 21s the azimuthal wavenumber of the shwave."," Repeating this test at higher resolutions indicates that successive swings from leading to trailing occur at an interval of $\tau = N_x/n_y$, where $n_y = 2$ is the azimuthal wavenumber of the shwave." + This is equivalent to ht)=2z/.Nr.," This is equivalent to $k_x(t) = +2\pi/\Delta x$." + The decay of the successive linear solutions with time is due to numerical diffusion., The decay of the successive linear solutions with time is due to numerical diffusion. + Figure 7 suggests (hat il is easier (o inject power into the simulation due to aliasing rather (han (o remove power due to numerical diffusion., Figure \ref{pap3f7} suggests that it is easier to inject power into the simulation due to aliasing rather than to remove power due to numerical diffusion. + We do not believe. however. (hat aliasing is affecting our high-resolution results.," We do not believe, however, that aliasing is affecting our high-resolution results." +" In addition. if we assume that the flow in our simulations can be modeled as two-dimensional Kolmogorov turbulence. then δν7AE,oE where 0r, is the rms velocity variation across a scale A."," In addition, if we assume that the flow in our simulations can be modeled as two-dimensional Kolmogorov turbulence, then $\delta v_{rms} \sim \lambda^ {1/3}$, where $\delta v_{rms}$ is the rms velocity variation across a scale $\lambda$." +" The velocity due to the mean shear ab these scales is O0sheap~qQA. and 9e,/OUshear~A77."," The velocity due to the mean shear at these scales is $\delta v_{shear} \sim q \Omega \lambda$, and $\delta v_{rms}/\delta v_{shear} \sim \lambda^{-2/3}$." + The velocities at the smallest scales are (hus dominated by turbulence rather than by the mean shear., The velocities at the smallest scales are thus dominated by turbulence rather than by the mean shear. + This conclusion is supported by the convergence of our numerical results at high resolution., This conclusion is supported by the convergence of our numerical results at high resolution. + Our model contains (wo additional numerical parameters: the size L and the initial turbulence amplitude o., Our model contains two additional numerical parameters: the size $L$ and the initial turbulence amplitude $\sigma$. + Figure 8 shows the evolution ol a lor several values of σ., Figure \ref{pap3f8} shows the evolution of $\alpha$ for several values of $\sigma$. + Eviclently for small enough values of o the a amplitude is reduced. but lor near-sonic initial Mach numbers (he a amplitude saturates (or at least the dependence on σ is greatly. weakened).," Evidently for small enough values of $\sigma$ the $\alpha$ amplitude is reduced, but for near-sonic initial Mach numbers the $\alpha$ amplitude saturates (or at least the dependence on $\sigma$ is greatly weakened)." + Figure 9 shows the evolution for several values of L but the same initial o and the identical initial power spectrum., Figure \ref{pap3f9} shows the evolution for several values of $L$ but the same initial $\sigma$ and the identical initial power spectrum. + For large enough L (he shear stress appears to be independent of L., For large enough $L$ the shear stress appears to be independent of $L$. + Finally. we have studied (he autocorrelation lunction of the potential vorticitv as a means ol characterizing structure inside the flow.," Finally, we have studied the autocorrelation function of the potential vorticity as a means of characterizing structure inside the flow." + Figure 10. shows the autocorrelation [function measured in the fiducial model and in an otherwise identical model with £L=3//., Figure \ref{pap3f10} shows the autocorrelation function measured in the fiducial model and in an otherwise identical model with $L = 8H$. + Eviclently the potential vorticitv is correlated over about one-half a scale height in radius. independent of the size of the model.," Evidently the potential vorticity is correlated over about one-half a scale height in radius, independent of the size of the model." + This supports the idea that compressive effects limit the size of the vortices. since the shear flow becomes supersonic across a vortex ol size ~Lf Colgate.Wencdroff.&Liska2001 ).," This supports the idea that compressive effects limit the size of the vortices, since the shear flow becomes supersonic across a vortex of size $\sim H$ \citep{bs95,li01}." +. The presence of long-lived vortices in weaklv-ionized disks may be an integral part of the angular momentum (iransport mechanism in these svstems., The presence of long-lived vortices in weakly-ionized disks may be an integral part of the angular momentum transport mechanism in these systems. + The kev result we have shown here is (hat compressibility of the flow is an extremely important factor in providing a significant. positivelv-correlated average shear stress will its associated outward transport of angular momentum.," The key result we have shown here is that compressibility of the flow is an extremely important factor in providing a significant, positively-correlated average shear stress with its associated outward transport of angular momentum." + Previous results using a local model have assumed incompressible flow, Previous results using a local model have assumed incompressible flow +"where T.E and D staud for temperature. E polarization aud £2 polarization. respectively. and the amplitudes τι are given by: The new independent] ceutered wait Gaussians 52...finY—T.E.B. ave independent] from the ]previous set HD. The pseudo-C,.","where $ T , E $ and $ B $ stand for temperature, $E$ polarization and $B$ polarization, respectively, and the amplitudes $ a_{\ell m} $ are given by: The new independent centered unit Gaussians $ h_{\ell m}^{Y} \; , \; +Y \equiv T, \; E, \; B $, are independent from the previous set $ g_{\ell m}^{X} \; , \; +X\equiv +,-,B $ ." + (that is Cr). can now be written as where with X.X'—T.E.B.," The $C_\ell$, (that is $\overline{C}_\ell$ ), can now be written as where with $ X, \; X' \equiv T, \; E, \; B $." + This second approach allows to use the same sky aud different noises. which is needed when cumulative chaunels are considered to reduce noise effects;," This second approach allows to use the same sky and different noises, which is needed when cumulative channels are considered to reduce noise effects." + For iustance. a cumulative channel formed by the LFI at 70 GIIz aud the two ΠΕΙ channels at 100 GITIz aud 113 GIIEz is obtained bv simply suunuiung the X?'s of Eq. (15))," For instance, a cumulative channel formed by the LFI at 70 GHz and the two HFI channels at 100 GHz and 143 GHz is obtained by simply summing the $\chi^2$ 's of Eq. \ref{chi2}) )" + relative to these three channels., relative to these three channels. + The above setup is based on the asstuption that the noise contribution of svstematic errors is preciscly assessed., The above setup is based on the assumption that the noise contribution of systematic errors is precisely assessed. + If this would uot be the case. bias effects would bo induced.," If this would not be the case, bias effects would be induced." + This can be simulated im the likelihood (7s of Eq. (191) , This can be simulated in the likelihood $\chi^2$ 's of Eq. \ref{chi2}) ) +"by using differcut uoises in the €, and in the covariance built with the test iultipoles €DO.", by using different noises in the $\overline{C}_\ell^{XX'}$ and in the covariance built with the test multipoles $C_\ell^{XX'}$. + That is. one should male (Μα) variations frou ND to sonie NIMM in Eq. (16))," That is, one should make (small) variations from $N_\ell^{XX}$ to some ${N'}_\ell^{XX}$ in Eq. \ref{Candx}) )" + while keeping them fixed in Eq. (191) (, while keeping them fixed in Eq. \ref{Amps}) ) ( +or viceversa) and study their iupact on the parameter determination of the test cosmological model.,or viceversa) and study their impact on the parameter determination of the test cosmological model. + lu our Monte Carlo Markov Chains (MCMC) simulations we take as fiducial model the ACDM r model. that is the standard ACDAL model augmented by the tensortoscalar ratio ras described in the introduction.," In our Monte Carlo Markov Chains (MCMC) simulations we take as fiducial model the $\Lambda$ $r$ model, that is the standard $\Lambda$ CDM model augmented by the tensor–to–scalar ratio $ r $ as described in the introduction." + We consider ΑΠΟΝΤΟ simmiations with both the ACDAIr aud the AC DAT model., We consider MCMC simulations with both the $\Lambda$ $r$ and the $\Lambda$ $r$ T model. + We deuote by ACDAIrT. the ACDM model iu which we impose the doublewell inflaton poteutial given in Eq. (1)).," We denote by $\Lambda$ $r$ T, the $\Lambda$ $r$ model in which we impose the double–well inflaton potential given in Eq. \ref{binon}) )," + as described iu the introduction aud iu Sect. 2.., as described in the introduction and in Sect. \ref{LGtheory}. + We consider two sets of best fit fiducial values for our parameters. as listed in Table 2.. where also the values of few other derived. paraucters are shown for illustrative purposes.," We consider two sets of best fit fiducial values for our parameters, as listed in Table \ref{tab2}, where also the values of few other derived parameters are shown for illustrative purposes." + Since r=0 in the first set. the model is just the AC DAL model.," Since $ r=0 $ in the first set, the model is just the $\Lambda$ CDM model." +" Iu the secoud set the values ο=0.0127 aud vy,=0.9611 ave chosen to lav on the theoretical curve kr—ris) dictated by the doublewell inflaton poteutial aud they correspond to the best fit value y=1.26 for the coupling (Destrictal.2008a) within the Ginshbure-Landau effective theory approach (see Eq. (1)))."," In the second set the values $ r = 0.0427 $ and $ n_s = +0.9614 $ are chosen to lay on the theoretical curve $ r=r(n_s) $ dictated by the double–well inflaton potential and they correspond to the best fit value $ y=1.26 $ for the coupling \citep{mcmc1} + within the Ginsburg-Landau effective theory approach (see Eq. \ref{binon}) ))." +" We then provide estimates of the errors in the measurements of the cosmological paramcters in the following wav: We consider two choices for the €, likelihood. one without the 2 modes aud one with the B modes aud take into account the white noise seusitivitv ofPlanck (LEI aud IIEI) in the 70. 100 and 113 CIIz channels."," We then provide estimates of the errors in the measurements of the cosmological parameters in the following way: We consider two choices for the $C_\ell-$ likelihood, one without the $ B $ modes and one with the $ B $ modes and take into account the white noise sensitivity of (LFI and HFI) in the 70, 100 and 143 GHz channels." + We also cousider a σπαΏνο chaunel whose \? is the sun of the 47s of the three chanucls above., We also consider a cumulative channel whose $ \chi^2 $ is the sum of the $ \chi^2 $ 's of the three channels above. + When using different channels iu he AICAIC analysis. we use different noise realizations while keeping the same sky. that is the same realization of the Gaussian process that generated the primordial fluctuations.," When using different channels in the MCMC analysis, we use different noise realizations while keeping the same sky, that is the same realization of the Gaussian process that generated the primordial fluctuations." + Tu our MCMC analysis we always take standard flat priors for the cosmological parameters., In our MCMC analysis we always take standard flat priors for the cosmological parameters. + In particular we assuue he flat priors 0<0.2 in the ACDM»r model aud 02.0, and galaxies of total mass M~108Mo need to form at zr=7.7."," For example, for a reionization epoch $z_s\sim 11$ and $z_r\sim 7$ and a homogeneous primordial magnetic field $B_0=1\nG$, our results indicate that galaxies of total mass $M\sim5 \times10^8\msun$ need to form at redshifts $z_F\gtrsim 2.0 $, and galaxies of total mass $M\sim 10^8\msun$ need to form at $z_F\gtrsim 7.7 $." + L.F.S.R. thanks the Brazilian agency CNPq for financial support (142394/2006-8)., L.F.S.R. thanks the Brazilian agency CNPq for financial support (142394/2006-8). + R.S.S. thanks the Brazilian agency FAPESP for financial support (2009/06770-2)., R.S.S. thanks the Brazilian agency FAPESP for financial support (2009/06770-2). + R.O.thanks FAPESP (06/56213-9) and the Brazilianagency CNPq (300414/82-0) for partial support., R.O.thanks FAPESP (06/56213-9) and the Brazilianagency CNPq (300414/82-0) for partial support. + We thank Joshua Frieman and Wayne Hu for helpful comments., We thank Joshua Frieman and Wayne Hu for helpful comments. + This research has made use ofNASA's Astrophysics Data System., This research has made use ofNASA's Astrophysics Data System. +presence of multiple spectral components.,presence of multiple spectral components. + The hotspot in the N plume shows a flat spectrum with àz0.5. consistent with a model in which it is produced by particle acceleration at the shock at the end of the N Jet: its spectrum has only steepened slightly by 15 GHz.," The hotspot in the N plume shows a flat spectrum with $\alpha \approx 0.5$, consistent with a model in which it is produced by particle acceleration at the shock at the end of the N jet; its spectrum has only steepened slightly by 15 GHz." + The immediately striking result of these measurements is the steep spectral index between 8 and 15 GHz in the southern plume., The immediately striking result of these measurements is the steep spectral index between 8 and 15 GHz in the southern plume. + We can be sure that this is not an artefact of poor sampling: the S plume lacks compact structure. and simulations show that we would not expect any flux on the scales of the observed emission to be missing from the 15-GHz maps.," We can be sure that this is not an artefact of poor sampling; the S plume lacks compact structure, and simulations show that we would not expect any flux on the scales of the observed emission to be missing from the 15-GHz maps." + It appears that there is a genuine break in the spectrum between 8 and 15 GHz in the southern plume which ts not present in the northern plume., It appears that there is a genuine break in the spectrum between 8 and 15 GHz in the southern plume which is not present in the northern plume. + As shown in refspix.. this effect is not limited to a single region in the plume. but is visible throughout.," As shown in \\ref{spix}, this effect is not limited to a single region in the plume, but is visible throughout." + The steep-spectrum ‘sheaths’ around the plumes. particularly the southern. plume. which were visible in the 8-GHz data presented in Paper 1. are missing in the 15-GHz images. although again simulated images show that the 15-GHz observations have sampling which should be adequate to reproduce them.," The steep-spectrum `sheaths' around the plumes, particularly the southern plume, which were visible in the 8-GHz data presented in Paper I, are missing in the 15-GHz images, although again simulated images show that the 15-GHz observations have sampling which should be adequate to reproduce them." + This implies that the sheath regions have very steep spectra between 8.4 and 15 GHz., This implies that the sheath regions have very steep spectra between 8.4 and 15 GHz. +" Using regions defined with on the 1.4—8.4-GHz spectral index map. in which the sheath region is well defined. I find that o27,2 for the sheaths around both north and south plumes. whereas N.15ovd."," Using regions defined with on the 1.4–8.4-GHz spectral index map, in which the sheath region is well defined, I find that $\alpha^{15}_{8.4} \ga 2$ for the sheaths around both north and south plumes, whereas $\alpha^{8.4}_{1.4} \sim 1$." +" It has recently been suggested (e.g. Katz-Stone Rudnick 1997)) that the jets in some FRI radio galaxies have a two-component structure. consisting of a flat-spectrum ""core jet and steep-spectrum surrounding “sheath”."," It has recently been suggested (e.g. Katz-Stone Rudnick \cite{kr}) ) that the jets in some FRI radio galaxies have a two-component structure, consisting of a flat-spectrum `core jet' and steep-spectrum surrounding `sheath'." + Katz-Stone et ((1999)) show that the same picture may apply to two WAT sources from the sample of O'Donoghue et ((1990))., Katz-Stone et \cite{krbo}) ) show that the same picture may apply to two WAT sources from the sample of O'Donoghue et \cite{o2e}) ). + The observed spectral steepening with distance from the core in FRI sources might therefore be unrelated to spectral ageing and expansion. as is frequently assumed: it might simply be a consequence of the increasing dominance of the sheath component.," The observed spectral steepening with distance from the core in FRI sources might therefore be unrelated to spectral ageing and expansion, as is frequently assumed; it might simply be a consequence of the increasing dominance of the sheath component." + To test whether such a picture is viable in130.. T constructed a spectral tomography gallery as discussed by Katz-Stone Rudnick: this involves generating a set of maps by subtracting a scaled version of the high-frequency map from the low-frequency map. so that for each pixel of the tomography map (41) we have where o; ts varied.," To test whether such a picture is viable in, I constructed a spectral tomography gallery as discussed by Katz-Stone Rudnick; this involves generating a set of maps by subtracting a scaled version of the high-frequency map from the low-frequency map, so that for each pixel of the tomography map $I_t$ ) we have where $\alpha_t$ is varied." + Features of a given spectral index vanish on the tomography map corresponding to that spectral index: if the apparent steepening in is due to varying blends of a flat- and steep-spectrum component. and the steep-spectrum component is relatively smooth. the plumes should appear more uniform in a tomography map with a spectral index corresponding to that of the flat-spectrum component. as the flat-spectrum component should then have vanished. leaving only a (scaled) version of the steep-spectrum component.," Features of a given spectral index vanish on the tomography map corresponding to that spectral index; if the apparent steepening in is due to varying blends of a flat- and steep-spectrum component, and the steep-spectrum component is relatively smooth, the plumes should appear more uniform in a tomography map with a spectral index corresponding to that of the flat-spectrum component, as the flat-spectrum component should then have vanished, leaving only a (scaled) version of the steep-spectrum component." + If there is no single. uniform flat-spectrum component. the plumes will still show structure for any value of o.," If there is no single, uniform flat-spectrum component, the plumes will still show structure for any value of $\alpha_t$." + The full gallery of tomography images ts not shown. but reftomol shows a representative example. made with the L and X-band maps taking ay=0.55.," The full gallery of tomography images is not shown, but \\ref{tomo1} shows a representative example, made with the L and X-band maps taking $\alpha_t = 0.55$." + It will be seen that the jets and N hotspot are oversubtracted. giving rise to negative flux densities on the tomography map — this 1s as expected. since their spectral index 1s about 0.5 (Paper 1).," It will be seen that the jets and N hotspot are oversubtracted, giving rise to negative flux densities on the tomography map – this is as expected, since their spectral index is about 0.5 (Paper I)." + In the N plume. there is still considerable structure in this image. but the S plume has a much more uniform surface brightness after subtracting the flat-spectrum component. suggesting that a two-component model of the source is close to being adequate here.," In the N plume, there is still considerable structure in this image, but the S plume has a much more uniform surface brightness after subtracting the flat-spectrum component, suggesting that a two-component model of the source is close to being adequate here." + This ts further illustrated in reftomo2.. which shows the results of spectral tomography on slices across the S plume: these show that. at least within 1.5 aremin of the core. the plume can be modelled as a superposition of a flat-spectrum component with a~0.55 and a broader steep-spectrum component with a~1.2. with the flat-spectrum component becoming progressively fainter with distance along the plume: this is consistent with the results of Katz-Stone et ((1999)).," This is further illustrated in \\ref{tomo2}, which shows the results of spectral tomography on slices across the S plume; these show that, at least within 1.5 arcmin of the core, the plume can be modelled as a superposition of a flat-spectrum component with $\alpha \sim 0.55$ and a broader steep-spectrum component with $\alpha +\sim 1.2$ , with the flat-spectrum component becoming progressively fainter with distance along the plume; this is consistent with the results of Katz-Stone et \cite{krbo}) )." + The spectrum of the flat-spectrum component. as estimated from the spectral index at which it disappears on tomography slices. appears to have steepened by 105 aresee from the core: this is true even after a rough correction is applied for the effects of the undersampling of the X-band data on large spatial scales (as assessed in section 3.1)).," The spectrum of the flat-spectrum component, as estimated from the spectral index at which it disappears on tomography slices, appears to have steepened by 105 arcsec from the core; this is true even after a rough correction is applied for the effects of the undersampling of the X-band data on large spatial scales (as assessed in section \ref{unders}) )." + The situation is certainly more complicated in the N plume. where there is 1n any case less evidence for a steep-spectrum sheath in the spectral index maps of Paper I: if a two-component model is to be viable there. it must allow for some spatial variation in the spectrum of the flat-spectrum component.," The situation is certainly more complicated in the N plume, where there is in any case less evidence for a steep-spectrum sheath in the spectral index maps of Paper I; if a two-component model is to be viable there, it must allow for some spatial variation in the spectrum of the flat-spectrum component." + But this would not be surprising. since there is much stronger evidence for ongoing particle acceleration in the N plume.," But this would not be surprising, since there is much stronger evidence for ongoing particle acceleration in the N plume." + I return to this point below., I return to this point below. + If there are two spectral components. what is the origin of the steep-spectrum material?," If there are two spectral components, what is the origin of the steep-spectrum material?" + Katz-Stone Rudnick identify several possibilities for the sheath in 4449., Katz-Stone Rudnick identify several possibilities for the sheath in 449. + There may be à two-component jet. with the steep-spectrum material only becoming visible at a flare point; or the steep-spectrum material may have evolved from the flatter-spectrum component through ageing. adiabatic expansion. diffusion into a region of lower magnetic field or a combination of these.," There may be a two-component jet, with the steep-spectrum material only becoming visible at a flare point; or the steep-spectrum material may have evolved from the flatter-spectrum component through ageing, adiabatic expansion, diffusion into a region of lower magnetic field or a combination of these." + Without additional low-frequency observations it is impossible to say whether the injection spectral indices of the two components are the same. so we cannot rule out a two-component plume in130..," Without additional low-frequency observations it is impossible to say whether the injection spectral indices of the two components are the same, so we cannot rule out a two-component plume in." + But it is certainly also possible that the sheath has evolved from the flatter-spectrum component., But it is certainly also possible that the sheath has evolved from the flatter-spectrum component. + Modelling of thesynchrotron spectrum does not allow me to rule out any of the, Modelling of thesynchrotron spectrum does not allow me to rule out any of the +PDS above (at ΤΟΝΟ).,PDS above (at ). + TEs were computed using the tecluiques described in Nowak et al. (, TLs were computed using the techniques described in Nowak et al. ( +1999a) between the 7-lO keV. lard aud 2-7 keV soft photons.,1999a) between the 7-40 keV hard and 2-7 keV soft photons. + Figure 1l shows the CCD of the four sources., Figure 1 shows the CCD of the four sources. + Fig., Fig. + 2 shows the correspouding PDS (top) aud TL spectra (bottom)., 2 shows the corresponding PDS (top) and TL spectra (bottom). + TLs were detected ouly from aud1UILTO5-LL. aud in their lowest/hardest intensity states (uamely their “islaud™ state).," TLs were detected only from and, and in their lowest/hardest intensity states (namely their “island” state)." + This is the first report of TLs from1U1728-21., This is the first report of TLs from. +. No TLs were detected iu their high states. with upper limits of 0.1-0.01 seconds between 1 aud 10 Iz: ie. a factor of 10 lareer than the values detected during their low states.," No TLs were detected in their high states, with upper limits of 0.1-0.01 seconds between 1 and 10 Hz; i.e. a factor of 10 larger than the values detected during their low states." + No TLs were detected from the two steady low state sources. aud the upper limits we derived are lower than the observed values for audIU1705-EL. indicating that the non detection of simular TLs is not due to a lack of scusitivity.," No TLs were detected from the two steady low state sources, and the upper limits we derived are lower than the observed values for and, indicating that the non detection of similar TLs is not due to a lack of sensitivity." + Looking at Fig., Looking at Fig. + 1 and 2. a few points can be drawn.," 1 and 2, a few points can be drawn." + First. TLs are uot associated with a sineular spectral state: and 1E1721-30152 occupy the same reeion of the CCD. aud ouly the former shows TLs.," First, TLs are not associated with a singular spectral state; and 2 occupy the same region of the CCD, and only the former shows TLs." + Second. although the overall shape of their PDS is broadly simular. there is one noticeable difference that slows up very clearly in the vy represcutation of the PDSs: that TLs are associated with a timing state in which the whole PDS is shifted towards high frequencies Ud are a factor of LO lavecr for and than for 1E1721-30152 aud GS1826-238)).," Second, although the overall shape of their PDS is broadly similar, there is one noticeable difference that shows up very clearly in the $\nu F \nu$ representation of the PDSs; that TLs are associated with a timing state in which the whole PDS is shifted towards high frequencies and are a factor of 10 larger for and than for 2 and )." + Third. when aud are high. TLs are sigmificautly detected at frequencies between and up to or slightly abovevopo.," Third, when and are high, TLs are significantly detected at frequencies between and up to or slightly above." + Fourth. although of lower significance than the effect. observed in the two BUs Cre N-1 aud €N2339-1 (Nowak ct al.," Fourth, although of lower significance than the effect observed in the two BHs Cyg X-1 and GX339-4 (Nowak et al." + 1999a.b). there is an indication that the TL decreases with frequency. especially for£U1728-31.," 1999a,b), there is an indication that the TL decreases with frequency, especially for." +. Finally. TEs do not depeud," Finally, TLs do not depend" +objects are located in the CC area belouging to early-type iiain-sequeuce (around OG-D2 V) aud carly-type giauts stars. hence they are expected to be part of the 6601 population and do uot suffer noticeable reddeniug: (b) the number of objects that le to the right of the reddenimg line for a O6-Os V star. they constitute the IR-excess objects and are the main interest for this study.,"objects are located in the CC area belonging to early-type main-sequence (around O6-B2 V) and early-type giants stars, hence they are expected to be part of the 604 population and do not suffer noticeable reddening; (b) the number of objects that lie to the right of the reddening line for a O6-O8 V star, they constitute the IR-excess objects and are the main interest for this study." + It is clear that the IB-exeess objects cover a larger area in the CC diagram of the NGC GO1 ceutral region than for the field region. aud the feld shows almost no objects redder than ~0.5: (ο) the location of the rec ejaut stars in the observed CC diagram. grouped around CJ-HY- 1.0 and IN)50.25. chanees due to the reddening introduced by 6601.," It is clear that the IR-excess objects cover a larger area in the CC diagram of the NGC 604 central region than for the field region, and the field shows almost no objects redder than $\sim$ 0.5; (c) the location of the red giant stars in the observed CC diagram, grouped around $\sim$ 1.0 and $\sim$ 0.25, changes due to the reddening introduced by 604." + This reflects in a relative over-deusity of reddened RCs when looking through 6601 and a relative absence of their uureddenued counterparts. seen as negative counts in the circled region marked iu the bottom IR excess iu MYSOs arise from heated dust and eas located in the very voung objects surroundings. being a cmeunstelar plenomena," This reflects in a relative over-density of reddened RGs when looking through 604 and a relative absence of their unreddened counterparts, seen as negative counts in the circled region marked in the bottom IR excess in MYSOs arise from heated dust and gas located in the very young objects' surroundings, being a circumstellar phenomena" +Carries away some momentum.,carries away some momentum. + Thus even in the case when there is no kick velocity a binary achieves an additional velocity (Blaauw.1960).., Thus even in the case when there is no kick velocity a binary achieves an additional velocity \cite{1960BAN....15..265B}. + Second. if the supernova explosion is asvmmetrie both the newly formed. compact. object maw receive a kick velocity which allects the orbit of the binary after the explosion as well as its center of mass velocity.," Second, if the supernova explosion is asymmetric both the newly formed compact object may receive a kick velocity which affects the orbit of the binary after the explosion as well as its center of mass velocity." + The [ate of a binary system in a supernova explosion depends on the value and. cirection of the kick velocity. on the orbital phase at which the explosion occurs. and on the parameters of the binary: the masses and orbital parameters e. and e.," The fate of a binary system in a supernova explosion depends on the value and direction of the kick velocity, on the orbital phase at which the explosion occurs, and on the parameters of the binary: the masses and orbital parameters $a$ , and $e$." + We present the population of compact object. binaries in the plane spanned by the center of mass velocity ofter the second supernova expolsion and time to merge in Figure IL.., We present the population of compact object binaries in the plane spanned by the center of mass velocity ofter the second supernova expolsion and time to merge in Figure \ref{vt}. + The orbital (Blaauw.1960). elfects are isolated and shown in the top left panel of Figure 1.. where we present the results of the simulation with a=O.," The orbital \cite{1960BAN....15..265B} effects are isolated and shown in the top left panel of Figure \ref{vt}, where we present the results of the simulation with $\sigma_v=0$." + There is a tail of long lived systems with Lifetimes much longer than the Llubble time and small velocities. stretching outside of the »undaries of the plot to the Lifetinies even of 107 vears.," There is a tail of long lived systems with lifetimes much longer than the Hubble time and small velocities, stretching outside of the boundaries of the plot to the lifetimes even of $10^{20}\,$ years." + These systems originally had large orbital separations. anc july interacted in the course of their binary lifetime.," These systems originally had large orbital separations, and hardly interacted in the course of their binary lifetime." + La he case when there are no kicks the center of mass velocity of the comapet object binary depends on the amount of mass lost in the supernova explosion., In the case when there are no kicks the center of mass velocity of the comapct object binary depends on the amount of mass lost in the supernova explosion. + In the extreme case of arge mass loss. the center of mass velocity approaches the orbital velocity at the moment of supernova explosion. anc it can never exceed it.," In the extreme case of large mass loss, the center of mass velocity approaches the orbital velocity at the moment of supernova explosion, and it can never exceed it." + The velocity of the system increases with increasing massloss. however the svstems that loose," The velocity of the system increases with increasing massloss, however the systems that loose" +and GALLEN? radiocheniücal experiments go to the lowest eucrgv aud heuce ueasure all of both fluxes. while the Hoiestake! radiochemical experimeut ueasures all of the SB spectrum but oulv part of the “Be flus. aud the Iuuiokaude! and Super-Kamiokande? scattering experiments measure only D fux.,"and \cite{ref:9} + radiochemical experiments go to the lowest energy and hence measure all of both fluxes, while the \cite{ref:10} radiochemical experiment measures all of the $^8$ B spectrum but only part of the $^7$ Be flux, and the \cite{ref:11} and \cite{ref:12} scattering experiments measure only $^8$ B flux." + Results vom all three actually intersect at a negative value of the * Be flux. vet “B is xodueed from ‘Be|p>SB5.," Results from all three actually intersect at a negative value of the $^7$ Be flux, yet $^8$ B is produced from $\rm^7Be+p\to\/^8B+\gamma$." + This problem cannot be avoided by one of the experiments being wroug., This problem cannot be avoided by one of the experiments being wrong. + Solar models which drastically change solar xoperties do not solve the problem. aud these models are severely coustrained w every accurate liclioscisimology 1ieasuremoeuts.," Solar models which drastically change solar properties do not solve the problem, and these models are severely constrained by very accurate helioseismology measurements." + A good solution to the solar 14. deficit is provided by oscillation into 1. ve. or vy. a sterile neutrino.," A good solution to the solar $\nu_e$ deficit is provided by oscillation into $\nu_\mu$, $\nu_\tau$, or $\nu_s$ , a sterile neutrino." + While this can be a ναι oscillation. requiring a lnass-squared difference Am?~1019 eV? and laree nüxiug between 7 and the other neutrino. more favored is a matter-cnhanced MSW! type of ⋅⋅ ∪↴∖↴↸⊳↕," While this can be a vacuum oscillation, requiring a mass-squared difference $\Delta +m^2\sim10^{-10}$ $^2$ and large mixing between $\nu_e$ and the other neutrino, more favored is a matter-enhanced \cite{ref:13} type of oscillation." +"∐⋜↧⊓∪∐∙⊟≻↥⋅⋜∏∕∕∣∪↥⋅↗∕⊤∐∐⋜↧↕↴∖↴↑⋜↧↑↸∖∙∆∣⊔↙−∣⇁∿↓∩⊽↾↸∖∖−⋜⋯≺↧∐∐⊼↕∐∶↴∙∷∖↴↸∖↕↑∐↸∖↥⋅ ⋅ 9 ↽↣⇁⋅≻ ⋅⋅ ⋅ sin∙⋅≽20,;~6⋅«↽10.7H or ~0.6⋅ are possible.⋅ whileH only the former. isH allowed for. ve."," For a $\nu_\mu$ or $\nu_\tau$ final state, $\Delta +m^2_{ei}\sim10^{-5}$ $^2$ and mixings either $\sin^22\theta_{ei}\sim6\times10^{-3}$ or $\sim0.6$ are possible, while only the former is allowed for $\nu_s$." +" The main change as a result of the new Super-Izanuiokaudoe data is that the lack of a day-night effect has reduced the parameter space for the larec-anele solution for the v,, or iz final state!! Pious produced iu the atmosphere would decay via πo>polyetMy| Mes 3ο that one would expect NM;|yy)=ING,mr). with a sinall correction for A decays."," The main change as a result of the new Super-Kamiokande data is that the lack of a day-night effect has reduced the parameter space for the large-angle solution for the $\nu_\mu$ or $\nu_\tau$ final \cite{ref:14} + Pions produced in the atmosphere would decay via $\pi\to\mu+\nu_\mu,\/\mu\to +e+\nu_\mu+\nu_e$ , so that one would expect $N(\nu_\mu+\bar\nu_\mu)=2N(\nu_e+\bar\nu_e)$, with a small correction for $K$ decays." + The (MydMadi(e|ve) ratio would be observed iu uudergronud experimeuts as p/e*. aud the result is far from the expected value.," The $(\nu_\mu+\bar\nu_\mu)/(\nu_e+\bar\nu_e)$ ratio would be observed in underground experiments as $\mu^\pm/e^\pm$, and the result is far from the expected value." + Because the caleulated pt and ο individual fluxes are kuown to whereas much of the uncertainty drops out in the ratio. the experiments utilize R=(μοιμοιµο.," Because the calculated $\mu^\pm$ and $e^\pm$ individual fluxes are known to $\sim15$ , whereas much of the uncertainty drops out in the ratio, the experiments utilize $R=(\mu/e)_{\rm Data}/(\mu/e)_{\rm Calc}$." +" While if once appeared that there was a discrepaney between water Choreukov detectors aud tracking calorimeters. the Soudan IE result#°| aereeC» with those from IMB"" Kanüokandel?and Super-Namiokaude!? While the statistical evidence for R being less than unitv is now quite colmpclling. it is the angular distributions of the ji aud © events which provide the primary evidencethat this deviation of AR from unity is explained bx neutrino oscillations."," While it once appeared that there was a discrepancy between water Cherenkov detectors and tracking \cite{ref:15} the Soudan II \cite{ref:16} agree with those from \cite{ref:17} + \cite{ref:18} and \cite{ref:19} + While the statistical evidence for $R$ being less than unity is now quite compelling, it is the angular distributions of the $\mu$ and $e$ events which provide the primary evidencethat this deviation of $R$ from unity is explained by neutrino oscillations." + This uon-flat distribution with angle of R was first observed in the higl-energy (>1.3 GeV) event sample frou Iuniokandoe. but has now beenconfirmed with better statistics in the similar data sample from Super-," This non-flat distribution with angle of $R$ was first observed in the high-energy $>1.3$ GeV) event sample from Kamiokande, but has now beenconfirmed with better statistics in the similar data sample from Super-Kamiokande." +" The data fit an oscillation hypothesis. usine Am?z2410.7 0V?, siu20~ 1. and is far from a non-oscillation. flat distribution."," The data fit an oscillation hypothesis, using $\Delta m^2\approx2\times10^{-3}$ $^2$ , $\sin^22\theta\approx1$ , and is far from a non-oscillation, flat distribution." + The low-cucrey Gz1.3 GeV) sample also agrees with the same oscillation parameters. but this," The low-energy $<1.3$ GeV) sample also agrees with the same oscillation parameters, but this" +The frames were combined with IRAF and processed with DAOPIIOT (Stetson1937).,The frames were combined with IRAF and processed with DAOPHOT \citep{st87}. +. A sample of the field is shown in Figure 2. allowing an impression of the level of crowcling.," A sample of the field is shown in Figure 2, allowing an impression of the level of crowding." + Point spread [functions were borrowed from the extragalactic distance scale Nev Project (IXennicutt.Mould.&Freedman.1995) and fitted to the images with ALLSTAR.," Point spread functions were borrowed from the extragalactic distance scale Key Project \citep{k95} + and fitted to the images with ALLSTAR." + The data underwent a second evele with stars found in the residual image., The data underwent a second cycle with stars found in the residual image. + The ALLSTAR files were then combined with DAOMASTER., The ALLSTAR files were then combined with DAOMASTER. + The number of stars detected on the four chips was 364T. 10.0230. 10.158 and 11.352. where chip 1 is the planetary camera.," The number of stars detected on the four chips was 3647, 10,030, 10,158 and 11,852, where chip 1 is the planetary camera." + Nine bright stars were used to determine aperture corrections to an accuracy of 0.01 mag., Nine bright stars were used to determine aperture corrections to an accuracy of 0.01 mag. + The calibration of Dolphin(2000) was emploved to (ranslorm (he color magnitude diagram (CMDJ) to the VI svstem., The calibration of \cite{do00} was employed to transform the color magnitude diagram (CMD) to the VI system. + There are spatial density. gradients across the WEPC? field in the point sources detected of20%., There are spatial density gradients across the WFPC2 field in the point sources detected of. +. Both the PC and WF chips are used., Both the PC and WF chips are used. + The stellar density increases in the field in the direction towards the center of the galaxy., The stellar density increases in the field in the direction towards the center of the galaxy. + The CAID is shown in Figure 3., The CMD is shown in Figure 3. + Stars have been exeluded if their color uncertainties exceed 0.5 mag., Stars have been excluded if their color uncertainties exceed 0.5 mag. + The CAID shows the lip of the red giant branch (TRGB) of NGC 4594., The CMD shows the tip of the red giant branch (TRGB) of NGC 4594. +" The TRGB is at I1 = 26.2 + 0.2 mag. corresponding to (in—M), = 30.15 + 0.2 mag (see (2008)))."," The TRGB is at I = 26.2 $\pm$ 0.2 mag, corresponding to $(m-M)_0$ = 30.15 $\pm$ 0.2 mag (see \cite{ms08}) )." + The population is an old one., The population is an old one. + NGC 4594 is al a distance of 29.95 + 0.18 mag according (o surface brightness [uctuation measurements by Tonrvetal. (2001).., NGC 4594 is at a distance of 29.95 $\pm$ 0.18 mag according to surface brightness fluctuation measurements by \cite{to01}. . + This is the distance we adopt., This is the distance we adopt. + The reddenineg is = 0.071 from Schlegeletal., The reddening is E(V-I) = 0.071 from \cite{sch}. +(1993).. From the distribution of giant branch colors a magnitude or so fainter (han M; = 4.0. it is (hus possible to measure the MDE. following Tlarvisetal.(2007).. who provide template giant branches for this purpose.," From the distribution of giant branch colors a magnitude or so fainter than $_I$ = –4.0, it is thus possible to measure the MDF, following \cite{hh07}, who provide template giant branches for this purpose." + The MDF is obtained by interpolation directly. in color-magnitude space and is shown in Figure 4., The MDF is obtained by interpolation directly in color-magnitude space and is shown in Figure 4. + The isochrone age was 12 Gyrs and the isochrone spacing was 0.15 dex in |Fe/1I]., The isochrone age was 12 Gyrs and the isochrone spacing was 0.15 dex in [Fe/H]. + Light hundred artificial stus with V1 = 1.75 mae and 26 < I < 28 were added to the FGOGW and FSIJW frames. ancl the measurement process was repeated.," Eight hundred artificial stars with V–I = 1.75 mag and 26 $<$ I $<$ 28 were added to the F606W and F814W frames, and the measurement process was repeated." + The average color error was 0.42 mag with little dependence on magnitude., The average color error was 0.42 mag with little dependence on magnitude. + The average I magnitude error was 0.44 mag., The average I magnitude error was 0.44 mag. + The color bias due to blending was measured αἱ 0.02 + 0.03. which is negligible.," The color bias due to blending was measured at –0.02 $\pm$ 0.03, which is negligible." + The process was repeated for V.I = 3. and the color error rose to 0.54 mag.," The process was repeated for V–I = 3, and the color error rose to 0.54 mag." + Since (he sensitivity of color to metallicity increases in (he red. (his increase is not an issue lor the MDF.," Since the sensitivity of color to metallicity increases in the red, this increase is not an issue for the MDF." + Incompleteness affects the MDE at the metal rich end., Incompleteness affects the MDF at the metal rich end. + However. this effect is modest: a [actor of (wo incompleteness in the solar metallicitv bin in Figure 4.," However, this effect is modest: a factor of two incompleteness in the solar metallicity bin in Figure 4." + But a small hieh metallicity tail with [Fe/H] > 0 may have been erased by incompleteness., But a small high metallicity tail with [Fe/H] $>$ 0 may have been erased by incompleteness. + Figure 5 results from photometry of a further 2400 artificial stars and shows completeness as a function ofI magnitude., Figure 5 results from photometry of a further 2400 artificial stars and shows completeness as a functionof I magnitude. +"where [is the bulk Lorentz factor of the jet. M, the mass ofthe ejecta. σ is a numerical [actor of orderunity. and Da, is the Lorentz [actor of randomly accelerated particles at the shock front.","where $\Gamma$ is the bulk Lorentz factor of the jet, $M_0$ the mass ofthe ejecta, $\sigma$ is a numerical factor of order, and $\Gamma_{\rm sh}$ is the Lorentz factor of randomly accelerated particles at the shock front." +". :The entrained. mass. mi. 15. given. by ima,=O72mpnz3j9. where © is. the jet. half opening5 angle.5 n the Sgas densitv. mjp is the mass of a proton. and £2 the distance traveled by the jet."," The entrained mass, $m_{\rm sw}$, is given by $m_{\rm sw} = \Theta^2 m_{\rm p} n \pi R^3/3 $, where $\Theta$ is the jet half opening angle, $n$ the gas density, $m_{\rm + p}$ is the mass of a proton, and $R$ the distance traveled by the jet." + We evolve Equ., We evolve Eqn. + 1 in 2-hour ime steps. using the inclination of the jet axis to the observers line of sight (8) to calculate the projected separation (6) between each jet ancl the central source: 0(/)=R(/)sin0/D.," \ref{eq:energy} in 2-hour time steps, using the inclination of the jet axis to the observer's line of sight $\theta$ ) to calculate the projected separation $\delta$ ) between each jet and the central source: $\delta(t^\prime) = R(t) {\rm sin}~\theta/D$." + Here. //214B(l)eos6/e is the observers time. which Lakes into account [or each jet the time delay between IHIT43s rest [rame and the frame of the observer.," Here, $t^\prime = t \pm R(t) {\rm cos}~\theta/c$ is the observer's time, which takes into account for each jet the time delay between H1743's rest frame and the frame of the observer." + Our full model requires just five parameters: D. 09. Dy. the launch date Z5. anc E. the effectiveenerev!.. Because of the association with the X-ray flare. the prior on the launch date is Caen to be MJD 5276645 days: we adopt a flat prior on 9. D. loe(Ty). ancl log(E ).," Our full model requires just five parameters: $D$, $\theta$, $\Gamma_0$, the launch date $T_0$, and $\tilde{E}$, the effective Because of the association with the X-ray flare, the prior on the launch date is taken to be MJD $52766 \pm 5$ days; we adopt a flat prior on $\theta$ , $D$, $\Gamma_0$ ), and $\tilde{E}$ )." + Our model is fitted. via a Markov. chain Monte Carlo (MCMC) routine developed usine the Metropolis-Hastines algorithm (LlastinesL970) which has been previously applied with {his jet model in Steiner&MeClintock(2012).., Our model is fitted via a Markov chain Monte Carlo (MCMC) routine developed using the Metropolis-Hastings algorithm \citep{MH} which has been previously applied with this jet model in \citet{Steiner_j1550jets}. + The chains are evolved until thev are well converged. using e2x10? elementstotal’.," The chains are evolved until they are well converged, using $\sim2\times10^5$ elements." + From the VLA data alone. the identification of the pair of radio sources is ambiguous.," From the VLA data alone, the identification of the pair of radio sources is ambiguous." + We have applied our model by attributing to the two radio sources each allowed combination of eastern jet. western jel. and core.," We have applied our model by attributing to the two radio sources each allowed combination of eastern jet, western jet, and core." + The most probable interpretation is (hat the (vo sources correspond to emission from the core and the western jet., The most probable interpretation is that the two sources correspond to emission from the core and the western jet. + Alternative pairings are ruled out al >97%. confidence by our model., Alternative pairings are ruled out at $>97\%$ confidence by our model. + The best fit achieved by the AICAIC run is shown in Figure 1. and reaches a goodness of fil \?/y=4.9/90.54.," The best fit achieved by the MCMC run is shown in Figure \ref{fig:fit} + and reaches a goodness of fit $\rchinu = 4.9/9 = 0.54$." + Obviously. further modification to the model is notneeded?.," Obviously, further modification to the model is not." +. Distributions for the model parameters are shown in Figure 2.., Distributions for the model parameters are shown in Figure \ref{fig:mcmc}. . + Of chief importance. we find that distance ancl inclination are well constrained: D=8.540.8 kpe ancl 7ie5e DeThis distance places H1742 near the Galactic center. which is expected. given ilsprojected," Of chief importance, we find that distance and inclination are well constrained: $D=8.5 \pm 0.8$ kpc and $i=75\degr +\pm 3\degr$ .This distance places H1743 near the Galactic center, which is expected, given itsprojected" +For years after the discovery of the first Gamma-Ray Burst (GRB) afterglow (van Paradijs et al..,"For years after the discovery of the first Gamma-Ray Burst (GRB) afterglow (van Paradijs et al.," + 1997). the smoothness of the optical afterglow light-curves has been considered one of the main GRB features (Laursen Stanek 2003).," 1997), the smoothness of the optical afterglow light-curves has been considered one of the main GRB features (Laursen Stanek 2003)." + Nowadays. thanks to the rapid follow up with robotic telescopes. it is possible to reconsider this paradigm and several examples of complex optical light-curves are known.," Nowadays, thanks to the rapid follow up with robotic telescopes, it is possible to reconsider this paradigm and several examples of complex optical light-curves are known." + The Gamma-Ray burst Optical Near-infrared Detector (GROND) is a seven-band simultaneous optical-NIR imager mounted on the 2.2 m MPI/ESO telescope at La Silla observatory (Greiner et al., The Gamma-Ray burst Optical Near-infrared Detector (GROND) is a seven-band simultaneous optical-NIR imager mounted on the 2.2 m MPI/ESO telescope at La Silla observatory (Greiner et al. + 2008)., 2008). + GROND is a unique instrument to study the optical spectral evolution associated to these complex light-curves (e.g. GRB 071031] Krühhler et al.," GROND is a unique instrument to study the optical spectral evolution associated to these complex light-curves (e.g., GRB 071031 Krühhler et al." + 2009 and GRB 080129 Greiner et al., 2009 and GRB 080129 Greiner et al. + 2009)., 2009). + In this paper. we report on the multi-wavelength observation of GRB 081029.," In this paper, we report on the multi-wavelength observation of GRB 081029." + This GRB is characterised by a very complex light-curve with à strong chromatic temporal evolution., This GRB is characterised by a very complex light-curve with a strong chromatic temporal evolution. + In the optical and near-infrared bands an extremely steep rebrightening. at around 3 ks after the trigger. suddenly interrupts the smooth early-time temporal evolution.," In the optical and near-infrared bands an extremely steep rebrightening, at around 3 ks after the trigger, suddenly interrupts the smooth early-time temporal evolution." +" Thanks to GROND we were able to observe this event simultaneously form the optical se//z to the near-infrared JHK, bands.", Thanks to GROND we were able to observe this event simultaneously form the optical $g^\prime r^\prime i^\prime z^\prime$ to the near-infrared $JHK_s$ bands. + This unprecedented temporal and spectral resolution allows a time-resolved analysis of the colour evolution., This unprecedented temporal and spectral resolution allows a time-resolved analysis of the colour evolution. + The analysis of the XRT light-curve excludes the presence of a similar rebrightening in the X-ray bands. which casts doubts on the common nature of the optical and X-ray afterglow emission.," The analysis of the XRT light-curve excludes the presence of a similar rebrightening in the X-ray bands, which casts doubts on the common nature of the optical and X-ray afterglow emission." + The existence of late-time rebrightenings in some GRB optical afterglows has been known since the dawn of afterglow observations (e.g.. the optical bump of GRB 970508 (Vietri 1998. Sokolov et al.," The existence of late-time rebrightenings in some GRB optical afterglows has been known since the dawn of afterglow observations (e.g., the optical bump of GRB 970508 (Vietri 1998, Sokolov et al." + 1998. Nardini et al.," 1998, Nardini et al." + 2006)) and several models have been proposed to account for deviations from a smooth power-law evolution in the optical light-curves (see $5))., 2006)) and several models have been proposed to account for deviations from a smooth power-law evolution in the optical light-curves (see \ref{model}) ). + Some of them. in the framework of standard external-shock afterglow model. invoke a discontinuity in the external medium density profile (e.g.. Dai Wu 2003; Lazzati et al.," Some of them, in the framework of standard external-shock afterglow model, invoke a discontinuity in the external medium density profile (e.g., Dai Wu 2003; Lazzati et al." + 2002: Nakar Piran 2003) some of them considering possible variations of the micro-physical parameters into the fireball (Kong et al., 2002; Nakar Piran 2003) some of them considering possible variations of the micro-physical parameters into the fireball (Kong et al. + 2010)., 2010). + In other cases a possible energy injection into the fireball (e.g.. Jóhhannesson et al.," In other cases a possible energy injection into the fireball (e.g., Jóhhannesson et al." + 2006: Fan Piran 2006) or complex jet geometry is considered (e.g.. Racusin et al.," 2006; Fan Piran 2006) or complex jet geometry is considered (e.g., Racusin et al." + 2009)., 2009). + In the late prompt model (Ghisellini et al., In the late prompt model (Ghisellini et al. + 2007. 2009: Nardini et a. 2010). a late-time activity of the central engine produces optical and X-ray radiation that is superposed on the standard external-shock afterglow emission.," 2007, 2009; Nardini et a. 2010), a late-time activity of the central engine produces optical and X-ray radiation that is superposed on the standard external-shock afterglow emission." + In $2 we present the available broad-band data set., In \ref{obs} we present the available broad-band data set. + | ο and in refsed we describe the complex optical and X-ray light-curves and we analyse the broad-band spectal evolution., In \ref{lc} and in \\ref{sed} we describe the complex optical and X-ray light-curves and we analyse the broad-band spectal evolution. + In $5. we study the possible origin of the optical rebrighteing. discussing the observed temporal and spectral properties of the afterglow of GRB 081029 in the framework of different physical models.," In \ref{model} we study the possible origin of the optical rebrightening, discussing the observed temporal and spectral properties of the afterglow of GRB 081029 in the framework of different physical models." + On 2008 October 29 at OL43:56 UT. the Burst Alert Telescope (BAT) triggered on a long burst (trigger=332931) (Sakamoto et al.," On 2008 October 29 at 01:43:56 UT, the Burst Alert Telescope (BAT) triggered on a long burst (trigger=332931) (Sakamoto et al." +" 2008) located at coordinates RAQ2000)2 23""097""0.Dec(J2000-- -068""10/4374 (Cummings et al."," 2008) located at coordinates ${\rm RA}({\rm J}2000)= 23^{\rm h} 07^{\rm m} 06^{\rm s} , {\rm Dec(J}2000) = -68\degr 10' 43\farcs4$ (Cummings et al." + 2008)., 2008). + The BAT mask-weighted light-curve is characterised by a single smooth peak starting around ss before trigger. peaking around 60ss after the trigger. and ending around ss after trigger.," The BAT mask-weighted light-curve is characterised by a single smooth peak starting around s before trigger, peaking around s after the trigger, and ending around s after trigger." + The 15-350 keV duration is Too=270445 ss. A simple power-law model provides a good fit of the time-integrated 15-350 keV spectrum with an index c=1.4340.18 (y.= 50.7/57dof)., The 15-350 keV duration is $T_{90}=270 \pm 45~$ s. A simple power-law model provides a good fit of the time-integrated 15–350 keV spectrum with an index $\alpha=1.43\pm 0.18$ $\chi^2=50.7/57 dof$ ). + In the same BAT energy range GRB 081029 has a fluence of 2.1+0.2x107°ere em”. and a peak flux of 0.5+0.2x1079ereems! (Cummings et," In the same BAT energy range GRB 081029 has a fluence of $2.1\pm 0.2\times 10^{-6}~ {\rm erg~cm}^{-2}$ , and a peak flux of $0.5\pm 0.2\times 10^{-6}~{\rm erg~cm^{-2}s^{-1}}$ (Cummings et" +ARGO-YBJ is an air shower detector optimized to observe sanall size showers. to be constructed iu the Yauehajine Laboratory (Tibet. China) at au altitude of 1300 τι as.,"ARGO-YBJ is an air shower detector optimized to observe small size showers, to be constructed in the Yangbajing Laboratory (Tibet, China) at an altitude of 4300 m a.s.l." + The experiment consists of à ~ T1471 m? core detector realised with a single laver οRPC s (©90% of active area). surrounded by au outer detector (~30% of active area) for a total size of ~ 1004100 m2.," The experiment consists of a $\sim$ $\times$ 74 $^2$ core detector realised with a single layer of RPC's $\sim 90\%$ of active area), surrounded by an outer detector $\sim 30\%$ of active area) for a total size of $\sim$ $\times$ 100 $^2$." + A lead converter 0.5 cm thick will cover uniformly the RPC plane in order to increase the wmuber of charge particles by conversion of shower photons iu c aud to reduce the time spread of the shower frout (Baccietal..1998)., A lead converter 0.5 cm thick will cover uniformly the RPC plane in order to increase the number of charged particles by conversion of shower photons in $e^{\pm}$ and to reduce the time spread of the shower front \cite{addendum}. +". ARGO-YBJ can image with high efficiency aud sensitivity atmospheric showers initiated by primarics of enuergles in the range 10 GeV: 500 TeV. Its nain physics eoals ave (Abbresciaetal.1996): Camuna-astronomy at LOO GeV energv threshold. with a scusitivity to detect ""nideutified poiut sources of inteusitv as low as 104 of the Crab Nebula: Canuna-Rav Durst physics. extending the pAatellite measurements at energies E> 10 CoV: p/p ratio inthe TeV energy range: Sun aud heliosphere phivsics."," ARGO-YBJ can image with high efficiency and sensitivity atmospheric showers initiated by primaries of energies in the range 10 $\div$ 500 TeV. Its main physics goals are \cite{proposal}: Gamma-astronomy at $\sim$ 100 GeV energy threshold, with a sensitivity to detect unidentified point sources of intensity as low as $10\%$ of the Crab Nebula; Gamma-Ray Burst physics, extending the satellite measurements at energies E $>$ 10 GeV; $\overline{p}/p$ ratio in the TeV energy range; Sun and heliosphere physics." + The etector assembling should start i 2000 aud data taking with the fist ~750 1? of RPC’s in 2001., The detector assembling should start in 2000 and data taking with the first $\sim 750$ $m^2$ of RPC's in 2001. + A hieh cnerey GRB is detectable if the Πο. of air showers from the eauunatravs is siguificaut larecr than the fluctuations of the backeround. due to showers from cosmic rays with arrival directious compatible with the burst position.," A high energy GRB is detectable if the number of air showers from the gamma-rays is significant larger than the fluctuations of the background, due to showers from cosmic rays with arrival directions compatible with the burst position." + A good augular resolution is of major nmuportauce du order to reduce the background and increase the detection seusitivitv., A good angular resolution is of major importance in order to reduce the background and increase the detection sensitivity. + The angular resolution and the effective arca of ARGO-YDJ to detect eiuirays as a function of the energv have Όσοι obtained by caus of simulations., The angular resolution and the effective area of ARGO-YBJ to detect gamma-rays as a function of the energy have been obtained by means of simulations. + For gauuna-ravs with energy as low as E — 10-20 GeV. the opening angle around the source direction iu which 70% of the signal showers are coutained ds 5," For gamma-rays with energy as low as E $\sim$ 10-20 GeV, the opening angle around the source direction in which $\%$ of the signal showers are contained is $\sim$ $^{\circ}$." + To evaluate the seusitivitv of ARGO-YDJ to detect GRBs. we considered a burst with a power law energy spectrum δαox»EU extending iu. the range 1 GeV οBinge. a duration Af=l s. aud a zenith anele ()—20.," To evaluate the sensitivity of ARGO-YBJ to detect GRBs, we considered a burst with a power law energy spectrum $dN/dE \propto E^{-\alpha}$ extending in the range 1 GeV $\div E_{max}$, a duration $\Delta t$ =1 s, and a zenith angle $\theta$ $^{\circ}$." +" The nust will eive a signal with a siguificance lavecr than standard deviations if the euergv fluence in the range 1 GeV iBaya, Is larger than a minium value E,,;,.", The burst will give a signal with a significance larger than 4 standard deviations if the energy fluence in the range 1 GeV $\div E_{max}$ is larger than a minimum value $_{min}$. +" Fig.l shows E,,;, as a function of E, for 3 spectral slopes.", Fig.1 shows $_{min}$ as a function of $E_{max}$ for 3 spectral slopes. +" For a generic duration At he màiniuu fluences detectable are given by Fri,At.", For a generic duration $\Delta t$ the minimum fluences detectable are given by $F_{min} \sqrt{\Delta t}$. +" Tn the energv ranee considered the sensitivity. is strongly dependent on the imaxiuuu οποιον of the spectimm £,,,4;.", In the energy range considered the sensitivity is strongly dependent on the maximum energy of the spectrum $E_{max}$. +" ARGO-YDJ can observe CRBs with enerev fluences of a few ' erg ou.if the energv spectrum extends at least up to ~ 200 CoV with a slope a <2: the müuinuuu detectable flueuce is ~ D if ES(4,~ BO GeV. This is of particular nuportanco. ποσο if CRB SOTDον are located at cosmological clistances, the lieh energv tail of the spectrum is affected by the Moyely interaction of Gammmarayvs with low euergv starlight photons in the iutergalactie space."," ARGO-YBJ can observe GRBs with energy fluences of a few $^{-6}$ erg $^{-2}$ if the energy spectrum extends at least up to $\sim$ 200 GeV with a slope $\alpha \leq$ 2; the minimum detectable fluence is $\sim$ $^{-5}$ if $E_{max}~\sim$ 30 GeV. This is of particular importance, since if GRB sources are located at cosmological distances, the high energy tail of the spectrum is affected by the $\gamma \gamma \rightarrow e^+ e^-$ interaction of gamma-rays with low energy starlight photons in the intergalactic space." + According to SalomonaudStecker(908).. at a distance corresponding to a redshift 2=0.1 the absorption is almost neclieible. while at 220.5 (1.0) the absorption becomes inportaut for photons of energy E > 100 (50) GeV. These values give au idea of the possible maxima euergv of the CRBs spectra as a function of their distance. aud from Fie.l one can infer the maxinuun sensitivity of ARGO-YDJ to detect cosinological GRBs.," According to \cite{abso}, at a distance corresponding to a redshift $z$ =0.1 the absorption is almost negligible, while at $z$ =0.5 (1.0) the absorption becomes important for photons of energy E $>$ 100 (50) GeV. These values give an idea of the possible maximum energy of the GRBs spectra as a function of their distance, and from Fig.1 one can infer the maximum sensitivity of ARGO-YBJ to detect cosmological GRBs." + The minimum observable ffiueuces cau )o compared with the fluences measured by EGRET in the MeV-1 GeV cnerey range: F—10/7:10 tere ? (Catellietal.1997).," The minimum observable fluences can be compared with the fluences measured by EGRET in the 1 MeV-1 GeV energy range: $F \sim +10^{-5} \div 10^{-4}$ erg $^{-2}$ \cite{egret}." +. Siuce EGRET spectral slopes à are uostlv ~ 2. one could expect fluences of the sue order of inaenitude at energies above 1 GeV. From Fie.l oue can conclude that ARGO-YDJ could detect GRBs with he same intensity of those observed by ECRET provided hat the euergey spectrum extends up to few tens of GeVs: he sensitivity increases by a factor 10 ," Since EGRET spectral slopes $\alpha$ are mostly $\sim$ 2, one could expect fluences of the same order of magnitude at energies above 1 GeV. From Fig.1 one can conclude that ARGO-YBJ could detect GRBs with the same intensity of those observed by EGRET provided that the energy spectrum extends up to few tens of GeVs; the sensitivity increases by a factor $\sim$ " +model. although within the observational upper limit.,"model, although within the observational upper limit." + This difference is due to the fact that oncarelli et al. (, This difference is due to the fact that Roncarelli et al. ( +2006). adopted: an observationally oriented. approach by excluding from (heir maps the extended sources detected by Chandra observations.,2006) adopted an observationally oriented approach by excluding from their maps the extended sources detected by Chandra observations. + This means (hat (heir estimate includes also the emission from unresolved clusters aud groups. (corresponding to our hot and dense WIIIM phases. respectively) that are instead excluded in our estimate.," This means that their estimate includes also the emission from unresolved clusters and groups (corresponding to our hot and dense WHIM phases, respectively) that are instead excluded in our estimate." + Aleasurements of the autocorrelation function for a set of NMM-Newton observations Galeazzietal.(2009) point to the fact that the A-Raa emission in (he 0.4—0.6 keV band from the WIIM is 1245% of the total extragalactie diffuse emission., Measurements of the autocorrelation function for a set of XMM-Newton observations \cite{Galeazzi09} point to the fact that the X-Ray emission in the $0.4-0.6$ keV band from the WHIM is $12\pm5\%$ of the total extragalactic diffuse emission. + Our models predict 10dc 156. 12dM. 1TdE1A. and 13dc156. in agreement with the observational data.," Our models predict $10\pm1\%$ , $12\pm1\%$, $17\pm1\%$, and $13\pm1\%$, in agreement with the observational data." + In order to understaud the dependence of flux. from metallicity and redshift of the sources. we calculated the average flux of each slice of the simulations and compared with (he results of our previous work Ursino," In order to understand the dependence of flux from metallicity and redshift of the sources, we calculated the average flux of each slice of the simulations and compared with the results of our previous work \cite{Ursino06}." +&Galeazzi(2006).. Figure G clearly shows that. while the overall photon budget is comparable between the old and new analvsis. the dependence on redshift behaves in very different wavs. being much sleeper in (he case based on Cen Ostriker (1999a) simulations.," Figure \ref{silicone-fluxredshift-whim} clearly shows that, while the overall photon budget is comparable between the old and new analysis, the dependence on redshift behaves in very different ways, being much steeper in the case based on Cen Ostriker (1999a) simulations." + Focusing on the data [rom the current. simulation. we see that the dependence from redshift changes with metallicity model.," Focusing on the data from the current simulation, we see that the dependence from redshift changes with metallicity model." + The four models show the sane trend. wilh a rather slow decrease of photon Εις at increasing redshift (compared to the older simulations). but the relative steepness is different.," The four models show the same trend, with a rather slow decrease of photon flux at increasing redshift (compared to the older simulations), but the relative steepness is different." + For the Boreani metallicity. photons coming [rom low redshift are ten times more than those coming from very hieh reclshilt. in the case of Croft metallicity the ratio of photons Irom near sources over photons [rom distant sources is around 20. and for the highest metallicity models this ratio is of the order of ~30.," For the Borgani metallicity, photons coming from low redshift are ten times more than those coming from very high redshift, in the case of Croft metallicity the ratio of photons from near sources over photons from distant sources is around 20, and for the highest metallicity models this ratio is of the order of $\sim30$." + since in our mocdels metallicity depends directly on density. (he metal abundance is higher in hieh density regions. where there is more star formation.," Since in our models metallicity depends directly on density, the metal abundance is higher in high density regions, where there is more star formation." + At low redshift. when the Universe is older. (here are more high density regions compared to the voung Universe. aud therefore there are more high metallicity regions.," At low redshift, when the Universe is older, there are more high density regions compared to the young Universe, and therefore there are more high metallicity regions." + This makes the difference between the abundance ol metals at low redshift and at high redshift bigger for those models where metallicity is stronger., This makes the difference between the abundance of metals at low redshift and at high redshift bigger for those models where metallicity is stronger. + This effect is due only to the relation between density and metallicity. ancl does nol depend on anv assumption on star formation history.," This effect is due only to the relation between density and metallicity, and does not depend on any assumption on star formation history." + We also investigated how the potential capability of a WILIIM dedicated future mission like EDGE Piroetal.(2009). or Xenia Hartmannetal.(2009)., We also investigated how the potential capability of a WHIM dedicated future mission like EDGE \cite{Piro09} or Xenia \cite{Hartmann09}. +. The (WEI) on EDGE (or Xenia - values in brackets) has a proposed field of view with diameter 1.5* (1.57). an angular resolution of 15° (107). an effective area of 580 (1000) cni? al 1 keV. and an energy resolution of 70 eV at 1: keV (70 eV at 0.5 keV).," The (WFI) on EDGE (or Xenia - values in brackets) has a proposed field of view with diameter $1.5^\circ$ $1.5^\circ$ ), an angular resolution of 15” (10”), an effective area of 580 (1000) $^2$ at 1 keV, and an energy resolution of 70 eV at 1 keV (70 eV at 0.5 keV)." + The (WES) on EDGE (Xenia) has a proposed field of view of 0.77x (1x 17). an angular resolution of 3.7 (2.5). an effective area of 1163 (1300) em? at 600 eV. and an enerev resolution of 3 (1)eV at 0.5 keV. We simulated an experiment similar to the WES.," The (WFS) on EDGE (Xenia) has a proposed field of view of $0.7^\circ\times0.7^\circ$ $1^\circ\times1^\circ$ ), an angular resolution of 3.7' (2.5'), an effective area of 1163 (1300) $^2$ at 600 eV, and an energy resolution of 3 (1)eV at 0.5 keV. We simulated an experiment similar to the WFS," +van der Hulst. 1993. Lee Irwin 1997. Wine Irwin 1997) resides in “supershells” and “worms”.,"van der Hulst 1993, Lee Irwin 1997, King Irwin 1997) resides in “supershells” and “worms”." + In. maps of the nearby spirals M31. and. M33 (Brinks Bajaja 1986. Deul den Lartog 1990). it is also found to be depleted in numerous LOO pc. 1 kpe holes”.," In maps of the nearby spirals M31 and M33 (Brinks Bajaja 1986, Deul den Hartog 1990), it is also found to be depleted in numerous 100 pc – 1 kpc “holes”." + Attempts to quantify this elaborate ISM structure are confronted. with questions of identification., Attempts to quantify this elaborate ISM structure are confronted with questions of identification. + Structures are interconnected. with. for example. denser regions of gas embedded: within filaments.," Structures are interconnected, with, for example, denser regions of gas embedded within filaments." + Llenee for example. potential sites of star formation cannot be picked out. without introducing a density threshold and thereby a bias to separate them from the underlving density Gelcl," Hence for example, potential sites of star formation cannot be picked out, without introducing a density threshold and thereby a bias to separate them from the underlying density field." + An alternative wav to analyze the ISM is with Fourier transform power spectra., An alternative way to analyze the ISM is with Fourier transform power spectra. + Applied to LIL emission maps of the Large and Small Magellanic Clouds. power laws over 2 orders of magnitude are found (Stanimirovie et al.," Applied to HI emission maps of the Large and Small Magellanic Clouds, power laws over $\sim$ 2 orders of magnitude are found (Stanimirovic et al." + 1999. Elmeereen. Ixim. Stavely-Smith 2001). providing another insight into the structure of the ISM. namely that as other observations have already suggested. it is likely to be turbulent.," 1999, Elmegreen, Kim, Stavely-Smith 2001), providing another insight into the structure of the ISM, namely that as other observations have already suggested, it is likely to be turbulent." + Clues about the energy sources for the stirring of the ISAL come from measurements of the sizes ancl velocities of shells., Clues about the energy sources for the stirring of the ISM come from measurements of the sizes and velocities of shells. + In. some cases stellar winds and supernovac are found to be adequate for creating the supershells. and LL holes.," In some cases stellar winds and supernovae are found to be adequate for creating the supershells, and HI holes." + In other cases larger quantities of energy are demanded. and then collisions of external clouds with the ealaxies are invoked CLenorio-Tagle 1981)., In other cases larger quantities of energy are demanded and then collisions of external clouds with the galaxies are invoked (Tenorio-Tagle 1981). + As for the diffuse ionized medium. although the energy. available from. O stars would be sullicient to account for its photoionization. a well-known. problem is that. photons from the O stars cannot travel far from their origin without being absorbed bv the molecular clouds and. HE halos surrounding them.," As for the diffuse ionized medium, although the energy available from O stars would be sufficient to account for its photoionization, a well-known problem is that photons from the O stars cannot travel far from their origin without being absorbed by the molecular clouds and HI halos surrounding them." + In that case the photons either reach larger distances by traveling through photoionized. conduits. carved out. by earlier supernovae or as suggested bv an alternative moclel they are additionally generated in turbulent mixing layers at the interfaces between hot. anc cold. gas., In that case the photons either reach larger distances by traveling through photoionized conduits carved out by earlier supernovae or as suggested by an alternative model they are additionally generated in turbulent mixing layers at the interfaces between hot and cold gas. + These are ubiquitous in the ISM. and have been invoked as an ellicient means to convert the thermal energy. &enerated. by shear Ilows to ionizing radiation (DBegelman Fabian 1990. Slavin. Shull Begelman 1993).," These are ubiquitous in the ISM, and have been invoked as an efficient means to convert the thermal energy generated by shear flows to ionizing radiation (Begelman Fabian 1990, Slavin, Shull, Begelman 1993)." + Ultimately the energy. source in the latter model is again the supernovae which create the hot eas., Ultimately the energy source in the latter model is again the supernovae which create the hot gas. + Reeent N-rav images from Chandra map out this hot. tenuous gas. predicted by Spitzer (1956). above and. below the ealactie plane of disk galaxies (Wang et al.," Recent X-ray images from Chandra map out this hot, tenuous gas, predicted by Spitzer (1956), above and below the galactic plane of disk galaxies (Wang et al." + 2001)., 2001). + Even without a heat source due to its long cooling time. once it is generated by supernovac. such gas can persist for millions of vears.," Even without a heat source due to its long cooling time, once it is generated by supernovae, such gas can persist for millions of years." + Cox Smith (1974) reasoned that given that OD stars occur in associations. it is likely that a supernovae will eo olf inside the hot cavity generated by a previous supernovae. hereby. rejuvenating it anc creating an even larger cavity.," Cox Smith (1974) reasoned that given that OB stars occur in associations, it is likely that a supernovae will go off inside the hot cavity generated by a previous supernovae, thereby rejuvenating it and creating an even larger cavity." + In this wav. successive supernovae can overlap creating a network of tunnels.," In this way, successive supernovae can overlap creating a network of tunnels." + Expanding at high speed. within these unnels. the hot gas can move above the galactic plane where it is either halted by insullicient speed to escape the galactic xotential. or bv an encounter with a large mass of cold. high density σας. or by ellicient mixing with cooler gas which increases its density thereby accelerating its raciiative energy OSSCS.," Expanding at high speed within these tunnels, the hot gas can move above the galactic plane where it is either halted by insufficient speed to escape the galactic potential, or by an encounter with a large mass of cold, high density gas, or by efficient mixing with cooler gas which increases its density thereby accelerating its radiative energy losses." + In light of this complex environment in which star ormation occurs. it is even more surprising that the Schmidt. law is so successful.," In light of this complex environment in which star formation occurs, it is even more surprising that the Schmidt law is so successful." + Le is in the context of his complexity. that we undertake a study of the star ormation rate in a multiphase ISM.," It is in the context of this complexity, that we undertake a study of the star formation rate in a multiphase ISM." + We restrict ourselves o a local study of the LSAL namely that of a ~ 1 κρο region.," We restrict ourselves to a local study of the ISM, namely that of a $\sim$ 1 $^3$ region." + Lhe earliest local study. which included supernovae eedback was done by Rosen Dregman (1995) in. two dimensions., The earliest local study which included supernovae feedback was done by Rosen Bregman (1995) in two dimensions. + They considered a segment of a galactic disk. aking into account a fixed external gravitational potential. rut neelecting rotational effects. self-gravitv. ancl magnetic ields.," They considered a segment of a galactic disk, taking into account a fixed external gravitational potential, but neglecting rotational effects, self-gravity, and magnetic fields." + In a three-dimensional model which included: the ellects of an external gravitational potential. rotation. and magnetic fields. IxXorpi et al. (," In a three-dimensional model which included the effects of an external gravitational potential, rotation, and magnetic fields, Korpi et al. (" +1999a.b) studied a supernova driven galactic dynamo.,"1999a,b) studied a supernova driven galactic dynamo." + Meanwhile. to investigate the clisk halo interaction. Avillez (2000) Followed the evolution of a seement of a galactic disk with an adaptive mesh refinemen code.," Meanwhile, to investigate the disk halo interaction, Avillez (2000) followed the evolution of a segment of a galactic disk with an adaptive mesh refinement code." + Unlike these stuclies. ours follows self-consistentLy zux in three dimensions both the gas and the stars. treating the alter as a svstem of collisionless particles subject to gravity.," Unlike these studies, ours follows self-consistently and in three dimensions both the gas and the stars, treating the latter as a system of collisionless particles subject to gravity." + tosen Dregman (1995) followed the stellar componen rut treated. the stars with the same Iuid. equations use or the eas thereby. making their Low more viscous than hat expected for a collisionless svstem ofparticles., Rosen Bregman (1995) followed the stellar component but treated the stars with the same fluid equations used for the gas thereby making their flow more viscous than that expected for a collisionless system of particles. + Withou star particles tageed with their ages. Rosen Breeman (1995) decided upon a supernovae rate for their simulation. hen proceeded to set olf supernovae with a probability of occurrence. correlated to the stellar density.," Without star particles tagged with their ages, Rosen Bregman (1995) decided upon a supernovae rate for their simulation, then proceeded to set off supernovae with a probability of occurrence correlated to the stellar density." + Avillez (2000) approached the issue by constructing an algorithm o distinguish between isolated anc clustered: supernovae., Avillez (2000) approached the issue by constructing an algorithm to distinguish between isolated and clustered supernovae. + For isolated. supernovae events. Avillez (2000) randomly determined the positions of supernovae in the clisk plane with rates based on observed ones.," For isolated supernovae events, Avillez (2000) randomly determined the positions of supernovae in the disk plane with rates based on observed ones." + To mimic clustered supernovae. a percentage of the supernovae sites were chosen to coincide with locations where there was a previous supernova.," To mimic clustered supernovae, a percentage of the supernovae sites were chosen to coincide with locations where there was a previous supernova." + In the Ixorpi et al. (, In the Korpi et al. ( +1999a.b) implementation there was a density criteria to determine the locations of isolated supernovae.,"1999a,b) implementation there was a density criteria to determine the locations of isolated supernovae." + In. both Avillez (2000) and. Ixorpi ο al. (, In both Avillez (2000) and Korpi et al. ( +1999a.h). supernovae occuring above the disk plane were placed in random locations with an exponentia distribution characterized by a scale height. also. adopte from observations.,"1999a,b), supernovae occuring above the disk plane were placed in random locations with an exponential distribution characterized by a scale height also adopted from observations." + Given that we are interested in the impact of supernovae feedback on star formation. we canno rely on these methods of modeling the supernovae locations.," Given that we are interested in the impact of supernovae feedback on star formation, we cannot rely on these methods of modeling the supernovae locations." + Insteack we require that the locations. ages. and masses of the star particles self-consistently determine the supernovae events.," Instead we require that the locations, ages, and masses of the star particles self-consistently determine the supernovae events." + X simple caleulation shows that a star with a velocity of 10 km/s will travel ~ LOO pe (e.g. the average size of a molecular cloud) in 1O Myr., A simple calculation shows that a star with a velocity of 10 km/s will travel $\sim$ 100 pc (e.g. the average size of a molecular cloud) in 10 Myr. + The. latter corresponds to a typical time delay between the birth and death of a star with M ~ SO M..., The latter corresponds to a typical time delay between the birth and death of a star with M $\sim$ 80 $_\odot$. + In a follow-up paper we explore how our results change when we neglect this time delay and instead allow the stars to explode as supernovae immecdiately after heir birth (Slvz. Devriendt. Dryan. Silk. preparation).," In a follow-up paper we explore how our results change when we neglect this time delay and instead allow the stars to explode as supernovae immediately after their birth (Slyz, Devriendt, Bryan, Silk, )." + Obviously a local model such as ours is of limited relevance or quantitative comparisons to the ISM in galaxies., Obviously a local model such as ours is of limited relevance for quantitative comparisons to the ISM in galaxies. + As ater detailed in section 6.. the limitations of our idealized x»indary conditions and the absence in our models of an external gravitational potential as well as of a shear low arising [rom rotation means that there are many 'undamental questions that we cannot address.," As later detailed in section \ref{discussion}, the limitations of our idealized boundary conditions and the absence in our models of an external gravitational potential as well as of a shear flow arising from rotation means that there are many fundamental questions that we cannot address." + Nevertheless we believe that for the purposes of studying the non-linear interplay between star formation and stellar feedback. our simple model vields important insights.," Nevertheless we believe that for the purposes of studying the non-linear interplay between star formation and stellar feedback, our simple model yields important insights." + The question we address is what. physical processes regulate the rate at which eas turns into stars in a, The question we address is what physical processes regulate the rate at which gas turns into stars in a +ab 2=3 with respect to the local one.,at $z=3$ with respect to the local one. + Moreover. we note that recent observations of GRB host galaxies at high-z (νήρο et al.," Moreover, we note that recent observations of GRB host galaxies at $z$ (Fynbo et al." + 2003) support the idea that GRBs might form. preferentially in low-metallicity environments., 2003) support the idea that GRBs might form preferentially in low-metallicity environments. + We have seen that the detection. of Cl1tDs at high redshift is a rare event., We have seen that the detection of GRBs at high redshift is a rare event. + Moreover. spectroscopic study. of these bursts requires a very rapid repointing of large erouncdbased. telescope.," Moreover, spectroscopic study of these bursts requires a very rapid re���pointing of large ground–based telescope." + Therefore. an cllicient procedure is needed in order to pickup in real time z GRBs.," Therefore, an efficient procedure is needed in order to pick–up in real time $z$ GRBs." + We propose to use the probability here computed to selec reliable zz5 candidates together with some promptlyavailable information provided. byοι. such as. burs duration. the lack of detection in the UVOT V. band. anc the low Galactic extinction.," We propose to use the probability here computed to select reliable $z\ge 5$ candidates together with some promptly--available information provided by, such as burst duration, the lack of detection in the UVOT $V$ band, and the low Galactic extinction." + We test the proposed procedure against the data obtained by in the last vear., We test the proposed procedure against the data obtained by in the last year. + Phree bursts match all our requirements. two being confirme ab ozzmD (Le. success rate = 66%)).," Three bursts match all our requirements, two being confirmed at $z\gsim 5$ (i.e. success rate $\gsim 66$ )." + Relaxing slightly our selection criteria. we identify other three cancidates.," Relaxing slightly our selection criteria, we identify other three candidates." + Therefore. the final sample consists in six bursts (success rate zo 33%)) with no lowredshift interloper identified up to now. showing that the proposed. procedure is quite ellicient. in selecting good z25 candidates.," Therefore, the final sample consists in six bursts (success rate $\gsim 33$ ) with no low–redshift interloper identified up to now, showing that the proposed procedure is quite efficient in selecting good $z\ge 5$ candidates." + We want to stress here that all quantities needed. for the selection. are available within a [ew hours from burst trigger. allowing a rapid pointing of S-m class telescope Lor spectroscopic followup studies.," We want to stress here that all quantities needed for the selection are available within a few hours from burst trigger, allowing a rapid pointing of 8-m class telescope for spectroscopic follow–up studies." + The propose procedure may be also used to identified. reliable targets for dedicated searches of CARB host galaxv at very high redshift., The propose procedure may be also used to identified reliable targets for dedicated searches of GRB host galaxy at very high redshift. + The detection of large number of very z bursts can be a fundamental tool to investigate the Universe up to the reionization era., The detection of large number of very $z$ bursts can be a fundamental tool to investigate the Universe up to the reionization era. +collisional cross sections and rate coefficients. using cilferent methods.,"collisional cross sections and rate coefficients, using different methods." + Fable Al shows a comparison of the resulting values ofσου at 74=10° 1. At temperatures higher than ~600 Ix. we have adopted the set of rovibrational H-LE» rate coefficients computed by. Mandy Martin (1993).," Table A1 shows a comparison of the resulting values of$\gamma_{20}$ at $\tg=10^3$ K. At temperatures higher than $\sim 600$ K, we have adopted the set of rovibrational $_2$ rate coefficients computed by Mandy Martin (1993)." + Phe corresponding cooling function has been determined. by Martin et al. (, The corresponding cooling function has been determined by Martin et al. ( +1996).,1996). + At lower temperatures. we have adopted the collisional coellicients recently computed by Forrey et al. (," At lower temperatures, we have adopted the collisional coefficients recently computed by Forrey et al. (" +"1997) that match those of Mandy Martin (1993) at 7=Lo? Ix. We have fitted the tabulated results by expressions like asl where 5,5 isin en +t. and the coellicients e; are listed in Fable A2.","1997) that match those of Mandy Martin (1993) at $T=10^3$ K. We have fitted the tabulated results by expressions like = ^3, where $\gamma_{J,J'}$ is in $^3$ $^{-1}$, and the coefficients $a_i$ are listed in Table A2." + Dillerent. choices (like. e. ο. Flower 1997a.b) are of course possible. and. produce cillerences of a factor ~2 in the cooling function.," Different choices (like, e. g. Flower 1997a,b) are of course possible, and produce differences of a factor $\sim 2$ in the cooling function." +" Lt is convenient to express the IH» cooling function jg, (in ere em? +) in the form given by Hollenbach Alclxee (1979). where Xa,(LEE) is the EFI cooling function. given. by Hollenbach Melxee (1979). 07 is the eritical density defined as niHi— and. ΑΗ)Q0] is the low-densitv limit of the cooling function. independent of the 4 density."," It is convenient to express the $_2$ cooling function $\Lambda_{{\rm +H}_2}$ (in erg $^3$ $^{-1}$ ) in the form given by Hollenbach McKee (1979), ] =, where $\Lambda_{{\rm H}_2}({\rm LTE})$ is the LTE cooling function given by Hollenbach McKee (1979), $n^{\rm cr}$ is the critical density defined as = and $\Lambda[n({\rm H})\rightarrow 0]$ is the low-density limit of the cooling function, independent of the H density." + The alter can be computed from the collisional ancl radiative deexcitation coellieients described above. and the result is well approximated by the expression over the range 10Ix 4 \kpc$ ). +"articles;é4 squares ⋅ en with⋅ strongerAAR SHAPBIHae distribution ,(decre⋅"," When particles move outwards (inwards) through the disk, they experience a weaker (stronger) gravitational potential, thus increasing (decreasing)." +" aaresmall, lessthan300pcevenwhenweconsiderthequartilerangeanthre"," However, changes in are small, less than $300$ pc even when we consider the quartile range at the extremes of." +rti end οκ uan a changesinth aandadramaticincreaseintheintercme quartilerangeatallAr.," The perturbed disks, by contrast, show larger changes in the median and a dramatic increase in the inter-quartile range at all." +".K' O8showthattheperturbed400pcdiskdevelopsatwor, solarannulustending componentverticalstructureinquantitativea greementwiththeobserwedi han σας askstrugtured.1-2kpc ΙΕΚ.", K08 show that the perturbed $400$ pc disk develops a two-component vertical structure in quantitative agreement with the observed thin/thick disk structure of the MW. +" SCPbroad AREFAr ncdiskiner easesit: at the solar annulus), but it can still be described by a single component model."," The perturbed $200$ pc disk increases its scale height (to $\approx 500 +\pc$ at the solar annulus), but it can still be described by a single component model." + This vertical heating by satellite perturbations is evident in Figure 9.., This vertical heating by satellite perturbations is evident in Figure \ref{fig:dr_dzmax}. +" Particles that have large positive hhave the largest increase inZmax,, which is plausibly a consequence of moving outwards to regions of lower disk surface density and thus weaker vertical restoring force."," Particles that have large positive have the largest increase in, which is plausibly a consequence of moving outwards to regions of lower disk surface density and thus weaker vertical restoring force." +" For i0, thetrendofmedianAzmax wwithAr tisapproximately flat, suggestionacancellationbetweentheef fectsofandiINGEA4%at Γι at smaller r and direct satellite-induced heating of those particles with the largest excursions."," For $<0$, the trend of median with is approximately flat, suggestion a cancellation between the effects of increased $\Sigma(r)$ at smaller $r$ and direct satellite-induced heating of those particles with the largest excursions." +" Figure 9 implies that stars with high metallicity for their age and present location should have preferentially largerZmax,, though the scatter is larger than the trend."," Figure \ref{fig:dr_dzmax} implies that stars with high metallicity for their age and present location should have preferentially larger, though the scatter is larger than the trend." +" The solar neighborhood is easier to study than other regions of the Galaxy, since high-precision spectroscopy is easier for brighter stars and parallax and proper motion measurements are more accurate at smaller distances."," The solar neighborhood is easier to study than other regions of the Galaxy, since high-precision spectroscopy is easier for brighter stars and parallax and proper motion measurements are more accurate at smaller distances." +" Some of the most detailed chemo-dynamic surveys, such as the GCS (Nordstrómetal.2004) and the Radial Velocity Experiment (RAVE,Steinmetz2006) concentrate on the solar neighborhood."," Some of the most detailed chemo-dynamic surveys, such as the GCS \citep{Nordstrom04} and the Radial Velocity Experiment \citep[RAVE, ][]{Steinmetz06} concentrate on the solar neighborhood." +" In this section, we repeat some of our earlier analysis specifically for stars that reside in the solar annulus (7kpc«τες9 kpc) at the end of each simulation."," In this section, we repeat some of our earlier analysis specifically for stars that reside in the solar annulus $7\kpc \leq \rfin \leq 9\kpc$ ) at the end of each simulation." +" This focus on the solar annulus also removes much of the impact of the bars that dominate evolution of the inner disk (r«3 kpc) in three of our simulations, though some particles from the bar region can migrate as far as the solar radius, and resonances between the bar and spiral structure may increase migration frequency (Minchev&Fa"," This focus on the solar annulus also removes much of the impact of the bars that dominate evolution of the inner disk $r < 3 +\kpc$ ) in three of our simulations, though some particles from the bar region can migrate as far as the solar radius, and resonances between the bar and spiral structure may increase migration frequency \citep{Minchev10}." +maey 2010).. Figure 10 shows the radius of formation (R¢orm)) easing g OM liauyinerqr ger m.," Figure \ref{fig:rform} shows the radius of formation ) distribution of particles residing in the solar annulus, marked by the vertical dashed lines." +" elu final dominated by stars born in the solar annulus, on either side,"," Only the isolated thick disk simulation predicts a final solar annulus dominated by stars born in the solar annulus, with tails extending $1$ $2 \kpc$ on either side." + The EAE migrate to the solar annulus from a wide range of formation radii., The broad distributions of the other three simulations show that their stars migrate to the solar annulus from a wide range of formation radii. +" The global ((Figure 3)) and solar annulus ddistributions of the isolated and perturbed thin disks are remarkably similar, despite the differences in migration mechanisms discussed in Section 3.2.."," The global (Figure \ref{fig:perdisks}) ) and solar annulus distributions of the isolated and perturbed thin disks are remarkably similar, despite the differences in migration mechanisms discussed in Section \ref{sec:orbits}." +" In the isolated thin disk, 32% of solar annulus particles originated at Rrorm<6kpc NaHιο10 kpc."," In the isolated thin disk, $32\%$ of solar annulus particles originated at $\leq 6 \kpc$ and $4\%$ at $\geq 10 \kpc$ ." + Corresponding numbers for the 36% and 3%., Corresponding numbers for the perturbed thin disk are $36\%$ and $3\%$. +" The ddistribution of the perturbed thick disk is slightly narrower, but it still broad with respect to the isolated thick disk."," The distribution of the perturbed thick disk is slightly narrower, but it still broad with respect to the isolated thick disk." + Figure 11 shows the correlations between aand ffor particles that end in the solar annulus., Figure \ref{fig:dcirc_dr_soln} shows the correlations between and for particles that end in the solar annulus. +" Consistent with results for the full disk (Figure 8)), the solar annulus particles in the isolated thick disk show no significant change in median rregardless ofAr."," Consistent with results for the full disk (Figure \ref{fig:dr_dcirc}) ), the solar annulus particles in the isolated thick disk show no significant change in median regardless of." +". In the isolated thin disk, the range of iis much larger, with a modest decrease in medianε."," In the isolated thin disk, the range of is much larger, with a modest decrease in median." +". The median ddrops at large positive bbecause particles move to less inclined orbits as they migrate outwards and disk heating has slightly modified the galaxy’s circular velocity curve, allowing outward moving particles to potentially increase circularity."," The median drops at large positive because particles move to less inclined orbits as they migrate outwards and disk heating has slightly modified the galaxy's circular velocity curve, allowing outward moving particles to potentially increase circularity." +" In the perturbed thick disk, there is a strong and nearly linear trend between aandAr.."," In the perturbed thick disk, there is a strong and nearly linear trend between and." +" Particles that migrated to the solar annulus from the outer disk haveexperienced substantial drops in circularity, while particles migrating from the inner disk show only modest"," Particles that migrated to the solar annulus from the outer disk haveexperienced substantial drops in circularity, while particles migrating from the inner disk show only modest" +ligure 2. plots the numerical results on the EL correlations measured at 2= 0. 0.5. 1 and 2 in the top-left. top-right. bottom-left and bottom-right panels. respectively.,"Figure \ref{fig:three} plots the numerical results on the EE correlations measured at $z=0$ , $0.5$, $1$ and $2$ in the top-left, top-right, bottom-left and bottom-right panels, respectively." + La each panel. the solid. dashed. and long dashed lines represent mn). qui) and (ή). respectively.," In each panel, the solid, dashed and long dashed lines represent $\eta_{\rm I}(r)$, $\eta_{\rm II}(r)$ and $\eta_{\rm III}(r)$, respectively." + “Phe dotted. line corresponds to the case of no correlation., The dotted line corresponds to the case of no correlation. + As can be seen. the nmiajor-axis correlations are strongest and the intermeciate-axis correlations are almost zero at all recshilts.," As can be seen, the major-axis correlations are strongest and the intermediate-axis correlations are almost zero at all redshifts." + To see the behaviorsof the EE correlations at. large distances. we plot giro) and gui(r) as solid dots with errors σι in the logarithmic scale in Figs 3. and 4.. respectively.," To see the behaviorsof the EE correlations at large distances, we plot $\eta_{\rm I}(r)$ and $\eta_{\rm III}(r)$ as solid dots with errors $\sigma_{\eta}$ in the logarithmic scale in Figs \ref{fig:corz} and \ref{fig:corz3}, respectively." + In each panel the solid. line represents the fitting mocel (see Section 3.4)., In each panel the solid line represents the fitting model (see Section 3.4). + For the estimation of ση. we divide the simulation volume into eight subvolumes cach of which has a linear size o£ 2505. Mpe and measure the EE correlations in each subvolume separatelv.," For the estimation of $\sigma_{\eta}$, we divide the simulation volume into eight subvolumes each of which has a linear size of $250h^{-1}$ Mpc and measure the EE correlations in each subvolume separately." + The errors. ση. are calculated as the standard deviation between realizations.," The errors, $\sigma_{\eta}$, are calculated as the standard deviation between realizations." + This estimation of errors accounts for both the cosmic variance and the Poisson noise., This estimation of errors accounts for both the cosmic variance and the Poisson noise. + Lt is also found that there exist non-neegligible correlations between radial bins at distance larger than 5h *\Ipe (sce Section 3.4).," It is also found that there exist non-negligible correlations between radial bins at distance larger than $5\,h^{-1}$ Mpc (see Section 3.4)." + As can be seen. the EL correlations are strongest at 2=2 and exist out to distances of 105. !IMpe.," As can be seen, the EE correlations are strongest at $z=2$, and exist out to distances of $10h^{-1}$ Mpc." + As z decreases. the correlations tend to decrease monotonically at all distance scales. indicating that the directions of the halo major and the minor axes tend to become randomized as 2 decreases.," As $z$ decreases, the correlations tend to decrease monotonically at all distance scales, indicating that the directions of the halo major and the minor axes tend to become randomized as $z$ decreases." + This result is consistent with the previous results obtained by Hopkinsetal.(2005)., This result is consistent with the previous results obtained by \citet{hop-etal05}. +.. Phe numerical results on the EL correlations measured at 2o0 are listed in Table 1.., The numerical results on the EE correlations measured at $z=0$ are listed in Table \ref{tab:EE_z0}. + To study how the EL correlations scale with halo mass. we measure mr) from two cdillerent mass bins with the mass threshold AZ.=142«1075TAR at z=0.," To study how the EE correlations scale with halo mass, we measure $\eta_{\rm I}(r)$ from two different mass bins with the mass threshold $M_{c}=1.42\times 10^{13}h^{-1}M_{\odot}$ at $z=0$." + Table 2. lists the numerical results and Figure ο. plots mir) at.=0 measured from the low-mass (Al< A) and the high-mass bin (AL> AL.) as solid dots in the top ancl the bottom panel. respectively.," Table \ref{tab:EE_m} lists the numerical results and Figure \ref{fig:corm} plots $\eta_{\rm I}(r)$ at $z=0$ measured from the low-mass $MM_{c}$ ) as solid dots in the top and the bottom panel, respectively." + As can be seen. the EI correlations of the high-mass halos are stronger at all clistances than that of the low- halos. which implies that the EL correlations increase as the halo mass increases.," As can be seen, the EE correlations of the high-mass halos are stronger at all distances than that of the low-mass halos, which implies that the EE correlations increase as the halo mass increases." + This finding is also consistent with the previous results obtained for the cluster alignments by Hopkinsetal.(2005)., This finding is also consistent with the previous results obtained for the cluster alignments by \citet{hop-etal05}. + We have alsomeasured the II cross-correlations. ger). between the low-mass and the high-mass halos.," We have alsomeasured the EE cross-correlations, $\eta_{C}(r)$ , between the low-mass and the high-mass halos." + Basically. we select halo pairs each of which consists of one halo [from the low-mass bin and one halo from the high-mass bin. and then," Basically, we select halo pairs each of which consists of one halo from the low-mass bin and one halo from the high-mass bin, and then" +"surrounding nebulae, explaining its absence in MNC4.","surrounding nebulae, explaining its absence in MNC4." + Once the central star evolves further it will heat up and ionise most or all of the now visible [O II] emission into [O III] to produce a more typical PN spectrum., Once the central star evolves further it will heat up and ionise most or all of the now visible [O II] emission into [O III] to produce a more typical PN spectrum. + The integrated [O III] flux is an important quantity for any extragalactic PN so that it may be added to the PNLF., The integrated [O III] flux is an important quantity for any extragalactic PN so that it may be added to the PNLF. + As the WFI data were taken in non-photometric conditions the measurement of [O III] fluxes for the new PNe requires a calibration based on PNe with known fluxes., As the WFI data were taken in non-photometric conditions the measurement of [O III] fluxes for the new PNe requires a calibration based on PNe with known fluxes. + RP2010 published an extensive catalogue of suitable [O III] fluxes for all PNe that overlap with the WFI observations., RP2010 published an extensive catalogue of suitable [O III] fluxes for all PNe that overlap with the WFI observations. + We adopt an error of 0.2 dex as recommended by RP2010 that includes all sources of error., We adopt an error of 0.2 dex as recommended by RP2010 that includes all sources of error. +" The calibrators are spread across the four sub-fields as follows: MG68 (30Dor1), SMP78 and MG60 (30Dor2), MG73 (30Dor3) and RP1037, MG65, Sal22, SMP77 and RP789 (30Dor4)."," The calibrators are spread across the four sub-fields as follows: MG68 (30Dor1), SMP78 and MG60 (30Dor2), MG73 (30Dor3) and RP1037, MG65, Sa122, SMP77 and RP789 (30Dor4)." + MG76 unfortunately fell into an inter-chip gap at the edge of the combined [O III] image of the 30Dor1 sub-field., MG76 unfortunately fell into an inter-chip gap at the edge of the combined [O III] image of the 30Dor1 sub-field. + We performed aperture photometry on the [O III] image of each PN using a circular aperture that included the most flux taking care as best we could to avoid field stars., We performed aperture photometry on the [O III] image of each PN using a circular aperture that included the most flux taking care as best we could to avoid field stars. + Sky subtraction was performed by subtracting the average counts from a set of identical sized apertures., Sky subtraction was performed by subtracting the average counts from a set of identical sized apertures. + The measured counts may include nebular or stellar continuum contributions and this is especially the case for the brightest PNe., The measured counts may include nebular or stellar continuum contributions and this is especially the case for the brightest PNe. + With only B and V images available these contributions cannot be safely subtracted as they both include substantial nebular contributions., With only $B$ and $V$ images available these contributions cannot be safely subtracted as they both include substantial nebular contributions. +" Instead, we have removed the"," Instead, we have removed the" +Average uncertainties in dust features were24...17%... ancl for the global fits for 555. 33109. and 55152. respectively.,"Average uncertainties in dust features were, and for the global fits for 55, 3109, and 5152, respectively." +" In addition to 1D spectra, 2D spectral maps from various wavelength regions were also eeneraled using CUDISMs mapping feature."," In addition to 1D spectra, 2D spectral maps from various wavelength regions were also generated using CUBISM's mapping feature." +" This procedure allows the user to specify ""peak"" and “continuum waveleneth intervals.", This procedure allows the user to specify “peak” and “continuum” wavelength intervals. + CUBISA then subtracts (he specified continuum from the peak. and creates a map of (he resulling emission.," CUBISM then subtracts the specified continuum from the peak, and creates a map of the resulting emission." + For maps covering spectral regions between 7.4 son and 7.6 pom. the overlap region between SLI and SL2. a more detailed method was needed.," For maps covering spectral regions between 7.4 $\mu$ m and 7.6 $\mu$ m, the overlap region between SL1 and SL2, a more detailed method was needed." + In (his case. maps were extracted separately in each slit ancl averaged together in the area of overlap before being combined.," In this case, maps were extracted separately in each slit and averaged together in the area of overlap before being combined." + As noted above. the galaxies in our sample were selected based on proximity and the presence of ongoing star formation.," As noted above, the galaxies in our sample were selected based on proximity and the presence of ongoing star formation." + These three clwarl imregulars span a modest range in metallicity (70.6 dex). but larger ranges in SER. dvnamical mass and absolute magnitude (Table 1)).," These three dwarf irregulars span a modest range in metallicity $\sim$ 0.6 dex), but larger ranges in SFR, dynamical mass and absolute magnitude (Table \ref{galaxysample}) )." + The ISM oxygen abundances have been determined through observations of HE II regions., The ISM oxygen abundances have been determined through observations of H II regions. + The temperature sensitive [O III] A4363 line was detected in each svstem. resulting in reliable abundance determinations.," The temperature sensitive [O III] $\lambda$ 4363 line was detected in each system, resulting in reliable abundance determinations." +" These abundancees are. 4 /""/og(O/1I1) = 00.1 for NGC 55 (Webster&Smith1983).. 4 00.07. for IC) 5152 (Leeetal.2003a).. and 00.33. for NGC33109 (Leeetal.2003b)."," These abundances are $+$ log(O/H) = $\pm$ 0.1 for NGC 55 \citep{Webster83}, $\pm$ 0.07 for IC 5152 \citep{Lee03a}, and $\pm$ 0.33 for 3109 \citep{Lee03b}." +. Previous investigations have studied (he luminosity of the 8 yam PAL feature via imaging., Previous investigations have studied the luminosity of the 8 $\mu$ m PAH feature via imaging. + Typically the IRAC band 1 or 2 images (al 3.6 jm and 4.5 pam. respectively) are assumed to accurately represent the underlving stellar continuum: these images are scaled and subtracted from the IRAC 8 ji image (see detailed discussion in 2006)).The resulting diffuse 8 jan emission (which includes contributions from the 6.2 jan. 7.7 jun and 8.6 jn PATI features) in these svstems scales approximately with the metallicity.," Typically the IRAC band 1 or 2 images (at 3.6 $\mu$ m and 4.5 $\mu$ m, respectively) are assumed to accurately represent the underlying stellar continuum; these images are scaled and subtracted from the IRAC 8 $\mu$ image (see detailed discussion in \nocite{Jackson06}) ).The resulting diffuse 8 $\mu$ m emission (which includes contributions from the 6.2 $\mu$ m, 7.7 $\mu$m and 8.6 $\mu$ m PAH features) in these systems scales approximately with the metallicity." + 33109 has the lowest gas-phase abundance (1256 Z.) and the lowest total diffuse 8 jin flux density. (0.06 Jv)., 3109 has the lowest gas-phase abundance $\sim$ $_{\odot}$ ) and the lowest total diffuse 8 $\mu$ m flux density (0.06 Jy). + 55152 is slightly more metal-rich. (1856 Z.) and harbors a larger total 8 jam fIux density (0.16 Jv)., 5152 is slightly more metal-rich $\sim$ $_{\odot}$ ) and harbors a larger total 8 $\mu$ m flux density (0.16 Jy). + Moving above the threshold metallicity (12 + log(O/II) ~ 8.0: 2005)). 555 (494 Z.) is an order of magnitude brighter in the IRAC 8 san band (1.4 Jv).," Moving above the threshold metallicity (12 $+$ log(O/H) $\simeq$ 8.0; \nocite{Engelbracht05}) ), 55 $\sim$ $_{\odot}$ ) is an order of magnitude brighter in the IRAC 8 $\mu$ m band (1.4 Jy)." + Note by examining Figure d. that our IH spectral maps cover only the regions of highest surface brightness 8 jm emission: the URS field of view encompasses 41%... 185. and of the intensity in the IRAC'S jan field of view for 555. 33109. and 55152. respectively," Note by examining Figure \ref{IRSoverlay} that our IRS spectral maps cover only the regions of highest surface brightness 8 $\mu$ m emission; the IRS field of view encompasses , , and of the intensity in the IRAC 8 $\mu$ m field of view for 55, 3109, and 5152, respectively" +Evidence for the existence of dark matter (DM) has been observed. in various astrophysical svstems. ranging [ron satellite dwarl galaxies to massive. galactic clusters. and cosmology.,"Evidence for the existence of dark matter (DM) has been observed in various astrophysical systems, ranging from satellite dwarf galaxies to massive galactic clusters and cosmology." +" Possible cold dark matter candidates arise from heoretical models conceived to extend the Standard Mocel of elementary. particles and. Weakly Interacting. Massive ""articles (WIALP) are the current main paradigm (see Feng(2010) [or a recent review on dark matter candidates).", Possible cold dark matter candidates arise from theoretical models conceived to extend the Standard Model of elementary particles and Weakly Interacting Massive Particles (WIMP) are the current main paradigm (see \citet{RevDM} for a recent review on dark matter candidates). + The fact that direct observation of dark matter particles las not vet been possible justifies all the elforts devoted to heir indirect. detection. Le. the observation of anomalous components in the cosmic rays spectrum that can be attributed to dark matter annihilation.," The fact that direct observation of dark matter particles has not yet been possible justifies all the efforts devoted to their indirect detection, i.e., the observation of anomalous components in the cosmic rays' spectrum that can be attributed to dark matter annihilation." + See Crockerctal.2007) [or examples of such searches in the 5-ray.. X-ray. radio and neutrino spectra.," See \citet{gamma_radio,gammaI,Xray,radioI,radioII,neutrino,multiI,multiII} for examples of such searches in the $\gamma$ -ray, X-ray, radio and neutrino spectra." + In fact. dark matter self-annihilation is expected. to ooduce several Standard: Model particles. among. which electrons and positrons that. by interacting with the galactic magnetic field. emit svnchrotron. radiation in the racio xd.," In fact, dark matter self-annihilation is expected to produce several Standard Model particles, among which electrons and positrons that, by interacting with the galactic magnetic field, emit synchrotron radiation in the radio band." + We can estimate the intensity of the emission coming rom a given direction in the sky hy adopting models or using measurements to describe the following quantities: he dark matter density. profile. whieh can be mocelled by using the results of halo formation numerical simulations: he magnetic field. estimated. through techniques such as he analysis of polarisation of radio and optical emission and rotation measures: and the interstellar raciation field and hydrogen distribution. which are needed to account for he electronpositron energy. losses.," We can estimate the intensity of the emission coming from a given direction in the sky by adopting models or using measurements to describe the following quantities: the dark matter density profile, which can be modelled by using the results of halo formation numerical simulations; the magnetic field, estimated through techniques such as the analysis of polarisation of radio and optical emission and rotation measures; and the interstellar radiation field and hydrogen distribution, which are needed to account for the electron/positron energy losses." + Phe comparison of this emission with the observed. radio emission then allows to impose constraints on the values of the dark matters mass. ma. and its thermally averaged annihilation cross section. oU).," The comparison of this emission with the observed radio emission then allows to impose constraints on the values of the dark matter's mass, $m_{\chi}$, and its thermally averaged annihilation cross section, $\langle \sigma_A v \rangle$." + In order for this method to provide reliable constraints. the values of all the involved parameters need to be known vers well. which often. does. not. happen.," In order for this method to provide reliable constraints, the values of all the involved parameters need to be known very well, which often does not happen." + Furthermore. ideally. the comparison between the theoretical result. and the observed. emission should be made after all the known astrophysical foreground has been subtracted from. the," Furthermore, ideally, the comparison between the theoretical result and the observed emission should be made after all the known astrophysical foreground has been subtracted from the" +fits (κος table 3)) aeree well with those obtained by the AIACTIO collaboration with a 3 vear baseline (Alcock et al.,fits (see table \ref{cand1}) ) agree well with those obtained by the MACHO collaboration with a 3 year baseline (Alcock et al. + L99T)). we will fx the level of he baseline flux. to hat obtaiue previously with the blended fit. to perform xwallax fits.," 1997b), we will fix the level of the baseline flux to that obtained previously with the blended fit, to perform parallax fits." + We fit sunultancously the red and blue ight curves allowing for parallax axd for the periodic nodulation described iu section 3., We fit simultaneously the red and blue light curves allowing for parallax and for the periodic modulation described in section 3. + Asstuing a bleudiug coefficient eji=0.71. our data allows us to exclude. at the CL. that du>0.05L.," Assuming a blending coefficient $c_{\rm bl} = 0.74$, our data allows us to exclude, at the CL, that $\delta u > 0.054$." + This vieksa lower bound on voth the projected transverse velocity of the defector: aud ou the projected Eiustein radius: We cau thus write: The high projected transverse velocity definitely excludes the possibility that the deflector is in the disk. of the \Glsv Wav. where the typical velocity dispersion is ~300 LOkui/s (Binney aud Tremaine 1987).," This yields a lower bound on both the projected transverse velocity of the deflector: and on the projected Einstein radius: We can thus write: The high projected transverse velocity definitely excludes the possibility that the deflector is in the disk of the Milky Way, where the typical velocity dispersion is $\sim 30-40$ km/s (Binney and Tremaine 1987)." + Moreover. a disk lens (ce.« 1/100) eeneratiug this event would have a nass Af>TOM!," Moreover, a disk lens (i.e. $x<1/100$ ) generating this event would have a mass $M>70{\rm +\;M_\odot}$!" + For a deflector in the halo. 6<2/3 at the confidence level (for a staudard halo) which requires the mass of the deflector AZ to be at least 0.3 AL... while for a deflector iu the SAIC. i£16021/10. the mass of the lens would be AY20.07AL...," For a deflector in the halo, $x<2/3$ at the confidence level (for a standard halo) which requires the mass of the deflector $M$ to be at least $0.3{\rm \;M_\odot}$ , while for a deflector in the SMC, if $1-x \simeq +1/10$, the mass of the lens would be $M\simeq 0.07 {\rm \;M_\odot}$." + This is illustrated iu figure 9.., This is illustrated in figure \ref{par_mx}. + It is possible for some parallax distortious to be largely cancelled out by bleudius effects., It is possible for some parallax distortions to be largely cancelled out by blending effects. + However. bleudiug distortions of light curves are always siunetric about the »omt of hiehest iagnification. while this is not the case. in general. of parallax distortions.," However, blending distortions of light curves are always symmetric about the point of highest magnification, while this is not the case, in general, of parallax distortions." + [t is only true when he velocity of the deflector is parallel or anti-parallel to he velocity of the Eart1 around t1ο Sun at the moment of Hehest maenification., It is only true when the velocity of the deflector is parallel or anti-parallel to the velocity of the Earth around the Sun at the moment of highest magnification. + Figure 1 )dlusrates the amount of lending required to compensate the effect of an increasing xuwallax while remaiming compatible with the observed ight curve., Figure \ref{parbl} illustrates the amount of blending required to compensate the effect of an increasing parallax while remaining compatible with the observed light curve. + All the »oiuts ploted vield a \?/cd.o.n for he fit within 1o of the wait value (157/158)., All the points plotted yield a $\chi^2/{\rm d.o.f.}$ for the fit within $1\sigma$ of the minimum value (157/158). + Note he two minima regious in the planes shown iu the Beure. one around an augle of ISO deerees between the xojected. velocities of the Earth aud of the deflector (full uarkers). while the other (empty markers) corresponds to a null angle.," Note the two minima regions in the planes shown in the figure, one around an angle of 180 degrees between the projected velocities of the Earth and of the deflector (full markers), while the other (empty markers) corresponds to a null angle." + The shaced area delinüits lending coetficieuts oereater than unitv. which is no physical.," The shaded area delimits blending coefficients greater than unity, which is not physical." + As shown iu Heure 10. da could be larger thau 0.05L. but oulv iu he unlikely case of alieunnent of velocities;," As shown in figure \ref{parbl}, $\delta u$ could be larger than 0.054, but only in the unlikely case of alignment of velocities." + We built a ikclihood based on the fit with xwallax. blending aud a nodulation ou the maguified sar. taking iuto account the xobabilitv that the aligniment of the Earth aud defiector velocities were parallel or auti-parallel.," We built a likelihood based on the fit with parallax, blending and a modulation on the magnified star, taking into account the probability that the alignment of the Earth and deflector velocities were parallel or anti-parallel." + This viclds the CL upper liit du«0.06 (which requiresa bleudius coefficient ej= 0.15).," This yields the CL upper limit $\delta u < +0.06$ (which requiresa blending coefficient $c_{\rm bl} = 0.45$ )." +" The projected velocity is then constrainedto be at least 190 Xin/s and equation 12 beconies""wy SESAdEmat-Γ 0.5.", The projected velocity is then constrainedto be at least 190 km/s and equation \ref{eqpar} becomes $\frac{M}{\rm M_\odot}\times \frac{x}{1-x} > 0.5$ . +As emphasised by Navakshinetal.(2009b).. there are wo distinctlv different: regimes.,"As emphasised by \cite{NayakshinEtal09b}, there are two distinctly different regimes." + Lo fyναι then the SMDLL grow arbitrarily quickly if provided with enough uel.," If $t_{\rm Salp} \ll t_{\rm dyn}$, then the SMBH grow arbitrarily quickly if provided with enough fuel." +" there is a SAIBLI feecing-feedback link that can limit he SMDBLEL mass. such as in the Wine(2003.2005) model. the atter then grows to the appropriate Ad, mass ancl remains here."," If there is a SMBH feeding-feedback link that can limit the SMBH mass, such as in the \cite{King03,King05} model, the latter then grows to the appropriate $M_\sigma$ mass and remains there." + Lf /sayfon. then the SMDLL is unable to grow sullicienthy quickly to reach its maximum (i.e. Mj). even if it is provided with ample fuel during the dynamical time of he system.," If $t_{\rm Salp} \gg t_{\rm dyn}$, then the SMBH is unable to grow sufficiently quickly to reach its maximum (i.e. $M_\sigma$ ), even if it is provided with ample fuel during the dynamical time of the system." + We now present two simulations that explore hese two regimes., We now present two simulations that explore these two regimes. + The initial condition used in this test is same as in 77.. except that the initial SALBLE mass dis. smaller. Adj—107AL...," The initial condition used in this test is same as in \ref{sec:underweight_fixed}, except that the initial SMBH mass is smaller, $M_{\rm bh} = 10^8 \msun$." +" As we found in §?? for this initial condition. the Ad, mass is about Ady=3OPAL.."," As we found in \ref{sec:critical_fixed} for this initial condition, the $M_\sigma$ mass is about $ M_0 = 3 \times 10^8 +\msun$." + The black hole thus needs to increase its mass by about a factor of το drive the shell out., The black hole thus needs to increase its mass by about a factor of 3 to drive the shell out. + Phe dynamical time of the shell is ανα7200 Alvrs. which gives the SAIBLE plenty of time to grow.," The dynamical time of the shell is $t_{\rm dyn} +\approx 200$ Myrs, which gives the SMBH plenty of time to grow." +" Figure 6 shows the mean racial velocity of gas (solid curve). the mean radius of the shell (dasb-dotted). the selferavity corrected velocity dispersion of the gas (dashed) and finally. the dotted curve shows the ratio of the black hole mass to the initial M,=Aly mass."," Figure \ref{fig:M0.01_R40_edd} shows the mean radial velocity of gas (solid curve), the mean radius of the shell (dash-dotted), the self-gravity corrected velocity dispersion of the gas (dashed) and finally, the dotted curve shows the ratio of the black hole mass to the initial $M_\sigma = M_0 $ mass." + The early phase of gas dynamics is quite similar to the underweight fixed mass case considered in §??.., The early phase of gas dynamics is quite similar to the underweight fixed mass case considered in \ref{sec:underweight_fixed}. +" Phe shell is contracting and the σας velocity dispersion grows with time. increasing the AZ, value (see the dashed curve in the figure)."," The shell is contracting and the gas velocity dispersion grows with time, increasing the $M_\sigma$ value (see the dashed curve in the figure)." + However. the SAIBLE grows even faster.," However, the SMBH grows even faster." + At around 90 Myrs the σας suddenly ects decelerated. and then accelerated. to positive velocity., At around 90 Myrs the gas suddenly gets decelerated and then accelerated to positive velocity. +" While this is as expected based on simple analytical expectations (Navakshinetal.2009b).. the SMBDBII mass at the time when gas velocity becomes positive is about 135LOPAL.. about a factor of 4 higher than the initial conliguration value. Al,=3107M..."," While this is as expected based on simple analytical expectations \citep{NayakshinEtal09b}, the SMBH mass at the time when gas velocity becomes positive is about $1.3\times 10^9 \msun$, about a factor of 4 higher than the initial configuration value, $M_\sigma = 3 \times 10^8 \msun$." + At the same time. he shell radius is much smaller at that moment than the initial value. increasing the self-gravity corrected AZ; value wea factor of about 2.5 to ~17.5«107M...," At the same time, the shell radius is much smaller at that moment than the initial value, increasing the self-gravity corrected $M_\sigma$ value by a factor of about 2.5 to $\sim 7.5 \times 10^8 \msun$." + H£ our models incluclecl star. formation and if à good fraction of gas was urned into stars then the resulting bulge. assuming the stars remain bound as the gas is blown away. would satisfy he Aly6 relation within a factor of two.," If our models included star formation and if a good fraction of gas was turned into stars then the resulting bulge, assuming the stars remain bound as the gas is blown away, would satisfy the $M_{\rm bh} - \sigma$ relation within a factor of two." + Llowever the οσο velocity dispersion would be higher than that of the uncerlving isothermal potential value., However the bulge velocity dispersion would be higher than that of the underlying isothermal potential value. +" We now repeat the run of 82? but shrinking the shells outer radius by a factor of four to Row=LO kpe and increasing the SMDBIUSs initial mass to Ad,=210M.", We now repeat the run of \ref{sec:large} but shrinking the shell's outer radius by a factor of four to $R_{\rm out} = 10$ kpc and increasing the SMBH's initial mass to $M_{\rm bh} = 2\times 10^8 \msun$. +" ‘This is about two thirds of the initial AZ, mass. and hence the black hole needs to increase in mass by only a small fraction to reverse the inflow of gas."," This is about two thirds of the initial $M_\sigma$ mass, and hence the black hole needs to increase in mass by only a small fraction to reverse the inflow of gas." + However. as Figure 7 demonstrates. the black hole's growth is too slow for this configuration of gas.," However, as Figure \ref{fig:M0.02_R10_edd} demonstrates, the black hole's growth is too slow for this configuration of gas." + As SMDII mass grows. so does the required ni; mass. since the shell contracts.," As SMBH mass grows, so does the required $m_\sigma$ mass, since the shell contracts." + In fact. when the shells mass exceeds the local dark matter mass the shell becomes sell-gravitating and the increase in moz accelerates. leaving no chance for the SMDBII to catch up.," In fact, when the shell's mass exceeds the local dark matter mass the shell becomes self-gravitating and the increase in $m_\sigma$ accelerates, leaving no chance for the SMBH to catch up." + The results of these experiments confirm that. the Salpeter time should be sulliciently. short compared to the, The results of these experiments confirm that the Salpeter time should be sufficiently short compared to the +be possible to observe the star move through the traditional DAV instability strip in a matter of only months or years. 107 times more rapidly than single DAVs. as the white dwarf photosphere cools between DN outbursts.,"be possible to observe the star move through the traditional DAV instability strip in a matter of only months or years, $10^8$ times more rapidly than single DAVs, as the white dwarf photosphere cools between DN outbursts." + GW Librae is a faint DN which called attention to itself for the first time in 1983 when its brightness increased by ~ 9 mag (Gonzállez 1983) — its only observed outburst., GW Librae is a faint DN which called attention to itself for the first time in 1983 when its brightness increased by $\sim$ 9 mag (Gonzállez 1983) – its only observed outburst. + The large amplitude of the outburst initially led to GW Lib being misclassified as a nova: however. subsequent spectroscopy (Duerbeck Sitter 1987: Ringwald. Naylor Mukai 1996) showed it to be a system with a very low mass-transfer rate.," The large amplitude of the outburst initially led to GW Lib being misclassified as a nova; however, subsequent spectroscopy (Duerbeck Sitter 1987; Ringwald, Naylor Mukai 1996) showed it to be a system with a very low mass-transfer rate." + GW Lib is almost certainly a member of the class of long outburst-interval. low mass-transfer-rute DNe known as the WZ Sagittae stars.," GW Lib is almost certainly a member of the class of long outburst-interval, low mass-transfer-rate DNe known as the WZ Sagittae stars." +" GW Lib's faintness (V 18) precluded interest in it for 14 years following its outburst. until we chanced upon its remarkable oroperties while conducting a high-speed-photometry survey of ""nt Southern Hemisphere CVs."," GW Lib's faintness $\sim$ 18) precluded interest in it for 14 years following its outburst, until we chanced upon its remarkable properties while conducting a high-speed-photometry survey of faint Southern Hemisphere CVs." + Its spectrum and its 1983 WZ-Sge-style superoutburst show beyond doubt that GW Lib is a CV. but the Fourier transform of its light-curve (Fig. 19) ," Its spectrum and its 1983 WZ-Sge-style superoutburst show beyond doubt that GW Lib is a CV, but the Fourier transform of its light-curve (Fig. \ref{fig:lcv}) )" +resembled hat of a nonradially pulsating single white dwarf., resembled that of a nonradially pulsating single white dwarf. + Nonradial oulsations had never been observed in an accreting white dwarf before (except possibly a single mode in the DOV primary of the CV AM CVn [Solheim et al., Nonradial pulsations had never been observed in an accreting white dwarf before (except possibly a single mode in the DOV primary of the CV AM CVn [Solheim et al. + 1998]): it had been assumed either hat accretion would keep the primaries of CVs too hot to pulsate. or that He in the accreted material would suppress pulsations.," 1998]); it had been assumed either that accretion would keep the primaries of CVs too hot to pulsate, or that He in the accreted material would suppress pulsations." + The DAV tor ZZ Cet) instability strip for (non-acereting) hydrogen-atmosphere white dwarfs (DAs) occurs between Toys of 11.000 and 12.500 K (Koester Holberg 20013. depending on the mixing length prescription used to describe convection.," The DAV (or ZZ Cet) instability strip for (non-accreting) hydrogen-atmosphere white dwarfs (DAs) occurs between $_{\rm eff}$ s of 11,000 and 12,500 K (Koester Holberg 2001), depending on the mixing length prescription used to describe convection." + The coolest DN primaries have surface temperatures of typically 15 000 K (Sion. Urban Lyons 2001).," The coolest DN primaries have surface temperatures of typically 15 000 K (Sion, Urban Lyons 2001)." + A spectroscopic study of GW Lib by Thorstensen et al. (, A spectroscopic study of GW Lib by Thorstensen et al. ( +2002) found an orbital period of 76.78 min — the shortest known orbital period for a CV with a hydrogen-rich donor (V485 Cen has a period of 59 min. but its companion has a low hydrogen content [Augusteijn et al.,"2002) found an orbital period of 76.78 min – the shortest known orbital period for a CV with a hydrogen-rich donor (V485 Cen has a period of 59 min, but its companion has a low hydrogen content [Augusteijn et al." + 1996])., 1996]). + This orbital period supports GW Lib’s status as a WZ Sve star., This orbital period supports GW Lib's status as a WZ Sge star. +" The WZ Sve stars. or ""TOADSs'. are the oldest DNe. and are characterized by very low mass-transfer rates. long outburst recurrent times and short orbital periods (e.g. Bailey 1979: O'Donoghue et al."," The WZ Sge stars, or `TOADs', are the oldest DNe, and are characterized by very low mass-transfer rates, long outburst recurrent times and short orbital periods (e.g. Bailey 1979; O'Donoghue et al." + 1991: Howell. Szkody Cannizzo 1995).," 1991; Howell, Szkody Cannizzo 1995)." + Along with the magnetic AM Her CVs. which also have low rates. WZ Spe stars are therefore the most likely CVs to harbour DAVs. because of their age (white dwarfs take 5 Gyr to cool to 12.500 K. depending on their mass [Chabrier et al.," Along with the magnetic AM Her CVs, which also have low rates, WZ Sge stars are therefore the most likely CVs to harbour DAVs, because of their age (white dwarfs take 0.5--5 Gyr to cool to 12,500 K, depending on their mass [Chabrier et al." + 2000]. and because of their low mass-transfer rate (so that compressional heating of the white dwarf's cores through accretion is small [Townsley Bildsten 200110.," 2000]), and because of their low mass-transfer rate (so that compressional heating of the white dwarf's cores through accretion is small [Townsley Bildsten 2001])." + Despite extensive photometry. no orbital modulation has been detected in GW Lib’s light-curves. suggesting that the system has a low inclination.," Despite extensive photometry, no orbital modulation has been detected in GW Lib's light-curves, suggesting that the system has a low inclination." + From the width of GW Lib's emission lines. Thorstensen et al. (," From the width of GW Lib's emission lines, Thorstensen et al. (" +"2002) infer an inclination of11"".",2002) infer an inclination of. + Thorstensen et al., Thorstensen et al. + also find an absolute magnitude for GW Lib of Ady TLS. adistance of 125 pe and a significant proper motion of 66+12 mas ," also find an absolute magnitude for GW Lib of $M_V$ 11.5, a distance of 125 pc and a significant proper motion of $66 \pm 12$ mas $^{-1}$." +Szkody. Desat Hoard (2000) found that spectra of GW Lib were roughly consistent with an effective temperature of 11.0004 1.000 K (assuming that of the flux came from the white dwarf). which put GW Lib in the DAV instability. strip.," Szkody, Desai Hoard (2000) found that spectra of GW Lib were roughly consistent with an effective temperature of $\pm$ 1,000 K (assuming that of the flux came from the white dwarf), which put GW Lib in the DAV instability strip." + However. Szkody et al. (," However, Szkody et al. (" +2002) then obtained a more accurate white dwarf surface temperature. with HST UV spectroscopy. of 14.700 K. which puts it well outside the traditional DAV instability strip.,"2002) then obtained a more accurate white dwarf surface temperature, with HST UV spectroscopy, of 14,700 K, which puts it well outside the traditional DAV instability strip." + This may imply a possible temporary heating of the white dwarf atmosphere due to an unobserved outburst (while the core and mean temperatures are much lower). or that the instability strip for accreting DAVs is different from that of single DAVs.," This may imply a possible temporary heating of the white dwarf atmosphere due to an unobserved outburst (while the core and mean temperatures are much lower), or that the instability strip for accreting DAVs is different from that of single DAVs." +" Indeed. the notion of an ""instability strip’ for accreting white dwarfs may be meaningless: instability strips are usually associated with groups of stars moving by single star evolution through a T.ar interval. but in accreting systems the mass transfer onto the white dwarf would very likely introduce very important additional parameters."," Indeed, the notion of an `instability strip' for accreting white dwarfs may be meaningless: instability strips are usually associated with groups of stars moving by single star evolution through a $_{\rm eff}$ interval, but in accreting systems the mass transfer onto the white dwarf would very likely introduce very important additional parameters." + GW Lib’s pulsation spectrum shows the unstable behaviour typical of the cool. large amplitude DA white dwarf pulsators.," GW Lib's pulsation spectrum shows the unstable behaviour typical of the cool, large amplitude DA white dwarf pulsators." + As white dwarfs evolve from the hot to the cool end of the DAV instability strip. their pulsation spectra become increasingly more complex and unstable. the amplitudes of their pulsation modes often changing dramatically from month to month (Kleinman et al.," As white dwarfs evolve from the hot to the cool end of the DAV instability strip, their pulsation spectra become increasingly more complex and unstable, the amplitudes of their pulsation modes often changing dramatically from month to month (Kleinman et al." + 1998)., 1998). + The amplitudes of the oscillations in GW Lib's light-curve are very small (~ 5-10 mmag)., The amplitudes of the oscillations in GW Lib's light-curve are very small $\sim$ 5-10 mmag). + However. as we expect approximately half the light from the system to be coming from the accretion dise (based on a comparison with the DN Z Cha). the intrinsic amplitude of the pulsations is likely to be greater.," However, as we expect approximately half the light from the system to be coming from the accretion disc (based on a comparison with the DN Z Cha), the intrinsic amplitude of the pulsations is likely to be greater." + As a result of its birth in a common envelope and its subsequent long history of accretion. it would not be surprising if GW Lib's primary were to have characteristics. and therefore a pulsation spectrum. different from those of single white dwarfs.," As a result of its birth in a common envelope and its subsequent long history of accretion, it would not be surprising if GW Lib's primary were to have characteristics, and therefore a pulsation spectrum, different from those of single white dwarfs." + We discuss below some issues which we believe may be of significance in the case of an accreting DAV., We discuss below some issues which we believe may be of significance in the case of an accreting DAV. + If a CV primary has a weak or absent magnetic field (as is the case of GW Lib. which does not appear as an X-ray source in the ROSAT All-Sky Survey Faint Source Catalogue Voges et al.," If a CV primary has a weak or absent magnetic field (as is the case of GW Lib, which does not appear as an X-ray source in the ROSAT All-Sky Survey Faint Source Catalogue [Voges et al." + 2000]. material from the dise. will accrete onto he equatorial regions of the star.," 2000]), material from the disc will accrete onto the equatorial regions of the star." + The white dwarf therefore develops an equatorial band which has a different temperature. rotational and chemical composition structure to the cooler. higher- regions of the star.," The white dwarf therefore develops an equatorial band which has a different temperature, rotational and chemical composition structure to the cooler, higher-latitude regions of the star." + The effect is especially pronounced after superoutbursts., The effect is especially pronounced after superoutbursts. + Sparks et al. (, Sparks et al. ( +1993) tind that after WZ Sge's,1993) find that after WZ Sge's +"Unfortunately, the low S/N in our data does not allow us to investigate the Balmer absorption in individual galaxy spectra.","Unfortunately, the low S/N in our data does not allow us to investigate the Balmer absorption in individual galaxy spectra." +" However, the strength of the Balmer absorption is a function of the age of the stellar population and is therefore expected to correlate with physical parameters of the galaxy such as stellar mass."," However, the strength of the Balmer absorption is a function of the age of the stellar population and is therefore expected to correlate with physical parameters of the galaxy such as stellar mass." + In order to investigate the effects of stellar absorption on our measurement we stack our spectra in bins of stellar mass and examine the effect of the Balmer absorption on the We stack, In order to investigate the effects of stellar absorption on our measurement we stack our spectra in bins of stellar mass and examine the effect of the Balmer absorption on the $EW(H\beta)$. + EW(H).our spectra into 7 mass bins., We stack our spectra into 7 mass bins. + We normalize each spectrum to the continuum by dividing by the median value of the continuum between 4800—4815A and 4900—49154., We normalize each spectrum to the continuum by dividing by the median value of the continuum between $4800-4815\AA$ and $4900-4915\AA$. + We then stack ~230 spectra in each mass bin by interpolating all spectra to have the same wavelength vector and take the median of the flux corresponding to each wavelength element., We then stack $\sim\!230$ spectra in each mass bin by interpolating all spectra to have the same wavelength vector and take the median of the flux corresponding to each wavelength element. + We get similar results if we take the mean rather than the median., We get similar results if we take the mean rather than the median. + The left panel of Figure 3 shows an example of a stacked spectrum., The left panel of Figure \ref{fig:ba} shows an example of a stacked spectrum. + We see that the H8 emission line sits on a broad absorption trough., We see that the $H\beta$ emission line sits on a broad absorption trough. + The correction accounts for the integrated flux of the EW(Hemissionf) line (red curve) that lies below the continuum (blue curve) and would not be included when measuring the in lower S/N spectra due to the absorption EW(Hcurve)., The $EW(H\beta)$ correction accounts for the integrated flux of the emission line (red curve) that lies below the continuum (blue curve) and would not be included when measuring the $EW(H\beta)$ in lower S/N spectra due to the absorption (green curve). +"B) To obtain a correction, we measure the (greenEW(Hf) for the stacked spectrum and corrected spectrum with the absorption removed."," To obtain a correction, we measure the $EW(H\beta)$ for the stacked spectrum and a corrected spectrum with the absorption removed." + The righta panel shows the correction to the EW(Hf) as a function of stellar mass., The right panel shows the correction to the $EW(H\beta)$ as a function of stellar mass. +" The red line is a linear least-square fit given by where x=log(M,.)—10.", The red line is a linear least-square fit given by where $x = log(M_{\ast}) - 10$. + EWeorr is the amount added to the to correct for underlying absorption., $EW_{corr}$ is the amount added to the $EW(H\beta)$ to correct for underlying absorption. + We emphasize EW(HB)that the correction given by equation 4 is sensitive to the fitting procedure., We emphasize that the correction given by equation \ref{eq:ewcorr} is sensitive to the fitting procedure. + A different method (using a smaller continuum window for example) may yield a different correction., A different method (using a smaller continuum window for example) may yield a different correction. + The median correction to the EW(HB) in our sample is 0.9., The median correction to the $EW(H\beta)$ in our sample is 0.9. + We note that this correction does not significantly effect our derived MZ relation owing to thefact that the median correction of 0.9 A is small compared to the median EW(H8) of 12.1 A., We note that this correction does not significantly effect our derived MZ relation owing to thefact that the median correction of 0.9 $\AA$ is small compared to the median $EW(H\beta)$ of 12.1 $\AA$. + This small correction translates to a median increase of 0.04 dex in metallicity., This small correction translates to a median increase of 0.04 dex in metallicity. + We perform a simple test in order to assess the effect of varying the spectral resolution on the Balmer absorption correction., We perform a simple test in order to assess the effect of varying the spectral resolution on the Balmer absorption correction. + We convolve our stacked spectra with gaussians of varying widths., We convolve our stacked spectra with gaussians of varying widths. + We find that the Balmer correction is sensitive to the spectral resolution., We find that the Balmer correction is sensitive to the spectral resolution. + The correction increases with smaller spectral resolution and the slope of the correction with respect to stellar mass flattens., The correction increases with smaller spectral resolution and the slope of the correction with respect to stellar mass flattens. + We speculate that the larger correction found by ? may be attributed to the lower spectral resolution of their data., We speculate that the larger correction found by \citet{Kobulnicky2003b} may be attributed to the lower spectral resolution of their data. +" In a future study, using higher quality data we hope to quantitatively establish the magnitude of this effect."," In a future study, using higher quality data we hope to quantitatively establish the magnitude of this effect." + We use the strong line diagnostics of KK04 as presented in KE08 in order to obtain an estimate of galaxy gas-phase metallicities., We use the strong line diagnostics of KK04 as presented in KE08 in order to obtain an estimate of galaxy gas-phase metallicities. + The diagnostics are based onthe? Reg theoretical calibrations., The diagnostics are based on the \citet{Kewley2002} $R_{23}$ theoretical calibrations. + In both diagnostics the metallicity is determined using the [ο and Oa ratios., In both diagnostics the metallicity is determined using the $R_{23}$ and $O_{32}$ ratios. + We calculate these ratios from our EWs such that and where EW([OII]) is for the doublet and EWY(([OIII]) is taken to be 1.33x[OH] EW([OIII]A5007)., We calculate these ratios from our EWs such that and where $EW([OII])$ is for the [OII] doublet and $EW([OIII])$ is taken to be $1.33 \times EW([OIII]\lambda5007)$ . + We have used the assumption that the ratio of the, We have used the assumption that the ratio of the +iregious In NGC 000. mainly in the spiral arms.,"regions in NGC 4303, mainly in the spiral arms." + The X-rav contour overlay over the Πα image in Fie., The X-ray contour overlay over the $\alpha$ image in Fig. + b reveals that the N-rav sources D. C. D. aud F coincide with rrogions. while sources A aud E are located near such reglons.," \ref{hrioveropt} reveals that the X-ray sources B, C, D, and F coincide with regions, while sources A and E are located near such regions." + Gas dynamical models of barred galaxies (Eueluaicr Gerhard 1997)) show strong eas acciunnulatiou at the tips of the bars due to corotation of the bar structure with the disk what should lead to cuhanced star formation., Gas dynamical models of barred galaxies (Englmaier Gerhard \cite{eng97}) ) show strong gas accumulation at the tips of the bars due to corotation of the bar structure with the disk what should lead to enhanced star formation. + oobservations as well as the existence of pronunent Ia features strikinely support the outcome of these models., observations as well as the existence of prominent $\alpha$ features strikingly support the outcome of these models. + The N-rav contours D aud F seein to arise from these reeious., The X-ray contours B and F seem to arise from these regions. + The X-ray iiaxiunun D is connected with another interesting feature of NCC L303: in the eastern part the ealactic avin secius to be deformed to a boomerane-like bow where source D hes at the beud but without any sjeuificaut brightening iu Io., The X-ray maximum D is connected with another interesting feature of NGC 4303: in the eastern part the galactic arm seems to be deformed to a boomerang-like bow where source D lies at the bend but without any significant brightening in $\alpha$. + The lower N-rvav contours of the nucleus indicate a possible extended source., The lower X-ray contours of the nucleus indicate a possible extended source. + Recent high-resolution. UV observations of the central region with the IIubble Space Telescope reveal a spiral-shapecl structure of inassive vouug (23 My) star-formune reeious with au outer radius of 225 pe (CÀ99))., Recent high-resolution UV observations of the central region with the Hubble Space Telescope reveal a spiral-shaped structure of massive young (2–3 Myr) star-forming regions with an outer radius of 225 pc \cite{col99}) ). + This structure cannot be resolved by WRI., This structure cannot be resolved by HRI. + Due to the low age of the star clusters almost no thermal X-ray eiission is expected at the ealactie uucleus (see Sect. D)., Due to the low age of the star clusters almost no thermal X-ray emission is expected at the galactic nucleus (see Sect. \ref{discussion}) ). + The extended X-ray coutours may originate frou additional sources at distances of about 1 kpc around the nucleus., The extended X-ray contours may originate from additional sources at distances of about 1 kpc around the nucleus. + No X-ray emission has been detected from the possible interaction companions NGC 1303 A and NCC 1292., No X-ray emission has been detected from the possible interaction companions NGC 4303 A and NGC 4292. +" Since the TIRT maxima are separated by ouly 50"".. aud because of the reasous 1ieutioned in Sect. 2.2.."," Since the HRI maxima are separated by only , and because of the reasons mentioned in Sect. \ref{pspcobs}," + the PSPC observations do uot allow to study the spectra of tle X-rav components of NCC [303 individually., the PSPC observations do not allow to study the spectra of the X-ray components of NGC 4303 individually. + ROSAT PSPC detected 505321. backgroung-subtracted. source counts fromm NGC L303 in a total integration time of 8135 sec., ROSAT PSPC detected $\pm$ 24 backgroung-subtracted source counts from NGC 4303 in a total integration time of 8135 sec. + The spectra of the source aud the backeroune are shown in Fig. 5.., The spectra of the source and the background are shown in Fig. \ref{pspcspec}. + We fitted the spectrum with several sinegle-component uodels; as Bremsstrahhme (BS). Raxinond-Suith model (BS). and a power law (PO). and a combined RS-PO nodel.," We fitted the spectrum with several single-component models, as Bremsstrahlung (BS), Raymond-Smith model (RS), and a power law (PO), and a combined RS-PO model." + The results are liste in Table 5.., The results are listed in Table \ref{fittab}. + A single power-law mode inplies the assmuption. that re active nucleus of NGC L803 dominates the N-rav uission.," A single power-law model implies the assumption, that the active nucleus of NGC 4303 dominates the X-ray emission." + Furthermore. the sources detected by the TRI iu the galactic disk would also have to be described with i6 same power lav.," Furthermore, the sources detected by the HRI in the galactic disk would also have to be described with the same power law." + The photon iudex in this model is T=3.2+0.2., The photon index in this model is $\Gamma$ $\pm$ 0.2. + The ciissiou of an AGN in the ROSAT energv band is best described bv a power law with a photon index of P—2.1: nevertheless some cases lave en observed with D.»3 (AICC 5-23-16: Mulcbaev et al. 1993:, The emission of an AGN in the ROSAT energy band is best described by a power law with a photon index of $\Gamma\sim$ 2.4; nevertheless some cases have been observed with $\Gamma>$ 3 (MCG –5-23-16: Mulchaey et al. \cite{mul93}; + Màn 335: πα et al. 1993))., Mkn 335: Turner et al. \cite{tur93}) ). + Hliglhi-iuass N-rav binaries (ΠΑΓΟ) found iu τοις star-foriuimg regions im the spiral arius have a similar spectral shape in the 0.12.1 keV energy range with a photou index of D 2.7 (Alavromatakis 19933)., High-mass X-ray binaries (HMXB) found in young star-forming regions in the spiral arms have a similar spectral shape in the 0.1–2.4 keV energy range with a photon index of $\Gamma\sim$ 2.7 (Mavromatakis \cite{mav93}) ). + The column deusitv of the absorbing commpoucut amounts to cu. which is bv a factor of 3 higher than the Galactic foreground ccolunun density (Dickey Lockman 1990. DL90)).," The column density of the absorbing component amounts to $^{-2}$, which is by a factor of 3 higher than the Galactic foreground column density (Dickey Lockman 1990, \cite{dic90}) )." + Nevertheless. self-absorption within NGC 13023 iust be expected. auc sinallscale deviations from the observe Galactic value by DL9U caunot be ruled out alu may result iu a hieher absorption from the. Milkv Way.," Nevertheless, self-absorption within NGC 4303 must be expected, and small-scale deviations from the observed Galactic value by \cite{dic90} cannot be ruled out and may result in a higher absorption from the Milky Way." + The resulting 0.12. keV. N-vav huuiunositv amounts to ere |., The resulting 0.1–2.4 keV X-ray luminosity amounts to erg $^{-1}$. + The flux portion from the sources outside the uuclear region as observed with the URI amounts to 1.1410! ore | du the case of a suele power-law ciuission model with [=3.2 using the corresponding⋅ ECF of⊳↽↽ cts cni?2 1., The flux portion from the sources outside the nuclear region as observed with the HRI amounts to $\sim$ erg $^{-1}$ in the case of a single power-law emission model with $\Gamma$ =3.2 using the corresponding ECF of cts $^2$ $^{-1}$. + Asinius. a nean X-ray luminosity of lO ore |! foy an IIMND. as observed in the Milkv Way (Fabbiauo ct al. 1982: ," Assuming a mean X-ray luminosity of $^{37}$ erg $^{-1}$ for an HMXB, as observed in the Milky Way (Fabbiano et al. \cite{fab82}; ;" +Watson 19903) would require an unlikely high umuber of 1100 ofthese systeis to produce the observed N-ray flu., Watson \cite{wat90}) ) would require an unlikely high number of 1400 of these systems to produce the observed X-ray flux. + The ratio of OB stars to IINUXDs is assunced to be ~500 (Fabbiauo et al. 19521)., The ratio of OB stars to HMXBs is assumed to be $\sim$ 500 (Fabbiano et al. \cite{fab82}) ). + This means that a total ΙΙΙ of OB stars would be required to account for the IININD X-ray flux in NGC 005., This means that a total number of OB stars would be required to account for the HMXB X-ray flux in NGC 4303. + Even if we consider to have 10° OB stars in NGC 1303. as observed e.g. iu Afku 297 (Benvenuti et al. 1979)).," Even if we consider to have $^{5}$ OB stars in NGC 4303, as observed e.g. in Mkn 297 (Benvenuti et al. \cite{ben79}) )," + it is still a factor of T higherthan expected., it is still a factor of 7 higherthan expected. + Moreover. this is the required nuuber onulv for the disksources aud would involve almost," Moreover, this is the required number only for the disksources and would involve almost" +we show the incompressible and compressible parts of the velocity field. respectively.,"we show the incompressible and compressible parts of the velocity field, respectively." + The incompressible part it strong., The incompressible part it strong. + It constitutes most of the velocity field thus it 15 not surprising that its scaling exponents are very similar to those observed in velocity., It constitutes most of the velocity field thus it is not surprising that its scaling exponents are very similar to those observed in velocity. + This is true in the case of subAlfvénnic models. because all curves in the middle left plot in Figure 6 are tightly covering the S-L scaling with D=1.," This is true in the case of subAlfvénnic models, because all curves in the middle left plot in Figure \ref{fig:expons_parts} are tightly covering the S-L scaling with $D=1$." + The similarity between the velocity and its solenoidal part is also confirmed in the case of superAlfvénnic models but only for subsonic case. when the role of shocks is strongly diminished.," The similarity between the velocity and its solenoidal part is also confirmed in the case of superAlfvénnic models but only for subsonic case, when the role of shocks is strongly diminished." + Two supersonic models show exponents following a scaling more closer to the S-L one with D=I. yet still with lower values," Two supersonic models show exponents following a scaling more closer to the S-L one with $D=1$, yet still with lower values" +were used to simultancously fit the two commponcuts in the next step.,were used to simultaneously fit the two components in the next step. + The composite bulec/disk fitting was done over the whole profile rauge for relatively simple profiles or. most often. after excluding complex features (bumps aud dips) at iutermediate radii.," The composite bulge/disk fitting was done over the whole profile range for relatively simple profiles or, most often, after excluding complex features (bumps and dips) at intermediate radii." + The sinuultaneous two-coniponent fit is based ou a non-linear least-squares iinimuization algoritlian to a function of two ecueralized exponentials., The simultaneous two-component fit is based on a non-linear least-squares minimization algorithm to a function of two generalized exponentials. + That is. we interactively fitted a fuuction withsir parameters. using as initial estimates the results from our ri pexpoucutial or exponential| fits. above.," That is, we interactively fitted a function with parameters, using as initial estimates the results from our $^{1/4}$ +exponential or exponential+exponential fits, above." + The form that we have adopted for the generalized exponential is the Sersic profile (Sersic 1968)) Mtr) beiug the surface brigltuess at radius r. Xj the ceutral surface brightucss aud the scale leugth.," The form that we have adopted for the generalized exponential is the Sersic profile \cite{sersic68}) ) $\Sigma(r)$ being the surface brightness at radius r, $\Sigma_{0}$ the central surface brightness and the scale length." + The sane formula can be written iu terms of surface niaenitudes (Note that im some studies the power Is used instead of n)., The same formula can be written in terms of surface magnitudes (Note that in some studies the power is used instead of n). + Sumaller values of à lead to more cuspy ceutral light distributions aud shallower profiles outwards. while progressively lavecr values of will produce flatter central light distributions aud truncated outer profiles (sce Figure 1)).," Smaller values of n lead to more cuspy central light distributions and shallower profiles outwards, while progressively larger values of will produce flatter central light distributions and truncated outer profiles (see Figure \ref{f1}) )." + The generalized. exponcutial function includes both the simple exponoeutial case (n=1) and the De Vaucouleurs profile using the trausfπμ PushSpon (the subscript referring to the De Vaucouleurs yaLaAlucters}.," The generalized exponential function includes both the simple exponential case =1) and the De Vaucouleurs profile using the transformations: _e, _e-8.325, (the subscript referring to the De Vaucouleurs parameters)." + Tn fact. as shown by Caonetal.1993.. the Sersic ornula can be expressed in terms of the radius enucircliug halfof the total luminosity aud the corresponding surface brightuess.," In fact, as shown by \cite{caon93}, the Sersic formula can be expressed in terms of the radius encircling half of the total luminosity and the corresponding surface brightness." + In order to do this. one can express he total Iuninuositv aud the surface brigltucss introducing wo coefficients that are functions of the exponent. à».," In order to do this, one can express the total luminosity and the surface brightness introducing two coefficients that are functions of the exponent $n$." + Then. for the range of values » that we fouud. we cau conrpute these coefficients by numerical iuteeration and fud two approximate formulas for their dependence onu ».," Then, for the range of values $n$ that we found, we can compute these coefficients by numerical integration and find two approximate formulas for their dependence on $n$." + We have done this. combining Caon s and our formulation. which eave to a very good approxinuatiou the following transformations between p.hi aud pionre for our data: We have used the errors iu ge (calculated as described in Chatzichristou1999)) for (Gaussian) weighting of he data points. estimating the goodness of fif and calculating errors for the fitted coefficients.," We have done this, combining Caon s and our formulation, which gave to a very good approximation the following transformations between $\mu,h$ and $\mu_{e},r_{e}$ for our data: We have used the errors in $\mu$ (calculated as described in \cite{thesis}) ) for (Gaussian) weighting of the data points, estimating the goodness of fit and calculating errors for the fitted coefficients." + Excep Oy cases where the light profiles were relatively simple and the initial paramcters well defined. we started by fixing the parameters for the best defined componeu and allowing the parameters for the second component o vary until a good fit was achieved.," Except for cases where the light profiles were relatively simple and the initial parameters well defined, we started by fixing the parameters for the best defined component and allowing the parameters for the second component to vary until a good fit was achieved." + Next we kep lis set of parameters fixed and varied the other and iterated this process uutil a good solution was approached., Next we kept this set of parameters fixed and varied the other and iterated this process until a good solution was approached. + At this point we allowed all six piuiuneters ο vary freely aud flually caleulated the errors for tle vest fit values., At this point we allowed all six parameters to vary freely and finally calculated the errors for the best fit values. + For most objects the fitted range for he expoucut was 0-2. which is the range usually ound in previous studies (see discussion im the next section).," For most objects the fitted range for the exponent was 0-2, which is the range usually found in previous studies (see discussion in the next section)." + There were however a few cases of very complex profiles. for which oue or both expoucuts iad to be kept fixed. iu order for the fits to couverec.," There were however a few cases of very complex profiles, for which one or both exponents had to be kept fixed, in order for the fits to converge." + The resuue1ο paranueters. that is. the exponentn. he characteristic scale lengths aud the corresponding surface brightuess levels µ are tabulated in Table 1.. where the subscripts andont denote. respectively. he inner (spheroidal) aud outer (disk) components.," The resulting parameters, that is, the exponent, the characteristic scale lengths and the corresponding surface brightness levels $\mu$ are tabulated in Table \ref{tab1}, where the subscripts and denote, respectively, the inner (spheroidal) and outer (disk) components." + Along with the fitted parameters. we also list in Table 2. the mean cllipticity and position angle Πορ:‘timated at a certain isophotal radius (listed in the sale table).," Along with the fitted parameters, we also list in Table \ref{tab2} the mean ellipticity and position angle estimated at a certain isophotal radius (listed in the same table)." + Since the outer isoplotes for many of our objects are distorted and/or show tidal features (tails Or one-sicler arms) aud strong spiral armis. it is not yosstble to «efiue a coluon characteristic brightucss evel or racius for estinating the disk ellipticities and positioi angles.," Since the outer isophotes for many of our objects are distorted and/or show tidal features (tails or one-sided arms) and strong spiral arms, it is not possible to define a common characteristic brightness level or radius for estimating the disk ellipticities and position angles." + Dustead. we inspected visually he direct nuages of al our objects aud compared hem to the fitted (clliptical) models. in order to fud he unaffected isophotes which are mostly located at he edge of the inner disk (avoiding bars and iuner vines}.," Instead, we inspected visually the direct images of all our objects and compared them to the fitted (elliptical) models, in order to find the unaffected isophotes which are mostly located at the edge of the inner disk (avoiding bars and inner rings)." +" Inevitably. the parameters estimated this wav are somewhat subjective aud should not be used to accurately estimate melimnatious for instance. but theyare judicative of the various subsamples aud have a statistical usefiulucss,"," Inevitably, the parameters estimated this way are somewhat subjective and should not be used to accurately estimate inclinations for instance, but they indicative of the various subsamples and have a statistical usefulness." + The ellipse fitting procedure. outlined earlier. was to all of appliedour objects for which either photometric information was available or which possessed well- morphologies.," The ellipse fitting procedure, outlined earlier, was applied to all of our objects for which either photometric information was available or which possessed well-resolved morphologies." + In the Appendix we preseut, In the Appendix we present +than anv of the viscuous timescales. so viscosity cloes not have time to change the angular momentum of a [uid particle (Cutler&LindblomLOST:Sawyer1989:Lindblom.win&Pethick 1982).,"than any of the viscuous timescales, so viscosity does not have time to change the angular momentum of a fluid particle \cite{cutler87,sawyer89,lindblom79,horn81,goodwin82}." +. Finally. we assume no material is ejected during the collapse.," Finally, we assume no material is ejected during the collapse." + Lt follows. from the conservation of j and the fact that 7 is a function of ze only before and after. collapse. that all particles. initially located. on a cvlindrical surface of radius cy [rom the rotation axis will end up being on a new cylindrical surface. of radius xe.," It follows, from the conservation of $j$ and the fact that $j$ is a function of $\varpi$ only before and after collapse, that all particles initially located on a cylindrical surface of radius $\varpi_1$ from the rotation axis will end up being on a new cylindrical surface of radius $\varpi_2$." + And the Solberg condition ensures that all particles initially inside the cylinder of radius σοι will collapse to the region inside the new cvlinder of radius zco., And the Solberg condition ensures that all particles initially inside the cylinder of radius $\varpi_1$ will collapse to the region inside the new cylinder of radius $\varpi_2$. + Lence the specifie angular momentum distribution Γης) of the new equilibrium configuration is the same as that of the pre-collapse white dwarf: here mc is the evlincdrical mass fraction defined by equation (9))., Hence the specific angular momentum distribution $j(m_{\varpi})$ of the new equilibrium configuration is the same as that of the pre-collapse white dwarf; here $m_{\varpi}$ is the cylindrical mass fraction defined by equation \ref{m:def}) ). + Dased οἱ these assumptions. we constructed equilibrium models of the collapsed objects with the same masses. total angular momenta anc j(m-) as the pre-collapse white chvarts.," Based on these assumptions, we constructed equilibrium models of the collapsed objects with the same masses, total angular momenta and $j(m_{\varpi})$ as the pre-collapse white dwarfs." + The gravitational collapse of a massive white dwarf is halted when the central density reaches nuclear density where the EOS becomes still., The gravitational collapse of a massive white dwarf is halted when the central density reaches nuclear density where the EOS becomes stiff. + Phe core bounces back and within a few milliseconds. a hot (Z220 Mev). lepton rich protoneutron star settles into hyvdrodynamie equilibrium.," The core bounces back and within a few milliseconds, a hot $T \ga 20~\rmn{Mev}$ ), lepton rich protoneutron star settles into hydrodynamic equilibrium." + During the so-called. Welvin-Llelmboltz cooling phase. the temperature and lepton number decrease due to neutrino emission and the protoneutron star. cools to a cold neutron star with temperature Z7«1Alev after several minutes.," During the so-called Kelvin-Helmholtz cooling phase, the temperature and lepton number decrease due to neutrino emission and the protoneutron star cools to a cold neutron star with temperature $T<1~\rmn{Mev}$ after several minutes." + Since the cooling timescale is much longer than the hvdrodynamical timescale. the protoneutron star can be regarded as in equasi-ecquilibrium.," Since the cooling timescale is much longer than the hydrodynamical timescale, the protoneutron star can be regarded as in quasi-equilibrium." +" The EOS of a protoneutron star is expressed in the form P=P(prs.d.). where s and 3, are the entropy. per barvon and lepton fraction respectively."," The EOS of a protoneutron star is expressed in the form $P=P(\rho;s,Y_e)$, where $s$ and $Y_e$ are the entropy per baryon and lepton fraction respectively." + As pointed out by Strobel. Seraah Weigel (1999).. the structure of à protoneutron star can be approximated by a constant s and 3; throughou the star. resulting in an effectively barotropic EOS.," As pointed out by Strobel, Scraab Weigel \shortcite{strobel99}, the structure of a protoneutron star can be approximated by a constant $s$ and $Y_e$ throughout the star, resulting in an effectively barotropic EOS." + We used (wo dillerentEOS for. densities. above QUeem7., We used two differentEOS for densities above $10^{10}~\rmn{g}~\rmn{cm}^{-3}$. + Phe first is one of the standard EOS for cok neutron stars., The first is one of the standard EOS for cold neutron stars. +" We adopt. the Bethe-Johnson EOS (Bethe&Johnson1974) for densities above Lottgcm"". aux BBP EOS (Bavm.Bethe&Pethick1971). for. densities in. the region. 107mοem10cm7."," We adopt the Bethe-Johnson EOS \cite{bethe74} for densities above $10^{14}~\rmn{g}~\rmn{cm}^{-3}$, and BBP EOS \cite{baym71} for densities in the region $10^{11}~\rmn{g}~\rmn{cm}^{-3}\ - \ 10^{14}~\rmn{g}~\rmn{cm}^{-3}$." + It turns ou hat the densities of these collapsed: stars are lower than 4107οem 7. and ideas about the EOS in this range iàve not changed very much since 1970s.," It turns out that the densities of these collapsed stars are lower than $4\times 10^{14}~\rmn{g}~\rmn{cm}^{-3}$ , and ideas about the EOS in this range have not changed very much since 1970's." +" The second is the EOS LPNS, ol Strobel ct al (1999)/suessmann/astro/eos/..", The second is the EOS $\rmn{LPNS}_{\rm YL04}^{\rm s2}$ of Strobel et al \shortcite{strobel99}. +. ‘This corresponds (ο ᾱ- protoneutron star 0.5ls alter core bounce., This corresponds to a protoneutron star $0.5 - 1~\rmn{s}$ after core bounce. +" It has an entropy per barvon s=2épy anda lepton fraction Y,—0.4. where Ap is Boltzmann's constant."," It has an entropy per baryon $s=2k_{\rm B}$ and a lepton fraction $Y_e=0.4$, where $k_{\rm B}$ is Boltzmann's constant." + We join both EOS to that of the pre-collapse white dwarf [or densities below 107gem.7., We join both EOS to that of the pre-collapse white dwarf for densities below $10^{10}~\rmn{g}~\rmn{cm}^{-3}$. + LHereafter. we shall call the first EOS the cold EOS. and the second one. the hotEOS.," Hereafter, we shall call the first EOS the cold EOS, and the second one, the hotEOS." + We compute the equilibrium. structure by. Hachisu's. self-consistent field method modified. so that pons)can be specified. (Smith&Centrella1992)..., We compute the equilibrium structure by Hachisu's self-consistent field method modified so that $j(m_{\varpi})$can be specified \cite{smith92}. . + The iteration scheme is based on the integrated static Euler equation (1)) written in the form where C' is the integration constant. and AZ and 4 are the total mass and angular momentum of the star respectively.," The iteration scheme is based on the integrated static Euler equation \ref{euler}) ) written in the form where $C$ is the integration constant, and $M$ and $J$ are the total mass and angular momentum of the star respectively." + Given an enthalpy distribution ; everywhere. the density distribution p; is caleulated by the LOS and the inverse of equation (43)).," Given an enthalpy distribution $h_i$ everywhere, the density distribution $\rho_i$ is calculated by the EOS and the inverse of equation \ref{enthalpy}) )." +" Next we compute the mass M; and cvlindrical mass fraction mz; by and solve the Poisson equation V7;=4xp; to obtain the gravitational potential Φε,"," Next we compute the mass $M_i$ and cylindrical mass fraction $m_{\varpi,i}$ by and solve the Poisson equation $\nabla^2 \Phi_i=4\pi G \rho_i$ to obtain the gravitational potential $\Phi_i$." +" We then update the enthalpy by equation (10)): with the parameters C5.4, and (J;1/ÀM;1X determined by specifying the central density pi and equatorial racius 2...", We then update the enthalpy by equation \ref{int:eluer2}) ): with the parameters $C_{i+1}$ and $(J_{i+1}/M_{i+1})^2$ determined by specifying the central density $\rho_c$ and equatorial radius $R_e$. + The procedure is repeated. until the enthalpy ancl density distribution converge to the desired degree of accuracy., The procedure is repeated until the enthalpy and density distribution converge to the desired degree of accuracy. +" To construct. the equilibrium. configuration with the same total mass ancl angular momentum as a pre-collapse white chyvarl we first compute a model of a non-rotating spherical neutron star. use its enthalpy distribution as an initial guess for the iteration scheme described above and build a configuration with slightly dillerent p, or Z4."," To construct the equilibrium configuration with the same total mass and angular momentum as a pre-collapse white dwarf, we first compute a model of a non-rotating spherical neutron star, use its enthalpy distribution as an initial guess for the iteration scheme described above and build a configuration with slightly different $\rho_c$ or $R_e$." +" Then the parameters p, and 2, are adjusted until we end up with a configuration having the correct total mass and angular momentuni.", Then the parameters $\rho_c$ and $R_e$ are adjusted until we end up with a configuration having the correct total mass and angular momentum. + Two numerical problems were encountered in. this procedure., Two numerical problems were encountered in this procedure. + The first problem is that when the angular momentunm J is increased. the star becomes Ilattened. and the iteration often oscillates among two or more states without converging.," The first problem is that when the angular momentum $J$ is increased, the star becomes flattened, and the iteration often oscillates among two or more states without converging." + This problem can be solved. by using a revised. iteration scheme suggested. by Pickett. Durisen Davis (1996).. in which only afraction of the revised enthalpy A; 4. h2επί8)h;4| hi. isused for the next iteration.," This problem can be solved by using a revised iteration scheme suggested by Pickett, Durisen Davis \shortcite{pickett96}, , in which only afraction of the revised enthalpy $h_{i+1}$ , $h'_{i+1}=(1-\delta)h_{i+1}+\delta h_{i}$ , isused for the next iteration." + Here 6« Lis à parameter controlling the change of enthalpy., Here $\delta<1$ is a parameter controlling the change of enthalpy. + We need. to use 90.95 for very BHattened configurations. and it takes 100900 iterations for the enthalpy and density distributions to converge.," We need to use $\delta > 0.95$ for very flattened configurations, and it takes $100 - 200$ iterations for the enthalpy and density distributions to converge." +structure found. with the International Ultraviolet. Explorer in this gravitational lens candidate indicates pronounced DAL structure in the high-ionization resonance lines of ο VI and N V.1240A.. Michalitsianos ct ((1907) performed. a comparison of [ar-UV. spectra. with data separated by nearly LO months. that. indicated: that changes occurred in both absorption ancl ionization levels associated with BAL structure in the QSO.,"structure found with the International Ultraviolet Explorer in this gravitational lens candidate indicates pronounced BAL structure in the high-ionization resonance lines of O VI and N V. Michalitsianos et (1997) performed a comparison of far-UV spectra, with data separated by nearly 10 months, that indicated that changes occurred in both absorption and ionization levels associated with BAL structure in the QSO." + We found this source to be non-variable during our 3.4 hr observation., We found this source to be non-variable during our $\sim$ 3.4 hr observation. +" ""his source is a HiBAAL with a balnicity incex of 460042.48 km s+ (Lamy et 22004).", This source is a HiBAL with a balnicity index of $\pm2.48$ km $^{-1}$ (Lamy et 2004). + This source did not show any significant mucrovariation over an observational run of AS hr and is non-variable according to the sealed Ετος., This source did not show any significant microvariation over an observational run of $\sim$ 3.8 hr and is non-variable according to the scaled $F$ -test. + Although the €-statistic showed it as a strong contender to have presented microvariability. that result appears to have been induced. because of its relatively bright. comparison stars. as discussed above.," Although the $C$ -statistic showed it as a strong contender to have presented microvariability, that result appears to have been induced because of its relatively bright comparison stars, as discussed above." + Significant. variations were noticed in the DLC over our observational run of ~ 4 hr., Significant variations were noticed in the DLC over our observational run of $\sim$ 4 hr. + Note that a coherent variability trend can be seen in both the quasarstar DLCs., Note that a coherent variability trend can be seen in both the quasar–star DLCs. + Statistical analyses using the C'-test. £ test and scaled f° test all stronely indicate the presence of microvariability.," Statistical analyses using the $C$ -test, $F-$ test and scaled $F-$ test all strongly indicate the presence of microvariability." + This LoBAL is in the Large Bright Quasar Survey. and was also detected in the Chandra BAL quasar survey (Cireen et 22001).," This LoBAL is in the Large Bright Quasar Survey, and was also detected in the Chandra BAL quasar survey (Green et 2001)." + We did not find any signature of microvariation in its DLO over an observational period of ~ 3.77 hr., We did not find any signature of microvariation in its DLC over an observational period of $\sim$ 3.77 hr. + This source has been extensively studied. for optical microvariabilitv., This source has been extensively studied for optical microvariability. + Barbieri et ((1984). click not find. any signature of variability in their observations., Barbieri et (1984) did not find any signature of variability in their observations. + In their search for intranight optical variability in RQOSOs., In their search for intranight optical variability in RQQSOs. + Gopal-Ixrishna et ((2000) observed this source twice for 5 hr cach time and on one of those nights. during which they had unfortunately sparse sampling. saw a hint of microvariation.," Gopal-Krishna et (2000) observed this source twice for 5 hr each time and on one of those nights, during which they had unfortunately sparse sampling, saw a hint of microvariation." + We have investigated this source for 3.8 hr. and the statistical analysis of its DLCs showed. clear. evidence of microvariability.," We have investigated this source for $\sim$ 3.8 hr, and the statistical analysis of its DLCs showed clear evidence of microvariability." + This LoBAL quasar has a balnicity index of 8021.53 km t+ (Trump et 22006)., This LoBAL quasar has a balnicity index of $\pm1.33$ km $^{-1}$ (Trump et 2006). + We observed this source for 3.5 hr but found. no overall evidence of microvariabilitv. although one star-QSO DLC was nominally variable.," We observed this source for $\sim$ 3.5 hr but found no overall evidence of microvariability, although one star-QSO DLC was nominally variable." + This is à LoAL QSO having a balnicity index of 7143743:1.66 kms + (Lrump et 22006)., This is a LoBAL QSO having a balnicity index of $\pm1.66$ km $^{-1}$ (Trump et 2006). + This bright quasar was found in the third. Hamburg Quasar Survey (Hagen ct 11999)., This bright quasar was found in the third Hamburg Quasar Survey (Hagen et 1999). + This source appeared to be variable in a 20 em radio study (Becker et 22000)., This source appeared to be variable in a 20 cm radio study (Becker et 2000). + We found it to be probably. variable over the course of an observing run of 2.7 hr., We found it to be probably variable over the course of an observing run of $2.7$ hr. + This source. also known as CSO τοῦ. is a strongly polarized (3.9 per cent) BALOSO (Cilenn ct 11994).," This source, also known as CSO 755, is a strongly polarized $\sim3.9$ per cent) BALQSO (Glenn et 1994)." + A stronely polarized continuum and unpolarized emission lines indicate that its polarization arises by scattering very near the central source. (Glenn. et 11994)., A strongly polarized continuum and unpolarized emission lines indicate that its polarization arises by scattering very near the central source (Glenn et 1994). + XNMM-Newton spectroscopy of this Luminous quasar gives a photon index of P=183qus and a flat (X-ray bright) intrinsic optical-X-ray spectral slope ofa... =1.51 (Shemmer et 22005)., XMM-Newton spectroscopy of this luminous quasar gives a photon index of $\Gamma =1.83^{+0.07}_{-0.06}$ and a flat (X-ray bright) intrinsic optical-X-ray spectral slope of $\alpha _{ox}=-1.51$ (Shemmer et 2005). + ‘The source shows evidence for intrinsic absorption. having a column density of N(LI) 12;1077 7.," The source shows evidence for intrinsic absorption, having a column density of N(H) $\sim 1.2 \times 10^{22}$ $^{-2}$." + This is among the lowest X-ray. columns measured for a BALQSO (Shemmoer ot al., This is among the lowest X-ray columns measured for a BALQSO (Shemmer et al. + 2005)., 2005). + We detected no signature of microvariability over à short run of ~ 2.9 hr., We detected no signature of microvariability over a short run of $\sim$ 2.9 hr. + | 535903 is also known as SBS | 541 as this source was discovered. in the Second. Byurakan Survey (Stepanyan et 11991)., $+$ 535903 is also known as SBS $+$ 541 as this source was discovered in the Second Byurakan Survey (Stepanyan et 1991). + It has many interesting properties: its DAL has a very high degree of ionization. (Telfer ct 11998). an associated absorption system and damped Lye (DLA) absorption system. and a strong X-ray. absorption (Green et 22001).," It has many interesting properties: its BAL has a very high degree of ionization (Telfer et 1998), an associated absorption system and damped $\alpha$ (DLA) absorption system, and a strong X-ray absorption (Green et 2001)." +" This bright high-redshift LiBAL 05Ο ""has very highly ionized DAXLs (including O VI. Ne VILL. and Si NIL: Peller et 11998) and appears to have an X-rav brightness typical for à non-BAL of its optical luminosity."," This bright high-redshift HiBAL QSO `has very highly ionized BALs (including O VI, Ne VIII, and Si XII; Telfer et 1998) and appears to have an X-ray brightness typical for a non-BAL of its optical luminosity." + Beehtold et ((2002) has found. intervening metal absorption systems at z = 1.41. 0.1558. and 0.72 along its line of sight.," Bechtold et (2002) has found intervening metal absorption systems at $z$ = 1.41, 0.1558, and 0.72 along its line of sight." + We found this source to be non-variable during our observation of ~4 hr., We found this source to be non-variable during our observation of $\sim 4$ hr. + This source was continuouslv observed lor ~3.7 hr., This source was continuously observed for $\sim3.7$ hr. + We [found this as a probably variable source. which makes this source another potentially good candidate for microvariability studies in the future.," We found this as a probably variable source, which makes this source another potentially good candidate for microvariability studies in the future." + Vhe results of our analysis are summarized in. Table 3: we applied both the C'-statistic and the scaled. £-test. as discussed. above (c.g. see Sect 4.2)).," The results of our analysis are summarized in Table \ref{tab:res}; we applied both the $C$ -statistic and the scaled $F$ -test, as discussed above (e.g., see Sect \ref{subs:stat}) )." + In the first. three columns we list the object name. number of cata points (Nisus). used. in. the. DLC and the duration. of our observation.," In the first three columns we list the object name, number of data points $N_{points}$ ) used in the DLC and the duration of our observation." + The fourth column lists the pair of C -values owed on starl and star2 (Iq. 1)), The fourth column lists the pair of $C$ -values based on star1 and star2 (Eq. \ref{eq:cvalue}) ) + while the fifth and sixth columns list the pair of A -values in the standard and scaled F-tvest., while the fifth and sixth columns list the pair of $F$ -values in the standard and scaled $F$ -test. + Columns 7 and 8. respectively. give £. for 0.95 and 1.99 confidence levels.," Columns 7 and 8, respectively, give $F_{c}$ for 0.95 and 0.99 confidence levels." + Columns 9. 10 and. LL respectively. ist the pairs of variability statuses using starl and star2 xwed on C'-statisties. the standard τοπ ancl the scaled f-test.," Columns 9, 10 and 11 respectively, list the pairs of variability statuses using star1 and star2 based on $C$ -statistics, the standard $F$ -test and the scaled $F$ -test." + Vhe status. based on both starl and star2 are listed separatelv rather than using their average value so as to," The status, based on both star1 and star2 are listed separately rather than using their average value so as to" +"histories, metallicities and dust attenuation strengths.","histories, metallicities and dust attenuation strengths." +" For a given galaxy, they evaluated the y? goodness-of-fit by comparing the observed photometry with each model, determined the relative weight for each model, and finally built a probability distribution function (PDF) for the model parameters."," For a given galaxy, they evaluated the $\chi^2$ goodness-of-fit by comparing the observed photometry with each model, determined the relative weight for each model, and finally built a probability distribution function (PDF) for the model parameters." + The average of the PDF is adopted as the a nominal estimate of the parameters., The average of the PDF is adopted as the a nominal estimate of the parameters. +" S07 show that the derived dust attenuation (the optical depth Ty) is sensitive to the assumed prior distribution of τν in the model library, so the prior distribution should be as realistic as possible."," S07 show that the derived dust attenuation (the optical depth $\tau_V$ ) is sensitive to the assumed prior distribution of $\tau_V$ in the model library, so the prior distribution should be as realistic as possible." +" To solve this problem, we estimate approximate values of the attenuation ty(gas) from the Balmer decrement F(Ha@)/F(H£) within the SDSS fiber and the Calzettietal.(2000) extinction curve, when both Ε(Πα) and F(H8) have S/N> 3."," To solve this problem, we estimate approximate values of the attenuation $\tau_V(gas)$ from the Balmer decrement $\alpha$ $\beta$ ) within the SDSS fiber and the \citet{Calzetti00} extinction curve, when both $\alpha$ ) and $\beta$ ) have $S/N>3$ ." +" When either Ε(Πα) or F(H8) has S/N«3, we adopt ty(star,fiber)/0.44 from the measurements of the attenuation of the stellar continuum of the galaxy provided in the MPA/JHU catalog (tauv.cont)."," When either $\alpha$ ) or $\beta$ ) has $S/N<3$, we adopt $\tau_V(star, fiber)/0.44$ from the measurements of the attenuation of the stellar continuum of the galaxy provided in the $\slash$ JHU catalog )." +" This parameter is obtained by fitting Bruzual Charlot (2003) population synthesis models to the stellar continuum; the reddening may then be estimated by determining the extra ""tilt"" that must be applied to the models in order to fit the shape of the observed spectrum.", This parameter is obtained by fitting Bruzual Charlot (2003) population synthesis models to the stellar continuum; the reddening may then be estimated by determining the extra “tilt” that must be applied to the models in order to fit the shape of the observed spectrum. +" The prior distribution of ry(gas) and u (ry(star) μ) values we adopt in our model library is tuned to reproduce the ry(star,fiber) predictions for the whole HI sample."," The prior distribution of $\tau_V(gas)$ and $\mu$ $\tau_V(star)=\tau_V(gas)\times\mu$ ) values we adopt in our model library is tuned to reproduce the $\tau_V(star, fiber)$ predictions for the whole HI sample." +" We adopt for ry(gas) a Gaussian distribution peaked at 1.78, with a width o=0.55, and we adopt for a Gaussian ditribution peaked at 0.44 (Calzettietal.2000), with a width c=0.4."," We adopt for $\tau_V(gas)$ a Gaussian distribution peaked at 1.78, with a width $\sigma=0.55$, and we adopt for $\mu$ a Gaussian ditribution peaked at 0.44 \citep{Calzetti00}, with a width $\sigma=0.4$." +" The Gaussian distribution for ry(gas) is trimmed so that it only spans values between 0 and 4, and the Gaussian distribution for u is trimmed so that it only spans values between 0 and 1."," The Gaussian distribution for $\tau_V(gas)$ is trimmed so that it only spans values between 0 and 4, and the Gaussian distribution for $\mu$ is trimmed so that it only spans values between 0 and 1." + Here we assume that the ry(star) does not change significantly throughout the galaxy., Here we assume that the $\tau_V(star)$ does not change significantly throughout the galaxy. +" In reality, the dust distribution in galaxies is more complicated than our simple model assumes."," In reality, the dust distribution in galaxies is more complicated than our simple model assumes." +" One issue is that for a typical galaxy, the relative attenuation between the inner disk, outer disk and bulge depends strongly on inclination (Tuffsetal. 2004)."," One issue is that for a typical galaxy, the relative attenuation between the inner disk, outer disk and bulge depends strongly on inclination \citep{Tuffs04}." +". However, this effect becomes most notable when the inclination is large (axis ratio b/a« 0.4), so this problem is much mitigated by excluding galaxies with b/a«0.4 from the samples (Section 2.1)) (Yipetal.2010)."," However, this effect becomes most notable when the inclination is large (axis ratio $b/a<0.4$ ), so this problem is much mitigated by excluding galaxies with $b/a<0.4$ from the samples (Section \ref{subsec:PSsample}) ) \citep{Yip10}." +". In the absence of more detailed information on the dust distribution in each galaxy, we believe our method gives results that are as accurate as possible."," In the absence of more detailed information on the dust distribution in each galaxy, we believe our method gives results that are as accurate as possible." +" To test the robustness of the sSFR derived from our SED fiting, we also measured sSFR directly from the SDSS fiber spectrum, and we compared this to the sSFR estimated within the 3 "" aperture using our SED fitting technique."," To test the robustness of the sSFR derived from our SED fitting, we also measured sSFR directly from the SDSS fiber spectrum, and we compared this to the sSFR estimated within the 3 $''$ aperture using our SED fitting technique." +" The SFR derived from the spectrum is calculated from the Ha luminosity, and corrected for dust using the Balmer decrement F(Ho)/F(Hp) and the Calzettial.(2000) extinction curve."," The SFR derived from the spectrum is calculated from the $\alpha$ luminosity, and corrected for dust using the Balmer decrement $\alpha$ $\beta$ ) and the \citet{Calzetti00} extinction curve." + The stellar mass inside the SDSS fiber is taken from the MPA/JHU catalog., The stellar mass inside the SDSS fiber is taken from the $\slash$ JHU catalog. +" For SED fitting, we take the SDSS fluxes within the fiber from the SDSS archive (fibercounts), measure the GALEX NUV fluxes and convolved SDSS u band and GALEX ΕΟΝ fluxes within 6 "" around the galaxy (approximately the FWHM of the GALEX NUV PSF)."," For SED fitting, we take the SDSS fluxes within the fiber from the SDSS archive (fibercounts), measure the GALEX NUV fluxes and convolved SDSS $u$ band and GALEX FUV fluxes within 6 $''$ around the galaxy (approximately the FWHM of the GALEX NUV PSF)." +" Then we use the u band fluxes (within the fiber aperture and from the convolved images) to normalize the GALEX FUV and NUV fluxes, so that we get consistent SED from the 7 bands within the 3"" aperture."," Then we use the $u$ band fluxes (within the fiber aperture and from the convolved images) to normalize the GALEX FUV and NUV fluxes, so that we get consistent SED from the 7 bands within the $''$ aperture." +" We see from Figure 7 that the two estimates generally agree with each other, with a lo scatter of ~0.39 dex."," We see from Figure \ref{fig:fibeffect} that the two estimates generally agree with each other, with a $\sigma$ scatter of $\sim$ 0.39 dex." + The offset between the two estimates exhibits weak systematic trends with both log SFR and ry., The offset between the two estimates exhibits weak systematic trends with both log SFR and $\tau_V$. +" The most discrepant results are obtained for galaxies with very low specific star formation rates, where the UV luminosities are low and may trace populations of stars that are not properly accounted for in standard population synthesis models (Conroy Gunn 2010)."," The most discrepant results are obtained for galaxies with very low specific star formation rates, where the UV luminosities are low and may trace populations of stars that are not properly accounted for in standard population synthesis models (Conroy Gunn 2010)." + We have also tested the effect of varying the adopted priors for ry ., We have also tested the effect of varying the adopted priors for $\tau_V$ . +" We confirm that the prior that is most similar to the real distribution (as calculated from the spectrum), gives the best fit."," We confirm that the prior that is most similar to the real distribution (as calculated from the spectrum), gives the best fit." +" We closely follow the procedure described in Lotzetal.(2004),, hereafter L04, to derive the asymmetry (A) and smoothness (6) parameters from the SDSS g-band images."," We closely follow the procedure described in \citet{Lots04}, hereafter L04, to derive the asymmetry $A$ ) and smoothness $S$ ) parameters from the SDSS $g$ -band images." + Both A and S are measured inside an aperture equal to 1.5 times the petrosian radius (rp)., Both $A$ and $S$ are measured inside an aperture equal to 1.5 times the petrosian radius $r_p$ ). + All neighboring objects are masked., All neighboring objects are masked. + A is a measure of the difference between a given galaxy image and the image rotated by 180 degrees about the object center (the center is determined by minimizing A)., $A$ is a measure of the difference between a given galaxy image and the image rotated by 180 degrees about the object center (the center is determined by minimizing $A$ ). + A higher value of A means that the galaxy is more asymmetric., A higher value of $A$ means that the galaxy is more asymmetric. +" $ is a measure of the difference between a given galaxy image and the image smoothed with a 0.27, wide boxcar kernel.", $S$ is a measure of the difference between a given galaxy image and the image smoothed with a $r_p$ wide boxcar kernel. + A higher value of S implies that the galaxy has amore clumpy morphology on scales equal to the kernel size., A higher value of $S$ implies that the galaxy has a more clumpy morphology on scales equal to the kernel size. + A and S are also calculated using regions of blank sky in the vicinity of the galaxy; the average values of A and S calculated for the background are subtracted from the measurements we make for the galaxy., $A$ and $S$ are also calculated using regions of blank sky in the vicinity of the galaxy; the average values of $A$ and $S$ calculated for the background are subtracted from the measurements we make for the galaxy. +" To make sure that our measurements are consistent with L04, we measure A and S for 41 galaxies from L04 with images available from the SDSS."," To make sure that our measurements are consistent with L04, we measure $A$ and $S$ for 41 galaxies from L04 with images available from the SDSS." + Our results are shown in Figure 8.., Our results are shown in Figure \ref{fig:as_lotz}. + We see that our parameters and those from L04 follow similar trends along the Hubble sequence., We see that our parameters and those from L04 follow similar trends along the Hubble sequence. +" There is quite close agreement between the A values, but our S values are typically four times smaller than those of Lotz — this is likely to be a reflection of thedifferent quality/resolution of the images or different details in the image processing steps in the two cases."," There is quite close agreement between the $A$ values, but our $S$ values are typically four times smaller than those of Lotz – this is likely to be a reflection of thedifferent quality/resolution of the images or different details in the image processing steps in the two cases." +" Nevertheless, our test shows that the relative trends in S are the same forboth sets of measurements, so these parameters are a useful diagnostic of relative changes in galaxy morphology."," Nevertheless, our test shows that the relative trends in $S$ are the same forboth sets of measurements, so these parameters are a useful diagnostic of relative changes in galaxy morphology." +We visually check all the images in our sample using the,We visually check all the images in our sample using the +We warmly thank Stephen Justham. Robert Laine. Stephen Blundell. Samuel Doolin. Paul Coodall aud Sebastian Perez for helpful discussions.,"We warmly thank Stephen Justham, Robert Laing, Stephen Blundell, Samuel Doolin, Paul Goodall and Sebastian Perez for helpful discussions." + I.D. thanks the Roval Society for a University Research. Fellowship., K.B. thanks the Royal Society for a University Research Fellowship. + Ρ.Π. is supported by the Gemini Observatory. which is operated by the Association of Universities for Research in Astronomy. Iuc.. on behalf of the international Gemini partnership of Argentina. Australia. Brazil. Canada. Chile. the United Winedom. aud the United States of America.," P.H. is supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, the United Kingdom, and the United States of America." + The referee is eratefully ackuowledeed for useful comments on the mamuscript., The referee is gratefully acknowledged for useful comments on the manuscript. +Data on other dynamical properties of the VLMBs are not yet available.,Data on other dynamical properties of the VLMBs are not yet available. +" Therefore, we do not include a study on e.g. the possible effects of cluster evolution on the VLMB eccentricity distribution."," Therefore, we do not include a study on e.g. the possible effects of cluster evolution on the VLMB eccentricity distribution." + We follow a similar method to the one described in ? to set up the clusters and systems in our simulations., We follow a similar method to the one described in \citet{Parker09} to set up the clusters and systems in our simulations. +" The clusters are designed to mimic a ‘typical’ star cluster, similar to Orion with N=2000 members and mass ~10? MMo."," The clusters are designed to mimic a `typical' star cluster, similar to Orion with $N = 2000$ members and mass $\sim 10^3$ $_\odot$." +" For each set of initial conditions, we create a suite of 10 simulations, corresponding to 10 clusters, identical apart from the random number seed used to initialise the simulations."," For each set of initial conditions, we create a suite of 10 simulations, corresponding to 10 clusters, identical apart from the random number seed used to initialise the simulations." + We set our clusters up as initially virialised Plummer spheres (7) as described by ?.., We set our clusters up as initially virialised Plummer spheres \citep{Plummer11} as described by \citet*{Aarseth74}. + The prescription in ? provides the positions and velocities of the centres of mass of the systems in the Plummer sphere., The prescription in \citet{Aarseth74} provides the positions and velocities of the centres of mass of the systems in the Plummer sphere. + The current half-mass radius of Orion is ppc (??7?)..," The current half-mass radius of Orion is pc \citep{McCaughrean94,Hillenbrand98,Kohler06}." +" However, ? argue that Orion was originally much denser and dynamical interactions (?,, ?;; ?,andreferences therein)) have caused it to expand to its current size."," However, \citet{Parker09} argue that Orion was originally much denser than it is now and that the effects of gas expulsion \citep*{Tutukov78,Hills80,Goodwin97,Kroupa01a,Goodwin06} and dynamical interactions \citealp{Kroupa99}, \citealp*{Berk07}; \citealp[][and references + therein]{Parker09}) ) have caused it to expand to its current size." +" We therefore adopt initial half-mass radii of ppc and ppc for the clusters in our simulations, thereby covering a wide range of cluster densities."," We therefore adopt initial half-mass radii of pc and pc for the clusters in our simulations, thereby covering a wide range of cluster densities." + Observations suggest that the ratio of stars with masses <11MMo to brown dwarfs is ~55:1 (e.g.?).., Observations suggest that the ratio of stars with masses $<$ $_\odot$ to brown dwarfs is $\sim$ 5:1 \citep[e.g.][]{Andersen08}. +" In our simulations, we place one sub-stellar system (either single or binary) in the cluster for every five stellar systems."," In our simulations, we place one sub-stellar system (either single or binary) in the cluster for every five stellar systems." +" It is thought that the star formation process should produce binary stars in preference to singles (??,andreferences therein).."," It is thought that the star formation process should produce binary stars in preference to singles \citep[][and references + therein]{Goodwin05,Goodwin07}." +" Therefore, all the clusters in our simulations are formed with aninitial stellar binary fraction, faena:=1 (i.e. all stars form in binary systems; there are no singles or triples, etc.),"," Therefore, all the clusters in our simulations are formed with aninitial stellar binary fraction, $f_{\rm stellar} = 1$ (i.e. all stars form in binary systems; there are no singles or triples, etc.)," +" where and S and B are the numbers of single and binary systems, respectively."," where and $S$ and $B$ are the numbers of single and binary systems, respectively." +" The mass of the primary star is chosen randomly from a? IMF of the form where m; = 0.106MMo, ma = 0.5MMo, and ma = MMe."," The mass of the primary star is chosen randomly from a \citet{Kroupa02} IMF of the form where $m_1$ = $_\odot$, $m_2$ = $_\odot$, and $m_3$ = $_\odot$." +" Note that the lower mass limit, mi, is higher than in our previous papers (e.g. ??).."," Note that the lower mass limit, $m_1$, is higher than in our previous papers \citep[e.g.][]{Parker09c,Parker09}. ." + This is to prevent a stellar binary or single star from having mass components (mp ms) that would overlap with the VLMBA data’.., This is to prevent a stellar binary or single star from having mass components $m_p$ $m_s$ ) that would overlap with the VLMBA . + In several, In several +given in Table 6 (see also Figure 13)).,given in Table \ref{MWfit} (see also Figure \ref{MW3}) ). +" The uncertainty on the coolest temperature is small because the that component contributes in both the FUV and soft X-rays, whereas in principle additional thermal components could be included in the fit; we note that the radius for this component is somewhat too small for a neutron star."," The uncertainty on the coolest temperature is small because the that component contributes in both the FUV and soft X-rays, whereas in principle additional thermal components could be included in the fit; we note that the radius for this component is somewhat too small for a neutron star." +" With the gap in the spectrum between the FUV and soft X-rays, we are thus not able to constrain the surface temperature better than in 83.1.3, 1.25x10°ρω.). - varices in /—1..2N spectral channels calculatexd using AL siuuples of real aud imaginary components of the instantaneous spectra.," Equation (18) is solved separately for each of $2 \times N$ real and imaginary sets of data providing estimates of $\widehat{\sigma^2_{M,real}(i)}$ and $\widehat{\sigma^2_{M,imag}(i)}$ - variances in $i=1,..N$ spectral channels calculated using $M$ samples of real and imaginary components of the instantaneous spectra." + Random values in the real and imaginary part of the iustantauceots spectruni are independent. so the sui of these estimates iu cach spectral chaunel eives the tota estimated power spectrum for cach spectral cheuel.," Random values in the real and imaginary part of the instantaneous spectrum are independent, so the sum of these estimates in each spectral channel gives the total estimated power spectrum for each spectral channel." + This “clean” power spectrums is represente in Fie., This “clean” power spectrum is represented in Fig. + 5b for L=50 time intervals., 5b for $L=50$ time intervals. +" In real observaloli cach of 7th time interval is equal to XN&ALAT seconds, where At=1/2Af is the iiput signal sample interval. Af is the bandwidth «of the iuput sienal."," In real observations each of $l-th$ time interval is equal to $N \times M \times \Delta t$ seconds, where $\Delta t=1/2\Delta f$ is the input signal sample interval, $\Delta f$ is the bandwidth of the input signal." +" Tn applications it is practical to find the solution to (18) when gj,=0 using the approach of stochastic approximation: HP—1..M."," In applications it is practical to find the solution to (18) when $\mu_{r}=0$ using the approach of stochastic approximation: $m=1,..M$." + Fig., Fig. + be aud 5d show he result of averaging L spectra in Fie., 5c and 5d show the result of averaging $L$ spectra in Fig. +" ba aud Sh for the ""dif ando “clean”vower spectra. respectively."," 5a and 5b for the “dirty” and “clean”power spectra, respectively." + The frequencies of iuterferences do no coiucide with the frequencies of spectral lines., The frequencies of interferences do not coincide with the frequencies of spectral lines. + It em therefore be seen that the coniponents with normal distribution (svstoeni nolse auk spectral lines} are utouched dy this RFI nitieation procedure., It can therefore be seen that the components with normal distribution (system noise and spectral lines) are untouched by this RFI mitigation procedure. + The sequence of pictux* in Fie., The sequence of pictures in Fig. + 6 similar to Fig., 6 similar to Fig. + 5 cemoustrate tl| result of conrputer simulation when the frequencies of interferences colucke with the frequencies of spectral lines., 5 demonstrate the result of computer simulation when the frequencies of interferences coincide with the frequencies of spectral lines. + Iun this case we again see that the restoration of the spectra is satisfactorY., In this case we again see that the restoration of the spectra is satisfactory. + Figures 5 aud 6 demonstrate how the aleorithin works with spectra., Figures 5 and 6 demonstrate how the algorithm works with spectra. + Towever experimental coustraiuts cid vot require the provision of estinates of Vvarbuice or vower spectu but did required the “clea” sigual in the temporal domain similar to the iuput sienal (the level of the signal. the bincdwidth).," However experimental constraints did not require the provision of estimates of variance or power spectrum but did required the “clean” signal in the temporal domain similar to the input signal (the level of the signal, the bandwidth)." +" Therefore running estimates of ""elesmnt nuxD odit power spectra are used for exponential weieliting of the runniug couples lnstantancous spectra: cach complex value of an instantaneous spectrum being imnultiplied. bx ccptP(r)30201). where Pt);=LN is the input spectral variance (power spectrum) iu the channel /. 62(/) is the estimate of the ""quiescent? power spectrum in the channel ¢ fouud from Eq. ("," Therefore running estimates of “clean” and “dirty” power spectra are used for exponential weighting of the running complex instantaneous spectra: each complex value of an instantaneous spectrum being multiplied by $exp(-P(i)/3\widehat{\sigma^2(i)})$, where $P(i), i=1,..N$ is the input spectral variance (power spectrum) in the channel $i$, $\widehat{\sigma^2(i)}$ is the estimate of the “quiescent” power spectrum in the channel $i$ found from Eq. (" +15).,18). + A corresponding delay must be iutroduced because of the time required to caleulate all 62)., A corresponding delay must be introduced because of the time required to calculate all $\widehat{\sigma^2(i)}$. + Then. after| the backward FFT. the signals iu the temporal domain cau be applied to TPDs or correlators.," Then, after the backward FFT, the signals in the temporal domain can be applied to TPDs or correlators." +" This auxiliary output was uxed to supply the ""elesut raw data in the observations described in Sections 1.", This auxiliary output was used to supply the “clean” raw data in the observations described in Sections 4. + 2 and 1L, 2 and 4. + 3., 3. + Figure? shows the inmipact of REI mutigation ou cross-correlation (radiointerforometric observations)., Figure 7 shows the impact of RFI mitigation on cross-correlation (radiointerferometric observations). + The aleoritlun in the block diagram shown iu Fie., The algorithm in the block diagram shown in Fig. +" 1 Was applied to two signals with the additional coherent Caussian component (0,= L1) emulatiug the noise from a radio source received at both sites of the radio iterferometcr.", 4 was applied to two signals with the additional coherent Gaussian component $\sigma_{s}=0.1$ ) emulating the noise from a radio source received at both sites of the radio interferometer. + Sporadic interference with the duty cevcle equal to 2 was concrated as frequeneyvanodiulated carrier aud was ideutical at both sies which is the worst Case scenario: LOO% correlates REI., Sporadic interference with the duty cycle equal to $0.2$ was generated as frequency-modulated carrier and was identical at both sites which is the worst case scenario: $100\%$ correlated RFI. + Iu reality hne impact of REI in radio interferometers is considerably reduced due to fringe stopping and delay trackue procedures (Thompson1982)., In reality the impact of RFI in radio interferometers is considerably reduced due to fringe stopping and delay tracking procedures \citep{thom82}. +. Figures τα aud 7b demoustrate three-cdimeusional time-frequency xeseutations of the input “dirty” aud “clean” power spectra on oue site. respectively.," Figures 7a and 7b demonstrate three-dimensional time-frequency presentations of the input “dirty” and “clean” power spectra on one site, respectively." + Deep “trouehs can appear iu the spectrum iu Fie., Deep “troughs” can appear in the spectrum in Fig. + Tb at the aces of interferencees duc to the exponential effect of weighting: when mterfereuce is strong the algorithin works similarly to the “thresholdingC» aud blanking”C» aleorithiuaC» but more smoothly and without thepriori knowledge Locessarv or the positionine of the threshold level., 7b at the places of interferences due to the exponential effect of weighting: when interference is strong the algorithm works similarly to the “thresholding and blanking” algorithm but more smoothly and without the knowledge necessary for the positioning of the threshold level. + Figures Tc and 7d give the averaged normalized cross-correlation functions corresponding to Fig., Figures 7c and 7d give the averaged normalized cross-correlation functions corresponding to Fig. +" Ta and Th. without aud wih RFI uütiseatiou. respectively,"," 7a and 7b, without and with RFI mitigation, respectively." + The central. parts of the, The central parts of the +"where £5, is the explosion energy in units of 10°! eres. A4 is the ejecta mass in units of 10M... and /, is the age in units of 10 days.","where $E_{51}$ is the explosion energy in units of $10^{51}$ ergs, $M_{e1}$ is the ejecta mass in units of $10\Msun$, and $t_1$ is the age in units of 10 days." +" The highest velocities occur just inside the reverse shock wave. where the velocity⋅⋅ is e,=ϱΤΝ-ΠΠ6.3⋅⋅x10EESΛΙ0.2ΙΟπια2,02ksfF."," The highest velocities occur just inside the reverse shock wave, where the velocity is $v_{rs}=0.978R_{cd}/t=6.3\times 10^3E_{51}^{0.4}M_{e1}^{-0.2}D_*^{-0.2}t_1^{-0.2}\kms$." + The applicability of the solution requires that ej&e. or E&PALPD<32., The applicability of the solution requires that $v_tls transition liberates a Ly, photon. which can excite the eround state. and there are always enough ow cherey plotous to ionize from an excited state."," The simplest way to take this effect into account is to write on equation for the ionization rate, the ratio of free electrons to the number of free protons plus hydrogen atoms: Each $2p \rightarrow 1s$ transition liberates a ${\rm Ly}_{\alpha}$ photon, which can excite the ground state, and there are always enough low energy photons to ionize from an excited state." +" The ransition to the eround state is final. when the uuuber of hese E.=>By,Bo photous is also diminished."," The transition to the ground state is final, when the number of these $E_{\gamma} \ge B_1 - B_2 \,$ photons is also diminished." +" Photous can escape from the Ly, line either by redshift or bv photon 2s > ds fransitions.", Photons can escape from the ${\rm Ly}_{\alpha}$ line either by redshift or by two--photon 2s $\rightarrow$ 1s transitions. +" lu a stationary state the nuubers of enütted aud absorbed Lx, photons are equal."," In a stationary state the numbers of emitted and absorbed ${\rm Ly}_{\alpha}\,$ photons are equal." +" Consequently. the ΜΠΡΟΣ of photous per mode iu the Ly, resonance line Is: Because of the general expansion of the Universe a frequency vy is shifted in wait time by where IT is the Hubbleparameter."," Consequently, the number of photons per mode in the ${\rm Ly}_{\alpha}$ resonance line is: Because of the general expansion of the Universe a frequency $\nu_0$ is shifted in unit time by where H is the Hubble–parameter." +" The nmuuber of reconibiuation photous removed from the lue by redshift in uult time is: Ou the other απ, the rate of twophoton decay in the 2s states has been caleulated by Spitzer Crecustein (1951)."," The number of recombination photons removed from the line by redshift in unit time is: On the other hand, the rate of two–photon decay in the 2s states has been calculated by Spitzer Greenstein (1951)." +" The umuber of net decays in wit time is with Ao.is8.227s l, "," The number of net decays in unit time is with $A_{2s,1s} = 8.227 s^{-1}$ ." +In thermal equilibrimn the munbers of twophoton decays aud the twophoton excitations are equal.," In thermal equilibrium the numbers of two–photon decays and the two–photon $1s \rightarrow 2s\,$ excitations are equal." +" At this point we have four unknown quantities: MieHosS42anda, aud four equations (103). (113). (133) and CLIEso we ave left with"," At this point we have four unknown quantities: $ n_{1s},n_{2s}, \gamma_{12} +\,{\rm and}\, n_e \,$ and four equations \ref{rec2s}) ), \ref{gamm}) ), \ref{rsr}) ) and \ref{rph2}) );so we are left with" +Astrophysics provides an increasing amount of independent indications that the dark matter of the universe is warm. so that the small-scale I[uctuations are damped out. by free streaming.,"Astrophysics provides an increasing amount of independent indications that the dark matter of the universe is warm, so that the small-scale fluctuations are damped out by free streaming." + This is most easily achieved by giving a keV mass to the DAL particle. in which case the preferred candidate is the sterile neutrino.," This is most easily achieved by giving a keV mass to the DM particle, in which case the preferred candidate is the sterile neutrino." + Support for warm dark matter (DM) comes from simulations of the number of satellite galaxies (Colin. Avila-Iteese Valenzuela 2000) and of disk. galaxy formation without the need for stellar feedback. (Sonuncr-Larsen Dolgov 2000). which both find that a DAL particle mass of about 1 keV is optimal: a significantly larger mass has little impact on galaxy formation. and a significantly smaller mass would lead to the well known cdilliculties faced by hot dark matter.," Support for warm dark matter (WDM) comes from simulations of the number of satellite galaxies (Colin, Avila-Reese Valenzuela 2000) and of disk galaxy formation without the need for stellar feedback (Sommer-Larsen Dolgov 2000), which both find that a DM particle mass of about 1 keV is optimal: a significantly larger mass has little impact on galaxy formation, and a significantly smaller mass would lead to the well known difficulties faced by hot dark matter." + A quantitative lower limit on the candidate WDAL particle mass is inferred. from the existence of a massive black hole at large redshift (Barkana. Haiman Ostriker 2001) and the requirement of. sulliciently early ealaxy formation to account for reionization of the universe and the observed. Ly-a forest. properties (Naravanan et al.," A quantitative lower limit on the candidate WDM particle mass is inferred from the existence of a massive black hole at large redshift (Barkana, Haiman Ostriker 2001) and the requirement of sufficiently early galaxy formation to account for reionization of the universe and the observed $\alpha$ forest properties (Narayanan et al." +" 2000). constraining the DM mass to be larger than 0.75 keV. A recent discussion of x-ray emission [rom decays of sterile neutrinos CXAbazajian. Fuller ""Tucker 2001) has imposed an upper limit of about 5 keV on the neutrino mass."," 2000), constraining the DM mass to be larger than 0.75 keV. A recent discussion of x-ray emission from decays of sterile neutrinos (Abazajian, Fuller Tucker 2001) has imposed an upper limit of about 5 keV on the neutrino mass." + Here we discuss a reinterpretation of these bounds on neutrino mass. and demonstrate that the proper inclusion of the neutrino momentum. arising from the specilic production temperature. reduces the allowed: sterile neutrino WDM mass to bein the range 2.6 keV κm«5 keV. Alb of these studies (Colin et. al.," Here we discuss a reinterpretation of these bounds on neutrino mass, and demonstrate that the proper inclusion of the neutrino momentum, arising from the specific production temperature, reduces the allowed sterile neutrino WDM mass to be in the range $2.6$ keV $< m< 5$ keV. All of these studies (Colin et al." + 2000: Somimer-Larsen Dolgov 2000: Barkana et al., 2000; Sommer-Larsen Dolgov 2000; Barkana et al. + 2001: Naravanan et al., 2001; Narayanan et al. + 2000) are based on the mass-depencdent cut-olf on small scales. produced by frec-streamineg.," 2000) are based on the mass-dependent cut-off on small scales, produced by free-streaming." + In the previously cited studies. a “conventional” WDA model was considered. for the underlving particle physies (see Bode. Ostriker ‘Turok (2001) and Sommer-Larsen. Dolgov (2000) [or recent overviews of such particle models).," In the previously cited studies, a “conventional” WDM model was considered for the underlying particle physics (see Bode, Ostriker Turok (2001) and Sommer-Larsen Dolgov (2000) for recent overviews of such particle models)." + In. such conventional WDAL models. the particles decouple in the carly Universe at. higher temperatures than do massless neutrinos.," In such conventional WDM models, the particles decouple in the early Universe at higher temperatures than do massless neutrinos." + Therefore they do not share the entropy release from the successive particle annihilations., Therefore they do not share the entropy release from the successive particle annihilations. +" Since they were relativistic at. decoupling. their. distribution. function. in momentum space is subsequently that ofa massless fermion. but with a temperature. Zi. which is given todav by where Z5,&1.946 Ix. 44,=100kms*\Ipe [oO is the present energy density of WDAL in units of the critical density. and may is the WDAT mass."," Since they were relativistic at decoupling, their distribution function in momentum space is subsequently that of a massless fermion, but with a temperature, $T_W$, which is given today by where $T_{\nu_0}\approx1.946$ K, $H_0 = 100 \, h \mbox{km} \, +\mbox{s}^{-1} \mbox{Mpc}^{-1}$, $\Omega_W$ is the present energy density of WDM in units of the critical density, and $m_W$ is the WDM mass." + Phe needed. entropy release in these conventional models is much bigger than allowed in the standard model. and such WD caneliclates should therefore have decoupled before a larger gauge group breaks down.," The needed entropy release in these conventional models is much bigger than allowed in the standard model, and such WDM candidates should therefore have decoupled before a larger gauge group breaks down." +is there excellent agreement between these values and the peaks in the redshift distribution. there are also three clear vallevs between the peaks.,"is there excellent agreement between these values and the peaks in the redshift distribution, there are also three clear valleys between the peaks." + Vallevs are expected here because no redshifts are predicted., Valleys are expected here because no redshifts are predicted. + They are not expected to drop to zero. however. because the preferred values will be sincared out by Doppler components.," They are not expected to drop to zero, however, because the preferred values will be smeared out by Doppler components." + Not ouly are the peaks periodic iu z — 0.62. they are pure harmonics above z = 0.," Not only are the peaks periodic in z = 0.62, they are pure harmonics above z = 0." + While possible causes for the vallevs at zg = 2.7 aud z = 3.5 have heen sugeested. no reason to suspect a valley at z = 1.03 has been suggested.," While possible causes for the valleys at z = 2.7 and z = 3.5 have been suggested, no reason to suspect a valley at z = 4.03 has been suggested." + It is concluded here that equ 2 appears to explain the redshift distribution in Fie 1 better than the other avguneuts that have so far been proffered., It is concluded here that eqn 2 appears to explain the redshift distribution in Fig 1 better than the other arguments that have so far been proffered. +" Furthermore. although it is possible. to sugeest explanations. forn the vallevs at z — 2.1 and 3.5. there is no way to prove that the reasons claimed+ are theiv. true cause,"," Furthermore, although it is possible to suggest explanations for the valleys at z = 2.7 and 3.5, there is no way to prove that the reasons claimed are their true cause." +" If there are actually no redshifts P""in the valleys. the selection cts vaised above cannot affect the result."," If there are actually no redshifts in the valleys, the selection effects raised above cannot affect the result." + Iu Fie 1 it needs to be kept in ήτα from the maenitudes involved. that if these hieh redshift objects have heen ejected from nearby low-redshift ealaxies. aud are therefore still associated with them. they iust be intrinsically several naguitudes0111 REMfainterIu thann normalBn galaxies.," In Fig 1 it needs to be kept in mind from the magnitudes involved, that if these high redshift objects have been ejected from nearby low-redshift galaxies, and are therefore still associated with them, they must be intrinsically several magnitudes fainter than normal galaxies." +"πα” DecauscTENay hey are therefore too fait to be detected at ALGearee (distancesistancos. theirlir cosinocosloeicalOgieal, OY (€distanceitane rodshitt colpoucuts will be quite stall relative the intrinsic: redshifts."," Because they are therefore too faint to be detected at large distances, their cosmological, or distance redshift components will be quite small relative to their intrinsic redshifts." +.⋅⋅ Iu⋅ this modelo the distribution in Fig l is therefore esseutiallv au lutrinsic redshift one., In this model the distribution in Fig 1 is therefore essentially an intrinsic redshift one. + If. as ds assunued dn this nodel. quasars are ejeced from active galaxies. and these galaxies are distributed unifoxiulv iu space. the same should lx frue for quasars.," If, as is assumed in this model, quasars are ejected from active galaxies, and these galaxies are distributed uniformly in space, the same should be true for quasars." + Distant, Distant +properties of the faint galaxy. population within groups (seee.g.Ixhosroshahietandreferences(herein) which could be among the driver of the group evolution.,"properties of the faint galaxy population within groups \citep[see e.g.][and references +therein]{Khosro04} which could be among the driver of the group evolution." + We used also (Pengetal.2002) to obtain an accurate mocleling of the surface photometry of each galaxy. which gives us (he parameters necessary (0 study galaxy scaling relations., We used also \citep{Peng02} to obtain an accurate modeling of the surface photometry of each galaxy which gives us the parameters necessary to study galaxy scaling relations. +" In particular we obtained the central surface brightness. jy. the hall-light radius. r,. the surface brightness at the effective radius. jr. and the Sersie profile shape parameter. 2? for the bulge component of the galaxies."," In particular we obtained the central surface brightness, $\mu_0$ , the half-light radius, $_e$, the surface brightness at the effective radius, $\mu_e$, and the Sersic profile shape parameter, $n$ for the bulge component of the galaxies." + The analvsis vielded (hat brighter objects exhibit twpical values of 5 in the range of 2xη<3.5 while the faint ealaxies part of which possibly belong to the NGC 4756 group have values »<2., The analysis yielded that brighter objects exhibit typical values of $n$ in the range of $ 2 \leq n \leq 3.5$ while the faint galaxies part of which possibly belong to the NGC 4756 group have values $n < 2$. + The dependence of n on the absolute magnitude of earlv-tvpe galaxies has been pointed oul in several studies (e.g.Prugniel&Simien1997)., The dependence of $n$ on the absolute magnitude of early-type galaxies has been pointed out in several studies \citep[e.g.][]{prusi97}. +. Our findings are also in agreement with results of similar studies e.g.such as that of IKhosroshahietal.(2004)., Our findings are also in agreement with results of similar studies e.g.such as that of \citet{Khosro04}. +. The coordinates of the bright group members (Mj;<—16.5 mag) and the dwarf galaxy candidates are given in Tables 6. and respectively together with the results of the surface photometry., The coordinates of the bright group members $_B < -16.5$ mag) and the dwarf galaxy candidates are given in Tables \ref{tab6} and \ref{tab7} respectively together with the results of the surface photometry. + It has to be emphasized however. that the method of using the Sersic profile shape parameter to idenüfyv. dwarl ealaxies possibly belonging to the group is prone to rather large uncertainties.," It has to be emphasized however, that the method of using the Sersic profile shape parameter to identify dwarf galaxies possibly belonging to the group is prone to rather large uncertainties." + It has to be expected therefore (hat a certain fraction of the objects listed in Table 7 are galaxies belonging to the background cluster., It has to be expected therefore that a certain fraction of the objects listed in Table \ref{tab7} are galaxies belonging to the background cluster. + A spectroscopic follow-up will give a definite answer., A spectroscopic follow-up will give a definite answer. +The relevant data about the confirmed bright members of (he NGC 4756group are summarized in Tables 3.. 4. and 5.. including three new members we found (o belong,"The relevant data about the confirmed bright members of the NGC 4756group are summarized in Tables \ref{tab3}, , \ref{tab4} and \ref{tab5}, , including three new members we found to belong" +of Ey=10?! eve.,"of $E_0 = +10^{51}$ erg." + This mechanical cucrey is injected by SNe after a few times 105 xii at this stage SNdriven bubbles propagate into the halo quenching further star formation. and the couversion of cold gas into stars is Iuuited bv the increasing fractional volume occupied by SN remnants.," This mechanical energy is injected by SNe after a few times $10^7\,$ yr: at this stage SN–driven bubbles propagate into the halo quenching further star formation, and the conversion of cold gas into stars is limited by the increasing fractional volume occupied by SN remnants." + To be conservative. we do not consider the possibility that very massive (222003.9. metal-free stars nuelt contribute both to metallicity and enerev input.," To be conservative, we do not consider the possibility that very massive $\approx 300 M_\odot$ ), metal-free stars might contribute both to metallicity and energy input." + Their effects have been discussed in detail by Sclineider (2002) and Schneider. Coretta Ferrara (2002) to which we refer to the reader for an exteusive description.," Their effects have been discussed in detail by Schneider (2002) and Schneider, Guetta Ferrara (2002) to which we refer to the reader for an extensive description." + Betore SN feedback occurs some fraction f; of the gas will be able to cool. fragment. and form stars.," Before SN feedback occurs some fraction $f_\star$ of the gas will be able to cool, fragment, and form stars." + As our formalisin does not include local feedback effects. this star formation efüciency must be considered as a free parameter of the model.," As our formalism does not include local feedback effects, this star formation efficiency must be considered as a free parameter of the model." +" Finally. a fraction f, of this euergv will be channeled at a constant rate into a sealaxv outflow over a timescale span of fop=33 Myr. ejecting eas iuto the ICM."," Finally, a fraction $f_w$ of this energy will be channeled at a constant rate into a galaxy outflow over a timescale span of $t_{\rm +OB} = 33$ Myr, ejecting gas into the IGM." + As we will show below 11). the most efficieut ICAL pollutors are objects with masses of a few times 105AZ... for which the fraction of eas that cau cool in a free-fall time is csscutially unity (MER).," As we will show below 1), the most efficient IGM pollutors are objects with masses of a few times $10^8 M_\odot$, for which the fraction of gas that can cool in a free-fall time is essentially unity (MFR)." + ence. this eas is readily available to be transformed iuto stars on short timescales.," Hence, this gas is readily available to be transformed into stars on short timescales." + This justifies the prompt star formation (starburst modo) approximation we have adopted. which therefore should be appropriate to the als of this study.," This justifies the prompt star formation (starburst mode) approximation we have adopted, which therefore should be appropriate to the aims of this study." + The outflows are modeled as spherical shells using a method that is based ou the approach described in SD. but with several important refuemeuts taken frou: MER. Ferrara. Pettini Shehekinov (2000). aud Mori. Ferrara Madau (2001: hereafter MEM).," The outflows are modeled as spherical shells using a method that is based on the approach described in SB, but with several important refinements taken from MFR, Ferrara, Pettini Shchekinov (2000), and Mori, Ferrara Madau (2001; hereafter MFM)." +" An outflow is driven out of the ealaxy by internal pressure and decelerated by inertia and the eravitational pull of the dark matter halo. both estimated in the thin shell approximation (Ostriker Mekoo 1988: οσα, Silk. Evrard 1993)."," An outflow is driven out of the galaxy by internal pressure and decelerated by inertia and the gravitational pull of the dark matter halo, both estimated in the thin shell approximation (Ostriker McKee 1988; Tegmark, Silk, Evrard 1993)." + The expansion of the shell. whose radius is denoted by Ry. is driven by the internal energy. £4. of the hot bubble eas.," The expansion of the shell, whose radius is denoted by $R_s$, is driven by the internal energy, $E_b$, of the hot bubble gas." +" The pressure of such a eas (with adiabatic iudex >= 5/3) is therefore D,=Ej/2x R2.", The pressure of such a gas (with adiabatic index $\gamma=5/3$ ) is therefore $P_b=E_b/2\pi R_s^3$ . +" Momentum and energv conservation vield the relevant evolutionary equations: Roa TER μας E,— Lit) le R?2R DP, Li. where the dots represent |time derivatives. the subscripts sandb indicate shell aud bubble quantities respectively. Ys=GALI(R.)RT. and p is the deusitv of the ambicut uediuu. taken to be the halo gas density within the virial radius and the mean ICM background density outside he virial radius."," Momentum and energy conservation yield the relevant evolutionary equations: = - - HR_s)^2 - _M - = L(t) - 4 R_s^2 P_b - L_c, where the dots represent time derivatives, the subscripts and indicate shell and bubble quantities respectively, $g_s\equiv +GM(R_s)/R_s^2$, and $\rho$ is the density of the ambient medium, taken to be the halo gas density within the virial radius and the mean IGM background density outside the virial radius." + These equatious reduce to those given in MER iu the regime in which the IIubble expausiou is weheible and reduce to those eiven in SD if the NEW. xofile is replaced by a point mass aud external pressure is neglected., These equations reduce to those given in MFR in the regime in which the Hubble expansion is negligible and reduce to those given in SB if the NFW profile is replaced by a point mass and external pressure is neglected. +" The cooling rate. £,.. is assumed here to be dominated woinverse Compton cooliug off CAIB photons (Dzeuchli Ostriker 1986). as eas radiative processes are much less efficicut i the low density 10? K xT105 K gas that drives the outflows."," The cooling rate, $L_c$, is assumed here to be dominated by inverse Compton cooling off CMB photons (Ikeuchi Ostriker 1986), as gas radiative processes are much less efficient in the low density $10^5$ K $\le T \le 10^8$ K gas that drives the outflows." + This approximation is expecially appropriate as the combined cooling processes produce varlatious of less than a few percent on the final size of the bubble (see Fig., This approximation is especially appropriate as the combined cooling processes produce variations of less than a few percent on the final size of the bubble (see Fig. + 6 of MER)., 6 of MFR). + The mechanical Iuninositv of SNe is giveu by — S26 —f) This assuptiou of à constant huuinositv over the burst is niost accurate for the larger galaxies in our παπαΊος. in which the stochastic variations of L(f) become Μα due to the larger number of SNe.," The mechanical luminosity of SNe is given by = 8.26 -t) ) f_w M. This assumption of a constant luminosity over the burst is most accurate for the larger galaxies in our simulations, in which the stochastic variations of $L(t)$ become smaller due to the larger number of SNe." +" We coustrain f, bv combining the overall efficiency of derived for the 24,105AF. object simulated by MEM with the mass scaling derived in Ferrara. Pettini Sbhchekiuov (2000). which was obtained by determining the fraction ofstarburst sites that can produce a blowout ina galaxy of a giveu mass."," We constrain $f_w$ by combining the overall efficiency of derived for the $2\times 10^8 M_\odot$ object simulated by MFM with the mass scaling derived in Ferrara, Pettini Shchekinov (2000), which was obtained by determining the fraction of starburst sites that can produce a blowout in a galaxy of a given mass." +" Thus. we choose f,(AM)=0.30p(AL)op(AL2.105AZ.) where pM) where Np—1<10""(OS/04MZA, is a dimensionless piruneter that scales according to the overall umber of SNe produced in a starburst. divided by the efficieucy f.."," Thus, we choose $f_w(M) = 0.3\delta_B(M)/\delta_B(M=2\times 10^8 M_\odot)$ where _B(M)= where $\tilde N_t \equiv 1.7 +\times 10^{-7} (\Omega_b/\Omega_M) M/M_\odot$ is a dimensionless parameter that scales according to the overall number of SNe produced in a starburst, divided by the efficiency $f_\star$." +" Within the virial radius a fixed fraction f,=0.5 of the eas is swept iuto the shell a value taken from the uuimerical simulations described in MEM."," Within the virial radius a fixed fraction $f_m = 0.5$ of the gas is swept into the shell, a value taken from the numerical simulations described in MFM." + Iu those experiments if is seen that after blowout. half of the initial nass contained iu the virial radius recollapsed to the center as a result of the multiple shell iuteractious leading to the formation of cold sheets.," In those experiments it is seen that after blow–out, half of the initial mass contained in the virial radius re–collapsed to the center as a result of the multiple shell–shell interactions leading to the formation of cold sheets." +" In this case the halo eax is asstuned to virialize to au isothermal distribution and settle down to a density profile pr)= ( Poy [e200)— e201) (Makino. Sasaki. Suto 1998). where the central. preburst gas deusity py is determined by the condition that the total harvouic mass fraction within the viral radius is equal to the cosmic average. vielding py=LLOS2pear Outside the virial radius the 0,4.shells expaud into the IIubble flow. sweeping up all of the barvons in their path."," In this case the halo gas is assumed to virialize to an isothermal distribution and settle down to a density profile (r)= ( _0) [v_e^2(0)- v_e^2(r)], (Makino, Sasaki, Suto 1998), where the central, preburst gas density $\rho_0$ is determined by the condition that the total baryonic mass fraction within the virial radius is equal to the cosmic average, yielding $\rho_0 = +11052 \rho_{\rm crit} \Omega_b.$ Outside the virial radius the shells expand into the Hubble flow, sweeping up all of the baryons in their path." +" Finally, when outflows slow down to the poiut that they are no longer supersonic. our approximations break down. and the shell is possibly fragmented by raudonm motions."," Finally, when outflows slow down to the point that they are no longer supersonic, our approximations break down, and the shell is possibly fragmented by random motions." + At this point we let the bubble expand with the Iubble flow., At this point we let the bubble expand with the Hubble flow. + To calculate the cooling tine of forminggalaxies (see 822). we use a simple estimate of the metallicity of," To calculate the cooling time of forminggalaxies (see 2), we use a simple estimate of the metallicity of" +The solar convection zone is highly turbulent and mixing is to be efficient.,The solar convection zone is highly turbulent and mixing is expected to be efficient. + Nevertheless. the Sun displays coherent expectedstructures encompassing many turbulent eddy scales.," Nevertheless, the Sun displays coherent structures encompassing many turbulent eddy scales." + A well-known ts the magnetic field of the Sun that is antisymmetricexample about the large-scaleequator and shows a 22 solar cycle (Stenflo&Vogel1986)., A well-known example is the large-scale magnetic field of the Sun that is antisymmetric about the equator and shows a 22 year solar cycle \citep{SV86}. +. Another prominent exampleyear in the Sun is the emergence of active regions., Another prominent example in the Sun is the emergence of active regions. + It 15 generally believed that active regions are the result of some non-axisymmetric instability of ~100KC magnetic fields in the tachocline (Gilman&Dikpati2000:Callyetal.2003;Par-frey&Menou 2007).," It is generally believed that active regions are the result of some non-axisymmetric instability of $\sim100\kG$ magnetic fields in the tachocline \citep{GD00,CDG03,PM07}." +. However. the existence of such strong fields remains debatable (Brandenburg2005).," However, the existence of such strong fields remains debatable \citep{B05}." +. A powerful tool for understanding the emergence of such large-scale structures from a turbulent background is mean-field dynamo theory (Moffatt1978;Parker1979;Krause&Radler 1980).," A powerful tool for understanding the emergence of such large-scale structures from a turbulent background is mean-field dynamo theory \citep{Mof78,Par79,KR80}." +. With the advent of powerful computers and numerical simulation tools. it has become possible to confront many of the mean-field predictions with direct simulations (Brandenburg&Subramanian2005).," With the advent of powerful computers and numerical simulation tools, it has become possible to confront many of the mean-field predictions with direct simulations \citep{BS05}." + Here we consider the idea that statistically steady. stratified. hydromagnetic turbulence with an initially uniform magnetic field is unstable to the negative effective magnetic pressure instability (NEMPI).," Here we consider the idea that statistically steady, stratified, hydromagnetic turbulence with an initially uniform magnetic field is unstable to the negative effective magnetic pressure instability (NEMPI)." + This instability is caused by the suppression of turbulent hydromagnetic pressure (the isotropic. part of combined Reynolds and Maxwell stresses) by the mean magnetic field (Kleeorinetal.1990;Rogach," This instability is caused by the suppression of turbulent hydromagnetic pressure (the isotropic part of combined Reynolds and Maxwell stresses) by the mean magnetic field \citep{KRR90,RK07}." +evskii&Kleeorin 2007).. At numbers and for sub-equipartition magnetic fields.large the Reynoldsnegative turbulent contribution can become so that the effective mean pressure (the sum of largeturbulent and non-turbulent magneticcontributions) appears negative.," At large Reynolds numbers and for sub-equipartition magnetic fields, the negative turbulent contribution can become so large that the effective mean magnetic pressure (the sum of turbulent and non-turbulent contributions) appears negative." + In a stratified medium. this results in the excitation of NEMPI that causes formation of large-scale inhomogeneous magnetic structures.," In a stratified medium, this results in the excitation of NEMPI that causes formation of large-scale inhomogeneous magnetic structures." + NEMPI ts similar to the large-scale dynamo instability. except that it only redistributes the total magnetic flux. creating large-scale concentrated magnetic flux regions at the expense of turbulent kinetic energy.," NEMPI is similar to the large-scale dynamo instability, except that it only redistributes the total magnetic flux, creating large-scale concentrated magnetic flux regions at the expense of turbulent kinetic energy." + Historically. the magnetic suppression of the Reynolds stress was first found by Ridler(1974) and Rüdiger (1974).," Historically, the magnetic suppression of the Reynolds stress was first found by \cite{Rae74} and \cite{Rue74}." +. Later. Rüdigeretal.(1986) considered the Maxwell stress and found the mean effective magnetic tension to be suppressed by mean fields.," Later, \cite{Rue86} considered the Maxwell stress and found the mean effective magnetic tension to be suppressed by mean fields." + However. these calculations were based on theory which is only valid at low fluid and magneticquasi-linear Reynolds numbers.," However, these calculations were based on quasi-linear theory which is only valid at low fluid and magnetic Reynolds numbers." + Kleeorinetal.(1990.1996) considered the combined Reynolds and Maxwell stresses at large Reynolds numbers and found a sign reversal of the effective mean magnetic pressure.," \cite{KRR90,KMR96} considered the combined Reynolds and Maxwell stresses at large Reynolds numbers and found a sign reversal of the effective mean magnetic pressure." + This result is based on the 7 approximation. and has been corroborated using the renormalization procedure (Kleeorin&Rogachevskit1994).," This result is based on the $\tau$ approximation, and has been corroborated using the renormalization procedure \citep{KR94}." + The magnetic suppression of the combined Reynolds and Maxwell stresses 1s quantified in terms of new turbulent mean-field coefficients that relate the components of the sum of Reynolds and Maxwell stresses to the mean magnetic field., The magnetic suppression of the combined Reynolds and Maxwell stresses is quantified in terms of new turbulent mean-field coefficients that relate the components of the sum of Reynolds and Maxwell stresses to the mean magnetic field. + These coefficients depend on the magnetic field and have now been determined in direct numerical simulations (DNS) for a broad range of different cases. including unstratified forced turbulence (Brandenburgetal.2010)... tsothermally stratified forced turbulence (Brandenburgetal.2011.here-after BKKR).. and turbulent convection (Kipyléetal.2011).," These coefficients depend on the magnetic field and have now been determined in direct numerical simulations (DNS) for a broad range of different cases, including unstratified forced turbulence \citep{BKR10}, isothermally stratified forced turbulence \citep[][hereafter BKKR]{BKKR11}, and turbulent convection \citep{KBKMR11}." +. These simulations have clearly demonstrated that the mean effective magnetic pressure Is negative for magnetic field strengths below about half the equipartition field strength., These simulations have clearly demonstrated that the mean effective magnetic pressure is negative for magnetic field strengths below about half the equipartition field strength. + However. these DNS studies did not find the actual instability.," However, these DNS studies did not find the actual instability." + With a quantitative parameterization 1n. place. it became possible to build mean-field models of stratified turbulence which clearly demonstrate exponential growth and saturation of NEMPI.," With a quantitative parameterization in place, it became possible to build mean-field models of stratified turbulence which clearly demonstrate exponential growth and saturation of NEMPI." + In view of applications to the formation of active in the Sun. such simulations were originally done for an regionsadiabatically stratified layer (Brandenburgetal. 2010).," In view of applications to the formation of active regions in the Sun, such simulations were originally done for an adiabatically stratified layer \citep{BKR10}." +. In addition. mean-field studies showed the existence of NEMPI even for isothermal stably stratified layers (Kemeletal. 2011).," In addition, mean-field studies showed the existence of NEMPI even for isothermal stably stratified layers \citep{KBKR11}." + This last result turned out to be important because it paved the way for this Letter where we demonstrate NEMPI through DNS., This last result turned out to be important because it paved the way for this Letter where we demonstrate NEMPI through DNS. + Once we establish the physical reality of this effect. it would be important to apply it to realistic solar models which include proper boundary conditions. realistic stratification. convective flux. and radiation transport.," Once we establish the physical reality of this effect, it would be important to apply it to realistic solar models which include proper boundary conditions, realistic stratification, convective flux, and radiation transport." + However. at this stage it 1s essential to isolate NEMPI as a physical effect under conditions that are as simple as possible.," However, at this stage it is essential to isolate NEMPI as a physical effect under conditions that are as simple as possible." +" We consider a domain of size £,«EL. in Cartesian", We consider a domain of size $L_x\times L_y\times L_z$ in Cartesian +Both algorithms are grid based. assuming a 2D grid over the galactic disc.,"Both algorithms are grid based, assuming a 2D grid over the galactic disc." + The first (hereafter CEL) selects clumps solely using a density threshold. whilst the second (hereafter CTE2) uses neighbour lists to assign the most dense grid cells and their neighbours to clumps.," The first (hereafter CF1) selects clumps solely using a density threshold, whilst the second (hereafter CF2) uses neighbour lists to assign the most dense grid cells and their neighbours to clumps." + For CE1. the density in each grid. cell is caleulated and all the cells above a certain density threshold. are selected.," For CF1, the density in each grid cell is calculated and all the cells above a certain density threshold are selected." + Cells that are adjacent. are erouped together ancl particles within these cells elassed as a clump., Cells that are adjacent are grouped together and particles within these cells classed as a clump. + CE2 was provided by Paul Clark and is based on the chump-lined method. of 2.., CF2 was provided by Paul Clark and is based on the clump-find method of \citet{Williams1994}. + The SPILL densities are firs smoothed onto a 2D grid., The SPH densities are first smoothed onto a 2D grid. + The grid cells are then ordere by decreasing density., The grid cells are then ordered by decreasing density. + For each cell in turn. the cell aux its neighbours. (subsequently removed from the List) are identified: as a clump. or assigned to a previously definec chump.," For each cell in turn, the cell and its neighbours (subsequently removed from the list) are identified as a clump, or assigned to a previously defined clump." + Again a density thresholel was set whieh remover low density cells., Again a density threshold was set which removed low density cells. + The properties of each clump are then calculated from the grid. cells rather than the actual SPL particles., The properties of each clump are then calculated from the grid cells rather than the actual SPH particles. + Since CE2 selects the most dense particles first. density. peaks tend to be separated into separate. clumps where they would otherwise constitute a single clump for CEL.," Since CF2 selects the most dense particles first, density peaks tend to be separated into separate clumps where they would otherwise constitute a single clump for CF1." + In both cases we used the density of the molecular gas. which as seen from Fig.," In both cases we used the density of the molecular gas, which as seen from Fig." + 4b largely rellects the underlving structure. and so we can compare the properties of these chumps with observed molecular clouds.," 4b largely reflects the underlying structure, and so we can compare the properties of these clumps with observed molecular clouds." + The clumps found using CTI are displaved. for. the multi-phase (Fig., The clumps found using CF1 are displayed for the multi-phase (Fig. + S) and the single-phase medium (Lig., 8) and the single-phase medium (Fig. + 9) for a subsection of the disc (the same section is shown in lig., 9) for a subsection of the disc (the same section is shown in Fig. + 2)., 2). + oth these figures are taken after LOO Myr., Both these figures are taken after 100 Myr. + The resolution of the οἱ for the algorithm. is 5 pc. and the density threshold for each cell is LOO AL.© ie. equivalent to à surface density o£ 9107 g em7.," The resolution of the grid for the algorithm is 5 pc, and the density threshold for each cell is 100 $_{\odot}$, i.e. equivalent to a surface density of $9 \times 10^{-4}$ g $^{-2}$." + Each clump consists of at least 30 SPL particles (corresponding to a total hydrogen mass of 5000 NL.) which lie within cells above the density threshold., Each clump consists of at least 30 SPH particles (corresponding to a total hydrogen mass of 5000 $_{\odot}$ ) which lie within cells above the density threshold. + Clumps with fewer particles are discarded., Clumps with fewer particles are discarded. + We also show the corresponding column density plots indicating the molecular gas column density (Figs 8 and 9. lower).," We also show the corresponding column density plots indicating the molecular gas column density (Figs 8 and 9, lower)." + There is à clear cillerence in structure of this section of the dise for the single ancl multi-phase gas., There is a clear difference in structure of this section of the disc for the single and multi-phase gas. + The multi-phase case shows many smaller clumps along the spiral arm. whilst the single-phase plot consists of 3 large clumps and several smaller clumps.," The multi-phase case shows many smaller clumps along the spiral arm, whilst the single-phase plot consists of 3 large clumps and several smaller clumps." + Over the whole disc. there are S383 clumps in the multi-phase calculation and 2066 in the single phase calculation.," Over the whole disc, there are 8383 clumps in the multi-phase calculation and 2066 in the single phase calculation." + Phe clump finding algorithm also picks out several clumps in the inter-arm regions in the multi-phase simulation. whereas there are none for the single-phase results.," The clump finding algorithm also picks out several clumps in the inter-arm regions in the multi-phase simulation, whereas there are none for the single-phase results." + These figures further show the general distribution of cold eas., These figures further show the general distribution of cold gas. + In the multi-phase simulation. the cold gas occupies a much smaller filling factor. located in small dense clumps. particularly in the inter-arm regions.," In the multi-phase simulation, the cold gas occupies a much smaller filling factor, located in small dense clumps, particularly in the inter-arm regions." + By contrast. in the single-phase case. the cold. gas is much more uniform. in the inter-arm regions.," By contrast, in the single-phase case, the cold gas is much more uniform in the inter-arm regions." + The second algorithm. CE2. generally produced smaller clumps. but with similar results.," The second algorithm, CF2, generally produced smaller clumps, but with similar results." + We now examine the properties of the clumps from. the single and multi-phase simulations., We now examine the properties of the clumps from the single and multi-phase simulations. + The results shown use CEL. but we discuss any differences with the second clump-finding algorithm.," The results shown use CF1, but we discuss any differences with the second clump-finding algorithm." + Again only clumps with 30 particles ave retained. and the clumps are located after 100 Myr.," Again only clumps with $> 30 $ particles are retained, and the clumps are located after 100 Myr." + The mass and radii for the clumps from the 2 simulations are shown in Fig., The mass and radii for the clumps from the 2 simulations are shown in Fig. + 10., 10. + At later times the clump masses increase or the multi-phase simulation increase. as there is a higher raction of HL». while those of the single phase simulation are similar.," At later times the clump masses increase for the multi-phase simulation increase, as there is a higher fraction of $_2$, while those of the single phase simulation are similar." + For both clump-finding algorithms. we take a column density. threshold 910 g em7," For both clump-finding algorithms, we take a column density threshold $9 \times 10^{-4}$ g $^{-2}$." + For CEL. this corresponcdecl to taking a grid. of resolution 5 pc and requiring that cach cell contains at least LOO AL. (of Le).," For CF1, this corresponded to taking a grid of resolution 5 pc and requiring that each cell contains at least 100 $_{\odot}$ (of $_2$ )." + For CEF2. we apply the same grid resolution. and a minimum column densitv of 0.001. ο em7? of Ls.," For CF2, we apply the same grid resolution, and a minimum column density of 0.001 g $^{-2}$ of $_2$." + With CEL. each clump corresponds to a group of SPII particles.," With CF1, each clump corresponds to a group of SPH particles." + The radii shown in Fig., The radii shown in Fig. + LO are determined by calculating the radius which contains 3/4 of the total clump mass. and thus the mass plotted is 3/4 of the total clump mass assigned bv the particles.," 10 are determined by calculating the radius which contains 3/4 of the total clump mass, and thus the mass plotted is 3/4 of the total clump mass assigned by the particles." + Using the full or 1/2 clump radii and masses merely shifts the distribution of clumps to higher or lower masses ane radii., Using the full or 1/2 clump radii and masses merely shifts the distribution of clumps to higher or lower masses and radii. + For CE2. we use the effective," For CF2, we use the effective" + seeen for of them., en for of them. +For a given luminosity. a relationship between the size of the emitting region ancl electron density can be determined.,"For a given luminosity, a relationship between the size of the emitting region and electron density can be determined." + Assuming the emitting region is spherical. the ion density equals that of the electrons. and a gas temperature of 10*—105 Ix. the radius of the emitting region based on Equation 5.14b and Figure 5.3 of Rvbicki&Lightinan(1979). is where fis the filling factor for the hot gas (LxBfeg).," Assuming the emitting region is spherical, the ion density equals that of the electrons, and a gas temperature of $10^7 - 10^8$ K, the radius of the emitting region based on Equation 5.14b and Figure 5.3 of \citet{randl} is where is the filling factor for the hot gas $\propto {\rm R}^3 f \epsilon_{\rm ff}$ )." + LW the luminosity of these sources in (he 0.58.0 keV band is completely due to thermal bremsstrahlung. assuming an electron density of ng—1 oE and f/=1. the size of the emitting regions ranges from 0.21 to 0.50 kpc.," If the luminosity of these sources in the 0.5–8.0 keV band is completely due to thermal bremsstrahlung, assuming an electron density of $\rm{n_e = 1}$ $^{-3}$ and $f = 1$, the size of the emitting regions ranges from 0.21 to 0.50 kpc." + These sizes of the X-ray emitne regions. deduced assuming dominance of bremsstrahlung emission. are consistent with our finding that most of our faint sources are unresolved byChandra.," These sizes of the X-ray emitting regions, deduced assuming dominance of bremsstrahlung emission, are consistent with our finding that most of our faint sources are unresolved by." + As discussed in Section 5.3.. if we assume Dc1.7 (the photon index of a typical unabsorbed AGN). the column density can be estimated from the hardness ratios.," As discussed in Section \ref{sec:coraltn}, if we assume $\Gamma \simeq 1.7$ (the photon index of a typical unabsorbed AGN), the column density can be estimated from the hardness ratios." + For many of the galaxies in our sample. the total column density estimated in this wav exceeds the Galactic value (see Table 4)).," For many of the galaxies in our sample, the total column density estimated in this way exceeds the Galactic value (see Table \ref{tab:hrs}) )." + This suggests that many of the galaxies in our sample may be absorbed AGNs with total Nj about 216 times the Galactic value ie. up to 7., This suggests that many of the galaxies in our sample may be absorbed AGNs with total $_{\rm H}$ about 2–16 times the Galactic value – i.e. up to $_{\rm H} \simeq 5 \times 10^{22}$ $^{-2}$. + These column density estimates could be inaccurate if absorption is patchy or if scattering [rom an ionizecl medium is significant. as in the cases of NGC 1063 (Matet and NGC 6240 (Ptaketal.2003).," These column density estimates could be inaccurate if absorption is patchy or if scattering from an ionized medium is significant, as in the cases of NGC 1068 \citep{matt} and NGC 6240 \citep{ptak}." +. Nevertheless. Compton-thick AGNs have been detected in several ULIRGs — e.g. IRAS 19254-7245 (Braitoetal.2003).. Mrk 231 Ptaketal. 2003).," Nevertheless, Compton-thick AGNs have been detected in several ULIRGs – e.g. IRAS 19254-7245 \citep{braito03}, Mrk 231 \citep{braito04, ptak}." +. If the intervening column density is 71000 or more times the Galactic value. then. Compton scattering will become important.," If the intervening column density is $\sim$ 1000 or more times the Galactic value, then Compton scattering will become important." + The qualitw of our data does not allow us to rule oul (his possibility., The quality of our data does not allow us to rule out this possibility. + We have obtained and analyzed X-ray. observations of 14 ULIRGs with theObservatory., We have obtained and analyzed X-ray observations of 14 ULIRGs with the. + Although all I4 galaxies were detected in the 0.58.0 keV enerev range. onlv (wo were bright enough lor traditional spectral fitting to be applicable.," Although all 14 galaxies were detected in the 0.5–8.0 keV energy range, only two were bright enough for traditional spectral fitting to be applicable." + Spectral analysis of these (wo galaxies (FOL572+0009 and Z11598-0112) with Sevfert 1 tvpe optical spectra shows that their soft. X-ray emissions are unresolved., Spectral analysis of these two galaxies (F01572+0009 and Z11598-0112) with Seyfert 1 type optical spectra shows that their soft X-ray emissions are unresolved. + There is a suggestion of an emission, There is a suggestion of an emission +ionizing clusters (MelIxee Williams 1997: Οσον Clarke 1998). in terms of a transition from ionization to densitv bounded regious (Beckman et al.,"ionizing clusters (McKee Williams 1997; Oey Clarke 1998), in terms of a transition from ionization to density bounded regions (Beckman et al." + 2000). aud iu terms of bleudiue introduced by observations at too low spatial resolution (Pleuss et al.," 2000), and in terms of blending introduced by observations at too low spatial resolution (Pleuss et al." + 2000): (2) steeper slopes iu the interarni regions of some spiral galaxies as compared to the axi regions. observed m some galaxies (SET: Rane 1992: Banfi et al.," 2000); (2) steeper slopes in the interarm regions of some spiral galaxies as compared to the arm regions, observed in some galaxies (KEH; Rand 1992; Banfi et al." + 1993: Thilker. Dri Walterbos 2000: Scoville et al.," 1993; Thilker, Braun Walterbos 2000; Scoville et al." + 2001). but not iu iiany others (I&uaponu et al.," 2001), but not in many others (Knapen et al." + 1993: Rozas et al., 1993; Rozas et al. + 1996a: I&napen 1998): (3) à correlation between the LF slopes aud the IIubble morphologica type. with the slopes being svstematically steeper in earbv-type galaxies (IKEIT: Banfi ct al.," 1996a; Knapen 1998); (3) a correlation between the LF slopes and the Hubble morphological type, with the slopes being systematically steeper in early-type galaxies (KEH; Banfi et al." + 1993): and (1) a loca imaxuunun in the LFs around logL(Illa)=38.6+0.1 eressD. interpreted as evidence for a change from au ionization to a density bounded regunae of regions of increasing huninosity by Beckman et al. (," 1993); and (4) a local maximum in the LFs around $\log L({\rm H}\alpha) = +38.6 \pm 0.1$ $^{-1}$, interpreted as evidence for a change from an ionization to a density bounded regime of regions of increasing luminosity by Beckman et al. (" +2000). but as au artifact of low resolution inagiug by Pleuss et al. (,"2000), but as an artifact of low resolution imaging by Pleuss et al. (" +2000).,2000). + From the theoretical poiut of view. the observationa differences of region LFs among galaxies have Όσοι reproduced in terms of evolutionary effects (c.g.. differeut ages. and SF histories}. and properties of the ionizing clusters such as different initial mass functions (IMEs) and the maxiuuun number of ionizing stars por cluster (c.g... von Hippel Bothun 1990: Feiusteiu 1997: Melee Williams 1997: Oey Clark 1997. 1998: Beckinan et al.," From the theoretical point of view, the observational differences of region LFs among galaxies have been reproduced in terms of evolutionary effects (e.g., different ages, and SF histories), and properties of the ionizing clusters such as different initial mass functions (IMFs) and the maximum number of ionizing stars per cluster (e.g., von Hippel Bothun 1990; Feinstein 1997; McKee Williams 1997; Oey Clark 1997, 1998; Beckman et al." + 2000: Scoville et al., 2000; Scoville et al. + 2001)., 2001). + It is eenerallv assumed that the shape and properties of the region LF directly reflec certain characteristics of the most recent SF history of tlic ealaxy., It is generally assumed that the shape and properties of the region LF directly reflect certain characteristics of the most recent SF history of the galaxy. + So far. all statistical studies of the properties of extragalactic regious have been performed on samples of disk regions. whereas the properties of nuclear an circmunuclear regions are relatively uuknownu. due to the combines effects. of liited spatial resolution aud blending.," So far, all statistical studies of the properties of extragalactic regions have been performed on samples of disk regions, whereas the properties of nuclear and circumnuclear regions are relatively unknown, due to the combined effects of limited spatial resolution and blending." +" The ceutral. kiloparsec scale. regions of disk galaxies. however, are interesting because of the usually icerease cireiununuclear or nuclear SF activity there. aud because the central regions act as excellent laboratories where. ce. SE aud eas flow processes i barred and non-birre ealaxies cau be studied iu detail (e.e.. review by IKnapenu 1999)."," The central, kiloparsec scale, regions of disk galaxies, however, are interesting because of the usually increased circumnuclear or nuclear SF activity there, and because the central regions act as excellent laboratories where, e.g., SF and gas flow processes in barred and non-barred galaxies can be studied in detail (e.g., review by Knapen 1999)." +" Even though sas fractious and star formation rates (SFRs) in the central regions can be siguificantlv chhanced. there is as vet no convinciug evidence that the SF processes in these regious are fundamentally different from those occuring in the disks of galaxies. nor for a different IME in the ceutral reeious of galaxies. or in fact in general ίσιο, reviews by Eliieereeu 1998: Cülinore 2001. but sce Eisenhauer 2001 for a differing view on the ΤΝΤ]."," Even though gas fractions and star formation rates (SFRs) in the central regions can be significantly enhanced, there is as yet no convincing evidence that the SF processes in these regions are fundamentally different from those occurring in the disks of galaxies, nor for a different IMF in the central regions of galaxies, or in fact in general (e.g., reviews by Elmegreen 1998; Gilmore 2001, but see Eisenhauer 2001 for a differing view on the IMF)." + We have used LS7T/NICMOS Pao images of the cireummnuclear reeious of a sample of 52 spiral and iregular ealaxies iu order to study the statistical properties of regions at high spatial resolution (130 pc).," We have used /NICMOS $\alpha$ images of the circumnuclear regions of a sample of 52 spiral and irregular galaxies in order to study the statistical properties of regions at high spatial resolution $1-30\,$ pc)." + We describe the sample. data. and production of the region catalogs in Section 2. aud the statistical properties of the reeious iu Section 3 and [.," We describe the sample, data, and production of the region catalogs in Section 2, and the statistical properties of the regions in Section 3 and 4." + We discuss our results and subunarize our couclusions iu Section 5., We discuss our results and summarize our conclusions in Section 5. + We have selected a sample of galaxies from the HST/NICAMOS Pao snapshot survey of πουν. galaxies as published by Bokker et al. (, We have selected a sample of galaxies from the /NICMOS $\alpha$ snapshot survey of nearby galaxies as published by Bökker et al. ( +1999). iniposiug the criteria that galaxies have morphological type S0/a or later. aud velocities of e<10001+.,"1999), imposing the criteria that galaxies have morphological type S0/a or later, and velocities of $v < 1000\,{\rm +km\,s}^{-1}$." + The Dókker et al. (, The Bökker et al. ( +1999) “snapshot” survey consists of galaxies selected at randoms from a master list taken from the Revised Shapley Ames Catalog (RSA) according toZZST scheduling couvenicuce.,1999) “snapshot” survey consists of galaxies selected at random from a master list taken from the Revised Shapley Ames Catalog (RSA) according to scheduling convenience. + Our sample contains a total of 52 ealaxies. aud is preseuted in Table 1. which lists the Dubble type. heliocentric velocity from the Nearby Galaxics Catalog (Tully 1988). morphological type. aud the distance from the Tully (1988) catalog assuniug fy=75kins1A\Ipc," Our sample contains a total of 52 galaxies, and is presented in Table 1, which lists the Hubble type, heliocentric velocity from the Nearby Galaxies Catalog (Tully 1988), morphological type, and the distance from the Tully (1988) catalog assuming $H_0 = 75\,{\rm km\,s}^{-1}\,{\rm Mpc}^{-1}$." + Iu terms of the morphological type. of the sample are galaxies with T=03 (that is. morphological types earlier than She). are galaxies with T=15 (SheSc) and galaxies with types T>5 (morphological types later than Sc).," In terms of the morphological type, of the sample are galaxies with $T = 0 - 3 $ (that is, morphological types earlier than Sbc), are galaxies with $T =4-5$ (Sbc--Sc) and galaxies with types $T > 5$ (morphological types later than Sc)." + According to tle preseuce or absence of a bar the saple is divided iuto: uubarred (A). strouely barred (B) and weakly barred (AB).," According to the presence or absence of a bar the sample is divided into: unbarred (A), strongly barred (B) and weakly barred (AB)." + We determined whetler there are distance biases within these subelasses. and found that the wealky barred ealaxies are at slightly larecr distances: galaxies with type AB are at a inedia distance of MMpce. πατος ealaxies at 5.6AIpc. aud strongly barred galaxies at MMpe.," We determined whether there are distance biases within these subclasses, and found that the weakly barred galaxies are at slightly larger distances: galaxies with type AB are at a median distance of Mpc, unbarred galaxies at Mpc, and strongly barred galaxies at Mpc." + We also found that the early-type galaxies iu our saniple are more distant: 7=(03 are at a median distance of MMpe. whereas £Z—Lo5aud T75 are at median distances of MAIpe aud MM»pc. respectively.," We also found that the early-type galaxies in our sample are more distant: $T=0-3$ are at a median distance of Mpc, whereas $T=4-5$ and $T >5$ are at median distances of Mpc and Mpc, respectively." + These biases are accounted for when we analyze propertics dependent on the distance. as detailed below.," These biases are accounted for when we analyze properties dependent on the distance, as detailed below." + hnuages were taken with the NIC3 camera (pixel size ppixel 1) of NICMOS ou theLST using the broad- FLGOW filter (equivalent to a erouud-based Z£-baud filter). aud the narrow-haud FLS7TN filter.," Images were taken with the NIC3 camera (pixel size $^{-1}$ ) of NICMOS on the using the broad-band F160W filter (equivalent to a ground-based $H$ -band filter), and the narrow-band F187N filter." +" The latter filter (AAZAz 1X) coutaius the emission line of Pad aud the adjaceut coutimmuu at 1.57 jn. The field of view of the Πω is 51.27«51.2"", which in our galaxies corresponds to the central 175peΌρο depending upon the distance to the galaxy."," The latter filter $\Delta \lambda/\lambda +\simeq 1\%$ ) contains the emission line of $\alpha$ and the adjacent continuum at $1.87\,\mu$ m. The field of view of the images is $51.2\arcsec \times 51.2\arcsec$, which in our galaxies corresponds to the central $175\,{\rm pc}- 5\,{\rm kpc}$, depending upon the distance to the galaxy." + The images were reduced following staudard procedures (see Alouso-Uerrero et al., The images were reduced following standard procedures (see Alonso-Herrero et al. + 2000 for more details)., 2000 for more details). + The aneular resolution (FWIIAL) of the NIC? images is0.37.. as measured from the poiut spread function (PSF) of stars iu the images.," The angular resolution (FWHM) of the NIC3 images is, as measured from the point spread function (PSF) of stars in the images." + This corresponds to typical spatial resolutions of between Lppe and ppc for the galaxies in our sample. using the distances given in Table 1.," This corresponds to typical spatial resolutions of between pc and pc for the galaxies in our sample, using the distances given in Table 1." + The flux calibration of the FIGOW aud FISTN images was performed using conversion factors based upon measurements of the standard star P330-E. taken duiug the Servicing Mission. Observatory. Verification (SMOV) progrann (M. J. Rieke. private communication 1999).," The flux calibration of the F160W and F187N images was performed using conversion factors based upon measurements of the standard star P330-E, taken during the Servicing Mission Observatory Verification (SMOV) program (M. J. Rieke, private communication 1999)." + Uufortuuatelv. there are no observations available of the contiuuuni adjacent to Pan. so we used the flux calibrated nuages at 1.641 as coutinume for the F187N nuages.," Unfortunately, there are no observations available of the continuum adjacent to $\alpha$, so we used the flux calibrated images at $1.6\,\mu$ m as continuum for the F187N images." + As discussed. tn Miiolino. et al. (, As discussed in Maiolino et al. ( +20003. ideally narrow-baud coutinuau inages on both sides of the οπήΙον liue are needed to perform an accurate continui subtraction which takes mto account the spatial distribution of the extinction.,"2000), ideally narrow-band continuum images on both sides of the emission line are needed to perform an accurate continuum subtraction which takes into account the spatial distribution of the extinction." +" We fine-tuned the scaliug of the coutimm,4", We fine-tuned the scaling of the continuum +The determination of the dust temperature in SALGs is thus very dillieult. and vet the derived SAIC) luminosity is a strong power of temperature.,"The determination of the dust temperature in SMGs is thus very difficult, and yet the derived SMG luminosity is a strong power of temperature." + Thus if dust temperatures are uncertain to just a factor of 2. the SM. luminosity. can be uncertain by more than an order of magnitude.," Thus if dust temperatures are uncertain to just a factor of 2, the SMG luminosity can be uncertain by more than an order of magnitude." + The addition of data points. or simply flux limits. at 70 and. 160/422 in the observed. frame will provide useful now constraints to the underlving dust. temperature and. start to solve this problem.," The addition of data points, or simply flux limits, at 70 and $\mu$ m in the observed frame will provide useful new constraints to the underlying dust temperature and start to solve this problem." + Pope ct al. (, Pope et al. ( +"2006). for example. use Spitzer data in the GOODS-N region combined. with the GOODS-N ""supermap'! to conclude that subnin sources on average have a cooler dust temperature than local ULIRGS.","2006), for example, use Spitzer data in the GOODS-N region combined with the GOODS-N 'supermap' to conclude that submm sources on average have a cooler dust temperature than local ULIRGs." + Similar conclusions are reached by Kovacs ct al. (, Similar conclusions are reached by Kovacs et al. ( +2006) auc Chapman et al. (,2006) and Chapman et al. ( +2005).,2005). + Ehis leads to an over-estimate of subnim source bolometric luminosities ifa local ULIIC: SED is assumed., This leads to an over-estimate of submm source bolometric luminosities if a local ULIRG SED is assumed. + Moreover. Efstathiou Itowan-lItobinson (2003) iive suggested. that some SAIGs have a much cooler dus emperature than would be the case if they were simply igh-redshift ULLIiCGs.," Moreover, Efstathiou Rowan-Robinson (2003) have suggested that some SMGs have a much cooler dust temperature than would be the case if they were simply high-redshift ULIRGs." + These svstems would be better fitte » a cool CE-—20.301k) cirrus-like SED. implying a lower redshift and less extreme star formation rate ancl far-LR uminosity than would otherwise be thought.," These systems would be better fitted by a cool $\sim$ 20–30K) cirrus-like SED, implying a lower redshift and less extreme star formation rate and far-IR luminosity than would otherwise be thought." + The overal range of galaxy properties in the SALG population is also still unclear., The overall range of galaxy properties in the SMG population is also still unclear. + While the bulk appear to lie at z~2.5. as founc w the spectroscopic followup of radio-identified SMCs by Chapman et al. (," While the bulk appear to lie at $\sim$ 2.5, as found by the spectroscopic followup of radio-identified SMGs by Chapman et al. (" +2005). even in that work several much lower redshift sources were found (eg.,"2005), even in that work several much lower redshift sources were found (eg." + SMM 030226.17|000624.5. aka.," SMM J030226.17+000624.5, aka." + CUDSS 35. which has a spectroscopic redshift of OSS (Clements et ab.," CUDSS 3.8, which has a spectroscopic redshift of 0.088 (Clements et al.," + 2004))., 2004)). + Some of these low redshift objects may in fact be foreground. eeavitational lenses of xickeround SAGs (Chapman et al..," Some of these low redshift objects may in fact be foreground gravitational lenses of background SMGs (Chapman et al.," + 2002)., 2002). + An examination of the optical-to-Far-L1t. SED of such sources would allow us o sav whether a lensed background: source is likely. or if he observed submm emission could be accounted for by the oesence of an unexpectedly large mass of cold. cirrusctype. dust at low redshift.," An examination of the optical-to-far-IR SED of such sources would allow us to say whether a lensed background source is likely, or if the observed submm emission could be accounted for by the presence of an unexpectedly large mass of cold, cirrus-type, dust at low redshift." + Despite much detailed study. the overall stellar population in SMCs remains dillicult to trace since the zu-Hi luminosity is clominatec by high mass voung stars.," Despite much detailed study, the overall stellar population in SMGs remains difficult to trace since the far-IR luminosity is dominated by high mass young stars." + Ixnowledge of this is important since it will indicate the evolutionary status of these svstems., Knowledge of this is important since it will indicate the evolutionary status of these systems. + This also relates to he initial mass function (AIF) of the underlving starburst., This also relates to the initial mass function (IMF) of the underlying starburst. + Baueh οἱ al. (, Baugh et al. ( +2005) have suggested that starbursts SMCs aave an LME skewed to high mass so that the overall stellar mass will be less than otherwise expected.,2005) have suggested that starbursts SMGs have an IMF skewed to high mass so that the overall stellar mass will be less than otherwise expected. + This is the only wav in which the SAIGs can be accounted for in their semi-analytic models of galaxy. formation., This is the only way in which the SMGs can be accounted for in their semi-analytic models of galaxy formation. + Since SMGs are far away and intrinsically optically faint. the presence of lower mass stars is poorly constrained by optical ancl near-Lht observations.," Since SMGs are far away and intrinsically optically faint, the presence of lower mass stars is poorly constrained by optical and near-IR observations." + The flux received. in the optical corresponds to the rest-frame UV ancl will also be dominated by voung stars., The flux received in the optical corresponds to the rest-frame UV and will also be dominated by young stars. + The 1.65 peak in the SED of normal galaxies due to the bulk of the stellar population (Sawicki. 2002) is redshiltec to μαι at ze 2.5 (Simpson Eisenhardt. 1999).," The $\mu$ m peak in the SED of normal galaxies due to the bulk of the stellar population (Sawicki, 2002) is redshifted to $\mu$ m at $\sim$ 2.5 (Simpson Eisenhardt, 1999)." + Observations in the mic-LR. from 3 to δ sam are thus ideally suited to placing constraints on the overall stellar mass of these systems (see eg.," Observations in the mid-IR, from 3 to 8 $\mu$ m are thus ideally suited to placing constraints on the overall stellar mass of these systems (see eg." + Borvs et al.," Borys et al.," + 2005)., 2005). + The Spitzer Space Observatory. with. instruments operating from 3.6 to. 160;mm (Werner et al..," The Spitzer Space Observatory, with instruments operating from 3.6 to $\mu$ m (Werner et al.," +. 2004) can provide the necessary micl-to-far-LR Fluxes required to fill the SED gap between observed. [rame wavelengths of 2// and S5Ofan required by the studies described above., 2004) can provide the necessary mid-to-far-IR fluxes required to fill the SED gap between observed frame wavelengths of $\mu$ m and $\mu$ m required by the studies described above. + SED fitting (eg., SED fitting (eg. + Rowan-Robinson et al. 2003) over this broad wavelength range can determine the role of obscured αν (Farrah et al.," Rowan-Robinson et al, 2003) over this broad wavelength range can determine the role of obscured AGN (Farrah et al.," + 2003). examine the nature of the dust emission. and examine the bulk of the stellar population.," 2003), examine the nature of the dust emission, and examine the bulk of the stellar population." + These same SED fitting methods are also capable of providing good photometric redshift estimates (lowan-Robinson et al.," These same SED fitting methods are also capable of providing good photometric redshift estimates (Rowan-Robinson et al.," + 2005: Babbedec et al.," 2005; Babbedge et al.," + 2006). especially if deep optical and/or near-LR. data are also available.," 2006), especially if deep optical and/or near-IR data are also available." + Previous attempts at photometric redshift estimation for SAIGs have set. only weak constraints on redshifts either using optical and near-H1 data (eg., Previous attempts at photometric redshift estimation for SMGs have set only weak constraints on redshifts either using optical and near-IR data (eg. + Clements et al..," Clements et al.," + 2004) or using a combination of racio and submam data (eg., 2004) or using a combination of radio and submm data (eg. + Arctxaga et al..," Aretxaga et al.," + 2007)., 2007). + The addition of Spitzer data allows for much more accurate redshift estimation. possibly as good as zz(L1|z) 0.04 (Rowan-Robinson et al 2007).," The addition of Spitzer data allows for much more accurate redshift estimation, possibly as good as $\Delta z / (1+z) \sim$ 0.04 (Rowan-Robinson et al 2007)." + The ellorts necessary to acquire spectroscopic redshifts for large samples of SMGs (c.g. Chapman et al., The efforts necessary to acquire spectroscopic redshifts for large samples of SMGs (e.g. Chapman et al. + 2005) might thus be avoiclect., 2005) might thus be avoided. + Spitzer studies o£ SCUBA sources to date have generally been based on relatively small samples of sources which are often. as here. pre-selected to have radio associations.," Spitzer studies of SCUBA sources to date have generally been based on relatively small samples of sources which are often, as here, pre-selected to have radio associations." + Ivison et al. (, Ivison et al. ( +2004) looked. at a sample of 9 NLAMDO selected sources (1.2mum) of which 4 were also SCUBA sources. while Fraver et al (2004) examinecl racio sources in the Spitzer First Look Survey of which 7 had z36 detections with SCUBA.,"2004) looked at a sample of 9 MAMBO selected sources (1.2mm) of which 4 were also SCUBA sources, while Frayer et al (2004) examined radio sources in the Spitzer First Look Survey of which 7 had $> 3\sigma$ detections with SCUBA." + Eeami et al. (, Egami et al. ( +2004) similarly looked at racio selected sources. this time in the Lockman Lole East GPO survev. of which 7 were SCUBA sources.,"2004) similarly looked at radio selected sources, this time in the Lockman Hole East GTO survey, of which 7 were SCUBA sources." + In all cases the SCUBA sources were found to have properties similar to hose expected of z=0.54 far-LR luminous galaxies., In all cases the SCUBA sources were found to have properties similar to those expected of z=0.5—4 far-IR luminous galaxies. + \Licl-LR. colours were used by νίκος et al., Mid-IR colours were used by Ivison et al. + ancl braver et al., and Frayer et al. + o identify AGN powered. sources. indicating that about of the SCUBA sources are starburst powered. a result confirmed. by URS mid-LR spectroscopy of smaller. samples (ce.," to identify AGN powered sources, indicating that about of the SCUBA sources are starburst powered, a result confirmed by IRS mid-IR spectroscopy of smaller samples (eg." + Valiante et al..," Valiante et al.," + 2007)., 2007). + An interesting aspect of the Ivison et al., An interesting aspect of the Ivison et al. + work is that nearly all of the NLAMBO/SCUD.A sources are identified at άμα at Dux limits comparable to those of he SWIRE survey discussed here., work is that nearly all of the MAMBO/SCUBA sources are identified at $\mu$ m at flux limits comparable to those of the SWIRE survey discussed here. + The largest Spitzer study of submim sources to date is that of Pope et al. (, The largest Spitzer study of submm sources to date is that of Pope et al. ( +"2006) using he GOODS-N Spitzer data and the GOODS-N. submm ""üaper-map'. which combines photometry. jigele-map and scan-map subnun observations into a single laree field (165 aremin?) (Borvs et al.","2006) using the GOODS-N Spitzer data and the GOODS-N submm 'super-map', which combines photometry, jiggle-map and scan-map submm observations into a single large field (165 $^2$ ) (Borys et al.," + 2003)., 2003). +" Of the 35 submim sources in the ""super-map 21 have secure Spitzer identifications with plausible counterparts for another 12.", Of the 35 submm sources in the 'super-map' 21 have secure Spitzer identifications with plausible counterparts for another 12. + An alternative. statistical approach to examining the subnin properties of Spitzer sources was conducted by Serjeant et. al. (," An alternative, statistical approach to examining the submm properties of Spitzer sources was conducted by Serjeant et al. (" +2004). who stacked SCUBA data from the SmJy survey (Scott et al..,"2004), who stacked SCUBA data from the 8mJy survey (Scott et al.," + 2002) at the positions of Spitzer sources in the Early Release Observations (IEgami et al..," 2002) at the positions of Spitzer sources in the Early Release Observations (Egami et al.," + 2004: Lluang et al..," 2004; Huang et al.," + 2004) to produce average subnini properties for various classes of Spitzer object., 2004) to produce average submm properties for various classes of Spitzer object. + Statistical detections are made for 5.8 and S ya. ancl marginally for 24m sources.," Statistical detections are made for 5.8 and 8 $\mu$ m, and marginally for $\mu$ m sources." + Dye ct al. (, Dye et al. ( +2006) produce similar results for objects in the CUDSS survey.,2006) produce similar results for objects in the CUDSS survey. + In summary. our understanding of the properties of submum sources in the Spitzer wavebancls is at à relatively carly stage.," In summary, our understanding of the properties of submm sources in the Spitzer wavebands is at a relatively early stage." + These results so far confirm that the submnm population is mace up of objects not too dissimilar from local. ULIRGs., These results so far confirm that the submm population is made up of objects not too dissimilar from local ULIRGs. + The rest of the paper is structured as follows., The rest of the paper is structured as follows. + In Section 2 we provide a brief summary. of the survey. data that is the basis for the current paper., In Section 2 we provide a brief summary of the survey data that is the basis for the current paper. + Section 3. describes our results for identifving SILADES/radio sources with SWIRE, Section 3 describes our results for identifying SHADES/radio sources with SWIRE + , +"electrous. the required CR electron pressure is negligible compared to the total bubble pressure. which may instead be dominated by other components. c.g.. thermal eas, CR protous. or magnetic fields. (","electrons, the required CR electron pressure is negligible compared to the total bubble pressure, which may instead be dominated by other components, e.g., thermal gas, CR protons, or magnetic fields. (" +2) Lf the gauunuaax enission is mainly due to CR protons. the required CR protou is uch higher. probably dominating the totalbubble pasenpressure.,"2) If the gamma-ray emission is mainly due to CR protons, the required CR proton pressure is much higher, probably dominating the total bubble pressure." + Oue of the main goals of this paper is to study the role of shear viscosity ou the evolution of the bubbles in the jet scenario., One of the main goals of this paper is to study the role of shear viscosity on the evolution of the bubbles in the jet scenario. +" This study is mainly motivatedby our xevious jet simulations presented in Paper L where the IWelvin-Uechuholtz (NID) aud. potential Ravleigh-Tavlor (RT) instabilities develop at the edees of the resulting CR nibbles, strikingly iuc with smooth edges ofthe observed. bubbles."," This study is mainly motivated by our previous jet simulations presented in Paper I, where the Kelvin-Helmholtz (KH) and potential Rayleigh-Taylor (RT) instabilities develop at the edges of the resulting CR bubbles, strikingly inconsistent with smooth edges of the observed bubbles." +c sen Sunoothbubble edges suggest hat the instabilities are effecively suppressed by some additioual which works ou sinall scales along he wholebubble pisses.surface.," Smooth bubble edges suggest that the instabilities are effectively suppressed by some additional physics, which works on small scales along the whole bubble surface." + Viscosity is an ideal candidate uechanisin to fulfill this purpose., Viscosity is an ideal candidate mechanism to fulfill this purpose. + Iu a fully ionized. uunagnuetized. thermal plasma. the dvuaic viscosity coefficient is (Bragiuskii 1958: 1962]): where fis the temperature of the plasiua in I&elviu aud In Ais the Coulomb logarithin.," In a fully ionized, unmagnetized, thermal plasma, the dynamic viscosity coefficient is \citealt{braginskii58}; ; \citealt{spitzer62}) ): where $T$ is the temperature of the plasma in Kelvin and $\text{ln }\Lambda$ is the Coulomb logarithm." + Oue important property of the viscosity is that it inercases dramatically with ofeas temperature (haX T?), One important property of the viscosity is that it increases dramatically with gas temperature $\mu_{\rm visc} \propto T^{5/2}$ ). + For exaniple. the value μις duereases from 0.06 to G000οcnts+ when teniperature ducreases from 109 to 105 Ik. As shown in Paper L the AGN event induces a stroug shock propagating iuto the hot halo gas. which heats the gas to tens to hundreds of keV at carly times.," For example, the value of $\mu_{\rm visc}$ increases from $0.06$ to $6000\text{ g cm}^{-1}\text{ s}^{-1}$ when temperature increases from $10^{6}$ to $10^{8}$ K. As shown in Paper I, the AGN jet event induces a strong shock propagating into the hot halo gas, which heats the gas to tens to hundreds of keV at early times." + The eas telmperature drops as the eas expauds into the halo. but even at the current time. the shocked gas still las teiiperatures of a few keV. Large viscosity in such hot eas av potentially plav a siguificaut role iu the evolutiou of the bubbles Guore generally AGNbubbles). in particular. suppressing the development of WI and RT instabilities.," The gas temperature drops as the gas expands into the halo, but even at the current time, the shocked gas still has temperatures of a few keV. Large viscosity in such hot gas may potentially play a significant role in the evolution of the bubbles (more generally AGN bubbles), in particular, suppressing the development of KH and RT instabilities." + Uukuown magnetic ficlds may suppress viscosity across Ποια lines. but as we show iu this paper. a very small fraction (less than 1'4)) of the viscosity im equation (5)) is capable of suppressing these iustabilities.," Unknown magnetic fields may suppress viscosity across field lines, but as we show in this paper, a very small fraction (less than ) of the viscosity in equation \ref{equvisc}) ) is capable of suppressing these instabilities." + Unlike the theories of accretion disks. where the role of viscosity is greatly appreciated. theoretical/mmucrica studies of ACNthe jets often ignore viscosity.," Unlike the theories of accretion disks, where the role of viscosity is greatly appreciated, theoretical/numerical studies of AGN jets often ignore viscosity." + One reason for this neglect is difficulty in attributing observationa features directly with the effects of viscosity: the smooth edges of the Ferinzbubbles may provide an unusua opportunity to place such observational constraints., One reason for this neglect is the difficulty in attributing observational features directly with the effects of viscosity; the smooth edges of the bubbles may provide an unusual opportunity to place such observational constraints. + Suiuilu smooth edges have also been observed iu many radio bubbles iu galaxy clusters. which motivate Revuoldsetal.(2005). to study the role of viscosity ou the evolution of buovantly rising bubbles.," Similar smooth edges have also been observed in many radio bubbles in galaxy clusters, which motivated \citet{reynolds05} to study the role of viscosity on the evolution of buoyantly rising bubbles." + These studies also found that modest levels of viscosity could stabilize Ravleigh-Tavlor and Iselvin-Uelmbolz instabilities. allowing the bubbles to maintain their integrity.," These studies also found that modest levels of viscosity could stabilize Rayleigh-Taylor and Kelvin-Helmholz instabilities, allowing the bubbles to maintain their integrity." + Towever. the uunuerical study of Revuoldsetal.(2005) only cousidered the buovaut rise of initially static bubbles. side-steppiug the initial jet-diiven inflation of the bubble.," However, the numerical study of \citet{reynolds05} only considered the buoyant rise of initially static bubbles, side-stepping the initial jet-driven inflation of the bubble." + As they acknowledge. besides excluding the effect of the jet on its surroundings (such as driving stroug shocks). this leaves out complex iuterual motions witlin the bubble whic' arise during the inflation phase.," As they acknowledge, besides excluding the effect of the jet on its surroundings (such as driving strong shocks), this leaves out complex internal motions within the bubble which arise during the inflation phase." + By directly simulatiue iasthe ACNME jet. we take such effects iio account.," By directly simulating the AGN jet, we take such effects into account." + We fiud iuter cktfows within the bubble contribute strongly to the development of fiuid instabilities at the bubble surface. aud cannot be ignored: indeed. viscosity plavs a critical role im mitigating sucht backfows.," We find that internal backflows within the bubble contribute strongly to the development of fluid instabilities at the bubble surface, and cannot be ignored; indeed, viscosity plays a critical role in mitigating such backflows." + Iu this paper. we adopt a constaut. isotropic Viscosity aud study how the results vary with different values of Viscosity mb a series of simulations (sce Table 1).," In this paper, we adopt a constant, isotropic viscosity and study how the results vary with different values of viscosity in a series of simulations (see Table 1)." + This simplified approach. which was also adopted by Revuoldsetal. 2005.. allows us to make a preliminary assessinenut of howbubble evolution might be affected by viscosity (seco Figure 2)).," This simplified approach, which was also adopted by \citealt{reynolds05}, allows us to make a preliminary assessment of how bubble evolution might be affected by viscosity (see Figure \ref{plot2}) )." + The true nature of viscosity here is hiehlv uucertain., The true nature of viscosity here is highly uncertain. + For instance. equation (5)) describes the isoticpic viscosity coefficient iu an munagnetizec. hot plasma.but the eas/plasima in aud outside the bubbles contains maguetic fields. which makes viscosity anisotropic. as it is chormously suppressed (bv a factor 10273 across field lines;," For instance, equation \ref{equvisc}) ) describes the isotropic viscosity coefficient in an unmagnetized hot plasma, but the gas/plasma in and outside the bubbles contains magnetic fields, which makes viscosity anisotropic, as it is enormously suppressed (by a factor $\sim 10^{23}$ ) across field lines." + The exact value of viscosity in a turbulent medi with taneled field Hues is uukuown. although perhaps in analogy with thermal conduction (Naravan&6Medyvedev2001). values ~130% of the Dragimski-Spitzer value are plausible.," The exact value of viscosity in a turbulent medium with tangled field lines is unknown, although perhaps in analogy with thermal conduction \citep{narayan01}, values $\sim 1-30\%$ of the Braginskii-Spitzer value are plausible." + The value couldbe considerably sinaller if the field is coherent: iustance. neurlv-parallel magnetic fold lines at the trbubble surface. as sugsested by sharpbubble edees (see Sec.," The value could be considerably smaller if the field is coherent: for instance, nearly-parallel magnetic field lines at the bubble surface, as suggested by sharp bubble edges (see Sec." + 3.2 of Paper I. sjenificauflv suppress momentum transport across mawbubble edges. although some fangliug of the field hereperhaps due to the instabilities itself.could still allow a non-neeligible value.," 3.2 of Paper I), may significantly suppress momentum transport across bubble edges, although some tangling of the field here–perhaps due to the instabilities itself–could still allow a non-negligible value." + The uature aud level of viscosity in thebubble iuterior are even more uncertain. as the thermal eas there is extremely hot aud underdeuse: the formal Coulonib niean free path: is so large that it is effectively collisiouless.," The nature and level of viscosity in the bubble interior are even more uncertain, as the thermal gas there is extremely hot and underdense; the formal Coulomb mean free path: is so large that it is effectively collisionless." + Thus. while we compare the values of viscosity that we use to theBragiuski-Spitzer value to illustrate its," Thus, while we compare the values of viscosity that we use to theBraginskii-Spitzer value to illustrate its" +Two spectra of this peculiar and strongly magnetic star were obtained with FEROS.,Two spectra of this peculiar and strongly magnetic star were obtained with FEROS. + The spectral lines show magnetic Zeeman splitting or broadening and rotational broadening., The spectral lines show magnetic Zeeman splitting or broadening and rotational broadening. + Rare earth clement lines found in the spectra include andtextscibL. among others.," Rare earth element lines found in the spectra include and, among others." + These lines are relatively weak in comparison with most peculiar stars., These lines are relatively weak in comparison with most peculiar stars. + Direct. measurements of the field. from. split. Zeeman components of the line reveal a magnetic field. modulus of κα for one spectrum ancl ΚΚ for a second observation., Direct measurements of the field from split Zeeman components of the line reveal a magnetic field modulus of kG for one spectrum and kG for a second observation. + In refsv158450. the spectral region with the line is shown together with a synthetic spectrum calculated or an kkC. field., In \\ref{sy158450} the spectral region with the line is shown together with a synthetic spectrum calculated for an kG field. + Despite the strong field only a small number of lines demonstrate Zeeman splitting., Despite the strong field only a small number of lines demonstrate Zeeman splitting. + The main reason is rotational broadening., The main reason is rotational broadening. + The line has doublet splitting corresponding to a magnetic field oEF9.9 κα. The longitucdinal magnetic field was found to vary oetween —2.92 to 0.51 ΚΚ over several days (Ixudrvavtsevetal. 2006)., The line has doublet splitting corresponding to a magnetic field of kG. The longitudinal magnetic field was found to vary between $-2.92$ to $+0.81$ kG over several days \citep{Kudr06}. +. Only four observations of this star have been xiblished. and they are consistent with the rotational period ound from the photometry.," Only four observations of this star have been published, and they are consistent with the rotational period found from the photometry." + reff158450 presents an amplitude spectrum of the ASAS xhotometry. while refbel58450 shows the longitudinal magnetic field. phased with the photometric S.524-d. period.," \\ref{ft158450} presents an amplitude spectrum of the ASAS photometry, while \\ref{be158450} shows the longitudinal magnetic field phased with the photometric 8.524-d period." + In the Catalogue ofComponents of Double and Multiple stars (Dommangetq&Ἂνς2002). this star is noted to be a binary star with a faint. mmag component at distance of aaresce.," In the Catalogue of Components of Double and Multiple stars \citep{Dommanget02}, this star is noted to be a binary star with a faint mag component at distance of arcsec." + Alartinez&Wurtz(1994) observed. 1158450 photometrically for about hh to search for rapid variations., \citet{Mart94} observed 158450 photometrically for about h to search for rapid variations. + This result was uncertain and further similar observations would be useful., This result was uncertain and further similar observations would be useful. + ‘This star has very strong lines of while other lines of rare earth elements such as are also present., This star has very strong lines of while other lines of rare earth elements such as are also present. + Zeeman splitting is visible in the line as shown in refsv 162316.., Zeeman splitting is visible in the line as shown in \\ref{sy162316}. +". ""Ehis line is a blend. but. comparison with a synthetic spectrum proves the presence of a magnetic field."," This line is a blend, but comparison with a synthetic spectrum proves the presence of a magnetic field." + The [line also shows a doublet structure of Zeeman components., The line also shows a doublet structure of Zeeman components. + Lines with low Landé factors are narrower than other lines., Lines with low Landé factors are narrower than other lines. + ASAS photometry shows variability with a probable rotation period of dd. A clear peak is visible in the amplitude, ASAS photometry shows variability with a probable rotation period of d. A clear peak is visible in the amplitude + =0.155... which here is more au estimate lor the sensitivity of the methoc used in the search [or variability. for additional fluctuations witha au amplitude much higher than this value would be required to significantly increase the minimum y7-stun inEq. 3.2.3.," =, which here is more an estimate for the sensitivity of the method used in the search for variability, for additional fluctuations witha an amplitude much higher than this value would be required to significantly increase the minimum $\chi^2$ -sum inEq. \ref{18}." + This data iu this enerey[n range[n] should contain a large[n] nunber of events. but are poteutially problematic because of the large width of the PSF.," This data in this energy range should contain a large number of events, but are potentially problematic because of the large width of the PSF." + Systematic problems were evident at lower euergies. aud we do uot know very well to what extent the data at 100-200 MeV are α[[οςος.," Systematic problems were evident at lower energies, and we do not know very well to what extent the data at 100–300 MeV are affected." + The scaling parameter of cilftse emission. Cj has best-lit values that are characterized by =0.132 so the scatter ini Csqug is tuarginally larger than the systematic error iu the absolute calibration.," The scaling parameter of diffuse emission, $\gm$, has best-fit values that are characterized by =0.132 so the scatter in $\gm$ is marginally larger than the systematic error in the absolute calibration." + The best-fit constaut Παν would be F(100—300MeV)) 229.9- forH whichη the minimal.η value ofH tlie V7> sum aud the eiauce probabilitymu ofH drawingH tlie measurect distribution given a coustaut [Iux. the gooduess-of-lit. would be," The best-fit constant flux would be ) = for which the minimal value of the $\chi^2$ sum and the chance probability of drawing the measured distribution given a constant flux, the goodness-of-fit, would be ." +of maguitude when the vortex weakens frou 4=2 to Y=3545.,of magnitude when the vortex weakens from $\chi=2$ to $\chi=3.5$. +" The strong dependence of migration rates on the backeround surface densitv profile opeus up the possibility of halting vortex migration at special locations in the disk. where the local eradieut of surface density is σα,"," The strong dependence of migration rates on the background surface density profile opens up the possibility of halting vortex migration at special locations in the disk, where the local gradient of surface density is small." + This is explored using a density profile as depicted in the top panel of Fie. 12.., This is explored using a density profile as depicted in the top panel of Fig. \ref{figbumpdens}. + The corresponding profile of a=—dlogX/dlosr is shown m the bottom panel of Fig. 12.., The corresponding profile of $\alpha=-d\log \Sigma/ d\log r$ is shown in the bottom panel of Fig. \ref{figbumpdens}. + From the discussion above we expect a vortex to mierate inwards outside r= ry. where ac0. and outward inside ¢=ry. where a<0.," From the discussion above we expect a vortex to migrate inwards outside $r=r_0$ , where $\alpha>0$, and outward inside $r=r_0$, where $\alpha<0$." + Iu this coufiguration. r=ry is an equilibrimn radius for migrating vortices.," In this configuration, $r=r_0$ is an equilibrium radius for migrating vortices." + We have put in a stroug vortex. with initial velocity erturbation amplitude of 3e./l over a scale Ly. at (fry=15 in a disk with My=O.lry.," We have put in a strong vortex, with initial velocity perturbation amplitude of $3c_s/4$ over a scale $H_0$, at $r/r_0=1.5$ in a disk with $H_0=0.1r_0$." + With such a strong vortex.we make sure it docs not dissipate before reaching the equilibrimm radius.," With such a strong vortex,we make sure it does not dissipate before reaching the equilibrium radius." + In Fig. 13..," In Fig. \ref{figbumpmig}," + we show he tine evolution of the orbital radius of the vortex (bottoni panel). the streneth of the vortex 5. (defined by he mininnun in the relative vortcusity perturbation. top xuel). aud the local value of à. (120iddle panel).," we show the time evolution of the orbital radius of the vortex (bottom panel), the strength of the vortex $S_\mathrm{v}$ (defined by the minimum in the relative vortensity perturbation, top panel), and the local value of $\alpha$ (middle panel)." + From the top pancl we see that the vortex gets weaker with respect to the backeround flow. partly because of uuuerical diffusion. partly because of the uueration itself.," From the top panel we see that the vortex gets weaker with respect to the background flow, partly because of numerical diffusion, partly because of the migration itself." + Since the vortex. being a negative perturbation iu vortcusity. is moving iuto a region of lower vorteusity. the relative perturbation is expected to go down. as observed in Fig. 13..," Since the vortex, being a negative perturbation in vortensity, is moving into a region of lower vortensity, the relative perturbation is expected to go down, as observed in Fig. \ref{figbumpmig}." + Results for two different resolutfious are shown iu Fig. 13:, Results for two different resolutions are shown in Fig. \ref{figbumpmig}; + the evolution of ὧν that appears similar iu both cases is due to nieration. while differences are most likely caused by uumnerical diffusion.," the evolution of $S_\mathrm{v}$ that appears similar in both cases is due to migration, while differences are most likely caused by numerical diffusion." + From the bottom) panel of Fie. 13..," From the bottom panel of Fig. \ref{figbumpmig}," + we see that uieration starts off fast. slows down over time. and alinost stalls at i5=ry.," we see that migration starts off fast, slows down over time, and almost stalls at $r=r_0$." + This slowing down of mieration is completely due to the decrease in à as depicted in the uiddle panel of Fig. 13.., This slowing down of migration is completely due to the decrease in $\alpha$ as depicted in the middle panel of Fig. \ref{figbumpmig}. + At rfry=1.5. αz:LL. giviug rise to fast inward mieration.," At $r/r_0=1.5$, $\alpha\approx 4$, giving rise to fast inward migration." +" As the vortex approaches he surface density παπα, à approaches zero and uieration slows down."," As the vortex approaches the surface density maximum, $\alpha$ approaches zero and migration slows down." + Since we obtain esseutiallv the sale result for both resolutions. we conclude that the wilting of inward wueration ix due to r=ry beine an equilibrium radius rather than due to the vortex dissipating.," Since we obtain essentially the same result for both resolutions, we conclude that the halting of inward migration is due to $r=r_0$ being an equilibrium radius rather than due to the vortex dissipating." + This therefore provides an example of vortex rapping at a surtace density bunip., This therefore provides an example of vortex trapping at a surface density bump. + We have ddeutiied a mechanism for angular iuonientuni exchange between ai vortex aud the surrounding Saseous disk. which leads to orbital nueration of the vortex.," We have identified a mechanism for angular momentum exchange between a vortex and the surrounding gaseous disk, which leads to orbital migration of the vortex." + The vortex excites spiral density waves Παπίας and outside its orbit that will iu eeneral be of unequal streugth., The vortex excites spiral density waves inside and outside its orbit that will in general be of unequal strength. + Geometrical effects favor the outer wave. while a backeround vorteusitv eracicut in the disk leads to an asvnunetric vortex. favoring the wave where the vortensitv is highest.," Geometrical effects favor the outer wave, while a background vortensity gradient in the disk leads to an asymmetric vortex, favoring the wave where the vortensity is highest." + For à constaut surface density disk. the two effects nearly cancel.," For a constant surface density disk, the two effects nearly cancel." + Whenever the waves are asvuuuetric. there is an associate angular momentum change in the region around the vortex.," Whenever the waves are asymmetric, there is an associate angular momentum change in the region around the vortex." + The vortex can either shrink. or change its orbital radius.," The vortex can either shrink, or change its orbital radius." + Numerical simulations imdicate that vortex mueration can be verv fast. especially for strong vortices enmibedded im thick disks. for which we found a migration time scale of a few LOO orbits for Ifj=üO.ley.," Numerical simulations indicate that vortex migration can be very fast, especially for strong vortices embedded in thick disks, for which we found a migration time scale of a few 100 orbits for $H_0=0.1 r_0$." + Migration slows down rapidly for vortices with size s Ep) solutions. where E is the conserved cuerey of the wine Land Eg is the eucrev for the traus-fast MIID wind."," \citet{Kennel83} classified the outgoing trans-Alfvénnic MHD wind solutions into a “critical” $E=E_{\rm F}$ ) solution, “sub-critical” $EE_{\rm F}$ ) solutions, where $E$ is the conserved energy of the wind and $E_{\rm F}$ is the energy for the trans-fast MHD wind." + To reach distant regions. the critical (frans-fast MIID wind) solution aud the swper-critical (sub-fast. MITD winds) solutions," To reach distant regions, the critical (trans-fast MHD wind) solution and the super-critical (sub-fast MHD winds) solutions" +"density and time. py and /4,. are those from equations (11) and (12). respectively: Finally. the exponent n is (o be set bv matching to observations.","density and time, $\rho_1$ and $t_1$, are those from equations (11) and (12), respectively: Finally, the exponent $n$ is to be set by matching to observations." + We stress (hat the prescription in equation (27) applies to low-mass stus., We stress that the prescription in equation (27) applies to low-mass stars. + The formation of massive objects is a separate phenomenon., The formation of massive objects is a separate phenomenon. +" In our model. this occurs only in the high-density. central region of (he final, minimum-enthalpy: state."," In our model, this occurs only in the high-density, central region of the final, minimum-enthalpy state." + Equation (27) contains a nondimensional efficiency [actor e., Equation (27) contains a nondimensional efficiency factor $\epsilon$. + Since only a traction of the cloud mass turis into stars. we expect € to be well under unity.," Since only a fraction of the cloud mass turns into stars, we expect $\epsilon$ to be well under unity." + IL. lor simplicity. we assume (his parameter to be (he same in all mass shells. (hen integration of equation (27) vields the total mass per unit (me in new stars: We may convenienUy recast (his formula in terms of the effective sound speed: llere. the nondimensional quantity Z is expressed using the (raditional. polvtropic variables: Our prescription gives a finite star formation rate lor clouds of arbitrarily low density.," If, for simplicity, we assume this parameter to be the same in all mass shells, then integration of equation (27) yields the total mass per unit time in new stars: We may conveniently recast this fornula in terms of the effective sound speed: Here, the nondimensional quantity ${\cal I}$ is expressed using the traditional, polytropic variables: Our prescription gives a finite star formation rate for clouds of arbitrarily low density." + This is clearly an oversimplification., This is clearly an oversimplification. + There is no evidence. for example. that HI clouds form stars at all.," There is no evidence, for example, that HI clouds form stars at all." + Even within the molecular domain. it may be that stars form only above some threshold densitv.," Even within the molecular domain, it may be that stars form only above some threshold density." + In (heir study of the Rosette cloud complex. Williamsetal.(1995) [ound that only chunps which are strongly sell-gravitating (as assessed bv comparison of velocity dispersions. masses. and sizes) have internal stars.," In their study of the Rosette cloud complex, \citet{w95} found that only clumps which are strongly self-gravitating (as assessed by comparison of velocity dispersions, masses, and sizes) have internal stars." +" While a more complete model should account for this threshold effect. we shall not include it explicitly. but. simply limit our discussion to sell-gravitating clamps 2,44)) Chat are capable of forming stars."," While a more complete model should account for this threshold effect, we shall not include it explicitly, but simply limit our discussion to self-gravitating clumps ) that are capable of forming stars." +"pulsar interior, the line density of electrons confined to a flux-tube of radius o is simply the volume electron number density ne times the cross-sectional area associated with the flux-tube: N/L=nerf’.","pulsar interior, the line density of electrons confined to a flux-tube of radius $\hat{\rho}$ is simply the volume electron number density $n_e$ times the cross-sectional area associated with the flux-tube: $N/L = n_e \pi \hat{\rho}^2$." +" When substituted, this gives in SI units."," When substituted, this gives in SI units." + Eq. (19)), Eq. \ref{fermi1dprim}) ) + is essentially Ruderman's formula (Ruderman 1971).., is essentially Ruderman's formula \citep{1971PhRvL..27.1306R}. . +" Assuming a typical magnetic field of 105T, and taking the electron number density from (8)), yields Notice that the Fermi energy increases with magnetic field strength: this is because the electron number density increases faster than the field strength, no matter which scaling model is chosen."," Assuming a typical magnetic field of $10^8$ T, and taking the electron number density from \ref{ne_geom}) ), yields Notice that the Fermi energy increases with magnetic field strength: this is because the electron number density increases faster than the field strength, no matter which scaling model is chosen." +" This is an important, if slightly counter-intuitive, result, since the influence of the magnetic field in expressions for ep such as Eq. (19))"," This is an important, if slightly counter-intuitive, result, since the influence of the magnetic field in expressions for $\epsilon_F$ such as Eq. \ref{fermi1dprim}) )" + suggest that an increasing magnetic field strength will lower the potential barrier at the poles., suggest that an increasing magnetic field strength will lower the potential barrier at the poles. +" However, this neglects the indirect influence of B on the electron number density: increasing field strengths must lead to increased matter compression, and this must be taken into account in the Fermi energy calculation."," However, this neglects the indirect influence of $B$ on the electron number density: increasing field strengths must lead to increased matter compression, and this must be taken into account in the Fermi energy calculation." +" Note that since the surface temperature of the pulsar 7; is below 10K, equivalent in energy terms to < 100eV, then (21)) is an acceptable approximation, since in this case it is self-evident that T»«Tp»."," Note that since the surface temperature of the pulsar $T_p$ is below $10^6$ K, equivalent in energy terms to $<100$ eV, then \ref{ef_simple}) ) is an acceptable approximation, since in this case it is self-evident that $T_p \ll T_F$." +" The calculations presented here assume a 1-D model for electron motion, and therefore preclude any contribution from Landau levels."," The calculations presented here assume a 1-D model for electron motion, and therefore preclude any contribution from Landau levels." +" The Appendix details the nature of the calculation where Landau levels must be included, and where the energies are intrinsically relativistic."," The Appendix details the nature of the calculation where Landau levels must be included, and where the energies are intrinsically relativistic." + The simple 1-D description of the electron transport requires careful treatment when the magnetic field is not homogeneous., The simple 1-D description of the electron transport requires careful treatment when the magnetic field is not homogeneous. +" Magnetic field emerges from the interior predominantly at the poles; this concentration of the field lines at specific points on the surface means that there must be significant curvature inside (and outside) the star, as the field emerges from inside the iron spherical shell."," Magnetic field emerges from the interior predominantly at the poles; this concentration of the field lines at specific points on the surface means that there must be significant curvature inside (and outside) the star, as the field emerges from inside the iron spherical shell." +" Electrons constrained in the 1-D model to follow these field lines are nevertheless inertial particles, and therefore cannot instantaneously change direction."," Electrons constrained in the 1-D model to follow these field lines are nevertheless inertial particles, and therefore cannot instantaneously change direction." +" However, they are also restricted in their perpendicular motion, since they have to satisfy the Landau quantization."," However, they are also restricted in their perpendicular motion, since they have to satisfy the Landau quantization." +" In the simple 1-D model, the electrons negotiate this magnetic field curvature in a non-quantal way, since scattering into Landau levels above the ground state is not permitted; therefore the electrons must change direction to follow the field direction, without any significant locally transverse excursions; momentum conservation must be provided by the crystal lattice, and the overall energy conservation must lead to electrons losing energy to the crystal as they negotiate the curve."," In the simple 1-D model, the electrons negotiate this magnetic field curvature in a non-quantal way, since scattering into Landau levels above the ground state is not permitted; therefore the electrons must change direction to follow the field direction, without any significant locally transverse excursions; momentum conservation must be provided by the crystal lattice, and the overall energy conservation must lead to electrons losing energy to the crystal as they negotiate the curve." +" The overall effect of the magnetic inhomogeneity must be to introduce a local ‘bunching’ of electron density along the magnetic field direction in the region of greatest local curvature, that is, near the magnetic poles."," The overall effect of the magnetic inhomogeneity must be to introduce a local `bunching' of electron density along the magnetic field direction in the region of greatest local curvature, that is, near the magnetic poles." + A schematic of the situation is shown in Figure 1., A schematic of the situation is shown in Figure 1. +" Such local density fluctuations will drive an electrostatic wave along the flux tube, accelerating (and decelerating) non-local electrons (ahead and behind the curved region) that populate this tube."," Such local density fluctuations will drive an electrostatic wave along the flux tube, accelerating (and decelerating) non-local electrons (ahead and behind the curved region) that populate this tube." +" Now either this is sufficient in itself to eject electrons at the end of the tube, where the surface exists, or the electrostatic wave itself evolves non-linearly and eventually breaks, leading to the ejection of a few relatively energetic particles ahead of the wave."," Now either this is sufficient in itself to eject electrons at the end of the tube, where the surface exists, or the electrostatic wave itself evolves non-linearly and eventually breaks, leading to the ejection of a few relatively energetic particles ahead of the wave." +" Either way, it seems that such a description has the requisite element of a parallel acceleration mechanism that is self-consistent, and not dependent on any frame-transformed field component."," Either way, it seems that such a description has the requisite element of a parallel acceleration mechanism that is self-consistent, and not dependent on any frame-transformed field component." +" It is worth distinguishing between the electron temperature and the electron energy; mono-energetic beams of electrons are formally cold (that is, possess zero temperature), yet can stream in the beam direction with significant energy."," It is worth distinguishing between the electron temperature and the electron energy; mono-energetic beams of electrons are formally cold (that is, possess zero temperature), yet can stream in the beam direction with significant energy." +" In the scenario outlined above, it is assumed that the mean energy of the electrons, including any directed streaming, is less than the Fermi energy, since otherwise a significant fraction of the interior electrons would simply leak out of the flux tube into the pulsar atmosphere at the surface."," In the scenario outlined above, it is assumed that the mean energy of the electrons, including any directed streaming, is less than the Fermi energy, since otherwise a significant fraction of the interior electrons would simply leak out of the flux tube into the pulsar atmosphere at the surface." +" Whilst this might solve the electron production problem, there remains the issue of identifying the physical process that causes such streaming."," Whilst this might solve the electron production problem, there remains the issue of identifying the physical process that causes such streaming." +" For the purposes of this article, therefore, we will assume that the electrons are mostly trapped in the iron crust, just as the free electrons are trapped in a metal in a natural terrestrial context."," For the purposes of this article, therefore, we will assume that the electrons are mostly trapped in the iron crust, just as the free electrons are trapped in a metal in a natural terrestrial context." +" As in the latter case, there needs to be a mechanism that provides the necessary energy for electrons to overcome the potential barrier at the interface between the pulsar surface and the vacuum (or atmosphere), before electrons can be liberated at the surface."," As in the latter case, there needs to be a mechanism that provides the necessary energy for electrons to overcome the potential barrier at the interface between the pulsar surface and the vacuum (or atmosphere), before electrons can be liberated at the surface." +" Thermionic emission seems implausible, since the surface temperature is less than one tenth of the Fermi temperature; hence our concentration onthe (self) electric field produced by charge concentrations of electrons in density waves."," Thermionic emission seems implausible, since the surface temperature is less than one tenth of the Fermi temperature; hence our concentration onthe (self) electric field produced by charge concentrations of electrons in density waves." +Our model naturally incorporates (he fact that the mass in high redshift sheets becomes partitioned up among filaments at later times. with filaments themselves being partitioned into halos.,"Our model naturally incorporates the fact that the mass in high redshift sheets becomes partitioned up among filaments at later times, with filaments themselves being partitioned into halos." + Clearly. the model is rich in spatial. temporal ancl spatio-temporal information.," Clearly, the model is rich in spatial, temporal and spatio-temporal information." + The kev output [rom (he triaxial collapse models is an estimate of the (wpical overdensity required Lor collapse along one. two ancl three axes by redshift z.," The key output from the triaxial collapse models is an estimate of the typical overdensity required for collapse along one, two and three axes by redshift $z$." + The dotted. curves in Figure 1. show how these three ‘harriers’ depend on mass., The dotted curves in Figure \ref{randomwalk} show how these three `barriers' depend on mass. + From bottom to top. the curves show These analvlic approximations to the barriers associated wilh collapse along one. two and three axes are reasonably accurate (οι.," From bottom to top, the curves show These analytic approximations to the barriers associated with collapse along one, two and three axes are reasonably accurate (c.f." + Figure 7))., Figure \ref{shethall}) ). +" They show that the critical overdensitv for ellipsoidal collapse along all three axes. 0,4. 15 larger (han in the spherical collapse model (for which this number is ὃς)."," They show that the critical overdensity for ellipsoidal collapse along all three axes, $\delta_{ec3}$, is larger than in the spherical collapse model (for which this number is $\delta_{sc}$ )." +" Lowever. collapse along just (wo axes requires an overdensily 942 Which is almost exactly (hat in the spherical model. and collapse along one axis only requires a smaller initial overdensitv. 04,4."," However, collapse along just two axes requires an overdensity $\delta_{ec2}$ which is almost exactly that in the spherical model, and collapse along one axis only requires a smaller initial overdensity, $\delta_{ec1}$." + In this model. tidal forces enhance collapse along the first axis ancl delay. collapse along the last axis relative to the spherical collapse model (Shethetal.2001)- the expressions above quantily these ellects.," In this model, tidal forces enhance collapse along the first axis and delay collapse along the last axis relative to the spherical collapse model \citep{SMT01}- —the expressions above quantify these effects." + Note that the differences among the three critical overdensiües are larger [for larger values of σ. corresponding to ellipsoids of lower masses.," Note that the differences among the three critical overdensities are larger for larger values of $\sigma$, corresponding to ellipsoids of lower masses." + Notice that these barrier shapes depend both on a0) ancl on 94(:2)., Notice that these barrier shapes depend both on $\sigma(m)$ and on $\delta_{sc}(z)$. + The presence of these two terms reflects the fact (hat the collapse depends on the expansion history of the universe. and on the initial spectrum of fluctuations.," The presence of these two terms reflects the fact that the collapse depends on the expansion history of the universe, and on the initial spectrum of fluctuations." + What is of particular importance in what follows is (hat the barrier shapes actually depend. not on ὃς and σ individually. but on the scaling variable v=[9.(z)/o(m)|?.," What is of particular importance in what follows is that the barrier shapes actually depend, not on $\delta_{sc}$ and $\sigma$ individually, but on the scaling variable $\nu=[\delta_{sc}(z)/\sigma(m)]^2$." + In the excursion set. approach. this implies that the mass functions of sheets. filaments and halos at any given time. in any given cosmology. ancl for anv given initial fluctuation spectrum. can all be scaled to universal funcüonal forms.," In the excursion set approach, this implies that the mass functions of sheets, filaments and halos at any given time, in any given cosmology, and for any given initial fluctuation spectrum, can all be scaled to universal functional forms." + Our next step is to provide analvlic approximations to these forms., Our next step is to provide analytic approximations to these forms. +On the other hand. if the cisk is filled with vortices that interact. merge and reform. those svinmetries are broken and augular momentum can be transported at moderate rates.,"On the other hand, if the disk is filled with vortices that interact, merge and reform, those symmetries are broken and angular momentum can be transported at moderate rates." + Thus. (here is a competition between mergers of vortices (hat would reduce (he number of vortices in a given radial band. and the formation of new vortices in unoccupied radial bands.," Thus, there is a competition between mergers of vortices that would reduce the number of vortices in a given radial band, and the formation of new vortices in unoccupied radial bands." + In order to understand how vortices are created and maintained. and whether thev are isolated or fill the disk. it is necessary to determine the sources of energy and vorticity.," In order to understand how vortices are created and maintained, and whether they are isolated or fill the disk, it is necessary to determine the sources of energy and vorticity." + IXlahr demonstrated Chat a elobally unstable radial entropy. gradient in a protoplanetary disk excited Rossby waves which also broke into large-scale vortices., \citet{klahr03} demonstrated that a globally unstable radial entropy gradient in a protoplanetary disk excited Rossby waves which also broke into large-scale vortices. + Decause the length scale of the entropy gradient was of order r. the horizontal scales of the vortices were much larger (han the thickness of the disk. and so the (hud velocities were supersonic.," Because the length scale of the entropy gradient was of order $r$, the horizontal scales of the vortices were much larger than the thickness of the disk, and so the fluid velocities were supersonic." + Acoustic waves and shocks rapidlv drain the kinetic energy. [rom such vortices., Acoustic waves and shocks rapidly drain the kinetic energy from such vortices. + We plan to extend (he racial domain in our simulations aud relax the shearing box boundary conditions so Chat we may investigate racial gradients as well., We plan to extend the radial domain in our simulations and relax the shearing box boundary conditions so that we may investigate radial gradients as well. + Coherent vortices located above and below (he midplane will significantly affect (he way dust settles into the midplane., Coherent vortices located above and below the midplane will significantly affect the way dust settles into the midplane. + Two-dimensional studies have shown that vortices are very efficient al capturing and concentrating dust particles (Darge&Sonuneria1995:Tangaetal.1996:delaFuenteMarcos&Baree 2001).," Two-dimensional studies have shown that vortices are very efficient at capturing and concentrating dust particles \citep{barge95,tanga96,fuentemarcos01}." +. If the vortices are located olf the midplane. will the dust grains be inhibited [rom settling into a thin. dense sublaver?," If the vortices are located off the midplane, will the dust grains be inhibited from settling into a thin, dense sublayer?" + If the vortices have a significant vertical velocity. will they be able to sweep up grains (hat have already settled into (he midplane?," If the vortices have a significant vertical velocity, will they be able to sweep up grains that have already settled into the midplane?" + We propose that the (rapping of dust in off-midplane vortices is analogous to the formation of hail in the Earth's atinosphere: turbulent vertical velocities prevent grains from falling out of the vortices until thev have grown to some critical mass., We propose that the trapping of dust in off-midplane vortices is analogous to the formation of hail in the Earth's atmosphere; turbulent vertical velocities prevent grains from falling out of the vortices until they have grown to some critical mass. + In future work. we plan to incorporate simple Lagrangian (racking of dust grains (delaFuente 2002).. as well as two-fluid models (Cuzzietal.1993:Johansen2004).," In future work, we plan to incorporate simple Lagrangian tracking of dust grains \citep{fuentemarcos02}, as well as two-fluid models \citep{cuzzi93,johansen04}." +. DP.S.M. thanks the support of NASA Grant NAG5-10664 and NSF Grant AST-0098465., P.S.M. thanks the support of NASA Grant NAG5-10664 and NSF Grant AST-0098465. + J.A.D. thanks the NSF for support via a Graduate Student. Fellowship while at Berkeley. and now with an Astronomy Astrophysics Postdoctoral Fellowship (NSF Grant 0302146).," J.A.B. thanks the NSF for support via a Graduate Student Fellowship while at Berkeley, and now with an Astronomy Astrophysics Postdoctoral Fellowship (NSF Grant AST-0302146)." +" He also thanks the support of the Kavli Institute for Theoretical Physics (hrough NSF Grant PILY-9907949,", He also thanks the support of the Kavli Institute for Theoretical Physics through NSF Grant PHY-9907949. + Computations were carried out at the San Diego Supercomputer Center using an NPACT aware., Computations were carried out at the San Diego Supercomputer Center using an NPACI award. + The authors would like to thank Berkeley graduate student Ἁνίαι Asay-Davis lor preparing the animations that appear in the electronic version of this paper: and Professors Eugene Chiang. Geoff Marcy. and Andrew Szeri [or useful comments on the early manuscript.," The authors would like to thank Berkeley graduate student Xylar Asay-Davis for preparing the animations that appear in the electronic version of this paper; and Professors Eugene Chiang, Geoff Marcy, and Andrew Szeri for useful comments on the early manuscript." +LAIC sample is limited at 24] by the sensitivity of MIPS to Aly brighter than 9.,LMC sample is limited at [24] by the sensitivity of MIPS to $M_{[24]}$ brighter than –9. + In spite of the presence of dust shells around the longer-period. stars at this wavelength. there is still some tendency towards a relation.," In spite of the presence of dust shells around the longer-period stars at this wavelength, there is still some tendency towards a relation." + The fluxes from the shorter-period variables remain photospheric., The fluxes from the shorter-period variables remain photospheric. + From As to 8 [am essentially the same AL log? sequences are repeated., From $K_S$ to 8 $\mu$ m essentially the same $M$ – $P$ sequences are repeated. + Though SGC2004 presented a 3]. vs logP diagram. and suggested that the sequences may persist at this wavelength. hey were not as obvious as here due to the smaller numbers of stars. the limited depth of the photometry ancl possibly ueher scatter in the colours.," Though SGC2004 presented a [7] vs $P$ diagram and suggested that the sequences may persist at this wavelength, they were not as obvious as here due to the smaller numbers of stars, the limited depth of the photometry and possibly higher scatter in the colours." + As expected. [rom theoretical models. the LM stars. xing of lower metallicity. tend to reach higher bIuminosities han the galactic ones.," As expected from theoretical models, the LMC stars, being of lower metallicity, tend to reach higher luminosities than the galactic ones." + This cllect was previously remarked on bv SCGC2004 [for the As band., This effect was previously remarked on by SGC2004 for the $K_S$ band. + Croenewegen ancl DBlomnmaert. (2005) point out also that the LMC contains ueher mass stars than the NCGC6522 field., Groenewegen and Blommaert (2005) point out also that the LMC contains higher mass stars than the NGC6522 field. + Phere are many additional subtle dillerences between the AZ. log? relations which are unfortunately cilficult to quantify because of the increased scatter due to depth elfects in 66522.," There are many additional subtle differences between the $M$, $P$ relations which are unfortunately difficult to quantify because of the increased scatter due to depth effects in 6522." + In the case of the Solar Neighbourhood sample. μαι magnitudes are not available and absolute 25//m magnitudes derived from LRAS are plotted instead.," In the case of the Solar Neighbourhood sample, $\mu$ m magnitudes are not available and absolute $\mu$ m magnitudes derived from IRAS are plotted instead." + In order to determine whether the slopes of the period-magnitude relations change with wavelength. straight [ines were fitted to several of the sequences visible in refPysmags..," In order to determine whether the slopes of the period-magnitude relations change with wavelength, straight lines were fitted to several of the sequences visible in \\ref{Pvsmags}." + Phe periods were assumed free of errors., The periods were assumed free of errors. + The nomenclature of the sequences is based on that of Ita ct al. (, The nomenclature of the sequences is based on that of Ita et al. ( +2004).,2004). + Only the LMC cata were used for this part of the investigation since they show the clearest: separations., Only the LMC data were used for this part of the investigation since they show the clearest separations. + Not all of Has sequences are separate enough to include in this analysis., Not all of Ita's sequences are separate enough to include in this analysis. + Even among those that are included. and are rather poorly defined ancl may be contaminated.," Even among those that are included, $^+$ and $^-$ are rather poorly defined and may be contaminated." + The parts of period-magnitude space used for fitting are shown in rofPysmags.peceandtheresullsaregivenindablel, The parts of period-magnitude space used for fitting are shown in \\ref{Pvsmags_spec} and the results are given in Table 1. + Phels PdataforLAlC starsgivenby sciO2004hacebeenineludedintheanalgsisforcoi, The $K_S$ $P$ data for LMC stars given by SGC2004 have been included in the analysis for completeness. + As in re[Pysmags.. stars with NLACTIO + amplitudes greater than 1.0 were taken to be Miras.," As in \\ref{Pvsmags}, stars with MACHO $r$ amplitudes greater than 1.0 were taken to be Miras." + Vhis level was chosen to include carbon Miras. which tend to have lower amplitudes than AM-types (see eg. Glass Llovd Evans 2003).," This level was chosen to include carbon Miras, which tend to have lower amplitudes than M-types (see e.g. Glass Lloyd Evans 2003)." + Most. Miras [all in the € region. though smaller aumplitο stars are also included.," Most Miras fall in the C region, though smaller amplitude stars are also included." + Objects with JKx1.6 were assumed to be carbon stars (though this is not an infallible criterion) and were not included in the linear fits., Objects with $J-K_S > 1.6$ were assumed to be carbon stars (though this is not an infallible criterion) and were not included in the linear fits. + Previous work such as that ofGlass et ((1987) and Feast et ((1989) suggested that O- and C-type Miras obey essentially the same relations ab dvs. though dillering at J and. // and consequently. in Ala.," Previous work such as that of Glass et (1987) and Feast et (1989) suggested that O- and C-type Miras obey essentially the same relations at $K_S$, though differing at $J$ and $H$ and consequently in $M_{\rm Bol}$." + Vhe carbon Miras in ro[fPysmags;pecscemltoliebetowtheM sterlincarfitallxz but to be above it at longer wavelengths., The carbon Miras in \\ref{Pvsmags_spec} seem to lie below the M-star linear fit at $K_S$ but to be above it at longer wavelengths. + However. it should be noted that the sample is a small one and that the Iv and WAAC data were not taken simultaneously.," However, it should be noted that the sample is a small one and that the $K_S$ and IRAC data were not taken simultaneously." + Table 1 shows that the stars show little scatter. (σ) around the derived. period-magnitucle relations. especially in the A and. D sequences.," Table 1 shows that the stars show little scatter $\sigma$ ) around the derived period-magnitude relations, especially in the A and B sequences." + The SIHVs of these sequences have the smallest amplitudes: the € sequence. however. contains some l[arge-amplitude variables (Miras) and can be expected to show more scatter.," The SRVs of these sequences have the smallest amplitudes; the C sequence, however, contains some large-amplitude variables (Miras) and can be expected to show more scatter." + For cach of the sequences Ao. A. ο .Cand D there is no systematic change in slope with wavelength.," For each of the sequences $^+$, $^-$, $^+$, $^-$, C and D there is no systematic change in slope with wavelength." + The colours of the samples are plotted against the principal and the very long periods in refPvscols.., The colours of the samples are plotted against the principal and the very long periods in \\ref{Pvscols}. + The most. conspicuous trend. is noticed in the log P Ixus - 24] diagram. where the SRVs show a very sharp onset of excess radiation at {ον 60d.," The most conspicuous trend is noticed in the log $P$ $K_{0,S}$ - [24] diagram, where the SRVs show a very sharp onset of excess radiation at $P$ $\sim$ 60d." + This is. in elfect. an exaggerated. version of what is seen in the 15/1 excess Hog? diagram olf Alard et ((2001).," This is, in effect, an exaggerated version of what is seen in the $\mu$ m excess $P$ diagram of Alard et (2001)." + Noteworthy again is the tendeney for many. SRVs to have very red. infrared colours. comparable to. or even greater than. those of the shorter-period. Miras.," Noteworthy again is the tendency for many SRVs to have very red infrared colours, comparable to, or even greater than, those of the shorter-period Miras." + Ht should be noted. however. from Fig l1 that they are not necessarily as luminous.," It should be noted, however, from Fig \ref{Pvsmags} that they are not necessarily as luminous." + The ολές with secondary. very long periods show clear evidence. particularly at 24 yam. for the existence of dust," The SRVs with secondary very long periods show clear evidence, particularly at 24 $\mu$ m, for the existence of dust" +unresolved source (c.f.,unresolved source (c.f. + Hasinger et al. 1992))., Hasinger et al. \cite{Hasinger92}) ). + Background spectra. extracted from an annulus around the source. were appropriately scaled and subtracted from the source spectra.," Background spectra, extracted from an annulus around the source, were appropriately scaled and subtracted from the source spectra." + The combined spectrum consists of 177 net source counts., The combined spectrum consists of 177 net source counts. + The spectrum was rebinned in order to have at least 15 counts per bin., The spectrum was rebinned in order to have at least 15 counts per bin. + For our spectral analysis we used he spectral fitting program (Kaastra et al. 1996))., For our spectral analysis we used he spectral fitting program (Kaastra et al. \cite{Kaastra96}) ). + Since we want to know whether the source qualifies as the potential stellar remnant associated with RCW 86. we fitted the spectrum with several emission models both with the interstellar absorption value fixed at =1.710?! 7. the typical absorption value for the X-ray emission of the supernova remnant (Vink et al. 1997)).," Since we want to know whether the source qualifies as the potential stellar remnant associated with RCW 86, we fitted the spectrum with several emission models both with the interstellar absorption value fixed at $= 1.7\, 10^{-21}$ $^{-2}$, the typical absorption value for the X-ray emission of the supernova remnant (Vink et al. \cite{Vink97}) )," + and with aas an additional free parameter., and with as an additional free parameter. + The results are listed. in Table 3.., The results are listed in Table \ref{spectral}. + The best fit values of ffor all models seem to be in favor of a low absorption column towards the source. but also models with fixed egive acceptable reduced 47? values.," The best fit values of for all models seem to be in favor of a low absorption column towards the source, but also models with fixed give acceptable reduced $\chi^2$ values." + The fact that models with three parameters result in very low reduced 47 values (i.e. far from the 4? expectation value). suggests that the statistics of the data is not really good enough to fit models with three or more parameters.," The fact that models with three parameters result in very low reduced $\chi^2$ values (i.e. far from the $\chi^2$ expectation value), suggests that the statistics of the data is not really good enough to fit models with three or more parameters." + All models provide reasonable fits to the data with only the thin plasma model with solar abundances and fixed Nj having a reduced 47 substantially larger than |., All models provide reasonable fits to the data with only the thin plasma model with solar abundances and fixed $N_{\rm H}$ having a reduced $\chi^2$ substantially larger than 1. + The spectrum appears to be rather soft as indicated by the steep power law index. [. and the low black body temperature.," The spectrum appears to be rather soft as indicated by the steep power law index, $\Gamma$, and the low black body temperature." + We searched the four PSPC observations for possible pulsations using the Rayleigh method (Buechert et al. 1983))., We searched the four PSPC observations for possible pulsations using the Rayleigh method (Buccheri et al. \cite{Buccheri}) ). + This method is one of the most sensitive methods and it does not involve any binning of the data., This method is one of the most sensitive methods and it does not involve any binning of the data. + A sensitive method is needed as the longest PSPC observations yielded only 101 events., A sensitive method is needed as the longest PSPC observations yielded only 101 events. +" We searched in each set for pulsations 1n the perioc range 0.02 to 300 s. sampling the frequency range with step of Έα with T, the total length of the observation."," We searched in each set for pulsations in the period range 0.02 to 300 s, sampling the frequency range with step of $1/T_{\rm obs}$ with $T_{\rm obs}$ the total length of the observation." + We compared the periodograms to look for peaks showing up ui two or more periodograms at or near the same period., We compared the periodograms to look for peaks showing up in two or more periodograms at or near the same period. + Such correlations were. however. not found.," Such correlations were, however, not found." + The peak values of the Rayleigh statistic. Z7?25. imply an upper limit to the pulsec fraction of ~20%..," The peak values of the Rayleigh statistic, $Z^2_1 \sim 28$, imply an upper limit to the pulsed fraction of $\sim $." + As for the variability on the timescales of month. at first sight there is little evidence for variability as all measured PSPC count rates are consistent with a count rate of (17.0+2.8)10? ents/s. However. if we convert the Einstein and ROSAT HRI count rates to PSPC count rates using the best fit power law model in Table 3. (the conversior factors are 4.9 and 2.7. respectively) we get the following PSPC count rates (in the same order as in Table 2) (5.8+1.9)10? ents/s. (5.7+2.7)10.7 ents/s. and (9.0+2.1)10.? ents/s. The dependence of the ROSAT HRI/PSPC conversion factor on the chosen model is small )). but the conversion factor for the Einstein HRI count rates is more model dependent. varying from 4.6 to 8.0.," As for the variability on the timescales of month, at first sight there is little evidence for variability as all measured PSPC count rates are consistent with a count rate of $(17.0\pm2.8)\ 10^{-3}$ cnts/s. However, if we convert the Einstein and ROSAT HRI count rates to PSPC count rates using the best fit power law model in Table \ref{spectral} + (the conversion factors are 4.9 and 2.7, respectively) we get the following PSPC count rates (in the same order as in Table \ref{positions}) ): $(5.8\pm 1.9)\ 10^{-3}$ cnts/s, $(5.7\pm 2.7)\ 10^{-3}$ cnts/s, and $(9.0\pm 2.1)\ 10^{-3}$ cnts/s. The dependence of the ROSAT HRI/PSPC conversion factor on the chosen model is small ), but the conversion factor for the Einstein HRI count rates is more model dependent, varying from 4.6 to 8.0." + Even taking into account the model uncertainties it is clear that the observations are not consistent with a constant source count rate. although it is a strange coincidence that low count rates were only observed by the HRI instruments.," Even taking into account the model uncertainties it is clear that the observations are not consistent with a constant source count rate, although it is a strange coincidence that low count rates were only observed by the HRI instruments." + Source contamination with the PSPC instrument seems unlikely. as no other unresolved sources are seen with the HRI instruments near the point source.," Source contamination with the PSPC instrument seems unlikely, as no other unresolved sources are seen with the HRI instruments near the point source." + Therefore. the ray source is very likely variable on a time scale of months to years.," Therefore, the X-ray source is very likely variable on a time scale of months to years." + So. could this X-ray source be the stellar remnant associated with RCW 86?," So, could this X-ray source be the stellar remnant associated with RCW 86?" + The radius of the star. as inferred from the black body fit. is 1.7 km at a distance of 2.8 kpe.," The radius of the star, as inferred from the black body fit, is 1.7 km at a distance of 2.8 kpc." + This is too small for a neutron star. but the spectrum may not be a black body.," This is too small for a neutron star, but the spectrum may not be a black body." + The X-ray luminosity ts lower than the luminosity of typical AXPs. but it is consistent with the surface luminosity of young neutron stars in case pion cooling is important (Umeda et al. 2000)).," The X-ray luminosity is lower than the luminosity of typical AXPs, but it is consistent with the surface luminosity of young neutron stars in case pion cooling is important (Umeda et al. \cite{Umeda}) )." + Also emission from a black hole accreting supernova fall back, Also emission from a black hole accreting supernova fall back +major and minor axis of 18 and15”.. respectively. implying a core radius. estimated from the eeonmeltric mean of the axis. of 0.42 pc (assuming a distance of 10.5 kpc).,"major and minor axis of 18 and, respectively, implying a core radius, estimated from the geometric mean of the axis, of 0.42 pc (assuming a distance of 10.5 kpc)." + The mass of the core determined [rom the 850 j/mi observations is 2x107M.., The mass of the core determined from the 850 $\mu$ m observations is $2\times10^3$. +. Deuther et al. (, Beuther et al. ( +2002b) detected class I] methanol and water masers near (he peak position of the dust core. suggesting (hat {his is à massive star forming region in an early stage of evolution.,"2002b) detected class II methanol and water masers near the peak position of the dust core, suggesting that this is a massive star forming region in an early stage of evolution." + The upper panel of Fig., The upper panel of Fig. + G shows a contour map of the 7 mm continuum enission observed with the VLA towards IRAS 19217-1651., \ref{fig-19217maps} shows a contour map of the 7 mm continuum emission observed with the VLA towards IRAS 19217+1651. + Most. of the emission arises [rom a sinele bright source. although there is evidence of a weaker component to the north.," Most of the emission arises from a single bright source, although there is evidence of a weaker component to the north." + VLA observations at centimeter wavelengths (X. U. and Ix bands) show that emission arises from two components.," VLA observations at centimeter wavelengths (X, U, and K bands) show that emission arises from two components." + This is illustrated in the bottom panel of Fig., This is illustrated in the bottom panel of Fig. +" 6 which presents a contour map of the emission observed αἱ 22.5 Gllz. showing that the emission arises [rom a bright compact component. (labeled A). with an angular size of0.16"". and a more extended. weaker component (labeled B) located ~1"" NE of component A. with an angular size of0."," \ref{fig-19217maps} + which presents a contour map of the emission observed at 22.5 GHz, showing that the emission arises from a bright compact component (labeled A), with an angular size of, and a more extended, weaker component (labeled B) located $\sim1\arcsec$ NE of component A, with an angular size of." +"8"".. The peak of the 7 mm source coincides with component A. The cross in both panels marks (he peak position of the large dust core.", The peak of the 7 mm source coincides with component A. The cross in both panels marks the peak position of the large dust core. + The radio continuum spectra of component A. in the range [rom 8.4 (to 43.4 GlIz. is shown in the upper panel of Figure 8..," The radio continuum spectra of component A, in the range from 8.4 to 43.4 GHz, is shown in the upper panel of Figure \ref{fig-spectra}." +" The spectra is reasonably well modeled (dotted line} by that of an homogeneous region of ionized gas with an enmüssion measure of 7.0x10 pe "" and an angular size of0.19""..", The spectra is reasonably well modeled (dotted line) by that of an homogeneous region of ionized gas with an emission measure of $7.0\times10^8$ pc $^{-6}$ and an angular size of. + The region of ionized gas is optically thick below 15 Gllz., The region of ionized gas is optically thick below 15 GHz. +" The total number of ionizing photons per second required to excite this region is 55x10"" I, which could be supplied by an 09.5 ZAMS star."," The total number of ionizing photons per second required to excite this region is $\times10^{47}$ $^{-1}$, which could be supplied by an O9.5 ZAMS star." + The total luminosity of the region inferred [rom the radio observations is 5.4x104L... which is close to the luminosity inferred from the IRAS observations of 7.9x10!L..," The total luminosity of the region inferred from the radio observations is $5.4\times 10^4$, which is close to the luminosity inferred from the IRAS observations of $7.9\times 10^4$." +. Possible explanations for the difference in luminosities is that a fraction of the ionizing stellar UY photons is absorbed by dust within the ullracompact HII region or that non-ionizing stars are present in (he region (or a combination of both)., Possible explanations for the difference in luminosities is that a fraction of the ionizing stellar UV photons is absorbed by dust within the ultracompact HII region or that non-ionizing stars are present in the region (or a combination of both). + Our analvsis of unpublished archive Spitzer observations show a single bright source associated with IRAS 19217--1651 that is detected in all four IRAC bands., Our analysis of unpublished archive Spitzer observations show a single bright source associated with IRAS 19217+1651 that is detected in all four IRAC bands. + The radio continuum spectra of component D. in the range of 3.4 to 22.5 Gllz. is consistent with a total [lux clensitv of 6.641.0 mJv at 43.4 GIIz. leaving a flux. density ol 43.841.0 mJy for component A at this lrecquency.," The radio continuum spectra of component B, in the range of 8.4 to 22.5 GHz, is consistent with a total flux density of $\pm$ 1.0 mJy at 43.4 GHz, leaving a flux density of $\pm$ 1.0 mJy for component A at this frequency." + The flat spectrum of component D is indicative of optically thin free-free emission., The flat spectrum of component B is indicative of optically thin free-free emission. + The direct interpretation of these data is that. since the total number of ionizing photons per second required (o excite this region is 6.9x10/5 I. we are observing an independent HII region ionized bv a D0.5 ZAMS star with a huninosity of 2.0x104L.," The direct interpretation of these data is that, since the total number of ionizing photons per second required to excite this region is $\times10^{46}$ $^{-1}$, we are observing an independent HII region ionized by a B0.5 ZAMS star with a luminosity of $2.0\times 10^4$." +.. However. the high angular resolution images (see the 22.5 GlIIz image in Fig.," However, the high angular resolution images (see the 22.5 GHz image in Fig." + 2) suggest that component D could be ionized gas outflowing from component A. Is this alternative possible?, 2) suggest that component B could be ionized gas outflowing from component A. Is this alternative possible? + The angular separation between components A and D is ~1 , The angular separation between components A and B is $\sim1{''}$ +Let us compare the coevolution and the above picture motivated by it with some pictures (or interpretations) and numerical simulation results of the ACDAL paradigm: that have been discussed in the literature.,Let us compare the coevolution and the above picture motivated by it with some pictures (or interpretations) and numerical simulation results of the $\LCDM$ paradigm that have been discussed in the literature. +" First. the continual erowth of the central stellar velocity dispersion and the stellar mass accompanying the growth of the halo over cosmic time would be inconsistent with a strictly ""stable core concept” for massive galaxies citealt LP03.Gac04)) even alter z=1."," First, the continual growth of the central stellar velocity dispersion and the stellar mass accompanying the growth of the halo over cosmic time would be inconsistent with a strictly “stable core concept” for massive galaxies \\citealt{LP03,Gao04}) ) even after $z=1$." +" However. the growth slopes for σ and M, are shallower for more massive haloes according to the abundance matching results (see Fie."," However, the growth slopes for $\sigma$ and $\Mstars$ are shallower for more massive haloes according to the abundance matching results (see Fig." + 4 and Fig. 9)), \ref{MvirV} and Fig. \ref{MhMs}) ). + lHlence a weakly evolving core of massive haloes would be consistent with our results., Hence a weakly evolving core of massive haloes would be consistent with our results. +" Second. the picture shares the concept of ""universal clensity profile” with the attractor hypothesis citealt LP03-CGao04))."," Second, the picture shares the concept of “universal density profile” with the attractor hypothesis \\citealt{LP03,Gao04}) )." + However. there is a clear distinction between the two.," However, there is a clear distinction between the two." + Phe attractor hypothesis assumes that the universal NEW profile is preserved or restored in hierarchical mereing of haloes (hosting galaxies) while the present picture assumes that the barvon-mocified: universal total density profile tthe GNEW profile) is preserved once it is created., The attractor hypothesis assumes that the universal NFW profile is preserved or restored in hierarchical merging of haloes (hosting galaxies) while the present picture assumes that the baryon-modified universal total density profile the GNFW profile) is preserved once it is created. + The latter property is supported by dissipationless merging simulations citealtBNOAISE ZINOG.NDBO9)).," The latter property is supported by dissipationless merging simulations \\citealt{BM04,KZK06,NTB09}) )." +paradigm?: Phe basic tenet of the ACDAL structure formation theory is the hierarchical mass assembly., The basic tenet of the $\LCDM$ structure formation theory is the hierarchical mass assembly. + What the theory predicts. is the. distribution of dark matter haloes., What the theory predicts is the distribution of dark matter haloes. + Connecting observed. galaxies. with theoretical dark haloes is a major goal. of cosmological research., Connecting observed galaxies with theoretical dark haloes is a major goal of cosmological research. + The cillieulty of testing the ACDAL paradigm arises [rom the complex phwsies of galaxy formation within the halo and the induced: modification of the halo structure., The difficulty of testing the $\LCDM$ paradigm arises from the complex physics of galaxy formation within the halo and the induced modification of the halo structure. + AX necessary condition for a successful. mociel is to reproduce the basic statistical properties of the observed local Universe. such as the luminosity. stellar mass and velocity. functions of galaxies and their. correlations (see TrujilloGiomezctal.20100).," A necessary condition for a successful model is to reproduce the basic statistical properties of the observed local Universe, such as the luminosity, stellar mass and velocity functions of galaxies and their correlations (see \citealt{TG10}) )." + However. a successful reproduction of the z=0 statistical properties of galaxies is not sullicient.," However, a successful reproduction of the $z=0$ statistical properties of galaxies is not sufficient." + A successful model must. predict correctly the evolution of the galaxy properties., A successful model must predict correctly the evolution of the galaxy properties. + Semi-analvtic models of galaxy formation have paid much attention on the ealaxy luminosity and stellar mass functions., Semi-analytic models of galaxy formation have paid much attention on the galaxy luminosity and stellar mass functions. + The current generation of these models can reproduce the z=0 functions reasonably well. but ful to match their observed. evolutions (see. e.g... Fontanotetal.2009:StringerCattaneoetal.2008)).," The current generation of these models can reproduce the $z=0$ functions reasonably well, but fail to match their observed evolutions (see, e.g., \citealt{Fon09,Str08,Cat08}) )." + The ealaxy luminosity. ancl stellar mass functions have much to do with the complex barvonic physics of star formations. ACN activities. leedbacks. etc.," The galaxy luminosity and stellar mass functions have much to do with the complex baryonic physics of star formations, AGN activities, feedbacks, etc." + Hence the evolutions of the galaxy. luminosity ancl stellar mass functions can only provide indirect. tests of the underlying ACDAL paradigm., Hence the evolutions of the galaxy luminosity and stellar mass functions can only provide indirect tests of the underlying $\LCDM$ paradigm. + The stellar velocity or velocity dispersion of the galaxy residing in the centre of a halo probes the gravitational potential of the barvon plus dark. matter system., The stellar velocity or velocity dispersion of the galaxy residing in the centre of a halo probes the gravitational potential of the baryon plus dark matter system. + Since the dark halo is expected to be modified in the course of the clissipational galaxy formation process citealtBlus6.Cine04.ItudOs. Aba09.TLis10)) and. the central potential is likely to be dominated by the baryonie matter. the velocity. (dispersion) function. evolution itself. is. not a direct. probe of the ACDAL paradigm. either.," Since the dark halo is expected to be modified in the course of the dissipational galaxy formation process \\citealt{Blu86,Gne04,Rud08,Aba09,Tis10}) ) and the central potential is likely to be dominated by the baryonic matter, the velocity (dispersion) function evolution itself is not a direct probe of the $\LCDM$ paradigm either." + However. the velocity. (dispersion) function is separated. from. much of the barvonic physics but has only to do with its dvnamical ellect.," However, the velocity (dispersion) function is separated from much of the baryonic physics but has only to do with its dynamical effect." + Hence. once the dynamical ellect of ealaxv formation is well accounted. for. the evolution of the velocity. (dispersion). function. olfers an usefu complementary probe of the structure formation. theory.," Hence, once the dynamical effect of galaxy formation is well accounted for, the evolution of the velocity (dispersion) function offers an useful complementary probe of the structure formation theory." + While it is challenging to measure reliably the evolution of the velocity (dispersion) function through conventiona ealaxy surveys. strong lensing statistics in a well-delinec survey provides an excellent. opportunity to constrain the evolution of the velocity (dispersion) function through the image splitting distributions (see Chae 2010)).," While it is challenging to measure reliably the evolution of the velocity (dispersion) function through conventional galaxy surveys, strong lensing statistics in a well-defined survey provides an excellent opportunity to constrain the evolution of the velocity (dispersion) function through the image splitting distributions (see \citealt{Cha10}) )." + Curren strong lensing statistics is limited by the small sample size., Current strong lensing statistics is limited by the small sample size. + However. future. cosmological surveys including (but no limited to) the Dark Enereyv Survey. the Large. Synoptic Survey “Telescope ancl the Square Wilometre Array wil increase dramatically the number of strong lenses (sce Oguri&Marshall 2010)) allowing to put tight constraints on the evolution of velocity (dispersion) functions.," However, future cosmological surveys including (but not limited to) the Dark Energy Survey, the Large Synoptic Survey Telescope and the Square Kilometre Array will increase dramatically the number of strong lenses (see \citealt{OM10}) ) allowing to put tight constraints on the evolution of velocity (dispersion) functions." + Through an abundance matching analysis of the lensing constrained VDE evolution along with the theoretical LLNLE and the observed SALE from galaxy surveys. we find. the ollowing.," Through an abundance matching analysis of the lensing constrained VDF evolution along with the theoretical HMF and the observed SMF from galaxy surveys, we find the following." +iintensity and has a large scatter.,intensity and has a large scatter. + ddoes not show any correlation with[Cm]., does not show any correlation with. +" A more quantitative analysis of the correlation between the different tracers andi]., is obtained by calculating the correlation coefficient (r) (Table 3))."," A more quantitative analysis of the correlation between the different tracers and, is obtained by calculating the correlation coefficient $r$ ) (Table \ref{tab_corrcoeff}) )." + For the entire region aand 24um aand um iintensities show around correlation with the intensities.," For the entire region and $\,\mu$ and $\,\mu$ intensities show around correlation with the intensities." +" For the region AHa,,i],, μπι, and um aare well correlated (r> 0.75) with[Cu]."," For the region $A$, $\,\mu$ m, and $\,\mu$ are well correlated $r>0.75$ ) with." +. The eemission is strongly correlated with the iintensity also on the south-western arm position., The emission is strongly correlated with the intensity also on the south-western arm position. + The iintensity ratio measured primarily in the rregion varies between 0.1-0.4 and this variation is significantly larger than the estimated uncertainties., The intensity ratio measured primarily in the region varies between 0.1–0.4 and this variation is significantly larger than the estimated uncertainties. +" In Fig. 8,,"," In Fig. \ref{fig_scatplot}," +" we plot the star formation rate (SFR), estimated from the um MMIPS data and the KPNO Ha data, as a function of the lintensity."," we plot the star formation rate (SFR), estimated from the $\,\mu$ MIPS data and the KPNO $\alpha$ data, as a function of the intensity." +" Positions within the selected regions A, B, and C are marked using differentsymbols and colours similar to Fig. 7.."," Positions within the selected regions $A$, $B$, and $C$ are marked using differentsymbols and colours similar to Fig. \ref{fig_allscats}." +" The SFR has been calculated from =[L(Ha)+0.031L(24)]x5.35107? in Mo yr“, where L(Ho)) is the lluminosity in Watt and L(24) is defined as vL, at um iin Watt (Calzettietal.2007)."," The SFR has been calculated from $~=~[L(H\alpha)~+~0.031L(24)]~\times~5.35~\times +10^{-35}$ in $\msun$ $^{-1}$, where ) is the luminosity in Watt and L(24) is defined as $\nu L_\nu$ at $\,\mu$ in Watt \citep{calzetti2007}." +. We have assumed a Kroupa(2001) initial mass function with a constant SFR over 100 Myr., We have assumed a \citet{kroupa2001} initial mass function with a constant SFR over 100 Myr. +" Here, we study the correlation on scales of 12"" corresponding to ppc."," Here, we study the correlation on scales of $12''$ corresponding to pc." +" On these small scales, we may start to see a break-up of any tight correlations between the various tracers of the SFR."," On these small scales, we may start to see a break-up of any tight correlations between the various tracers of the SFR." +" Viewing at all pixels we find a steepening of the slope in the log-log plots from regions where both the SFR and aare weak, to regions where both are strong."," Viewing at all pixels we find a steepening of the slope in the log–log plots from regions where both the SFR and are weak, to regions where both are strong." +" Towards the rregion (A), we find an almost linear relation between log(SFR) and log([C m])), with a good correlation, r=0.90 and the fitted slope is 1.48+0.26, i.e. the SFR goes as tto the power 1.48."," Towards the region $A$ ), we find an almost linear relation between $\log$ (SFR) and $\log$ ), with a good correlation, $r=0.90$ and the fitted slope is $\pm$ 0.26, i.e. the SFR goes as to the power 1.48." + Region B shows a correlation coefficient of 0.64 and region C shows no correlation., Region $B$ shows a correlation coefficient of 0.64 and region $C$ shows no correlation. + Boquienetal.(2010b) have obtained a linear fit to the total infrared (TIR) luminosity as a function of the luminosity in the PACS 160um bband for the entire M333 galaxy.," \citet{boquien2010b} have obtained a linear fit to the total infrared (TIR) luminosity as a function of the luminosity in the PACS $\,\mu$ band for the entire 33 galaxy." +" The TIR is the total infrared intensity, integrated between | um and mmm."," The TIR is the total infrared intensity, integrated between $1\,\mu$ m and mm." +" It is about a factor 2 (Rubinetal.2009) larger than the FIR continuum which is integrated between 42.7 and um. Boquienetal.(2010b) derived the TIR from fits of Draineetal.(2007) models to the MIPS, PACS, and SPIRE FIR data."," It is about a factor 2 \citep{rubin2009} larger than the FIR continuum which is integrated between 42.7 and $\mu$ m. \citet{boquien2010b} derived the TIR from fits of \citet{draineli2007} + models to the MIPS, PACS, and SPIRE FIR data." + And they find a tight linear relation between the two quantities: logLr=axlogLieo+b with a = 1.013+0.008 and b= 0.429+0.097.," And they find a tight linear relation between the two quantities: ${\rm log} L_{\rm TIR} = a +\times {\rm log} L_{160} + b$ with $a$ = $\pm$ 0.008 and $b$ = $\pm0.097$." +" We have used this relation to derive the TIR intensity at each position of the mapped region, at a resolution of 12"".."," We have used this relation to derive the TIR intensity at each position of the mapped region, at a resolution of ." +" To check that this is a valid approach, we independently derived the TIR at individual positions by fitting a greybody to the MIPS, PACS, and SPIRE data, smoothed to"," To check that this is a valid approach, we independently derived the TIR at individual positions by fitting a greybody to the MIPS, PACS, and SPIRE data, smoothed to" +We wish to compare our sample of LEGOs to a sample of faint Lyman Break Galaxies (LBGs) in order to determine the similarities and differences of the two populations of high-redshift galaxies.,We wish to compare our sample of LEGOs to a sample of faint Lyman Break Galaxies (LBGs) in order to determine the similarities and differences of the two populations of high-redshift galaxies. + First. we want to know if our LEGOs would be detected as LBGs and so we apply the LBG selection criteria for U-band drop-outs of Wadadekar et al. (," First, we want to know if our LEGOs would be detected as LBGs and so we apply the LBG selection criteria for $U$ -band drop-outs of Wadadekar et al. (" +2006: 0B>1.0. UD»5D V|l3andDV< 1.2) as well as the criteria of Madauetal. (,"2006; $U-B > 1.0$, $U-B > B-V + 1.3$ and $B-V < 1.2$ ) as well as the criteria of Madau et al. (" +1996: UCBD»1. UB>B7|12 and B—i« 1.5) to our sample.,"1996; $U-B > 1.3$, $U-B > B-i + 1.2$ and $B-i < 1.5$ ) to our sample." + However. our C-band data. and in the case of the faintest candidates also the HST data. is too shallow to get a useful measurement on the (D colour.," However, our $U$ -band data, and in the case of the faintest candidates also the HST data, is too shallow to get a useful measurement on the $U-B$ colour." + Instead. we take the best fit spectrum from the SED fitting (see Fig. 9))," Instead, we take the best fit spectrum from the SED fitting (see Fig. \ref{plotsed}) )" + and convolve it with the C (F300W). B and V filter sensitivities and calculate the colours.," and convolve it with the $U$ (F300W), $B$ and $V$ filter sensitivities and calculate the colours." + Forthis model spectrum. these colours become {ὁB=LOB VV=0.21 and Boi=0.69 which well satisfy the selection criteria for Ü- band drop-outs. see Fig. 13..," Forthis model spectrum, these colours become $U-B = 4.51$, $B-V = 0.24$ and $B-i = 0.69$ which well satisfy the selection criteria for $U$ -band drop-outs, see Fig. \ref{lbgcol2}." + However. many of our LEGOs are very faint and the stacked D magnitude is fainter than the lower limit of the selection of Madau et al. (," However, many of our LEGOs are very faint and the stacked $B$ magnitude is fainter than the lower limit of the selection of Madau et al. (" +1996). and about half of our sample are fainter than the V cut-off in the sample of Wadadekar et al. (,"1996), and about half of our sample are fainter than the $V$ cut-off in the sample of Wadadekar et al. (" +2006). see Fig. 14..,"2006), see Fig. \ref{lbgcol}." + Secondly. we wish to compare the observed optical colours (restframe UV colours) of our LEGOs to the LBGs in order to establish if our LEGO candidates have the same UV continuum colours as LBGs on the red side of the Lyman break.," Secondly, we wish to compare the observed optical colours (restframe UV colours) of our LEGOs to the LBGs in order to establish if our LEGO candidates have the same UV continuum colours as LBGs on the red side of the Lyman break." + In Fig. 14..," In Fig. \ref{lbgcol}," + we plot the colours of the two samples of faint LBGs published by Wadadekar et al. (, we plot the colours of the two samples of faint LBGs published by Wadadekar et al. ( +2006) and Madau et al. (,2006) and Madau et al. ( +1996) against the colours of our candidates.,1996) against the colours of our candidates. + All samples are drawn from survey data-sets such as GOODS-S and HDF-N. hence there ts no bias in photometry.," All samples are drawn from survey data-sets such as GOODS-S and HDF-N, hence there is no bias in photometry." +" In the plot. we see that the LEGO candidates are drawn from a fainter sub-sample of the high-redshift galaxy population,"," In the plot, we see that the LEGO candidates are drawn from a fainter sub-sample of the high-redshift galaxy population." + However. for the brighter candidates among our sample. the LEGOs appear to have UV colours similar to LBG galaxies.," However, for the brighter candidates among our sample, the LEGOs appear to have UV colours similar to LBG galaxies." + We have performed deep narrow-band imaging of part of the GOODS-S field., We have performed deep narrow-band imaging of part of the GOODS-S field. + The image revealed a set of 24 LEGO candidates. at a redshift of + 3.15.," The image revealed a set of 24 LEGO candidates, at a redshift of $z \approx 3.15$ ." + Of these. three candidates have been observed spectroscopically and are confirmed.," Of these, three candidates have been observed spectroscopically and are confirmed." +blue stragelers occurs.,blue stragglers occurs. + In earlier work. Benz Llills (L987) performed. an SPLL simulation. using 1024 particles. and concluded that collision products are fully mixed. (ic. the resulting star is chemically homogeneous).," In earlier work, Benz Hills \shortcite{BH87} + performed an SPH simulation using 1024 particles, and concluded that collision products are fully mixed (i.e. the resulting star is chemically homogeneous)." + Ten vears later. these simulations were repeated but with a factor of 10-50 more particles (Lombardietal.1996).," Ten years later, these simulations were repeated but with a factor of 10-50 more particles \cite{LRS96}." +. Because of the higher resolution. it became clear that collision products are NOT chemically homogeneous. but instead. retain some memory of the chemical profile of the parent stars of the collision.," Because of the higher resolution, it became clear that collision products are NOT chemically homogeneous, but instead retain some memory of the chemical profile of the parent stars of the collision." + We feel confident that such a fundamental change in our understanding will not happen again when we increase the resolution. but we want to be sure.," We feel confident that such a fundamental change in our understanding will not happen again when we increase the resolution, but we want to be sure." + Alore importantly. we performed these high resolution calculations to answer two fundamoental questions about the structure of the collision products. immediately after. the collision.," More importantly, we performed these high resolution calculations to answer two fundamental questions about the structure of the collision products immediately after the collision." + Phe first involves the structure of the outer layers of the star. and the second is concerned. with the material which is thrown olf by the star during the collision itself.," The first involves the structure of the outer layers of the star, and the second is concerned with the material which is thrown off by the star during the collision itself." + ‘There has been some debate in the literature recently about whether the collision product has a surface convection zone shortly. after the end of the collision., There has been some debate in the literature recently about whether the collision product has a surface convection zone shortly after the end of the collision. + Phe presence of such a convection zone could have ramifications for both the surface chemical abundances and the rotation rate of the star when it reaches its main sequence (Leonard&Livio 1995)., The presence of such a convection zone could have ramifications for both the surface chemical abundances and the rotation rate of the star when it reaches its main sequence \cite{LL95}. +. Previous SPL simulations and subsequent evolution alculations have shown that no convection zone exists at re end of the collision. nor does. it appear during the initial thermal relaxation of the star (Lombardietal.1996:Sillsctal. 1997).," Previous SPH simulations and subsequent evolution calculations have shown that no convection zone exists at the end of the collision, nor does it appear during the initial thermal relaxation of the star \cite{LRS96,SLBDRS97}." +. However. members of the community argue that the previous simulations are unable to resolve the outermost regions of the star well at all. clue to their low particle number and use of cqual-mass particles (Livio. private communication).," However, members of the community argue that the previous simulations are unable to resolve the outermost regions of the star well at all, due to their low particle number and use of equal-mass particles (Livio, private communication)." + In this paper. we resolve this issue bv increasing the resolution of our simulations in the outer regions of the parent stars in particular. and by using variable mass particles.," In this paper, we resolve this issue by increasing the resolution of our simulations in the outer regions of the parent stars in particular, and by using variable mass particles." + We are also interested in following the material which is thrown olf from the stars during the collision., We are also interested in following the material which is thrown off from the stars during the collision. + We have discovered. using previous generation simulations. that blue stragelers which are formed by an oll-axis collision have an angular momentum. problem (Sillsctal.2001).," We have discovered, using previous generation simulations, that blue stragglers which are formed by an off-axis collision have an angular momentum problem \cite{SFLRW01}." +.. Namely. these stars retain too much of their angular momentum. and have no apparent way of losing it during their thermal relaxation phase after the collision.," Namely, these stars retain too much of their angular momentum, and have no apparent way of losing it during their thermal relaxation phase after the collision." + As a result. the collision products spin up during their collapse to the main sequence. and inevitably rotate faster than their break-up velocity.," As a result, the collision products spin up during their collapse to the main sequence, and inevitably rotate faster than their break-up velocity." + Such collision products can never become blue stragelers. since they tear themselves apart before they reach the main sequence.," Such collision products can never become blue stragglers, since they tear themselves apart before they reach the main sequence." + We wish to follow the lost material with greater resolution. to study the amount of angular momentum that this material carries away with it.," We wish to follow the lost material with greater resolution, to study the amount of angular momentum that this material carries away with it." + We also wish to follow the outermost material of the parent stars to see if some of it forms a disk around the collision product., We also wish to follow the outermost material of the parent stars to see if some of it forms a disk around the collision product. + LE so. then we can plausibly suggest that magnetic locking to a clisk is responsible for removing angular momentum from the collision product.," If so, then we can plausibly suggest that magnetic locking to a disk is responsible for removing angular momentum from the collision product." + Ins refmethock we describe the methods used to model the stellar collisions and their subsequent evolution., In \\ref{method} we describe the methods used to model the stellar collisions and their subsequent evolution. + We present our results in refresults.. and discuss their implications in refsummarv..," We present our results in \\ref{results}, and discuss their implications in \\ref{summary}." + The simulations of stellar. collisions discussed. in lis paper were performed using the smoothecl particle ivdrodvnamics (SPII) method. (Benz1990:Monaghanrm992).," The simulations of stellar collisions discussed in this paper were performed using the smoothed particle hydrodynamics (SPH) method \cite{B90,M92}." +. Our three dimensional code uses a tree to solve for 10 gravitational forces and to find the nearest. neighbours (Benzοἱal.1990)., Our three dimensional code uses a tree to solve for the gravitational forces and to find the nearest neighbours \cite{BBCP90}. +.. We use the standard form of artificial Pdscositv with a=1 ancl? =2.5. and an adiabatie equation of state.," We use the standard form of artificial viscosity with $\alpha=1$ and $\beta=2.5$, and an adiabatic equation of state." + The. thermodynamic quantities are evolved. by ollowing the change in internal energy., The thermodynamic quantities are evolved by following the change in internal energy. + Both the smoothing enegth and the number of neighbourscan change in time and space., Both the smoothing length and the number of neighbourscan change in time and space. + Phe smoothing length is varied to keep the number of neighbours approximately constant ( 50 for the low resolution runs. and ~ 200 for the million particle run).," The smoothing length is varied to keep the number of neighbours approximately constant $\sim$ 50 for the low resolution runs, and $\sim$ 200 for the million particle run)." + The code is the parallel version of the code described in detail in Bate. Bonnell Price (1995).," The code is the parallel version of the code described in detail in Bate, Bonnell Price \shortcite{BBP95}." +. It was parallelized. using OpenAL. and was run on the SCL Origin 3000 operated. ολ) the Ulx Astrophysical Fluids Facility (ΕΝΑΕΡΙΟ) based at the University of Leicester.," It was parallelized using OpenMP, and was run on the SGI Origin 3000 operated by the UK Astrophysical Fluids Facility (UKAFF) based at the University of Leicester." + We modelled collisions between two equalmass stars., We modelled collisions between two equal–mass stars. + We chose a mass of 0.6 Al. as a representative. but. no extreme. mass for elobular cluster stars.," We chose a mass of 0.6 $M_{\odot}$ as a representative, but not extreme, mass for globular cluster stars." + The initial stellar models were calculated using the Yale stellar evolution code (YREC. Guenther ct al.," The initial stellar models were calculated using the Yale stellar evolution code (YREC, Guenther et al." + 1992). and had a metallicity of Z=0.001 and an age of 15 Gye.," 1992), and had a metallicity of Z=0.001 and an age of 15 Gyr." + ithe goal of the simulation is to investigate the detailed structure of the collision product. then it is crucial to begin. with a realistic stellar mode rather than a polvtrope or other approximation (Sills&Lombardi 1997).," If the goal of the simulation is to investigate the detailed structure of the collision product, then it is crucial to begin with a realistic stellar model rather than a polytrope or other approximation \cite{SL97}." +. Phe particles were initially cistributed on an equallyspaced eric. ancl their masses were varied. unti the density. profile matched that of the stellar model.," The particles were initially distributed on an equally–spaced grid, and their masses were varied until the density profile matched that of the stellar model." + By using uncqual mass particles. we increase the resolution in the outer. low density regions of the star.," By using unequal mass particles, we increase the resolution in the outer, low density regions of the star." + This is importan [or resolving the outer lavers of the collision products (to determine if there is a convection zone or not) ane for following the material which is thrown off during the collision., This is important for resolving the outer layers of the collision products (to determine if there is a convection zone or not) and for following the material which is thrown off during the collision. + The stars were given a relative velocity at infinity of py —10 km/s. which is a reasonable value for globular cluster stars.," The stars were given a relative velocity at infinity of $v_{\infty}$ =10 km/s, which is a reasonable value for globular cluster stars." +" They. were set up on almost parabolic orbits with a »ericentre separation rp,—0 for the head-on collisions. anc Γρο. BH. for the off-axis collisions. ("," They were set up on almost parabolic orbits with a pericentre separation $r_p=0$ for the head-on collisions, and $r_p$ =0.25 $R_{\odot}$ for the off-axis collisions. (" +Lhe radius of the main sequence star is 0.612. 2),The radius of the main sequence star is $0.61 R_{\odot}$ .) + Most collisions are expectec o happen during interactions involving binary stars (Hut& 1983).. so the stars are on bound. and usually highly elliptical. orbits.," Most collisions are expected to happen during interactions involving binary stars \cite{HB83}, , so the stars are on bound, and usually highly elliptical, orbits." + For both the head-on and oll-axis collisions. he number of particles was varied between LO 000 ancl 300," For both the head-on and off-axis collisions, the number of particles was varied between 10 000 and 300" +(1985). and derived by Dalcanton. Spergel Summers (1997) and de Jong Lacey (1999a.b 2000) using the Fall Efstathiou (1980) disk-galaxy formation mocdel.,"(1985), and derived by Dalcanton, Spergel Summers (1997) and de Jong Lacey (1999a,b 2000) using the Fall Efstathiou (1980) disk-galaxy formation model." + Note that the new term contains a normalisation cocllicicnt : ensuring that ó. M and à are identical to the traditional Schechter parameters.," Note that the new term contains a normalisation coefficient $\frac{1}{\sqrt{2\pi}\sigma_{\mu}}$ ensuring that $\phi^*$ , $M^*$ and $\alpha$ are identical to the traditional Schechter parameters." + We choose to fit the BBE to the data shown in Cross et al. (, We choose to fit the BBF to the data shown in Cross et al. ( +2001): this is the largest available data set.,2001); this is the largest available data set. + This BBD was derived from a subset of 45.000 galaxies from the two-degree field galaxy recdshift survey (see Cross et al.," This BBD was derived from a subset of 45,000 galaxies from the two-degree field galaxy redshift survey (see Cross et al." + 2001 [or details). and is shown on Fig.," 2001 for details), and is shown on Fig." + 1. (thin contours)., \ref{fig1} (thin contours). + Also shown in Fig., Also shown in Fig. + 1. is the selection boundary derived rom visibility theory (shaded region. see Appendix D of Cross et al.," \ref{fig1} is the selection boundary derived from visibility theory (shaded region, see Appendix B of Cross et al." + 2001)., 2001). + In the shaded region insullicient. volume is surveyed to make any meaningful statement of the space-densities., In the shaded region insufficient volume is surveyed to make any meaningful statement of the space-densities. + The BBF can be fitted to the BBD by mininisine the 7 of the model compared to the data., The BBF can be fitted to the BBD by minimising the $\chi^2$ of the model compared to the data. + The BBE is à non-lincar six parameter equation and to find the minimum. we use the Levenberg-Marquardt: Method. (see Press et al.," The BBF is a non-linear six parameter equation and to find the minimum, we use the Levenberg-Marquardt Method (see Press et al." + 1986)., 1986). + The data provided. (see Cross ct al., The data provided (see Cross et al. + 2001) is binned as in Table C2 of Cross et al. (, 2001) is binned as in Table C2 of Cross et al. ( +2001) using those bins whose values are binned on à minimum of 25 galaxies.,2001) using those bins whose values are binned on a minimum of 25 galaxies. +" The best fit parameters we derive are: O°=(0.02064 7. ALSlogh=(1972+0.04) mag. a=1.05x0.02. 5,=0.281x0.007. pe=(21.90-Ε0.01) mag ? and e,=0.517d0.006."," The best fit parameters we derive are: $\phi^*=(0.0206 \pm 0.0009)h^3$ $^{-3}$ , $M^*-5\log\,h=(-19.72 \pm 0.04)$ mag, $\alpha=-1.05 \pm 0.02$, $\beta_{\mu}=0.281 \pm 0.007$, $\mu_e^*=(21.90 +\pm 0.01)$ mag $^{-2}$ and $\sigma_{\mu}=0.517 \pm 0.006$." + ΔΙ errors are le errors., All errors are $1\sigma$ errors. + Fig., Fig. + 1. shows the BBE for these parameters (thick lines) overlaid on the data (thin contour lines)., \ref{fig1} shows the BBF for these parameters (thick lines) overlaid on the data (thin contour lines). + The errors in the parameters were found using a Monte-Carlo simulation. that is the observed distribution was randomised within the quoted le errors and the BBE fit re-derived.," The errors in the parameters were found using a Monte-Carlo simulation, that is the observed distribution was randomised within the quoted $1\sigma$ errors and the BBF fit re-derived." + The final BBE fit vields a X7 value of 164. for v=49. where & is the no.," The final BBF fit yields a $\chi^{2}$ value of 164, for $\nu=49$, where $\nu$ is the no." + of data points - no., of data points - no. + of parameters., of parameters. + This gives a likelihood of 26.10H., This gives a likelihood of $2.6\times10^{-14}$. + Ilence. although the BBE appears to describe the BBD. the fit is poor.," Hence, although the BBF appears to describe the BBD, the fit is poor." + It is important to understand: where the dillerences are occurring., It is important to understand where the differences are occurring. + From Fig., From Fig. + d. we see that the model fits the cata well brightwards of Ad=18. and less well in fainter bins.," \ref{fig1} we see that the model fits the data well brightwards of $M=-18$, and less well in fainter bins." + The errors become comparable to the space density faintwards of AL=——16. so the main error in the fit occurs in the range: 1625Al>1s.," The errors become comparable to the space density faintwards of $M=-16$, so the main error in the fit occurs in the range: $-16>M>-18$." + The data (Fig. 1)), The data (Fig. \ref{fig1}) ) + show an upturn towards the faint end in this range whereas the Schechter function. gradually. Dattens towards the faint end., show an upturn towards the faint end in this range whereas the Schechter function gradually flattens towards the faint end. + Thus it is the Schechter function. part that does not describe the data well., Thus it is the Schechter function part that does not describe the data well. + Note that the BBE provides Schechter parameters comparable to the range from previous SULVONS., Note that the BBF provides Schechter parameters comparable to the range from previous surveys. + The model fits the data well in the surface brightness direction. implving that a Gaussian distribution is a good deseription. of the space density as a function of surface brightness. for a constant absolute magnitude.," The model fits the data well in the surface brightness direction, implying that a Gaussian distribution is a good description of the space density as a function of surface brightness, for a constant absolute magnitude." + Table 1. compares our BBE with the de Jong Lacey (2000) BBE which was determined for Sh-Sclm galaxies only., Table \ref{table1} compares our BBF with the de Jong Lacey (2000) BBF which was determined for Sb-Sdm galaxies only. + As de Jong Lacey use confidence intervals for their errors. we have quoted. 20 errors rather than le errors for our values.," As de Jong Lacey use confidence intervals for their errors, we have quoted $2\sigma$ errors rather than $1\sigma$ errors for our values." + We converted. their. half-light. radii parameters to our elective surface brightness. parameters., We converted their half-light radii parameters to our effective surface brightness parameters. + De Jong Lacey fit disks and exponential bulges to their data. taking into account inclination and internal extinction.," De Jong Lacey fit disks and exponential bulges to their data, taking into account inclination and internal extinction." + In Appendix A. we estimate the uncertainty in our results due to not taking this into account and find that the error is O.1 mag in Ale and ~0.55 mag 2 in fH.," In Appendix A, we estimate the uncertainty in our results due to not taking this into account and find that the error is $\sim0.1$ mag in $M*$ and $\sim0.55$ mag $^{-2}$ in $\mu_e^*$." + We note that the de Jong Lacey (2000) parameters are their total galaxy parameters. not their cisk-only galaxy parameters.," We note that the de Jong Lacey (2000) parameters are their total galaxy parameters, not their disk-only galaxy parameters." + In cach case. these have been converted to 5;- band magnitudes using 2f=1.7 mag from de Jong Lacey (2000). and 6;2D.0.28(D.—V) (Maddox. Efstathiou Sutherland. 1990). using a value of (D.Y)=0.5 for a late tvpe spiral (Coleman. Wu Weedman. 1980. Driver et al.," In each case, these have been converted to $b_j$ -band magnitudes using $B-I = 1.7$ mag from de Jong Lacey (2000), and $b_j=B-0.28(B-V)$ (Maddox, Efstathiou Sutherland 1990), using a value of $(B-V)=0.5$ for a late type spiral (Coleman, Wu Weedman, 1980, Driver et al." + 1994)., 1994). + Finally we convert from 444=65 km tAlpe + to Hy—100 km ! +., Finally we convert from $H_0 = 65$ km $^{-1}$ $^{-1}$ to $H_0 = 100$ km $^{-1}$ $^{-1}$ . + In addition. the de Jong Lacey sample has tighter selection criteria and more accurate CCD photometry (£0.05 magcompared to 0.2 mag). but it only includes late-type galaxies and has a redshift completeness of compared to >90% for the 20E€GHBS.," In addition, the de Jong Lacey sample has tighter selection criteria and more accurate CCD photometry $\pm 0.05$ magcompared to $\pm 0.2$ mag), but it only includes late-type galaxies and has a redshift completeness of compared to $>90$ for the 2dFGRS." +" In spite of this. we find a similar spread in fr (a, = 0.52 q.v."," In spite of this, we find a similar spread in $\mu$ $\sigma_{\mu}$ = $0.52$ q.v." + 0.61) and wefind that the avalues of the (wo surveys are equal within the, $0.61$ ) and wefind that the $\alpha$values of the two surveys are equal within the + (e.g..Piran2005a:Meszarosreferencestherein)... &Ostriker1978:BlandfordEichler1987)).— 2006.andreferencestherein).. (Keshetetal.2008;Spitkovsky2008b).," \citep[e.g.,][and references therein]{Piran:05a,Meszaros:06}. \citealt{Bell:78,Blandford:78,Blandford:87}) \citep[e.g.,][and references therein]{Achterberg:01,Ellison:02,Niemiec:06}, \citep{Keshet:08,Spitkovsky:08}." +. large scale magnetic field is present in the shock upstream., large scale magnetic field is present in the shock upstream. + Inverse Compton cooling of the nonthermal electrons imposes an upper limit on the energy of electrons that are accelerated by DSA (e.g..Li&Waxman2006).," Inverse Compton cooling of the nonthermal electrons imposes an upper limit on the energy of electrons that are accelerated by DSA \citep[e.g.,][]{Li:06}." +. Since higher energy ions reach farther from the shock into the shock upstream. there may exist a region in the shock upstream devoid of nonthermal electrons that still contains nonthermal ions: we restrict our analysis to this region.," Since higher energy ions reach farther from the shock into the shock upstream, there may exist a region in the shock upstream devoid of nonthermal electrons that still contains nonthermal ions; we restrict our analysis to this region." + In the reference frame in which the shock upstream is at rest. the nonthermal ions are beamed forward within the narrow angle ~[7!. where [<>| is the shock Lorentz factor.," In the reference frame in which the shock upstream is at rest, the nonthermal ions are beamed forward within the narrow angle $\sim \Gamma^{-1}$, where $\Gamma\gg 1$ is the shock Lorentz factor." + The upstream plasma responds to the forward-beamed nonthermal tons by developing a return current (see.e.g..Thode&Sudan1975;Spicer&Sudan1984.andreferencestherein) which flows toward the shock.," The upstream plasma responds to the forward-beamed nonthermal ions by developing a return current \citep[see, e.g.,][and references therein]{Thode:75,Spicer:84} which flows toward the shock." + The return current cancels the charge separation between the nonthermal ions that reach farther from the shock and the nonthermal electrons that are confined closer to the shock by the inverse Compton losses., The return current cancels the charge separation between the nonthermal ions that reach farther from the shock and the nonthermal electrons that are confined closer to the shock by the inverse Compton losses. + If the upstream plasma is weakly magnetized. the flow of return current across a weak magnetic field accelerates the upstream plasma transversally. r.e.. perpendicular to the direction of shock propagation. which creates inhomogeneities in. the plasma (Revilleetal.2006:Pelletier.Lemoine.&Mar-cowith 2008):: this is a relativistic version of the mechanism discussed by Bell(2004.2005).," If the upstream plasma is weakly magnetized, the flow of return current across a weak magnetic field accelerates the upstream plasma transversally, i.e., perpendicular to the direction of shock propagation, which creates inhomogeneities in the plasma \citep{Reville:06,Pelletier:08}; this is a relativistic version of the mechanism discussed by \citet{Bell:04,Bell:05}." +. We show that even when the upstream magnetic field is weak. these density inhomogeneities may be sufficient to generate a stronger magnetic field in the shock downstream via vorticity production at the shock transition (Goodman&MacFadyen2007:Siront&Goodman 2007).," We show that even when the upstream magnetic field is weak, these density inhomogeneities may be sufficient to generate a stronger magnetic field in the shock downstream via vorticity production at the shock transition \citep{Goodman:08,Sironi:07}." +. This process converts the bulk kinetic energy of the shock downstream into vortical and magnetic energy., This process converts the bulk kinetic energy of the shock downstream into vortical and magnetic energy. + An advantage of this process Is that it can take place even when the circumburst medium ts uniform and therefore it is relevant for. as required by observations.both long and short GRBs (Nakar 2007).," An advantage of this process is that it can take place even when the circumburst medium is uniform and therefore it is relevant for, as required by observations,both long and short GRBs \citep{Nakar:07}. ." + Alternative sources of vorticity that were previously discussed, Alternative sources of vorticity that were previously discussed +a particular dataset identifier is known and can be resolved to an online resource.,a particular dataset identifier is known and can be resolved to an online resource. + Upon successful verification. the identifier would be incorporated into the paper with a link to a resolution service provided by ADS (rather than a simple link to the current. URL for the resource).," Upon successful verification, the identifier would be incorporated into the paper with a link to a resolution service provided by ADS (rather than a simple link to the current URL for the resource)." + This model provides a level of redirection which can be used to properly (rack a dataset ic and when it moves from one archive to another. and allows (he resolver (o provide options should multiple versions of a data product be available.," This model provides a level of redirection which can be used to properly track a dataset if and when it moves from one archive to another, and allows the resolver to provide options should multiple versions of a data product be available." + A complete description of this implementation ean be found in Aecomazzietal.(2007).., A complete description of this implementation can be found in \cite{2007ASPC..376..467A}. + Elements of this architecture are similar to the Digital Object Identifier standard used for the persistent linking; of scholarly publications. which is discussed in section 4.," Elements of this architecture are similar to the Digital Object Identifier standard used for the persistent linking of scholarly publications, which is discussed in section 4." + Ilowever. this svstem was designed to be fully managed by the astronomical community requiring a minimal level of effort for institutional bus-in.," However, this system was designed to be fully managed by the astronomical community requiring a minimal level of effort for institutional buy-in." + Six vears have passed since (he introduction of (he dataset linking infrastructure. so now is a good time to take stock of this effort.," Six years have passed since the introduction of the dataset linking infrastructure, so now is a good time to take stock of this effort." + From a svsten design point of view. some ol the features that made the implementation of this svstem attractive have. in retrospect. proven to be obstacles to its long-term success.," From a system design point of view, some of the features that made the implementation of this system attractive have, in retrospect, proven to be obstacles to its long-term success." + Chief among all problems with the registration of dataset identifiers has been enforcing (heir persistence., Chief among all problems with the registration of dataset identifiers has been enforcing their persistence. + Since data products ultimately reside within archives that participate in the ADEC but which are run independently of each other. ihe implementation and maintenance of services (hat. provide access to the data is lelt to the archives themselves.," Since data products ultimately reside within archives that participate in the ADEC but which are run independently of each other, the implementation and maintenance of services that provide access to the data is left to the archives themselves." + Given (hat the thrust of this elfort is completely voluntary. there is no contract or reward svstem which can be leveraged to enforce the long-term resolution of and access (ο a particular dataset.," Given that the thrust of this effort is completely voluntary, there is no contract or reward system which can be leveraged to enforce the long-term resolution of and access to a particular dataset." + Experience shows that unless requirements for the preservation ol these linking services become part of the archive operations. a simple system upgrade is enough to break valuable links to dataset resources.," Experience shows that unless requirements for the preservation of these linking services become part of the archive operations, a simple system upgrade is enough to break valuable links to dataset resources." + As an example. over 200 dataset identifiers which were published in a 2004 ApJ Supplement special issue on the Spitzer Space Telescope are no longer resolvable due to a change in the Spitzer Science Center interface.," As an example, over 200 dataset identifiers which were published in a 2004 ApJ Supplement special issue on the Spitzer Space Telescope are no longer resolvable due to a change in the Spitzer Science Center interface." + Unfortunately the adoption aud use of dataset identifiers in (he literature has not been a success storv., Unfortunately the adoption and use of dataset identifiers in the literature has not been a success story. + Citations to datasets began appearing in 2005 and increased in the following two vears. peaking in 2007. before decreasing in 2008 and finally going down to zero in 2009 (see fie.," Citations to datasets began appearing in 2005 and increased in the following two years, peaking in 2007, before decreasing in 2008 and finally going down to zero in 2009 (see fig." + 2)., 2). + The reasons for this reversal are not entirely clear. but can probably be attributed to a variety of factors.," The reasons for this reversal are not entirely clear, but can probably be attributed to a variety of factors." + First and foremost. even though the ADEC approved a policy encouraging archives and users to make an effort to more widely publish dataset identifiers. auiecdotal evidence shows a low level of awareness [rom scientists ol this possibility.," First and foremost, even though the ADEC approved a policy encouraging archives and users to make an effort to more widely publish dataset identifiers, anecdotal evidence shows a low level of awareness from scientists of this possibility." +"T Tauri stars are considered to resenade our Suu at au age of a fe""v nullion vears.",T Tauri stars are considered to resemble our Sun at an age of a few million years. + Studies of their surrounding eas and dust can therefore provide important clues on the carly evolution of the solar nebula., Studies of their surrounding gas and dust can therefore provide important clues on the early evolution of the solar nebula. + Tt is well established through surveys at iuyared aud müilieter waveleieths that most T Tauri stars lave ciretuustollar disks with masses of ~10?10.1 AE. and sizes of ~100— AU (see overviews by Beckwith&Sarecut1996.. Dutrev et 1]996. Muudy et 22000).," It is well established through surveys at infrared and millimeter wavelengths that most T Tauri stars have circumstellar disks with masses of $\sim 10^{-3} - 10^{-1}$ $_{\odot}$ and sizes of $\sim +100-400$ AU (see overviews by \cite{BS96}, Dutrey et 1996, Mundy et 2000)." + I1 addition to serviug as a conduit for mass accretion outo the voung star. the disks also provide a reservolrof eas aud dust for the formation of potential plauctary svsteiis (Shu et J993).," In addition to serving as a conduit for mass accretion onto the young star, the disks also provide a reservoir of gas and dust for the formation of potential planetary systems (Shu et 1993)." + Theories of disk evoluion depend strongly ou the racial and vertical temperature structure of the disks (o... Hartinaun et 1]998). but these parameters are still poorly constrained by the available observations.," Theories of disk evolution depend strongly on the radial and vertical temperature structure of the disks (e.g., Hartmann et 1998), but these parameters are still poorly constrained by the available observations." +" We report here the results of a deep survey for the lowest two pure rotational lines of Πο, the J=2 >0 S(O) line at 28.218 yan aud the J=3>1 SCL) transition at 17.035 son. using the Short Wavelength Spectrometer (SWS) on board theObservatory (ISO)."," We report here the results of a deep survey for the lowest two pure rotational lines of $_2$, the $J$ $2\to0$ S(0) line at 28.218 $\mu$ m and the $J=3\to1$ S(1) transition at 17.035 $\mu$ m, using the Short Wavelength Spectrometer (SWS) on board the (ISO)." + Ii cluission. the IT» lines originate from levels at 509.9 I& and 1015.1 IS above eround and are thus excellerit tracers of the “wari (£7; 80 IN) eas in disks. especially in the interesting πιner part where Jovian planes qnav form.," In emission, the $_2$ lines originate from levels at 509.9 K and 1015.1 K above ground and are thus excellent tracers of the “warm” $T$ 80 K) gas in disks, especially in the interesting inner part where Jovian planets may form." + I» has the advantage that it dominates the mass budget aud that it does not deplee onto erains. contrary to CO.," $_2$ has the advantage that it dominates the mass budget and that it does not deplete onto grains, contrary to CO." + Moreover. the lines are optically thin up to very. high coluunu densitics owiug to t1ο μα Eiustein ο coefficieuts for electric quadrupole transitions. so that the modeling of the radiative transfer is simple.," Moreover, the lines are optically thin up to very high column densities owing to the small Einstein $A$ coefficients for electric quadrupole transitions, so that the modeling of the radiative transfer is simple." + Tere we preseut Πω pure rotational line observations of the GG Tau system. which is situated at the οσο of the Taurus-Auriga cloud complex at a distance of approximately 110 pe (IXenvonctal.199 1)).," Here we present $_2$ pure rotational line observations of the GG Tau system, which is situated at the edge of the Taurus-Auriga cloud complex at a distance of approximately 140 pc \cite{KDH}) )." +" CC Tau consists of two close binary pairs separated by 10"". or 1100 AU."," GG Tau consists of two close binary pairs separated by $''$, or 1400 AU." + The main binary GC Tau A has a separation of ~35 AU (Chez et 14997) and is composed of a I&7 and a MO.5 star (White et 1999). both classified as cuussiou-line or “classical” T Tauri stars by Herbig Bell (1988) with an estimated acerction rate of δν SAL. + Uartimann et 11998).," The main binary GG Tau A has a separation of $\sim 35$ AU (Ghez et 1997) and is composed of a K7 and a M0.5 star (White et 1999), both classified as emission-line or “classical” T Tauri stars by Herbig Bell (1988) with an estimated accretion rate of 2 $\times$ $^{-8}$ $_{\odot}$ $^{-1}$ (Hartmann et 1998)." + The GG Tau D binary is comprised of au Απο and MT. star separated by ~200 AU., The GG Tau B binary is comprised of an M5 and M7 star separated by $\sim 200$ AU. + The age of the GC Tau svstei is estimated to be ~1.5 Myis by White et (1999). usine the evolutionary models of Baratte ct (1998) and assuming the four stars to be coeval.," The age of the GG Tau system is estimated to be $\sim 1.5$ Myrs by White et (1999), using the evolutionary models of Baraffe et (1998) and assuming the four stars to be coeval." + Ilieh spatial resolution mages taken iu the near iufrared show that each of the stars in the GG. Tau A svstem has associated circuuustcllar material within a radius of less than 10 AU (Boddier et 11996)., High spatial resolution images taken in the near infrared show that each of the stars in the GG Tau A system has associated circumstellar material within a radius of less than 10 AU (Roddier et 1996). + These stars are located within a cavity of radius ~200 AU cleared by the dynamical interaction of the, These stars are located within a cavity of radius $\sim 200$ AU cleared by the dynamical interaction of the +hence an overall hieh level of lound in these svstems.,hence an overall high level of found in these systems. + In particular. at hieh enerev clensiGes variousprocesses come mto play.," In particular, at high energy densities various come into play." + In addition. in some maegnetically-dominated environments wilh low ambient plasma clensily. e.g.. in pulsar magnetospheres ancl in Active Galactic Nucleus (AGN) jets. one often has to deal withreconnection.," In addition, in some magnetically-dominated environments with low ambient plasma density, e.g., in pulsar magnetospheres and in Active Galactic Nucleus (AGN) jets, one often has to deal with." + And finally. at the most extreme end of high energv density astrophysical reconnection in environments such as magnetar magnetospheres and central eneines and inner jets of Ganma-hayv Bursis — the energy density is so high. corresponding to radiation temperatures in tens of keV. or equivalently. magnetic fields of 107 Gauss and more. that. in addition to all (he radiative processes mentioned above. should become important. inside the reconnection laver (??)..," And finally, at the most extreme end of high energy density astrophysical reconnection — in environments such as magnetar magnetospheres and central engines and inner jets of Gamma-Ray Bursts — the energy density is so high, corresponding to radiation temperatures in tens of keV, or equivalently, magnetic fields of $10^{12}$ Gauss and more, that, in addition to all the radiative processes mentioned above, should become important inside the reconnection layer \citep{Uzdensky_MacFadyen-2006, Uzdensky-2008}." + In the present paper. however. we shall concentrate solely on the role of radiative effects in reconnection and will leave the relativistic ellects ancl pair creation for a future study.," In the present paper, however, we shall concentrate solely on the role of radiative effects in reconnection and will leave the relativistic effects and pair creation for a future study." + In general. radiation mav have several important ellects on magnetic reconnection cdvnamices. the most important ones being radiative cooling of (he reconnection laver (optically thick or optically thin). radiation pressure. and Compton drag (i.e. (he radiative resistivity due to collisions between. electrons and. photons. as opposed to electrons and ious as in Classical Spitzer resistivitv).," In general, radiation may have several important effects on magnetic reconnection dynamics, the most important ones being radiative cooling of the reconnection layer (optically thick or optically thin), radiation pressure, and Compton drag (i.e., the radiative resistivity due to collisions between electrons and photons, as opposed to electrons and ions as in classical Spitzer resistivity)." + To the best of our knowledge. these aspects of radiative magnetic reconnection have not been adequately explored so far. even though (μον are critical [or several outstanding problems in modern high-energy astroplivsies.," To the best of our knowledge, these aspects of radiative magnetic reconnection have not been adequately explored so far, even though they are critical for several outstanding problems in modern high-energy astrophysics." + There is only a handful of relerences on (he subject of reconnection in the presence of radiation (?????).. and clearly much more work needs to be done.," There is only a handful of references on the subject of reconnection in the presence of radiation \citep{Dorman_Kulsrud-1995, Uzdensky_MacFadyen-2006, Uzdensky-2008, Jaroschek_Hoshino-2009, Nalewajko_etal-2010}, and clearly much more work needs to be done." + Thus. there is a clear astvophvsical motivation for further effort in (his area.," Thus, there is a clear astrophysical motivation for further effort in this area." + In addition. we believe that Chis topic should be of strong interest to experimental (IED) Physics — a new exciüng branch of modern physics that emerged in recent vears (e.g..?)..," In addition, we believe that this topic should be of strong interest to experimental High-Energy-Density (HED) Physics — a new exciting branch of modern physics that emerged in recent years \citep[e.g.,][]{Drake-2006-book}." + We (therefore anticipate a rapid progress in IED reconnection studies facilitated by the advent. of new computational anc experimental tools ancl capabilities developed in the WED Physics community. including powerful lasers ancl Z pinches.," We therefore anticipate a rapid progress in HED reconnection studies facilitated by the advent of new computational and experimental tools and capabilities developed in the HED Physics community, including powerful lasers and Z pinches." + In fact. several ILED reconnection experimental studies utilizing laser-procluced plasmas wilh eauss magnetic field have already been reported (??)..," In fact, several HED reconnection experimental studies utilizing laser-produced plasmas with mega-gauss magnetic field have already been reported \citep{Nilson_etal-2006, Li_etal-2007}." + In this paper we are making (he first steps towards building up intuition about the role of radiation effects in Iligh-Energv-Densitv. magnetic reconnection., In this paper we are making the first steps towards building up intuition about the role of radiation effects in High-Energy-Density magnetic reconnection. + Namely. here we concentrate on the simplest case. corresponding to relatively modest energy clensilies. where one needs to include only one of the above-mentioned effects racliative cooling.," Namely, here we concentrate on the simplest case, corresponding to relatively modest energy densities, where one needs to include only one of the above-mentioned effects — radiative cooling." + In general. prompt radiative cooling in both optically thin and optically thick regimes greatly affects the energv balance and hence the dvnamies of the reconnection laver.," In general, prompt radiative cooling in both optically thin and optically thick regimes greatly affects the energy balance and hence the dynamics of the reconnection layer." + Different radiation cooling mechanisms mav be important in different astrophysical situations. e.g.. (1) svnchrotron," Different radiation cooling mechanisms may be important in different astrophysical situations, e.g., (1) synchrotron" +time. the departure of these stars from the general trend of other active stars.,"time, the departure of these stars from the general trend of other active stars." + {From their membership in young stellar associations or moving groups and/or lithium abundance. we have shown that most of the stars in the upper branch of the above mentioned relationships are indeed young stars.," >From their membership in young stellar associations or moving groups and/or lithium abundance, we have shown that most of the stars in the upper branch of the above mentioned relationships are indeed young stars." +" This is also confirmed by their position in the logFy, 4B-V) diagram.", This is also confirmed by their position in the $\log F_\mathrm{H\alpha}$ $B$ $V$ ) diagram. + The remaining stars in the upper branch are flare stars., The remaining stars in the upper branch are flare stars. + We have proved that a single flare event occurring during the observation cannot account for the deviation observed in the flux-flux relationships., We have proved that a single flare event occurring during the observation cannot account for the deviation observed in the flux–flux relationships. + However. a plausible explanation for this deviation may be the hypothesis of nanoflare heating. which suggests that the quiescent state of the star is the result of the superposition of multiple small flares.," However, a plausible explanation for this deviation may be the hypothesis of nanoflare heating, which suggests that the quiescent state of the star is the result of the superposition of multiple small flares." + Regardless of whether the explanation is the age of the stars or such nanoflare heating. and given that all the upper branch stars are in the (magnetic activity) saturation regime. it is our belief that their ditferent behaviour in the flux-flux relationships is a consequence of a shared physical phenomenon.," Regardless of whether the explanation is the age of the stars or such nanoflare heating, and given that all the upper branch stars are in the (magnetic activity) saturation regime, it is our belief that their different behaviour in the flux–flux relationships is a consequence of a shared physical phenomenon." + These stars probably have a magnetie structure that ditfers in some way from that of the less active stars., These stars probably have a magnetic structure that differs in some way from that of the less active stars. + The authors acknowledge support from the Spanish Ministerio de Educaciónn y Ciencia (currently the Ministerio de Ciencia e Innovaciónny under the grant FPI2Z0061465-00592 (Programa Nacional Formaeiónn Personal Investigador) and projects AYA2008-00695 (Programa Nacional de Astronomíaa y Astrofissica). AstroMadrid S2009/ESP-1496.," The authors acknowledge support from the Spanish Ministerio de Educaciónn y Ciencia (currently the Ministerio de Ciencia e Innovaciónn), under the grant FPI20061465-00592 (Programa Nacional Formaciónn Personal Investigador) and projects AYA2008-00695 (Programa Nacional de Astronomíaa y Astrofíssica), AstroMadrid S2009/ESP-1496." + J. Lóppez-Santiago acknowledges support by the Spanish Ministerio de Ciencia e Innovaciónn under grant AYA2008-06423-CO3-03., J. Lóppez-Santiago acknowledges support by the Spanish Ministerio de Ciencia e Innovaciónn under grant AYA2008-06423-C03-03. + This research has made use of the SIMBAD database and VizieR catalogue access tool. operated at CDS. Strasbourg. France.," This research has made use of the SIMBAD database and VizieR catalogue access tool, operated at CDS, Strasbourg, France." + The stellar and line parameters are published in electronic format only., The stellar and line parameters are published in electronic format only. + Table A4.. available at the CDS. contains the name of the star (column #11). the right ascension and declination (columns #22 and #33). the spectral type (column #44). the colour index (B-V) (column #55). and any important note on each star (column The chromospheric activity results arelisted in two ditterent tables.," Table \ref{tab:parameters}, available at the CDS, contains the name of the star (column 1), the right ascension and declination (columns 2 and 3), the spectral type (column 4), the colour index $B$ $V$ ) (column 5), and any important note on each star (column The chromospheric activity results arelisted in two different tables." + Table AS contains the excess emission EW as measured in the subtracted spectrum. whereas Table AG. includes the excess fluxes derived in this work.," Table \ref{tab:activity_ew} contains the excess emission EW as measured in the subtracted spectrum, whereas Table \ref{tab:activity_flux} includes the excess fluxes derived in this work." + In both tables. column £11 is the name of the star.," In both tables, column 1 is the name of the star." + In columns #22. #33. #44. £55. #66 and #77. the excess emission (or fluxes) for Ca K. Can H. Hec and Ca IRT 48498AÀ.. Ca," In columns 2, 3, 4, 5, 6 and 7, the excess emission (or fluxes) for Ca K, Ca H, $\alpha$ and Ca IRT $\lambda$ , Ca" +"where U; and U, ave both 3x3 unitary matrices such that C; arises [rom the diagonalization of the charged lepton mass matrix GV) while C, diagonalizes the neutrino mass malrix (19).",where $U_l$ and $U_{\nu}$ are both $\times$ 3 unitary matrices such that $U_l$ arises from the diagonalization of the charged lepton mass matrix $(M_l)$ while $U_\nu$ diagonalizes the neutrino mass matrix $(M_\nu)$. +" For three lepton generations. (he 3x3 unilary matrix Ü in Particle DataGroup (PDC) [3]. parametrization is given by where sy, = sinfqa. Cy, = cos£45 with £44 being the reactor angle. sq» = sin£5. cys = cosAy with Fy being the solar angle. so, = sinfs4. Co, = cos854 with 054 being the atmospheric mixing anele and ὁ is the Dirac-tvpe CP violating phase."," For three lepton generations, the $\times$ 3 unitary matrix $U$ in Particle DataGroup (PDG) \cite{3} parametrization is given by where $s_{13}$ = $\sin \theta_{13}$, $c_{13}$ = $\cos \theta_{13}$ with $\theta_{13}$ being the reactor angle, $s_{12}$ = $\sin \theta_{12}$ , $c_{12}$ = $\cos \theta_{12}$ with $\theta_{12}$ being the solar angle, $s_{23}$ = $\sin \theta_{23}$, $c_{23}$ = $\cos \theta_{23}$ with $\theta_{23}$ being the atmospheric mixing angle and $\delta$ is the Dirac-type CP violating phase." + The phase matrix y = diag(l.«ways?>€/02/2) contains the Majorana-tvpe CP violating phases αι and ay which do not affect neutrino oscillations and are not directly accessible to experimental scrutinv al present.," The phase matrix $\wp$ = $(1,e^{i \alpha_1/2},e^{i \alpha_2/2})$ contains the Majorana-type CP violating phases $\alpha_1$ and $\alpha_2$ which do not affect neutrino oscillations and are not directly accessible to experimental scrutiny at present." + Current data is consistent with the tribimaximal CEDM) mixing | which has been derived using family svmmetries [5]., Current data is consistent with the tribimaximal (TBM) mixing \cite{4} which has been derived using family symmetries \cite{5}. +". In addition to Γον. there are other mixing schemes which can reproduce the observed leptonic mixing pattern which include the two Golden Ratio (GR) mixing schemes where the mixing angles are lor GR: 04» = tan!(1/4). 854 = z/4. 644 = 0 [6].. GR2: Ay = cos1/2). 854 — g/4. 80,5, — 0 [7] where ; = (1+v/5)/2. Hexagonal Mixing (11M): 64» = 7/6. 65; — /7/4. A, — 0 [5].. Dimaximal Mixing (DM): 845 = w/d. bo, = x/4. 044 = 0 [9]."," In addition to TBM, there are other mixing schemes which can reproduce the observed leptonic mixing pattern which include the two Golden Ratio (GR) mixing schemes where the mixing angles are for GR1: $\theta_{12}$ = $\tan^{-1}(1/\varphi)$, $\theta_{23}$ = $\pi/4$, $\theta_{13}$ = 0 \cite{6}, GR2: $\theta_{12}$ = $\cos^{-1}(\varphi/2)$, $\theta_{23}$ = $\pi/4$ , $\theta_{13}$ = 0 \cite{7} where $\varphi$ = $(1+\sqrt{5})/2$, Hexagonal Mixing (HM): $\theta_{12}$ = $\pi/6$, $\theta_{23}$ = $\pi/4$, $\theta_{13}$ = 0 \cite{8}, Bimaximal Mixing (BM): $\theta_{12}$ = $\pi/4$, $\theta_{23}$ = $\pi/4$, $\theta_{13}$ = 0 \cite{9}." +. MI (hese mixing schemes can arise from mass independent textures also known as form diagonalizable textures |10]. and lead to a predictive neutrino mass matrix structure which contains just five parameters (the three neutrino masses and (xo Majorana phases)., All these mixing schemes can arise from mass independent textures also known as form diagonalizable textures \cite{10} and lead to a predictive neutrino mass matrix structure which contains just five parameters (the three neutrino masses and two Majorana phases). + All the above mixing scenarios have the same predictions for the reactor aud abmospheric mixing angles viz 044 = (0 and Go; = 7/4. whereas (heir predictions lor the solar mixing angle 645 are different.," All the above mixing scenarios have the same predictions for the reactor and atmospheric mixing angles viz $\theta_{13}$ = 0 and $\theta_{23}$ = $\pi/4$ , whereas their predictions for the solar mixing angle $\theta_{12}$ are different." + Thus. theabove mixing matrices are common upto a mixing matrix arising from a mu-tain svmnmeltric neutrino mass matrix.," Thus, theabove mixing matrices are common upto a mixing matrix arising from a mu-tau symmetric neutrino mass matrix." + Ht is highly unlikely. that anv of the above mixing schemes is exact since there are already hints of a non-zero, It is highly unlikely that any of the above mixing schemes is exact since there are already hints of a non-zero + m = Pah. where a is the dimensionless integration constant which can be determined via surface mass clensity (or pressure) at fixed A.,"then, solving the differential equation \ref{eq17}) ) with respect to $\sigma$, we obtain = hence m = R, where $\alpha$ is the dimensionless integration constant which can be determined via surface mass density (or pressure) at fixed $R$." + The surface energy density determined by (3)) appears to be the 2D analogue of the cosmological o0 component from the Sec., The surface energy density determined by \ref{eq22}) ) appears to be the 2D analogue of the cosmological $T^0_0$ component from the Sec. + ??. if one takes into account the reduction of dimensionalitv., \ref{sec:intro} if one takes into account the reduction of dimensionality. + This is an expected result: from the viewpoint of (he 2D observer “living” on the shell it seems for him to be the whole universe with the scale factor A., This is an expected result: from the viewpoint of the 2D observer “living” on the shell it seems for him to be the whole universe with the scale factor $R$. + Thus. our 2D πιά model indeed not only considers the established (race properties of (hie texture siress-energv tensor but also restores its components for the surface case.," Thus, our 2D fluid model indeed not only considers the established trace properties of the texture stress-energy tensor but also restores its components for the surface case." + In this connection the inlegratGon constant a obtains the sense of the (squared) topological charge η., In this connection the integration constant $\alpha$ obtains the sense of the (squared) topological charge $\eta$. + The topological nature of the textures will brightly show itself at the end of of this section when we will study the texture fInid singular lavers with the vanishing total gravitational mass-enerev., The topological nature of the textures will brightly show itself at the end of of this section when we will study the texture fluid singular layers with the vanishing total gravitational mass-energy. + Equations .. (3)) and (3)) together with the choice of the signs e» completely determine the motion of the (hin-wall texture., Equations \ref{eq19}) ) and \ref{eq23}) ) together with the choice of the signs $\epsilon_\pm$ completely determine the motion of the thin-wall texture. + In conventional general relativity it is usually supposed that lasses are noineealive., In conventional general relativity it is usually supposed that masses are nonnegative. + Llowever. keeping in mind possible wormhole and quanti extensions of the theory 9].. we will not restrict ourselves by positive values and consider general case of arbitrary (rea) masses.," However, keeping in mind possible wormhole and quantum extensions of the theory \cite{man}, we will not restrict ourselves by positive values and consider general case of arbitrary (real) masses." + Then forbidden ancl permitted signs of this values can be determined from table 2.., Then forbidden and permitted signs of this values can be determined from table \ref{tab-2}. + Let us find now the trajectories of 2D textures., Let us find now the trajectories of 2D textures. + Integrating (3)) we obtain the iranscendenta equation for fi(7) 7//AL = JUM) = JUS/M).," Integrating \ref{eq19}) ) we obtain the transcendental equation for $R(\tau)$ /M = J (R/M) - J (R_0/M)," +"Note that this section is related to the ideal case R= x. but all equations can be straightforwardly rewritten for a finite 7221x roplaciug & by Aj,. bounding each inteeral and adapting normalisation.","Note that this section is related to the ideal case $R = \infty$ , but all equations can be straightforwardly rewritten for a finite $R$ by replacing $k$ by $k_{ln}$, bounding each integral and adapting normalisation." + The formulas arising from this adaptation are used iu the next sections., The formulas arising from this adaptation are used in the next sections. + Although the three approaches described in ?? are theoretically equivalent. their estimates and uunuerical luplementatious take differeut foris.," Although the three approaches described in \ref{sub:3equiv} are theoretically equivalent, their estimates and numerical implementations take different forms." +" Estimating the £/,,,, cocfficieuts using the mcthod naturally requires the radial dimension to be discretisecd.", Estimating the $f_{\ell mn}$ coefficients using the method naturally requires the radial dimension to be discretised. + Tudeed. the first step is to compute the spherical harmonic transform ou a set of shells located at radial values Fs.FN..," Indeed, the first step is to compute the spherical harmonic transform on a set of shells located at radial values $r_1, \dots, r_{N_{layers}}$." + Iun cach laver. the coefiicieuts fi) are estimated.," In each layer, the coefficients $f_{\ell m}(r_i)$ are estimated." +" Althoueh it is possible to perform, a raw estimate for the later harimoics transform. it is often advisable to use a robust 2D discretisation scheme (of Nuus) pixels for the i-th shell) aud to take advantage of the related high-performance algorithms."," Although it is possible to perform a raw estimate for the later harmonics transform, it is often advisable to use a robust 2D discretisation scheme (of $N_{pix}(i)$ pixels for the $i$ -th shell) and to take advantage of the related high-performance algorithms." + Aneular space is hence discretised into nodes{(riων)=(rey) aud the field is approximated on cach node. giving firi.γρ).," Angular space is hence discretised into nodes $(r_i,\theta_p,\phi_p)=(r_i,{\boldsymbol{\gamma}}_q)$ and the field is approximated on each node, giving $\tilde{f}(r_i,{\boldsymbol{\gamma}}_p)$." +" The spherical harmonic decomposition m the th shell becomes and the ual cocficicnts are obtained: by performing the folkNing .rical Bessel decomposition: With ""is method. radial aud augular spaces are discretised and both transforms are approximated."," The spherical harmonic decomposition in the $i$ -th shell becomes and the final coefficients are obtained by performing the following spherical Bessel decomposition: With this method, radial and angular spaces are discretised and both transforms are approximated." + For the approach. a 2D scheme on the sphere was required as well.," For the approach, a 2D scheme on the sphere was required as well." + As previously. this scheme defines a set of γην Zones (pixels) related to angular nodes Hu ," As previously, this scheme defines a set of $N_{pix}$ zones (pixels) related to angular nodes $\boldsymbol{\gamma}_q$ ." +πας denotes the points of the survey located in the solid angle corresponding to the q-th zone of the scheme. we perform thespherical Bessel Transform (raw estimate) in cach zoue and cach of these intermediate maps is decomposed! iuto spherical havmouic (spherical Warionics Trausfori) which gives the Fouricr-Bessel coetficieuts With the reverse method. one can avoid to discretise racdia space.," If $G_q$ denotes the points of the survey located in the solid angle corresponding to the $q$ -th zone of the scheme, we perform the spherical Bessel Transform (raw estimate) in each zone and each of these intermediate maps is decomposed into spherical harmonic (spherical Harmonics Transform) which gives the Fourier-Bessel coefficients With the reverse method, one can avoid to discretise radial space." + Moreover. this oue-shell pixclisation of the skv (thus wd on physical solid angles) allows for a natural treatiuent of radial distortions (redslüft. relativistic) aud masking effects.," Moreover, this one-shell pixelisation of the sky (thus based on physical solid angles) allows for a natural treatment of radial distortions (redshift, relativistic) and masking effects." + Using iultiple resolutions at differcut radial values. as would be possible with the forward method. is uuch more questionable.," Using multiple resolutions at different radial values, as would be possible with the forward method, is much more questionable." + The three inethods to estimate the spherical Fourier-Bessel decomposition cau therefore also |ο expressed. for a discrete 3D survey. sinnnuarised schematicallybelow: Note that iu practice. the range of (.Εν0) is finite. which imtroduces an additional approximation.," The three methods to estimate the spherical Fourier-Bessel decomposition can therefore also be expressed for a discrete 3D survey, summarised schematicallybelow: Note that in practice, the range of $(l,m,n)$ is finite, which introduces an additional approximation." +" ere. ( and ware restricted to [0.6,,,,] aud |1Hmax] respectively."," Here, $\ell$ and $n$ are restricted to $[0,\ell _{max}]$ and $[1,n_{max}]$ respectively." + Given f. in goes from ( to f.," Given $\ell$, $m$ goes from $-\ell$ to $\ell$." + For a survey that probes a field by ON discrete poiuts. the raw method is the natural estimate of the Fouricr-Bessel coctiicicuts.," For a survey that probes a field by $N$ discrete points, the raw method is the natural estimate of the Fourier-Bessel coefficients." +" Towever. suce cach point contributes to the calculation of every coefiicieut fry, (8Fan. n). πμ. is proportional to ΑΕuus|LPP which canbe highly. problematic for large survevs."," However, since each point contributes to the calculation of every coefficient $\tilde{f}_{\ell mn}$ $\forall \ l,m,n$ ), computation time is proportional to $N \cdot n_{max} ( \ell _{max} + 1)^2/2$, which can be highly problematic for large surveys." + Tn the forward method. the repeated spherical harmonic transforms take advantage οἳ tesselation schemes aud high-performance algorithms such as those provided bv TEALPix |?]] IGLOO |7] or GLESP |? ||.," In the forward method, the repeated spherical harmonic transforms take advantage of tesselation schemes and high-performance algorithms such as those provided by HEALPix \cite{gorski:2004by}] ], IGLOO \cite{igloo}] ] or GLESP \cite{glesp}] ]." + Roughly speaking. the umuber of nodes to be considered is reduced from Noto ON. aud the use of fast spherical harmonic ransforius on these sclicies senificautlv decreases computation time.," Roughly speaking, the number of nodes to be considered is reduced from $N$ to $N_{pix}$, and the use of fast spherical harmonic transforms on these schemes significantly decreases computation time." + Ilowever. this axoach requires the three-dimieusioual space to be divide into shells O(57;).," However, this approach requires the three-dimensional space to be divided into shells $\Omega(r_i)$." + Both radial aud aneular cdinensions are discretised. and the survey is approximated on :ji actual 3D eyid.," Both radial and angular dimensions are discretised, and the survey is approximated on an actual 3D grid." + Iu practice. this approximation deteriorates he accuracy of the estimated Fourier-Bessel coefficients.," In practice, this approximation deteriorates the accuracy of the estimated Fourier-Bessel coefficients." + Furthermore. «designing a meauiugful racia iscrcetixation is a difficult task.," Furthermore, designing a meaningful radial discretisation is a difficult task." +" For equal-area the area of each pixel ou the i-thshell is parameterpixelisatious,ln? Ay4G)."," For equal-area pixelisations, the area of each pixel on the $i$ -thshell is $4\pi r_i^2/N_{pix}(i)$ ." + With TEALPix. the side angular may onlv be increased bv a factor 2. which changes the uuuber of pixels bv a factor of |," With HEALPix, the $n_{side}$ angular parameter may only be increased by a factor 2, which changes the number of pixels by a factor of 4" +by a photon-photon collision generated pair plasma which is stabilized at high redshift deep inside the photon orbit bv an Eelelington limit radiation pressure generated hy an equipartition magnetic field. intrinsic to the MECO.,by a photon-photon collision generated pair plasma which is stabilized at high redshift deep inside the photon orbit by an Eddington limit radiation pressure generated by an equipartition magnetic field intrinsic to the MECO. + The surface value of the AIECO intrinsic magnetic field is calculated by cquating the synchrotron generated photon pressure (x H1) to the gravitational force per unit area. which is proportional to the density.," The surface value of the MECO intrinsic magnetic field is calculated by equating the synchrotron generated photon pressure $\propto B^4$ ) to the gravitational force per unit area, which is proportional to the density." + Since the density is inversely. proportional to the square of the MISCO mass. M. the internal magnetic field scales as AL? and the MECO magnetic moment. fr. scales as AdΛοινADT.," Since the density is inversely proportional to the square of the MECO mass, $M$, the internal magnetic field scales as $M^{-1/2}$ and the MECO magnetic moment, $\mu$, scales as $M^{-1/2}(2GM/c^2)^3 +\propto M^{5/2}$." + In the following. lor NS. GBC and AGN. we will assume the existence of a gas pressure dominated. ecometrically thin accretion disk (Shakura Sunvacy 1973).," In the following, for NS, GBHC and AGN, we will assume the existence of a gas pressure dominated, geometrically thin accretion disk (Shakura Sunyaev 1973)." + For gas pressure dominance. it has been shown (ce.g.. Merloni Fabian 2002) that the hard. x-ray spectral tail and reflection features of the low state spectrum can be adequately explained. by reprocessing of the soft hermal disk photons in an accretion disk corona (ADC).," For gas pressure dominance, it has been shown (e.g., Merloni Fabian 2002) that the hard x-ray spectral tail and reflection features of the low state spectrum can be adequately explained by reprocessing of the soft thermal disk photons in an accretion disk corona (ADC)." + The physical size of a corona is Consistent with limits found or the source of the power-law x-ray emissions of LAINB (Church Balucitisska-Chureh 2003)., The physical size of a corona is consistent with limits found for the source of the power-law x-ray emissions of LMXB (Church Balucińsska-Church 2003). +" ]t has been suggested. however. (Αακο, Faleke Fender 2001. Faleke. EIxOrrding Alarkoll 2003) that. the power-law X-ray emissions might originate in a jet."," It has been suggested, however, (Markoff, Falcke Fender 2001, Falcke, Körrding Markoff 2003) that the power-law x-ray emissions might originate in a jet." + Plat or inverted spectrum svnchrotron radio- infrared emissions are generally believed to originate in jets and low state jets have oen resolved. (Stirling ct al., Flat or inverted spectrum synchrotron radio- infrared emissions are generally believed to originate in jets and low state jets have been resolved (Stirling et al. + 2001) and studied over a wide range of luminosity variation (Corbel et al., 2001) and studied over a wide range of luminosity variation (Corbel et al. + 2000. 2003).," 2000, 2003)." + As a result of these outllows. it has been pointed out. (Fender. Gallo Jonker 2003) that the low quiescent luminosities of GDLIC cannot be taken as evidence of advective accretion lows (ΑΟΑΛΛΟ) through event horizons and as noted hy Abramowicz. IxIuznialk and Lasota (2002) there is presently no other observational evidence of event horizons.," As a result of these outflows, it has been pointed out (Fender, Gallo Jonker 2003) that the low quiescent luminosities of GBHC cannot be taken as evidence of advective accretion flows (ADAF) through event horizons and as noted by Abramowicz, Kluzniak and Lasota (2002) there is presently no other observational evidence of event horizons." + Whether or not the x-ravs originate in the jet. there is a strong coupling between x-ray. ancl radio emissions that must be related. to the accretion Dow. and. jet. structure.," Whether or not the x-rays originate in the jet, there is a strong coupling between x-ray and radio emissions that must be related to the accretion flow and jet structure." + AX universal low state racio X-ray correlation (Lgx L) (Gallo. Fender Pooley 2003) with a cutoll at the Iow/high state transition (Fender et al.," A universal low state radio / X-ray correlation $L_R \propto L_x^{0.7}$ ) (Gallo, Fender Pooley 2003) with a cutoff at the low/high state transition (Fender et al." + 1999. Tannenbaunm et al.," 1999, Tannenbaum et al." + 1972. Corbel οἱ al.," 1972, Corbel et al." + 2003) has been found for GBIIC and NS ( Migliari ct al., 2003) has been found for GBHC and NS ( Migliari et al. + 2008)., 2003). +> X similar radio / x-ray correlation (Alerloni. lHleinz Di Matteo. 2003. Falcke. Wworrding Markoll. 2003) and its suppression at. the ransition to the hieh/solt state (Maccarone. Gallo Fender 2003) have been shown to hold for AGN as well.," A similar radio / x-ray correlation (Merloni, Heinz Di Matteo 2003, Falcke, Körrding Markoff, 2003) and its suppression at the transition to the high/soft state (Maccarone, Gallo Fender 2003) have been shown to hold for AGN as well." + These radio / X-ray luminosity correlations have been examined or scale invariant jets (Lleing Sunvacy 2003. hereafter 11503). vielding constraints on the accretion processes.," These radio / X-ray luminosity correlations have been examined for scale invariant jets (Heinz Sunyaev 2003, hereafter HS03), yielding constraints on the accretion processes." + In he context of 11803. Merloni. Heinz Di Matteo (2003) (Llereafier MIIDO3) have examined their correlation for compatibility with various accretion Dow models and found »tter Consisteney with an ADAE. / jet model than with racliatively cllicient disk. / jet or pure jet mocels.," In the context of HS03, Merloni, Heinz Di Matteo (2003) (Hereafter MHD03) have examined their correlation for compatibility with various accretion flow models and found better consistency with an ADAF / jet model than with radiatively efficient disk / jet or pure jet models." + An ADAP/jet model (Meier. 2001) can also account or the low/high spectral state transition as a transition rom an ADAE to a standard thin disk., An ADAF/jet model (Meier 2001) can also account for the low/high spectral state transition as a transition from an ADAF to a standard thin disk. + lt relies on a rapid black hole spin to provide energy to drive the jet., It relies on a rapid black hole spin to provide energy to drive the jet. + The model predicts that stable high/soft states would. not exist for GIN more massive than 710747. (Meier 2001) or. with more generous allowance for hysteresis effects. ~4LOPAL. (Maccarone. Gallo Fender 2008).," The model predicts that stable high/soft states would not exist for AGN more massive than $7 \times 10^4 M_\odot$ (Meier 2001) or, with more generous allowance for hysteresis effects, $\sim 4\times 10^6 M_\odot$ (Maccarone, Gallo Fender 2003)." + The theoretical mass limit occurs because the Ededineton scaled luminosity at which a thin disk (constrained to match a raciatively inellicient ΑΟΛΙ accretion rate) becomes radiation dominated is mass dependent., The theoretical mass limit occurs because the Eddington scaled luminosity at which a thin disk (constrained to match a radiatively inefficient ADAF accretion rate) becomes radiation dominated is mass dependent. + Since the high/soft state nevertheless appears to exist in AGN more massive han 6«107A7.. the ADAE. transition model cannot. be regarded: as established.," Since the high/soft state nevertheless appears to exist in AGN more massive than $6 \times 10^7 M_\odot$, the ADAF transition model cannot be regarded as established." + Understanding the origin of the mass limit error of the model remains an open question (Maccarone. Gallo Fencer 2003).," Understanding the origin of the mass limit error of the model remains an open question (Maccarone, Gallo Fender 2003)." + Black hole models that rely entirely on the jet. to srocluce the power-law x-ray emissions may have dilliculties with constraints on the physical size of a jet., Black hole models that rely entirely on the jet to produce the power-law x-ray emissions may have difficulties with constraints on the physical size of a jet. + For clipping sources the size of the region of the low state power-law xoduction has been found (Church Balueitisska-Church 2003) to be x101(0 em., For dipping sources the size of the region of the low state power-law production has been found (Church Balucińsska-Church 2003) to be $\leq 10^9$ cm. + In aclelition.PI there is. the enigma. ofB the size of the hard spectral. producing region increasing while he jet dies in the high state.," In addition, there is the enigma of the size of the hard spectral producing region increasing while the jet dies in the high state." + Lt is also unclear how black hole and NS behaviours could be so similar with the magnetic iclds of even the weakly magnetized atoll class NS being capable of disrupting the inner accretion disk., It is also unclear how black hole and NS behaviours could be so similar with the magnetic fields of even the weakly magnetized atoll class NS being capable of disrupting the inner accretion disk. + On the other mane. we will show that our MECO moclel. with a raciatively ellicient disk. will provide a superior fit to the radio / X-ray correlations and. provide a mass scale invariant cutoll at the ugh/solt state transition while permitting racdio-infrared and some of the x-ray luminosity to originate in a jet.," On the other hand, we will show that our MECO model, with a radiatively efficient disk, will provide a superior fit to the radio / X-ray correlations and provide a mass scale invariant cutoff at the high/soft state transition while permitting radio-infrared and some of the x-ray luminosity to originate in a jet." + In the magnetic propeller model. the inner clisk and magnetosphere radius. rj. determines the spectral state.," In the magnetic propeller model, the inner disk and magnetosphere radius, $r_m$, determines the spectral state." + Very low to quiescent states correspond to an inner accretion clisk raclius outside the light evlinder., Very low to quiescent states correspond to an inner accretion disk radius outside the light cylinder. + In the low/hard/racdio-loud/jet-producing state of the active propeller regime. the inner disk radius lies between light evlincer and Ixeplerian CO-rotation radii.," In the low/hard/radio-loud/jet-producing state of the active propeller regime, the inner disk radius lies between light cylinder and Keplerian co-rotation radii." + Most. and perhaps all. of the accretion How is ejected in the low/harc state.," Most, and perhaps all, of the accretion flow is ejected in the low/hard state." + The high/soft state corresponds to an inner disk inside the co-rotation radius with the How of accreting matter able to reach the central object. where it produces an ultrasoft. thermal spectral component., The high/soft state corresponds to an inner disk inside the co-rotation radius with the flow of accreting matter able to reach the central object where it produces an ultrasoft thermal spectral component. + The cooling of the accretion disk corona and the ormer base of the jet by the soft photons also contributes o à softening of the x-ray spectrum., The cooling of the accretion disk corona and the former base of the jet by the soft photons also contributes to a softening of the x-ray spectrum. + The whole complex of spectral state switch phenomoena is related to the cessation or regeneration. of magnetospherically driven. outflow. and oesence or absence of dominant soft emissions [rom a central source., The whole complex of spectral state switch phenomena is related to the cessation or regeneration of magnetospherically driven outflow and presence or absence of dominant soft emissions from a central source. + The inner clisk temperature is generally high enough to xoduce a very diamagnetie plasma at the magnetopause., The inner disk temperature is generally high enough to produce a very diamagnetic plasma at the magnetopause. + Surface currents on the inner disk distort the magnetopause and they also substantially shield the trailing disk such hat the region of strong disk-magnetosphere interaction is mostly confined to a ring or torus. of width dr and half height ff.," Surface currents on the inner disk distort the magnetopause and they also substantially shield the trailing disk such that the region of strong disk-magnetosphere interaction is mostly confined to a ring or torus, of width $\delta r$ and half height $H$." + Vhis shielding leaves most of the disk under the influence of its own internal shear dyvnamo fields. (e.g. Balbus llawlev 1998. Balbus 2003).," This shielding leaves most of the disk under the influence of its own internal shear dynamo fields, (e.g. Balbus Hawley 1998, Balbus 2003)." + At the inner cisk radius the magnetic field of the central MIEC'O is much stronger than the shear dvnamo field generatedwithin the inner acerction disk., At the inner disk radius the magnetic field of the central MECO is much stronger than the shear dynamo field generatedwithin the inner accretion disk. + In MIID approximation. the force density on the inner ring is P=(NoD) Bide.," In MHD approximation, the force density on the inner ring is $F_v = (\nabla \times B) \times B / 4\pi$ ." + For simplicity. we assume," For simplicity, we assume" +the svstem. even for fractal particles.,"the system, even for fractal particles." + Even though the variation in the properties of the evolving distribution due to porous particles are incorporated directly into the kernel. ancl are lolded into the integration of the explicit approach. the effects of fractal aggregates can. nonetheless. affect which moments characterize what properties in the semi-implicit (or implicit) approach.," Even though the variation in the properties of the evolving distribution due to porous particles are incorporated directly into the kernel, and are folded into the integration of the explicit approach, the effects of fractal aggregates can, nonetheless, affect which moments characterize what properties in the semi-implicit (or implicit) approach." + For example. (he wavelength-independent opacity expressed in Eq. (," For example, the wavelength-independent opacity expressed in Eq. (" +32) takes the form &=(προπιο26D.)Aloep/AM.,32) takes the form $\kappa = (\pi r_o^2/m_o^{2/D})M_{2/D}/M_1$. + It should be noted that (he value D=2 represents a special case in (hat (he relative velocities in the Epstein regime do not depend on the mass of the fractal particle., It should be noted that the value $D=2$ represents a special case in that the particle-to-particle relative velocities in the Epstein regime do not depend on the mass of the fractal particle. + Indeed. this would seem to indicate that fractal growth can proceed unabated with (he corresponding stopping time of the fluffy aggregate remaining the same as that of a single monomer. which would have a significant effect on other particle properties.," Indeed, this would seem to indicate that fractal growth can proceed unabated with the corresponding stopping time of the fluffy aggregate remaining the same as that of a single monomer, which would have a significant effect on other particle properties." + In. particular. the waveleneth-independent opacity for D=2 is constant.," In particular, the wavelength-independent opacity for $D=2$ is constant." + However. impacts will eventually lead to compaction or even fragmentation depending on the relative velocities 2007)..," However, impacts will eventually lead to compaction or even fragmentation depending on the relative velocities \citep[e.g.,][]{orm07b}." + Both Iractal grains and non-Iractal particles in (he same mass distribution can be ireated in the explicit approach without any modifications. while a piecewise fit to the integrated kernel ο(1) 2.2.2) can be used in order (ο account for the change in regimes in the semi-inmplicit approach.," Both fractal grains and non-fractal particles in the same mass distribution can be treated in the explicit approach without any modifications, while a piecewise fit to the integrated kernel $C_k(m)$ 2.2.2) can be used in order to account for the change in regimes in the semi-implicit approach." + We have demonstrated an approach to solving the collisional coagulation equation with an arbitrary collisional kernel which should be useful in cases when it is only necessary {ο keep (rack of general properties of the distribution., We have demonstrated an approach to solving the collisional coagulation equation with an arbitrary collisional kernel which should be useful in cases when it is only necessary to keep track of general properties of the distribution. + This approach involves solving a finite set of coupled differential equations in terms of the integer moments of the particle size distribution., This approach involves solving a finite set of coupled differential equations in terms of the integer moments of the particle size distribution. + The number of equations (and (ius moments) needed depends on (he number of properties being (tracked., The number of equations (and thus moments) needed depends on the number of properties being tracked. + The advantage of the moments method approach is that il allows for considerable savings in computational (me compared to direct integration of the coagulation equation. which requires keeping (rack of every particle size al every spatial location and timestep.," The advantage of the moments method approach is that it allows for considerable savings in computational time compared to direct integration of the coagulation equation, which requires keeping track of every particle size at every spatial location and timestep." + In this paper we have specifically studied (he growth of the largest particle under the assumption that the particle size distribution is a powerlaw: however. the technique can be extended to track other properties of the distribution that may change with time.," In this paper we have specifically studied the growth of the largest particle under the assumption that the particle size distribution is a powerlaw; however, the technique can be extended to track other properties of the distribution that may change with time." + There are many reasons to believe (hiat a powerlaw size distribution is a natural endestate of particle growth. especially those with equal mass per decade. because thev have sell- properties (Cuzzi&Weilenschilling2006).," There are many reasons to believe that a powerlaw size distribution is a natural end-state of particle growth, especially those with equal mass per decade, because they have self-preserving properties \citep{cuz06}." +. With (hie assumption of a powerlaw distribution. we have provided two different. approaches to solving the moment equations.," With the assumption of a powerlaw distribution, we have provided two different approaches to solving the moment equations," +Figure 1 shows the overall structure of the continuum emission from Arp220 as observed with VLBI.,Figure 1 shows the overall structure of the continuum emission from Arp220 as observed with VLBI. + The sensitivity level achieved in this image is significantly better than earlier efforts (Smith et al..," The sensitivity level achieved in this image is significantly better than earlier efforts (Smith et al.," + 1998a; Rovilos et al..," 1998a; Rovilos et al.," + 2003). aud represents the current state of the art in high sensitivity radio imaging.," 2003), and represents the current state of the art in high sensitivity radio imaging." + As a result of the sharply reduced. noise levels. we have been able to detect 49 continuum point sources in Arp 220 (29 in the west nucleus. ancl 20 in (he east).," As a result of the sharply reduced noise levels, we have been able to detect 49 continuum point sources in Arp 220 (29 in the west nucleus, and 20 in the east)." + From the current observations. we note the following pertinent features of the structure:," From the current observations, we note the following pertinent features of the structure:" +in which we have assumed that the nucleus is at heliocentric distance /2 and is spherical. of density p. radius r and non-rotating.,"in which we have assumed that the nucleus is at heliocentric distance $R$ and is spherical, of density $\rho$ , radius $r$ and non-rotating." + Also. G is the gravitational constant and. M. is the mass of the Sun.," Also, $G$ is the gravitational constant and $M_{\odot}$ is the mass of the Sun." + The dimensionless quantity » depends upon the grain shape. composition and porosity but is principally a funetion of particle size. e.," The dimensionless quantity $\beta$ depends upon the grain shape, composition and porosity but is principally a function of particle size, $a$." +" As a useful first approximation. we take JcL/a,. where a, is the grain radius expressed in microns (Bohren ΕΠ 1983)."," As a useful first approximation, we take $\beta \sim 1/a_{\mu}$, where $a_{\mu}$ is the grain radius expressed in microns (Bohren and Huffman 1983)." + Then. the condition for a grain to be lost to raciation pressure becomes p = 2000 ke m and expressing the nucleus radius in km and the heliocentric distance in AU. we find the eritieal radius for grain loss to be lhm Equation (17)) (also plotted in Figure 5)) shows that. for example. a 1 km radius object αἱ R= 3 AU would lose dust grains smaller than about à~ 1 jan. Optically active particles (a> 0.1 pom) can be swept away throughout the asteroid belt provided their parent bodies are smaller (han about 10 km.," Then, the condition for a grain to be lost to radiation pressure becomes Substituting $\rho$ = 2000 kg $^{-3}$ and expressing the nucleus radius in km and the heliocentric distance in AU, we find the critical radius for grain loss to be Equation \ref{amu}) ) (also plotted in Figure \ref{critical}) ) shows that, for example, a 1 km radius object at $R$ = 3 AU would lose dust grains smaller than about $a \sim$ 1 $\mu$ m. Optically active particles $a \ge$ 0.1 $\mu$ m) can be swept away throughout the asteroid belt provided their parent bodies are smaller than about 10 km." + Larger particles can be lost if the nucleus is rotating and has an aspherical shape., Larger particles can be lost if the nucleus is rotating and has an aspherical shape. + The above considerations are simplistic in that Chev take no account of the direction of the radiation pressure acceleration relative to the nucleus., The above considerations are simplistic in that they take no account of the direction of the radiation pressure acceleration relative to the nucleus. + Grains releasecl on the lor instance. will be pushed back into the nucleus by radiation pressure [rom above.," Grains released on the day-side, for instance, will be pushed back into the nucleus by radiation pressure from above." + On the other hand. grains released near the terminator will feel a net [orce in a direction determined by (he vector sum of the local gravitational acceleration and radiation pressure acceleration.," On the other hand, grains released near the terminator will feel a net force in a direction determined by the vector sum of the local gravitational acceleration and radiation pressure acceleration." + These erains have the potential to escape., These grains have the potential to escape. + The principal limitation to efficacy of radiation pressure sweeping is. as will electrostatic launch. set by contact Lorces (hat hold small particles to the asteroicl surface.," The principal limitation to efficacy of radiation pressure sweeping is, as with electrostatic launch, set by contact forces that hold small particles to the asteroid surface." + If these forces can be overcome. then radiation pressure sweeping can plav a role across (he asteroid belt for 10 kin sizedasteroids and smaller.," If these forces can be overcome, then radiation pressure sweeping can play a role across the asteroid belt for 10 km sizedasteroids and smaller." + The Κον observational property of these objects is that the activity is recurrent. (Isieh, The key observational property of these objects is that the activity is recurrent (Hsieh +controversy whether observed low-mass haloes around dwarf galaxies have core-like shallow profiles (?)).,controversy whether observed low-mass haloes around dwarf galaxies have core-like shallow profiles \citealt{CorePIDwarfGalaxy2011}) ). +" In the simple scenarios presented below and in our line-of-sight lensing simulations (see 85 and 86), we model perturbing haloes either as truncated singular isothermal or truncated NFW profiles, normalized with their masses and truncated at their virial radii."," In the simple scenarios presented below and in our line-of-sight lensing simulations (see $\S$ 5 and $\S$ 6), we model perturbing haloes either as truncated singular isothermal or truncated NFW profiles, normalized with their masses and truncated at their virial radii." +" We follow the convention of defining the virial radius as rooo, the radius within which the mean halo density is 200 times the critical density of the Universe (at the appropriate redshift z)."," We follow the convention of defining the virial radius as $r_{200}$, the radius within which the mean halo density is 200 times the critical density of the Universe (at the appropriate redshift $z$ )." + The mass enclosed within rooo is denoted as Maoo., The mass enclosed within $r_{200}$ is denoted as $M_{200}$. +" For the NFW profile, the concentration parameter is Cogo=rooo/Ts, where rs is the scale radius."," For the NFW profile, the concentration parameter is $C_{200} \equiv r_{200}/r_{\rm s}$, where $r_{\rm s}$ is the scale radius." + This parameter is thought to correlate with mass M»oo and redshift z., This parameter is thought to correlate with mass $M_{200}$ and redshift $z$. +" A number of relations have been proposed in the literature, based on N-body simulations."," A number of relations have been proposed in the literature, based on $N$ -body simulations." +" In this work, we adopt the concentration-mass relation of ? (hereafter M08) wherever we model perturbers as truncated NFW profiles."," In this work, we adopt the concentration-mass relation of \citet{Maccio08CM} (hereafter M08) wherever we model perturbers as truncated NFW profiles." +" The fitting formula (for a WMAP-1 cosmology, close to that of the Millennium-II simulation) is given by: where H?(z)=Hé[Qa+Qm(1z)?]."," The fitting formula (for a WMAP-1 cosmology, close to that of the Millennium-II simulation) is given by: where $H^2(z)=H_0^2 [\Omega_\Lambda+\Omega_m(1+z)^3]$." + The concentration-mass relation of ? was used by ?? to study how line-of-sight haloes (10°Mo«€m< 10°Mo) contribute to the flux anomaly problem.," The concentration-mass relation of \citet{BullockNFWC2001} was used by \citet{Metcalf2005a,Metcalf2005b} to study how line-of-sight haloes $10^{6}M_{\odot} \leqslant m \leqslant 10^{9}M_{\odot}$ ) contribute to the flux anomaly problem." +" The adopted fitting formula was given by (?)): To compare with ??,, we also perform our analysis"," The adopted fitting formula was given by \citealt{Metcalf2005b}) ): To compare with \citet{Metcalf2005a,Metcalf2005b}, , we also perform our analysis" +opacities.,. +. lu the deep 1iterior of RGB stars. thermal conduction by electrons serves as an important means of erey 1laisfer.," In the deep interior of RGB stars, thermal conduction by electrons serves as an important means of energy transfer." +" The thermal coucductivity uuder these conditions tlierefore serves to establish the tiperature [n]oO""adieut in red giaut interiors auc determine when the core becomes hot enoug1 to ignite helju", The thermal conductivity under these conditions therefore serves to establish the temperature gradient in red giant interiors and determine when the core becomes hot enough to ignite helium. + C'ouductive opacities are one [9] e most significant sources of uncertainty ou tlie upper RGB. so a close examination of or eurreli iderstanding in this area is appropriate.," Conductive opacities are one of the most significant sources of uncertainty on the upper RGB, so a close examination of our current understanding in this area is appropriate." + There are essentially two treatvents of condLCive opaci: avallable [or use in red giant models: the tabulated values of Hubbard&Laipe(1969) and te more recent caleulatious of Hohetal.(1983)., There are essentially two treatments of conductive opacity available for use in red giant models: the tabulated values of \citet{hubbard} and the more recent calculations of \citet{itoh83}. +. However. as Catelatοἱal.(1996 OIL out. tie [tohetal.(1983) calculatious were mace for conditions characteristic of wilte clwarls and neiron stars: red giant cores do not fall within their range of validity.," However, as \citet{cat96} point out, the \citet{itoh83} calculations were made for conditions characteristic of white dwarfs and neutron stars; red giant cores do not fall within their range of validity." +" S»ecifically. the Iohetal. results are preseuted as au analytic fitting formula in terms of the paralneter which cha""acterizes the strength of the electrostatic interaction between ious in a plasuia."," Specifically, the \citeauthor{itoh83} results are presented as an analytic fitting formula in terms of the parameter which characterizes the strength of the electrostatic interaction between ions in a plasma." + Here e is he electron charge. Z is the atomic number. Ay; is the Boltzinanu coustant. aud rο”... he ion-sphiere radius with 5»; tle number ceusity of ious.," Here $e$ is the electron charge, $Z$ is the atomic number, $k_B$ is the Boltzmann constant, and $r = [3/(4 \pi n_i)]^{1/3}$ is the ion-sphere radius with $n_i$ the number density of ions." + The domain where 2<0S.171 'epresenits natter in the liqid metal phase. while τς2 corresponds more typically to a Boltzall eas.," The domain where $2 \lesssim +\Gamma \lesssim 171$ represents matter in the liquid metal phase, while $\Gamma \lesssim 2$ corresponds more typically to a Boltzmann gas." +" The itting [oruula o ""μοιetal.(1983). intended for application to deuse matter in tle liquid metal ghase. js valic ouly iu the ratgeo 2«/Np<160. while in red giant cores D is cousideraby lower."," The fitting formula of \citet{itoh83} intended for application to dense matter in the liquid metal phase, is valid only in the range $2 +\le \Gamma \le 160$, while in red giant cores $\Gamma$ is considerably lower." + Applying he reslts of Itohetal.(1983 to RGB stars therelore requires extrapolaing lthe fitting ormula from |icticl inetal concitious to Boltzimam gas οςuxditions. aud it is not clear how 1Mwh error liis extrapola1O introduces.," Applying the results of \citet{itoh83} to RGB stars therefore requires extrapolating the fitting formula from liquid metal conditions to Boltzmann gas conditions, and it is not clear how much error this extrapolation introduces." + Because o ulis. Caelanetal.(1996 conclude that the Lampe(1969) values are to )e preferre |: present.," Because of this, \citet{cat96} + conclude that the \citet{hubbard} values are to be preferred at present." + The treatment of condiClive opacity in our stellar evolutio1 calculaious is based on the Hubbard&Lampe(1969). tables. along wihb the elatis‘istic extension proviled by Canuto(1970) for higher densities.," The treatment of conductive opacity in our stellar evolution calculations is based on the \citet{hubbard} tables, along with the relativistic extension provided by \citet{canuto} for higher densities." + Specifically. we empον a set of analvtic fitting Oornmiulas rou Sweigart (LO73):: for logpx5.8. we use Sweigarts fit to tle Hubyard&Lamye tables. while for logp>6.0 we Ilse Sweigart's fit to the Camto relativistic opacities.," Specifically, we employ a set of analytic fitting formulas from \citet{sweig}; ; for $\log \rho \le 5.8$, we use Sweigart's fit to the \citeauthor{hubbard} tables, while for $\log \rho \ge 6.0$ we use Sweigart's fit to the Canuto relativistic opacities." + For 5.84.5$ keV (Mushotzky 2004 and reference within), even though medium temperature clusters, $2-4$ keV, have abundances of $\sim 0.4$ (Baumgartner et al." + 2005)., 2005). + Phere seems to be a slight redshift dependence: NMM ancl Chandra show no evolution in Fe abundances up to z&OS (e.g. Mushotzky. 2004 and reference within).," There seems to be a slight redshift dependence; XMM and Chandra show no evolution in Fe abundances up to $z\approx0.8$ (e.g., Mushotzky 2004 and reference within)." + However. a certain degree of enrichment must have occurred.," However, a certain degree of enrichment must have occurred." + Balestra et al. (, Balestra et al. ( +2007) found that the average iron content of IC eas at 2=O0 is a factor ~2 higher than at 2=~ 1.2.,2007) found that the average iron content of IC gas at $z=0$ is a factor $\sim 2$ higher than at $z=\sim1.2$ . + Several low-redshilt. bright X-ray groups were shown by Finoguenoy Ponman (1999) to have Fe abundances of =0.8 at radii higher than 100 κρο," Several low-redshift, bright X-ray groups were shown by Finoguenov Ponman (1999) to have Fe abundances of $\lesssim 0.3$ at radii higher than $\sim 100$ kpc." + For almost anv kind of abundance gradient and evolution the CXRB contributions of high mass groups and clusters is between our derivec values for of20 ancl ;1=0.3., For almost any kind of abundance gradient and evolution the CXRB contributions of high mass groups and clusters is between our derived values for $A=0$ and $A=0.3$. + The impact of using à mass function dillerent than PS was explored by re»eating the calculations with the ST mass function. which is characterised. by higher abuncances of hieh-mass halos ir1 the mass range AL>»4-10 ht M. with respect (o 11e Corresponding numbers predicted: by the PS mass funcion.," The impact of using a mass function different than PS was explored by repeating the calculations with the ST mass function, which is characterised by higher abundances of high-mass halos in the mass range $M>4\cdot10^{13}$ $_{0.7}^{-1}$ $_{\odot}$ with respect to the corresponding numbers predicted by the PS mass function." + The enhanced. abundances result. in appreciably higher intensity levels that possibly exceed the measured SRB range for high values of Cy... even in ACDAL., The enhanced abundances result in appreciably higher intensity levels that possibly exceed the measured XRB range for high values of $C_{gas}$ even in $\Lambda$ CDM. + Clearly. given that not all of the NRB in the O48Ex1 keV energy range is due to high-mass groups and. clusters. this implied excess provides a very tight constraint on the maximum. value of Coo. (," Clearly, given that not all of the XRB in the $0.4\lesssim E \lesssim 1$ keV energy range is due to high-mass groups and clusters, this implied excess provides a very tight constraint on the maximum value of $C_{gas}$. (" +Note that the mass range of the Jenkins et al. (,Note that the mass range of the Jenkins et al. ( +2001) mass function. which was deduced from N-bocky simulations. is irrelevant to our work here.),"2001) mass function, which was deduced from N-body simulations, is irrelevant to our work here.)" + Lf Coos7C'oyr. where Cpa is the concentration parameter. the NRB can put strong constrains on the value of the concentration parameter.," If $C_{gas}\approx C_{DM}$, where $C_{DM}$ is the concentration parameter, the XRB can put strong constrains on the value of the concentration parameter." + Finally. we note that whereas we have accounted. for emission. from. groups and clusters. our treatment does not include emission. from the filamentary WIILM.," Finally, we note that whereas we have accounted for emission from groups and clusters, our treatment does not include emission from the filamentary WHIM." + With temperatures ~10° or slightly higher. WIIIM. emission could also contribute somewhat to the CARB.," With temperatures $\sim 10^6$ or slightly higher, WHIM emission could also contribute somewhat to the CXRB." + Clearly. any aciditional contributionwill only strengthen our conclusions on the viability of alternative models in which the predicted spectral bumpexceeds the observed range.," Clearly, any additional contributionwill only strengthen our conclusions on the viability of alternative models in which the predicted spectral bumpexceeds the observed range." + We wish to thank the anonymous referee for a thorough, We wish to thank the anonymous referee for a thorough +F(e) in order to solve (2)) (????)..,"$F(\psi)$ in order to solve \ref{eq:gra2}) ) \citep{uch81,ham83,bro98,lit01}." + However. this approach leads (ο an inconsistency.," However, this approach leads to an inconsistency." + In the perfectly conducting limit. material is frozen (ο magnetic Ποιά lines.," In the perfectly conducting limit, material is frozen to magnetic field lines." + Hence (he mass dM=2adefdspir(s).dls\frsinave}! enclosed between two adjacent παν surfaces c ancl idrdo (where the integral is along a field line) equals the mass enclosed before accretion plus any mass added during accretion.material (??7)..," Hence the mass $dM = 2\pi d\psi \int ds\, \rho[r(s),\theta(s)] + r\sin\theta |\nabla\psi|^{-1}$ enclosed between two adjacent flux surfaces $\psi$ and $\psi+d\psi$ (where the integral is along a field line) equals the mass enclosed before accretion plus any mass added during accretion, \citep{mou74,mel01,pay04}. ." +" To calculate & correctly. one must specily (LU/de according to the global accretion plivsies. with Fv) following from otherwise. if F(v) is specified. αλα changes as a function of M, in a manner that inconsistently leads to cross-field transport."," To calculate $\psi$ correctly, one must specify $dM/d\psi$ according to the global accretion physics, with $F(\psi)$ following from otherwise, if $F(\psi)$ is specified, $dM/d\psi$ changes as a function of $M_{\rm a}$ in a manner that inconsistently leads to cross-field transport." + The functional form of Fe). determined through (3)). changes as M4 increases.," The functional form of $F(\psi)$, determined self-consistently through \ref{eq:gra4}) ), changes as $M_{\rm a}$ increases." + This property. newly recognized in the context of magnetic burial (??).. has an important astrophysical consequence: il produces a greater hvdromagnetie deformation Chan predicted by previous authors. because polar (accreting) and equatorial (nonaccretng) flux. (tubes maintain siric(idlv separate identities through (3)). without exchanging material. aud hence the equatorial magnetic field is highly compressed.," This property, newly recognized in the context of magnetic burial \citep{mel01,pay04}, has an important astrophysical consequence: it produces a greater hydromagnetic deformation than predicted by previous authors, because polar (accreting) and equatorial (nonaccreting) flux tubes maintain strictly separate identities through \ref{eq:gra4}) ), without exchanging material, and hence the equatorial magnetic field is highly compressed." + We solve (2)) and (23)) simultaneously for eG.) ancl p(r.9) subject to the line-tving (Dirichlet) boundary. condition ο.6)=vysin?@ at the stellar surface. such that the footpoints of magnetic field lines are anchored to the heavy. highly conducting crust (??)..," We solve \ref{eq:gra2}) ) and \ref{eq:gra4}) ) simultaneously for $\psi(r,\theta)$ and $\rho(r,\theta)$ subject to the line-tying (Dirichlet) boundary condition $\psi(R_\ast,\theta)=\psi_\ast \sin^2\theta$ at the stellar surface, such that the footpoints of magnetic field lines are anchored to the heavy, highly conducting crust \citep{mel01,pay04}." +" We adopt a mass-Iux distribution. (c)=IMSe""pet9)FL that embodies the essence of disk accretion. namely that the accreted mass is distributed. rather evenly within the polar flux tube 01 (Dekeusteim Mileroii 1981).," The Lagragian MOND field equations lead to a modified version of Poisson's equation given by where $\rho$ is the density, $a_{0}$ is a universal acceleration of the order of $10^{-8}$ cm $^{-2}$, and $\mu(x)$ is some interpolating function with the property that $\mu(x)=x$ for $x\ll 1$ and $\mu(x)=1$ for $x\gg 1$ (Bekenstein Milgrom 1984)." + To a good approximation. thereal acceleration at the iidplaue of a isolated. flattened axisviunietrical svsten. g. às related with the Newtonian acceleration. ga. by: The two most popular choices for the interpolating function are the “simple” p-function. sugeested ly FEiunaey Binney (2005). and the “standard” p-functiou proposed by Mileroii (1983).," To a good approximation, the acceleration at the midplane of a isolated, flattened axisymmetrical system, $\vecg$, is related with the Newtonian acceleration, $\vecg_{N}$, by: The two most popular choices for the interpolating function are the “simple” $\mu$ -function, suggested by Famaey Binney (2005), and the “standard” $\mu$ -function proposed by Milgrom (1983)." + For à sample of galaxies having a gradual transition from the Newtonian luit in the inner regions to the MOND limit iu the outer parts. Famacy ct al. (," For a sample of galaxies having a gradual transition from the Newtonian limit in the inner regions to the MOND limit in the outer parts, Famaey et al. (" +2007) aud Saunders Noordermecr (2007) conclude that the plausability of the relative stellar mass-to-lieht ratios for bulge and disk. as well as the ecuerally siualler global AZ/L. lend support to the simple j77fuuction (see also Weijmans et al.,"2007) and Sanders Noordermeer (2007) conclude that the plausability of the relative stellar mass-to-light ratios for bulge and disk, as well as the generally smaller global $M/L$, lend support to the simple $\mu$ -function (see also Weijmans et al." + 2008 and Gentile et al., 2008 and Gentile et al. + 2011)., 2011). + Certainly Holl is uot at isolation: it d8 oe1ibbeded in the external gravitational field of ΑΙΣΙ evou, Certainly HoII is not at isolation; it is embbeded in the external gravitational field of M81 group. + Since the modified Poissou equation is nonlinear. the internal acceleration of a system depends on the external acceleration field goa (Bokeusteiu Mileroi 1981).," Since the modified Poisson equation is nonlinear, the internal acceleration of a system depends on the external acceleration field $\vecg_{\rm ext}$ (Bekenstein Milgrom 1984)." + Iu order to quantity the external Ποια effect (EFE) it is important to compare the internal and external accelerations.," In order to quantity the external field effect (EFE), it is important to compare the internal and external accelerations." + Assuming that the ADSL group is bound. the exterual acceleration is 0.7.«LO! cm P7 (IGuacheutsev- ct al.," Assuming that the M81 group is bound, the external acceleration is $0.7\times 10^{-10}$ cm $^{-2}$ (Karachentsev et al." + KE2002)., 2002). + The1 [Toll internal+ accelerations are of ς10. ems ? aud 2&109 em 7 at R=T7 kpe aud R=20 kpc. respectively.," The HoII internal accelerations are of $6\times 10^{-10}$ cm $^{-2}$ and $2\times 10^{-10}$ cm $^{-2}$ at $R=7$ kpc and $R=20$ kpc, respectively." + Thus. EFE should be small at R<10 kpe.," Thus, EFE should be small at $R<10$ kpc." + Iudecd. the fiatuess of the rotation curve of WoT would be incompatible ith Πο being dominated by the external field.," Indeed, the flatness of the rotation curve of HoII would be incompatible with HoII being dominated by the external field." +3031. NGC 4579. and NGC 5033. in contrast to Sevfert 1s which show iron Ix emission at 6.4. keV. The center energy. of the irongenerally Ix lines in NGC 3031 and NGC 4579 are 6.7 keV. (Ishisaki et al.,"3031, NGC 4579, and NGC 5033, in contrast to Seyfert 1s which generally show iron K emission at 6.4 keV. The center energy of the iron K lines in NGC 3031 and NGC 4579 are 6.7 keV (Ishisaki et al." + 1996: Terashima et al., 1996; Terashima et al. + 19982). which is significantly higher than Sevlert 1s. while that of NGC 5038 is 6.4 keV Clerashima οἱ al.," 1998a), which is significantly higher than Seyfert 1s, while that of NGC 5033 is 6.4 keV (Terashima et al." + 1998b)., 1998b). + These iron line are possibly due to dilference of physical states of accretion disksproperties between LLAGNs and luminous ACGNs., These iron line properties are possibly due to difference of physical states of accretion disks between LLAGNs and luminous AGNs. + 3.2 N-rav. variability and black hole mass Rapid time on time scales less than one cay is generally observed in luminous variability 1 ealaxies., 3.2 X-ray variability and black hole mass Rapid time variability on time scales less than one day is generally observed in luminous Seyfert 1 galaxies. + Lt is well known that lower σον[ο 1 tend to Sevfertshow larger amplitude and shorter timeLuminosity scale galaxies 1993: Nandra et al., It is well known that lower luminosity Seyfert 1 galaxies tend to show larger amplitude and shorter time scale variability (Lawrence Papadakis 1993; Nandra et al. + 19972), 1997a). + We variabilitysearched for (Lawrenceshort-term Papadakis on time scales less than one clay for the galaxies in the present variabilit, We searched for short-term variability on time scales less than one day for the galaxies in the present sample. +yOnly two low luminosity Sevlert 1 ealaxies (NGC 3031 and NGC 5033) sample.indicate variability on time scale of sec (Ishisaki et al., Only two low luminosity Seyfert 1 galaxies (NGC 3031 and NGC 5033) indicate variability on time scale of $\sim10^4$ sec (Ishisaki et al. + 1996: Terashima et al., 1996; Terashima et al. + 1998b)., 1998b). + Phus small amiplitτα or no detectable is quite common in LLACGNSs. and luminosity. dependence of variability variabilityproperties observed in luminous Sevfert 1s are no seen in LLAGN with luminosities below ~5«107.," Thus small amplitude or no detectable variability is quite common in LLAGNs, and luminosity dependence of variability properties observed in luminous Seyfert 1s are no longer seen in LLAGN with luminosities below $\sim5\times10^{41}$." + One longer of such difference between luminous and less eresluminous the possibility of disk is between these two ACGNsclassesis that(Ptak et al., One possibility of such difference between luminous and less luminous AGNs is that the structure of an accretion disk is different between these two classes (Ptak et al. + structure1998)., 1998). + anAlternatively.aceretion i£ the dillerentvariability time scale reflects the size of the emitting the variability on longer time scales would infer X-raysystem size and region.larger black hole mass.," Alternatively, if the variability time scale reflects the size of the X-ray emitting region, the variability on longer time scales would infer larger system size and larger black hole mass." + We attempt to largermeasure black bole masses in LLAGNs from X-ray variability using the method by Havashida et al. (, We attempt to measure black hole masses in LLAGNs from X-ray variability using the method by Hayashida et al. ( +1998).,1998). + Llavashicda et al. (, Hayashida et al. ( +1998) defined a new variabilitv time scale: the frequency. at which power (frequeney) crosses a certain level. where a (normalizednormalized spectral density)« is defined as the power spectral divided by the power spectralsource densityintensity,"1998) defined a new variability time scale: the frequency at which (normalizedpower spectral density) $\times$ (frequency) crosses a certain level, where a normalized power spectral density is defined as the power spectral density divided by the averaged source intensity squared." + Hf we assume that densitythe black hole masses are averaged.linearly proportional to the squared. time scale and that the mass of N-I is 104... which is used as a variabilityreference we can estimate the black€vg hole mass Πλ... point," If we assume that the black hole masses are linearly proportional to the variability time scale and that the mass of Cyg X-1 is $M_{\odot}$, which is used as a reference point, we can estimate the black hole mass in AGNs." +.We estimate the black hole masses from light curves of bright LLAGNs (NGC 1097. 3031. 3998. 4579. 5033. 4258) under an additional the spectral density for ΕλαΝο are same as luminous AGNs. Le. assumption:the power-spectralpower slope is àz 2.," We estimate the black hole masses from light curves of bright LLAGNs (NGC 1097, 3031, 3998, 4579, 5033, 4258) under an additional assumption: the power spectral density for LLAGNs are same as luminous AGNs, i.e. the power-spectral slope is $\alpha\approx2$ ." + We obtained lower limit, We obtained lower limit +As has been the case in the past. new data on this source raise as many questions as they answer.,"As has been the case in the past, new data on this source raise as many questions as they answer." + We lack an understanding of how PSR egenerates such a fast-moving and collimated outflow over such large scales. nor is it clear why such a striking feature is not seen in most other PWNe.," We lack an understanding of how PSR generates such a fast-moving and collimated outflow over such large scales, nor is it clear why such a striking feature is not seen in most other PWNe." + We have also not addressed the nature of the interaction between this outflow and the surrounding SNR: a forthcoming paper will present an analysis of X-ray emission from the rregion. which may better elucidate the physical conditions associated with this process.," We have also not addressed the nature of the interaction between this outflow and the surrounding SNR; a forthcoming paper will present an analysis of X-ray emission from the region, which may better elucidate the physical conditions associated with this process." + While we have outlined a self-consistent model in which the ares seen near the pulsar are wisps as in the Crab. we have no explanation for why these features are only seen on one side of the pulsar (it is important to realize that the nature of the Crab’s wisps are themselves still a matter of heated debate).," While we have outlined a self-consistent model in which the arcs seen near the pulsar are wisps as in the Crab, we have no explanation for why these features are only seen on one side of the pulsar (it is important to realize that the nature of the Crab's wisps are themselves still a matter of heated debate)." + We clearly need to extend our coverage to other wavelengths and additional epochs if we are to better understand the observed structures., We clearly need to extend our coverage to other wavelengths and additional epochs if we are to better understand the observed structures. + Finally. the process which produces the innermost X-ray features is completely unknown. and will also require further study.," Finally, the process which produces the innermost X-ray features is completely unknown, and will also require further study." + To conclude. we comment that for many decades the Crab Nebula has been the focus of almost all efforts to understand the process by which pulsars couple to their environment.," To conclude, we comment that for many decades the Crab Nebula has been the focus of almost all efforts to understand the process by which pulsars couple to their environment." + With data such as those presented here. we can now finally extend such studies to a wider sample of sources.," With data such as those presented here, we can now finally extend such studies to a wider sample of sources." +The combination of astrometric and spectroscopic data makes it possible to find a complete orbital solution.,The combination of astrometric and spectroscopic data makes it possible to find a complete orbital solution. +" However, the result can be misleading or wrong, if the significance of the solution is not verified."," However, the result can be misleading or wrong, if the significance of the solution is not verified." +" For significant orbits the derived parameters, e.g. the companion mass, and their errors are valid."," For significant orbits the derived parameters, e.g. the companion mass, and their errors are valid." +" For low-significance orbits, the derived parameters and their errors are very probably false."," For low-significance orbits, the derived parameters and their errors are very probably false." +" Therefore, the distribution function for the companion mass of a low-significance orbit cannot be used to derive an upper and lower mass limits."," Therefore, the distribution function for the companion mass of a low-significance orbit cannot be used to derive an upper and lower mass limits." + The question is then turned to the definition of a significant orbit., The question is then turned to the definition of a significant orbit. +" In the literature, various significance estimators (e.g. F-test or permutation test) and detection limits are employed."," In the literature, various significance estimators (e.g. F-test or permutation test) and detection limits are employed." + We use a 3-o detection limit based on the permutation test and deem orbits at less than 2-σ unreliable., We use a $\sigma$ detection limit based on the permutation test and deem orbits at less than $\sigma$ unreliable. + For a 2-σ orbit we adopt a reduced validity and expect that the mass limits do hold., For a $\sigma$ orbit we adopt a reduced validity and expect that the mass limits do hold. +" In principle, it is possible to derive the upper mass limit for any companion by employing simulations similar to the one described in Sect. 3.8.1.."," In principle, it is possible to derive the upper mass limit for any companion by employing simulations similar to the one described in Sect. \ref{sec:simulation}." + Such simulation is extremely elaborate and its application to the list of host stars with undetected astrometric motion is beyond the scope of this paper., Such simulation is extremely elaborate and its application to the list of host stars with undetected astrometric motion is beyond the scope of this paper. +" However, we showed that an orbit is detected at better than 3-c significance, when its semimajor axis amounts to ~70 of the measurement precision, if the Hipparcos observations cover one complete orbit."," However, we showed that an orbit is detected at better than $\sigma$ significance, when its semimajor axis amounts to $\sim$$70$ of the measurement precision, if the Hipparcos observations cover one complete orbit." +" Including an additional confidence margin, we thus claim that the signature of a fully covered orbit would have been detected, if its semimajor axis equalled the single-measurement precision."," Including an additional confidence margin, we thus claim that the signature of a fully covered orbit would have been detected, if its semimajor axis equalled the single-measurement precision." +" Hence, an upper limit to the companion mass can be set by enforcing the equation a=σι for orbits with significance below 2-σ and Nor>1."," Hence, an upper limit to the companion mass can be set by enforcing the equation $a = \sigma_\Lambda$ for orbits with significance below $2$ $\sigma$ and $N_\mathrm{orb} > 1$." +" For all objects in our sample we are able to obtain an orbital solution from the combination of the radial-velocity orbit and the Hipparcos astrometric data, but not all of these orbits are credible."," For all objects in our sample we are able to obtain an orbital solution from the combination of the radial-velocity orbit and the Hipparcos astrometric data, but not all of these orbits are credible." +" To distinguish a real orbit from meaningless output of the fitting procedure, we use the permutation test to evaluate the orbit significance."," To distinguish a real orbit from meaningless output of the fitting procedure, we use the permutation test to evaluate the orbit significance." + This results in the detection of 6 orbits having high significance above 2-σ (Tables 7 and 8))., This results in the detection of 6 orbits having high significance above $\sigma$ (Tables \ref{tab:sol2sigma} and \ref{tab:mass2sigma}) ). + The orbits of 5 objects have moderate significance between 2-σ and 3-o-., The orbits of 5 objects have moderate significance between $\sigma$ and $\sigma$ . +" Three orbits have low significancebetween l-o and 2-σ and the orbits of 17 objects have very-low significance (< 1-c, Table 10))”.."," Three orbits have low significancebetween $\sigma$ and $\sigma$ and the orbits of 17 objects have very-low significance $<\!1$ $\sigma$, Table \ref{tab:insignificantOrbits})." +" The Tables 3,, 9,, and 10 list the spectroscopic and astrometric elements of the adopted orbital solution together with the orbit significance and give additional information: Nop is the number of orbits covered by the Hipparcos observations, σι is the median Hipparcos single-measurement precision, asini is the minimum astrometric semimajor axis, Mz (3-0) are upper and lower companion-mass limits at 3-c', dye, is the semimajor axis of the relative orbit, Xsed is the reduced chi-square value of the adopted 7-parameter solution, and the Null probability gives the result of the F-test."," The Tables \ref{tab:KeplerOrbits}, , \ref{tab:target2sigma}, and \ref{tab:insignificantOrbits} list the spectroscopic and astrometric elements of the adopted orbital solution together with the orbit significance and give additional information: $N_{\mathrm{orb}}$ is the number of orbits covered by the Hipparcos observations, $\sigma_\Lambda$ is the median Hipparcos single-measurement precision, $a \sin i$ is the minimum astrometric semimajor axis, $M_2$ $\sigma$ ) are upper and lower companion-mass limits at $\sigma$, $a_\mathrm{rel}$ is the semimajor axis of the relative orbit, $\chi^2_{7,\mathrm{red}}$ is the reduced chi-square value of the adopted 7-parameter solution, and the Null probability gives the result of the F-test." + The quoted errors correspond to Monte-Carlo based 1-c-confidence intervals., The quoted errors correspond to Monte-Carlo based $\sigma$ -confidence intervals. +" For orbits with significance below 2-σ and provided that the orbital period is fully covered by Hipparcos observations, we derived the upper limit to the companions mass M»up-iim by enforcing the equation a=σλ (cf."," For orbits with significance below $2$ $\sigma$ and provided that the orbital period is fully covered by Hipparcos observations, we derived the upper limit to the companions mass $M_{2,\mathrm{up-lim}}$ by enforcing the equation $a = \sigma_\Lambda$ (cf." + Sect. ??))., Sect. \ref{sec:mlim}) ). + Clear orbital signatures are detected for six target stars., Clear orbital signatures are detected for six target stars. +" The orbit significances exceed 99.7%, which we adopt as criterion for undoubtful detection."," The orbit significances exceed $99.7 \%$, which we adopt as criterion for undoubtful detection." + The orbits show a large variety in size (a=2.3—35 mas) and inclination (;=12—173°) and reveal companion masses ranging from 90M; to 0.52Mo.," The orbits show a large variety in size $a=2.3-35$ mas) and inclination $i = 12-173 ^{\circ}$ ) and reveal companion masses ranging from $90 \,M_J$ to $0.52 \, M_{\odot}$." + The obtained relative precision on the companion mass is typically of the order of 10 and does not include any contribution of the primary-mass uncertainty., The obtained relative precision on the companion mass is typically of the order of 10 and does not include any contribution of the primary-mass uncertainty. +" The visualisation of Hipparcos astrometric data is not very intuitive, because positions are measured in one dimension only, ie. along the scan-angle orientation y."," The visualisation of Hipparcos astrometric data is not very intuitive, because positions are measured in one dimension only, i.e. along the scan-angle orientation $\psi$." + We choose a representation similar to ? and the resulting stellar astrometric orbits are shown in Fig. 20.., We choose a representation similar to \cite{Torres:2007kx} and the resulting stellar astrometric orbits are shown in Fig. \ref{fig:orbits}. +" For better display, we compute normal points for each satellite orbit number."," For better display, we compute normal points for each satellite orbit number." +" Their values and errors are given by the mean and standard-deviation of the Hipparcos abscissae obtained during one given satellite orbit, respectively."," Their values and errors are given by the mean and standard-deviation of the Hipparcos abscissae obtained during one given satellite orbit, respectively." + Normalpoints are used only for the visualisation and not during the orbit adjustment., Normalpoints are used only for the visualisation and not during the orbit adjustment. +" We prove that orbit detections are also possible in apparently difficult conditions, such as incomplete orbit coverage by the satellite (Νοιν=0.5 for HD 43848) and an instrument precision comparable to the the orbit size 164427A))."," We prove that orbit detections are also possible in apparently difficult conditions, such as incomplete orbit coverage by the satellite $N_{orb}=0.5$ for HD 43848) and an instrument precision comparable to the the orbit size )." + The final 7-parameter fit for the detected orbits has an acceptable reduced chi-square value κας=0.8—1.2) in all but one case.," The final 7-parameter fit for the detected orbits has an acceptable reduced chi-square value $\chi^2_{7,\mathrm{red}} = 0.8-1.2)$ in all but one case." +" For HD 17289 this value is very small at 0.3 and the Hipparcos precision is unusually large at 7.2 mas, which may indicate that the astrometric errors for this star are overestimated."," For HD 17289 this value is very small at 0.3 and the Hipparcos precision is unusually large at 7.2 mas, which may indicate that the astrometric errors for this star are overestimated." +" As for the radial-velocity measurements, the light emitted by the actual stellar companion of this star may have disturbed the Hipparcos observations."," As for the radial-velocity measurements, the light emitted by the actual stellar companion of this star may have disturbed the Hipparcos observations." + Three out of these six stars have non-standard Hipparcos solutions., Three out of these six stars have non-standard Hipparcos solutions. +" Thus, first indications for the astrometric disturbance induced by the companion were already detected during the standard Hipparcos data analysis."," Thus, first indications for the astrometric disturbance induced by the companion were already detected during the standard Hipparcos data analysis." +" An additional outcome of the companion solution are refined positions, distances, and proper motions of the objects (Table 7))."," An additional outcome of the companion solution are refined positions, distances, and proper motions of the objects (Table \ref{tab:sol2sigma}) )." +" For 5 stars the parallax estimate becomes more precise, whereas its value is compatible within the error bars."," For 5 stars the parallax estimate becomes more precise, whereas its value is compatible within the error bars." + Only the parallax of HIP 103019 is1.9mas larger than the value given by the new reduction., Only the parallax of HIP 103019 is1.9mas larger than the value given by the new reduction. +" Changes in position and proper motion are of the order of 1 mas and 1 mas yr, with extrema of 41 mas and 22 mas yr, respectively."," Changes in position and proper motion are of the order of 1 mas and 1 mas $^{-1}$ , with extrema of 41 mas and 22 mas $^{-1}$ , respectively." +asteroseismic fits (Bischoff-Kim et al.,asteroseismic fits (Bischoff-Kim et al. +" 2008; Castanheira Kepler 2008), using the BIC, only one fit among 6 comes out superior."," 2008; Castanheira Kepler 2008), using the BIC, only one fit among 6 comes out superior." + But that is a fit to a single mode star using 4 parameters., But that is a fit to a single mode star using 4 parameters. + It is difficult to argue for the significance of such a fit., It is difficult to argue for the significance of such a fit. +" It is illuminating to also look at the parameters (mass and effective temperature) of models that did not fit quite as well, but were still fits."," It is illuminating to also look at the parameters (mass and effective temperature) of models that did not fit quite as well, but were still good fits." + , Fig. +3 is a of where all the models that fit to goodbetter than Fig.opmg=plot1.0s lie in parameter space., \ref{f3} is a plot of where all the models that fit to better than $\rm \sigma_{RMS} = 1.0 \; s$ lie in parameter space. + The best fit models follow a negatively sloping trend in the mass versus effective temperature plane., The best fit models follow a negatively sloping trend in the mass versus effective temperature plane. + This is a direct consequence of Eq. 2.., This is a direct consequence of Eq. \ref{eq2}. +" To fit a fixed set of observed higher temperature models must compensate with a lower periods,mass in order to keep the appropriate average period spacing."," To fit a fixed set of observed periods, higher temperature models must compensate with a lower mass in order to keep the appropriate average period spacing." + This trend frequently shows up in white dwarf asteroseismology (e.g. Bischoff-Kim et al., This trend frequently shows up in white dwarf asteroseismology (e.g. Bischoff-Kim et al. + 2008; Castanheira Kepler 2008)., 2008; Castanheira Kepler 2008). + The band of acceptable model fits in that plane misses the 1-c spectroscopic box completely., The band of acceptable model fits in that plane misses the $\sigma$ spectroscopic box completely. +" However, we do not consider this a failure as it is well known that the He I lines in the DB change only weakly with temperature."," However, we do not consider this a failure as it is well known that the He I lines in the DB instability region change only weakly with temperature." +" Thus, small instabilitycalibrationregion effects can easily throw the temperature by many times the formal 1-sigma fitting error."," Thus, small calibration effects can easily throw the temperature by many times the formal 1-sigma fitting error." +" The mass of our best fit models, on the other hand, corresponds well with the mass determined from the"," The mass of our best fit models, on the other hand, corresponds well with the mass determined from the" +The system temperature on (he blank skv is then given by: where ων.ϱ) is the calibration temperature of the noise diode and is a function of lrequenceyv. G7) aud polarisation (p).,"The system temperature on the blank sky is then given by: where $T_{cal}(\nu,p)$ is the calibration temperature of the noise diode and is a function of frequency $\nu$ ) and polarisation $p$ )." + Instead. of ων.p)we adopted (he mean 4p) value across the entire bandpass.," Instead of $T_{cal}(\nu,p)$we adopted the mean $T_{cal}(p)$ value across the entire bandpass." + Throughout the observing run the svsten temperature (integrated over (he entire bandwidth observed) varied between IXIx in optimal conditions to IXIx in the worst cases. depending on elevation and the water vapour content of the alimosphere.," Throughout the observing run the system temperature (integrated over the entire bandwidth observed) varied between K in optimal conditions to K in the worst cases, depending on elevation and the water vapour content of the atmosphere." + Each sean was inspected by eve in order (to weed out bad or abnormal looking} scals., Each scan was inspected by eye in order to weed out bad or abnormal looking scans. + The data were reduced using (wo independent methods., The data were reduced using two independent methods. + The first method used the GDTIDL-routine GETNOD. which takes theOFF signal [rom one scan and subtracts il from the signal in the neishbouring scan. and vice versa.," The first method used the GBTIDL-routine GETNOD, which takes the signal from one scan and subtracts it from the signal in the neighbouring scan, and vice versa." +" In (his scheme the spectra are calibrated onto the antenna temperature scale Following: where ON;;—(ÜN.,,1,,;,+ΟΝΕ)3 and OFF;;1—(OFFton+ΟΕΕ)/3. and j. 9 represent the beam and sean number. respectively,"," In this scheme the spectra are calibrated onto the antenna temperature scale following: where ${\tt ON_{i,j}} = ({\tt ON}_{calon}+{\tt ON}_{caloff})/2$ and ${\tt OFF_{i,j+1}} = ({\tt OFF}_{calon}+{\tt OFF}_{caloff})/2$, and $i$, $j$ represent the beam and scan number, respectively." +" Thus (wo neighbouring scans result in (wo independent spectra. Z,,,;(7.p) and Ty.)1(7.p)."," Thus two neighbouring scans result in two independent spectra, $T_{ant,j}(\nu,p)$ and $T_{ant,j+1}(\nu,p)$." + All the difference spectra are then averaged. weighted according to their svstem temperature. to produce the final difference spectrum for each polarisation.," All the difference spectra are then averaged, weighted according to their system temperature, to produce the final difference spectrum for each polarisation." + As an alternative reduction scheme. we used the method of Lainline et ((2006) which involves constructing a baseline template for each signal from a best-fit linear combination ol its neighbouring OFF signals.," As an alternative reduction scheme, we used the method of Hainline et (2006) which involves constructing a baseline template for each signal from a best-fit linear combination of its neighbouring signals." + We can write this as, We can write this as +mechanism that naturally provides these requirements (although lately some interesting new candidates where suggested). and that can naturally explain a large fraction of the observed features.,"mechanism that naturally provides these requirements (although lately some interesting new candidates where suggested), and that can naturally explain a large fraction of the observed features." + Observationally we already. have great 10 keV - 1 MeV. data set and a large number of oplical - X-ray observations (hat coincide with the end of the prompt emission of long GRBs., Observationally we already have great $10$ keV - $1$ MeV data set and a large number of optical - X-ray observations that coincide with the end of the prompt emission of long GRBs. + The only hope that I can see lor observational breakthrough in the near future is by Fermi. which already. provided useful information that stronelv disfavor inverse Compton by relativistic electrons as the source of (he prompt emission.," The only hope that I can see for observational breakthrough in the near future is by Fermi, which already provided useful information that strongly disfavor inverse Compton by ultra-relativistic electrons as the source of the prompt emission." + But. so far. Fermi observations did not pointed towards the correct model. while they. did raise up new open questions.," But, so far, Fermi observations did not pointed towards the correct model, while they did raise up new open questions." + If such breakthrough will not take place. (hen a theoretical study of the existing models that are still viable aud clevelopment of new ones. are the most promising way (o understand the prompt enission.," If such breakthrough will not take place, then a theoretical study of the existing models that are still viable and development of new ones, are the most promising way to understand the prompt emission." + The late afterglow is generated during (and almost certainly by) the interaction with the circum burst medium., The late afterglow is generated during (and almost certainly by) the interaction with the circum burst medium. + This statement is robustly based on the deceleratecl expansion of the afterglow image of GRB 030329., This statement is robustly based on the decelerated expansion of the afterglow image of GRB 030329. + It is also strongly supported by the light curve ancl spectral allerelow evolution. which show a continuous power-law decay (in both the flux and peak frequency) ancl variability time scales (hat increase will (ime.," It is also strongly supported by the light curve and spectral afterglow evolution, which show a continuous power-law decay (in both the flux and peak frequency) and variability time scales that increase with time." + By far. the most popular alterglow model is the external forward shock model. aud in mv view il is very likely that the afterglow emission. at least starting a few hours after the burst. is generated by forward external shock.," By far, the most popular afterglow model is the external forward shock model, and in my view it is very likely that the afterglow emission, at least starting a few hours after the burst, is generated by forward external shock." + The major success of this model is that with a very simple parametrization (of only a few [ree parameters) il encompasses (he gross observed alterglow properties over eight orders of magnitude in frequency. aud. four orders ol magnitude in time., The major success of this model is that with a very simple parametrization (of only a few free parameters) it encompasses the gross observed afterglow properties over eight orders of magnitude in frequency and four orders of magnitude in time. + However. an examination of the fine details shows that the model is fay [rom being complete.," However, an examination of the fine details shows that the model is far from being complete." + The simple model is not compatible with the detailed observations of many bursts (e.g.. the exact spectral and temporal power-law indices).," The simple model is not compatible with the detailed observations of many bursts (e.g., the exact spectral and temporal power-law indices)." + There is a set of observations (especially during the first 10*—107 s). which ave difficult to explain bv forward shock emission even by significantly complicating the simple model.," There is a set of observations (especially during the first $10{^3}-10^{4}$ s), which are difficult to explain by forward shock emission even by significantly complicating the simple model." + Some examples are X-ray flares. X-ray plateaus ancl some chromatic breaks.," Some examples are X-ray flares, X-ray plateaus and some chromatic breaks." + Diflerent extensions of the basic model are, Different extensions of the basic model are +dy anda broad. toroidal field profile of the fori The initial pressure aud temperature are chosen such that the initial state is iu iuagnoeto-hwdrostatie aud magneto-geostroplic balauce.,$u_0$ and a broad toroidal field profile of the form The initial pressure and temperature are chosen such that the initial state is in magneto-hydrostatic and magneto-geostrophic balance. + The parameter à is set to uuity for the simulations preseuted here. corresponding to a peak dimensional field strength of about 10 kG. toward the high cud of the range expected to exist iu the tachocline (AIGDOT).," The parameter $\alpha$ is set to unity for the simulations presented here, corresponding to a peak dimensional field strength of about 40 kG, toward the high end of the range expected to exist in the tachocline (MGD07)." + Cdobal magneto-shear iustabilities also occur for weaker fields but they take longer to develop., Global magneto-shear instabilities also occur for weaker fields but they take longer to develop. + The iutial equilibrium state is perturbed by adding a raudoi. nall-scale velocity field.," The initial equilibrium state is perturbed by adding a random, small-scale velocity field." + Unlike the siauulations prescuted im ALGDOT. we mnaintain the ciferential rotation through the forcing term defined in equation (1)).," Unlike the simulations presented in MGD07, we maintain the differential rotation through the forcing term defined in equation \ref{eq:Fu}) )." +" An example of the subsequent evoution in the absence of maeuetic forcing GF,= 0) is shown in Figure 1..", An example of the subsequent evolution in the absence of magnetic forcing $\FF_p = {\bf 0}$ ) is shown in Figure \ref{onlyshear}. + The spatial resolution used for this case is Ny. NV... N. = 128. 256. 210.," The spatial resolution used for this case is $N_\theta$, $N_\phi$, $N_z$ = 128, 256, 210." + Figue losrows the components of the magnetic cherey integraed over the volume of the shell., Figure \ref{onlyshear} shows the components of the magnetic energy integrated over the volume of the shell. + One, One +lines. bottom panel). but compared to V336 Tau. it shows a centrally peaked profile.,"lines, bottom panel), but compared to V836 Tau, it shows a centrally peaked profile." + Although the signal-to-noise ratio of the spectrum is limited. weak stellar photospheric features appear to be present.," Although the signal-to-noise ratio of the spectrum is limited, weak stellar photospheric features appear to be present." + In the bottom panel of Figure 7. we show the CO enission from 115 alter correction for a stellar photospherie contribution. following the approach described in 83.1.," In the bottom panel of Figure 7, we show the CO emission from 15 after correction for a stellar photospheric contribution, following the approach described in 3.1." + The stellar photospheric model assumes an Allard stellar atmosphere model wilh a gravity of logy=4.0. an ellective temperature of KIX to match the Ix5 spectral ivpe of 115 (IHerbig Bell 1983). a stellar rotational velocity esin’=12.5kms! (Hartmann. Soderblom. Stauffer 1987). and an observed (topocentric) radial velocity of —39.8kms!. which is appropriate for the measured stellar radial velocity (Hartmann. et 11987) and the observation date.," The stellar photospheric model assumes an Allard stellar atmosphere model with a gravity of $\log g = 4.0$, an effective temperature of K to match the K5 spectral type of 15 (Herbig Bell 1988), a stellar rotational velocity $v \sin i =12.5\kms$ (Hartmann, Soderblom, Stauffer 1987), and an observed (topocentric) radial velocity of $-39.8 \kms$, which is appropriate for the measured stellar radial velocity (Hartmann et 1987) and the observation date." + A veiling of 2.5 times the stellar continuum roughly reproduces the strength of the stellar photospheric features near the 10 P30 line., A veiling of 2.5 times the stellar continuum roughly reproduces the strength of the stellar photospheric features near the 1–0 P30 line. + This level of veiling is also consistent with the veiling at 5jmi implied by the SED (e.g.. Furlan οἱ al.," This level of veiling is also consistent with the veiling at $5\micron$ implied by the SED (e.g., Furlan et al." + 2006)., 2006). + Subtractüng the veiled stellar photospheric component produces a disk CO emission prolile (hat is even more centrally peaked 77. bottom panel).," Subtracting the veiled stellar photospheric component produces a disk CO emission profile that is even more centrally peaked 7, bottom panel)." + In addition to its low stellar accretion rate. 115 is also similar to V836 Tau in that it has the characteristics of a transition object with a weak near-inlrarecd continuum and an oplically (hick outer disk (e.¢.. Bergin οἱ 22004: Espaillat et 22007).," In addition to its low stellar accretion rate, 15 is also similar to V836 Tau in that it has the characteristics of a transition object with a weak near-infrared continuum and an optically thick outer disk (e.g., Bergin et 2004; Espaillat et 2007)." + Its properties therefore probe empirically how both the reduction in small grains and reduced heating might affect the CO fundamental emission from the disk., Its properties therefore probe empirically how both the reduction in small grains and reduced accretion-related heating might affect the CO fundamental emission from the disk. + The LkCa115 spectrum shows that in at least some cases. these effects do not racially truncate the CO fundamental emission within 1 AU.," The 15 spectrum shows that in at least some cases, these effects do not radially truncate the CO fundamental emission within 1 AU." + To summarize. the double-peaked line profile of the CO fundamental emission [rom V836 Tan maw indicate that the gaseous disk extends from close to the star (~0.05 AU) out toa physical truneation radius (~0.4 AU).," To summarize, the double-peaked line profile of the CO fundamental emission from V836 Tau may indicate that the gaseous disk extends from close to the star $\sim 0.05$ AU) out to a physical truncation radius $\sim 0.4$ AU)." + If the gaseous disk in V836 Tou is instead continuous bevond (his radius. the double-peaked CO profile would indicate a sudden truncation of the CO emission bevond a radius of AAU.," If the gaseous disk in V836 Tau is instead continuous beyond this radius, the double-peaked CO profile would indicate a sudden truncation of the CO emission beyond a radius of AU." + As discussed in 84.2. an abrupt decrement in excitation is not expected empirically. since (he majority of CO emission profiles observed (o date (both (vpical classical T Tauri stars aud transition objects like 115) show centrally peaked CO profiles with no comparable decrement in excitation wilh radius.," As discussed in 4.2, an abrupt decrement in excitation is not expected empirically, since the majority of CO emission profiles observed to date (both typical classical T Tauri stars and transition objects like 15) show centrally peaked CO profiles with no comparable decrement in excitation with radius." + llowever. a truncated emission profile may result from either an (anomalously) steep temperature gradient or departures trom LTE that become important in low accretion rate svslenms.," However, a truncated emission profile may result from either an (anomalously) steep temperature gradient or departures from LTE that become important in low accretion rate systems." + These two possible explanations can be explored and potentially distinguished with a higher signal-to-noise spectrum that measures the strengths of the r=21 lines., These two possible explanations can be explored and potentially distinguished with a higher signal-to-noise spectrum that measures the strengths of the $v$ =2–1 lines. + A theoretical study of the possibility of non-LTE CO level populations would also be welcome in sorling out whether an excitation ellect is a possible explanation for the outer radius of the emission., A theoretical study of the possibility of non-LTE CO level populations would also be welcome in sorting out whether an excitation effect is a possible explanation for the outer radius of the emission. + Adcditional observations of low accretion rate sources would be useful in exploring, Additional observations of low accretion rate sources would be useful in exploring +no significant dillerence between B and. € in terms of the local σας density ng. or in terms of the local ionizing luminosity Q/tar 2) (,"no significant difference between B and C in terms of the local gas density $_{H}$, or in terms of the local ionizing luminosity $\pi$ $^{2}$. (" +Note: since OL]/OLLI is also sensitive to redenning. this result reinforces result. 1.),"Note: since [OII]/[OIII] is also sensitive to redenning, this result reinforces result 1.)" + 3., 3. + Ixnot € is a lactor of ~2 brighter than knot D: taking into account results 1 and 2. the most natural explanation is that there is a higher mass of warm ionizecl gas on the SIE side of the nucleus than on the NW. in agreement with the original scenario suggested by MeCarthy. Van Breugel Wapahi (1991). and also in agreement with conclusions reached by Humphrey. ct al. (," Knot C is a factor of $\sim$ 2 brighter than knot B: taking into account results 1 and 2, the most natural explanation is that there is a higher mass of warm ionized gas on the SE side of the nucleus than on the NW, in agreement with the original scenario suggested by McCarthy, Van Breugel Kapahi (1991), and also in agreement with conclusions reached by Humphrey et al. (" +2007) in the case of the 2=2.57 radio galaxy PAS 0828|193.,2007) in the case of the $=$ 2.57 radio galaxy TXS 0828+193. + We note that. the radio properties of AIRC 0406-244 are consistent with this explanation: compared to the NW radio hotspot. the SE hotspot has a lower radio polarization and higher rotation measure (Carilli ct al.," We note that the radio properties of MRC 0406-244 are consistent with this explanation: compared to the NW radio hotspot, the SE hotspot has a lower radio polarization and higher rotation measure (Carilli et al." +" 1997). consistent with being viewed through a comparatively larger column of magneto-ionized eas,"," 1997), consistent with being viewed through a comparatively larger column of magneto-ionized gas." + Finally. we suggest that high spatial resolution images of emission from molecular gas. neutral Livelrogen and dust would be useful to explore further the nature of the side-to-side asvmmetries in this and other powerful radio galaxies.," Finally, we suggest that high spatial resolution images of emission from molecular gas, neutral Hydrogen and dust would be useful to explore further the nature of the side-to-side asymmetries in this and other powerful radio galaxies." + For instance. does the cold phase of the interstellar medium show a similar brightness asymmetry. and is this correlated with the radio lobe-Iength asymmetry?," For instance, does the cold phase of the interstellar medium show a similar brightness asymmetry, and is this correlated with the radio lobe-length asymmetry?" + 1n AIRC 040€244. the alignment between the superbubbles and the biconical ionizing radiation field of the AGN has allowed: the superbubbles to be seen in emission.," In MRC 0406-244, the alignment between the superbubbles and the biconical ionizing radiation field of the AGN has allowed the superbubbles to be seen in emission." + It is unclear whether this alignment is by chance or whether the racio/optical axis defines the preferred axis of this kind. of outtlow., It is unclear whether this alignment is by chance or whether the radio/optical axis defines the preferred axis of this kind of outflow. + In this section we ask. what if the superbubbles were not within the ionization cones?," In this section we ask, what if the superbubbles were not within the ionization cones?" + Le. what if the bubbles expand bevond. or are misaligned with. the cones. and what would be their observational characteristics?," I.e., what if the bubbles expand beyond, or are misaligned with, the cones, and what would be their observational characteristics?" + 20115 outside of the ionizing radiation field of the active nucleus. the superbubbles would likely have a low ionization fraction. and thus might not be detectable in. emission.," Being outside of the ionizing radiation field of the active nucleus, the superbubbles would likely have a low ionization fraction, and thus might not be detectable in emission." + Llowever. if the covering factor of the superbubble structure is sullicient (Le. 20.1). then the high expected column density of the bubbles. estimated to be 610! em in the case of AIRC 0406-244 (63.3). would render them detectable via absorption lines such as LLL Lvo.," However, if the covering factor of the superbubble structure is sufficient (i.e., $\ga$ 0.1), then the high expected column density of the bubbles, estimated to be $\ga 6 \times10^{14}$ $^{-2}$ in the case of MRC 0406-244 $\S$ 3.3), would render them detectable via absorption lines such as HI $\alpha$." + We would also expect the absorption lines to be blushifted relative to he line emission from the EELRB. due to expansion of the superbubbles. as well as spatially extended.," We would also expect the absorption lines to be blushifted relative to the line emission from the EELR, due to expansion of the superbubbles, as well as spatially extended." + Such observation properties are similar to those shown »v manv of the LEE absorbers that are often detected in front of Hz:(e.g. IHotttgering οἱ al., Such observation properties are similar to those shown by many of the HI absorbers that are often detected in front of HzRG (e.g. Rötttgering et al. + JOD: van Ojik et al., 1995; van Ojik et al. + OT4: 'entericci et al., 1997; Pentericci et al. + 2001: Jarvis et à s, 2001; Jarvis et al. +5103: Wilman et al., 2003; Wilman et al. +"""n2 Villar-Alartin ct al.", 2004; n et al. + 2007: Hum et al., 2007; Humphrey et al. + 2008b). cads us to suggest that the superbubbles in MIC! 0406-244 and the LL absorbers in front of some other HzIt€: might be similar phenomena.," 2008b), which leads us to suggest that the superbubbles in MRC 0406-244 and the HI absorbers in front of some other HzRG might be similar phenomena." + If the bubbles have swept up most of the cool/warm. interstellar eas. and if the expansion of the bubbles proceeds at the velocities implied. by the emission line. kinematics (several hundred km s17: e.g. Taniguchi et al.," If the bubbles have swept up most of the cool/warm interstellar gas, and if the expansion of the bubbles proceeds at the velocities implied by the emission line kinematics (several hundred km $^{-1}$: e.g., Taniguchi et al." + 2001). then the majority of the extendedl gas could leave the ionization cones (and host galaxy) on a timescale of ~107 vr.," 2001), then the majority of the extended gas could leave the ionization cones (and host galaxy) on a timescale of $\sim 10^{8}$ yr." + We speculate that we may be witnessing the destruction of the extended: emission line region of AIRC 0406-244. and the ealaxys transition to join the 1/3 of luminous radio galaxies that emit radio and optical continua. but no detectable emission lines (Aliley De Breuck 2008).," We speculate that we may be witnessing the destruction of the extended emission line region of MRC 0406-244, and the galaxy's transition to join the 1/3 of luminous radio galaxies that emit radio and optical continua, but no detectable emission lines (Miley De Breuck 2008)." + We thank the referee. Patrick MleCarthy. for his comments on the manuscript.," We thank the referee, Patrick McCarthy, for his comments on the manuscript." + LB was supported by the CONACTL erant .-50296., LB was supported by the CONACyT grant J-50296. + MIVAL acknowledges support. from the Spanish S de Eclucacionn v Ciencia through the erants AYA2004-02708 and ÀYA2007-64712.. and. from FEDER ren," MVM acknowledges support from the Spanish Ministerio de Educaciónn y Ciencia through the grants AYA2004-02703 and AYA2007-64712, and from FEDER funds." +the other hand. reveals that the coldest part of the molecular heart-shaped structure is located toward the Compact Ridge.,"the other hand, reveals that the coldest part of the molecular heart-shaped structure is located toward the Compact Ridge." +" All the emission peaks of these lines. (CH3CN(12,-0 1ο). SOs(2155o-214 2) Xv» D. and HC3N(37-36)(0-7=1)). are well concentrated in the southeast sector of the filamentary CO structure and are aligned with the band of highest HC3N(37- 36)(v;z1)line width. see Figure 5."," All the emission peaks of these lines, $_3$ $_9$ $_9$ ), $_2$ $_{2,20}$ $_{1,21}$ $\nu_2$ =1), and $_3$ $\nu_7$ =1)), are well concentrated in the southeast sector of the filamentary CO structure and are aligned with the band of highest $_3$ $\nu_7$ =1)line width, see Figure 5." +" Note that the ground state Ime CH3CN(12,-119) is not coincident with any of the submillimeter or radio continuum sources located in this region.", Note that the ground state line $_3$ $_9$ $_9$ ) is not coincident with any of the submillimeter or radio continuum sources located in this region. + We show the kinematies of the molecular gas within. the Hot Core and the Compact Ridge regions in Figure 5 where moment one (integrated weighted velocity) and two (integratec velocity dispersion squared) maps of the vibrationally excited resp., We show the kinematics of the molecular gas within the Hot Core and the Compact Ridge regions in Figure 5 where moment one (integrated weighted velocity) and two (integrated velocity dispersion squared) maps of the vibrationally excited resp. + ground state emission from the CH;CN(1I2;-013) anc HC5;N(37-36)(05;21) lines are displayed., ground state emission from the $_3$ $_3$ $_3$ ) and $_3$ $\nu_7$ =1) lines are displayed. + The moment one maps show that the blueshifted molecular gas is concentratec in the northeast part of the heart-shaped structure. while the redshifted gas is located on the northwest part.," The moment one maps show that the blueshifted molecular gas is concentrated in the northeast part of the heart-shaped structure, while the redshifted gas is located on the northwest part." + The origi of the runaway stars and of the filamentary structure is well placed in between. in the middle of the northern lobes of the heart-shaped structure as defined by CH3CN(123-013).," The origin of the runaway stars and of the filamentary structure is well placed in between, in the middle of the northern lobes of the heart-shaped structure as defined by $_3$ $_3$ $_3$ )." + The emission of HCxN(37-36)(v;21) 1s totally blueshifted with respect to ambient and shows a velocity gradient with northeast-southwest orientation., The emission of $_3$ $\nu_7$ =1) is totally blueshifted with respect to ambient and shows a velocity gradient with northeast-southwest orientation. + The moment two maps surprisingly reveal filamentary structures that clearly point towards the dynamical origin., The moment two maps surprisingly reveal filamentary structures that clearly point towards the dynamical origin. + These filaments are reminiscent of the filamentary CO(2-1) emission found by that might have been caused by the ejection of material upon the dynamical disintegration of the young stellar system BN.7. and n.," These filaments are reminiscent of the filamentary CO(2-1) emission found by that might have been caused by the ejection of material upon the dynamical disintegration of the young stellar system , and ." + Note that the largest linewidths are located closest to this origin., Note that the largest linewidths are located closest to this origin. + We think that maybe the — km s! blushifted component found in HCiN(G37-36)(9 21) and CH:OH(74 3-643) Is excited for one filament that collided with a slightly different velocity toward this position.," We think that maybe the $-$ 4 km $^{-1}$ blushifted component found in $_3$ $\nu_7$ =1) and $_3$ $_{4,3}$ $_{4,3}$ ) is excited for one filament that collided with a slightly different velocity toward this position." +" An overlay of the HCiN(37-36)(v;21). the CH:OH(T7, 3-641) A (v,22). and the submillimeter continuum emission on the 11.7 um infrared emission from the Orion KL region is displayed in Figure 6."," An overlay of the $_3$ $\nu_7$ =1), the $_3$ $_{4,3}$ $_{4,3}$ ) $^-$ $\nu_t$ =2), and the submillimeter continuum emission on the 11.7 $\mu$ m infrared emission from the Orion KL region is displayed in Figure 6." + Included in this image are the positions of the four radio sourcesBN.£.n. and(22?).," Included in this image are the positions of the four radio sources, and." +. The map shows a lack of correspondence between the centimeter. submillimeter. and mid-infrared continuum sources.," The map shows a lack of correspondence between the centimeter, submillimeter, and mid-infrared continuum sources." + This poor coincidence suggests that they might be of different nature., This poor coincidence suggests that they might be of different nature. + We found three groups of similar sourees in the Orion KL region which we describe as follows: As the mid-infrared shows a good correspondence with the hot molecular gas traced by the vibrationally/torsionally excited emission. it would not necessarily be reprocessed emission escaping through inhomogeneities in. the dense material but could be due to heating by shock compression that destroyed the dust grains.," We found three groups of similar sources in the Orion KL region which we describe as follows: As the mid-infrared shows a good correspondence with the hot molecular gas traced by the vibrationally/torsionally excited emission, it would not necessarily be reprocessed emission escaping through inhomogeneities in the dense material but could be due to heating by shock compression that destroyed the dust grains." + The reason that vibrationally/torsionally exeited lines are observed only towards IRS2 might be that only this spot has density or temperature high enough to be sufficiently excited., The reason that vibrationally/torsionally excited lines are observed only towards IRS2 might be that only this spot has density or temperature high enough to be sufficiently excited. + In Figure | one can see that towards the position of this emission the highly extineted and dense Extended Ridge ts located., In Figure 1 one can see that towards the position of this emission the highly extincted and dense Extended Ridge is located. + Molecular lines that trace colder gas. such as NH3(4.4). are not present where the mid-infrared and vibrationally/torsionally excited molecular emission ts located. see Figure 5 of?.," Molecular lines that trace colder gas, such as $_3$ (4,4), are not present where the mid-infrared and vibrationally/torsionally excited molecular emission is located, see Figure 5 of." +". We note that the Submillimeter source “Compact Ridge"" (SMMI) seems to be surrounded with mid-infrared emissio25 oriented in approximately the direction of the dynamical origi> but without associated hot molecular gas."," We note that the Submillimeter source ""Compact Ridge"" (SMM1) seems to be surrounded with mid-infrared emission oriented in approximately the direction of the dynamical origin but without associated hot molecular gas." + It is interesting to. mention that most of the eastern OH maser spots mapped by show good coincidence with the vibrationally/torsionally excited emission reported here., It is interesting to mention that most of the eastern OH maser spots mapped by show good coincidence with the vibrationally/torsionally excited emission reported here. + Moreover. part of the OH maser emission seems to cover the submillimeter source SMM3= just às the vibrationally/torsionally excited emission does.," Moreover, part of the OH maser emission seems to cover the submillimeter source SMM3 just as the vibrationally/torsionally excited emission does." + This further argues in favor of the infrared emission being produced by shocks that heated the dust., This further argues in favor of the infrared emission being produced by shocks that heated the dust. + The presence and peculiar properties of radio sourceJ add substantially to the complexity of the KL region's appearance., The presence and peculiar properties of radio source add substantially to the complexity of the KL region's appearance. + One might think that the molecular outflow from { is heating the Orion KL Hot Core because it lies along the same orientation as thevibrationally/torsionally excited lines., One might think that the molecular outflow from is heating the Orion KL Hot Core because it lies along the same orientation as thevibrationally/torsionally excited lines. + However. if it were one would expect the largest linewidths in," However, if it were one would expect the largest linewidths in" +slight discrepancy could indicate that the newly formed stars are concentrated at the center of the cloud.,slight discrepancy could indicate that the newly formed stars are concentrated at the center of the cloud. + In this case their emission could be more attenuated than the eemission., In this case their emission could be more attenuated than the emission. +" From the radio flux, we compute an ionizing photon rate of 2x10?!s7!, which, for a young (1-2 Myr) burst corresponds to a stellar mass of ~4x10* based on Starburst99 models."," From the radio flux, we compute an ionizing photon rate of $\rm 2\times 10^{51} \, s^{-1}$, which, for a young (1-2 Myr) burst corresponds to a stellar mass of $\sim 4 \times +10^4~$ based on Starburst99 models." + This stellar mass is of the virial mass of the compact ssource., This stellar mass is of the virial mass of the compact source. +" In this section we argue that, for both the extended emission and the compact molecular source, the H2 line emission is shock powered."," In this section we argue that, for both the extended emission and the compact molecular source, the $_2$ line emission is shock powered." + We also estimate the bolometric Hz luminosity for both emission components., We also estimate the bolometric $_{2}$ luminosity for both emission components. +" In this section, we discuss the excitation of the H» gas and the nature of the Hz emission for the extended emission and the compact source."," In this section, we discuss the excitation of the $_2$ gas and the nature of the $_{2}$ emission for the extended emission and the compact source." + We focus on the near-IR lines within the K-band using spectral diagnostics that do not depend on extinction., We focus on the near-IR lines within the $K$ -band using spectral diagnostics that do not depend on extinction. + The H» excitation diagrams for the extended emission and the compact Η2 source are presented in Fig. 8.., The $_{2}$ excitation diagrams for the extended emission and the compact $_{2}$ source are presented in Fig. \ref{fig:exc}. +" We obtain two estimates of the gas temperature, the first by fitting the Hy population in the rotational states of the v=1 vibrational state, and the second from the ratio between the J=1 level of the v=1 and v=2 states."," We obtain two estimates of the gas temperature, the first by fitting the $_{2}$ population in the rotational states of the v=1 vibrational state, and the second from the ratio between the J=1 level of the v=1 and v=2 states." +" For the compact H» source we find 1700 K and 2300 K, respectively, and for the extended emission 900 K and 2700 K. The molecular gas has a range of temperatures."," For the compact $_{2}$ source we find $1700$ K and $2300$ K, respectively, and for the extended emission $900$ K and $2700$ K. The molecular gas has a range of temperatures." + Most, Most +Ay=1.9 towards this sightline. te. close to the asymptotic value shown by Fig. 4..,"$A_V = 1.9$ towards this sightline, i.e. close to the asymptotic value shown by Fig. \ref{fig:4}." + The likely reason for such an abrupt asymptoting is that. at the distance of the Perseus arm (the only major dusty structure encountered beyond | kpe along this line of sight). a Galactic latitude of b.=—4.04 corresponds to a distance of ~140 pe below the midplane. and little cumulative dust obscuration is expected farther out.," The likely reason for such an abrupt asymptoting is that, at the distance of the Perseus arm (the only major dusty structure encountered beyond 1 kpc along this line of sight), a Galactic latitude of $b=-4.04^{\circ}$ corresponds to a distance of $\sim 140$ pc below the midplane, and little cumulative dust obscuration is expected farther out." + According to Fig. 4..," According to Fig. \ref{fig:4}," + IACPN could be located at any distance from «1 kpe (the formal best fit to the uprising section of the curve) to z8 kpe (the limit where there are adequate stellar data)., IACPN could be located at any distance from $<$ 1 kpc (the formal best fit to the uprising section of the curve) to $\gtrsim$ 8 kpc (the limit where there are adequate stellar data). + The error bars of the stellar and the PN data overlap at 2c and the plateau of interstellar extinction along this line of sight precludes a thrustworthy estimation. of the extinction distance to this PN., The error bars of the stellar and the PN data overlap at $2\sigma$ and the plateau of interstellar extinction along this line of sight precludes a thrustworthy estimation of the extinction distance to this PN. + Secondly. the relationship between He-surface brightness and nebular radius (S— 7) of ??. was used.," Secondly, the relationship between $\alpha$ -surface brightness and nebular radius $S - r$ ) of \citet{frew06,frew10} was used." + IACPN is almost circular. and its dimensions. measured directly from the Ho IPHAS image at the 10 percent of peak-brightness contour. following the procedure of ?.. are 10.5 x 9.7 aresec.," IACPN is almost circular, and its dimensions, measured directly from the $\alpha$ IPHAS image at the 10 percent of peak-brightness contour, following the procedure of \citet{tylenda03}, are 10.5 $\times$ 9.7 arcsec." + The total Πα flux was calculated from the wide-slit Hf flux (Section 2.2) and the Balmer decrement of 5.5 + 0.2. resulting in log F(Hao) = -12.73 + 0.05.," The total $\alpha$ flux was calculated from the wide-slit $\beta$ flux (Section 2.2) and the Balmer decrement of 5.5 $\pm$ 0.2, resulting in log $\alpha$ ) = $-12.73$ $\pm$ 0.05." + The He flux was also independently estimated from the IPHAS calibrated He image after subtracting the contribution of the two adjacent [Nu]] lines as measured form the spectrum. yielding log F(Ha) = -12.96 + 0.22. in fair agreement with the spectroscopically determined value.," The $\alpha$ flux was also independently estimated from the IPHAS calibrated $\alpha$ image after subtracting the contribution of the two adjacent ] lines as measured form the spectrum, yielding log $\alpha$ ) = $-12.96$ $\pm$ 0.22, in fair agreement with the spectroscopically determined value." + We will adopt the better determined spectroscopic value in the following., We will adopt the better determined spectroscopic value in the following. + The resulting He surface brightness is log SCHa) = --00 + 0.06 ergcem™ ss7'ssr7!., The resulting $\alpha$ surface brightness is log $\alpha$ ) = $-4.00$ $\pm$ 0.06 $^{-2}$ $^{-1}$ $^{-1}$. + After dereddening this value using Ay = 1.7 £ 0.2 mag and the extinction law of Fitzpatrick (2004) with Ry = 3.1. we find the physical radius of the PN to be ppe. using the mean Ha S$—-r relation of ?..," After dereddening this value using $A_{V}$ = 1.7 $\pm$ 0.2 mag and the extinction law of Fitzpatrick (2004) with $R_{V}$ = 3.1, we find the physical radius of the PN to be pc, using the mean $\alpha$ $S - r$ relation of \cite{frew06}." + The mean- equation (?.Frewetal.2011.inpreparation) was used. which ts applicable to round. optically-thick PN. viz.:," The mean-trend equation \citep[][ Frew et al. 2011, in preparation]{frew08} was used, which is applicable to round, optically-thick PN, viz.:" + The resulting distance is 12.8 + 3.7 kpe., The resulting distance is 12.8 $\pm$ 3.7 kpc. + The quoted uncertainty in the distance includes the formal dispersion of the relation (+28%:: 2)) which is the dominant error term. added in quadrature with the estimated uncertainties of the integrated Ha flux. mean diameter. and reddening of the PN.," The quoted uncertainty in the distance includes the formal dispersion of the relation $\pm$; \citealt{frew08}) ) which is the dominant error term, added in quadrature with the estimated uncertainties of the integrated $\alpha$ flux, mean diameter, and reddening of the PN." + The corresponding galacto-centric distance 1s Dee=20.843.8 kpe if a distance to the Sun of 8.0+0.6 kpe (?) is assumed., The corresponding galacto-centric distance is $_{GC} = 20.8\pm3.8$ kpc if a distance to the Sun of $8.0\pm0.6$ kpc \citep{ghez08} is assumed. + At 12.8 kpe from the Sun. IACPN is located about | kpe off the plane of the Galactic disk.," At 12.8 kpc from the Sun, IACPN is located about 1 kpc off the plane of the Galactic disk." + That is a large height indeed. but we note that the well-known flaring of the outer disk (seee.g.?) allows a high probability of thin disk objects being located even at this offset from the mid-plane.," That is a large height indeed, but we note that the well-known flaring of the outer disk \citep[see e.g.][]{gyuk99} allows a high probability of thin disk objects being located even at this offset from the mid-plane." + Using the ? prescription. the thin disk scale height at Doo: = 20.8 kpe is in excess of 1 kpe (even if the solar neighbourhood scale height is reduced in line with the ? result).," Using the \citet{gyuk99} prescription, the thin disk scale height at $_{GC}$ = 20.8 kpc is in excess of 1 kpc (even if the solar neighbourhood scale height is reduced in line with the \citet{juric08} result)." + We will adopt for LACPN the S—r distance of 12.8 kpe., We will adopt for IACPN the $S - r$ distance of 12.8 kpc. + At Dec =20.8 kpe. it would be one of the most distant planetary nebula from the Galactic Centre for which à distance has been determined (c.f. ??))," At $_{GC}$ =20.8 kpc, it would be one of the most distant planetary nebula from the Galactic Centre for which a distance has been determined (c.f. \citealt{acker94,ssv08}) )" + and the farthest PN from the Galactic Centre with measured abundances (??)).," and the farthest PN from the Galactic Centre with measured abundances \citealt{maciel09,henry10}) )." + IACPN is a low density planetary nebula with an emission line spectrum typical of a moderate excitationType IL PN (Class3of?).., IACPN is a low density planetary nebula with an emission line spectrum typical of a moderate excitationType II PN \citep[Class 3 of][]{dopita90}. + This. together with its strong stratification. apparent from to (Fig. 2)).," This, together with its strong stratification, apparent from to (Fig. \ref{fig:2}) )," + suggests that it is composed of a moderately massive nebula hosting a relatively hot star., suggests that it is composed of a moderately massive nebula hosting a relatively hot star. + The ionised hydrogen mass of the nebula. derived from its Hf flux. electron temperature. radius. and distance. is M= 0.4 M...," The ionised hydrogen mass of the nebula, derived from its $\beta$ flux, electron temperature, radius, and distance, is M= 0.4 $_{\odot}$." + The nebular expansion velocity (17 km s! ) and the physical radius (0.31 pe at the distance of 12.8 kpe) lead to a kinematic age of 17800 yr., The nebular expansion velocity (17 km $^{-1}$ ) and the physical radius (0.31 pc at the distance of 12.8 kpc) lead to a kinematic age of 17800 yr. + Such à large kinematical age would point to à low mass central star if a luminosity larger. than ~300-500 L. is required (cf.2).., Such a large kinematical age would point to a low mass central star if a luminosity larger than $\sim300-500$ $_{\odot}$ is required \citep[cf.][]{blocker95}. +" To crudely estimate the central star mass. we follow the prescriptions of ?. for a N/O abundance ratio as given in Table 3.. finding m,,=0.6 M,. and an age for the progenitor star of - Gyr (if Case A from ? is assumed)."," To crudely estimate the central star mass, we follow the prescriptions of \citet{maciel10} for a N/O abundance ratio as given in Table \ref{tab:abund}, finding $_{cs} = 0.6$ $_{\odot}$ and an age for the progenitor star of $\sim$ 4 Gyr (if Case A from \citealt{maciel10} is assumed)." + However. given the several uncertain parameters involved (central star luminosity and temperature. kinematical vs. real age). no precise estimate of the stellar mass can be derived.," However, given the several uncertain parameters involved (central star luminosity and temperature, kinematical vs. real age), no precise estimate of the stellar mass can be derived." + We have ran several simple Cloudy (?) photoionisatior models using spherical or shell geometry and the model atmospheres of ?.., We have ran several simple Cloudy \citep{ferland98} photoionisation models using spherical or shell geometry and the model atmospheres of \citet{rauch03}. +" We assumed a nebula with an outer radius of 0.31 pe. hydrogen density of 200 em. anc chemical abundances 0.3 dex below those labelled in Cloudy as “planetary nebula""."," We assumed a nebula with an outer radius of 0.31 pc, hydrogen density of 200 $^{-3}$, and chemical abundances 0.3 dex below those labelled in Cloudy as “planetary nebula”." + This implies that the input models have 12+log(O/H)=8.34 and He/H=0.1. close to our measured values.," This implies that the input models have 12+log(O/H)=8.34 and He/H=0.1, close to our measured values." + On the other hand.the model abundances of N. Ar. and S are 0.1-0.3 dex above our derived values. whereas the model abundance of Ne is 0.2 dex below the value listed 1 Table 3..," On the other hand,the model abundances of N, Ar, and S are 0.1-0.3 dex above our derived values, whereas the model abundance of Ne is 0.2 dex below the value listed in Table \ref{tab:abund}. ." + Since the abundances of these elements are more uncertain. and since our comparison is based on the He and O ions. this should be à good approximation for our purposes.," Since the abundances of these elements are more uncertain, and since our comparison is based on the He and O ions, this should be a good approximation for our purposes." +"30% of the bulge mass in galaxies with AZ,~10 M. and as low as 15% in galaxies with A,Me=3-410 AL.",$30 \%$ of the bulge mass in galaxies with $M_* \sim 10^9$ $_{\odot}$ and as low as $15 \%$ in galaxies with $M_* > M_C=3 \times 10^{10}$ $_{\odot}$. + The quiescent component is associated with stars previously formed in gaseous discs according to the Schmict-Ixennicutt [aw and later being accded to the spheroid during major mergers., The quiescent component is associated with stars previously formed in gaseous discs according to the Schmidt-Kennicutt law and later being added to the spheroid during major mergers. + We find that the fraction of quiescent stars dominates bulges and elliptical galaxies., We find that the fraction of quiescent stars dominates bulges and elliptical galaxies. +" For galaxies above the critical mass scale. the fraction of quiescent stars becomes constant at a value of AZ,AM;~85%. the result of mergers. minor as well as major. only introducing small deviations as soon as galaxies are more massive than Me."," For galaxies above the critical mass scale, the fraction of quiescent stars becomes constant at a value of $M_q/M_{bul} \sim 85 \%$, the result of mergers, minor as well as major, only introducing small deviations as soon as galaxies are more massive than $M_C$." + The fraction of stars in bulges and discs shows a remarkable relation with the galaxy mass scale., The fraction of stars in bulges and discs shows a remarkable relation with the galaxy mass scale. + At galaxy masses below Ae we find only a weak redshift dependency and a decreasing fraction of stars in bulges with decreasing mass.," At galaxy masses below $M_C$, we find only a weak redshift dependency and a decreasing fraction of stars in bulges with decreasing mass." + However. at masses above Me: we find a strong redshift dependence.," However, at masses above $M_C$ we find a strong redshift dependence." + At higher. redshifts. the fraction of stars. in rulges becomes largcr in massive galaxies.," At higher redshifts, the fraction of stars in bulges becomes larger in massive galaxies." + This means that he most massive galaxies around at each redshift are likely be elliptical galaxies and that only at. later times do massive spiral galaxies start occurring., This means that the most massive galaxies around at each redshift are likely to be elliptical galaxies and that only at later times do massive spiral galaxies start occurring. +" Furthermore. our simulations indicate that mergers cacding to remnants with mass larecr than Λίο always include progenitors with bulges and that more than 50% of he mass in progenitorsDo of mass Al,Me is in bulges."," Furthermore, our simulations indicate that mergers leading to remnants with mass larger than $M_C$ always include progenitors with bulges and that more than $50 \% $ of the mass in progenitors of mass $M_* \sim M_C$ is in bulges." +5 Lhis las an important influence on the role of ACGN-feedback as hese bulges will harbour super-massive black holes., This has an important influence on the role of AGN-feedback as these bulges will harbour super-massive black holes. + Looking at the environmental dependence. we find that only galaxies less massive than Ae: show cdillerences.," Looking at the environmental dependence, we find that only galaxies less massive than $M_C$ show differences." + This is mainly related to the dilferent epoch at which these galaxies assembled., This is mainly related to the different epoch at which these galaxies assembled. + Xssembly is faster in high density environments resulting in larger merger components in. bulges., Assembly is faster in high density environments resulting in larger merger components in bulges. + Cialaxies above Ales do not show any significant environmental dependency because of continued merger activity in contrast o smaller galaxies., Galaxies above $M_C$ do not show any significant environmental dependency because of continued merger activity in contrast to smaller galaxies. + Recently Springel&Lernquist(2005). suggested. that mergers between extremely gas-rich clises could lead to the ormation of a disc galaxy during a major merger., Recently \citet{sh05} suggested that mergers between extremely gas-rich discs could lead to the formation of a disc galaxy during a major merger. + The authors argued that these kind of merecrs are likely to occur at high redshifts., The authors argued that these kind of mergers are likely to occur at high redshifts. + However. our simulations indicate hat the maximum. eas fraction is at 40% in mergers at high redshift anc most likely between ορ30% for a wide range of masses and redshifts.," However, our simulations indicate that the maximum gas fraction is at $\sim 40 \%$ in mergers at high redshift and most likely between $20 \% - 30 \%$ for a wide range of masses and redshifts." + In. general the eas raction in mergers is à decreasing function of mass., In general the gas fraction in mergers is a decreasing function of mass. + At very arge masses and at high redshifts a small population of eas rich massive mergers occurs. which tends slightly deviate from this trend.," At very large masses and at high redshifts a small population of gas rich massive mergers occurs, which tends to slightly deviate from this trend." + A reason for these events in our simulation could be associated with missing feedback fron AGNs., A reason for these events in our simulation could be associated with missing feedback from AGNs. + Fhose massive gas-rich mergers at high redshift are likely to have progenitors with black holes., Those massive gas-rich mergers at high redshift are likely to have progenitors with black holes. + Simulations by Springcl&Llernquist(2005). show that in general the merger. component is more centrally concentrated than the quiescent component., Simulations by \citet{sh05} show that in general the merger component is more centrally concentrated than the quiescent component. + The elfective radius of the merger component in their simulation is 5.7 times smaller than that of the quiescent. component., The effective radius of the merger component in their simulation is $\sim 5.7$ times smaller than that of the quiescent component. + ‘This suggest an interesting behaviour for the sizes of two galaxies of the same mass but dillerent merger component., This suggest an interesting behaviour for the sizes of two galaxies of the same mass but different merger component. + The remnant [rom the merger including less gas and hence less merger component will have a larger sizes., The remnant from the merger including less gas and hence less merger component will have a larger sizes. + As we have shown above remnants at higher redshifts have larger merger fractions., As we have shown above remnants at higher redshifts have larger merger fractions. + This and the observational indication that disc galaxies at higher redshifts are smaller. might be able to account. for the observed size-evolution of elliptical galaxies (Dacklictal.2005:‘Trujilloetal.," This and the observational indication that disc galaxies at higher redshifts are smaller might be able to account for the observed size-evolution of elliptical galaxies \citep{da05,tru05}." +2005) We would. like to thank Hgnacio ‘Trujillo αμα Emanucle Daddi for pointing out the high redshift. data., We would like to thank Ignacio Trujillo and Emanuele Daddi for pointing out the high redshift data. + Sl& acknowledges. funding. by the PPARC VPheoretical Cosmology. Rolling Grant., SK acknowledges funding by the PPARC Theoretical Cosmology Rolling Grant. +"contraction arguments suggest that the dark matter should become more centrally concentrated than a pure NFW profile, as the gas which formed the stellar component shrinks towards the center — we are ignoring this effect (see Padmanabhan et al.","contraction arguments suggest that the dark matter should become more centrally concentrated than a pure NFW profile, as the gas which formed the stellar component shrinks towards the center – we are ignoring this effect (see Padmanabhan et al." + 2004; Schulz et al., 2004; Schulz et al. + 2010; Treu et al., 2010; Treu et al. + 2010 for recent analyses of other samples in which this effect is included)., 2010 for recent analyses of other samples in which this effect is included). +" On the other hand, observations suggest that galaxies have a cored rather than a cuspy halo (e.g. Salucci et al."," On the other hand, observations suggest that galaxies have a cored rather than a cuspy halo (e.g. Salucci et al." + 2007) — even an uncontracted NFW profile is too steep., 2007) – even an uncontracted NFW profile is too steep. +" To proceed further, we assume that: followings Shankar et al.! ("," To proceed further, we assume that: following Shankar et al. (" +2006).,2006). +! This makes Notice that big galaxies are likely to have some scatter around this number (i.e. 30)., This makes Notice that big galaxies are likely to have some scatter around this number (i.e. 30). +" In fact for smaller values, our conclusion. that the stars dominate. the mass willH be stronger."," In fact for smaller values, our conclusion that the stars dominate the mass will be stronger." +" We demonstrate that the mass within rg, is dominated by the stars, not the dark matter."," We demonstrate that the mass within $r_{ap}$ is dominated by the stars, not the dark matter." +" For My,c10?Mo, rs=Tyir/c&60 kpc, and the NFW mass within rap is approximately 30M.(rap/rs)”/2.86, whereas the stellar mass within rap is slightly less than M,/2."," For $M_{vir}\approx 10^{13}M_\odot$, $r_s = r_{vir}/c \approx 60$ kpc, and the NFW mass within $r_{ap}$ is approximately $30M_*\,(r_{ap}/r_s)^2/2.86$, whereas the stellar mass within $r_{ap}$ is slightly less than $M_*/2$ ." +" Since rap/rs<1, the total mass within Tap is dominated by the stellar mass."," Since $r_{ap}/r_s\ll 1$, the total mass within $r_{ap}$ is dominated by the stellar mass." +" Consequently, σο is⋅ also dominated⋅by the stellar mass."," Consequently, $\sigma_{0}$ is also dominatedby the stellar mass." + We show this. explicitly⋅⋅ in⋅ Figure⋅ 1.., We show this explicitly in Figure \ref{fig:disp}. . +" The left hand panel Shows cios(r) , obtained from equation 7,, 8,, for an elliptical galaxy with M,=10’?Mo and re=6 kpc."," The left hand panel shows $\sigma_{los}(r)$ , obtained from equation \ref{eq:sigma2}, \ref{eq:sigma2los}, for an elliptical galaxy with $M_\star=10^{12}M_\odot$ and $r_e= 6$ kpc." + We see that the contribution from the dark matter component is always much smaller than that of the stellar component (o« of)., We see that the contribution from the dark matter component is always much smaller than that of the stellar component $\sigma_{los}^{DM}\ll \sigma_{los}^\star$ ). + Then we show that o7 is always negligible compared to oo observed (right hand panel)., Then we show that $\sigma_0^{DM}$ is always negligible compared to $\sigma_0$ observed (right hand panel). +" Since σὸ=σύ?o9""?, within our assumptions, the measured value of oo --provides a good estimate of M., without being contaminated by the dark matter component."," Since $\sigma_{0}^2 = \sigma_0^{\star \ 2} + \sigma_0^{DM\ 2}$, within our assumptions, the measured value of $\sigma_0$ provides a good estimate of $M_*$, without being contaminated by the dark matter component." +" The effect of DM is⋅ small, we can evaluate it and correct the estimation of oj by assuming equation 13.."," The effect of DM is small, we can evaluate it and correct the estimation of $\sigma_0^{\star}$ by assuming equation \ref{eq:mvir30}." + On average the dark matter component contributes to less than 596 to the total velocity dispersion (Table 2))., On average the dark matter component contributes to less than $5\%$ to the total velocity dispersion (Table \ref{tab:results}) ). + Now we build a new stellar mass estimatorthat exploits the quantity co., Now we build a new stellar mass estimatorthat exploits the quantity $\sigma_{0}$. + The Jeans equation implies that the quantity Ταρσῷ should be proportional to a function of Tap/Te., The Jeans equation implies that the quantity $r_{ap} \sigma_{0}^2$ should be proportional to a function of $r_{ap}/r_e$. +" If we set the actual value of A plotted in Figure 2 can befitted by: As acheck, note that if the power-law above had slope —1, then M.ος Τεσὸ; this isthe scaling that is usually"," If we set the actual value of $\lambda$ plotted in Figure \ref{fig:lambda} can befitted by: As acheck, note that if the power-law above had slope $-1$ , then $M_*\propto r_e\sigma_{0}^2$ ; this isthe scaling that is usually" +Exa of the iinatiouscattering diameters inferred for nxividual objects indicates that some of the larecst scattering diameters result from ACN for which no neasurenients exist below 1 CGIIz.,Examination of the scattering diameters inferred for individual objects indicates that some of the largest scattering diameters result from AGN for which no measurements exist below 1 GHz. + In order hat these not bias our result. we removed these :uid repeated the νο test analysis.," In order that these not bias our result, we removed these and repeated the K-S test analysis." + There is LO change in the result. that the scattering ciaeers for the scintillating and nou-sciutillatiue ACN are consistent with having been drawn from he same distribution.," There is no change in the result, that the scattering diameters for the scintillating and non-scintillating AGN are consistent with having been drawn from the same distribution." + Both the mean aud the nediai scattering diameter for scintillating and ron-scintillating sotrees Is approximately 2 mas (Table 2))., Both the mean and the median scattering diameter for scintillating and non-scintillating sources is approximately 2 mas (Table \ref{tab:stats}) ). + Frou the entire sample. 37 ACN )) lave ueasured redshifts.," From the entire sample, 37 AGN ) have measured redshifts." +" There appears to be little differeico du the redshüft distribution of the sciutilating aud Πολ]πο]itillatingΑνν, with he twο. populations having similar means an nediais (Table 2))."," There appears to be little difference in the redshift distribution of the scintillating and non-scintillating, with the two populations having similar means and medians (Table \ref{tab:stats}) )." + Figure l1 shows the distribution of the scattering diameers as a fiction of redshif., Figure \ref{fig:z} shows the distribution of the scattering diameters as a function of redshift. + We have determined. the correlation ETWECuu the scattering cjuueters and redshifts ‘Or the entire. sample. as well as splitting 1 into f1ο two populations. scintillating and nonu-sciutilating.," We have determined the correlation between the scattering diameters and redshifts for the entire sample, as well as splitting it into the two populations, scintillating and non-scintillating." + There is no correlation of the scatteri18o ciaeer with redshift for the cnutire sample., There is no correlation of the scattering diameter with redshift for the entire sample. + There iav be a marginal correlation. at the couficece level. between the scattering diameters and redshift. in the opposite seuse for the scintillating and nou-scintillating sources.," There may be a marginal correlation, at the confidence level, between the scattering diameters and redshift, in the opposite sense for the scintillating and non-scintillating sources." + That is. the scattering diameters of scintillating (uou-scintillating) ACN may become smaller (larger) at higher redshifts.," That is, the scattering diameters of scintillating (non-scintillating) AGN may become smaller (larger) at higher redshifts." + Tn one sense. our results are broadly cousisteut with what is known about intraday variability aud," In one sense, our results are broadly consistent with what is known about intraday variability and" +srockucect by the sinking σας (e.g. λος&Llernquist19001: aab&Burkert 2001)).,"produced by the sinking gas (e.g., \citealt{mihos96}; ; \citealt{naab01}) )." + This mass congregation makes he gravitational potential well of the galaxy steeper. thus »ompting a change of the stellar orbits.," This mass congregation makes the gravitational potential well of the galaxy steeper, thus prompting a change of the stellar orbits." + Specifically. it »vcomes more axisvmimetric and. less triaxial.," Specifically, it becomes more axisymmetric and less triaxial." + Phe lack of support for box orbits makes the minor-axis tubes more »opulated. thus producing clisey orbits.," The lack of support for box orbits makes the minor-axis tubes more populated, thus producing discy orbits." + The properties of the LOSVDSs are also allected by the oesence of eas (e.e Naabetal.2006:: CGonzález-Carcíaetal. 2006)).," The properties of the LOSVDs are also affected by the presence of gas (e.g., \citealt{naab06}; \citealt{garcia06}) )." + The local correlations between fyi. and ep.)fo observed. for our low-Iuminosity galaxies. is reproduced. in numerical simulations by superimposing a cold stellar disc component in the outer regions (io. 2 Lr) of the spheroidal body (Naab&Burkert 20013).," The local correlations between $h_{3,4}$ and $v_{rot}/\sigma$ observed for our low-luminosity galaxies, is reproduced in numerical simulations by superimposing a cold stellar disc component in the outer regions (i.e., $\geq 1 r_{e}$ ) of the spheroidal body \citealt{naab01}) )." + The transfer. of angular momentum between stars and eas (e.g. λος&Llern-«quist. 1996)) and. the redistribution of angular momentum from larger radii to inner radii produce a net increase of the rotational velocity of the galaxy.," The transfer of angular momentum between stars and gas (e.g., \citealt{mihos96}) ) and the redistribution of angular momentum from larger radii to inner radii produce a net increase of the rotational velocity of the galaxy." + The elliciency of gas consumption is also found to be responsible in allecting the shape of the isophotes (e.g. Bekki&Shiova 1997)).," The efficiency of gas consumption is also found to be responsible in affecting the shape of the isophotes (e.g., \citealt{bekki97}) )." + Disey isophotes are more likely formed in galaxies with gradual star formation. whereas galaxies with a rapid starburst tend to have boxy isophotes.," Discy isophotes are more likely formed in galaxies with gradual star formation, whereas galaxies with a rapid starburst tend to have boxy isophotes." + The almost solar value of the a ο] abundance: ratios displayed by our galaxies (Paper LL) favours this idea., The almost solar value of the $\alpha$ /Fe] abundance ratios displayed by our galaxies (Paper II) favours this idea. + The observed. abundance values are a consequence of the low star formation elliciency in our galaxies. thus leading to an extended star-forming episode (2:1 Gyr).," The observed abundance values are a consequence of the low star formation efficiency in our galaxies, thus leading to an extended star-forming episode $\geq 1$ Gyr)." + In conclusion. the kinematic and photometric results of our analvsis are in good. agreement with the interpretation of the stellar population findings in Paper LL.," In conclusion, the kinematic and photometric results of our analysis are in good agreement with the interpretation of the stellar population findings in Paper II." + They sugges that an early star-forming collapse with a mass-depencen star-formation elliciency is the main mechanisms acting in the formation of these low-luminosity earlv-tvpe galaxics., They suggest that an early star-forming collapse with a mass-dependent star-formation efficiency is the main mechanisms acting in the formation of these low-luminosity early-type galaxies. + Galaxy mergers may also produce some of the observe features., Galaxy mergers may also produce some of the observed features. + We now compare our results to merger simulations bv Naab&Burkert(2003).. Naabetal.(2006). and Coxeal. (2006).," We now compare our results to merger simulations by \cite{naab03}, \cite{naab06} and \cite{cox06}." +. Naab&Burkert(2003) used à large set of collisionless N-body simulations to investigate the fundamenta statistical properties. of merger remnants., \cite{naab03} used a large set of collisionless $N$ -body simulations to investigate the fundamental statistical properties of merger remnants. + Simulations involve dissipationless binary mergers ofdisc galaxies with mass ratios of 1:1. 2:1. 3:1. 4:1.," Simulations involve dissipationless binary mergers of disc galaxies with mass ratios of 1:1, 2:1, 3:1, 4:1." + Projection ellects are taken into account and the bulge components of the progenitor disces are left to evolve until they coalesce before. the kincmatic and photometric properties of the simulated carly-vpe galaxies are measured., Projection effects are taken into account and the bulge components of the progenitor discs are left to evolve until they coalesce before the kinematic and photometric properties of the simulated early-type galaxies are measured. + Naabetal.(2006). re-simulated the merger remnants of aab&Burkert(2003) with an aciditional gas component in he progenitor disc galaxies., \cite{naab06} re-simulated the merger remnants of \cite{naab03} with an additional gas component in the progenitor disc galaxies. + They considered only mergers of galaxies with mass ratios of 1:1 and 3:1., They considered only mergers of galaxies with mass ratios of 1:1 and 3:1. + Each progenitor jas LO percent of the total mass of the stellar dise replaced ον gas. but substantial heating processes prevent gas cooling and hence star formation.," Each progenitor has 10 percent of the total mass of the stellar disc replaced by gas, but substantial heating processes prevent gas cooling and hence star formation." + The gas is allowed to set into an equilibrium state before the disc galaxies are merged., The gas is allowed to set into an equilibrium state before the disc galaxies are merged. + The study of Coxetal.(2006) considers mergers of cqual-mass disc galaxies., The study of \cite{cox06} considers mergers of equal-mass disc galaxies. + Pwo sets of numerical simulations are generated. to compare the statistical properties of earlv-tv galaxies formed. by. clissipationless and. dissipational mergers., Two sets of numerical simulations are generated to compare the statistical properties of early-type galaxies formed by dissipationless and dissipational mergers. +pe. Progenitor galaxies can contain a purely exponential stellar. disc with a null fraction. of sas. or disc where 40 percent of the total mass is in the orm of gas.," Progenitor galaxies can contain a purely exponential stellar disc with a null fraction of gas, or disc where 40 percent of the total mass is in the form of gas." + Gas-rich. mergers include radiative cooling of eas. star formation. feedback processes and induced growth of massive central black holes.," Gas-rich mergers include radiative cooling of gas, star formation, feedback processes and induced growth of massive central black holes." + The orbits of the merging »ogenitors are identical to. those. explored. by Naab.&Durkert(2003) and Naabctal.(2006)... allowing a clirect comparison of results.," The orbits of the merging progenitors are identical to those explored by \cite{naab03} and \cite{naab06}, , allowing a direct comparison of results." + In Fig. 15..," In Fig. \ref{histo1b}," + we show the distribution of the anisotropy xwanmeter of our sample in comparison with the predictions of Naab&Burkert(2003).. Naalbctal.(2006)— and Coxetal.(2006).," we show the distribution of the anisotropy parameter of our sample in comparison with the predictions of \cite{naab03}, \cite{naab06} and \cite{cox06}." +.. The distribution of our low-luminosity ealaxies has a median value of (eu.συον0.56 and the values span the range 0.4 - 2.0., The distribution of our low-luminosity galaxies has a median value of $(v_{max}/\sigma_{0})^{*}$$\sim 0.86$ and the values span the range 0.4 - 2.0. + The distributions of simulated: remnants have significantly dillerent. median values for the degree of rotational support with respect to our galaxy sample., The distributions of simulated remnants have significantly different median values for the degree of rotational support with respect to our galaxy sample. + However. there exists a tendency for mergers with increasingly different mass ratios to produce more isotropically supported. galaxies.," However, there exists a tendency for mergers with increasingly different mass ratios to produce more isotropically supported galaxies." + “Phe predictions of Naabetal.(2006) and Coxetal.(2006) show that an additional gas component in the progenitor cliscs has a significant impact on the galaxy dynamical support., The predictions of \cite{naab06} and \cite{cox06} show that an additional gas component in the progenitor discs has a significant impact on the galaxy dynamical support. + This dissipative Component increase the amount of rotation and therefore. ordered: motion in the remnants., This dissipative component increase the amount of rotation and therefore ordered motion in the remnants. + The results of a Smirnov (INS) test show that our observed ealaxies and galaxies simulated by Coxctal.(2006). have a difference in their anisotropy parameter. distributions significant at to level., The results of a $-$ Smirnov (KS) test show that our observed galaxies and galaxies simulated by \cite{cox06} have a difference in their anisotropy parameter distributions significant at $\sigma$ level. + On the other hand. remnants of mergers with mass ratios of 4:1 simulated by Naab&Burkert(2003). and merger models of Naabetal.(2006) with mass ratios 3:1 with progenitors having LO percent. of eas appear similarly. distributed to our sample galaxies at almost the GO per cent level.," On the other hand, remnants of gas-free mergers with mass ratios of 4:1 simulated by \cite{naab03} and merger models of \cite{naab06} with mass ratios 3:1 with progenitors having 10 percent of gas appear similarly distributed to our sample galaxies at almost the 60 per cent level." + In Fig. 16..," In Fig. \ref{histo3b}," + the observed. distribution of the isophote-shape parameter By (the disevness/boxiness parameter) is compared to merger predictions., the observed distribution of the isophote-shape parameter $\overline{B_{4}}$ (the discyness/boxiness parameter) is compared to merger predictions. + The sample. galaxies have cisev-shapecl isophotes. with a distribution. median value of By= 0.30.," The sample galaxies have discy-shaped isophotes, with a distribution median value of $\overline{B_{4}} =$ 0.30." + Lhe dissipationless models of Naab&δικοί(2003). produce merger remnants with more ciscev isophotes when progenitors of increasingly dLETerent miss ratio are considered., The dissipationless models of \cite{naab03} produce merger remnants with more discy isophotes when progenitors of increasingly different mass ratio are considered. + On the other hand. 1ο simulations of Naabetal.(2006). suggest that the presence of a gas component in the progenitors is responsible for changing he stellar orbits of the remnant.," On the other hand, the simulations of \cite{naab06} suggest that the presence of a gas component in the progenitors is responsible for changing the stellar orbits of the remnant." + In this case. progenitors with a mass ratio 3:1 and. 10 percent of a gas component xoduce remnants with a small amount of discy. Isophotes.," In this case, progenitors with a mass ratio 3:1 and 10 percent of a gas component produce remnants with a small amount of discy isophotes." + A IWS test marginally rejects at the 70 per cent level the ivpothesis that dissipationless merger with mass ratios of 2:1 and LO per cent gas-vich mergers with mass ratios 3:1 wave the same distribution of our sample galaxies., A KS test marginally rejects at the 70 per cent level the hypothesis that dissipationless merger with mass ratios of 2:1 and 10 per cent gas-rich mergers with mass ratios 3:1 have the same distribution of our sample galaxies. + The simulations of Coxetal.(2006). show that. equal-mass »wogenitors with 40 percent of gas ancl merger-induced star formation produce remnants with significantly discey isophotes., The simulations of \cite{cox06} show that equal-mass progenitors with 40 percent of gas and merger-induced star formation produce remnants with significantly discy isophotes. + The INS test confirms that the degree of disevness of the simulated galaxies is inconsistent with that one of the observed. galaxies., The KS test confirms that the degree of discyness of the simulated galaxies is inconsistent with that one of the observed galaxies. + We note that the inclination angle under which the galaxy is observed. might alfect the evaluation of the isophotes’s shape (i.e. projection elfects)., We note that the inclination angle under which the galaxy is observed might affect the evaluation of the isophotes's shape (i.e. projection effects). + 1n conclusion. the kinematic and. isophotal shape predictions [rom merger models examined arein less good agreement. with our results.," In conclusion, the kinematic and isophotal shape predictions from merger models examined arein less good agreement with our results." + Although we suggest that mergingis unlikely to be the main ealaxy formation mechanism of our galaxies. comparison with the model predictions provides us with some constraints on the merger," Although we suggest that mergingis unlikely to be the main galaxy formation mechanism of our galaxies, comparison with the model predictions provides us with some constraints on the merger" +dispersions.,dispersions. + Phere can be stars much vounger and older than this average age among the Ποια stars’., There can be stars much younger and older than this average age among the `field stars'. + On careful. inspection of Fig., On careful inspection of Fig. + 3b and Fig., 3b and Fig. + 4b. one may notice the distinct holes [oft in the centers of the distributions after the possible MG members removed.," 4b, one may notice the distinct holes left in the centers of the distributions after the possible MG members removed." + This confirms the fact implied by the term ‘possible’. and suggests a substantial amount of the MG stars are really not M members.," This confirms the fact implied by the term `possible', and suggests a substantial amount of the MG stars are really not MG members." + Any individual svstems being older than the common age of the MG. could. be. selected. out às. non-members with the ages predicted by the stellar evolution. but this process (o0 does not to remove all of the non-members since there isguarantee still a possibility that a Ποια star. with a similar age as the AIG. occupies the same velocity space fulfilling the kinematical criteria to be a possible member.," Any individual systems being older than the common age of the MG could be selected out as non-members with the ages predicted by the stellar evolution, but this process too does not guarantee to remove all of the non-members since there is still a possibility that a field star, with a similar age as the MG, occupies the same velocity space fulfilling the kinematical criteria to be a possible member." + Nevertheless. our prime concern is to divide current CAB sample into two distinct age groups in order to compare the physical parameters then investigate the reasons behind if there is any noticeable dillerence.," Nevertheless, our prime concern is to divide current CAB sample into two distinct age groups in order to compare the physical parameters then investigate the reasons behind if there is any noticeable difference." +" Although. both the ""MC and. field. stars! are not. very homogeneous to represent (wo different ages. we found current grouping satisfactory Lor this study."," Although, both the `MG' and `field stars' are not very homogeneous to represent two different ages, we found current grouping satisfactory for this study." + The physical parameters of the chromospherically active binaries are Disted. in. Table. 4., The physical parameters of the chromospherically active binaries are listed in Table 4. + The columns are self explanatory ancl indicate the spectral type. SB (indicating single or double lined binary or whether within a multiple system). orbital period. eccentricity. mass ratio. mass of the primary. mass function. and radii of components.," The columns are self explanatory and indicate the spectral type, SB (indicating single or double lined binary or whether within a multiple system), orbital period, eccentricity, mass ratio, mass of the primary, mass function, and radii of components." + Phe data were collected primarily from the same literature where the radial velocities were taken., The data were collected primarily from the same literature where the radial velocities were taken. + ]ntending to compile binaries according ο known evolutionary stages of luminosity classification. the whole sample has been divided into three groups.," Intending to compile binaries according to known evolutionary stages of luminosity classification, the whole sample has been divided into three groups." + The first group is called °C? which contains binaries with at least one component being a giant., The first group is called `G' which contains binaries with at least one component being a giant. + A giant classification in the spectral typo. if pit exists.. or otherwise.. one of⋅ the radiiM being. six solar radii or bigger. were accepted. as criteria to form the C7 group.," A giant classification in the spectral type, if it exists, or otherwise, one of the radii being six solar radii or bigger, were accepted as criteria to form the `G' group." + The group of the sub giants ‘SCO were formed from the rest of the sample with a similar criteria: a sub giant classification in the spectral type. or at least one component being bigger than two solar radii.," The group of the sub giants `SG' were formed from the rest of the sample with a similar criteria; a sub giant classification in the spectral type, or at least one component being bigger than two solar radii." + After forming the giants and sub giants. the rest of the sample is called main sequence symbolized with “ALS.," After forming the giants and sub giants, the rest of the sample is called main sequence symbolized with `MS'." + All three groups contain almost equal numbers of “ALCO and field stars’., All three groups contain almost equal numbers of `MG' and `field stars'. +a brighter AM*.,a brighter $M^{\ast}$. + This could explain the clillerences between group ancl field galaxies., This could explain the differences between group and field galaxies. +" On the other hand. the ""lu band result. is not unexpected since this band is closely related to the current star formation. and galaxies in svstems are likely to have lower or suppressed star formation rates (see for instance Martinezetal.2002a))."," On the other hand, the $\ub$ band result, is not unexpected since this band is closely related to the current star formation, and galaxies in systems are likely to have lower or suppressed star formation rates (see for instance \citealt{m02}) )." + In this subsection we study how the LF depends on group masses., In this subsection we study how the LF depends on group masses. + A previous analysis on {his matter was done by Ekeetal.(2004b) using the 2dFCRS Percolation-Inferred Galaxy Group catalog (2PIGG: Ekeetal. 2004a)).," A previous analysis on this matter was done by \citet{eke04b} + using the 2dFGRS Percolation-Inferred Galaxy Group catalog (2PIGG; \citealt{eke04a}) )." + Thev split their group sample into three mass bins and compute the corresponding LFs using the standard ως and the STY methods., They split their group sample into three mass bins and compute the corresponding LFs using the standard $1/V_{\rm max}$ and the STY methods. + Though their high mass bin is statistically poor aud does not follow the same trend as the lower mass ones. (hey conclude that A and a decrease when mass increases.," Though their high mass bin is statistically poor and does not follow the same trend as the lower mass ones, they conclude that $M^{\ast}$ and $\alpha$ decrease when mass increases." + Given (he large number of eroups we have identified in DRA. we expect to obtain a more detailed description on this subject.," Given the large number of groups we have identified in DR4, we expect to obtain a more detailed description on this subject." + We have split the full sample of 20.22 groups into 6 mass bins defined to have roughly the same number of groups (2200)., We have split the full sample of $z\le0.22$ groups into 6 mass bins defined to have roughly the same number of groups $\sim 2200$ ). + The details of this selection can be seen in Table 2.., The details of this selection can be seen in Table \ref{stymass}. + The large number of galaxies in the samples allows the determination of LEs with a high level of confidence. even when we are splitting (he sample into several bins.," The large number of galaxies in the samples allows the determination of LFs with a high level of confidence, even when we are splitting the sample into several bins." +" In Figure ""3. we show the resulting (""tr band LF for each mass bin.", In Figure \ref{lfmasa} we show the resulting $\rb$ band LF for each mass bin. + As it can be seen from Figure 3.. the LEs are well fitted by Schechter finetions for all masses (see parameters in Table 2)).," As it can be seen from Figure \ref{lfmasa}, the LFs are well fitted by Schechter functions for all masses (see parameters in Table \ref{stymass}) )." + In order to simplify the reader interpretation of the results. we show the values ol Al* a (Figure 4)) and. M and à as a function of the mass (Figure 5)).," In order to simplify the reader interpretation of the results, we show the values of $M^{\ast}$ $\alpha$ (Figure \ref{isomasa}) ) and $M^{\ast}$ and $\alpha$ as a function of the mass (Figure \ref{amm}) )." + Figure 4 displavs the lo and 26 confidence ellipses according to STY computations., Figure \ref{isomasa} displays the $1\sigma$ and $2\sigma$ confidence ellipses according to STY computations. + Y-axis error-hars in Figure 5 are the projections of the la joint error ellipse onto each axis of Figure 4.. while x-axis error-bars are the semi-nterquartile range of (he median mass.," Y-axis error-bars in Figure \ref{amm} + are the projections of the $\sigma$ joint error ellipse onto each axis of Figure \ref{isomasa}, , while x-axis error-bars are the semi-interquartile range of the median mass." + There are two clear and continuous trends: a brghtening of M and a simultaneous steepening of a as mass increases., There are two clear and continuous trends: a brightening of $M^{\ast}$ and a simultaneous steepening of $\alpha$ as mass increases. + A/* changes in ~0.75magnitudes while a varies in 0.4. over two orders of magnitude i group mass.," $M^{\ast}$ changes in $\sim 0.75$magnitudes while $\alpha$ varies in 0.4, over two orders of magnitude in group mass." + We have done (he same calculations for the other SDSS bands., We have done the same calculations for the other SDSS bands. + The best-litting Schechter parameters are in Table 3.., The best-fitting Schechter parameters are in Table \ref{stymassband}. +" We found the same global trends in all bands. with some differences for the ""tu band."," We found the same global trends in all bands, with some differences for the $\ub$ band." + In this case we observe a brightening of M* ol ~0.4 magnitudes. significantly smaller than the 0.75 magnitudes value for the other bands.," In this case we observe a brightening of $M^{\ast}$ of $\sim 0.4$ magnitudes, significantly smaller than the $\sim0.75$ magnitudes value for the other bands." + This is not unexpected. since the 0.1“cu band is sensitive to star formation. ie.. σεInmiinosity lunction is apoor indicator of the underlying mass distribution.," This is not unexpected, since the $\ub$ band is sensitive to star formation, i.e., $\ub$luminosity function is apoor indicator of the underlying mass distribution." + The faint end slope variation with mass is roughly (he same. 0.5. for all bands.," The faint end slope variation with mass is roughly the same, $\sim0.5$ , for all bands." +pilot survey galaxies have an hhalo of the scale seen in NGC 891. we find that all of the pilot survey targets show varying indications of cold gas in their halos.,"pilot survey galaxies have an halo of the scale seen in NGC 891, we find that all of the pilot survey targets show varying indications of cold gas in their halos." + The lack of a prominent halo in UGC 2082 may not be a surprising result: the star formation rate is low. and the galaxy 15 Isolated.," The lack of a prominent halo in UGC 2082 may not be a surprising result: the star formation rate is low, and the galaxy is isolated." + Apart from the possibility of significant primordial accretion. à ready source for creating a gaseous halo does not seem to be present in this target.," Apart from the possibility of significant primordial accretion, a ready source for creating a gaseous halo does not seem to be present in this target." + Nonetheless. we find several distinct extraplanar features (these are noted in and are visible in Figures | and 2)).," Nonetheless, we find several distinct extraplanar features (these are noted in and are visible in Figures \ref{figure:u2082} and \ref{figure:pvdiagram_u2082}) )." + These clouds may be a sign of cold gas accretion., These clouds may be a sign of cold gas accretion. + Two of the pilot galaxies that are located in denser environments have a much less regular sstructure., Two of the pilot galaxies that are located in denser environments have a much less regular structure. + Clearly. the case of NGC 672 is a complicated one — the strong interaction with its companion IC 1727 has spread eemission throughout the system.," Clearly, the case of NGC 672 is a complicated one – the strong interaction with its companion IC 1727 has spread emission throughout the system." + This is a dramatic case of interaction-induced accretion., This is a dramatic case of interaction-induced accretion. + Another interacting system but at a later stage. NGC 925 seems to have interacted with a gas-rich companion sometime in its recent past. resulting in stripped material surrounding the main disk.," Another interacting system but at a later stage, NGC 925 seems to have interacted with a gas-rich companion sometime in its recent past, resulting in stripped material surrounding the main disk." + Whether the culprit is the faint blob at the southern edge of the galaxy. the object found to the north (as described in refsubsection:n0925)). or some other entity. is not yet clear.," Whether the culprit is the faint blob at the southern edge of the galaxy, the object found to the north (as described in \\ref{subsection:n0925}) ), or some other entity, is not yet clear." + NGC 925 also seems to possess aat lagging velocities with respect to the main disk., NGC 925 also seems to possess at lagging velocities with respect to the main disk. + The anomalous component in NGC 925 has a similar. mass and kinematic lag when compared to the same feature in NGC 2403., The anomalous component in NGC 925 has a similar mass and kinematic lag when compared to the same feature in NGC 2403. + Another target to compare with existing observations is the large edge-on NGC 4565. which does not show evidence of a prominent halo component.," Another target to compare with existing observations is the large edge-on NGC 4565, which does not show evidence of a prominent halo component." + Can this lack be explained?, Can this lack be explained? + In comparison with NGC 591. the differences in the global parameters of the two galaxies all tend to be in the sense in which one would indeed expect a larger halo im NGC 891. if gaseous halos are induced primarily by star. formation-driven galactic fountain flows.," In comparison with NGC 891, the differences in the global parameters of the two galaxies all tend to be in the sense in which one would indeed expect a larger halo in NGC 891, if gaseous halos are induced primarily by star formation-driven galactic fountain flows." + Under that assumption. the most important properties of a galaxy for determining whether a," Under that assumption, the most important properties of a galaxy for determining whether a" +We will also show that an unstable star of a small value of 3 eventually settles down to a nonaxisvmmetrie quasi-stationary state. which is a strong emitter of quasi-periodic eravitational waves.,"We will also show that an unstable star of a small value of $\beta$ eventually settles down to a nonaxisymmetric quasi-stationary state, which is a strong emitter of quasi-periodic gravitational waves." + The paper is organized as follows., The paper is organized as follows. + In Section 2. we describe our methods in numerical analysis.," In Section 2, we describe our methods in numerical analysis." + La Section 3. the numerical results are presented.," In Section 3, the numerical results are presented." + Section 4 is devoted to a summary and discussion., Section 4 is devoted to a summary and discussion. + Throughout this paper. we use the geometrical units of ο—e=1 where € and e denote the gravitational constant and the light velocity.," Throughout this paper, we use the geometrical units of $G=c=1$ where $G$ and $c$ denote the gravitational constant and the light velocity." + We set a differentially rotating star in equilibrium. ancl investigate the dynamical stability.," We set a differentially rotating star in equilibrium, and investigate the dynamical stability." + Rotating stars in equilibrium. are modeled. using the polvtropic equations of state as P=Wp! where P. p. I and b=1|fn denote the pressure. densitv. polvtropic constant and. acdiabatic index.," Rotating stars in equilibrium are modeled using the polytropic equations of state as $P=K\rho^{\Gamma}$ where $P$, $\rho$, $K$ and $\Gamma=1+1/n$ denote the pressure, density, polytropic constant and adiabatic index." + In this paper. we choose n=1. 3/2. and 5/2 (P=2. 5/5. and 7/5).," In this paper, we choose $n=1$, 3/2, and 5/2 $\Gamma=2$, 5/3, and 7/5)." + As the angular velocity. profile (zc). we choose the j-constant-like law as and the so-called Ixepler-Iike law as where cf is a constant. and QO the angular velocity at the symmetric axis.," As the angular velocity profile $\Omega(\varpi)$ , we choose the so-called $j$ -constant-like law as = and the so-called Kepler-like law as = _0 where $A$ is a constant, and $\Omega_0$ the angular velocity at the symmetric axis." + Phe parameter οἱ controls the steepness of the angular velocity profile: For smaller values of zl. the profile is steeper and for cl=ox the rigid rotationis recovered.," The parameter $A$ controls the steepness of the angular velocity profile: For smaller values of $A$ , the profile is steeper and for $A \rightarrow \infty$, the rigid rotationis recovered." + In the present work. the values of iA are chosen among the range OL<4—MIxm where £44 is the equatorial radius of rotating stars.," In the present work, the values of $A$ are chosen among the range $0.1 \leq \hat A \equiv A/R_{\rm eq} \leq 1$ where $R_{\rm eq}$ is the equatorial radius of rotating stars." +" For therotation laws (1)) ancl (2)). © at large evlindrical radius asvmptotically behaves as zc2 and zcBED""7. oc"," For therotation laws \ref{omegaj}) ) and \ref{omegak}) ), $\Omega$ at large cylindrical radius asymptotically behaves as $\varpi^{-2}$ and $\varpi^{-3/2}$." +uThis is. the reason why we refer to the profiles (1)) and (2)) as the j-constant-like and Ixepler-IHike laws., This is the reason why we refer to the profiles \ref{omegaj}) ) and \ref{omegak}) ) as the $j$ -constant-like and Kepler-like laws. + In the limit of 1:OQ with the profile (13). the specific angular momentum becomes constant everywhere and © diverges at zc=0.," In the limit of $A \rightarrow 0$ with the profile \ref{omegaj}) ), the specific angular momentum becomes constant everywhere and $\Omega$ diverges at $\varpi=0$." + We note that this profile has been often used in studies of nonaxisvmmetric instabilities in tori and annuli (Papaloizou&Pringle1984:GoodmanNaravan19858:Tohline&Hachisu1990:Andalib 1997).," We note that this profile has been often used in studies of nonaxisymmetric instabilities in tori and annuli \cite{PP,GN,TH,AT}." +. In this paper. however. we do not consider tori and annuli and focus only on spheroidal stars for which the density is not zero at zc= 0.," In this paper, however, we do not consider tori and annuli and focus only on spheroidal stars for which the density is not zero at $\varpi=0$ ." + μιας. we cannot adopt this limiting profile.," Thus, we cannot adopt this limiting profile." + In terms of 3=T/[W]| and AL one rotating star is determined. for a given rotational profile and. polvtropic index.," In terms of $\beta=T/|W|$ and $\hat A$, one rotating star is determined for a given rotational profile and polytropic index." + Thus. in the following. we often refer to these two parameters to specify a rotating star.," Thus, in the following, we often refer to these two parameters to specify a rotating star." + Here. ZY and M are defined. as por--- where p and ó are the mass density and the Newtonian eravitational potential.," Here, $T$ and $W$ are defined as d^3x ^2 d^3x, where $\rho$ and $\phi$ are the mass density and the Newtonian gravitational potential." +" Fo specify a particularmodel. we may choose the axis ratio of the rotating starsC, instead of 3."," To specify a particularmodel, we may choose the axis ratio of the rotating stars$C_a$ instead of $\beta$." +" Mere €, is delined as the ratio of the polar radius hj to the equatorial radius. feq. Le. €,=Byfi."," Here $C_a$ is defined as the ratio of the polar radius $R_p$ to the equatorial radius $R_{\rm eq}$, i.e., $C_a=R_p/R_{\rm eq}$." +" For the equations of state and the angular velocity. profiles that we study in this paper. the value of C, monotonically decreases with increase of 3 for a given set of wl and η."," For the equations of state and the angular velocity profiles that we study in this paper, the value of $C_a$ monotonically decreases with increase of $\beta$ for a given set of $\hat A$ and $n$." +" This is the reason that C, can be a substitute for 3.", This is the reason that $C_a$ can be a substitute for $\beta$. + To investigate πο dynamical stability against nonaxisvmumetric bar-mode deformations. we have performed the numerical simulation as well as the linear stability analysis.," To investigate the dynamical stability against nonaxisymmetric bar-mode deformations, we have performed the numerical simulation as well as the linear stability analysis." + Below we explain the methods for our numerical computation separately., Below we explain the methods for our numerical computation separately. + In the hyvedrodsnamie simulation. we initially superimpose a nonaxisvmmetric density perturbation to an axisvmmetric equilibrium star.," In the hydrodynamic simulation, we initially superimpose a nonaxisymmetric density perturbation to an axisymmetric equilibrium star." + We focus mainly on a fundamental bar-mode. and simply add the node-Iess density perturbation of the form where po(ze.2) denotes the density of the axisvmmoetric configuration and 9 constant.," We focus mainly on a fundamental bar-mode, and simply add the node-less density perturbation of the form = ,z) where $\rho_0(\varpi,z)$ denotes the density of the axisymmetric configuration and $\delta$ constant." + Throughout this paper. we choose à= 0.1.For simplicitv. the velocity is left tobe unperturbed at /— 0.," Throughout this paper, we choose $\delta=0.1$ For simplicity, the velocity is left tobe unperturbed at $t=0$ ." +" The growth of the bar-mode can be followedby monitoring the distortion parameter as On | )""?.(6) where IT μυ and Ji)(2)—ονιτ) denotes the quacdrupole moment defined by = α patat"," The growth of the bar-mode can be followedby monitoring the distortion parameter as ( + , where _+ , and $I_{ij}~(i,j=x,y,z)$ denotes the quadrupole moment defined by = d^3x x^i x^j." + Ilere. a—Gr.g. 2).Simulations are performed. using a 3D numerical hyerodsnamic implementation in Newtonian," Here, $x^i=(x, y, z)$ .Simulations are performed using a 3D numerical hydrodynamic implementation in Newtonian" +"The trausfer equation of polarized radiation reads (Zhelezuvakovetal.1971:Jones.1955) Q. C aud ⊲V ire the2 usual Stokes parameters. 71. X (7pfr)“vpdsalo.the svuchrotron optical depth. 7where is the sourceJ£. fiction. o is the azimuthal projection augle of the magnetic field ou the sky aud the coefficiouts of chiissivity (e. ει). absorptivity (Gy. Ce). convertibility (C, ) aud rotativity (65) are given by: where Qexe]σοιο.” aro the ratios- of couvertibilitiessDdee (4) aud rotativities∙∙∙ (0) of. the cold (e) aud relativisticPE. (6r) plasiuas eiven by: The trauster cocticicuts have been generalized to iuclude coutributious from both electronand positron plasmas but they asstme au isotropic pitch-angle distribution of the radiating particles.","The transfer equation of polarized radiation reads \citep{zhe74,jon88} +: where $I$ , $Q$, $U$ and $V$ are the usual Stokes parameters, $\tau\propto (\nu_{B}/\nu)^{\alpha +5/2}\nu_{B}^{-1}$ is the synchrotron optical depth, $J$ is the source function, $\phi$ is the azimuthal projection angle of the magnetic field on the sky and the coefficients of emissivity $\epsilon_{q}$ , $\epsilon_{v}$ ), absorptivity $\zeta_{q}$ , $\zeta_{v}$ ), convertibility $\zeta_{q}^{*}$ ) and rotativity $\zeta_{v}^{*}$ ) are given by: where $\zeta_{v,q}^{*(c)}/\zeta_{v,q}^{*(r)}$ are the ratios of convertibilities $(q)$ and rotativities $(v)$ of the cold $(c)$ and relativistic $(r)$ plasmas given by: The transfer coefficients have been generalized to include contributions from both electronand positron plasmas but they assume an isotropic pitch-angle distribution of the radiating particles." + We also neglected circular emissivitv ει and absorptivity ος (JonesandO'Dell1977a)., We also neglected circular emissivity $\epsilon_{v}$ and absorptivity $\zeta_{v}$ \citep{jon77a}. +". In the above equations. à; are umber densities of cold/relativistic clectrous ( Jorpositrous (| ).vp—eB siu(/2zicis the Larinor frequency. 2; is the low-cucrey cut-off Loreutz factor of relativistic particles. 7)=seg is the frequeney corresponding to radiating particles of enerey ο ο is the svuchrotrou-thinspectral index which also defines the slope of the relativistic particle energy distribution ασ}x57""1, 0 js the anele between the line of sight aud the direction of the maguetic field aud e7. 67. 677 and ο are the proportionality coefficients which are tabulated in JonesaudO'Dell(1977a)."," In the above equations, $n_{c,r}^{+,-}$ are number densities of cold/relativistic electrons $(-)$ or positrons $(+)$, $\nu_{B}=eB\sin\theta/2\pi m_{e}c$ is the Larmor frequency, $\gamma_{i}$ is the low-energy cut-off Lorentz factor of relativistic particles, $\nu_{i}=\gamma_{i}^{2}\nu_{B}$ is the frequency corresponding to radiating particles of energy $\sim\gamma_{i}m_{e}c^{2}$, $\alpha$ is the synchrotron-thinspectral index which also defines the slope of the relativistic particle energy distribution $n(\gamma)\propto\gamma^{-2\alpha -1}$, $\theta$ is the angle between the line of sight and the direction of the magnetic field and $\epsilon_{\alpha}^{q}$, $\zeta_{\alpha}^{q}$, $\zeta_{\alpha}^{*q}$ and $\zeta_{\alpha}^{*v}$ are the proportionality coefficients which are tabulated in \citet{jon77a}." +. We inteerated the radiative trauster equations using the Cash-harp cmbedded Runee-hutta fifth-order method with an adaptive stepsize control (Pressetal.1992)., We integrated the radiative transfer equations using the Cash-Karp embedded Runge-Kutta fifth-order method with an adaptive stepsize control \citep{pre92}. + Computations were performed by integrating transfer equatious in a piece-wise homogeneous medium., Computations were performed by integrating transfer equations in a piece-wise homogeneous medium. + The physical conditions in cach cell. ic.. orientation of the maguetic field vector. were chosen using the random ΠΟ: ecucration method of L'Ecuver in the implementation provided by Pressetal.(1992).," The physical conditions in each cell, i.e., orientation of the magnetic field vector, were chosen using the random number generation method of L'Ecuyer in the implementation provided by \citet{pre92}." +. This method is particularly suited for our purposes as it generates loue-period sequences of random nuubers aud thus prevents any spurious correlations., This method is particularly suited for our purposes as it generates long-period sequences of random numbers and thus prevents any spurious correlations. +" We assumed a coustant streneth of the variable B-ficld component but allowed its solid anele distribution to beuniformwithin 0€(0°.1807) aud oC( Ορ). where £cos20?(oo.)=2p. Lis the average of cos20 in the interval (| 0,.0,)."," We assumed a constant strength of the variable $\mathbf{B}$-field component but allowed its solid angle distribution to beuniformwithin $\theta\in +(0^{\rm o}, 180^{\rm o})$ and $\phi\in (-\phi_{o},\phi_{o})$ , where $\langle\cos2\phi\rangle_{(-\phi_{o},\phi_{o})}=2p-1$ is the average of $\cos 2\phi$ in the interval $(-\phi_{o},\phi_{o})$ ." +" We also superimposed a weak coustant and unidirectional coniponeut |B,|=9|B| on the variable iiagnetic field.", We also superimposed a weak constant and unidirectional component $|\mathbf{B}_{u}|=\delta |\mathbf{B}|$ on the variable magnetic field. +In the blast wave frame the external density #;=D»; and sweep-up occurs at a rate Sew- D».,"In the blast wave frame the external density $n_{i} = \Gamma +\,n_{\rm i}^\ast$ and sweep-up occurs at a rate ) = ." + As we have seen in the preceding section. the relativistic electrons and protons get very quickly isotropised and lose little energy in the process.," As we have seen in the preceding section, the relativistic electrons and protons get very quickly isotropised and lose little energy in the process." + This has two consequences: the sweep-up Is a source of isotropic. quasi-monoenergetie protons and electrons with Lorentz factor D in the blast wave frame.," This has two consequences: the sweep-up is a source of isotropic, quasi-monoenergetic protons and electrons with Lorentz factor $\Gamma$ in the blast wave frame." + The tsotropisation also provides a momentum transfer from the ambient medium to the blast wave., The isotropisation also provides a momentum transfer from the ambient medium to the blast wave. + In a time interval ó? the blast wave sweeps up a momentum of ] annlof which is transferred from the swept-up particles to the whole system with mass doge hae) where the density and relativistic mass of the energetic particles yoo havem to be added to that of the thermal plasma., In a time interval $\delta t$ the blast wave sweeps up a momentum of = ^2 t which is transferred from the swept-up particles to the whole system with mass }= + ) where the density and relativistic mass of the energetic particles = ) have to be added to that of the thermal plasma. + Therefore. the blast wave will tend to move backwards and its Lorentz factor relative to the ambient medium is reduced to which can easily be integrated numerically.," Therefore, the blast wave will tend to move backwards and its Lorentz factor relative to the ambient medium is reduced to = which can easily be integrated numerically." + For à highly relativistic blast wave we can expand the blast wave equation of motion and derive the timescale for slowing down, For a highly relativistic blast wave we can expand the blast wave equation of motion and derive the timescale for slowing down. + In the laboratory frame this timescale is longer by a factor I., In the laboratory frame this timescale is longer by a factor $\Gamma$. + We may also integrate the inverse of the slow-down rate to derive the observed time frame of the deceleration. that is the time at which the blast wave would be observed with a particular. Lorentz factor.," We may also integrate the inverse of the slow-down rate to derive the observed time frame of the deceleration, that is the time at which the blast wave would be observed with a particular Lorentz factor." + This may be interesting to compare results of VLBI observations of blazars., This may be interesting to compare with the results of VLBI observations of blazars. + In. the radiativeWith. the.regime. 1.9. when the internal energy is radiated away quickly. we may neglect the mass loading for D>>1 and obtain where we have assumed an interstellar medium with a constant density #;.," In the radiative regime, i.e. when the internal energy is radiated away quickly, we may neglect the mass loading for $\Gamma\gg 1$ and obtain where we have assumed an interstellar medium with a constant density $n_{\rm i}^\ast$." +In Fig., In Fig. + 2 we show typical solutions of the integral Eq.(82))., \ref{timeplot} we show typical solutions of the integral \ref{slow}) ). + The observed time needed for à deceleration to Lorentz factors [ of a few is independent of the initial Lorentz factor [yz»E. and it varies much less strongly with the aspect angle than did the initial Doppler factor.," The observed time needed for a deceleration to Lorentz factors $\Gamma$ of a few is independent of the initial Lorentz factor $\Gamma_0 \gg \Gamma$, and it varies much less strongly with the aspect angle than did the initial Doppler factor." + We can also calculate the distance traveled by the blast wave., We can also calculate the distance traveled by the blast wave. + For this we replace the retardation factor in Eq.(82)) by jc and we obtain for DjoE , For this we replace the retardation factor in \ref{slow}) ) by $\beta c$ and we obtain for $\Gamma_0 \gg \Gamma$ +"fit had reduced \5,,=1.61 for 11. degrees of freedom (see Figure 3)).",fit had reduced $\chi^2_{\mathrm{dof}} = 1.61$ for 11 degrees of freedom (see Figure \ref{fig:spectra}) ). + The probability οἱ obtaining such avalue of \? or larger under the hypothesis that the model is correct is very low. P(\?>17.75)=0.088.," The probability of obtaining such avalue of $\chi^2$ or larger under the hypothesis that the model is correct is very low, $P(\chi^2 \ge 17.75 ) = 0.088$." +" The fit was ereatly improved by the addition of a Gaussian emission line: in this case the fit had X3,—0.56 for & degrees of freedom (see Figure 3)).", The fit was greatly improved by the addition of a Gaussian emission line; in this case the fit had $\chi^2_{\mathrm{dof}} = 0.56$ for 8 degrees of freedom (see Figure \ref{fig:spectra}) ). + The probability of obtaining such a value of A? or larger under the hypothesis that the model is correct is P(\7>4.75)=.784., The probability of obtaining such a value of $\chi^2$ or larger under the hypothesis that the model is correct is $P(\chi^2 \ge 4.75 ) = .784$. + The line enerev was E=13.09£0.25 keV. Note that a line at a similar energv was found by Gavriiletal.(2002) in the first burst discovered from (his source., The line energy was $E=13.09\pm0.25$ keV. Note that a line at a similar energy was found by \citet{gkw02} in the first burst discovered from this source. + To fimily establish (he significance of this feature. we performed (he following Monte Carlo simulation inXPSEC.," To firmly establish the significance of this feature, we performed the following Monte Carlo simulation in." +. We generated 10000 Lake spectra drawn [rom a simple blackbody model having the same background aud exposure as our data set., We generated 10000 fake spectra drawn from a simple blackbody model having the same background and exposure as our data set. + We fit the simulated data to a blackbody model and to a blackbody plus emission line model and compared the 4? difference between the two., We fit the simulated data to a blackbody model and to a blackbody plus emission line model and compared the $\chi^2$ difference between the two. + To ensure we were sensitive lo narrow lines when Πο our blackbody plus emission line model we stepped through different line energies from 2 to 30 keV in steps of 0.2 keV ancl velit our spectrum holding the line energy fixed and recorded the lowest A? value returned., To ensure we were sensitive to narrow lines when fitting our blackbody plus emission line model we stepped through different line energies from 2 to 30 keV in steps of 0.2 keV and refit our spectrum holding the line energy fixed and recorded the lowest $\chi^2$ value returned. + In our simulations only LL events had a 4? difference greater or equal to the one found Irom our data., In our simulations only 11 events had a $\chi^2$ difference greater or equal to the one found from our data. + Thus. the probability of obtaining a spectral feature of equal signilicance by random chance is 0.0011.," Thus, the probability of obtaining a spectral feature of equal significance by random chance is $\sim +0.0011$." + The significance of the spectral feature reported for this source by Gavrilletal.(2002) al (his enerev was 0.0008., The significance of the spectral feature reported for this source by \citet{gkw02} at this energy was $\sim 0.0008$. + Since these were independent measurements. the probability of finding (vo spectral features at the same energv bv random chance is 8.3xLO‘. thus the emission line al ~13 keV is genuine.," Since these were independent measurements, the probability of finding two spectral features at the same energy by random chance is $\sim 8.8\times +10^{-7}$, thus the emission line at $\sim$ 13 keV is genuine." + In order to compare the energetics of this burst to those emitted in 2001 we measured its peak flux aud (ence., In order to compare the energetics of this burst to those emitted in 2001 we measured its peak flux and fluence. + The first step in (his analvsis was to model the background count rate., The first step in this analysis was to model the background count rate. + First we extracted an instrumental background for the entire observation usingpcabackest., First we extracted an instrumental background for the entire observation using. +. The function can only estimate the background rate every 16 5 seconds. so we interpolated to finer resolution bv modeling the background rate as a 5th order polynomial.," The function can only estimate the background rate every 16 s seconds, so we interpolated to finer resolution by modeling the background rate as a 5th order polynomial." + We then added the average non-burst count. rate to this model., We then added the average non-burst count rate to this model. + We estimated this value by subtracting our interpolated model from our data and then measuring (he average count rate over the same interval used to estimate the background in (he spectral evolution analvsis., We estimated this value by subtracting our interpolated model from our data and then measuring the average count rate over the same interval used to estimate the background in the spectral evolution analysis. + The 220 keV peak flux was determined from the event data using a box-car integrator of width 1/A/., The 2–20 keV peak flux was determined from the event data using a box-car integrator of width $1/\Delta t$. +" We used A?=64 ms and A/=/, (fordetailsonthefIux 2004).."," We used $\Delta t =64$ ms and $\Delta t = t_r$ \citep[for details on the flux calculation algorithm, +see][]{gkw04}. ." + At each step of the boxcar we subtracted the total number of background counts as determined by integrating our background moclel, At each step of the boxcar we subtracted the total number of background counts as determined by integrating our background model +To show more detailed influence of magnetic Ποια we list the maxinunm evaporation rates and (the corresponding radii lor dillerent;7 values in the upper part of Table 1..,To show more detailed influence of magnetic field we list the maximum evaporation rates and the corresponding radii for different$\beta$ values in the upper part of Table \ref{mdot-r}. +" The data can be linearly fitted by loginj,=0.143/.9—1.579 aud logΌμως=—1.150/;2+2.299."," The data can be linearly fitted by $\log \dot m_{\rm max}=0.143/ + \beta-1.579$ and $\log r_{\rm max}=-1.750/\beta+2.299$." +" ""Theoretical works have shown (hat the chaotic magnetic field would suppress Che heat conduction in the plasma (Tao 1995: Chandran Cowlevy 1998: Naravan Mecdvedevy 2001).", Theoretical works have shown that the chaotic magnetic field would suppress the heat conduction in the plasma (Tao 1995; Chandran Cowley 1998; Narayan Medvedev 2001). + Recent work reports that the coeffident of heat conduction can be reduced. to one fifth of the Spitzer value (Naravan Alecdvedey 2001)., Recent work reports that the coefficient of heat conduction can be reduced to one fifth of the Spitzer value (Narayan Medvedev 2001). + We caleulate the i—r relation [or different & with both the 2-T model and 1-LI models., We calculate the $\dot{m}-r$ relation for different $\kappa$ with both the 2-T model and 1-T models. + The 2-T results do not include the irracdiation/Conmptonization effects since we are more interested in (he influence caused by ihe heat conduction., The 2-T results do not include the irradiation/Comptonization effects since we are more interested in the influence caused by the heat conduction. +of the combined effect of heat conduction and irradiation/Comptonization one can reler to the work of \lever-Holmeister Mever (2006)., the combined effect of heat conduction and irradiation/Comptonization one can refer to the work of Meyer-Hofmeister Meyer (2006). + Fi, Fig. +e.4 shows the dependence of the ri—r relation on & based on the 2-T model., \ref{2T_kappa} shows the dependence of the $\dot{m}-r$ relation on $\kappa$ based on the 2-T model. + The solid line represents (he standard case with #=5uy. .," The solid line represents the standard case with $\kappa=\kappa_{\rm Sp} + $, ." + The dot-dashed line and the long-dashed line correspond to &=0.55up. and &=0.2555. respectively.," The dot-dashed line and the long-dashed line correspond to $\kappa=0.5 \kappa_{\rm Sp}$, and $\kappa=0.2 \kappa_{\rm Sp}$, respectively." + For comparison. a curve with Ho—Bay dn the I-T model is also shown as a short-dashed line.," For comparison, a curve with $\kappa= \kappa_{\rm Sp}$ in the 1-T model is also shown as a short-dashed line." + Fig., Fig. + 4. looks very similar to Fig. 3.., \ref{2T_kappa} looks very similar to Fig. \ref{2T_beta}. + The location of the maximal evaporation rate moves inward with the decrease of &. but the maximal evaporation rate is insensitive to &.," The location of the maximal evaporation rate moves inward with the decrease of $\kappa$, but the maximal evaporation rate is insensitive to $\kappa$." + Detailed values of our calculation aud 1e corresponding linearly fitting results are listed in the lower half of Table 1.., Detailed values of our calculation and the corresponding linearly fitting results are listed in the lower half of Table \ref{mdot-r}. + Comparing 1e filling results for both the cases of magnetic pressure ancl heat conduction. we find that the influence of magnetic field is much stronger than that of the heat conduction.," Comparing the fitting results for both the cases of magnetic pressure and heat conduction, we find that the influence of magnetic field is much stronger than that of the heat conduction." + Note that the chaotic magnetic field tends to decrease the heat conduction bv cleflecting the motion of electrons and the inclusion of magnetic field would greatly reduce the disk truneation radius iough both 7 and &. Well show a composite result in the next subsection., Note that the chaotic magnetic field tends to decrease the heat conduction by deflecting the motion of electrons and the inclusion of magnetic field would greatly reduce the disk truncation radius through both $\beta$ and $\kappa$ We'll show a composite result in the next subsection. + The 1-T results with different & values are plotted in Fie. 5..," The 1-T results with different $\kappa$ values are plotted in Fig. \ref{1T_kappa}," + which shows (the similar tendency as the influence of 7., which shows the similar tendency as the influence of $\beta$ . + Due to the decoupling of electrons and ionsin the inner region. the 1-T results are less meaningful than the 2-T results.," Due to the decoupling of electrons and ionsin the inner region, the 1-T results are less meaningful than the 2-T results." +Noο that in al cases photometric colors were sclected according to the new Luge logg relations derived iu Sect. L2..,Note that in all cases photometric colors were selected according to the new $T_{\rm eff}$ $\log g$ relations derived in Sect. \ref{TGrelations}. + ExCUSIVE coniyarisous of these relatious with various other Teg color scales have been published ia nuuerous studies (ee...Alonsoetal.1999b:Houdashelt200:vere&Clem2003:RamirezMeléndez 2005b).," Extensive comparisons of these relations with various other $T_{\rm eff}$ –color scales have been published in numerous studies \citep[e.g.,][]{A99, H00, SF00, WLB02, VC03, RM05b}." +. Some of hese relatious (BaSeL 2.2. À99. II00. SFOO. and VCny were also emiploved im our comparison of the observed axd heoretical colors of lae-tvpe eius a Solar metallicity (Paper D.," Some of these relations (BaSeL 2.2, A99, H00, SF00, and VC03) were also employed in our comparison of the observed and theoretical colors of late-type giants at Solar metallicity (Paper I)." + Àtogether. this provides a further reference ist for à conirpari«1 of the new T; COor and color scales with similar relatious available i the literature.," Altogether, this provides a further reference list for a comparison of the new $T_{\rm eff}$ –color and color–color scales with similar relations available in the literature." + Conmparisous of the new Z7. log gcolor rolatious sed onPHOENIX. aud coors (Tables 6 aud 7)) with the miblishec Jig color relaIOUS are eiven lu Fig.," Comparisons of the new $T_{\rm eff}$ $\log g$ –color relations based on, and colors (Tables \ref{TGPhoenixMarcs} and \ref{TGAtlas}) ) with the published $T_{\rm eff}$ –color relations are given in Fig." + δ (Tig οςdor planes) and Fie., \ref{figTCplanes-1.0} $T_{\rm eff}$ –color planes) and Fig. + 9 {ς'olorcolor planes) at|M/II|= 1.0.:iid. correspondiuelv. in Figs.," \ref{figCCplanes-1.0} (color–color planes) at $\MoH=-1.0$, and, correspondingly, in Figs." + 10 and 11 at [M/TI|=2.0 (all coniparisons are uade with respect to the scale o' A99)., \ref{figTCplanes-2.0} and \ref{figCCplanes-2.0} at $\MoH=-2.0$ (all comparisons are made with respect to the scale of A99). + We discuss the trends at these two metalicities in the sections below., We discuss the trends at these two metalicities in the sections below. + On the whole. tie agreenient between different Tig color relations is &oot in all Tuy color planes (Fig. 8)).," On the whole, the agreement between different $T_{\rm eff}$ –color relations is good in all $T_{\rm eff}$ –color planes (Fig. \ref{figTCplanes-1.0}) )." + Typical differences are well within ATi~SO ας with somewhat larger deviations in the Tig (7Iv) plane.," Typical differences are well within $\Delta T_{\rm eff} \sim80$ K, with somewhat larger deviations in the $T_{\rm eff}$ $(J-K)$ plane." + Except for the scales of SE10 and BaSeL 3.1 (which start to deviate below Tig~11 OTS and ~L300 TIN. correspondingly). reasonably goo agreenient is also seen in the τω (5V) plane (note hat effective temperaturecoor relations differ cousideradv amore in this plane at Solar imoetallicitv: see Paper D.," Except for the scales of SF00 and BaSeL 3.1 (which start to deviate below $T_{\rm +eff}\sim4100$ K and $\sim4300$ K, correspondingly), reasonably good agreement is also seen in the $T_{\rm eff}$ $(B-V)$ plane (note that effective temperature–color relations differ considerably more in this plane at Solar metallicity; see Paper I)." + I is worthwhile uoting that t1e slopes of SFOO aud BaSeL 3.Ἰ scales are clearly cüffereu from those of other relatiojs du his Digg color plane., It is worthwhile noting that the slopes of SF00 and BaSeL 3.1 scales are clearly different from those of other relations in this $T_{\rm eff}$ –color plane. + The agreeneut heween different relations is very eood 1ji the fig (VI) plane. typically to £50 IIs. with somewhat larecr deviatious for he scales based on BaScL axl] COors.," The agreement between different relations is very good in the $T_{\rm +eff}$ $(V-I)$ plane, typically to $\pm50$ K, with somewhat larger deviations for the scales based on BaSeL and colors." + There is also a goo consistency beween differe Tia color scales in tp Tog (CA) plane (to E80 WI). though effective aniooratures predicted by the Tig cok reation of A99 are slightly ower than those resuline fro otjr relations.," There is also a good consistency between different $T_{\rm +eff}$ –color scales in the $T_{\rm eff}$ $(V-K)$ plane (to $\pm80$ K), though effective temperatures predicted by the $T_{\rm eff}$ –color relation of A99 are slightly lower than those resulting from other relations." + Iu spite of t1ο reasonably good agreement between the different Tig color scaes iu general there is a clear indication hat effective te3uperatures predicted bv the Tig color relatiois based o isvuthetic colors (100.ATLAS.MARCS. PHOENIX) are typically slightly higher than those inferred from the empirical relations (i.c.. those of A99. DaSeL 2.2 and 3.1. SFOO. VCO3. ΠΑΛΙΟΣ).," In spite of the reasonably good agreement between the different $T_{\rm eff}$ –color scales in general, there is a clear indication that effective temperatures predicted by the $T_{\rm +eff}$ –color relations based on synthetic colors (H00, ) are typically slightly higher than those inferred from the empirical relations (i.e., those of A99, BaSeL 2.2 and 3.1, SF00, VC03, RM05)." + This offset is seen in all Zi color planes and is hugest in the Tig (BVIp ane. where the average cdiffercuce between the predictions of theoretical aud empirical relations amounts to 100 IKIS (similar offset i eeu iu the Tag 67.A) plane too. thougiiu this case the comparison can oulv be made with the semi-enipirica BaSel 2.2 aud 3.1 scales).," This offset is seen in all $T_{\rm eff}$ –color planes and is largest in the $T_{\rm +eff}$ $(B-V)$ plane, where the average difference between the predictions of theoretical and empirical relations amounts to $\sim100$ K (similar offset is seen in the $T_{\rm eff}$ $(J-K)$ plane too, though in this case the comparison can only be made with the semi-empirical BaSel 2.2 and 3.1 scales)." + The ouly exception in this seise ds the scale of BCSs9: theoretical colors of DOGS) aro verv dndar to those precictecL din enipirical reations 1- he Tur (BVy and Tig (V.I) planes., The only exception in this sense is the scale of BG89: theoretical colors of BG89 are very similar to those predicted by empirical relations in the $T_{\rm eff}$ $(B-V)$ and $T_{\rm eff}$ $(V-I)$ planes. + In tιο 1.g (VWI) pane. the BOs) relaticπι s sinilar to he otlICY scaes baselon svuthetic colors. while in the Tig (JK)p ane it precicts effective temperatures that are coisicleralv higher han those resulting from other Tig coor relatio1s.," In the $T_{\rm eff}$ $(V-K)$ plane, the BG89 relation is similar to the other scales based on synthetic colors, while in the $T_{\rm eff}$ $(J-K)$ plane it predicts effective temperatures that are considerably higher than those resulting from other $T_{\rm eff}$ –color relations." + It shoul he not«cο that tιο. AND scale occtpics an intermediate position iu us sense in all Tig color aues. providing a coupromise between the predicloli of theoretica and empirica Tar color relatious.," It should be noted that the A99 scale occupies an intermediate position in this sense in all $T_{\rm eff}$ –color planes, providing a compromise between the predictions of theoretical and empirical $T_{\rm eff}$ –color relations." + That is. effective temperatures οἼνοιι w the À99 scale eenerallv ead to be lower than those oeiven bv Zig color rela10119 sed on SVLhetic colors. witjan average offset of aout ~6 Ην. On the other haid. they are higher by 1p to 5iην] (Τομ (BV3 plane) than effective temperaures XCicted by the enmipirieal scales.," That is, effective temperatures given by the A99 scale generally tend to be lower than those given by $T_{\rm eff}$ –color relations based on synthetic colors, with an average offset of about $\sim60$ K. On the other hand, they are higher by up to $\sim50$K $T_{\rm +eff}$ $(B-V)$ plane) than effective temperatures predicted by the empirical scales." + Ivansetal.(20n) rave reached sniilar conchisious in their conrparison o‘the effective temperatures of RGB stars in the globular chster AIS derived usine the Tig (BV) scales of A99. SFOO and Π0ῦ.," \citet{I01} have reached similar conclusions in their comparison of the effective temperatures of RGB stars in the globular cluster M5 derived using the $T_{\rm eff}$ $(B-V)$ scales of A99, SF00 and H00." + While there are some hiuts that the A99 scale tends to predict slightly lower Tuy tiu other Tig color relations a Solar uetallicity (Paper D. at [ALU]=1.0 asinular treud is seen oulv in the Tig (V.AK) plane (it is interesting to note in this respect tha the Tig s predicted by A99 scaes at [NIj=2.0 are indeccd lower than those resulting fronm other Dig color relalous: see Sect; 5.2.2)).," While there are some hints that the A99 scale tends to predict slightly lower $T_{\rm eff}$ than other $T_{\rm eff}$ –color relations at Solar metallicity (Paper I), at $\MoH=-1.0$ a similar trend is seen only in the $T_{\rm +eff}$ $(V-K)$ plane (it is interesting to note in this respect that the $T_{\rm eff}$ 's predicted by A99 scales at $\MoH=-2.0$ are indeed lower than those resulting from other $T_{\rm +eff}$ –color relations; see Sect. \ref{MoH=-2.0}) )." + While the RAIO5 scale) (which Is an exteusion and update of he A99 relations) predicts slightly (1erent effectiveΣ temperaures tha1 do the A99 relations. differences between the two scales are always within X50IKEK. A slightly larecr discrepaicv is seen in the Τιμ (VA) plane. especialy af Ta&1300 II. Note. however. that the transformation cquations of Carpeuter(2001) used bv us to convert (VIWovtass colors of RM to the Jomson-C'o1sius-Cilass svstei (see Sect.," While the RM05 scale (which is an extension and update of the A99 relations) predicts slightly different effective temperatures than do the A99 relations, differences between the two scales are always within $\pm50$ K. A slightly larger discrepancy is seen in the $T_{\rm eff}$ $(V-K)$ plane, especially at $T_{\rm +eff}\ga4300$ K. Note, however, that the transformation equations of \citet{C01} used by us to convert $(V-K)_{\rm 2MASS}$ colors of RM05 to the Johnson-Cousins-Glass system (see Sect." + 2 for details) were ¢lerived utilizi19 OL va part of the 2\TASS survey data avaiable at that tnue., \ref{synthcolors} for details) were derived utilizing only a part of the 2MASS survey data available at that time. + Nevertheess. a slüft of Α/ΤWy=0L1 is needed to compensate for a difference of 5bUTKI& betwee ithe A99 aud RAL5 relations (Fie.," Nevertheless, a shift of $\Delta (V-K)=0.1$ is needed to compensate for a difference of $50$ K between the A99 and RM05 relations (Fig." + δος]. which is quite lar9e to be explained by uuceraiuties in the transformation οquations.," \ref{figTCplanes-1.0}c c), which is quite large to be explained by uncertainties in the transformation equations." + We fiud no cear evidence that he Tig color relations based on the BaSeb 3.1 colors would 1udec represent al luprovelment owy the DaSeL 2.2 scales at [M/TI|= 1.0., We find no clear evidence that the $T_{\rm eff}$ –color relations based on the BaSeL 3.1 colors would indeed represent an improvement over the BaSeL 2.2 scales at $\MoH=-1.0$ . + Iu fact. the scales npoving BaSeL 2.2 colors seca to be in better agreement with the general treus seen in the Tag (BOW) aneL Ta (17) planes at DarS1500 IN. Otherwise. the two scaes behave very similarly. especially," In fact, the scales employing BaSeL 2.2 colors seem to be in better agreement with the general trends seen in the $T_{\rm eff}$ $(B-V)$ and $T_{\rm eff}$ $(V-I)$ planes at $T_{\rm eff}\la4500$ K. Otherwise, the two scales behave very similarly, especially" +a result. nag ds determined by the neutral fraction qj du the redshift ranec ZEN<2OX ix.,"a result, $\tau_{\rm eff}$ is determined by the neutral fraction $x_{\rm HI}$ in the redshift range $z_{\rm Ly\alpha,in}^i \leq z \leq z_{\rm S}$ ." + Since μι at liel-: Is uncertain. we assume that ayy is constant iu the above range for simplicity.," Since $x_{\rm HI}$ at $z$ is uncertain, we assume that $x_{\rm HI}$ is constant in the above range for simplicity." + The real cji might vary significantly in the redshift range. so that the assumed ο should © regarded as an effective mean value inchudiug such a variation (hereafter n ).," The real $x_{\rm HI}$ might vary significantly in the redshift range, so that the assumed $x_{\rm HI}$ should be regarded as an effective mean value including such a variation (hereafter $x_{\rm HI}^{\rm eff}$ )." + Iu Figures 3a3d. we show Zn; for the Lf. J. IT. aud K- as a functiou of the source redshift.," In Figures 3a–3d, we show $\Delta m_i$ for the $I$, $J$, $H$, and $K$ -bands as a function of the source redshift." + The continu in the observers L-band is not absorbed bv the ICA jieutral hydrogen at all when the source redshift is less han about 25., The continuum in the observer's $L$ -band is not absorbed by the IGM neutral hydrogen at all when the source redshift is less than about 25. + Although we assmued that the spectra shape is proportioual to vο- in the paucls. the results are much robust for the chanee of the spectral shape as roted above.," Although we assumed that the spectral shape is proportional to $\nu^{-1/2}$ in the panels, the results are much robust for the change of the spectral shape as noted above." +" The solid curves iu these panels are loci of Aim; for a given 4f as a function of the source redshit τμ, ", The solid curves in these panels are loci of $\Delta m_i$ for a given $x_{\rm HI}^{\rm eff}$ as a function of the source redshift $z_{\rm S}$. +"For example. siuce tio,=5 for [baud the IG absorption iu J[-banud is about 5 mae for the source a ty=7 if the effective neutral fraction m in the redshif range 5€iX Tis dÜ7."," For example, since $z_{\rm Ly\alpha,in}^I=5$ for $I$ -band, the IGM absorption in $I$ -band is about 5 mag for the source at $z_{\rm S}=7$ if the effective neutral fraction $x_{\rm HI}^{\rm eff}$ in the redshift range $5 \leq z \leq 7$ is $10^{-5}$." + Two dotted vertical lines in cach panel of Figure 3 indicate the redshifts when the Lya break enters and goes out of the each baud width τρ aud .~Lyeout’ respectively).," Two dotted vertical lines in each panel of Figure 3 indicate the redshifts when the $\alpha$ break enters and goes out of the each band width $z_{\rm Ly\alpha,in}^i$ and $z_{\rm Ly\alpha,out}^i$, respectively)." +" As seeu iu Figure d. if the ICAI is Sienificautly ucutral. the source with τμ>d""Lyesout cannot be detected through the filter / (ie. drop-out)."," As seen in Figure 1, if the IGM is significantly neutral, the source with $z_{\rm S} > z_{\rm Ly\alpha,out}^i$ cannot be detected through the filter $i$ (i.e. )." + ILowever. we can detect such a source if the universe is liehlv ionized.," However, we can detect such a source if the universe is highly ionized." + This is because the countiuuuu below the Ίνα break remains as shown in Figure 2., This is because the continuum below the $\alpha$ break remains as shown in Figure 2. + Suppose we observe a source with iy>d~Lyeour through the /£ and jy filters and assume that the radiation through 7 filter is not affected by any intervening absorption (.c. An;= 0).," Suppose we observe a source with $z_{\rm S}>z_{\rm Ly\alpha,out}^i$ through the $i$ and $j$ filters and assume that the radiation through $j$ filter is not affected by any intervening absorption (i.e. $\Delta m_j=0$ )." +" From equation (12). the expected magnitude through the ;/ filter is For example. we consider the case of /=I. j=1, and τμ=7."," From equation (12), the expected magnitude through the $i$ filter is For example, we consider the case of $i=I$, $j=L$, and $z_{\rm S}=7$." + We find that the apparent L maguitude of the afterglow of the GRB at τα=7 for 1 hour after the prompt burst is about Ll mag from Figure. 1., We find that the apparent $L$ magnitude of the afterglow of the GRB at $z_{\rm S}=7$ for 1 hour after the prompt burst is about 14 mag from Figure 4. +" Thus. the apparent £ maguitude is expected to be 22 mag because the iutvinsic ££=3.1mae for d hour (ie. the case xv U?gqpn Table 3) and AI~5 mae if n""—10"" in the redshift range 5<2x7."," Thus, the apparent $I$ magnitude is expected to be 22 mag because the intrinsic $I-L=3.1$mag for 1 hour (i.e. the case $\propto \nu^{-1/2}$ in Table 3) and $\Delta I\sim 5$ mag if $x_{\rm HI}^{\rm eff}=10^{-5}$ in the redshift range $5 \leq z \leq 7$." + We can reach 5-0 detection ofthe source with £=22 mae bx oulv three müuutes exposure with a S-an class telescope., We can reach $\sigma$ detection of the source with $I=22$ mag by only three minutes exposure with a 8-m class telescope. + Interestingly the assumed nm is nuila to the value reported bv Whiteetal.(2003) from the CamuPeterson trough in the spectra of 5>6 quasars., Interestingly the assumed $x_{\rm HI}^{\rm eff}$ is similar to the value reported by \cite{whi03} from the Gunn–Peterson trough in the spectra of $z>6$ quasars. + Siuluw aremuent can be done for other aids., Similar argument can be done for other bands. + Therefore. in general the detection of the source with −⋅ filter js San trastaGaray ↑∐⋜↧↑↑∐↸∖∏∐↕↖⇁↸∖↥⋅↴∖↴↸∖↕∐↑∐↸∖↥⋅↸∖≼↧↴∖↴∐↕↕⋟↑↥⋅⋜⋯∶↴∙⊾↸∖−∙∣∟↖↽↙⇝↕↕↓∿−∙∿−∙↔∖↽⋅∖⊳∖ ∙↴⊣∕⊳∙∟↖↽↙⋅⊳⋅↗⊓⊺↑↕∐∪∏∶↴∙∐↑↕∐∏↑∪∣↕↴∖↑∐∏∪⋅↖∶↴∙∪∪≼↧∩↕≺∐∐∩ is highly ionized. ie. mu lin that redshift raus.," Therefore, in general, the detection of the source with $z_{\rm S}>z_{\rm Ly\alpha,out}^i$ through the filter $i$ is the very good evidence that the universe in the redshift range $z_{\rm Ly\alpha,in}^i \la z \la z_{\rm S}$ is highly ionized, i.e. $x_{\rm HI}^{\rm eff} \ll 1$ in that redshift range." + Conversely. the detection enables us to estimate πμ aud cq.," Conversely, the detection enables us to estimate $\tau_{\rm eff}$ and $x_{\rm HI}^{\rm eff}$." + Finally. we note here that Figure 3 is also useful for any other sources (e.e.. QSOs) because Ai; is almost incependeut of the source spectrin.," Finally, we note here that Figure 3 is also useful for any other sources (e.g., QSOs) because $\Delta m_i$ is almost independent of the source spectrum." + Tere we discuss how we can confirm or refute αινὰ scenario: the universe was reionized twice., Here we discuss how we can confirm or refute Cen's scenario: the universe was reionized twice. + Iu the scenario. the first complete ionization at 2~20 is followed bv the partially iouized epoch at :~10.," In the scenario, the first complete ionization at $z\sim 20$ is followed by the partially ionized epoch at $z\sim 10$." + Therefore. we should check whether the neutral fraction at 2~20 is very low or not and whether the fraction at 2~10 is almost unity or not.," Therefore, we should check whether the neutral fraction at $z\sim 20$ is very low or not and whether the fraction at $z\sim 10$ is almost unity or not." + To do so. the best observation is ae spectroscopy in the NTR bands.," To do so, the best observation is the spectroscopy in the NIR bands." + As shown iu Fig., As shown in Fig. + we of section 3. the reionization historv is imprinted iu ιο observed. continuum.," 2 of section 3, the reionization history is imprinted in the observed continuum." + However. the seusitivity of the spectroscopy is in eeneral mmch less than that of the photometric observations.," However, the sensitivity of the spectroscopy is in general much less than that of the photometric observations." + Hence we discuss the way using 16 NIR photometrics., Hence we discuss the way using the NIR photometries. +" Tn the previous section. we have shown that the letection of the GRB afterglows through a filter / bevoud ve Lye drop-out redshift (C15, )proves the ionization of the universe around. if,ag "," In the previous section, we have shown that the detection of the GRB afterglows through a filter $i$ beyond the $\alpha$ drop-out redshift $z_{\rm Ly\alpha,out}^i$ )proves the ionization of the universe around $z_{\rm Ly\alpha,out}^i$ ." +From the characteristic redshifts for the NIR filters sunuuarized in Table 2. the T. J. HT. aud Iv filters axe the suitable to check the ionization state at 2~5 S. 811. 1115. aud. 1520. respectively.," From the characteristic redshifts for the NIR filters summarized in Table 2, the $I$, $J$, $H$, and $K$ filters are the suitable to check the ionization state at $z\sim 5$ –8, 8–11, 11–15, and 15–20, respectively." + Thos. the null detection of the GRD afterglows of zy~11 in J-haud indicates an high neutral fraction iu 8X:11.," Thus, the null detection of the GRB afterglows of $z_{\rm S}\sim 11$ in $J$ -band indicates an high neutral fraction in $8 \la z \la 11$." + On the other haud. we detect the CRB afterglows of n0 203a A-baud if the IGM in 15S2S20 is ionized.," On the other hand, we detect the GRB afterglows of $z_{\rm S}\sim 20$ in $K$ -band if the IGM in $15 \la z \la 20$ is ionized." + { and Z£-baud surveys are also very imniportaut to assess the relonization historv of the universe., $I$ and $H$ -band surveys are also very important to assess the reionization history of the universe. + We cau coustrain the latest reionization epoch by observing the CRB afterelows at +=6 through F-baud., We can constrain the latest reionization epoch by observing the GRB afterglows at $z\ga 6$ through $I$ -band. + In stummary. we can examine the relonization historv bv checking whether the high-: CRB afterelows drop out of the NIR filters or not.," In summary, we can examine the reionization history by checking whether the $z$ GRB afterglows drop out of the NIR filters or not." + Tn the rest of this subsection. woe discuss what is the difference between Cems scenario and others.," In the rest of this subsection, we discuss what is the difference between Cen's scenario and others." +" To demonstrate the main feature. we assunue two schematic relonization histories: (1) single gradual reionization and (2) double sudden reionizations. which are shown iu Figure 5 as the solid. aud. dashed curves. respectively,"," To demonstrate the main feature, we assume two schematic reionization histories; (1) single gradual reionization and (2) double sudden reionizations, which are shown in Figure 5 as the solid and dashed curves, respectively." + These histories are based on two observational coustraiuts: (1) the neutral fraction of lvdrogen egi~10.7 at z~6 from the Camu-Peterson trough fouud iu the :26 quasars spectra (Beckeretal.2001:White2003)... and (2) the beginning of the reionization is :20 from the large opacity of the electron scattering suggested byIWAZAP (Ixogutctal.2003).," These histories are based on two observational constraints; (1) the neutral fraction of hydrogen $x_{\rm HI}\sim 10^{-5}$ at $z\sim 6$ from the Gunn-Peterson trough found in the $z>6$ quasars spectra \citep{bec01,whi03}, and (2) the beginning of the reionization is $z\sim 20$ from the large opacity of the electron scattering suggested by \citep{kog03}." +. For the double reiouizatious. we also cousider different values of μι d the first reiouization epoch.," For the double reionizations, we also consider different values of $x_{\rm HI}$ in the first reionization epoch." + Iu Figure 6. we show the expected NIR colors as a function of the source redshift for the afterglow spectruu fooxovU? case (the observing time lessthan several hours. see Table 3).," In Figure 6, we show the expected NIR colors as a function of the source redshift for the afterglow spectrum $f_\nu \propto \nu^{-1/2}$ case (the observing time lessthan several hours, see Table 3)." + We find differences between the single and double reionizatious iu the fF (paucl jal) aud WL (panel 01) colors., We find differences between the single and double reionizations in the $I-J$ (panel [a]) and $K-L$ (panel [d]) colors. + Iu panel (a). the CRBafterglows up to BS09B cau be seen in both of the 7 aud J bauds for the siugle roeionization case. whereas the Fo color of ty>7.1 afterelows diverges m the double reionizatiou case. Le. the sources drop out of the Z-baud.," In panel (a), the GRBafterglows up to $z_{\rm S} \sim 8$ can be seen in both of the $I$ and $J$ bands for the single reionization case, whereas the $I-J$ color of $z_{\rm S} > 7.1$ afterglows diverges in the double reionization case, i.e. the sources drop out of the $I$ -band." + This reflects the difference of the increasing rate of the neutral fraction around +~6 in two reionization histories., This reflects the difference of the increasing rate of the neutral fraction around $z\sim6$ in two reionization histories. +" The drop-out redshift iu the double reionization case is determined hy As(ldEisahop)=AGOd nao) Where A, audAG are the rest-frame waveleusth of the Ίσα aud Ly) lines. aud Leon IS the sudden reiouization redshift (Taian 1999).."," The drop-out redshift in the double reionization case is determined by $\lambda_{\beta}(1+z_{\rm S,drop})=\lambda_{\alpha}(1+z_{\rm reion})$ , where $\lambda_{\alpha}$ and$\lambda_{\beta}$ are the rest-frame wavelength of the $\alpha$ and $\beta$ lines, and $z_{\rm reion}$ is the sudden reionization redshift \citep{hai99}. ." + In our case. nio= 6.," In our case, $z_{\rm reion}=6$ ." + It is worth to noting that, It is worth to noting that +criterion is strongly depenlent on the star formation rate. which may be systematically affected oe1 clusters (e.e.. Iennicutt 1983. Moss Whittle 1993. IKoopiuaun Kenney 1998b).,"criterion is strongly dependent on the star formation rate, which may be systematically affected in clusters (e.g., Kennicutt 1983, Moss Whittle 1993, Koopmann Kenney 1998b)." + Van deu -)oreli based his DDO classifications solely ou apparent bulec-to-«disk ratios (11uch as the Yerkes classification (Morgan 1958) is based primarily ou a visual light concentration parameter) aud oetroduced the term ‘anemic’ to refer to galaxies with weak star formation., Van den Bergh based his DDO classifications solely on apparent bulge-to-disk ratios (much as the Yerkes classification (Morgan 1958) is based primarily on a visual light concentration parameter) and introduced the term `anemic' to refer to galaxies with weak star formation. + Bothun (1982) stressed the use of quantitative paranueters. such as the bulec-to-disk ratio. to better trace the underline stellar mass distribution of the galaxw aud avoid dependence on visually striking star formation characteristics. as well as 1esolutiou effects.," Bothun (1982) stressed the use of quantitative parameters, such as the bulge-to-disk ratio, to better trace the underlying stellar mass distribution of the galaxy and avoid dependence on visually striking star formation characteristics, as well as resolution effects." + Recent studies (Dressler ct al., Recent studies (Dressler et al. + 199[: van deu Bereh al., 1994; van den Bergh et al. + 1996) have affirmed that a relatively sinaller fraction of distant galaxies fits the ITubble classification. and several eroups (c.@.. Abraham ct al.," 1996) have affirmed that a relatively smaller fraction of distant galaxies fits the Hubble classification, and several groups (e.g., Abraham et al." + 1991: Fukueita et al., 1994; Fukugita et al. + 1995: Tashimoto ot al., 1995; Hashimoto et al. + 1998) have adopted «puautitative parameters. such as ceutral elt coucentration. to trace morphological type.," 1998) have adopted quantitative parameters, such as central light concentration, to trace morphological type." + Howeyor. no quantitative test of the IIubble classification has vet been made for nearby cluster galaxies.," However, no quantitative test of the Hubble classification has yet been made for nearby cluster galaxies." + Iu this paper. we explore whether the Ibubble types of nearby. isolated and cluster galaxies correlate with quantitative measures of the ceutral light concentration aud star formation activity.," In this paper, we explore whether the Hubble types of nearby isolated and cluster galaxies correlate with quantitative measures of the central light concentration and star formation activity." + This work is part of a series on the comparative star formation propertics of Vireo Cluster aud isolated 8galaxies., This work is part of a series on the comparative star formation properties of Virgo Cluster and isolated galaxies. + A full discussion of star formation properties in the two samples is eiveui in Koopiiaun Iseunev (1998)., A full discussion of star formation properties in the two samples is given in Koopmann Kenney (1998b). + The data for the 81 galaxies presented iu this paper are extracted from a larger study of Virgo Cluster and isolated spirals., The data for the 84 galaxies presented in this paper are extracted from a larger study of Virgo Cluster and isolated spirals. + The 55 Virgo S0-Sed galaxies have BY « 13 (Mg < -18 for an asstuned distance of 16 Mpc). iunclinatious less than 757. aud a range iu position in the cluster.," The 55 Virgo S0-Scd galaxies have $_T^0$ $<$ 13 $_B$ $<$ -18 for an assumed distance of 16 Mpc), inclinations less than $^{\circ}$, and a range in position in the cluster." +" Because the main inteut was to study the star formation properties of Virgo Cluster ealaxies. the spiral subtypes are observed to a relatively lieh level of completeness. while ος are incomplete (Sc:ον, Sb:.. Sa:50%.. SO: )). aud therefore not represcutative of the Virgo SO population."," Because the main intent was to study the star formation properties of Virgo Cluster galaxies, the spiral subtypes are observed to a relatively high level of completeness, while S0's are incomplete (Sc:, Sb:, Sa:, S0: ), and therefore not representative of the Virgo S0 population." + The 29 isolated galaxies were carefully selected. frou low deusity regions. outsidegroups. as defined by Tully (1987) aud Gourgoulhon. Cliaimaraux. Fouqué (1992).," The 29 isolated galaxies were carefully selected from low density regions, outside, as defined by Tully (1987) and Gourgoulhon, Chamaraux, Fouqué (1992)." + All isolated ealaxies have lme«M-eht velocity < 2000 kins . Mp -1δ. and Tully (1987) density parameter < 0.3 eal Mpc.," All isolated galaxies have line-of-sight velocity $<$ 2000 km $^{-1}$ , $_B$ $<$ -18, and Tully (1987) density parameter $<$ 0.3 gal $^3$." +" Approximately equal numbers of isolated S0. Sa. Sb. aud Se galaxies were observed (completcness within selection criteria for Sc: Sh:25%.. Sa:τν, aud SO: hus the relative fr:ictions of the isolated nibble types are not representative of the eeneral isolated population. dn which SO aud Sa galaxies are relatively rare."," Approximately equal numbers of isolated S0, Sa, Sb, and Sc galaxies were observed (completeness within selection criteria for Sc:, Sb:, Sa:, and S0: ); thus the relative fractions of the isolated Hubble types are not representative of the general isolated population, in which S0 and Sa galaxies are relatively rare." + Observations were made between 1986 and 1996 at the KPNO 0.911. CTIO 0.912. CTIO 1.51). and WIYN 3.514. telescopes.," Observations were made between 1986 and 1996 at the KPNO 0.9m, CTIO 0.9m, CTIO 1.5m, and WIYN 3.5m telescopes." + All galaxies were observed iu broadband R aud in a filter of bandwidth: 70-80. aapxopriate for the redshitted Πα line., All galaxies were observed in broadband R and in a filter of bandwidth 70-80 appropriate for the redshifted $\alpha$ line. + Images were fiux calibrated using spectrophotometric sandard stars. combined with observatious of Landolt standards.," Images were flux calibrated using spectrophotometric standard stars, combined with observations of Landolt standards." + Contiuuuu-free Πα | [N H (hereafter abbreviated as Ho). inmiages were obtained by subtracting scaled BR. images from the ine nuages.," Continuum-free $\alpha$ + [N II] (hereafter abbreviated as $\alpha$ ), images were obtained by subtracting scaled R images from the line images." + B aud Πα surface photometry aud total fluxes were mneasured usines procedures in IRAF and with an IDL based surface photometry program (IXoopiuanu ct al., R and $\alpha$ surface photometry and total fluxes were measured using procedures in IRAF and with an IDL based surface photometry program (Koopmann et al. + 1005)., 1998). + A] surface briehtuess profiles were adjusted to face ou by assmuine CO)ete transparency alc a fixed inclination derived from the outer BR isophotes., All surface brightness profiles were adjusted to face on by assuming complete transparency and a fixed inclination derived from the outer R isophotes. + The oversimplified assuniption«of complete transparency is necessary in the absence of extinction values for other galaxies. hit should uot systematically affect theresults since the Virgo Cluster," The oversimplified assumption of complete transparency is necessary in the absence of extinction values for other galaxies, but should not systematically affect theresults since the Virgo Cluster" +is coniplex - a double power-law or simular: 3) the electrou aneular distribution is anisotropic: 1) the flare produces enough EUV/SXRB photous for the wildly relativistic ICS to be effective.,is complex - a double power-law or similar; 3) the electron angular distribution is anisotropic; 4) the flare produces enough EUV/SXR photons for the mildly relativistic ICS to be effective. + Sources in which ICS plays a siguificaut role are likely rare., Sources in which ICS plays a significant role are likely rare. + Poteutial cases ας be analyzed in soie detail., Potential cases must be analyzed in some detail. + Such analyses would be ereatly aide we the availability of imaging and spectroscopic— data at both IIXR/z-rav cnereies and centimeter/millimeter radio wavelengths., Such analyses would be greatly aided by the availability of imaging and spectroscopic data at both $\gamma$ -ray energies and centimeter/millimeter radio wavelengths. + We note that limited microwave observations are available for the event discussed in $55.3:?.. who fiud that the radio cussion is broadly consisteut with the bremsstrabhine interpretation. point out that the electrous that produce the 17 CdIz enuüssiou have energies of order 1.2 MeV. These are the same mildly relativistic electrons that could be respousible for ICS. if it is relevant. in the mildly relativistic regime.," We note that limited microwave observations are available for the event discussed in 5.3;, who find that the radio emission is broadly consistent with the bremsstrahlung interpretation, point out that the electrons that produce the 17 GHz emission have energies of order 1.2 MeV. These are the same mildly relativistic electrons that could be responsible for ICS, if it is relevant, in the mildly relativistic regime." + It is well known that a close relationship between ICS aud svuchrotron cluission exists for isotropic distributions of electrous and photons., It is well known that a close relationship between ICS and synchrotron emission exists for isotropic distributions of electrons and photons. + The ratio of the svuchrotrou power Payne to the ICS power Pres is equal to the ratio+ of. the magnetic+ enerev deusitv. ap=D/8xP* aud the photon energy deusitv apn: One could in principle use joint radio and IIXR observations to determine whether ICS iu the mildly relativistic τοσο is relevant., The ratio of the synchrotron power $P_{synch}$ to the ICS power $P_{ICS}$ is equal to the ratio of the magnetic energy density $u_B = B^2/8\pi$ and the photon energy density $u_{ph}$: One could in principle use joint radio and HXR observations to determine whether ICS in the mildly relativistic regime is relevant. + (ναι that auisotropic electron distributions may be an important clement iu determining the relevance of ICS. the above relationship would need to be recast to the specifies of the electrou anisotropy.," Given that anisotropic electron distributions may be an important element in determining the relevance of ICS, the above relationship would need to be recast to the specifics of the electron anisotropy." +" It is bevond the scope of this paper to investigate whether the INR and radio observations of flares can be reconciled iu the framework of nuüldlv relativistic ICS, but it is inportaut to eniphasize that the sale electrons are responsible for the radio cussion aud the photon up-scatter iu this case and both mechauisins would jointly inupose strong constraints on the electron distribution."," It is beyond the scope of this paper to investigate whether the HXR and radio observations of flares can be reconciled in the framework of mildly relativistic ICS, but it is important to emphasize that the same electrons are responsible for the radio emission and the photon up-scatter in this case and both mechanisms would jointly impose strong constraints on the electron distribution." + We thank Dr. Alec MacKinnon. Dr. Samun Ixrucker. and the anouviunous referee for useful comments that led to improvements to the paper.," We thank Dr. Alec MacKinnon, Dr. Sämm Krucker, and the anonymous referee for useful comments that led to improvements to the paper." + The National Radio Astronomy Observatory ds a facility of the National Science Foundation operated muder cooperative agreement by Associated Universities. Inc. CHTANTTI is a collaborative project involving George Mason University. the Universtv of Michigan (USA) and the University of Cambridge (UIS).," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. CHIANTI is a collaborative project involving George Mason University, the University of Michigan (USA) and the University of Cambridge (UK)." + DC acknowledges support by NSF erant ACGS-1010652 to the University of Virginia., BC acknowledges support by NSF grant AGS-1010652 to the University of Virginia. +"radius. renorimalizing the value of Pg with npMinne the correlation P;Pp holds (with DD and D, = 0.05 and 0.002. respectively: see Table 3)).","radius, renormalizing the value of $P_B$ with $n_B = n_{\rm inn}$, the correlation $P_J - P_B$ holds (with $P^V_{\rho}$ and $P_{\rho}$ = 0.03 and 0.002, respectively; see Table \ref{tab3}) )." + The quasi linear dependence is niüutaimed. although with a sleltly higher scatter. and with an intercept (aud thus a conversiou efficiency) increased by a factor of ~ 5.," The quasi linear dependence is maintained, although with a slightly higher scatter, and with an intercept (and thus a conversion efficiency) increased by a factor of $\sim$ 5." + Following BBCOS. we looked for possible relationships between the jet power aud the sinele quautities defining Pp through Eq. (," Following BBC08, we looked for possible relationships between the jet power and the single quantities defining $P_B$ through Eq. (" +1).,1). + No correlation was fod between P; and the temperature at the Bondi radius., No correlation was found between $P_J$ and the temperature at the Bondi radius. +" A correlation P;ϱ αιμαθος only when the whole sample is cousidered iP,= 0,03) but with a huge scatter (rius = 0.81). an --indication that the highest jet powers are in ecneral found oe1 the deusest (at heir Bondi radius) coronac."," A correlation $P_J - n_B$ emerges only when the whole sample is considered $P_{\rho} = 0.03$ ) but with a large scatter (rms = $0.81$ ), an indication that the highest jet powers are in general found in the densest (at their Bondi radius) coronae." + A stronger relationship of P; with Mp is couverselv present as VArown bv the right panel of Fig., A stronger relationship of $P_J$ with $M_{BH}$ is conversely present as shown by the right panel of Fig. + 2. aud in Table 3.., \ref{pjpb} and in Table \ref{tab3}. + The slope of the fit (@z2.2+0.1 for he full sample and azxlor0.1 for the Vireo sub-sanuple) aerees with that predicte by the dependence of the accretion rate from Mg., The slope of the fit $a \approx 2.2\pm0.4$ for the full sample and $a \approx 1.7\pm0.4$ for the Virgo sub-sample) agrees with that predicted by the dependence of the accretion rate from $M^2_{BH}$. + We must remark however that the scatter of the correlation P; - Afpy is larger than for the P; - Pp relation., We must remark however that the scatter of the correlation $P_J$ - $M_{BH}$ is larger than for the $P_J$ - $P_B$ relation. + From these arguments i is clear that the mass of the SMDIT is the dominant parameter in driving the accretion Xxocess and powering the jet. but that the density at the Bondi radius plavs an important role. reducing the scatter of the correlation.," From these arguments it is clear that the mass of the SMBH is the dominant parameter in driving the accretion process and powering the jet, but that the density at the Bondi radius plays an important role, reducing the scatter of the correlation." + Bahuaverdeetal.(2008). found that the different. levels of unclear activity are related to global differences iu 1ο structure of the ealactic hot coronae., \citet{balmaverde08alias} found that the different levels of nuclear activity are related to global differences in the structure of the galactic hot coronae. + Tncleed. a relation links the jet power with the corona ατα surface xiehtuess. albeit with a large scatter.," Indeed, a relation links the jet power with the corona X-ray surface brightness, albeit with a large scatter." + This suggests jit a substantial variation iu the jet power must be acconipanied by a global change iu its ISM. properties., This suggests that a substantial variation in the jet power must be accompanied by a global change in its ISM properties. + As the temperature is quite uniforui across the ISM.L. ie density in the external region is the most relevant xuaneter that could be related to the accretion process occurmnue in the core.," As the temperature is quite uniform across the ISM, the density in the external region is the most relevant parameter that could be related to the accretion process occurring in the core." +" We here re-examine this Ίππο, but oeistead of cousidering the surface brightuess of the corona. we measured its ce-projected deusitv at a fixed radius of lkpe. μοι ~ 1 2 orders of anaguitude larger than the Boudi radius. interpolating the neighboring poiuts iu the density profile."," We here re-examine this issue, but instead of considering the surface brightness of the corona, we measured its de-projected density at a fixed radius of 1 kpc, $n_{\rm 1 kpc}$ , $\sim$ 1 – 2 orders of magnitude larger than the Bondi radius, interpolating the neighboring points in the density profile." + Iu Fig., In Fig. + 3. we compare ποιο With Pp., \ref{pbalfa} we compare $n_{\rm 1 kpc}$ with $P_B$. +" For the complete sample of 27 galaxies. the correlation analysis between Pp aud tiie provides D,=0.05 aud awιτοι. The residuals have a rims of 0.8 dex."," For the complete sample of 27 galaxies, the correlation analysis between $P_B$ and $n_{\rm 1 kpc}$ provides $P_{\rho} = 0.05$ and $a \approx 1.7 \pm +0.4$ The residuals have a rms of 0.8 dex." + A μίαν relation is present also between P; aud iic., A similar relation is present also between $P_J$ and $n_{\rm 1 kpc}$. + The inclusion of the four low-power VCC ealaxics is crucial to unveil the connection between these quantities. because it extends the range covered by doth variables. providing the necessary leverage o the data.," The inclusion of the four low-power VCC galaxies is crucial to unveil the connection between these quantities, because it extends the range covered by both variables, providing the necessary leverage to the data." + We thus coufirim that the evel of AGN activity is counected with the overall properties of the hot corona., We thus confirm that the level of AGN activity is connected with the overall properties of the hot corona. + The rather loose relation between accretion rate iud corona density is not surprising., The rather loose relation between accretion rate and coronal density is not surprising. + ΗΕ vpical sound speeds of ~500 km lo the outer (1 kpc) aud Inner regions (rg~10LOO pc) of the ISM are causally connected on dynamical timescales ou the order of a few 109 years.," Indeed, assuming typical sound speeds of $\sim 500$ km $^{-1}$, the outer (1 kpc) and inner regions $r_B \sim 10 - 100$ pc) of the ISM are causally connected on dynamical timescales on the order of a few $10^6$ years." + The large scatter observed cau be related to events occurring inside the ISM on shorter timescales., The large scatter observed can be related to events occurring inside the ISM on shorter timescales. + These could be of external origin. e.g. transicut changes due to mergers or iuteractious with the ISM. but the accretion flow cau also be affected “frou inside. e.g. due to a variable release of jet kinetic energy iuto the corona.," These could be of external origin, e.g. transient changes due to mergers or interactions with the ISM, but the accretion flow can also be affected `from inside', e.g. due to a variable release of jet kinetic energy into the corona." + We now look for possible relationships between the je power (strictly connected to the nuclear activity) of the Virgo CoreC aud their location within the cluster. aud in particular with respect to the dominant galaxies of Vireo A and B (see Table 1)).," We now look for possible relationships between the jet power (strictly connected to the nuclear activity) of the Virgo CoreG and their location within the cluster, and in particular with respect to the dominant galaxies of Virgo A and B (see Table \ref{tab1}) )." + In Fie., In Fig. + we compare P; with (eft panel) the three dinieusiona distance of cach ealaxy with respect to its relative sub-cluster dominar colmponent and Gieht panel) also in terms of difference of recession velocity., \ref{fig4} we compare $P_J$ with (left panel) the three dimensional distance of each galaxy with respect to its relative sub-cluster dominant component and (right panel) also in terms of difference of recession velocity. + A suggestive trend between distance from thedominant ealaxy of cach subcluster aud jet power emerges: ealaxies located closer to the center of cach sub-cluster, A suggestive trend between distance from thedominant galaxy of each subcluster and jet power emerges; galaxies located closer to the center of each sub-cluster +in amplitude anc photon cnerev. is remarkable.,"in amplitude and photon energy, is remarkable." + The temperature of the heated [aver increases only very. weakly with increasing energv Lux., The temperature of the heated layer increases only very weakly with increasing energy flux. + The cutoll energy increases somewhat with distance from the hole. but again this is dependence is rather weak.," The cutoff energy increases somewhat with distance from the hole, but again this is dependence is rather weak." + On account of the mocdoest optical depth of the Laver. the spectrum shows a prominent contribution from unscatterecl soft photons from the reprocessing depth 7.," On account of the modest optical depth of the layer, the spectrum shows a prominent contribution from unscattered soft photons from the reprocessing depth $\tau_{\mathrm b}$." + This peak is smeared out somewhat when the spectra are convolved over distance from the hole. at a given accretion rate.," This peak is smeared out somewhat when the spectra are convolved over distance from the hole, at a given accretion rate." + TFhis is shown in figure 6.., This is shown in figure \ref{conv}. + With an acamittedly somewhat simplified radiative transfer model E have shown that heating of a cool disk by protons from an ion supported advection torus produces X-ray spectra (hat are. very reminiscent. of the hard. spectra of acercting black holes., With an admittedly somewhat simplified radiative transfer model I have shown that heating of a cool disk by protons from an ion supported advection torus produces X-ray spectra that are very reminiscent of the hard spectra of accreting black holes. + Like the Maraschi ancl Llaarelt, Like the Maraschi and Haardt +so the elfective complex gain for a distant source is not the same as that at the pointing centre ancl varies with time in a different way.,so the effective complex gain for a distant source is not the same as that at the pointing centre and varies with time in a different way. + We used the procedure to remove the olfending source from the (i.0) data for each configuration before combining them.," We used the procedure to remove the offending source from the $(u,v)$ data for each configuration before combining them." + Finally. we corrected for variations in core [ux density and amplitude scale. between observations as described in(2006b).," Finally, we corrected for variations in core flux density and amplitude scale between observations as described in." +. J2000 coordinates are used. throughout this paper., J2000 coordinates are used throughout this paper. + LL positions from archival data were originally in the 12190548) system. then (uv) coordinates were recaleulated for 2000 before imaging.," If positions from archival data were originally in the B1950 system, then (u,v,w) coordinates were recalculated for J2000 before imaging." + The astrometry for cach of the sources was set using the A-configuration observations. referenced to a nearby phase calibrator in the usual manner.," The astrometry for each of the sources was set using the A-configuration observations, referenced to a nearby phase calibrator in the usual manner." + Thereafter. the position of the compact core was held constant. during the process of array combination.," Thereafter, the position of the compact core was held constant during the process of array combination." + The observations of. SS4 in 1980 and. 1981 used an earlier ancl less accurate value of the position of the phase calibrator B1236|077 (alias J1239|075) than that currently given in the VLA calibrator manual., The observations of 84 in 1980 and 1981 used an earlier and less accurate value of the position of the phase calibrator B1236+077 (alias J1239+075) than that currently given in the VLA calibrator manual. + We have updated the, We have updated the +Early work on black hole accretion disks poiuted out the possibility that magnetic stresses iehlt exert a torque ou the inner parts of the accretion disk (Page Thorne 1971. Thorne 1971. Rufini Wilson 1975. Iiug Lasota 1977).,"Early work on black hole accretion disks pointed out the possibility that magnetic stresses might exert a torque on the inner parts of the accretion disk (Page Thorne 1974, Thorne 1974, Ruffini Wilson 1975, King Lasota 1977)." +" ILowever. in virtually every recent account of the dvuaudes of accretion disks arouud black holes. it has been asstuned that there is no stress at the disk iunuer οσο, which should occur very close to the radius of the marginally stable orbit. r,,;."," However, in virtually every recent account of the dynamics of accretion disks around black holes, it has been assumed that there is no stress at the disk's inner edge, which should occur very close to the radius of the marginally stable orbit, $r_{ms}$." + That this should be so was variously argued on the basis that the plunging matter in the region of uustable orbits has too little inertia O affect the disk. or rapidly becomes causally discounected from the disk. or that such stresses were due to relative weak transport processes that could uot compete wi the huge eravitational forces pulling matter away fro the disk.," That this should be so was variously argued on the basis that the plunging matter in the region of unstable orbits has too little inertia to affect the disk, or rapidly becomes causally disconnected from the disk, or that such stresses were due to relatively weak transport processes that could not compete with the large gravitational forces pulling matter away from the disk." + Receutlv this view has been questioned (I&krolik 1999) on the basis that magnetic fields are the likely agent of torque in accretiou disks (Balbus Tawley 1998)., Recently this view has been questioned (Krolik 1999) on the basis that magnetic fields are the likely agent of torque in accretion disks (Balbus Hawley 1998). + If this is so. and thei streneth in the plineine region is what would be expected on the basis of fiux-frecziug. they should be stroug enough iu that zone to both make the Alfvénn speed relativistic (postponing the point of causal ecoupliug) aud exert forces competitive with gravity.," If this is so, and their strength in the plunging region is what would be expected on the basis of flux-freezing, they should be strong enough in that zone to both make the Alfvénn speed relativistic (postponing the point of causal decoupling) and exert forces competitive with gravity." + If matter inside the mareinally stable orbit docs. oedeed. remain maguctically connected to the disk. it can exert a sizable torque on the the portion of the disk containing the field-lue footpoiuts.," If matter inside the marginally stable orbit does, indeed, remain magnetically connected to the disk, it can exert a sizable torque on the the portion of the disk containing the field-line footpoints." + Camunie (1999) has VAtown that. within the confines of a highlv-icdealized model of inflow dynaines. this torque can cousiderablv cuhance the amount of energy released in the disk.," Gammie (1999) has shown that, within the confines of a highly-idealized model of inflow dynamics, this torque can considerably enhance the amount of energy released in the disk." + Iu fact. even if there were no continuing accretion. field hues attached to the event horizon of a spinning black hole and ruuniug through the disk could exert torques of a very simular character (Blandford 1998. D.NL. Eardley. private conuuunication).," In fact, even if there were no continuing accretion, field lines attached to the event horizon of a spinning black hole and running through the disk could exert torques of a very similar character (Blandford 1998, D.M. Eardley, private communication)." +" We will call this situation the ""iufinite efiicicney Laut.”"," We will call this situation the “infinite efficiency limit.""" + A corollary of torque ou the inner edge of the disk is an increase in the outward augular momentum flux., A corollary of torque on the inner edge of the disk is an increase in the outward angular momentum flux. + In a ine-xteady state. this additional augular ποιοται fli. uust be couveved bv additional stress.," In a time-steady state, this additional angular momentum flux must be conveyed by additional stress." + Additional local dissipation must accompany the additional stress., Additional local dissipation must accompany the additional stress. +" It is ie principal object of this paper to compute how this lissipation is distributed through the disk. aud examine 16 consequences for observable properICs,"," It is the principal object of this paper to compute how this dissipation is distributed through the disk, and examine the consequences for observable properties." + Tuue-steady torques at ry. are nof the only way that uerev nav be transmitted from the ]duugiue regiou to ie disk=the torque may be variable. it may be delivered wer a range of radii. aud there may be radial forces exerted wat carry no angular momentum.," Time-steady torques at $r_{ms}$ are not the only way that energy may be transmitted from the plunging region to the disk—the torque may be variable, it may be delivered over a range of radii, and there may be radial forces exerted that carry no angular momentum." + However. in this paper. we will restrict our attention to this simplest possible case.," However, in this paper, we will restrict our attention to this simplest possible case." + Novikov Thorne (1973) and Page Thorne (1971) showed how the surface brightucss aud vertically-integrated stress in the fluid frame for a. time-steady. ecolmectrically thin. relativistic accretion disk could be written as the Newtomian forms multiplied by correction factors that approach unity at laree radius.," Novikov Thorne (1973) and Page Thorne (1974) showed how the surface brightness and vertically-integrated stress in the fluid frame for a time-steady, geometrically thin, relativistic accretion disk could be written as the Newtonian forms multiplied by correction factors that approach unity at large radius." + Iu the notation of Page Thorue (197D). conservation of angular," In the notation of Page Thorne (1974), conservation of angular" +available.,available. +" The RGS dispersion gratings cover the 5—35 wwavelength range (2.48—0.35kkeV), although we obtained useful signal only in the 5—26 rrange (2.48—0.48 kkeV)."," The RGS dispersion gratings cover the $5 - 35$ wavelength range $2.48-0.35$ keV), although we obtained useful signal only in the $5 - 26$ range $2.48-0.48$ keV)." +" The RGS data are piled-up, but in a dispersion instrument, piled-up events at a discrete wavelength increase in pulse height amplitude by an integer multiple of the intrinsic energy."," The RGS data are piled-up, but in a dispersion instrument, piled-up events at a discrete wavelength increase in pulse height amplitude by an integer multiple of the intrinsic energy." +" Furthermore, since the softness of the source precludes any intrinsic photons from higher spectral orders, we can confidently identify events that occur within the higher order spectral masks for an on-axis point source as piled-up first order photons."," Furthermore, since the softness of the source precludes any intrinsic photons from higher spectral orders, we can confidently identify events that occur within the higher order spectral masks for an on-axis point source as piled-up first order photons." + This is verified by line matching of the piled-up events using the first order response matrix., This is verified by line matching of the piled-up events using the first order response matrix. + Source events dominate over background and scattered source light in the first three orders., Source events dominate over background and scattered source light in the first three orders. +" Consequently we added events within the second and third order extraction masks to the first order events, thus reclaiming the piled-up events and increasing the signal-to-noise of the spectra."," Consequently we added events within the second and third order extraction masks to the first order events, thus reclaiming the piled-up events and increasing the signal-to-noise of the spectra." +" In a first step, we compared our SEDs with the observation of vviaXSPEC."," In a first step, we compared our SEDs with the observation of via." +. We let the neutral hydrogen column density ΛΗΤ and vvary as free parameters[οτι2] inXSPEC.," We let the neutral hydrogen column density $N_\mathrm{H\,I}$ $^{-2}$ ] and vary as free parameters in." +. determines and logNur=20.58.," determines and $\log N_\mathrm{H\,I} = 20.58$." +" In (top panel), we show this fit."," In (top panel), we show this fit." + The reader may miss the typical residuals at the bottom of the plots., The reader may miss the typical residuals at the bottom of the plots. +" Since our models do not include all the elements with all the lines that may be exhibited in the observation, the residuals are not that helpful like in comparisons of simple models where continuum slope and a handful of strategic lines has to be reproduced."," Since our models do not include all the elements with all the lines that may be exhibited in the observation, the residuals are not that helpful like in comparisons of simple models where continuum slope and a handful of strategic lines has to be reproduced." +" Thus, we decided to omit the residual plots generally."," Thus, we decided to omit the residual plots generally." +" Instead, the reader should judge the strengths of prominent lines and absorption edges with respect to the (estimated) local flux continuum."," Instead, the reader should judge the strengths of prominent lines and absorption edges with respect to the (estimated) local flux continuum." +" As expected, a solar composition does not well represent the white dwarf spectrum inSgr."," As expected, a solar composition does not well represent the white dwarf spectrum in." +. The flux at wavelengths smaller than iis far too low., The flux at wavelengths smaller than is far too low. +" n test calculations, we decreased the carbon abundance to 1.0([X]denoteslog|mass fraction/solarmassfraction] [C]==-of species X angtollao[C —2.0."," In test calculations, we decreased the carbon abundance to $-$ 1.0 ([X] denotes log [mass fraction / solar mass fraction] of species X) and to $-$ 2.0." +" We achieved a much better fit at [C]==- 2.0,, andlogNg;=20.54 for A«26sAfig:xspechhecno."," We achieved a much better fit at $-$ 2.0, and $\log N_\mathrm{H\,I} = 20.54$ for $\lambda < 26$." +". We wondered whether the small wavelength interval (18—38 AA)) of our RGS spectra leads in the fit procedure to a smaller Ng; than found by ?,logNyr = 21.60, obtained fitting the a LETG spectrum (18—58 AA))."," We wondered whether the small wavelength interval $18 - 38$ ) of our RGS spectra leads in the fit procedure to a smaller $N_\mathrm{H\,I}$ than found by \citet[][$\log N_\mathrm{H\,I} = 21.60, obtained fitting the a LETG spectrum $18 - 58$ )." +" In we show however, that we fitted the LETG spectrum of March 19, 2003 and used the same wavelength range as ?,, deriving and logNur=20.95 for the [C]==- ΚΚ 2.0model."," In we show however, that we fitted the LETG spectrum of March 19, 2003 and used the same wavelength range as \citet{PEA05}, deriving and $\log N_\mathrm{H\,I} = 20.95$ for the $-$ 2.0 model." +"AdecreasingNy, from March to April is consistent with intrinsic absorption of the ejecta clearing up."," A decreasing $_\mathrm{H\,I}$ from March to April is consistent with intrinsic absorption of the ejecta clearing up." +" Before we start now with a detailed analysis, we mention that the calibration of the instruments that were used to obtain our data is still an issue."," Before we start now with a detailed analysis, we mention that the calibration of the instruments that were used to obtain our data is still an issue." + Different calibration products (response matrices and effective areas) may play an important role on the results obtained from fits to X-ray spectra., Different calibration products (response matrices and effective areas) may play an important role on the results obtained from fits to X-ray spectra. +" Cross calibration between instruments has improved over the years (see, but there is yet room for further improvement."," Cross calibration between instruments has improved over the years \citep[see, e.g\.][]{BBR06,BBR08} + but there is yet room for further improvement." +" While the wavelength scale of X-ray gratings instruments is generally very well known, the effective areas of these instruments are less well calibrated."," While the wavelength scale of X-ray gratings instruments is generally very well known, the effective areas of these instruments are less well calibrated." +" For example, a comparison between the continuum calibrations of the gratings and CCD instruments on board by ? shows deviations between the RGS and the EPIC-pn of kkeV and about deviations are still smaller than the deviations between data and model caused by simplifications in the"," For example, a comparison between the continuum calibrations of the gratings and CCD instruments on board by \citet{SEA08} + shows deviations between the RGS and the EPIC-pn of keV and about deviations are still smaller than the deviations between data and model caused by simplifications in the" +N132D is located in the LMC which makes the distance determination easier.,N132D is located in the LMC which makes the distance determination easier. +" Here, we will assume D=50 kpc (Panagiaetal.1991;vanderMarel,Alves,Hardy&Suntzeff 2002)."," Here, we will assume $D$ =50 kpc \citep[][]{Panagia91,Marel02}." +". Determining the age of the explosion, however, proves less straight forward than the case of the earlier studied 1E 0102.2-7219 in the SMC."," Determining the age of the explosion, however, proves less straight forward than the case of the earlier studied 1E 0102.2-7219 in the SMC." +" Currently, there are no proper motion measurements of the expansion rate of the ejecta."," Currently, there are no proper motion measurements of the expansion rate of the ejecta." + The only age estimates are based on size and radial velocity measurements., The only age estimates are based on size and radial velocity measurements. +" Since these require some kind of assumption about the 3D shape of the SNR, they are much more uncertain."," Since these require some kind of assumption about the 3D shape of the SNR, they are much more uncertain." +" Current age estimates range from ~1300 years to ~3000 years and above (Morse,Winkler&Kirshner 1995).", Current age estimates range from $\sim$ 1300 years \citep[][]{Lasker80} to $\sim$ 3000 years and above \citep[][]{Morse95}. +". Let us first explore the consequences of making different age estimates on the resulting 3D map, before studying in detail our best estimate of the 3D shape of N132D in Section ??.."," Let us first explore the consequences of making different age estimates on the resulting 3D map, before studying in detail our best estimate of the 3D shape of N132D in Section \ref{Sec:ring}." +" As we discuss in the next Section, the bulk of the oxygen-rich ejecta trace out a ring tilted with respect to the line of sight, a model that is broadly in agreement with that of Lasker(1980)."," As we discuss in the next Section, the bulk of the oxygen-rich ejecta trace out a ring tilted with respect to the line of sight, a model that is broadly in agreement with that of \citet{Lasker80}." +". Taking the distance to the LMC to be D=50 kpc, the effect of different age estimates will be to either expand or contract the ejecta along the line of sight (z-axis)."," Taking the distance to the LMC to be $D=50$ kpc, the effect of different age estimates will be to either expand or contract the ejecta along the line of sight (z-axis)." +" In Fig. 6,,"," In Fig. \ref{fig:angle}," +" we have projected the 3D map on an X’Y’Z coordinate system, where Z is the line of sight direction, with the Earth to the top of the Figure, and Y! is in the ejecta ring plane."," we have projected the 3D map on an X'Y'Z coordinate system, where Z is the line of sight direction, with the Earth to the top of the Figure, and Y' is in the ejecta ring plane." +" In the three left hand panels of this figure, we plot the projection of the 3D map assuming an age of 2000, 2500 and 3000 years (from left to right), and on the right hand panel the view in the plane of the sky, which obviously does not depend on the age estimate."," In the three left hand panels of this figure, we plot the projection of the 3D map assuming an age of 2000, 2500 and 3000 years (from left to right), and on the right hand panel the view in the plane of the sky, which obviously does not depend on the age estimate." +" Assuming that the central ring is indeed a true ring, its projected size in the X’-Z plane should equal its long axis in the X’-Y’ plane (or equivalently, the X-Y plane)."," Assuming that the central ring is indeed a true ring, its projected size in the X'-Z plane should equal its long axis in the X'-Y' plane (or equivalently, the X-Y plane)." + 'This can be estimated in Fig. 6.., This can be estimated in Fig. \ref{fig:angle}. +" In the top view, we have plotted a 12 pc ruler in grey shades, which we find to be the length of the long axis of the ejecta in this plane."," In the top view, we have plotted a 12 pc ruler in grey shades, which we find to be the length of the long axis of the ejecta in this plane." +" We did not take the knot in consideration in this process, since it may lie beyond the reverse shock."," We did not take the knot in consideration in this process, since it may lie beyond the reverse shock." + We have then plotted the same linear scale of 12 pc in a grey shade on every three projections on the X’-Z plane (left panels )., We have then plotted the same linear scale of 12 pc in a grey shade on every three projections on the X'-Z plane (left panels ). +" Clearly, the 2000 years estimate has a ring too small by ~2pc, while on the other hand the 3000 years estimate ring is too big by —2 pc."," Clearly, the 2000 years estimate has a ring too small by $\sim$ 2pc, while on the other hand the 3000 years estimate ring is too big by $\sim$ 2 pc." +" The central estimate of 2500 years has a ring that extends over the same distance, ~12 pc, in the X’-Z plane as it does in the X’-Y’ plane."," The central estimate of 2500 years has a ring that extends over the same distance, $\sim$ 12 pc, in the X'-Z plane as it does in the X'-Y' plane." +" With this age estimate, the ring will then be a true circle, with a radius of —12 pc, and tilted by ~25 degrees with respect to the line of sight."," With this age estimate, the ring will then be a true circle, with a radius of $\sim$ 12 pc, and tilted by $\sim 25$ degrees with respect to the line of sight." +" Thus, an age of 2500 years is our preferred estimate, which will be used in the remaining Sections of this paper."," Thus, an age of 2500 years is our preferred estimate, which will be used in the remaining Sections of this paper." +" We should also mention here that Lasker(1980) found a good fit to the ejecta shape assuming a ring tilted at e45 degrees, which is consistent with our results, bearing in mind that his age estimate for the SNR was only ~1300 years."," We should also mention here that \cite{Lasker80} found a good fit to the ejecta shape assuming a ring tilted at $\sim 45$ degrees, which is consistent with our results, bearing in mind that his age estimate for the SNR was only $\sim 1300$ years." +" Adopting an age of T=2500 years for N132D, and a distance D=50 kpc (Panagiaetal.1991),, gives the following transformation to our data cube axis units: TThe resulting data cube provides the 3D map of the oxygen-rich ejecta in SNR N132D. In Fig. 7,,"," Adopting an age of $T$ =2500 years for N132D, and a distance $D$ =50 kpc \citep{Panagia91}, gives the following transformation to our data cube axis units: The resulting data cube provides the 3D map of the oxygen-rich ejecta in SNR N132D. In Fig. \ref{fig:3dproj}," +" we present side, front and top projections of this 3D map."," we present side, front and top projections of this 3D map." +" The rainbow color ramp is linear in the number of counts per pixels, and ranges from 18-60, 60-120 and >120 for the top, middle and bottom rows respectively."," The rainbow color ramp is linear in the number of counts per pixels, and ranges from 18-60, 60-120 and $\geq$ 120 for the top, middle and bottom rows respectively." +" For the projection along the Z axis, the low velocity data, with -100 km s! «€ v, < 100 km s! have been skipped to avoid filling the figure with emission which would obscure the salient structural features."," For the projection along the Z axis, the low velocity data, with -100 km $^{-1}$ $\leq$ $_r$ $\leq$ 100 km $^{-1}$ have been skipped to avoid filling the figure with emission which would obscure the salient structural features." +" For the side and frontprojections, the Earth is to the top of the plot."," For the side and frontprojections, the Earth is to the top of the plot." +" A 2 pc scale is shown for information, which is also the inter-ticks distance."," A 2 pc scale is shown for information, which is also the inter-ticks distance." +" At the estimated age and distance of N132D, v,.—1000 km s~! corresponds to 2.55 pc, or 1 pc corresponds to 391.39 km s~! in radial velocity."," At the estimated age and distance of N132D, $v_r$ =1000 km $^{-1}$ corresponds to 2.55 pc, or 1 pc corresponds to 391.39 km $^{-1}$ in radial velocity." +" In the front and side views, the vertical stripes are due to field stars, while the horizontal plane is due to the low velocity gas in SNR N132D. The ejecta have an approximately circular symmetry in the side and front views."," In the front and side views, the vertical stripes are due to field stars, while the horizontal plane is due to the low velocity gas in SNR N132D. The ejecta have an approximately circular symmetry in the side and front views." +" In comparison, in the top view, they seem to form an ellipse with major axis in the NE-SW direction."," In comparison, in the top view, they seem to form an ellipse with major axis in the NE-SW direction." + This suggests that the ejecta have the shape of a tilted ring., This suggests that the ejecta have the shape of a tilted ring. + Note that the blue-shifted material has a higher velocities than the red-shifted material., Note that the blue-shifted material has a higher velocities than the red-shifted material. + This results in a mean radial velocity of the oxygen-rich knots which is blue-shifted with respect to the systemic velocity of the surrounding ISM by several hundreds of kilometers per second., This results in a mean radial velocity of the oxygen-rich knots which is blue-shifted with respect to the systemic velocity of the surrounding ISM by several hundreds of kilometers per second. + This has been noticed in previous studies (Lasker1980;Suther-land&Dopita 1995a).," This has been noticed in previous studies \citep[][]{Lasker80,Sutherland95a}." +". The ISM knots, previously identified in Section ??,, display smaller radial velocities, of the order of a few hundred km s~!."," The ISM knots, previously identified in Section \ref{sec:orich}, , display smaller radial velocities, of the order of a few hundred km $^{-1}$ ." + These are disposed in a ring pattern in the plane of the sky., These are disposed in a ring pattern in the plane of the sky. + The resulting shape of the O-rich, The resulting shape of the O-rich +to be considerably smaller than that of the observed profile.,to be considerably smaller than that of the observed profile. + Moreover. while the red dip can be reproduced quite well. the depth of the blue one is much smaller than in the observation.," Moreover, while the red dip can be reproduced quite well, the depth of the blue one is much smaller than in the observation." + The only way to increase the width of the profile is to assume a larger Doppler width. but. in this case. the three peak structure is rapidly lost.," The only way to increase the width of the profile is to assume a larger Doppler width, but, in this case, the three peak structure is rapidly lost." + We investigated the effect of à microturbulent magnetic field. as well as the effect of dichroism. but they both do not seem to be able to explain the disagreement between our theoretical result and the observation.," We investigated the effect of a microturbulent magnetic field, as well as the effect of dichroism, but they both do not seem to be able to explain the disagreement between our theoretical result and the observation." + Nevertheless. it is important to point out that the lower level of this line. being polarizable irrespective of the hyperfine structure (J;= 2). is found to be as polarized as the upper level (depolarizing collisions have been neglected in this investigation).," Nevertheless, it is important to point out that the lower level of this line, being polarizable irrespective of the hyperfine structure $J_{\ell}=2$ ), is found to be as polarized as the upper level (depolarizing collisions have been neglected in this investigation)." + This circumstance explains why the lower-level Hanle effect is so clearly evident in this line., This circumstance explains why the lower-level Hanle effect is so clearly evident in this line. + In conclusion. the physical origin of the observed three-peak Q/7 profile of this scandium line does not seem to be the mere presence of hyperfine structure.," In conclusion, the physical origin of the observed three-peak $Q/I$ profile of this scandium line does not seem to be the mere presence of hyperfine structure." + We may speculate that an additional physical mechanism ts at work (such as. for instance. PRD effects).," We may speculate that an additional physical mechanism is at work (such as, for instance, PRD effects)." + However. if this turns out to be the case. it would be of interest to investigate the influence," However, if this turns out to be the case, it would be of interest to investigate the influence" +The amplitude parameter. denoted σε when relerring to thers linear density [Inctuation in spheres of radius 8t\Mpe at z=0. is not easily determined since the mass distribution cannot be directly observed.,"The amplitude parameter, denoted $\sigma_8$ when referring to the linear density fluctuation in spheres of radius $8h^{-1}$ Mpc at $z=0$, is not easily determined since the mass distribution cannot be directly observed." + As a result. this parameter is not vel accurately known.," As a result, this parameter is not yet accurately known." +" Recent observations suggest an amplitude Chat ranges in value trom σς0.7 to a high. value of a,0.9—1.", Recent observations suggest an amplitude that ranges in value from $\sigma_8\sim 0.7$ to a `high' value of $\sigma_8\sim 0.9-1$. + While the difference in the reported values is only around50%.. the impact on structure formation aud evolution is much larger. since the latter depends exponentially on az.," While the difference in the reported values is only around, the impact on structure formation and evolution is much larger, since the latter depends exponentially on $\sigma_8^2$." + The low amplitude values are suggested by current observationsof (he CMD spectrum of fInetuations CNetterfieldοἱal.2002:SieversetBondRuhl2002).," The low amplitude values are suggested by current observationsof the CMB spectrum of fluctuations \citep{netterfield, sievers02, bondea02, ruhlea02}." +. llowever. this ox determination is degenerate wilh (he unknown optical depth at reionization: if the optical depth were underestimated. then ox would be aswell!.," However, this $\sigma_8$ determination is degenerate with the unknown optical depth at reionization: if the optical depth were underestimated, then $\sigma_8$ would be as." +. Recent observations of the present-day cluster abundance as well as cosmic shear lensing measurements have also suggested that ox~0.7 (e.g.Jarvisοἱal.2003:Hlamanaet2002:Seljak 2001)..," Recent observations of the present-day cluster abundance as well as cosmic shear lensing measurements have also suggested that $\sigma_8\sim 0.7$ \citep[e.g.][]{jarvis03, hamana02, sel01}. ." +" llowever. these measures provide a degenerate relation between (he amplitude o, and the mass-density parameter O,,: σκοςzz0.33 (Ikebeetal.2002:Baheall2003:al.2003:Seljak 2001).."," However, these measures provide a degenerate relation between the amplitude $\sigma_8$ and the mass-density parameter $\Omega_m$: $\sigma_8 \Omega_m^{0.6}\approx 0.33$ \citep{ike02, SDSSmf03, jarvis03, sel01}. ." +" The amplituce σς~0.7 is implied only if ,,~0.3.", The amplitude $\sigma_8\sim 0.7$ is implied only if $\Omega_m \sim 0.3$. +" IE O,,~0.2. as is suggested by some observations (e.g.Carlberg.Yee&Ellingson1997:BaheallFan1993:Bahealletal.2000:Wilson.2001:Ikebe2002:Reiprich&Dohringer 2002).. then (he amplitude is σε0.9—1."," If $\Omega_m \sim 0.2$, as is suggested by some observations \citep[e.g.][]{CYE97, bah98, bah00, wklc01, ike02, rei02}, then the amplitude is $\sigma_8\sim 0.9-1$." +" Early results Irom the Sloan Digital Skv Survey (SDSS) cluster data (Dalcalletal.2003) use the shape of the observed cluster mass Iunction {ο break the degeneracy between the parameters and find ox=0.963 and Q,,=0.19qm."," Early results from the Sloan Digital Sky Survey (SDSS) cluster data \citep{SDSSmf03} + use the shape of the observed cluster mass function to break the degeneracy between the parameters and find $\sigma_8 =0.9^{+0.3}_{-0.2}$ and $\Omega_m =0.19^{+0.08}_{-0.07}$." + sinilar results have recently been obtained from (he temperature function of a large sample of X-ray clusters (Ikebeοἱal.2002:Reiprich&Bohringer2002).," Similar results have recently been obtained from the temperature function of a large sample of X-ray clusters \citep{ike02, rei02}." +". Most of the recent cluster normalization observations. as well as cosmic shear lensing measurements suggest ox 0.9—1 if Q,,220.2 (Jarvisetal.2003:Hamana2002.anclthereferencesabove)..."," Most of the recent cluster normalization observations, as well as cosmic shear lensing measurements suggest $\sigma_8\simeq 0.9-1$ if $\Omega_m \simeq 0.2$ \citep[][and the references above]{jarvis03, hamana02}." +" Combining ο CAD measurements with (he SDSS cluster mass function vields intermediate values of og=0.76£0.09 and Q,,=0.26ης CMelchiorriοἱal.2003).", Combining current CMB measurements with the SDSS cluster mass function yields intermediate values of $\sigma_8 =0.76\pm 0.09$ and $\Omega_m =0.26^{+0.06}_{-0.07}$ \citep{MBBS03}. +". The evolution of cluster abundance will (me. especially for (he most massive clusters. breaks the degeneracy between o4 and KQ,, (e.g.Peebles.Daly&Juszkiewiez1939:Eke.ColeDahcall&Fan1998:DonahueVoit1999:IIenryv. 2000)."," The evolution of cluster abundance with time, especially for the most massive clusters, breaks the degeneracy between $\sigma_8$ and $\Omega_m$ \citep[e.g.][]{PDJ89, ECF96, OB97, BFC97, CMYE97, bah98, DV99, Henry00}." +".. This evolution depends strongly on cx. and only weakly on O,, or other parameters."," This evolution depends strongly on $\sigma_8$, and only weakly on $\Omega_m$ or other parameters." + The expected abundance of massiveclusters al ze0.5—1 differs between Gaussian models with oy=0.6 and og=1 by orders- nearly inclepencently of other parameters (Fan.Bahcall&Cen1997. e.," The expected abundance of massiveclusters at $z\sim 0.5-1$ differs between Gaussian models with $\sigma_8=0.6$ and $\sigma_8=1$ by orders-of-magnitude, nearly independently of other parameters \citep[e.g.]{FBC97}. ." +"g.).. ""Therefore. this method provides a uniquely powerful tool in estimating theamplitude asx."," Therefore, this method provides a uniquely powerful tool in estimating theamplitude $\sigma_8$ ." +The integrated flux measured from the 71. resolution data cube (see Fig. HI[[,The integrated flux measured from the $71^{''}$ resolution data cube (see Fig. \ref{fig:overlay}[ [ +AD is 59.6 Jy,A]) is $59.6$ Jy. + The HI mass obtained from the integrated profile is1.30«107M. Land the Mlui/Ly ratio is found to be ~4.7 in solar units.," The HI mass obtained from the integrated profile is${\rm{1.30 \times{10}^{8}M_\odot}}$, and the ${\rm{M_{HI}/L_{B}}}$ ratio is found to be $\sim 4.7$ in solar units." + This estimate of the HI mass (which is dominated by he WSRT data) is slightly (— 1.50) lowertian the value of 1.6+0.2107ML. that was obtained in Paper I. On comparing Fig., This estimate of the HI mass (which is dominated by the WSRT data) is slightly $\sim 1.5\sigma$ ) lower than the value of ${\rm{1.6\pm0.2 \times{10}^{8}M_\odot}}$ that was obtained in Paper I. On comparing Fig. + | with the —40 map made using only the GMRT data Gin EFigure |A] of Paper D. we find that using the combined data set from WSRT. GMRT and DRAO. we could recover the faint. more extended outer envelope of HI distribution.," \ref{fig:overlay} with the $\sim 40^{''}$ map made using only the GMRT data (in Figure 1[A] of Paper I), we find that using the combined data set from WSRT, GMRT and DRAO, we could recover the faint, more extended outer envelope of HI distribution." + The HI envelope extends to 14.6 . at a level of ~1107 7 Le. ~ 8.8 times," The HI envelope extends to $\sim14.6^{'}$ , at a level of $\sim 1 \times 10^{19}$ $^{-2}$ i.e. $\sim$ 8.8 times" +"in the present study leads to our result on og being, typically, somewhat higher for a given value of (see |6.3)).","in the present study leads to our result on $\sigma_8$ being, typically, somewhat higher for a given value of (see )." +" Our result on is in excellent agreement with current constraints based on cluster data and references therein) and the power spectrum of galaxies in the 2dF galaxy redshift survey and Sloan Digital Sky Survey (SDSS),, as wellet as the combination of CMB data with a variety of external constraints⋅"," Our result on is in excellent agreement with current constraints based on cluster data and references therein) and the power spectrum of galaxies in the 2dF galaxy redshift survey and Sloan Digital Sky Survey (SDSS), as well as the combination of CMB data with a variety of external constraints." +⋅ Our result on og is marginally lower than that determined by weak lensing tomography in the Cosmic Evolution Survey and by the observed number (COSMOS;density of Masseyoptically-selectedetαἱ 12007)groups and clusters in the 2dF and SDSS surveysal., Our result on $\sigma_8$ is marginally lower than that determined by weak lensing tomography in the Cosmic Evolution Survey and by the observed number density of optically-selected groups and clusters in the 2dF and SDSS surveys. +||2007).. The joint constraints on and og from the luminosity function data using our standard priors (purple contours) are compared with those of WMAP (blue) in the left panel of, The joint constraints on and $\sigma_8$ from the luminosity function data using our standard priors (purple contours) are compared with those of WMAP (blue) in the left panel of. +" Since the WMAP results are marginalized over ns, we also FigureJ].show the XLF results using our weak n, prior as dot-dashed lines, although the difference from the standard results is small."," Since the WMAP results are marginalized over $n_s$, we also show the XLF results using our weak $n_s$ prior as dot-dashed lines, although the difference from the standard results is small." +" The right panel displays constraints on and w obtained independently from the XLF (purple), WMAP (blue), SNIa data (green) and cluster data (red)."," The right panel displays constraints on and $w$ obtained independently from the XLF (purple), WMAP (blue), SNIa data (green) and cluster data (red)." +" Our new XLF results are consistent with each of these independent data sets, and with the cosmological-constant model (w= —1)."," Our new XLF results are consistent with each of these independent data sets, and with the cosmological-constant model $w=-1$ )." +" The marginalized results from the X-ray luminosity function data are Qm=0.24*005, gg=0.85*0:36 and w=���1.4*0 bp."," The marginalized results from the X-ray luminosity function data are $\Omegam=0.24^{+0.15}_{-0.07}$, $\sigma_8=0.85^{+0.13}_{-0.20}$ and $w=-1.4^{+0.4}_{-0.7}$ )." + We now consider the improvement over a combined, We now consider the improvement over a combined +"However, the detection of those events among the Gaia data will not be easy.","However, the detection of those events among the Gaia data will not be easy." +" Gaia will observe more than one billion objects all over the sky, and each object will be independently detected around eighty times during the mission, comprising a total of around 1012 astrometric, spectrophotometric, and spectroscopic observations (after detection, the observations are multiplexed in the focal plane)."," Gaia will observe more than one billion objects all over the sky, and each object will be independently detected around eighty times during the mission, comprising a total of around $10^{12}$ astrometric, spectrophotometric, and spectroscopic observations (after detection, the observations are multiplexed in the focal plane)." +" Consequently, finding the OAs events among all that data can be a quite challenging task."," Consequently, finding the OAs events among all that data can be a quite challenging task." +" In Gaia data processing, a system called AlertPipe is being implemented to deal with alerts of transient events."," In Gaia data processing, a system called AlertPipe is being implemented to deal with alerts of transient events." +" It is foreseen to operate as follows: first candidate alerts are classified using Gaia data, then sources are cross-matched with available catalogues through Virtual Observatory or local copies and further classified, and finally the alerts are stored on an alert server and released to the community as VOEvents (Hodgkin&Wyrzykowski2011;vanLeeuwenetal. 2011)."," It is foreseen to operate as follows: first candidate alerts are classified using Gaia data, then sources are cross-matched with available catalogues through Virtual Observatory or local copies and further classified, and finally the alerts are stored on an alert server and released to the community as VOEvents \citep{HodgkinWyrzykowski2011, vanLeeuwen2011}." +". Algorithms are under analysis for dealing with GRBs (Wyrzykowski, 2012 priv."," Algorithms are under analysis for dealing with GRBs (Wyrzykowski, 2012 priv." +" comm.),"," comm.)," + but no performance figures are available at the present moment., but no performance figures are available at the present moment. +" Based on Gaia data, the duration of the OA can be roughly estimated from the flux variation between two subsequent observations: if the event is detected during the transit of the first telescope, it will be re-observed 106.5 minutes later when Gaia’s second telescope re-observes the field."," Based on Gaia data, the duration of the OA can be roughly estimated from the flux variation between two subsequent observations: if the event is detected during the transit of the first telescope, it will be re-observed 106.5 minutes later when Gaia's second telescope re-observes the field." +" Moreover, the light curve will be sampled several times during the transit of each telescope, since at each column of Gaia’s focal plane an independent magnitude measurement will be performed (measurements are spaced by 4.4s)."," Moreover, the light curve will be sampled several times during the transit of each telescope, since at each column of Gaia's focal plane an independent magnitude measurement will be performed (measurements are spaced by 4.4s)." +" The light curve alone may not be enough to distinguish between GRB afterglows and other optical transient sources, as noted by Japelj&Gomboc(2011)."," The light curve alone may not be enough to distinguish between GRB afterglows and other optical transient sources, as noted by \citet{Japelj2011}." +". However, as these events have power law like SEDs and no quiescent counterpart, this information should also be considered."," However, as these events have power law like SEDs and no quiescent counterpart, this information should also be considered." + Further analysis of Gaia’s BP/RP low-dispersion are needed to distinguish between different transients with similar characteristics., Further analysis of Gaia's BP/RP low-dispersion are needed to distinguish between different transients with similar characteristics. +" To perform transient event classification, AlertPipe uses several algorithms, including bayesian classifiers, template matching, and self-organizing maps (HodgkinWyrzykowski 2010)."," To perform transient event classification, AlertPipe uses several algorithms, including bayesian classifiers, template matching, and self-organizing maps \citep{HodgkinWyrzykowski2010}." +. A possible way to search for such objects within a large survey is to look for signatures of afterglows from Pop III stars., A possible way to search for such objects within a large survey is to look for signatures of afterglows from Pop III stars. +" Two important characteristics of these objects are the total energy of Pop III GRBs, which can be much higher than those of Pop I/II GRBs, and the active duration time of their jet, which can be much longer than Pop I/II GRB jets due to the larger progenitor star."," Two important characteristics of these objects are the total energy of Pop III GRBs, which can be much higher than those of Pop I/II GRBs, and the active duration time of their jet, which can be much longer than Pop I/II GRB jets due to the larger progenitor star." +" Consequently, the detection of GRBs with very high E; and very long duration could be indicative of such objects (Suwa&Ioka2011;Tomaetal.2011).."," Consequently, the detection of GRBs with very high $E_{iso}$ and very long duration could be indicative of such objects \citep{suwa2011,toma2011}." +" Thus, they should appear as quasi-steady point sources in the radio survey observations."," Thus, they should appear as quasi-steady point sources in the radio survey observations." + But the indication should be complemented with the constraint on the metal abundances in the surrounding medium with high-resolution IR and X-ray spectroscopy., But the indication should be complemented with the constraint on the metal abundances in the surrounding medium with high-resolution IR and X-ray spectroscopy. +" Since we do not have any observation of these objects, we have to rely on theoretical models to compare the data."," Since we do not have any observation of these objects, we have to rely on theoretical models to compare the data." +" A way to look for such objects that is worth future investigation is the use of automatic light curve classifiers, which are widely implemented for classifying supernovae and transients in general (Johnson&deSouza2012).."," A way to look for such objects that is worth future investigation is the use of automatic light curve classifiers, which are widely implemented for classifying supernovae and transients in general \citep{johnson2006,kuznetsova2007,poznanski2007,rodney2009,falck2010,newling2011,richards2011,sako2011,ishida2012}." +" In principle, the theoretical model could work as a training set for the classifier, which would be then applied to surveys to identify possible candidates for further spectroscopical follow up."," In principle, the theoretical model could work as a training set for the classifier, which would be then applied to surveys to identify possible candidates for further spectroscopical follow up." + These OAs event will be detected by the Gaia data processing pipeline just like any other transient., These OAs event will be detected by the Gaia data processing pipeline just like any other transient. +" The timescales for raising the alerts are very dependent on specificities of the Gaia dataflow, but it is foreseen that, in the worst case, the data will be available for analysis by AlertPipe 24h after the observation."," The timescales for raising the alerts are very dependent on specificities of the Gaia dataflow, but it is foreseen that, in the worst case, the data will be available for analysis by AlertPipe 24h after the observation." + The alerts will thus be raised no later than 48h after the Gaia observation (Wyrzykowski&Hodgkin2011)., The alerts will thus be raised no later than 48h after the Gaia observation \citep{WyrzykowskiHodgkin2011}. +". Nonetheless, it is not yet clear if AlertPipe by itself will be able to determine the nature of the transient as an OA."," Nonetheless, it is not yet clear if AlertPipe by itself will be able to determine the nature of the transient as an OA." +" Moreover, due to the design of the mission dataflow, real-time identification will not be possible, but further identification of OAs using data from satellites/telescopes operating on other wavelengths may be possible, as VOEvents will be created by the Gaia data processing alert system."," Moreover, due to the design of the mission dataflow, real-time identification will not be possible, but further identification of OAs using data from satellites/telescopes operating on other wavelengths may be possible, as VOEvents will be created by the Gaia data processing alert system." +" Also, OAs could be identified if they trigger X-ray detectors, such as Swift’s BAT (Barthelmyetal. 2005),, Fermi’s LAT (Atwoodetal.2009),, which is foreseen to operate until 2018, or future instruments, such as SVOM (Schanneetal. 2010).."," Also, OAs could be identified if they trigger X-ray detectors, such as Swift's BAT \citep{Barthelmy2005}, , Fermi's LAT \citep{Atwood2009}, which is foreseen to operate until 2018, or future instruments, such as SVOM \citep{Schanne2010}. ." +" Finally, the same may also be observed by other large-scale optical surveys on Earth, e.g., LSST (Ivezicetal.2008) and Pan-STARRS (Kaiseretal.2002),, improving the sampling of the events’ light curve and providing information on other optical bands."," Finally, the same may also be observed by other large-scale optical surveys on Earth, e.g., LSST \citep{Ivezic2008} and Pan-STARRS \citep{Kaiser2002}, improving the sampling of the events' light curve and providing information on other optical bands." + It is important to emphasize that our knowledge concerning first stars and their GRBs is still quite incomplete., It is important to emphasize that our knowledge concerning first stars and their GRBs is still quite incomplete. +" Many of their properties (e.g., characteristic mass, SFR and efficiency to trigger GRBs) are still very uncertain, and more reliable information can only come once a detection is confirmed."," Many of their properties (e.g., characteristic mass, SFR and efficiency to trigger GRBs) are still very uncertain, and more reliable information can only come once a detection is confirmed." +" Recently, Hosokawaetal. (2011), performing state-of-the-art radiation- simulations, showed that the typicalmass ofprimordial stars could be ~ 43Mo, i.e., less massive than originally expected by theoretical models."," Recently, \citet{hosokawa2011}, performing state-of-the-art radiation-hydrodynamics simulations, showed that the typicalmass ofprimordial stars could be $\sim 43 M_{\odot}$ , i.e., less massive than originally expected by theoretical models." + Their, Their +outburst fluence is correlated with duration.,outburst fluence is correlated with duration. +" The exceptions are the 2006 and 1967 outbursts, which are long but of low fluence."," The exceptions are the 2006 and 1967 outbursts, which are long but of low fluence." + The UV light curve of the 2006 outburst is unique in its coverage and thus cannot be compared to previous outbursts., The UV light curve of the 2006 outburst is unique in its coverage and thus cannot be compared to previous outbursts. + However the ratio of the maximum flux to that in the final observation (approximately quiescence; the AAVSO magnitude was ~00.2 mag above the quiescent level) is 71.5 (=2.2 magnitudes) whereas the ratio of the flux at 2600 bbetween outburst and quiescence was 225 (=3.6 magnitudes; Bianchini 11983; Rosino 11982)., However the ratio of the maximum flux to that in the final observation (approximately quiescence; the AAVSO magnitude was 0.2 mag above the quiescent level) is 7.5 (=2.2 magnitudes) whereas the ratio of the flux at 2600 between outburst and quiescence was 28 (=3.6 magnitudes; Bianchini 1983; Rosino 1982). +" The amplitude of the UV outburst is thus around 1.5 magnitudes less than expected from previous data, as has already been noted for the optical data."," The amplitude of the UV outburst is thus around 1.5 magnitudes less than expected from previous data, as has already been noted for the optical data." +" By analogy with the optical data, we assume this implies a lower outburst flux rather than increased quiescent flux."," By analogy with the optical data, we assume this implies a lower outburst flux rather than increased quiescent flux." +" This is a surprising result, since the typical UVOT count rate was nearly an order of magnitude higher than that reported by Vrielmann ((2005)."," This is a surprising result, since the typical UVOT count rate was nearly an order of magnitude higher than that reported by Vrielmann (2005)." +" To investigate, we downloaded the pipeline -OM products from the SScience Archive and examined the uvwl data (ObsID 0154550201)."," To investigate, we downloaded the pipeline -OM products from the Science Archive and examined the uvw1 data (ObsID 0154550201)." +" We found the count rate to be much higher than claimed by Vrielmann ((2005), and comparable to or higher than in our ddata."," We found the count rate to be much higher than claimed by Vrielmann (2005), and comparable to or higher than in our data." +" Given that the ddata were taken on the rise of the outburst, not the peak, we conclude that XMM--OM data are consistent with the idea that the UV emission in the 2006 outburst was fainter than in previous outbursts."," Given that the data were taken on the rise of the outburst, not the peak, we conclude that -OM data are consistent with the idea that the UV emission in the 2006 outburst was fainter than in previous outbursts." +" We also searched the OM data for evidence of spin-period modulation, since this is clearly seen in our Swift--UVOT data, but was reported as absent by Vrielmann ((2005)."," We also searched the OM data for evidence of spin-period modulation, since this is clearly seen in our -UVOT data, but was reported as absent by Vrielmann (2005)." +" There is weak evidence for spin-period modulation in the OM data, with an amplitude$33%.."," There is weak evidence for spin-period modulation in the OM data, with an amplitude." + The presence of spin-period modulation in the UV emission is thus not peculiar to the 2006 outburst., The presence of spin-period modulation in the UV emission is thus not peculiar to the 2006 outburst. +" While the UV light curve is clearly correlated with the optical one, the X-ray light curve is not."," While the UV light curve is clearly correlated with the optical one, the X-ray light curve is not." +" By eye, some possible anti-correlation or time-delayed correlation, with the UVOT data seems possible."," By eye, some possible anti-correlation or time-delayed correlation, with the UVOT data seems possible." +" We thus performed a Discrete Correlation Function analysis between the UVOT and XRT data, however no correlation was found above the 1.8-c level."," We thus performed a Discrete Correlation Function analysis between the UVOT and XRT data, however no correlation was found above the $\sigma$ level." +" 'The 1983, 1996 and 2002 outbursts of GK Per were all monitored in the X-rays with different satellites (Watson 11985; Hellier 22004)."," The 1983, 1996 and 2002 outbursts of GK Per were all monitored in the X-rays with different satellites (Watson 1985; Hellier 2004)." + The most extensive dataset prior to that presented here is unpublished monitoring of the 2002 outburst., The most extensive dataset prior to that presented here is unpublished monitoring of the 2002 outburst. + In Fig., In Fig. + [] we show the X- flux evolution from these 3 outbursts in addition to the ddata from 2006.," \ref{fig:xrayob} + we show the X-ray flux evolution from these 3 outbursts in addition to the data from 2006." +" As can be seen, there is no systematic X- evolution seen during outbursts, unlike in the optical."," As can be seen, there is no systematic X-ray evolution seen during outbursts, unlike in the optical." + 'The 2006 outburst is however fairly typical in its relative flux evolution., The 2006 outburst is however fairly typical in its relative flux evolution. +" The 2-10 keV flux during oobservation 009 (the observation during which the X-ray flux was greatest) was erg ss| (La=8.7x1035 erg s !), which is consistent with the peak hard X-ray fluxes seen in previous outbursts (e.g. 1983, Watson 11985; 1989, Ishida 11992; 1996, Hellier 22004)."," The 2–10 keV flux during observation 009 (the observation during which the X-ray flux was greatest) was erg $^{-1}$ $L_x=8.7\tim{33}$ erg $^{-1}$ ), which is consistent with the peak hard X-ray fluxes seen in previous outbursts (e.g. 1983, Watson 1985; 1989, Ishida 1992; 1996, Hellier 2004)." +" In 2007 September Swift--XRT observed GK Per in quiescence for calibration purposes (unfortunately, the UVOT was not in operation)."," In 2007 September -XRT observed GK Per in quiescence for calibration purposes (unfortunately, the UVOT was not in operation)." + The 2-10 keV flux in this observation was erg ss (Lz=6.1x10% erg !! s!) aa factor of 14 lower than in outburst., The 2–10 keV flux in this observation was erg $^{-1}$ $L_x=6.1\tim{32}$ erg $^{-1}$ ) a factor of 14 lower than in outburst. +! This is similar to the 2-10 keV quiescent fluxes of erg ss! and erg ss! reported by!! Norton ((1988)., This is similar to the 2–10 keV quiescent fluxes of erg $^{-1}$ and erg $^{-1}$ reported by Norton (1988). +" Thus, unlike the optical and UV, both the peak 2-10 keV flux and the outburst/quiescence 2-10 keV flux ratio seen in this"," Thus, unlike the optical and UV, both the peak 2–10 keV flux and the outburst/quiescence 2–10 keV flux ratio seen in this" +around the galaxy’s center.,around the galaxy's center. + The velocity curve in the central slit. NUC (Fig. 3..," The velocity curve in the central slit, NUC (Fig. \ref{far}," +" central panel). has a full amplitude of ~400 ""land shows a general reflection symmetry: starting from the center. the velocity rises rapidly on both sides by ~200 reaching a peak at r~ 0711 from the center."," central panel), has a full amplitude of $\sim 400$ and shows a general reflection symmetry: starting from the center, the velocity rises rapidly on both sides by $\sim 200$ reaching a peak at $r \sim$ 1 from the center." + This trend is followed by a small decrease and a substantially constant value at larger radu., This trend is followed by a small decrease and a substantially constant value at larger radii. + Line emission and velocity dispersion are strongly peaked and smoothly decrease from the nucleus outwards., Line emission and velocity dispersion are strongly peaked and smoothly decrease from the nucleus outwards. + The behavior seen in the off-nuclear slits is qualitatively similar to what is seen at the NUC location (Fig. 3..," The behavior seen in the off-nuclear slits is qualitatively similar to what is seen at the NUC location (Fig. \ref{far}," + left and right panels). but with smaller velocity amplitude and. more important. a less extreme velocity gradient.," left and right panels), but with smaller velocity amplitude and, more important, a less extreme velocity gradient." + Both the amplitude and gradient decrease at increasing distance of the slit center from the nucleus. with a behavior characteristic of gas rotating in à circumnuclear disk.," Both the amplitude and gradient decrease at increasing distance of the slit center from the nucleus, with a behavior characteristic of gas rotating in a circumnuclear disk." + Ground-based photometric and kinematical studies (Demoulin-Ulrichetal.1984:Bertola1991) show that NGC 5077 exhibits a gaseous disk with the major axis roughly orthogonal to the galaxy photometric major axis (PA ~107).," Ground-based photometric and kinematical studies \citep{demoulin84, bertola91} show that NGC 5077 exhibits a gaseous disk with the major axis roughly orthogonal to the galaxy photometric major axis (PA $\sim 10^\circ$ )." +" The gas tsophotes show twisting and a marked warp on the W side at r 20""(Caonetal.2000).", The gas isophotes show twisting and a marked warp on the W side at $r \sim$ \citep{caon00}. +. The gas has a fairly symmetric and smooth rotation curve at PA = 108° (~ major axis of the tonized gas distribution) with a half amplitude of ~270 at r~ 13”., The gas has a fairly symmetric and smooth rotation curve at PA = $108^\circ$ $\sim$ major axis of the ionized gas distribution) with a half amplitude of $\sim 270$ at $r \sim$ . + At PA = 10°. the stellar rotation curve exhibits a counter-rotating core (7€ 5.," At PA = $10^\circ$, the stellar rotation curve exhibits a counter-rotating core $r \leq$ )." + Along this axis. the gas rotates in the same direction as the stellar nucleus and shows a small-seale central velocity plateau.," Along this axis, the gas rotates in the same direction as the stellar nucleus and shows a small-scale central velocity plateau." + The velocity curves for this galaxy are complex (see Fig. 4))., The velocity curves for this galaxy are complex (see Fig. \ref{group2}) ). + On the nuclear slit. the. velocity apparently shows a general rotational trend. with redshift on the left and blueshift on the right side of the diagram.," On the nuclear slit, the velocity apparently shows a general rotational trend, with redshift on the left and blueshift on the right side of the diagram." + The same large-scale rotation 15 observable on the off-nuclear slit positions., The same large-scale rotation is observable on the off-nuclear slit positions. + Smaller scale high-amplitude (~ 200 ) velocity oscillations are also clearly visible., Smaller scale high-amplitude $\sim$ 200 ) velocity oscillations are also clearly visible. + In the SW region at rx 0744 the position-velocity diagrams of NUC and the adjacent S1 slit show a trend that is inconsistent with gas in regular rotation around the galaxy’s center (see Fig. 4..," In the SW region at $r \leq$ 4 the position-velocity diagrams of NUC and the adjacent S1 slit show a trend that is inconsistent with gas in regular rotation around the galaxy's center (see Fig. \ref{group2}," + second upper panel)., second upper panel). + In this region the velocity curves diverge. reaching a separation of ~ 300 kms7'at r- 0722.," In this region the velocity curves diverge, reaching a separation of $\sim$ 300 at $r \sim$ 2." + The over-plot of the position velocity diagrams suggests an expanding bubble of gas., The over-plot of the position velocity diagrams suggests an expanding bubble of gas. + Summarizing. we find that NGC 5077 shows a line emission consistent with a circumnuclear gas disk in Keplerian rotation around the galaxy’s center.," Summarizing, we find that NGC 5077 shows a line emission consistent with a circumnuclear gas disk in Keplerian rotation around the galaxy's center." + For the remaining two objects. the trend of their velocity curves cannot be ascribed to the regular rotation of a nuclear gas disk.," For the remaining two objects, the trend of their velocity curves cannot be ascribed to the regular rotation of a nuclear gas disk." + The position-velocity diagrams of IC 989 indicate the presence of a counter-rotating gas component., The position-velocity diagrams of IC 989 indicate the presence of a counter-rotating gas component. + Modeling this configuration would require (at least) a warped geometry for the disk. which cannot be constrained with the present data.," Modeling this configuration would require (at least) a warped geometry for the disk, which cannot be constrained with the present data." + By these considerations. only NGC 5077 is a suitable candidate for providing a successful SMBH mass measurement.," By these considerations, only NGC 5077 is a suitable candidate for providing a successful SMBH mass measurement." + Our modeling code. deseribed in detail in Marconi (2003).. was used to fit the observed rotation curves of NGC 5077.," Our modeling code, described in detail in \citet{marconi03_2}, was used to fit the observed rotation curves of NGC 5077." + The code computes the rotation curves of the gas assuming that the gas is rotating in circular orbits within a thin disk in the galaxy potential., The code computes the rotation curves of the gas assuming that the gas is rotating in circular orbits within a thin disk in the galaxy potential. + The gravitational potential has two components: the stellar potential (whose mass distribution will be determined in Sec. 4.1)).," The gravitational potential has two components: the stellar potential (whose mass distribution will be determined in Sec. \ref{stelle}))," + characterized by its mass-to-light ratio and a dark mass concentration (the black hole). spatially," characterized by its mass-to-light ratio and a dark mass concentration (the black hole), spatially" +method 1 or 2 results in svstematically underestimating the ratios by roughly .05-.10 dex.,method 1 or 2 results in systematically underestimating the ratios by roughly .05-.10 dex. + Therefore. in order to minimize uncertainües in determining in low metallicitv svstenis. one clearly should derive and from separately.," Therefore, in order to minimize uncertainties in determining in low metallicity systems, one clearly should derive and from separately." + A comparison of our temperature parameterizations (eqs. [|5]], A comparison of our temperature parameterizations (eqs. \ref{eq:tn210}] ] + and [9]]) with those of pag92 and izo94 in Figure 3. shows good agreement among the three functions at a density of 10*.. where the pag92 and izo94 formulations are based on photoionization models by SEasiiska(1990)... most of which have = I0cm7.," and \ref{eq:to210}] ]) with those of pag92 and izo94 in Figure \ref{teplot} shows good agreement among the three functions at a density of 10, where the pag92 and izo94 formulations are based on photoionization models by \cite{stasinska90}, most of which have = 10." + On the other haud. for a density of 100 ? the agreement between our results (eqs. [10]]," On the other hand, for a density of 100 $^{-3}$ the agreement between our results (eqs. \ref{eq:tn2100}] ]" + and |11]]) and pag92 and izo94 is less salisfactory., and \ref{eq:to2100}] ]) and pag92 and izo94 is less satisfactory. + For (he temperature formulation by sta96. there is relatively poor agreement with our low density results for and}.. although the agreement is better lor our results for a density of 100 em. especially in the case of).," For the temperature formulation by sta96, there is relatively poor agreement with our low density results for and, although the agreement is better for our results for a density of 100 $^{-3}$, especially in the case of." +. Dilferences between the values obtained. wilh sta96 and our method are due to the fact that sta96 constitutes an extrapolation to lower metallicites of the published relation., Differences between the values obtained with sta96 and our method are due to the fact that sta96 constitutes an extrapolation to lower metallicites of the published relation. + In addition. the latter is based on simulations of IE I regions created by an evolving group of stars. while we use single non-evolving star sinnlations.," In addition, the latter is based on simulations of H II regions created by an evolving group of stars, while we use single non-evolving star simulations." + Finally. our method uses independent relations for and )with respect to7).," Finally, our method uses independent relations for and with respect to." +. To test the impact of the density. effect on our final values. we used equation (1)) to calculate this ratio for each of our sample objects for the two densitv regimes. n1O and nl100.," To test the impact of the density effect on our final values, we used equation \ref{eq:ionabun}) ) to calculate this ratio for each of our sample objects for the two density regimes, n10 and n100." + The results are shown in the upper left panel of Figure 7.. where the n100 regime (ordinate) is plotted against the n10 reeime (abscissa).," The results are shown in the upper left panel of Figure \ref{n2os}, where the n100 regime (ordinate) is plotted against the n10 regime (abscissa)." + Clearly. the points closely follow the diagonal line corresponding to equal values of in both cases.," Clearly, the points closely follow the diagonal line corresponding to equal values of in both cases." +" Further comparisons of our temperature method with the three literature results just discussed. are shown in the remaining panels of Figure Ἐν,", Further comparisons of our temperature method with the three literature results just discussed are shown in the remaining panels of Figure \ref{n2os}. + In each case we have calculated values at a density of 10 cm-3 for our sample objects using both our temperature method (vertical axis) and that of pag92 (upper right). iz094 (lower left). aud sta96 (lower right). shown on the horizontal axis in each eraph.," In each case we have calculated values at a density of 10 ${-3}$ for our sample objects using both our temperature method (vertical axis) and that of pag92 (upper right), izo94 (lower left), and sta96 (lower right), shown on the horizontal axis in each graph." + The diagonal lines show the one-to-one relation., The diagonal lines show the one-to-one relation. + Note the particularly poor agreement between our method and those of pag92 ancl iz094. especially lor values below -1.2.," Note the particularly poor agreement between our method and those of pag92 and izo94, especially for values below -1.2." + This disagreement can be easily (traced to the relatively low temperatures predicted by pag92 and izo94 when exceeds 14000 IX. resulüng in hieher and lower ratios than ours.," This disagreement can be easily traced to the relatively low temperatures predicted by pag92 and izo94 when exceeds 14000 K, resulting in higher $^+$ and lower ratios than ours." + On the other haad. the apparently closer agreement wilh sta96 arises because their parameterizations lor both and are offset [rom our curves bv roughly the same amount in each case. resulting in relatively little difference in our computed ratios.," On the other hand, the apparently closer agreement with sta96 arises because their parameterizations for both and are offset from our curves by roughly the same amount in each case, resulting in relatively little difference in our computed ratios." + Since in general the only sensitive line flix ratio available [rom observations is the ratio στις) Fuzz. we assumed that was equal to throughout the observed IL IL regions.," Since in general the only sensitive line flux ratio available from observations is the ratio $I_{6716}$ $I_{6731}$, we assumed that was equal to throughout the observed H II regions." + For 42 low metallicity svstenis in our sample the ratio was detected with, For 42 low metallicity systems in our sample the ratio was detected with +(1997).,. +. An asvmptotie analvsis of the Grac-Shalranov equation can vield the structure of the flow at large distances [rom the source. as in and Shuetal.(1995).," An asymptotic analysis of the Grad-Shafranov equation can yield the structure of the flow at large distances from the source, as in \citet{hn89, hn03} + and \citet{shu95}." +. Because of the difficulties in finding analvtical solutions to the flow structure. it has become common in recent vears (o attack (he problem with time-dependent numerical simulations.," Because of the difficulties in finding analytical solutions to the flow structure, it has become common in recent years to attack the problem with time-dependent numerical simulations." + Two different approaches have been taken in developing mnunerical models of jet launching [rom aceretion disks including the accretion disk as part of the simulation. or treating (he disk as a fixed boundary condition.," Two different approaches have been taken in developing numerical models of jet launching from accretion disks — including the accretion disk as part of the simulation, or treating the disk as a fixed boundary condition." + We have chosen the latter approach for our study and will focus on it., We have chosen the latter approach for our study and will focus on it. + We reler the reader to Shibata&Uchida(1986).. Stone& (1994).. Matsumotoetal. (1996).. and vonRekowski&Drandenburg(2004). [or exanples of models which include the clisk.," We refer the reader to \citet{su86}, , \citet{sn94}, \citet{m96}, and \citet{vonR04} for examples of models which include the disk." + For cases where the disk is treated as a fixed rotating boundary [or the simulation. it is important that the hydromagnelic euantities are specified on the disk in a sell-consistent manner.," For cases where the disk is treated as a fixed rotating boundary for the simulation, it is important that the hydromagnetic quantities are specified on the disk in a self-consistent manner." + Several different approaches have been taken for specibving both the iniGal and boundary conditions for numerical simulations of magnetocentrifugal jet launching., Several different approaches have been taken for specifying both the initial and boundary conditions for numerical simulations of magnetocentrifugal jet launching. + Usivugovaelal.(1995) performed. simulations demonstrating the acceleration and collimation of a jet from a disk with a hot (plasma ; parameter “> 1) corona., \citet{u95} performed simulations demonstrating the acceleration and collimation of a jet from a disk with a hot (plasma $\beta$ parameter $\gg1$ ) corona. + Their simulations did 100 reach steady-state. allhough it is unclear whether this is a feature of their model or the result of terminating the simulation before it became stationary.," Their simulations did not reach steady-state, although it is unclear whether this is a feature of their model or the result of terminating the simulation before it became stationary." + A similar study (Romanovaetal.1997). using a stronger magnetic field and a cold (9< 1) corona resulted in stationary wind solutions: however the wind was at best poorly collimated., A similar study \citep{r97} using a stronger magnetic field and a cold $\beta<1$ ) corona resulted in stationary wind solutions; however the wind was at best poorly collimated. + (1997a.b) also use a corona that can be described as cold. ancl two different. initial nagnelic configurations: a potential (current-free) field (Ouved&ον1997a).. ancl a uniform. vertical (parallel to rotation axis) field (Ouved&πανί1997b).," \citet{op97a,op97b} also use a corona that can be described as cold, and two different initial magnetic configurations: a potential (current-free) field \citep{op97a}, and a uniform, vertical (parallel to rotation axis) field \citep{op97b}." +. Both cases exhibit acceleration ancl collimation. but the former comes to a steady-state. while the latter is characterized by episodie behavior.," Both cases exhibit acceleration and collimation, but the former comes to a steady-state, while the latter is characterized by episodic behavior." + However. in a follow-up paper (Ouved&Puclritz1999).. thev arene that it is not the initial magnetic configuration but rather (he mass loading at the base of the wind that determines whether a given model will reach steady-state or display episodic behavior.," However, in a follow-up paper \citep{op99}, they argue that it is not the initial magnetic configuration but rather the mass loading at the base of the wind that determines whether a given model will reach steady-state or display episodic behavior." + Their conclusions are based on simulations they performed for different values of mass load. for both the potential and uniform field configurations. INrasnopolsky.Blanclford (1999)," Their conclusions are based on simulations they performed for different values of mass load, for both the potential and uniform field configurations. \citet{klb99}," +.. herealter referred (o as IXKLD99. also performed cold simulations in an initially potential field. with an important modification.," hereafter referred to as KLB99, also performed cold simulations in an initially potential field, with an important modification." + Γον pinned the foot points of the wind-Iaunching field lines on the disk. but left the field lines [ree to vary in the racial and azimuthal directions both on the disk and away [rom the disk in the wind zone.," They pinned the foot points of the wind-launching field lines on the disk, but left the field lines free to vary in the radial and azimuthal directions both on the disk and away from the disk in the wind zone." + These degrees of freedom are needed to prevent sharp discontinuities Irom developing betweenthe disk boundary and (the magnetocentrigual wind for the case of a spherical boundary)., These degrees of freedom are needed to prevent sharp discontinuities from developing betweenthe disk boundary and the magnetocentrigual wind \\citealt{bt99} for the case of a spherical boundary). +We have already shown the strong spatial association of magnetic transients with the WLE kernels.,We have already shown the strong spatial association of magnetic transients with the WLF kernels. + Figure T((/op)) shows (he consecutive difference magnetogram and white-lieht images of the AR NOAA 11158 during the peak phase UUT) of the X2.2 flare., Figure \ref{LineProf}( ) shows the consecutive difference magnetogram and white-light images of the AR NOAA 11158 during the peak phase UT) of the X2.2 flare. + We selected a quiel (P4) aud. a transient (P5) location as marked by the arrows., We selected a quiet $_1$ ) and a transient $_2$ ) location as marked by the arrows. + Figure 7((c- shows the line profiles at these two locations., Figure \ref{LineProf}( (c-d) shows the line profiles at these two locations. + Solid (dashed) curve represents the line profile during the pre (peak) phase of the flare., Solid (dashed) curve represents the line profile during the pre (peak) phase of the flare. + These curves were obtained from a four term Gaussian fitting (except for the peak profile at P» where such a fitting was not possible)., These curves were obtained from a four term Gaussian fitting (except for the peak profile at $_2$ where such a fitting was not possible). + It is evident (hat the line profile turned. to emission al the wavelength: .NA—-34.4mamA and became broader during the peak phase of the flare as compared to the pre-IIare phase., It is evident that the line profile turned to emission at the wavelength $\Delta\lambda$ and became broader during the peak phase of the flare as compared to the pre-flare phase. + This change in the line profile shape is expected to be (he main reason for the observed. flare associated sign reversal of magnetic [Iux and the enhancement of Doppler velocity αἱ the location P» during (he peak phase of the flare., This change in the line profile shape is expected to be the main reason for the observed flare associated sign reversal of magnetic flux and the enhancement of Doppler velocity at the location $_2$ during the peak phase of the flare. + No such change was found at Py taken as a relerence location [ar away from the flare., No such change was found at $_1$ taken as a reference location far away from the flare. + From the WAU spectral line-prolile data. we now attempt to explain (he reason for these transients.," From the HMI spectral line-profile data, we now attempt to explain the reason for these transients." + In (he SDO/IIMI measurements. magnetogram aud Dopplergram maps ol the full disk Sun are computed from the phase of the Fourier (ransform (first component) of the line profile values.," In the SDO/HMI measurements, magnetogram and Dopplergram maps of the full disk Sun are computed from the phase of the Fourier transform (first component) of the line profile values." + The phase is determined [or the LCP and RCP components independently. €xl the Dopplererams and magnetograms are constructed [rom the mean and cdillerence. respectively (Schouetal.2012).," The phase is determined for the LCP and RCP components independently, and the Dopplergrams and magnetograms are constructed from the mean and difference, respectively \citep{Schou2012}." +. However. (he standard procedure assumes only a moderate line shift due to Doppler velocity ancl Zeeman splitting.," However, the standard procedure assumes only a moderate line shift due to Doppler velocity and Zeeman splitting." + The regions having laree changes in the line profile shape. e.g.. line reversal. ancl laree shifts would not be covered by the algorithin. resulting in artifacts in (hese measurements.," The regions having large changes in the line profile shape, e.g., line reversal, and large shifts would not be covered by the algorithm, resulting in artifacts in these measurements." + For this large N2.2 flare. the spectral line core at the locations of the transient. evidently (turned. Irom absorption (o emission.," For this large X2.2 flare, the spectral line core at the locations of the transient evidently turned from absorption to emission." +" Therefore. it is difficult to get ""correct"" values of magnetic [lux and Doppler velocity. using the above algorithm."," Therefore, it is difficult to get “correct” values of magnetic flux and Doppler velocity using the above algorithm." + In the following. we have used a (wo point algorithm to illustrate the result of the observed spectral line reversal at the transient locations.," In the following, we have used a two point algorithm to illustrate the result of the observed spectral line reversal at the transient locations." +" The magnetic [Iux and. Doppler velocily values can be computed from the line intensities in (he LCP and RCP as follow: Let |LOP.RCP0 .P—U90...,5 be the line intensities in the (wo circular polarizations. LCP and RCP. at the six wavelength positions. AA;=68.87—172.0. centered around the Fe spectral line."," The magnetic flux and Doppler velocity values can be computed from the line intensities in the LCP and RCP as follow: Let $I_i^{\rm LCP,RCP}$, $i=0, \ldots, 5$ be the line intensities in the two circular polarizations, LCP and RCP, at the six wavelength positions, $\Delta\lambda_i=68.8\,i-172.0$, centered around the Fe spectral line." + Then the mean intensities in the blue and red wings of the line can be written as. and," Then the mean intensities in the blue and red wings of the line can be written as, and" +"bright low-ionization knots are embedded within a faint envelope around a bright inner shell, e.g., 22392 and 77354 2010).","bright low-ionization knots are embedded within a faint envelope around a bright inner shell, e.g., 2392 and 7354 ." +". As for these two PNe, the relatively low velocity differences measured for the knots of the envelope of 66369 would suggest that they lay at different latitudes with respect to the symmetry axis of the barrel, but mostly on a weavy disk-like or flattened structure, as for 22392 and 77354."," As for these two PNe, the relatively low velocity differences measured for the knots of the envelope of 6369 would suggest that they lay at different latitudes with respect to the symmetry axis of the barrel, but mostly on a weavy disk-like or flattened structure, as for 2392 and 7354." +" The relative sizes of the regions dominated by ionized material and molecules and dust are illustrated in Figure 12 that displays the normalized surface brightness profiles in the Ho and [N τή, WHT LIRIS Hs, and IRAC 4.5 and 8.0 jum images."," The relative sizes of the regions dominated by ionized material and molecules and dust are illustrated in Figure \ref{prof.han2h2i4i8} that displays the normalized surface brightness profiles in the $\alpha$ and [N ], WHT LIRIS $_2$, and IRAC 4.5 and 8.0 $\mu$ m images." + The comparison between these profiles confirms that the surface brightness profiles of the inner shell of 66369 of the optical Ha emission line and mid-IR IRAC 4.5 and 8.0 um bands are very similar in shape and extent., The comparison between these profiles confirms that the surface brightness profiles of the inner shell of 6369 of the optical $\alpha$ emission line and mid-IR IRAC 4.5 and 8.0 $\mu$ m bands are very similar in shape and extent. +" The mid-IR and optical profiles start to depart from each other at the edge of the inner shell: the emission from Ha and [N ri] drops considerably in an annular region between aand ((i.e., the inner regions of the envelope), while the emission in the IRAC 4.5 and 8.0 um bands stays higher and the Ha profile shows increased emission."," The mid-IR and optical profiles start to depart from each other at the edge of the inner shell: the emission from $\alpha$ and [N ] drops considerably in an annular region between and (i.e., the inner regions of the envelope), while the emission in the IRAC 4.5 and 8.0 $\mu$ m bands stays higher and the $_2$ profile shows increased emission." +" On the contrary, on the oouter rim of the envelope, the emission in the Ho and [N 1] lines is enhanced, while the emission in the IRAC 4.5 and 8.0 um bands flattens and then decays smoothly."," On the contrary, on the outer rim of the envelope, the emission in the $\alpha$ and [N ] lines is enhanced, while the emission in the IRAC 4.5 and 8.0 $\mu$ m bands flattens and then decays smoothly." + There is no H» emission in this range of radial distances., There is no $_2$ emission in this range of radial distances. + 'The comparison of the relative shapes and extents of these different surface brightness profiles is relevant to the understanding of the physical structure of 66369., The comparison of the relative shapes and extents of these different surface brightness profiles is relevant to the understanding of the physical structure of 6369. + Its inner shell is mostly ionized and thus the emission in the IRAC 4.5 and 8.0 jum bands is dominated by ionic emission., Its inner shell is mostly ionized and thus the emission in the IRAC 4.5 and 8.0 $\mu$ m bands is dominated by ionic emission. +" The shell is enclosed by a series of “tadpole” or “cometary” knots whose prominent low-excitation [N 11] and molecular He emission at their heads result in bright [N τῇ and He peaks at c13""..", The shell is enclosed by a series of “tadpole” or “cometary” knots whose prominent low-excitation [N ] and molecular $_2$ emission at their heads result in bright [N ] and $_2$ peaks at $\simeq$. +" The inner shell is surrounded by a region dominated by molecular material, the inner rim of the envelope between ~17” and ~25”.."," The inner shell is surrounded by a region dominated by molecular material, the inner rim of the envelope between $\sim$ and $\sim$." +" This region, outside the bright inner shell and beyond the annular region defined by the tails of the “cometary” knots, seems to be a real PDR."," This region, outside the bright inner shell and beyond the annular region defined by the tails of the “cometary” knots, seems to be a real PDR." +" The relative brightening of the emission in the IRAC 4.5 and 8.0 wm bands at these radial distances is very likely due to molecular H2 emission, although a contribution from continuum dust or PAH emissions is also very likely as noted in other PNe2008)."," The relative brightening of the emission in the IRAC 4.5 and 8.0 $\mu$ m bands at these radial distances is very likely due to molecular $_2$ emission, although a contribution from continuum dust or PAH emissions is also very likely as noted in other PNe." +". Finally, the outer rim of the envelope is again dominated by ionic emission, but we note that low-excitation emission dominates."," Finally, the outer rim of the envelope is again dominated by ionic emission, but we note that low-excitation emission dominates." + This may explain the flattening of the emission in the IRAC 4.5 and 8.0 wm emission due to an additional contribution of ionic emission., This may explain the flattening of the emission in the IRAC 4.5 and 8.0 $\mu$ m emission due to an additional contribution of ionic emission. + It is finally worth noting that sources with comparable He and H1 Zanstra temperatures are likely to be ionisation bound and enveloped by a shell of neutral material., It is finally worth noting that sources with comparable He and H Zanstra temperatures are likely to be ionisation bound and enveloped by a shell of neutral material. +" This leads to a correlation between the Zanstra ratio Tz(He 11)/Tz(H 1), and mid-IR extent outside of the ionised shell2011)."," This leads to a correlation between the Zanstra ratio $_Z$ (He $_Z$ (H ), and mid-IR extent outside of the ionised shell." +". 66369 seems to be a peculiar case of this correlation: whereas the emission from molecular material causes a larger dimension of its inner shell at mid-IR, wavelenghts, the presence of ionized material in its singular envelope results in very similar final optical and mid-IR dimensions."," 6369 seems to be a peculiar case of this correlation: whereas the emission from molecular material causes a larger dimension of its inner shell at mid-IR wavelenghts, the presence of ionized material in its singular envelope results in very similar final optical and mid-IR dimensions." +" In § refneb,,orpsecwenotedthelargejumpinthe|N ii]to[O iii|ratioattheflamenta", In \\ref{neb_morp_sec} we noted the large jump in the [N ] to [O ] ratio at the filamentary structures that enclose the eastern and western extensions of the inner shell of 6369. +, Given that these structures are at the tips of +"from the orbital solution. besides Το, logg. Vig sin£. [Fe/H] and micro-turbulent velocity. also the ratio of the luminosity of the two components is considered a free parameter.","from the orbital solution, besides $T_{\rm eff}$ , $\log g$, $V_{\rm +rot}$ $\sin i$, [Fe/H] and micro-turbulent velocity, also the ratio of the luminosity of the two components is considered a free parameter." + The y procedure allows a firm identification of the location. in the erid space. of the absolute minimum.," The $\chi^2$ procedure allows a firm identification of the location, in the grid space, of the absolute minimum." + Around it the grid is interpolated to a finer step and the position of the minimum is re-fitted and calculated to a greater accuracy., Around it the grid is interpolated to a finer step and the position of the minimum is re-fitted and calculated to a greater accuracy. + The absence of a total eclipse. however. prevents us from observing the spectrum of the occulting star alone and makes it difficult to measure with confidence the micro-turbulent velocity. which we find constrained between 1.7 and 2 km s7!.," The absence of a total eclipse, however, prevents us from observing the spectrum of the occulting star alone and makes it difficult to measure with confidence the micro-turbulent velocity, which we find constrained between 1.7 and 2 km $^{-1}$ ." + We obtain for the metallicity [Fe/H]=+0.02+0.05., We obtain for the metallicity $\pm$ 0.05. +" A comparison between the results obtained with the orbital solution (Typ. logg) and the atmospheric analysis (Tar. loge. Vi, sin? and |Fe/H]) is presented in Table 3. while in Figure 3 an example of the goodness of fit is shown."," A comparison between the results obtained with the orbital solution $T_{\rm eff}$ , $\log g$ ) and the atmospheric analysis $T_{\rm eff}$, $\log g$, $V_{\rm rot}$ $\sin i$ and [Fe/H]) is presented in Table 3, while in Figure 3 an example of the goodness of fit is shown." + The above orbital and atmospheric analyses have provided us with accurate masses. radit. temperatures. and. assuming T..=5770 K. luminosities of the components of V570 Per. which allow us to directly place them on the theoretical Το L/L.. plane We compare on the Temperature/Luminosity plane the position of the two components of V570 Per (from the orbital solution in Table 2) with the tracks from thePadova (Bertelli et al.," The above orbital and atmospheric analyses have provided us with accurate masses, radii, temperatures, and, assuming $T_{\odot}$ =5770 K, luminosities of the components of V570 Per, which allow us to directly place them on the theoretical $T_{\rm eff}$, $L/L_{\odot}$ plane We compare on the Temperature/Luminosity plane the position of the two components of V570 Per (from the orbital solution in Table 2) with the tracks from thePadova (Bertelli et al." + 1994.Fagotto et al.," 1994,Fagotto et al." + 1994. Girardi etal.," 1994, Girardi etal." + 2000). Geneva," 2000), Geneva" +Thermal conduction has been suggested to be an iuportant process in galaxy clusters for quite sole time (Dertschinger Meiksiu 1986: Malvshikin 2001: Brigheuti Alathews 2002: Voigt 2002: Fabian. Voigt Morris 2002).,"Thermal conduction has been suggested to be an important process in galaxy clusters for quite some time (Bertschinger Meiksin 1986; Malyshkin 2001; Brighenti Mathews 2002; Voigt 2002; Fabian, Voigt Morris 2002)." + Tlowever it is not clear as to how domiuaut it would be since nmagetie fields would suppress the conduction co-cfiicient by a large amount from the classical Spitzer value., However it is not clear as to how dominant it would be since magetic fields would suppress the conduction co-efficient by a large amount from the classical Spitzer value. + However. recent theoretical works by Naravan Medvedev (2001). Chandran Maron (200D. Loeb (2002) and several others sugeests that conduction could be as high as to of the Spitzer value in the presence of a tangled aud turbulent magnetic field.," However, recent theoretical works by Narayan Medvedev (2001), Chandran Maron (2004), Loeb (2002) and several others suggests that conduction could be as high as to of the Spitzer value in the presence of a tangled and turbulent magnetic field." + Motivated by these results we adopt the suppression factor f—0.1., Motivated by these results we adopt the suppression factor $f=0.1$. + The flux due to thermal conduction Froud is giveu bv where & ds the Spitzer couductivitv with the Coulomb logaritlin luÀ=37. approprite for ICAL temperature and density.," The flux due to thermal conduction $F_{\rm cond}$ is given by where $\kappa$ is the Spitzer conductivity with the Coulomb logarithm $\ln\lambda = 37$, approprite for ICM temperature and density." + The iutracluster gas is assuned to be in quasi-hydrostatic equilibrium at all times since cooling is uot precipitous at these radii and the heating is mild., The intracluster gas is assumed to be in quasi-hydrostatic equilibrium at all times since cooling is not precipitous at these radii and the heating is mild. + The eas enutropv per particle is S = | , The gas entropy per particle is S = + ). +"2odbylutten(12)———_ where στPfpl, is the ""entropy index” and > is the adiabatic iudex."," where $\sigma \equiv P_{\rm \scriptscriptstyle gas}/\rho_{\rm +\scriptscriptstyle gas}^{\rm \scriptscriptstyle \gamma}$ is the “entropy index” and $\gamma$ is the adiabatic index." +" The particle uunuber deusitv of the gas. p.ds given by 9—py.fn, Divi"," The particle number density of the gas, $n$, is given by $n = \rho_{\rm \scriptscriptstyle gas}/\mu m_{\rm +\scriptscriptstyle p}$." +"ng each timestep Af. the entropy of a given mass shell changes by an amount AS=hs = τν edota) After evaluating the change in the eutropy iudex of cach mass shell of gas due to heating. cooling aud conduction after a time Af using equation (2.3)). the new cutropy iudex of cach shell is calculated using =o, CM) | Ao(AL) where o,CU)=Pooofpl, is the default cutropy index."," During each timestep $\Delta t$, the entropy of a given mass shell changes by an amount S = = - - t. After evaluating the change in the entropy index of each mass shell of gas due to heating, cooling and conduction after a time $\Delta t$ using equation \ref{eq:del_S}) ), the new entropy index of each shell is calculated using = (M) + (M) where $ \sigma_{\rm \scriptscriptstyle 0}(M) = P_{\rm \scriptscriptstyle +gas0}/\rho_{\rm \scriptscriptstyle gas0}^{\rm \scriptscriptstyle \gamma}$ is the default entropy index." + The svstem relaxes to a new state of lydrostatic equilibrium with a new density aud temperature profile., The system relaxes to a new state of hydrostatic equilibrium with a new density and temperature profile. + After updating the function 60CM) for cach mass shell. we solve the equatious Dol to determine the new deusitv aud temperature profiles at time t|Af.," After updating the function $\sigma (M)$ for each mass shell, we solve the equations = = to determine the new density and temperature profiles at time $t+\Delta t$." + The boundary conditious imposed on these equations are that (1) the pressure at the boundary of the cluster. ry. Is constant and is equal to the initial pressure at fo DO. Peri) = coustaut = P4). aud (2) the eax lass Within +. at all times is the mass contained within r4 for the default profile at the initial time. 1.6.. Morand=Maru)1333Ma GS).," The boundary conditions imposed on these equations are that (1) the pressure at the boundary of the cluster, $r_{\rm \scriptscriptstyle out}$, is constant and is equal to the initial pressure at $r_{\rm +\scriptscriptstyle 200}$, i.e., $P\,(r_{\rm \scriptscriptstyle out})$ = constant = $P_{\rm \scriptscriptstyle gas0}$ $r_{\rm \scriptscriptstyle +200}$ ), and (2) the gas mass within $r_{\rm \scriptscriptstyle out}$ at all times is the mass contained within $r_{\rm \scriptscriptstyle 200}$ for the default profile at the initial time, i.e., $M_{\rm \scriptscriptstyle g} +(r_{\rm \scriptscriptstyle out}) = M_{\rm \scriptscriptstyle g0}(r_{\rm +\scriptscriptstyle 200}) = 0.1333M_{\rm \scriptscriptstyle dm} (r_{\rm +\scriptscriptstyle 200})$ ." + It is mnaportant to uote here that μμ increases as the cluster eas ects heated aud spreads out., It is important to note here that $r_{\rm \scriptscriptstyle out}$ increases as the cluster gas gets heated and spreads out. +" The observed eas eutropy S(re) at Ors, aud at ir, ds then calculated using Tir)fn?(r)."," The observed gas entropy ${\cal S}$ $r$ ) at $0.1r_{\rm \scriptscriptstyle +200}$ and at $r_{\rm \scriptscriptstyle 500}$ is then calculated using (r)." + The updated values of o(AL) aud pressure of the ICM Dore) are used to calculate the heating and cooling rates and the conduction flux for the next time step.," The updated values of $\sigma (M)$ and pressure of the ICM $P_{\rm +\scriptscriptstyle gas}(r)$ are used to calculate the heating and cooling rates and the conduction flux for the next time step." +" Tlus is continued. for a curation of f,,,,.", This is continued for a duration of $t_{\rm \scriptscriptstyle heat}$. + After that the ισαπιο source is switched off. putting H = 0.," After that the heating source is switched off, putting ${\cal H}$ = 0." +" The cooling rate and conduction flux coutiuue to be calculated to pdate the function c(M) at subsequent timesteps. aud je livdvostatic structure is correspondiuelv evolved for a uration of fyfica.) Where f,, is the IIubble time."," The cooling rate and conduction flux continue to be calculated to update the function $\sigma (M)$ at subsequent timesteps, and the hydrostatic structure is correspondingly evolved for a duration of $t_{\rm +\scriptscriptstyle H} - t_{\rm \scriptscriptstyle heat}$ , where $t_{\rm +\scriptscriptstyle H}$ is the Hubble time." + Note iat rua decreases during this time since the iutracluster eas loses cutropy and shrinks.," Note that $r_{\rm +\scriptscriptstyle out}$ decreases during this time since the intracluster gas loses entropy and shrinks." + The only free parameters in our calculation are the energy injection rate aud ie time τα over which the ‘effervescent heating” of 16 ICAL takes place., The only free parameters in our calculation are the energy injection rate and the time $t_{\rm \scriptscriptstyle heat}$ over which the “effervescent heating” of the ICM takes place. +" After evolving the eas for the total vailable time. f,~1.35«101"" years. we check whether 1e entropy. at 0.1655, aud reo. match the observed values. and adjust parameters accordingly."," After evolving the gas for the total available time, $t_{\rm +\scriptscriptstyle H} \sim 1.35\times 10^{10}$ years, we check whether the entropy at $0.1r_{\rm \scriptscriptstyle 200}$ and $r_{\rm +\scriptscriptstyle 500}$ match the observed values, and adjust parameters accordingly." +" Iu this wav. we explore le paraiueter space of aud fi... or rather a single ree parameter. Le. the total energev. £a(Litheat or differeut cluster masses so that the cutropy (after « 1029 vears) at Q.1rs,, and ru, matches the observed values."," In this way, we explore the parameter space of and $t_{\rm \scriptscriptstyle heat}$ or rather a single free parameter, i.e. the total energy, $E_{\rm agn}=\langle L\rangle t_{\rss heat}$ for different cluster masses so that the entropy (after $\times$ $^{10}$ years) at $0.1r_{\rm +\scriptscriptstyle 200}$ and $r_{\rm \scriptscriptstyle 500}$ matches the observed values." + For muuerical stability of the code. the couduction term. is inteerated using timesteps that satisfv the appropriate Courant condition.," For numerical stability of the code, the conduction term is integrated using timesteps that satisfy the appropriate Courant condition." +" The Courant condition for conduction 15 (),5)", The Courant condition for conduction is 0.5. + The timesteps. At. used in equation (12) to update the eutropv of the eas and calculate its pressure. temperature and deusitv profiles abways obey the above Couraut condition (Buszkowski Beechuan 2002: Stone. Pringle Beechuan 1999).," The timesteps, $\Delta t$, used in equation (12) to update the entropy of the gas and calculate its pressure, temperature and density profiles always obey the above Courant condition (Ruszkowski Begelman 2002; Stone, Pringle Begelman 1999)." + The temperature decrement of CAIB dueto the SZ effect is directly proportional to the Comptonparameter (y)., The temperature decrement of CMB dueto the SZ effect is directly proportional to the Comptonparameter $y$ ). + For a spherically sxaunetrie cluster. the Conmipton parameter Is Given by," For a spherically symmetric cluster, the Compton parameter is given by" +"curve in the A Qy plane. where Qy=afOg/z6G, represents the condition Qa;=1 for different values of the disk scale height parameter 2.","curve in the $\lambda$ $ Q_T$ plane, where $Q_T = +a f \Omega_K/\pi G \Sigma_0$ represents the condition $Q_M=1$ for different values of the disk scale height parameter $\beta$." + The thick curve corresponds to 2=1 and the thin curves correspond to ;2—0 and o=V2. which is the maximum value allowed or a thermally supported disk (S07).," The thick curve corresponds to $\beta=1$ and the thin curves correspond to $\beta=0$ and $\beta=\sqrt{2}$, which is the maximum value allowed for a thermally supported disk (S07)." +" For each value of ». the portion of the plane below the corresponding curve represents (he region of parameter space lor which disks are unstable in the presence of magnetic effects (Qa,<1)."," For each value of $\beta$, the portion of the plane below the corresponding curve represents the region of parameter space for which disks are unstable in the presence of magnetic effects $Q_M<1$ )." + Above the curve. Qu; is larger than unity. and (he disk is stable.," Above the curve, $Q_M$ is larger than unity, and the disk is stable." + The ellects of magnetic pressure and magnetic tensioni make a cisk nore stable compared to its unmagnetized counterpart. whereas (he effects of subkeplerian rotation destabilize (he disk.," The effects of magnetic pressure and magnetic tension make a disk more stable compared to its unmagnetized counterpart, whereas the effects of subkeplerian rotation destabilize the disk." + For /=1. the line Q4=1 delines the boundary for stability in the absence of magnetic effects.," For $f=1$, the line $Q_T = 1$ defines the boundary for stability in the absence of magnetic effects." + The same curves also show the value of the inverse of the unction M defined in equation (5-3))., The same curves also show the value of the inverse of the function ${\cal M}$ defined in equation \ref{defM}) ). +" Next we define the benchmark disk mass Mq, integrating the critical surface density when there are not magnetic effects. qo"," Next we define the benchmark disk mass $M_{\rm max}$ integrating the critical surface density when there are not magnetic effects, 2." +Ila As shown by many authors (starting with Adams οἱ al., As shown by many authors (starting with Adams et al. + 1983). if one uses the observed spectral enerev distributions of T ‘Tauri star/clisk svstems to specily the radial distribution of temperature. aid hence the sound speed profile ¢(a). the mass scales resulting from equation (5-4)) lie in the range M4 = 0.38 1 ALL.Le. masses comparable to those of the central stars.," 1988), if one uses the observed spectral energy distributions of T Tauri star/disk systems to specify the radial distribution of temperature, and hence the sound speed profile $a(\varpi)$, the mass scales resulting from equation \ref{maxzero}) ) lie in the range $M_{\rm max}$ = 0.3 – 1 $M_\odot$,i.e., masses comparable to those of the central stars." + Note that this benchmark mass scale is calculated by assuming that (Q4: = 1 throughout (he disk. ancl(hus represents an upper Επί on the disk mass that can be stable.," Note that this benchmark mass scale is calculated by assuming that $Q_T$ = 1 throughout the disk, andthus represents an upper limit on the disk mass that can be stable." + In practice. the Toomre parameter depends on radius. Q4ίσα). so that much of the disk will have larger Qy and hence smaller surface densitv (han used in (his exercise.," In practice, the Toomre parameter depends on radius, $Q_T = Q_T (\varpi)$, so that much of the disk will have larger $Q_T$ and hence smaller surface density than used in this exercise." +" Considerations of elobal stability show that the maximum disk mass is lower. e.g.. the maximum clisk mass (hat is stable to a class of 2 = 1 modes is given by Mj/GM,+4Mg)=3/40 (Shu et al."," Considerations of global stability show that the maximum disk mass is lower, e.g., the maximum disk mass that is stable to a class of $m$ = 1 modes is given by $M_d / (M_\ast + M_d) = 3/4\pi$ (Shu et al." + 1990)., 1990). + Nonetheless. (his mass scale of equation (5-4)) provides an interesting benchmark.," Nonetheless, this mass scale of equation \ref{maxzero}) ) provides an interesting benchmark." + For the case of magnetized disks. the maximum mass is increased. as shown below.," For the case of magnetized disks, the maximum mass is increased, as shown below." + With the inclusion of magnetic effects. the maximum cisk mass that is stable to gravitational perturbations takes the form 2d (28) Vf Pe," With the inclusion of magnetic effects, the maximum disk mass that is stable to gravitational perturbations takes the form 2 ( ) f )^2 +" +"Curiously, the lens probability in the spherical case at small separations is actually higher than in the elliptical case.","Curiously, the lens probability in the spherical case at small separations is actually higher than in the elliptical case." + This is a consequence of the magnification bias., This is a consequence of the magnification bias. + A source placed at the center of a lens with circular symmetry forms an Einstein ring; this degeneracy means that sources placed near the center will have both of their images highly magnified., A source placed at the center of a lens with circular symmetry forms an Einstein ring; this degeneracy means that sources placed near the center will have both of their images highly magnified. +" A similar lens with ellipticity, however, does not have this degeneracy."," A similar lens with ellipticity, however, does not have this degeneracy." +" Although sources placed inside and near the astroid caustic will be strongly magnified, a source slightly outside the astroid caustic does not produce such high magnifications since it maps to transition loci rather than critical curves (?))."," Although sources placed inside and near the astroid caustic will be strongly magnified, a source slightly outside the astroid caustic does not produce such high magnifications since it maps to transition loci rather than critical curves \cite{finch02}) )." +" This effect implies that if a lens with circular symmetry is deformed into an elliptical lens such that the average image separation stays fixed, the magnification bias for doubles is drastically reduced while the high magnification bias for quads may or may not compensate for this reduction."," This effect implies that if a lens with circular symmetry is deformed into an elliptical lens such that the average image separation stays fixed, the magnification bias for doubles is drastically reduced while the high magnification bias for quads may or may not compensate for this reduction." +" Whether the total bias cross section is increased or reduced by ellipticity depends on the type of bias used, and on the density profile of the lens."," Whether the total bias cross section is increased or reduced by ellipticity depends on the type of bias used, and on the density profile of the lens." +" For our lens model, if the “second brightest image” bias is used (as in fig. 7))"," For our lens model, if the “second brightest image” bias is used (as in fig. \ref{fig:dpdtheta-spherical-comp}) )" +" the total cross section will be lower than in the spherical case, whereas if the total magnification bias is used it will be roughly the same."," the total cross section will be lower than in the spherical case, whereas if the total magnification bias is used it will be roughly the same." +" Hence, depending on which type of bias is appropriate for a set of observed lens systems, the assumption of spherical galaxies may result in a slight overestimate of the total lensing probability."," Hence, depending on which type of bias is appropriate for a set of observed lens systems, the assumption of spherical galaxies may result in a slight overestimate of the total lensing probability." +" In calculating all the results presented thus far, we ignored the effect of scatter in the mass-luminosity relation and in halo concentrations."," In calculating all the results presented thus far, we ignored the effect of scatter in the mass-luminosity relation and in halo concentrations." + The question naturally arises as to how scatter effects the lensing probabilities., The question naturally arises as to how scatter effects the lensing probabilities. + To investigate this we calculate the total lensing probability assuming spherical galaxies and halos., To investigate this we calculate the total lensing probability assuming spherical galaxies and halos. +" The result is fig. 7,,"," The result is fig. \ref{fig:dpdtheta-spherical-comp}," + with the total lensing probability in the elliptical case (from fig. 1)), with the total lensing probability in the elliptical case (from fig. \ref{fig:dpdtheta-aligned-corr}) ) + being plotted for comparison., being plotted for comparison. +" For the spherical concentrations of halos we used the ? model, assigning log-normal scatter around the median with standard deviation σ=0.3."," For the spherical concentrations of halos we used the \cite{bullock01} model, assigning log-normal scatter around the median with standard deviation $\sigma = 0.3$." +" We also assumed log-normal scatter in mass-luminosity with a standard deviation Σ=0.25, as derived in ?.."," We also assumed log-normal scatter in mass-luminosity with a standard deviation $\Sigma = 0.25$, as derived in \cite{cooray05}." + Scatter in mass-luminosity has the effect of increasing the total lens probability by ~11%.., Scatter in mass-luminosity has the effect of increasing the total lens probability by $\approx$. +" Scatter in concentration increases the contribution of the dark matter to the lensing probability, and has a noticeable effect at separations as small as 2""."," Scatter in concentration increases the contribution of the dark matter to the lensing probability, and has a noticeable effect at separations as small as $2''$." +" While including scatter in these relations will not have a profound effect on image multiplicities, the concentration scatter will probably increase the quad fraction slightly in the middle region (~2""-10"") since the dark matter halos produce higher quad and cusp fractions than the galaxies."," While including scatter in these relations will not have a profound effect on image multiplicities, the concentration scatter will probably increase the quad fraction slightly in the middle region $\approx 2''$ $10''$ ) since the dark matter halos produce higher quad and cusp fractions than the galaxies." +" We have shown that the distribution of strong lensing image multiplicities offers new possibilities for constraining correlations between galaxies and their host dark matter halos—in particular, adiabatic contraction and the degree of axial alignment."," We have shown that the distribution of strong lensing image multiplicities offers new possibilities for constraining correlations between galaxies and their host dark matter halos—in particular, adiabatic contraction and the degree of axial alignment." +" Since varying the amount of alignment makes a considerable difference in the quad/double ratio, and given that the observed ratio is so high, one might expect galaxies and halos to be quite closely aligned."," Since varying the amount of alignment makes a considerable difference in the quad/double ratio, and given that the observed ratio is so high, one might expect galaxies and halos to be quite closely aligned." +" Simulations seem to support this (?,, ?)), and indeed there is some observational evidence from lensing: ? used mass profile modeling of 20 lenses from the CfA-Arizona Space Telescope Lens Survey (CASTLES) to show that the mass and light distributions were aligned within (A62)!?«10° where @ is the projected alignment angle."," Simulations seem to support this \cite{bailin05}, \cite{kazantzidis04}) ), and indeed there is some observational evidence from lensing: \cite{kochanek02} used mass profile modeling of 20 lenses from the CfA-Arizona Space Telescope Lens Survey (CASTLES) to show that the mass and light distributions were aligned within $\langle \Delta \theta^2\rangle^{1/2} < +10^\circ$ where $\theta$ is the projected alignment angle." +" The distribution of image multiplicities provides a simple method, far less time-consuming than individual lens modeling, that can be applied to a large statistical sample of lenses."," The distribution of image multiplicities provides a simple method, far less time-consuming than individual lens modeling, that can be applied to a large statistical sample of lenses." + This method also has the advantange that the data for each individual lens does not have to be very high quality., This method also has the advantange that the data for each individual lens does not have to be very high quality. + The disadvantage is that we have to include all correlations and enviromental effects that are either constrained by other data or directly obtained from theory., The disadvantage is that we have to include all correlations and enviromental effects that are either constrained by other data or directly obtained from theory. + One important caveat to keep in mind is that alignment of the major/minor axes of galaxy and halo does not necessarily imply that the axes will be aligned., One important caveat to keep in mind is that alignment of the major/minor axes of galaxy and halo does not necessarily imply that the axes will be aligned. +" The projected axes can also be misaligned if the galaxy and halo have differing triaxialities (?)), analogous to the phenomenon of ""isophote twist""."," The projected axes can also be misaligned if the galaxy and halo have differing triaxialities \cite{keeton97}) ), analogous to the phenomenon of “isophote twist”." + Our method constrains the alignment of the projected axes., Our method constrains the alignment of the projected axes. +" If the projected axes are shown to be closely aligned, then we can draw the strong conclusion that the major/minor axes of galaxy and halo are aligned, and that the triaxial galaxy and halo shapes are similar on average."," If the projected axes are shown to be closely aligned, then we can draw the strong conclusion that the major/minor axes of galaxy and halo are aligned, and that the triaxial galaxy and halo shapes are similar on average." + There are several ways in which our model can be improved., There are several ways in which our model can be improved. +" First, a fully triaxial model for adiabatic contraction. from simulations is required."," First, a fully triaxial model for adiabatic contraction from simulations is required." +" We used analytic fitting functions from the ? model of adiabatic contraction that was derived from halos with spherically averaged density profiles, extending it to triaxial halos by making the replacement r>R where R is the triaxial radius."," We used analytic fitting functions from the \cite{gnedin04} model of adiabatic contraction that was derived from halos with spherically averaged density profiles, extending it to triaxial halos by making the replacement $ r +\rightarrow R$ where $R$ is the triaxial radius." + But this is clearly only an approximation that may break down at high ellipticity., But this is clearly only an approximation that may break down at high ellipticity. + The predicted lensing probability for cusps may differ significantly when a more accurate model of adiabatic contraction is used., The predicted lensing probability for cusps may differ significantly when a more accurate model of adiabatic contraction is used. +" In addition, we have neglected the contribution from spiral galaxies."," In addition, we have neglected the contribution from spiral galaxies." + This is partly justified by the fact that at least of galaxy lensing is thought to be due to ellipticals (?))., This is partly justified by the fact that at least of galaxy lensing is thought to be due to ellipticals \cite{moeller07}) ). +" However, since disk galaxies viewed edge-on can have extremely high projected ellipticities, their effect on image multiplicities may be substantial."," However, since disk galaxies viewed edge-on can have extremely high projected ellipticities, their effect on image multiplicities may be substantial." +" We have also not included scatter in the mass-luminosity relation and in halo concentration, the effects of which were discussed in the previous section."," We have also not included scatter in the mass-luminosity relation and in halo concentration, the effects of which were discussed in the previous section." +" Although the image multiplicities are not drastically effected by the scatter, it is"," Although the image multiplicities are not drastically effected by the scatter, it is" +Figure |. shows 5. caleulated using the value of Jj for N=20kx and LAL The choice of these values of NU is soniewhnat arbitrary. but as one can see from figure 3.. we obtained simular figures with different choices of V.,"Figure \ref{fig:deslope} shows $\gamma$, calculated using the value of $\beta$ for $N=20{\rm K}$ and 1M. The choice of these values of $N$ is somewhat arbitrary, but as one can see from figure \ref{fig:defig}, we obtained similar figures with different choices of $N$." + We could use a least-square fit. but decided against it since there is no obvious reason to assign equal weights to results with different jV.," We could use a least-square fit, but decided against it since there is no obvious reason to assign equal weights to results with different $N$ ." + We can see that + indeed increases as {ορ increases., We can see that $\gamma$ indeed increases as $|E_b|$ increases. +" Even at E, 8.5 has not couverged to a final value."," Even at $E_b=-8$, $\gamma$ has not converged to a final value." + If we could extend the calculation to higher values of £5. we would be able to determine whether or not 5 really approaches unitv.," If we could extend the calculation to higher values of $E_b$, we would be able to determine whether or not $\gamma$ really approaches unity." + Uunfortunatelv. it would be too time consuming. even on a GRAPE-6. to further extend the calculations. eiven that the hardening rate is so simall for large NV.," Unfortunately, it would be too time consuming, even on a GRAPE-6, to further extend the calculations, given that the hardening rate is so small for large $N$." + From the current simulations. we can sately conclude that the hardening rate ο) depends onu the nuniber of particles Ne aud the power iudex of the dependence 5 munerically obtained is larger than 0.7.," From the current simulations, we can safely conclude that the hardening rate $\beta$ depends on the number of particles $N$, and the power index of the dependence $\gamma$ numerically obtained is larger than 0.7." + The umunucrical result is consistent with the simple loss-cone arguineut. which predicts >=1.," The numerical result is consistent with the simple loss-cone argument, which predicts $\gamma=1$." + The results given in the previous subsection demonstrate clearly that the hardening rate depends ou the nuuber of particles., The results given in the previous subsection demonstrate clearly that the hardening rate depends on the number of particles. + Iu this aud following subsections. we will check whether this result is really reliable.," In this and following subsections, we will check whether this result is really reliable." + First we look at the effect of the softening., First we look at the effect of the softening. + The relatively large and constant softeniug used iun our standard runs has the effect of suppressing two-body relaxation., The relatively large and constant softening used in our standard runs has the effect of suppressing two-body relaxation. + In particular. iu the core of the ealaxy. the effective Coulomb logaritlun might be very αμα]. resulting iu unphysical suppression of the relaxation effect.," In particular, in the core of the galaxy, the effective Coulomb logarithm might be very small, resulting in unphysical suppression of the relaxation effect." + Since the timescale of the loss-cone refill is related to the relaxation timescale. it is crucial to express the relaxation with a reasonable accuracy.," Since the timescale of the loss-cone refill is related to the relaxation timescale, it is crucial to express the relaxation with a reasonable accuracy." + To test the effect of the softening. we performed several runs with a much smaller softening leneth.," To test the effect of the softening, we performed several runs with a much smaller softening length." + Figure 5 shows the result., Figure \ref{fig:ebeps} shows the result. + For N=2«107. reducing € by a factor of 100 resulted in only a small increase in the hardening rate.," For $N=2\times 10^5$, reducing $\epsilon$ by a factor of 100 resulted in only a small increase in the hardening rate." + Furthermore. in the case of rus with N=105. the change in the softening has practically no effect on the hardening rate.," Furthermore, in the case of runs with $N=10^6$, the change in the softening has practically no effect on the hardening rate." + Thus. we can safelv couclude that the effect of the softemime is. if amy. sufficiently sinall that it docs not affect the results in the previous section.," Thus, we can safely conclude that the effect of the softening is, if any, sufficiently small that it does not affect the results in the previous section." + Before the loss cone is depleted. the hardceuime rate is expected to be proportional to the central deusitv of the parent galaxy.," Before the loss cone is depleted, the hardening rate is expected to be proportional to the central density of the parent galaxy." + After the loss cone is depleted. the hardening rate is determined by the timescale at which the stars close to tle loss cone diffuse iuto the cone.," After the loss cone is depleted, the hardening rate is determined by the timescale at which the stars close to the loss cone diffuse into the cone." + Thus. here again. the hardening timescale is expected to depend ou the initial ceutral density.," Thus, here again, the hardening timescale is expected to depend on the initial central density." + Fiewe 6 shows the results of runs with different initial ealaxy models., Figure \ref{fig:ebphi} shows the results of runs with different initial galaxy models. + As expected. the hardening is faster for models with deeper ceutral potential (hielkd central deusitv).," As expected, the hardening is faster for models with deeper central potential (higher central density)." + However. for all runs the hardening rate depends on the number of particles.," However, for all runs the hardening rate depends on the number of particles." + Figure 7 shows the growth rate ο) as a function of the iuifial central deusitv of the pareut galaxy. py.," Figure \ref{fig:phide} shows the growth rate $\beta$ as a function of the initial central density of the parent galaxy, $\rho_{0,0}$." + In the carly phase (£5=— 1). fis roughly proportional to p for pocMO.," In the early phase $E_b=-1$ ), $\beta$ is roughly proportional to $\rho$ for $\rho < 10^2$." + For higher p or for later phases the dependence is solnewhat weaker. prestunably because the black hole binary already has ejected nearby stars. thereby reducing the ceutral density.," For higher $\rho$ or for later phases the dependence is somewhat weaker, presumably because the black hole binary already has ejected nearby stars, thereby reducing the central density." + Tn the previous subsections we have secu that the behavior of the hardening rate is consistent with the loss cone argument., In the previous subsections we have seen that the behavior of the hardening rate is consistent with the loss cone argument. + Iu this subsection. we directly investigate whether or not the loss cone is actually depleted.," In this subsection, we directly investigate whether or not the loss cone is actually depleted." + Figure ὃ shows the distribution of particles in the CE.) plane. where E is the specific energy aud 4 is the specific total angular momentum.," Figure \ref{fig:ej1M} shows the distribution of particles in the $(E,J)$ plane, where $E$ is the specific energy and $J$ is the specific total angular momentum." + We use the coordinate origin as the refercuce point for the augular moment., We use the coordinate origin as the reference point for the angular momentum. + We alsotried to use the center of mass of the black hole binary. but that resulted iu practically iudistinguishable figures.," We alsotried to use the center of mass of the black hole binary, but that resulted in practically indistinguishable figures." +" Παο, we can clearly see that the number of"," Here, we can clearly see that the number of" +the deconvolved: maps is not free. from svstematic ellects either.,the deconvolved maps is not free from systematic effects either. + Phe problems with stopping criteria discussed in section 4.2. are of particular importance. since the extendec emission is quite sensitive to exactly when the deconvolution is terminated.," The problems with stopping criteria discussed in Section \ref{crits} are of particular importance, since the extended emission is quite sensitive to exactly when the deconvolution is terminated." + We therefore believe the best way to caleulate spectra indices for the compact sources is to use the photometry presented in Section 6.. which was obtained by integrating over appropriate regions in the deconvolved maps calibrate: in Jv/aresec.," We therefore believe the best way to calculate spectral indices for the compact sources is to use the photometry presented in Section \ref{phot}, which was obtained by integrating over appropriate regions in the deconvolved maps calibrated in $^2$." + Values calculated in this wav appear in ‘Table 2.. together with values of 2 calculated at various temperatures.," Values calculated in this way appear in Table \ref{betas}, together with values of $\beta$ calculated at various temperatures." + We have also constructed spectral index maps made from the undeconvolved images. in order to examine the extended structure.," We have also constructed spectral index maps made from the undeconvolved images, in order to examine the extended structure." + Figure ὃ shows the map of spectral index a. (5x UU). computed. from the raw maps.," Figure \ref{alphafig1} shows the map of spectral index $\alpha$, $F_\nu \propto \nu^{\alpha}$ ), computed from the raw maps." + This map has been recalibrated into 2/aresec7., This map has been recalibrated into $^2$. + The mmap has been degraded to the same resolution asS5Ofm., The map has been degraded to the same resolution as. +. This smoothing is another cause of possible systematic elfects. and the correct smoothing was found by minimising the resulting artefacts by a process of trial ancl error.," This smoothing is another cause of possible systematic effects, and the correct smoothing was found by minimising the resulting artefacts by a process of trial and error." + The RATS deviation from the mean of the. clouds spectral index. measured in a region between 4A. 4B and 4C. is (LOS.," The RMS deviation from the mean of the cloud's spectral index, measured in a region between 4A, 4B and 4C, is 0.08." + This value was used as an estimate of the random error in extended regions of the spectral index map., This value was used as an estimate of the random error in extended regions of the spectral index map. + The compact sources are seen in Figure S. to have lower spectral index than the surrounding material., The compact sources are seen in Figure \ref{alphafig1} to have lower spectral index than the surrounding material. + Values ofà for the sources in the SI map are twpically 3 for 4X or 3.5 for 4B and 4€. compared to 4.1 for the cloud.," Values of $\alpha$ for the sources in the SI map are typically 3 for 4A or 3.5 for 4B and 4C, compared to 4.1 for the cloud." + A region of low spectral index is seen extending from. 4A. roughly perpendicular to the 4X disk axis.," A region of low spectral index is seen extending from 4A, roughly perpendicular to the 4A disk axis." + This region corresponds to the outflow seen in molecular line emission bv BSDGALA., This region corresponds to the outflow seen in molecular line emission by BSDGMA. + The difference in a between the outflow region and the surrounding cloud is approximately 0.5. and is therefore significant compared to the RATS error for the loud.," The difference in $\alpha$ between the outflow region and the surrounding cloud is approximately 0.5, and is therefore significant compared to the RMS error for the cloud." + Since the outIow is not a compact source. it is dillicult to see how beam ellects could have produced this result.," Since the outflow is not a compact source, it is difficult to see how beam effects could have produced this result." + We conclude that the 4A outflow has a lower spectral index than 1e surrounding cloud., We conclude that the 4A outflow has a lower spectral index than the surrounding cloud. + Computing values for à from the photometry of Section 6.. and comparing these to values measured for the cloud from the SL map discussed above. we see again that 4A has a significantly lower a than the cloud.," Computing values for $\alpha$ from the photometry of Section \ref{phot}, and comparing these to values measured for the cloud from the SI map discussed above, we see again that 4A has a significantly lower $\alpha$ than the cloud." +" The 4B a is comparable to the σος, and 4€ is even a little higher."," The 4B $\alpha$ is comparable to the cloud, and 4C is even a little higher." + This gives us more confidence that the 4A spectral index is eenuinely low. but lends no support to the idea that 4D or 4€ have significantly lower spectral index than the cloud.," This gives us more confidence that the 4A spectral index is genuinely low, but lends no support to the idea that 4B or 4C have significantly lower spectral index than the cloud." + Below. we discuss the various physical causes which could give rise to these spectral index. variations.," Below, we discuss the various physical causes which could give rise to these spectral index variations." + Provided we assume the emission is optically thin. we can write the spectral index as à=2|5. where 3 is he dust opacity spectral index and 5 is a [actor taking account of the departure from the Ttavleigh-Jeans law at ow temperatures. which is always negative ancl becomes significant for temperatures. below about 50K. We have aken account of this correction when calculating the .7 values presented in the various tables and used in Section 6..," Provided we assume the emission is optically thin, we can write the spectral index as $\alpha = 2 + \beta + \gamma$, where $\beta$ is the dust opacity spectral index and $\gamma$ is a factor taking account of the departure from the Rayleigh-Jeans law at low temperatures, which is always negative and becomes significant for temperatures below about 50K. We have taken account of this correction when calculating the $\beta$ values presented in the various tables and used in Section \ref{phot}." + The temperature of the HUXSA sources was estimated w SADR to be 331x. based on a fit to the SED measured at millimetre and submillimetre wavelengths.," The temperature of the IRAS4 sources was estimated by SADRR to be 33K, based on a fit to the SED measured at millimetre and submillimetre wavelengths." + A temperature of around. 30Ix. therefore seems most Likely for the compact, A temperature of around 30K therefore seems most likely for the compact + , +low-signal-to-nolise spectrum.,low-signal-to-noise spectrum. + To investigate a broad. emission line. we fitted the MEG and WEG first order spectra binned at resolution with a mocdel consisting of a power-law. blackbody auc a Gaussian line near 1 keV. The line width σ was fixed at 100 eV. The lit gives a center enerev of 1.0220.03 keV and the EW of I8xz7 eV. The energy is consistent with the results [rom but the EW is smadler.," To investigate a broad emission line, we fitted the MEG and HEG first order spectra binned at resolution with a model consisting of a power-law, blackbody and a Gaussian line near 1 keV. The line width $\sigma$ was fixed at 100 eV. The fit gives a center energy of $1.02\pm0.03$ keV and the EW of $18\pm7$ eV. The energy is consistent with the results from but the EW is smaller." + Although the detected absorption lines with the EWs of 1 eV cannot be seen in speclva with medium energv resolution. the predicted. absorption edges may be apparent.," Although the detected absorption lines with the EWs of $\sim$ 1 eV cannot be seen in spectra with medium energy resolution, the predicted absorption edges may be apparent." + We speculate that the 1 keV feature is an artifact of the edges., We speculate that the 1 keV feature is an artifact of the edges. + In order (o investigate this point. we add both the inferred UTA ancl the edges [rom the low and high-£ warm absorbers. fixing (he parameters to be best-lit values. to the model.," In order to investigate this point, we add both the inferred UTA and the edges from the low and $\xi$ warm absorbers, fixing the parameters to be best-fit values, to the model." + The spectral modelabsori inXSPEC was used for the model of the edges of warm absorbers., The spectral model in was used for the model of the edges of warm absorbers. + Then. the center energy of the broad line: becomes 1.02.4;vy0.05 keVM and the EW 7o]becomes 947mi eV.r Although-. the decrease oft the EWun is not statistically significant. the EW is smaller and nearly consistent with zero.," Then, the center energy of the broad line becomes $1.02^{+0.05}_{-0.04}$ keV and the EW becomes $9{\pm7}$ eV. Although the decrease of the EW is not statistically significant, the EW is smaller and nearly consistent with zero." + Furthermore. the fit with the two warm absorbers was not significantly improved by adding the broad line component to the model (35 significance by F-test).," Furthermore, the fit with the two warm absorbers was not significantly improved by adding the broad line component to the model (85 significance by F-test)." + Thus the 1 keV. feature appears {ο be consistent wilh being an artifact of the warm absorber. allhough we cannot completely rule out a broad emission line or blends of many narrow absorption lines.," Thus the 1 keV feature appears to be consistent with being an artifact of the warm absorber, although we cannot completely rule out a broad emission line or blends of many narrow absorption lines." + From our IIIEZEGS observation. we confirmed the presence of the soft excess.," From our HETGS observation, we confirmed the presence of the soft excess." + Η we fitted the excess wilh blackbody model. the best-fit temperature is 0.124 keV. No prominent narrow emission lines are observed around 1 keV. We detected an edge-like feature at 0.712 keV in the source rest frame.," If we fitted the excess with blackbody model, the best-fit temperature is 0.124 keV. No prominent narrow emission lines are observed around 1 keV. We detected an edge-like feature at 0.712 keV in the source rest frame." + The preferred interpretation of this feature is combination of the O Ix-edge and a inunber of the L-absorption lines from the slightly ionized iron. which suggests a warm absorber with £~I and Nu eLO?! 7..," The preferred interpretation of this feature is combination of the O K-edge and a number of the L-absorption lines from the slightly ionized iron, which suggests a warm absorber with $\xi\sim1$ and $N$ $~\sim10^{21}$ $^{-2}$." + These properties are roughly consistent with those of the UV absorber., These properties are roughly consistent with those of the UV absorber. + We also detected narrow absorption lines of Ovii. οVILL NeIx. NeX. and Mg αἱ the svstemic velocity.," We also detected narrow absorption lines of O, O, Ne, Ne, and Mg at the systemic velocity." + From these lines. another warm absorber having log£e 2 and Nu e107! 7 is required.," From these lines, another warm absorber having $\log\xi\sim$ 2 and $N$ $~\sim10^{21}$ $^{-2}$ is required." +IJXPNO 2.1in teescope(?)..,KPNO 2.1m telescope\citep{Ge2010}. + Note that the S/N can be further increased by conducting tmultiple iudependent measurements aud increasiug instrument througlput., Note that the S/N can be further increased by conducting multiple independent measurements and increasing instrument throughput. + We would like to express our deepest gratitude to the anorvinous referee o ‘this paper. without whot there woud not have been this paper.," We would like to express our deepest gratitude to the anonymous referee of this paper, without whom there would not have been this paper." + We acknowledge the support from NSF with grant NSF AST-0T05139. NASA with grant NNNOTAPLIG (Origins. UCF-UF SRI xogram. DoD ARO Cooperative Ag'eeinent WOIINFE-09-2-0017. SDSS UL consortitin. Dharma Encowinent Foundation and the Unive‘sity of Floida.," We acknowledge the support from NSF with grant NSF AST-0705139, NASA with grant NNX07AP14G (Origins), UCF-UF SRI program, DoD ARO Cooperative Agreement W911NF-09-2-0017, SDSS III consortium, Dharma Endowment Foundation and the University of Florida." + Fuudiug or SDSS-ILI (http:/www.sdss3.org/)) has bee1 provided by he Alfred P. Sloan Foundation. the Participaine Iustitutions. the National Science Fouxclation. aud the U.S. Departileit ol Energy. Ollice of Scieuc7," Funding for SDSS-III ) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science." + SDSS-ILL is managed by the Astrophysical Research Consortiuu for the Participating Iustitutον of the SDSS-IIE Collaboration including the University of Arizona. the Braziian Participation Group. Brookhaven National Laboratory. University of Cambricee. Carnegie Mellon Universiv. University of ΕΙorida. the French Participation Group. he Germ:ui Participatio1 Group. Harvard University. tle Iustituto de Astrofisica de Canarias. the Àichigau 9ate/Notre Datve/JINA Participation Group. Johus Hopkius University. Lawrence Berkeley Naional Laboratory. Max Planck Institute for Astrophysics. Max Planck Lustitute for Extraterrestrial |hysics. New Mexico Stae Uulversity. New York Uuiversity. Ohio State University. Peuusylvauia 5ate University. University of Portsmouμ. Princeton University. the Spanish Participation Croup. Uuiversity of Tokyo. University of Utali. Vanderbilt University. Uuiversity of Vireinia.e University of Washington.e aud Yale University.," SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University." +The observations were carried. out using TEXES in its high-resolution mode 80.000) with a wwide slit on the Gemini North telescope on 29-30 October 2007 under program LD ,"The observations were carried out using TEXES in its high-resolution mode $R=80,000$ ) with a wide slit on the Gemini North telescope on 29-30 October 2007 under program ID GN-2007B-C-5." +The background sky. emission was removed by noclding the source along the slit and subtracting adjacent nod positions., The background sky emission was removed by nodding the source along the slit and subtracting adjacent nod positions. + We corrected for telluric absorption wilh observations ol a CAla obtained at a similar airmass as that of the science targets (the difference in airniass was < 0.2)., We corrected for telluric absorption with observations of $\alpha$ CMa obtained at a similar airmass as that of the science targets (the difference in airmass was $< 0.2$ ). + The spectra were flux calibrated using the low resolution spectra reported. by Furlan et ((2006)., The spectra were flux calibrated using the low resolution spectra reported by Furlan et (2006). + Roughly every 10 minutes. we took a serles of calibration Lames including blank sky. ancl an ambient temperature blackbody.," Roughly every 10 minutes, we took a series of calibration frames including blank sky and an ambient temperature blackbody." + The blackbody observations were used for flatfielding the data. while the sky emission line observations were used [or wavelength: calibration.," The blackbody observations were used for flatfielding the data, while the sky emission line observations were used for wavelength calibration." + The standard TEXES pipeline (Lacy et 22002) which produces waveleneth-calibrated one dimensional spectra. was used to reduce the data.," The standard TEXES pipeline (Lacy et 2002) which produces wavelength-calibrated one dimensional spectra, was used to reduce the data." + The wavelength solutions have an accuracy in velocity of ~Lkms|!, The wavelength solutions have an accuracy in velocity of $\sim 1\kms$. + One challenge associated with these observations is (hat the [Nell] line at 12.81 jim falls in a gap between two TEXES spectral orders., One challenge associated with these observations is that the [NeII] line at 12.81 $\mu$ m falls in a gap between two TEXES spectral orders. + By Gilling a mirror within the instrument. we are able to cover the gap by shifting the spectrum on the detector and (thereby accessing the Nell} line at the long wavelength end of one order or the short wavelength end of the next order.," By tilting a mirror within the instrument, we are able to cover the gap by shifting the spectrum on the detector and thereby accessing the [NeII] line at the long wavelength end of one order or the short wavelength end of the next order." + In the first case. the blaze efficiency rises toward the blue side of the line. while in the second ease. it rises toward the red side of the line.," In the first case, the blaze efficiency rises toward the blue side of the line, while in the second case, it rises toward the red side of the line." + During the night of 29 October. we shifted the optics to enhance the sensitivity on the red side of the [Nell] line.," During the night of 29 October, we shifted the optics to enhance the sensitivity on the red side of the [NeII] line." + We spent 2590 seconds of on-source integration time on GAL Aur and 3238 seconds on AA Tau in this instrument setup., We spent 2590 seconds of on-source integration time on GM Aur and 3238 seconds on AA Tau in this instrument setup. + The observed GAL Aur line appeared narrow. svnunetric. and centered at the stellar velocity while the emission from AA Tau was broad ancl vedward of the stellar velocity.," The observed GM Aur line appeared narrow, symmetric, and centered at the stellar velocity while the emission from AA Tau was broad and redward of the stellar velocity." + This led us to search for a line profile component that might be present blueward of the AA Tau stellar velocity on the following night., This led us to search for a line profile component that might be present blueward of the AA Tau stellar velocity on the following night. + We spent 2331 seconds of on-source integration Gime on AA Tau on the night of 30 October 2007. with our optics shifted to enhance the sensitivity on the blue side of the [Nell] line.," We spent 2331 seconds of on-source integration time on AA Tau on the night of 30 October 2007, with our optics shifted to enhance the sensitivity on the blue side of the [NeII] line." + The AA Tau data from the two separate nights were combined by interpolating onto a common wavelength scale aud. in the spectral regions where data Irom both nights were available. weighting the contribution [rom each night.," The AA Tau data from the two separate nights were combined by interpolating onto a common wavelength scale and, in the spectral regions where data from both nights were available, weighting the contribution from each night." + The weighting was used to account [or the varving noise across (he spectra in the overlap region: (he variation resulted primarily from the rising or falling blaze elliciency., The weighting was used to account for the varying noise across the spectra in the overlap region; the variation resulted primarily from the rising or falling blaze efficiency. + We therefore weighted each data point inversely. as the square of (he noise. which was calculated assuming (hat photon noise dominates.," We therefore weighted each data point inversely as the square of the noise, which was calculated assuming that photon noise dominates." + This weiehting is appropriate if the noise in the (wo spectra being combined add in euadrature., This weighting is appropriate if the noise in the two spectra being combined add in quadrature. + In practice. (he exact value of the weighting [actor had little effect on the combined spectrum.," In practice, the exact value of the weighting factor had little effect on the combined spectrum." +rate for the subsonic settling solution is determined by an inner boundary condition.,rate for the subsonic settling solution is determined by an inner boundary condition. + In that problem. a whole family of settling solutions exists.," In that problem, a whole family of settling solutions exists." + Each member of the family has a cilferent mass accretion rate. and it is the manner in which the gas cools ancl condenses on the accreting star that determines which particular solution. be. which 5. is selected.," Each member of the family has a different mass accretion rate, and it is the manner in which the gas cools and condenses on the accreting star that determines which particular solution, i.e., which $\dot m$, is selected." + We expect the same situation to apply to our problem., We expect the same situation to apply to our problem. + Unfortunately. this means that in order to estimate mowe have to solve the full. coupled hydrodynamic. and raciative transfer equations in the boundary. laver region next to the neutron star. with proper boundary. conditions.," Unfortunately, this means that in order to estimate $\dot m$ we have to solve the full coupled hydrodynamic and radiative transfer equations in the boundary layer region next to the neutron star, with proper boundary conditions." + We have not vet succeeded in this dillieult exercise., We have not yet succeeded in this difficult exercise. + The second problem that needs to be addressed: is the stability of the hot settling Low solution., The second problem that needs to be addressed is the stability of the hot settling flow solution. + Because the solution is hot. optically thin ancl satisfies the energy balance condition (5)). it is similar in. many noD to the hot solution discovered. by Shapiro et. al. ," Because the solution is hot, optically thin and satisfies the energy balance condition \ref{energy}) ), it is similar in many respects to the hot solution discovered by Shapiro et al. (" +AV,1976). + The latter is known be thermally very (c.g. Piran 1978)). and so one wonders whether the hot settling How might also be unstable.," The latter is known to be thermally very unstable (e.g., \citealp{P78}) ), and so one wonders whether the hot settling flow might also be unstable." + Phe thermal stability depends. in. particular. on the viscosity. prescription. chosen. as illustrated below (we thank the refe [or this simple argument).," The thermal stability depends, in particular, on the viscosity prescription chosen, as illustrated below (we thank the referee for this simple argument)." + With the prescription v=ecz/Ogree the low is unstable because qoxT while qxVT.," With the prescription $\nu=\alpha +c_s^2/\Omega_K$ the flow is unstable because $q^+\propto T$ while $q^-\propto\sqrt T$." + ence. a local increase of temperature results in an increase of the net heating rate q which leads to a further temperature increase.," Hence, a local increase of temperature results in an increase of the net heating rate $q^+ - q^-$ which leads to a further temperature increase." + However. for the viscosity. prescription given in equation (4)). we have qxVExqd .so that the Low is marginally stable.," However, for the viscosity prescription given in equation \ref{nu}) ), we have $q^+\propto\sqrt T\propto q^-$, so that the flow is marginally stable." + A more detailed analysis of the problem is bevonc the scope of the present paper., A more detailed analysis of the problem is beyond the scope of the present paper. + We finally comment on the relationship of the hot settling How discussed. in this paper to the subsonic propeller How described by Lkhsanov(2001.2003).," We finally comment on the relationship of the hot settling flow discussed in this paper to the subsonic propeller flow described by \citet{I01,I03}." +. Both Hows describe the braking action of hot gas on a spinning neutron star., Both flows describe the braking action of hot gas on a spinning neutron star. + The propeller Dow has been discussed. in connection with a stronely magnetized neutron star. while the hot settling flow was developed. to. model. acecretion onto an unmagnetizecl neutron star. but this is not a large distinction.," The propeller flow has been discussed in connection with a strongly magnetized neutron star, while the hot settling flow was developed to model accretion onto an unmagnetized neutron star, but this is not a large distinction." + The main cillerence between the two solutions is in the treatment of the energy. equation., The main difference between the two solutions is in the treatment of the energy equation. + In. Ikhsanov's subsonic propeller flow. the heating rate of the accreting eas through viscous dissipation is much larger than the radiative cooling rate.," In Ikhsanov's subsonic propeller flow, the heating rate of the accreting gas through viscous dissipation is much larger than the radiative cooling rate." + The eas becomes convective and isentropic. with density falling as +," The gas becomes convective and isentropic, with density falling as $r^{-3/2}$." + The solution is in some sense related to an adsyection-dominated accretion [ow (Naravan et al., The solution is in some sense related to an advection-dominated accretion flow (Narayan et al. + 1997) or a convection-dominated accretion ον(Naravan. lgumenshcehev Abramowicz 2000: Quataert Cruzinov 2000).," 1997) or a convection-dominated accretion flow (Narayan, Igumenshchev Abramowicz 2000; Quataert Gruzinov 2000)." + In contrast. the hot settling flow. as well as the two other solutions described in this paper. satisfy detailed: energy balance at each radius.," In contrast, the hot settling flow, as well as the two other solutions described in this paper, satisfy detailed energy balance at each radius." + The viscous heating at cach point is exactly balanced by local radiative cooling via optically thin bremsstrahlung. as indicated in equation (5) of the present paper.," The viscous heating at each point is exactly balanced by local radiative cooling via optically thin bremsstrahlung, as indicated in equation (5) of the present paper." + Furthermore. the density [alls olf ase7? and kr2I7? for solutions 1l and 2 rather than +2. the entropy. of the eas increases outward. and the gas is convectively stable (AINOL)," Furthermore, the density falls off as $r^{-2}$ and $r^{-7/2}$ for solutions 1 and 2 rather than $r^{-3/2}$, the entropy of the gas increases outward, and the gas is convectively stable (MN01)." + The authors are grateful. to the referee. for. helpful suggestions. and RN thanks Lars Uernquist for. useful discussions.," The authors are grateful to the referee for helpful suggestions, and RN thanks Lars Hernquist for useful discussions." + This work was supported in part bv NASA erant NAC5-107, This work was supported in part by NASA grant NAG5-10780. +Generic inflationary models predict that the initial,Generic inflationary models predict that the initial +attributed to the power-law component and is consistent with a constant thermal component.,attributed to the power–law component and is consistent with a constant thermal component. + The spectral properties of aare in full agreement with those observed in the other three persistent Be binary pulsars 4U 03524309. RX JO146.9+6121 and RX J1037.5-5647. thus confirming that the spectral component is à common property of this type of sources.," The spectral properties of are in full agreement with those observed in the other three persistent Be binary pulsars 4U 0352+309, RX J0146.9+6121 and RX J1037.5–5647, thus confirming that the spectral component is a common property of this type of sources." + Moreover. we have shown that the same type of feature has been detected also in other low-luminosity and long—period pulsars: therefore it is an ubiquitous phenomenon which requires further investigations.," Moreover, we have shown that the same type of feature has been detected also in other low–luminosity and long--period pulsars; therefore it is an ubiquitous phenomenon which requires further investigations." +"ew: =pand2d= 2£70""3Thou OM —dol!4362(p|HCN2CSd:(qu1)/SEThusalso ","Then $-\xi^2{d\theta \over d \xi} = \mu$ and ${d\mu \over +d\xi} = \xi^2 \theta^n$ , also $\xi^3{d\theta^{n+1} \over +d\xi}=(n+1)\xi^2\theta^n\xi^2{d\theta \over d\xi}/\xi = - +(n+1){\mu \over \xi} \ \ {d\mu \over d\xi}$." +Now write c=@| and take e to obey Furthermore choose oy so that ο20 at x., Thus Now write $\psi = \theta + \psi_1$ and take $\psi$ to obey Furthermore choose $\psi_1$ so that $\psi \rightarrow 0$ at $\infty$. + Ἠαιος where Tence which gives Ritter’s foriiulaNow Frou tables of polvtropes, Hence where Hence which gives Ritter's formulaNow From tables of polytropes +following fits we decided to use the photon imdoex and the normalization fixed to the best fit values found in Sl.,following fits we decided to use the photon index and the normalization fixed to the best fit values found in S4. + We leave the neutral ion Ίνα line fiux and centroid energy free to vary. since it is much easier to detect variability iu this slap feature with respect to a continuum component.," We leave the neutral iron $\alpha$ line flux and centroid energy free to vary, since it is much easier to detect variability in this sharp feature with respect to a continuum component." + This is a consistency test: even the common ΟΥ10111 of the iron Ίνα line aud he reflection component in our model. any variation of the former would invalidate our asstuuption.," This is a consistency test: given the common origin of the iron $\alpha$ line and the reflection component in our model, any variation of the former would invalidate our assumption." + Adopting the model described above. we then fitted the other three spectra and the new 2007 data.," Adopting the model described above, we then fitted the other three spectra and the new 2007 data." + In all cases. we found very good fits (sce Table 2 and Fie. 2)).," In all cases, we found very good fits (see Table \ref{bestfits} and Fig. \ref{bestplots}) )." + Allowing the frozen parameters to vary does not seuificautlv-[p improve. the fits* (whose reduced 47D are already very close to unitv). but only eularges he statistical uncertainties on the pariuneters.," Allowing the frozen parameters to vary does not significantly improve the fits (whose reduced $\chi^2$ are already very close to unity), but only enlarges the statistical uncertainties on the parameters." + All he main parameters of the model appears to be constant among the observations., All the main parameters of the model appears to be constant among the observations. + Iu particular. he neutral iron We line does not show auv sienificant variation. thus beiug consistent with our asstunption that the reprocessed coupoucuts roni Comptou-thick material are indecd coustaut.," In particular, the neutral iron $\alpha$ line does not show any significant variation, thus being consistent with our assumption that the reprocessed components from Compton-thick material are indeed constant." + As expected. no significant variability is found in the flux aud inodelizatioun of the sof Nouv cnussion. either.," As expected, no significant variability is found in the flux and modelization of the soft X-ray emission, either." + Therefore. he clear variability observed amoung he observations has to be ascribed to the vchavior of the iuner column density. the ouly xumanieter which sieuificantly changes between he observations (see Table 2. and Fig. 3)).," Therefore, the clear variability observed among the observations has to be ascribed to the behavior of the inner column density, the only parameter which significantly changes between the observations (see Table \ref{bestfits} and Fig. \ref{nhplot}) )." + The variatiou (from Tos71077 to L1«1075 7) )etwoeenu $2 aud 83 occurs in roughly 5 mouths., The variation (from $7\times10^{23}$ to $1.1\times10^{24}$ $^{-2}$ ) between S2 and S3 occurs in roughly 5 months. + A much shorter timescale. the 23 days separating he first from the second observation. witnesses another significant variation. from around 1.5 to τς10° cm 2.," A much shorter timescale, the 23 days separating the first from the second observation, witnesses another significant variation, from around $4.5$ to $7\times10^{23}$ $^{-2}$ ." + A still shorter timescale (ess than a dav) characterizes the variation from 3.3!ud to LIOSs1075 2 aneasured. between NMMUT and S1., A still shorter timescale (less than a day) characterizes the variation from $3.3^{+0.4}_{-0.5}$ to $4.4^{+0.3}_{-0.2}\times10^{23}$ $^{-2}$ measured between XMM07 and S1. + Iu conclusion. our best fit iiodoel allows us to ascribe inost of the observed spectral variability in NGC 7582 to the rapid changes of the colin deusitv of this internal absorber.," In conclusion, our best fit model allows us to ascribe most of the observed spectral variability in NGC 7582 to the rapid changes of the column density of this internal absorber." + On the other haud. there are some hints of variability of the primary contiuuuni intensity. but they are nof conclusive. given the large errors.," On the other hand, there are some hints of variability of the primary continuum intensity, but they are not conclusive, given the large errors." + The fowrth and latest observation caught the source at the lowest state. but this iudeed. allowed us to have a clearer view of the reprocessing coniponents of its spectrum. which apparently are those of a typical Sevtert 2.," The fourth and latest observation caught the source at the lowest state, but this indeed allowed us to have a clearer view of the reprocessing components of its spectrum, which apparently are those of a typical Seyfert 2." + The resulting scenario applies well to all other ταν observations of NGC 7582. the different states bemeg due ouly to the variability of the colum density of the imuer absorber.," The resulting scenario applies well to all other X-ray observations of NGC 7582, the different states being due only to the variability of the column density of the inner absorber." + In this section. we will discuss in detail the implications on the complex geometry of the absorbers required iu his source.," In this section, we will discuss in detail the implications on the complex geometry of the absorbers required in this source." + The intrinsic nuclear euission appears obscured * oa very large column density Gust below the ‘canonical Comptou-thick limit)., The intrinsic nuclear emission appears obscured by a very large column density (just below the `canonical' Compton-thick limit). + The spectra yclow 10 keV is therefore dominated by a Comptou reflection component aud the relative irou line., The spectrum below 10 keV is therefore dominated by a Compton reflection component and the relative iron line. + Both the fiux of the reflection component aud of he iron Lue are consistent with beiug coustaut diving the monitoring campaign and with he values found ia observations. he older dating back to 2001.," Both the flux of the reflection component and of the iron line are consistent with being constant during the monitoring campaign and with the values found in observations, the older dating back to 2001." + The material that xoduces. both comiponeuts is likely o be quite ar away from the nuclear X-ray cutting source. oossiblv in the classic pe-seale ‘torus’ mvoked im Unification Models (?)..," The material that produces both components is likely to be quite far away from the nuclear X-ray emitting source, possibly in the classic pc-scale `torus' invoked in Unification Models \citep{antonucci93}." + These reprocessing conipoueuts appears to (0 obseured by a second absorber. which must ο located farther away.," These reprocessing components appears to be obscured by a second absorber, which must be located farther away." + Its column density is rot well constrained iu the spectra. but is cousistent with the oue measured byNewton.. around 15s1072 cnPον," Its column density is not well constrained in the spectra, but is consistent with the one measured by, around $4-5\times10^{22}$ $^{-2}$." + It can ve identified with a laree scale obscuration. as he dust lanes commonly observed in galaxies.," It can be identified with a large scale obscuration, as the dust lanes commonly observed in galaxies." + Tudeed. the combined analysis of aud Ἱμασος clearly detected such a dust lane also in the N-vavs. with a column density consistent with the one required. by the spectral fits (2)..," Indeed, the combined analysis of and images clearly detected such a dust lane also in the X-rays, with a column density consistent with the one required by the spectral fits \citep{bianchi07b}." + Iu this case. the preseuce of a second. Compton-tlin absorber. as invoked iu simple modifications of the Unified Models (asin.2.audreferencestherein).. is directly observed.," In this case, the presence of a second, Compton-thin absorber, as invoked in simple modifications of the Unified Models \citep[as in][and references therein]{matt00b}, is directly observed." +" The soft N-rav enuüssou. as reported bv 7? thanks to the well-exposed Reflection Crating Spectrometer(RGS) high resolution spectra, appears dominated by cussion lines of"," The soft X-ray emission, as reported by \citet{pico07} thanks to the well-exposed Reflection Grating Spectrometer(RGS) high resolution spectra, appears dominated by emission lines of" +of the frozen-in field theorem is the conservation of magnetic flux inside the fluid.,of the frozen-in field theorem is the conservation of magnetic flux inside the fluid. +" This conservation principle does not imply that the conductive fluid cannot pass through magnetic field lines, only that the magnetic field lines entering a given fluid element are equal in number to those leaving the element at all times."," This conservation principle does not imply that the conductive fluid cannot pass through magnetic field lines, only that the magnetic field lines entering a given fluid element are equal in number to those leaving the element at all times." +" On the condition that the shape and the size of the conductive fluid do not change, two frozen examples are respectively shown in Fig."," On the condition that the shape and the size of the conductive fluid do not change, two frozen examples are respectively shown in Fig." + 6 and Fig., 6 and Fig. + 7., 7. +" In general, if the magnetic field intensity in the direction of travel of the conductive fluid changes, the conductive fluid will be acted upon by the frozen resistance."," In general, if the magnetic field intensity in the direction of travel of the conductive fluid changes, the conductive fluid will be acted upon by the frozen resistance." +" Further, when an individual charged particle crosses a magnetic field the Lorentz force will compel it to gyrate around the magnetic field lines."," Further, when an individual charged particle crosses a magnetic field the Lorentz force will compel it to gyrate around the magnetic field lines." +" However, within the conductive fluid, the appearances of polarization charges and a polarization electric field create a very different situation."," However, within the conductive fluid, the appearances of polarization charges and a polarization electric field create a very different situation." + Under some special conditions such as those illustrated in Figs., Under some special conditions such as those illustrated in Figs. +" 2, 4 and 5, the polarized electric field can counteract the Lorentz force and allow the conductive fluid to cross the magnetic field without any resistance."," 2, 4 and 5, the polarized electric field can counteract the Lorentz force and allow the conductive fluid to cross the magnetic field without any resistance." +" 'To illustrate the above analysis, we conducted a series of magnetohydrodynamic experiments."," To illustrate the above analysis, we conducted a series of magnetohydrodynamic experiments." + The main materials used in our experiments were liquid mercury and solid magnets., The main materials used in our experiments were liquid mercury and solid magnets. +" The mercury simulated the plasma, while the magnet simulated the pulsar."," The mercury simulated the plasma, while the magnet simulated the pulsar." +" For the sake of simplicity and clarity, our experiments were recorded as videos which are available at YouTube."," For the sake of simplicity and clarity, our experiments were recorded as videos which are available at YouTube." +" Briefly, the mercury is placed in a cylindrical trough surrounding a rotating platform with a receptacle for the solid magnet."," Briefly, the mercury is placed in a cylindrical trough surrounding a rotating platform with a receptacle for the solid magnet." + 'The experiments were divided into two subgroups., The experiments were divided into two subgroups. + 'The first consisted of three pairs of experiments whose purpose was to ascertain the conditions under which the magnet can drive rotation in the surrounding mercury., The first consisted of three pairs of experiments whose purpose was to ascertain the conditions under which the magnet can drive rotation in the surrounding mercury. + In each experiment our basis for comparison was an ατα cylindrically symmetric magnet whose magnetic axis is the same as the axis of rotation., In each experiment our basis for comparison was an: a cylindrically symmetric magnet whose magnetic axis is the same as the axis of rotation. + The three experiment pairs were as follows:, The three experiment pairs were as follows: +for their generation — remains elusive.,for their generation — remains elusive. + The tradiGonal theoretical approach to explaining the generation ol large-scale magnetic fields is via mean field electrodynanmies (see.forexample.Moffatt1978:KrauseRacller 1930).. an elegant theory of magnetohvdrodsanamie (ATID) turbulence in which the evolution of the mean (large-scale) field is governed bv a mean induction equation of the form where By represents (he mean magnetic field. Uy ihe mean velocitv. € the mean electromotive force (emf) and 7 the magnetic diffusivity.," The traditional theoretical approach to explaining the generation of large-scale magnetic fields is via mean field electrodynamics \citep[see, for example,][]{Moffatt78,KR80}, an elegant theory of magnetohydrodynamic (MHD) turbulence in which the evolution of the mean (large-scale) field is governed by a mean induction equation of the form where $\bfB_0$ represents the mean magnetic field, $\bfU_0$ the mean velocity, $\bfcalE$ the mean electromotive force (emf) and $\eta$ the magnetic diffusivity." + The term describing the mean en) which is the distinctive feature of equation (1)) in comparison wilh the unaveraged induction equation. is defined by where wu and 6 represent the (small-scale) [lactuating velocity and magnetic fields. and angle brackets denote a spatial average over intermediate scales.," The term describing the mean emf, which is the distinctive feature of equation \ref{eq:mean_ind}) ) in comparison with the unaveraged induction equation, is defined by where $\bfu$ and $\bfb$ represent the (small-scale) fluctuating velocity and magnetic fields, and angle brackets denote a spatial average over intermediate scales." + The closure of equation (1)) is usually brought about by postulating an expansion of € in terms of By and its spatial derivatives. where α and 8 are pseuco-lensors: Iughes&Proctor(2010) discuss a more general expansion procedure involving also temporal derivatives of the mean field.," The closure of equation \ref{eq:mean_ind}) ) is usually brought about by postulating an expansion of $\bfcalE$ in terms of $\bfB_0$ and its spatial derivatives, where $\bfalpha$ and $\bfbeta$ are pseudo-tensors; \citet{HP10} discuss a more general expansion procedure involving also temporal derivatives of the mean field." +" In the kinematic reeime. in which the field is assumed to exert no back-reaction on the flow. the components aj, and J), depend solely on the properties of the velocity. field and on the magnetic diffusivitv."," In the kinematic regime, in which the field is assumed to exert no back-reaction on the flow, the components $\alpha_{ij}$ and $\beta_{ijk}$ depend solely on the properties of the velocity field and on the magnetic diffusivity." +" The svamnietric part of the e tensor (the so-called *a-effect) leads to field amplification. and can be non-zero ouly inflows that lack vrellectional svinmetry. such as helical flows: in its simplest isotropic Dorm. in which 9),= σέ. the scalar 9 can be"," The symmetric part of the $\bfalpha$ tensor (the so-called $\alpha$ -effect') leads to field amplification, and can be non-zero only inflows that lack reflectional symmetry, such as helical flows; in its simplest isotropic form, in which $\beta_{ijk} = \beta \epsilon_{ijk}$ , the scalar $\beta$ can be" +halo er. is softened. by replacing 2 with vH7|0. where c2x 2hpe.,"halo $v_c$ is softened by replacing $R$ with $\sqrt{R^2+\epsilon^2}$, where $\epsilon\simeq2kpc$ ." + Phe Coulomb logarithm A was set to à constant (=)., The Coulomb logarithm $\Lambda$ was set to a constant $=8$ ). + We tried two prescriptions for the satellite mass mau: 1) the ‘virial’ mass m.(/). more exactly the mass of satellite particles within the original virial radius at the identification time: and 2) the selt-bound mass msa(£). defined in Section 7??7..," We tried two prescriptions for the satellite mass $m_{sat}$: 1) the `virial' mass $m_v(t)$, more exactly the mass of satellite particles within the original virial radius at the identification time; and 2) the self-bound mass $m_b(t)$, defined in Section \ref{sec:sb}." + The former was found to give the best results (a similar conclusion was reached by Navarro. Frenk White 1995). and was used for the results described.," The former was found to give the best results (a similar conclusion was reached by Navarro, Frenk White 1995), and was used for the results described." + The results are shown in Figure 4.., The results are shown in Figure \ref{fig:friction}. + Here we show the ratio of the theoretically predicted. to the measured quantities in terms of the median over all satellites in each mass bins (the same mass bins as defined for Figure 3))., Here we show the ratio of the theoretically predicted to the measured quantities in terms of the median over all satellites in each mass bins (the same mass bins as defined for Figure \ref{fig:orbits}) ). + In all cases the theoretical. prediction is rather good. for the two smallest. mass bins. and fails for the large mass satellites as they approach the centre.," In all cases the theoretical prediction is rather good for the two smallest mass bins, and fails for the large mass satellites as they approach the centre." + This is not surprising since the assumptions behind the simple orbit model break down when Al(2?) is comparable with ma., This is not surprising since the assumptions behind the simple orbit model break down when $M(R)$ is comparable with $m_{sat}$. + Lhe most drastic ellect. of the breakdown of the assumptions is the plunging of the theoretical orbits of the large satellites towards the centre of the parent cluster. with J/(7) and cCr) tending rapidly to zero.," The most drastic effect of the breakdown of the assumptions is the plunging of the theoretical orbits of the large satellites towards the centre of the parent cluster, with $J(\tau)$ and $\epsilon(\tau)$ tending rapidly to zero." + Even for these most massive satellites. however. the evolution up to 2 Gyr of ΕΤ) and (to a lesser extent) J(7) is wellenough reproduced by the theoretical calculations.," Even for these most massive satellites, however, the evolution up to $\sim 2$ Gyr of $R(\tau)$ and (to a lesser extent) $J(\tau)$ is wellenough reproduced by the theoretical calculations." + Thus. the decay. times can be accurately precieted.," Thus, the decay times can be accurately predicted." +ralio of radio to UV flux to characterize the radio loudness. The value of RL for each object in our sample is listed in Table 3..,"ratio of radio to UV flux to characterize the radio loudness, The value of RL for each object in our sample is listed in Table \ref{tab-flux}." + A histogram of these values and the distribution of RL with z for the sample objects are shown in Figure 15.., A histogram of these values and the distribution of RL with $z$ for the sample objects are shown in Figure \ref{fig:rl}. + The division between radio loud aud radio quiet was chosen to be RL=1.0., The division between radio loud and radio quiet was chosen to be RL=1.0. + The resulting values of log|J(54)] for these subsamples are listed in Table 4.., The resulting values of $J(\nu_{0})$ ] for these subsamples are listed in Table \ref{table-jnu}. + There is no significant trend for log|J(4))] to appear larger for radio loud objects than for radio quiet objects., There is no significant trend for $J(\nu_{0})$ ] to appear larger for radio loud objects than for radio quiet objects. + We performed (he maximum likelihood calculation for the case of a non-zero cosmological constant., We performed the maximum likelihood calculation for the case of a non-zero cosmological constant. + This means that the observer-QSO ancl absorber-OQS8O huninosity distances (hat appear in the relationship between w and 2 (BDO) must be calculated numerically [rom the expression: where (Peebles. 1993) as this integral cannot be reduced to an analytical form for (2440.," This means that the observer-QSO and absorber-QSO luminosity distances that appear in the relationship between $\omega$ and $z$ (BDO) must be calculated numerically from the expression: where (Peebles, 1993) as this integral cannot be reduced to an analytical form for $\Omega_{\Lambda} \neq 0$." +" The caleulations in the sections above assume (Q4,.04) = (1.0.0.0)."," The calculations in the sections above assume $\Omega_{\rm M}$ $\Omega_{\Lambda}$ ) = (1.0,0.0)." +" Here. we perform the maximum likelihood search lor (n) using (Q4,04) = (0.3.0.7)."," Here, we perform the maximum likelihood search for $J(\nu_{0}$ ) using $\Omega_{\rm M}$ $\Omega_{\Lambda}$ ) = (0.3,0.7)." + For a QSO at z=0.5 with a Lyman limit {his density of 0.1 j6(Jy. an absorber at z=0.43. and an assumed background of Jay )J= —22..," For a QSO at $z=0.5$ with a Lyman limit flux density of 0.1 $\mu$ Jy, an absorber at $z=0.48$, and an assumed background of $J(\nu_{0})$ $=-22$ .," + this (Q4.04) results in a value of o that is ~25% smaller Chan that inlerred in the 4=0 case., this $\Omega_{\rm M}$ $\Omega_{\Lambda}$ ) results in a value of $\omega$ that is $\sim 25$ smaller than that inferred in the $\Omega_{\Lambda}=0$ case. +" Unlike all (he other solutions performed. we ignore redshift path associated with metal lines and use all redshifts between z7;, and ~z£... Wax? "," Unlike all the other solutions performed, we ignore redshift path associated with metal lines and use all redshifts between $z_{\rm min}^{q}$ and $z_{\rm max}^{q}$ ." +"This does not change the results significantly. but cuts down the computation (time substantially,"," This does not change the results significantly, but cuts down the computation time substantially." + The results are listed in Table 4 and are plotted in Figure 11.., The results are listed in Table \ref{table-jnu} and are plotted in Figure \ref{fig:lowzcomp}. +" For comparison. we also give the solutions for J(,) Iound using the standard parameters. (04,04) = (1.0.0.0). with this redshift path neglected."," For comparison, we also give the solutions for $J(\nu_{0})$ found using the standard parameters, $\Omega_{\rm M}$ $\Omega_{\Lambda}$ ) = (1.0,0.0), with this redshift path neglected." + We find that (Q34.04) = (0.3.0.7). does not change the value of (24) derived significantly [rom the value found using (34.04) = (1.0.0.0).," We find that $\Omega_{\rm M}$ $\Omega_{\Lambda}$ ) = (0.3,0.7), does not change the value of $J(\nu_{0})$ derived significantly from the value found using $\Omega_{\rm M}$ $\Omega_{\Lambda}$ ) = (1.0,0.0)." + We performed a slightly modified re-analvsis of the Scott et (2000b) sample of objects al z~2 and— found little effect at hieh redshift as well., We performed a slightly modified re-analysis of the Scott et (2000b) sample of objects at $z \sim 2$ and found little effect at high redshift as well. + The solution found for (234.04) = (1.0.0.0) was ιτ—21.09ins while for (34.04) = (0.3.0.1).," The solution found for $\Omega_{\rm M}$ $\Omega_{\Lambda}$ ) = (1.0,0.0) was $J(\nu_{0})$ $=-21.09^{+0.20}_{-0.17}$, while for $\Omega_{\rm M}$ $\Omega_{\Lambda}$ ) = (0.3,0.7)," +final population of terrestrial planets formed and should be considered when these planets are involved.,final population of terrestrial planets formed and should be considered when these planets are involved. + We also have studied. the οσοι produced. by. the collisions between the embryos. where we find that most of the planets sulfer less than 5 impacts during its formation. which means that in most of the cases primordial spins of planets are randomly. determined. by a very. [ον impacts sullered. during accretion.," We also have studied the effects produced by the collisions between the embryos, where we find that most of the planets suffer less than 5 impacts during its formation, which means that in most of the cases primordial spins of planets are randomly determined by a very few impacts suffered during accretion." + We also take special attention to final spin state. which means planetary obliquities and rotation periods. where we found that the distribution of obliquities of final planets is well expressed. by an isotropic distribution. result. tha confirms those obtained previously by other authors Aenoretal.(1999):Kokubo&Ida(2007). and. is independen on the planetary mass.," We also take special attention to final spin state, which means planetary obliquities and rotation periods, where we found that the distribution of obliquities of final planets is well expressed by an isotropic distribution, result that confirms those obtained previously by other authors \citet{b13,b14} and is independent on the planetary mass." + ‘Phis fact is in marked contras o the terrestrial planets in our own Solar System. whose current spin axes are more or less perpendicular to their orbital planes (except for Venus).," This fact is in marked contrast to the terrestrial planets in our own Solar System, whose current spin axes are more or less perpendicular to their orbital planes (except for Venus)." + However. the spin axis of he terrestrial planets strongly depends on the gravitationa »erturbations from the other planets of the Solar System hat create a large chaotic zone for their obliquities.," However, the spin axis of the terrestrial planets strongly depends on the gravitational perturbations from the other planets of the Solar System that create a large chaotic zone for their obliquities." + So all of he terrestrial planets could have experienced large. chaotic variations in obliquity in their history. and this is why their obliquities can not be considered. as primordial (Laskar&tobutelSeen199c .," So all of the terrestrial planets could have experienced large, chaotic variations in obliquity in their history, and this is why their obliquities can not be considered as primordial \citep{b36}." + S0 presentthe fact that the terrestrial planets in our Solar obliquities O° does not necessarily indicate a problem with the model considered. here., So the fact that the terrestrial planets in our Solar System present obliquities $\sim 0^{\circ}$ does not necessarily indicate a problem with the model considered here. + Other studies such as body and atmospheric tides and core-mantle friction among others. must be taken into account [or explaining the present obliquities of the terrestrial planets.," Other studies such as body and atmospheric tides and core-mantle friction among others, must be taken into account for explaining the present obliquities of the terrestrial planets." + Regarding the findings on the rotation period. we found that the primordial rotation periods of terrestrial planets are dependent on the semi major axis. which means on the region where the embryos were formed and evolved.," Regarding the findings on the rotation period, we found that the primordial rotation periods of terrestrial planets are dependent on the semi major axis, which means on the region where the embryos were formed and evolved." + On the one hand. we note a very small population of planets with small rotation periods (less than 0.5 honrs). which are very rare planets. because at that rotation periods the spin angular velocities are high enough to overcome the critical rotation angular velocity for rotation instability.," On the one hand we note a very small population of planets with small rotation periods (less than $\sim 0.5 \; hours$ ), which are very rare planets, because at that rotation periods the spin angular velocities are high enough to overcome the critical rotation angular velocity for rotation instability." + On the other hand there are a large. population of embryos with rotation periods until 210000fos., On the other hand there are a large population of embryos with rotation periods until $\simeq 10000 \; hours$. + These planets with laree rotation periods probably acquired then mainly by the accretion of planetesimals. while those with shorter periods need one or more impacts for acquire that spin.," These planets with large rotation periods probably acquired them mainly by the accretion of planetesimals, while those with shorter periods need one or more impacts for acquire that spin." + Another important result. is that we have found a large population of planets with the characteristics of the ‘Terrestrial Planets. and our results suggest that they did not acquire their rotation period only by the accretion of planetesimals. but during one or more impacts during their formation.," Another important result is that we have found a large population of planets with the characteristics of the Terrestrial Planets, and our results suggest that they did not acquire their rotation period only by the accretion of planetesimals, but during one or more impacts during their formation." +"low-resolution (8z 10°, AA~1 À)) spectrum of HE 2347—4342 at A€1174Á.","low-resolution $R \approx 10^3$ , $\Delta \lambda \sim 1$ ) spectrum of HE $-$ 4342 at $\lambda \le 1174$." +" In principle, the COS/G140L wavelength coverage extends to very low wavelengths (~400 À))."," In principle, the COS/G140L wavelength coverage extends to very low wavelengths $\sim400$ )." +" However, the combination of low instrumental effective area, Acg~10 cm? at A ((McCandliss€1030 22010) and interstellar absorption by atomic and molecular hydrogen limit the working wavelength coverage."," However, the combination of low instrumental effective area, $A_{\rm eff} \sim 10$ $^{2}$ at $\lambda \la 1030$ (McCandliss 2010) and interstellar absorption by atomic and molecular hydrogen limit the working wavelength coverage." +" For the aabsorption toward HE 2347—4342, we present G140L data from 1030 SsA<1174A,, corresponding to zyere2.39—2.87."," For the absorption toward HE $-$ 4342, we present G140L data from 1030 $\la \lambda \le$ 1174, corresponding to $z_{\rm HeII} \approx 2.39-2.87$." +" We cross-calibrated the G140L segment-B spectrum with the short-wavelength data from G130M, finding that the flux calibration is better than in the overlap region."," We cross-calibrated the G140L segment-B spectrum with the short-wavelength data from G130M, finding that the flux calibration is better than in the overlap region." + 'The data were then used to extendour investigation of the ionization state in the IGM down to zpgar=2.39 (1030 À))., The data were then used to extendour investigation of the ionization state in the IGM down to $z_{\rm HeII} = 2.39$ (1030 ). +" Figure 3 provides a comparison among three spectrographs: COS/G130M, COS/G140L, and ((LiF1 and LiF2 channels)."," Figure 3 provides a comparison among three spectrographs: COS/G130M, COS/G140L, and (LiF1 and LiF2 channels)." +" There is a fair amount of agreement in fluxes among these instruments, although the bbackgrounds at 1160-1187 are obviously incorrect."," There is a fair amount of agreement in fluxes among these instruments, although the backgrounds at 1160–1187 are obviously incorrect." + This comparison givesus confidence in using G140L data down to 1030, This comparison givesus confidence in using G140L data down to 1030 . +"The first equation is just the advection of 5b, along the y direction. the second equation is a which enforces V«b=0.","The first equation is just the advection of $b_x$ along the $y$ direction, the second equation is a which enforces $\grad \cdot \bvec = 0$." + The key point to note here is that to enforce V-5b=0 we must ise the same EMF computed iu the advection step during the coustraint step: otherwise Vb=0 will only be zero up to truucation error., The key point to note here is that to enforce $\grad \cdot \bvec = 0$ we must use the same EMF computed in the advection step during the constraint step; otherwise $\grad \cdot \bvec = 0$ will only be zero up to truncation error. +" We accomplish this by fiucliug a secoud order accurate. ipwiud EMF v,6, for the advection step to update 6,. aud then inunediately use this same EMF or the coustraint step to update b."," We accomplish this by finding a second order accurate, upwind EMF $v_y +b_x$ for the advection step to update $b_x$, and then immediately use this same EMF for the constraint step to update $b_y$." + 2? first store the EME's over the entire 3D grid. then average he EMPE's. aud then update the field.," \citet{1998ApJ...509..244R} + first store the EMF's over the entire 3D grid, then average the EMF's, and then update the field." + We coustruct the EMP using Jin aud Xin's (1995) TWD uethod. which is described iu the appendix.," We construct the EMF using Jin and Xin's (1995) TVD method, which is described in the appendix." +" Note that the velocity D must be interpolated to he same position as the magnetic field 57.45"" with secoud order accuracy."," Note that the velocity $v^y_{ijk}$ must be interpolated to the same position as the magnetic field $b^x_{i-1/2,j,k}$ with second order accuracy." +" Jin aud Xiu's (1995) symmetric iuethod introduces a ""Παν freeziug speed” c. which must be ereater than or equal to the maximum speed at which information cau travel."," Jin and Xin's (1995) symmetric method introduces a “flux freezing speed"" $c$, which must be greater than or equal to the maximum speed at which information can travel." + Since we are holding the fluidvariables fixed. the flux freezing speed for the advection-coustraint equation is just e=[ey].," Since we are holding the fluidvariables fixed, the flux freezing speed for the advection-constraint equation is just $c=|v_y|$." + Now we brielly describe the fluid. update., Now we briefly describe the fluid update. + A more complete discussion is given in ?.., A more complete discussion is given in \citet{2003PASP..115..303T}. + The magnetic field is held fixed. aud iuterpolated to grid centers with secoud order accuracy.," The magnetic field is held fixed, and interpolated to grid centers with second order accuracy." + Let τε=ply.pese) represent the volume averaged quantities positioned at the center of each cell.," Let $\uvec=(u_1,u_2,u_3,u_4,u_5)=(\rho,\rho v_x,\rho v_y,\rho v_z,e)$ represent the volume averaged quantities positioned at the center of each cell." +" For advection aloug the ;e direction. the Euler. continuity. aud euergy ecquations can be written iu flux conservative fori as ""ET NV —Ui2li where the flux vector is given by and the pressure is determined by p—(51)(epe?/209/2)."," For advection along the $x$ direction, the Euler, continuity, and energy equations can be written in flux conservative form as _t + _x = 0 where the flux vector is given by and the pressure is determined by $p=(\gamma-1)(e-\rho v^2/2 - b^2/2)$." + We hold the magnetic field fixed duriug the [uid update. ancl interpolate 6 to cell centers for secoud order accuracy.," We hold the magnetic field fixed during the fluid update, and interpolate $\bvec$ to cell centers for second order accuracy." + Eq.21 can be solved by syiuuetric TVD. described in the appeucis.," \ref{eq:euler} can be solved by symmetric TVD, described in the appendix." + The flux freezing speed is: taken to be e=[e|+(5p/p/02g/p)9 F7. which⋅ is⋅ the maximum⋅ speed information⋅⋅⋅ can travel ?..," The flux freezing speed is taken to be $c=|v_x|+(\gamma p/\rho + b^2/\rho)^{1/2}$ , which is the maximum speed information can travel ." +The new formula (52)) allows us to deduce the mass of the galaxy [rom its absolute magnitude and ean be easily particularizec in different pass-bands.,The new formula \ref{massgalaxy}) ) allows us to deduce the mass of the galaxy from its absolute magnitude and can be easily particularized in different pass-bands. + As an example. with the data of SDSS in the five bands reported in Table 2... My. as in equation (16) of and HR as in Figure 15.. we have The method here suggested to deduce the mass of the galaxy. can be compared with the formula that comes out from the Twlly-Fisher relation. see Tully&Fisher(1977). and Tullyetal.(1998).," As an example, with the data of SDSS in the five bands reported in Table \ref{para_physical_SDSS_data} +, ${M}_{bol,\sun}$ as in equation (16) of \cite{blanton} and $R$ as in Figure \ref{masse}, we have The method here suggested to deduce the mass of the galaxy can be compared with the formula that comes out from the Tully-Fisher relation, see \cite{Tully1977} and \cite{Tully1998}." +. In the Tully-Fisher framework the mass of a rotating galaxy can be parameterisecl as where Vy is the rotational velocity expressed in Ansee MeGaugh(2005).," In the Tully-Fisher framework the mass of a rotating galaxy can be parameterised as where $V_f$ is the rotational velocity expressed in $\frac{Km}{s}$,see \cite{McGaugh2005}." +. The mass to light ratio in our framework scales xLY! with a depending on the selected catalog and band., The mass to light ratio in our framework scales $\propto L^{(1/a) -1}$ with $a$ depending on the selected catalog and band. +" This ratio oscillates . referring to the SDSS data. between a mininnun dependence in the g* band. uxxL""?! and a maximum dependence in the /* band. »xLP "," This ratio oscillates , referring to the SDSS data, between a minimum dependence in the $g^*$ band, $\frac{\mathcal{M}}{L}\propto L^{-0.24}$ and a maximum dependence in the $i^*$ band, $\frac{\mathcal{M}}{L}\propto L^{-0.42}$." +"A comparison should be made with +!xL'"" in vanderMarel(1991). [or a sample of 37 bright elliptical galaxies: Chis result was obtained by implementing axisvnuuetric dvnamical models.", A comparison should be made with $\frac{\mathcal{M}}{L}\propto L^{0.35}$ in \cite{vandermarel1991} for a sample of 37 bright elliptical galaxies; this result was obtained by implementing axisymmetric dynamical models. + The completeness of the mass sample of the galaxies belonging to a given catalog can be evaluated in the following wav., The completeness of the mass sample of the galaxies belonging to a given catalog can be evaluated in the following way. + The limiting apparent magnitude is known. and is different for each catalog.," The limiting apparent magnitude is known, and is different for each catalog." + In the case of the SDSS (G7 band) is m=17.6. see )..," In the case of the SDSS $r^*$ band) is $m$ =17.6, see \cite{blanton}." + The corresponding absolute limiting magnitude is computed and inserted in equation (52))., The corresponding absolute limiting magnitude is computed and inserted in equation \ref{massgalaxy}) ). +" The limiting mass lor galaxies. Mfg, is where ¢)2 is the radial distance expressed in fin/s."," The limiting mass for galaxies, ${\mathcal M}_L$ ,is where $c_Lz$ is the radial distance expressed in $km/s$ ." + In order tosee how Che parameter 2 influences the limiting mass. Table 7 reports the range of observable masses as a function of z.," In order tosee how the parameter $z$ influences the limiting mass, Table \ref{para_limiting} reports the range of observable masses as a function of $z$ ." +At the time of writing approximately 250 extrasolar planets have been discovered. of which about 30 are members of binary or multiple stellar systems (Eggenberger et al.,"At the time of writing approximately 250 extrasolar planets have been discovered, of which about 30 are members of binary or multiple stellar systems (Eggenberger et al." + 2004: Mugrauer et al., 2004; Mugrauer et al. + 2007)., 2007). + Most of the planets found in binaries orbit around one of the stellar component in so-called S-type orbits. and the majority of binaries harbouring planets have orbital separations ap=100 AU.," Most of the planets found in binaries orbit around one of the stellar component in so–called S–type orbits, and the majority of binaries harbouring planets have orbital separations $a_b \ge 100$ AU." + There are. however. exceptions to these cases.," There are, however, exceptions to these cases." +" The short period binary systems Gliese 86. y Cepheir and HD41004 have a,~20 AU. and contain planets orbiting at I - 2 AU from the central star (Eggenberger et al."," The short period binary systems Gliese 86, $\gamma$ Cephei and HD41004 have $a_b \sim 20$ AU, and contain planets orbiting at 1 - 2 AU from the central star (Eggenberger et al." + 2004: Mugrauer Neuhauser 2005)., 2004; Mugrauer Neuhauser 2005). + Although there are no known planets which orbit around both stellar companions in a binary system consisting of main sequence stars (1.8. circumbinary planets on so-called P-type orbits). there are two systems which indicate that the formation of circumbinary planets is feasible.," Although there are no known planets which orbit around both stellar companions in a binary system consisting of main sequence stars (i.e. circumbinary planets on so–called P-type orbits), there are two systems which indicate that the formation of circumbinary planets is feasible." +" The first is the circumbinary planet with mass i,=2.5 M; and orbital radius 23 AU observed in the radio pulsar PSR 1620-26 (Sigurdsson et al.", The first is the circumbinary planet with mass $m_p=2.5$ $_{J}$ and orbital radius 23 AU observed in the radio pulsar PSR 1620-26 (Sigurdsson et al. + 2003)., 2003). +" The second is the m,=2.44 M, planet orbiting about the system composed of the star HD202206 and its 17.4 M; brown dwarf companion (Udry et al.", The second is the $m_p=2.44$ $_{J}$ planet orbiting about the system composed of the star HD202206 and its 17.4 $_J$ brown dwarf companion (Udry et al. + 2002)., 2002). + The lack of observed cireumbinary planets is probably due to the fact that short period binaries are usually rejected from observational surveys., The lack of observed circumbinary planets is probably due to the fact that short period binaries are usually rejected from observational surveys. + The observation of planets in binary systems ts consistent with detections of circumstellar dises in. binary. systems., The observation of planets in binary systems is consistent with detections of circumstellar discs in binary systems. + Several circumbinary discs have been detected around spectroscopic binaries such as DQ Tau. AK Sco. and GW Orit.," Several circumbinary discs have been detected around spectroscopic binaries such as DQ Tau, AK Sco, and GW Ori." + The circumbinary dise around GG Tau has been directly imaged (Dutrey et al., The circumbinary disc around GG Tau has been directly imaged (Dutrey et al. + 1994). revealing the presence of a tidally truncated inner cavity generated by the central binary.," 1994), revealing the presence of a tidally truncated inner cavity generated by the central binary." + The existence of these circumbinary discs opens up the possibility of circumbinary planets forming., The existence of these circumbinary discs opens up the possibility of circumbinary planets forming. + Combining the observations of cireumbinary disces. with the fact that ~50% of solar-type stars are members of binaries (Duquennoy Mayor 1991). suggests that circumbinary planets are probably common.," Combining the observations of circumbinary discs, with the fact that $\sim 50 \%$ of solar-type stars are members of binaries (Duquennoy Mayor 1991), suggests that circumbinary planets are probably common." + To date there has been a relatively modest amount of theoretical work examining planet formation in binary systems., To date there has been a relatively modest amount of theoretical work examining planet formation in binary systems. + Results from previous studies suggest that planetesimal aceretion should be possible in regions of both circumstellar (Marzari Scholl 2000: Thebault et al., Results from previous studies suggest that planetesimal accretion should be possible in regions of both circumstellar (Marzari Scholl 2000; Thebault et al. + 2006) and circumbinary dises (Moriwaki Nakagawa 2004: Scholl et al., 2006) and circumbinary discs (Moriwaki Nakagawa 2004; Scholl et al. + 2007)., 2007). + Quintana Lissauer (2006) simulated the late stages of terrestial planet formation in eireumbinary discs., Quintana Lissauer (2006) simulated the late stages of terrestial planet formation in circumbinary discs. + They found that planetary systems similar to those around single stars can be formed around binaries. provided the ratio of the binary apocentre distance to planetary orbit is <0.2.," They found that planetary systems similar to those around single stars can be formed around binaries, provided the ratio of the binary apocentre distance to planetary orbit is $\le 0.2$." + In general binaries with larger maximum separations lead to planetary systems with fewer planets., In general binaries with larger maximum separations lead to planetary systems with fewer planets. + The evolution of a low mass planetary core embedded in à circumbinary dise. was investigated recently by Pierens Nelson (2007) (hereafter referred to as Paper D., The evolution of a low mass planetary core embedded in a circumbinary disc was investigated recently by Pierens Nelson (2007) (hereafter referred to as Paper I). +" This work examined the migration and long term orbital evolution of planets with masses of a,= 5. IO and 20 M. under the action of disc torques."," This work examined the migration and long term orbital evolution of planets with masses of $m_p=$ 5, 10 and 20 $M_\oplus$ under the action of disc torques." + It was found that the inward drift of a planet undergoing type | migration is stopped at the edge of the cavity formed by the binary., It was found that the inward drift of a planet undergoing type I migration is stopped at the edge of the cavity formed by the binary. + This halting of migration is due to positive corotation torques operating which can counterbalance negative Lindblad torques., This halting of migration is due to positive corotation torques operating which can counterbalance negative Lindblad torques. + Such an effect is known to be at work in accretion dise regions where there Is a strong positive gradient of the surface density (Masset et al., Such an effect is known to be at work in accretion disc regions where there is a strong positive gradient of the surface density (Masset et al. + 2006)., 2006). + Interestingly. Pierens Nelson (2007) showed that the stopping of migration in circumbinary dises occurs in a regtor of long-term dynamical stability. suggesting that such planets may be able to survive there over long times. or at least remait in the dise for long enough to form a gas giant planet.," Interestingly, Pierens Nelson (2007) showed that the stopping of migration in circumbinary discs occurs in a region of long-term dynamical stability, suggesting that such planets may be able to survive there over long times, or at least remain in the disc for long enough to form a gas giant planet." + The evolution of giant planets in eircumbinary dises was considerec by Nelson (2003)., The evolution of giant planets in circumbinary discs was considered by Nelson (2003). + In this paper. we extend the model presented in Paper I by considering the evolution of multiple planets embeddec in à circumbinary disc.," In this paper, we extend the model presented in Paper I by considering the evolution of multiple planets embedded in a circumbinary disc." + Here. we wish to examine how multiple planets interact with each other if they form at large distance from the binary and successively migrate towarc the cavity edge.," Here, we wish to examine how multiple planets interact with each other if they form at large distance from the binary and successively migrate toward the cavity edge." + In particular. we want to look at whether or not the trapping of a planet at the cavity edge. and the subsequent migration of additional planets to its vicinity lead to growth of the planet through collisions. the formation of mean motion resonances. or destablisation of the system through gravitational scattering.," In particular, we want to look at whether or not the trapping of a planet at the cavity edge, and the subsequent migration of additional planets to its vicinity lead to growth of the planet through collisions, the formation of mean motion resonances, or destablisation of the system through gravitational scattering." +" To address these issues. we first consider a system which consists of a pair of planets with masses of i,= 5. 10 and"," To address these issues, we first consider a system which consists of a pair of planets with masses of $m_p=$ 5, 10 and" +forward. boosting its velocity up to and. beyond. escape velocity.,"forward, boosting its velocity up to and beyond escape velocity." + The material emerges. from the magnetosphere and sails out of the binary svstem., The material emerges from the magnetosphere and sails out of the binary system. + This process etficientlv extracts energv and angular momentum from the white chvarl. transferring it via the long-range magnetic field to he stream material. which is expelled from the svstem.," This process efficiently extracts energy and angular momentum from the white dwarf, transferring it via the long-range magnetic field to the stream material, which is expelled from the system." + The ejected outflow consists of a broad equatorial fan of materia aunched over a range of azimuths on the side away from the Ix star., The ejected outflow consists of a broad equatorial fan of material launched over a range of azimuths on the side away from the K star. + The material stripped from the gas stream and threace »v the field [lines has a dillerent fate. one which we believe eives rise to the radio and X-ray emission.," The material stripped from the gas stream and threaded by the field lines has a different fate, one which we believe gives rise to the radio and X-ray emission." + This materia co-rotates with the magnetosphere while accelerating along iebld lines either. toward or away from. the white cdwarl under the inlluences of gravity and centrifugal forces., This material co-rotates with the magnetosphere while accelerating along field lines either toward or away from the white dwarf under the influences of gravity and centrifugal forces. + The small fraction of the total mass transfer that leaks below he co-rotation radius at 5Ry aceretes down. [elk ines producing the surface hotspots responsible for the 33s oscillations., The small fraction of the total mass transfer that leaks below the co-rotation radius at $\sim5~R_{\rm wd}$ accretes down field lines producing the surface hotspots responsible for the 33s oscillations. + Particles outside co-rotation remain trappe ong enough to accelerate up to relativistic energies through magnetic pumping. eventually reaching a sullicient. energy density to break away from the magnetosphere (Ixuijpersetal. LO97).," Particles outside co-rotation remain trapped long enough to accelerate up to relativistic energies through magnetic pumping, eventually reaching a sufficient energy density to break away from the magnetosphere \cite{kuijpers97}." +. The resulting ejection of balls of relativistic magnetized plasma is thought to give rise to the flaring radio emission (Bastian.Dulk&Chanmugam1988a:Bas-tian.Dulk&Chanmugam LOSSb).," The resulting ejection of balls of relativistic magnetized plasma is thought to give rise to the flaring radio emission \cite{bastian88a,bastian88b}." +. This paper addresses the optical anc ultraviolet variability seen in AL) Aqr., This paper addresses the optical and ultraviolet variability seen in AE Aqr. + In many studies the lighteurves exhibit dramatic Hares. with 1-10 minute rise and fall times (Patterson1979:vanParadijs.Kraakman&Ameron-σος1989:Bruch1901:Welsh.Lorne&Oke 1993).," In many studies the lightcurves exhibit dramatic flares, with 1-10 minute rise and fall times \cite{patterson79,paradijs89,bruch91,welsh93}." +. The Hares seem to come in clusters or avalanches of many super-imposed. individual [lares separated by quiet intervals. of &eraciuallv declining line and continuum emission (IE5racleous&Lorne1996:Patterson 1979).," The flares seem to come in clusters or avalanches of many super-imposed individual flares separated by quiet intervals of gradually declining line and continuum emission \cite{eracleous96,patterson79}." +. “Phese quiet. and [laring states tvpically last a few hours., These quiet and flaring states typically last a few hours. + Power spectra compute rom the lighteurves have a power-law form. with larger amplitudes on longer timescales.," Power spectra computed from the lightcurves have a power-law form, with larger amplitudes on longer timescales." + Elsworth&James(1982) [ound that the index in clx was -l., \scite{elsworth82} found that the index in $A\propto\nu^{\alpha}$ was -1. + That is. tha he amplitude of the flare or Llieker varies inversely as he frequency of its occurence.," That is, that the amplitude of the flare or flicker varies inversely as the frequency of its occurence." + Bruch(1992) examinec several datasets and found values for o in the range 0.71 1.64., \scite{bruch92} examined several datasets and found values for $\alpha$ in the range $-0.71$ $-1.64$. + Such power-law spectra are often. associated with »hysical processes involving self-organized criticality. for example earthquakes. snow or sandpile avalanches (Bak 1996).," Such power-law spectra are often associated with physical processes involving self-organized criticality, for example earthquakes, snow or sandpile avalanches \cite{bak96}." +. Similar red noise power spectra are seen in active galaxies. X-ray binaries. and other cataclysmic variables. and is therefore regarded: as characteristic of accreting sources in general.," Similar red noise power spectra are seen in active galaxies, X-ray binaries, and other cataclysmic variables, and is therefore regarded as characteristic of accreting sources in general." + However. flickering in other cataclysmic variables typically has an amplitude of (Bruch 1992).. contrasting with factors of several in AL! qr.," However, flickering in other cataclysmic variables typically has an amplitude of \cite{bruch92}, contrasting with factors of several in AE Aqr." + 1£ the mechanism is the same. then it must be weaker or dramatically eluted in other svstenis.," If the mechanism is the same, then it must be weaker or dramatically diluted in other systems." + The optical and ultraviolet: spectra of the IS. Aqr ares are not understood. at. present except in the most general terms., The optical and ultraviolet spectra of the AE Aqr flares are not understood at present except in the most general terms. + The lines and continua rise and fall together. with little change in the equivalent. widths or ratios of the emission lines (Eracleous&Lorne1996).," The lines and continua rise and fall together, with little change in the equivalent widths or ratios of the emission lines \cite{eracleous96}." +. This suggests hat the fares represent changes in the amount of material involved. more than changes in. physical conditions., This suggests that the flares represent changes in the amount of material involved more than changes in physical conditions. + The Balmer emission lines decay somewhat more slowly than the optical continuum perhaps revealing a recombination time delay (Welsh.Horne&Gomer1998)., The Balmer emission lines decay somewhat more slowly than the optical continuum – perhaps revealing a recombination time delay \cite{welsh98}. +. Ultraviolet. spectra rom LIST reveal a wide range of lines representing a diverse mux of ionization states and densities., Ultraviolet spectra from HST reveal a wide range of lines representing a diverse mix of ionization states and densities. + Eracleous&Llorne(19096) conclude: thus setting ai lower limit on the density range in the Uaring region., \scite{eracleous96} conclude: thus setting a lower limit on the density range in the flaring region. + Such spectra suggest. shocks., Such spectra suggest shocks. + “Phe emission. is. unusually weak. suggesting non-solar abundances.," The emission is unusually weak, suggesting non-solar abundances." + For example. carbon depletion may occur if CNO-processed. material is being transferred. from. the secondary star. which is an evolved star being whittled down by Roche lobe overflow.," For example, carbon depletion may occur if CNO-processed material is being transferred from the secondary star, which is an evolved star being whittled down by Roche lobe overflow." + So far no quantitative fts to the spectra have been achieved either by shock or photo-ionization models., So far no quantitative fits to the spectra have been achieved either by shock or photo-ionization models. + IUIS observations by Jameson.Wine&Sherrington(1980) derive an emission measure (VgV7) from Lye of 10m7., IUE observations by \scite{jameson80} derive an emission measure $V_{\rm HII}N_{\rm e}^{2}$ ) from $\alpha$ of $10^{61}~\mbox{m}^{-3}$. + UDVBI colour photometry. of [ares bv BeskrovnavaetaL(1996). &ive colour indices close to those for a blackbody in the 15000 20000Ix range with an emitting area 1079n., UBVRI colour photometry of flares by \scite{beskrovnaya96} give colour indices close to those for a blackbody in the $15~000$ $20~000$ K range with an emitting area $\sim10^{16}~\mbox{m}^{2}$. + What mechanism triggers these dramatic optical ancl ultraviolet. flares?, What mechanism triggers these dramatic optical and ultraviolet flares? + Clues come from. multi-waveleneth co-variability. and. orbital kinematics., Clues come from multi-wavelength co-variability and orbital kinematics. + Simultaneous VLA and optical observations show that the radio lux variations occur on similar timescales but are not. correlated with the optical anc ultraviolet. flares. which therefore require a clilferent mechanism CXbada-Simonetal.1995).," Simultaneous VLA and optical observations show that the radio flux variations occur on similar timescales but are not correlated with the optical and ultraviolet flares, which therefore require a different mechanism \cite{abada-simon95}." + Lt was proposed that the [ares represent modulations of the accretion rate onto the white cwarL. so that. they should be correlated with N-ray variability.," It was proposed that the flares represent modulations of the accretion rate onto the white dwarf, so that they should be correlated with X-ray variability." + Some correlation was found. but the correlation is not high.," Some correlation was found, but the correlation is not high." + However. LST observations discard this model. because the ultraviolet oscillation amplitude is unmoved by transitions between the «quiet. ancl [laring states (IE£racleous.&Llorne1996).," However, HST observations discard this model, because the ultraviolet oscillation amplitude is unmoved by transitions between the quiet and flaring states \cite{eracleous96}." +.. This disconnects the origins of the oscillations and Lares. and the oscillations arise [rom accretion onto the white dwarl. so the lares must arise elsewhere.," This disconnects the origins of the oscillations and flares, and the oscillations arise from accretion onto the white dwarf, so the flares must arise elsewhere." + Further clues come from emission line kinematics., Further clues come from emission line kinematics. + The emission line profiles may be. roughly. described as broad Caussianswith widths ~1000 kms+. though they often exhibit kinks and sometimes multiple peaks.," The emission line profiles may be roughly described as broad Gaussianswith widths $\sim1~000$ km $^{-1}$, though they often exhibit kinks and sometimes multiple peaks." + Detailed study olf the Balmer lines (Welsh.Horne&Comer1998). indicates that the new light appearing during a are can have emission lines shifted from the line centroid and somewhat narrower. ~300 km +.," Detailed study of the Balmer lines \cite{welsh98} indicates that the new light appearing during a flare can have emission lines shifted from the line centroid and somewhat narrower, $\sim300$ km $^{-1}$ ." + Individual Bares therefore. occupy. only a subset of the entire emission-line region., Individual flares therefore occupy only a subset of the entire emission-line region. + The emission line centroid velocities vary sinusoldally with orbital phase. with semi-amplitudes ~200 km + and maximum redshift near phase 70.8," The emission line centroid velocities vary sinusoidally with orbital phase, with semi-amplitudes $\sim200$ km $^{-1}$ and maximum redshift near phase $\sim$ 0.8" +"force CMaedoer 2003)) which acts horizoutallv. ie. r/(Q5P Vo), oue obtainsB the Bfollowing. coefficientm This expression. despite ifs differeuce with respect fo Eq. (8)).","force \cite{Mturb03}) ) which acts horizontally, i.e. $t_{\mathrm{diff}} \, \approx\, {r}/({\Omega_2 \, V_2} )^{1/2}$ , one obtains the following coefficient This expression, despite its difference with respect to Eq. \ref{o2}) )," +" leads to sula uunerica values for the horizoutal turmleuce in stellar models (Mathisetal. 2001)). while the original estimate (Zahn 1992)) leads to a coefficient Dy, smaller by four orders of a 1naenitucdo."," leads to similar numerical values for the horizontal turbulence in stellar models \cite{MathisPZ04}) ), while the original estimate (Zahn \cite{Zahn92}) ) leads to a coefficient $D_{\mathrm{h}}$ smaller by four orders of a magnitude." +" The expression of 14, requires that we know the vertica aud horizontal coupoucuts C5 and V of the velocity of meridional circulation.", The expression of $\nu_{\mathrm{h}}$ requires that we know the vertical and horizontal components $U_2$ and $V_2$ of the velocity of meridional circulation. + Tf not. some approximations are eiven in the Appcucdix.," If not, some approximations are given in the Appendix." + We examine what happens to the condition (5)) or Solbere-Ioiluid criterion in case of thermal diffusivity and lorizoutal turbulence., We examine what happens to the condition \ref{gsfmu}) ) or Solberg-Hoiland criterion in case of thermal diffusivity and horizontal turbulence. + For that let us start from the BiuntVaisalla frequency in a rotating star at colatitude Ü If it is negative. the medium is unstable.," For that let us start from the Brunt–Väiisällä frequency in a rotating star at colatitude $\vartheta$ If it is negative, the medium is unstable." + Vi is the internal eracdicut iu a displaced fluid clement. while V is the eracicut in the ambient medium.," $\nabla_{\mathrm{int}}$ is the internal gradient in a displaced fluid element, while $\nabla$ is the gradient in the ambient medium." +" These eradieuts obey to the relations (Alaeder 1995)) For a fluid clement movingC» at velocity Poi:ο over a distance (, D=Pef6cf(68). where Pe is the Peclet προς. Lie. the ratio of the hermal to the dynamical timescale."," These gradients obey to the relations \cite{M95}) ) For a fluid element moving at velocity $v$ over a distance $\ell$ , $\Gamma=Pe/6=v \ell/(6 K)$, where $Pe$ is the Peclet number, i.e. the ratio of the thermal to the dynamical timescale." + [ois the ratio of the energy. transported to the οποιον lost on the way f., $\Gamma$ is the ratio of the energy transported to the energy lost on the way $\ell$. + The jorizoutal turbulence adds it» contribution to the radiative heat transport aud TP becomes (Talon&Ζαΐπι 1997)) The ratio DAT.| 1)iu Eq. (12)), The horizontal turbulence adds its contribution to the radiative heat transport and $\Gamma$ becomes \cite{TZ97}) ) The ratio $\Gamma/(\Gamma+1)$ in Eq. \ref{G+1}) ) + is the fraction of the energy transported., is the fraction of the energy transported. +" The GSP instability problem is 2D with two different coupled geoirctrics: the cvlindrical oue associated to the rotation with the restoring force being along ὃς aud the spherical one where the eutropy aud chemical straticatiou restoring force is along 6, that explains the in Eq. (113)."," The GSF instability problem is 2D with two different coupled geometries: the cylindrical one associated to the rotation with the restoring force being along $\widehat{\mathbf e}_s$ and the spherical one where the entropy and chemical stratication restoring force is along $\widehat{\mathbf e}_r$ that explains the $\,\vartheta$ in Eq. \ref{Ncomplet}) )," + which gives the radial component of the total restoring force., which gives the radial component of the total restoring force. + The following foriiula for No in spherical ecometry iu the case of a shiellular rotation QC) can be obtained: starting: with: Eq. (2)::, The following formula for $N^2_{\Omega}$ in spherical geometry in the case of a shellular rotation $\overline{\Omega}(r)$ can be obtained: starting with Eq. \ref{ineg}) ): + N5=?=lIisto?)VistO?)2. and then introducing splerical coordinates.," $N^2_{\Omega}=\frac{1}{s^3} \frac{{\rm d}(s^4\Omega^2)}{{\rm d}s} +=\frac{1}{s^3} \vec{\nabla}(s^4\Omega^2)\cdot \widehat{\mathbf e}_s$ and then introducing spherical coordinates." + Frou now on. in order to simplify the problem. we will focus ou the equatorial plane (0=7/2). in which case we simply have: The horizontal turbulence also makes some exchanges between a inoviug fluid clement with composition given by Hine aud its surroundings with nean molecular weight yr.," From now on, in order to simplify the problem, we will focus on the equatorial plane $\vartheta= \pi/2$ ), in which case we simply have: The horizontal turbulence also makes some exchanges between a moving fluid element with composition given by $\mu_{\mathrm{int}}$ and its surroundings with mean molecular weight $\mu$." +" Tt f, is the amount of ji trausported expressed 1i fraction of the external 8eradieut. oue las Ono canVu also write fy,τμαμ!1). where E, is the ratio of amount of jj transported to that lost by the fluid clement ou its wav."," If $f_{\mu}$ is the amount of $\mu$ transported expressed in fraction of the external gradient, one has One can also write $f_{\mu}= \Gamma_{\mu}/(\Gamma_{\mu}+1)$, where $\Gamma_{\mu}$ is the ratio of amount of $\mu$ transported to that lost by the fluid element on its way." + Thus. oue has to be compared to the first partof Eq. 12.," Thus, one has to be compared to the first partof Eq. \ref{G+1}." +. If N?<0. the inediu is unstable. thus the instability coucition at the equator becomes The situation is DIIsimilar to the effect of horizoutal turbulence in the case of the shear instability (Talon&Zahu 1997)).," If $N^2 < 0$, the medium is unstable, thus the instability condition at the equator becomes The situation is similar to the effect of horizontal turbulence in the case of the shear instability \cite{TZ97}) )." + The turbulent eddies with the largest sizes c=ef/6 are those which eive the largest contribution to the vertical transport., The turbulent eddies with the largest sizes $x=v \ell/6$ are those which give the largest contribution to the vertical transport. +" For these eddics. the equalityiu (18)) is satisfied. which gives The cINID,ciffusiou coefficieut by Dythe CSF instability is Dog= 2a. obtained from the solution of this second order equation. which may also be written. We notice several interesting properties."," For these eddies, the equalityin \ref{rim}) ) is satisfied, which gives The diffusion coefficient by the GSF instability is $D_{\mathrm{GSF}}=(1/3) v \ell=2x$ , obtained from the solution of this second order equation, which may also be written, We notice several interesting properties." +A possible source of energy injection is the power emitted by a spinning-down newly-born magnetar (Dai&Lu1998;Zhang&Mészáros2001:CorsiMeészaros2009) that refreshes the forward shock (see Dall'Ossoetal.2011. for an analytic treatment of this problem).,"A possible source of energy injection is the power emitted by a spinning-down newly-born magnetar \citep{1998A&A...333L..87D,2001ApJ...552L..35Z,2009ApJ...702.1171C} that refreshes the forward shock (see \citealt{2011A&A...526A.121D} for an analytic treatment of this problem)." + We appliedthe solution of Dall'Ossoetal.(2011) to our sample (details are given in Appendix ??)). and we find that it fits the observed light curves well enough.," We appliedthe solution of \citet{2011A&A...526A.121D} to our sample (details are given in Appendix \ref{app_magnetar}) ), and we find that it fits the observed light curves well enough." + This is independent of the presence of flares (see Table B 1). provided that the light curve’s normal decay agrees with the forward shock modelpredictions?.," This is independent of the presence of flares (see Table \ref{tab_magnetar}) ), provided that the light curve's normal decay agrees with the forward shock model." +. The major advantage of this interpretation is that all the plateau properties are directly related to the central engine and. consequently. to the prompt emission.," The major advantage of this interpretation is that all the plateau properties are directly related to the central engine and, consequently, to the prompt emission." + This explains the connection between the plateau energy and the prompt emission energy., This explains the connection between the plateau energy and the prompt emission energy. + The basic information can be derived from two main quantities: the magnetic field B and the period P of the pulsar., The basic information can be derived from two main quantities: the magnetic field $B$ and the period $P$ of the pulsar. +" In particular. they are all that is neededto explain the anticorrelation between the plateau luminosity L, and the second break time 75»=f, found by Dainottietal.(2008. 2010).."," In particular, they are all that is neededto explain the anticorrelation between the plateau luminosity $L_p$ and the second break time $t_{b2}=t_p$ found by \citet{2008MNRAS.391L..79D,2010ApJ...722L.215D}. ." + Starting from the distributions of B and P from our sample (see Appendix ??)). we obtained the normalisation. the slope. and the scatter of the observed anticorrelatio (Fig. 6;," Starting from the distributions of $B$ and $P$ from our sample (see Appendix \ref{app_magnetar}) ), we obtained the normalisation, the slope, and the scatter of the observed anticorrelation (Fig. \ref{LTcorr};" + for details see Appendix ??))., for details see Appendix \ref{app_magnetar}) ). + We underline that these distributions are within the range of values expected for newly born. millisecond spinning magetars (Duncan& 1992)..," We underline that these distributions are within the range of values expected for newly born, millisecond spinning magnetars \citep{1992ApJ...392L...9D}." + We plot in Fig., We plot in Fig. +" 6. the luminosity at the break time L(tp,) of Type Ia light curves in the rest frame energy banc corresponding to =2.29. and we find that they follow the same luminosity-time anticorrelation and that they can be interpreted as the spin-down luminosity of a millisecond pulsar for the same distribution of B and P as for Type II."," \ref{LTcorr} the luminosity at the break time $L(t_{b1})$ of Type Ia light curves in the rest frame energy band corresponding to $\tilde{z}=2.29$, and we find that they follow the same luminosity-time anticorrelation and that they can be interpreted as the spin-down luminosity of a millisecond pulsar for the same distribution of $B$ and $P$ as for Type II." + We add to Fig., We add to Fig. + 6 last Type Ib observation as a lower limit on the end of the injection phase and an upper limit on the luminosity., \ref{LTcorr} last Type Ib observation as a lower limit on the end of the injection phase and an upper limit on the luminosity. + The possibility of having injection times up to 10° s. as observed in Type Ib light curves. is allowed within reasonable values of the magnetic field and period (see Fig. 6)).," The possibility of having injection times up to $10^5$ s, as observed in Type Ib light curves, is allowed within reasonable values of the magnetic field and period (see Fig. \ref{LTcorr}) )." +" However. the upper limit on luminosity found for some Type Ib is much lower than the expected one. unless we assume that the injection time is z10° s, We argue that a different beaming factor and/or efficiency in converting the spin-down power in X-rays may account for such Type Ib light curves."," However, the upper limit on luminosity found for some Type Ib is much lower than the expected one, unless we assume that the injection time is $\gtrsim 10^6$ s. We argue that a different beaming factor and/or efficiency in converting the spin-down power in X-rays may account for such Type Ib light curves." + The main constraints of the magnetar model is related to the energy budget., The main constraints of the magnetar model is related to the energy budget. + The maximum energy emitted in such a model is a few 1077 erg and limited by the maximum rotation energy attainable by a rotating neutron star (Usov 1992).. , The maximum energy emitted in such a model is a few $10^{52}$ erg and limited by the maximum rotation energy attainable by a rotating neutron star \citep{1992Natur.357..472U}. . +The energy budget strongly depends on the uncertain estimate of the jet angle. however in a few cases the released energy may be high enough to challenge the nodel (Cenkoetal.2010)..," The energy budget strongly depends on the uncertain estimate of the jet angle, however in a few cases the released energy may be high enough to challenge the model \citep{2010ApJ...711..641C}." + The plateau phase in the accretion model of Kumaretal.(2008) is triggered if the progenitor star has a core-envelope structure., The plateau phase in the accretion model of \citet{2008MNRAS.388.1729K} is triggered if the progenitor star has a core-envelope structure. + An analysis of Type II light curves with this model has been presented by Cuietal.(2010).., An analysis of Type II light curves with this model has been presented by \citet{2010MNRAS.401.1465C}. + They inferred properties of the progenitor star based on the timescales and energeties. although they assume that the initial steep decay is not produced by the central engine.," They inferred properties of the progenitor star based on the timescales and energetics, although they assume that the initial steep decay is not produced by the central engine." + This approach is very effective in obtaining some indications about the progenitor star structure., This approach is very effective in obtaining some indications about the progenitor star structure. + In Sect., In Sect. + 2? we show that a quasi-linear correlation exists between shallow decay energy and the prompt emission total energy for the light curves with and without flares. extending the relation between the plateau energy and the prompt emission energy observed in 15—150 keV previously found by Liangetal.(2007) (seealsoCuietal.2010).," \ref{energy} we show that a quasi-linear correlation exists between shallow decay energy and the prompt emission total energy for the light curves with and without flares, extending the relation between the plateau energy and the prompt emission energy observed in $15-150$ keV previously found by \citet{2007ApJ...670..565L} \citep[see also][]{2010MNRAS.401.1465C}." + It implies that the progenitor star has a self-similar structure. with a constant envelope-to-core mass ratio ~0.02+0.03.," It implies that the progenitor star has a self-similar structure, with a constant envelope-to-core mass ratio $\sim 0.02\div 0.03$." + This is valid for Type IL. as shown by Cuietal.(2010).. but also for Type Ia. where similar injection times (see Table 2)) point to similar dimensions of the progenitor star.," This is valid for Type II, as shown by \citet{2010MNRAS.401.1465C}, but also for Type Ia, where similar injection times (see Table \ref{tab_median}) ) point to similar dimensions of the progenitor star." + The slightly different distribution in the power-law indices of the two cases (see Table 2)) can be ascribed to a possibly different typical accretion rate of the envelope (see e.g. Kumaretal.2008.. their Fig.," The slightly different distribution in the power-law indices of the two cases (see Table \ref{tab_median}) ) can be ascribed to a possibly different typical accretion rate of the envelope (see e.g. \citealt{2008MNRAS.388.1729K}, their Fig." + 7)., 7). + However. in Sect.," However, in Sect." + 2? we show that the shallow decay in Type Ib is closely related to the one in Types Ia and II., \ref{class} we show that the shallow decay in Type Ib is closely related to the one in Types Ia and II. + This poses severe problems to this scenario., This poses severe problems to this scenario. + In fact. itis very difficult to obtain a shallow decay duration z107 s. since such an extended envelope is more probably ejected during the main burst (Kumaretal.2008).," In fact, it is very difficult to obtain a shallow decay duration $\gtrsim 10^4$ s, since such an extended envelope is more probably ejected during the main burst \citep{2008MNRAS.388.1729K}." + The forward shock emission is expected to give a significant contribution to the X-ray light curve after the fading of the prompt emission (seee.g.Zhangetal.2006.andref-erences therein)..., The forward shock emission is expected to give a significant contribution to the X-ray light curve after the fading of the prompt emission \citep[see e.g.][and references therein]{2006ApJ...642..354Z}. + The shape of the light curve depends on the density profile of the ambient medium (Sarietal.1998;Chevalier&Li2000) and the temporal and spectral indices should satisfy specific closure relations (Zhang&Mészáros 2004)..," The shape of the light curve depends on the density profile of the ambient medium \citep{1998ApJ...497L..17S,2000ApJ...536..195C} and the temporal and spectral indices should satisfy specific closure relations \citep{2004IJMPA..19.2385Z}." + Figure 7. shows that 80% of Type II light curves matches the expectations of the standard afterglow model in the slow cooling regime within 1c. 90% of the second segment of Type Ia. and 77% of Type O0 light curves.," Figure \ref{abI} shows that $80\%$ of Type II light curves matches the expectations of the standard afterglow model in the slow cooling regime within $1 \sigma$, $90\%$ of the second segment of Type Ia, and $77\%$ of Type 0 light curves." + This connection is favoured in Type Ia and IL light curves by the absence of spectral variation during the transition. from the previous injection phase (see Fig. 2))., This connection is favoured in Type Ia and II light curves by the absence of spectral variation during the transition from the previous injection phase (see Fig. \ref{BETAtype}) ). + If we include Type II GRBs of the sample analysed in Marguttietal. (2011)... we find that 84% are consistent with one of the above cases.," If we include Type II GRBs of the sample analysed in \citet{2011MNRAS.410.1064M}, , we find that $84\%$ are consistent with one of the above cases." + If the origin of the plateau phase is injectionof energy from a millisecond pulsar into the forward shock (Dall'Osso therein). after theplateau we expect that the light curves follow the standard afterglow scenario. as we find for the majority of cases.," If the origin of the plateau phase is injectionof energy from a millisecond pulsar into the forward shock \citep[][and references therein]{2011A&A...526A.121D}, , after theplateau we expect that the light curves follow the standard afterglow scenario, as we find for the majority of cases." + Alternatively. the accretion," Alternatively, the accretion" +permeates massive galaxies and galaxy clusters.,permeates massive galaxies and galaxy clusters. + Essentially. this conceptuatises AGN feedback as ai control svstem. similar to a thermostat (ef.?7)..," Essentially, this conceptualises AGN feedback as a control system similar to a thermostat \citep[c.f.][]{stats}." + This approach can be highly informative: ACN) feedback. is an extremely complex phenomenon which depends on poorly understood physical. processes occurring across a huge range of spatial scales., This approach can be highly informative; AGN feedback is an extremely complex phenomenon which depends on poorly understood physical processes occurring across a huge range of spatial scales. + As vet. numerical hyerodvnanmic simulations co not include sullicient. physical processes to naturally. reproduce observations without being complemented. by additional numerical prescriptions.," As yet, numerical hydrodynamic simulations do not include sufficient physical processes to naturally reproduce observations without being complemented by additional numerical prescriptions." + Yet. even if the simulations were physically complete. the outcomes would. still need. to be interpreted.," Yet, even if the simulations were physically complete, the outcomes would still need to be interpreted." + For this reason. we investigate AGN feedback in. the most general wav. by expressing its overall effect in terms of well-defined. global quantities. ancl comparing the main results with observations.," For this reason, we investigate AGN feedback in the most general way, by expressing its overall effect in terms of well-defined global quantities, and comparing the main results with observations." + For example. consider the simplest case. in which AGN heating is regulated only by negative fecdback.," For example, consider the simplest case, in which AGN heating is regulated only by negative feedback." + Negative feedback. can be defined as a response which occurs to oppose its cause., Negative feedback can be defined as a response which occurs to oppose its cause. + Pherefore. unless forced to do otherwise. it will tend to minimise deviations from some equilibrium condition.," Therefore, unless forced to do otherwise, it will tend to minimise deviations from some equilibrium condition." + Thus. in general. a system regulated purelv by negative feedback: will rapidly tend: towards a steady state in which the controller is permanently. active ab a constant value.," Thus, in general, a system regulated purely by negative feedback will rapidly tend towards a steady state in which the controller is permanently active at a constant value." + Notably. this does not appear to be the case for AGN feedback. and it is imperative to note that minimising deviations from an equilibrium state is only one measure of the performance of feedback.," Notably, this does not appear to be the case for AGN feedback, and it is imperative to note that minimising deviations from an equilibrium state is only one measure of the performance of feedback." + Depending on additional constraints it can also be favourable to minimise other quantities. such as the energy. invested in controlling the svstem.," Depending on additional constraints it can also be favourable to minimise other quantities, such as the energy invested in controlling the system." + Importantly. à system regulated. by feedback subject to additional constraints generally. behaves quite dilferently to the simplest. case described above.," Importantly, a system regulated by feedback subject to additional constraints generally behaves quite differently to the simplest case described above." + The choice of constraint adopted in. this article is influenced by (wo. principle sets of. observations., The choice of constraint adopted in this article is influenced by two principle sets of observations. + In particular. radio data (e.g.777). can be used to infer the fraction of time (duty evele) an AGN spends. producing kinetic outllows. which couple strongly to the ambient gas.," In particular, radio data \citep[e.g.][]{best05,best08,shab08} can be used to infer the fraction of time (duty cycle) an AGN spends producing kinetic outflows, which couple strongly to the ambient gas." + Vherefore. a feedback. model which vields continual and constant heating would appear to be inconsistent with data.," Therefore, a feedback model which yields continual and constant heating would appear to be inconsistent with data." + In addition. any appropriate model must also grow black oles of the masses we observe.," In addition, any appropriate model must also grow black holes of the masses we observe." + For example. ?. found that. in some cases. the accretion cnerey liberated. in. growing he supermassive black holes at cluster centres seems to be insullicient to have olfset the ICM. X-ray. luminosity over he lifetimes of the clusters.," For example, \cite{smbh04} found that, in some cases, the accretion energy liberated in growing the supermassive black holes at cluster centres seems to be insufficient to have offset the ICM X-ray luminosity over the lifetimes of the clusters." + Phat is. the some black hole masses are lower than expected.," That is, the some black hole masses are lower than expected." + As a result. the aim of this article is to find a plausible constraint which forces a simple eedback svstem to exhibit features that are broadly similar o these observations: heating should. proceed in the form of discrete events and at low black hole growth rates. while still balancing gas cooling.," As a result, the aim of this article is to find a plausible constraint which forces a simple feedback system to exhibit features that are broadly similar to these observations; heating should proceed in the form of discrete events and at low black hole growth rates, while still balancing gas cooling." + Guided. by. these observations. we investigate an enerectically favourable. model in which feedback heating acts to balance gas cooling. but is also constrained to minimise the total energy output of the system.," Guided by these observations, we investigate an energetically favourable model in which feedback heating acts to balance gas cooling, but is also constrained to minimise the total energy output of the system." + This means that. feedback. minimises the sum. of the energy. racdiated bv the N-rav emitting gas the energy injected by the AGN. which is equivalent. to balancing gas cooling with the minimum black hole growth.," This means that feedback minimises the sum of the energy radiated by the X-ray emitting gas the energy injected by the AGN, which is equivalent to balancing gas cooling with the minimum black hole growth." + Such constraints are implemoented. with the minimum number of assumptions. by emploving optimal control theory7.," Such constraints are implemented, with the minimum number of assumptions, by employing optimal control theory." +.. Using this approach. we also show that the constraint. prevents continuous. constant AGN power output. but. favours discrete AGN outbursts with a duty evcle which depends. only on the. feedback strength.," Using this approach, we also show that the constraint prevents continuous, constant AGN power output, but favours discrete AGN outbursts with a duty cycle which depends only on the feedback strength." + “Pherefore. despite being. largely: empirical. the constraint warrants investigation as a baseline node! against which both observations and numerical simulations can be compared.," Therefore, despite being largely empirical, the constraint warrants investigation as a baseline model against which both observations and numerical simulations can be compared." + Llowever. we note that there may. be other equally. plausible interpretations. and explanations. of these observations.," However, we note that there may be other equally plausible interpretations, and explanations, of these observations." + The outline of the article is as follows., The outline of the article is as follows. + Section 2 outlines a simple. feedback model., Section 2 outlines a simple feedback model. + In. Section 3. we investigate the ellect of the mimumunm. energy. constraint which is implemented using optimal control theory.," In Section 3, we investigate the effect of the mimumum energy constraint which is implemented using optimal control theory." + The findings are discussed in section + and summarised in section 5., The findings are discussed in section 4 and summarised in section 5. + Current interpretation of observations suggests that. raclio AGN heating is related. to the cooling rate of the hot.X-ray emitting gas (e.g.2???) which itself must evolve according to the dillerence between the ACN heating and eas cooling rates.," Current interpretation of observations suggests that radio AGN heating is related to the cooling rate of the hot,X-ray emitting gas \citep[e.g.][]{best05,birzan,dunn05,nulsen2007}, which itself must evolve according to the difference between the AGN heating and gas cooling rates." + The precise details of the interaction between a collimated AGN outflow and the ambient. gas mav be relevant on kiloparsec scales. but are. much. less so on larger scales. since the injected. energy is eventually dissipated more or less isotropically (see2)..," The precise details of the interaction between a collimated AGN outflow and the ambient gas may be relevant on kiloparsec scales, but are much less so on larger scales, since the injected energy is eventually dissipated more or less isotropically \citep[see][]{heinz06a}." + Therefore. on arge spatial scales. GN heating can be approximated. as supplying thermal energy alone (c.g.2?) and it is reasonable o expect the heating/cooling system to be explicable by a relatively simple model.," Therefore, on large spatial scales, AGN heating can be approximated as supplying thermal energy alone \citep[e.g.][]{pope09,fabj} and it is reasonable to expect the heating/cooling system to be explicable by a relatively simple model." + In terms of general expectations. radiative cooling from the hot gas is a positive feedback »oCess - as οποιον ds radiated. the gas loses pressure support. contracts and radiates at an accelerating rate.," In terms of general expectations, radiative cooling from the hot gas is a positive feedback process - as energy is radiated, the gas loses pressure support, contracts and radiates at an accelerating rate." + As à result. the Nth time derivative. dPLsfd. must. itself x: related to Lx(/). in some wav.," As a result, the $N$ th time derivative, ${\rm d}^{\rm N}L_{\rm + X}/{\rm d}t^{\rm N}$, must itself be related to $L_{\rm X}(t)$, in some way." + Conversely. heating will cause the N-ray. emitting gas to expand. thereby reducing its luminositv.," Conversely, heating will cause the X-ray emitting gas to expand, thereby reducing its luminosity." + With this in mind. and without making any unnecessary assumptions. suppose that /7(/) and Lx(/) can be related. by a continuous time. linear. N-th orderdifferential equation of the form Note that. in its present form. equation (1)) is a generic description for the variation of the X-ray Iuminosity. Lx(1). in response to an externally applied: heating rate. (0).," With this in mind, and without making any unnecessary assumptions, suppose that $H(t)$ and $L_{\rm X}(t)$ can be related by a continuous time, linear, $N$ -th orderdifferential equation of the form Note that, in its present form, equation \ref{eq:1}) ) is a generic description for the variation of the X-ray luminosity, $L_{\rm X}(t)$, in response to an externally applied heating rate, $H(t)$." + Llowever. heating rates derived. from observations of X-ray cavities inflated by ACN seem to correlate with the X-rav luminosity of the host cluster (e.g. 27).. suggesting Lf(/)x Lx(E).," However, heating rates derived from observations of X-ray cavities inflated by AGN seem to correlate with the X-ray luminosity of the host cluster \citep[e.g.][]{birzan,dunn08}, , suggesting $H(t) \propto L_{\rm + X}(t)$ ." + Furthermore. ? (seealso2). showed that ACN in," Furthermore, \cite{raff08} \citep[see also][]{cav08} showed that AGN in" +as soon as they are formed. hence the absence of a filtered flux in the corresponding models (see 5).,"as soon as they are formed, hence the absence of a filtered flux in the corresponding models (see 5)." + Finally. damping also depends strongly on the Brunt-.—Viiiisillaé frequency (Eq. 7).," Finally, damping also depends strongly on the Brunt-V\""aiis\""all\""a frequency (Eq. \ref{optdepth}) )," +" whose thermal part is given by Vm 6 =|-(Inp/dIn7T)p,.Vette)and other symbols have their dn,= usual meaning."," whose thermal part is given by ^2 = with $\delta = -(\partial \ln \rho/\partial \ln T)_{P,\mu}$, and other symbols have their usual meaning." + From Fig., From Fig. + 4. we see that during the PMS. the star's contraction leads to an increase in gravity and a reduction of the pressure scale height. which produce a large increase in N57 when combined.," \ref{fig:BVI} we see that during the PMS, the star's contraction leads to an increase in gravity and a reduction of the pressure scale height, which produce a large increase in ${N_T}^2$ when combined." + Later. during the giant phase. the expansion of the outer layers produces a large decrease in Ny? outside the hydrogen-buming shell.," Later, during the giant phase, the expansion of the outer layers produces a large decrease in ${N_T}^2$ outside the hydrogen-burning shell." + More important. core contraction produces a major increase inside this shell; in fact. Ny? becomes so large there that (low-frequeney) waves will be unable to cross that boundary.," More important, core contraction produces a major increase inside this shell; in fact, ${N_T}^2$ becomes so large there that (low-frequency) waves will be unable to cross that boundary." + A large angular momentum deposition is expected there. provided there is differential above. to produce a bias in inlthe local wave flux.," A large angular momentum deposition is expected there, provided there is differential rotation above to produce a bias in the local wave flux." +" Lmintl.(2@7,)""""}). use to describe IGW properties is (3) extensively described (Papers I and II. and TCOS)."," The formalism we use to describe IGW properties is extensively described elsewhere (Papers I and II, and TC05)." + where N- is recall the main features of our model and discuss — convection zone. principles.," Here, we only recall the main features of our model and discuss the critical physical principles." + depth varies as. angular momentum evolution. the relevant (Goldreich & Nicholson filteredangular momentum luminosity slightly We integrate this envelope (hereafter CE).," In terms of angular momentum evolution, the relevant parameter is the filtered angular momentum luminosity slightly below the convection envelope (hereafter CE)." +" To get that momentum luminosity luminosity. need to obtain the spectrum of excited — £, i57 waves."," To get that luminosity, we first need to obtain the spectrum of excited waves." + As we did in previous studies. we apply the Goldreich. Murray Kumar (1994) formalism to IGWs to calculate this spectrum.," As we did in previous studies, we apply the Goldreich, Murray Kumar (1994) formalism to IGWs to calculate this spectrum." +" The energy flux per unit frequency 7 is then where & and [/(£+D]72,. are the radial and horizontal displacement wave functions. which are normalized to unit €Dergy flux just below the convection zone. ¥,. is the convective Velocity. L=aijHp the radial size of an energy bearing turbulent eddy. r,s L/w. the characteristic convective me. and /,, is the radial size of the largest eddy at depth 7 with characteristic frequency of w or higher (5,= "," The energy flux per unit frequency ${\cal F}_E$ is then where $\xi_r$ and $[\ell(\ell+1)]^{1/2}\xi_h$ are the radial and horizontal displacement wave functions, which are normalized to unit energy flux just below the convection zone, $v_c$ is the convective velocity, $L=\alpha_{\rm MLT} H_P$ the radial size of an energy bearing turbulent eddy, $\tau_L \approx L/v_c$ the characteristic convective time, and $h_\omega$ is the radial size of the largest eddy at depth $r$ with characteristic frequency of $\omega$ or higher $h_\omega = L \min\{1, (2\omega\tau_L)^{-3/2}\}$ )." +"The radial waveην numberτς £, is palerelated torotation the horizontal wave number 4;, by k 3.d'a 1)ΓΗ) the BruntVüusállà frequency.", The radial wave number $k_r$ is related to the horizontal wave number $k_h$ by k_r^2 = -1 k_h^2 = -1 where $N^2$ is the Brunt-Väiisällä frequency. + In the Here. we only mode is evanescent and the penetration the eritical physical V£(£ - 1).," In the convection zone, the mode is evanescent and the penetration depth varies as $\sqrt{\ell \lp \ell +1 \rp}$." +" Themomentumflux per unit frequency 7; is then related to the kinetic energy flux by , . u 1989: Talon & Matias 1997)."," The momentum flux per unit frequency ${\cal F}_J$ is then related to the kinetic energy flux by (Goldreich Nicholson 1989; Zahn, Talon Matias 1997)." + is the quantity horizontally to get an angular below the convection we first, We integrate this quantity horizontally to get an angular momentum luminosity _J = 4 r^2 +"The sum in equation (117)) can be transformed into an integral as follows Changing the integration variable q to 7=""m and defining Wa and A=eal- one can wrile with From equations (118)). (120)) and (121)) we obtain where g(A)is given by ⊳↔⊲↥∐≺∢≼↲⋅≀⋮∣∣⋗⋗⊥↕∐⊔∐↲↕⋅≀↧↴∐≸≟≼↲∪↓⋟≼↲⇀↸↕↽≻≼↲↕⋅↕∐∐↲↕∐≀↧↴↥≼⇂≀↧↴⋯⋅∖∖↽≼↲≼↲∐↓↕↽≻↥∪⋡∖↽↳∖↡≼↲↥⊳∖⇁∪∐≀↧↴∐≼⇂ ⇀∖↕∪↕⋅∪∠≀↧↴↕↽≻↕↽≻↕⋅∪⇀↸↕∐⋯↥↕∪∐∏ to calculate (he inteeral in equation (124)).","The sum in equation \ref{app3-z2}) ) can be transformed into an integral as follows Changing the integration variable $q$ to $x=\sqrt{\frac{\bar{A}}{\stackrel{}{\tilde{f}}}}\,q$ , and defining $x_0=2\sqrt{\frac{\bar{A}}{\stackrel{}{\tilde{f}}}}\,\omega_0$ and $\lambda =\frac{\hat{A}}{\stackrel{}{\bar{A}}}$, one can write with From equations \ref{app3-z0}) ), \ref{app3-z3}) ) and \ref{app3-intG}) ) we obtain where $g(\lambda)$ is given by Since $x_0\gg 1$ in the range of experimental data, we employ Nelson and Moroz approximation \cite{Nelson} + to calculate the integral in equation \ref{app3-g}) )." + We find Thus weobtain, We find Thus weobtain + The resulting coherence function is shown by the markers in Fig. 3..," The resulting coherence function is shown by the markers in Fig. \ref{coh_test}," + where diamoncds denote deata points and triangles denote ppoints., where diamonds denote data points and triangles denote points. + The coherence measurements in this plot have been corrected for Poisson noise effects in the high signal-to-noise limit given by Vaughan&Nowak(1997)., The coherence measurements in this plot have been corrected for Poisson noise effects in the high signal-to-noise limit given by \citet{Vaughan_coh}. +. The solid. and dotted lines represent the scatter expected. for cach data set. estimated under the assumptions that will be explained in Sec. 3.3..," The solid and dotted lines represent the scatter expected for each data set, estimated under the assumptions that will be explained in Sec. \ref{significance}." +" The measured. coherence is high (~ 0.9) for the entire frequency. range up to ~LO ""Hz.", The measured coherence is high $\sim 0.9$ ) for the entire frequency range up to $\sim 10^{-3}$ Hz. + At higher frequencies. the coherence drops. drastically. (the highest-frequeney point is negative. not shown in the plot) but the expected scatter inercases significantly. makine coherence measurements in this range unreliable.," At higher frequencies, the coherence drops drastically (the highest-frequency point is negative, not shown in the plot) but the expected scatter increases significantly, making coherence measurements in this range unreliable." + ligure 4. shows the lag spectrum over the frequency. range where the measured coherence is high. ic. below ~2.107 llz. as lags measured in cases of low coherence are not meaningful.," Figure \ref{lags_tot} shows the lag spectrum over the frequency range where the measured coherence is high, i.e. below $\sim 2 + \times + 10^{-3}$ Hz, as lags measured in cases of low coherence are not meaningful." + Positive lag values indicate that the soft band eads the hard., Positive lag values indicate that the soft band leads the hard. + Significant lags are detected. between 10 με.," Significant lags are detected between $\sim 10^{-5} + -10^{-3}$ Hz." + The aand lag spectra match. well at. the frequencies. where they overlap. around LO1 Hz.," The and lag spectra match well at the frequencies where they overlap, around $10^{-4}$ Hz." + Phe lag spectrum appears to be requency-dependent. where larger time laes are associated with longer time-scale [uctuations. similar to what has been observed in other AGN ancl DIIXNBDs (see Sec. 5.1)).," The lag spectrum appears to be frequency-dependent, where larger time lags are associated with longer time-scale fluctuations, similar to what has been observed in other AGN and BHXRBs (see Sec. \ref{comparison}) )." + The ags spectrum in the frequency range between 2;10.7 and 2.104 Lz resembles the shape of a power law., The lags spectrum in the frequency range between $2\times 10^{-5}$ and $2 \times 10^{-4}$ Hz resembles the shape of a power law. + However. at lower and higher frequencies. the measured lags decrease noticeably below the extension of a power law fitted to the lag spectrum in this central frequency. range.," However, at lower and higher frequencies, the measured lags decrease noticeably below the extension of a power law fitted to the lag spectrum in this central frequency range." + A single power law fit to the lag spectrum over the whole frequeney range shown in Fig. 4..," A single power law fit to the lag spectrum over the whole frequency range shown in Fig. \ref{lags_tot}," +" vields a best-fitting mocel τι)=OOLf"". with a yt=62 for LE dof (solid. [ine in Fig. 4))."," yields a best-fitting model $\tau(f)=0.04f^{-0.9}$, with a $\chi^2=62$ for 14 dof (solid line in Fig. \ref{lags_tot}) )." + This is clearly an unacceptable fit and leaves the best-delinec lag measurements well above the fitted curve., This is clearly an unacceptable fit and leaves the best-defined lag measurements well above the fitted curve. +" Restricting the fitting range to 1075.! lly produces a similar power law. τς)=0.5f"""". with a yo=9.9 for 5 dol. shown by the dotted line in the same ligure."," Restricting the fitting range to $\sim 10^{-5}-5\times +10^{-4}$ Hz produces a similar power law, $\tau(f)=0.5f^{-0.7}$, with a $\chi^2=9.9$ for 5 dof, shown by the dotted line in the same figure." + The measured lags above ancl below this range fall [ar below the extension of the power law fit. so the lag spectrum resembles a broad hump.," The measured lags above and below this range fall far below the extension of the power law fit, so the lag spectrum resembles a broad hump." + A much better fit to the entire frequency range was obtained by using a single-bend power law model., A much better fit to the entire frequency range was obtained by using a single-bend power law model. + The best fitting values for the low frequency ancl high frequeney slopes (az and ay respectively) are 0 and. -4. while the bend is at a frequeney of 210? Lz.," The best fitting values for the low frequency and high frequency slopes $\alpha_L$ and $\alpha_H$ respectively) are 0 and -4, while the bend is at a frequency of $2 \times 10^{-4}$ Hz." + This tat time lag spectrum. bending to a very steep high frequency slope model produces a X7=10.9 for 16 dof.," This flat time lag spectrum, bending to a very steep high frequency slope model produces a $\chi^2= 10.9$ for 16 dof." + The significance of the deviations from a simple power law and the goodness of fit of the bending. power Law model were assessed through the Monte Carlo simulations discussed in the following section., The significance of the deviations from a simple power law and the goodness of fit of the bending power law model were assessed through the Monte Carlo simulations discussed in the following section. + A power law lag spectrum could be distorted. by sampling ancl observational noise ellects., A power law lag spectrum could be distorted by sampling and observational noise effects. +. We used. Monte. Carlo simulations to test the possibilities that the measured. [ag spectrum deviates from a power law only by these effects and that the drops observed in the coherence function are, We used Monte Carlo simulations to test the possibilities that the measured lag spectrum deviates from a power law only by these effects and that the drops observed in the coherence function are +There are currently à number of interstellar dust. models that satisfy the usual observational constraints with different grain size distribution (Mathis et al.,There are currently a number of interstellar dust models that satisfy the usual observational constraints with different grain size distribution (Mathis et al. +" 1977. Nim Alartin 1995. Weingartner Draine 2000. Witt. 1999),"," 1977, Kim Martin 1995, Weingartner Draine 2000, Witt 1999)." + AIL size distributions have a large range of grain sizes. they are either continuous or in a multi-mode distribution. and most of (he mass is contained in the largest grains.," All size distributions have a large range of grain sizes, they are either continuous or in a multi-mode distribution, and most of the mass is contained in the largest grains." + No grain size distribution postulated for the diffuse interstellar medium incorporates large grains in (he numbers specified in Sect., No grain size distribution postulated for the diffuse interstellar medium incorporates large grains in the numbers specified in Sect. + 3.2. and all would recquire similar modifications as we carried out with the MIN distribution in order to produce a satisfactory fit to the N-rax halo of Nova Cveni 1992.," 3.2, and all would require similar modifications as we carried out with the MRN distribution in order to produce a satisfactory fit to the X-ray halo of Nova Cygni 1992." + We conclude from (his that our result is not a peculiar consequence of (he assumed size distribution., We conclude from this that our result is not a peculiar consequence of the assumed size distribution. + All models utilize similar amounts of the refractory elements (Snow Witt 1995.1996).The optical properties of the MIN model are determined by the assumed Composition in terms of silicate and graphite grains will densities specilied in Sect.," All models utilize similar amounts of the refractory elements (Snow Witt 1995,1996).The optical properties of the MRN model are determined by the assumed composition in terms of silicate and graphite grains with densities specified in Sect." + 3.2 and optical constants as given by Draine and Lee (1934)., 3.2 and optical constants as given by Draine and Lee (1984). + As shown by Mathis et al. (, As shown by Mathis et al. ( +1995). adopting different compositions. especially for the carbonaceous component of the erains. as well as composite ancl porous structures instead of homogeneous. compact grains produces some variation in the overall halo intensity. but it does not significantly affect the profile shape.,"1995), adopting different compositions, especially for the carbonaceous component of the grains, as well as composite and porous structures instead of homogeneous, compact grains produces some variation in the overall halo intensity, but it does not significantly affect the profile shape." + This was confirmed bv (the Mie-caleulations for porous particles bv Smith Dwek (1993) as well., This was confirmed by the Mie-calculations for porous particles by Smith Dwek (1998) as well. + We conclude from this that our result concerning the need for a erain size distribution extended {ο larger sizes is independent of the assumed composition. eiven (he normal constraints. nainlv [rom depletion studies and the study of grain band emissions and absorptions.," We conclude from this that our result concerning the need for a grain size distribution extended to larger sizes is independent of the assumed composition, given the normal constraints, mainly from depletion studies and the study of grain band emissions and absorptions." + The presence of larger grains in our NMBN distribution bevond the MIN limit of 0.25 yan does not seem to impose an additional mass requirement bevond that set by the canonical Galactic dust-to-gas ratio. and thus our result does not further compound the problem of the apparent mismatch between (he amounts of refractory elements required bv," The presence of larger grains in our XMRN distribution beyond the MRN limit of 0.25 $\mu$ m does not seem to impose an additional mass requirement beyond that set by the canonical Galactic dust-to-gas ratio, and thus our result does not further compound the problem of the apparent mismatch between the amounts of refractory elements required by" +Furthermore. when the moon orbital period is stall. an asyimunetry arises in the bottom of the transit. shown by the downward arrows in Figure 3..,"Furthermore, when the moon orbital period is small, an asymmetry arises in the bottom of the transit, shown by the downward arrows in Figure \ref{fig:planetas_com_lua}." + This asyiumetry is geueratecd when the ioon is eclipsed by the planet., This asymmetry is generated when the moon is eclipsed by the planet. + may also happen if at the start of the trausit tle moon is already behind (or in frout) of the planet. but falls out of eclipse during the trausit.," It may also happen if at the start of the transit the moon is already behind (or in front) of the planet, but falls out of eclipse during the transit." + The width aud intensity ol this signal depends ou the moou's relative orbital period. radius. aud also ou the position augle ο of the moon with respect to the planet at the initial transit time.," The width and intensity of this signal depends on the moon's relative orbital period, radius, and also on the position angle $\varphi$ of the moon with respect to the planet at the initial transit time." + Figure L presents the moceled light curve produced by a trausiting Saturu-like planet around a star with solar parameters (left panel)., Figure \ref{fig:planetas_com_aneis} presents the modeled light curve produced by a transiting Saturn-like planet around a star with solar parameters (left panel). + To eulance the sigual produced by the ring presence. their size were augmented by (right pane," To enhance the signal produced by the ring presence, their size were augmented by (right panel)." + The main elfect of the planetary ring system is to increase the covered area of the stellar surface., The main effect of the planetary ring system is to increase the covered area of the stellar surface. + The result of which is to deepen the transit light curve., The result of which is to deepen the transit light curve. + Moreover. the trausit shape becomes rouuder at the ingress aud egress iustauts. than if no rines are present.," Moreover, the transit shape becomes rounder at the ingress and egress instants, than if no rings are present." + Both these [actors depend strougly ou the ring trausparency. being larger in the case of more opaque riugs. as expectect.," Both these factors depend strongly on the ring transparency, being larger in the case of more opaque rings, as expected." + Au interesting ellect. appears when the rine size is increased., An interesting effect appears when the ring size is increased. + In this case. the lieht curve becomes more triaugular.e similar to the liehte curves produced duringMm 0eraziuge eclipses of binary star systelus.," In this case, the light curve becomes more triangular, similar to the light curves produced during grazing eclipses of binary star systems." + [f the star lias one or more spots on its surface. similar to suuspots. Silva(2003) has shown that the photometric ligit curve during a planetary trausit will display a small “bump”.," If the star has one or more spots on its surface, similar to sunspots, \citet{Silva2003} has shown that the photometric light curve during a planetary transit will display a small “bump""." + This occurs because wheu the planet occults a darker reeione of the stellar surface. occupied by the spot. there is," This occurs because when the planet occults a darker region of the stellar surface, occupied by the spot, there is" +huncred for the introduction of only three aclelitional degrees of freedom in the fit.,hundred for the introduction of only three additional degrees of freedom in the fit. + For NGC 1399. 4472 and. 4649. the use of the two temperature model results in a significant increase in the inferred. metallicity of the X-ray gas in the galaxies. from values of 0.2.—0.4 solar with spectral model D. to values consistent with (or slightly exceeding) the solar value. with spectral model D. This is in agreement with the results. previously-reported by. Buote Fabian (1998: see also Buote 1999).," For NGC 1399, 4472 and 4649, the use of the two temperature model results in a significant increase in the inferred metallicity of the X-ray gas in the galaxies, from values of $0.2-0.4$ solar with spectral model B, to values consistent with (or slightly exceeding) the solar value, with spectral model D. This is in agreement with the results previously-reported by Buote Fabian (1998; see also Buote 1999)." + For AIST. NGC 4696 and. NGC 4636. we found. that the fits were further significantly improved by allowing the abundances of various individual elements to be included as acdelitional free parameters in the fits. (," For M87, NGC 4696 and NGC 4636, we found that the fits were further significantly improved by allowing the abundances of various individual elements to be included as additional free parameters in the fits. (" +With spectral mocel D. all elements ave linked to vary in the same ratio. relative to their solar values).,"With spectral model D, all elements are linked to vary in the same ratio, relative to their solar values)." + Improvements in the measured. 47 values of several hundred were obtained for these objects by allowing the abundances of Mg. Si and S to be included as [ree parameters in the fits (with only a single extra degree of freedom being associated. with each extra clement included as a [ree [it parameter).," Improvements in the measured $\chi^2$ values of several hundred were obtained for these objects by allowing the abundances of Mg, Si and S to be included as free parameters in the fits (with only a single extra degree of freedom being associated with each extra element included as a free fit parameter)." + The results on the individual clement abuncdances for. MIST ancl NGC 4696 are discussed bv Allen (1999)., The results on the individual element abundances for M87 and NGC 4696 are discussed by Allen (1999). + Phe results for NGC 4636 are detailed in Section 6., The results for NGC 4636 are detailed in Section 6. + The results on the power-law components detected in the ASCA spectra are. summarized. in ‘Table 4., The results on the power-law components detected in the ASCA spectra are summarized in Table 4. + In all cases the introduction of the power-law component into the two-temperature models (models D anc E) leads to a highly significant improvement in the fit., In all cases the introduction of the power-law component into the two-temperature models (models D and F) leads to a highly significant improvement in the fit. + For guidance. a reduction in 7 of AY?~10 with the introduction. of the power-law component (2 extra fit parameters) is significant at approximately the 99 per cent confidence level (for a Lit," For guidance, a reduction in $\chi^2$ of $\Delta \chi^2 \sim 10$ with the introduction of the power-law component (2 extra fit parameters) is significant at approximately the 99 per cent confidence level (for a fit" +the hydrodynamical variables at a.,the hydrodynamical variables at $a$. +" After that the corresponding density, pressure and velocity profile in the mask are computed."," After that the corresponding density, pressure and velocity profile in the mask are computed." + For 7<1 the shocks form very close to the second star., For $\eta \ll 1$ the shocks form very close to the second star. +" In this case, the mask of the star has to be as small as possible so that the shocks can form properly (?).."," In this case, the mask of the star has to be as small as possible so that the shocks can form properly \citep{1998MNRAS.300..479P}." + However a minimum length of 8 computational cells per direction is needed to obtain spherical symmetry of the winds., However a minimum length of 8 computational cells per direction is needed to obtain spherical symmetry of the winds. + We thus fix the size of the masks to 8 computational cells in each direction for the highest value of refinement., We thus fix the size of the masks to 8 computational cells in each direction for the highest value of refinement. + We performed tests with a single star for different sizes of the mask ranging from 0.03a to 1.5a., We performed tests with a single star for different sizes of the mask ranging from $a$ to $a$. + The tests were performed for nz=128 and 4 levels of refinement., The tests were performed for $n_x=128$ and 4 levels of refinement. + The resulting density profiles all agree with the analytic solution with less than 1 96 offset., The resulting density profiles all agree with the analytic solution with less than 1 $\%$ offset. +" The surrounding medium is filled with a density pa»=10*p(a) and pressure P;,,=0.1P(a).", The surrounding medium is filled with a density $\rho_{amb}=10^{-4}\rho(a)$ and pressure $P_{amb}=0.1P(a)$. + This initial medium is pushed away by the winds., This initial medium is pushed away by the winds. +" Simulations with different pam» and Pam» show the same final result, to round-off precision."," Simulations with different $\rho _{amb}$ and $P_{amb}$ show the same final result, to round-off precision." + The size of the computational domain varies between /po;=2a and [νου=80a according to the purpose of the simulation., The size of the computational domain varies between $l_{box}=2a$ and $l_{box}=80a$ according to the purpose of the simulation. +" Except where stated otherwise, we took Mi=Μο—107*5, M;=Ma30, vs»=2000 s! and η was varied by changing v5,1.Hence, our low momentum flux ratios can imply very high velocities for the first wind."," Except where stated otherwise, we took $\dot{M_1}=\dot{M_2}=10^{-7}$, $\mathcal{M}_1=\mathcal{M}_2=30$, $v_{\infty 2}=2000$ $^{-1}$ and $\eta$ was varied by changing $v_{\infty 1}$ .Hence, our low momentum flux ratios can imply very high velocities for the first wind." + In this section we study the dependence on η of the geometry of the interaction zone., In this section we study the dependence on $\eta$ of the geometry of the interaction zone. +" We discuss he analytic solutions for the colliding wind geometry, in 2D and 3D, to which we compare our simulations."," We discuss he analytic solutions for the colliding wind geometry, in 2D and 3D, to which we compare our simulations." + Simulations are performed with adiabatic and isothermal equations of state., Simulations are performed with adiabatic and isothermal equations of state. + In both cases the numerical diffusion introduced by the solver is sufficient to quench the development of instabilities., In both cases the numerical diffusion introduced by the solver is sufficient to quench the development of instabilities. + Section ?? deals with high resolution simulations of the development of these instabilities., Section \ref{instabilities} deals with high resolution simulations of the development of these instabilities. + The overall structure of the colliding wind binary is given in Fig. 1.., The overall structure of the colliding wind binary is given in Fig. \ref{fig:geometry}. + The density map shows two shocks separating the free winds from the shocked winds., The density map shows two shocks separating the free winds from the shocked winds. + The shocked winds from both stars are separated by a contact discontinuity., The shocked winds from both stars are separated by a contact discontinuity. + The Bernouilli relation is preserved across shocks hence across the first shock., The Bernouilli relation is preserved across shocks hence across the first shock. + The subscript s refers to quantities in the shocked region and we have neglected the thermal pressure in the unshocked wind due to its high Mach number., The subscript $s$ refers to quantities in the shocked region and we have neglected the thermal pressure in the unshocked wind due to its high Mach number. + A similar equation holds for the second shock., A similar equation holds for the second shock. + The Bernouilli relation is constant in each shocked region but discontinuous at the CD., The Bernouilli relation is constant in each shocked region but discontinuous at the CD. +" There, Pi,=Pos by definition and vj,=vo,O on the line-of-centres so that the two Bernouilli equations combine to give Pis¥2o1=ροκ with p; the value of the density on each side of the contact discontinuity."," There, $P_{1s}\equiv P_{2s}$ by definition and $v_{1s}=v_{2s}=0$ on the line-of-centres so that the two Bernouilli equations combine to give $\rho_{1s}v_{\infty 1}^2=\rho_{2s}v_{\infty 2}^2$, with $\rho_s$ the value of the density on each side of the contact discontinuity." +"σος, Assuming that the density is constant in each shocked region on the binary axis (the numerical simulations carried out below show this is a verygood approximation) then where pi (p2) is the value of the density at the first(second) shock.", Assuming that the density is constant in each shocked region on the binary axis (the numerical simulations carried out below show this is a verygood approximation) then where $\rho_{1}$ $\rho_2$ ) is the value of the density at the first(second) shock. + The above relation states the balance of ram pressures (?).., The above relation states the balance of ram pressures \citep{Stevens:1992on}. + Using Eqs. (1)), Using Eqs. \ref{eq:eta}) ) +" and (6)) then yields where 7; is the distance between the first star and the first shock and r2, the distance between the second star and the second shock."," and \ref{eq:rho}) ) then yields where $r_1$ is the distance between the first star and the first shock and $r_2$, the distance between the second star and the second shock." +" If the shock is thin then r1+r27a and the distance of the CD to the second star is Note that, fora given η<1, the contact discontinuity is closer to the second star for a 2D geometry than for a 3D geometry."," If the shock is thin then $r_1+r_2\approx a$ and the distance $R_s\approx r_2$ of the CD to the second star is Note that, for a given $\eta \leq 1$, the contact discontinuity is closer to the second star for a 2D geometry than for a 3D geometry." +" The shock positions are not easily derived away from the line-of-centres, where the density is not constant in the shocked winds."," The shock positions are not easily derived away from the line-of-centres, where the density is not constant in the shocked winds." +" Analytic solutions have been derived based on the thin shell hypothesis, which considers both shocks and the contact discontinuity are merged into one single layer."," Analytic solutions have been derived based on the thin shell hypothesis, which considers both shocks and the contact discontinuity are merged into one single layer." +" ? (see also ?,, ? and ?)) derive the following equation for the shape of the interaction region by assuming that it is located where the ram pressures normal to the shell balance: The same analysis for the 2D structure (Eq. 6))"," \citet{Stevens:1992on} (see also \citealt{Luo:1990mp}, \citealt{1993MNRAS.261..430D} and \citealt{Antokhin:2004hi}) ) derive the following equation for the shape of the interaction region by assuming that it is located where the ram pressures normal to the shell balance: The same analysis for the 2D structure (Eq. \ref{eq:rho}) )" +" leads to ?,, extending the work of ?,, found an analytical solution in the thin shell limit based on momentum conservation (hence, taking"," leads to \citet{Canto:1996jj}, , extending the work of \cite{Wilkin:1996ud}, , found an analytical solution in the thin shell limit based on momentum conservation (hence, taking" +The dark grey lines overplotted in Fig.,The dark grey lines overplotted in Fig. + 3 show evolutionary tracks for the intermediate metallicity of the LMC with 250 kkm/s by Brott et (2010) for masses of 15. 20. 30. 40 and M...," \ref{VROT_GG} show evolutionary tracks for the intermediate metallicity of the LMC with $\varv_{\rm rot}=250$ km/s by Brott et (2010) for masses of 15, 20, 30, 40 and $M_\odot$." + The black dots on the tracks represent evolutionary time-steps of 10° tick-markedyears. and are intended to facilitate the comparison with observations.," The black tick-marked dots on the tracks represent evolutionary time-steps of $10^5$ years, and are intended to facilitate the comparison with observations." + In Sect. 3..," In Sect. \ref{s_hook}," + we highlighted the steep drop in the rotation rates of massive stars. but we have yet to provide an explanation for ," we highlighted the steep drop in the rotation rates of massive stars, but we have yet to provide an explanation for it." +question is whether the absence of rapidly rotating B The black supergiants is the result of BSB. or if the cooler slow rotators form an entirely separate population from the hotter MS stars.," The question is whether the absence of rapidly rotating B supergiants is the result of BSB, or if the cooler slow rotators form an entirely separate population from the hotter MS stars." + The cool objects (red asterisks) in refV ROTGGandtheH RDof Fig., The cool objects (red asterisks) in \\ref{VROT_GG} and the HRD of Fig. + Aaresupergiantsofluminosityclassi.," \ref{HRD_GG} are supergiants of luminosity class, whilst the fast rotators are dominated by dwarfs (blue pluses)." + whi —whichhavesomehowlosttheirangularmomentum -ontheotherhand.," Although it is by no means obvious that supergiants cannot be in a H burning phase, the division in $g$ might imply that we have a population of rapidly rotating MS objects on the one hand, whilst observing a population of slowly rotating evolved supergiants -- which have somehow lost their angular momentum -- on the other hand." +Currently. wedonothavesuf ficient," Currently, we do not have sufficient information with respect to the evolutionary state of these cool supergiants." +informationwi," In principle, this part of the HRD can be populated with the products of binary evolution, although this would normally not be expected to lead to slowly rotating stars." +thres Gorblue—loopstars. butthekexpointisthatwithinthecontexto Fthetwope ," Alternatively, one could envision the cooler objects to be the product of single star evolution, e.g. post-RSG or blue-loop stars, but the key point is that within the context of the two population interpretation, they are core H burning." +"A potential distinguishing factor between the ""two population scenario” and BSB is that of the chemical abundances.", A potential distinguishing factor between the “two population scenario” and BSB is that of the chemical abundances. + We present LMC N abundances versus effective temperature in Fig. 5..," We present LMC N abundances versus effective temperature in Fig. \ref{nitrogen}," + noting that N abundances could only be derived for a subset of our objects shown in Figs., noting that N abundances could only be derived for a subset of our objects shown in Figs. + 3 and 4.., \ref{VROT_GG} and \ref{HRD_GG}. + As the LMC baseline [N/H] equals ~6.9. the vast majority of slow rotators is found to be strongly N enhaneed.," As the LMC baseline [N/H] equals $\sim$ 6.9, the vast majority of slow rotators is found to be strongly N enhanced." + Although rotating models can in principle account for large N abundances. the fact that such a large number of the cooler objects is found to be N enriched suggests an evolved nature for these stars.," Although rotating models can in principle account for large N abundances, the fact that such a large number of the cooler objects is found to be N enriched suggests an evolved nature for these stars." + The second explanation for the steep drop in rotation rates is that both the objects cooler and hotter than 0000 K reside on the MS. and that it is BSB that explains the slow rotation of the cooler B supergiants.," The second explanation for the steep drop in rotation rates is that both the objects cooler and hotter than 000 K reside on the MS, and that it is BSB that explains the slow rotation of the cooler B supergiants." + The main argument for BSB is that it is predicted at the temperature where the rotational velocities are found to drop steeply., The main argument for BSB is that it is predicted at the temperature where the rotational velocities are found to drop steeply. + The evolutionary tracks in ref HRDGindicatethattheMS forthehighestmassstarsindeedappearsrat Jumptemperatureat22 kkK. andbevond.," The evolutionary tracks in \\ref{HRD_GG} indicate that the MS for the highest mass stars indeed appears rather broad, reaching as far as the BS-Jump temperature at kK, and beyond." +Therefore. masslossseentscapal," Therefore, mass loss seems capable of removing a considerable amount of angular momentum during the MS evolution for the highest mass stars." +situation (ef.2)...,situation \citep[cf.][]{king.2010}. + First. the black hole is embedded: in he gravitational potential of a galaxy that ds. orders of magnitude more massive than it: this means that the eravitational force acting on the accretion Low is dominate ov the mass of the galaxy rather than the black hole and so Moon Will be à similar number of orders of magnitude oll he true AMpg (we show this explicitlv in Hobbs et al.," First, the black hole is embedded in the gravitational potential of a galaxy that is orders of magnitude more massive than it; this means that the gravitational force acting on the accretion flow is dominated by the mass of the galaxy rather than the black hole and so $\dot M_{\rm Bondi}$ will be a similar number of orders of magnitude off the true $\dot M_{\rm BH}$ (we show this explicitly in Hobbs et al.," + in reparation)., in preparation). + Second. anv astrophysically realistic accretion low will have some angularD momentum. violating5 one of he key assumptions made in calculatingὃν Αμα.," Second, any astrophysically realistic accretion flow will have some angular momentum, violating one of the key assumptions made in calculating $\dot M_{\rm Bondi}$." + Phis is important because it implies that infalling material wil settle onto a circular orbit whose radius foie is set by the angular momentum of the material with respect to the black hole (c£.2).., This is important because it implies that infalling material will settle onto a circular orbit whose radius $R_{\rm circ}$ is set by the angular momentum of the material with respect to the black hole \citep[cf.][]{hobbs.etal.2010a}. + In particular. it means that only the very lowest angular material will be available to feed the black hole because the timescale required for viscous transport of material through the clise is of order a Llubble time on scales of order 2~1LOpe (see.forexemple.2)..," In particular, it means that only the very lowest angular material will be available to feed the black hole because the timescale required for viscous transport of material through the disc is of order a Hubble time on scales of order $R\sim 1-10\rm pc$ \citep[see, for example, ][]{king.2010}." + This is à very restrictive condition because it is not. straightforward. for infalling gas to lose its angular momentum other than by colliding with other gas. which leads to angular momentuni cancellation.," This is a very restrictive condition because it is not straightforward for infalling gas to lose its angular momentum other than by colliding with other gas, which leads to angular momentum cancellation." + Therefore. angular momentum provides an ellicient natural barrier to accretion by the black hole. and so must be accounted for when estimating Alp. These arguments make clear that the Boncli-Llovle method cannot provide a reliable estimate of Aly in galaxy formation simulations.," Therefore, angular momentum provides an efficient natural barrier to accretion by the black hole, and so must be accounted for when estimating $\dot M_{\rm BH}$ These arguments make clear that the Bondi-Hoyle method cannot provide a reliable estimate of $\dot M_{\rm BH}$ in galaxy formation simulations." + Lf feedback from black holes plays as important a role in galaxy formation as we expect it to 77). then it is crucial that we devise an alternative method for estimating Alou in galaxy formation simulations that overcomes the problems that beset the Bondi-Llovle method.," If feedback from black holes plays as important a role in galaxy formation as we expect it to \citep[e.g.][]{bower.etal.2006,croton.etal.2006}, then it is crucial that we devise an alternative method for estimating $\dot M_{\rm BH}$ in galaxy formation simulations that overcomes the problems that beset the Bondi-Hoyle method." + In this short. paper. we introduce our new “accretion disc. particle” method. (hereafter the ADP method). for estimating Alou in galaxy formation simulations. which accounts naturally for the angular momentum of infalling material.," In this short paper, we introduce our new “accretion disc particle” method (hereafter the ADP method) for estimating $\dot M_{\rm BH}$ in galaxy formation simulations, which accounts naturally for the angular momentum of infalling material." + We use a collisionless accretion disc particle (ADD) to model the black hole and its accretion disc., We use a collisionless accretion disc particle (ADP) to model the black hole and its accretion disc. + The black hole accretes if and only if gas comes within the accretion radius Pace of the ADI. at which point it is captured and added to the aceretion disc that Leeds the black hole on a viscous timescale fee.," The black hole accretes if and only if gas comes within the accretion radius $R_{\rm acc}$ of the ADP, at which point it is captured and added to the accretion disc that feeds the black hole on a viscous timescale $t_{\rm visc}$." + In this way the black hole. will accrete only the lowest angular momentum material [rom its surroundings., In this way the black hole will accrete only the lowest angular momentum material from its surroundings. + The lavout of this paper is as follows., The layout of this paper is as follows. + We describe the main features of the ADP method in . showinghowlheacerelionral eL. onto the ADP is linked to the black hole accretion rate Alpu.," We describe the main features of the ADP method in \\ref{sec:accretion_models}, showing how the accretion rate $\dot M_{\rm acc}$ onto the ADP is linked to the black hole accretion rate $\dot M_{\rm BH}$ ." + Ins relsee:feedback— we discuss brielly our monentun-cdriven feedback model (e£2). as well as our implementation of the quasar pre-heating model of ?.. , In \\ref{sec:feedback} we discuss briefly our momentum-driven feedback model \citep[cf.][]{nayakshin.power.2010} as well as our implementation of the quasar pre-heating model of \citet{sazonov.etal.2005}. . +The accretion rate Alou estimated using the ADP method is very cillerent from one estimated. using the Bondi-Hovle method., The accretion rate $\dot M_{\rm BH}$ estimated using the ADP method is very different from one estimated using the Bondi-Hoyle method. + We show this clearly in refsec:results using simple idealised numerical simulations. designed to illustrate the kev dillerences between the ADP and. Bonedi-Llovle methods for. estimating Alay.," We show this clearly in \\ref{sec:results} using simple idealised numerical simulations, designed to illustrate the key differences between the ADP and Bondi-Hoyle methods for estimating $\dot M_{\rm BH}$." + These simulations follow the collapse of an initially rotating shell of gas onto a black hole embedded in an isothermal ealactic potential., These simulations follow the collapse of an initially rotating shell of gas onto a black hole embedded in an isothermal galactic potential. + Finally we summarise our results in refsec:sununary and we discuss the implications for galaxy ormation simulations and the Afpy—e relation in re[sec:iconclusions.., Finally we summarise our results in \\ref{sec:summary} and we discuss the implications for galaxy formation simulations and the $M_{\rm BH}-\sigma$ relation in \\ref{sec:conclusions}. + The main features of the ADP are illustrated in Fig 1.., The main features of the ADP are illustrated in Fig \ref{fig:accretion_model}. + Phe ADP is collisionless and consists of a sink particle (2?) with an accretion radius Lace., The ADP is collisionless and consists of a sink particle \citep{bate.1995} with an accretion radius $R_{\rm acc}$. + Race is a free parameter of the simulation but in general it is desirable to set it to the smallest. resolvable scale in the simulation. which will be of order the gravitational softening length of the gas particles.," $R_{\rm acc}$ is a free parameter of the simulation but in general it is desirable to set it to the smallest resolvable scale in the simulation, which will be of order the gravitational softening length of the gas particles." + The total mass of the sink particle is equal to the sum of the masses of the black hole. A/py. and its accretion cisc. Moise.," The total mass of the sink particle is equal to the sum of the masses of the black hole, $M_{\rm BH}$, and its accretion disc, $M_{\rm disc}$." + Phe aceretion dise is assumed to be tightly bound to the black hole and is thus a property of the sink particle rather than a separate cntity., The accretion disc is assumed to be tightly bound to the black hole and is thus a property of the sink particle rather than a separate entity. + Accretion onto the black hole in the ADP method is a two-stage process., Accretion onto the black hole in the ADP method is a two-stage process. + First. any gas that crosses the accretion radius {μυς is removed from the computational domain and added to the aceretion disc.," First, any gas that crosses the accretion radius $R_{\rm acc}$ is removed from the computational domain and added to the accretion disc." + In the classical sink-particle method. of 7.. the acercted gas would. be added: to the black hole immediately. but in an astrophwysically realistic situation. the finite non-zero angular momentum of the acereted gas leads to the formation. of an accretion disc before the gas can accrete onto the black hole.," In the classical sink-particle method of \citet{bate.1995}, the accreted gas would be added to the black hole immediately, but in an astrophysically realistic situation, the finite non-zero angular momentum of the accreted gas leads to the formation of an accretion disc before the gas can accrete onto the black hole." + Here. we assume that gas is added to the accretion disc after a time that is of order the dvnamical timescale fay at Pace., Here we assume that gas is added to the accretion disc after a time that is of order the dynamical timescale $t_{\rm dyn}$ at $R_{\rm acc}$. + Second. gas is transported through the accretion disc and is added to the blackhole.," Second, gas is transported through the accretion disc and is added to the blackhole." + In. principle. we could describe the evolution of the accretion disc by the standard viscous disc evolution equations (see.forexample.Chap- ?).. ," In principle, we could describe the evolution of the accretion disc by the standard viscous disc evolution equations \citep[see, for example, +Chapter 5 of][]{frank.king.raine}. ." +However. neithertheory nor observation tell us what themagnitude of the dise viscosity should be anc so," However, neithertheory nor observation tell us what themagnitude of the disc viscosity should be and so" +"phases exist with comparable pressure. it is convenient to use a definition based on the ratio of the ionizing photon pressure to eas pressure ντο]. Mel&ee Tarter LOst)): where rds the distance to the central σοι source. vis the eas density. T the gas temperature. L, the differential lunünositv. rj the frequeney at the Lyman linut. aud the other sviubols have their usual meanimes.","phases exist with comparable pressure, it is convenient to use a definition based on the ratio of the ionizing photon pressure to gas pressure Krolik, McKee Tarter \cite{KMT1981}) ): where $r$ is the distance to the central continuum source, $n$ is the gas density, $T$ the gas temperature, $L_{\nu}$ the differential luminosity, $\nu_{\rm L}$ the frequency at the Lyman limit, and the other symbols have their usual meanings." +C» Another common definition is the ratio of the ionizingn photon deusitv to the eas deusity. The relation between these two ionization parameters depends on the shape of the ionizing spectrum.," Another common definition is the ratio of the ionizing photon density to the gas density, The relation between these two ionization parameters depends on the shape of the ionizing spectrum." +" For the canonical AGN spectu in (sce Woods 1996)). which we adopt for this work. where T, is the eas temperature in units of 10119. Comparison with Roos (1992)) shows that our adopte spectruni is neither particularly soft or hard."," For the canonical AGN spectrum in (see Woods \cite{W1996}) ), which we adopt for this work, where $T_{4}$ is the gas temperature in units of $10^{4}$ K. Comparison with Roos \cite{R1992}) ) shows that our adopted spectrum is neither particularly soft or hard." +" In Figure 1— we show the thermal equilibrimiu. curve for he assumed ACN ο as a ""unction of temperature and ionization parameters. = ak C"," In Figure \ref{fig:teq} we show the thermal equilibrium curve for the assumed AGN spectrum as a function of temperature and ionization parameters, $\Xi$ and $U$." +LA OW temperatures photoionization 1catius aud cooling due to line excitation aud recombination are in near balance., At low temperatures photoionization heating and cooling due to line excitation and recombination are in near balance. + A hieh temperatures. the equilirit arises frou the balance of Compton heating and cooling.," At high temperatures, the equilibrium arises from the balance of Compton heating and cooling." + The exact shape of the thermal equilibrium curve at nteriuediate temperatures is a complicated function of the inradiating spectra the assumed abundances and thermal processes I&rolik 1981)). aud varies substantially from source to source.," The exact shape of the thermal equilibrium curve at intermediate temperatures is a complicated function of the irradiating spectrum, the assumed abundances and thermal processes Krolik \cite{KMT1981}) ), and varies substantially from source to source." + Since we are not modelling a specific object. we do not concern ourselves with the details of this part of the equilibrium curve.," Since we are not modelling a specific object, we do not concern ourselves with the details of this part of the equilibrium curve." + To obtain cool gas in thermal equilibriun we require ionization parameters =10., To obtain cool gas in thermal equilibrium we require ionization parameters $\Xi \ltsimm 10$. + As noted by Perry Dysou (1985)). shocked gas cooled back to equilibrium can have a value of 5 uuch lower than its pre-shock value.," As noted by Perry Dyson \cite{PD1985}) ), shocked gas cooled back to equilibrium can have a value of $\Xi$ much lower than its pre-shock value." + This is )ecause the post-shock density aud pressure cau be much ereater than the pre-shock value., This is because the post-shock density and pressure can be much greater than the pre-shock value. + Therefore. stroug shocks can create conditions for the gas to cool to tenmiperatures uuch lower than the surrounding ambicut temperature.," Therefore, strong shocks can create conditions for the gas to cool to temperatures much lower than the surrounding ambient temperature." + The crucial question is whether the shocked eas remains at high deusities aud pressures for long cuough to cool roni its post-shock temperature to T~2«10! K. Ta our earlber ID work (Pittard al. 2001)) we demonstrated hat this was possible for a supernova iu a characteristic ACN euvironnoeut., The crucial question is whether the shocked gas remains at high densities and pressures for long enough to cool from its post-shock temperature to $T \sim 2 \times 10^{4}$ K. In our earlier 1D work (Pittard \cite{PDFH2001}) ) we demonstrated that this was possible for a supernova in a characteristic AGN environment. + Iun the uext section we present results from 2D simulations of à SNR evolving in an ACN cuviromuent., In the next section we present results from 2D simulations of a SNR evolving in an AGN environment. + We have computed models with ambient densitics Po10.10«n.7 aud with AGN wind speeds5.," We have computed models with ambient densities $n = 10^{5},10^{6} \pcm3$ and with AGN wind speeds." + The initial radius. expausion speed. aud age of the SNR iu our models is specified iu Table 1 for cach of the ambient densities.," The initial radius, expansion speed, and age of the SNR in our models is specified in Table \ref{tab:init_radius_age} for each of the ambient densities." + All 1nodels have the same ionization paranaueter and temperature for the ambient inedia (S=150 T=1.33«10 K) uuless otherwise stated.," All models have the same ionization parameter and temperature for the ambient medium $\Xi \approx 150$, $T = 1.33 \times 10^{7}$ K) unless otherwise stated." + We further assuned that the central contimmiun source ds distaut enough that he flux of ionizing racdiatiou is constant over our computational volume., We further assumed that the central continuum source is distant enough that the flux of ionizing radiation is constant over our computational volume. + The SNR was evolved. until the wressuure of the shocked eas drops to the point where it is no longer able to exist in the cool phase (1~105 IK)., The SNR was evolved until the pressure of the shocked gas drops to the point where it is no longer able to exist in the cool phase $T \sim 10^{4}$ K). + As the reiinant expands we periodically reerid our model to a coarser set of exids., As the remnant expands we periodically regrid our model to a coarser set of grids. + Iu Fies, In Figs. + 2 and 3 we show the evolution of a SNR expanding iuto a stationary ocnvironneut with »=10%eni7., \ref{fig:nw6_rho} and \ref{fig:nw6_temp} we show the evolution of a SNR expanding into a stationary environment with $n = 10^{6} \pcm3$ . + The shocked gas rapidly loses energy. first through inverse Compton scattering. and then through free-free and Lue cooling. aud is compressed into a relatively thin zone with the uushocked ejecta dominating the remnant volune.," The shocked gas rapidly loses energy, first through inverse Compton scattering, and then through free-free and line cooling, and is compressed into a relatively thin zone with the unshocked ejecta dominating the remnant volume." + The shocked eas has a fractional, The shocked gas has a fractional +The Verv Large Array (VLA) is an imaging array located on the plains of San Augustin in west-central New Mexico.,The Very Large Array (VLA) is an imaging array located on the plains of San Augustin in west-central New Mexico. + It consists of a total of 27 antennas. each 25 meters in diameter. wilh nine antennas distributed along each of three equilangular arms extending oul to 21 km from the center.," It consists of a total of 27 antennas, each 25 meters in diameter, with nine antennas distributed along each of three equilangular arms extending out to 21 km from the center." + The array. provides diffracon-limited images of astronomical objects in all Stokes parameters. wilh a maxinuun resolution at 1.4 GlIIz of 1.4 arcseconds. and at 45 Gllz of 0.05 areseconds.," The array provides diffraction-limited images of astronomical objects in all Stokes parameters, with a maximum resolution at 1.4 GHz of 1.4 arcseconds, and at 45 GHz of 0.05 arcseconds." + Detailed descriptions of the VLA as originally constructed can be found in |1] and [2]., Detailed descriptions of the VLA as originally constructed can be found in [1] and [2]. + The VLA was designed and built in the 1970s. and utilized the best technology of that time.," The VLA was designed and built in the 1970s, and utilized the best technology of that time." + The telescope. upon completion in 1980. could observe in four frequency. bands. utilizing state-of-the-art crvogenically cooled receivers. TEOL circular waveguide to transport the analog signals of 200 MIIz bandwidth [rom the most distant. antennas to the central location without amplification and. most notably. a digital correlator capable of producing up lo 512 spectral channels spanning 3 MIIZ for each of the 351 baselines. or full-polarization continuum correlations at two [requencies simultaneously with 50 MlIz bandwidth.," The telescope, upon completion in 1980, could observe in four frequency bands, utilizing state-of-the-art cryogenically cooled receivers, TE01 circular waveguide to transport the analog signals of 200 MHz bandwidth from the most distant antennas to the central location without amplification and, most notably, a digital correlator capable of producing up to 512 spectral channels spanning 3 MHz for each of the 351 baselines, or full-polarization continuum correlations at two frequencies simultaneously with 50 MHz bandwidth." + The VLA increased astronomical capabilities by one or more orders of magnitude over all preceding radio telescopes in sensitivity. resolution. frequency. coverage. speed. flexibility. aud imaging ficlelity.," The VLA increased astronomical capabilities by one or more orders of magnitude over all preceding radio telescopes in sensitivity, resolution, frequency coverage, speed, flexibility, and imaging fidelity." + The design of the VLA was heavily influenced by both the available technology of the 1970s. and the kev scientific questions of that era. which included imaging the Doppler-shiltec emission from neutral hvdrogen [rom local galaxies and resolving the bright continuum emission of distant quasars. radio galaxies. ancl supernova remnants.," The design of the VLA was heavily influenced by both the available technology of the 1970s, and the key scientific questions of that era, which included imaging the Doppler-shifted emission from neutral hydrogen from local galaxies and resolving the bright continuum emission of distant quasars, radio galaxies, and supernova remnants." + The VLA has been spectacularly successful both in addressing these questions. and in its application to a wide range of astrophvsical problems unknown or unanticipated in the 1970s.," The VLA has been spectacularly successful both in addressing these questions, and in its application to a wide range of astrophysical problems unknown or unanticipated in the 1970s." + It has been so successful in (his latter area. because il was designed as a general purpose. reconfigurable array.," It has been so successful in this latter area because it was designed as a general purpose, reconfigurable array." + However. the VLA has changed very little since 1980.," However, the VLA has changed very little since 1980." + Although most of the receiver bands have seen improvements in sensitlivitv. and [our new receiving svstenis have been added. the arrays original signal transmission svstem and correlator remain unchanged.," Although most of the receiver bands have seen improvements in sensitivity, and four new receiving systems have been added, the array's original signal transmission system and correlator remain unchanged." + In {he approximately 30 vears since the VLA was designed. there have been enormous advances in technology. particularly in digital communication and signal processing capabilities.," In the approximately 30 years since the VLA was designed, there have been enormous advances in technology, particularly in digital communication and signal processing capabilities." + Over (he same interval. (he kev scientific questions have also undergone great. changes. requiring telescopes wilh ever greater emphasis on sensitivity. wider Irequency coverage. faster surveving capabilities. more spectral capabilities. higher imaging fidelity. aad Laster response to transient enission.," Over the same interval, the key scientific questions have also undergone great changes, requiring telescopes with ever greater emphasis on sensitivity, wider frequency coverage, faster surveying capabilities, more spectral capabilities, higher imaging fidelity, and faster response to transient emission." + One can respond to (hese challenges in two wavs: by designing wholly new imstruments. or by utilizing modern technologies to upgrade. ancl expand. the worlds preeminent existing telescopes.," One can respond to these challenges in two ways: by designing wholly new instruments, or by utilizing modern technologies to upgrade, and expand, the world's preeminent existing telescopes." + Taking the latter approach has resulted in the Expanded Very Large Array, Taking the latter approach has resulted in the Expanded Very Large Array +Οι. hence the feedback.,"$\Theta_1$, hence the feedback." + In the dual lossy source coding with feedforward setting we consider. O4 plavs the role of a lossy description of (he source sequence. and we will need (NX:Y) bits per source svinbol to represent it with high enough accuracy.," In the dual lossy source coding with feedforward setting we consider, $\Theta_1$ plays the role of a lossy description of the source sequence, and we will need $I(X;Y)$ bits per source symbol to represent it with high enough accuracy." +" In order to be able to generate AX, (lossv reconstruction of 35) thedecoder needs (o know the Y""! on top of the (quantized representation of the) lossy description O4. hence the feecllorward."," In order to be able to generate $X_n$ (lossy reconstruction of $Y_n$ ) thedecoder needs to know the $Y^{n-1}$ on top of the (quantized representation of the) lossy description $\Theta_1$, hence the feedforward." + Fix the block size n. and set R=ZCNX:Y)ο some 9>0.," Fix the block size $n$, and set $R = I(X;Y)+\delta$ for some $\delta>0$." +" Let (45,TE be an open partition of Z into equi-sized intervals. ancl let a,, be the midpoint of %,,."," Let $\{\m{J}_m\}_{m=1}^{\lfloor 2^{nR}\rfloor}$ be an open partition of $\m{I}$ into equi-sized intervals, and let $a_m$ be the midpoint of $\m{J}_m$." + Denote the set of all midpoints by τς., Denote the set of all midpoints by $A_n$ . + We are now ready to describe the compression protocol., We are now ready to describe the compression protocol. +The infrared images also show what appears to be a wide ring at 10-20 AU.,The infrared images also show what appears to be a wide ring at 10–20 AU. +" We can see from Figure 5 that this ring consists mostly of grains with s 3r_n$." + Secxxl Condition is the azimuthal extension of the emission region., Second condition is the azimuthal extension of the emission region. + We use the magnetic azinmutlia augle of the ootprint of field line (i.e.. the poiuo whe'e mmaenetic field lile penetrates the neutrou star surface o characterize the field liue for giver Nop»," We use the magnetic azimuthal angle of the footprint of field line (i.e., the point where magnetic field line penetrates the neutron star surface) to characterize the field line for given $r_{ov}$." + Raclial distance to the null clarge surface ou the [iek ines significantly depeuds on the maguetic azimuthal augle., Radial distance to the null charge surface on the field lines significantly depends on the magnetic azimuthal angle. + Iu the outer eap ος]. most of the j»alrs are created around tje null surace (TCS08).," In the outer gap model, most of the pairs are created around the null surface (TCS08)." + We expect that the eap activity Is related he distance to the null surface., We expect that the gap activity is related to the distance to the null surface. + Altiough the current density should je cletermined by [n]oOobal conditious. there is uo stidly of the th'ee-dimeusional magnetosphere of a1 inclined rotator.," Although the current density should be determined by global conditions, there is no study of the three-dimensional magnetosphere of an inclined rotator." +" In ihi yaper. we assume hat tie. field. lines of both outward and. imward emissiOll ale active ouly ift ‘aclial distance to ull str[ace ry, Issjiorter than Rye."," In this paper, we assume that the field lines of both outward and inward emission are active only ifthe radial distance to null surface $r_n$ is shorter than $R_{LC}$." + The azimuthal constrait| is automatically satisfied for outward eimission because the radial extensio Leives ry«Htpe., The azimuthal constraint is automatically satisfied for outward emission because the radial extension gives $r_n < R_{LC}$. + However. for inwar emission the condition becomes stro.&.," However, for inward emission the condition becomes strong." +" The radial extensio brerccmin(3ry.Re) allows lor t 'eelous r«pe on the field lines with ry,>νο."," The radial extension $r_s < r < \min(3r_n, R_{LC})$ allows for the regions $r < R_{LC}$ on the field lines with $r_n > R_{LC}$." + They a‘e not active. so that the correspouclioO 'eelous should e excluded.," They are not active, so that the corresponding regions should be excluded." +" The eritical value Br, was obt:üued by fitting to Vela pulsar (TCSOs).", The critical value $3r_n$ was obtained by fitting to Vela pulsar (TCS08). + [t is not straightforwardilo to apply it tο other sources., It is not straightforward to apply it to other sources. +" The ueau free path A(r) of the palr creation ILOCeSS |pelwee1 the 5-ray aud tlerual X-ray enisslons roni the stellar surface is estimated as A(r)ο.721BAO0)T, (Tangeetal.2008)."," The mean free path $\lambda(r)$ of the pair creation process between the $\gamma$ -ray and thermal X-ray emissions from the stellar surface is estimated as $\lambda (r) \sim 5.6 +P^{13/21}(B_s/10^{12}G)^{-2/7} r$ \citep{Ta08}." +". The value at the null pointis A(r,) fouud to je in a range of (2-3)ry lor our sainRmes.", The value at the null pointis $\lambda(r_n)$ found to be in a range of $(2$ $3)r_n$ for our samples. +" Our lieli curves especially peak positions are not clangect even by adopting 2r, as tlie ouer bo=idary [or inward emission.", Our light curves especially peak positions are not changed even by adopting $2r_n$ as the outer boundary for inward emission. + Spatial distribution of the emissivity is approximate by the step function-tvpe. but the peak positions weakly depend ou the detaid elissiviy cdistributiou.," Spatial distribution of the emissivity is approximated by the step function-type, but the peak positions weakly depend on the detailed emissivity distribution." + We assuiue that the overall struct='e ofthe light curve co1105 Lie [rom the emissivity distribution. but froma bunch ofmany fiekd lines i he observation. that iW.. Callsics.," We assume that the overall structure of the light curve comes not from the emissivity distribution, but from a bunch of many field lines in the observation, that is, caustics." + Tle appearance of caustics strongly depends ou the observational viewing angle € and tle iuelsity cisribution., The appearance of caustics strongly depends on the observational viewing angle $\xi$ and the intensity distribution. +" In this paper. we focus ou the peak phases of the ight curve. so we acloyt a simple. uniform emissivity along all inagneti€ field lines. which is indepeudent. of bot1 the1iagnetic azimuthal angle 6,5, aud the altitude rj."," In this paper, we focus on the peak phases of the light curve, so we adopt a simple, uniform emissivity along all magnetic field lines, which is independent of both the magnetic azimuthal angle $\phi_{m}$ and the altitude $r_{ov}$." + The fittiug does not completely reproduce the «Pbservatious so. iu Section L a simple improvemeit to the emissivity distribution is couside'ed which leads to a πιό better fit.," The fitting does not completely reproduce the observations so, in Section 4, a simple improvement to the emissivity distribution is considered which leads to a much better fit." + We now explain our fittingOm method., We now explain our fitting method. +" For fixed inclination angleOm a and viewiug angle € the light CULVE as a uuction of phase © depends ouly ou the atitude r,,."," For fixed inclination angle $\alpha $ and viewing angle $\xi$, the light curve as a function of phase $\phi$ depends only on the altitude $r_{ov}$ ." + The intersity is calculated in the πω”...L364? witha bin width of 0.02., The intensity is calculated in the range $ r_{ov}< 1.36^{1/2}$ witha bin width of 0.02. + There a‘e no significaut caustics for large roy., There are no significant caustics for large $ r_{ov}$ . +changed at ϐ>2 aresec. where the best-fitting amplitude is 5244174.10+.,"changed at $\theta>2$ arcsec, where the best-fitting amplitude is $52.4\pm 17.4\times +10^{-4}$." + This implies that. at z—1 2. faint X-ray sources (AGN and starbursts) in general (Le. not only the very reddened ones) cluster with LEROs.," This implies that, at $z\sim 1$ –2, faint X-ray sources (AGN and starbursts) in general (i.e. not only the very reddened ones) cluster with EROs." + We also calculated the eross-correlation of the sources with the separate plZRO and dsfl£ItO. subsamples (Figure 16b). and fitted the same Function as above at 2.0—0—20 arcsec.," We also calculated the cross-correlation of the sources with the separate pERO and dsfERO subsamples (Figure 16b), and fitted the same function as above at $2.0\leq \theta\leq 20$ arcsec." +" At the A,x21.5 limit the best-fit zl, are 34.53:27.0.10.1 (pEROs) and 30.2224.210+ (elsfEROs) neither measurement is a 2e detection and there is no significant dillerence between the two. so a larger sample will be needed. to investigate the dependence on spectral lvpe."," At the $K_s\leq 21.5$ limit the best-fit $A_{\omega}$ are $34.5\pm 27.0\times 10^{-4}$ (pEROs) and $39.2\pm 24.2\times +10^{-4}$ (dsfEROs) – neither measurement is a $2\sigma$ detection and there is no significant difference between the two, so a larger sample will be needed to investigate the dependence on spectral type." + Almaini et al. (, Almaini et al. ( +2003) cross-correlatecl bright sub-mum (SCUBA) sources and. X-rav (Chandra) sources on. the ELAIS:N2 field ancl detected. a signal at 40. significance. with a mean cross-correlation function. of ~0.6 at non-zero separations of 5«6<100 aresec.,"2003) cross-correlated bright sub-mm (SCUBA) sources and X-ray ) sources on the ELAIS:N2 field and detected a signal at $4\sigma$ significance, with a mean cross-correlation function of $\sim 0.6$ at non-zero separations of $5< \theta< 100$ arcsec." + However. while the bright. sub-nim sources are generally at high. redshifts e.g. Chapman et al. (," However, while the bright sub-mm sources are generally at high redshifts – e.g. Chapman et al. (" +2003) find. an interquartile range LO<22.8 fora spectroscopic sample of LO the source AN(z) is peakecl at only 20.7 (Calli et al.,"2003) find an interquartile range $1.9< z < +2.8$ for a spectroscopic sample of 10 – the source $N(z)$ is peaked at only $z\simeq 0.7$ (Gilli et al." + 2003. fromthe CDES 1 MS6ec survey).," 2003, from the CDFS 1 MSec survey)." + Part of the cross-correlation could be due to gravitational lensing of the sub-nim sources by lower redshift large-scale structure. traced by the X-ray sources (Almaini et al.," Part of the cross-correlation could be due to gravitational lensing of the sub-mm sources by lower redshift large-scale structure, traced by the X-ray sources (Almaini et al." + 2003b. and in prep.)," 2003b, and in prep.)." + On the other hand. the X-ray source IN(z) also has an extended: high-z tail. with 20 per cent at 2.21.5.," On the other hand, the X-ray source $N(z)$ also has an extended $z$ tail, with $\sim 20$ per cent at $z>1.5$." + Furthermore these high-z. X-ray. sources are clustered. with Ας) spikes at 2=1.618 and z=2.572. and some of the faintest sources are themselves detections (Alexander ct al.," Furthermore these $z$ X-ray sources are clustered, with $N(z)$ spikes at $z=1.618$ and $z=2.572$, and some of the faintest sources are themselves detections (Alexander et al." + 2003)., 2003). + Hence. it is probable that a real clustering together of sub-mim anc X-ray sources is. also contributing.," Hence, it is probable that a real clustering together of sub-mm and X-ray sources is also contributing." + Fortunately. lensing cllects will be much less significant in the case of our source ERO correlation.," Fortunately, lensing effects will be much less significant in the case of our source – ERO correlation." + Firstly. the elleet of lensing on the observed surface density of any type of source depends on its number count slope: for a power-law 4ΝmΞ the cumulative count to magnitude m is modified. by a muliplicative factor 677: where yr is the lensing magnification (Almaini ct al.," Firstly, the effect of lensing on the observed surface density of any type of source depends on its number count slope; for a power-law ${dN\over + dm}=\gamma$ the cumulative count to magnitude $m$ is modified by a muliplicative factor $\mu^{2.5\gamma - 1}$ , where $\mu$ is the lensing magnification (Almaini et al." + 2003b)., 2003b). + The sub-mm number counts are extremely steep. 521. whereas the majority of the EROs are at. A19.25 with *>0.16.," The sub-mm number counts are extremely steep, $\gamma\simeq 1$, whereas the majority of the EROs are at $K_s>19.25$ with $\gamma\simeq 0.16$." + Lensing of so1.25- near a cluster would then enhance the probability of finding a sub-mam source by 40 per cent but the number of EROs by 10 per cent., Lensing of $\mu\simeq 1.25$ near a cluster would then enhance the probability of finding a sub-mm source by 40 per cent but the number of EROs by 10 per cent. + Secondly. the redshifts of EROs (e.g. Cimatti et al.," Secondly, the redshifts of EROs (e.g. Cimatti et al." + 2002a. 2002b) show much more overlap with the sources than do the sub-mim sources.," 2002a, 2002b) show much more overlap with the sources than do the sub-mm sources." + Llenee. we interpret. our cross-correlation as evidence that these galaxies do trace the same large-scale structures.," Hence, we interpret our cross-correlation as evidence that these galaxies do trace the same large-scale structures." +" We identify a sample of 198. EROs. defined here as ""EEdy.3.92 galaxies. to a limit A;=22 on public ESO/GOODS data covering 504 avemin? of the Chandra Deep Field South CCDES)."," We identify a sample of 198 EROs, defined here as $I_{775}-K_s>3.92$ galaxies, to a limit $K_s=22$ on public ESO/GOODS data covering 50.4 $\rm arcmin^2$ of the Chandra Deep Field South (CDFS)." + Of these. 179 are brighter than an estimated completeness limit of A;=21.5.," Of these, 179 are brighter than an estimated completeness limit of $K_s=21.5$." + The number counts of EROs flatten markedly at Aστ 19.5. from *=0.59+011 to 5=0.1640.05.," The number counts of EROs flatten markedly at $K_s\simeq 19.0$ –19.5, from $\gamma\simeq 0.59\pm 0.11$ to $\gamma\simeq 0.16\pm 0.05$." + As we previously reported. counts of EROs are significantly. lower than predicted by a model in which all present-day 12/80 galaxies have undergone pure luminosity evolution (PLE).," As we previously reported, counts of EROs are significantly lower than predicted by a model in which all present-day E/S0 galaxies have undergone pure luminosity evolution (PLE)." + At dy.20. the ERO counts fall below even a non-evolving 15/80 model. suggesting that the comoving number density (and not only the mass or luminosity) of redpassive galaxies is lower at z=>1.," At $K_s>20$, the ERO counts fall below even a non-evolving E/S0 model, suggesting that the comoving number density (and not only the mass or luminosity) of red/passive galaxies is lower at $z\geq 1$." +" The ERO counts can be fitted much more closely by our ""merging and negative density evolution’ (M-DIZ) moclel (Paper D. in which a local luminosity function. for [2/80 ealaxies is evolved through a combination of (i) passive L' evolution. Gi) merging at an evolving rate based. on an observational estimate (Patton et al."," The ERO counts can be fitted much more closely by our `merging and negative density evolution' (M-DE) model (Paper I), in which a local luminosity function for E/S0 galaxies is evolved through a combination of (i) passive $L^*$ evolution, (ii) merging at an evolving rate based on an observational estimate (Patton et al." + 2002). ancl (iii) a gradual decrease. with redshift in the comoving number density of red/passsive galaxies. parameterized as 2...," 2002), and (iii) a gradual decrease with redshift in the comoving number density of red/passsive galaxies, parameterized as $R_{\phi}$." +" The best-fitting £75,2 O0.49(+0.06) corresponds to a 42/61/68 per cent reduction in & at 2=1/2/3.", The best-fitting $R_{\phi}\simeq -0.49(\pm 0.06)$ corresponds to a 42/61/68 per cent reduction in $\phi^*$ at $z=1/2/3$. + This could be interpreted. as ao =Lp Lraction. of⋅ the present clay CODIOVIDE. number density of E/80 galaxies forming at z>3 and the remainder from mergers and. interactions of blucr galaxies (e.g. spirals) over all intermediate redshifts., This could be interpreted as a $\sim {1\over 3}$ fraction of the present day comoving number density of E/S0 galaxies forming at $z>3$ and the remainder from mergers and interactions of bluer galaxies (e.g. spirals) over all intermediate redshifts. +" We investigate the clustering of the CDES EROs and detect a 3o signal in the angular correlation. function. wí(8).at AN,=21.22 limits."," We investigate the clustering of the CDFS EROs and detect a $>3\sigma$ signal in the angular correlation function, $\omega(\theta)$, at $K_s=21-22$ limits." + Phe w(9) amplitudes. combined with those from previous studies of ERO clustering (Paper ]: Daddi et al.," The $\omega(\theta)$ amplitudes, combined with those from previous studies of ERO clustering (Paper I; Daddi et al." + 2000: Firth et al., 2000; Firth et al. + 2002). are interpreted using models based on the Limber's formula integration of our “ALDE model IN(z) for EROs.," 2002), are interpreted using models based on the Limber's formula integration of our `M-DE' model $N(z)$ for EROs." + The w(@) scaling of EROs at A.=I8 22 limits is welblitted with either comoving (c=— 1.2) clustering and a correlation radius ro=125(41.2)h+ Alpe. or stable clustering {ο= 0) and ro=214(+2.0)b.+ Alpe.," The $\omega(\theta)$ scaling of EROs at $K=18$ –22 limits is well-fitted with either comoving $\epsilon=-1.2$ ) clustering and a correlation radius $r_0=12.5(\pm +1.2)~h^{-1}$ Mpc, or stable clustering $\epsilon=0$ ) and $r_0=21.4(\pm 2.0)~h^{-1}$ Mpc." + Our sample appears to be insulliciently large for us to either confirm or exclude the recent claim that pl£ltOs are more clustered at z21 than dsfEROs (Dacleli et al., Our sample appears to be insufficiently large for us to either confirm or exclude the recent claim that pEROs are more clustered at $z\simeq 1$ than dsfEROs (Daddi et al. + 2002)., 2002). + Por Cull A-IHimited samples of galaxies. ο(0) is consistent the locally measured. correlation radius of rj=5.85h Alpe. with little or no clustering evolution. «c— 0.40.," For full $K$ -limited samples of galaxies, $\omega(\theta)$ is consistent the locally measured correlation radius of $r_0=5.85~h^{-1}$ Mpc, with little or no clustering evolution, $\epsilon\simeq -0.4$ –0." + In contrast. EROs are even more clustered. than local giant GLc L) ellipticals (with ro28P1 Alpe). implving that if the EROs are cirect progenitors of the E/SOs. they undergo strong clustering evolution (c< 1.2).," In contrast, EROs are even more clustered than local giant $L>L^*$ ) ellipticals (with $r_0\simeq 8~h^{-1}$ Mpc), implying that if the EROs are direct progenitors of the E/S0s, they undergo strong clustering evolution $\epsilon\leq -1.2$ )." + Vhis could be part of the same process as the ο) evolution. if the oldest EROs form as strongly clustered. massive sub-mun sources. while the vounger EROs. added ad lowerredshift. form [from less strongly clustered. clisk ealaxies and progessively dilute the red-galaxy £r) down to its present-day value.," This could be part of the same process as the $\phi^*$ evolution, if the oldest EROs form as strongly clustered, massive sub-mm sources, while the younger EROs, added at lowerredshift, form from less strongly clustered disk galaxies and progessively dilute the red-galaxy $\xi(r)$ down to its present-day value." + This scenario may be supported by aa |weliminary ‘COMBO 17. findingT (Phleps| and Moeisenheimer 2002) that ESh type galaxies show a rapid increase of, This scenario may be supported by a a preliminary `COMBO 17' finding (Phleps and Meisenheimer 2002) that E–Sb type galaxies show a rapid increase of +from the over-expaucled star sets (he periodicity.,from the over-expanded star sets the periodicity. +" The (vpical mass in the maximum part of the envelope. when 7,2000Ix. is Moyc4xOups. where ο is the stellar radius in the over-expanded state. and oo~I."," The typical mass in the maximum over-expanded part of the envelope, when $T_p \simeq 2000 \K$, is $M_{OE} \simeq 4 \pi \beta R_{OE}^3 \rho_p$, where $R_{OE}$ is the stellar radius in the over-expanded state, and $\beta \sim 1$." + Using the scaling in equation (6) gives Mop~0.02..., Using the scaling in equation (6) gives $ M_{OE} \simeq 0.02 M_\odot$. + For a mass loss rate Mop. this part of the envelope will be depleted in a (ime The mass loss rate of ~10.TAL.vr. tis observed at the upper AGB. and it is in accord wilh Wachter et al. (," For a mass loss rate $\dot M_{OE}$, this part of the envelope will be depleted in a time The mass loss rate of $\sim 10^{-4} M_\odot \yr^{-1}$ is observed at the upper AGB, and it is in accord with Wachter et al. (" +2002) for these parameters.,2002) for these parameters. + The depletion time of the over-expauded envelope may set the period of the semi-periodie ares: a large fraction of the over-extended envelope mass is lost in the wind. such that the star shrinks and mass loss rate drops.," The depletion time of the over-expanded envelope may set the period of the semi-periodic arcs: a large fraction of the over-extended envelope mass is lost in the wind, such that the star shrinks and mass loss rate drops." + When the photospheric temperature rises again (o 3000Ix. another over-expaaxded phase starts.," When the photospheric temperature rises again to $\sim 3000 \K$, another over-expanded phase starts." + The exact conditions for the occurrence of this speculative evele should be determined by stellar evolutionary numerical code. possibly including rotation and magnetic activity.," The exact conditions for the occurrence of this speculative cycle should be determined by stellar evolutionary numerical code, possibly including rotation and magnetic activity." + The much cooler over-expanded envelope is more susceptible to some mechanisms which enhance dust formation. e.g.. shocks bv convective cells and magnetic cool spots.," The much cooler over-expanded envelope is more susceptible to some mechanisms which enhance dust formation, e.g., shocks by convective cells and magnetic cool spots." + In particular. 1 is enough Chat during the over-expancled state (he temperature above magnetic cool spots be only slightly lower to substantially enhance dust. formation. hence mass loss rate.," In particular, it is enough that during the over-expanded state the temperature above magnetic cool spots be only slightly lower to substantially enhance dust formation, hence mass loss rate." + If magnetic spols are concentrated in the equatorial plane. this may increase (he mass loss rate (here. leading to axisvimmeltric mass loss.," If magnetic spots are concentrated in the equatorial plane, this may increase the mass loss rate there, leading to axisymmetric mass loss." +" Because the total mass loss rate increases as well (see previous subsection). this leads (o a positive correlation between mass loss rate and deviation from spherical mass loss,"," Because the total mass loss rate increases as well (see previous subsection), this leads to a positive correlation between mass loss rate and deviation from spherical mass loss." + Another effect is in svstems where a companion at a large orbital separation accretes [rom the AGB wind. forms an accretion disk. and blows collimated [ast wind (CEW: or two jets).," Another effect is in systems where a companion at a large orbital separation accretes from the AGB wind, forms an accretion disk, and blows collimated fast wind (CFW; or two jets)." + The hieher mass loss rate and slower wind velocity. because of lower escape velocity. will make such a mechanism much more likely to occur (Soker 2001).," The higher mass loss rate and slower wind velocity, because of lower escape velocity, will make such a mechanism much more likely to occur (Soker 2001)." + There is a group of post-AGB stars (or stars about to leave the AGB). which have a binary companion and a circumbinary disk: most of these stars are classilied as RV Tauri stars. (Mass et 22005: De Ruvter et 22005). ancl most svstems have their orbital period," There is a group of post-AGB stars (or stars about to leave the AGB), which have a binary companion and a circumbinary disk; most of these stars are classified as RV Tauri stars, (Mass et 2005; De Ruyter et 2005), and most systems have their orbital period" +to as ring-like structures surrounding the pore. are used for this analysis.,"to as ring-like structures surrounding the pore, are used for this analysis." + We emphasize that the following results should not be taken as trying to globalize the properties and behavior of the flows around all solar pores but as a preliminar and simplistic case in which we can compare two pores of our sample under similar conditions (size. shape. polarity among others) and apply the above-mentioned method of computing velocities in ribbons around them.," We emphasize that the following results should not be taken as trying to globalize the properties and behavior of the flows around all solar pores but as a preliminar and simplistic case in which we can compare two pores of our sample under similar conditions (size, shape, polarity among others) and apply the above-mentioned method of computing velocities in ribbons around them." + In a future work we will conduct a study to be able to compare more general cases., In a future work we will conduct a study to be able to compare more general cases. + Figure 10 panels)) plots the speeds versus distance to the pore border., Figure \ref{magvel_pore} ) plots the speeds versus distance to the pore border. +" The velocity magnitudes increment. às a function of this distance: 1) the mean value of speeds increments rapidly at distances ranging from ~ 0715 to 074; 2) in the range 074 - 170 the variation curve is flatter, 3) in the range 170 - 16 we again obtain very sharp increments.", The velocity magnitudes increment as a function of this distance: 1) the mean value of speeds increments rapidly at distances ranging from $\sim$ $\farcs$ 15 to $\farcs$ 4; 2) in the range $\farcs$ 4 - $\farcs$ 0 the variation curve is flatter; 3) in the range $\farcs$ 0 - $\farcs$ 6 we again obtain very sharp increments. + Up to this distance from the pore border. we observe the same behavior in both pores.," Up to this distance from the pore border, we observe the same behavior in both pores." + Nevertheless. the mean speed values at l6 are quite different (250 3390 m κ.," Nevertheless, the mean speed values at $\farcs$ 6 are quite different (250 390 m $^{-1}$ )." + At further distances (> 176) the trend in the mean velocity magnitudes differs substantially., At further distances $>$ $\farcs$ 6) the trend in the mean velocity magnitudes differs substantially. + We must bear in mind that the flows around the pore can also be affected by the intrinsic characteristics of every single pore and by the contribution from other sources in the neighbourhood. ppores 1n the vicinity.," We must bear in mind that the flows around the pore can also be affected by the intrinsic characteristics of every single pore and by the contribution from other sources in the neighbourhood, pores in the vicinity." + The proper motions in solar active regions displaying pores are analyzed from high-resolution time series of images., The proper motions in solar active regions displaying pores are analyzed from high-resolution time series of images. + The observing material stems from coordinated ground-based anc space observations., The observing material stems from coordinated ground-based and space observations. + Thus. part of this material was acquirec with the Swedish 1-m Solar Telescope. and reconstructed by employing the novel MFBD and MOMFBD techniques to achieve image resolutions near the diffraction limit.," Thus, part of this material was acquired with the Swedish 1-m Solar Telescope, and reconstructed by employing the novel MFBD and MOMFBD techniques to achieve image resolutions near the diffraction limit." + The other part of the data stems from the solar telescope Οἱ board the satellite., The other part of the data stems from the solar telescope on board the satellite. + The long duration. stability anc high-resolution of the time series achieved by enable us to study dynamical properties of the photospheric horizontal flows along periods of time much longer than those typically reachable from ground-based observations which are restricted by varying seeing The local correlation technique applied to the time series allowed us to track the proper motions of structures in. solar active regions and particularly in the areas nearby solar pores.," The long duration, stability and high-resolution of the time series achieved by enable us to study dynamical properties of the photospheric horizontal flows along periods of time much longer than those typically reachable from ground-based observations which are restricted by varying seeing The local correlation technique applied to the time series allowed us to track the proper motions of structures in solar active regions and particularly in the areas nearby solar pores." + Proper motions have been tracked in a variety of active regions for periods of typically 20-60 min but also one for several hours., Proper motions have been tracked in a variety of active regions for periods of typically 20-60 min but also one for several hours. + We conclude that the flow patterns derived from different observational sets are consistent among each other in the sense that they show the determinant and overall influence of exploding events in the granulation around the pores and in the whole FOV., We conclude that the flow patterns derived from different observational sets are consistent among each other in the sense that they show the determinant and overall influence of exploding events in the granulation around the pores and in the whole FOV. + Motions toward the pores in their nearest vicinity are the dominant characteristic we claim to observe systematically., Motions toward the pores in their nearest vicinity are the dominant characteristic we claim to observe systematically. + Thus. we do not find any trace of moat flow in the wide sample of pores studied.," Thus, we do not find any trace of moat flow in the wide sample of pores studied." + The motions at the periphery of the pores are basically influenced by the external plasma flows deposited by the exploding events. as suggested by other authors in previous works (Sobotkaetal..1999:Roudier.Bonet&Sobotka.2002;SankarasubramanianRimmele. 2003).," The motions at the periphery of the pores are basically influenced by the external plasma flows deposited by the exploding events, as suggested by other authors in previous works \citep{sobotka1999, roudier2002, sankara2003}." +. In addition. the horizontal velocity magnitudes are clearly lower (< 0.3 km s! ) in the nearest locations surrounding the pores and. in general. in the more nagnetized regions in the FOV. as expected due to the mhibition of convection taking Our results are also in agreement with recently developed 3D radiative magnetohydrodynamie simulations of pore-like magnetic structures that report downflows surrounding them. maintained by horizontal flows towards the simulated. pore (Cameronetal..2007).," In addition, the horizontal velocity magnitudes are clearly lower $<$ 0.3 km $^{-1}$ ) in the nearest locations surrounding the pores and, in general, in the more magnetized regions in the FOV, as expected due to the inhibition of convection taking Our results are also in agreement with recently developed 3D radiative magnetohydrodynamic simulations of pore-like magnetic structures that report downflows surrounding them, maintained by horizontal flows towards the simulated pore \citep{cameron2007}." +. Moreover. we interpret the dividing line between radial inward and outward motions. found by Dengetal.(2007) outside the residual pore in the last stage of a decaying sunspot. as corresponding to the location of the centres of divergence of the exploding events around the pore.," Moreover, we interpret the dividing line between radial inward and outward motions, found by \cite{deng2007} outside the residual pore in the last stage of a decaying sunspot, as corresponding to the location of the centres of divergence of the exploding events around the pore." + The outward motions these authors describe. which are not in the immediate surroundings of the pore but separatec by the annular inward motion. would then correspond not to moat flows but to the outward flows originated in the regular mesh of divergence centers around the pore.," The outward motions these authors describe, which are not in the immediate surroundings of the pore but separated by the annular inward motion, would then correspond not to moat flows but to the outward flows originated in the regular mesh of divergence centers around the pore." +In Table A6.. we give the absolute flux at the stellar surface and its error for the late-K and M stars of the FEROSOS observing run.,"In Table \ref{tab:activity_flux}, we give the absolute flux at the stellar surface and its error for the late-K and M stars of the FEROS05 observing run." + We refer the reader to L$10 and MAIO for a compilation of the fluxes of the rest of the stars., We refer the reader to LS10 and MA10 for a compilation of the fluxes of the rest of the stars. + X-ray flux is a direct measure of stellar activity because it is unlikely to include contributions from other sources such as the basal atmosphere (22).," X-ray flux is a direct measure of stellar activity because it is unlikely to include contributions from other sources such as the basal atmosphere \citep{1991A&A...252..203R,1992A&A...258..432S}." + Therefore. in addition to the optical data. we searched for X-ray counterparts of the stars in our sample in the ROSAT All Sky Survey (RASS) catalogue.," Therefore, in addition to the optical data, we searched for X-ray counterparts of the stars in our sample in the ROSAT All Sky Survey (RASS) catalogue." + For this purpose we followed ?.., For this purpose we followed \citet{2009A&A...499..129L}. + We cross-correlated our total stellar sample with the ROSAT AII-SKy Survey Bright Source Catalogue (RASS-BSC) and the Faint Source Catalogue (RASS-FSC) using a search radius of 30 aresec to account for the ROSAT X-ray object coordinate determination accuracy., We cross-correlated our total stellar sample with the ROSAT All-Sky Survey Bright Source Catalogue (RASS-BSC) and the Faint Source Catalogue (RASS-FSC) using a search radius of 30 arcsec to account for the ROSAT X-ray object coordinate determination accuracy. + We found 243 counterparts for the sample of 298 stars., We found 243 counterparts for the sample of 298 stars. + To determine the X-ray fluxes. we used the count energy flux conversion factor (CF) relation found by 9? where AR is the hardness-ratio of the star in the ROSAT energy band 0.1—2.4 Κον detined as HR=(H-S)/(H+S8) with H and S being the counts in the detector channels 11—49 and 52-201. respectively.," To determine the X-ray fluxes, we used the count rate-to-energy flux conversion factor $CF$ ) relation found by \citet{1995ApJ...450..392S} + where $HR$ is the hardness-ratio of the star in the ROSAT energy band 0.1–2.4 KeV, defined as $HR = (H - S)/(H+S)$ with $H$ and $S$ being the counts in the detector channels 11–49 and 52–201, respectively." + X-ray fluxes were determined by multiplying the CF value by the count-rate of the sources in the same band., X-ray fluxes were determined by multiplying the $CF$ value by the count-rate of the sources in the same band. + Note that the fluxes determined in this way are observed fluxes. but not surface fluxes.," Note that the fluxes determined in this way are observed fluxes, but not surface fluxes." + Fluxes were then transformed into luminosities using the distances from the star to the Earth., Fluxes were then transformed into luminosities using the distances from the star to the Earth. + Since the CF and the count rate (CA) are defined for the ROSAT energy band 0.1—2.4. KeV. the X-ray uminosity Lx is also integrated in this band.," Since the $CF$ and the count rate $CR$ ) are defined for the ROSAT energy band 0.1–2.4 KeV, the X-ray luminosity $L_{\rm X}$ is also integrated in this band." + To obtain surface X-ray fluxes we used the computed uminosities and the stellar radius., To obtain surface X-ray fluxes we used the computed luminosities and the stellar radius. + Since the stars in the sample are dwarfs (see L$10. MAIO and Table A4). the radius were estimated by using a ZAMS calibration.," Since the stars in the sample are dwarfs (see LS10, MA10 and Table \ref{tab:parameters}) ), the radius were estimated by using a ZAMS calibration." + The number of matches between our sample and the RASS decreases with increasing distance., The number of matches between our sample and the RASS decreases with increasing distance. + For instance. ? observed that. or their sample. at 4.<40 ppe. approximately of the stars were eross-identified. while at V.€50 ppc. only half of them had an RASS counterpart.," For instance, \citet{2009A&A...499..129L} observed that, for their sample, at $d \le 40$ pc, approximately of the stars were cross-identified, while at $d \le 50$ pc, only half of them had an RASS counterpart." + This suggests that some X-ray emitters at large distances are lost as a consequence of the flux limit of the RASS. producing a bias in our X-ray sample.," This suggests that some X-ray emitters at large distances are lost as a consequence of the flux limit of the RASS, producing a bias in our X-ray sample." + Note that the MAIO sample is limited to 25 pe and this effect should be negligible., Note that the MA10 sample is limited to 25 pc and this effect should be negligible. + In the following we address the subject of flux—flux relationships from a classical point of view and make no distinction between stars., In the following we address the subject of flux–flux relationships from a classical point of view and make no distinction between stars. + In Figs., In Figs. + 3. and 4+ we compare pairs of fluxes of different chromospheric lines for all the stars in our sample., \ref{fig:flux_all} and \ref{fig:flux_ha} we compare pairs of fluxes of different chromospheric lines for all the stars in our sample. + For those stars observed more than once we plot the median value determined by us with all the observations and an error bar representing the maximum deviation from it., For those stars observed more than once we plot the median value determined by us with all the observations and an error bar representing the maximum deviation from it. + Power-law relationships between pairs of lines have beendetermined by fitting the data to a relation of the ypewhere Fy and Εν are the fluxes of two ditferent lines and οἱ and c» are the fitting parameters., Power-law relationships between pairs of lines have beendetermined by fitting the data to a relation of the typewhere $F_{\rm 1}$ and $F_{\rm 2}$ are the fluxes of two different lines and $c_{\rm 1}$ and $c_{\rm 2}$ are the fitting parameters. + We used the method explained in ? to determine cj. c» and their errors.," We used the method explained in \citet{1990ApJ...364..104I} + to determine $c_{\rm 1}$, $c_{\rm 2}$ and their errors." + The bisector of the two possible ordinary least squares regressions (Y on X and X on Y) was determined in each case., The bisector of the two possible ordinary least squares regressions (Y on X and X on Y) was determined in each case. + The ordinary least squares bisector regression is the best solution when the goal is to estimate the underlying functional relation between the variables completestudyofthe problem).," The ordinary least squares bisector regression is the best solution when the goal is to estimate the underlying functional relation between the variables \citep[see][for a complete study of +the problem]{1990ApJ...364..104I}." +" In Table 2. we present the results for c, and c». This table also ists the values of the slope (co) previously obtained in different studies by other authors (222222)."," In Table \ref{tab:flux_rel} we present the results for $c_1$ and $c_2$ This table also lists the values of the slope $c_2$ ) previously obtained in different studies by other authors \citep{1989ApJ...337..964S,1995A&A...294..165M, +1996A&A...312..221M,1996ASPC..109..657M,2005PhDT........14B,2010A&A...520A..79M}." + Comparing columns £55 and #77 in Table 2. we observe that the values obtained for the linear tit of the data in this work are compatible. taking uncertainties into account. with those previously reported for single F. G and early-K stars for all chromospheric indicators.," Comparing columns 5 and 7 in Table \ref{tab:flux_rel} we observe that the values obtained for the linear fit of the data in this work are compatible, taking uncertainties into account, with those previously reported for single F, G and early-K stars for all chromospheric indicators." + It is important to mention hat while this study is based on single active stars. ? is focused on active binary stars.," It is important to mention that while this study is based on single active stars, \citet{1995A&AS..114..287M} is focused on active binary stars." + However. the ditferences obtained in the atter cases are not more noticeable than those obtained when one compares the results obtained in this work and other single based studies.," However, the differences obtained in the latter cases are not more noticeable than those obtained when one compares the results obtained in this work and other single star-based studies." + The values obtained for the slopes in the relationships between xirs of logarithmic fluxes follow the trend that has previously been reported. £e. the larger the difference in atmospheric height at which the compared lines form. the larger the value of the slope.," The values obtained for the slopes in the relationships between pairs of logarithmic fluxes follow the trend that has previously been reported, $i.e.$ the larger the difference in atmospheric height at which the compared lines form, the larger the value of the slope." + This result has been obtained before using not only chromospheric indicators (2).. but also transition region (222)— and coronal diagnostics (22)..," This result has been obtained before using not only chromospheric indicators \citep{1996ASPC..109..657M}, , but also transition region \citep{1986A&A...154..185O,1991A&A...251..183S,1996ASPC..109..657M} and coronal diagnostics \citep{1989ApJ...337..964S,1996ASPC..109..657M}." + It is important to mention that after measuring excess EW. we applied the Ha £W criterion (2). to ensure that no stars with an," It is important to mention that after measuring excess $EW$ , we applied the $\alpha$ $EW$ criterion \citep{2003AJ....126.2997B} to ensure that no stars with an" +like GRB 980425 is unlikely to happen any time soon. even assuming that the association is real. and consequently. the question of whether Type Ib-Ic SNe can produce extremely faint GRBs is likely to remain open for a long time.,"like GRB 980425 is unlikely to happen any time soon, even assuming that the association is real, and consequently, the question of whether Type Ib-Ic SNe can produce extremely faint GRBs is likely to remain open for a long time." + Earlier studies have shown that gamma-ray bursts can be separated into two classes: short. harder. more variable bursts; and long. softer. smoother bursts (see. e.g.. Lamb. Graziant Smith 1993: Kouveliotou et al.," Earlier studies have shown that gamma-ray bursts can be separated into two classes: short, harder, more variable bursts; and long, softer, smoother bursts (see, e.g., Lamb, Graziani Smith 1993; Kouveliotou et al." + 1993)., 1993). + Recently. Mukherjee et al. (," Recently, Mukherjee et al. (" +1999) have provided evidence for the possible existence of a third class of bursts. based on these same properties of duration. hardness and smoothness properties of the bursts.,"1999) have provided evidence for the possible existence of a third class of bursts, based on these same properties of duration, hardness and smoothness properties of the bursts." +" Also. the hardest long bursts exhibit a pronounced deviation from the -3/2 power-law required for a homogeneous spatial distribution of sources. whereas the short bursts and the softest long bursts do not (Pizzichini 1995; Kouveliotou 1996; Belli 1997, 1999; Tavani 1998)."," Also, the hardest long bursts exhibit a pronounced deviation from the -3/2 power-law required for a homogeneous spatial distribution of sources, whereas the short bursts and the softest long bursts do not (Pizzichini 1995; Kouveliotou 1996; Belli 1997, 1999; Tavani 1998)." + These results contradict the expectation that the most distant bursts should be the most affected by cosmological energy redshift and time dilation., These results contradict the expectation that the most distant bursts should be the most affected by cosmological energy redshift and time dilation. + Some bursts show considerable high-energy (EF>300 keV) emission whereas others do not. but it is doubtful that this difference signifies two separate GRB classes. since a similar difference in behavior 15 seen for peaks within a burst (Pendleton et al.," Some bursts show considerable high-energy $E > 300$ keV) emission whereas others do not, but it is doubtful that this difference signifies two separate GRB classes, since a similar difference in behavior is seen for peaks within a burst (Pendleton et al." + 1998)., 1998). + It is not clear whether the short and long classes. and the other differences among various burst properties. reflect distinct burst mechanisms. or whether they are due to beaming-or some other property of the bursts—and different viewing angles.," It is not clear whether the short and long classes, and the other differences among various burst properties, reflect distinct burst mechanisms, or whether they are due to beaming--or some other property of the bursts–and different viewing angles." +" Some theorists say. however. that the ""collapsar"" or ""hypernova model cannot explain the short bursts (see. e.g.. Woosley 1999)."," Some theorists say, however, that the “collapsar” or “hypernova” model cannot explain the short bursts (see, e.g., Woosley 1999)." + Because of observational. selection. effects. all of the GRBs that have been detected by the BeppoSAX GRBM and observed by the WFC have been long bursts.," Because of observational selection effects, all of the GRBs that have been detected by the BeppoSAX GRBM and observed by the WFC have been long bursts." + It may be possible for BeppoSAX to revise its GRB detection algorithm 1n order to detect short bursts., It may be possible for BeppoSAX to revise its GRB detection algorithm in order to detect short bursts. + We also expect that HETE-2 will detect short bursts and determine their positions (Kawai et al., We also expect that HETE-2 will detect short bursts and determine their positions (Kawai et al. +" 1999, Ricker et al."," 1999, Ricker et al." + 1999)., 1999). + If so. follow-up observations may well lead to a breakthrough in our understanding of the nature of the short bursts similar to that which has occurred for the long bursts.," If so, follow-up observations may well lead to a breakthrough in our understanding of the nature of the short bursts similar to that which has occurred for the long bursts." + A nightmare I sometimes have is that HETE-2 provides accurate positions. for a number of short bursts. but the positions are not coincident with any host galaxies because the bursts are due to merging compact object binaries that have drifted away from their galaxy of origin (see below).," A nightmare I sometimes have is that HETE-2 provides accurate positions for a number of short bursts, but the positions are not coincident with any host galaxies because the bursts are due to merging compact object binaries that have drifted away from their galaxy of origin (see below)." + And furthermore. the bursts exhibit no soft X-ray. optical. or radio afterglows because any envelope that the progenitors of the compact objects might have expelled has been left behind. and the intergalactic medium is too tenuous to dissipate efficiently the energy in the relativistic external shock that is widely thought to be the origin of GRB afterglows.," And furthermore, the bursts exhibit no soft X-ray, optical, or radio afterglows because any envelope that the progenitors of the compact objects might have expelled has been left behind, and the intergalactic medium is too tenuous to dissipate efficiently the energy in the relativistic external shock that is widely thought to be the origin of GRB afterglows." + The redshifts of such bursts would be difficult. if not impossible. to determine. since they could not be inferred from the redshift of any host galaxy. nor constrained by the observation of absorption-line systems in the spectrum of any optical afterglow.," The redshifts of such bursts would be difficult, if not impossible, to determine, since they could not be inferred from the redshift of any host galaxy, nor constrained by the observation of absorption-line systems in the spectrum of any optical afterglow." + On a more positive note. future radio. optical. and X-ray observations of GRB afterglows and host galaxies. may well lead to the identification of new subelasses of GRBs.," On a more positive note, future radio, optical, and X-ray observations of GRB afterglows and host galaxies, may well lead to the identification of new subclasses of GRBs." + The detection of burst X-ray and optical afterglows has led in eight cases to identification of the likely host galaxy by positional coincidence with the optical afterglow., The detection of burst X-ray and optical afterglows has led in eight cases to identification of the likely host galaxy by positional coincidence with the optical afterglow. + At Ro=25.526. the typical R-band magnitudes of these galaxies. galaxies cover of the sky for ground-based observations. because of smearing of the galaxy images due," At $R = 25.5 -26$, the typical R-band magnitudes of these galaxies, galaxies cover of the sky for ground-based observations, because of smearing of the galaxy images due" +he two best-fit planes. i.e. (7.5) —(31. LR) and (176° 53°). respectively (Euctal.2010).. (,"the two best-fit planes, i.e., $l$ $b$ $311\arcdeg$ $-14\arcdeg$ ) and $176\arcdeg$, $-53\arcdeg$ ), respectively \citep{Luetal10}. (" +2) The stellar oinaries are initially set on orbits with scmimajor axes of EUNT 0.5pc. aud this range is adopted accorlue o the observational exteuts of the CWS disk.,"2) The stellar binaries are initially set on orbits with semimajor axes of $a_{\rm out,i}\sim$ $-$ $\pc$, and this range is adopted according to the observational extents of the CWS disk." + We note rere that the extents of the structure associated with he second plane are not clear., We note here that the extents of the structure associated with the second plane are not clear. + Nevertheless. we assunue hat it is iu the same rauge as the CWS disk.," Nevertheless, we assume that it is in the same range as the CWS disk." + Adopting a slightly larger range (sav. from O.Olpe to l1pe) «ους tot affect the results presented in this section and uext section. (," Adopting a slightly larger range (say, from $0.04\pc$ to $1\pc$ ) does not affect the results presented in this section and next section. (" +3) The distribution of Cour; Of these binaries is assunied to follow the same surTace density. distriltion as that of stars in the CWS disk fisci)~aout.i2° (Euetal.2009:Bartko2009). . C,"3) The distribution of $a_{\rm out,i}$ of these binaries is assumed to follow the same surface density distribution as that of stars in the CWS disk $f(a_{\rm out,i}) \sim a_{\rm out,i}^{-2.3}$ \citep{LuJ09,Bartko09a}. (" +D) The distribution of the initial periapsis of the stellar binaries should depend ou detailed mechanisius leading to the injection.,4) The distribution of the initial periapsis of the stellar binaries should depend on detailed mechanisms leading to the injection. + It is not clear how bound binarics (iu fje outer disk region) are delivered to the mauuediate vicinity of the ceutral MDIT., It is not clear how bound binaries (in the outer disk region) are delivered to the immediate vicinity of the central MBH. + Nevertheless. the mechanism respousible for the small orbital angular ποιοτι of tje stellar binary may fall iuto the two extreme categories discussed. below.," Nevertheless, the mechanism responsible for the small orbital angular momentum of the stellar binary may fall into the two extreme categories discussed below." + Table 2. lists the above miolels aud. the settings of a few reated parameters., Table \ref{tab:tab2} lists the above models and the settings of a few related parameters. +" According to the models (i.c.. the ""UDB model. the ""LP inodel. aud the “RW” nodel). we use Moute Carlo simulations to obtain both he OCDE aud the eCDE."," According to the models (i.e., the “UB” model, the “LP” model, and the “RW” model), we use Monte Carlo simulations to obtain both the $\Theta$ CDF and the $v$ CDF." +" For each Ίοςlel. the total umber of the three-body experiments is 101,"," For each model, the total number of the three-body experiments is $10^4$." + We ouly record those cases in which the masses of ejected stars are i ithe mass range (SAL... LAL.) oftre detectec IIVSs if not specified. and then calculate both the distzibution of the iuclination aneles with respect to he central planes of their pareut population aud the velcity distritions.," We only record those cases in which the masses of ejected stars are in the mass range $3\msun, 4\msun$ ) of the detected HVSs if not specified, and then calculate both the distribution of the inclination angles with respect to the central planes of their parent population and the velocity distributions." + To compare with fi6 Observeious summarized in Section 77.. the selec‘tion effecs quust be carefully considered.," To compare with the observations summarized in Section \ref{sec:obs}, , the selection effects must be carefully considered." + As shown in Figure 10.. most IIVSs are detected diu Calactoceiride distances from 25kpc to 130kpc which is partly due to fιο detection lait aud partly due to the limut in the survey. area.," As shown in Figure \ref{fig:f10}, most HVSs are detected in Galactocentric distances from $25\kpc$ to $130\kpc$ which is partly due to the detection limit and partly due to the limit in the survey area." + In the NINIT survev of IIVSs bv Brownetal.(2009a).. the IIVS candidates are selected by a cutoff in the racial velocity. Le. ye>275lans|.," In the MMT survey of HVSs by \citet{Brown09a}, the HVS candidates are selected by a cutoff in the radial velocity, i.e., $v_{\rm rf}\ga275 \kms$." + To account for these selection effects; we adopt the Galactic poeutial model listed iu Section ?? aud simulate the racial distribution of IIVSs under the assuuption of a constan IIVS ejection rate for cachof the above iiodels. which apears to be compatible," To account for these selection effects, we adopt the Galactic potential model listed in Section \ref{sec:obs} and simulate the radial distribution of HVSs under the assumption of a constant HVS ejection rate for eachof the above models, which appears to be compatible" +Dézardetal.(2002) [or Jupiter and by Griffith&Yelle(1999). for Gliese 229D because the updated rate coefficients were not previously available.,\citet{bezard2002} for Jupiter and by \citet{griffith1999} for Gliese 229B because the updated rate coefficients were not previously available. +" The above scheme (15)) also cliffers Tom Chat proposed by Visscheretal.(2010) for CO — CIL; in Jupiters (roposphere. mostly due to differences in our selected reaction rate coefficients for II4-ΟΠ---CL,+II50 (Mosesοἱal.2011). and CIL;+OIMCII;OIL (Jasperetal.2007)."," The above scheme \ref{comech}) ) also differs from that proposed by \citet{visscher2010icarus} for CO $\rightarrow$ $_{4}$ in Jupiter's troposphere, mostly due to differences in our selected reaction rate coefficients for $\textrm{H}+\textrm{CH}_{3}\textrm{OH} \rightarrow \textrm{CH}_{3} + \textrm{H}_{2}\textrm{O}$ \citep{moses2011} and $\textrm{CH}_{3} + \textrm{OH} \xrightarrow{\textrm{M}} \textrm{CH}_{3}\textrm{OH}$ \citep{jasper2007}." +. Indeed. if we adopt the updated rate coefficients Lor our Jupiter models. (he reaction scheme for CO destruction in Jupiters (roposphere is identical to the scheme (15)) described above for Gliese 229D. These revisions will also have some implications regarding the Jovian deep water abundance inferred from CO chenistiry. which we briefly discuss in relssCOJupiter. below.," Indeed, if we adopt the updated rate coefficients for our Jupiter models, the reaction scheme for CO destruction in Jupiter's troposphere is identical to the scheme \ref{comech}) ) described above for Gliese 229B. These revisions will also have some implications regarding the Jovian deep water abundance inferred from CO chemistry, which we briefly discuss in \\ref{ss CO Jupiter} below." + In any case. the rate-limiting reaction candliclates identified in Visscheretal.(2010). all quench in the same vicinity in (he atmosphere of Gliese 229D and are therelore expected to vield roughly similar results for the quench CO abundance if our adopted rate coellicients for any of (he reactions in scheme (15)) are in serious error.," In any case, the rate-limiting reaction candidates identified in \citet{visscher2010icarus} all quench in the same vicinity in the atmosphere of Gliese 229B and are therefore expected to yield roughly similar results for the quench CO abundance if our adopted rate coefficients for any of the reactions in scheme \ref{comech}) ) are in serious error." + Furthermore. we emphasize that reaction (15ee) is much more likely to be (he rate-limiting step than the reaction II» proposed by Prinn&Barshay(1977)... which is too slow to play any significant role in CO quenching kinetics (e.g..Dean&Westmoreland1987:Yungetal.1985:2005:Jasperοἱal.2007) because (here are faster. alternative patliwavs (such as scheme 15)) for CO destruction in hydrogen-dominated substellar atmospheres.," Furthermore, we emphasize that reaction \ref{comech}e e) is much more likely to be the rate-limiting step than the reaction $\textrm{H}_{2}+\textrm{H}_{2}\textrm{CO}\rightarrow +\textrm{CH}_{3}+\textrm{OH}$ proposed by \citet{prinn1977}, which is too slow to play any significant role in CO quenching kinetics \citep[e.g.,][]{dean1987,yung1988,deavillezpereira1997,xia2001,krasnoperov2004,baulch2005,jasper2007} because there are faster, alternative pathways (such as scheme \ref{comech}) ) for CO destruction in hydrogen-dominated substellar atmospheres." +" Although the overall reaction scheme and/or the rate-limiting reaction for CO—Cl, conversion may differ lor objects with different compositions or thermal profiles. we expect (he above scheme to play an important role in the atmospheres of relatively cool(4.6. Ave) substellar objects (such as T ciwarls or cool giant planets) with near-solar metallicities and element abuucdanuce ratios (e.g.. » solar C/O)."," Although the overall reaction scheme and/or the rate-limiting reaction for $\textrm{CO}\rightarrow\textrm{CH}_{4}$ conversion may differ for objects with different compositions or thermal profiles, we expect the above scheme to play an important role in the atmospheres of relatively cool, $X_{\textrm{CH}_{4}} \approx X_{\Sigma\textrm{C}}$ ) substellar objects (such as T dwarfs or cool giant planets) with near-solar metallicities and element abundance ratios (e.g., $\sim$ solar C/O)." + ILowever. under some conditions the CO quenching mechanism mav bypass CLO altogether via the following mechanism:," However, under some conditions the CO quenching mechanism may bypass $_{3}$ OH altogether via the following mechanism:" +Iu low-SB regions. the key feature for an instimment is the ratio of background level to effective area (7)..,"In low-SB regions, the key feature for an instrument is the ratio of background level to effective area \citep{ettoriwfxt}." + In this respect. //PSPC is a amore scusitive iustrument than /NIS.," In this respect, /PSPC is a more sensitive instrument than /XIS." + Frou the tota backeround level (see Fig. 2)), From the total background level (see Fig. \ref{backfit}) ) + we get a value of |x counts t d 7 cur7 for this quautity (0.1-2.0 keV bind). which is almost a factor of two lower thai for /NIS (sceFie.5of?)..," we get a value of $4\times10^{-7}$ counts $^{-1}$ $^{-1}$ $^{-2}$ $^{-2}$ for this quantity (0.4-2.0 keV band), which is almost a factor of two lower than for /XIS \citep[see Fig. 5 of ][]{mitsuda}." + As stated in G09. the mass parameters derived. frou the data appear to be incousisteut with other results.," As stated in G09, the mass parameters derived from the data appear to be inconsistent with other results." + We performed a miass analysis using the density profile and the temperature profiles from various satellites(Suzahu..NALAL. aud Swift. seo Appendix A).," We performed a mass analysis using the density profile and the temperature profiles from various satellites, and , see Appendix A)." + Interestingly. we see that all satellites except fud a value of royy that is larger than 2 Mpc (~25% leger than the value estimated by (091. correspouding to a differcuce of a factor of 2 iu the virial mass.," Interestingly, we see that all satellites except find a value of $r_{200}$ that is larger than 2 Mpc $\sim25\%$ larger than the value estimated by G09), corresponding to a difference of a factor of 2 in the virial mass." + For aud umeasurements the difference in rogo is statistically highlv significant. at more than 6 and 5o. respectively (κου Appendix A for details).," For and measurements the difference in $r_{200}$ is statistically highly significant, at more than 6 and $\sigma$, respectively (see Appendix A for details)." + Since there is no compelling reason to prefer one set of nieasureineuts with respect to another. we are forced to conclude that. tre scale radius in PISS 0715-191 is curreutly affected by a svstematic indetermination of roughly.," Since there is no compelling reason to prefer one set of measurements with respect to another, we are forced to conclude that the scale radius in PKS 0745-191 is currently affected by a systematic indetermination of roughly." + It goes almost without saving that any estimate ofthe fraction of the virial radius reached by N-rav ineasurements will have to take this ieetermination iuto account., It goes almost without saying that any estimate of the fraction of the virial radius reached by X-ray measurements will have to take this indetermination into account. + Thus is no siia Lissue., This is no small issue. + Depending on whetler weassunae tje or the virial radius we have tiat the PSPC surface brightuess micasurements extend to 1.031599 or 0.Srogo., Depending on whether weassume the or the virial radius we have that the PSPC surface brightness measurements extend to $1.03r_{200}$ or $0.8r_{200}$. + Finally. altrough we caunot xefer oue esΠατο of rogo f» another. there are areuimoeuts avorme tje ueasuremieut over the ouc.," Finally, although we cannot prefer one estimate of $r_{200}$ to another, there are arguments favoring the measurement over the one." + First of all. we have two inclepeudent measurements hat are consistent with one another and iucousisteut with he one.," First of all, we have two independent measurements that are consistent with one another and inconsistent with the one." + Secondly. the aud profiles are consistent with mean cluster temperature profiles neasured with (?).. (?).. and (?).. and with predictions from simulatiois (eo...2).," Secondly, the and profiles are consistent with mean cluster temperature profiles measured with \citep{sabrina}, \citep{lm08}, and \citep{vikhlinin06}, and with predictions from simulations \citep[e.g.,][]{roncarelli}." + This is not the case for the profile. which shows a 1iuch nore rapid and significant decline.," This is not the case for the profile, which shows a much more rapid and significant decline." + This is an imiportat »oiut since. as discussed in the Appeudix. the difference in rogy follows from the difference in the shape of the radial eni])oratiure xofiles.," This is an important point since, as discussed in the Appendix, the difference in $r_{200}$ follows from the difference in the shape of the radial temperature profiles." + We have reported OUL analysis οἱ ali archival //PSPC observation of the ealaxy cluster PISS 0715-191., We have reported our analysis of an archival /PSPC observation of the galaxy cluster PKS 0745-191. + We have found that the surtace-brightuess profile extracted frou PSPC data is statistically inconsistent with the result from (109 at high significance (7.70)., We have found that the surface-brightness profile extracted from PSPC data is statistically inconsistent with the result from G09 at high significance $7.7\sigma$ ). + At large radii (>13.5) rcm). the predicted count rate exceeds the PSPC data by a factor of 2.1 3.," At large radii $>13.5$ arcmin), the predicted count rate exceeds the PSPC data by a factor of $2.1-3$ ." + This differcuce is most likely due to a problem in the modelne of the backeround iu the, This difference is most likely due to a problem in the modeling of the background in the +To date. about 25 extrasolar planets with masses less than 10M. and commonly referred to as super-Earths have been discovered (e.g. http://exoplanet.eu).,"To date, about $25$ extrasolar planets with masses less than $10\;M_\oplus$ and commonly referred to as super-Earths have been discovered (e.g. )." + Although two of them. Corot-7b (Légger et al.," Although two of them, Corot-7b (Légger et al." + 2009: Queloz et al., 2009; Queloz et al. + 2009) and GJ 1214b (Charbonneau et al., 2009) and GJ 1214b (Charbonneau et al. + 2009) were detected via the transit method. most of them were found by high-precision radial velocity surveys.," 2009) were detected via the transit method, most of them were found by high-precision radial velocity surveys." + It is expected that the number of observed super-Earths will considerably increase in the near future with the advent of space observatories Corot and Kepler., It is expected that the number of observed super-Earths will considerably increase in the near future with the advent of space observatories Corot and Kepler. + Interestingly. Kepler team has recently announced the discovery of ~170 multi-planet systems candidates (Lissauer et al.," Interestingly, Kepler team has recently announced the discovery of $\sim 170 $ multi-planet systems candidates (Lissauer et al." + 2011). although these need to be confirmed by follow-up programs.," 2011), although these need to be confirmed by follow-up programs." + Previous to Kepler results. four multi-planet systems contaming at least two super-Earths had been detected around PSR B1257+12. HD 69830. GJ 581 and HD 40307.," Previous to Kepler results, four multi-planet systems containing at least two super-Earths had been detected around PSR B1257+12, HD 69830, GJ 581 and HD 40307." + For the sytems around main-sequence stars (HD 69830. GJ 581. HD 40307). the observed period ratios between two adjacent low-mass planets are quite far from strict commensurability.," For the sytems around main-sequence stars (HD 69830, GJ 581, HD 40307), the observed period ratios between two adjacent low-mass planets are quite far from strict commensurability." + However. the planetary system that is orbiting the radio pulsar PSR B1257+12 exhibits two planets with masses 3.9 M. and 4.3 Mz in a 3:2 mean motion resonance (Konacki Wolszezan 2003).," However, the planetary system that is orbiting the radio pulsar PSR B1257+12 exhibits two planets with masses $3.9$ $ M_\oplus$ and $4.3$ $M_\oplus$ in a 3:2 mean motion resonance (Konacki Wolszczan 2003)." + Papaloizou Szuszkiewiez (2005) showed that. for this system. the existence of such a resonance can be understood by a model in which two low-mass planets with mass ratio close to unity undergo convergent type I migration (e.g. Ward 1997; Tanaka et al.," Papaloizou Szuszkiewicz (2005) showed that, for this system, the existence of such a resonance can be understood by a model in which two low-mass planets with mass ratio close to unity undergo convergent type I migration (e.g. Ward 1997; Tanaka et al." + 2002) while still embedded in a gaseous laminar disk until capture in that resonance occurs., 2002) while still embedded in a gaseous laminar disk until capture in that resonance occurs. + More generally. these authors found that. for more disparate mass ratios and provided that convergent migration occurs. the evolution of a system of two planets in the |—4 M. nass range Is likely to result in the formation of high first-order commensurabilities p+ Isp with p>3.," More generally, these authors found that, for more disparate mass ratios and provided that convergent migration occurs, the evolution of a system of two planets in the $1-4$ $M_\oplus$ mass range is likely to result in the formation of high first-order commensurabilities $p+1$ $p$ with $p\ge 3$." + Studies aimed at examining the interaction of many embryos within protoplanetary disks also suggest that capture in resonance between adjacent cores through type | migration appears as a natural outcome of such a system (MeNeil et al., Studies aimed at examining the interaction of many embryos within protoplanetary disks also suggest that capture in resonance between adjacent cores through type I migration appears as a natural outcome of such a system (McNeil et al. + 2005; Cresswell Nelson 2006)., 2005; Cresswell Nelson 2006). + This. combined with the fact that the majority of super-Earths are found in multiplanetary systems (Mayor et al.," This, combined with the fact that the majority of super-Earths are found in multiplanetary systems (Mayor et al." + 2009). would suggest that systems of resonant super-Earths are common.," 2009), would suggest that systems of resonant super-Earths are common." + The fact that most of the multiple systems of super-Earths observed so far do not exhibit mean motion resonances may be explained by a scenario in which strict commensurability is lost due to cireularization through tidal interaction with the central star as the planets migrate inward and pass through the disk inner edge (Terquem Papaloizou Moreover. it is expected that in presence of strong disk turbulence. effects arising from stochastic density flucuations will prevent super-Earths from. staying in a resonant configuration.," The fact that most of the multiple systems of super-Earths observed so far do not exhibit mean motion resonances may be explained by a scenario in which strict commensurability is lost due to circularization through tidal interaction with the central star as the planets migrate inward and pass through the disk inner edge (Terquem Papaloizou Moreover, it is expected that in presence of strong disk turbulence, effects arising from stochastic density flucuations will prevent super-Earths from staying in a resonant configuration." + It is indeed now widely accepted that à source of anomalous viscosity due to turbulence 1s required to account for the estimated accretion rates for Class IL T Tauri stars. which are typically ~107? Mayr! (Sicilia-Aguilar et al.," It is indeed now widely accepted that a source of anomalous viscosity due to turbulence is required to account for the estimated accretion rates for Class II T Tauri stars, which are typically $\sim 10^{-8}$ $_{\odot}$ $^{-1}$ (Sicilia-Aguilar et al." + 2004)., 2004). + The origin of turbulence is believed to be related to the magneto-rotational instability (MRI. Balbus Hawley 1991) for which a number of studies (Hawley et al.," The origin of turbulence is believed to be related to the magneto-rotational instability (MRI, Balbus Hawley 1991) for which a number of studies (Hawley et al." + 1996; Brandenburg et al., 1996; Brandenburg et al. + 1996) have shown that the non-linear outcome of this instability is MHD turbulence with an effective viscous stress parameter a ranging between ~5x107 anc ~0.1. depending on the magnetic field amplitude and topology.," 1996) have shown that the non-linear outcome of this instability is MHD turbulence with an effective viscous stress parameter $\alpha$ ranging between $\sim 5\times 10^{-3}$ and $\sim 0.1$, depending on the magnetic field amplitude and topology." + So far. the effects of stochastic density fluctuations i1 the disk on the evolution of two-planet systems has received little attention.," So far, the effects of stochastic density fluctuations in the disk on the evolution of two-planet systems has received little attention." + Rem Papaloizou (2009) developed ar analytical model and performed N-body simulations of two-planet systems subject to external stochastic forcing and showed that turbulence can produce systems in meat motion resonance with broken apsidal corotation. explaining thereby the resonant configuration of the HD 128311 system.," Rein Papaloizou (2009) developed an analytical model and performed N-body simulations of two-planet systems subject to external stochastic forcing and showed that turbulence can produce systems in mean motion resonance with broken apsidal corotation, explaining thereby the resonant configuration of the HD $128311$ system." + Adams et al. (, Adams et al. ( +2008) examined the effets of turbulent torques on the survival of resonances using a pendulum model with an additional stochastic fore£z term.,2008) examined the effets of turbulent torques on the survival of resonances using a pendulum model with an additional stochastic forcing term. + They found that mean motion resonances are generally disrupted by turbulence within disk lifetimes., They found that mean motion resonances are generally disrupted by turbulence within disk lifetimes. + Lecoaiet et al. (, Lecoanet et al. ( +2009) extended this,2009) extended this +been addressed much in the past ~ 10 years since the publication of Paper I (see ??. for recent examples of the ZOE for spheroids and bulges. respectively).,"been addressed much in the past $\sim$ 10 years since the publication of Paper I (see \citealt{Zar06,Gad09} for recent examples of the ZOE for spheroids and bulges, respectively)." + However. in that work. the origin of the ZOE and the gap between stellar and galactic systems was not addressed. so this analysis is offered here.," However, in that work, the origin of the ZOE and the gap between stellar and galactic systems was not addressed, so this analysis is offered here." + This paper is organized as follows., This paper is organized as follows. + In the next section. we review the 2VT hypothesis and possible evidence for it.," In the next section, we review the 2VT hypothesis and possible evidence for it." + We outline the interplay between dissipation. the 2VT. and the ZOE in Section 3..," We outline the interplay between dissipation, the 2VT, and the ZOE in Section \ref{Interplay}." + Finally. we discuss our results (Section 4)).," Finally, we discuss our results (Section \ref{Discussion}) )." + In this section we revisit the 2VT formulation and study the evidence for it based on a statistical analysis of the 2VT fittings to a wide range of astrophysical objects., In this section we revisit the 2VT formulation and study the evidence for it based on a statistical analysis of the 2VT fittings to a wide range of astrophysical objects. + The properties of regular nearby galaxies are slowly evolving at present. after a presumably previous and complex gas-rich protogalactic stage.," The properties of regular nearby galaxies are slowly evolving at present, after a presumably previous and complex gas-rich protogalactic stage." + Thus. observables such as surface brightness. effective radius. mean velocity dispersion. and luminosity can be used to specify the parameters of these objects.," Thus, observables such as surface brightness, effective radius, mean velocity dispersion, and luminosity can be used to specify the parameters of these objects." + At the same time. when considering galaxies as stationary self-gravitating systems. their physical properties should at some level reflect an equilibrium state through the virial relation. roool! (using the one-component virial theorem. 1VT). which implies that only two of a great number of observables are independent.," At the same time, when considering galaxies as stationary self-gravitating systems, their physical properties should at some level reflect an equilibrium state through the virial relation, $r_e \propto \sigma_0^2I_e^{-1}$ (using the one-component virial theorem, 1VT), which implies that only two of a great number of observables are independent." +" Actually. the FP describes a global relation of virial type. 5r,xwilh but. differently from IVT. with exponents A~1.53 and B-—-0.79 for elliptical galaxies observed in the near-infrared (?).."," Actually, the FP describes a global relation of virial type, $r_e \propto \sigma_0^AI_e^{B}$ but, differently from 1VT, with exponents $A\sim 1.53$ and $B \sim -0.79$ for elliptical galaxies observed in the near-infrared \citep{Pah98}." + This means that there 1s no direct mapping between the virial plane and the FP., This means that there is no direct mapping between the virial plane and the FP. + The reason for the difference of these relations (also called the FP tilt) is a question of current debate involving different hypotheses such as the non-homology of ellipticals properties or a mass-luminosity ratio variable with the total luminosity (see. for instance. 222222)).," The reason for the difference of these relations (also called the FP tilt) is a question of current debate involving different hypotheses such as the non-homology of ellipticals properties or a mass-luminosity ratio variable with the total luminosity (see, for instance, \citealt{Cap95,Cap97,Hjo95,Cio96, Kri97,Bek98}) )." + ? suggests that the FP tilt could be a combination of stellar population plus non-homology effects. while ? points out scaling relations of ellipticals might be the combined result of cosmological collapse plus dissipative merging.," \cite{Tru04} suggests that the FP tilt could be a combination of stellar population plus non-homology effects, while \citet{Lan05} points out scaling relations of ellipticals might be the combined result of cosmological collapse plus dissipative merging." + When extending the problem to other scales and systems. we find a similar situation: the cosmic virial plane deseribed by the IVT. defined as the ensemble of all possible collapsed objects of all masses and radi (2).. does not coincide with the observationally determined cosmic metaplane. as shown in Paper 1. This metaplane is also tilted with respect to the virial expectations.," When extending the problem to other scales and systems, we find a similar situation: the cosmic virial plane described by the 1VT, defined as the ensemble of all possible collapsed objects of all masses and radii \citep{Bur97}, does not coincide with the observationally determined cosmic metaplane, as shown in Paper I. This metaplane is also tilted with respect to the virial expectations." + This problem is mitigated in Paper I by adding a term to the virial equilibrium equation considering the gravitational energy due to the interaction of dark and. baryonic components., This problem is mitigated in Paper I by adding a term to the virial equilibrium equation considering the gravitational energy due to the interaction of dark and baryonic components. + Applying the 2VT to stellar and galaxy systems. they find," Applying the 2VT to stellar and galaxy systems, they find" + These features are the result of the preseuce of extended caustics which are associated with binary lenses., These features are the result of the presence of extended caustics which are associated with binary lenses. + The large maeifications which result whe a caustic sweeps across a source has proved to be a powerful diagnostic of not only stellar sysclus CAeol 1996: Tau. Park. Wim Chane 2000: IlevrovskY.. Sasselov Loeb 2000). but also. at high optical depths. structure at the heart of quasars (Winubsgauss Paczvüsski 1991: Lewis Belle 1998: Àeol Ixrolik 1999: Delle Lewis 2000).," The large magnifications which result when a caustic sweeps across a source has proved to be a powerful diagnostic of not only stellar systems (Agol 1996; Han, Park, Kim Chang 2000; Heyrovský,, Sasselov Loeb 2000), but also, at high optical depths, structure at the heart of quasars (Wambsganss Paczyńsski 1991; Lewis Belle 1998; Agol Krolik 1999; Belle Lewis 2000)." + Causties in such networks are comprised of; catastrophes. (Schucider. Elilers Falco J992). combiningi in regious to form higher order catastrophes.," Caustics in such networks are comprised of catastrophes' (Schneider, Ehlers Falco 1992), combining in regions to form higher order catastrophes." + As hey donunate the caustic structure formed by a binary leus in the followingC» analysis it is assmmed that the source star and planet are swept by a fold caustic., As they dominate the caustic structure formed by a binary lens in the following analysis it is assumed that the source star and planet are swept by a fold caustic. + It is assumed hat he caustic is straight in the vicinity of the planet., It is assumed that the caustic is straight in the vicinity of the planet. + As a point source is swept bv a fold caustic. the uaeuification at a locatione is giveu by where \/g is the vstrength” of the caustic. 6. d8 the location of the caustic and f(r} is the step function.," As a point source is swept by a fold caustic, the magnification at a location $x$ is given by where $\sqrt{g}$ is the “strength” of the caustic, $x_c$ is the location of the caustic and $H(x)$ is the step function." + The background maguification. ων. is due to other lensed images. not associated with the caustic crossing. formed by the binary lens.," The background magnification, $\mu_o$, is due to other lensed images, not associated with the caustic crossing, formed by the binary lens." +" In the following study it is assumed that j4,—1.", In the following study it is assumed that $\mu_o=1$. +" Au exiuniuation of Equation 1 reveals that as the caustic crosses the point sotwee. where eue,—0. the resulting maeuification is infinite."," An examination of Equation \ref{caustic} reveals that as the caustic crosses the point source, where $x-x_c=0$, the resulting magnification is infinite." + With auv finite source. however. integrating the maenification distribution over the source results in a finite naenification. smoothing out the iuicroleusiug Lelt curve in the vicinity of the caustic (see inset box in Fig. 1)).," With any finite source, however, integrating the magnification distribution over the source results in a finite magnification, smoothing out the microlensing light curve in the vicinity of the caustic (see inset box in Fig. \ref{fig1}) )." + T16 peak magnification in the light curve for a source swep by a fold caustic is eivenby where Ry is the radius of the source. aud fois a fon actor that accounts for the specific ecometry of the source (Chang 1981).," The peak magnification in the light curve for a source swept by a fold caustic is givenby where $R_s$ is the radius of the source, and $f$ is a form factor that accounts for the specific geometry of the source (Chang 1984)." + For a uuiformly circular source. f=1.39.," For a uniformly circular source, $f=1.39$." + With regards to the work presented in Sect. ??..," With regards to the work presented in Sect. \ref{ideal}," + hese parameters are chosen such that γω~10. a value typical for miuicrolensed stars of a Solar radius iu he Galactic Bulge (Lewis Ibata 2000).," these parameters are chosen such that $\mu_{peak}\sim70$, a value typical for microlensed stars of a Solar radius in the Galactic Bulge (Lewis Ibata 2000)." + The results iu his paper are simply scalable to other stellar radii and caustic strengths using Equation 2.., The results in this paper are simply scalable to other stellar radii and caustic strengths using Equation \ref{peakmag}. + The planet ix also represented as a circular disk that colmpletely obscures a fraction of light from the star., The planet is also represented as a circular disk that completely obscures a fraction of light from the star. +" fiducial planetary radii were investigated. wi hk,= "," fiducial planetary radii were investigated, with $R_p =$ " +NNNOSAQJ3AG. The National Center for the Atmospheric Research is sponsored by the National Science Foundation.,NNX08AQ34G. The National Center for the Atmospheric Research is sponsored by the National Science Foundation. +would expect LMC stars to He at the position of the second velocity peak we observe in the Eastern fields.,would expect LMC stars to lie at the position of the second velocity peak we observe in the Eastern fields. + This seems somewhat less likely because we find that the secondary peaks in our data contain about the same number of stars as the primary velocity peaks. and therefore appear more likely to be associated with the SMC velocity structure than the LMC.," This seems somewhat less likely because we find that the secondary peaks in our data contain about the same number of stars as the primary velocity peaks, and therefore appear more likely to be associated with the SMC velocity structure than the LMC." +" Since our easternmost fields are closer to the LMC than the 0.9 kpe eastern field. we would expect the LMC contribution (if it causes the secondary peak) to increase ""outward? from the SMC. unlike the observations."," Since our easternmost fields are closer to the LMC than the 0.9 kpc eastern field, we would expect the LMC contribution (if it causes the secondary peak) to increase `outward' from the SMC, unlike the observations." + It is of course very likely that some LMC stars are actually superposed over the SMC. but they can probably be securely separated out only by chemical tagging.," It is of course very likely that some LMC stars are actually superposed over the SMC, but they can probably be securely separated out only by chemical tagging." + One striking feature we observe in our data is a broad metallicity distribution centered on [Fe/H] ~1.2. extending from —2.5 to solar or even slightly supersolar values.," One striking feature we observe in our data is a broad metallicity distribution centered on [Fe/H] $\sim -1.2$, extending from $-2.5$ to solar or even slightly supersolar values." + This is very similar to what observed in the LMC by Munozetal.(2006) and in Sagittarius by Monacoetal.(2005) and may suggest a very similar chemical evolution pattern in most dwarf galaxies., This is very similar to what observed in the LMC by \cite{munoz06} and in Sagittarius by \cite{monaco05} and may suggest a very similar chemical evolution pattern in most dwarf galaxies. +" In fact the abundance distribution we observe in the SMC is also very similar to that measured for the M31 ""giant stream"" population. with a peak near [Fe/H] ~1 and tails to high and low metallicities (Kochetal.2008)."," In fact the abundance distribution we observe in the SMC is also very similar to that measured for the M31 “giant stream” population, with a peak near [Fe/H] $\sim -1$ and tails to high and low metallicities \citep{koch08}." +. The ingestion of massive galaxies such as the SMC has been invoked to explain the wide metallicity distribution and the presence of metal-rich stars in the M31 halo (see e.g.. al. 2008)).," The ingestion of massive galaxies such as the SMC has been invoked to explain the wide metallicity distribution and the presence of metal-rich stars in the M31 halo (see e.g., \citealt{koch08}) )." + In the case of the SMC there is the question of how a galaxy massive enough to host such metal-rich stars could have been accreted by the SMC without more significant disruption of the SMC (but see Tsujimoto&Bekki 2009))., In the case of the SMC there is the question of how a galaxy massive enough to host such metal-rich stars could have been accreted by the SMC without more significant disruption of the SMC (but see \citealt{tsujimoto09}) ). + The broad metallicity distribution may instead imply the presence of multiple stellar generations., The broad metallicity distribution may instead imply the presence of multiple stellar generations. + It is known that the SMC has undergone recent star formation. possibly induced by encounters with the LMC. after a long period of quiescence (Harris&Zaritsky20," It is known that the SMC has undergone recent star formation, possibly induced by encounters with the LMC, after a long period of quiescence \citep{harris04}." +04)... Carreraetal.(2008). claim that there is a metal abundance gradient in the SMC and suggest that this is due to the presence of younger stars in the centre of this galaxy., \cite{carrera08} claim that there is a metal abundance gradient in the SMC and suggest that this is due to the presence of younger stars in the centre of this galaxy. + We find that the main population of the SMC does not exhibit a metal abundance gradient (Parisi2010).. but that in the inner fields to the North and South there is a contribution from more metal-rich stars. with peak metallicity around [Fe/H] ~—0.6.," We find that the main population of the SMC does not exhibit a metal abundance gradient \citep{parisi08,parisi10}, but that in the inner fields to the North and South there is a contribution from more metal-rich stars, with peak metallicity around [Fe/H] $\sim -0.6$." + Noél&Gallart(2007) find evidence for an intermediate age population in their fields to the South out to 6.5 kpe. while a younger stellar population is detected by Harris&Zaritsky(2004) along the Magellanic Bridge.," \cite{noel07} find evidence for an intermediate age population in their fields to the South out to 6.5 kpc, while a younger stellar population is detected by \cite{harris04} along the Magellanic Bridge." + The presence of more metal-rich stars forming a separate peak in the inner fields resembles the picture of Carreraetal.(2008) where a recent burst of star formation has led to self-enrichment in the inner regions., The presence of more metal-rich stars forming a separate peak in the inner fields resembles the picture of \cite{carrera08} where a recent burst of star formation has led to self-enrichment in the inner regions. + The approximate North-South trend is roughly in the directions of the Bridge and Stream features and it is tempting to speculate that the interactions that created these gaseous features are also responsible for the star formation episodes., The approximate North-South trend is roughly in the directions of the Bridge and Stream features and it is tempting to speculate that the interactions that created these gaseous features are also responsible for the star formation episodes. + A wider and larger spectroscopic survey will allow us to clarify the structure and kinematics of the SMC. explore the existence of metallicity gradients. search for a metal poor halo and detect the presence of streams.," A wider and larger spectroscopic survey will allow us to clarify the structure and kinematics of the SMC, explore the existence of metallicity gradients, search for a metal poor halo and detect the presence of streams." +is chosen to bring e. continuously (to zero al the edge of the launching region. as required by our boundary conditions.,"is chosen to bring $v_z$ continuously to zero at the edge of the launching region, as required by our boundary conditions." + We adopt a softened power-law form lor the distribution of the vertical component of magnetic field D.(25) on the launching surface where the parameter D controls the strength of the magnetic field. and ay the spatial distribution.," We adopt a softened power-law form for the distribution of the vertical component of magnetic field $B_{z}(\varpi)$ on the launching surface where the parameter $B_{0}$ controls the strength of the magnetic field, and $\alpha_{B}$ the spatial distribution." + It is also smoothed by the spine function ίσο)., It is also smoothed by the spline function ${\cal S}(\varpi)$. + To complete the specification of the launching conditions. we adopt the following form for the mass density distribution where (he parameter Dy controls the rate of mass loacling aud αμ (he spatial distribution.," To complete the specification of the launching conditions, we adopt the following form for the mass density distribution where the parameter $D_0$ controls the rate of mass loading and $\alpha +_m$ the spatial distribution." + Allofour calculations within s3D are carried out in dimensionless units for convenience. but it is instructive to redimensionalize the hwdromagnetic «quantities at the end of the simulation for comparison will observational results.," All of our calculations within 3D are carried out in dimensionless units for convenience, but it is instructive to redimensionalize the hydromagnetic quantities at the end of the simulation for comparison with observational results." +" For our application to YSOs. we set the stellar mass M,=LM. and the softening radius 2,=0.1AU. which vield a characteristic velocity-: scale.. the Keplerian74a velocity-: αἱ —zy. /G.M.—/z,m=94kms-|."," For our application to YSOs, we set the stellar mass $M_{*}= 1\solarmass$ and the softening radius $\varpi_{g}=0.1\AU$, which yield a characteristic velocity scale, the Keplerian velocity at $\varpi_{g}$, $\sqrt{GM_{*}/\varpi_{g}}=94\,\kms$." + {The scales. fort. other. quantities can be determined once the magnetic field strength at the gravitational softening racius. By. is specified.," The scales for other quantities can be determined once the magnetic field strength at the gravitational softening radius, $B_0$, is specified." + We begin with a detailed description of our reference run in3.1... to which the rest of our simulations are compared.," We begin with a detailed description of our reference run in, to which the rest of our simulations are compared." +" In relloacdinagn we present a series of simulations in which only the total mass loading of the wind. M, is varied from the relerence run."," In \\ref{loadmagn} we present a series of simulations in which only the total mass loading of the wind, $\dot{M}_{w}$, is varied from the reference run." + Finally in relloaddist we present a smaller group of simulations where the total mass load is fixed. but its distribution over the launching surface varies.," Finally in \\ref{loaddist} we present a smaller group of simulations where the total mass load is fixed, but its distribution over the launching surface varies." +The dvnamical structure of (he Kuiper Bell suggests that the outer solar svstem experienced a phase of planetesimal-driven migration in its early history(Fernandez&Ip1984:Malho-ira.1993.1995:Lahn&Malhotra1999;Levisonetal. 20083)..,"The dynamical structure of the Kuiper Belt suggests that the outer solar system experienced a phase of planetesimal-driven migration in its early history\citep{Fernandez:1984p61,Malhotra:1993p244,Malhotra:1995p79,Hahn:1999p122,Levison:2008p690}." + Pluto and other Kuiper belt objects that are trapped in mean motion resonances (MMBs) with Neptune are explained bv the outward migration of Neptune due to interactions wilh a more massive primordial planetesimal disk in the outer regions of the solar svstem (Malhotra1993.1995)..," Pluto and other Kuiper belt objects that are trapped in mean motion resonances (MMRs) with Neptune are explained by the outward migration of Neptune due to interactions with a more massive primordial planetesimal disk in the outer regions of the solar system \citep{Malhotra:1993p244,Malhotra:1995p79}." + In addition. the so-called the scattered disk of the Kuiper belt can also be explained by the outwiud migration of Neptune (Ilahn&Malhotva2005).. or by the effects of a high eccentricity phase of ice giant planet evolution during the outward migration of Neptune 2008)..," In addition, the so-called the scattered disk of the Kuiper belt can also be explained by the outward migration of Neptune \citep{Hahn:2005p4122}, or by the effects of a high eccentricity phase of ice giant planet evolution during the outward migration of Neptune \citep{Levison:2008p690}." + The basic premise of planetesimal-criven migration is (hat the giant. planets formed in a more compact configuration (han we find them today. and that (hey were surrounded bv a massive (o50 M.) disk of unaccreted icy planetesimals that was (he progenitor of the currently observed. Kuiper belt. (Ilan.&Malhotra1999)..," The basic premise of planetesimal-driven migration is that the giant planets formed in a more compact configuration than we find them today, and that they were surrounded by a massive $\sim50\Mearth$ ) disk of unaccreted icy planetesimals that was the progenitor of the currently observed Kuiper belt \citep{Hahn:1999p122}." + When planetesimals are preferentially scattered either inward (toward the Sun) or outward (away from the Sun). nel orbital angular momentum is transferred between the disk and the large body. causing a drift in the large body's semimajor axis (Fernandez&Ip1984:Ixirshetal.2009).," When planetesimals are preferentially scattered either inward (toward the Sun) or outward (away from the Sun), net orbital angular momentum is transferred between the disk and the large body, causing a drift in the large body's semimajor axis \citep{Fernandez:1984p61,Kirsh:2009p2746}." +. In many simulations of giant planet migration. icv planetesimals are preferentially scattered. inward by each of the three outer giant planets (Saturn. Uranus. and Neptune) causing (hese planets to migrate outward.," In many simulations of giant planet migration, icy planetesimals are preferentially scattered inward by each of the three outer giant planets (Saturn, Uranus, and Neptune) causing these planets to migrate outward." + Due to Jupiters large mass. planetesimals (hat encounter Jupiter are preferentially ejected out of the solar svstem. leading to a net loss of mass [rom the solar svslem and an inward migration of Jupiter.," Due to Jupiter's large mass, planetesimals that encounter Jupiter are preferentially ejected out of the solar system, leading to a net loss of mass from the solar system and an inward migration of Jupiter." + Planetesimal-diiven giant planet migration has been suggested as a cause of the Late lleavv. Bombardment (LIB) (Gomesοἱal.2005:Stromet 2005).. however the link," Planetesimal-driven giant planet migration has been suggested as a cause of the Late Heavy Bombardment (LHB) \citep{Gomes:2005p51,Strom:2005p80}, , however the link" +are numerically converged in Appendix A and at various points in Section 3..,are numerically converged in Appendix A and at various points in Section \ref{results}. + The ealeulations were performed on the University of Exeter Supercomputer. an SGI Altix ICE 8200.," The calculations were performed on the University of Exeter Supercomputer, an SGI Altix ICE 8200." + The collapse of each molecular cloud core up until the formation of the stellar core proceeds in a manner that is qualitatively similar to those reported from previous three-dimensional calculations without magnetic fields and using barotropic equations of state (22222) for both the barotropic and radiation hydrodynamical calculations presented here.," The collapse of each molecular cloud core up until the formation of the stellar core proceeds in a manner that is qualitatively similar to those reported from previous three-dimensional calculations without magnetic fields and using barotropic equations of state \citep{Bate1998, SaiTom2006, SaiTomMat2008, MacInuMat2010, MacMat2011} for both the barotropic and radiation hydrodynamical calculations presented here." + Fig. L..," Fig. \ref{evolutions}," +" gives the evolution with time of the maximum density and temperature for clouds with different initial rotation rates. with each calculation performed using 10"" particles (except for the baratropic 7=0.04 case)."," gives the evolution with time of the maximum density and temperature for clouds with different initial rotation rates, with each calculation performed using $10^6$ particles (except for the baratropic $\beta=0.04$ case)." + The initial collapse is isothermal until the maximum density exceeds 101 & em using the barotropic equation of state., The initial collapse is isothermal until the maximum density exceeds $10^{-13}$ g $^{-3}$ using the barotropic equation of state. + Using radiation hydrodynamics the evolutions to this density are also almost isothermal., Using radiation hydrodynamics the evolutions to this density are also almost isothermal. + However. slight heating when using radiation hydrodynamics does slow the collapse marginally. leading to the times taken to form the first 1ydrostatic cores being sightly longer(zz0.010.015 ty) than in he corresponding barotropic calculations.," However, slight heating when using radiation hydrodynamics does slow the collapse marginally, leading to the times taken to form the first hydrostatic cores being slightly longer $\approx 0.01-0.015~{\rm t}_{\rm ff}$ ) than in the corresponding barotropic calculations." + In the radiation hydrodynamical calculations. as the heating rate in the central regions exceeds the rate at which the gas can cool. he gas begins to heat up and the collapse enters an almost adiabatic johase where the temperaure rises as the gas is compressed.," In the radiation hydrodynamical calculations, as the heating rate in the central regions exceeds the rate at which the gas can cool, the gas begins to heat up and the collapse enters an almost adiabatic phase where the temperature rises as the gas is compressed." + This is mimicked in the barotropic calculations by the change in the value of η from | to 7/5 (equation 12)., This is mimicked in the barotropic calculations by the change in the value of $\eta$ from 1 to $7/5$ (equation \ref{eta}) ). +" This increasing temperature leads o the formation of a pressure-supported ""first hydrostatic core’ (2).. which ean be seen in Fig."," This increasing temperature leads to the formation of a pressure-supported `first hydrostatic core' \citep{Larson1969}, which can be seen in Fig." + |. when the initial collapse stalls with central (maximum) densities ~10.1 gem. and temperatures of zz30—120 K. depending on the degree of rotational support (i.e. cores that rotate more quickly have lower maximum temperatures).," \ref{evolutions} when the initial collapse stalls with central (maximum) densities $\sim 10^{-11}$ g $^{-3}$ and temperatures of $\approx 30-120$ K, depending on the degree of rotational support (i.e. cores that rotate more quickly have lower maximum temperatures)." + Aguin. apart from the small offset in the time of first core formation. the barotropic and radiation hydrodynamical calculations give very similar results to this point.," Again, apart from the small offset in the time of first core formation, the barotropic and radiation hydrodynamical calculations give very similar results to this point." + Without rotation 62.=0). the first core has an initial mass of z5 Jupiter masses (Mj) and a radius of z5 AU (inagree- ," Without rotation $\beta=0$ ), the first core has an initial mass of $\approx 5$ Jupiter masses $_{\rm J}$ ) and a radius of $\approx 5$ AU \citep[in agreement with][]{Larson1969}." +However. with higher initial rotation rates of the molecular cloud core. the first cores become progressively more oblate (Figures 2.. 3.. and 4)).," However, with higher initial rotation rates of the molecular cloud core, the first cores become progressively more oblate (Figures \ref{images_D_barotropic}, , \ref{images_xyD}, and \ref{images_xzD}) )." +" For example. with 7=0.005 using radiation hydrodynamics, before the onset of dynamical instability. the first core has a radius of zz20 AU and a major to minor axis ratio of e+] (first panel in each third row of Figs."," For example, with $\beta = 0.005$ using radiation hydrodynamics, before the onset of dynamical instability, the first core has a radius of $\approx 20$ AU and a major to minor axis ratio of $\approx$ 4:1 (first panel in each third row of Figs." + 3 and 4)., \ref{images_xyD} and \ref{images_xzD}) ). + With 7=0.01. the first core has a radius of z30 AU and a major to minor axis ratio of 6:1 (fourth rows of these figures).," With $\beta=0.01$, the first core has a radius of $\approx 30$ AU and a major to minor axis ratio of $\approx$ 6:1 (fourth rows of these figures)." + Thus. for the higher rotation rates. the first core is actually a pre-stellar dise. without a central object.," Thus, for the higher rotation rates, the first core is actually a pre-stellar disc, without a central object." + As pointed out by 2.. 2.. and ?.. the disc actually formsbefore the star.," As pointed out by \cite{Bate1998}, \cite{MacInuMat2010}, and \cite{Bate2010}, , the disc actually forms the star." + For the very highest rotation rates G3=0.04). the first core actually takes the form of a torus or ring (first panel in each bottom row of Figs.," For the very highest rotation rates $\beta=0.04$ ), the first core actually takes the form of a torus or ring (first panel in each bottom row of Figs." + 3. and 45» in which the central density is lower than the maximum density., \ref{images_xyD} and \ref{images_xzD}) ) in which the central density is lower than the maximum density. + The evolution of the first core up until the point of stellar core formation depends on its rotation rate., The evolution of the first core up until the point of stellar core formation depends on its rotation rate. + Non-rotating and slowly rotating cores evolve as they accrete mass from the surrounding infalling envelope with their central densities and temperatures increasing (Figs., Non-rotating and slowly rotating cores evolve as they accrete mass from the surrounding infalling envelope with their central densities and temperatures increasing (Figs. + | and S.. calculations with ο50.001).," \ref{evolutions} and \ref {first_core_time}, calculations with $\beta \le 0.001$ )." +" In the radiation hydrodynamical calculations. when the central emperature exceeds zz.2000 Κ. molecular hydrogen begins to ""issociate. leading to a second hydrodynamic collapse deep within ye first core (?).."," In the radiation hydrodynamical calculations, when the central temperature exceeds $\approx 2000$ K, molecular hydrogen begins to dissociate, leading to a second hydrodynamic collapse deep within the first core \citep{Larson1969}." +" The formation of the stellar core occurs just a ew yeurs after the onset of the second collapse. during which the maximum density increases from ~LO7 to 20.1 gem and 19 maximum temperature increases from zz2000 to >60.000 K. The stellar core is formed with a mass of AZ,z1.5 Mj and a radius of 2.&2 R.."," The formation of the stellar core occurs just a few years after the onset of the second collapse, during which the maximum density increases from $\sim 10^{-8}$ to $\gsim 0.1$ g $^{-3}$ and the maximum temperature increases from $\approx 2000$ to $>60,000$ K. The stellar core is formed with a mass of $M_{\rm sc} \approx 1.5$ $_{\rm J}$ and a radius of $R_{\rm sc} \approx 2$ $_\odot$." + Without rotation. the stellar core accretes 1e remnant of the first core in which it is embedded in z10 years and then aceretes the envelope (2).. though with three-dimensional calculations we only follow the calculations for zz50.—LOO years after stellar core formation.," Without rotation, the stellar core accretes the remnant of the first core in which it is embedded in $\approx 10$ years and then accretes the envelope \citep{Larson1969}, though with three-dimensional calculations we only follow the calculations for $\approx 50-100$ years after stellar core formation." + Although these stages are qualitatively the. same in the barotropic calcuations. there is a much greater difference in the evolution of the first core between the barotropic and radiation hydrodynamical calculations than for the phase of the collapse prior to first core formation.," Although these stages are qualitatively the same in the barotropic calcuations, there is a much greater difference in the evolution of the first core between the barotropic and radiation hydrodynamical calculations than for the phase of the collapse prior to first core formation." + To make this clear. in Fig.," To make this clear, in Fig." + 5. the time evolution of maximum density and maximum temperature during the calculations is replotted with /=0 set to the time of stellar core formation (defined as the time when the maximum density reaches 10. ¢ em. )., \ref{first_core_time} the time evolution of maximum density and maximum temperature during the calculations is replotted with $t=0$ set to the time of stellar core formation (defined as the time when the maximum density reaches $10^{-3}$ g $^{-3}$ ). + This allows us to clearly see the amount of time spent between first core formation and stellar core formation in each of the calculations., This allows us to clearly see the amount of time spent between first core formation and stellar core formation in each of the calculations. + The barotropic results are plotted using dashed lines. while the solid lines give the radiation hydrodynamical results.," The barotropic results are plotted using dashed lines, while the solid lines give the radiation hydrodynamical results." + The evolution time of the first core or pre-stellar dise is longer using radiation hydrodynamics than using the barotropic equation of state in all cases. by factors of 453 except for the most rapidly-rotating case.," The evolution time of the first core or pre-stellar disc is longer using radiation hydrodynamics than using the barotropic equation of state in all cases, by factors of $1.5-3$ except for the most rapidly-rotating case." + This is because ct1e. barotropic equation of state consistently underestimates the temperature of the gas. providing less pressure support to the gas and. thus. allowing it to enter the second collapse phase earlier.," This is because the barotropic equation of state consistently underestimates the temperature of the gas, providing less pressure support to the gas and, thus, allowing it to enter the second collapse phase earlier." + The consistent temperature underestimate can be seen clearly in Fig., The consistent temperature underestimate can be seen clearly in Fig. + 6 whichplots the maximum temperature versus maximum density for each of the radiation hydrodynamical ealeulations and compares this to the barotropic equation of state (dashed black solid line).," \ref{temp_vs_density} + whichplots the maximum temperature versus maximum density for each of the radiation hydrodynamical calculations and compares this to the barotropic equation of state (dashed black solid line)." + The lines from the radiation hydrodynamical calculationsalmost lie on top of one another. but from densities of 10.7! to," The lines from the radiation hydrodynamical calculationsalmost lie on top of one another, but from densities of $10^{-11}$ to" +vvalues are unreliable.,values are unreliable. + However. if we fit the data from cach camera separately. without adding svstematic uncertainties. we reach the same conclusion: that the soft pulse is mainly a change in visible emitting area. and not a change in absorption.," However, if we fit the data from each camera separately, without adding systematic uncertainties, we reach the same conclusion: that the soft pulse is mainly a change in visible emitting area, and not a change in absorption." + Since the 00.712 keV softness ratio is ellectively a ratio of the blackbody emission to the plasma emission. we have also computed the 4//5512 keV softness ratio. which is sensitive to spectral changes in the harder plasma emission.," Since the 0.7–12 keV softness ratio is effectively a ratio of the blackbody emission to the plasma emission, we have also computed the 5–12 keV softness ratio, which is sensitive to spectral changes in the harder plasma emission." + This ratio (Fig. 2)), This ratio (Fig. \ref{fig:spin}) ) + shows little variation other than a hardening at phases 00.00.2. near the maximum of the hard pulse.," shows little variation other than a hardening at phases 0.0–0.2, near the maximum of the hard pulse." + We thus extracted and compared spectra for the phase regions 0.00.2 and 0.40.9., We thus extracted and compared spectra for the phase regions 0.0–0.2 and 0.4–0.9. + Fitting the model to. the two phase regions independently gave a total ool 1253 11.10: in this section vvalues are for energies above 0.7 keV only: again. this does not allect. the AD values).," Fitting the model to the two phase regions independently gave a total of 1253 1.10; in this section values are for energies above 0.7 keV only; again, this does not affect the $\Delta\chisq$ values)." + Constraining the absorption (simple and partial covering) to have the same value in cach phase region gave an identical oof 1253. implving no absorption change.," Constraining the absorption (simple and partial covering) to have the same value in each phase region gave an identical of 1253, implying no absorption change." + Alternatively. requiring the normalisations of the MEKALS to be the same in cach region worsened tto 1530 (422 L34).," Alternatively, requiring the normalisations of the s to be the same in each region worsened to 1530 = 1.34)." + Thus we conclude that the hardening near tux maximum is caused by a change in the ratio of the soft and hard ccomponents., Thus we conclude that the hardening near flux maximum is caused by a change in the ratio of the soft and hard components. + At all other phase regions there appears to be little or no change in the ratios of the two ccomponents. nor in the absorption.," At all other phase regions there appears to be little or no change in the ratios of the two components, nor in the absorption." + This is despite the [act that the overall Dux level changes considerably. over these phase regions., This is despite the fact that the overall flux level changes considerably over these phase regions. + Similar results. that the hard pulse does not show much energy dependence. were reported. using data by de Martino ((2004).," Similar results, that the hard pulse does not show much energy dependence, were reported using data by de Martino (2004)." +Dust grains play an important role in the formation and evolution of galaxies.,Dust grains play an important role in the formation and evolution of galaxies. + Dust grains control the energy balance in the interstellar medium (ISM) by absorbing stellar light and reemitting it in far infrared (FIR)., Dust grains control the energy balance in the interstellar medium (ISM) by absorbing stellar light and reemitting it in far infrared (FIR). + Also. the surface of dust grains is a site or an efficient formation of Hz molecules (e.g.Cazaux&Tielens2004.. which aet as an effective coolant in metal-poor ISM.," Also, the surface of dust grains is a site for an efficient formation of $_2$ molecules \citep[e.g.][]{cazaux04}, which act as an effective coolant in metal-poor ISM." + Those effects of dust turn on even at ~1% of the solar metallicity according to he calculation by Hirashita&Ferrara(2002)... who argue that the star formation rate is enhanced because of the first dust enrichment in the history of galaxy evolution.," Those effects of dust turn on even at $\sim 1$ of the solar metallicity according to the calculation by \citet{hirashita02}, who argue that the star formation rate is enhanced because of the first dust enrichment in the history of galaxy evolution." +" The first sources of dust in he Universe are Type II (core-collapse) supernovae (SNe II) or our instability supernovae (PISNe). since the lifetimes of their orogenitors are short (~10"" yr)."," The first sources of dust in the Universe are Type II (core-collapse) supernovae (SNe II) or pair instability supernovae (PISNe), since the lifetimes of their progenitors are short $\sim 10^6$ yr)." + In the local Universe. dust grains are also produced by evolved low mass stars (Gehrz1989). but this production mechanism requires much longer €. Gyr) imescales.," In the local Universe, dust grains are also produced by evolved low mass stars \citep{gehrz89}, but this production mechanism requires much longer $\ga 1$ Gyr) timescales." + The first dust supplied by SNe Π or PISNe may 1.trigger he formation of low-mass stars via dust cooling (Schneider2003:Omukaietal. 2005).," The first dust supplied by SNe II or PISNe may trigger the formation of low-mass stars via dust cooling \citep{schneider03,omukai05}." + To quantify the above effects of dust in the early stages of galaxy evolution. it is crucial to know how much dust and what species of grains form in supernovae (SNe).," To quantify the above effects of dust in the early stages of galaxy evolution, it is crucial to know how much dust and what species of grains form in supernovae (SNe)." + It has been suggested by some observations of nearby SNe that dust is indeed produced in SNe. although the quantity of formec dust is still debated2007).," It has been suggested by some observations of nearby SNe that dust is indeed produced in SNe, although the quantity of formed dust is still debated." + By treating the nucleation and accretion in SNe. the dust composition and size distribution are theoretically calculated (Kozasa.Hasegawa.&Nomoto1989.199]).," By treating the nucleation and accretion in SNe, the dust composition and size distribution are theoretically calculated \citep*{kozasa89,kozasa91}." +. Recently. in order to examine the effects of dust in Population III (Pop ΠΙΟ objects. the formation of dust in SNe II and PISNe is extensively examined (Todini&Ferrara2001:: Nozawaetal.2003.hereafter NO3.. Schneider.Ferrara.&Salvaterra 20049).," Recently, in order to examine the effects of dust in Population III (Pop III) objects, the formation of dust in SNe II and PISNe is extensively examined \citealt{todini01}; \citealt[hereafter N03]{nozawa03}, \citealt{schneider04}) )." + The motivation for considering PISNe comes from some evidence indicating that the stars formed from metal-free gas. Population IIT (PopIID) stars. are very massive with a characteristic mass of a few hundrec solar masses (e.g.Nakamura&Umemura2001:BrommLarson 20043.," The motivation for considering PISNe comes from some evidence indicating that the stars formed from metal-free gas, Population III (PopIII) stars, are very massive with a characteristic mass of a few hundred solar masses \citep[e.g.][]{nakamura01,bromm04}." +. Such massive stars are considered to begin pair creation of electron and positron after the helium burning phase. and finally an explosive nuclear reaction disrupts the whole stars (Fryer.Woosley.&Heger2001:Woosley 2002).," Such massive stars are considered to begin pair creation of electron and positron after the helium burning phase, and finally an explosive nuclear reaction disrupts the whole stars \citep{fryer01,heger02}." +. This explosion is callec PISN., This explosion is called PISN. + Recently. the hypothesis that the dust formation is dominatec by SNe II and/or PISNe at high redshift (2) is observationally examined for some objects.," Recently, the hypothesis that the dust formation is dominated by SNe II and/or PISNe at high redshift $z$ ) is observationally examined for some objects." + We expect that at 2>5. when the cosmic age is less than | Gyr. the main sources of dust grains are SNe II and PISNe (e.g.Dwek.Galliano.&Jones2007).," We expect that at $z>5$, when the cosmic age is less than 1 Gyr, the main sources of dust grains are SNe II and PISNe \citep[e.g.][]{dwek07}." +. Extinction curves can be used to investigate the dust properties (e.g.Mathis1990)., Extinction curves can be used to investigate the dust properties \citep[e.g.][]{mathis90}. +. By using a sample of broad absorption line (BAL) quasars. Maiolinoetal.20048). show that the extinction properties of the low-z (2.« 4) sample is different from those of the high-z {5 4.9) sample.," By using a sample of broad absorption line (BAL) quasars, \citet{maiolino04a} show that the extinction properties of the $z$ $z<4$ ) sample is different from those of the $z$ $z>4.9$ ) sample." + This result is suggestive. of a change in the dust production mechanism in the course of, This result is suggestive of a change in the dust production mechanism in the course of +clusters. the presence of the soft X-ray excess might be a wide-spread phenomenon among the massive clusters. as indicated by first results on NAINENewtou REFLEN-DXL survey (Zhane ct al.,"clusters, the presence of the soft X-ray excess might be a wide-spread phenomenon among the massive clusters, as indicated by first results on XMM-Newton REFLEX-DXL survey (Zhang et al." + 2003)., 2003). + We lave discovered oxveen lue cussion associated witli he outskirts of the Coma cluster., We have discovered oxygen line emission associated with the outskirts of the Coma cluster. + These data show that he previously observed soft X-ray excess iu this cluster is due to thermal cussion frou a wari gas. possibly the one-sought WIIDN," These data show that the previously observed soft X-ray excess in this cluster is due to thermal emission from a warm gas, possibly the long-sought WHIM." +"L Typical parameters characterizing he cuttingc» material are ai teniperature ~0.2 keV. abundance 0.1 solar. and density ~50f,poitea:"," Typical parameters characterizing the emitting material are a temperature $\sim0.2$ keV, abundance $\sim0.1$ solar, and density $\sim 50 f_{\rm baryon} \rho_{\rm critical}$." + The thermodvuaimical state of the gas iu the Coma filament reduces the star-formation rate of the embedded spiral galaxics. providing an explanation to the presence of the passive spirals iu the SDSS survey in this region (Coto et al.," The thermodynamical state of the gas in the Coma filament reduces the star-formation rate of the embedded spiral galaxies, providing an explanation to the presence of the passive spirals in the SDSS survey in this region (Goto et al." + 2003)., 2003). +both the satellite observations (Paschinannetal.1981:Gosling1982:Sckopke1983) and the theory/simulation studies lor super-critical Mach number shocks 1982).,"both the satellite observations \citep{Pas81,Gos82,Sck83} and the theory/simulation studies for super-critical Mach number shocks \citep{Ler82}." +. A part of the incoming ions is reflected due to both the polarization electrostatic field and the compressed magnetic field in shock downstream., A part of the incoming ions is reflected due to both the polarization electrostatic field and the compressed magnetic field in shock downstream. + The magnetic overshoot structure can be found around ΑΟων)~248., The magnetic overshoot structure can be found around $X/(c/\omega_{pe}) \sim 248$. +" In addition to such ion dynamics around this shock (transition region. we find the electron hole in theelectron. phase space diagram in CX.0,,) around ΑΟ)e223. and its corresponding electrostatic solitary. wave (ESW) in (the electric field ο,"," In addition to such ion dynamics around this shock transition region, we find the electron hole in theelectron phase space diagram in $(X, U_{ex})$ around $X/(c/\omega_{pe}) \sim 223$, and its corresponding electrostatic solitary wave (ESW) in the electric field $E_x$." + Other ESWs in the erowing phase can be also found in the foreside of the largest ESW structure., Other ESWs in the growing phase can be also found in the foreside of the largest ESW structure. + Shimadaancl discussed that those localized structures are excited by Duneman instability between the reflected ious and the incoming electrons (Papadopoulos1988:CareillaudPa-padopoulos19388:Dieckmannetal. 2000a.b).," \citet{Non00} discussed that those localized structures are excited by Buneman instability between the reflected ions and the incoming electrons \citep{Pap88,Car88,Die00a,Die00b}." +. The simulation result in Figure 1 is basically same as that obtained by ShimadaandHoshino(2000) and Selimitzetal.(2001)., The simulation result in Figure 1 is basically same as that obtained by \citet{Non00} and \citet{Schm01}. +. Looking at the electron hole structure in (he shock (ransition region in details. we find that some electrons are accelerated and gain a laree amount οἱ energv.," Looking at the electron hole structure in the shock transition region in details, we find that some electrons are accelerated and gain a large amount of energy." + After the strong acceleration in the shock transition region. the electrons are transported downstream.," After the strong acceleration in the shock transition region, the electrons are transported downstream." + Figure 2 shows the downstream electron energy spectrum., Figure 2 shows the downstream electron energy spectrum. + The energy 5=vlcAde)n is normalized by the incident electron bulk energy 24=1/1—(09/0)?e» 1.03., The energy $\gamma = \sqrt{1 + (U_e/c)^2}$ is normalized by the incident electron bulk energy $\gamma_0 = 1/\sqrt{1 - (v_0/c)^2} \sim 1.03$ . + The spectrum is superposed over 538 snapshots for the (ime interval from wy.=535 to 1815., The spectrum is superposed over 538 snapshots for the time interval from $\omega_{pe}t=535$ to $1815$. + The line is (he Maxwellian fit for the spectrum. and the bottom dotted line is the one-count level. which is (he reciprocal of the number of snapshots of 1/538 in this case.," The dot-dashed line is the Maxwellian fit for the spectrum, and the bottom dotted line is the so-called one-count level, which is the reciprocal of the number of snapshots of $1/538$ in this case." + Although the statistics of the nonthermal high enerev tail is not good. but we can Clearly find (he enhancement of (he nonthermal population above the Maxwellian level over /u>15. ShimadaandH," Although the statistics of the nonthermal high energy tail is not good, but we can clearly find the enhancement of the nonthermal population above the Maxwellian level over $\gamma/\gamma_0 > 1.8$." +oshino(2000) also obtained (hat the similar suprathermal energy spectrum for the high Mach number shock of M4710., \citet{Non00} also obtained that the similar suprathermal energy spectrum for the high Mach number shock of $M_A \sim 10$. +" In addition. they found (hat the suprathermal electrons are nol generated [or a low Mach number case of Af,~3. and the spectrum is well fitted bv a thermal Maxwellian."," In addition, they found that the suprathermal electrons are not generated for a low Mach number case of $M_A \sim 3$, and the spectrum is well fitted by a thermal Maxwellian." + With regard (o the electron energy spectrum obtained by these simulations. a hieh Mach number shock seems to be a candidate for producing hieh energv electrons.," With regard to the electron energy spectrum obtained by these simulations, a high Mach number shock seems to be a candidate for producing high energy electrons." + Belore discussing the mechanism producing the suprathermal electrons. we would like lo give a comment that Che suprathermal electron energy is much larger than the potential energy of ESW.," Before discussing the mechanism producing the suprathermal electrons, we would like to give a comment that the suprathermal electron energy is much larger than the potential energy of ESW." +" The potential energy FO...οNes can be estimated as 0.26m,c. where we have assumed En~ 20). the width of ESW. Aww~ορ. Tron Figure 1."," The potential energy $e \phi_{\rm esw} = e E_{\rm esw} \Delta_{\rm esw}$ can be estimated as $20 (\omega_{ce}/\omega_{pe})(v_0/c) m_e c^2 \sim 0.26 m_e c^2$ , where we have assumed $E_{\rm esw} \sim 20 E_0$ , the width of ESW, $\Delta_{\rm esw} \sim c/\omega_{pe}$ from Figure 1." + Other simulation parameters are ανω=1/19 and y/o= 1/4., Other simulation parameters are $\omega_{ce}/\omega_{pe} = 1/19$ and $v_0/c = 1/4$ . + Then we getihe increment of the Lorentz [actor normalized by the initial Lorentz [actor as, Then we getthe increment of the Lorentz factor normalized by the initial Lorentz factor as +discussed. observing magnetic field amplification due to the WILT.,"discussed, observing magnetic field amplification due to the KHI." + In fact. the NIL setup is routinely used to test MIID models (Mignoneetal.2009:Beckwith2011).. but the connection between the MIID description aud the fully kinetic picture is still missing (Cruzinov2011).," In fact, the KHI setup is routinely used to test MHD models \citep{mignone09, beckwith11}, but the connection between the MHD description and the fully kinetic picture is still missing \citep{gruzinov11}." +. However. the IKI contains intrinsically kinetic features. and so far 3D fully kinetic ab initio simulations have not been reported.," However, the KHI contains intrinsically kinetic features, and so far 3D fully kinetic ab initio simulations have not been reported." + In (his Letter. we present the first sell-consistent 2D PIC simulations of the IXILE for both subrelativistic ancl relativistic scenarios of shearing unmaegnetized electron-proton. plasma clouds.," In this Letter, we present the first self-consistent 3D PIC simulations of the KHI for both subrelativistic and relativistic scenarios of shearing unmagnetized electron-proton plasma clouds." + We show that the KIT] contains important kinetic features which are not captured in previous 3D MIID simulations (Xeppensetal.1999:Zhang2009:Mignone2009:Beekwithetal. 2011).. namely the transverse KIT dvnaimics. and the generation of a arge-scale DC magnetic field al the shear region.," We show that the KHI contains important kinetic features which are not captured in previous 3D MHD simulations \citep{keppens99,macfadyen09,mignone09,beckwith11}, namely the transverse KHI dynamics, and the generation of a large-scale DC magnetic field at the shear region." + This large-scale field can reach mG levels or (vpical parameters of (he interaction of a relativistic flow with the interstellar medium (ISAT)., This large-scale field can reach mG levels for typical parameters of the interaction of a relativistic flow with the interstellar medium (ISM). + Furthermore. our generalization of the IKI linear theory (Gruzinoy2008) to include arbitrary density jumps between the shearing flows allows us to conclude that the onset of the instability is robust to this asymmetry.," Furthermore, our generalization of the KHI linear theory \citep{gruzinov08} to include arbitrary density jumps between the shearing flows allows us to conclude that the onset of the instability is robust to this asymmetry." + The NII can therefore operate in shears within the ejecta (similar densitv. flows) and also between the ejecta and the surrounding ISM (relative density ratios of 1— 10). and it will likely operate at the same level (or stronger) than the Weibel instability. even for moderate velocity shears.," The KHI can therefore operate in shears within the ejecta (similar density flows) and also between the ejecta and the surrounding ISM (relative density ratios of $1-10$ ), and it will likely operate at the same level (or stronger) than the Weibel instability, even for moderate velocity shears." + In. Section 2. we explore the density jumps effect on the behavior ancl features of the instability.," In Section 2, we explore the density jumps effect on the behavior and features of the instability." + The 3D PIC simulation results are presented. ancl disceussed in detail in Section 3., The 3D PIC simulation results are presented and discussed in detail in Section 3. + In Section 4. we discuss the saturation levels of the magnetic field. and conclusions are drawn in Section 5.," In Section 4, we discuss the saturation levels of the magnetic field, and conclusions are drawn in Section 5." + The WII linear theory. outlined in (Gruzinov2008).. is based on the relativistic fIuicd formalism of plasmas coupled with Maxwell's equations. and was analyzed Lor the particular case where the two shearing flows have equal densities.," The KHI linear theory, outlined in \citep{gruzinov08}, is based on the relativistic fluid formalism of plasmas coupled with Maxwell's equations, and was analyzed for the particular case where the two shearing flows have equal densities." + Realistic shears. however. are more likely to occur between different density flows (IHardeeetal.1992:Kvause 2002)..," Realistic shears, however, are more likely to occur between different density flows \citep{hardee92,krause03}. ." + We have extended the analvsis presented in (Gruzinov2008) for shearing plasma [lows with uniform densities p» and ». and counter-velociües +c) ancl —iy. respectively.," We have extended the analysis presented in \citep{gruzinov08} for shearing electron-proton plasma flows with uniform densities $n_+$ and $n_-$, and counter-velocities $+\vec v_0$ and $-\vec v_0$, respectively." + Here. the protons are considered Bree-streaming whereas (he electron [Iuid «quantities and fields are linearly perturbed.," Here, the protons are considered free-streaming whereas the electron fluid quantities and fields are linearly perturbed." + The dispersionrelation for electromagnetic waves, The dispersionrelation for electromagnetic waves +surface (e.g.222222)..,"surface \citep[e.g.][]{Howe1999, Chaplin2003, Chaplin2004b, Chaplin2004, Jimenez2004, Chaplin2007}." +" Sun-as-a-star observations are most sensitive to the sectoral components of a mode, which, because of the spatial structure of the mode, show greater sensitivity to equatorial regions as [ increases."," Sun-as-a-star observations are most sensitive to the sectoral components of a mode, which, because of the spatial structure of the mode, show a greater sensitivity to equatorial regions as $l$ increases." +" Therefore, sincea at solar maximum the solar activity is also concentrated at low latitudes, /—2 and 3 modes experience a larger shift than the /20 and 1 modes (when observed in data)."," Therefore, since at solar maximum the solar activity is also concentrated at low latitudes, $l=2$ and 3 modes experience a larger shift than the $l=0$ and 1 modes (when observed in Sun-as-a-star data)." + Fig., Fig. +" 1 shows that, for each /, there is shorter-term, quasi-biennial structure on top of the dominant 11-yr trend and we now study this structure in more detail."," \ref{figure[freq shifts]} shows that, for each $l$, there is shorter-term, quasi-biennial structure on top of the dominant 11-yr trend and we now study this structure in more detail." + We begin by assessing whether the quasi-biennial structure observed in the frequency shifts represent a significant QBO., We begin by assessing whether the quasi-biennial structure observed in the frequency shifts represent a significant QBO. + The significance of the seismic QBO was assessed by computing periodograms of the raw frequency shifts., The significance of the seismic QBO was assessed by computing periodograms of the raw frequency shifts. + When assessing the statistical significance of the seismic QBO we used the frequency shifts observed in the dd independent time series as artifacts can be introduced when using overlapping subsets., When assessing the statistical significance of the seismic QBO we used the frequency shifts observed in the d independent time series as artifacts can be introduced when using overlapping subsets. + Overlaps in the subsets mean that the periodograms are modulated by a sinc squared function whose first zero was at 1.0yr! i.e. the inverse of the time difference between independent subsets.," Overlaps in the subsets mean that the periodograms are modulated by a sinc squared function whose first zero was at $1.0\,\rm yr^{-1}$ i.e. the inverse of the time difference between independent subsets." +" This makes it difficult to determine whether any significant periodicities are present in the overlapping data, particularly above 0.5yr!."," This makes it difficult to determine whether any significant periodicities are present in the overlapping data, particularly above $0.5\,\rm yr^{-1}$." + The mean frequency shift was subtracted before each periodogram was calculated and the data were oversampled by a factor of 10., The mean frequency shift was subtracted before each periodogram was calculated and the data were oversampled by a factor of 10. + The results are shown in Fig. 2.., The results are shown in Fig. \ref{figure[periodograms]}. + Also plotted in Fig., Also plotted in Fig. +" 2 are the 1pper cent false alarm significance levels (?),, which were determined using Monte Carlo simulations."," \ref{figure[periodograms]} are the per cent false alarm significance levels \citep{Chaplin2002}, which were determined using Monte Carlo simulations." +" 100,000 noise time series were simulated, using a normal distribution random number generator, to mimic those plotted in Fig. 1.."," 100,000 noise time series were simulated, using a normal distribution random number generator, to mimic those plotted in Fig. \ref{figure[freq shifts]}." + The standard deviation of each point in the time series was taken as the 1c error associated with the rotational splittings plotted in Fig. 1.., The standard deviation of each point in the time series was taken as the $1\sigma$ error associated with the rotational splittings plotted in Fig. \ref{figure[freq shifts]}. + Periodograms of the time series were calculated and the distribution of the amplitudes observed in the simulated periodograms was used to define the pper cent false alarm significance levels., Periodograms of the time series were calculated and the distribution of the amplitudes observed in the simulated periodograms was used to define the per cent false alarm significance levels. + The large peaks in each panel of Fig., The large peaks in each panel of Fig. + 2 at 0.09yr“! are the signal from the 11-yr cycle.," \ref{figure[periodograms]} at $0.09\,\rm yr^{-1}$ are the signal from the 11-yr cycle." + The /=2 and 3 high-frequency-range periodograms show a significant peak (at a pper cent false alarm level) at a frequency of ~0.5yr.," The $l=2$ and 3 high-frequency-range periodograms show a significant peak (at a per cent false alarm level) at a frequency of $\sim0.5\,\rm yr^{-1}$." +" This is the same frequency as the seismic QBO observed by, for example, ?.."," This is the same frequency as the seismic QBO observed by, for example, \citet{Fletcher2010}." +" However, we note that ? also observed a significant peak at ~0.5yr“! in low-frequency-range frequency shifts that were averaged over 0<|2."," However, we note that \citeauthor{Fletcher2010} also observed a significant peak at $\sim0.5\,\rm yr^{-1}$ in low-frequency-range frequency shifts that were averaged over $0\le l\le2$." +" However, there is no evidence for a significant signal at the same frequency in the low-frequency range observed here."," However, there is no evidence for a significant signal at the same frequency in the low-frequency range observed here." + We have improved our analysis techniques since ?.., We have improved our analysis techniques since \citeauthor{Fletcher2010}. +" However, it is possible that this has introduced some destructive interference with noise that has reduced the amplitude of the signal."," However, it is possible that this has introduced some destructive interference with noise that has reduced the amplitude of the signal." + Alternatively the improved analysis could have removed constructive, Alternatively the improved analysis could have removed constructive +ignition is preferred.,ignition is preferred. + We expect this range to be reasonably broad for 4U 1636-536 because of the rapid stellar rotation., We expect this range to be reasonably broad for 4U 1636-536 because of the rapid stellar rotation. +" As accretion rate increases LI ignitionstabilizes"".. and there is à transition to Lle-ienitecl bursts."," As accretion rate increases H ignition, and there is a transition to He-ignited bursts." + Above the transition ignition moves back to the equator., Above the transition ignition moves back to the equator. + Within this picture the Group 1 and Group 2 bursts are mixed 11Πο bursts triggered by olf-equatorial LE ignition., Within this picture the Group 1 and Group 2 bursts are mixed H/He bursts triggered by off-equatorial H ignition. + We would expect similar numbers of bursts to be triggered in the northern and. southern hemispheres., We would expect similar numbers of bursts to be triggered in the northern and southern hemispheres. + We therefore sugeest that most of the Group | bursts. which have negative convexities. ignite in the northern hemisphere. while most of the Group 2 bursts ignite in the southern hemisphere (lor which positive convexities are morelikelv)'.," We therefore suggest that most of the Group 1 bursts, which have negative convexities, ignite in the northern hemisphere, while most of the Group 2 bursts ignite in the southern hemisphere (for which positive convexities are more." +. The two groups should have similar peak Uuxes and rise times. in accordance with our observations.," The two groups should have similar peak fluxes and rise times, in accordance with our observations." + The properties of the »oursts in these groups are in accordance with those expected or mixed. Πο bursts triggered) by LL ignition: low peak luxes. rise times of a [ew seconds. and clurations longer han 10s.," The properties of the bursts in these groups are in accordance with those expected for mixed H/He bursts triggered by H ignition: low peak fluxes, rise times of a few seconds, and durations longer than 10s." + The value of 4 at which the transition takes place (= 0.03) is perhaps a little higher than expected (n Peng.Brown&Truran. (2007).. for example. LE ignition no longer rigeers mixed HLe bursts above z Exldington). but he precise values of the transitions will depend on factors such as heating [from the deep crust. and is not a perfect measure of accretion rate.," The value of $\gamma$ at which the transition takes place $\gamma \approx 0.03$ ) is perhaps a little higher than expected (in \citet{PBT}, for example, H ignition no longer triggers mixed H/He bursts above $\approx$ Eddington), but the precise values of the transitions will depend on factors such as heating from the deep crust, and $\gamma$ is not a perfect measure of accretion rate." +" The Group 3 bursts would in this picture be triggered by lle ignition on the equator,", The Group 3 bursts would in this picture be triggered by He ignition on the equator. + At acceretion rates immecdiately above the transition one would. expect the bursts το be nearly pure He. with the amount of II. involved. in the bursts increasing as accretion rate rises.," At accretion rates immediately above the transition one would expect the bursts to be nearly pure He, with the amount of H involved in the bursts increasing as accretion rate rises." + The properties of the Group 3 bursts are in line with those expected. for Lle-dominated bursts: high peak Duxes (with radius expansion). rise times l s. and durations ©10 s. We note that a transition to short rise time radius expansion bursts at a few percent of the Exddington rate was also seen in the ENOSAT data (Lewinetal.1987).," The properties of the Group 3 bursts are in line with those expected for He-dominated bursts: high peak fluxes (with radius expansion), rise times $\lesssim 1$ s, and durations $\lesssim 10$ s. We note that a transition to short rise time radius expansion bursts at a few percent of the Eddington rate was also seen in the EXOSAT data \citep{L}." +. A transition from mixed HII burning triggered by LI ignition. to He burning. should resu tin a drop in burst rate and an increase in alpha (the ratic» of the energy. released by stable burning between the burs sto the energy released," A transition from mixed H/He burning triggered by H ignition, to He burning, should result in a drop in burst rate and an increase in alpha (the ratio of the energy released by stable burning between the bursts to the energy released" +barvouic slope. which is difficult to interpret.,"baryonic slope, which is difficult to interpret." + We feel that this limited applicability warus. that a more general calculation may provide a different connection between the DM aud gaseous barvouic profiles Au interesting possibility now appears. namely hat one can use our results to infer the dark uatter profiles frou observations of the barvouic xofile.," We feel that this limited applicability warns, that a more general calculation may provide a different connection between the DM and gaseous baryonic profiles An interesting possibility now appears, namely that one can use our results to infer the dark matter profiles from observations of the baryonic profile." + This method cau be used. quite generally o inter the DAL distribution. and is therefore conrplemieutary to other methods such as lensing observations.," This method can be used quite generally to infer the DM distribution, and is therefore complementary to other methods such as lensing observations." + Lot us say we have observed a xuwvonie sphere with profile paron- (Lewisetal.2003))). (Navarrectal.1996:Moore 2.1.. (Eisenetal.2002:Aelia (Corbelli2003).," Let us say we have observed a baryonic sphere with profile $\beta_{\rm baryon}$ \citep{lewis03}) \citep{nfw96,moore99}. \ref{sec:sphere}. \citep{hansen02,aghanim03}. \citep{corb03}." +. Peebles(1972) (Balicall&Wolf1976) (Young1980) (Freitag&Benz2002)..," \cite{peebles72} \citep{bahcall76} \citep{young80} + \citep{freitag02}." +aL(dlrrgardb) lor several different impact parameter values.,$d\Gamma/(dlnr_{gal}db)$ for several different impact parameter values. +" We calculate dIf(ln,db) with and without the effect of eravitational focusing (solid and dashed lines respectively).", We calculate $d\Gamma/(dlnr_{gal}db)$ with and without the effect of gravitational focusing (solid and dashed lines respectively). + The latter is obtained by multiplvsing equation. (16)) by the eravitational focusing cnhancement term. before the integration., The latter is obtained by multiplying equation \ref{eq:dgamma_final}) ) by the gravitational focusing enhancement term before the integration. + As expected. eravitational focusing is negligible at small Galactic radii since typical stellar encounters involve high. relative velocities.," As expected, gravitational focusing is negligible at small Galactic radii since typical stellar encounters involve high relative velocities." + As the typical relative velocities decrease with increasing Cialactic radius. the enhancement to the collision rate [rom gravitational focusing becomes important.," As the typical relative velocities decrease with increasing Galactic radius, the enhancement to the collision rate from gravitational focusing becomes important." + The figure also shows that eravitational focusing becomes less important with increasing impact parameter since the eravitational attraction between the stars is weaker., The figure also shows that gravitational focusing becomes less important with increasing impact parameter since the gravitational attraction between the stars is weaker. + Fig., Fig. +" Sbb shows the cumulative differential collision rate (integrated. over rg) per impact. parameter as a function ofr,""", \ref{fig:diff_coll_rate}b b shows the cumulative differential collision rate (integrated over $r_{gal}$ ) per impact parameter as a function of $r_{gal}$. + Again. we plot the results with and without gravitational focusing and for the same impact parameters.," Again, we plot the results with and without gravitational focusing and for the same impact parameters." + To caleulate the mass loss rate from stars due to collisions within the Galactic center. we multiply equation (16)) by the fraction of mass lost. per collision. ελ). and compute the multidimensional integral.," To calculate the mass loss rate from stars due to collisions within the Galactic center, we multiply equation \ref{eq:dgamma_final}) ) by the fraction of mass lost per collision, $\Delta(\gamma)$, and compute the multi-dimensional integral." + We calculate the total mass loss rate from both the perturbed and perturber stars by simply interchanging the “pro and “ped” labels and re-performing 1e calculation., We calculate the total mass loss rate from both the perturbed and perturber stars by simply interchanging the “pr” and “pd” labels and re-performing the calculation. + We first compute the cdillerential mass loss rate for indirect. collisions., We first compute the differential mass loss rate for indirect collisions. + The mass loss per collision is given by: The coetficients. for the polynomial depend. on. the polytopic index of the perturbed star (and thus on its mass) ancl are taken from Table 1.., The mass loss per collision is given by: The coefficients for the polynomial depend on the polytopic index of the perturbed star (and thus on its mass) and are taken from Table \ref{tab:coeffs}. + We multiply equation (19)) and equation (16)) and simplify the integration., We multiply equation \ref{eq:mass_loss}) ) and equation \ref{eq:dgamma_final}) ) and simplify the integration. + In principle. b should go to o. but we cut olf the integral at Bye=20 as we find that the results converge well before this point.," In principle, b should go to $\infty$, but we cut off the integral at $\tilde b_{max}=20$ as we find that the results converge well before this point." +" The velocity integral is also cut olf at. 0,4 due to the fact that 2N(5) becomes zero below ~=0.98.", The velocity integral is also cut off at $\tilde v_{max}$ due to the fact that $\Delta (\gamma)$ becomes zero below $\gamma = 0.98$. + This cut-oll ≼∙∪↓⋅↓⋅⋖⋅≱∖↓≻∪⊔∠⇂≱∖↿∪∣⇁⋯⋯∶ -Ve.MDoelanes, This cut-off corresponds to $\tilde v_{max} = \frac{(\tilde M_{pr})_{max}}{0.98\tilde b_{min}^2}$. +" We. mav safely⋅ throw away the exponential. as 05,422«267Pyar)Dp For] the range ofe Fryar that we consider.", We may safely throw away the exponential as $\tilde v_{max}^2 \ll \tilde \sigma^2(\tilde r_{gal})$ for the range of $\tilde r_{gal}$ that we consider. +" Phus. the integral that we evaluate is: Lor direct. collisions. M,EMPot) is caleulated given the prescription ANC.in Sec.2.3.."," Thus, the integral that we evaluate is: For direct collisions, $\Delta(\tilde{b}, \tilde{M}_{pr}, \tilde{M}_{pd}, \tilde{v}_{rel})$ is calculated given the prescription in \ref{sec:mass_loss_direct}." +" To evaluate the multidimensional integral. we make the approximation of evaluating 2, at P4=26."," To evaluate the multidimensional integral, we make the approximation of evaluating $\Delta_{pd}$ at $\tilde{v}_{rel}=2\tilde{\sigma}$." +" The factor of à, thus comes out of the 5, integral. so that the P4 integral can be performed analytically: We evaluate the remaining integrals numerically."," The factor of $\Delta_{pd}$ thus comes out of the $\tilde{v}_{rel}$ integral, so that the $\tilde{v}_{rel}$ integral can be performed analytically: We evaluate the remaining integrals numerically." + Once values for o. Advi and Adie. are specified. equations (20)) ancl (21)) can be integrated to obtain the mass loss rate as à function of Galactic radius.," Once values for $\alpha$, $M_{min}$ and $M_{max}$ are specified, equations \ref{eq:mass_loss_indir}) ) and \ref{eq:mass_loss_dir}) ) can be integrated to obtain the mass loss rate as a function of Galactic radius." +" To show how he mass loss rate profiles vary with Adin. M, and a. weplot dAlαι,| lor direct collisions in Fig."," To show how the mass loss rate profiles vary with $M_{min}$, $M_{max}$ and $\alpha$, weplot $d\dot{M}/dlnr_{gal}$ for direct collisions in Fig." + 9. and vary hese parameters., \ref{fig:dmdot_dlnr_v_r} and vary these parameters. + In the figure. we have evaluated M; at 1.05. 0.5 and ΝΕ. Mus at το. 100. 125M. and à from 1.00 o 2.5 in equal increments.," In the figure, we have evaluated $M_{min}$ at 0.05, 0.5 and $_{\odot}$, $M_{max}$ at 75, 100, $_{\odot}$ and $\alpha$ from 1.00 to 2.5 in equal increments." +" The parameter. M,,;, increases vertically from the bottom panel to the top. M, increases rorizontally from. the feft. panel to the right. anc in each »del à increases from the bottom to the top."," The parameter $M_{min}$ increases vertically from the bottom panel to the top, $M_{max}$ increases horizontally from the left panel to the right, and in each panel $\alpha$ increases from the bottom to the top." + We have indicated a Salpeter-Iike mass function (a=2.29. AL;=VSAL. and Ado.= 125M.) with the dashed line.," We have indicated a Salpeter-like mass function $\alpha =2.29$, $M_{min} =0.5M_{\odot}$ and $M_{max} =125M_{\odot}$ ) with the dashed line." + Mass oss is extensive and approximately constant until about rj; of 10. Ἶρο and then drops dramatically., Mass loss is extensive and approximately constant until about $r_{gal}$ of $10^{-2}$ pc and then drops dramatically. + This drop relleets hat fact that collisions are less frequent at larger. raclii since star densities and relative velocities drop., This drop reflects that fact that collisions are less frequent at larger radii since star densities and relative velocities drop. + The amount of mass lost for any direct collision also. decreases. with ealactic radius since A decreases with decreasing relative velocities., The amount of mass lost for any direct collision also decreases with galactic radius since $\Delta$ decreases with decreasing relative velocities. +" Note that the profiles are approximately constant as a Function of Mu. so that the choice o£ M,;, determines the extent of the mass loss rate."," Note that the profiles are approximately constant as a function of $M_{max}$ , so that the choice of $M_{min}$ determines the extent of the mass loss rate." + 1n Fig., In Fig. + 10. we show the contributions to dMΕμ , \ref{fig:dir_indir} we show the contributions to $d\dot{M}/dlnr_{gal}$ +recently discovered a large correction to the galaxy. bias in numerical simulations of(οὐ primordial non-Ciaussianity.,recently discovered a large correction to the galaxy bias in numerical simulations of primordial non-Gaussianity. + Further numerical and theoretical work has confirmed this result (Matarrese&Verde2008:Slosaretal.AfshordiClannantonio&Porciani 2009).," Further numerical and theoretical work has confirmed this result \citep{MatarreseVerde2008, SlosarEtal2008, AfshordiTolley2008, McDonald2008, GrossiEtal2008, TaruyaKoyamaMatsubara2008, PillepichPorcianiHahn2010, DesjacquesSeljakIliev2009, GiannantonioPorciani2009}." +. The constraints obtained from power spectrum measurement of highly biased objects in current data-sets. are already comparable to the CALB results (Slosaretal.2008:Desjacques&Seljalk2010a). and the prospects For detecting local primordial non-Ciaussianity with galaxy clustering look exciting (Dalaletal.2008:Car-2009:Desjacques&Seljalk 2010a).," The constraints obtained from power spectrum measurement of highly biased objects in current data-sets are already comparable to the CMB results \citep{SlosarEtal2008, DesjacquesSeljak2010}, and the prospects for detecting local primordial non-Gaussianity with galaxy clustering look exciting \citep{DalalEtal2008, CarboneVerdeMatarrese2008, Seljak2009, Slosar2009, VerdeMatarrese2009, DesjacquesSeljak2010}." +. At this point. analyses of the galaxy bispectrum preceeding the work of Dalaletal.(2008) must. be updated: to account for the non- correction to the galaxy bias.," At this point, analyses of the galaxy bispectrum preceeding the work of \citet{DalalEtal2008} must be updated to account for the non-Gaussian correction to the galaxy bias." + In fact. a rigorous analysis of the galaxy power spectrum and bispectrum in presence of local non-Ciaussianity is in order.," In fact, a rigorous analysis of the galaxy power spectrum and bispectrum in presence of local non-Gaussianity is in order." + First steps in this direction have been taken by Jeong&Ixomatsu(2009) and Sefusatti(2009) with a preliminary comparison with simulations in Nishimichietal.(2009)., First steps in this direction have been taken by \citet{JeongKomatsu2009B} and \citet{Sefusatti2009} with a preliminary comparison with simulations in \citet{NishimichiEtal2009}. +. In this perspective. we will consider the measurement ol several triangular configurations of the bispeetrun on mildly nonlinear scales. with both Gaussian and non-Gaussian initial conditions of the local tvpe.," In this perspective, we will consider the measurement of several triangular configurations of the bispectrum on mildly nonlinear scales, with both Gaussian and non-Gaussian initial conditions of the local type." +. Although he matter bispectrum is not. directly observable with racers of the large-scale. structure. it ijs instructive to assess the extent to which perturbation theory. describes he shape dependence of the matter three-point function in the presence of non-Gaussianity of the local tvpe.," Although the matter bispectrum is not directly observable with tracers of the large-scale structure, it is instructive to assess the extent to which perturbation theory describes the shape dependence of the matter three-point function in the presence of non-Gaussianity of the local type." + This analysis will be useful when considering the complication ought by biasing. which will be accdressed in a forthcoming xublieation.," This analysis will be useful when considering the complication brought by biasing, which will be addressed in a forthcoming publication." + Measurements of the matter power spectrum with local non-Gaussianity can be found in Pillepichctal.(2010):Desjacquesetal. (2009).. where the small corrections at mildly: nonlinear scales predicted. in the framework of »erturbation theory by Taruüvaetal.(2008). are observed.," Measurements of the matter power spectrum with local non-Gaussianity can be found in \citet{PillepichPorcianiHahn2010, DesjacquesSeljakIliev2009}, , where the small corrections at mildly nonlinear scales predicted in the framework of perturbation theory by \citet{TaruyaKoyamaMatsubara2008} are observed." + In the case of the matter bispectrum. measurements in simulations with Gaussian initial conditions are shown in Scoecimarroetal.(1998):Lou(2005):Pan(2007):Smithetal.(2008):Guo&Jing (2009).. with Smithetal.(2008) considering. in aclelition. redshift space predictions in the context of the halo model.," In the case of the matter bispectrum, measurements in simulations with Gaussian initial conditions are shown in \citet{ScoccimarroEtal1998, HouEtal2005, PanColesSzapudi2007, SmithShethScoccimarro2008, GuoJing2009A}, with \citet{SmithShethScoccimarro2008} considering, in addition, redshift space predictions in the context of the halo model." + By contrast. the only measurement so far of the matter (and halo) bispeetrun in simulations with local non-Gaussian initial conditions can be found in Nishimichietal.(2009).. where a relatively small subset of isosceles triangular configurations is considered.," By contrast, the only measurement so far of the matter (and halo) bispectrum in simulations with local non-Gaussian initial conditions can be found in \citet{NishimichiEtal2009}, where a relatively small subset of isosceles triangular configurations is considered." + We will compare our measurements with predictions of the matter bispectrum at. the one-loop approximation in Eulerian perturbation theory., We will compare our measurements with predictions of the matter bispectrum at the one-loop approximation in Eulerian perturbation theory. + A comparison of one-loop results with the bispectrum extracted: from. simulations with Caussian initial conditions is shown in Scoccimarroetal. (1998).. whereas a comparison of the cllect of primordial non-Gaussianity with the. tree-level prediction of perturbation theory is performed. in. Nishimichictal.etal.2000:Ixomatsu&Sperecl2001) for “squeezed” isosceles configurations at 2=0 with AsOLAlpe+ only.," A comparison of one-loop results with the bispectrum extracted from simulations with Gaussian initial conditions is shown in \citet{ScoccimarroEtal1998}, whereas a comparison of the effect of primordial non-Gaussianity with the tree-level prediction of perturbation theory is performed in \citet{NishimichiEtal2009} for “squeezed” isosceles configurations at $z=0$ with $k\lesssim 0.1\kMpc$ only." + Here. we will extend the analysis to include several triangular configurations covering the range of scales 0.002=&z0.3Alpe+ and redshifts z=0. 1 and 2.," Here, we will extend the analysis to include several triangular configurations covering the range of scales $0.002\lesssim k \lesssim 0.3\kMpc$ and redshifts $z=0$, $1$ and $2$." + This will allow us to broadly test the accuracy of one-loop perturbation theory in the mildly: nonlinear regime., This will allow us to broadly test the accuracy of one-loop perturbation theory in the mildly nonlinear regime. + We will also discuss the validity of two phenomenological prescriptions for the nonlinear bispectrum with Ciaussian initial conditions. namely the fitting function of Scoccimarro&Couchman(2001) and the formula of Panetal.(2007) based. on a sealing transformation.," We will also discuss the validity of two phenomenological prescriptions for the nonlinear bispectrum with Gaussian initial conditions, namely the fitting function of \citet{ScoccimarroCouchman2001} and the formula of \citet{PanColesSzapudi2007} based on a scaling transformation." + This paper is organized as follows., This paper is organized as follows. + In section 2 we summarize previous results on the predictions of the matter power spectrum and bispectrum in. cosmological perturbation theory for both Gaussian and. local. non-Gaussian initial perturbations., In section \ref{sec:theory} we summarize previous results on the predictions of the matter power spectrum and bispectrum in cosmological perturbation theory for both Gaussian and local non-Gaussian initial perturbations. + In section 3. we describe the N-bocly simulations and the bispectrum estimator employed. in our analvsis whereas. in section ει. we present our measurements of the matter bispectrum and compare them to one-loop predictions in. perturbation theory.," In section \ref{sec:sims} we describe the N-body simulations and the bispectrum estimator employed in our analysis whereas, in section \ref{sec:results}, we present our measurements of the matter bispectrum and compare them to one-loop predictions in perturbation theory." + Finally. we conclude in section 5..," Finally, we conclude in section \ref{sec:conclusions}." + ln this section. we summarize previous results on the nonlinear. evolution. of the matter correlators às deseribecd specifically by Eulerian Perturbation Theory (PL).," In this section, we summarize previous results on the nonlinear evolution of the matter correlators as described specifically by Eulerian Perturbation Theory (PT)." + The quantity of interest. the matter overcensity 9. is obtained. as a perturbative solution to the continuity ancl Euler equations. anc Poisson equation relating matter perturbations and the gravitational potential.," The quantity of interest, the matter overdensity $\d$, is obtained as a perturbative solution to the continuity and Euler equations, and Poisson equation relating matter perturbations and the gravitational potential." + ποσο equations fully determine the evolution of the matter density ane velocity fields. once the initial conditions are given in terms of the primordial correlators.," These equations fully determine the evolution of the matter density and velocity fields, once the initial conditions are given in terms of the primordial correlators." + Other approaches such as Lagrangian Perturbation Fheory. for instance. have also been studied in the literature.," Other approaches such as Lagrangian Perturbation Theory, for instance, have also been studied in the literature." + We refer the reader to Scoccimarro(2000). for a study of the matter bispectrum in Lagrangian Perturbation Vheory with Gaussian. initial conditions and to Dernardeauetal.(2002) for a complete review of cosmological perturbation theory., We refer the reader to \citet{Scoccimarro2000B} for a study of the matter bispectrum in Lagrangian Perturbation Theory with Gaussian initial conditions and to \citet{BernardeauEtal2002} for a complete review of cosmological perturbation theory. + Our N-body simulations of the matter density. evolution assumefocal non-Gaussian initial conditions., Our N-body simulations of the matter density evolution assume non-Gaussian initial conditions. + Vhis model of primordial non-Ciaussianity is defined by thelocat expression in position space for the Dardeen's curvature perturbations ® (Salopek&Bond1990.1991:Ganguietal.L994:Verde OQ((x)) = ó((x) | well describes inflationary models in which the non-Gaussianityis produced by local mechanisms on superhorizon scales (seeBartoloetal.2004:Liguori therein). ," This model of primordial non-Gaussianity is defined by the expression in position space for the Bardeen's curvature perturbations $\Phi$ \citep{SalopekBond1990, SalopekBond1991, GanguiEtal1994, VerdeEtal2000, KomatsuSpergel2001} + ) = ) + well describes inflationary models in which the non-Gaussianityis produced by local mechanisms on superhorizon scales \citep[see][and references therein]{BartoloEtal2004, LiguoriEtal2010, Chen2010, ByrnesChoi2010}. ." +The definition of corresponds to a very specifie functional form of the bispectrum and trispectrum of the initial curvature perturbations., The definition of corresponds to a very specific functional form of the bispectrum and trispectrum of the initial curvature perturbations. + One finds the following, One finds the following +The paper is organized in the following manner: Sectioi 3 describes the sample and the data used: Sectior 24 deseribes the data reduction procedure; Section 4 illustrates the broad-band and spectral fitting procedures in general and for each individual source: Section 5 1s devoted to the discussion of the different spectral components found and their possible correlations.,The paper is organized in the following manner: Section 2 describes the sample and the data used; Section 3 describes the data reduction procedure; Section 4 illustrates the broad-band and spectral fitting procedures in general and for each individual source; Section 5 is devoted to the discussion of the different spectral components found and their possible correlations. + Finally. in Section 6 we report our coiclusions.," Finally, in Section 6 we report our conclusions." + Throughout this paper we assume a flat ACDM cosmology with ( Oy. Q4)=(0.3. 0.7) and a Hubble constant of 70 km s! Mpe! (Bennett et al.," Throughout this paper we assume a flat $\Lambda$ CDM cosmology with ( $\Omega_{\rm M}$, $\Omega_{\rm\Lambda}) = (0.3$, 0.7) and a Hubble constant of 70 km $^{-1}$ $^{-1}$ (Bennett et al." + 2003)., 2003). + The sample analyzed in the present work is extracted from the Bassani et al. (, The sample analyzed in the present work is extracted from the Bassani et al. ( +2006) survey. updated to include à number of optical classifications. obtained. afterwards. (see. Bassani. Malizia and Stephen 2006).,"2006) survey, updated to include a number of optical classifications obtained afterwards (see Bassani, Malizia and Stephen 2006)." + The sample includes Seyfert 1.5 galaxies with a 20-100 keV flux less than 5 mCrab. for which data were available at the time of writing.," The sample includes Seyfert 1-1.5 galaxies with a 20-100 keV flux less than 5 mCrab, for which data were available at the time of writing." + From the sample we have excluded sources already studied over a similar broad energy band. i.e.. eight type 1-1.5 Seyfert galaxies listed in Bassani et al. (," From the sample we have excluded sources already studied over a similar broad energy band, i.e., eight type 1-1.5 Seyfert galaxies listed in Bassani et al. (" +2006) survey are below the chosen threshold flux: four (NGC 4593. NGC 0814. MKN 6 and MCG-6-30-15) have already been studied (Perola et al.,"2006) survey are below the chosen threshold flux: four (NGC 4593, NGC 6814, MKN 6 and MCG-6-30-15) have already been studied (Perola et al." + 2002. Molina et al.," 2002, Molina et al." + 2006. Malizia et al.," 2006, Malizia et al." + 2003a. Guainazzi et al.," 2003a, Guainazzi et al." +" 1999, respectively) and the remaining four (2E. 1853.71534. ESO 323-G077. ESO 511-G030 and IGR 16119-06036) had no data available or public at the time this analysis was conducted."," 1999, respectively) and the remaining four (2E 1853.7+1534, ESO 323-G077, ESO 511-G030 and IGR J16119-6036) had no data available or public at the time this analysis was conducted." + All nine objects in the sample have been detected in X-rays before. but with the exception of 4U 1344-60. the available data were of poorer quality or limited to soft energy ranges (Le.. below 3 keV) than those presented here.," All nine objects in the sample have been detected in X-rays before, but with the exception of 4U 1344-60, the available data were of poorer quality or limited to soft energy ranges (i.e., below 3 keV) than those presented here." + None of the objects in the present sample had spectral information available in the soft gamma-ray range prior to this study. except 4U. 1344-60 (Beckmann et al.," None of the objects in the present sample had spectral information available in the soft gamma-ray range prior to this study, except 4U 1344-60 (Beckmann et al." + 2006)., 2006). + Overall we can conclude that the sample used in this work is representative of the population of type | AGN detected by above 20 keV and consists of objects poorly studied so far., Overall we can conclude that the sample used in this work is representative of the population of type 1 AGN detected by above 20 keV and consists of objects poorly studied so far. + The data presented here consist of several pointings performed by the low-energy instrument IBIS/ISGRI Soft Gamma-Ray; Lebrun et al., The data presented here consist of several pointings performed by the low-energy instrument IBIS/ISGRI Soft Gamma-Ray; Lebrun et al. + 2003) between revolution 12 and 429. re. the period from launch (October 2002) to the end of April 2006.," 2003) between revolution 12 and 429, i.e. the period from launch (October 2002) to the end of April 2006." + The IBIS/ISGRI images for each available pointing were generated in various energy bands using the ISDC off-line scientific analysis software OSA version 5.] (see e.g.. Goldwurm et al. (," The IBIS/ISGRI images for each available pointing were generated in various energy bands using the ISDC off-line scientific analysis software OSA version 5.1 (see e.g., Goldwurm et al. (" +2003) for the ISGRI data analysis within OSA).,2003) for the ISGRI data analysis within OSA). + Count rates at the position of the source were extracted from individual images in order to provide light curves in various energy bands: from these light curves average fluxes were then estimated and combined to obtain the source spectrum (see Bird et al., Count rates at the position of the source were extracted from individual images in order to provide light curves in various energy bands; from these light curves average fluxes were then estimated and combined to obtain the source spectrum (see Bird et al. + 2006. 2007. for details).," 2006, 2007, for details)." + In Table | we report the list of objects analyzed and the relevant information for each of them such as. the coordinates for epoch J2000. the optical classification. the redshift. the Galactic column density. the 20-40 keV flux as reported in. Bird et al. (," In Table \ref{sample} we report the list of objects analyzed and the relevant information for each of them such as, the coordinates for epoch J2000, the optical classification, the redshift, the Galactic column density, the 20-40 keV flux as reported in Bird et al. (" +2007) and the optical identification references.,2007) and the optical identification references. + For each AGN. we checkec in the field of view (typically a radius of 15’ ) for the presence of sources which might contribute to the high energy flux.," For each AGN, we checked in the field of view (typically a radius of $\arcmin$ ) for the presence of sources which might contribute to the high energy flux." + Except for IGR J07597-3842. no bright sources were found.," Except for IGR J07597-3842, no bright sources were found." + At ~ 4’ from the nuclear position of IGR JO7597-3842. a bright point-like source is clearly detected in the image .," At $\sim$ $\arcmin$ from the nuclear position of IGR J07597-3842, a bright point-like source is clearly detected in the image ." + Its spectrum is dominated by a strong soft component. while the 10 keV flux is only 6 x107™ erg em7? s7!: therefore we do not expect this source to contribute significantly to the flux.," Its spectrum is dominated by a strong soft component, while the 2-10 keV flux is only 6 $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$; therefore we do not expect this source to contribute significantly to the flux." + Finally. we remind the reader that while are snap-shot observations. provides an average spectrum over many ks exposures spanning a few years period.," Finally, we remind the reader that while are snap-shot observations, provides an average spectrum over many ks exposures spanning a few years period." + All objects in the sample have been observed between March and August 2006., All objects in the sample have been observed between March and August 2006. + The data have been processed startingfrom, The data have been processed startingfrom +is comparable to that of the TSI comparisous. though the model fares less well with respect to the SIM data.,"VIRGO is comparable to that of the TSI comparisons, though the model fares less well with respect to the SIM data." + As indicated by the correlation eradieuts. the model appears to underestimate the variability by between 10 and20%.," As indicated by the correlation gradients, the model appears to underestimate the variability by between 10 and." +. We cousider the derived from SIM data to he less reliable. mainly because the data follow a slight degradation-like loue-term trend.," We consider the derived from SIM data to be less reliable, mainly because the data follow a slight degradation-like long-term trend." + Tis is again most obvious at the begiuuime of λίαν, This is again most obvious at the beginning of May. +", A correlation analysis with data after May 11 yields a slope of 1.11 with respect to the model. aud agrees well with our fiudiugs for the blue VIRGO filter."," A correlation analysis with data after May 11 yields a slope of 1.11 with respect to the model, and agrees well with our findings for the blue VIRGO filter." + During 2001. the solar UV spectra aud its variability was also recorded with the UARS/SUSIM iustrunceut.," During 2004, the solar UV spectrum and its variability was also recorded with the UARS/SUSIM instrument." + Tn this section. we compare these measurements with the SORCE/SIM measurements aud the model calculations for wavelougths between 170 aud 320 um.," In this section, we compare these measurements with the SORCE/SIM measurements and the model calculations for wavelengths between 170 and 320 nm." + Fig., Fig. + 7 shows a plot of the normalised standard deviation for data aud model calculations between Alay 1 aud July 31 in 2001., \ref{fig:SOR_SUS} shows a plot of the normalised standard deviation for data and model calculations between May 1 and July 31 in 2004. + Iu order to reduce confusion iu the plot. we have binned the SORCE/SIM and UARS/SUSIM data in the wavelength domain before carrying out the variability analysis.," In order to reduce confusion in the plot, we have binned the SORCE/SIM and UARS/SUSIM data in the wavelength domain before carrying out the variability analysis." + The binning factors are detailed in the caption of Fig. 7.., The binning factors are detailed in the caption of Fig. \ref{fig:SOR_SUS}. + A uuuber of striking features are apparent iu the plot. aud are discussed below.," A number of striking features are apparent in the plot, and are discussed below." + The SORCE/SIAL and SATIRE data show a luge Increase m variability at about 205 niu., The SORCE/SIM and SATIRE data show a large increase in variability at about 205 nm. + This is most likely due to Aland Ca opacity edges between 200 aud 210 n1., This is most likely due to Al and Ca opacity edges between 200 and 210 nm. + A significant decrease of the solay brightuess temperature around this waveleneth was already observed. by Widingctal.(1970) based ou data from rocket fights., A significant decrease of the solar brightness temperature around this wavelength was already observed by \citet{widing70} based on data from rocket flights. + It is very noticeable. however. that the variability recorded by UARS/SUSIM is 1uuch lower than both the SORCE/SIM aud the SATIRE variability.," It is very noticeable, however, that the variability recorded by UARS/SUSIM is much lower than both the SORCE/SIM and the SATIRE variability." + While the UARS/SUSIM Increase nüght appear weakened because of the higher (instrumental) variability seen above 200 nm and the ower velocity resolution. we expect the SUSIM data t) vest reflect the solar variability below 200 imu during he time period considered here.," While the UARS/SUSIM increase might appear weakened because of the higher (instrumental) variability seen above 200 nm and the lower velocity resolution, we expect the SUSIM data to best reflect the solar variability below 200 nm during the time period considered here." + The main reason for he (excessive) Aucrease in variability of the SATIRE uodel is the breakdown of the LTE assumuptious aud the use of opacity distribution fuuctious (ODFs) rather than detailed line-opacitv caleulatious., The main reason for the (excessive) increase in variability of the SATIRE model is the breakdown of the LTE assumptions and the use of opacity distribution functions (ODFs) rather than detailed line-opacity calculations. + Iu the case of SIME. the juup in variability is uot surprising either. as its detector is not expected to perform well at these wavelenetls (see Sec. 3.1.1)).," In the case of SIM, the jump in variability is not surprising either, as its detector is not expected to perform well at these wavelengths (see Sec. \ref{sec:instru_sim_uv}) )." + Better results should be provided bx SORCE/SOLSTICE., Better results should be provided by SORCE/SOLSTICE. + Iu the waveleneth region between 210 and 290 nu. the agreement between the model caleulatious aud the SIM nieasurenmaents is varied.," In the wavelength region between 210 and 290 nm, the agreement between the model calculations and the SIM measurements is varied." + While some features such as the Me h&kk limes (280 nii). aud the regions from 220 to 232 uu. Tou 255 to 270 aud above 290 nui match well. other waveleneth regions show large disagrecnieuts. see. ess the lines of Mg at 285 mu. or the complex sets of lines around 210 and 250 mm.," While some features such as the Mg k lines (280 nm), and the regions from 220 to 232 nm, from 255 to 270 and above 290 nm match well, other wavelength regions show large disagreements, see, e.g., the lines of Mg at 285 nm, or the complex sets of lines around 240 and 250 nm." + As above. these disagreeimieuts are due mainly to the assumption of LTE aud the use of ODFs (I&urucz1992)..," As above, these disagreements are due mainly to the assumption of LTE and the use of ODFs \citep{kurucz92missing_uv}." + Uncertainties in the model atinospheres also coutzibute. though probably to a muuch sinaller extent. since the differences are largest at the wavelengths of stroug Ines showing strong NLTE effects.," Uncertainties in the model atmospheres also contribute, though probably to a much smaller extent, since the differences are largest at the wavelengths of strong lines showing strong NLTE effects." + Thus the difference in the behaviour of the Me and Ale resonance nes can be explained quite well if NLTE effects are taken iuto account (Uitenbrock&Briand1995)., Thus the difference in the behaviour of the Mg and Mg resonance lines can be explained quite well if NLTE effects are taken into account \citep{uitenbroek1995}. +. Overall. the aercement between SIM. and SUSIM is reasonably eood between about 210 and 290 mm.," Overall, the agreement between SIM and SUSIM is reasonably good between about 210 and 290 nm." + While the variability recorded with SUSIM is higher due to its lower sensitivity. the features recovered agree well aud the measured relative variabilities are uot too different.," While the variability recorded with SUSIM is higher due to its lower sensitivity, the features recovered agree well and the measured relative variabilities are not too different." + Above 200 iui UARS/SUSIM shows a relatively poor response that swamps he solar variability ou mid to short-teri. time scales., Above 290 nm UARS/SUSIM shows a relatively poor response that swamps the solar variability on mid to short-term time scales. + The responsivity aud noise characteristics of SUSIM have been well documented aud are discussed. e.g. in Woodsctal. (1996)..," The responsivity and noise characteristics of SUSIM have been well documented and are discussed, e.g., in \citet{woods-et-al-96}. ." +Evolution of the potential plays a minor role in the case of super structures.,Evolution of the potential plays a minor role in the case of super structures. +" Hence, the effect on the galaxy redshift is different from the RS effect or the ISW effect."," Hence, the effect on the galaxy redshift is different from the RS effect or the ISW effect." +" The compensated cluster (void) in changes the redshift of a z,~0.6 background galaxy by Az,=2.8x107? (—1.7x 107?) in the EdS universe and by Az=12x107? x1079) in the universe.", The compensated cluster (void) in changes the redshift of a $z_\mathrm{s} \simeq 0.6$ background galaxy by $\Delta z_\mathrm{s} = 2.8\times10^{-5}$ $-1.7\times10^{-5}$ ) in the EdS universe and by $\Delta z_\mathrm{s} = 1.2\times10^{-5}$ $-7.5\times10^{-6}$ ) in the universe. +" Although measuring(—7.5 such redshift differences is not completely out of technical reach, the fact that there is not a standard redshift to compare with makes it impossible to measure this effect on individual galaxies."," Although measuring such redshift differences is not completely out of technical reach, the fact that there is not a standard redshift to compare with makes it impossible to measure this effect on individual galaxies." +" Since it is a systematic perturbation to galaxy redshifts, one might be able to detect the effect by comparing the galaxy redshift distribution with and without intervening structures."," Since it is a systematic perturbation to galaxy redshifts, one might be able to detect the effect by comparing the galaxy redshift distribution with and without intervening structures." +" However, many issues come into play."," However, many issues come into play." +" For example, magnification by the very foreground structures also affects how background galaxies are selected into the sample and thus change the galaxy redshift distribution perhaps more significantly."," For example, magnification by the very foreground structures also affects how background galaxies are selected into the sample and thus change the galaxy redshift distribution perhaps more significantly." +" While the absolute time delay due to foreground structures is not directly observable, one can obtain the relative time delay between images of a strongly lensed source either by actual measurements with a variable source or by estimation with a lens model."," While the absolute time delay due to foreground structures is not directly observable, one can obtain the relative time delay between images of a strongly lensed source either by actual measurements with a variable source or by estimation with a lens model." + This could have allowed a short cut to the that has to run for decades., This could have allowed a short cut to the that has to run for decades. +" Assuming for the moment that the potential does not evolve, i.e., AT—0 in(4),, we have = where Atg is the 1+2,Hs,,(22)relative time delay observed at z=0."," Assuming for the moment that the potential does not evolve, i.e., $\Delta T=0$ in, we have = =, where $\Delta t_0$ is the relative time delay observed at $z=0$." +" For a source at z,=1, the velocity difference corresponding to a time delay of one year is —1.8cms~!."," For a source at $z_\mathrm{s} = 1$, the velocity difference corresponding to a time delay of one year is $-1.8\,\mathrm{cm\,s}^{-1}$." + The evolution of the lens potential also contributes to the redshift difference., The evolution of the lens potential also contributes to the redshift difference. +" Because lenses are more or less virialized structures, one might approximate them as static objects in physical space and determine their potential evolution in the expanding universe."," Because lenses are more or less virialized structures, one might approximate them as static objects in physical space and determine their potential evolution in the expanding universe." + One might also stack CMB measurements behind a large number of similar lenses to determine the potential evolution., One might also stack CMB measurements behind a large number of similar lenses to determine the potential evolution. +" For comparison, the gives (Loeb1998) z)]]"," For comparison, the gives \citep{loeb98} + ]." +.(23) Here= —Ato125 is the— time between two epochs of measurements., Here $\Delta t_0$ is the time between two epochs of measurements. +" In the universe, H,SHo(1+z) at zsS2.5, so the direction of the redshift change in the strong-lensing case is opposite to the at z,<2.5."," In the universe, $H_\mathrm{s} \lesssim H_0(1+z)$ at $z_\mathrm{s} \lesssim 2.5$, so the direction of the redshift change in the strong-lensing case is opposite to the at $z_\mathrm{s} \lesssim 2.5$." +" The amplitude in the strong- case is almost an order of magnitude larger than that in thetest,, making the former comparatively easier to measure for the same Ato."," The amplitude in the strong-lensing case is almost an order of magnitude larger than that in the, making the former comparatively easier to measure for the same $\Delta t_0$ ." +" Moreover, the requires extremely high-precision absolute calibration of the instruments over a few decades, which is more difficult than high-precision relative measurements performed at the same time using the same instrument in the strong lensing case."," Moreover, the requires extremely high-precision absolute calibration of the instruments over a few decades, which is more difficult than high-precision relative measurements performed at the same time using the same instrument in the strong lensing case." +" Unfortunately as Loeb pointed out, differences in the conditions(1998) of the images (e.g. shape, magnification, noise, etc.)"," Unfortunately, as \citet{loeb98} pointed out, differences in the conditions of the images (e.g., shape, magnification, noise, etc.)" +" of the same galaxy could already cause larger differences in the redshift measurements; even more fproblematically, proper motion of the lens could induce a difference in image redshifts (Birkinshaw&Gull1983) far exceeding that associated with the time delay."," of the same galaxy could already cause larger differences in the redshift measurements; even more problematically, proper motion of the lens could induce a difference in image redshifts \citep{birkinshaw83} far exceeding that associated with the time delay." +" Therefore, even though the strong lensing case has a few advantages, it is still impractical to use the redshift difference and time delay between images of a strongly lensed source to measure the Hubble expansion at the source redshift."," Therefore, even though the strong lensing case has a few advantages, it is still impractical to use the redshift difference and time delay between images of a strongly lensed source to measure the Hubble expansion at the source redshift." +" 'This work was supported by the Bairen program from the Chinese Academy of Sciences, the National Basic Research Program of China grant No."," This work was supported by the Bairen program from the Chinese Academy of Sciences, the National Basic Research Program of China grant No." +" 2010CB833000, and the National Natural Science Foundation of China grant No."," 2010CB833000, and the National Natural Science Foundation of China grant No." + 11033005., 11033005. + We require the curvature function K of the model structures to have a continuous second derivative with respect to r., We require the curvature function $K$ of the model structures to have a continuous second derivative with respect to $r$. +" For compensated models, we specify K directly «"," For compensated models, we specify $K$ directly. ," +"(Al where Ky=61,07 and ὅτι is the initial overdensity of region I. For uncompensated models, we let the initial overdensity 9; follow the H?7Qm,same form as K Ky replaced by and then use Equations (2)), and (2)) to obtain K."," where $\KI = \dIi {a_i^2 H_i^2} \Omega_\mathrm{m}$, and $\dIi$ is the initial overdensity of region I. For uncompensated models, we let the initial overdensity $\delta_i$ follow the same form as $K$ (with $\KI$ replaced by $\dIi$ ) and then use Equations \ref{eq:rho}) ), \ref{eq:Ri}) ), and \ref{eq:RdotS}) ) to obtain $K$." +" We choose ry for uncompensated (withmodels so that the δι)uncompensated overdensity profiles (2)),roughly match those of compensated models in the central region.", We choose $\rII$ for uncompensated models so that the uncompensated overdensity profiles roughly match those of compensated models in the central region. + The left panel of shows overdensity profiles of the compensated (dotted lines) and uncompensated (solid cluster models., The left panel of shows overdensity profiles of the compensated (dotted lines) and uncompensated (solid lines) cluster models. +" For both models, the initial overdensity of region I at a; is set to δι;=7.0x107+, so that lines)dy=0.36 at redshift z=0.5 to match the mean overdensity of overdense regions of the clusters found in (2008)."," For both models, the initial overdensity of region I at $a_i$ is set to $\dIi=7.0\times10^{-4}$, so that $\dI = 0.36$ at redshift $z=0.5$ to match the mean overdensity of overdense regions of the clusters found in \citet{granett08}." +. The density of the uncompensated cluster grows with time everywhere., The density of the uncompensated cluster grows with time everywhere. + The void models behave similarly but with inverted profiles and smaller amplitudes., The void models behave similarly (not shown) but with inverted profiles and smaller amplitudes. +" Moreover, the uncompensated void develops slightly positive(not shown)overdensity (6< |d;|) at rZry at late time."," Moreover, the uncompensated void develops slightly positive overdensity $\delta \ll |\dI|$ ) at $r \gtrsim \rII$ at late time." + The right panel of illustrates the evolutionof the function R/ar for the compensated cluster (solid lines) and the compensated void (dotted lines)., The right panel of illustrates the evolutionof the function $R/ar$ for the compensated cluster (solid lines) and the compensated void (dotted lines). +" The void has ój;——5.5x1074and 6;=—0.19 at 2= 0.5, matching the"," The void has $\dIi=-5.5\times 10^{-4}$and $\dI = -0.19$ at $z = 0.5$ , matching the" +Alost spectroscopically normal. single b-type clwarl stars are very constant in brightness.,"Most spectroscopically normal, single F-type dwarf stars are very constant in brightness." +" IHecently. a number of E-(ype stars on. or just above. the main sequence Lh the Lertzsprung-Russcllwd._2 (UR)> Diagram1.uu havenyyg. beenνα been""n shown. to be photometrically variable. up to 0.1 magnitude on time scales of several hours to tens of hours."," Recently, a number of F-type stars on, or just above, the main sequence in the Hertzsprung-Russell (HR) Diagram have been been shown to be photometrically variable, up to 0.1 magnitude on time scales of several hours to tens of hours." + The first. of these to be identified was the bright southern star. > Doradus (Cousins Warren 1963).," The first of these to be identified was the bright southern star, $\gamma$ Doradus (Cousins Warren 1963)." + It was most recently studied by Balona (1994a). and. by Jalona. Wrisciunas Cousins (1994b).," It was most recently studied by Balona (1994a) and by Balona, Krisciunas Cousins (1994b)." + A number of other stars of similar s»ectral type and luminosity class have been independently icentified to be variable in brightness., A number of other stars of similar spectral type and luminosity class have been independently identified to be variable in brightness. + This includes LID 164615 (Abt. Jollineer Burke 1983). four peculiar variables in the open cluster NGC 2516 (Antonello Mantegazza 1986). LID 96008 (Lampens 1987: Matthews 1990). 9 Aurigae (Ixrisciunas and Guinan 1990: Ixrisciunas 1993). WD 111829 (Mantegazza. Poretti Antonello 1991: note correct LID number). and WD 224638 and LID 224945 (Mantegazza Poretti 1991: Mantegazza. Poretti Zorbi 1994).," This includes HD 164615 (Abt, Bollinger Burke 1983), four peculiar variables in the open cluster NGC 2516 (Antonello Mantegazza 1986), HD 96008 (Lampens 1987; Matthews 1990), 9 Aurigae (Krisciunas and Guinan 1990; Krisciunas 1993), HD 111829 (Mantegazza, Poretti Antonello 1991; note correct HD number), and HD 224638 and HD 224945 (Mantegazza Poretti 1991; Mantegazza, Poretti Zerbi 1994)." + Because these stars have such similar spectral tvpes and absolute magnitudes. hence temperatures. and densities. it is sensible to study their similarities under the assumption that they constitute a new group of variables.," Because these stars have such similar spectral types and absolute magnitudes, hence temperatures and densities, it is sensible to study their similarities under the assumption that they constitute a new group of variables." + Antonello Mantegazza (1986) first suggested that the slowly varving. Fo. stars in. NGC Xm2516- might. be undergoing: non-radial pulsations., Antonello Mantegazza (1986) first suggested that the slowly varying F stars in NGC 2516 might be undergoing non-radial pulsations. + However. they felt that such a notion would. be dillicult to νο because the expected: racial velocity and color variations would: “probably be] bevond the present precision of measurements.”," However, they felt that such a notion would be difficult to verify because the expected radial velocity and color variations would “probably [be] beyond the present precision of measurements.”" + They suggested star spots and. ellipsoidally. shapec stars as other possibilities., They suggested star spots and ellipsoidally shaped stars as other possibilities. + Waclkens (1991) independently suggested. that one of the stars mentioned above. LD 96008. was undergoing non-radial pulsations.," Waelkens (1991) independently suggested that one of the stars mentioned above, HD 96008, was undergoing non-radial pulsations." + Hlowever. Mantegazza Poretti (1994) have recently shown that ID 96008 exhibits smooth radial velocity variations with a poriod equal to twice the photometrie period.," However, Mantegazza Poretti (1994) have recently shown that HD 96008 exhibits smooth radial velocity variations with a period equal to twice the photometric period." + It is almost certain that LLL 96008 is an ellipsoidal star with a close companion (likely to be an M5 dwarf star), It is almost certain that HD 96008 is an ellipsoidal star with a close companion (likely to be an M5 dwarf star). + The reason for the suggestion that one or more of these stars is undergoing non-radial pulsations is that a star with, The reason for the suggestion that one or more of these stars is undergoing non-radial pulsations is that a star with +the latitudinal dependence of the seismic QBO. using low-/ modes. by examining the frequency shifts observed in modes of ditferent 7.,"the latitudinal dependence of the seismic QBO, using $l$ modes, by examining the frequency shifts observed in modes of different $l$." + ? used the green coronal emission line at nnm observed between 1939 and 2005 to examine the spatial distribution of the QBO., \citet{Vecchio2009} used the green coronal emission line at nm observed between 1939 and 2005 to examine the spatial distribution of the QBO. + They found that the signal was strong in polar regions and weaker around the equator., They found that the signal was strong in polar regions and weaker around the equator. + We make use of Sun-as-a-star (Doppler velocity) observations. which are sensitive to p modes with the largest horizontal scales tor lowest /).," We make use of Sun-as-a-star (Doppler velocity) observations, which are sensitive to p modes with the largest horizontal scales (or lowest $l$ )." + Resolved helioseismic observations allow higher-/ modes to be observed., Resolved helioseismic observations allow $l$ modes to be observed. + However. in general these modes are more localized than are the low-/ modes and hence sensitive to local conditions.," However, in general these modes are more localized than are the $l$ modes and hence sensitive to local conditions." + This has the potential to confuse the discussion of patterns on a large scale. which is what interests us here.," This has the potential to confuse the discussion of patterns on a large scale, which is what interests us here." + Furthermore. the method used in the determination of frequencies for the high-/ modes is ditteren from that used at low / because of the influence of mode leakage. which occurs because the spatial filters are not perfect due to only half of the Sun being observed.," Furthermore, the method used in the determination of frequencies for the $l$ modes is different from that used at low $l$ because of the influence of mode leakage, which occurs because the spatial filters are not perfect due to only half of the Sun being observed." + Although analysis based on combinec data sets is done. great care has to be taken to minimize systematic discrepancies (e.g.??).," Although analysis based on combined data sets is done, great care has to be taken to minimize systematic discrepancies \citep[e.g.][]{Chaplin2004b, Chaplin2004a}." + Therefore. in this paper. we assess wha information concerning the location of the QBO can be obtained from low-/ modes alone.," Therefore, in this paper, we assess what information concerning the location of the QBO can be obtained from $l$ modes alone." + The structure of the remainder of this paper is as follows: Section ?? deseribes the data used in this paper., The structure of the remainder of this paper is as follows: Section \ref{section[data]} describes the data used in this paper. + The /-dependence of the raw frequency shifts is discussed in Section ??.., The $l$ -dependence of the raw frequency shifts is discussed in Section \ref{section[freq shifts]}. + In Section ?? we assess whether the observed seismic QBO is strong enough to be significant when the frequencies are examined for each / individually.," In Section \ref{subsection[significance +of QBO]} we assess whether the observed seismic QBO is strong enough to be significant when the frequencies are examined for each $l$ individually." + Then. in Section ??.. the /-dependence and frequency dependence of the seismic QBO is discussed.," Then, in Section \ref{section[QBS]}, the $l$ -dependence and frequency dependence of the seismic QBO is discussed." + In Section ??. we use simple models to try and constrain the latitudinal dependence of the seismic QBO., In Section \ref{section[models]} we use simple models to try and constrain the latitudinal dependence of the seismic QBO. + Finally the main results are summarized in Section ??.., Finally the main results are summarized in Section \ref{section[discussion]}. + The Birmingham Solar-Oscillations Network (BISON) makes Sun-as-a-star (unresolved) Doppler velocity observations., The Birmingham Solar-Oscillations Network (BiSON) makes Sun-as-a-star (unresolved) Doppler velocity observations. + We have used the BiSON data to investigate whether a seismic QBO is present in the frequencies of modes with O60s and Fy>2xLOPere 7s ! could certainly heat up the ambient plasma to 7> 10*IX bv the dissipation of the N-waves even in a flow tube with the areal expansion of μας=5. bx balancing with the losses of the radiative cooling. the downward thermal conduction. and the adiabatie loss by the solar wind.," We have found that the acoustic waves with $\tau\ge 60$ s and $F_{\rm w,0} +\ge 2\times 10^5$ erg $^{-2}$ $^{-1}$ could certainly heat up the ambient plasma to $T\ge 10^6$ K by the dissipation of the N-waves even in a flow tube with the areal expansion of $f_{\rm max}=5$, by balancing with the losses of the radiative cooling, the downward thermal conduction, and the adiabatic loss by the solar wind." + Due to its dissipative character. the dissipation of N-waves effectively. works in the inner corona and reproduces the density profile observed in the streamer region.," Due to its dissipative character, the dissipation of N-waves effectively works in the inner corona and reproduces the density profile observed in the streamer region." + However. il cannot contribute to the heating of (he outer corona. since most of the wave energy is damped within a region of few-tenth of the solar radius even if one considers the waves with a long period of 7= 300s. As a result. it is impossible to explain the observed temperature profile and flow velocity of the low-speed wind only by Chat process.," However, it cannot contribute to the heating of the outer corona, since most of the wave energy is damped within a region of few-tenth of the solar radius even if one considers the waves with a long period of $\tau=300$ s. As a result, it is impossible to explain the observed temperature profile and flow velocity of the low-speed wind only by that process." + Therefore. other mechanisnis with the larger dissipation leneth should play a role cooperatively in the coronal heating and the acceleration of the low-speed wind.," Therefore, other mechanisms with the larger dissipation length should play a role cooperatively in the coronal heating and the acceleration of the low-speed wind." + sinall-scale reconnection events and spicules also predict 5generation of fast shock waves (Lee&Wu2000:Lee2001:Hollweg1932).. though we have concentrated on the role of the N-waves (slow shocks along the magnetic lield line) excited by those events in (his paper.," Small-scale reconnection events and spicules also predict generation of fast shock waves \citep{lw00,lee01,hol82}, though we have concentrated on the role of the N-waves (slow shocks along the magnetic field line) excited by those events in this paper." + The dissipation length of the fast shocks must be larger than N-waves with the identical period. since their phase speed is 2vy. which is much larger Chan that of the N-waves (o ος) for low-2 coronal plasma.," The dissipation length of the fast shocks must be larger than N-waves with the identical period, since their phase speed is $\gtrsim v_{\rm A}$, which is much larger than that of the N-waves $\sim c_{\rm s}$ ) for $\beta$ coronal plasma." +" Hence. cooperation with the fast shocks would give a more distant. location of Tia, to match the observed temperature profile (fig.9)). and would let the acceleration of the wind flow continue in the outer corona. as suggested by observation ol the streamer belt. 10))."," Hence, cooperation with the fast shocks would give a more distant location of $T_{\rm max}$ to match the observed temperature profile \ref{fig:obste}) ), and would let the acceleration of the wind flow continue in the outer corona, as suggested by observation of the streamer belt \ref{fig:obsvl}) )." + Finally. we had better remark an issue on anisotropic ancl selective heating of ions.," Finally, we had better remark an issue on anisotropic and selective heating of ions." + According to recent observations (Strachanetal.2002).. O VI ions in the streamer have hieh perpendicular kinetic temperature. though (his is not so extreme as that observed in (he hieh-speed wind.," According to recent observations \citep{ssp02}, O VI ions in the streamer have high perpendicular kinetic temperature, though this is not so extreme as that observed in the high-speed wind." + Our results show that the deposition of energv and momentum Irom the N-waves to the ambient gas is completed in the region of rS 1.5/.. where the particles are," Our results show that the deposition of energy and momentum from the N-waves to the ambient gas is completed in the region of $r\lesssim 1.5 R_{\odot}$ , where the particles are" +"As expected, in ~20% of the deviant cases the pointings have fallen close to the coronagraphic hole.","As expected, in $\sim20\%$ of the deviant cases the pointings have fallen close to the coronagraphic hole." + T'he profiles are clustered around the Q2-A positions., The profiles are clustered around the Q2-A positions. +" With time, the precise position of the hole wanders by about one pixel."," With time, the precise position of the hole wanders by about one pixel." +" However, its position (x,y) is typically 73.5, 213.5 with a soft edge that can extend to a radius of 7 pixels."," However, its position (x,y) is typically 73.5, 213.5 with a soft edge that can extend to a radius of 7 pixels." + Data that were affected by the presence of the coronagraph were excluded., Data that were affected by the presence of the coronagraph were excluded. + The remaining flagged profiles show >2c deviations at radii of €2 pixels., The remaining flagged profiles show $>2\sigma$ deviations at radii of $\leq2$ pixels. +" As the NIC2 polarizers have an effective wavelength of 1.9954m, and the effective primary aperture is 2.281 m (as defined by the NIC2 pupil the theoretical PSF core diameter is 07222 or 2.91 mask),pixels (PSF FWHM = 071185, 2.44 pixels); NIC2 critically samples the PSF."," As the NIC2 polarizers have an effective wavelength of $1.995\micron$, and the effective primary aperture is 2.281 m (as defined by the NIC2 pupil mask), the theoretical PSF core diameter is 22 or 2.91 pixels (PSF FWHM = 185, 2.44 pixels); NIC2 critically samples the PSF." +" As these profiles are only deviant within the diffraction limit of the instrument, and are within 2c of the average profiles at radii >2 pixels, i.e., the effects are negated by increasing the aperture size, they are not excluded from further study."," As these profiles are only deviant within the diffraction limit of the instrument, and are within $2\sigma$ of the average profiles at radii $>2$ pixels, i.e., the effects are negated by increasing the aperture size, they are not excluded from further study." + The processes of flagging and inspecting deviant profiles was repeated until all profiles fell within 2c of the average., The processes of flagging and inspecting deviant profiles was repeated until all profiles fell within $2\sigma$ of the average. +" At each iteration, excluded profiles were removed from the original average."," At each iteration, excluded profiles were removed from the original average." +" In the worst case, only three profiles (from 12) were rejected."," In the worst case, only three profiles (from 12) were rejected." +" In polarimetric analyses, the accuracies that are achievable are determined by the signal-to-noise ratio (S/N) of the data."," In polarimetric analyses, the accuracies that are achievable are determined by the signal-to-noise ratio (S/N) of the data." +" Therefore, in order to estimate the effects of background noise, the twelve NIC2 images in each polarizer were combined, after precise astrometric registration, into a single median image."," Therefore, in order to estimate the effects of background noise, the twelve NIC2 images in each polarizer were combined, after precise astrometric registration, into a single median image." +" In all cases, images were first aligned using the spacecraft pointing information provided in the headers of the raw files."," In all cases, images were first aligned using the spacecraft pointing information provided in the headers of the raw files." + This co-registered the images with a relative precision of a few tenths of a pixel., This co-registered the images with a relative precision of a few tenths of a pixel. +" Subsequent ""fine"" alignments of the inter-visit images were performed using an apodized bi-cubic re-sampling of the stellar PSF cores onto a 32x (in both x and y) larger grid.", Subsequent “fine” alignments of the inter-visit images were performed using an apodized bi-cubic re-sampling of the stellar PSF cores onto a $\times$ (in both x and y) larger grid. + The re-sampled individual images were then shifted to a common fiducial position by the difference in centroids found iteratively with least-squares 2D Gaussian profile fitting., The re-sampled individual images were then shifted to a common fiducial position by the difference in centroids found iteratively with least-squares 2D Gaussian profile fitting. + This process was repeated three times and converged all re-registered image centroids to a few thousandths of a pixel., This process was repeated three times and converged all re-registered image centroids to a few thousandths of a pixel. + The pixel-to-pixel noise in the combined polarimetric total intensity images (Stokes J) was found by measuring (in each image) the standard deviation in the “background” region., The pixel-to-pixel noise in the combined polarimetric total intensity images (Stokes $I$ ) was found by measuring (in each image) the standard deviation in the “background” region. +" The region was close enough to the target that all 12 backgrounds from the individual images contributed to the combined image, but sufficiently far out sono flux from the target itself contributed to the background."," The region was close enough to the target that all 12 backgrounds from the individual images contributed to the combined image, but sufficiently far out sono flux from the target itself contributed to the background." +" A 151x pixel sub-array region, centered on the target was used."," A $151\times151$ pixel sub-array region, centered on the target was used." + Flux from the diffraction spikes was masked., Flux from the diffraction spikes was masked. +" To find the region beyond which the target did not contribute to the background, square masks, increasing in size iteratively, were placed in the photometric aperture."," To find the region beyond which the target did not contribute to the background, square masks, increasing in size iteratively, were placed in the photometric aperture." +" As the mask was incremented (in 2 pixel lengths and widths) from 90 to 100 pixels, earlier mask standard deviations ceased to decrease, and (smallerboth the size)median and mean were consistent with zero."," As the mask was incremented (in 2 pixel lengths and widths) from 90 to 100 pixels, earlier (smaller mask size) standard deviations ceased to decrease, and both the median and mean were consistent with zero." +" Therefore, a square mask of 100x pixels, plus a diffraction spike mask, were used and noise statistics were computed on 10660 pixels."," Therefore, a square mask of $100\times100$ pixels, plus a diffraction spike mask, were used and noise statistics were computed on 10660 pixels." +" In all cases, the peak pixels (with instrument intensities of several thousand counts per second) typically have a lo noise of 0.1 to 0.2 counts per second; the per pixel data is photon noise dominated."," In all cases, the peak pixels (with instrument intensities of several thousand counts per second) typically have a $1\sigma$ noise of 0.1 to 0.2 counts per second; the per pixel data is photon noise dominated." +" As shown by ?,hereafter $A99), the S/N ratio averaged across the three polarizers ((S/N),) times the required polarization degree (p) determines the accuracy to which polarimetry can be performed (oy) in the photon noise dominated regime."," As shown by \citet[][hereafter SA99]{1999PASP..111.1298S}, , the S/N ratio averaged across the three polarizers $\langle{\rm S/N}\rangle_k$ ) times the required polarization degree $p$ ) determines the accuracy to which polarimetry can be performed $\sigma_p$ ) in the photon noise dominated regime." +" Equation 1,, taken from SA99 (theirsection 7.4), demonstrates the relationship"," Equation \ref{equ:sanda}, , taken from SA99 (theirsection 7.4), demonstrates the relationship" +"remains below the critical value. interactions between oligarchs are less chaotic even when M,2M.","remains below the critical value, interactions between oligarchs are less chaotic even when $\Sigma_l \gtrsim \Sigma_s$." + Interactions among 2 or 3 oligarchis produce a small merger rate which eventually vields a svstem with lower mass planets compared to more massive disks., Interactions among 2 or 3 oligarchs produce a small merger rate which eventually yields a system with lower mass planets compared to more massive disks. + Although chvnamical interactions among the ensemble of oligarchs produce terrestrial mass planets in all disks. more massive disks vield more massive planets.," Although dynamical interactions among the ensemble of oligarchs produce terrestrial mass planets in all disks, more massive disks yield more massive planets." +" Our results sugeest a maximum. MASS. Hyg,~ li2m. [forB My4~ δ16⋅↽ g 97 and m,,,,~ 0.10.2i m. lor. Ma~ 12 e@ 7."," Our results suggest a maximum mass, $m_{max} \sim$ 1–2 $m_{\oplus}$ for $\Sigma_0 \sim$ 8–16 g $^{-2}$ and $m_{max} \sim$ 0.1–0.2 $m_{\oplus}$ for $\Sigma_0 \sim$ 1–2 g $^{-2}$." + Because voung stars appear {ο have a wide range of initial disk masses. we expect a wide range in (he masses of terrestrial planets in exosolar svstems.," Because young stars appear to have a wide range of initial disk masses, we expect a wide range in the masses of terrestrial planets in exosolar systems." + In. future studies. we plan to address (his issue in more detail.," In future studies, we plan to address this issue in more detail." + In terresirial planet formation. the Gransitions between different stages of growth produce distinct waves through the disk.," In terrestrial planet formation, the transitions between different stages of growth produce distinct waves through the disk." + During the transition from orcerly growth to runaway erowth. the increase in (he collision rate rapidly propagates from the inner edge of the disk to the outer edge.," During the transition from orderly growth to runaway growth, the increase in the collision rate rapidly propagates from the inner edge of the disk to the outer edge." + This transition is rapid and takes <10? vr to move from 0.4 AU to 2 AU., This transition is rapid and takes $\lesssim 10^5$ yr to move from 0.4 AU to 2 AU. + Although less rapid. the transitions from runaway (ο oligarchie growth aud from oligarehic to chaotic growth also propagate from the inner disk to the outer disk.," Although less rapid, the transitions from runaway to oligarchic growth and from oligarchic to chaotic growth also propagate from the inner disk to the outer disk." + During the transition to chaotic growth. dvnanmical interactions tend to produce more chaotic orbils at the outer edee of the disk.," During the transition to chaotic growth, dynamical interactions tend to produce more chaotic orbits at the outer edge of the disk." + This behavior depends on (he surface density. eraclient., This behavior depends on the surface density gradient. +" In disks will steep densitv gradients. X~Nya"" with nZ 3/2. chaotic interactions propagate slowly outward."," In disks with steep density gradients, $\Sigma \sim \Sigma_0 a^{-n}$ with $n \gtrsim$ 3/2, chaotic interactions propagate slowly outward." + In disks with shallower density gradients. »< 1. dynamical interactions tend to concentrate more mass in the outer part of the disk.," In disks with shallower density gradients, $n \lesssim$ 1, dynamical interactions tend to concentrate more mass in the outer part of the disk." +" This difference in behavior is set bv the growtli rate. ~P/Nca""7, where P is the orbital period: the wave of growth propagates more rapidly through disks with shallower densitv. gradients (e.g.Lissaner LOST)."," This difference in behavior is set by the growth rate, $\sim P/\Sigma \sim a^{n+3/2}$, where $P$ is the orbital period: the wave of growth propagates more rapidly through disks with shallower density gradients \citep[e.g.][]{lis87}. ." + These results have several interesting consequences for the evolution of planets in the terrestrial zone (seealsoIXominami&Ida2002)., These results have several interesting consequences for the evolution of planets in the terrestrial zone \citep[see also][]{kom02}. +. The (transition rom oligarchie to chaotic erowth occurs on timescales. a lew Myr. well before radiometric evidence suggests the formation of the Earth was [αν complete (e.g..Yinetal.2002).," The transition from oligarchic to chaotic growth occurs on timescales, $\sim$ a few Myr, well before radiometric evidence suggests the formation of the Earth was fairly complete \citep[e.g.,][]{yin02}." +. Planets are also fully formecl well before the estimated. time of the Late Heavy. Bombardment. ~ 100300 Myr alter (he formation of (he Sun (e.g..Tera.Papanastassiou.&Wasserbure19174:Hartinann1980:Ryder2002:Noeberl2003) Throughout the chaotic growth phase. our ealeulations produce many Dunar- to objects on highly eccentric orbits.," Planets are also fully formed well before the estimated time of the Late Heavy Bombardment, $\sim$ 100–300 Myr after the formation of the Sun \citep[e.g.,][]{ter74, +har80, ryd02, koe03} + Throughout the chaotic growth phase, our calculations produce many lunar- to Mars-sized objects on highly eccentric orbits." + These objects are good candidates for the giant impactor that collided with the Earth to produce the Moon (Παπά&Davis1975:Cameron&Ward1976:Benz.Slattery.1936;Canup. 2004a.b).," These objects are good candidates for the `giant impactor' that collided with the Earth to produce the Moon \citep{har75b,cam76,ben86,can04a,can04b}." +. As we complete calculations with fragmentation and migration. predicted mass and eccentricityv distributions for these objects will vield betterestimates for the probability of these events.," As we complete calculations with fragmentation and migration, predicted mass and eccentricity distributions for these objects will yield betterestimates for the probability of these events." +We note that since the CFL phase traisition occi* onlv once in a given star. there is only one giant burst in our model.,"We note that since the CFL phase transition occurs only once in a given star, there is only one giant burst in our model." + However. if we asse solie form of heatiig. then it is possible tliat he quark star can revert to a nou-CFL stae wherein superconcductiviy is lost. aud the interior unaguetic fiekl les are uo longer constrailec to the vorices.," However, if we assume some form of heating, then it is possible that the quark star can revert to a non-CFL state wherein superconductivity is lost, and the interior magnetic field lines are no longer constrained to the vortices." + Then presuuably the cdsuaimies tliat initially caused the magnetic dipole axis ο ημαigh wi1 tlie rotation axis. we speculate. sliould Once agaln ensue to some exten.," Then presumably the dynamics that initially caused the magnetic dipole axis to misalign with the rotation axis, we speculate, should once again ensue to some extent." + Thus we alow or the »ossibility of stbsequeit misalieniueut of he magnetic axis that. upou furher coolit& back |)elow te decoUinement eimperature. cau trigeerMD he sale yrocess as before to [n]oOive subsequert bu‘sts.," Thus we allow for the possibility of subsequent misalignment of the magnetic axis that, upon further cooling back below the deconfinement temperature, can trigger the same process as before to give subsequent bursts." + οe melt expect these bursts streuet15 d[9] depeud on the amount of heatingD> and resuling inisalieutrent., One might expect these bursts strengths to depend on the amount of heating and resulting misalignment. + Possible sources of subsequent lieTenD>oO Cal include accretion [rom a cΟΠΙΡαΙΟ. impact roni the accretion of a small bdy. or the clark stafo passiig through a higher density region iu the IS.," Possible sources of subsequent heating can include accretion from a companion, impact from the accretion of a small body, or the quark star passing through a higher density region in the ISM." + This eads to the precdictiou that 'acli enision should pick up again sightly before the subsecueut bursts. proviecd tlere is a favou‘al line-of-sigit.," This leads to the prediction that radio emission should pick up again slightly before the subsequent bursts, provided there is a favourable line-of-sight." + The accirate measurement of the temperature in tje star in these sibsequent bLs WOld now allow obse‘vations of the decoulinement temyerature. which has elucec QCD physiClsl: nO ar.," The accurate measurement of the temperature in the star in these subsequent bursts would now allow observations of the deconfinement temperature, which has eluded QCD physicists so far." + The qtuescent plase is due to vortex expulsion from spiu-down auc subseqient. annihilation through magnetic recyunection near the surface., The quiescent phase is due to vortex expulsion from spin-down and subsequent annihilation through magnetic reconnection near the surface. + The muuber of vortices decrease slowly with leadiug to contilous. quiescent energy release which can last for 10% to 10! vears (see Ouved et al.," The number of vortices decrease slowly with spin-down leading to continuous, quiescent energy release which can last for $10^3$ to $10^4$ years (see Ouyed et al." + 2001 for more details)., 2004 for more details). + Iu the light of the results preseuted above we will now discuss our model predictions and olTer our interoretation of the open issues listed iu L, In the light of the results presented above we will now discuss our model predictions and offer our interpretation of the open issues listed in \ref{sec:open_issues}: : + Iu the light of the results preseuted above we will now discuss our model predictions and olTer our interoretation of the open issues listed iu Ll, In the light of the results presented above we will now discuss our model predictions and offer our interpretation of the open issues listed in \ref{sec:open_issues}: : +showing the explicit relation between our expression and the more common form of equation (13) from (L991).,showing the explicit relation between our expression and the more common form of equation (13) from \citet{bras91}. +" Tu extremely degenerate matter, cPy=duP/dlup|s aud if not careful the important term is missed."," In extremely degenerate matter, $\,\chi_\rho \approx \Gamma_1 = d \ln P / d \ln \rho \arrowvert_{S}$ and if not careful the important term is missed." +" We thus rewrite the expression for the adiabaticx, exponent in terms of x, plus a iiall correction teri After an expansion in the sinall quantities aud prestumine ο].=0. we fud Now for electron degenerate matter and ideal ious Also. as we take the ious to be ideal we have Iu degenerate y,—xg, Is between 1/2 aud 5/3 depeudiug ou the relativity parameter."," We thus rewrite the expression for the adiabatic exponent in terms of $\chi_\rho$ plus a small correction term After an expansion in the small quantities and presuming $d T/dz=0$, we find Now for electron degenerate matter and ideal ions Also, as we take the ions to be ideal we have In degenerate $\chi_\rho = -\chi_{\mu_e}$ is between 4/3 and 5/3 depending on the relativity parameter." + Finally where the last step is valid oulv if is a trace., Finally where the last step is valid only if is a trace. + With this expression we have so that. for relativistic matter.," With this expression we have so that, for relativistic matter," +to theXMM data. we obtained the calibration files indicated as necessary for this observation by the on-line software toolcifbuild.,"to the data, we obtained the calibration files indicated as necessary for this observation by the on-line software tool." + We used the Science Analysis Software (SAS- package to reprocess the pn. MOSI. and MOS2 data using andemproc. yielding photon event lists for the three instruments.," We used the Science Analysis Software (SAS-10.0.0) package to reprocess the pn, MOS1, and MOS2 data using and, yielding photon event lists for the three instruments." + Although proton flares sometimes cause portions of observations to have very high backgrounds. we did not find evidence for proton flares. and we were able to use the full exposure time.," Although proton flares sometimes cause portions of observations to have very high backgrounds, we did not find evidence for proton flares, and we were able to use the full exposure time." + We used the SAS tool to produceXMM energy spectra for IGR J16167-4957., We used the SAS tool to produce energy spectra for IGR J16167–4957. + We used standard event filtering and included photons within an aperture with a 30” radius., We used standard event filtering and included photons within an aperture with a $30^{\prime\prime}$ radius. + We took background spectra from the nearest source-free region of the CCD., We took background spectra from the nearest source-free region of the CCD. + For the MOS detectors. we used the 0.1-10 keV bandpass. and for the pn detector. we used the 0.2-12 keV bandpass.," For the MOS detectors, we used the 0.1–10 keV bandpass, and for the pn detector, we used the 0.2–12 keV bandpass." +" The observing log can be found in Table 1.. and the targets are now presented in order of R.A. This is classified as an ‘ironclad’ IP (according to the IP catalogue version 2009a) with both an established spin and orbital period. in the optical (P,=5063.5 s and Pos=0014520 8 respectively (2)))."," The observing log can be found in Table \ref{observing_log}, and the targets are now presented in order of R.A. This is classified as an `ironclad' IP (according to the IP catalogue version 2009a) with both an established spin and orbital period in the optical $P_{spin}=563.5$ s and $P_{orb}=14\,520$ s respectively \citep{bonnetbidaud07}) )." + Further to this ? report observations which clearly show spin modulated variability below 2 keV. but not above it.," Further to this \citet{anzolin09} report observations which clearly show spin modulated X-ray variability below 2 keV, but not above it." + No hard X-ray detections of the white dwarf spin period have been reported., No hard X-ray detections of the white dwarf spin period have been reported. + report spectra over a similar energy range.," \citet{tomsick08} + report spectra over a similar energy range." + 10025 was observed over two consecutive days with a total of 7776 s good time in PCU2 (see Table 1))., J0023 was observed over two consecutive days with a total of 776 s good time in PCU2 (see Table \ref{observing_log}) ). + The 2-10 keV energy band raw count rate varied between 2.0-6.1 ct s! and the background count rate was 2.9-4.0 ct s!. The mean background subtracted count rate in the 2-10 keV band was 0.7 et s!., The 2–10 keV energy band raw count rate varied between 2.0–6.1 ct $^{-1}$ and the background count rate was 2.9–4.0 ct $^{-1}$ The mean background subtracted count rate in the 2–10 keV band was 0.7 ct $^{-1}$. + The cleaned power spectrum of the 2-10 keV light curve (Fig. 1)), The ed power spectrum of the 2–10 keV light curve (Fig. \ref{J0023_cleaned}) ) + has a peak at 153 cyeles day! (where the 563.5 s spin period would be expected to be seen). however. this is in a forest of peaks. each with à similar power to the “noise” seen elsewhere.," has a peak at 153 cycles $^{-1}$ (where the 563.5 s spin period would be expected to be seen), however, this is in a forest of peaks, each with a similar power to the `noise' seen elsewhere." + The peak at ~10 cycles day”! is too close to the length of some of the data sets to be considered legitimate here., The peak at $\sim$ 10 cycles $^{-1}$ is too close to the length of some of the data sets to be considered legitimate here. + The 2-10 keV light curve folded at the previously identified spin. period is shown in Fig., The 2–10 keV light curve folded at the previously identified spin period is shown in Fig. + 2. where a single peaked modulation is seen., \ref{J0023_2_10_folded} where a single peaked modulation is seen. + Folding the light curve in different energy bands gives a trend of increasing modulation depth with increasing energy (summarised in Table 2))., Folding the light curve in different energy bands gives a trend of increasing modulation depth with increasing energy (summarised in Table \ref{J0023_modulation_depth}) ). + Folding the data at the 145520 s orbital period gives an indication of a double peaked modulation. however this is by no means conclusive.," Folding the data at the 520 s orbital period gives an indication of a double peaked modulation, however this is by no means conclusive." + The parameters of the spectral models used to fit the 10023 X-ray spectrum are shown in Table 3.., The parameters of the spectral models used to fit the J0023 X-ray spectrum are shown in Table \ref{spectral_fits}. + In both cases the column density had to be pegged to a lower limit., In both cases the column density had to be pegged to a lower limit. +An iron emission line is clearly present and the spectrum is hard. as shown in Fig. 3..,"An iron emission line is clearly present and the spectrum is hard, as shown in Fig. \ref{J0023_spectrum}. ." +velow about 10! 7. Field,below about $10^4$ $^{-3}$. +&Partridge(1961) μηου considered the case in which Lyman-a 'adiation is effectively destroyed by collisional conversion of 2p states to 2s (followed by 2-photon decay to the ground state)., \citet{fie61} further considered the case in which $\alpha$ radiation is effectively destroyed by collisional conversion of $2p$ states to $2s$ (followed by 2-photon decay to the ground state). + The cousequeut overpopulation of 2p states then led to tlie precdictiou hat the 9.9 GHz lines would appear iu stimulated emission in HII regious. (, The consequent overpopulation of $2p$ states then led to the prediction that the 9.9 GHz lines would appear in stimulated emission in HII regions. ( +This also inuplied that he 1.1 GHz lines would appear in absorption.),This also implied that the 1.1 GHz lines would appear in absorption.) + Myers&Barrett(1972) used the Haystack 37-2 'adiotelescope with a 16-chaunuel filter bauk spauuiug 1 GHz iu frequency to search for the 9.9 GHz ines. but cid not find auy lines in excess of 0.1 Ix autenua temperature.," \citet{mye72} used the Haystack 37-m radiotelescope with a 16-channel filter bank spanning 1 GHz in frequency to search for the 9.9 GHz lines, but did not find any lines in excess of 0.1 K antenna temperature." + Ershov(1987). estimated he streneths of both sets of lines in Orion A aud W3(OH) uuder the assumption that the 2p states are ueeglieibly populated with respect to 2519., \citet{ers87} estimated the strengths of both sets of lines in Orion A and W3(OH) under the assumption that the $2p$ states are negligibly populated with respect to $2s_{1/2}$. + The major variation in the predietions arises from tlie uncertain density of Lyiuau-a radiation in HII regions. which in turu is deteriniued by the processes that destroy Lyiman-a radiatiou.," The major variation in the predictions arises from the uncertain density of $\alpha$ radiation in HII regions, which in turn is determined by the processes that destroy $\alpha$ radiation." + Lu addition to the couversion of 2p to 2s states via collisions. other processes are likely to be important.," In addition to the conversion of $2p$ to $2s$ states via collisions, other processes are likely to be important." + Resonautly scattered Lyiman-a photons uudergo a diffusion in frequency aud μιαν thus acquire a significant probability of escaping the HII region cue the much lower optical depth iu the line wines (Cox&Matthews1960:Spitzer1078).," Resonantly scattered $\alpha$ photons undergo a diffusion in frequency and may thus acquire a significant probability of escaping the HII region due the much lower optical depth in the line wings \citep{cox69,spi78}." +. Systematic gas motions within the region (e.g. expausion) can also contribute to the migration of Lymau-a photous away from line center., Systematic gas motions within the region (e.g. expansion) can also contribute to the migration of $\alpha$ photons away from line center. + The cdomiuaut removal mechanism. however. is absorption by dust within the HII region 1978)..," The dominant removal mechanism, however, is absorption by dust within the HII region \citep{kap70,spi78}. ." + This last fact greatly simplilies tle estimation of the Lyuiu-a deusity., This last fact greatly simplifies the estimation of the $\alpha$ density. + In this paper. we obtain formulae lor the 2s and 2p populatious[un in au ΠΠ region under a yarameterization that characterizes the rate of 2p production by Lymanu-a absorption in terms of the rate of 2p production through recombination (Section 2).," In this paper, we obtain formulae for the $2s$ and $2p$ populations in an HII region under a parameterization that characterizes the rate of $2p$ production by $\alpha$ absorption in terms of the rate of $2p$ production through recombination (Section 2)." + Existing iuodels for dust in HII 'eelons aud planetary nebulae are then used to place tight coustraints ou the Lyimanu-a deusity auc thus the 2p production rate by Lyman-a pliotous (Sectiou 3)., Existing models for dust in HII regions and planetary nebulae are then used to place tight constraints on the $\alpha$ density and thus the $2p$ production rate by $\alpha$ photons (Section 3). + The radiative trausler problem or the fiue structure lines is tlien solved for a uniform region (Section 1)., The radiative transfer problem for the fine structure lines is then solved for a uniform region (Section 4). + We obtain approximate oedicted line streuetls for various HIE regions. compact components. aud planetary uebulae uider he justified assumption that Lymau-a pumping of the 2p states is uegligible (Section 5).," We obtain approximate predicted line strengths for various HII regions, compact components, and planetary nebulae under the justified assumption that $\alpha$ pumping of the $2p$ states is negligible (Section 5)." + High emission measure HII regions and/or planetary nebulae are most likely to yield detectable lines., High emission measure HII regions and/or planetary nebulae are most likely to yield detectable lines. + Spitzer&Cireeustein(1951) estimated that between 0.30 and 0.35 of all recombiuations ln au HII region reach the 2s state., \citet{spi51} estimated that between 0.30 and 0.35 of all recombinations in an HII region reach the $2s$ state. + Includiug the effects of collisious aud the 2-photon decay rate. the rate equation for the 2s stateis where f is the fraction of recombinatious producing the 2s state aid à is the recombination coellicient.," Including the effects of collisions and the 2-photon decay rate, the rate equation for the $2s$ stateis where $f$ is the fraction of recombinations producing the $2s$ state and $\alpha$ is the recombination coefficient." +" The collision coellicieuts. C,Pp and C' speeive the appropriate rates at which atoms are trauslerrecd [rom 2p to 2s aud [rom 2s to 2p. respectively."," The collision coefficients, $C_{ps}$ and $C_{sp}$ ,give the appropriate rates at which atoms are transferred from $2p$ to $2s$ and from $2s$ to $2p$ , respectively." + These rates are clominated by collisions, These rates are dominated by collisions +"the clements ofD are referred to as ""Catenokls aud “Displacements.”",the elements of${\bf D}$ are referred to as “Catenoids” and “Displacements.” +" DGRT describe an inversion whereby one can estimate the individual components. and thus measure two ""Hexious: where @ is the complex derivative operator: Figure 77 is reproduced frou BORT aud shows the effect of a first or second flexion on a circular source."," BGRT describe an inversion whereby one can estimate the individual components, and thus measure two “flexions”: where $\partial$ is the complex derivative operator: Figure \ref{fg:shapes} is reproduced from BGRT and shows the effect of a first or second flexion on a circular source." + An object with first flexion. JF. appears skewed. while an object with second flexion. 6. appears arced. especially if the imaee has an induced shear as well.," An object with first flexion, ${\cal F}$, appears skewed, while an object with second flexion, ${\cal G}$, appears arced, especially if the image has an induced shear as well." + The first flexion has an 0=I rotational svuuuetrv. aud thus behaves like a vector.," The first flexion has an $m=1$ rotational symmetry, and thus behaves like a vector." + In particular. it is a direct tracer of the eradieut of the convergeuce: where Fy is the real component aud νο is the imaginary wart (as with the second flexion aud. as the standard convention. with shear).," In particular, it is a direct tracer of the gradient of the convergence: where ${\cal F}_1$ is the real component and ${\cal F}_2$ is the imaginary part (as with the second flexion and, as the standard convention, with shear)." + The secoud flexion has au i=3 rotational svuuuetry. hough unlike the first Hexionu. it has no simple plysical interpretation like that of the first flexion.," The second flexion has an $m=3$ rotational symmetry, though unlike the first flexion, it has no simple physical interpretation like that of the first flexion." + It is. however. roughly proportional to the local derivative of the nagnitude of the shear.," It is, however, roughly proportional to the local derivative of the magnitude of the shear." + A more complete discussion of Hexion formatlisin can be found in DGRT., A more complete discussion of flexion formalism can be found in BGRT. + Measurement of flexion ultimately requires very accurate knowledge of the distribution of helt in an iniagc., Measurement of flexion ultimately requires very accurate knowledge of the distribution of light in an image. + The shapelets (Refreeier 2003: Refregier Bacou 2003) method of image reconstruction deconiposes ani imnaee ito 2D Termite polvnomial bases: This technique has a πα of very natural advantages., The shapelets (Refregier 2003; Refregier Bacon 2003) method of image reconstruction decomposes an image into 2D Hermite polynomial bases: This technique has a number of very natural advantages. + Iu the abseuce of a PSF. all shapelet coefficients. will have equal noise.," In the absence of a PSF, all shapelet coefficients will have equal noise." + Moreover. the basis set is quite localized (Πίο polvuomials have a Gaussian smoothing filter). and thus is ideal for modeling galaxies.," Moreover, the basis set is quite localized (Hermite polynomials have a Gaussian smoothing filter), and thus is ideal for modeling galaxies." +" Furthermore. the generating “step-up and “step-down” operators for the Termite polvnonuals are simply combinations of the οτε, and ; operators."," Furthermore, the generating “step-up” and “step-down” operators for the Hermite polynomials are simply combinations of the $x_i$, and $\partial_i$ operators." +" Refregicr (2003) shows that if we decompose a source Πμασο, f. iuto shapelet cocfiicicuts. the transformation to a lensed image iav be expressed quite simply as: where the various lensing operators are: a! and « are the normal step-yp and step-down operators. and the subscript refers to the directional component of the cocticicut ιο, 1 for the first or x-component. aud 2 for the second. or v-component)."," Refregier (2003) shows that if we decompose a source image, $f$, into shapelet coefficients, the transformation to a lensed image may be expressed quite simply as: where the various lensing operators are: $\hat{a}^{\dagger}$ and $\hat{a}$ are the normal step-up and step-down operators, and the subscript refers to the directional component of the coefficient (i.e. 1 for the first or x-component, and 2 for the second, or y-component)." + Note that iu the weak feld lit. these operators indicate that power will be trausferred between coefficieuts with indices [An]|=2. which preserves syinmetry as well as keeping the nuage representation in shapelet space compact.," Note that in the weak field limit, these operators indicate that power will be transferred between coefficients with indices $|\Delta n|+|\Delta m|=2$, which preserves symmetry as well as keeping the image representation in shapelet space compact." + Tn Goldberg Bacon (2005). similar (albeit more complicated) transforms were found relating the derivatives of shear.," In Goldberg Bacon (2005), similar (albeit more complicated) transforms were found relating the derivatives of shear." + We will not reproduce the full ecoud order operators here. as they are written in full in the earlier work. but we will poiut out some kev features.," We will not reproduce the full second order operators here, as they are written in full in the earlier work, but we will point out some key features." + First. some of the clemenuts in the operators lave au explicit dependence ou the (Guileused) quadrupole moments of the ight distribution.," First, some of the elements in the operators have an explicit dependence on the (unlensed) quadrupole moments of the light distribution." + This is duc to a relatively subtle effect rot present in shear analysis., This is due to a relatively subtle effect not present in shear analysis. + Since the flexion signal is asvuuuetrc. the ceuter of brightness iu the muage plaue will ono longer necessarily correspond to the center of xiehtuess iu the source plane. aud since the shapelet decomposition is performed around the ceuter of light. we weed to correct for this.," Since the flexion signal is asymmetric, the center of brightness in the image plane will no longer necessarily correspond to the center of brightness in the source plane, and since the shapelet decomposition is performed around the center of light, we need to correct for this." + Most important. though. is the fact that second. order chsing terms vield trausfer of power between indices witli An|||Am|= 1 or 3.," Most important, though, is the fact that second order lensing terms yield transfer of power between indices with $|\Delta n|+|\Delta m|=$ 1 or 3." +" To second order. then. a lensed nuage can be expressed as: Flexion analysis assunies (as does shear analvsis) that the iutriusic flexion is random. and thus all ""odd"" (defined as niii) moments are expected to be zero."," To second order, then, a lensed image can be expressed as: Flexion analysis assumes (as does shear analysis) that the intrinsic flexion is random, and thus all “odd” (defined as n+m) moments are expected to be zero." +" Thus. frou a set of shapelet cocficicuts. a best estimate for the flexion signal may be found via (7 mininization. whore: Vignama IS the covariance matrix of the shapelet coefficients and ρω is the ""uuleused estimate of a shapelet cocticient."," Thus, from a set of shapelet coefficients, a best estimate for the flexion signal may be found via $\chi^2$ minimization, where: $V_{n_1m_1 n_2m_2}$ is the covariance matrix of the shapelet coefficients, and $\mu_{nm}$ is the “unlensed” estimate of a shapelet coefficient." + For odd modes. this is zero.," For odd modes, this is zero." +" For eveu modes. the relative effect of shear is typically wich smaller than the iutrinsic ellipticity of an image, thus it males seuse to set yan= fu."," For even modes, the relative effect of shear is typically much smaller than the intrinsic ellipticity of an image, thus it makes sense to set $\mu_{nm}=f_{nm}$ ." +" ""Though the form looks quite complicated. conceptually. computiue the flexion is very straightforward."," Though the form looks quite complicated, conceptually, computing the flexion is very straightforward." + A simplified pipeline may be written as follows:, A simplified pipeline may be written as follows: +"The masses of the neutron star and secondary star can be computed from the optical mass function. the mass ratio. and the inclination (CCIx98): Using our lo limits on the inclination (7=62.5° 44°) we find AM,=L7S40.23Af. and Al,=O.GO40.13M...","The masses of the neutron star and secondary star can be computed from the optical mass function, the mass ratio, and the inclination (CCK98): Using our $1\sigma$ limits on the inclination $i=62.5^{\circ}\pm 4^{\circ}$ ) we find $M_x=1.78\pm 0.23\,M_{\odot}$ and $M_c=0.60\pm 0.13\,M_{\odot}$." +" The extreme range of allowed inclinations (49°<7< ) implies an extreme mass range allowed for the neutron star ol L420.10AZ...—M,x2.58EO21M.."," The extreme range of allowed inclinations $49^{\circ}\le i\le 73^{\circ}$ ) implies an extreme mass range allowed for the neutron star of $1.42\pm 0.10\,M_{\odot} +\le M_x\le 2.88\pm 0.21\,M_{\odot}$." +" Since the values of the optical mass function ancl the mass ratio were fairly well determined by €CCIN98. the largest uncertainty on AZ, is the value of the inclination 7 one 'hooses."," Since the values of the optical mass function and the mass ratio were fairly well determined by CCK98, the largest uncertainty on $M_x$ is the value of the inclination $i$ one chooses." + Thus it is instructive to see how the mass of the =ieutron star varies as a function of the inclination., Thus it is instructive to see how the mass of the neutron star varies as a function of the inclination. + We plot in Figure S. the mass of the neutron star as a function of 10 inclination., We plot in Figure \ref{massplot} the mass of the neutron star as a function of the inclination. + We also indicate the lo errors at. several llferent inclinations., We also indicate the $1\sigma$ errors at several different inclinations. +" The mass of the neutron star in Cvg X-2 is consistent at the lo level with the canonical neutron gaar mass of 1.35. (CPhorsett Chakrabarty 1998). for inclinations greater than TO"".", The mass of the neutron star in Cyg X-2 is consistent at the $1\sigma$ level with the canonical neutron star mass of $1.35_{\odot}$ (Thorsett Chakrabarty 1998) for inclinations greater than $70^{\circ}$. + Llowever. the fits to the light curves ect increasingly worse as the inclination grows larger jun z68 tthe sharp increase in x7 displaved in Figure 5)). so it is unlikeA iat the inclination of €vg X-2 is much larger than z687.," However, the fits to the light curves get increasingly worse as the inclination grows larger than $\approx 68^{\circ}$ the sharp increase in $\chi^2$ displayed in Figure \ref{crosscut}) ), so it is unlikely that the inclination of Cyg X-2 is much larger than $\approx +68^{\circ}$." +" At the lower value of the lo inclination range for our model with the unirradiateddisc (7= 58.5). the neutron star mass is M,=2.0040.15AZ. . which is more than 4e larger than the canonical mass of 1.35M..."," At the lower value of the $1\sigma$ inclination range for our model with the unirradiateddisc $i=58.5^{\circ}$ ), the neutron star mass is $M_x=2.00\pm 0.15\,M_{\odot}$ which is more than $4\sigma$ larger than the canonical mass of $1.35\,M_{\odot}$." + For most ofthe parameter space in ;. f(M). and q. the mass of the neutron star in Cvg X-2 exceeds the average mass of the neutron stars in binary radio pulsars.," For most of the parameter space in $i$, $f(M)$, and $q$, the mass of the neutron star in Cyg X-2 exceeds the average mass of the neutron stars in binary radio pulsars." + Thus Cve N-2 contains a rare example of a “massive” neutron star., Thus Cyg X-2 contains a rare example of a “massive” neutron star. + Perhaps the best-known example of a massive neutron star is the hieh-mass X-ray binary Vela X-1 (4U. 0900-40)., Perhaps the best-known example of a massive neutron star is the high-mass X-ray binary Vela X-1 (4U 0900-40). + Vela N-1 is an eclipsing system. and the neutron star is an X-ray pulsar.," Vela X-1 is an eclipsing system, and the neutron star is an X-ray pulsar." +" Dynamical mass measurements by van lxerkwijk et ((1995b) gave a mass of M,=1.9ο. confidence limits).", Dynamical mass measurements by van Kerkwijk et (1995b) gave a mass of $M_x=1.9^{+0.7}_{-0.5}$ confidence limits). +" A later analysis of LUE spectra by Stickland et (1997) eave a mass consistent with 1ΕΛ. (1.342M4.xAl,X153Af. )."," A later analysis of IUE spectra by Stickland et (1997) gave a mass consistent with $1.4\,M_{\odot}$ $1.34\,M_{\odot} +\la M_x\la 1.53\,M_{\odot}$ )." +" However. a recent. reanalysis of the UV data (Barziv et 11998. in preparation) gives Al,=LOAL.. consistent with the result of van Werkwijk et ((1995b)."," However, a recent reanalysis of the UV data (Barziv et 1998, in preparation) gives $M_x=1.9\,M_{\odot}$, consistent with the result of van Kerkwijk et (1995b)." +". Barziv ct ((1998. in preparation) also find A4,=L9.M. from optical spectra."," Barziv et (1998, in preparation) also find $M_x=1.9\,M_{\odot}$ from optical spectra." + Phe range of derived: masses by. clilferent groups is an indication of the cdillicultv in analvzing the radial velocity curves of a high-mass companion star such as the one in Vela N-1., The range of derived masses by different groups is an indication of the difficulty in analyzing the radial velocity curves of a high-mass companion star such as the one in Vela X-1. + Another example of a possible massive neutron star is the eclipsing high-mass X-rav binary 4U 1700-37., Another example of a possible massive neutron star is the eclipsing high-mass X-ray binary 4U 1700-37. + The companion star (MID. 153919) is an OGf star with a strong wind., The companion star (HD 153919) is an O6f star with a strong wind. +" Lleap Corcoran (1992) find M,=1840.442..."," Heap Corcoran (1992) find $M_x=1.8\pm 0.4\,M_{\odot}$." + However. 4U 1700-31 does not pulse and its N-ray spectrum is harder than the spectra of typical X-ray pulsars.," However, 4U 1700-37 does not pulse and its X-ray spectrum is harder than the spectra of typical X-ray pulsars." + This lack of “neutron star signatures” has led Brown. Weingartner. Wijers (1996) to speculate that 4U 1700-37 contains a “low-mass” black hole rather than a neutron star.," This lack of “neutron star signatures” has led Brown, Weingartner, Wijers (1996) to speculate that 4U 1700-37 contains a “low-mass” black hole rather than a neutron star." + ltecent computations of the neutron star and black hole initial mass function bx Timmes. Woosley. Weaver (1996) indicate that Type IE supernovae give rise to à. bimocal distribution. of initial neutron star masses.," Recent computations of the neutron star and black hole initial mass function by Timmes, Woosley, Weaver (1996) indicate that Type II supernovae give rise to a bimodal distribution of initial neutron star masses." + The average masses for the two peaks are 1.26+0.06AL. and 1.73+0.08AZ. . respectively.," The average masses for the two peaks are $1.26\pm 0.06 \,M_{\odot}$ and $1.73\pm 0.08\,M_{\odot}$ , respectively." + Type Ib supernovae tend to produce neutron stars in the lower mass range., Type Ib supernovae tend to produce neutron stars in the lower mass range. + Ehe masses derived bv Tinumnes et ((1996) clo not include mass that. may fall back onto the neutron star shortly alter the supernova explosion., The masses derived by Timmes et (1996) do not include mass that may fall back onto the neutron star shortly after the supernova explosion. + “Phe mean mass for the lower-niass distribution of 1.260.06AL. agrees well with the mean mass of the binary radio pulsars of 1.35d:0.04AZ. determined by Fhorsett Chakrabarty (1908).," The mean mass for the lower-mass distribution of $1.26\pm 0.06\,M_{\odot}$ agrees well with the mean mass of the binary radio pulsars of $1.35\pm 0.04\,M_{\odot}$ determined by Thorsett Chakrabarty (1998)." + Phe mass of the neutron star in (νο X-2 scems to be significantly larger than both of these masses., The mass of the neutron star in Cyg X-2 seems to be significantly larger than both of these masses. +" llowever. the neutron star mass of AZ,=I1.78d0.23M. &iven above agrees well with the mean mass of 1.733:0.08AJ. derived by Timmes et ((1996) for the higher-mass peak of their bimocdal distribution."," However, the neutron star mass of $M_x=1.78\pm 0.23 +\,M_{\odot}$ given above agrees well with the mean mass of $1.73\pm 0.08\,M_{\odot}$ derived by Timmes et (1996) for the higher-mass peak of their bimodal distribution." + Vhus the current mass of the neutron star in (νο X-2 mieht simply be the mass at its formation (within the framework of the models of λος et ((1996))., Thus the current mass of the neutron star in Cyg X-2 might simply be the mass at its formation (within the framework of the models of Timmes et (1996)). + Alternatively. Zhang. Strohmayer. Swank (1997) point out that one would. expect massive neutron stars to exist in systems where a neutron star formed. at =LAM. has been accreting at the Ecelington rate for extended. periods of time.," Alternatively, Zhang, Strohmayer, Swank (1997) point out that one would expect massive neutron stars to exist in systems where a neutron star formed at $\approx 1.4\,M_{\odot}$ has been accreting at the Eddington rate for extended periods of time." + HE the kilohertz QPOs observed in Cvg X-2 and other neutron star LMXDs can be interpreted as the frequeney of the last stable orbit of the inner accretion disc. then the neutron star masses in some X-ray. binaries could be as large as z2M..," If the kilohertz QPOs observed in Cyg X-2 and other neutron star LMXBs can be interpreted as the frequency of the last stable orbit of the inner accretion disc, then the neutron star masses in some X-ray binaries could be as large as $\approx 2\,M_{\odot}$." + Assuming the neutron stars were formed at xL4Al.. the =OGAL. of extra matter is not an unreasonable amount to accrete in zz107 vears (Zhang et 14997).," Assuming the neutron stars were formed at $\approx 1.4\,M_{\odot}$, the $\approx 0.6\,M_{\odot}$ of extra matter is not an unreasonable amount to accrete in $\approx 10^8$ years (Zhang et 1997)." + One would basically have to know how long (νο X-2 has been accreting at near Exdcdington rates in order to determine whether the neutron star formed at “low mass” (21.8 M.) or high mass” (21.7 M.).," One would basically have to know how long Cyg X-2 has been accreting at near Eddington rates in order to determine whether the neutron star formed at “low mass” $\approx 1.3\,M_{\odot}$ ) or “high mass” $\approx 1.7\,M_{\odot}$ )." + Ht remains to be seen i£ a reliable age estimate can be derived [rom a binary evolution mioclel of this system., It remains to be seen if a reliable age estimate can be derived from a binary evolution model of this system. + According to Wing et ((1997). à companion star mass ofat least zz0.75A. is needed to maintain steady accretion in à neutron star low-mass X-ray binary like (νο X-2.," According to King et (1997), a companion star mass of at least $\approx 0.75\,M_{\odot}$ is needed to maintain steady accretion in a neutron star low-mass X-ray binary like Cyg X-2." +" If AL,>05M... then Ad,>LSSM. at the confidence level CCCINO9S). which would require an inclination lower than about 607. near the lower end of the le inclination range."," If $M_c> +0.75\,M_{\odot}$, then $M_x> 1.88\,M_{\odot}$ at the confidence level (CCK98), which would require an inclination lower than about $60^{\circ}$, near the lower end of the $1\sigma$ inclination range." + We find AZ.=0.600.19AL. (1o) using 7=62.5°E 4. which is ©lo smaller than minimum AL. of Kine et (1997).," We find $M_c=0.60\pm 0.13\,M_{\odot}$ $1\sigma$ ) using $i=62.5^{\circ}\pm +4^{\circ}$ , which is $\approx 1\sigma$ smaller than minimum $M_c$ of King et (1997)." + Ehe. extreme range of allowed inclinations (49xPs 73°) implics an extreme mass range allowed for the secondary star of O48S+0.00Al.3.5$ Gpc is included, with the $L=\Lcrit, \Lmin$ and $\Lmax$ cases labelled as before." + It is clear from these pQs that departures from standard cosmology are too sinall to have a significant effect ou eiher LSS or BBN., It is clear from these plots that departures from standard cosmology are too small to have a significant effect on either LSS or BBN. +" For £«L4, the density of dark euergv relative to that iu staard cosmologv.", For $L<\Lcrit$ the density of dark energy relative to that in standard cosmology. +" For L2L4. even the largest possible iucrease in dark-energw deusitv (corresponding to the shortest-lived universe with L= L,4,) is far too modest relative to the matter density at ον=1 to interfere with structure formation. aud completely negligible relative to raciatiou-cucrey density at z=1000."," For $L>\Lcrit$, even the largest possible increase in dark-energy density (corresponding to the shortest-lived universe with $L=\Lmin$ ) is far too modest relative to the matter density at $z\gtrsim1$ to interfere with structure formation, and completely negligible relative to radiation-energy density at $z\gtrsim1000$." + Thus these tests do not place meaningful constraints ou the theory., Thus these tests do not place meaningful constraints on the theory. + Fig., Fig. + 2 (bottom) shows that the largest departures from standard theory are found near 2~1. raising the possibility that strouger constraints might be obtained by use of the SNIa maguitude-redshift relation.," 2 (bottom) shows that the largest departures from standard theory are found near $z\sim1$, raising the possibility that stronger constraints might be obtained by use of the SNIa magnitude-redshift relation." + Supernovac are now being routinely monitored at Dodb (Riess et al., Supernovae are now being routinely monitored at $z\sim1$ (Riess et al. + 2006). providing a scusitive testbed for alternative theories of eravitv with time-varving dark-cucrey density (see for example Fui 2006).," 2006), providing a sensitive testbed for alternative theories of gravity with time-varying dark-energy density (see for example Fukui 2006)." +iive [fewer particles. so we have chosen to [it to the cumulative profile instead.),"have fewer particles, so we have chosen to fit to the cumulative profile instead.)" + Our choice of an exponential ofile is motivated by Van de Weveaert Van [Ixampen 1993 who noted that an exponential profile provided a very &ood [it to their volds., Our choice of an exponential profile is motivated by Van de Weygaert Van Kampen 1993 who noted that an exponential profile provided a very good fit to their voids. + Figure 13. shows the density profiles. of voids. in he CLIE simulation with a range of values for the mean void overdensity., Figure \ref{SystematicDensityProfiles} shows the density profiles of voids in the GIF simulation with a range of values for the mean void overdensity. + As can be seen. varying the overdensity hreshold in the range chosen here does not systematically alter the density. profiles.," As can be seen, varying the overdensity threshold in the range chosen here does not systematically alter the density profiles." + Figure 14. shows density profiles of four GLP voids going out to a distance of 505. Ape from their centers., Figure \ref{LargeDensityProfilesGIF} shows density profiles of four GIF voids going out to a distance of $50h^{-1}$ Mpc from their centers. + The void edges are marked with a small vertical line., The void edges are marked with a small vertical line. + Although there are some variations in the profiles. all voids have very sharp edges.," Although there are some variations in the profiles, all voids have very sharp edges." + The densities peak at the ellective radius. and the enclosed clensities rise above the threshold.," The densities peak at the effective radius, and the enclosed densities rise above the threshold." + This is consistent with the visual impressions of voids discussed earlier. where one sees that voids are very well defined by the haloes which populate their boundaries.," This is consistent with the visual impressions of voids discussed earlier, where one sees that voids are very well defined by the haloes which populate their boundaries." + It also agrees qualitatively with the results in. Van cde Weveacrt Van Wkampen (1993)., It also agrees qualitatively with the results in Van de Weygaert Van Kampen (1993). + What is more. Benson et al (2003) and Llovle Voecley 2004 see similar behaviour for voids outlined by the galaxy distribution in a semi-analvtic galaxy formation model and in the 2dECGIS. respectively (see Figure 11: in Benson et al (2003) and Figure 4 in Hovle Vogcley 2004).," What is more, Benson et al (2003) and Hoyle Vogeley 2004 see similar behaviour for voids outlined by the galaxy distribution in a semi-analytic galaxy formation model and in the 2dFGRS, respectively (see Figure 11 in Benson et al (2003) and Figure 4 in Hoyle Vogeley 2004)." + Gottlóbber et al (2003) investigated the z=0 void halo mass function using a set of highresolution simulations of individual voids., Gottlöbber et al (2003) investigated the $z=0$ void halo mass function using a set of high–resolution simulations of individual voids. + They find that both the normalization and the shape of the cumulative mass function are cillerent from those of the nonvoid halo mass function., They find that both the normalization and the shape of the cumulative mass function are different from those of the non–void halo mass function. + Their nieasurements are in qualitative agreement with mocdoels for this dependence by Mo White (1996) ancl Sheth ‘Tormen (2002). although there are cilferences in detail.," Their measurements are in qualitative agreement with models for this dependence by Mo White (1996) and Sheth Tormen (2002), although there are differences in detail." + Also see Patiri ct al (2004) who used the simulations run by Gottlóbber et al (2003) to model mass functions in. voids., Also see Patiri et al (2004) who used the simulations run by Gottlöbber et al (2003) to model mass functions in voids. + For our study. of the mass function. we use the CIE2 simulation. which has the highest mass resolution.," For our study of the mass function, we use the GIF2 simulation, which has the highest mass resolution." + We identify haloes using a friendsof (fof) group finder with a linking length. of 0.2 times the mean interparticle separation. and require that haloes have at least 10 particles.," We identify haloes using a friends–of–friends (fof) group finder with a linking length of 0.2 times the mean interparticle separation, and require that haloes have at least 10 particles." + At.=0. we find void haloes by picking those halocs whose centresofmass lic within a We then mark those particles that are in a void at =( and run the fof group finder on them at earlier redshifts.," At $z=0$, we find void haloes by picking those haloes whose centres–of–mass lie within a We then mark those particles that are in a void at $z=0$ and run the fof group finder on them at earlier redshifts." + Vhis means that we clo not require that 2=0 void haloes be located inside a void at earlier times., This means that we do not require that $z=0$ void haloes be located inside a void at earlier times. + Our choice is dictated by the fact that the void volume fraction evolves rapidly (ef., Our choice is dictated by the fact that the void volume fraction evolves rapidly (c.f. + Section 3.2)): choosing only haloes that are inside voids at carly times would reduce he size of our high redshift halo samples significantly., Section \ref{VoidVolumeFunction}) ); choosing only haloes that are inside voids at early times would reduce the size of our high redshift halo samples significantly. + TFhus. what we are really showing is the mass function of the high-z »ojenitors of halos which are in voids at z=0.," Thus, what we are really showing is the mass function of the $z$ projenitors of halos which are in voids at $z=0$." + ligure 15. compares the mass function of all haloes with hat of haloes whose particles lie in a void. at = 0.The ot indicates that haloes that end up in à void at z=0 oobablv located at the very edges of a void — undergo slightly more evolution than haloes with the same mass elsewhere., Figure \ref{MassFunctionGIF2_2} compares the mass function of all haloes with that of haloes whose particles lie in a void at $z=0$ .The plot indicates that haloes that end up in a void at $z=0$ – probably located at the very edges of a void – undergo slightly more evolution than haloes with the same mass elsewhere. + Figure 167 shows this point a Little jt more clearly by plotting the ratios of the mass fuctions shown in Figure 15. for zΞ0/z—1 and z21/2—2., Figure \ref{MassFunctionGIF2_3} shows this point a little bit more clearly by plotting the ratios of the mass fuctions shown in Figure \ref{MassFunctionGIF2_2} for $z=0/z=1$ and $z=1/z=2$. + Note hat if vou look at all haloes. for small halo masses there are less haloes at later redshift (2= 0) than at the earlier redshift (2= 1).," Note that if you look at all haloes, for small halo masses there are less haloes at later redshift $z=0$ ) than at the earlier redshift $z=1$ )." + The small simulation volume and the resulting modest halo sample sizes do not allow more detailed studies of this., The small simulation volume and the resulting modest halo sample sizes do not allow more detailed studies of this. + We will readdress the void halo mass function in a later study that will make use of à much largersimulation., We will re–address the void halo mass function in a later study that will make use of a much largersimulation. +be the canonical momentum conjugate to q.,be the canonical momentum conjugate to $\q$. + We seek that will be canonically conjugate to Q., We seek that will be canonically conjugate to $\Q$. + Let us write Using the identity (4)) we can rewrite the middle terni as rep(dQ'ΚΟ)].," Let us write Using the identity \ref{trperm}) ) we can rewrite the middle term as $\tr{\p\,(d\Q^*\,\k\,\Q)^*}$." +" Since p—p! and (9ΚΩ)""=Q'( R)dQtheterm becomes becomes repQ'kdQ]."," Since $\p=-\p^*$ and $(d\Q^*\,\k\,\Q)^*=\Q^*\,(-\k)\,d\Q$ the term becomes becomes $\tr{\p^*\Q^*\k\,d\Q}$." + Thus we have Now if we define we have which is to say p:dq=PdQ.," Thus we have Now if we define we have which is to say, $\p\cdot d\q=\P\cdot d\Q$." + Provided. the Hamiltonian depends on P.Q only through Ῥ.α and. not on the gauge c. the transformation (P.Q)(p.q) is canonical.," Provided the Hamiltonian depends on $\P,\Q$ only through $\p,\q$ and not on the gauge $\psi$, the transformation $(\P,\Q)\rightarrow(\p,\q)$ is canonical." + To get an explicit expression for p. we multiply (22)) on the left by QR. obtaining Note that while we have to be careful about the order of multiplication when 2.3. are involved. real numbers like Q commute with evervthing.," To get an explicit expression for $\p$, we multiply \ref{Pdef}) ) on the left by $\Q^*\k$ , obtaining Note that while we have to be careful about the order of multiplication when $\i,\j,\k$ are involved, real numbers like $Q^2$ commute with everything." + Since p has no real part. reQ'kP]=0 identicallv.," Since $\p$ has no real part, $\tr{\Q^*\k\P}=0$ identically." + We can think of it as a formal constant of motion resulting [rom invariance with respect to t., We can think of it as a formal constant of motion resulting from invariance with respect to $\psi$. + That P (as defined in Equation 22.. or equivalentIv) completes a canonical transformation is a standard. part of WS theory. but the derivation of the canonical condition using quaternion identities appears to be new.," That $\P$ (as defined in Equation \ref{Pdef}, or equivalently) completes a canonical transformation is a standard part of KS theory, but the derivation of the canonical condition using quaternion identities appears to be new." + Let us now write the Ixepler Hamiltonian in terms of INS variables., Let us now write the Kepler Hamiltonian in terms of KS variables. + Multiplving each of (11)) and (22)) bv its quaternion conjugate. we have and substituting these gives We now use a device known in Hamiltonian dynamics as a Poincaré time transformation.," Multiplying each of \ref{Qtoq}) ) and \ref{Pdef}) ) by its quaternion conjugate, we have and substituting these gives We now use a device known in Hamiltonian dynamics as a Poincaré time transformation." + This involves introducing a fictitious time variable s. whose relation to / we choose to be Since Q? is the radial distance in the Kepler problen. (28)) is in fact Ixepler's equation. and s is the eccentric anomaly.," This involves introducing a fictitious time variable $s$, whose relation to $t$ we choose to be Since $Q^2$ is the radial distance in the Kepler problem,\ref{kepeq}) ) is in fact Kepler's equation, and $s$ is the eccentric anomaly." + In the fictitious time variable s. the equations of motion are given by à new Llamiltonian with / being the constant initial value of 41.," In the fictitious time variable $s$, the equations of motion are given by a new Hamiltonian with $E$ being the constant initial value of $H$." + The time-ransformecd E Hamiltonian is zero along à trajectory. but its partial derivatives are not zero.," The time-transformed $\Gamma$ Hamiltonian is zero along a trajectory, but its partial derivatives are not zero." + The Hamiltonian E is remarkable indeed., The Hamiltonian $\Gamma$ is remarkable indeed. + For ££«0 (bound orbits) it is à harmonic oscillator., For $E<0$ (bound orbits) it is a harmonic oscillator. + Since Q has four components. E is like a mass on an isotropic spring in four ]5uclidean dimensions.," Since $\Q$ has four components, $\Gamma$ is like a mass on an isotropic spring in four Euclidean dimensions." + Thus the well-known fact that the o»und. Ixepler. problem has a dynamical. O(4) symmetry., Thus the well-known fact that the bound Kepler problem has a dynamical $O(4)$ symmetry. + For the unbound case. the svmimetry group. is dilferent: ormally the Lorentz group. but with a physical meaning completely different from. special relativity.," For the unbound case, the symmetry group is different: formally the Lorentz group, but with a physical meaning completely different from special relativity." + Andperhaps most importantly—Hamilton's equations for EL are. well-ohaved even at GQ=0 fa collision)., And—perhaps most importantly—Hamilton's equations for $\Gamma$ are well-behaved even at $Q=0$ (a collision). + This is known as regularization and was the original motivation for WS theory., This is known as regularization and was the original motivation for KS theory. + The etfectof an external force F is simple., The effectof an external force $\F$ is simple. + From (22)) it ollows immediately that EZ will acd an extra contribution of 2kQF to dP/dt. which amounts to a contribution of 2QkQF to dP/ds.," From \ref{Pdef}) ) it follows immediately that $\F$ will add an extra contribution of $-2\k\Q\F$ to $d\P/dt$, which amounts to a contribution of $-2Q^2\k\Q\F$ to $d\P/ds$." + Provided the external force is singular. the equations of motion in s remain regular.," Provided the external force is non-singular, the equations of motion in $s$ remain regular." + Application. of IWS regularization to N-body simulations involve expressing the gravitating svstem either as a trec-like hierarchy of coupled two-body systems (7). or as a chain (??)..," Application of KS regularization to $N$ -body simulations involve expressing the gravitating system either as a tree-like hierarchy of coupled two-body systems \citep{1989ApJS...71..871J} or as a chain \citep{1990CeMDA..47..375M,1993CeMDA..57..439M}." + The basic idea can be described using the threc- problem with all masses unity., The basic idea can be described using the three-body problem with all masses unity. + Here again. quaternions enable a concise formulation.," Here again, quaternions enable a concise formulation." + 1n relative coordinates. the Hamiltonian for three unit eravitating masses can be written (cf.Eq.12in2). as plus an additional potential V(qu.qs).," In relative coordinates, the Hamiltonian for three unit gravitating masses can be written \cite[cf. Eq. 12 in][]{1974CeMec..10..185A} as plus an additional potential $V(\q_1,\q_2)$." +" Llere ασια. expresses the position of the first ancl second. body relative to the zeroth body. while p,. express the momenta of the first ane second bodies in the p.barvcentric frame."," Here $\q_1,\q_2$ expresses the position of the first and second body relative to the zeroth body, while $\p_1,\p_2$ express the momenta of the first and second bodies in the barycentric frame." + Meanwhile. V(qi.q.) expresses the mutual interaction of the first and second. bodies. plus any external potential.," Meanwhile, $V(\q_1,\q_2)$ expresses the mutual interaction of the first and second bodies, plus any external potential." + Wecan regard V(qi.q.) as an external potential. and. since we already know how to deal withexternal forces. we set V. aside and concentrate on Lf.," Wecan regard $V(\q_1,\q_2)$ as an external potential, and since we already know how to deal withexternal forces, we set $V$ aside and concentrate on $H$ ." + Now we introduce IWS variables αιΟΙΚΟΙ and so on., Now we introduce KS variables $\q_1=\Q_1^*\k\Q_1$ and so on. +" Defining we can write p,ps as [au L/(40102).", Defining we can write $\p_1\cdot\p_2$ as $\Pi/(4Q_1^2Q_2^2)$ . + Applying a Poincaré time transformation gives where { is the value of df., Applying a Poincaré time transformation gives where $E$ is the value of $H$ . + The E Hamiltonian. has no denominators. and is thus regular for collisions with the zeroth body. (," The $\Gamma$ Hamiltonian has no denominators, and is thus regular for collisions with the zeroth body. (" +We assume V remains regular. that,"We assume $V$ remains regular, that" +There are two important dilfereuces between space-based aud grouud-based data—oue obvious aud oue more subtle—that suggestMOD that a spacec-based observatory is likely to make use of larger pixels (relative to the PSF FWHM) than a grouud-based imager: The strict eutol of the Airy PSF at &=2D/A also means that space-borne observatories will be relatively insensitive to pixel respouse fuuctions that depart [rom the ideal unit-square moclel.,There are two important differences between space-based and ground-based data—one obvious and one more subtle—that suggest that a spaced-based observatory is likely to make use of larger pixels (relative to the PSF FWHM) than a ground-based imager: The strict cutoff of the Airy PSF at $k=2D/\lambda$ also means that space-borne observatories will be relatively insensitive to pixel response functions that depart from the ideal unit-square model. + If the PRE has structure at wavelengths <1/5 the pixel spacing. it will be irrelevant. since the PSF does not pass spatial frequencies much smaller than the FWHAL which will be close to the pixel size.," If the PRF has structure at wavelengths $\lesssim 1/5$ the pixel spacing, it will be irrelevant, since the PSF does not pass spatial frequencies much smaller than the FWHM, which will be close to the pixel size." + Similarly. subtle pixel-to-pixel variatious in the PRE will not matter if they occur at high spatial frequencies.," Similarly, subtle pixel-to-pixel variations in the PRF will not matter if they occur at high spatial frequencies." +" Iu velvesults we will quantify the effect of a sharply bouided: ""dead zone” within each pixel. which can be taken as an extreme case of intrapixel variation."," In \\ref{results} we will quantify the effect of a sharply bounded “dead zone” within each pixel, which can be taken as an extreme case of intrapixel variation." +lag in the evolution of the system.,lag in the evolution of the system. +" When the gainer loses enough angular momentum that Q/Q,«1 mass accretion resumes.", When the gainer loses enough angular momentum that $\Omega/\Omega_k < 1$ mass accretion resumes. + InFig., InFig. + [6] we show the evolution of the system with initial masses 5 and 3Mo and orbital period of 5d. The ὅΜο star evolves off the main sequence when it exhausts hydrogen in its core and moves towards the Hertzsprung gap where it fills its Roche lobe and rapidly transfers most of its envelope to its less massive companion.," \ref{evol1} we show the evolution of the system with initial masses $5$ and $3\,\rm{M}_{\odot}$ and orbital period of $5\,$ d. The $5\,\rm M_\odot$ star evolves off the main sequence when it exhausts hydrogen in its core and moves towards the Hertzsprung gap where it fills its Roche lobe and rapidly transfers most of its envelope to its less massive companion." + It becomes established as a red giant when its mass has fallen to 0.67Ms.," It becomes established as a red giant when its mass has fallen to $0.67\,\rm{M}_{\odot}$." + Our models show that this final mass is almost independent of 6 (0.675M for 6=1 falling to 0.665Mo for 8=0.5).," Our models show that this final mass is almost independent of $\beta$ $0.675\,\rm{M}_{\odot}$ for $\beta=1$ falling to $0.665\,\rm{M}_{\odot}$ for $\beta=0.5$ )." +" Meanwhile, the gainer moves up the main sequence as mass transfer proceeds."," Meanwhile, the gainer moves up the main sequence as mass transfer proceeds." + In Fig., In Fig. + [ba the dashed line is the evolutionary track of the 5M; and the solid line that of the 3M star.," \ref{evol1}a a the dashed line is the evolutionary track of the $5\,\rm M_\odot$ and the solid line that of the $3\,\rm{M}_{\odot}$ star." + The mass accretion rate Macc for B=0.9 is plotted against time in Fig., The mass accretion rate $\dot{M}_{\rm acc}$ for $\beta = 0.9$ is plotted against time in Fig. + lobb. It is larger during the early stages and slows sharply after 10? yr as the loser reaches the giant branch.," \ref{evol1}b b. It is larger during the early stages and slows sharply after $10^5\,$ yr as the loser reaches the giant branch." + The gainer reaches hydrostatic equilibrium on a dynamical time-scale and then thermodynamic equilibrium on the Kelvin-Helmholtz time-scale., The gainer reaches hydrostatic equilibrium on a dynamical time-scale and then thermodynamic equilibrium on the Kelvin–Helmholtz time-scale. + The variation of the accreting star's radius over the same time interval is plotted in Fig., The variation of the accreting star's radius over the same time interval is plotted in Fig. + (6c and its angular velocity in Fig., \ref{evol1}c c and its angular velocity in Fig. +" [ófld when the magnetic field strength is B,=1.5 kG. Recall that the variation of angular velocity is caused by the interaction between the torques of the wind, the accretion and the disc together with radius changes of the star."," \ref{evol1}d d when the magnetic field strength is $B_{\rm s}=1.5\,$ kG. Recall that the variation of angular velocity is caused by the interaction between the torques of the wind, the accretion and the disc together with radius changes of the star." + After the phase of rapid mass transfer (q7 0.2) the slowing torques dominate., After the phase of rapid mass transfer $q \approx 0.2$ ) the slowing torques dominate. + The location of the donor in the H-R diagram (see Fig. |1])), The location of the donor in the H–R diagram (see Fig. \ref{figalgolhr}) ) + shows that it is still at its minimum luminosity reached following mass transfer., shows that it is still at its minimum luminosity reached following mass transfer. +" For this system, this phase corresponds to an effective temperature of log,)(Te¢/K)=3.66 and luminosity of logi9(L/Lo)=2.25."," For this system, this phase corresponds to an effective temperature of $\log_{10} (T_{\rm + eff}/{\rm K}) = 3.66$ and luminosity of $\log_{10} (L/{\rm L_\odot}) +=2.25$." +" The angular velocities computed for the same initial system but varying @ and B, are shown in Fig. [ή.", The angular velocities computed for the same initial system but varying $\beta$ and $B_{\rm s}$ are shown in Fig. \ref{figB1}. +" As expected a larger B, creates larger torques for the same f and hence smaller angular velocities Q/Q;, at a similar point in the evolution.", As expected a larger $B_{\rm s}$ creates larger torques for the same $\beta$ and hence smaller angular velocities $\Omega/\Omega_k$ at a similar point in the evolution. +" For the same B, but smaller B there is more mass lost in the wind and again smaller €2/€) but then the evolution of the system is highly non-conservative.", For the same $B_{\rm s}$ but smaller $\beta$ there is more mass lost in the wind and again smaller $\Omega/\Omega_k$ but then the evolution of the system is highly non-conservative. +" The most important result we find here is that when B,=1 kG the gainer does not reach its critical spin rate if it loses pper cent of the mass transferred from its companion."," The most important result we find here is that when $B_{\rm s}\gtrsim 1\,$ kG the gainer does not reach its critical spin rate if it loses per cent of the mass transferred from its companion." + In such a case a classical Algol as observed today is produced., In such a case a classical Algol as observed today is produced. + For decreasing £ the final mass ratio is larger for the same initial mass., For decreasing $\beta$ the final mass ratio is larger for the same initial mass. + We also applied our models to a system with initial masses of 3.2+2M and period P= 5d. This is typical of the progenitors considered for Algol (8 Per) itself 1997)...," We also applied our models to a system with initial masses of $3.2+2\,\rm{M}_{\odot}$ and period $P=5\,$ d. This is typical of the progenitors considered for Algol $\beta$ Per) itself \citep{tout1997}. ." + The models are shown in Figs., The models are shown in Figs. + |8} and gr., \ref{evol2} and \ref{figB2}. . +non-axisymmetrie and three-dimensional models.,non-axisymmetric and three-dimensional models. + Various authors have evaluated the extra power that needs to be continuously dissipated deep in the convective interior of hot Jupiters to explain their inflated radii (e.g.. Gu. Bodenheimer Lin 2004. Burrows et al.," Various authors have evaluated the extra power that needs to be continuously dissipated deep in the convective interior of hot Jupiters to explain their inflated radii (e.g., Gu, Bodenheimer Lin 2004, Burrows et al." + 2007. Ibgui et al.," 2007, Ibgui et al." + 2009)., 2009). + While Batygin Stevenson (2010) emphasize such a deep deposition scenario. our own ohmic dissipation models say little about this scenario since we only calculate currents and ohmie dissipation in the superficial atmospheric region of the planet.," While Batygin Stevenson (2010) emphasize such a deep deposition scenario, our own ohmic dissipation models say little about this scenario since we only calculate currents and ohmic dissipation in the superficial atmospheric region of the planet." + However. another means by which hot Jupiter radii can be inflated is by slowing down their rate of contraction. through modifications to the thermal structure of their overlaying atmospheres which act as boundary conditions for the cooling isentropic interiors.," However, another means by which hot Jupiter radii can be inflated is by slowing down their rate of contraction, through modifications to the thermal structure of their overlaying atmospheres which act as boundary conditions for the cooling isentropic interiors." + Indeed. Guillot Showman (2002) argue that. if ~1% of the stellar insolation flux were deposited at pressures of tens of bars deep in the atmosphere. this would slow down cooling sufficiently to explain the inflated radit of hot Jupiters.," Indeed, Guillot Showman (2002) argue that, if $\sim 1\%$ of the stellar insolation flux were deposited at pressures of tens of bars deep in the atmosphere, this would slow down cooling sufficiently to explain the inflated radii of hot Jupiters." + While Guillot Showman (2002) suggested that a downward flux of kinetic energy could in principle achieve such energy deposition. our Fig.," While Guillot Showman (2002) suggested that a downward flux of kinetic energy could in principle achieve such energy deposition, our Fig." + 2 indicates that this ts in fact naturally achieved by ohmic dissipation in our atmospheric models. with or without drag. for à magnetic field strength Be 106. More specifically. Guillot Showman (2002) describe an evolutionary model in which 2.4«107? W are deposited at a location centered around 21 bar in the atmosphere of HD 209458b. which can explain its observed inflated radius.," 2 indicates that this is in fact naturally achieved by ohmic dissipation in our atmospheric models, with or without drag, for a magnetic field strength $B \gsim 10$ G. More specifically, Guillot Showman (2002) describe an evolutionary model in which $2.4 \times 10^{20}$ W are deposited at a location centered around 21 bar in the atmosphere of HD 209458b, which can explain its observed inflated radius." + This is achieved by the two ohmic dissipation models represented by the upper dashed and solid lines in our Fig., This is achieved by the two ohmic dissipation models represented by the upper dashed and solid lines in our Fig. + 2., 2. + In fact. since even more ohmic power is dissipated deeper in. we anticipate that models with fields even weaker than 10 G. possibly as low as 3 G. will be able to meet the inflated radius requirement for HD 209458b.," In fact, since even more ohmic power is dissipated deeper in, we anticipate that models with fields even weaker than $10$ G, possibly as low as 3 G, will be able to meet the inflated radius requirement for HD 209458b." + This leads us to conclude that ohmic dissipation deep in the atmospheres of hot Jupiters. which indirectly taps into the kinetic energy of dragged winds driven by stellar insolation higher up. is a promising scenario to explain the inflated radii of hot Jupiters.," This leads us to conclude that ohmic dissipation deep in the atmospheres of hot Jupiters, which indirectly taps into the kinetic energy of dragged winds driven by stellar insolation higher up, is a promising scenario to explain the inflated radii of hot Jupiters." + In thisLetter. we have computed the rate of ohmic dissipation in representative. three-dimensional atmospheric circulation models of the hot Jupiter HD 209458b.," In this, we have computed the rate of ohmic dissipation in representative, three-dimensional atmospheric circulation models of the hot Jupiter HD 209458b." + We find that. for a fiducial magnetic field strength of 3 G. ohmie dissipation starts dominating over stellar insolation heating at levels deeper than a few bars.," We find that, for a fiducial magnetic field strength of 3 G, ohmic dissipation starts dominating over stellar insolation heating at levels deeper than a few bars." +" The spatial non-uniformity of this extra source of heat could induce Joule-driven circulation in the deep layers traditionally considered as ""inert"".", The spatial non-uniformity of this extra source of heat could induce Joule-driven circulation in the deep layers traditionally considered as “inert”. + For a magnetic field strength >10 G. our models also indicate that enough heat is deposited at pressures of several tens of bars to slow down cooling sufficiently that the inflated radii of hot Jupiters can be explained.," For a magnetic field strength $\gsim 10$ G, our models also indicate that enough heat is deposited at pressures of several tens of bars to slow down cooling sufficiently that the inflated radii of hot Jupiters can be explained." + Our results hence suggest that magnetic interactions in hot Jupiter atmospheres play à fundamental coupling role for the dynamies and the thermal evolution of these planets., Our results hence suggest that magnetic interactions in hot Jupiter atmospheres play a fundamental coupling role for the dynamics and the thermal evolution of these planets. + As such. our work calls for the problem to be treated more consistently: magnetic drag affects wind speeds and induces currents. while the ohmic dissipation of these currents can generate a deep atmospheric circulation which could. in turn. feedback on the circulation. higher up.," As such, our work calls for the problem to be treated more consistently: magnetic drag affects wind speeds and induces currents, while the ohmic dissipation of these currents can generate a deep atmospheric circulation which could, in turn, feedback on the circulation higher up." + Indeed. the extra heat source might also enhance convection in the night side. which might in turn enhance cooling.," Indeed, the extra heat source might also enhance convection in the night side, which might in turn enhance cooling." + These various ingredients. will have to be incorporated consistently in circulation. models for a better assessment of their influence on the structure and the evolution of hot Jupiters., These various ingredients will have to be incorporated consistently in circulation models for a better assessment of their influence on the structure and the evolution of hot Jupiters. + Some diversity may naturally arise from variations in the magnetic field strength and geometry of different planets., Some diversity may naturally arise from variations in the magnetic field strength and geometry of different planets. + We thank Tristan Guillot for useful discussions. and Adam Burrows. Jeremy Goodman and the referee Douglas Lin for helpful comments on our manuscript.," We thank Tristan Guillot for useful discussions, and Adam Burrows, Jeremy Goodman and the referee Douglas Lin for helpful comments on our manuscript." + This work was supported in part by the National Science Foundation under Grant No., This work was supported in part by the National Science Foundation under Grant No. + ΡΗΥΟΣ-51164., PHY05-51164. +(2007).. can be relatively well described by the so-called cubic solution (the second derivative of vis non-zero). see vanIEerkwijkaudIaplau(2007).,", can be relatively well described by the so-called cubic solution (the second derivative of $\nu$ is non-zero), see \cite{vkk2007}." +. Spectral changes before this date are not verv large (Πάναetal.2006:vanI&erkwijkaudἹναρίαν2007).," Spectral changes before this date are not very large \citep{hetal2006, vkk2007}." +. After MD 52821 the iniug solution is well described by a periodic function. see vanWerkwijkandKaplan(2007) (these authors studied several models with aud without a elitch iu their two papers) aud spectral changes follow this lav. too (Eaberletal.2006)certain.," After MJD 52821 the timing solution is well described by a periodic function, see \cite{vkk2007} + (these authors studied several models with and without a glitch in their two papers), and spectral changes follow this law, too \citep{hetal2006}." +.. Based on that. I SugeestOO that he timing residuals wieght be also explained by a model without (or with small) precession before the glitch. and strong precession after.," Based on that, I suggest that the timing residuals might be also explained by a model without (or with small) precession before the glitch, and strong precession after." + However. this particular uodel has never been tested quantitatively against observational data.," However, this particular model has never been tested quantitatively against observational data." + Glitches naturally can produce hermal afterglows (Iliranoetal.1997)., Glitches naturally can produce thermal afterglows \citep{hetal1997}. +. About Loe8 10575 eres can be released iu a elitch (in the case of RN J0720.1-3125 according to estimates of the increase in spin frequency o» vauRAerkwijketal.2007 this value is closer to 107 ere)., About $10^{38}$ – $10^{43}$ ergs can be released in a glitch (in the case of RX J0720.4-3125 according to estimates of the increase in spin frequency by \citealt{vketal2007} this value is closer to $10^{38}$ erg). + However. Hirano et al.," However, Hirano et al." + showed that a thermal response of a NS to a elitch cannot produce a s11o0thi cluperature liucrease on the time scale of vears., showed that a thermal response of a NS to a glitch cannot produce a smooth temperature increase on the time scale of years. + If surface temperature is Increased just bv few percent. as it is required by vanERerkwijketal.(2007).. then the xiehteniung lasts just for few davs (this correspoucds to weak energy release).," If surface temperature is increased just by few percent, as it is required by \cite{vketal2007}, then the brightening lasts just for few days (this corresponds to weak energy release)." + If we require a temperature rise or a long time. then the effect is too strong (IIiranoetal. 1997).," If we require a temperature rise for a long time, then the effect is too strong \citep{hetal1997}." +. So. I conclude that spectral changes ou a long time scale should be attributed to precession of he NS.," So, I conclude that spectral changes on a long time scale should be attributed to precession of the NS." + Glitches of ANPs (xd soft eamuna-repeaters) can be differeut in nature with respect to radio pulsar elitclies. as the former can be related to crust fracture due to superstronug maenetic field.," Glitches of AXPs (and soft gamma-repeaters) can be different in nature with respect to radio pulsar glitches, as the former can be related to crust fracture due to superstrong magnetic field." + Still. the origin of a elitch is not important for our discussion here. “," Still, the origin of a glitch is not important for our discussion here. “" +Normal” elitches are quite «οποια for long period pulsars. for example. PSR J181l1-171 with spin period about 1 seconds demonstrated a elitch CJaussenaud.Stappers 2006).,"Normal” glitches are quite common for long period pulsars, for example, PSR J1814-1744 with spin period about 4 seconds demonstrated a glitch \citep{js2006}." +. So. RN J0720.1-3125 can οLBch not only via the mechiuisii operating din magnetars. but also due to convenient mechanisnis proposed for normal radio pulsars.," So, RX J0720.4-3125 can glitch not only via the mechanism operating in magnetars, but also due to convenient mechanisms proposed for normal radio pulsars." + For them one can estimate the reccurence time followingC» AlparaudBavkal(1991)., For them one can estimate the reccurence time following \cite{ab1994}. +. ↕↕≯↑∐↸∖∶↴∙⊾∐↑↸⊳∐∪↕⋟↕⊰⊸∖⊽⋅↧∩⊤⊇∩∙↓≓∶≩⊔⋅↱⊐↕↴∖↴≼⋯∖↑∪↿∐∏≻↕↕∐∐∐∶↴⋁∙ ↑↕∐∖∐∏↴∖↴↕∐∶↴∙⊾↴∖↴↑⋜⋯≼↧⋜∐⋅≼↧↕≯∪↥⋅∐⋯↕⋜∥∖⋖⋎↻⋜∐⋅⋜⋯≼↧↕≧⋜↧⋅↖⇁↨↘↽⋜↧↕↕∩∩⊔ ∪∐↸∖∪↴⋝↑⋜↧↕∐↴∖↴↑∐⋜↧↑↑∐↸∖↥⋅↸∖↸⊳↸⊳⋯⋅↸∖∐↸⊳↸∖↑↕⊔↸∖↴⋝↸∖↑↖↖↽↸∖↸∖∐↑↖↖⇁∪ ↴∖↴⋯⊳↸⊳↸∖↴∖↴↕↖↽↸∖∶↴∙⊾∐↑↸⊳↕∐∖↴∖↴↕↴∖↴∶ Parameter 6Q is the critical value of the differeuce between the rotation frequencics of normal matter aud the superfluid at a boundary ler.," If the glitch of RX J0720.4-3125 is due to unpinning, then using standard formulae \citep{ab1994} one obtains that the reccurence time between two succesive glitches is: Parameter $\delta \Omega$ is the critical value of the difference between the rotation frequencies of normal matter and the superfluid at a boundary layer." +" 6Q itself can be estimated as (Alpar Bavkal 19910): here J, is the effective molent of inertia of the region of a pinning laver.", $\delta \Omega$ itself can be estimated as (Alpar Baykal 1994): here $I_{\mathrm{p}}$ is the effective moment of inertia of the region of a pinning layer. + Combining these two formulac one obtains the relation for the time between elitcles: where fis the age of a pulsar. f£=0/2Q.," Combining these two formulae one obtains the relation for the time between glitches: where $t$ is the age of a pulsar, $t=\Omega/2\, \dot \Omega$." + Surprisingly. the time is about 10 vears for RN 1θτου.63125.," Surprisingly, the time is about 10 years for RX J0720.4-3125." + Le. it is quite probable to observe one since the discovery of this object., I.e. it is quite probable to observe one since the discovery of this object. + Then. oue can expect to see simular pheuonienae in other Magnificent seven objects.," Then, one can expect to see similar phenomenae in other Magnificent seven objects." + Tlowever. they are less studied. aud may be some elitches are missed.," However, they are less studied, and may be some glitches are missed." + Still. o produce luninosity aud spectral clhaueges. il to generate Tkachenko waves. it is probably more natural to have a elitch due to a starquake.," Still, to produce luminosity and spectral changes, and to generate Tkachenko waves, it is probably more natural to have a glitch due to a starquake." + Iu the case of the quake model (ΑραiuxDavkal1991). the time between glitelies is longer. about 300 vears for RX 10190.1-3125.," In the case of the quake model \citep{ab1994} + the time between glitches is longer, about 300 years for RX J0720.4-3125." + The estimate above was obtained assumniue standard values (AlparaudBavkal1991) 4=107 ere. 10 ?. B210/7 ere. aud 1—107 ο au? Then. we can be just lucky to find a elitch iu ~10 vears of observations (but note. that it is not the only NDINS observed).," The estimate above was obtained assuming standard values \citep{ab1994} $A=10^{52}$ erg, $\phi=10^{-3}$ , $B=10^{48}$ erg, and $I\sim 10^{45}$ g $^2$ Then, we can be just lucky to find a glitch in $\sim 10$ years of observations (but note, that it is not the only XDINS observed)." + Or. in NDINS quakes do not follow the foriuula for radio pulsars.," Or, in XDINS quakes do not follow the formula for radio pulsars." +" vanderkwidjkctal.(2007) xoposed that an accretion episode can be responsible for spectral chanecs after a ""elite? in RN J0720.63125.", \cite{vketal2007} proposed that an accretion episode can be responsible for spectral changes after a “glitch” in RX J0720.4-3125. + E think that us Is uot a very probable reason for the origin of the oelitch and corresponding changes., I think that this is not a very probable reason for the origin of the glitch and corresponding changes. + It is hardly possible to inaeime that if we observe such au episode just after 10 vears of observations. other episodes were uot frequent during the evolution of this source.," It is hardly possible to imagine that if we observe such an episode just after 10 years of observations, other episodes were not frequent during the evolution of this source." + With frequent episodes of accretion of lieht. clements a NS should, With frequent episodes of accretion of light elements a NS should +vary When rogo is reset to new values within au expected royy range.,vary when $r_{200}$ is reset to new values within an expected $r_{200}$ range. + We consider a nuniber of galaxy clusters with kuown redshifts as leus candidates;, We consider a number of galaxy clusters with known redshifts as lens candidates. + As a beuchluunark system. we consider RXJI317-1115. a high ταν hundnositv cluster at :=0.5 that has been widely studied in weak and strong leusing.," As a benchmark system, we consider RXJ1347-1145, a high X-ray luminosity cluster at $z=0.45$ that has been widely studied in weak and strong lensing." + BRNJI2IT-1115. has a pair of ares at redshift 0.5. located at approximated 235 arc sec fromm the eravitational ceuter of the cluster.," RXJ1347-1145 has a pair of arcs at redshift 0.8, located at approximated 35 arc sec from the gravitational center of the cluster." + We also consider a cluster discovered bv Wittinauetal.(2003). at 2=0.68 that appears o have a pair of ares at 7 arc sec at an unconfirmed redshift., We also consider a cluster discovered by \citet{wittman} at $z=0.68$ that appears to have a pair of arcs at 7 arc sec at an unconfirmed redshift. + To cousider a range of lens redshifts. we also iuclude Abel 1151 at 2=0.2. whose weak. lensing signal is reported in Cyprianoetal.(2001) aud RDCS1252.9-2027. a lieh redshift cluster (2= 1.21) with a weak lensing wecasurement from UST πασάς reported in Lombardietal.(2005)..," To consider a range of lens redshifts, we also include Abel 1451 at $z=0.2$, whose weak lensing signal is reported in \citet{cypriano} and RDCS1252.9-2927, a high redshift cluster $z=1.24$ ) with a weak lensing measurement from HST imaging reported in \citet{lombardi}." + We note that the mass density inferred from the weak lensing measurements of these clusters has fallen to essentially zero at a projected radius in the lens plane by approximately 3.5 Alpe., We note that the mass density inferred from the weak lensing measurements of these clusters has fallen to essentially zero at a projected radius in the lens plane by approximately 3.5 Mpc. + Therefore. in our standard comparisons. we choose the SIS trumeation radii of 3.5 Alpe. the siue as the NEW cases. although iu some comparisons we allow for a range of truncation radii," Therefore, in our standard comparisons, we choose the SIS truncation radii of $3.5$ Mpc, the same as the NFW cases, although in some comparisons we allow for a range of truncation radii." + 3.5 Mpe is eenerallv a factor of 10 to 50 larger than the scale radius. Eq. 23..," $3.5$ Mpc is generally a factor of 10 to 50 larger than the scale radius, Eq. \ref{scalerad}." + For the purposes of iuteeratiug the null ecoclesics. we re-scale the tine and radial coordinates: Iu the # coordinate. the observer receives the liebt rays f=1. and the metric is rescaled by an overall factor which. of course. does not alter the null geodesics.," For the purposes of integrating the null geodesics, we re-scale the time and radial coordinates: In the $t'$ coordinate, the observer receives the light rays $t' = 1$, and the metric is rescaled by an overall factor which, of course, does not alter the null geodesics." + We use a rav shooting technique to determine the observation angle for a given positioning and set of lens miodel parameters., We use a ray shooting technique to determine the observation angle for a given positioning and set of lens model parameters. +" For exiuuploe. if the Einstein ring angle is fixed. iucreasing 86, or ¢ will cause the true light rav to cross the optical axis closer to the lens."," For example, if the Einstein ring angle is fixed, increasing $\sigma_v$ or $c$ will cause the true light ray to cross the optical axis closer to the lens." + This allows us to vary oue model paracter at a time for a given Elustein ring angle. using Newtons method to determine the parameter value to a high accuracy. limited essentially by the quality of the ODE inteeration scheme.," This allows us to vary one model parameter at a time for a given Einstein ring angle, using Newton's method to determine the parameter value to a high accuracy, limited essentially by the quality of the ODE integration scheme." + We integrate the null gcodesic equations using an adaptive stepsize Runec-hutta-Fellbere [1-5 method based on the implementation im Pressetal.(1995)., We integrate the null geodesic equations using an adaptive stepsize Runge-Kutta-Fehlberg 4-5 method based on the implementation in \citet{nrc}. +. This allows us to monitor the error in each step and maintain a known. and s1nall. accumulated error in the integration.," This allows us to monitor the error in each step and maintain a known, and small, accumulated error in the integration." + We purposefullv slow the integration (over he affine paralcter) as we approach the source location. where the adaptive stepsize algorithii would naturally take large steps. in order to carefully stop at the source position.," We purposefully slow the integration (over the affine parameter) as we approach the source location, where the adaptive stepsize algorithm would naturally take large steps, in order to carefully stop at the source position." + The principal source oferror iu our metlocl is iu stopping at the source position., The principal source of error in our method is in stopping at the source position. +" With the observer at o=0 aud source at oy. we integrate over the affine parauueter until o=o,ce, aud determine whether r=rice, where r; is the known loeus »ositiou."," With the observer at $\phi=0$ and source at $\phi_f$, we integrate over the affine parameter until $\phi = +\phi_f \pm \epsilon_\phi$ and determine whether $r = r_l \pm +\epsilon_r$ where $r_l$ is the known lens position." + Based ouwhether ris less thanor ereater han ry. we accept or change initial values at he observer.," Based on whether $r$ is less than or greater than $r_l$, we accept or change initial values at the observer." + In practice. we fud that the eror introduced by. this stopping condition is orders of nagnitude ereater than the error accumulated imn he ODE inteeration.," In practice, we find that the error introduced by this stopping condition is orders of magnitude greater than the error accumulated in the ODE integration." + In the materials below. the error bars on the nunucerical iutegration are derived ron this known error source.," In the materials below, the error bars on the numerical integration are derived from this known error source." + We consider results frou the numerical integration of the null geodesic equations. Eq. &..," We consider results from the numerical integration of the null geodesic equations, Eq. \ref{ODES}," + to be the “correct” results from leusine which we compare he thin-lens models to., to be the “correct” results from lensing which we compare the thin-lens models to. +" As an estimate of the error in our ODE inteeration. we first set the Einstein ring angle to known value. 0r. and solve or the parameter value (either 6, or ο)."," As an estimate of the error in our ODE integration, we first set the Einstein ring angle to known value, $\theta_E$, and solve for the parameter value (either $\sigma_v$ or $c$ )." + We hen solve backwards for the Eiusteiu ring angle our nunerical integration predicts eiven these xuwaneter values. and subtract from the original specified ang5," We then solve backwards for the Einstein ring angle our numerical integration predicts given these parameter values, and subtract from the original specified angle." + The difference. which should be zero. is an estimate of the error our methods allow.," The difference, which should be zero, is an estimate of the error our methods allow." + Figure 1 shows this error estimate for a SIS model of δι17-1115. a cluster at 2=0.15. with ares frou aol=OS source.," Figure \ref{consist_n_sis:fig} shows this error estimate for a SIS model of RXJ1347-1145, a cluster at $z=0.45$ with arcs from a $z=0.8$ source." + The error values are all small aud show relatively little treucl., The error values are all small and show relatively little trend. + Similar results are obtained in the NEW models., Similar results are obtained in the NFW models. +As demonstrated by ?.. who present a detailed semi-analytic analysis of galactic outflows. the galaxy wind-IGM interaction can be approximately described at early times as a spherically expanding. self-similar blastwave or ‘bubble’.,"As demonstrated by \citet*{samuietal08}, who present a detailed semi-analytic analysis of galactic outflows, the galaxy wind-IGM interaction can be approximately described at early times as a spherically expanding, self-similar blastwave or `bubble'." + The model used to deseribe this bubble is based on that presented in 2.. which describes the adiabatic interaction of strong stellar winds with the interstellar medium.," The model used to describe this bubble is based on that presented in \citet{weaveretal77}, which describes the adiabatic interaction of strong stellar winds with the interstellar medium." + This is related to the original Sedov-Taylor blastwave solution (see. e.g.. 22)) but describes the shock evolution under rather than instantaneous energy injection. making it being better suited to cases with ongoing starburst activity.," This is related to the original Sedov-Taylor blastwave solution (see, e.g., \citealp{landaulifshitz59,ostrikermckee88}) ) but describes the shock evolution under rather than instantaneous energy injection, making it being better suited to cases with ongoing starburst activity." + The ?. model retains self-similarity by not introducing a characteristic timescale to the stellar wind bubble. and it is this property that allows it to be applied equally well to the galaxy interaction despite the greater energies of this regime.," The \citet{weaveretal77} model retains self-similarity by not introducing a characteristic timescale to the stellar wind bubble, and it is this property that allows it to be applied equally well to the galaxy wind-IGM interaction despite the greater energies of this regime." +" At time /=0 star formation processes initiate the expulsion of a galaxy wind. which we approximate as having constant mass outflow rate M, leading to a mechanical energy injection rate given by where oy is the net wind outflow velocity."," At time $t=0$ star formation processes initiate the expulsion of a galaxy wind, which we approximate as having constant mass outflow rate $\dot{M}_{\mw}$ leading to a mechanical energy injection rate given by where $v_{\mw}$ is the net wind outflow velocity." + All quantities will be expressed in relation to a fiducial value ον=LO? +. motivated by observations of intermediate-to-high redshift winds for objects with extreme star formation rates (22222)..," All quantities will be expressed in relation to a fiducial value $v_{\mw} = 10^3$ $^{-1}$, motivated by observations of intermediate-to-high redshift winds for objects with extreme star formation rates \citep{rubinetal10, weineretal09,capaketal08,blandhawthornetal07,adelbergeretal03}." +" Following 2... 2. and ?.. we relate the wind mass outflow A, to the star formation rate AL, using the dimensionless wind mass loading parameter 7j (adopting a fiducial value of | in all calculations). so that M,=Ms."," Following \citet{aguirreetal01}, \citet{springelhernquist03}, , and \citet{dallavecchiaschaye08}, we relate the wind mass outflow $\dot{M}_{\mw}$ to the star formation rate $\dot{M}_*$ using the dimensionless wind mass loading parameter $\eta$ (adopting a fiducial value of 1 in all calculations), so that $\dot{M}_{\mw} = \eta \dot{M}_* $." + The total energy injected by the wind into the system is thus The mechanical luminosity £L. can be related to the total energy available from core collapse supernovae via the wind energy fraction where es. is the kinetic energy injected per M. of stars ormed citealpdallaveechiaschaye08))., The total energy injected by the wind into the system is thus The mechanical luminosity $L_{\mw}$ can be related to the total energy available from core collapse supernovae via the wind energy fraction where $\epsilon_{\textrm{SN}}$ is the kinetic energy injected per $_{\odot}$ of stars formed \\citealp{dallavecchiaschaye08}) ). +" Assuming a 2. initial mass function. hese authors adopt a value cs,21.510ergM1: for our fiducial values of e and η this implies a wind energy fraction of foσε 0.55."," Assuming a \citet{chabrier03} initial mass function, these authors adopt a value $\epsilon_{\textrm{SN}} \simeq 1.8 \times 10^{42} \textrm{erg} \textrm{M}^{-1}_{\odot}$: for our fiducial values of $v_{\mw}$ and $\eta$ this implies a wind energy fraction of $f_{\mw} \simeq 0.55$ ." + This is slightly larger than the value of 0.4 adopted by ? for more moderately star-forming systems., This is slightly larger than the value of $0.4$ adopted by \citet{dallavecchiaschaye08} for more moderately star-forming systems. + It should be cautioned hat the exact value of f. appropriate for supernovae in high-redshift hyper-starburst regions is unclear. and so all results will be presented with scaling relations for the parameters c and 7).," It should be cautioned that the exact value of $f_{\mw}$ appropriate for supernovae in high-redshift hyper-starburst regions is unclear, and so all results will be presented with scaling relations for the parameters $v_{\mw}$ and $\eta$." + The interaction ofthe wind with the IGM can be split into four shysically distinet zones at increasing radial distance + from the bubble centre: a) the free-streaming wind immediately on exit from he hyper-starburst region: b) a region of shocked galaxy wind: ο) a shell of shocked IGM plasma: d) the ambient IGM surrounding he hyper-starburst host galaxy (22)).," The interaction of the wind with the IGM can be split into four physically distinct zones at increasing radial distance $r$ from the bubble centre: a) the free-streaming wind immediately on exit from the hyper-starburst region; b) a region of shocked galaxy wind; c) a shell of shocked IGM plasma; d) the ambient IGM surrounding the hyper-starburst host galaxy \citealp{weaveretal77,samuietal08}) )." + We model the unshocked IGM in zone d) as ionized hydrogen of homogeneous density p., We model the unshocked IGM in zone d) as ionized hydrogen of homogeneous density $\rho_d$. +" In order to estimate a value for this density in a hyper-starburst galaxy. we make use of measurements for the clustering bias bi, of high-redshift SDSS-DRS quasars given in ?:: large molecular gas reservoirs and hyper-starburst events are often associated with quasi-stellar objects (QSOs). radio galaxies. or other indications of active galactic nuclei see also Section 22.. Table 1»."," In order to estimate a value for this density in a hyper-starburst galaxy, we make use of measurements for the clustering bias $b_{\mQs}$ of high-redshift SDSS-DR5 quasars given in \citet{shenetal09}: large molecular gas reservoirs and hyper-starburst events are often associated with quasi-stellar objects (QSOs), radio galaxies, or other indications of active galactic nuclei; see also Section \ref{sect:targets}, Table \ref{tab:targets}) )." +" These authors find a bias of b=12.96+2.09 for the sample of 1788 objects in their highest redshift bin: 3.5=3.84). and we thus choose a fiducial modelling value of b,=13."," These authors find a bias of $b_{\mQs} = 12.96 \pm 2.09$ for the sample of 1788 objects in their highest redshift bin: $3.5 < z < 5.0$ (median $z=3.84$ ), and we thus choose a fiducial modelling value of $b_{\mQs} = 13$." +" We also assume that the IGM in the region immediately surrounding the starburst is biased in the same way. giving where ρουμ and δι, are the current-epoch critical density and baryon density parameter respectively. and ὁ is the dimensionless density perturbation."," We also assume that the IGM in the region immediately surrounding the starburst is biased in the same way, giving where $\rho_{\mcrit}$ and $\Omega_{\mb}$ are the current-epoch critical density and baryon density parameter respectively, and $\delta$ is the dimensionless density perturbation." + We approximate this perturbation in the star formation environment as ὁ5-180. the mean overall matter density perturbation for a collapsed halo.," We approximate this perturbation in the star formation environment as $\delta \simeq 180$, the mean overall matter density perturbation for a collapsed halo." + The outer radius of an adiabatically expanding (non-radiative). spherical blastwave under constant energy injection is given by where 3?=O.SS2S8 is a constant estimated via numerical calculation (2)..," The outer radius of an adiabatically expanding (non-radiative), spherical blastwave under constant energy injection is given by where $\beta = 0.8828$ is a constant estimated via numerical calculation \citep{ostrikermckee88}." + Equation is the only dimensionally correct combination of the system variables in this time and distance scale-free problem. and its power law form is therefore required: this self-similar evolution will cease only after radiative losses become significant (see Section ?2?)).," Equation is the only dimensionally correct combination of the system variables in this time and distance scale-free problem, and its power law form is therefore required; this self-similar evolution will cease only after radiative losses become significant (see Section \ref{sect:cooling}) )." +" Using a flat. WMAP S-year best-fitting ACDM cosmology (2). and the value O1,=0.044+0.01 (2). we may rewrite equation in terms of fiducial values for a hyper-starburst shockwave system as follows: It can be seen that bubble radius will quickly extend significantly beyond the star forming regions into the surrounding IGM."," Using a flat, WMAP 5-year best-fitting $\Lambda$ CDM cosmology \citep{komatsuetal09} and the value $\Omega_{\mb} = 0.044 \pm 0.01$ \citep{sanchezetal09}, we may rewrite equation in terms of fiducial values for a hyper-starburst shockwave system as follows: It can be seen that bubble radius will quickly extend significantly beyond the star forming regions into the surrounding IGM." + The pressure and density structure within the bubble is also approximately self-similar (22).. and can therefore be described in terms of the dimensionless radial parameter £=Πο).," The pressure and density structure within the bubble is also approximately self-similar \citep{weaveretal77,samuietal08}, , and can therefore be described in terms of the dimensionless radial parameter $\xi = r/R_2(t)$." + At the very edge of the shock (£= 1). the gas quantities are determined by the Rankine-Hugoniot conditions for a strong shock boundary: where {ο=cléto/edé. and for the monatomic gas we have adiabatic index .=5/3 (see 2).," At the very edge of the shock $\xi=1$ ), the gas quantities are determined by the Rankine-Hugoniot conditions for a strong shock boundary: where $\dot{R}_2 \equiv \dif R_2/ \dif t$, and for the monatomic gas we have adiabatic index $\gamma = 5/3$ (see \citealp{landaulifshitz59}) )." +" Using this value gives an edge- density of p»=4p, and pressure /=3p,τὸ4.", Using this value gives an edge-of-shock density of $\rho_2 = 4 \rho_d$ and pressure $P_2 = 3 \rho_d \dot{R}^2_2 / 4$. + Within the outer shock radius. ? find that the density p(£) decreases inwards and drops suddenly to zero at the contact surface 0.8642». the interface between the shocked IGM in zone c) and the shocked wind in zone b).," Within the outer shock radius, \citet{weaveretal77} find that the density $\rho(\xi)$ decreases inwards and drops suddenly to zero at the contact surface $R_c = 0.86 R_2$ , the interface between the shocked IGM in zone c) and the shocked wind in zone b)." +" The pressure at this surface is //(£=0.59, 5. and these scalings hold while the expansion remains adiabatic."," The pressure at this surface is $P(\xi = 0.86) = 0.59 \rho_d \dot{R}^2_2$ , and these scalings hold while the expansion remains adiabatic." +Fora perfect gas the tSZ effect may be estimated by integrating the pressure along a line-of-sight path through the bubble: a model for the pressure structure throughout must therefore be adopted.,Fora perfect gas the tSZ effect may be estimated by integrating the pressure along a line-of-sight path through the bubble; a model for the pressure structure throughout must therefore be adopted. + An exact model may be calculated numerically (22). but ultimately the accuracy of such a model will rely on the physical conditions matching those describedabove uuniform ambient IGMdensity py or constant input star- power Ly). which is unlikely.," An exact model may be calculated numerically \citep{weaveretal77,dokuchaev02} but ultimately the accuracy of such a model will rely on the physical conditions matching those describedabove uniform ambient IGMdensity $\rho_d$ or constant input star-formation power $L_{\mw}$ ), which is unlikely." + Instead. for the purposes," Instead, for the purposes" +The gravity waves play an important role in studying the coupling of lower and upper solar atmospheric regions and are therefore of tremendous inter-disciplinary interest.,The gravity waves play an important role in studying the coupling of lower and upper solar atmospheric regions and are therefore of tremendous inter-disciplinary interest. + The gravity waves in the Sun can be divided into two types. namely. (1) the internal gravity waves. may be confined to the solar interior. and (11) the atmospheric gravity waves. which are related to the photosphere and chromosphere. and may be further beyond.," The gravity waves in the Sun can be divided into two types, namely, (i) the internal gravity waves, may be confined to the solar interior, and (ii) the atmospheric gravity waves, which are related to the photosphere and chromosphere, and may be further beyond." + In general. the observation of gravity mode oscillations of the Sun would provide a wealth of information about the energy-generating region. which is poorly probed by the p-mode oscillations.," In general, the observation of gravity mode oscillations of the Sun would provide a wealth of information about the energy-generating region, which is poorly probed by the p-mode oscillations." + In addition. the internal g-modes of the Sun are the most powerful tool for the investigation of the solar core. and a way to solve. for instance. the neutrino problem.," In addition, the internal g-modes of the Sun are the most powerful tool for the investigation of the solar core, and a way to solve, for instance, the neutrino problem." + It hàs been suggested that the turbulent convection below the photosphere will generate the high order. non-radial g-mode oscillations (internal gravity waves) (Meyer and Schmidt. 1967; Stix. 1970).," It has been suggested that the turbulent convection below the photosphere will generate the high order, non-radial g-mode oscillations (internal gravity waves) (Meyer and Schmidt, 1967; Stix, 1970)." + There are theoretical studies earlier on gravity waves by various groups (Whitaker. 1963. Lighthill. 1967. Stein. 1967 and Schmieder. 1977).," There are theoretical studies earlier on solar-atmospheric gravity waves by various groups (Whitaker, 1963, Lighthill, 1967, Stein, 1967 and Schmieder, 1977)." + In Frazier's (1968) diagrams. the traces of internal gravity waves may be present.," In Frazier's (1968) diagrams, the traces of internal gravity waves may be present." + Deubner (1974) observed the generation of internal gravity waves by individual granules., Deubner (1974) observed the generation of internal gravity waves by individual granules. + Cram (1978) has investigated the evidence of low. but significant. power at frequencies relevant to internal gravity waves.," Cram (1978) has investigated the evidence of low, but significant, power at frequencies relevant to internal gravity waves." + He had also concluded from the studies of the phase lag between successive layers. that there was an upward energy flux.," He had also concluded from the studies of the phase lag between successive layers, that there was an upward energy flux." + In addition. Brown and Harrison (1980) have observed the indications of the possible existence of trapped gravity waves by analyzing the brightness fluctuations of the visible continuum.," In addition, Brown and Harrison (1980) have observed the indications of the possible existence of trapped gravity waves by analyzing the brightness fluctuations of the visible continuum." + These internal gravity waves. by-products of the granulation. are expected to be fairly common and may not be negligible in the energy balance of," These internal gravity waves, by-products of the granulation, are expected to be fairly common and may not be negligible in the energy balance of" +free parameter.,free parameter. + The values of the Coulomb logarithm obtained from these N-body simulations are InCA)~2—7., The values of the Coulomb logarithm obtained from these $N$ -body simulations are $\ln(\Lambda)\sim 2-7$. + In differentially rotating gas or stellar disks. the torque is provided by the flow in the corotation region and by angular momentum transfer at Lindblad resonances (e.g..Gol-dreich&TremaineQuinnGoodman 1986).," In differentially rotating gas or stellar disks, the torque is provided by the flow in the corotation region and by angular momentum transfer at Lindblad resonances \citep[e.g.,][]{Goldreich:80,Quinn:86}." +. Disk clusters with masses 1980:M=10.. have Roche tidal radii rj~[GM/(IOIn|? that are smaller than the thickness of the disk.," Disk clusters with masses $M\lesssim 10^6\,M_\odot$ have Roche tidal radii $r_{\rm t}\sim [GM/(d\Omega/d\ln R)^2]^{1/3}$ that are smaller than the thickness of the disk." +" In /dthis Ryregime. the disk torque is a generalization of the ""Type I torque acting on small planets in protoplanetary disks (e.g..Tanakaetal.2002:D'Angelo2003;Baruteau to non-Keplerian disks and is proportional to where X is the (8)surface density of the gas or stellar disk. and σ is the gas sound speed or the stellar velocity dispersion in the disk."," In this regime, the disk torque is a generalization of the “Type I” torque acting on small planets in protoplanetary disks \citep[e.g.,][]{Tanaka:02,DAngelo:03,Baruteau:08} + to non-Keplerian disks and is proportional to where $\Sigma$ is the surface density of the gas or stellar disk, and $\sigma$ is the gas sound speed or the stellar velocity dispersion in the disk." + In what follows we take the constant of proportionality 1n equation (8)) to be equal to unity., In what follows we take the constant of proportionality in equation \ref{eq:torque_disk}) ) to be equal to unity. + This choice seems consistent with the numerical calibration of the torque in a collisionless particle disk by Donner&Sundelius(1993) and Wahdeetal.(1996) if the gravitational softening employed in their calculations is equated with the vertical thickness of the disk.," This choice seems consistent with the numerical calibration of the torque in a collisionless particle disk by \citet{Donner:93} and \citet{Wahde:96} + if the gravitational softening employed in their calculations is equated with the vertical thickness of the disk." + Finally. we note that Milosavljevié(2004) argued against the migratory scenario in disks on the grounds of long migration times.," Finally, we note that \citet{Milosavljevic:04} argued against the migratory scenario in disks on the grounds of long migration times." + There. migration from a distant location in the disk was envisioned. and the treatment ignored the enhancement in dynamical friction force due to the stellar accumulation of earlier migrating clusters in the central kiloparsee of the galaxy.," There, migration from a distant location in the disk was envisioned, and the treatment ignored the enhancement in dynamical friction force due to the stellar accumulation of earlier migrating clusters in the central kiloparsec of the galaxy." + In the present picture. clusters migrate from a range of radii in the galactic disk. but only those that form closest to the galactic center reach the center and merge with the nuclear cluster.," In the present picture, clusters migrate from a range of radii in the galactic disk, but only those that form closest to the galactic center reach the center and merge with the nuclear cluster." + The timescale on which a cluster is disrupted in the galactic tidal field has been determined. empirically by modeling the luminosity and age functions of clusters in nearby disk galaxies (see.e.g..Lamersetal.2005a.b).," The timescale on which a cluster is disrupted in the galactic tidal field has been determined empirically by modeling the luminosity and age functions of clusters in nearby disk galaxies \citep[see, + e.g.,][]{Lamers:05a,Lamers:05b}." +. Theoretical models tracking stellar and dynamical evolution of a cluster in a tidal field (e.g..Gielesetal.2008;&Baumgardt2008) have reproduced the observationally inferred variation of the dissolution time with cluster mass. ο: where ~0.62 (Boutloukos&Lamers2003:deGrisAnders 2006).," Theoretical models tracking stellar and dynamical evolution of a cluster in a tidal field \citep[e.g.,][]{Gieles:08a, Gieles:08b} have reproduced the observationally inferred variation of the dissolution time with cluster mass, =, where $\gamma\approx 0.62$ \citep{Boutloukos:03,deGrijs:06}." +. The normalization fj varies between galaxies. which seems to be a consequence of the variation in the tidal field strength and of cluster-scale density inhomogeneities of the galactic environment.," The normalization $t_0$ varies between galaxies, which seems to be a consequence of the variation in the tidal field strength and of cluster-scale density inhomogeneities of the galactic environment." + Gielesetal.(2008) assessed the role of the tidal field by comparing cluster lifetimes in several galaxies with the inverse angular frequency of circular orbits at observed cluster radit and found consistency with the linear relation αννQ7!.," \citet{Gieles:08a} assessed the role of the tidal field by comparing cluster lifetimes in several galaxies with the inverse angular frequency of circular orbits at observed cluster radii and found consistency with the linear relation $t_{\rm dis}\propto +\Omega^{-1}$." +" The residual variation of ty, between galaxies has been ascribed to disruption by giant molecular clouds (Gielesetal.2006a.andreferencestherein) which we ignore."," The residual variation of $t_{\rm dis}$ between galaxies has been ascribed to disruption by giant molecular clouds \citep[][and + references therein]{Gieles:06a} which we ignore." + The tidal radius really depends on the degree of differential rotation. |2[GM/(dO/dInRy|? (e.g..Quinn&Goodman 1986).. and thus one would expect that /jx R[*. L," The tidal radius really depends on the degree of differential rotation, $r_{\rm + t}=[GM/(d\Omega/d\ln R)^2]^{1/3}$ \citep[e.g.,][]{Quinn:86}, and thus one would expect that $t_0\propto|d\Omega/d\ln R|^{-1}$ ." +amersetal.(20052). modeled the observed cluster/d in M33 and found. at an arbitrary. radius. tofaΩΙ) populationwith fagi;Μαι70.16.," \citet{Lamers:05a} modeled the observed cluster population in M33 and found, at an arbitrary radius, $t_0\approx f_{\rm dis}/\Omega(R)$ with $f_{\rm dis,M33}\approx 0.16$." + The coefficient. ο. which can be separately inferred from the observed young cluster populations and from theoretical calculations. encapsulates the detailed mass loss mechanics in a cluster embedded in a galactic tidal field and evolving through internal two-body relaxation.," The coefficient $f_{\rm dis}$, which can be separately inferred from the observed young cluster populations and from theoretical calculations, encapsulates the detailed mass loss mechanics in a cluster embedded in a galactic tidal field and evolving through internal two-body relaxation." + From the theoretical viewpoint. the coefficient depends on the initial stellar mass function. on the initial cluster structure. and on the (possibly time-dependent) gravitational potential within and near the cluster.," From the theoretical viewpoint, the coefficient depends on the initial stellar mass function, on the initial cluster structure, and on the (possibly time-dependent) gravitational potential within and near the cluster." + Under idealized assumptions. the coefficient has been estimated with N-body simulations (PortegiesZwartetal.1998.2002:Baumgardt&Makino2003).," Under idealized assumptions, the coefficient has been estimated with $N$ -body simulations \citep{PortegiesZwart:98,PortegiesZwart:02,Baumgardt:03}." +". The theoretical estimate fq,~0.3 in Lamersetal.(2005a).. which is based on the results of Baumgardt&Makino(2003).. is larger than the empirical value."," The theoretical estimate $f_{\rm dis}\sim 0.3$ in \citet{Lamers:05a}, which is based on the results of \citet{Baumgardt:03}, is larger than the empirical value." + The clusters originating in M33’s central disk could be denser and more resistant to tidal disruption than those in the sample ofLamersetal.(2005a)., The clusters originating in M33's central disk could be denser and more resistant to tidal disruption than those in the sample of\citet{Lamers:05a}. +. The above relations were obtained for clusters originating in à galactic disk., The above relations were obtained for clusters originating in a galactic disk. +" For lack of an equivalent empirical result for spheroidal starbursts. we assume that these relations hold universally and adopt the crude relation to =[T where we|| estake| fj,20.2."," For lack of an equivalent empirical result for spheroidal starbursts, we assume that these relations hold universally and adopt the crude relation t_0 =, where we take $f_{\rm dis} = 0.2$." +" We have compared our simplified form of the dissolution timescale defined in equations (9)) and (10)) for a cluster with initial mass M=10.. and angular velocity O(7)=0)7]7, where ΛοςΜ.ο)+Λάρι) Is the total[GMa initial)/ galactic mass within a sphere of radius r (see Section 3n. with the timescale from etal.(2005a.b).. whereLass ή=ΠΜοM.) MMLamers 2003). 4=yr«ο57!(5/1yr?99 (Lamersetal.2005b).. and (5=fui(rr! and found it m be consistent to within 20% 1n the range£X of radi where we find that significant cluster migration takes place."," We have compared our simplified form of the dissolution timescale defined in equations \ref{eq:time_dis}) ) and \ref{eq:t_zero}) ) for a cluster with initial mass $M=10^5\,M_\odot$ and angular velocity $\Omega(r)=[G M_{\rm + gal,0}(r)/r^3]^{1/2}$, where $M_{\rm + gal,0}(r)=M_{\star,0}(r)+M_{\rm DM}(r)$ is the total initial galactic mass within a sphere of radius $r$ (see Section \ref{sec:input}) ), with the timescale from \citet{Lamers:05a,Lamers:05b}, where $t'_{\rm + dis}=t'_4(M/10^4\,M_\odot)^\gamma$ \citep{Boutloukos:03}, $t'_4=1.355 +\,\textrm{ yr}\times 10^{4 \gamma}\gamma^{-1}(t'_0/1\,\textrm{ + yr})^{0.967}$ \citep{Lamers:05b}, and $t'_0 = f_{\rm + dis}\Omega(r)^{-1}$, and found it to be consistent to within $20\%$ in the range of radii where we find that significant cluster migration takes place." + Here we deseribe our models for the initial density profile of a spheroidal galaxy (Section 3.1)) and a disk galaxy (Section 3.2))., Here we describe our models for the initial density profile of a spheroidal galaxy (Section \ref{subsec:spheroidal}) ) and a disk galaxy (Section \ref{subsec:disk}) ). + The initial density lacks a stellar nucleus: its innermost baryonic density profile is an extrapolation from larger radit., The initial density lacks a stellar nucleus; its innermost baryonic density profile is an extrapolation from larger radii. + Then in Section 3.3.. we describe our method of distributing initial clusters consistent with these surface density profiles and modeling cluster mass redistribution during. migration and dissolution.," Then in Section \ref{subsec:redistribution}, we describe our method of distributing initial clusters consistent with these surface density profiles and modeling cluster mass redistribution during migration and dissolution." + We include the growing central cluster mass in the mass distribution affecting subsequent migrating clusters. but we ignore the response of the dark matter halo to the baryonic collapse and subsequent mass redistribution by cluster migration.," We include the growing central cluster mass in the mass distribution affecting subsequent migrating clusters, but we ignore the response of the dark matter halo to the baryonic collapse and subsequent mass redistribution by cluster migration." + Photometry of spheroidal galaxies in the nearby universe (Cotéetal.2006:Ferrarese2006a;Kormendy 2009).. combined with the fact that in these relatively old stellar systems the stellar mass-to-light ratios do not vary significantly within. galaxies. has shown that their mass surface density profiles are well described by a model (Balcells Cade URES UR ," Photometry of spheroidal galaxies in the nearby universe \citep{Cote:06,Ferrarese:06a,Kormendy:09}, , combined with the fact that in these relatively old stellar systems the stellar mass-to-light ratios do not vary significantly within galaxies, has shown that their mass surface density profiles are well described by a two-component model \citep{Balcells:03,Graham:03} + (R) = (R) + ." +"The Sérrsic law component Xs448)xexpl-(R/R7] (Caonetal. 1993)..where 75 is the Sérrsic index and R, "," The Sérrsic law component $ +\Sigma_{\rm Sersic}(R) \propto \exp[-(R/R_{\rm s})^{1/n}] +$ \citep{Caon:93}, ,where $n$ is the Sérrsic index and $R_{\rm s}$ " +"to our results. their of estimationthe median stellar 11ass is very consistent with ours. logAL./AL..=10.00.21, at Mpc21.0. which is our faintest bin.","to our results, their estimation of the median stellar mass is very consistent with ours, $\log{M_*/M_\odot}=10.0\pm0.2$, at $M_{UV}\sim-21.0$, which is our faintest bin." + 2Further conrparisoun is nof possible at this time as ouly +20 ealaxies iu their sample are bright enough to be iu ours., Further comparison is not possible at this time as only $\approx$ 20 galaxies in their sample are bright enough to be in ours. + Unlike stellar mass. we find no correlation between the imediau age of the stellar population and the UV huunositv.," Unlike stellar mass, we find no correlation between the median age of the stellar population and the UV luminosity." + The best-fit age values (200-100. Mr in all cases). sugeest that the majority of galaxies are donunated by vouug star-fornune populations not just in their rest-frame UV light. but also iu their rest-frame optical to ucar-infrared light that is considerably vouuser than the age of the Universe— at DoBT (mlgGyr:ego7).," The best-fit age values (200-400 Myr in all cases), suggest that the majority of galaxies are dominated by young star-forming populations -- not just in their rest-frame UV light, but also in their rest-frame optical to near-infrared light – that is considerably younger than the age of the Universe at $z\sim3.7$ \citep[$\approx 1.7$ Gyr: e.g.,][]{papovich01}." + Assuming exponentially declining SFUs would generally make best-fit ages even vouugcr., Assuming exponentially declining SFHs would generally make best-fit ages even younger. + The voung ages are inferred from the weak Balmer breaks between the H- and Ivs-haucd. aud are," The young ages are inferred from the weak Balmer breaks between the $H$ - and $K_S$ -band, and are" +preferred to combine the field ancl MG. systems. that is. re-arrange the total sample into six sub-groups according to their OAM. (7).,"preferred to combine the field and MG systems, that is, re-arrange the total sample into six sub-groups according to their OAM $J$ )." + In this way we expected to see the cllect of mixing voung stars erroneously into the field svstems., In this way we expected to see the effect of mixing young stars erroneously into the field systems. + In other words: what would happen if MG. svstems were not selected out of a sample?, In other words: what would happen if MG systems were not selected out of a sample? + The kinematical ages of the six sub-groups of the total sample (ALC|Field) have been re-computed from their space velocity dispersions as was done for the field stars., The kinematical ages of the six sub-groups of the total sample (MG+Field) have been re-computed from their space velocity dispersions as was done for the field stars. + The assigned. ages of MC systems in cach group is ignored in this process., The assigned ages of MG systems in each group is ignored in this process. + The kinematical ages ancl mean OAAIs of these newly formed sub-groups are shown for comparison in Fig., The kinematical ages and mean OAMs of these newly formed sub-groups are shown for comparison in Fig. + | together with a line (dashed) fitted using the least squares method., 1 together with a line (dashed) fitted using the least squares method. + The steeper inclination of the dashed line in Fig., The steeper inclination of the dashed line in Fig. + 1 indicates there is faster. OAM evolution among the total sample (114) in comparison to the evolution (solid lino) within the field CABs., 1 indicates there is faster OAM evolution among the total sample (114) in comparison to the evolution (solid line) within the field CABs. + Of course. faster evolution is just an illusion because cach sub-group of the total sample contains voung stars with small space velocities with respect to LS (Local Standard of Rest).," Of course, faster evolution is just an illusion because each sub-group of the total sample contains young stars with small space velocities with respect to LSR (Local Standard of Rest)." + Therefore. the mean dispersions of the total sample sub-eroups are reduced.," Therefore, the mean dispersions of the total sample sub-groups are reduced." + Smaller dispersions. on the other hand. correspond to smaller kinematical ages.," Smaller dispersions, on the other hand, correspond to smaller kinematical ages." + With smaller ages. the higher inclination were produced.," With smaller ages, the higher inclination were produced." + Accordingly. it can be concluded: that the rate of decrease of OAAL would. be overestimated if voung ALG group stars were left in the Therefore. we conclude that the sub-groups in Table 53 are corrected for this error.," Accordingly, it can be concluded that the rate of decrease of OAM would be overestimated if young MG group stars were left in the Therefore, we conclude that the sub-groups in Table 3 are corrected for this error." + As a result. the solid line in Fig.," As a result, the solid line in Fig." + 1 shows the corrected OAM evolution among the CADs., 1 shows the corrected OAM evolution among the CABs. + Nevertheless. this correction associated with removing possible MG. members [from a sample is still a first. orcler Correction.," Nevertheless, this correction associated with removing possible MG members from a sample is still a first order correction." + ‘This is. because the kinematical criteria for determining the moving group members do not constitute proof of membership since there is always a possibility that members and non-menibers could share the same velocity space., This is because the kinematical criteria for determining the moving group members do not constitute proof of membership since there is always a possibility that members and non-members could share the same velocity space. + Ixaratas et ((2004) believed non-members are negligible in number and cdo not. spoil the statistics., Karataş et (2004) believed non-members are negligible in number and do not spoil the statistics. + Thereore. further purification by selecting out non members rom the possible ALG members. which requires independent wool of a different age or chemical composition. was not attempted.," Therefore, further purification by selecting out non members from the possible MG members, which requires independent proof of a different age or chemical composition, was not attempted." + Since it is possible that some small number of icldl stars were erroneously selected as MG. members. the inclination of the solid line in Fig.," Since it is possible that some small number of field stars were erroneously selected as MG members, the inclination of the solid line in Fig." + 1 can be considered a ower limit., 1 can be considered a lower limit. + This is because. if erroneously selected MG stars with smaller space velocity were put back into field stars. the ages of the sub-groups would have been Iowered accordingly.," This is because, if erroneously selected MG stars with smaller space velocity were put back into field stars, the ages of the sub-groups would have been lowered accordingly." + Because this second. order correction was not. applied. we can onlv estimate that the OAAL evolution among the field CADs could be little faster. but not slower than the evolution implied in Fig.," Because this second order correction was not applied, we can only estimate that the OAM evolution among the field CABs could be little faster, but not slower than the evolution implied in Fig." + 1., 1. + The observed: OAM decrease among the field CABs requires mass loss to carry OAM oul ob the systems dn order to have a reducing ellect on the orbital periods. unless there are mechanisms which do not require mass loss., The observed OAM decrease among the field CABs requires mass loss to carry OAM out of the systems in order to have a reducing effect on the orbital periods unless there are mechanisms which do not require mass loss. + One possibility. is the direct loss of binary binding energy by stellar encounters in the galactic space which is expected be effective down to few days period (Stepien. 11995: Chez. Neugebauer 11993).," One possibility is the direct loss of binary binding energy by stellar encounters in the galactic space which is expected to be effective down to few days period (Stepien 1995; Ghez, Neugebauer 1993)." + Likely it is negligible. but the other .possibility. is. [riction between the binary components and circum binarv material in Ixeplerian orbits.," Likely it is negligible, but the other possibility is friction between the binary components and circum binary material in Keplerian orbits." + Lt is not the scope of this study to solve which mechanism is dominant and what are he contributions to the orbital period evolution., It is not the scope of this study to solve which mechanism is dominant and what are the contributions to the orbital period evolution. + Indeed. the statistics in ‘Table 3 clearly indicate that total masses and orbital periods also decrease with stellar kinematical ages similar to OAM evolution.," Indeed, the statistics in Table 3 clearly indicate that total masses and orbital periods also decrease with stellar kinematical ages similar to OAM evolution." +" The age dependence of the orbital periods (P) and mean total masses (AZ=Al,|M3») of the field. CABs are plotted. in Fig.", The age dependence of the orbital periods $(P)$ and mean total masses $(M= M_{1} + M_{2})$ of the field CABs are plotted in Fig. + 2. where the age dependence of J is also shown for à comparison.," 2, where the age dependence of $J$ is also shown for a comparison." + The linear trend lines fitted by least squares indicate the first order approximations to describe the changes at P. M and J.," The linear trend lines fitted by least squares indicate the first order approximations to describe the changes at $P$, $M$ and $J$." + With similar arguments stated for J. the decreasing rates of systemic masses (AZ) and orbital periods (2?) could also be considered as lower limits.," With similar arguments stated for $J$, the decreasing rates of systemic masses $M$ ) and orbital periods $P$ ) could also be considered as lower limits." + With ages less than 0.6 Cir. the MG. group CABs are plotted as a voungest eroup in Fie.," With ages less than 0.6 Gyr, the MG group CABs are plotted as a youngest group in Fig." + 2., 2. + It is possible to claim hat their position does not support the general trend of the itted lines reasonably as their position appears lower than he position expected., It is possible to claim that their position does not support the general trend of the fitted lines reasonably as their position appears lower than the position expected. + This again could be explained by the »ollution of a limited number of older stars in MC., This again could be explained by the pollution of a limited number of older stars in MG. + The true members of MG would have agreed the general trends., The true members of MG would have agreed the general trends. + Orbital period data in Fig., Orbital period data in Fig. + 2b indicate that the orbital xeriod changes (HP/di) at the vounger ages are Laster., 2b indicate that the orbital period changes $(dP/dt)$ at the younger ages are faster. + Such a trend. however. will not. be consistent with the orbital," Such a trend, however, will not be consistent with the orbital" +such as acceleration between ingress and egress.,such as acceleration between ingress and egress. + However. detection of the secoudary eclipse οιο using Spitzer photometry) is potentially the most scusitive coustraiut ou the ecceutricity of the orbit (Charbonneauetal.2005:Deineetal.," However, detection of the secondary eclipse (e.g., using Spitzer photometry) is potentially the most sensitive constraint on the eccentricity of the orbit \citep{charb, deming}." + 2005).. Spitzer observations of ILAT-P-11 spanning the time of secoudary eclipse were obtained by BR. Barry (Spitzer program 60063). but those data are still uuder analysis.," Spitzer observations of HAT-P-11 spanning the time of secondary eclipse were obtained by R. Barry (Spitzer program 60063), but those data are still under analysis." + Tadeed. it is possible that the secoucdary eclipse of this relatively cool planet will prove too weak to be detectable in the Spitzer data.," Indeed, it is possible that the secondary eclipse of this relatively cool planet will prove too weak to be detectable in the Spitzer data." + Therefore. for all of our transit fits. we fix the orbital eccentricity aud argument of periastron at the values derived by BLO. except that we alter w by Ls0-deerees. as per the difference between w for radial velocity observations (orbit of the star) and w for transits (orbit of the planet).," Therefore, for all of our transit fits, we fix the orbital eccentricity and argument of periastron at the values derived by B10, except that we alter $\omega$ by 180-degrees, as per the difference between $\omega$ for radial velocity observations (orbit of the star) and $\omega$ for transits (orbit of the planet)." + We compute transif curves using a new version of the Mandel&σοι(2002)— algorithius.," We compute transit curves using a new version of the \citet{mandel} + algorithms." + This new version includes the effects of a non-circular orbit. calculating the ska-projected distance of the planet from the center of the stellar disk by solving the elliptical ecometry.," This new version includes the effects of a non-circular orbit, calculating the sky-projected distance of the planet from the center of the stellar disk by solving the elliptical geometry." + We also specifically verified that our code can reproduce the obseved radial velocities for this svstem (BIO IDirauoetal.2001:Winnet 20103).," We also specifically verified that our code can reproduce the obseved radial velocities for this system (B10 \citealp{hirano, winn}) )." + The new code is also faster than previous versions., The new code is also faster than previous versions. + We fit theoretical transit curves to the transit data using a Markov. Chain Monte. Carlo (MCMC) alegorithiu (Ford 2005).., We fit theoretical transit curves to the transit data using a Markov Chain Monte Carlo (MCMC) algorithm \citep{ford}. + We use the Moetropolis-ILlastiues aleorithu with Gibbs sampling., We use the Metropolis-Hastings algorithm with Gibbs sampling. + We adjust the step size for cach variable so as to obtain acceptance rates between and60. and we un our chains for 10° samples.," We adjust the step size for each variable so as to obtain acceptance rates between and, and we run our chains for $10^6$ samples." + Prior to starting each AICAIC chain. we re-scale the eror bars for the data to insure that the best reduced 47 will be close to unity.," Prior to starting each MCMC chain, we re-scale the error bars for the data to insure that the best reduced $\chi^2$ will be close to unity." + This helps to insure that the errors calculated from the posterior distributions are realistic., This helps to insure that the errors calculated from the posterior distributions are realistic. + The re-scaling factor was approximately 2 for the binned Isepler data., The re-scaling factor was approximately 2 for the binned Kepler data. + For the ground-based data. we adopt error bars equal to the observed scatter in the data. so uo scaling is necessary.," For the ground-based data, we adopt error bars equal to the observed scatter in the data, so no re-scaling is necessary." + We discard the first of each chain ΣΕ the posterior distributions., We discard the first of each chain when tabulating the posterior distributions. + To verify convergence. we compare the posterior distributions from four chains that have different starting values aud slightlv different step sizes.," To verify convergence, we compare the posterior distributions from four chains that have different starting values and slightly different step sizes." + Since our code is new. we tested it i several wavs.," Since our code is new, we tested it in several ways." + These tests began with simple ποσα. problems such as fitting to an average of a series of uuuboers. aud fitting to data that scatter around a straight line.," These tests began with simple numerical problems such as fitting to an average of a series of numbers, and fitting to data that scatter around a straight line." + Our final test was to generate svuthetic transit data by adding noise to theoretical transit curves based on the Maudel&Ασοι(20023. formmlae. and fitting to those svuthetic transits to verify that we recover the system parameters that were used to generate the svuthetic data.," Our final test was to generate synthetic transit data by adding noise to theoretical transit curves based on the \citet{mandel} formulae, and fitting to those synthetic transits to verify that we recover the system parameters that were used to generate the synthetic data." +" Ideally. we would like ft to all of the individual trausit curves simultaneously, allowing the central transit times to be free parameters in the fit."," Ideally, we would like fit to all of the individual transit curves simultaneously, allowing the central transit times to be free parameters in the fit." + HTowever. the spot crossings that contanuuate individual transits force us to fit to the binned aud cleaned transit (Figure 6).," However, the spot crossings that contaminate individual transits force us to fit to the binned and cleaned transit (Figure 6)." + One caveat to this procedure is that imperfections in the mutual phasiugs of the transits could potentially broaden aud distort the binned transit., One caveat to this procedure is that imperfections in the mutual phasings of the transits could potentially broaden and distort the binned transit. + To check our result. we combined the transits two wars.," To check our result, we combined the transits two ways." + First. we use our new ephemeris (Sec.," First, we use our new ephemeris (Sec." + 6) to shift cach transit to a common phase., 6) to shift each transit to a common phase. + Second. we use the raw individual ceutral transit times from the bisector analyses to phase the trausits.," Second, we use the raw individual central transit times from the bisector analyses to phase the transits." + We performed all of our AICNIC fits to binned transits coustructed using both methods. aud found agreement within the raucom errors.," We performed all of our MCMC fits to binned transits constructed using both methods, and found agreement within the random errors." + We are coufident that pliasiug crrors do not coutamunate our results to a significant deeree., We are confident that phasing errors do not contaminate our results to a significant degree. + We report the fit results from the ephemeris phasing. because it eiiplovs the constraint that the transit times should be strictly periodic in the abseuce of planetary perturbations.," We report the fit results from the ephemeris phasing, because it employs the constraint that the transit times should be strictly periodic in the absence of planetary perturbations." +" Our MCMC fits to the binned and cleaned IKepler data (Figure 6) include 6 variables in the fit: a/Ry. ,/Π.. orbital inclination. quadratic and linear limb darkenius cocfücients. and a correction to transit center time."," Our MCMC fits to the binned and cleaned Kepler data (Figure 6) include 6 variables in the fit: $a/R_s$, $R_p/R_s$, orbital inclination, quadratic and linear limb darkening coefficients, and a correction to transit center time." + The latter is expected to be zero because the stacking aud biuuiug procedures alieued. the individual I&epler trausits to the commuon trausit-centered time frane., The latter is expected to be zero because the stacking and binning procedures aligned the individual Kepler transits to the common transit-centered time frame. + Within the errors. the AICAIC fits retrieved a central time correction consistent with zero.," Within the errors, the MCMC fits retrieved a central time correction consistent with zero." + We performed a second iudepenudoeut set of MCMC fits to the Kepler data by fixiug the Liuab-arkeuing coefficieuts at their iiodel-atinospliere values., We performed a second independent set of MCMC fits to the Kepler data by fixing the limb-darkening coefficients at their model-atmosphere values. + We tabulate best-fit values for the svstemi parameters bv averaging over the last 500.000 samples for four independent MCMC chains.," We tabulate best-fit values for the system parameters by averaging over the last 800,000 samples for four independent MCMC chains." +" As a check ou those best-fit values, we implemented an iudepondeut (7 minimization solution using a Levenbere-Marquardt alegoritlin."," As a check on those best-fit values, we implemented an independent $\chi^2$ minimization solution using a Levenberg-Marquardt algorithm." + Our cle error limits equal the values where high aud low-side tails of the NCMC posterior distributions contained of the total samples., Our $\pm1\sigma$ error limits equal the values where high and low-side tails of the MCMC posterior distributions contained of the total samples. + The error limits were close to sviunietric on each side of the distributions Chigh- aud low-side errors typically aeree within ))., The error limits were close to symmetric on each side of the distributions (high- and low-side errors typically agree within ). + We conservatively adopt the greater value as the svuuuetric error for cach fitted parameter., We conservatively adopt the greater value as the symmetric error for each fitted parameter. + The best-fit values and errors ave listed iu Table 1. except for the quadratic Buib darkening cocfitcicut that has little inipact on our analysis.," The best-fit values and errors are listed in Table 1, except for the quadratic limb darkening coefficient that has little impact on our analysis." + The best-fit trausit curve is plotted over the binned transit data in Figure 6. together with the curve expected from the DIO discovery parameters.," The best-fit transit curve is plotted over the binned transit data in Figure 6, together with the curve expected from the B10 discovery parameters." + The exouud-based data give us ai opportunity to check xuanueters such as Bb darkeniug over au extended waveleugth range., The ground-based data give us an opportunity to check parameters such as limb darkening over an extended wavelength range. +" Moreover. the ereatlv reduced Bub darkening in the J-baud results in sharp ingress aud cercss ines, aud that sharp definition of the transit duration will xove to be useful. as we discuss in Sec."," Moreover, the greatly reduced limb darkening in the J-band results in sharp ingress and egress times, and that sharp definition of the transit duration will prove to be useful, as we discuss in Sec." + 8. and as Colon(2009). predicted.," 8, and as \citet{colon} + predicted." + However. because the eromud- data do not have photometric precision comparable o the Kepler data. we fud it prudent to restrict the eround-based fits to extract fewer paraimecters.," However, because the ground-based data do not have photometric precision comparable to the Kepler data, we find it prudent to restrict the ground-based fits to extract fewer parameters." + For the J-hand. we set the quadratic Biub-darkeuing cocfitcicut o equal the model atinosphere prediction (0.211). aud we set the DB-band quadratic cocficient to zero as noted above.," For the J-band, we set the quadratic limb-darkening coefficient to equal the model atmosphere prediction $0.244$ ), and we set the B-band quadratic coefficient to zero as noted above." + Anticipating our results. we find rough agreecineut )etwoeen the fits aud the model atmosphere lnib-darkeuiug xedietious.," Anticipating our results, we find rough agreement between the fits and the model atmosphere limb-darkening predictions." + The quadratic portion of the luab-darkenine las a nudnor effect compared to the linear cocfficieut. especially in B-band where the strong limb darkening is well approximated by the linear law.," The quadratic portion of the limb-darkening has a minor effect compared to the linear coefficient, especially in B-band where the strong limb darkening is well approximated by the linear law." + Note that Southworth found linear Linh darkening to be adequate for the, Note that \citet{southworth} found linear limb darkening to be adequate for the +field profile out side the bodies are eiven by (D.LiaudJ.D.Barrow (2007))) Hence the correspondiusg poteutial euergv of the ΠΟΙΟΤΟ is The bound ou the streugth of the interaction to be eiven as follows Writing Eq (113) ,field profile out side the bodies are given by \cite{26}) ) Hence the corresponding potential energy of the interaction is The bound on the strength of the interaction to be given as follows Writing Eq. \ref{17}) ) +for every one of the test bodies. we ect Tere peas is energy deusity of the vacuum iuside the chamber.," for every one of the test bodies, we get Here $\rho_{vac}$ is energy density of the vacuum inside the chamber." +" Iu the experiment performed im (J.Is.Iloskiuse£ef (1985))). for a typical test body with mass Hs.8dOgr and radius àzlem the density p, aud . respectively.: ↑∐∖↻∪↑↸∖∐⊓⋜↧↕≼↕≻↙∐⋜↧↖↽↸∖↴⋝↸∖↸∖∐∪↴⋝↑⋜⊔∐↸∖≺↧∩∙⋅↱⊐∙↙∕∣⋮↙⋅∣⊔⊽⋟⋅↓∩−∣"," In the experiment performed in \cite{35}) ), for a typical test body with mass $m_c\approx 40gr$ and radius $r_c\approx 1cm$ the density $\rho_c$ and the potential $\Phi_c$ have been obtained $9.5gr/{cm}^3,\, 10^{-27}$ respectively." + Furthermore. the pressure in the vacuum chamber have been reported 3.&410.N1 which: is: equivalent to peas29LS<10H'grfei?.," Furthermore, the pressure in the vacuum chamber have been reported $3\times 10^{-8}mmHg$ which is equivalent to $\rho_{vac}\approx4.8\times 10^{-14}gr/{cm}^3$." + Substituting the upon values iu to (30)) and. combining with (29)) result iu the bound Which if we replace p.=1.7«102060) 2. with substitute iu to Eq. (31))," Substituting the upon values in to\ref{32}) ) and combining with \ref{31}) ) result in the bound Which if we replace $\rho_c=1.7\times 10^{-26}{cm}^{-2}$ , with substitute in to Eq. \ref{33}) )" + we can obtain e«2«10OR. Iu this paper we have coustrained FR) model of eravities. using the renowned equivalence between rese dnodels aud scaler tensor theories.," we can obtain $\epsilon<2\times10^{-3}R_c $ In this paper we have constrained $f(R)$ model of gravities, using the renowned equivalence between these models and scaler tensor theories." + Mostly. iu us representation from FO) theory there is a stroug coupling of the scalar field with the matter sector.," Mostly, in this representation from $f(R)$ theory there is a strong coupling of the scalar field with the matter sector." + We wave used from the chameleon mechanisi to suppress us coupling., We have used from the chameleon mechanism to suppress this coupling. +" We have shown that in order to the uodel (3)) be consistent with the preseut local eravitv experiments. the paramcters ε aud £A, should satisty 1e following conditions."," We have shown that in order to the model \ref{11}) ) be consistent with the present local gravity experiments, the parameters $\epsilon$ and $R_c$ should satisfy the following conditions." + Whereas. the structure of this paper is perturbation state of general relativity. hence € should be small.," Whereas, the structure of this paper is perturbation state of general relativity, hence $\epsilon$ should be small." +" Therefore. we suggest A. must be the same order of peo=102060,2. where with this value of [δι we have found that the model (3)) is consistent with the thiu-shell and EP conditions for ο<1035 as well as it is cousisteut with fifth force."," Therefore, we suggest $R_c$ must be the same order of $\rho_e = 10^{-26} cm^{-2}$, where with this value of $R_c$, we have found that the model \ref{11}) ) is consistent with the thin-shell and EP conditions for $\epsilon\lesssim 10^{-14}$, as well as it is consistent with fifth force." + At the moment. as a result applying the above values from €. we obtain SppN=lcLIS«10 ον ," At the moment, as a result applying the above values from $\epsilon$, we obtain $\gamma_{PPN}\simeq1\mp1.13\times 10^{-5}$ ." +That is remarkable that this value of 2;ppy are nearly equal to what is required by observation., That is remarkable that this value of $\gamma_{PPN}$ are nearly equal to what is required by observation. + It should be implied that the above resul is achieved under the assumption that pone«pin , It should be implied that the above result is achieved under the assumption that $\rho_{out}\ll\rho_{in}\ll \frac{\Phi_c R_c}{\epsilon}$ . +Therefore. thestudied model is a viable fCGR) model which satisfied EP aud Solar Svsteii bounds auc it has very stualldeviation from the general relativity.," Therefore, thestudied model is a viable $f(R)$ model which satisfied EP and Solar System bounds and it has very smalldeviation from the general relativity." +The flix of gamma-rays expected in the IC: model for the emission region within the diauneter of 1around the cluster center (Eq.(13))) aud the Fermi observational data. are shown in Fig. 3..,The flux of gamma-rays expected in the IC model for the emission region within the diameter of around the cluster center \ref{spec_e}) )) and the Fermi observational data are shown in Fig. \ref{gamma_IC}. + We fined that the optical photons emitted Irom the core of GC (see Eq. (, We find that the optical photons emitted from the core of GC (see Eq. ( +6)) does not contribute significantly in (he gamama-ray flux. produced by the inverse Compton scaltering because their density decreases rapidly away [rom (he core and the diffusion mean [ree path (see Eq.(20) below) is much larger than the size of the core.,6)) does not contribute significantly in the gamma-ray flux produced by the inverse Compton scattering because their density decreases rapidly away from the core and the diffusion mean free path (see Eq.(20) below) is much larger than the size of the core. + One can see from this figure that the data can equally be interpreted either by scattering on relic (solid line). IR. (dashed line) or optical photons (dash-dotted line).," One can see from this figure that the data can equally be interpreted either by scattering on relic (solid line), IR (dashed line) or optical photons (dash-dotted line)." + The three peaks on each of (hese lines correspond to scattering on relic. IR. and optical photons. respectively.," The three peaks on each of these lines correspond to scattering on relic, IR, and optical photons, respectively." + Since the characteristic energies of soft photons from relic. IR and optical components are different to make them to be scattered to GeV range one should use electrons with different energies in accordance with Eq. (13)).," Since the characteristic energies of soft photons from relic, IR and optical components are different to make them to be scattered to GeV range one should use electrons with different energies in accordance with Eq. \ref{IC_ph_en}) )." + The energv parameter [rom Eq. (9)), The energy parameter from Eq. \ref{inj}) ) +" corresponding to the relic scattering to be responsible for explanation of FERMI data is E7*""*nj=0.7 TeV. to the IR scaltering is £njik—0.15 TeV. and to the optical scattering is £77.Hjop=0.02 TeV. As one can see [rom this figure LAT. MAGIC and even HESS are able to detect the predicted excesses in (he energv range above 10 GeV except the case when the GeV gamma-ray enission is produced by scattering on optical photons (the dash-dotted line)."," corresponding to the relic scattering to be responsible for explanation of FERMI data is $E_{inj}^{relic} += 0.7$ TeV, to the IR scattering is $E_{inj}^{IR} = 0.15$ TeV, and to the optical scattering is $E_{inj}^{op} = 0.02$ TeV. As one can see from this figure LAT, MAGIC and even HESS are able to detect the predicted excesses in the energy range above 10 GeV except the case when the GeV gamma-ray emission is produced by scattering on optical photons (the dash-dotted line)." + However (hese excesses depend on the nature of the soft photons., However these excesses depend on the nature of the soft photons. + In general IR photons give (he strongest excess in 30 GeV range., In general IR photons give the strongest excess in 30 GeV range. + If this flux level is detected. it supports that the GeV ganuna-ravs have IC origin.," If this flux level is detected, it supports that the GeV gamma-rays have IC origin." + On the other hand. if the excess is found but significantly weaker than the predicted level of IC model.," On the other hand, if the excess is found but significantly weaker than the predicted level of IC model." + Then part of GeV gamnma-rays may still come from CR mechanism as predicted by Venter De Jager (2009)., Then part of GeV gamma-rays may still come from CR mechanism as predicted by Venter De Jager (2009). +" We also want to remark (hat although the upward scattered relic photons can fit the Fermi data. it requires £;,; larger (han the estimated"," We also want to remark that although the upward scattered relic photons can fit the Fermi data, it requires $E_{inj}$ larger than the estimated" +Some websites tuaimtain a consistency to their HTML format such that quick information cau be extractec with a simple script.,Some websites maintain a consistency to their HTML format such that quick information can be extracted with a simple script. + For example. the following script grabs the J2000 coords for a galaxy from NED: Note that the object name is all the words after the comuuaud (e.g. 4881).," For example, the following script grabs the J2000 coords for a galaxy from NED: Note that the object name is all the words after the command (e.g. )." + The parsiug is done by NED. the webpage is piped back to the script.," The parsing is done by NED, the webpage is piped back to the script." + The script then splits by carriage returis looking for the line that has the coordinates., The script then splits by carriage returns looking for the line that has the coordinates. + The secret here is that NED always maintains the same ‘look’. aud the coordinates are always ou the line with unique kleutifiers Equatorial’ and *J2000°.," The secret here is that NED always maintains the same 'look', and the coordinates are always on the line with unique identifiers 'Equatorial' and 'J2000'." + Again. is thisnot an elegant method to communicatewith a data archive. but it is the simplest.," Again, this is not an elegant method to communicate with a data archive, but it is the simplest." + Some iuvestiuent in time Is spent decocling the source hypertext of the webpage to find the particular set of lines from which to extract the values., Some investment in time is spent decoding the source hypertext of the webpage to find the particular set of lines from which to extract the values. + Thus. this method is hardly efficient if one ueeds more iulormation than a simple set of coordinates.," Thus, this method is hardly efficient if one needs more information than a simple set of coordinates." + To capture the full collection of data on a galaxy. NED ollers au XML output to their queries.," To capture the full collection of data on a galaxy, NED offers an XML output to their queries." + Iu order to access the XML file. one simply. chanees the URL by addiug «αλ.," In order to access the XML file, one simply changes the URL by adding all""." +" This returns the entire set of NED data on the query galaxy in au easy to parse ΛΙ, format.", This returns the entire set of NED data on the query galaxy in an easy to parse XML format. + NED also offers several XML files for photometry data. reference data. etc (see the tools website lor a suite of NED scripts).," NED also offers several XML files for photometry data, reference data, etc (see the tools website for a suite of NED scripts)." + To work with the returning XML file. Python has a number of XML modules.," To work with the returning XML file, Python has a number of XML modules." + However. this project has constructed one that better matches astronomical data aud is discussed iu the next section.," However, this project has constructed one that better matches astronomical data and is discussed in the next section." + Storage of data in NAIL format closely uiimiues the HTML format that make up webpages through the use of tags to ideutify each data element., Storage of data in XML format closely mimics the HTML format that make up webpages through the use of tags to identify each data element. + Each element (or data atom) has attributes. data and," Each element (or data atom) has attributes, data and" +"under the assumption of axisymmetry, and adopt a spherical polar coordinate system (1,6,à), with a stellar object of M,= at the origin such that the gravitational potential 0.5Mgis $;=—G/r, neglecting the self-gravity of the gas.","under the assumption of axisymmetry, and adopt a spherical polar coordinate system $(r, \theta, \phi)$, with a stellar object of $M_\ast=0.5\msun$ at the origin such that the gravitational potential is $\Phi_g= - GM_\ast/r$, neglecting the self-gravity of the gas." +" Self-gravity willM, be included in a follow-up work, where we will evolve the magnetized core from its formation to collapse in a self-consistent manner."," Self-gravity will be included in a follow-up work, where we will evolve the magnetized core from its formation to collapse in a self-consistent manner." +" For this initial study, we aim to capture the essence of the problem of magnetic suppression of disk formation in the simplest possible way, by adopting uniform distributions for the initial gas density and magnetic field, and to study the effects of a new ingredient, resistivity, in this simplest problem."," For this initial study, we aim to capture the essence of the problem of magnetic suppression of disk formation in the simplest possible way, by adopting uniform distributions for the initial gas density and magnetic field, and to study the effects of a new ingredient, resistivity, in this simplest problem." +" At time t=0, we fill the computation domain between rj;=1.5x10!cm and Το=1.5x10!""cm with a uniform density po=1.4x1071?gcm? (corresponding to n(H3)=3.0x10* cm?), so that the total envelope mass is "," At time $t=0$, we fill the computation domain between $r_i=1.5\times 10^{14}\cm$ and $r_o=1.5\times 10^{17}\cm$ with a uniform density $\rho_0=1.4\times 10^{-19}\gram\cm^{-3}$ (corresponding to $n(\Htwo)=3.0\times 10^4\cm^{-3}$ ), so that the total envelope mass is $1\msun$." +"For simplicity, we assume that the gas stays 1Mg.isothermal, with an isothermal sound speed a=(p/p)/?2x10cms""! (corresponding to a temperature of about 10 K)."," For simplicity, we assume that the gas stays isothermal, with an isothermal sound speed $a=(p/\rho)^{1/2}=2\times 10^4\cm\second^{-1}$ (corresponding to a temperature of about $10\kelvin$ )." +" For theinitial rotation, we adopt the following prescription: where we choose vg9=2x104cms!, c is the cylindrical radius, and cv,=3x1015cm."," For theinitial rotation, we adopt the following prescription: where we choose $v_{\phi,0}=2\times 10^4\cm\second^{-1}$, $\varpi$ is the cylindrical radius, and $\varpi_c=3\times 10^{15}\cm$." + The softening of the rotational profile inside the cylindrical radius c. is to prevent the angular speed from becoming singular near the rotation axis., The softening of the rotational profile inside the cylindrical radius $\varpi_c$ is to prevent the angular speed from becoming singular near the rotation axis. +" Since the inner radius of our computational domain is 10AU, we are concerned with the formation or suppression of relatively large disks (of tens of AU or more) only."," Since the inner radius of our computational domain is $10\au$, we are concerned with the formation or suppression of relatively large disks (of tens of AU or more) only." +" Our initial rotation is relatively fast: Goodmanetal.(1993) estimated observationally that the ratio of rotational to gravitational energies for dense NHs cores is typically ~0.02, which would imply vg~3xl0?cms""! for our setup."," Our initial rotation is relatively fast: \citet{gbfm93} + estimated observationally that the ratio of rotational to gravitational energies for dense $\N\Hydrogen_3$ cores is typically $\sim 0.02$, which would imply $v_\phi \sim +3\times 10^3\cm\second^{-1}$ for our setup." + Our choice of a faster rotational speed is conservative in that it is harder to remove a larger initial angular momentum through magnetic braking (see also Mellon&Li 2008))., Our choice of a faster rotational speed is conservative in that it is harder to remove a larger initial angular momentum through magnetic braking (see also \citealp{ml08}) ). +" The calculations are done with a new version of Zeus, dubbed “ZeusTW”."," The calculations are done with a new version of Zeus, dubbed “ZeusTW”." +" ZeusTW, written in idiomatic Fortran95, is based on the “Zeus36” code (Krasnopolsky,Li,&Blandford1999, 2003),, itself derived from Zeus3D (LCA version 3.4.2: Clarke,Norman,&Fiedler 1994)); Zeus36 is parallel by domain decomposition, and utilizes dynamic memory for its field and grid arrays."," ZeusTW, written in idiomatic Fortran95, is based on the “Zeus36” code \citep{klb99,klb03}, itself derived from Zeus3D (LCA version 3.4.2: \citealp{cnf94}) ); Zeus36 is parallel by domain decomposition, and utilizes dynamic memory for its field and grid arrays." +" A small memory pool of temporary arrays replaces the worker arrays of Zeus3D, increasing programming flexibility at essentially zero runtime cost."," A small memory pool of temporary arrays replaces the worker arrays of Zeus3D, increasing programming flexibility at essentially zero runtime cost." +" ZeusTW adds to Zeus36 the ability to solve many non-ideal MHD problems in an explicit form, covering the ohmic, Hall, and ambipolar diffusion terms."," ZeusTW adds to Zeus36 the ability to solve many non-ideal MHD problems in an explicit form, covering the ohmic, Hall, and ambipolar diffusion terms." +" To treat the ohmic term relevant for this paper, we used a resistivity algorithm based on Fleming,Stone,&Hawley (2000),, which includes subcycling."," To treat the ohmic term relevant for this paper, we used a resistivity algorithm based on \citet{fsh00}, which includes subcycling." +" We tested the code by diffusing an initial Gaussian profile in Cartesian geometry, in one, two, and three dimensions."," We tested the code by diffusing an initial Gaussian profile in Cartesian geometry, in one, two, and three dimensions." +" We also tested slightly different forms of the algorithm as changing the operator splitting by calculating the (suchcurrent density J before or after the magnetic field B is updated), and different subcycling prescriptions (such as varying the maximum number of ohmic subcycles from 1 to 100)."," We also tested slightly different forms of the algorithm (such as changing the operator splitting by calculating the current density $\vJ$ before or after the magnetic field $\vB$ is updated), and different subcycling prescriptions (such as varying the maximum number of ohmic subcycles from 1 to 100)." + The code passed all of these tests., The code passed all of these tests. +" We adopt the standard hydro outflow boundary conditions at both the inner and outer (radial) boundaries of the computation domain (these boundary conditions impose continuity of material outflowing the grid, helping to reduce artificial reflections of waves at boundaries)."," We adopt the standard hydro outflow boundary conditions at both the inner and outer (radial) boundaries of the computation domain (these boundary conditions impose continuity of material outflowing the grid, helping to reduce artificial reflections of waves at boundaries)." +" We use 400 non-uniformly spaced grid points in the radial direction, corresponding to a smallest radial grid size drmin=3x10!?cm (or 0.2 AU) and a ratio of adjacent zone sizes of 1.017."," We use $400$ non-uniformly spaced grid points in the radial direction, corresponding to a smallest radial grid size $dr_{\rm min}=3\times 10^{12}\cm$ (or $0.2\au$ ) and a ratio of adjacent zone sizes of $1.017$." +" We use 180 uniform zones in the 0 direction, corresponding to a minimum polar grid size of 2.6x10?cm, comparable to the smallest radial grid size."," We use 180 uniform zones in the $\theta$ direction, corresponding to a minimum polar grid size of $2.6\times 10^{12}\cm$, comparable to the smallest radial grid size." +" With this setup, we obtain a rotationally supported disk of radius rg~400AU and mass mq7:0.01M at a time t=10135 in the absence of magnetic braking; the time is comparable to the duration of the deeply embedded Class 0 phase (Andréetal.2000,, see, however, Evansetal.2009 who concluded that the duration is "," With this setup, we obtain a rotationally supported disk of radius $r_d\approx 400\au$ and mass $m_d\approx 0.01\msun$ at a time $t=10^{12}\second$ in the absence of magnetic braking; the time is comparable to the duration of the deeply embedded Class 0 phase \citealp{awb00}, see, however, \citealp{e09} + who concluded that the duration is longer)." +A snapshot of the disk is shown in Figure 1.. The longer, A snapshot of the disk is shown in Figure \ref{hydro}. . +).hydrodynamic disk is resolved in the radial direction by more than 200 zones., The hydrodynamic disk is resolved in the radial direction by more than 200 zones. +" We have experimented with coarser grids (e.g., a total of 200 radial zones and"," We have experimented with coarser grids (e.g., a total of $200$ radial zones and" +2003).. which takes into account the effect of multiple collisions on (he intensity ol the emitted radiation.,", which takes into account the effect of multiple collisions on the intensity of the emitted radiation." + The influence of the LPAI effect for the bremsstrahlung emisivity of the electrosphere has been discussed in Jaikunaretal.(2004b) and it has been shown that the elect of the dense medium can reduce the emissivity by (wo orders of magnitude., The influence of the LPM effect for the bremsstrahlung emisivity of the electrosphere has been discussed in \citet{Ja04b} and it has been shown that the effect of the dense medium can reduce the emissivity by two orders of magnitude. + It is the purpose of the present paper to consider a svstematic analysis of the LPAI effect in the electrosphere of (he bare quark stars., It is the purpose of the present paper to consider a systematic analysis of the LPM effect in the electrosphere of the bare quark stars. + In particular. we would like to point oul the effect of the electric field at the quark star surface on the electromagnetic radiation [rom the electrosphere.," In particular, we would like to point out the effect of the electric field at the quark star surface on the electromagnetic radiation from the electrosphere." + The presence of the electric field considerably reduces the magnitude of the LPAI effect (lor example. the critical LPM frequency ds reduced. due to the electric field. from 1 GeV to a few MeV).," The presence of the electric field considerably reduces the magnitude of the LPM effect (for example, the critical LPM frequency is reduced, due to the electric field, from $1$ GeV to a few MeV)." + The radiation properties of the electrosphere essentially depend on (the value of the electric potential at the quark star surface., The radiation properties of the electrosphere essentially depend on the value of the electric potential at the quark star surface. + For high values of the electric potential (of the order of 16—20 MeV. or higher). the electrosphere can be considered. from the point of view of the LPAI effect. as a Chick medium. and radiation is strongly. suppressed in almost ihe entire volume of the electrosphere.," For high values of the electric potential (of the order of $16-20$ MeV or higher), the electrosphere can be considered, from the point of view of the LPM effect, as a thick medium, and radiation is strongly suppressed in almost the entire volume of the electrosphere." + On the other hand. for small values of the surface electrostatic potential of the quark star the electrosphere becomes thin and the suppression ellect can be ignored.," On the other hand, for small values of the surface electrostatic potential of the quark star the electrosphere becomes thin and the suppression effect can be ignored." + The present paper is organized as follows., The present paper is organized as follows. + In Section HE we review the basic formalism and (he main results describing (he radiation spectrum of the individual electrons by taking into account the LPAI effect., In Section II we review the basic formalism and the main results describing the radiation spectrum of the individual electrons by taking into account the LPM effect. + The emissivity and energy f[Iux of the electrosphere is obtained in Section ILI., The emissivity and energy flux of the electrosphere is obtained in Section III. + We discuss and conclude our results in Section IV., We discuss and conclude our results in Section IV. + Throughout this paper we use (lie natural svstem of units. with e—fhbg=1.," Throughout this paper we use the natural system of units, with $c=\hbar =k_B=1$." + In the present Section we shall review some of the basic definitions and physical processes related (o the electromagnetic radiation emission the of electrons in the dense electron laver al (he surface of a quark stir., In the present Section we shall review some of the basic definitions and physical processes related to the electromagnetic radiation emission the of electrons in the dense electron layer at the surface of a quark star. + In particular. we shall describe in some details (he mechanisis of electromagnetic radiation suppression due to the Landau-Pomeranchuk-Migdal effect. in the case of electrons in a dense medium (Landau&Pomeranchuk1953:Migdal1956)... with and without the presence of an external electric field.," In particular, we shall describe in some details the mechanisms of electromagnetic radiation suppression due to the Landau-Pomeranchuk-Migdal effect in the case of electrons in a dense medium \citep{LaPo53,Mi56}, with and without the presence of an external electric field." + This effect plavs an essential role in the calculation of the radiation emission from the electrosphere of the quark star., This effect plays an essential role in the calculation of the radiation emission from the electrosphere of the quark star. +Ilunsberger. Charlton and Zaritsky 1996). which tend to have steep luminosity functions (Ilunsberger. Charlton Zaritsky 1998). though (μον are not usually thought to be as brighte as the objects in our LFs.,"Hunsberger, Charlton and Zaritsky 1996), which tend to have steep luminosity functions (Hunsberger, Charlton Zaritsky 1998), though they are not usually thought to be as bright as the objects in our LFs." + For the largeste exeroups there may be a modest flatteninge of the slope again. perhaps rellecting the smaller number of clwarls seen in some very dense environments (Boveeetal.2001).," For the largest groups there may be a modest flattening of the slope again, perhaps reflecting the smaller number of dwarfs seen in some very dense environments \citep{boyce01}." +. When attempting to interpret the observed (rends. we should also consider the appropriateness ol our measure of the group or cluster environment.," When attempting to interpret the observed trends, we should also consider the appropriateness of our measure of the group or cluster environment." + A group's total mass is evidently a critical measure. as halo mass is the key variable in structure formation models (Press& seq.: Yangetal. 2005b)).," A group's total mass is evidently a critical measure, as halo mass is the key variable in structure formation models \citealt{press74} ; \citealt{yang05b}) )." + The total Iuminositv has been demonstrated to be a good measure of total stellar mass and total halo mass (Padillaetal.2004:Yang2005c).," The total luminosity has been demonstrated to be a good measure of total stellar mass and total halo mass \citep{padilla04,yang05c}." +. One could argue that the total 2 band Iuminositv would be preferable to the 5 band luminosity. as il is less subject to contributions from short term star formation. and that the A band would be better still: A band LFs should also more closely. reflect the mass distribution of the individual group galaxies (e.g. Cole et al.," One could argue that the total $R$ band luminosity would be preferable to the $B$ band luminosity, as it is less subject to contributions from short term star formation, and that the $K$ band would be better still; $K$ band LFs should also more closely reflect the mass distribution of the individual group galaxies (e.g. Cole et al." + 2001)., 2001). + In fact. 2 aud. f£ group. luminosities (urn out to be well correlated so experiments dividing the sample by group. A magnitudes presentis (he same picture as Chat already discussed. while A band data is not vel available for a large enough sample to overcome statistical uncertainties (though see Ekeetal.2005 for a current analysis).," In fact, $B$ and $R$ group luminosities turn out to be well correlated so experiments dividing the sample by group $R$ magnitudes presents the same picture as that already discussed, while $K$ band data is not yet available for a large enough sample to overcome statistical uncertainties (though see \citealt{eke05} + for a current analysis)." + We could also divide the groups purely by multiplicity. though (iis will bring in additional (or at least different) selection effects. and theoretically is expected to have wide. poissonian. variations [or a given halo mass (e.g. NKravisovetal.2004:Yang 2005d)). or by a dvnanmücal measure such as velocity dispersion (Christlein2000:Ekeetal.2004b) or parameters such as X-ray [lux (Milesοἱal.2004).," We could also divide the groups purely by multiplicity, though this will bring in additional (or at least different) selection effects, and theoretically is expected to have wide, poissonian, variations for a given halo mass (e.g. \citealt{kravtsov04,yang05d}) ), or by a dynamical measure such as velocity dispersion \citep{christlein00,eke04b} or parameters such as X-ray flux \citep{miles04}." +.. We defer a discussion of this and of a wider range of group properties to a subsequent paper., We defer a discussion of this and of a wider range of group properties to a subsequent paper. + To sum up. the results of our study suggestex that changese in the egalaxv population take place mostly among (he lower Iuminosity groups ancl are consistent will the changes being broughtex about by mergere//interaction-induced accretion and star formation suppression.," To sum up, the results of our study suggest that changes in the galaxy population take place mostly among the lower luminosity groups and are consistent with the changes being brought about by merger/interaction-induced accretion and star formation suppression." + We have arguede that the observed changese in LF parameters are not merely a selection elfect due to the total available luminosity., We have argued that the observed changes in LF parameters are not merely a selection effect due to the total available luminosity. + The processes appear to be largely complete once the group Iuminosityv reaches a threshold value ήν2—22.5 (with projected densities of a few giant galaxies per Mpc?)., The processes appear to be largely complete once the group luminosity reaches a threshold value $M^G_{b_J} \simeq -22.5$ (with projected densities of a few giant galaxies per $^2$ ). + This is similar to earlier observations in groups and clusters (Ixodamaοἱal.al. 2005)..," This is similar to earlier observations in groups and clusters \citep{kodama01,dominguez02,martinez02,kodama05,sabatini05,tanaka05}." +" The ""threshold huminositv may arise during the growth of groups. when the internal velocity dispersion becomes so large as to inhibit further interactions despite the increased galaxy density."," The `threshold' luminosity may arise during the growth of groups, when the internal velocity dispersion becomes so large as to inhibit further interactions despite the increased galaxy density." + Hf (he more massive groups then coalesce to produce clusters (as, If the more massive groups then coalesce to produce clusters (as +[ive parsecs across. it nestles at the edge. of the giant molecular cloud in. Orion. about 470 pe away. ane its spectacular appearance has mace it a familiar astronomical image.,"five parsecs across, it nestles at the edge of the giant molecular cloud in Orion, about 470 pc away, and its spectacular appearance has made it a familiar astronomical image." + At its centre are the four bright Trapezium stars. of which. the most massive..Ori. is. by [ar⋅ the dominant. source of UV radiation in the cluster.," At its centre are the four bright Trapezium stars, of which the most massive, is by far the dominant source of UV radiation in the cluster." + There is evidence to suggest that the majority of stars in the ONC have cireumstellar disks., There is evidence to suggest that the majority of stars in the ONC have circumstellar disks. + Over 40 have now been observed. directly. with theTelescope. either sillhouctted against the background. nebula or. embedded inside a bright ionized envelope of matter (a proplvd) (AleCaughrean&O'Dell1996:OWongBally.O'Dell&AleCaughrean 2000).," Over 40 have now been observed directly with the, either sillhouetted against the background nebula or embedded inside a bright ionized envelope of matter (a proplyd) \cite{MccOde96,OdeWon96,BalOdeMcc00}." +. The existence. of many more can be inferred. from an excess in the near infrared continuum emission [rom stars in the cluster., The existence of many more can be inferred from an excess in the near infrared continuum emission from stars in the cluster. + Measurements wv Hilleabrand et al., Measurements by Hillenbrand et al. + (1998). found evidence for clisks around 5590 per cent of their sample of ~ 1600 stars. ancl more recently. Lada et al.," \shortcite{Hil+98} found evidence for disks around 55–90 per cent of their sample of $\sim$ 1600 stars, and more recently, Lada et al." + (inpress). have narrowed this fraction ο NO50 per cent in their observations., \shortcite{Lad+**} have narrowed this fraction to 80–85 per cent in their observations. + In this paper we present the results of N-bocky simulations of the ONC using Aarseth’s code (Aarseth2000).. and their implications Lor clisk destruction » photocvaporation ancl stellar encounters.," In this paper we present the results of $N$ -body simulations of the ONC using Aarseth's code \cite{Aar00}, and their implications for disk destruction by photoevaporation and stellar encounters." + Such an approach is necessary to properly calculate the effects. of whotoevaporation. because the mass loss rate from a clisk due to an incident UV [ux is determined by its clistanee from he flux source.," Such an approach is necessary to properly calculate the effects of photoevaporation, because the mass loss rate from a disk due to an incident UV flux is determined by its distance from the flux source." + Phe model we use for this. due to Johnstone. llollenbach Bally (1998).. Stórrzer IHollenbach (1999) and references in Hollenbach. Yorke Johnstone (2000).. is in agreement with measurements made by Henney ODell (1999).. who found mass loss rates of ~410AL.vr+ [rom proplyds close toOri.," The model we use for this, due to Johnstone, Hollenbach Bally \shortcite{JohHolBal98}, Störrzer Hollenbach \shortcite{StoHol99} + and references in Hollenbach, Yorke Johnstone \shortcite{HolYorJoh00}, , is in agreement with measurements made by Henney O'Dell \shortcite{HenOde99}, who found mass loss rates of $\sim 4 \times 10^{-7}\,\msol\,\mbox{yr}^{-1}$ from proplyds close to." + LE these objects have spent the whole age of the ONC in this environment. their initial masses must have been greater than 0.5M. and we might expect to see some disks today with a non-negligible fraction of this mass present.," If these objects have spent the whole age of the ONC in this environment, their initial masses must have been greater than $0.8\,\msol$, and we might expect to see some disks today with a non-negligible fraction of this mass present." + However mm-wavelength observations of cisks in the ONC indicate (Ladaetal.1996:Ballyοἱ1908) clisk masses no greater than 0.02AL.” Phe paradox might be resolved if wwas born only very recently at most 5r101 vrago — or if» the dynamics of the ONC were such that the proplyvels seen close to ttoday have spent most of their lives elsewhere in the eluster. as has been suggested by Stórrzer LHollenbach (1999).," However mm-wavelength observations of disks in the ONC indicate \cite{Lad+96,Bal+98} disk masses no greater than $0.02\,\msol$ The paradox might be resolved if was born only very recently – at most $5 \times 10^{4}\,\mbox{yr}$ ago – or if the dynamics of the ONC were such that the proplyds seen close to today have spent most of their lives elsewhere in the cluster, as has been suggested by Störrzer Hollenbach \shortcite{StoHol99}." +. We investigate this possibility in simulations in which the cluster undergoes a collapse [rom cold initial conditions., We investigate this possibility in simulations in which the cluster undergoes a collapse from cold initial conditions. + The relevance of cluster dynamics for the destruction of disks bv stellar encounters is even. more readily apparent., The relevance of cluster dynamics for the destruction of disks by stellar encounters is even more readily apparent. + A full dynamical simulation is necessary (0 improve on analytic approximations in which stars remain in the same density environment throughout the life of the cluster (e.g. Clarke Pringle (1991)))., A full dynamical simulation is necessary to improve on analytic approximations in which stars remain in the same density environment throughout the life of the cluster (e.g. Clarke Pringle \shortcite{ClaPri91}) ). + Until recently however. I-bodvy Codes suppressed strongly gravitationally focused encounters by smoothing the gravitational field. on small scales.," Until recently however, $N$ -body codes suppressed strongly gravitationally focused encounters by smoothing the gravitational field on small scales." + 1n the ONC. typical encounters are gravitationally focused at impact parameters less than 160 AU. so a proper evaluation of svstenis on the scale. of interest. for planet formation could not be mace with such codes.," In the ONC, typical encounters are gravitationally focused at impact parameters less than 160 AU, so a proper evaluation of systems on the scale of interest for planet formation could not be made with such codes." + In this work we useNBODYG. which represents the state of the art in dynamical simulation on a commercial hardware platform. and which incorporates two-bods. regularisation algorithms to hanelle close encounters without smoothing.," In this work we use, which represents the state of the art in dynamical simulation on a commercial hardware platform, and which incorporates two-body regularisation algorithms to handle close encounters without smoothing." + Although the ONC is relatively close. the large aniounts of gas and dust. present and the bright emission from the ‘Trapezitm stars have until recently hidden: much of its population. and. prevented us from. accurately measuring its kinematics.," Although the ONC is relatively close, the large amounts of gas and dust present and the bright emission from the Trapezium stars have until recently hidden much of its population, and prevented us from accurately measuring its kinematics." + In the past decade. however. deep ane high resolution studies at optical wavelengths. (Prosseretal.1994). and adaptive optical techniqes in the infrared (MeCaughrean&Stauller1994). have greatly improved our understanding of the cluster’s size and composition.," In the past decade, however, deep and high resolution studies at optical wavelengths \cite{Pro+94} and adaptive optical techniqes in the infrared \cite{MccSta94} have greatly improved our understanding of the cluster's size and composition." + llillenbrand Llartmann (1998) detected: 3500. stars down to mass 0.1AL: within 2.5pe of the eluster centre.," Hillenbrand Hartmann \shortcite{HilHar98} detected 3500 stars down to mass $0.1\,\msol$ within $2.5\,\mbox{pc}$ of the cluster centre." + A subsequent survey of the central 0.7pew2 (Llillenbrand&Carpenter2000) down to mass 0.02δν found an additional 20 per cent stars in that region.," A subsequent survey of the central $0.7 \times 0.7\,\mbox{pc}^2$ \cite{HilCar00} down to mass $0.02\,\msol$ found an additional 20 per cent stars in that region." + The overall mass spectrum was found to be similar to that of the Galactic field., The overall mass spectrum was found to be similar to that of the Galactic field. + In this work we therefore consider a population of 4000 stars. with a mean mass of around 0.5AL; though the true population is probably higher still.," In this work we therefore consider a population of 4000 stars, with a mean mass of around $0.5\,\msol$ – though the true population is probably higher still." + Jones Walker (LOSS) measured a (threc-dimensional) velocity. dispersion σ=4.3+0.5kms [or about 1000 stars distributed within 2pc of the centre.," Jones Walker \shortcite{JonWal88} measured a (three-dimensional) velocity dispersion $\sigma = 4.3 \pm 0.5\,\mbox{km}\,\mathrm{s}^{-1}$ for about 1000 stars distributed within $2\,\mbox{pc}$ of the centre." + Combined with a half-mass radius [4= lpc. this gives a crossing time d.=2Ryfo0.5Myr.," Combined with a half-mass radius $R_{\mathrm{h}} = 1\,\mbox{pc}$ , this gives a crossing time $T_{\mathrm{c}} = 2R_{\mathrm{h}} / \sigma +\approx 0.5\,\mathrm{Myr}$." + The age of the cluster is cüllicult to determine. but cata from Llillenbrand (1907)— and Lillenbrancl Carpenter (2000). suggest that perhaps 85 per cent of its stars are less than 2Myr old. (with a mean age of ~0.5 Myr).," The age of the cluster is difficult to determine, but data from Hillenbrand \shortcite{Hil97} and Hillenbrand Carpenter \shortcite{HilCar00} suggest that perhaps 85 per cent of its stars are less than $2\,\mbox{Myr}$ old (with a mean age of $\sim +0.8\,\mbox{Myr}$ )." + The cluster thus seems to be dynamically voung — a few crossing times old., The cluster thus seems to be dynamically young – a few crossing times old. + Using these parameters. a rough calculation of the virial ratio (kinetic energy. / potential οποιον) ofthe cluster gives a value of about 1.5.," Using these parameters, a rough calculation of the virial ratio (kinetic energy / potential energy) of the cluster gives a value of about 1.5." + Some authors have concluded: [rom this that either the ONC must be unbound and expanding. or there must be a significant amount of gas or stars perhaps low-mass binary companions — present ancl not seen (Jones&Walker1988:Tianetal.1996:LHillenbrand]lartmann1998:Ixroupa 2000).," Some authors have concluded from this that either the ONC must be unbound and expanding, or there must be a significant amount of gas or stars -- perhaps low-mass binary companions – present and not seen \cite{JonWal88,Tia+96,HilHar98,Kro00}." +.. LLowever. reasonable errors in the observational parameters can casily account for an error of over 50 per cent in this calculation.," However, reasonable errors in the observational parameters can easily account for an error of over 50 per cent in this calculation." + The density profile of the eluster is very much that of arelaxed system. to the extent that Hillenbrand llartmann(1998) were able to fit a Kine mocel characteristic of elobular clusters many relaxation times old το their data.," The density profile of the cluster is very much that of arelaxed system, to the extent that Hillenbrand Hartmann\shortcite{HilHar98} were able to fit a King model -- characteristic of globular clusters many relaxation times old – to their data." +xedieted in the barvonic outflow model. where Ry he initial radius where the outflow is accelerated (e.g.Zhang&Peer2009:Fan 2010).,"predicted in the baryonic outflow model, where $R_0$ is the initial radius where the outflow is accelerated \citep[e.g.][]{ZP09,Fan10}." +. Oue may arene that he photosphere radiation peaksat the observed E., One may argue that the photosphere radiation peaksat the observed $E_{\rm p}$. + Such a scenario. however. Is head to account for the N-ray spectrum Fyκble ," Such a scenario, however, is hard to account for the X-ray spectrum $F_\nu \propto \nu^{-0.32\pm 0.03}$." +Below we discuss a ΤΗ.possi maguetic dissipation scenario hat would interpret ARE 100316D pronipt enission., Below we discuss a possible magnetic dissipation scenario that would interpret XRF 100316D prompt emission. +" Dv comparing the pam deusity (X+7. r js the radial distance from the ceutral source) aud the density required for co-votation (x&.1 bevoud the light ονποσα of the compact object). one can estimate the radius at which the MIID condition. breaks down. which reads ÉFAHHIDvDEREN10Limbtn,nmCni where 6 is the ratio of the magnetic energv flux to the particle euerev flux. Ty is the bulk Lorentz factor of the outflow. fran~P ds the mnüunmna variability timescale of the central engine (Zhane&Mészáros2002:Fanctal.2005:Cao&Fan 2006).."," By comparing the pair density $\propto r^{-2}$, $r$ is the radial distance from the central source) and the density required for co-rotation $\propto r^{-1}$ beyond the light cylinder of the compact object), one can estimate the radius at which the MHD condition breaks down, which reads $r_{\rm MHD} \sim 5\times 10^{15} L_{47}^{1/2} +\sigma_{1.6}^{-1}t_{v,m,-2} \Gamma_{\rm i,1.5}^{-1} ~{\rm cm}$, where $\sigma$ is the ratio of the magnetic energy flux to the particle energy flux, $\Gamma_{\rm i}$ is the bulk Lorentz factor of the outflow, $t_{v,m} \sim P$ is the minimum variability timescale of the central engine \citep{ZM02,Fan05,Gao06}. ." + Devoud this radius. intense electromagnetic waves are generated aud outflowiug particles are accelerated (Usov1991:Lxutikov&Black-man 2001).," Beyond this radius, intense electromagnetic waves are generated and outflowing particles are accelerated \citep{Usov94,Lyutikov01}." +. Part of the Povuting flix euergv is converted to radiation., Part of the Poynting flux energy is converted to radiation. + At rypp. the comoving maguctic fields Dygip can be estimated as νο~20Coyσέ5G. where $<1 reflects the cficiency of magnetic energv dissipation.," At $r_{\rm MHD}$, the comoving magnetic fields $B_{\rm +MHD}$ can be estimated as $B_{\rm MHD}\sim 20~ \xi \sigma_{1.6} +t_{v,m,-2}^{-1}~{\rm G}$, where $\xi\leq 1$ reflects the efficiency of magnetic energy dissipation." + When imaeuetic dissipation occurs. a fraction e. of the dissipated comoving magnetic energev would be eventually converted to the comoving kinetic energv of the electrous.," When magnetic dissipation occurs, a fraction $\varepsilon_{\rm e}$ of the dissipated comoving magnetic energy would be eventually converted to the comoving kinetic energy of the electrons." + Electrons may be linearly accelerated in the electric fields or stochastically accelerated im the random electromagnetic fields., Electrons may be linearly accelerated in the electric fields or stochastically accelerated in the random electromagnetic fields. +" One may assuie that the accelerated electrons formi a single power-law distribution in enerev. Le. dufds.Xx5.""( for 5.2tea. Where CALL he estimated as rt,73.5«104σι aud C,cdz,/05)pSean2)/(p1)."," One may assume that the accelerated electrons form a single power-law distribution in energy, i.e. $dn/d\gamma_{\rm e} \propto +\gamma_{\rm e}^{\rm -p}$ for $\gamma_{\rm e}>\gamma_{\rm e,m}$, where $\gamma_{\rm e,m}$ can be estimated as $\gamma_{\rm e,m}\sim +3.5\times 10^{4}~\sigma_{1.6} C_p$, and $C_p \equiv +(\varepsilon_e/0.5)(p-2)/(p-1)$." +" At mip. the correspondingον. svuchrotron radiation frequency is (Fanctal.2005) The cooling Lorentz factor can be estimated by σαςL5«lor,G'xiup which gives a svuchrotron cooling frequency Bip):rewnp~6Sstot!TzTey4LοςBayένω ο."," At $r_{\rm MHD}$, the corresponding synchrotron radiation frequency is \citep{Fan05} + The cooling Lorentz factor can be estimated by $\gamma_{\rm e,c}\sim +4.5\times 10^{19}\Gamma_{\rm i} /(r_{\rm MHD} B_{\rm MHD}^2)$, which gives a synchrotron cooling frequency $\nu_{\rm c,MHD}\sim 6\times 10^{14}~{\rm Hz}~\Gamma_{\rm +i,1.5}^{5}L_{47}^{-1} \xi^{-3}\sigma_{1.6}^{-1}t_{\rm v,m,-2}$ ." +" The observed XRT spectzuni can be approximated by Fyx»UvUd which is close to the fast cooling spectrum vL7, suggesting ΙΟXπο (t is straightforward to show that for the fiducial parameters adopted iu this work the svuchrotrou selt-absorptiou is below the optical baud)."," The observed XRT spectrum can be approximated by $F_\nu \propto +\nu^{-0.3\sim-0.4}$, which is close to the fast cooling spectrum $\nu^{-1/2}$, suggesting $\nu_{\rm c,MHD}\lesssim + 10^{17}~{\rm Hz}$ (it is straightforward to show that for the fiducial parameters adopted in this work the synchrotron self-absorption is below the optical band)." + Ou the other hand. the non-detection of prompt cussion by UVOT (Starlingctal.2010) favors a high cooling frequency Meant2.1«lo! Ez.," On the other hand, the non-detection of prompt emission by UVOT \citep{Starling10} favors a high cooling frequency $\nu_{\rm c,MHD} \sim 2.4\times 10^{17}$ Hz." + As shown in L.. the svuchrotron radiation model with such a high MoM cau roughly account for the data.," As shown in \ref{fig:SED}, , the synchrotron radiation model with such a high $\nu_{\rm c,MHD}$ can roughly account for the data." + We then eet a constraiut Substituting this iuto eq.(2)) we eot Within such a scenario. ds defined bw jb [Eq.(2))].," We then get a constraint Substituting this into \ref{eq:nu_m}) ) we get Within such a scenario, $E_{\rm p}$ is defined by $\nu_{\rm m,MHD}$ \ref{eq:nu_m}) )]." +" An observed evolving£), may bo understood by invoking a decreasing e. which £i,is consistent with the magnetic field dissipation hvpothesis."," An observed evolving $E_{\rm p}$ may be understood by invoking a decreasing $\sigma$ , which is consistent with the magnetic field dissipation hypothesis." +" Por p>£),/h (where fis Plauck’s coustaut). the spectra is Fy,xwee, Iw "," For $\nu>E_{\rm p}/h$ (where $h$ is Planck's constant), the spectrum is $F_\nu \propto \nu^{-p/2}$ ." +typical variability timescale of the raciation powered by the maguetic energy dissipation cau be estimated as which is much larger than the rotation period P~10τις of the magnetar. inüplviug that the pulsation of the ceutral euneiue is undetectable.," The typical variability timescale of the radiation powered by the magnetic energy dissipation can be estimated as which is much larger than the rotation period $P \sim 10~{\rm ms}$ of the magnetar, implying that the pulsation of the central engine is undetectable." + So far the nearby supcruova-associated CRBs. except GRB 030329. are found to be intrinsically uuder-unuiuous.," So far the nearby supernova-associated GRBs, except GRB 030329, are found to be intrinsically under-luminous." + Thev share the similarities such /as low isotropic energies auc smooth light curves. but differ in sole aspects;," They share the similarities such as low isotropic energies and smooth light curves, but differ in some aspects." + For example. GRD 980125 aud. CRB 31203 have shorter durations aud higher £s than NRF 060218 aud XRF 100316D. The uuderlviug physical oocesses that result im these differences are uot well nuderstood.," For example, GRB 980425 and GRB 031203 have shorter durations and higher $E_{\rm p}$ 's than XRF 060218 and XRF 100316D. The underlying physical processes that result in these differences are not well understood." + Through supernova modeling. it is fouud hat CRB 980125 and GRB 031203 have a progeuitor star massive enough to form a black hole (Dengetal.2005:Mazzalietal. 200Ga).. while NRF 060218 has a ess Inassive progenitor that most plausibly produces a jeutron star (Mazzaliet:2006b).," Through supernova modeling, it is found that GRB 980425 and GRB 031203 have a progenitor star massive enough to form a black hole \citep{Deng05,Mazzali06a}, while XRF 060218 has a less massive progenitor that most plausibly produces a neutron star \citep{Mazzali06b}." +. The hnunumositv and the duration of NRF 100316D. are consistent with he radiation from a neutron star with a dipole magnetic field By~«105 C aud a rotation period P~10 us.," The luminosity and the duration of XRF 100316D are consistent with the radiation from a neutron star with a dipole magnetic field $B_{\rm p} +\sim 3\times 10^{15}$ G and a rotation period $P \sim 10$ ms." + This secus 3to point towards a hypothesis that two types of central eugines define the apparent dichotomw of the SN-associated LL-GRBs. i.e. black hole cugines give rise to “shorter” aud “harder” GRBs such as GRB 980125 and GRB 031205. while magnuetar engines give rise to very long and soft NRFs such as NRF 060218 aud. AREF 100316D?.. Adding in SN data makes the scenario more complicated.," This seems to point towards a hypothesis that two types of central engines define the apparent dichotomy of the SN-associated LL-GRBs, i.e. black hole engines give rise to “shorter"" and “harder"" GRBs such as GRB 980425 and GRB 031203, while magnetar engines give rise to very long and soft XRFs such as XRF 060218 and XRF 100316D. Adding in SN data makes the scenario more complicated." + Although SN 2006aj associated with NRF 000515 does not conflict with a slow maenuctar central euge. SN POLObL associated with NRF 1005316D. iav be too cherectic to be interpreted with a slow magnetar central cheine.," Although SN 2006aj associated with XRF 060218 does not conflict with a slow magnetar central engine, SN 2010bh associated with XRF 100316D may be too energetic to be interpreted with a slow magnetar central engine." + [fit is coufirmed that the kinetic energy of SN 2010bL is in excess of 1003 ere. neither the neutrino enerev nor the magnetar spin τε1ου cre) are adequate to power the SN.," If it is confirmed that the kinetic energy of SN 2010bh is in excess of $10^{52}$ erg, neither the neutrino energy nor the magnetar spin energy $\sim 10^{50}$ erg) are adequate to power the SN." +" A salieut CHENfeature of the dipole spindown formula (Τα.ΠΠ is that if one shifts the time zero point (e.g. f= τμ). the spindown law still applies. with the initial angular frequency re-defined as OY=0) aud the characteristic spindown time scale ve-defined as 7=1.6«107D,3105“Lis Rt."," A salient feature of the dipole spindown formula \ref{eq:E_inj}] ]) is that if one shifts the time zero point (e.g. $t'=t - t_0$ ), the spindown law still applies, with the initial angular frequency re-defined as $\Omega'=\Omega(t'=0)$, and the characteristic spindown time scale re-defined as $\tau'_0=1.6\times 10^4 B_{\rm p,14}^{-2} {\Omega'_4}^{-2} I_{45} +R_{s,6}^{-6}$ ." +" This sugeests that the observed. plateau feature can he still interpreted if the iitial period is much shorter than 10 us. sav. Jyo laus. if the time zeropoint is mach earlierhau uj, 5005s (c.f 0)."," This suggests that the observed plateau feature can be still interpreted if the initial period is much shorter than 10 ms, say, $P_0 \sim 1$ ms, if the time zeropoint is much earlierthan $T_{\rm trig}-500$ s (i.e. $t=0$ )." + This is because a power-law decay light curve may show au artificial plateau in the og-log space. if the zero time is uais-placedto a later," This is because a power-law decay light curve may show an artificial plateau in the log-log space, if the zero time is mis-placedto a later" +provide a better understanding of stellar differential rotation.,provide a better understanding of stellar differential rotation. + Next. we investigated angular velocity dillerence al the surface.," Next, we investigated angular velocity difference at the surface." + The X effect. causes spatial difference in the rotation profile. while turbulent. viscosity reduces the difference.," The $\Lambda$ effect causes spatial difference in the rotation profile, while turbulent viscosity reduces the difference." + Aneular velocity difference AQ is determined in eq. (49)).," Angular velocity difference $\Delta\Omega$ is determined in eq. \ref{deltaomega}) )," + which is then used to investigate differential rotation in rapicly rotating stars., which is then used to investigate differential rotation in rapidly rotating stars. + Since stellar rotation is close to the Tavlor-Proudman state. and the radiative core is rotating rigidly. differential rotation is concentrated at low latitudes with large stellar angular velocity.," Since stellar rotation is close to the Taylor-Proudman state, and the radiative core is rotating rigidly, differential rotation is concentrated at low latitudes with large stellar angular velocity." + This concentration leads to a stuall A@ in eq. (49))., This concentration leads to a small $\Delta\theta$ in eq. \ref{deltaomega}) ). + Therefore. only at low latitudes our model is consistent with stellar observations.," Therefore, only at low latitudes our model is consistent with stellar observations." + Our conclusions are as follows: (1) Differential rotation approaches the Proudman state when stellar rotation is faster than solar rotation. (, Our conclusions are as follows: (1) Differential rotation approaches the Taylor-Proudman state when stellar rotation is faster than solar rotation. ( +2) Entropy gradient generated by the attached subadiabatie laver beneath the convection zone becomes relatively small with a large stellar angular velocity. (,2) Entropy gradient generated by the attached subadiabatic layer beneath the convection zone becomes relatively small with a large stellar angular velocity. ( +3) Turbulent. viscosity and turbulent angular momentum transport determine the spatial difference of angular velocity AQ. (,3) Turbulent viscosity and turbulent angular momentum transport determine the spatial difference of angular velocity $\Delta\Omega$. ( +4) The results of our mean field model can explain observations οἱ stellar differential Our [future work will focus on the stellar MIID dynamo.,4) The results of our mean field model can explain observations of stellar differential Our future work will focus on the stellar MHD dynamo. + Several investigations have been conducted on the stellar dnamo using a kinematic diamo framework (Dikpatietal.Charbonnean&Saar2001:MossSokoloff2009:Jouveetal. 2010)..," Several investigations have been conducted on the stellar dynamo using a kinematic dynamo framework \citep{2001ASPC..248..235D,2001ASPC..248..189C,2009A&A...497..829M,2010A&A...509A..32J}." + Since. under such a framework. only the magnetic induction equation is solved using a given. velocity lied. solving a linear equation. such analvsis does not give sufficient information on the strength of the dvnamo-generated stellar magnetic field.," Since, under such a framework, only the magnetic induction equation is solved using a given velocity field, solving a linear equation, such analysis does not give sufficient information on the strength of the dynamo-generated stellar magnetic field." + To obtain the full aanplitude of the stellar magnetic field. the feedback to the velocity [iekd is required. ie.. an MIID Iramework.," To obtain the full amplitude of the stellar magnetic field, the feedback to the velocity field is required, i.e., an MHD framework." + Adopting a similar approach to Rempel(2006).. we can use the results of this paper to investigate the strength of the stellar magnetic field.," Adopting a similar approach to \cite{2006ApJ...647..662R}, we can use the results of this paper to investigate the strength of the stellar magnetic field." + Recent observations of the strength ol the magnetic field generated by stellar differential rotation have been conducted using, Recent observations of the strength of the magnetic field generated by stellar differential rotation have been conducted using +The mniportauce of the ionizing background on he eas dvuanües and hence the star-formation history of ealaxies has loug been recognized 1992).. and studied both uunercallv and seimiaualvticallv 20023... (,"The importance of the ionizing background on the gas dynamics and hence the star-formation history of galaxies has long been recognized , and studied both numerically and semianalytically . (" +Ini this paper we take “ionizing backeround” to refer to both he heating aud IL/IIe ionization effects of the 13.6 eV - 10) keV portion of the external radiation field experienc4(i bv galaxies at variois epochs: ie. the energies whic1 can ionize IT aud other species but have a large οποιοo1 cross-section to sieuilBcantle affect the gas properties.),"In this paper we take “ionizing background” to refer to both the heating and H/He ionization effects of the 13.6 eV - 100 keV portion of the external radiation field experienced by galaxies at various epochs; i.e., the energies which can ionize H and other species but have a large enough cross-section to significantly affect the gas properties.)" + ILowever. although the ivdrodynuannic simulation ot ealaxies has become someπιο of a cottage industry 1 recent vcars (see for a review wit1 special focus on disk 8ealaxies). relatively little atteutio1 has been paid to the 'Orni of ionizing background which js used.," However, although the hydrodynamic simulation of galaxies has become something of a cottage industry in recent years (see for a review with special focus on disk galaxies), relatively little attention has been paid to the form of ionizing background which is used." + The default optio1 (seen receutlv in aud 2008.. among others) ls generalv à version of t1ο UV. background of (1996).," The default option (seen recently in and , among others) is generally a version of the UV background of ." +. Those authors modeled the QSO ckerouvl and the effects of reprocessing by Lwa orest clouds., Those authors modeled the QSO background and the effects of reprocessing by $\alpha$ forest clouds. +" They fit the redslüft «ependence of the II photoionization rate with a generalized Gaussian of the orm (1SEexp|(22,7?SI: for their parameters (B=0.73. 2.=2: S$=1.9 in the original paper). he intensity declines steeply above :=3 and the ckeround is negligible bevoud +=7."," They fit the redshift dependence of the H photoionization rate with a generalized Gaussian of the form $(1+z)^B \exp{[-(z-z_c)^2/S]}$; for their parameters $B=0.73$, $z_c=2.3$, $S=1.9$ in the original paper), the intensity declines steeply above $z=3$ and the background is negligible beyond $z=7$." + There is. however. a history of simulations using jonizing backgrounds with a less steep redshift dependence.," There is, however, a history of simulations using ionizing backgrounds with a less steep redshift dependence." + is one such exaniple: they performed |P SPII particle siiulatious resampled from a larger P?N I simulation. together with a UV backeround that was costant at hieh redshitt.," is one such example: they performed $40^3$ SPH particle simulations resampled from a larger $^3$ M simulation, together with a UV background that was constant at high redshift." + They found that the final amouut of cooled gas was reduced by up to half. with lIate-accreted gas preferentially affected. conrpared to no backgrounm.," They found that the final amount of cooled gas was reduced by up to half, with late-accreted gas preferentially affected, compared to no background." + Moreover. recent evidence such as the independent obscyvatious of the optical depth to electron scattering and the Lyman alpha Canu-Peterson trough have put increasingly tight constraints on fιοrejonization history of the universe.," Moreover, recent evidence such as the independent observations of the optical depth to electron scattering and the Lyman alpha Gunn-Peterson trough have put increasingly tight constraints on thereionization history of the universe." + Iu particular. exiuuine the Lye effective opical depth using 856 quasar spectra. aud fiud an esseutiallv flat ionization rate o1 tto:L2 (see Fie.," In particular, examine the $\alpha$ effective optical depth using 86 quasar spectra, and find an essentially flat ionization rate out to $z=4.2$ (see Fig." + 1 aud the «ISCUSSIOM nu 822.1]g22 below): these authors have thus proposed a new UV backegrouud. described in2009).. which we investigate here.(," \ref{fig:spectra} and the discussion in 2.1 below); these authors have thus proposed a new UV background, described in, which we investigate here.," +2009)... using 1733 quasars from SDSS. similarly fud a flat ionization rate for 2<12. albeit with a shehtly different normalization.," using 1733 quasars from SDSS, similarly find a flat ionization rate for $2AL.)z2004,/10*MN).8 for 106M_{\rm g})\approx +20(M_{\rm g}/10^7 \, \rm M_{\odot})^{-0.7}$ for $10^610°AT, is ~HO100."," The predicted number of dark clouds with $M_{\rm g}>10^6 \, \rm +M_{\odot}$ is $\sim 50-100$." + À fraction of the observed CIIVCs can thus be associated with the simall-miass DAL halos., A fraction of the observed CHVCs can thus be associated with the small-mass DM halos. + Within central 50 Ipc. however. the umuuber of halos with such σας nminsses is only ~2.5.," Within central $50$ kpc, however, the number of halos with such gas masses is only $\sim 2-5$." + We cannot therefore explain 25 CTIVCs observed by within this radius around M31., We cannot therefore explain 25 CHVCs observed by within this radius around M31. + It is possible that sinulatious underpredict the number of stuall-inass halos due to overmereime., It is possible that simulations underpredict the number of small-mass halos due to overmerging. + To check this will require hieher-+vesolution sinulatious., To check this will require higher-resolution simulations. + Ou the other liaud. we did not take iuto account processes such as rani pressure stripping. which would further reduce the umber of halos with eas.," On the other hand, we did not take into account processes such as ram pressure stripping, which would further reduce the number of halos with gas." + Another possibilitv is that most of the observed M31: CTIWCs are gas clouds in tidal streams. such as the AMaecllanic Stream. and are uot associated with distinct dark matter halos(?).," Another possibility is that most of the observed M31 CHVCs are gas clouds in tidal streams, such as the Magellanic Stream, and are not associated with distinct dark matter halos." +. Possible astroplivsical solutions to the “missing satellite problem” have been cousidered in the last several vears., Possible astrophysical solutions to the “missing satellite problem” have been considered in the last several years. + Tere we discuss the main differences of our wnodel aud the models proposed in previous studies.T," Here we discuss the main differences of our model and the models proposed in previous studies.," +S72S and discussed the formation aud evolution of chwart galactic satellites using scii-analytic models of different deerees of sophistication., and discussed the formation and evolution of dwarf galactic satellites using semi-analytic models of different degrees of sophistication. +" The conclusion reached by all these studies is that the extragalactic UV background can ercatly suppress the eas accretion and star formation in the majority of low-nass (Vi,30kins +) halos."," The conclusion reached by all these studies is that the extragalactic UV background can greatly suppress the gas accretion and star formation in the majority of low-mass $V_{\rm m}\lesssim +30\ \rm km\,s^{-1}$ ) halos." +" A siuall fraction of the dwarf halos that harbors stellar svstemis was απο, to lave formed (es assembled VAsiguificaut fraction of their mass) before reionization. when the level of UV radiajon was low."," A small fraction of the dwarf halos that harbors stellar systems was assumed to have formed (i.e., assembled significant fraction of their mass) before reionization, when the level of UV radiation was low." + Tus is because i all of these studies the naxiuuni circuar velocity of siDhalos was asstumedl to )0 constant as he mass ds ticalvy stripped., This is because in all of these studies the maximum circular velocity of subhalos was assumed to be constant as the mass is tidally stripped. + There was thus a simple ouc-to-one mapping between the circular velocity observed at 2=0 and at the time of accretion., There was thus a simple one-to-one mapping between the circular velocity observed at $z=0$ and at the time of accretion. +" Our results show that this assumption is incorrect??),.", Our results show that this assumption is incorrect. + Another kev difference is that tidal mass loss in our model can occur before a halo is accreted by the host. as a result of interactions with other halos.," Another key difference is that tidal mass loss in our model can occur before a halo is accreted by the host, as a result of interactions with other halos." + These effects are not accounted for im auv of the seimi-aualvtic nodels., These effects are not accounted for in any of the semi-analytic models. + The implicit assuuiption in the above models is that the μα] systems would be able to retain the accreted eas aud orn stars after reionization., The implicit assumption in the above models is that the small systems would be able to retain the accreted gas and form stars after reionization. +" This assuuiption was justified at the time. as the first calculations of photoevaporation of eas indicated that halos with Vi,210kms| might retain heir eas(?7)."," This assumption was justified at the time, as the first calculations of photoevaporation of gas indicated that halos with $V_{\rm m}\gtrsim 10\rm\ km\,s^{-1}$ might retain their gas." +. More recent caleulations. however. show that he eas could be gradually removed frou: halos of up to ΈτοςmBOlaus1(?)..," More recent calculations, however, show that the gas could be gradually removed from halos of up to $V_{\rm +max}\approx 30\rm\ km\,s^{-1}$." + In Πο of this result. the previous uodels would not be able to explain the formation aud xoperties of huninous dwarfs. as the star formation in small halos would be suppressed after reionization.," In light of this result, the previous models would not be able to explain the formation and properties of luminous dwarfs, as the star formation in small halos would be suppressed after reionization." + It would lius be difficult to explain the more exteuded star formation ustorics derived for many dSph galaxies in the Local Caroup(7)., It would thus be difficult to explain the more extended star formation histories derived for many dSph galaxies in the Local Group. + Iu our model. the sinallinass dwarts are identified wit[um he halos that were relatively massive at lLieh redshift aud could retain the eas and form stars after reionization.," In our model, the small-mass dwarfs are identified with the halos that were relatively massive at high redshift and could retain the gas and form stars after reionization." + The star formation histories of dwarfs are thus more extended. iu better accord with observations.," The star formation histories of dwarfs are thus more extended, in better accord with observations." + As noted in the previous section. our niodoel is also insensitive to the epoch of reionization and can acconmnodate early reionization suggested by results of the satellite(?).," As noted in the previous section, our model is also insensitive to the epoch of reionization and can accommodate early reionization suggested by results of the satellite." +. Our model and all of the models discussed above are qualitatively differcut from the proposal of??., Our model and all of the models discussed above are qualitatively different from the proposal of. +. These authors argued that the masximaun circular velocity of the Local Group dwarts may be svstematically underestimated because it is derived from the stellar velocity dispersion witlin radii considerably smaller than myax. the radius at which the mania halo velocity. τμ is reached?).," These authors argued that the maximum circular velocity of the Local Group dwarfs may be systematically underestimated because it is derived from the stellar velocity dispersion within radii considerably smaller than $r_{\rm max}$, the radius at which the maximum halo velocity, $V_{\rm m}$ is reached." +.ü2suggestedthatthe., suggested that the luminous dwarfs may be harbored by the most massive satellites of the DM halos. + ifthedwarfsindecdoccupytwclecorsomostinass/ echalos," This has an important physical implication: if the dwarfs indeed occupy twelve or so most massive halos, then there exists a certain mass scale below which galaxy formation is completely suppressed." +",thenthere AL... one has to explain why some fraction of inall halos managed to light wp the stars. while most others did not."," If, on the other hand, the dwarf galaxies occupy satellites with a variety of masses $\sim 10^7-10^{10}\ \rm +M_{\odot}$ ), one has to explain why some fraction of small halos managed to light up the stars, while most others did not." + If the idea of is correct. our results indicate that circular velocities of davarf spheroidal halos should have been even larger (bv a factor of two or more) than the values interred from the current observations.," If the idea of is correct, our results indicate that circular velocities of dwarf spheroidal halos should have been even larger (by a factor of two or more) than the values inferred from the current observations." + This could make halos of some galaxies uncomfortably massive., This could make halos of some galaxies uncomfortably massive. + For example. derive the maxinnun circular velocity for the Draco in the range 35.SSdans+.," For example, derive the maximum circular velocity for the Draco in the range $\sim 35-55\rm\ +km\,s^{-1}$." + This plies the pre-aceretion values of Via2TOkus+ and the pre-accvetion niass coniparable to those of M32. NCC 205. and NE.," This implies the pre-accretion values of $V_{\rm +max}\gtrsim 70\rm\ km\,s^{-1}$ and the pre-accretion mass comparable to those of M32, NGC 205, and M33." + The fact that Wuuinosity of Draco is aliiost four orders of magnitude lower than Iuninosities of these galaxies woul preseut a major puzzle., The fact that luminosity of Draco is almost four orders of magnitude lower than luminosities of these galaxies would present a major puzzle. + Iu addition. the radial distribution of the most massive satellites should be consistent with the observed radia distribution of the MW satellites.," In addition, the radial distribution of the most massive satellites should be consistent with the observed radial distribution of the MW satellites." + We fud that iu our simulatious the radial distribution of subhalos with largest Vaids between that of the Iuniuous satelites aud all DA sateites shown iu Figure 8.., We find that in our simulations the radial distribution of subhalos with largest $V_{\rm m}$ is between that of the luminous satellites and all DM satellites shown in Figure \ref{fig:rdlg}. + Ina study « ta larger sample of cluster halos. find that the radial «istribution of the os lassive lalos is even more extender than that of the snaer nass objects.," In a study of a larger sample of cluster halos, find that the radial distribution of the most massive halos is even more extended than that of the smaller mass objects." + A similar point was mace recently by7. who used seii-aualvtic nodels for s1yhalo population tosrow that the radial distribution of he most massive halo sds more extended than that of the ATW satellites at &Ὢσ level.," A similar point was made recently by, who used semi-analytic models for subhalo population to show that the radial distribution of the most massive halos is more extended than that of the MW satellites at $\gtrsim 3\sigma$ level." + A caveat to this argument is tratthe sample of ADlkv Way satellites may be incomplete at large distances and amore faint dwarf galaxies will be discovered iu the, A caveat to this argument is thatthe sample of Milky Way satellites may be incomplete at large distances and more faint dwarf galaxies will be discovered in the +nucro-plivsics has not included into hvdrodsnamic simulations. the study to the behaviors ol species by using multi-I[Iuid models may be worthwhile.,"micro-physics has not included into hydrodynamic simulations, the study to the behaviors of species by using multi-fluid models may be worthwhile." + With consideration of the process radiative transfer. this paper aims (o caleulate planetarv atomic hydrogen ancl proton loss rates through the solution to their mass. momentum and energy equations.," With consideration of the process radiative transfer, this paper aims to calculate planetary atomic hydrogen and proton loss rates through the solution to their mass, momentum and energy equations." + A great deal of microscopic physics processes are covered in (he mass and momentum equations (Section 2.1)., A great deal of microscopic physics processes are covered in the mass and momentum equations (Section 2.1). + The code is designed for ordinary equations wilh one or more critical points (Section 2.2)., The code is designed for ordinary equations with one or more critical points (Section 2.2). + We use Henvey method to calculate these equations (Section 2.4)., We use Henyey method to calculate these equations (Section 2.4). + The results are presented in Section 3., The results are presented in Section 3. + OL especial interest are what makes atomic IIvdrogen and proton decoupling (Section 4.1)?, Of especial interest are what makes atomic Hydrogen and proton decoupling (Section 4.1)? + In Section 4.2 we discuss the properties of ionized wind and fit (he mass loss rate as a function of UV flux., In Section 4.2 we discuss the properties of ionized wind and fit the mass loss rate as a function of UV flux. + We summarize mv results in Section.5 The model describes (he steady state. radial expansion of plasma containing three species: atomic hvdrogen (h). proton (p) and electron (e).," We summarize my results in Section.5 The model describes the steady state, radial expansion of plasma containing three species: atomic hydrogen (h), proton (p) and electron (e)." + Each species has its own continuitv and momentum equations and is described bv a particle density nm. and velocity us., Each species has its own continuity and momentum equations and is described by a particle density $n_{s}$ and velocity $u_{s}$. + l do not include ffs in this model because the thermosphere of close-in planet should be composed primarily of H1 and Jf., I do not include $H_{2}$ in this model because the thermosphere of close-in planet should be composed primarily of H and $H^{+}$. + The location of transition from ο to IH is about at Lip (Yelle 2004)., The location of transition from $H_{2}$ to H is about at $R_{P}$ (Yelle 2004). +" In addition. with the assumption of T;=T,T;. only one energy equation for electron is given in (he calculations."," In addition, with the assumption of $T_{h}=T_{p}=T_{e}$, only one energy equation for electron is given in the calculations." + As this model deals with a mixture of atomic hydrogen and. proton. the following processes are considered: photoionization. recombination ancl charge exchange.," As this model deals with a mixture of atomic hydrogen and proton, the following processes are considered: photoionization, recombination and charge exchange." + The most, The most +insights for Figure 5 and the editor for additional comments.,insights for Figure 5 and the editor for additional comments. + KW acknowledges the support of an ARC Australian Research Fellowship and a PPARC visiting fellowship., KW acknowledges the support of an ARC Australian Research Fellowship and a PPARC visiting fellowship. + Consider a power series where The series is convergent for c«L1 if the ratio of thecoefficients JC1|/]C5|€1 for sullicientIy large n., Consider a power series where The series is convergent for $x <1$ if the ratio of thecoefficients $|C_{n+1}|/|C_{n}| \leq 1$ for sufficiently large $n$. + As the convergent radius of f(r)is infinite., As the convergent radius of $f(x)$is infinite. + Moreover. for p20 Llence. τω&1 for àol.," Moreover, for $x>0$ Hence, $|f(x)| < 1$ for $x \rightarrow 0^{^+}$." +" For the ""Ieaky aceretion column with a specific mass Flux ao=p(le 779). where jp=(1οὁTey the accretion luminosity is"," For the “leaky” accretion column with a specific mass flux $\sigma = \mu (1-e^{-\tau/\tau_{\rm m}})$ , where $\mu = (1-e^{-1/4\tau_{\rm m}})^{-1}$ , the accretion luminosity is" +of ~1590%.,of $\sim 15-90\%$. + Therefore. since galaxies with outer rings have presumably had: no tidal interactions in the past (see above). present AGN activity (which lasts [ow PMs) is very unlikelyexception to be due to interactions (NGC but2685 is the possible since it has an outer ring is also cross-classilicd as peculiar).," Therefore, since galaxies with outer rings have presumably had no tidal interactions in the past $\sim$ Gyr (see above), present AGN activity (which lasts few $\times$ 10Myrs) is very unlikely to be due to interactions (NGC 2685 is the possible exception since it has an outer ring but is also cross-classified as peculiar)." + Furthermore. if tical interactions generated the activity observed in our control group (no rings. < TOALpe). it is indistinguishable rom activity due to secular processes.," Furthermore, if tidal interactions generated the activity observed in our control group (no rings, $<70$ Mpc), it is indistinguishable from activity due to secular processes." + Note that we can conclude the same thing from the Group 1 AGN hack in Fig. 2..," Note that we can conclude the same thing from the Group 1 AGN back in Fig. \ref{fig:mass1}," + where AGN in. clisk-clominatecl anc (presumably idallv) disrupted hosts have a very. similar spread. in Lys and Lx., where AGN in disk-dominated and (presumably tidally) disrupted hosts have a very similar spread in $L_{IR}$ and $L_{X}$. + Phe RS and T-statistic tests on AGN at «TOALpe also reveal no significant dillerence in Mpgg between those rost galaxies with and without outer rings (RORY). when we take into account uncertainty in the mass estimates.," The RS and T-statistic tests on AGN at $<70$ Mpc also reveal no significant difference in $M_{BH}$ between those host galaxies with and without outer rings $^{\prime}$ ), when we take into account uncertainty in the mass estimates." + Therefore it seems likely that the ACN in our sample have αι. approximately their present AMgg for a long time as MMu recen aloes (c.g. Wormendy&Ixenni-(2006):HMetal.," Therefore it seems likely that the AGN in our sample have had approximately their present $M_{BH}$ for a long time as suggested by recent simulations (e.g. \citet{b24,b43,b42,b41}) )." +"{"" eIf MRtidal interactions are not the main driver of AUN in our saniple. this suggests a number of possible explanations."," If tidal interactions are not the main driver of AGN activity in our sample, this suggests a number of possible explanations." +" The most likely explanation is that the timescale for activity driven hy processes internal to the galaxy (/;,;) is much smaller than the timescale for activity driven by processes external to the ealaxy (F4). or bingmLua."," The most likely explanation is that the timescale for activity driven by processes internal to the galaxy $t_{int}$ ) is much smaller than the timescale for activity driven by processes external to the galaxy $t_{ext}$ ), or $t_{int}\ll t_{ext}$." + dM is easy to see that estimates of rapid. bar dissolution times ancl galaxy rotation speeds (Bagleyetal.2009) are much shorter than the expected dynamical timescales of tidal interactions., It is easy to see that estimates of rapid bar dissolution times and galaxy rotation speeds \citep{b73} are much shorter than the expected dynamical timescales of tidal interactions. + For mgalaxies in the WAS sample within TOALpe.1 outer ring structures (not collisional) are found in only ~104 (48/479) of normal 5galaxies. but are much more common in Sevlert AGN host galaxies(19/57) (Hunt.&Malkan1999," For galaxies in the IRAS sample within 70Mpc, outer ring structures (not collisional) are found in only $\sim 10\%$ (48/479) of normal galaxies, but are much more common in Seyfert AGN host galaxies (19/57) \citep{b10}." +) An intruiging possibility is that tidal interactions actually disrupt the action of bars so that both ring formation and AGN activity are inhibited. which would be consistent with conclusions from recent optical ancl N-ray studies of ACN (Alartinezetal20)Os:Arnoldal.," An intruiging possibility is that tidal interactions actually disrupt the action of bars so that both ring formation and AGN activity are inhibited, which would be consistent with conclusions from recent optical and X-ray studies of AGN \citep{b92,b75}." +2009)... A simple test of this hypothesis is that the occurrence of AGN in recently disrupted barred. spiral hosts should. be lower than the occurrence of AGN among all barred spiral hosts., A simple test of this hypothesis is that the occurrence of AGN in recently disrupted barred spiral hosts should be lower than the occurrence of AGN among all barred spiral hosts. + We shall return to this hypothesis in future work., We shall return to this hypothesis in future work. + In Melxernanetal.(2009) we discussed biases in our sample and our results. particularly with reference to the all-sky IRAS (12-100pum) and. soft. X-ray (ROSAT) surveys.," In \citet{b99} we discussed biases in our sample and our results, particularly with reference to the all-sky IRAS $\micron$ ) and soft X-ray (ROSAT) surveys." + We pointed out that in a heterogeneous sample such as ours. there are many biases. generally in favour of more luminous. local AGN. and against less luminous. more distant AGN.," We pointed out that in a heterogeneous sample such as ours, there are many biases, generally in favour of more luminous, local AGN, and against less luminous, more distant AGN." + Lere we briefly review some of the more important. biases. but see cello(2008) for warnings about heterogeneous samples of AGN in general and. Melxernanetal.(2009). for more detailed discussion of most of the present. sample.," Here we briefly review some of the more important biases, but see \citet{b95} for warnings about heterogeneous samples of AGN in general and \citet{b99} for more detailed discussion of most of the present sample." + On one hand. since we consider the reported observed AGN luminosity. we are biased against hiehly obscured AGN (particularly at ninoslarger distances).," On one hand, since we consider the reported observed AGN luminosity, we are biased against highly obscured AGN (particularly at larger distances)." + We also introduce error into estimates. since non-MGN host ealaxy contributions to the luminosity are included. in the observed. luminosity in most cases.," We also introduce error into luminosity estimates, since non-AGN host galaxy contributions to the luminosity are included in the observed luminosity in most cases." + (X further error in luminosity estimates is introduced since internal and Galactic absorption corrections are. not svsteniaticalA reported for all sources., A further error in luminosity estimates is introduced since internal and Galactic absorption corrections are not systematically reported for all sources. + On the other hand. an advantage of using observed. luminosity is that we avoid. assumptions about the central engine. of AGN in order to. estimate the intrinsic ACN) luminosity.," On the other hand, an advantage of using observed luminosity is that we avoid assumptions about the central engine of AGN in order to estimate the intrinsic AGN luminosity." + Furthermore. all but. the highest. resolution observations of the closest AGI include non-AGN contributions.," Furthermore, all but the highest resolution observations of the closest AGN include non-AGN contributions." + By using. the observed αν luminosity. we avoid the dillicult. (and. mocdel-dependent) problem. of de-coupling the non-AGN contribution (which may be significant in many lower-Iuminosity AGN in our sample).," By using the observed AGN luminosity, we avoid the difficult (and model-dependent) problem of de-coupling the non-AGN contribution (which may be significant in many lower-luminosity AGN in our sample)." + So. all our Luminosity estimates include a non-AG component of variable size.," So, all our luminosity estimates include a non-AGN component of variable size." + For example. in the N-ray. band. the non-AGN component may consist of hot. clilluse gas. ray binaries or ULXs in the host galaxy.," For example, in the X-ray band, the non-AGN component may consist of hot, diffuse gas, X-ray binaries or ULXs in the host galaxy." + In the Ht band. the non-AGN component may consist of star-forming regions or warm dust in the host galaxy.," In the IR band, the non-AGN component may consist of star-forming regions or warm dust in the host galaxy." + Our heterogeneous sample also introduces an obvious observation bias: many AGN have been observed. in. the 2-10keV. X-rav. band. but were not seen with LRAS(or at least had upper limits)., Our heterogeneous sample also introduces an obvious observation bias; many AGN have been observed in the 2-10keV X-ray band but were not seen with IRAS (or at least had upper limits). + Likewise. some ItXS-cdetected AGN have not been observed in the 2-IOkeV band (or only have upper limits).," Likewise, some IRAS-detected AGN have not been observed in the 2-10keV band (or only have upper limits)." + None of these AGN have been included. in, None of these AGN have been included in +eravitatioually to make a prestellar core before it re-expauds.,gravitationally to make a prestellar core before it re-expands. + For both the traditional picture of supercritical core ormation and the scenario we propose. the magnetic fied remalus relatively stationary while tle ueutrals move inward. within the biel density regious.," For both the traditional picture of supercritical core formation and the scenario we propose, the magnetic field remains relatively stationary while the neutrals move inward, within the high density regions." + For the traditioual pictire. the iuward wettral inotions are cue to sinall-scale within the core.," For the traditional picture, the inward neutral motions are due to small-scale self-gravity within the core." + For shock-incducecl core formation. the inward motious of neutrals owes to large-scale couvergiug supe‘sonic flows within GMCSs (whicl may ultimately be driven by large-scale sell-gravity withiu the cloud).," For shock-induced core formation, the inward motions of neutrals owes to large-scale converging supersonic flows within GMCs (which may ultimately be driven by large-scale self-gravity within the cloud)." + Transient ambipolar cliffusio is paricularly importa because without it. post-shock regions in GMCs ypleally have very sinall iiass-o-imagnetic [ux ratios.," Transient ambipolar diffusion is particularly important because without it, post-shock regions in GMCs typically have very small mass-to-magnetic flux ratios." + Thus. the regious with the shortest gravitatioal timescales (at. high density. ¢ue to shocks) would be prevented from collapsing by magnetic fields. which are also eiiauced by shocks.," Thus, the regions with the shortest gravitational timescales (at high density, due to shocks) would be prevented from collapsing by magnetic fields, which are also enhanced by shocks." + Our utuuerical simulations show a peak in the uiass-to-Iux ratio. produced by transient aibipolar diffusiyn.," Our numerical simulations show a peak in the mass-to-flux ratio, produced by transient ambipolar diffusion." + For strong shocks (egΌλο sullicient) and low encieli ionization [fractioL. OUL resits suggest that supercritical cores car be produced.," For strong shocks $v_0/v_{\mathrm{A},0}$ sufficient) and low enough ionization fraction, our results suggest that supercritical cores can be produced." + Based ou our simulation resilts and aialvses. our nain conclusions are as folOWS?," Based on our simulation results and analyses, our main conclusions are as follows:" +Massive star lormation in the Milkv. Way and in external galaxies takes place in a wide range of circumstances.,Massive star formation in the Milky Way and in external galaxies takes place in a wide range of circumstances. + In (he current Universe. perhaps (he most extreme star formation lakes place in “Super Star Clusters” (55Cs). which mav be the forerunners of globular clusters (e.g.. Whitmore 2002).," In the current Universe, perhaps the most extreme star formation takes place in “Super Star Clusters” (SSCs), which may be the forerunners of globular clusters (e.g., Whitmore 2002)." + Individual SSCs may have ionizing fluxes equal to Chat of 10° to 10! OT-equivalent stars within diameters of just a few parsecs (Whilmoreetal.Turneretal.2000:Johnson&Nobulnicky2003:Beck 2004).," Individual SSCs may have ionizing fluxes equal to that of $10^3$ to $10^4$ O7-equivalent stars within diameters of just a few parsecs \citep{whi99,tur00,joh03,tur04}." +. The initial mass functions in SSCs have been reported to be top-heavy: however. studies of initial mass functions are affected by crowcling in the fields ancl mass segregation in clusters 2005).," The initial mass functions in SSCs have been reported to be top-heavy; however, studies of initial mass functions are affected by crowding in the fields and mass segregation in clusters \citep{whi02,elm05}." +. Therefore. the total masses of SSCs may be uneertain by an order of magnitude. but it appears that at least some SSC's have total masses of 10211. to LOYAL..," Therefore, the total masses of SSCs may be uncertain by an order of magnitude, but it appears that at least some SSCs have total masses of $10^5M_\odot$ to $10^6M_\odot$." + If they are in Woll-Ravet. galaxies. such as (he galaxies (hat are the subjects of this paper. the SSC's may form most of their mass into stars on a lime scale of 5x10° vr 1992)..," If they are in Wolf-Rayet galaxies, such as the galaxies that are the subjects of this paper, the SSCs may form most of their mass into stars on a time scale of $\times 10^6$ yr \citep{kru92}." + Thus their star formation rates per unit area may be above 102M. | 7. or 10M. ! 7. a factor of at least 1000 higher than the average value in larger-area starbursts (ILeckman2005).," Thus their star formation rates per unit area may be above $10^{-2}M_\odot$ $^{-1}$ $^{-2}$, or $10^{4}M_\odot$ $^{-1}$ $^{-2}$, a factor of at least 1000 higher than the average value in larger-area starbursts \citep{hec05}." +. There are a variety of means of estimating the stellar content. star formation rate. or supernova rale in starbursis.," There are a variety of means of estimating the stellar content, star formation rate, or supernova rate in starbursts." + For example. one may count ionizing photons by measuring ihe Πα luminosity in a starburst galaxy or an SSC.," For example, one may count ionizing photons by measuring the $\alpha$ luminosity in a starburst galaxy or an SSC." + IIowever. such a method may greatly underestimate the number of ionizing photons. if the SSC is heavily obseured by dust.," However, such a method may greatly underestimate the number of ionizing photons, if the SSC is heavily obscured by dust." + A more reliable method of counting ionizing photons may be from the study. of thermal radio emission. although this also may be subject to Iree-[ree absorption. leakage through a porous interstellar medium. or absorption of ionizing photons by dust.," A more reliable method of counting ionizing photons may be from the study of thermal radio emission, although this also may be subject to free-free absorption, leakage through a porous interstellar medium, or absorption of ionizing photons by dust." + Mid-inlrared imaging also may measure the total energv output in an SSC. although Che resolution of such imaging often is not adequate to isolate individual SSCs.," Mid-infrared imaging also may measure the total energy output in an SSC, although the resolution of such imaging often is not adequate to isolate individual SSCs." + Globally. either Eu-infrared or radio powers of galaxies may sullice to estimate (heir total star-formation rate (Condon1992 )..," Globally, either far-infrared or radio powers of galaxies may suffice to estimate their total star-formation rate \citep{con92}, ," +The positions of the sources in our VLBA images were determined using a two-dimensional Gaussian fitting procedure (task JMFIT in AIPS) and are given in 11.,The positions of the sources in our VLBA images were determined using a two-dimensional Gaussian fitting procedure (task JMFIT in AIPS) and are given in 1. + JMFIT provides an estimate of the position error based on the expected theoretical astrometric precision of an interferometer (Condon 1997); these errors are quoted in columns 4 and 6 of 11., JMFIT provides an estimate of the position error based on the expected theoretical astrometric precision of an interferometer (Condon 1997); these errors are quoted in columns 4 and 6 of 1. +" To obtain the astrometric parameters [rom these data, we used the SVD-decomposition fitting scheme described by Loinard et (02007)."," To obtain the astrometric parameters from these data, we used the SVD–decomposition fitting scheme described by Loinard et (2007)." +" The necessary barycentric coordinates of the Earth, as well as the Julian date of each observation, were calculated using the Interactive Computer Almanac (MICA) distributed as a CD ROM by the US Naval Observatory."," The necessary barycentric coordinates of the Earth, as well as the Julian date of each observation, were calculated using the Multi-year Interactive Computer Almanac (MICA) distributed as a CD ROM by the US Naval Observatory." + The reference epoch was taken at the mean of our observations: JD 2454765.98 = J2008.90., The reference epoch was taken at the mean of our observations: JD 2454765.98 $\equiv$ J2008.90. +" Since EC 95a is only detected three times, it would be very hazardous to fit the observed positions with a combination of parallax and proper motions."," Since EC 95a is only detected three times, it would be very hazardous to fit the observed positions with a combination of parallax and proper motions." +" Thus, we will concentrate here on the EC 95b component."," Thus, we will concentrate here on the EC 95b component." + Two fits were performed., Two fits were performed. +" In the first one, we assumed a linear and uniform proper motion."," In the first one, we assumed a linear and uniform proper motion." +" The best fit under this assumpton is shown on the left panel of 44, and yields the following astrometric elements: The corresponding⋅ distance⋅ is⋅ !i»ANONpc."," The best fit under this assumption is shown on the left panel of 4, and yields the following astrometric elements: The corresponding distance is $^{+38.8}_{-32.9}$." +" Note, however, that the post-fit5 rms are somewhat large: 0.28 and 0.21 in right ascension and declination, respectively."," Note, however, that the post-fit rms are somewhat large: 0.28 and 0.21 in right ascension and declination, respectively." +" Indeed, 44 shows that the observed positions often do not coincide with the positions expected [rom the best fit."," Indeed, 4 shows that the observed positions often do not coincide with the positions expected from the best fit." +" We saw earlier that two sources are detected in our VLBA images, and that those sources are likely to trace two associated active stars."," We saw earlier that two sources are detected in our VLBA images, and that those sources are likely to trace two associated active stars." +" Under these circumstances, it is to be expected that they will be in gravitational interaction, and that their motions will be accelerated rather than uniform,"," Under these circumstances, it is to be expected that they will be in gravitational interaction, and that their motions will be accelerated rather than uniform." +" As a consequence, we performed another fit including a uniform acceleration term (similar to that included in the fit to the T Tau data; see Loinard et 22007)."," As a consequence, we performed another fit including a uniform acceleration term (similar to that included in the fit to the T Tau data; see Loinard et 2007)." +" This fit is shown on the right panel of 44, and yields the following parameters:"," This fit is shown on the right panel of 4, and yields the following parameters:" +Since the pioneeriug work of Black&Dalgarno(10ΤΤ).. observations of diffuse iuolecular clouds continue to motivate aud «Lhalleuge efforts to model the thermal balance and cljienudstrv of interstellar eas dliunnmated by UV photons.,"Since the pioneering work of \cite{BD77}, observations of diffuse molecular clouds continue to motivate and challenge efforts to model the thermal balance and chemistry of interstellar gas illuminated by UV photons." + Models allow observers to determine physical coucitious from their data and observations contribute to nrodels by quautifving plysical processes of general relevance to studies of matter in space such as IIo formatioi. photo-clectric heating. aud cosmic ray lonization.," Models allow observers to determine physical conditions from their data and observations contribute to models by quantifying physical processes of general relevance to studies of matter in space such as $_2$ formation, photo-electric heating, and cosmic ray ionization." + Many modes of well characterized lines of sight have been preseuted (c.c.intheastvears:Zsared&Federman2003:LePetietal.2001:Shaw 2006).," Many models of well characterized lines of sight have been presented \citep[e.g. in the last years:][]{Zsargo,LRH,Shaw06}." +. They are successful in reproducing nauv observables apart from sole noecular abundances. most conspicuously CII!. which points to out-of-cquilibrimm chemistry.," They are successful in reproducing many observables apart from some molecular abundances, most conspicuously $^+$, which points to out-of-equilibrium chemistry." + This molecular lon. and several of the molecular species conumnonlv oserved in diffuse molecular clouds such as CTL. ΟΠ aud CO! may be produced by MIID. shocks (Draine&Watz.1986:PineaudesForetsetal.Flower&PineaudesForets. 1998). and small scale vortices (Joilaijietabl.1998:Falearoneal.2006) where Πο is heated bv tie localized. dissipation o: the eas turbulent kiictic energy;," This molecular ion, and several of the molecular species commonly observed in diffuse molecular clouds such as CH, OH and $^+$ may be produced by MHD shocks \citep{DK86,Pineau86,Flower}, and small scale vortices \citep{Joulain98,Falga06} + where $_2$ is heated by the localized dissipation of the gas turbulent kinetic energy." + Turbulent transport betweeu the cold and wari neutra medium iav also siguificautlv nupact the cheuistry of diffuse clouds (Lesaffreeal.. 2007)., Turbulent transport between the cold and warm neutral medium may also significantly impact the chemistry of diffuse clouds \citep{Lesaffre07}. +. Tudepencdent voof eas chemistry. the presence of IT» at higher temperaures than that set by UW and cosuiüc- heating of diffuse molecular clouds. may be probed through observations of the IT» level populations (Ceccli-Pestellinictal.," Independently of gas chemistry, the presence of $_2$ at higher temperatures than that set by UV and cosmic-rays heating of diffuse molecular clouds, may be probed through observations of the $_2$ level populations \citep{CCD}." +. 2006).. A correlation between CIT! aud rotationally excited Is was found by using Copernicus observations., A correlation between $^+$ and rotationally excited $_2$ was found by using Copernicus observations. + Falgaroneetal. reported he detection of the S(O) to S(3) IT» lines -ji a lune of siel towards the immer Culaxyv away frou PAar forming reeius., \cite{Falga05} reported the detection of the S(0) to S(3) $_2$ lines in a line of sight towards the inner Galaxy away from star forming regions. +" They interpret their observation as ""videuce for traces ο[varia molecular eas m the diffuse oeπο mecii.", They interpret their observation as evidence for traces of warm molecular gas in the diffuse interstellar medium. + But the interpretation of the wealth of Ilo. observatious provided bv the FUSE satellite is still a matter o οvate., But the interpretation of the wealth of $_2$ observations provided by the FUSE satellite is still a matter of debate. +" Cayctal.(2002) mcled FUSE IL, observations of three stars i Cliuuacleon using the Meudon Photou Dominated Regions (PDR) 1nodel (LeBourlotetal.1993).", \cite{GBNPHF} modeled FUSE $_2$ observations of three stars in Chamaeleon using the Meudon Photon Dominated Regions (PDR) model \citep{JGED}. +.. Thev show tha the inodel cannot account for Il) column deusjos dn rotational states with J>2., They show that the model cannot account for $_2$ column densities in rotational states with $\rm J>2$. + A lareer sample of Πο FUSE servations (Τὰ1801etal.202:Cull1uolial.2005:Wakker.2t 016)... including 2 of tje 2 Chamacleou ines of sight of Cayetal.(2002).. iwe been analyzed ithe basis of moce calculations preseuted by Browningetal. (2003).," A larger sample of $_2$ FUSE observations \citep{Tumlinson,GillShull05,Wakker06}, including 2 of the 3 Chamaeleon lines of sight of \cite{GBNPHF}, have been analyzed on the basis of model calculations presented by \cite{BTS}." +". Their model. like other PDR models. takes into accouit he formation of IL, o1 gradus. its pjoto-dissociatio1 by absorption of rexrant UV photons. raclative transfer aid vibrational/rotational excitation resulting from colisions. Πω formation aud UV. puuipiug."," Their model, like other PDR models, takes into account the formation of $_2$ on grains, its photo-dissociation by absorption of resonant UV photons, radiative transfer and vibrational/rotational excitation resulting from collisions, $_2$ formation and UV pumping." +" Unlike the latest PDR unodels (ShawetaL.2005:LePetitetaL.2006 i), the Browningoeal.(2003) model does not derive he eas temperature from he thermal valance between ισαιο and cooling Xocesses,"," Unlike the latest PDR models \citep{Shaw05,LNHLR}, the \cite{BTS} model does not derive the gas temperature from the thermal balance between heating and cooling processes." + Browimgetal.(2003) istead consider gas teniperature as a model 21ΠΟΤΟ independent of he deusitv. incident radiation field aud cloud shiclding (total extinction).," \cite{BTS} instead consider gas temperature as a model parameter independent of the density, incident radiation field and cloud shielding (total extinction)." + They conclude vat Πο observations caniof be accounted for with a sinele isotherma slab of eas., They conclude that $_2$ observations cannot be accounted for with a single isothermal slab of gas. + They propose sohtions where ie data are fittd with absorption from two plysically oeidependent gas lavers wih distinct temperatures. UV ---DIunuuationus ancL columm deusities.," They propose solutions where the data are fitted with absorption from two physically independent gas layers with distinct temperatures, UV illuminations and column densities." + A cold (xLOO Ts) ‘Oleιοί conutrjbutes most of the total Ilo column eusitv while a warmer (~200 I&) aud thinner compoveut witha higher UV field helps populate the high J states.," A cold $\le 100\, $ K) component contributes most of the total $_2$ column density while a warmer $\sim 200 \, $ K) and thinner component with a higher UV field helps populate the high J states." + For, For +From this follows that the acceleration. process is favored in those scenarios in which the injection of Alfvénn waves occurs on relatively small scales to start with.,From this follows that the acceleration process is favored in those scenarios in which the injection of Alfvénn waves occurs on relatively small scales to start with. + One injection orocess in which this condition is fulfilled is provided by the so-calledLighthilf mechanism (Ixato 1968: σος Henriksen 1984). which can convert some fraction of the large scale luicl turbulence on the larger scales into Alfvénn waves on smaller scales.," One injection process in which this condition is fulfilled is provided by the so-called mechanism (Kato 1968; Eilek Henriksen 1984), which can convert some fraction of the large scale fluid turbulence on the larger scales into Alfvénn waves on smaller scales." + Following Fujita ct al. (, Following Fujita et al. ( +2003) and Paper L. we assume in our caleulation that [uid turbulence is injected on arge scales. for instance excited by a merger event. and that heLighlhill mechanism couples the fluid. turbulence with MED turbulence on smaller scales.,"2003) and Paper I, we assume in our calculation that fluid turbulence is injected on large scales, for instance excited by a merger event, and that the mechanism couples the fluid turbulence with MHD turbulence on smaller scales." +" We mace the assumption rere that the spectrum of the [uid turbulence (not the MED urbulenee) is in the form of a power law in the range rr,< x_{\rm T}$, $x_{\rm T}$ being the wavenumber at which the transition from large-scale ordered turbulence to small-scale disordered turbulence occurs." + This transition is usually assumed to take place at the Tavlor scale (eéilek Henriksen 1984). hp~LSSRY where the IHevnolds number is eiven by R=laryfi. and my is the kinetic viscosity.," This transition is usually assumed to take place at the Taylor scale (Eilek Henriksen 1984), $l_{\rm T} \sim l_o (15 / {\cal R} )^{1/2}$, where the Reynolds number is given by ${\cal R} =l_o v_{\rm f}/\nu_{\rm K}$, and $\nu_{\rm K}$ is the kinetic viscosity." + The fraction of the Druid turbulence racdiated in the form of MIID modes is small for all but the larger eddies. near the Taylor scale.," The fraction of the fluid turbulence radiated in the form of MHD modes is small for all but the larger eddies, near the Taylor scale." + Therefore theLighihilf radiation may be expected to not. disrupt the fluid. spectrum., Therefore the radiation may be expected to not disrupt the fluid spectrum. + The rate of raciation theLighlhill mechanism into Alfvénn waves of wavenumber A is (Eilek Henriksen 1984: Fujita et αἱ20091 Paper 1]: where p€vy. with £/ the energy density of the ILuid turbulence. and As discussed above. the main new ingredient. added in this paper. compared. with the caleulations presented in. Paper Lis the presence of secondary. electrons (and. positrons). as ecncrated in the hadronic inclastic interactions of cosmic ravs with the thermal gas in the ICM.," The rate of radiation the mechanism into Alfvénn waves of wavenumber $k$ is (Eilek Henriksen 1984; Fujita et al.2003; Paper I): where $\rho \sim {\cal E}_t / v_f^2$, with ${\cal E}_t$ the energy density of the fluid turbulence, and As discussed above, the main new ingredient added in this paper, compared with the calculations presented in Paper I is the presence of secondary electrons (and positrons), as generated in the hadronic inelastic interactions of cosmic rays with the thermal gas in the ICM." +" The decay. chain that we consider is (Blasi Colalrancesco 1999): The spectrum of secondary electrons and positrons with energv £5. is given by the convolution of the spectra of protons. AN(E,). with the spectrum of pions produced. in a single cosmic ray interaction at energy. fy. ο and with the distribution of leptons from the pion clecay. BY(hb). (ο... Aloskalenko Strong. 1998): where στ). is the inclusive cross section for pion production. £7, is the threshold energy. for the process to occur and the distribution of electrons anc positrons is given by where LO(hybyLE.) is the spectrum of clectrons/positrons from the decay of a muon of energy. {νι produced in the decay of a pion with energy. ££."," The decay chain that we consider is (Blasi Colafrancesco 1999): The spectrum of secondary electrons and positrons with energy $E_e$ is given by the convolution of the spectra of protons, $N(E_p)$, with the spectrum of pions produced in a single cosmic ray interaction at energy $E_p$, $F_{\pi} (E_{\pi},E_p)$ ) and with the distribution of leptons from the pion decay, $F_e^{\pm}(E_e,E_{\pi})$, (e.g., Moskalenko Strong, 1998): where $\sigma^{\pm}(E_p)$ is the inclusive cross section for pion production, $E_{tr}$ is the threshold energy for the process to occur and the distribution of electrons and positrons is given by: where $F_e^{\pm}(E_e,E_\mu,E_\pi)$ is the spectrum of electrons/positrons from the decay of a muon of energy $E_\mu$ produced in the decay of a pion with energy $E_\pi$." +" At largefe) values of ££,/ the dillerential cross section is sulliciently well described by the so-called Feynman scaling. with small deviations which can easily be taken into account."," At large values of $E_p$ the differential cross section is sufficiently well described by the so-called Feynman scaling, with small deviations which can easily be taken into account." + In the low energy. part. when the reaction occurs close to 1e threshold. and in general at laboratory energies smaller jun LO GeV. the experimental data on pion production we rather poor. and the scaling behaviour is violated.," In the low energy part, when the reaction occurs close to the threshold, and in general at laboratory energies smaller than $\sim 10$ GeV, the experimental data on pion production are rather poor, and the scaling behaviour is violated." + Since in this paper we are going to caleulate the spectrum. of 16 reaccelerated. secondary electrons ancl positrons. we are orced to use à source term which correctly describes the μα»ectrum of the injected leptons over a broad energy. range (107. 1073.," Since in this paper we are going to calculate the spectrum of the reaccelerated secondary electrons and positrons, we are forced to use a source term which correctly describes the spectrum of the injected leptons over a broad energy range $\gamma \sim 10^2-10^5$ )." + A practical and useful approach to both the ugh energy and low energy regimes was proposed in Dernier (1986a) and reviewed by Moskalenko Strong (1998). and is based on the combination of the isobaric model (Stecker 1970) and scaling. model (Bacdhwar ct al..," A practical and useful approach to both the high energy and low energy regimes was proposed in Dermer (1986a) and reviewed by Moskalenko Strong (1998), and is based on the combination of the isobaric model (Stecker 1970) and scaling model (Badhwar et al.," +. 1977: Stephens Bachwar 1981)., 1977; Stephens Badhwar 1981). + Here we briellv describe the formalism and approximations used in our calculations and provide the main equations., Here we briefly describe the formalism and approximations used in our calculations and provide the main equations. +" In the Stecker's model the pion production due to pp collisions near threshold is mediated by the excitation of the A,H» isobar. which subsequantly decays into a nucleon ancl a pion."," In the Stecker's model the pion production due to $pp$ collisions near threshold is mediated by the excitation of the $\Delta_{3/2}$ isobar, which subsequantly decays into a nucleon and a pion." + In this case the spectrum of pions produced in a, In this case the spectrum of pions produced in a +comm.).,"comm.)," + of which 2 were rejected as outliers (see Fig. 10)).," of which 2 were rejected as outliers (see Fig. \ref{fig:c1calib}) )," + and 16 hot subdwarfs from an updated version of the catalogof ?).., and 16 hot subdwarfs from an updated version of the catalogof \cite{Kilkennyetal:1988}. . + The 16 error of the calibration is 0.15 mmag.," The $1\,\sigma$ error of the calibration is $0.15$ mag." + c; can be used as a gravity indicator for early-type stars. since 1t measures the strength of the Balmer discontinuity.," $c_1$ can be used as a gravity indicator for early-type stars, since it measures the strength of the Balmer discontinuity." + In many stellar applications of the HES. it is not possible to generate large enough training and test samples from spectra present on HES plates.," In many stellar applications of the HES, it is not possible to generate large enough training and test samples from spectra present on HES plates." + This ts because usually the target objects are very rare., This is because usually the target objects are very rare. + Therefore. we have developed methods to generate learning samples by simulations. using either model spectra. or slit spectra.," Therefore, we have developed methods to generate learning samples by simulations, using either model spectra, or slit spectra." + In this paper we will use the simulations for the development of selection criteria., In this paper we will use the simulations for the development of selection criteria. +" In later papers we will use sets of simulated spectra as learning samples for selection of e.g. metal-poor stars by automatic spectral classification,", In later papers we will use sets of simulated spectra as learning samples for selection of e.g. metal-poor stars by automatic spectral classification. + The conversion of model spectra. or slit spectra. to objective-prism spectra consists of five steps: Step (4) ensures that objects of any brightness can be simulated.," The conversion of model spectra, or slit spectra, to objective-prism spectra consists of five steps: Step (4) ensures that objects of any brightness can be simulated." + The B; magnitude range corresponding to a given S/Ncan be read from Fig. 6.., The $B_J$ magnitude range corresponding to a given $S/N$can be read from Fig. \ref{SNofBJ}. . +particular cases the following specifications for smoothing were used: € = 5x107' and 200 d normals for the emission-wing RVs measured by both methods. and € = 1X107'° and 200 d normals for the RVs measured on the absorption core.,"particular cases the following specifications for smoothing were used: $\epsilon$ = $\times$ $^{{-16}}$ and 200 d normals for the emission-wing RVs measured by both methods, and $\epsilon$ = $\times$ $^{{-16}}$ and 200 d normals for the RVs measured on the absorption core." + These particular choices of ε make the smoothing function follow only the secular RV variations., These particular choices of $\epsilon$ make the smoothing function follow only the secular RV variations. + The solid lines in the three panels of Fig., The solid lines in the three panels of Fig. + 6. show the estimated long-term changes. which were then substracted from the original RVs.," \ref{13hahe} show the estimated long-term changes, which were then substracted from the original RVs." + These prewhitened RVs were than searched for periodicity from 3000700 down to 055 with the program HEC?7 (also written by PH). based on the PDM technique developed by ?..," These prewhitened RVs were than searched for periodicity from 0 down to 5 with the program HEC27 (also written by PH), based on the PDM technique developed by \citet{stell78}." + The 8-statistics periodograms for the manually and automatically measured emission RVs are plotted in Figs., The $\theta$ -statistics periodograms for the manually and automatically measured emission RVs are plotted in Figs. + 7 and 8.. respectively.," \ref{thetajn} and \ref{thetamr}, respectively." + The upper panels in both plots show the range of periods from 3000700 down to 50400. while the periods from 2400 down to 0155 are shown in the lower panels.," The upper panels in both plots show the range of periods from 0 down to 0, while the periods from 0 down to 5 are shown in the lower panels." + The periodograms are flat. with 8 close to a value of | for all periods between 2 and 50 d. which is why we do not show these parts of the perrodograms in the figures.," The periodograms are flat, with $\theta$ close to a value of 1 for all periods between 2 and 50 d, which is why we do not show these parts of the periodograms in the figures." + One can see that the combination of RVs from several observatories. which are different from each other in their local times. safely excluded the one-day aliases.," One can see that the combination of RVs from several observatories, which are different from each other in their local times, safely excluded the one-day aliases." + The deepest minimum in both periodograms at a frequency fox 0.004910 d7! corresponds to a period of P = 2203/00., The deepest minimum in both periodograms at a frequency $f$ $\approx$ 0.004910 $^{\rm -1}$ corresponds to a period of $P$ $\approx$ 0. + The two shallower peaks at lower frequencies in Figs., The two shallower peaks at lower frequencies in Figs. + 7. and 8 correspond to the integer multiples of the 203 d period.," \ref{thetajn} + and \ref{thetamr} correspond to the integer multiples of the 203 d period." + The 203 d period was also detected in the measured RVs of other spectral lines. though with a larger scatter in the RV curves.," The 203 d period was also detected in the measured RVs of other spectral lines, though with a larger scatter in the RV curves." + These additional results are presented in the online Appendix., These additional results are presented in the online Appendix. + Since no obvious signs of the secondary companion are seen in the spectrum. we adopted as a single-line spectroscopic binary.," Since no obvious signs of the secondary companion are seen in the spectrum, we adopted as a single-line spectroscopic binary." + We derived a number of orbital solutions for the emission RVs. prewhitened for the long-term changes with HECI3.," We derived a number of orbital solutions for the emission RVs, prewhitened for the long-term changes with HEC13." + We used the program SPEL (written by Dr. J. Horn and never published) for this purpose., We used the program SPEL (written by Dr. J. Horn and never published) for this purpose. +" The program has already been used in several previous studies. e.g.. ??., 2.. ?.. and ??.."," The program has already been used in several previous studies, e.g., \citet{hec1983, hec1984}, \citet{koubsky1985}, \citet{stefl1990}, and \citet{horn1992, horn1994}." + Our first goal was to decide whether the orbital eccentricity found by ? is real or whether the orbit is actually circular as concluded by ?.., Our first goal was to decide whether the orbital eccentricity found by \citet{hec2000} is real or whether the orbit is actually circular as concluded by \citet{mirosh2002}. + In Table 4. the eccentric-orbit solutions for the manually and automatically measured emission-wing RVs are compared., In Table \ref{elementhec} the eccentric-orbit solutions for the manually and automatically measured emission-wing RVs are compared. + ? have pointed out that observational uncertainties may cause the estimated eccentricity to be biased when the eccentricity is low., \citet{ls71} have pointed out that observational uncertainties may cause the estimated eccentricity to be biased when the eccentricity is low. +" The probability that the true eccentricity is zero can be calculated. and this is given in the column “L-S test""."," The probability that the true eccentricity is zero can be calculated, and this is given in the column ”L-S test”." + If this probability is greater than 0.05 we accept the hypothesis that the true eccentricity Is zero at a confidence level., If this probability is greater than 0.05 we accept the hypothesis that the true eccentricity is zero at a confidence level. + To shed more light on the problem. we split both manually and automatically measured RVs into a number of data subsets. each of them covering a time interval not longer than three consecutive orbital periods and containing enough observations to define the orbital RV curve.," To shed more light on the problem, we split both manually and automatically measured RVs into a number of data subsets, each of them covering a time interval not longer than three consecutive orbital periods and containing enough observations to define the orbital RV curve." + We used the original. not the prewhitened RVs.," We used the original, not the prewhitened RVs." + The phase diagrams for a period P = 2034552 for all selected data subsets are shown in Fig. 9.., The phase diagrams for a period $P$ = 52 for all selected data subsets are shown in Fig. \ref{subsets}. + We derivec the elliptical-orbit solutions for them. again testing the reality of the non-zero orbital eccentricity after ?..," We derived the elliptical-orbit solutions for them, again testing the reality of the non-zero orbital eccentricity after \citet{ls71}. ." +" To always finc the solution with the smallest rms error. we started the trial solutions for each subset with initial values of c). for four possible orientations of the orbit. namely 45°. 1357. 225°. and 315°,"," To always find the solution with the smallest rms error, we started the trial solutions for each subset with initial values of $\omega$ for four possible orientations of the orbit, namely $^{\circ}$, $^{\circ}$, $^{\circ}$, and $^{\circ}$." + The corresponding orbital elements for the selected subsets. together with the Lucy-Sweeney test. are summarized i7 Table 5. for manually measured RVs and in Table 6 for automatically measured RVs.," The corresponding orbital elements for the selected subsets, together with the Lucy-Sweeney test, are summarized in Table \ref{subtabman} for manually measured RVs and in Table \ref{subtabaut} for automatically measured RVs." + The results show very convineingly that the true orbit must be circular (or has a very low eccentricity. which is beyond the accuracy limitof our data).," The results show very convincingly that the true orbit must be circular (or has a very low eccentricity, which is beyond the accuracy limitof our data)." + Although the L-S test detected a definite eccentricity for several subsets. the individual values of the longitude of," Although the L–S test detected a definite eccentricity for several subsets, the individual values of the longitude of" +me in electronic form.,me in electronic form. + In addition. I am very. pleased to thank the referee lor constructive comments and helpful suggestions that improved (he manuscript.," In addition, I am very pleased to thank the referee for constructive comments and helpful suggestions that improved the manuscript." + This work was supported bv the National Science Foundation under NSF contracts AST-0406844 and AST-0708463., This work was supported by the National Science Foundation under NSF contracts AST-0406844 and AST-0708468. +bv generating a sample of 10000. galaxies.,by generating a sample of $10 000$ galaxies. + Two galaxies are selected which correspond to lens parameters which are only slightly cifferent., Two galaxies are selected which correspond to lens parameters which are only slightly different. + Phus we have considered only pairs of galaxies separated by lessthan 0.2 in the lens plane., Thus we have considered only pairs of galaxies separated by lessthan $0.2$ in the lens plane. + To simplify the presentation we shall use the following notation., To simplify the presentation we shall use the following notation. + In Fig.9 we have plotted the average5 value of AL as a function of ALys., In \ref{rpf1} we have plotted the average value of $\Delta\Gamma$ as a function of $\Delta\Gamma_{12}$. +" H£ there is no measurement error. the error on he retrieved E is roughly equal to the dillerence between the values of Py, and."," If there is no measurement error, the error on the retrieved $\Gamma$ is roughly equal to the difference between the values of $\Gamma_{g_1}$ $\Gamma^{g_2}$." +" If on the other hand one plotsthe same curve but for a population of galaxies when a measurement error of 2.5"" is mace. then the error on E is noticeably greater. and around 15 204."," If on the other hand one plotsthe same curve but for a population of galaxies when a measurement error of $2.5^o$ is made, then the error on $\Gamma$ is noticeably greater, and around $15-20\%$ ." +" In order to establish the precision on e, necessary to establish P up to a certain level of accuracy. we rave plotted the mean value of ALP against Aa. for pairs of galaxies satisfving M»«1054."," In order to establish the precision on $\alpha_s$ necessary to establish $\Gamma$ up to a certain level of accuracy, we have plotted the mean value of $\Delta\Gamma$ against $\Delta\alpha_s$ for pairs of galaxies satisfying $\Delta\Gamma_{12}<10\%$." + Indeed. one sees that just one yale of nearby galaxies whose polarization vields o; with 5° accuracy. allows E to be determined with an accuracy of 25% without making any assumptions about the form of the lens., Indeed one sees that just one pair of nearby galaxies whose polarization yields $\alpha_s$ with $5^o$ accuracy allows $\Gamma$ to be determined with an accuracy of $25\%$ without making any assumptions about the form of the lens. + Evidently. if one has a large number of galaxy pairs. that it is »ossible to still further reduce this error.," Evidently, if one has a large number of galaxy pairs, that it is possible to still further reduce this error." + One should also not that if one has several pairs of neighbouring galaxies. the number of equations in (19)) is greater han the number of unknowns. and one should use statistical techniques for the determination of the lens parameters.," One should also not that if one has several pairs of neighbouring galaxies, the number of equations in \ref{deuxgal}) ) is greater than the number of unknowns, and one should use statistical techniques for the determination of the lens parameters." + Once E has been determined. it is still necessary to determine the convergence & and the shear 5. which are the parameters directly linked to the mass density distribution in the lens plane.," Once $\Gamma$ has been determined, it is still necessary to determine the convergence $\kappa$ and the shear $\gamma$, which are the parameters directly linked to the mass density distribution in the lens plane." + These parameters can be obtained from equation (7)). which can be written in the form If we now average the above relation over a subset S of galaxies having the same value of s. either because they are sullicienthy close together or because ofsome symmetry (all the galaxies can be used and not only those with a measured," These parameters can be obtained from equation \ref{s2}) ), which can be written in the form If we now average the above relation over a subset $S$ of galaxies having the same value of $\kappa$ , either because they are sufficiently close together or because ofsome symmetry (all the galaxies can be used and not only those with a measured" +than twice the radius of all galaxies brighter than Rz18.,than twice the radius of all galaxies brighter than R=18. + This strongly limits the GC contamination shown for example in B9S., This strongly limits the GC contamination shown for example in B95. + However. intergalactic GCs or GCs distant from galaxy centres can still be present. as demonstrated by Rhode & Zepf (2004: RZ04).," However, intergalactic GCs or GCs distant from galaxy centres can still be present, as demonstrated by Rhode $\&$ Zepf (2004: RZ04)." + According to these authors. the GC number density profile could have a small (but non negligible) contribution to number counts outside the regions masked in our analysts.," According to these authors, the GC number density profile could have a small (but non negligible) contribution to number counts outside the regions masked in our analysis." + If we apply our masking to the RZO4+ M86 data. we find that the remaining GCs (distant from their parent galaxy) are - 80 times less numerous than the whole population.," If we apply our masking to the RZ04 M86 data, we find that the remaining GCs (distant from their parent galaxy) are $\sim$ 80 times less numerous than the whole population." + In order to estimate a GC LF in our fields. we assumed the M86 population of GCs to be typical of all galaxies brighter than R=18 in the Coma CS.," In order to estimate a GC LF in our fields, we assumed the M86 population of GCs to be typical of all galaxies brighter than R=18 in the Coma CS." + It will only be used to give us a rough estimate of the GC LF., It will only be used to give us a rough estimate of the GC LF. + Then. rescaling the surface densities to the Coma cluster distance. we were able to generate the GC LF," Then, rescaling the surface densities to the Coma cluster distance, we were able to generate the GC LF" +1988).,. +. To compare the sources in our sample to these previous results. ro; was determined from the 9.7 um silicate features in our sample.," To compare the sources in our sample to these previous results, $\tau_{9.7}$ was determined from the 9.7 $\mu$ m silicate features in our sample." + An estimation of the error on these measurements was done by taking different reasonable continua and determining the effect on τω., An estimation of the error on these measurements was done by taking different reasonable continua and determining the effect on $\tau_{9.7}$. + The E(J—K) colour excesses were determined by taking the (J-K) colour observed by 2MASS (Skrutskieetal..2006) and subtracting the intrinsic (J-K) colour from Koornneef(1983)., The $E$ $-$ K) colour excesses were determined by taking the $-$ K) colour observed by 2MASS \citep{2MASS06} and subtracting the intrinsic $-$ K) colour from \citet{Koornneef83}. +. If the spectral type of the source is unknown. we assume it Is à GO-M4 giant. with an average intrinsic (J-K) colour of about 0.8] magnitudes (consistent with Chiaretal. (2007))).," If the spectral type of the source is unknown, we assume it is a G0–M4 giant, with an average intrinsic $-$ K) colour of about 0.81 magnitudes (consistent with \citet{Chiar07}) )." + The errors were estimated by taking into account the uncertainty in the spectral type and thus the intrinsic (J-K) colour., The errors were estimated by taking into account the uncertainty in the spectral type and thus the intrinsic $-$ K) colour. + The results are listed in Table 2. and Fig., The results are listed in Table \ref{tab:resultstauvsEJK} and Fig. + 7. shows these results together with the Galactic line-of-sight and the results from Chiaretal.(2007) for the diffuse and molecular sightlines separately., \ref{fig:tauvsEJK} shows these results together with the Galactic line-of-sight and the results from \citet{Chiar07} for the diffuse and molecular sightlines separately. + Our measurements are in agreement with the results found by Chiaretal.(2007) ascan be seen in Fig. 7.., Our measurements are in agreement with the results found by \citet{Chiar07} ascan be seen in Fig. \ref{fig:tauvsEJK}. + Please note. that two of our measurements are forof Chiaretal.(2007).. namely: and and we have replaced their measurements by ours in Fig. 7..," Please note, that two of our measurements are for \citet{Chiar07}, namely: and and we have replaced their measurements by ours in Fig. \ref{fig:tauvsEJK}." + The two measurements for agree within the uncertainty., The two measurements for agree within the uncertainty. + For the measurement was done by Whittetetal.(1988) from a relatively noisy. ground based spectrum. so the error on their measured r5; 1s quite large (approximately 0.08 in 7).," For the measurement was done by \citet{Whittet88_2} from a relatively noisy, ground based spectrum, so the error on their measured $\tau_{9.7}$ is quite large (approximately 0.08 in $\tau$ )." + Moreover. they did not correct for photospheric gas phase S1O. We also included the Galactic line-of-sight in Fig.," Moreover, they did not correct for photospheric gas phase SiO. We also included the Galactic line-of-sight in Fig." + (upper panel)., \ref{fig:tauvsEJK} (upper panel). + For this we used r9;23.25 2004:Minetal..2007) and το ;/E(J-K)20.71985)..," For this we used $\tau_{9.7}$ =3.25 \citep{Kemper04, Min07} and $\tau_{9.7}$ $E$ $-$ K)=0.7." + The Galactic line-of-sight is exceptional. since it is the only one for which 75; versus E(J-K) lies above the diffuse ISM correlation.," The Galactic line-of-sight is exceptional, since it is the only one for which $\tau_{9.7}$ versus $E$ $-$ K) lies above the diffuse ISM correlation." + This sightline probes the local ISM as well as the inner parts of our Galaxy in contrast to the other sightlines which only probe the local ISM., This sightline probes the local ISM as well as the inner parts of our Galaxy in contrast to the other sightlines which only probe the local ISM. + Since there are relatively fewer C-rich stars (as compared to O-rich stars) around the Galactie than in the outer regions of our Galaxy. the abundance of dust is probably also lower around the Galactic (Roche&Aitken. 1985). ," Since there are relatively fewer C-rich stars (as compared to O-rich stars) around the Galactic than in the outer regions of our Galaxy, the abundance of dust is probably also lower around the Galactic \citep{Roche85}. ." +This would explain the relatively high το ;/E(J—K) ratio for this particular line-of-sight. since carbon rich dustof the extinction.," This would explain the relatively high $\tau_{9.7}$ $E$ $-$ K) ratio for this particular line-of-sight, since carbon rich dust the extinction." + Furthermore. there is one molecular cloud source (indicated by the arrow in Fig. 7))," Furthermore, there is one molecular cloud source (indicated by the arrow in Fig. \ref{fig:tauvsEJK}) )" + that seems to agree very well with the diffuse ISM correlation despite the high value for E(J—K). was observed with Spitzer in the c2d legacy program spectrum is shown in Fig. 8..," that seems to agree very well with the diffuse ISM correlation despite the high value for $E$ $-$ K), was observed with Spitzer in the c2d legacy program spectrum is shown in Fig. \ref{fig:sst18}." + Prominent ice features are present at about 6 and 6.85 jm caused by H3O and CH:OH + NH7 ice respectively (BoogertEhrenfreund.2004;vanDishoeck. 2004).," Prominent ice features are present at about 6 and 6.85 $\mu$ m caused by $_{2}$ O and $_{3}$ OH + $_{4}^{+}$ ice respectively \citep{Boogert04,Dishoeck04}." +. The latter also has a feature at about 9.7 uim. which increases the depth of the9.7 jm silicate feature We note the large differences in the strength of the ice bands between the spectrum in Fig.," The latter also has a feature at about 9.7 $\mu$ m, which increases the depth of the9.7 $\mu$ m silicate feature We note the large differences in the strength of the ice bands between the spectrum in Fig." + 8 and the4 molecular cloud sightlines shown in Fig. 2.. ," \ref{fig:sst18} and the4 molecular cloud sightlines shown in Fig. \ref{fig:spectra1}, ," +for similar values of E(J-K)., for similar values of $E$ $-$ K). + The trajectory of auy photon emitted from a flare with bulk motion at this point can be specified by two motion constants. Le. the component of augular momentum parallel to the sviunietry. axis / aud the Carter constant Q. which can be derived from the direction of the photon momentum iud the comoving tetrad: where py is the photon momentium at this location. aud τας is the bulk velocity of the flare at this point as expressed in € À5)).,"Then the components of the comoving tetrad associated with this point are: The trajectory of any photon emitted from a flare with bulk motion at this point can be specified by two motion constants, i.e. the component of angular momentum parallel to the symmetry axis $l$ and the Carter constant $Q$, which can be derived from the direction of the photon momentum and the comoving tetrad: where ${\bf p}_{s}$ is the photon momentum at this location, and ${\bf u}_{s}$ is the bulk velocity of the flare at this point as expressed in ( \ref{eq:system3}) )." + Based on equations (A5)}). (AG)) aud (À7)). we can obtain where," Based on equations \ref{eq:system3}) ), \ref{eq:system4}) ) and \ref{eq:system5}) ), we can obtain where" +we analyze data frou these observations. made available though the public archive.,"we analyze data from these observations, made available though the public archive." + Thing data on wwere acquired on 2000 Feb Ll with the inagine Iheh Resolution Camera (HBRC-I: Miuray. et al., Timing data on were acquired on 2000 Feb 11 with the imaging High Resolution Camera (HRC-I; Murray et al. + 1997). a auultichannel plate detector with an effective time resolution degraded to ~Lams due to a known timing error.," 1997), a multichannel plate detector with an effective time resolution degraded to $\sim 4$ ms due to a known timing error." + The IRC is seusitive to N-ravs in the cucrey rauge 110 keV: no useful spectral information is available., The HRC is sensitive to X-rays in the energy range $0.1-10$ keV; no useful spectral information is available. +" The target was placed near (228"") the optical axis where the telescope nürror poiut-spread fuuctiou (PSF) has half power radius (the radius enclosing of the total source counts) of ~075 for energies E«—6 keV. The IIRC-I overssmuuples the PSF with pixels 071318 on a side. which allows the pulsar to be isolated frou any smroundius enüsson such as the pulsar wind nebulae (DWNe) typically found associated with vouug pulsars observed by (o... see Gotthelf 2001)."," The target was placed near $\approx 28^{\prime\prime}$ ) the optical axis where the telescope mirror point-spread function (PSF) has half power radius (the radius enclosing of the total source counts) of $\sim 0.\!^{\prime\prime}5$ for energies $E < 6$ keV. The HRC-I oversamples the PSF with pixels $0.\!^{\prime\prime}1318$ on a side, which allows the pulsar to be isolated from any surrounding emission such as the pulsar wind nebulae (PWNe) typically found associated with young pulsars observed by (e.g., see Gotthelf 2001)." + Data were also obtained with the Advanced CCD hnaging Spectrometer (ACTS: Burke et al., Data were also obtained with the Advanced CCD Imaging Spectrometer (ACIS; Burke et al. + 1997). which has resolution ΑΕ~0.1 at 1 keV scaling as 1/V/E over itx 0.2.10 keV active band-pass.," 1997), which has resolution $\Delta E / E \sim 0.1$ at 1 keV scaling as $1 / \sqrt{E}$ over its 0.2–10 keV active band-pass." + The pulsar was observed on 2000 Aug tl aud positioned ou the backilluminated $3 chip of the ACIS-S array. offset by 0/5 from the aim-poit. where the PSF is mudersamipled by the 071920«L920 CCD pixels.," The pulsar was observed on 2000 Aug 14 and positioned on the back-illuminated S3 chip of the ACIS-S array, offset by $0\farcm5$ from the aim-point, where the PSF is undersampled by the $0.\!^{\prime\prime}4920 \times +0.\!^{\prime\prime}4920$ CCD pixels." +" Data were collected in the nominal timine with3.211 s exposures between CCD readouts. aud 1 mode,""FAINT"" spectral mode."," Data were collected in the nominal timing mode, with 3.241 s exposures between CCD readouts, and in “FAINT” spectral mode." + The standardChendre screcuineg criteria produced total usable exposure time of 16.8 ks aud 11.3 ks for the TRC and ACTS data sets. respectively.," The standard screening criteria produced a total usable exposure time of 46.8 ks and 14.3 ks for the HRC and ACIS data sets, respectively." + These resulted iu a simular ΠΡΟ of detected photons frou the source. aud the inages made from the two iustrunents are found to be consistent.," These resulted in a similar number of detected photons from the source, and the images made from the two instruments are found to be consistent." + The ACTS image. restricted to the 0:3.Ss keV energv band to reduce instruiieutal backeround. reveals a poiut-lke X-arav source at the radio pulsar position auc four nearby faint N-rav sources that are coincikdeut with USNO stars to sub-arcsecond accuracy.," The ACIS image, restricted to the $0.3 - +8$ keV energy band to reduce instrumental background, reveals a point-like X-ray source at the radio pulsar position and four nearby faint X-ray sources that are coincident with USNO stars to sub-arcsecond accuracy." +" TheChandra position of ua=Lite127,073, 6=LE29708""E. »""(2000.0) with RAIS error (75.positi"," The position of is $\alpha += 17^{\rm h} 09^{\rm m} 42^{\rm s}.73$, $\delta = -44^{\circ} +29^{\prime} 08\farcs4$ (J2000.0) with RMS error $0\farcs5$." +on Thisis iu aereciueut with precise racio timing of Wane et al.(, This is in agreement with the precise radio timing position of Wang et al. ( +2000. see Table1).,"2000, see Table 1)." + To look for evidence of extended cussion around wwe constructed a radial profile. the distribution of counts per uuif area in the WRC as a function of distance from the pulsar.," To look for evidence of extended emission around we constructed a radial profile, the distribution of counts per unit area in the HRC as a function of distance from the pulsar." + For courparison. we analyzed a 23 ksChandra observation of the mullisecoud pulsar PSR JOL371715 observed at the ain-poiut of the WRC just two davs later (Zavlin et al.," For comparison, we analyzed a 23 ks observation of the millisecond pulsar PSR J0437–4715 observed at the aim-point of the HRC just two days later (Zavlin et al." + 2002)., 2002). + PSR JOL371715 is an isolated poiu source with a spectrum similar to that of (Cas shown iu 1) thus providing a realistic example of the im-orbit poiut-spread function.," PSR J0437–4715 is an isolated point source with a spectrum similar to that of (as shown in 4), thus providing a realistic example of the in-orbit point-spread function." +" Figure 5. displays the two radial profiles after adjusting for differcut backerouiu iuteusities. sampled in aui auuulus of 30""«crk« 607where the backeroundis flat."," Figure \ref{fig:profile} displays the two radial profiles after adjusting for different background intensities, sampled in an annulus of $30^{\prime\prime} < r < 60^{\prime\prime}$ where the background is flat." + We then normalized the two profiles to the peak inteusity withinkr«170., We then normalized the two profiles to the peak intensity within $r <1.\!^{\prime\prime}0$. +" While the majority of the cussion is poiut-like.there is clearly diffuse cussion out to a radius of zz20"","," While the majority of the emission is point-like, there is clearly diffuse emission out to a radius of $\approx 20^{\prime\prime}$." +" There is also a bump of enlaces emission. between 11«kr23"".", There is also a bump of enhanced emission between $11^{\prime\prime} < r < 23^{\prime\prime}$. +" This result is cousisten with the analvsis of these databy Dodsou Colap (2002). who displaved extended emissiou out to zz5"", and is mareimally cousisteut with the decomposition of the TRI image deduced by Finley ct al. ("," This result is consistent with the analysis of these data by Dodson Golap (2002), who displayed extended emission out to $\approx +5^{\prime\prime}$, and is marginally consistent with the decomposition of the HRI image deduced by Finley et al. (" +1998).,1998). +" In order to make a direct comparison with the eenerev baud. we also extracted photous from the ACIS nuage in the rauge in22.0 keV. After backeround subtraction. we fiud in,513 photons in the ACTS from the point source (radius and 383 nebular photons iu the aunulus 175κrk«20%,"," In order to make a direct comparison with the energy band, we also extracted photons from the ACIS image in the range $0.2-2.0$ keV. After background subtraction, we find 513 photons in the ACIS from the point source (radius $1.\!^{\prime\prime}5$ ), and 383 nebular photons in the annulus $1.\!^{\prime\prime}5 < r < 20^{\prime\prime}$." + We searched for a pulsed signal frou Hu the URC data using time-tageecd photon cveuts extracted from an 3/0 radius aperture. centered. on the N-rav pulsar position., We searched for a pulsed signal from in the HRC data using time-tagged photon events extracted from an $3.\!^{\prime\prime}0$ radius aperture centered on the X-ray pulsar position. + This aperture effectively excludes uost of the diffuse emission from the putative surrounding svuchrotron nebub: furthermore. less than of the photons in this aperture are backeround eveuts.," This aperture effectively excludes most of the diffuse emission from the putative surrounding synchrotron nebula; furthermore, less than of the photons in this aperture are background events." + The arrival times of the 821 selected photous were corrected o the solar system barveenter using the JPL-DE200 ephemeris aud the radio timime position., The arrival times of the 824 selected photons were corrected to the solar system barycenter using the JPL-DE200 ephemeris and the radio timing position. + We then eeucrated a periodograii using the Z? statistic (Rayleigh est) on a range of test frequencies centered on the xedieted. pulsar frequency derived from a fit to radio observations from the Parkes Observatory archives (Wane et al., We then generated a periodogram using the $Z_1^2$ statistic (Rayleigh test) on a range of test frequencies centered on the predicted pulsar frequency derived from a fit to radio observations from the Parkes Observatory archives (Wang et al. + 2000) that span the A-ray observation., 2000) that span the X-ray observation. + The residual deviations of the radio pulse arrival times from the fitted quadratic ephemeris in Table 1 are less than 1 ins. including one observation that occured 21 days before the X-ray observation.," The residual deviations of the radio pulse arrival times from the fitted quadratic ephemeris in Table 1 are less than 1 ms, including one observation that occurred 24 days before the X-ray observation." + The kuown dispersion nicasure was used to correct the radio pulse arrival times to infinite frequency for absolute phase comparison with tle N-rav pulse., The known dispersion measure was used to correct the radio pulse arrival times to infinite frequency for absolute phase comparison with the X-ray pulse. + The X-ray periodograim is shown in Figure 6.., The X-ray periodogram is shown in Figure \ref{fig:periodogram}. + We fiud a peak at f=9.r75ssUsS£0.0000026 Iz (epoch 51585.31101 MID) which. within the quoted uncertainty range. is identical to the coutemmporancous radio frequency. f=9.7588097 Iz.," We find a peak at $f = 9.7588088 \pm +0.0000026$ Hz (epoch 51585.34104 MJD) which, within the quoted uncertainty range, is identical to the contemporaneous radio frequency, $f = 9.7588097$ Hz." + The Zi statistic for this peak is 20.51. which has a probability of chance occurrence of «107.," The $Z_1^2$ statistic for this peak is 20.54, which has a probability of chance occurrence of $3.5 \times 10^{-5}$." + The light cwve. shown iu Figure 7.. is broad aud single peaked with a pulsed fraction of 23%46%.," The light curve, shown in Figure \ref{fig:lightcurve}, is broad and single peaked with a pulsed fraction of $23\% \pm 6\%$." + Accordingthe to convention. the pulsed fraction is defined as ratio of counts above the minima iu the liebt curve to the total counts.," According to convention, the pulsed fraction is defined as the ratio of counts above the minimum in the light curve to the total counts." + This detection is consistent with the previous upper limits of< (from the ΠΠ (Finley ct al., This detection is consistent with the previous upper limits of $<29$ from the HRI (Finley et al. + 1998) andThe<18% from the PSPC (Becker et al., 1998) and $<18$ from the PSPC (Becker et al. + 1995)., 1995). + latter did not resolve the pulsar from the nebula. therefore. it represents a true upper limit of <31%van seien the contribution of diffuse photous measured im the ACTS image as described in 82.," The latter did not resolve the pulsar from the nebula, therefore, it represents a true upper limit of $<31\%$ given the contribution of diffuse photons measured in the ACIS image as described in 2." + The arrival time of the radio pulse is consistent with occurs at the center of the broad N-rav. peak., The arrival time of the radio pulse is consistent with occurring at the center of the broad X-ray peak. + This is uot thecase for the ECRET 5-xav pulse. which is ceutered zz0.37 evcles after the racio pulse ((Thompson et al.," This is not the case for the EGRET $\gamma$ -ray pulse, which is centered $\approx 0.37$ cycles after the radio pulse (Thompson et al." + 1996)., 1996). + To characterize the energy. dependence of the emission from the pulsar aud its putative wind nebula. we analyzed spectral data obtained with the ACTS detector.," To characterize the energy dependence of the emission from the pulsar and its putative wind nebula, we analyzed spectral data obtained with the ACIS detector." + Pulsar and PWN source counts spectra were extracted from two concentric regions. a circle of radius 1” and an," Pulsar and PWN source counts spectra were extracted from two concentric regions, a circle of radius $1^{\prime\prime}$ and an" +produced per unit of stellar Iuminosity. (less than 0.02 dex).,produced per unit of stellar luminosity (less than 0.02 dex). + For reasons fully explained in the next section. we expect that (he Iraction of ionizing photons absorbed by the dust should scale as the product (ΟΙ). for a given grain model.," For reasons fully explained in the next section, we expect that the fraction of ionizing photons absorbed by the dust should scale as the product ${\cal +U}({\rm O}/{\rm H})$, for a given grain model." + Therefore in Figure (1) we have plotted (his quantity against the computed ratio of Balmer IL? fluxes. with and without the inclusion of dust.," Therefore in Figure (1) we have plotted this quantity against the computed ratio of Balmer ${\beta}$ fluxes, with and without the inclusion of dust." + The (wo families of curves are shown. one with of the C locked in PAII-like molecules. and the other with of the C locked in such molecules.," The two families of curves are shown, one with of the C locked in PAH-like molecules, and the other with of the C locked in such molecules." + The families of models with al 0.4 times solar abundance (open circles). 1.0 (imes solar abundance (erossed circles) and 2 times solar abundance (filled circles) lie close to each other for each grain composition.," The families of models with at 0.4 times solar abundance (open circles), 1.0 times solar abundance (crossed circles) and 2 times solar abundance (filled circles) lie close to each other for each grain composition." + This gives us confidence that the G(O/II) scaling [actor is correct. to first order.," This gives us confidence that the ${\cal U}({\rm O}/{\rm H})$ scaling factor is correct, to first order." + The lareest dust absorption is found [or (he models with extreme metallicity and ionisalion parameter (οἱ=0.0133 and Z= 2Z.)., The largest dust absorption is found for the models with extreme metallicity and ionisation parameter ${\cal U}=0.0133$ and $Z=2Z_{\odot}$ ). + In practice rreeions are rarely encountered wilh such a high ionization parameter (Dopita]xewlev&Dopita 2002).," In practice regions are rarely encountered with such a high ionization parameter \citep{Dopita00, Kewley02}." +. Therefore. we conclude on the basis of our models (hat accounting for the effect of dust absorption in determining star formation rates is both a significant. ancl important correction. but that dust rarely dominates in the absorption of the EUV photons in normal rreglons.," Therefore, we conclude on the basis of our models that accounting for the effect of dust absorption in determining star formation rates is both a significant and important correction, but that dust rarely dominates in the absorption of the EUV photons in normal regions." + It is sell-evident (hat greater dust content will enable the dust to compete more efficiently with (he eas for the EUV Lyman continuum photons., It is self-evident that greater dust content will enable the dust to compete more efficiently with the gas for the EUV Lyman continuum photons. + The dust content is determined by the balance of grain formation and grain destruction processes. but it should. to first order. scale as (he metalliitv. Z.," The dust content is determined by the balance of grain formation and grain destruction processes, but it should, to first order, scale as the metallicity, $Z$." + We have taken Chis as an assumption of our models by using (he same set of depletion factors in all models., We have taken this as an assumption of our models by using the same set of depletion factors in all models. + LLowever. it is not so immediately apparent (hat for hieh ionizalion parameter. (he dust becomes again relatively more important in the competition for absorption of the ionizing photons.," However, it is not so immediately apparent that for high ionization parameter, the dust becomes again relatively more important in the competition for absorption of the ionizing photons." + This result is reaclily established., This result is readily established. + After Dopita οἱ al. (, After Dopita et al. ( +"2002a). the local absorption of ionizing photons by the ionized plasma is sinplv equal to ihe local recombination rate: where n is the density in (he ionizecl plasma. 5, =(he)NIALCA)dA is the local photon density from the ionizing source 7s 1). and a(7,) is the recombination coellicient.","2002a), the local absorption of ionizing photons by the ionized plasma is simply equal to the local recombination rate: where $n$ is the density in the ionized plasma, $S_{*}$ $=\left( hc\right) +^{-1}\int \lambda I\left( \lambda \right) d\lambda $ is the local photon density from the ionizing source $^{-2}$ $^{-1}$ ), and $\alpha \left( +T_{e}\right) $ is the recombination coefficient." + Here.," Here," +(2) The distribution of the possible values of the local smoothness parameter à is directly related to matter distribution in our (3) The variance of à depends on the matter power spectrum.,(2) The distribution of the possible values of the local smoothness parameter $\tilde{\alpha}$ is directly related to matter distribution in our (3) The variance of $\tilde{\alpha}$ depends on the matter power spectrum. + It provides a «quantitative guidance in the use of Dver-Roeder distances to illustrate the effect of gravitational lensing of point sources., It provides a quantitative guidance in the use of Dyer-Roeder distances to illustrate the effect of gravitational lensing of point sources. + For example. instead of arbitrary values of à. one should use à values which are one or (wo standard deviations away [rom the mean value of (à)=1.," For example, instead of arbitrary values of $\tilde{\alpha}$, one should use $\tilde{\alpha}$ values which are one or two standard deviations away from the mean value of $\langle \tilde{\alpha}\rangle=1$." + Next. we derive (he variance of à in terms of the matter power spectitun.," Next, we derive the variance of $\tilde{\alpha}$ in terms of the matter power spectrum." + This is done through the relation of à to the reduced convergence 5 derived in Sec, This is done through the relation of $\tilde{\alpha}$ to the reduced convergence $\eta$ derived in Sec. +IL.,III. + In Sec, In Sec. +"U1. we have shown that Ay), is the (rue minimum convergence and corresponds to the minimum magnilication 5,5. While 545, 1s the approximation lo Ay,;,, in the weak lesning limit.","III, we have shown that $\tilde{\kappa}_{min}$ is the true minimum convergence and corresponds to the minimum magnification $\mu_{min}$, while $\kappa_{min}$ is the approximation to $\tilde{\kappa}_{min}$ in the weak lesning limit." + This suggests that we need to use 7=L+r//Fil. instead of 7=L4/8/87. as (he reduced convergence.," This suggests that we need to use $\tilde{\eta}=1+\kappa/|\tilde{\kappa}_{min}|$, instead of $\eta=1+\kappa/|\kappa_{min}|$, as the reduced convergence." + Subsecquently. we modify the formulae in Valageas(2000) as follows.," Subsequently, we modify the formulae in \cite{Valageas00} + as follows." + The convergence & (Dernardeau.Waerbeke.anclMellier1997:Kaiser1998). is modified io beBO Eq.(4)) is Ain (see E«.(2))). which does correspond to the minimum magnification (see I5q.(3))).," The convergence $\kappa$ \citep{Bernardeau97,Kaiser98} + is modified to be, where $z_s$ is the sourceredshift, $\delta= +(\rho-\overline{\rho})/\overline{\rho}$, and (z, z_s)= (1+z)^2 ) is $\tilde{\kappa}_{min}$ (see \ref{eq:kapdef}) )), which does correspond to the minimum magnification (see \ref{eq:mumin}) ))." + The variance of 7j is similar (to that of η (Valageas 2000).. and given by," The variance of $\tilde{\eta}$ is similar to that of $\eta$ \citep{Valageas00}, , and given by" +at G.2V. and 26° super-catastrophically disrupted the target leaving a largest remnant of ouly 0.008ντι.,at $6.2V_{\rm esc}$ and $26^{\circ}$ super-catastrophically disrupted the target leaving a largest remnant of only $0.008 M_{\rm Earth}$. + There were a total of 3686 collisious by planetesinials and embryos diving the erowth of the 52 planets in group 2., There were a total of 3686 collisions by planetesimals and embryos during the growth of the 52 planets in group 2. + Of these. 3112 collisions were bv plauctesimals.," Of these, 3142 collisions were by planetesimals." + As in eroup 1. the analytic model predicts that about of planetesimial collisions will lead to partial accretion.," As in group 1, the analytic model predicts that about of planetesimal collisions will lead to partial accretion." + The simmlatious by considered a wider range of dynamical configurations for Jupiter aud Saturn. which produced a slishtlv wider distribution of Hupact velocities (Figure 2BB) compared to group 1.," The simulations by considered a wider range of dynamical configurations for Jupiter and Saturn, which produced a slightly wider distribution of impact velocities (Figure \ref{fig:vimpact}B B) compared to group 1." + Iu addition. the initial masses of the embryos was sinaller.," In addition, the initial masses of the embryos was smaller." + As a result. a couple of percent of plauctesimals impacts ed to erosion of the erowing planet.," As a result, a couple of percent of planetesimals impacts led to erosion of the growing planet." + For collisions iun the xuwtial accretion regime. the menn accretion efficiency is shelitly lower in group 2 aud the tail of low efficiency events is more pronounced than in eroup 1 (Figure 3BB).," For collisions in the partial accretion regime, the mean accretion efficiency is slightly lower in group 2 and the tail of low efficiency events is more pronounced than in group 1 (Figure \ref{fig:acceff}B B)." + Overall. the probabilities of different collision outcomes or plauetesinal mipacts are simular iu eroups 1 and 2 jecause of the simular mass ratios and mipact velocity distributions (Table 1)).," Overall, the probabilities of different collision outcomes for planetesimal impacts are similar in groups 1 and 2 because of the similar mass ratios and impact velocity distributions (Table \ref{tab:outcomes}) )." + Again. most of the plauetesinial uit-and-+run eveuts result iu catastrophic disruption of he projectile.," Again, most of the planetesimal hit-and-run events result in catastrophic disruption of the projectile." + Compared to the giaut mipacts in eroup 1. eroup 2 eiut impacts have more partial accretion events and sjenificauflv more enbryvos are croded ia hit-aud-aruu events.," Compared to the giant impacts in group 1, group 2 giant impacts have more partial accretion events and significantly more embryos are eroded in hit-and-run events." + The difference is primarily a result of the fact that the mitial enibrvos were smaller iu the sinulatious by(2009)., The difference is primarily a result of the fact that the initial embryos were smaller in the simulations by. +". The larger mass ratio between the embrwvos and erowing planet leads to more cases of fragmentation of the smaller body aud fewer erazing iupacts,", The larger mass ratio between the embryos and growing planet leads to more cases of fragmentation of the smaller body and fewer grazing impacts. + of giant nupacts in eroup 2 have ><0.1. but ouly of eroup 1 git impacts have such a large nass contrast (Figure 1)).," of giant impacts in group 2 have $\gamma < 0.1$, but only of group 1 giant impacts have such a large mass contrast (Figure \ref{fig:gamma}) )." + Of the 151 hit-aud-aun eiant impacts iu eroup 2. 75 projectiles were eroded (50% and 29 projectiles suffered. catastrophic disruption 1].level fragmicutation )).," Of the 151 hit-and-run giant impacts in group 2, 75 projectiles were eroded ), and 29 projectiles suffered catastrophic disruption level fragmentation )." +" The three erosive eiaut nupacts in this group removed 16. 6. and of the material from tarect bodies with imitial masses of 0.08. 0.50 aud Ra0.724th. respectively,"," The three erosive giant impacts in this group removed 16, 6, and of the material from target bodies with initial masses of 0.08, 0.50 and $0.72 M_{\rm Earth}$, respectively." + The crosive events all occurred in the eccentric Jupiter aud Saturn (EIS) eroup of simulations with inipact velocities between 2.1 aud 3.2..., The erosive events all occurred in the eccentric Jupiter and Saturn (EJS) group of simulations with impact velocities between 2.1 and $3.2 V_{\rm esc}$. + Because partial accretion is the most common outcome of non-grazius collisions. a significant fraction of elaut iupacts result iu potentially observable changes in the bulk composition of a planet (Table 13).," Because partial accretion is the most common outcome of non-grazing collisions, a significant fraction of giant impacts result in potentially observable changes in the bulk composition of a planet (Table \ref{tab:outcomes}) )." + For collisions between differentiated bodies. the core-to-uantle mass ratio changes during both partial accretion aud erosion events.," For collisions between differentiated bodies, the core-to-mantle mass ratio changes during both partial accretion and erosion events." + For the large final planets in group 2. a or ercater increase in the mass fraction of the core. νο: occured in about of all eiut impacts aud in about of last eiaut iupacts.," For the large final planets in group 2, a or greater increase in the mass fraction of the core, $f_{\rm + core}$, occured in about of all giant impacts and in about of last giant impacts." + Considering all 1165 elaut impacts outo 161 planets in 10 planet formation simulations. the outcomes are approximately evenly split between partial accretion. eraze-and-merec. aud düt-and-run.," Considering all 1165 giant impacts onto 161 planets in 40 planet formation simulations, the outcomes are approximately evenly split between partial accretion, graze-and-merge, and hit-and-run." + Erosive events. including super-catastroplic disruption. occur about of the tine.," Erosive events, including super-catastrophic disruption, occur about of the time." + Iu the hit-aud-arun eveuts. about half of the projectiles are eroded aud about are catastroplically clisruptecl.," In the hit-and-run events, about half of the projectiles are eroded and about are catastrophically disrupted." +" The equal likelihood. of partial accretion. eraze-aid-moree, and hit-and-run is a result of the rauge of mass ratios and impact velocities for giant mipacts;"," The equal likelihood of partial accretion, graze-and-merge, and hit-and-run is a result of the range of mass ratios and impact velocities for giant impacts." + (τοι the iupact velocity distribution iu eroup 3. the velocity axis of a collision outcome map max be scaled by probability.," Given the impact velocity distribution in group 3, the velocity axis of a collision outcome map may be scaled by probability." + Iu Figure 5.. both axes are scaled by probability: hence. the area of each collision outcome (denoted by colors) is directly proportional to their probability.," In Figure \ref{fig:collmapequal}, both axes are scaled by probability; hence, the area of each collision outcome (denoted by colors) is directly proportional to their probability." + The L[ panels span the rauge of giant impact nass ratios in eroup 3 of eveuts have ~>0.03 but a few eibrvo-oubrvo collisions have mass ratios as extronie as 1:55)., The 4 panels span the range of giant impact mass ratios in group 3 of events have $\gamma>0.03$ but a few embryo-embryo collisions have mass ratios as extreme as 1:55). + Note that. over the course of the ecutive simulation. the mass ratio of a giant inpact is about equally likely to fall anwwhere between 0.03 and 1 (Figure LCC).," Note that, over the course of the entire simulation, the mass ratio of a giant impact is about equally likely to fall anywhere between 0.03 and 1 (Figure \ref{fig:gamma}C C)." + Even when considering just the largest final plaucts (eroup 2). giant iupacts may be any mass ratio (ce. a collision between two 0.LAgary bodies).," Even when considering just the largest final planets (group 2), giant impacts may be any mass ratio (e.g., a collision between two $0.4 M_{\rm Earth}$ bodies)." + However. the last eiaut impact onto target bodies greater than about OSAug are dominated by mass ratios less than 0.1 (Figure A.TFF).," However, the last giant impact onto target bodies greater than about $0.8 M_{\rm Earth}$ are dominated by mass ratios less than 0.1 (Figure \ref{fig:group3vels}F F)." + The collision maps fully scaled dy probability emphasize the importance of the eraze-aud-auerge regie even though it is a narrow regiuue in absolute ipact velocity., The collision maps fully scaled by probability emphasize the importance of the graze-and-merge regime even though it is a narrow regime in absolute impact velocity. +" The scaled figures also cuuphasize that partial accretion of the projectile is the most common outcome for non-graziug collisions: recall that the accretion cficiency peaks at about for all giant impacts (Figure ος ο),", The scaled figures also emphasize that partial accretion of the projectile is the most common outcome for non-grazing collisions; recall that the accretion efficiency peaks at about for all giant impacts (Figure \ref{fig:acceff}C C). + As shown in Figure 5.. hit-and-run eveuts occur about 1/3 of the time aud the projectile is eroded when the projectile mass is less than about of the arect.," As shown in Figure \ref{fig:collmapequal}, hit-and-run events occur about 1/3 of the time and the projectile is eroded when the projectile mass is less than about of the target." + Note that the boundary between eraze-uidauerge aud he adjacent partial accretion and hit-and-run regiuues derived by is generally in good agreement with other simulations with ~=1., Note that the boundary between graze-and-merge and the adjacent partial accretion and hit-and-run regimes derived by is generally in good agreement with other simulations with $\gamma=1$. + However. he simulations of rubble pile collisions with ~=0.5 using the pkderav code found a nuch narrower eraze-and-nuieree reeime compared to the voundary derived frou SPU simulations of fluid. bodies.," However, the simulations of rubble pile collisions with $\gamma=0.5$ using the pkdgrav code found a much narrower graze-and-merge regime compared to the boundary derived from SPH simulations of fluid bodies." + More work is needed to wuderstand the boundaries of the eraze-andauerge regine and its dependence ou material xoperties., More work is needed to understand the boundaries of the graze-and-merge regime and its dependence on material properties. + As shown iu Table 1.. the last giant impact was ikelv to be erosive (554)) or to be a hit-aud-au- ) compared to all eiaut. impacts.," As shown in Table \ref{tab:outcomes}, the last giant impact was more likely to be erosive ) or to be a hit-and-run ) compared to all giant impacts." + The dvuunuical stimiug bv the last remaining planets leads to higher nuüpact velocities near the eund of planet formation conrpared to the total time average., The dynamical stirring by the last remaining planets leads to higher impact velocities near the end of planet formation compared to the total time average. + In Figure 2CC. uote that the distribution of impact velocites is more weighted to values 2L2500. for the last impact (erev filled histoeraun) compared to all giant nupacts (black histogram).," In Figure \ref{fig:vimpact}C C, note that the distribution of impact velocites is more weighted to values $>1.25 V_{\rm esc}$ for the last impact (grey filled histogram) compared to all giant impacts (black histogram)." + For the same reason. more of the projectiles in the last giaut hit-and-run event are eroded compared to all eiaut inipacts (35 out of GO events).," For the same reason, more of the projectiles in the last giant hit-and-run event are eroded compared to all giant impacts (35 out of 60 events)." + Note that the collisious considered iun groups 13 are ouly those that coutributed to the formation of the final planets., Note that the collisions considered in groups 1–3 are only those that contributed to the formation of the final planets. + At the beeinuine of the simulation. there should have been maux collisions between planctesimals. but they were not uodclecd.," At the beginning of the simulation, there should have been many collisions between planetesimals, but they were not modeled." + The collision outcome map for impacts between planetesinals with a mass ratio, The collision outcome map for impacts between planetesimals with a mass ratio +The quasar core is unresolved and well-detected.,The quasar core is unresolved and well-detected. +" Counts were extracted from a 1.5"" radius, circular region centered on the quasar position (α == 12220333.9; 6 == 443112), and background counts, estimated from an annulus 10""—20"" with the same center, were subtracted yielding 726-27 (0.3—8 keV) net counts (Table 3))."," Counts were extracted from a $''$ radius, circular region centered on the quasar position $\alpha$ = 33.9; $\delta$ = 12), and background counts, estimated from an annulus $10''-20''$ with the same center, were subtracted yielding $\pm$ 27 $-$ 8 keV) net counts (Table \ref{tb:counts}) )." +" A point source correction was applied for flux estimates using the CIAO tool arfcorr, which applies an energy-dependent PSF correction appropriate for the extraction region to the ARF (effective area) file."," A point source correction was applied for flux estimates using the CIAO tool arfcorr, which applies an energy-dependent PSF correction appropriate for the extraction region to the ARF (effective area) file." + The counts were grouped to yield a minimum of 15 per bin to perform spectral fitting., The counts were grouped to yield a minimum of 15 per bin to perform spectral fitting. +" A single, absorbed power-law spectral fit in the energy range (0.3—8 keV) shows absorption consistent with the Galactic 21.29x102° cm? (?),, which was accordingly fixed to this value."," A single, absorbed power-law spectral fit in the energy range $-$ 8 keV) shows absorption consistent with the Galactic $\times 10^{20}$ $^{-2}$ \citep{1992ApJS...79...77S}, which was accordingly fixed to this value." +" The resulting best fit slope, Γ--1.640.08 (X2,,~0.74, 42 degrees of freedom (dof)) is consistent with those generally reported for high-redshift, radio-loud quasars (e.g. ??,, ?,, Figure 3aa, ?))."," The resulting best fit power-law slope, $\Gamma = 1.64\pm0.08$ $\chi^2_{red} \sim +0.74$, 42 degrees of freedom (dof)) is consistent with those generally reported for high-redshift, radio-loud quasars (e.g. \citet{2011ApJ...738...53S,2006MNRAS.366..339B}, \citet{2005ApJS..156...13M}, , Figure \ref{fg:AGNfit}a a, \citet{1997ApJ...478..492C}) )." +" There is an emission line apparent at energy, E~2.5 keV, consistent with cold Fe Κα in the rest frame of the quasar."," There is an emission line apparent at energy, $\sim 2.5$ keV, consistent with cold Fe $\alpha$ in the rest frame of the quasar." +" Although only marginally significant, addition of a narrow Gaussian line at 2.5kkeV improves the fit, while a higher energy line kkeV, approximating ionized Fe) is clearly inconsistent."," Although only marginally significant, addition of a narrow Gaussian line at keV improves the fit, while a higher energy line keV, approximating ionized Fe) is clearly inconsistent." +" A spectral fit including a narrow line with energy, E=2.5 keV yields an EW=172+110 eeV with a power-law slope I'=1.66+0.08 (x2,4v0.70, 41 dof)."," A spectral fit including a narrow line with energy, $= 2.5$ keV yields an $172 \pm 110$ eV with a power-law slope $\Gamma = 1.66 \pm 0.08$ $\chi^2_{red} \sim +0.70$, 41 dof)." +" Given the large errors, the line energy and equivalent width are consistent with those reported for detected Fe Κα emission in radio-loud quasars (2100 eV, ?))."," Given the large errors, the line energy and equivalent width are consistent with those reported for detected Fe $\alpha$ emission in radio-loud quasars 100 eV, \citet{2006ApJ...642..113G}) )." + There is a suggestion (Figure 3bb) of further emission lines around 0.8 and 0.5 keV which roughly align with highly-ionized Si and Mg features ina photoionized spectrum in the quasar rest-frame., There is a suggestion (Figure \ref{fg:AGNfit}b b) of further emission lines around 0.8 and 0.5 keV which roughly align with highly-ionized Si and Mg features ina photoionized spectrum in the quasar rest-frame. + However they are not significant in this low-count, However they are not significant in this low-count +Drissenetal.(2000) have usedHST and eerouncd-based observatious to obtain CMDs of NGC 2363 aud discuss its star formation history and that of ueigliboring star clusters.,\citet{Dr00} have used and ground-based observations to obtain CMDs of NGC 2363 and discuss its star formation history and that of neighboring star clusters. + However. their analysis was mostly restricted to young stellar populations.," However, their analysis was mostly restricted to young stellar populations." + Of note is the discovery of a rare luminous blue variable (LBV) star in NGC 2366 by Drisseuetal.(1997). eeast of NGC 2363. aud presetuly the brighest optical source in the galaxy.," Of note is the discovery of a rare luminous blue variable (LBV) star in NGC 2366 by \citet{Dr97}, east of NGC 2363, and presently the brightest optical source in the galaxy." + The LBV star has been erupting since 199[., The LBV star has been erupting since 1994. + Drisseneal.(2001) lave monitored the photometric and spectroscopic time variatious of the LBV star wih theHST aid have coustructed a physical model for it., \citet{Dr01} have monitored the photometric and spectroscopic time variations of the LBV star with the and have constructed a physical model for it. + The general properties axl evolutiouary status οNGC 2366 liave been ciscussecl by Noeske (2000)., The general properties and evolutionary status of NGC 2366 have been discussed by \citet{No00}. +. They have used photometric and spectroscopic ground-based observatio1s to put coustraiuts on tlie age of tle oder stellar populatious i NGC 2366., They have used photometric and spectroscopic ground-based observations to put constraints on the age of the older stellar populations in NGC 2366. + Noeskeetal.(2000) concluded that the light of Νας 2366 is cominuated by stellar ;»opulatiouns with age not exceecdiiο 3 Cyr. significantly lower than the typical age of Z 5 Cyr cerived for the uuderlyiug stellar comj»onent of other dwarl galaxies.," \citet{No00} concluded that the light of NGC 2366 is dominated by stellar populations with age not exceeding 3 Gyr, significantly lower than the typical age of $\ga$ 5 Gyr derived for the underlying stellar component of other dwarf galaxies." + However their couclusious are based ou populatio svithesis of spectroscopic observaions. theHST oervallons o| Drisseneal.(2000.2001) no beiug deep enough for studying old stellar populalous.," However their conclusions are based on population synthesis of spectroscopic observations, the observations of \citet{Dr00,Dr01} not being deep enough for studying old stellar populations." + To reirecly 1le Situation. we have obtained «leep AST Wide Fiekl auc Planetary C'amer: (2(WEPC2 V and { iuages of NGC 2366.," To remedy the situation, we have obtained deep Wide Field and Planetary Camera 2 (WFPC2) $V$ and $I$ images of NGC 2366." + We use these data to look anew at both vouug aud old stellar poptlatious of he cometary cdwarl galaxy. aud discuss its evolutionary status., We use these data to look anew at both young and old stellar populations of the cometary dwarf galaxy and discuss its evolutionary status. + We describe the observations i1 Sect., We describe the observations in Sect. + 2., 2. + The distance to NGC 2366 is derived in Sect., The distance to NGC 2366 is derived in Sect. + 3., 3. + The stellar populations aud sta ‘formation history of NGC 2366 are discussed in Sect., The stellar populations and star formation history of NGC 2366 are discussed in Sect. + {., 4. + We summarize our finclinesOm in Sect., We summarize our findings in Sect. + 5., 5. + We have obtainedHST i1mages of NGC 2366 on 2000 December 12 during cycle 9 with the WEPC?2 through filters F555\ Vaud Fsliw. which we wi] refer to hereafter as V aud J.," We have obtained images of NGC 2366 on 2000 December 12 during cycle 9 with the WFPC2 through filters F555W and F814W, which we will refer to hereafter as $V$ and $I$." + The observatious were broken iuto ive subexposures in the V. filer aud into three subexposures in the f filter to permit identification and removal of cosmic rays., The observations were broken into five subexposures in the $V$ filter and into three subexposures in the $I$ filter to permit identification and removal of cosmic rays. + The total exposure tine was 6700s in V aud LLOOs in {., The total exposure time was 6700s in $V$ and 4100s in $I$. + The galaxy was positioned so that 1je brightest H region NGC 2363 is located in the PC fratje. to lase advantage [rom its twice as good spatial resolution.," The galaxy was positioned so that the brightest H region NGC 2363 is located in the PC frame, to take advantage from its twice as good spatial resolution." + The WEPC2 was orieuted in order the major axis of the galaxy. lies aloig the ciagonals of the PC and WES [rames., The WFPC2 was oriented in order the major axis of the galaxy lies along the diagonals of the PC and WF3 frames. + The scale of tιο WEPC? is 070016 per pixel in the PC frame and 01105 per pixel in ihe WF frames., The scale of the WFPC2 is 046 per pixel in the PC frame and 102 per pixel in the WF frames. +" Because he considerable major axis of NGC 2366 (aj. ~ QU"")) is larger than the combined diagonal lengths of the PC and WE3 frames (~ 160"")). the norihermost paris of the ealaxycould not be image."," Because the considerable major axis of NGC 2366 $a_{I_{25}}$ $\sim$ ) is larger than the combined diagonal lengths of the PC and WF3 frames $\sim$ ), the northermost parts of the galaxycould not be imaged." + Preliminary processing of the raw images including correctious for flat-Helding was done at, Preliminary processing of the raw images including corrections for flat-fielding was done at +predicted in this Letter distinguished. easily since they follows the high energy. (soft. N-rav) tail of the FUY lares (see also Wang. Li Alésszérros 2006). which is unexpected in any alternative model.,"predicted in this Letter can be distinguished easily since they follows the high energy (soft X-ray) tail of the FUV flares (see also Wang, Li Mésszárros 2006), which is unexpected in any alternative model." + Our prediction could be tested by the cooperation of and GLAST., Our prediction could be tested by the cooperation of and GLAST. + ‘This is possible asSwiff NICE usually slews to the GRB source in 100 seconds and. the field of view of the GLAST burst monitor (BAI) is all sky. not oceultecl by the earth and the Large Area Telescope (LAT) will slew to the GRB direction automatically in 5 minutes.," This is possible as XRT usually slews to the GRB source in $\sim 100$ seconds and, the field of view of the GLAST burst monitor (GBM) is all sky not occulted by the earth and the Large Area Telescope (LAT) will slew to the GRB direction automatically in $\sim 5$ minutes." + The physical process is as follows: A few minutes after he end of the prompt + ray emission. the central engine »ecomes active again and this renewed. activity gives. rise (cither via internal shocks or via magnetic dissipation) to a strong FUV flare.," The physical process is as follows: A few minutes after the end of the prompt $\gamma-$ ray emission, the central engine becomes active again and this renewed activity gives rise (either via internal shocks or via magnetic dissipation) to a strong FUV flare." + At this time the original ejecta that iis produced the CRB haspropagated into the circum-)urst matter., At this time the original ejecta that has produced the GRB haspropagated into the circum-burst matter. + The blast waves obtained a Blandford-Mcelxee xofile with a strong shock wave in its [ront (sce Fig. 1))., The blast waves obtained a Blandford-McKee profile with a strong shock wave in its front (see Fig. \ref{fig:Cartoon}) ). + Phe ]are PUY photons cannot be detected on earth as they are absorbed by the neutral LEvdrogen., The flare FUV photons cannot be detected on earth as they are absorbed by the neutral Hydrogen. + However. its high energy (soft N-rav) tail might be seen.," However, its high energy (soft X-ray) tail might be seen." + As the FUN photons catch up with the blast wave they cool the shock heated electrons hrough external inverse C'ompoton (EIC) scattering., As the FUV photons catch up with the blast wave they cool the shock heated electrons through external inverse Compoton (EIC) scattering. + A very small fraction of the FUY photons is boosted to a much uigher frequency. typically in sub-CGeV. range.," A very small fraction of the FUV photons is boosted to a much higher frequency, typically in sub-GeV range." + This can he observed as a sub-GeV. [are, This can be observed as a sub-GeV flare. + The basic mechanism is radiation produced. inside the ejecta at a small radius is Comptonized in the external blast wave at a much Larger. radius., The basic mechanism is radiation produced inside the ejecta at a small radius is Comptonized in the external blast wave at a much larger radius. + Beloborocoy (2005) considered. first. this elfect for Comptonization of prompt 10 keV photons in the reverse shock of the blast. wave.," Beloborodov (2005) considered, first, this effect for Comptonization of prompt 100 keV photons in the reverse shock of the blast wave." + The Comptonization of the prompt photons in the forward shock was investigated by Fan et al. (, The Comptonization of the prompt photons in the forward shock was investigated by Fan et al. ( +2005b).,2005b). + Wang ct al. (, Wang et al. ( +2006) considered a scenario in which X-ray photons [rom X-ray flares are upscattered to GeV ancl higher energies.,2006) considered a scenario in which X-ray photons from X-ray flares are upscattered to GeV and higher energies. + llowever. as we discuss later the observed X-ray Hare Duxes may be too low to produce a significant. observable CoV signal.," However, as we discuss later the observed X-ray flare fluxes may be too low to produce a significant observable GeV signal." + PUY Uares. that we discuss here. are motivated. by the very soft spectrum. of the observed: X-ray Lares.," FUV flares, that we discuss here, are motivated by the very soft spectrum of the observed X-ray flares." + Their fluence is not constrained. by current observations ancl the sub-CieV. flare that we predict is the only wav known to explore their existence., Their fluence is not constrained by current observations and the sub-GeV flare that we predict is the only way known to explore their existence. +" Furthermore. as we show below. a FUY Ποσο comparable to the [luence of current X-ray ]ares will produce a signal that can be observed by GLAST We focus on the FUV Dares taking place at 1001000 seconds after the burst since (1) +), decreases rapidly with ime."," Furthermore, as we show below, a FUV fluence comparable to the fluence of current X-ray flares will produce a signal that can be observed by GLAST We focus on the FUV flares taking place at $100-1000$ seconds after the burst since (i) $\gamma_m$ decreases rapidly with time." + At later times. the scattered. photons are not in the veh energy range. (," At later times, the scattered photons are not in the high energy range. (" +i) The carly FUY fares are relatively energetic and contain more seed. photons.,ii) The early FUV flares are relatively energetic and contain more seed photons. + For our purpose the total number of seed. photons (rather than the total energv) is more important as this determine the total number of high energy. (upscattered) οποίος., For our purpose the total number of seed photons (rather than the total energy) is more important as this determine the total number of high energy (upscattered) photons. + To obtain a reliable estimate of the number of detected photons we need to calculate the probability. of upscattered of a seed photon by the forward shock electrons. i.c.. the optical depth of these electrons refsecidepth)).," To obtain a reliable estimate of the number of detected photons we need to calculate the probability of upscattered of a seed photon by the forward shock electrons, i.e., the optical depth of these electrons \\ref{sec:depth}) )." + We also need to estimate the number of the Hare photons refsec:photon))., We also need to estimate the number of the flare photons \\ref{sec:photon}) ). + A simple estimate of these factors vields. for an ISM surrouncling: where 2 ds the radius of the forward shock. my the surrounding density. ν is the Uuence of the seed FUY photons’ [lare and με is their tvpical frequency.," A simple estimate of these factors yields, for an ISM surrounding: where $R$ is the radius of the forward shock, $n_0$ the surrounding density, ${\cal F}$ is the fluence of the seed FUV photons' flare and $\nu_{uv}$ is their typical frequency." +" S. is the detectors area and S,ο is the effective area of Large Area Telescope (LAT) onboard GLAST.", $S$ is the detectors area and $S_{\rm _{GLAST}}\sim 8000{\rm cm^2}$ is the effective area of Large Area Telescope (LAT) onboard GLAST. +" Here and throughout this text. the convention Q,=Q/IO0* has been acloptecl in ces units."," Here and throughout this text, the convention $Q_x=Q/10^x$ has been adopted in cgs units." + Later we elaborate on these estimates., Later we elaborate on these estimates. + We also need to take into account the important correction caused by the anisotropic emission of the scattered photons (in the comoving frame of the shocked material). which has been ignored. previously (see eqs. (12--14))," We also need to take into account the important correction caused by the anisotropic emission of the scattered photons (in the comoving frame of the shocked material), which has been ignored previously (see eqs. \ref{eq:j}- \ref{eq:f_cor}) )" + for details)., for details). + In the standard GRB afterglow mocel (e.g. Sari. Piran Naravan 1998: Piran 1999) the blast wave propagates into a constant density ISM.," In the standard GRB afterglow model (e.g. Sari, Piran Narayan 1998; Piran 1999) the blast wave propagates into a constant density ISM." +" In thiscase where ££ ds the isotropic. kinetic energy. of the initial GRB outllow. €,=13(p2)/3(p D)]. p~2.3 is the power-law index of the shocked electrons. / is the observer's timescale in units of second. z is the redshift of the burst. c. and cg represent the fractions of shock energy. given to the electrons and. magnetic filed. respectively."," In thiscase where $E_k$ is the isotropic kinetic energy of the initial GRB outflow, $C_p\equiv 13(p-2)/[3(p-1)]$ , $p\sim 2.3$ is the power-law index of the shocked electrons, $t$ is the observer's timescale in units of second, $z$ is the redshift of the burst, $\epsilon_e$ and $\epsilon_B$ represent the fractions of shock energy given to the electrons and magnetic filed, respectively." +" The Lorentz factor of the cooling electrons is where Y ids the Compton parameter. which is a sum of the synchrotron self-Compton. (SSC) parameter You, and the ELC parameter $,4,,."," The Lorentz factor of the cooling electrons is where $Y$ is the Compton parameter, which is a sum of the synchrotron self-Compton (SSC) parameter $Y_{_{SSC}}$ and the EIC parameter $Y_{_{EIC}}$ ." + Following FanPiran (2006: see Appendix A). 3...=[d(1|Yos)|ναVeedP1Lμηνfee $/2. where η= (e.g. Sari. Naravan Piran 1996).," Following FanPiran (2006; see Appendix A), $Y_{_{SSC}}\simeq +\{-(1+Y_{_{EIC}})+\sqrt{(1+Y_{_{EIC}})^2+4\eta +\eta_{_{KN}}\epsilon_e/\epsilon_B}\}/2$ , where $\eta=\min\{1,(\gamma_m/\gamma_c)^{(p-2)}\}$ (e.g. Sari, Narayan Piran 1996)." + The, The +"In this work, we have shown Lor the first ime that coronagraphic white-light images can be employed to esumate the shock compression ratio X not only at a single latitude and altitude (as in previous works), but all over the observed shock front.","In this work, we have shown for the first time that coronagraphic white–light images can be employed to estimate the shock compression ratio $X$ not only at a single latitude and altitude (as in previous works), but all over the observed shock front." +" The compression ratios computed for an event observed by have been used to esumate the Allvénnic Mach numbers for perpendicular, parallel and oblique shocks."," The compression ratios computed for an event observed by }/LASCO-C2 have been used to estimate the Alfvénnic Mach numbers for perpendicular, parallel and oblique shocks." +" The results show that at earlier umes the CME-driven shock is supereriuical at the top of the shock and suberiucal at the flanks, with the supercritical region disappearing with time."," The results show that at earlier times the CME-driven shock is supercritical at the top of the shock and subcritical at the flanks, with the supercritical region disappearing with time." +" The above results suggest the overall evolution qualitatively shown in Figure 3, with the CME-driven shock primarily super-criucal in its earlier phase (and hence an ellicient parücle accelerator)."," The above results suggest the overall evolution qualitatively shown in Figure 3, with the CME-driven shock primarily super-critical in its earlier phase (and hence an efficient particle accelerator)." +" In the following minutes, às the shock progressively lose its energy, the supereritical region becomes narrower and narrower, with the particle acceleration site progressively more localized in space."," In the following minutes, as the shock progressively lose its energy, the supercritical region becomes narrower and narrower, with the particle acceleration site progressively more localized in space." +" At the end of the process, the whole shock becomes suberiucal, so that no more efficient high energy particle acceleration 15 possible."," At the end of the process, the whole shock becomes subcritical, so that no more efficient high energy particle acceleration is possible." +" While the present result for a single event supports SEP generation at the CME/shock Iront in the higher corona, type HI emission at the CME flanks is sull expected in the lower corona due to interaction with nearby streamers (e.g.. Mancuso Raymond 2004), so that a more extended study will be required in order to draw a definite conclusion."," While the present result for a single event supports SEP generation at the CME/shock front in the higher corona, type II emission at the CME flanks is still expected in the lower corona due to interaction with nearby streamers (e.g., Mancuso Raymond 2004), so that a more extended study will be required in order to draw a definite conclusion." + These results have very important implications on the localization of parucle acceleration sites during CMEs and on the temporal evolution of SEP fluxes in CME-driven shocks., These results have very important implications on the localization of particle acceleration sites during CMEs and on the temporal evolution of SEP fluxes in CME–driven shocks. + A.B. acknowledges support from ASI/INAF 1/023/09/0 contract., A.B. acknowledges support from ASI/INAF I/023/09/0 contract. + SOHO 1s a project of international cooperation between ESA and NASA., SOHO is a project of international cooperation between ESA and NASA. +of and both lving within an ionized gas halo of dimension 4 arcmin (~9 pe) (Anantharamaiah. Pedlar Coss 1999).,"of and both lying within an ionized gas halo of dimension $\sim$ 4 arcmin $\sim$ 9 pc) (Anantharamaiah, Pedlar Goss 1999)." + Optical. ultraviolet. and soft N-rav observations of are curtailed due to heavy interstellar absorption in the line of sight. whereas hard X-ray to > -ray observations have provided only limited. information due to the lack of instruments allording sullicient spatial resolution.," Optical, ultraviolet, and soft X-ray observations of are curtailed due to heavy interstellar absorption in the line of sight, whereas hard X-ray to $\gamma$ -ray observations have provided only limited information due to the lack of instruments affording sufficient spatial resolution." + \laver-Llasselwander (1998). detected a significant. CieV. 5- pav source towards the with EGRET with a spatial accuracy of 0.2 deg (2I; 2852 = 3EG J1746| 2852. re-designated in Hartman 1999).," Mayer-Hasselwander \shortcite{Mayer1998} detected a significant GeV $\gamma$ -ray source towards the with EGRET with a spatial accuracy of 0.2 deg (2EG $-$ 2852 = 3EG $-$ 2852, re-designated in Hartman 1999)." + Melia (1908a. b) and Fatuzzo Alelia (2003). suggest that the 5-ravs may originate in East. although other possibilities. for example the candidate source may be Ser A or other point/dilluse sources. cannot be exeluded.," Melia (1998a, b) and Fatuzzo Melia (2003) suggest that the $\gamma$ -rays may originate in , although other possibilities, for example the candidate source may be Sgr $^*$ or other point/diffuse sources, cannot be excluded." + In the soft. N-rav. band. below 3 keV. although major part of the emission is absorbed. (Watsonοἱal.1981) andROSAT (Predehl Trümmper 1994) have detected a dilluse emission extending for ~20 arcmin.," In the soft X-ray band below 3 keV, although major part of the emission is absorbed, \cite{Watson1981} and (Predehl Trümmper 1994) have detected a diffuse emission extending for $\sim$ 20 arcmin." + The detailed structure in the close vicinity of Ser A was left unknown., The detailed structure in the close vicinity of Sgr A was left unknown. + In the harder X-ray band of 210 keV. withthe moderate spatial resolution of (the half power diameter (LIPD) οἱ 3 aremin). Wovama (1996) were not able to resolve Ser] 2AC. but did. see extended emissionun (2ET]«wf 3) with. a peak in surface brightness coinciding with Ser .," In the harder X-ray band of 2–10 keV, withthe moderate spatial resolution of (the half power diameter (HPD) of 3 arcmin), Koyama \shortcite{Koyama1996} were not able to resolve Sgr $^*$, but did see extended emission $2'\times3'$ ) with a peak in surface brightness coinciding with Sgr $^*$ ." + The spectrum of the extended. emission was found to have many emission lines from hiehly ionized atoms including both helium(Lo)-like ancl hyvedrogen(E)-Hike iron., The spectrum of the extended emission was found to have many emission lines from highly ionized atoms including both helium(He)-like and hydrogen(H)-like iron. + The overall spectral form is very similar to that of the hot plasma which is observed over the entire region except for the absence of a 6.4-keV line from neutral iron (Ixovama 1996: Maecda 1998: Sakano 2002)., The overall spectral form is very similar to that of the hot plasma which is observed over the entire region except for the absence of a 6.4-keV line from neutral iron (Koyama 1996; Maeda 1998; Sakano 2002). + A observation also confirmed the result (Sidoli&Mereghetti1999)., A observation also confirmed the result \cite{Sidoli_M1999}. +. Alore recently this region has been observed. by ACIS in. the hard X-ray band. at a spatia resolution of 0.5 aresec (Baganoll 2003: Maeda 2002) and Ser was resolved in the X-ray. band for the irst time (DaganolEctal.2003)., More recently this region has been observed by /ACIS in the hard X-ray band at a spatial resolution of 0.5 arcsec (Baganoff 2003; Maeda 2002) and Sgr $^*$ was resolved in the X-ray band for the first time \cite{Baganoff2003}. +. Intriguingly Baganoll (2004) have claimed on the basis of the most recen 1.5 Als observation. that. during quiescence the X-ray emission detected. from Ser X is slightly extended.," Intriguingly Baganoff (2004) have claimed on the basis of the most recent 0.5 Ms observation, that during quiescence the X-ray emission detected from Sgr $^*$ is slightly extended." + lHlowever. the peculiar X-ray Hares seen from the exac ocation of Ser A in both (Baganoll 2001) ancNALAL-New/on observations (CCGoldwurm 2002:Porquet 2003). are almost certainly modest Iuminosity outbursts on Ser A itself.," However, the peculiar X-ray flares seen from the exact location of Sgr $^*$ in both (Baganoff 2001) and observations (Goldwurm 2002;Porquet 2003), are almost certainly modest luminosity outbursts on Sgr $^*$ itself." + In the observation. bright dilfuse X-ray emission from was also cdetected and. resolved (Alaedactal.2002).," In the observation, bright diffuse X-ray emission from was also detected and resolved \cite{Maeda2002}." +. Phe X-ray. emission associated with fills the inner part of the non-thermal radio shell and has a spectrum characteristic of thin thermal emission at a temperature Al2 keV and a metal abundance Z~4 (Maecctal.2002)., The X-ray emission associated with fills the inner part of the non-thermal radio shell and has a spectrum characteristic of thin thermal emission at a temperature $kT\sim 2$ keV and a metal abundance $Z\sim 4$ \cite{Maeda2002}. +. As one of the Guaranteed. Time programmes. we have conducted. a survey of the region with NALAL-New/lon. including the field of Ser A.," As one of the Guaranteed Time programmes, we have conducted a survey of the region with , including the field of Sgr $^*$." + The mirrors and CCD imagine instruments oller an excellent. effective area as well as good energy. resolution GNEE~0.02 at 5.9 keV) and moderate spatial resolution (75 aresec)., The mirrors and CCD imaging instruments offer an excellent effective area as well as good energy resolution ${\Delta}E/E\sim0.02$ at 5.9 keV) and moderate spatial resolution $\sim$ 5 arcsec). + With this capability. we obtained spectra of excellent quality fromEast.," With this capability, we obtained spectra of excellent quality from." + Ehe first quick-Iook result of and its surroundings has been reported. in Sakano (900280)., The first quick-look result of and its surroundings has been reported in Sakano (2003b). + In this paper. we report our detailed results on as derived. from the observations and discuss their implications.," In this paper, we report our detailed results on as derived from the observations and discuss their implications." + We adopt a distance of S.0 kpc to theCentre throughout this paper (Reid1993)., We adopt a distance of 8.0 kpc to the throughout this paper \cite{Reid1993}. +. We focus on the observation of the Ser A region carried out on 2001 September 4 as part of a survey of the whole region. (see Warwick 2002 and Sakano 20020) and specifically concentrate on the results. from the European Photon Imaging. Camera (EPIC)., We focus on the observation of the Sgr A region carried out on 2001 September 4 as part of a survey of the whole region (see Warwick 2002 and Sakano 2003c) and specifically concentrate on the results from the European Photon Imaging Camera (EPIC). + Phe EPLC instrument comprises of two MOS CCD cameras (MOSI and 2: Turner 2001) ancl one pn CCD camera (Strüderetal.2001).. which work simultaneously.," The EPIC instrument comprises of two MOS CCD cameras (MOS1 and 2; Turner 2001) and one pn CCD camera \cite{Struder2001}, which work simultaneously." + The MOS and pn CCDs were operated in Full Frame and Extended Full Frame mocoe. respectively. with the medium ilter selected.," The MOS and pn CCDs were operated in Full Frame and Extended Full Frame mode, respectively, with the medium filter selected." + We have carried. out the data reduction and filtering with the Standard Analysis Software. (SAS) ουσ., We have carried out the data reduction and filtering with the Standard Analysis Software ) Ver.5.4. + A oweliminary screening. of the data was applied. to exclude intervals of high instrumental background. (based. on the ull-Licld light. curve above LO keV. which is dominated. by xwiicle background events).," A preliminary screening of the data was applied to exclude intervals of high instrumental background (based on the full-field light curve above 10 keV, which is dominated by particle background events)." + “Phe elfective exposure times or MOSI. 2 and pn after filtering are 23.0 ks. 23.1 ks. and 19.7 ks. respectively.," The effective exposure times for MOS1, 2 and pn after filtering are 23.0 ks, 23.1 ks, and 19.7 ks, respectively." + lor cach event. we accepted the pixel patterns of 0 (single to quadruple events) for MOS.," For each event, we accepted the pixel patterns of 0--12 (single to quadruple events) for MOS." + For pn. we only accepted. the single event (pattern of 0). because of the calibration uncertainties for other pixel patterns in the pn Extended Full Frame moce.," For pn, we only accepted the single event (pattern of 0) because of the calibration uncertainties for other pixel patterns in the pn Extended Full Frame mode." + lig., Fig. +" laa and b show images of the region encompassing the Ser A complex measured. respectively, in the hard (210 keV) and soft (0.5.1.43 keV) NX-rav bands with the MOSI12 cameras."," \ref{fig:img}a a and b show images of the region encompassing the Sgr A complex measured, respectively, in the hard (2–10 keV) and soft (0.5–1.4 keV) X-ray bands with the MOS1+2 cameras." + The highest surface brightness feature in the hard band coincides with the location of Ser X. the central massive black hole.," The highest surface brightness feature in the hard band coincides with the location of Sgr $^*$, the central massive black hole." + We find that the emission around Ser A? is not point-like and that Ser A® itself is not. resolved., We find that the emission around Sgr $^*$ is not point-like and that Sgr $^*$ itself is not resolved. + CGoldwurm et al. (, Goldwurm et al. ( +2002) have reported the occurrence of an X-ray [lare from Ser X at the very end ofthisobservation. but here we have specifically excluded data taken during this timeinterval [rom our analysis.,"2002) have reported the occurrence of an X-ray flare from Sgr $^*$ at the very end ofthisobservation, but here we have specifically excluded data taken during this timeinterval from our analysis." + According to recent. results. (Baganollctal. 2003).. Ser Ais the brightest individual sourcein thecentral 10 aresee region. however.," According to recent results \cite{Baganoff2003}, , Sgr $^*$is the brightest individual sourcein thecentral 10 arcsec region, however," +"To second. order in the Ποια��ς forces. taking into account that the average of the stochastic forces in the unperturbed state vanishes. and summing on the jj subindex to obtain the global elfect. we ect: where is the correlation matrix (see Appencix A: the symbol stands for the tensorial product of vectors Fyi- and ""nBo. he average is on the unperturbed states of particles à and ? and the invariance of the correlation matrix under time ranslation has been taken into account).","To second order in the fluctuating forces, taking into account that the average of the stochastic forces in the unperturbed state vanishes, and summing on the $i_{\mu}$ subindex to obtain the global effect, we get: where is the correlation matrix (see Appendix A; the symbol $\otimes$ stands for the tensorial product of vectors $\mbox{\boldmath $ $}_{i_{\gamma}}^{\alpha}$ and $\mbox{\boldmath $ $}_{ j_{\delta}}^{\beta}$, the average is on the unperturbed states of particles $\alpha$ and $\beta$ and the invariance of the correlation matrix under time translation has been taken into account)." + Because in the προος state two dilferent. particles are not correlated. he correlation matrix defined in the previous equation vanishes if az2.," Because in the unperturbed state two different particles are not correlated, the correlation matrix defined in the previous equation vanishes if $\alpha \neq \beta$." + This has been taken into account to deduce eq. (0-1) , This has been taken into account to deduce eq. \ref{dEgen}) ) +from eq. (33))., from eq. \ref{dEaver}) ). + Note that because for s>af he correlations vanish. thelower limit of the integrals can oe extended up to o.," Note that because for $s \ge \delta t$ the correlations vanish, thelower limit of the integrals can be extended up to $-\infty$." + Eq. (84)), Eq. \ref{dEgen}) ) + is the expression of the global instantaneous energy variation of subsystem. se due o the fluctuating forces of subsystem vv., is the expression of the global instantaneous energy variation of subsystem $\mu$ due to the fluctuating forces of subsystem $\nu$. + Phe integrand in he first term of the r.h.s., The integrand in the first term of the r.h.s. + of eq. (34)), of eq. \ref{dEgen}) ) + is invariant uncer ime reversal., is invariant under time reversal. + Extending the integral to positive s. this erm is the corresponding power spectrum at zero frequency (Wiener-Ixhintchine theorem. see Reif 1965 and DMO92) ancl. consequently. itis positive and represents a heating term of class jp particles due to the Huctuating forces caused by ν xuwticles.," Extending the integral to positive $s$, this term is the corresponding power spectrum at zero frequency (Wiener-Khintchine theorem, see Reif 1965 and BM92) and, consequently, it is positive and represents a heating term of class $\mu$ particles due to the fluctuating forces caused by $\nu$ particles." + It is of order O(4)1. relative to the second erm., It is of order $O({1 \over N}) \ll 1$ relative to the second term. + Terms of this kind will be neglected in this work., Terms of this kind will be neglected in this work. + The second term can be either positive or negative. depending on he sign of (2;μι ," The second term can be either positive or negative, depending on the sign of $(\beta_{\tilde{\nu}} - \beta_{\nu})$." +In the next section it will be explicitly calculated for jr.ip=D.5.," In the next section it will be explicitly calculated for $\mu, \nu = B, S$." + Enerev Lows between the satellite anc the background. as a result of either the global energy. variation of the satellite particles due to the [uctuating forces of the background. or. conversely. the elobal energy. variation of the background particles due to the Huetuating forces of the satellite.," Energy flows between the satellite and the background as a result of either the global energy variation of the satellite particles due to the fluctuating forces of the background, or, conversely, the global energy variation of the background particles due to the fluctuating forces of the satellite." + Phese Iluxes are given by eq. (84)), These fluxes are given by eq. \ref{dEgen}) ) + when f(xp., when $\mu \neq \nu$. + Let us first. calculate the clleet due to the stochastic forces of the background., Let us first calculate the effect due to the stochastic forces of the background. + This term could causean energy Ilux responsible for the satellite deacceleration., This term could causean energy flux responsible for the satellite deacceleration. + Iq. 34)), Eq. \ref{dEgen}) ) + with =SiD and neglecting the heating term. gives: where the correlation matrix is given by eq. CXI0))," with $\mu = S, \nu = B$ and neglecting the heating term, gives: where the correlation matrix is given by eq. \ref{A10}) )" + with o—D oand —0=., with $\alpha = B$ and $\gamma = \delta = S$ . + In the case of a point-like satellite with ms3mg. Js7g ancl then the satellite loses energy to the background.," In the case of a point-like satellite with $m_S \gg m_B$, $\beta_{S} \ll \beta_{B}$ and then the satellite loses energy to the background." + In our case. however. it is not excluded in principle that 747g and then the energy would [ow from the background to the satellite.," In our case, however, it is not excluded in principle that $\beta_{S} > \beta_{B}$ and then the energy would flow from the background to the satellite." + The integralover ds in eq. (36)), The integralover $ds$ in eq. \ref{EBS}) ) + can be caleulated taking into account eq. CX10)), can be calculated taking into account eq. \ref{A10}) ) + and the equality: where Ay is the projection of vector on the plane normal to vector V., and the equality: where $ \mbox{\boldmath $ $}_{\perp}$ is the projection of vector $ \mbox{\boldmath $ $}$ on the plane normal to vector $\mbox{\boldmath $ $} $. +" In our case cither — vj. vy, or = vj. (soo eq. (ΑΟ "," In our case either $\mbox{\boldmath $ $} \equiv \mbox{\boldmath $ $}_{j_{S}} - +\mbox{\boldmath $ $}_{h_{B}}$ or $\mbox{\boldmath $ $} \equiv +\mbox{\boldmath $ $}_{j_{S}}$, (see eq. \ref{A10}) ))," +and = rj. τιν 0r rj. Tv.," and $\mbox{\boldmath $ $} \equiv \mbox{\boldmath $ $}_{j_{S}} - +\mbox{\boldmath $ $}_{h_{B}}$ or $\mbox{\boldmath $ $} \equiv \mbox{\boldmath $ $}_{j_{S}} - +\mbox{\boldmath $ $}^{ '}$." +" We obtain: where the sum on a generic subindex. 4,. means A, times the average on velocity and positions of class à particles. and is carried. out by means of the distribution function given in eq. (27))."," We obtain: where the sum on a generic subindex, $i_{\alpha}$, means $N_{\alpha}$ times the average on velocity and positions of class $\alpha$ particles, and is carried out by means of the distribution function given in eq. \ref{fMax}) )." + To proceed. further. we recall that the velocity distribution. of background. particlesis assumed. to. be Alaxwellian with zero mean and dispersion ag. and the velocity distribution of the satellite particles has mean equal to the satellite center of mass velocity. veays. and dispersion as.," To proceed further, we recall that the velocity distribution of background particlesis assumed to be Maxwellian with zero mean and dispersion $\sigma_B$ , and the velocity distribution of the satellite particles has mean equal to the satellite center of mass velocity, $\mbox{\boldmath $ $}_{CMS}$ , and dispersion $\sigma_S$ ." +" Phe integration over dv),,, elves:", The integration over $d \mbox{\boldmath $ $}_{h_{B}}$ gives: +Da. respectively.,"$n_{\rm d}$, respectively." +" If densitics of neutral hydrogen atoms. protons. and electrons. are represented by rye. iy. and DS. respectively, we have mye=(loη and s,= in terms of the ionization degree. we. which varies with the radius. r. frou the central exciting source."," If densities of neutral hydrogen atoms, protons, and electrons, are represented by $n_{\rm H^0}$, $n_{\rm p}$, and $n_{\rm e}$ , respectively, we have $n_{\rm H^0}=(1-x)n_{\rm H}$ and $n_{\rm p}=n_{\rm +e}=xn_{\rm H}$ in terms of the ionization degree, $x$, which varies with the radius, $r$, from the central exciting source." + Iu addition. we assune the frequencies of all LC photous to be that of the Lyman limit. that is. all quantities are treated monochromatically iu our trausfer model.," In addition, we assume the frequencies of all LC photons to be that of the Lyman limit, that is, all quantities are treated monochromatically in our transfer model." + This is because we obtain oulv the uuuber of LC photous from observations of recombination lines or thermal radio enissions from IT regions., This is because we obtain only the number of LC photons from observations of recombination lines or thermal radio emissions from H regions. + We introduce a dineusiouless radius. y=rfRs. where Reis the classical Stronuueren radius which is defined as Tere Nee is the intrinsic production rate of LC photons of the central source. and ap is the Case D recombination cocficient of hydrogen.," We introduce a dimensionless radius, $y=r/R_{\rm S}$, where$R_{\rm S}$ is the classical Strömmgren radius which is defined as Here $N_{\rm LC}$ is the intrinsic production rate of LC photons of the central source, and $\alpha_B$ is the Case B recombination coefficient of hydrogen." + We consider the change of the number of LC photons passing through the shell whose inner aud outer radii are y aud y| dy. vespectively.," We consider the change of the number of LC photons passing through the shell whose inner and outer radii are $y$ and $y+dy$ , respectively." +" If the number of LC photous entering the shell per unit tine denotes το). its change in the shell is where sy and sq are cross sections for LC photous of neutral hydrogen atoms aud dust eraius. respectively. wods the dust albedo for these photons. aud a, is the recombination cocficicnt to the erouud state of hydrogen."," If the number of LC photons entering the shell per unit time denotes $N_{\rm LC}(y)$, its change in the shell is where $s_{\rm H}$ and $s_{\rm d}$ are cross sections for LC photons of neutral hydrogen atoms and dust grains, respectively, $\omega$ is the dust albedo for these photons, and $\alpha_1$ is the recombination coefficient to the ground state of hydrogen." + We neglect the asvuunetric effect of the dust scattering for sinplicitv., We neglect the asymmetric effect of the dust scattering for simplicity. + Since the shell is in ionization equilibrium. where ay is the cocticicut of lyvdrogen recombination to all levels.," Since the shell is in ionization equilibrium, where $\alpha_A$ is the coefficient of hydrogen recombination to all levels." + We note that à4.ap=04., We note that $\alpha_A-\alpha_B=\alpha_1$. + By equation (3)) and replacing aye with (Lordy. equation (2)) is reduced to where This is a correction term for existence of dust eras in the uchula.," By equation \ref{eq2-2}) ) and replacing $n_{\rm H^0}$ with $(1-x)n_{\rm H}$, equation \ref{eq2-1}) ) is reduced to where This is a correction term for existence of dust grains in the nebula." + If we define the total (gas | dust) optical depth for LC photons as we obtain Neatly)=Npce.," If we define the total (gas + dust) optical depth for LC photons as we obtain $N_{\rm LC}(y)=N_{\rm LC}\,e^{-\tau}$." + Then equation (3)) is reduced to ~ ⋅ ⋅ ⋅↴ ⋅⋅⋜∐⊔∖⊼⊓⋅↸∖⋯↸∖↸⊳⋜↧↴∖↴↸∖↑∐⋜↧↑∐∪≼⊔↕↴∖↴↕↴∖↴↕∐↴∖↴↕≼∐∖↑↕∐∖↸⊳⋜↕↖⇁↕↑↖⇁⋅↴∖↴↥⋅⋜⊔∐∏↴∖↴∙ where eds the helt speed., Then equation \ref{eq2-2}) ) is reduced to Now we define the ionization parameter as where $c$ is the light speed. + Then equatious (6)) aud (7)) are reduced to and respectively., Then equations \ref{eq2-5.1}) ) and \ref{eq2-3}) ) are reduced to and respectively. + Finally. we determine two recombination coeficicuts of hydrogen. o4 aud ap.," Finally, we determine two recombination coefficients of hydrogen, $\alpha_A$ and $\alpha_B$ ." + The cocficients are a fiction of the electron temperature. T; (Spitzer1978).," The coefficients are a function of the electron temperature, $T_{\rm +e}$ \citep{spi78}." +. Fitting values in Table 5.2 of Spitzer(1978).. we can approximate them to the following equation: for 20001.zT.Z1600018. where ¢=4 or B. aud ay=2.10 and ep1.61.," Fitting values in Table 5.2 of \cite{spi78}, we can approximate them to the following equation; for $2000\,{\rm K} \la T_{\rm e} \la 16000\,{\rm K}$, where $i=A$ or $B$, and $a_A=2.40$ and $a_B=1.64$." + The uncertainties of values determined by these equation are less than for the above range of T..., The uncertainties of values determined by these equation are less than for the above range of $T_{\rm e}$. + Let us estimate the dust effect that appears in the term. X.," Let us estimate the dust effect that appears in the term, $X$ ." + We adopt the dust extinction law in the Galactic interstellar οςια (ISM) developed dy Weineartucr&Draine (2001).. who have derived a size-distributiou function of dust erains composed of carbonaceous aud silicate populations by Draine&Lee(1981) auc Li&Draine (2001).," We adopt the dust extinction law in the Galactic interstellar medium (ISM) developed by \cite{wei01}, who have derived a size-distribution function of dust grains composed of carbonaceous and silicate populations by \cite{dl84} and \cite{li01}." +. Their carbonaceous erain includes PATI (polvevclic aromatic hydrocarbon) iiolecules., Their carbonaceous grain includes PAH (polycyclic aromatic hydrocarbon) molecules. + Weingartucr&Draine(2001) have developed the extinction laws for various valuesof By. which is the ratio of the visual extinction to color excess.," \cite{wei01} have developed the extinction laws for various valuesof $R_V$, which is the ratio of the visual extinction to color excess." + We approximate the optical depths for LC photons bv hydrogen and dust to those at 912A., We approximate the optical depths for LC photons by hydrogen and dust to those at 912. +". According to Weimeartucr&Draine(2001).. the dust cross sections per uit hydrogen nucleus at 912 iic. nas πο 2.515«10.23 σαι”. 1.676«10.23 οι”, and 1.087«10.7! cin. for Ry=3.1. L0. and 5.5. We note that these values are calibrated by lyδι=2.610. το”. where Ay is the livdrogeu column density."," According to \cite{wei01}, the dust cross sections per unit hydrogen nucleus at 912 i.e. $n_{\rm d}s_{\rm d}^{\rm 912\AA}/n_{\rm H}$ are $2.515 \times 10^{-21}$ $^2$, $1.676 \times 10^{-21}$ $^2$, and $1.087 \times 10^{-21}$ $^2$, for $R_V=3.1$, 4.0, and 5.5, We note that these values are calibrated by $A_I/N_{\rm +H}=2.6\times10^{-22}$ $^2$, where $N_{\rm H}$ is the hydrogen column density." + Also. the dust albedos at 912 aare 0.2[51. 0.269L. and 0.2989 for Ry=3.1. L0. aud 5.5. respectively.," Also, the dust albedos at 912 are 0.2451, 0.2694, and 0.2989 for $R_V=3.1$, 4.0, and 5.5, respectively." + If we adopt sp—(G341015 cu’. equation (5)) is reduced to Tere. we introduce a parameter for the dust distribution. the dineusionlessdust cavitys radius. gq. because the dust distribution+may have a radial+ dependence as stronely suggested in the literature (81).," If we adopt $s_{\rm H}^{\rm 912\AA} = 6.3\times10^{-18}$ $^2$ , equation \ref{eq2-5}) ) is reduced to Here, we introduce a parameter for the dust distribution, the dimensionlessdust cavity's radius, $y_{\rm d}$, because the dust distributionmay have a radial dependence as strongly suggested in the literature 1)." + Forsimplicity. we consider ⋀∖∪↖↖↖↖↸∖≼∐∖∱∐∐∖↑∐↸∖↕∪↕∐∠⋜↧⊓∪∐↻⋜⋯⋯∐∖↑↸∖↥⋜↧↴∖ aud the eas-dust ratio is ⋅constant outside of- it.," Forsimplicity, we consider an extremecase that no dust is inside the cavity's radius, $y_{\rm d}$ , and the gas-dust ratio is constant outside ofit." +-That - the dust term. IX. ds zero within yy. aud coustaut value _ outsideσεν ;ofὰ it.IBEage⋅ο We∙ad," That is, the dust term, $X$ , is zero within $y_{\rm d}$ , and constant value shown above outside ofit." +-That - the dust term. IX. ds zero within yy. aud coustaut value _ outsideσεν ;ofὰ it.IBEage⋅ο We∙ado," That is, the dust term, $X$ , is zero within $y_{\rm d}$ , and constant value shown above outside ofit." +-That - the dust term. IX. ds zero within yy. aud coustaut value _ outsideσεν ;ofὰ it.IBEage⋅ο We∙adop," That is, the dust term, $X$ , is zero within $y_{\rm d}$ , and constant value shown above outside ofit." +-That - the dust term. IX. ds zero within yy. aud coustaut value _ outsideσεν ;ofὰ it.IBEage⋅ο We∙adopt," That is, the dust term, $X$ , is zero within $y_{\rm d}$ , and constant value shown above outside ofit." +change in the observed two-day interval.,change in the observed two-day interval. + Evidence for the existence of the filament back on July 1st was presented in the BBSO Ha images (see Fig. 1))., Evidence for the existence of the filament back on July 1st was presented in the BBSO $\alpha$ images (see Fig. \ref{Fig:BBfil}) ). + This readily shows that the process that created the filament occurred well before our observations., This readily shows that the process that created the filament occurred well before our observations. +" We tentatively identify this previously existing filament with the spine region in our observations, and remark on the fact that it showed almost no evolution during our observing campaign."," We tentatively identify this previously existing filament with the spine region in our observations, and remark on the fact that it showed almost no evolution during our observing campaign." +" However, the PIL region was not inactive in this time lapse from the 3rd to the 5th of July."," However, the PIL region was not inactive in this time lapse from the 3rd to the 5th of July." + MDI line-of-sight magnetograms show a widening (on July 3rd) and a narrowing (on July 5th) of the opposite polarities of the AR., MDI line-of-sight magnetograms show a widening (on July 3rd) and a narrowing (on July 5th) of the opposite polarities of the AR. + The photospheric longitudinal magnetic field obtained with TIP-II on July 3rd also indicates a wide separation of both polarities compared to the more compact PILs observed on July 5th., The photospheric longitudinal magnetic field obtained with TIP-II on July 3rd also indicates a wide separation of both polarities compared to the more compact PILs observed on July 5th. +" On this day, the field of view included not only the spine region, but also the newly appeared orphan penumbrae and pores."," On this day, the field of view included not only the spine region, but also the newly appeared orphan penumbrae and pores." + This region has a magnetic topology different from that of the spine discussed before., This region has a magnetic topology different from that of the spine discussed before. + The upper panels of Fig., The upper panels of Fig. + 10 show chromospheric field lines with a normal polarity configuration (above y~ 15”)).," \ref{Fig:vector5jul} show chromospheric field lines with a normal polarity configuration (above $y \sim +15$ )." +" The horizontal fields there are stronger than in the spine, reaching up to GG (see ?).."," The horizontal fields there are stronger than in the spine, reaching up to G \citep[see][]{kuckein09}." + This normal polarity configuration suggests the presence of field lines that directly connect opposite polarities., This normal polarity configuration suggests the presence of field lines that directly connect opposite polarities. +" On the other hand, and most noticeably, in the lower panels of Fig. 10,configuration."," On the other hand, and most noticeably, in the lower panels of Fig. \ref{Fig:vector5jul},." +" The strengths of these PIL-aligned fields are large, in the range of GG. Now, the shear is seen in the photosphere, below the chromospheric arching field lines in a normal configuration."," The strengths of these PIL-aligned fields are large, in the range of G. Now, the shear is seen in the photosphere, below the chromospheric arching field lines in a normal configuration." +" If a flux rope above the photosphere were found in the spine region, a similar flux rope would be necessarily sitting underneath it, at photospheric heights."," If a flux rope above the photosphere were found in the spine region, a similar flux rope would be necessarily sitting underneath it, at photospheric heights." + Note that a simple potential arcade model can be excluded here since for such a configuration., Note that a simple potential arcade model can be excluded here since for such a configuration. +" In the scenario that we suggest, the Helium Stokes profiles would be mapping the top arching field lines with a normal configuration, while the axis of the rope, with"," In the scenario that we suggest, the Helium Stokes profiles would be mapping the top arching field lines with a normal configuration, while the axis of the rope, with" +were identical to (he Tppii=1 simulation. in order to verify that (he spectral hardening al radio [requencies is indeed partially a consequence of our magnetic field parametrization.,"were identical to the $\tau_{\rm T, BLR} = 1$ simulation, in order to verify that the spectral hardening at radio frequencies is indeed partially a consequence of our magnetic field parametrization." + Fie., Fig. + 9 shows that the impact of a strong external Compton component on the optical and X-rav light curves is very moderate., \ref{ext_lc} shows that the impact of a strong external Compton component on the optical and X-ray light curves is very moderate. + In. particular. the light curves at. energies below the svuehrotron cutoff remain virtually unchanged.," In particular, the light curves at energies below the synchrotron cutoff remain virtually unchanged." + However. a strong external Compton component. dominating the bolometric luminosity τμ20.1 in our case) leads to a significantly faster decay of the light curves at N-rav energies bevond the svnchrotron entoll.," However, a strong external Compton component, dominating the bolometric luminosity $\tau_{\rm T, BLR} \gtrsim 0.1$ in our case) leads to a significantly faster decay of the light curves at X-ray energies beyond the synchrotron cutoff." + Just as the light curves. also the X-ray spectral hysteresis characteristics remain virtually unchanged. even in the case of a stronely dominant external Compton component. except for a moderate softening of the local spectrum in (he decaving phase of the flare at energies bevond the svnchrotron cutolf (see Fig. 10)).," Just as the light curves, also the X-ray spectral hysteresis characteristics remain virtually unchanged, even in the case of a strongly dominant external Compton component, except for a moderate softening of the local spectrum in the decaying phase of the flare at energies beyond the synchrotron cutoff (see Fig. \ref{ext_hic}) )." + The value of the electron injection spectral index g should be rather easily determined by measuring (he time-averaged oplical N-ray spectral index of the strongly cooled svnchrotron spectrum., The value of the electron injection spectral index $q$ should be rather easily determined by measuring the time-averaged optical – X-ray spectral index of the strongly cooled synchrotron spectrum. + As illustrated in Fig. 11..," As illustrated in Fig. \ref{q_intspectra}," + this spectral change is accompanied by a shift of the σος peak towards higher frequencies as (he injection spectrum hardens: For q>2.5. the SSC peak is. located at exsec55164. While. forB g«i 2.5. itn shiftsate towards essec5564.L7 ," this spectral change is accompanied by a shift of the SSC peak towards higher frequencies as the injection spectrum hardens: For $q > 2.5$ , the SSC peak is located at $\epsilon_{\rm SSC} \sim \gamma_1^2 \epsilon_{\rm sy}$, while for $q < 2.5$ , it shifts towards $\epsilon_{\rm SSC} \sim +\gamma_2^2 \epsilon_{\rm sy}$." +As illustrated in Fig. 12..," As illustrated in Fig. \ref{q_lc}," + the characteristics of the light curves are only marginally different [or different. values of q., the characteristics of the light curves are only marginally different for different values of $q$. + The X-ray spectral hysteresis al N-rayv. energies below the svnchrotron cutoff is obviously shifted according to the change in injection spectral index. but its basic Doaracteristies remain unchanged (see Fig. 13)).," The X-ray spectral hysteresis at X-ray energies below the synchrotron cutoff is obviously shifted according to the change in injection spectral index, but its basic characteristics remain unchanged (see Fig. \ref{q_hic}) )." + An interesting qualitative change of the spectral hysteresis can be seen for energies just above the svuchrotron cutoll: While for hare Meclron injection spectra (q« 2.5). the peak flux is reached al a steep local X-ray spectrum i.e. (he spectrum is dominated by (he svnchrotron component at the (time of peak flux). a soft injection spectrum (q7 2.5) leads to a hard local spectral index at the time of peak flux (i.e. (he spectrum is dominated by (he SSC component at that time).," An interesting qualitative change of the spectral hysteresis can be seen for energies just above the synchrotron cutoff: While for hard electron injection spectra $q < 2.5$ ), the peak flux is reached at a steep local X-ray spectrum (i.e. the spectrum is dominated by the synchrotron component at the time of peak flux), a soft injection spectrum $q > 2.5$ ) leads to a hard local spectral index at the time of peak flux (i.e. the spectrum is dominated by the SSC component at that time)." + In order to investigate the influence of the duration of the electron. injection event causing the flare. we have performed simulations with 3 different. values of /;j. where we kept the total energv input during the flare constant. (simulations no.," In order to investigate the influence of the duration of the electron injection event causing the flare, we have performed simulations with 3 different values of $t_{\rm inj}$, where we kept the total energy input during the flare constant (simulations no." + 2. 11. aud 12).The üime-averaged SEDs [rom those simulations are virtually indistinguishable.," 2, 11, and 12).The time-averaged SEDs from those simulations are virtually indistinguishable." + Fig., Fig. +14 shows,\ref{duration_lc} shows +"this line provides no information on the snow line, which is located close to the star, near R~1 AU in this model (see Fig. 1)).","this line provides no information on the snow line, which is located close to the star, near $R\sim 1$ AU in this model (see Fig. \ref{temp_and_abun}) )." +" At an inclination 4=0° (face-on disk), the line width is determined by the turbulent velocity óv and the line opacity."," At an inclination $i=0^\circ$ (face-on disk), the line width is determined by the turbulent velocity $\delta v$ and the line opacity." +" The center of the line is strongly self-absorbed for no freeze-out, since the emission produced at Ny~10??—1035 cm? is absorbed by the upper layers."," The center of the line is strongly self-absorbed for no freeze-out, since the emission produced at $N_{\rm H}\sim +10^{22}-10^{23}$ $^{-2}$ is absorbed by the upper layers." + These regions are sub-thermally excited because the densities are low (ng<10? cm?)., These regions are sub-thermally excited because the densities are low $n_{\rm H}<10^8$ $^{-3}$ ). +" Self-absorption occurs, but to a lesser extent, when freeze-out is included and the residual water vapor abundance is z;(H53O0)—10-5."," Self-absorption occurs, but to a lesser extent, when freeze-out is included and the residual water vapor abundance is $x_f$ $_2$ $10^{-8}$." + Even for z;(H530)—10- the line is still optically thick.," Even for $x_f$ $_2$ $10^{-10}$, the line is still optically thick." +" For finite inclination 10,angles, i=30? and 60°, flux loss at line center can also occur for the freeze-out model with a water vapor abundance r;(H3O)=10-719."," For finite inclination angles, $i=30^\circ$ and $60^\circ$, flux loss at line center can also occur for the freeze-out model with a water vapor abundance $x_f({\rm H_2O})=10^{-10}$." + This is most clearly seen for the case óv=0.5 km s-!., This is most clearly seen for the case $\delta v= 0.5$ km $^{-1}$. +" This is not a signature of the snow line, since the flux loss occurs for i=60°, for example, for velocities v<2 km s, corresponding to radii R>50 AU."," This is not a signature of the snow line, since the flux loss occurs for $i=60^\circ$, for example, for velocities $v<2$ km $^{-1}$, corresponding to radii $R>50$ AU." +" In Fig. 3,,"," In Fig. \ref{noise_added_model}," + we test how well the shape of the 119— line can be measured byHerschel., we test how well the shape of the $1_{10}-1_{01}$ line can be measured by. +" The model is shown in black, and a lo noise level of 0.5 mK has been added in green."," The model is shown in black, and a $\sigma$ noise level of 0.5 mK has been added in green." + The sensitivity of theHerschel detectors at 1113.34 GHz is about four times less than at 556.936 GHz., The sensitivity of the detectors at 1113.34 GHz is about four times less than at 556.936 GHz. +" According to the time estimator for theHerschel Space Observatory (http://www.esac.esa.int), a lo noise level of 0.5 and 2.0 mK can be obtained at the frequencies of the 119—191 ortho and 111—00ο para transition, respectively, in about 4 hours of observing time, when frequency switching is used and a spectral resolution of 1 km s~! is requested."," According to the time estimator for the Space Observatory (http://www.esac.esa.int), a $\sigma$ noise level of 0.5 and 2.0 mK can be obtained at the frequencies of the $1_{10}-1_{01}$ ortho and $1_{11}-0_{00}$ para transition, respectively, in about 4 hours of observing time, when frequency switching is used and a spectral resolution of 1 km $^{-1}$ is requested." +" Thus one should be able to determine the width, and to some degree the shape of the 149—191 ortho-H3O line."," Thus one should be able to determine the width, and to some degree the shape of the $1_{10}-1_{01}$ $_2$ O line." +" However, the effect of self-absorption due to high opacities will be hard to distinguish for low turbulent velocities (óv<1.0 km 1) at this resolution."," However, the effect of self-absorption due to high opacities will be hard to distinguish for low turbulent velocities $\delta v \leq 1.0$ km $^{-1}$ ) at this resolution." + The para line is not a good candidate as the ortho transition for obtaining a line shape at the same noise level because of the decrease in sensitivity., The para line is not a good candidate as the ortho transition for obtaining a line shape at the same noise level because of the decrease in sensitivity. +" The line profiles and integrated intensities of the 110—{οι and its ratio with the 11;—Ooo transition are affected by inclination angle, turbulent broadening, and the residual water vapor abundance after freeze-out."," The line profiles and integrated intensities of the $1_{10}-1_{01}$ and its ratio with the $1_{11}-0_{00}$ transition are affected by inclination angle, turbulent broadening, and the residual water vapor abundance after freeze-out." +" The dust opacity, which is influenced by grain growth and settling, can also play a role, although our study of these effects indicates that this is less important than the variables just mentioned."," The dust opacity, which is influenced by grain growth and settling, can also play a role, although our study of these effects indicates that this is less important than the variables just mentioned." +" T'hus the models are degenerate in the sense that different parameter sets give the same line shapes and intensities, due to the high opacities in these lines."," Thus the models are degenerate in the sense that different parameter sets give the same line shapes and intensities, due to the high opacities in these lines." +" Unfortunately, these are the only lines to be observed in the WISH program."," Unfortunately, these are the only lines to be observed in the WISH program." +" Observing higher excitation transitions would help, but the decrease in sensitivity with frequency means that only line fluxes and not line shapes can be determined byHerschel observations."," Observing higher excitation transitions would help, but the decrease in sensitivity with frequency means that only line fluxes and not line shapes can be determined by observations." +" At a velocity resolution of 1 km s-!, it would takeHerschel about 4 hours to get the 1o noise level down to 2 mK for transition frequencies around ~1100 GHz."," At a velocity resolution of 1 km $^{-1}$, it would take about 4 hours to get the $\sigma$ noise level down to 2 mK for transition frequencies around $\sim 1100$ GHz." +" In a similar observation around ~1700 GHz, the noise level would be 8 mK. Inspection of Table 1 shows that higher transitions may be observable withHerschel."," In a similar observation around $\sim 1700$ GHz, the noise level would be 8 mK. Inspection of Table 1 shows that higher transitions may be observable with." +" We will now focus on the 312—303 transition at 1097.37 GHz and the 201—212 transition at 1661.01 GHz, although other lines may also have diagnostic value."," We will now focus on the $3_{12}-3_{03}$ transition at 1097.37 GHz and the $2_{21}-2_{12}$ transition at 1661.01 GHz, although other lines may also have diagnostic value." + Fig., Fig. +" 4 plots the ratios of these two lines to the fundamental 119—191 transition, and shows that the ratios can distinguish between different levels of water vapor in the freeze-out zone."," \ref{ratios} plots the ratios of these two lines to the fundamental $1_{10}-1_{01}$ transition, and shows that the ratios can distinguish between different levels of water vapor in the freeze-out zone." +" The model results for no freeze-out are found in the right upper part of the figure, where there are three segments for inclination 0?, 30? and 60?; each segment consists of two values of the turbulent velocity, óv=0.5 and 2.0 km s~!."," The model results for no freeze-out are found in the right upper part of the figure, where there are three segments for inclination $i=0^\circ$ , $30^\circ$ and $60^\circ$; each segment consists of two values of the turbulent velocity, $\delta v=0.5$ and $2.0$ km $^{-1}$." + Similar sets for r;=10-5 (middle part) and v;=10-!? (left lower part) are clearly in a different part of the diagram and do not overlap with each other., Similar sets for $x_f = 10^{-8}$ (middle part) and $x_f = 10^{-10}$ (left lower part) are clearly in a different part of the diagram and do not overlap with each other. + The variations due to inclination and turbulent velocity are smaller than those associated with freeze-out., The variations due to inclination and turbulent velocity are smaller than those associated with freeze-out. + We have shown that it should be possible to observe some far-infrared rotational lines of water with the HIFT instrument onHerschel that are produced in regions between radii R~10—100 AU., We have shown that it should be possible to observe some far-infrared rotational lines of water with the HIFI instrument on that are produced in regions between radii $R\sim 10-100$ AU. + The current scheduled observations of the 110—191 and 111—Ooo transitions would provide information on the spatial distribution of water and on turbulence if the inclination of the disk is known., The current scheduled observations of the $1_{10}-1_{01}$ and $1_{11}-0_{00}$ transitions would provide information on the spatial distribution of water and on turbulence if the inclination of the disk is known. +" The ratios of these lines are quite similar for the different models (~0.9— 1.0), which is due to the high opacities in both lines."," The ratios of these lines are quite similar for the different models $\sim 0.9-1.0$ ), which is due to the high opacities in both lines." + The line shapes of the 119—101 transition for different water vapor residuals in the freeze- zone are quite similar at the same inclination angle., The line shapes of the $1_{10}-1_{01}$ transition for different water vapor residuals in the freeze-out zone are quite similar at the same inclination angle. +" When measurements of the 119—191 line are combined with higher transitions, such as the 315—393, and 221—212 "," When measurements of the $1_{10}-1_{01}$ line are combined with higher transitions, such as the $3_{12}-3_{03}$ , and $2_{21}-2_{12}$ " +The rising Ne abundance with increasing temperature observed in active regions could be mimiced by an ion population error in Ne IX. but (he requirecl errors are again of order a [actor of 2 al temperatures of logZ~6.6. or a shift in the Ne IX ion population curve toward higher temperatures by oor so.,"The rising Ne abundance with increasing temperature observed in active regions could be mimiced by an ion population error in Ne IX, but the required errors are again of order a factor of 2 at temperatures of $\log T\sim 6.6$, or a shift in the Ne IX ion population curve toward higher temperatures by or so." + Such a shift would also require commenstuate changes in the Ne X population. and it seems difficult to introduce such a change in Ne without invoking similar changes in (he O ion balance.," Such a shift would also require commensurate changes in the Ne X population, and it seems difficult to introduce such a change in Ne without invoking similar changes in the O ion balance." + The calculations presented here employ the most recent ion balance assessment currently available (Bryansetal.2009).. and it seems highly unlikely that residual errors of such magnitude remain.," The calculations presented here employ the most recent ion balance assessment currently available \citep{Bryans.etal:09}, and it seems highly unlikely that residual errors of such magnitude remain." + We have also repeated the abundance calculations for the ionization equilibria of Mazzottaetal.(1993). and Arnaud&Rothenflig(1985)., We have also repeated the abundance calculations for the ionization equilibria of \cite{Mazzotta.etal:98} and \citet{Arnaud.Rothenflug:85}. +. The latter result in slighilv lower temperatures from Fe XVII and Fe XVIII lines by about 0.1 dex. and systematically higher Ne/O abundance ratios bv a similar amount. but the abundance trends are unaffected (see also below).," The latter result in slightly lower temperatures from Fe XVII and Fe XVIII lines by about 0.1 dex, and systematically higher Ne/O abundance ratios by a similar amount, but the abundance trends are unaffected (see also \\ref{s:saturated} below)." + Desaiοἱal.(2005). found the Fe XVIII Al4.21 resonance line strength: predicted. by CIILANTI v4.2 and other databases appeared lower by rrelative to the A93.92 resonance 2p—2s line compared with the ratio observed in Capella., \citet{Desai.etal:05} found the Fe XVIII $\lambda 14.21$ resonance line strength predicted by CHIANTI v4.2 and other databases appeared lower by relative to the $\lambda 93.92$ resonance $2p-2s$ line compared with the ratio observed in Capella. + More recent. Fe XVIII electron. collisional excitation calculations have been published by Witthoeftetal.(2007)., More recent Fe XVIII electron collisional excitation calculations have been published by \citet{Witthoeft.etal:07}. +. Using these data. DelZanna(2006) finds good agreement between observed and predicted Fe XVIII line strengths.," Using these data, \citet{Del_Zanna:06} finds good agreement between observed and predicted Fe XVIII line strengths." + It is these data that are included in CHIANTI v6.0.1 used here., It is these data that are included in CHIANTI v6.0.1 used here. + We conclude that atomic data errors are a very unlikely explanation for the observed temperature trend in Ne/O. and (hat it is (he underlying abundance ratio itself which is responsible.," We conclude that atomic data errors are a very unlikely explanation for the observed temperature trend in Ne/O, and that it is the underlying abundance ratio itself which is responsible." + We noted in rels:abunrats that the mean Ne/O abundance ratio indicated by the data in Figure 4. is somewhat lower than the assessments of Asplindetal.(2005.2009) ancl (1993)..," We noted in \\ref{s:abunrats} that the mean Ne/O abundance ratio indicated by the data in Figure \ref{f:abuns} is somewhat lower than the assessments of \citet{Asplund.etal:05,Asplund.etal:09} and \citet{Grevesse.Sauval:98}." + The mean ratio would tend to reconciliation with these values were the estimated aclive region temperatures to be svstematically too high by ~0.15 dex or so., The mean ratio would tend to reconciliation with these values were the estimated active region temperatures to be systematically too high by $\sim 0.15$ dex or so. + In this regard. the ionization balance of Arnaud&Rothenflig(1985). provides better agreement with the solar assessments than (hat of Bryansοἱal. (2009)..," In this regard, the ionization balance of \citet{Arnaud.Rothenflug:85} provides better agreement with the solar assessments than that of \citet{Bryans.etal:09}. ." + ILowever. the trend with temperature cannot be erased by plausible adjustments of the estimated temperatures: the scatter in the," However, the trend with temperature cannot be erased by plausible adjustments of the estimated temperatures: the scatter in the" +The log of the observations is even in Table 1.,The log of the observations is given in Table 1. + The data reduction was done with the Exteuded Scientific Aualvsis System (Zinuucrinann et YZ Cue was detecte in every pointing. the countrate was determined by applying a maxinuun-likelihood technique which compares the observed photon distribution with the point spread function of the WRI (Cruddace et The resulting couutrates are giveu in Table 1.," The data reduction was done with the Extended Scientific Analysis System (Zimmermann et YZ Cnc was detected in every pointing, the countrate was determined by applying a maximum-likelihood technique which compares the observed photon distribution with the point spread function of the HRI (Cruddace et The resulting countrates are given in Table 1." + YZ Cue is much brighter than the backeround countrate: the errors in the countrate are therefore dominated by Poisson statistics on the detected muuber of source counts., YZ Cnc is much brighter than the background countrate; the errors in the countrate are therefore dominated by Poisson statistics on the detected number of source counts. + We investigate the variation of the N-vav flux of YZ Cue through the outburst evele. and also on the orbital timescale.," We investigate the variation of the X-ray flux of YZ Cnc through the outburst cycle, and also on the orbital timescale." + In Figure 1 we show the optical lighiteurve of YZ Cue roni April 5 to 26. 1998. as deteriued by the American Association of Variable Star Observers. together with he DRI countrates listed in Table 1.," In Figure 1 we show the optical lightcurve of YZ Cnc from April 5 to 26, 1998, as determined by the American Association of Variable Star Observers, together with the HRI countrates listed in Table 1." + The optical ightcurve shows maxima of ordinary outbursts occurring on 22150912 aud 22150921. aud a superouthurst naxinnun near 22150930.," The optical lightcurve shows maxima of ordinary outbursts occurring on 2450912 and 2450921, and a superoutburst maximum near 2450930." + Tn comparing the N-rav countrates with the optical iehteurves we remark on three features of Fig., In comparing the X-ray countrates with the optical lightcurves we remark on three features of Fig. + 1., 1. + First. he URI countrates are lower during the optical outbursts han in the quiescent intervals.," First, the HRI countrates are lower during the optical outbursts than in the quiescent intervals." + Second. in both quiesceut iutervals that we cover. the couutrate is lower in the later observation.," Second, in both quiescent intervals that we cover, the countrate is lower in the later observation." + Third. i both outbursts that we cover. the Πο wm lower m the later oheermration.," Third, in both outbursts that we cover, the countrate is lower in the later observation." + The distuibution of the photons over the energv channels of the TRI is the same for the observations taking diving outburst as for those taken cing quiescence., The distribution of the photons over the energy channels of the HRI is the same for the observations taking during outburst as for those taken during quiescence. + Comparison of the distributions obtained for the first observatious during outburst tthose of April 8 aud 16) with those obtained during the later outburst observations (of April 10 and 15) sugecsts that the decrease im X-rays is niareduallv less a the lower cuereies. tthat the spectrun becomes slightly softer as the optical outburst proceeds.," Comparison of the distributions obtained for the first observations during outburst those of April 8 and 16) with those obtained during the later outburst observations (of April 10 and 18) suggests that the decrease in X-rays is marginally less at the lower energies, that the spectrum becomes slightly softer as the optical outburst proceeds." + The significance of this softening is marginal. but it suffices to show that the decrease of the N-ray flux cannot be due to the disappearance of an ultra-soft colpoucut.," The significance of this softening is marginal, but it suffices to show that the decrease of the X-ray flux cannot be due to the disappearance of an ultra-soft component." + Tn accordance with these findines. we iuterpret the change in TRI countrates divine the outburst cvcle as a change mainly in the amount of gas that cuits kkeV photons.," In accordance with these findings, we interpret the change in HRI countrates during the outburst cycle as a change mainly in the amount of gas that emits $~$ keV photons." + This amount drops gradually during quiescence. more dramatically iu the begimuing of an outburst. and eradually again as the outburst proceeds.," This amount drops gradually during quiescence, more dramatically in the beginning of an outburst, and gradually again as the outburst proceeds." + We have searched. for short-term variability by dividing the individual observations m smaller intervals., We have searched for short-term variability by dividing the individual observations in smaller intervals. + For the outburst data we determine the average couutrate during cach ROSAT orbit: for the higher couutrate curing quiescenceo We use bius of sx. Figure 2 show the resulting liehteurves., For the outburst data we determine the average countrate during each ROSAT orbit; for the higher countrate during quiescence we use bins of s. Figure 2 show the resulting lightcurves. + Significant variation is present both diving outburst and during quiesceunce., Significant variation is present both during outburst and during quiescence. + During carly ordinary outburst (April 8.16) the variation appears dominated by a long-term decline.," During early ordinary outburst (April 8,16) the variation appears dominated by a long-term decline." + No orbital variation is apparent in any of the outburst data., No orbital variation is apparent in any of the outburst data. + During quiescence. the flux level at a given orbital phase varies as much as the overall variation.," During quiescence, the flux level at a given orbital phase varies as much as the overall variation." + We have folded the variation on the orbital period of 0.08692dd. and find uo siguificaut variation ou the orbital period. in1 quiescence or in1 outburst.," We have folded the variation on the orbital period of d, and find no significant variation on the orbital period, in quiescence or in outburst." + Any orbital variation is less than the inmegular variations seen in Fie., Any orbital variation is less than the irregular variations seen in Fig. + 2., 2. + To compare our observations with previous ROSAT PSPC observations. we note that for à 2-3kkeV thermal Προςπι as found for YZ Cuc by Vau Teescling VVeybunt (1991) the ROSAT PSPC (channels 50-201) countrate is similar to the Eimstein IPC countrate. and about twice the ROSAT TRI couutrate.," To compare our observations with previous ROSAT PSPC observations, we note that for a keV thermal spectrum as found for YZ Cnc by Van Teeseling Verbunt (1994) the ROSAT PSPC (channels 50-201) countrate is similar to the Einstein IPC countrate, and about twice the ROSAT HRI countrate." + From the results listed iu Table 1. we therefore expect countrates in the ROSAT PSPC (ch.550-201) or Eiustein IPC of 0.22-0.17 cts/s in quicscence aud of (.017-0.025 cts/s during outburst.," From the results listed in Table 1, we therefore expect countrates in the ROSAT PSPC 50-201) or Einstein IPC of 0.22-0.17 cts/s in quiescence and of 0.047-0.025 cts/s during outburst." + The Al-Sky Survey observation was obtained from 10 to 12 October 1990. dduving the outburst which ponlked on Octobov TO {2or¢t]o TOGO)," The All-Sky Survey observation was obtained from 10 to 12 October 1990, during the outburst which peaked on October 10 (Bortle 1990)." + The conmtvato (41, The countrate (in + The conmtvato (41), The countrate (in + (e.g.2) (e.g.?).. (e.g.?).. (e.g.?)..," \cite[e.g.][]{Haa96} \cite[e.g.][]{Efs92}, \cite[e.g.][]{Hui97}, \cite[e.g.][]{Rau97a}." + (??) (22??) (?).. 2>2. (??) Ha (e.g.??).. (e.g.??)..," \citep{Sch03,Fau08a} \citep{Gal95,Hop04,Hop07,Bou09} \citep{Dav01}, $z>2$ \citep{Mad99,Fau08b} \citep{Loe95,Fau08c} $\alpha$ \cite[e.g.][]{Car82,Bat88}, \cite[e.g.][]{Cen94,Rau97b}." + difficult or impossible at low redshift., difficult or impossible at low redshift. + We are motivated to constrain the current model with a different. low redshift measurement.," We are motivated to constrain the current model with a different, low redshift measurement." + Instead of using Lyman-« forest features. we pursue a measurement of the UVB powered. Ha emission that should occur in the outskirts of local disk galaxies.," Instead of using $\alpha$ forest features, we pursue a measurement of the UVB powered, $\alpha$ emission that should occur in the outskirts of local disk galaxies." + As a secondary motivation. the kinematics of Ha at distances beyond HI data are important probes to the total dark halo masses in nearby disk galaxies (?)..," As a secondary motivation, the kinematics of $\alpha$ at distances beyond HI data are important probes to the total dark halo masses in nearby disk galaxies \citep{Chr08}." + Galactic disks are optically thick to Lyman limit photons and maintain their observed HI distributions through self-shielding against the UVB., Galactic disks are optically thick to Lyman limit photons and maintain their observed HI distributions through self-shielding against the UVB. + As recognized for decades (???).. the influence of the UVB may be investigated in the extreme outskirts of disks where the self-shielding begins to fail.," As recognized for decades \citep{Sun69,Fel69,Boc77}, the influence of the UVB may be investigated in the extreme outskirts of disks where the self-shielding begins to fail." + These early works sought to measure this effect through disk truncation in HI., These early works sought to measure this effect through disk truncation in HI. + However. there appear to be cases with (??) and without (???) HI truncations above the critical column density predicted using current UVB estimates. implying that other processes may strip gas and mimic the result.," However, there appear to be cases with \citep{Cor89,vGo93} and without \citep{Wal97,Car98,Oos07} HI truncations above the critical column density predicted using current UVB estimates, implying that other processes may strip gas and mimic the result." + Moreover. reaching the UVB implied truncation thresholds in 21 em measured HI would require rather long observations with current facilities.," Moreover, reaching the UVB implied truncation thresholds in 21 cm measured HI would require rather long observations with current facilities." + A more robust signature of the UVB strength would be the detection of the Ha in these outskirt regions.Hahas been found at such radii before in actively starformingandwarped galaxies by ?(hereafterBFQ)with Fabry-Perot staring measurements., A more robust signature of the UVB strength would be the detection of the $\alpha$ in these outskirt regions.$\alpha$has been found at such radii before in actively starformingandwarped galaxies by \citet{Bla97} (hereafterBFQ)with Fabry-Perot staring measurements. + However. the iHa)2.3410. 1? erg/s/em?/LI ," However, the $\mu(H\alpha)=2.3\times$ $^{-19}$ $^2$ " +could be the result of disruption of chemical network brought on bv the infusion of atomic hydrogen to the shocked gas by repeated shocks. as atomic hydrogen rapidly destrovs many ol the intermediate molecules in the reaction network.,"could be the result of disruption of chemical network brought on by the infusion of atomic hydrogen to the shocked gas by repeated shocks, as atomic hydrogen rapidly destroys many of the intermediate molecules in the reaction network." + To derive an estimate of IIC] column density from the low signal-to-noise detection. we use ΠΛΟΙΟ simulation to reproduce an TIC] line of 0.2 IX with a FWIIM of 10 citepvanDishoeck1993..," To derive an estimate of HCl column density from the low signal-to-noise detection, we use RADEX simulation to reproduce an HCl line of 0.2 K with a FWHM of 10 \\citep{vanDishoeck1993}." + The resulting ICT column density of 3xLO’ 7. when compared to an ecolumn density of 1x107? (vanDishoeck.Jansen.&Phillips1993). leads to an LLC] abundance of 3x101.," The resulting HCl column density of $3\times10^{12}$ $^{-2}$, when compared to an column density of $1\times10^{22}$ \citep{vanDishoeck1993}, leads to an HCl abundance of $3\times10^{-10}$." + Again. the weak IICI line emission [rom 1C443 Chump GI may be the result of relatively low IC] abundance ancl ecolumu density.," Again, the weak HCl line emission from IC443 Clump G1 may be the result of relatively low HCl abundance and column density." + More observations of similar cores are needed (o confirm that shocked gas mav have a somewhat lower HIC] abundance compared to other similarly dense gas in star forming regions. PDRs. aud Ultra-compact HII regions.," More observations of similar cores are needed to confirm that shocked gas may have a somewhat lower HCl abundance compared to other similarly dense gas in star forming regions, PDRs, and Ultra-compact HII regions." + Ultra-compact LIT regions with reasonably high emission measures have proven to be a lreasure (rove for detecting HC] absorption (see Figure 4))., Ultra-compact HII regions with reasonably high emission measures have proven to be a treasure trove for detecting HCl absorption (see Figure \ref{fig:spectra4}) ). + Such cases twpically involve a delicate balance between a emission feature and an absorption feature., Such cases typically involve a delicate balance between a emission feature and an absorption feature. + Our forthcoming paper (Yoshidaetal.2010) will discuss these cases., Our forthcoming paper \citep{hiro2010} will discuss these cases. + In Figure 2. we shown that the IC line profile for IRC+10216 could be adequately fit by (wo Gaussians centered al —17.3 ‘ancl —27.4 rrespectivelv. indicating that the ILC] emission is associated with a cireumstellar shell with an expansion velocity of 4.8|.," In Figure \ref{fig:spectra2} we shown that the HCl line profile for IRC+10216 could be adequately fit by two Gaussians centered at $-17.8$ and $-27.4$ respectively, indicating that the HCl emission is associated with a circumstellar shell with an expansion velocity of 4.8." +" The HC] emission is likely [rom a densitv-enhanced shell at. 215"" ", The HCl emission is likely from a density-enhanced shell at $\sim$ +where (0). is the phase of Qu. ancl describes the phase shift taking place curing the two coupling processes.,"where $\Phi(Q_0)$ is the phase of $Q_0$, and describes the phase shift taking place during the two coupling processes." +" Equation (34)) gives a second order polynomial in w,. which physical solution is: where owe defined two frequencies typical of the adveetive-acoustic evele and of the horizontal propagation: Note that in principle & depends on the frequency. therefore. Equation (35)) gives explicitly. the [requenevy only if we know the value of 9."," Equation \ref{eq:phaseQ}) ) gives a second order polynomial in $\omega_r$, which physical solution is: where we defined two frequencies typical of the advective-acoustic cycle and of the horizontal propagation: Note that in principle $\Phi$ depends on the frequency, therefore Equation \ref{eq:w_aac}) ) gives explicitly the frequency only if we know the value of $\Phi$." + In the following of this subsection. we suppose 9?=O0 which turns out to be a good approximation in this tov model.," In the following of this subsection, we suppose $\Phi=0$ which turns out to be a good approximation in this toy model." + This is not always true in the spherical model as will be ciscussed in Section 5.2.2.., This is not always true in the spherical model as will be discussed in Section \ref{sec:SASI_spectrum}. + ligure 7 compares this analvtical result with cigenmodes computed numerically., Figure \ref{fig:toyspectrum_aac} compares this analytical result with eigenmodes computed numerically. + Phe agreement is very eood both with advective-acoustic modes and. with the full modes (Le. the modes that verify Equation (5))). in the regime of propagative acoustic waves.," The agreement is very good both with advective-acoustic modes and with the full modes (i.e. the modes that verify Equation \ref{eq:QR}) )), in the regime of propagative acoustic waves." + “Phe left panel shows that the approximations mace are valid. and that there is no significant phase shift.," The left panel shows that the approximations made are valid, and that there is no significant phase shift." + The right panel shows that the frequeney of the full modes is cüictated by the acdvective-acoustic evele. as could be expected from the results of ?..," The right panel shows that the frequency of the full modes is dictated by the advective-acoustic cycle, as could be expected from the results of \citet{foglizzo09}." + One can nonetheless notice that the purely acoustic evele has an influence on the growth rate of the modes. (especially those close to marginal stability. (211). since the unstable modes are not exactly the same on the two panels.," One can nonetheless notice that the purely acoustic cycle has an influence on the growth rate of the modes (especially those close to marginal stability, \citep{foglizzo09}) ), since the unstable modes are not exactly the same on the two panels." +" Ehe origin of the stable a,=1 mode at very low frequency. which does not. coincide with any curve. is rather uncertain (it lies in the regime of evanescent acoustic waves. which is not described by Equation (35)))."," The origin of the stable $n_x=1$ mode at very low frequency, which does not coincide with any curve, is rather uncertain (it lies in the regime of evanescent acoustic waves, which is not described by Equation \ref{eq:w_aac}) ))." + From Figure 7 and Equation (35)). one may notice that two successive modes sharing the same transverse structure are separated by a frequeney. dillerence that is close to the frequency of a vertical advective-acoustic evele Wane.," From Figure \ref{fig:toyspectrum_aac} and Equation \ref{eq:w_aac}) ), one may notice that two successive modes sharing the same transverse structure are separated by a frequency difference that is close to the frequency of a vertical advective-acoustic cycle $\omega_{\rm aac}$." +" This is exact in the case of one-dimensional modes. but only approximative for m,=0."," This is exact in the case of one-dimensional modes, but only approximative for $n_x\neq 0$." + Indeeda transverse advective-acoustie mode has a slightly higher frequeney than the corresponding LD mode (hy a factor ab most 1/(1AM) for a propagative mode)., Indeeda transverse advective-acoustic mode has a slightly higher frequency than the corresponding 1D mode (by a factor at most $1/(1-\M)$ for a propagative mode). + Γι» higher frequeney may sccm counterintuitive at first sight. because the geometrical path along which the waves propagate during one ονο]ο is longer.," This higher frequency may seem counterintuitive at first sight, because the geometrical path along which the waves propagate during one cycle is longer." + Εις longer path is the reason why the duration of the evele increases with inclination in Equation (33)) giving the growth rate., This longer path is the reason why the duration of the cycle increases with inclination in Equation \ref{eq:wi_aac}) ) giving the growth rate. + Llowever this duration corresponds to the group velocity of acoustic waves. while the frequency is determined by a phase relation.," However this duration corresponds to the group velocity of acoustic waves, while the frequency is determined by a phase relation." + The evele time relevant to the frequency is thus given by the phase speed., The cycle time relevant to the frequency is thus given by the phase speed. + Phe vertical phase speed of an acoustic wave increases with inclination. because the wave fronts get closer to the vertical direction.," The vertical phase speed of an acoustic wave increases with inclination, because the wave fronts get closer to the vertical direction." + This explains the higher frequeney of non radial modes., This explains the higher frequency of non radial modes. + The frequency of the purely acoustic modes. can be obtained by a very similar method to that usec for the adyvective-acoustic modes., The frequency of the purely acoustic modes can be obtained by a very similar method to that used for the advective-acoustic modes. +" For this purpose. one combines Equations (25)) and (27)) to obtain: where Tacs ds the duration. of a one-climensional purely acoustic evele (A.=0): ὃν taking the argument of this complex equation. we obtain: [rom which one can deduce the following expression for the frequeney of purely acoustic modes: where wae: is the frequency associated to a vertical acoustic propagation: Equation (41)) is analogous to the frequency of the acoustic modes of a rectangular box with periodic boundary conditions in .r and rellexive boundary conditions in z (it is only slightly mocilied by advection): Thus as argued in Section 3. if the number of wavelengths in the transverse direction (n,) increases. the frequeney increases typically by wre, corresponding to a propagation time in the transverse clirection."," For this purpose, one combines Equations \ref{eq:R}) ) and \ref{eq:R0}) ) to obtain: where $\tau_{{\rm ac}z}$ is the duration of a one-dimensional purely acoustic cycle $k_x=0$ ): By taking the argument of this complex equation, we obtain: from which one can deduce the following expression for the frequency of purely acoustic modes: where $\omega_{{\rm ac}z}$ is the frequency associated to a vertical acoustic propagation: Equation \ref{eq:w_acoustic}) ) is analogous to the frequency of the acoustic modes of a rectangular box with periodic boundary conditions in $x$ and reflexive boundary conditions in $z$ (it is only slightly modified by advection): Thus as argued in Section \ref{sec:radial_time}, if the number of wavelengths in the transverse direction $n_x$ ) increases, the frequency increases typically by $\omega_{{\rm ac}x}$ corresponding to a propagation time in the transverse direction." + Similarly if the number of waveleneth in the vertical direction (77. ) increases. the frequency increases typically by aye: Corresponding to an acoustic propagation along the vertical direction.," Similarly if the number of wavelength in the vertical direction $n_z$ ) increases, the frequency increases typically by $\omega_{{\rm ac}z}$ corresponding to an acoustic propagation along the vertical direction." +" Equation (41)) (with &= 0) is compared with the numerically computed cigenmoces in Figure δι,", Equation \ref{eq:w_acoustic}) ) (with $\Phi=0$ ) is compared with the numerically computed eigenmodes in Figure \ref{fig:toyspectrum_acoustic}. + Ht agrees with the purely acoustic modes. (all stable). showing here again that the approximation of small growth rate holds and that the phase shift is not very significant.," It agrees with the purely acoustic modes (all stable), showing here again that the approximation of small growth rate holds and that the phase shift is not very significant." + By contrast. the frequency. of the full modes do not match the purely. acoustic prediction.," By contrast, the frequency of the full modes do not match the purely acoustic prediction." + This confirms that the unstable modes are not dominated by the purely acoustic evele. and that the study of the frequency spectrum enables to discriminate between the two mechanisms.," This confirms that the unstable modes are not dominated by the purely acoustic cycle, and that the study of the frequency spectrum enables to discriminate between the two mechanisms." + Although the purely acoustic cevele does not determine the mode frequencies. ib can be observed from Figure S that the acoustic timescale inlluences the modes stability.," Although the purely acoustic cycle does not determine the mode frequencies, it can be observed from Figure \ref{fig:toyspectrum_acoustic} that the acoustic timescale influences the modes stability." + Indeed. the full modes in the vicinity of an acoustic branch are more likely to be unstable than the other modes.," Indeed, the full modes in the vicinity of an acoustic branch are more likely to be unstable than the other modes." +" Furthermore. the most unstable mioces (for a given n,) are all close to the branch 5n.= 0."," Furthermore, the most unstable modes (for a given $n_x$ ) are all close to the branch $n_z=0$ ." + These observations can be interpreted by two phenomena., These observations can be interpreted by two phenomena. + First. a constructive interference. between the purely. acoustic and advyective-acoustic eveles takes place when the mode frequeney (determined by the acdveetive-acoustic evele)," First, a constructive interference between the purely acoustic and advective-acoustic cycles takes place when the mode frequency (determined by the advective-acoustic cycle)" +Since 1997 — 40 gamma-ray burst (GRB) optical afterglows (OAs) have been discovered (see the GRB compilation of J. )).,Since 1997 $\sim$ 40 gamma-ray burst (GRB) optical afterglows (OAs) have been discovered (see the GRB compilation of J. ). + GRBs generally occur in subluminous host galaxies with redshifts ranging from 2=0.1685 (GRB 030329: Hjorth et al. 2003)), GRBs generally occur in subluminous host galaxies with redshifts ranging from $z=0.1685$ (GRB 030329; Hjorth et al. \cite{Hjor03}) ) + to =150 (GRB 000131: Andersen et al. 20000)., to $z=4.50$ (GRB 000131; Andersen et al. \cite{Ande00}) ). + Most of the GRB hosts are subluminous and have bluer optical/near-IR colours than the local galaxies or the typical galaxies detected by the Infrared Space Observatory (ISO) and the Submillimeter Common-User Bolometer Array (SCUBA) (e.g. Le Floc’h et al. 2003)), Most of the GRB hosts are subluminous and have bluer optical/near-IR colours than the local galaxies or the typical galaxies detected by the Infrared Space Observatory (ISO) and the Submillimeter Common-User Bolometer Array (SCUBA) (e.g. Le Floc'h et al. \cite{LeFl03}) ). + The afterglow of GRB 000418 was discovered in the near-infrared (NIR) 2.5 days after the gamma-ray event (Klose et al. 2000a))., The afterglow of GRB 000418 was discovered in the near-infrared (NIR) 2.5 days after the gamma-ray event (Klose et al. \cite{Klos00a}) ). + The optical counterpart was rather faint (2=21.63 2.[5 days after the GRB) in comparison to other afterglows (see Fig.," The optical counterpart was rather faint $R=21.63$, $2.48$ days after the GRB) in comparison to other afterglows (see Fig." + 3 of Gorosabel et al., 3 of Gorosabel et al. + 2002a for comparison purposes)., \cite{Goro02a} for comparison purposes). + The R-band light curve decayed as t17? typical of OAs (Klose et al. 2000b)).," The $R$ -band light curve decayed as $t^{-1.22}$ typical of OAs (Klose et al. \cite{Klos00b}) )," + flattening off at a level of R~21 due to the underlying host galaxy (Bloom et al. 2000))., flattening off at a level of $R \sim 24$ due to the underlying host galaxy (Bloom et al. \cite{Bloo00}) ). + The afterglow ts one of the reddest(2IV= 1) detected to date (see Fig., The afterglow is one of the reddest $R-K=4$ ) detected to date (see Fig. + 2 of Gorosabel et al. 2002b))., 2 of Gorosabel et al. \cite{Goro02b}) ). + Klose et al. (2000b)), Klose et al. \cite{Klos00b}) ) + suggested that the red colour is caused by reddening due to dust extinction in the host galaxy and they estimated an extinction of “ly—0.9 mag.," suggested that the red colour is caused by reddening due to dust extinction in the host galaxy and they estimated an extinction of $A_{\rm V} \sim +0.9$ mag." + Berger et al. (2001)), Berger et al. \cite{Berg01}) ) + found Ayo0.E mag for the OA., found $A_{\rm V} \sim 0.4$ mag for the OA. + HST/STIS observations performed on 4.17 UT June 2000 (46.76 days after the GRB) revealed that the OA occurred in a very compact host galaxy with a half-light radius of ~0713 (Metzger et al. 2000)), HST/STIS observations performed on 4.17 UT June 2000 (46.76 days after the GRB) revealed that the OA occurred in a very compact host galaxy with a half-light radius of $\sim 0\farcs13$ (Metzger et al. \cite{Metz00}) ) + corresponding to about 1 kpe., corresponding to about 1 kpc. + The redshift of the host galaxy was determined to be 1.115 (Bloom et al. 2002.. 2003)).," The redshift of the host galaxy was determined to be $z=1.118$ (Bloom et al. \cite{Bloo02}, \cite{Bloo03}) )." + A preliminary DV RT-band SED fitting analysis showed that the host galaxy SED can be fitted with starburst galaxy templates. but not with an evolved stellar population (Gorosabel et al. 2001)).," A preliminary $BVRI$ -band SED fitting analysis showed that the host galaxy SED can be fitted with starburst galaxy templates, but not with an evolved stellar population (Gorosabel et al. \cite{Goro01}) )." + This result has, This result has +example) new planetary nebulae which would be of interest to someone.,example) new planetary nebulae which would be of interest to someone. + The technique as implemented was (o search all (he 894 north ancl 894 south survey fields visually. for objects resembling the known Andromeda dwarf spheroidals aud Tucana. that is of very low surface brightness and large (one to several minutes of arc in size).," The technique as implemented was to search all the 894 north and 894 south survey fields visually, for objects resembling the known Andromeda dwarf spheroidals and Tucana, that is of very low surface brightness and large (one to several minutes of arc in size)." + In addition. any object which appeared to be resolving into faint stus was included.," In addition, any object which appeared to be resolving into faint stars was included." + To screen out plate defects and reflection nebulae. candidates were required to be on both red and blue copies of the field.," To screen out plate defects and reflection nebulae, candidates were required to be on both red and blue copies of the field." +" At the same time. each field was rated as ""good"" (no apparent Galactic interference). “troublesome” (Galactic nebulosity. present. but not covering the whole plate. averaging to something like 50%)). or ""poor"" (little or no freedom from the Milkv. Way) io provide a rough estimate of Galactic obscuration."," At the same time, each field was rated as “good” (no apparent Galactic interference), “troublesome” (Galactic nebulosity present, but not covering the whole plate, averaging to something like ), or “poor” (little or no freedom from the Milky Way) to provide a rough estimate of Galactic obscuration." + A total of 338 real objects were listed from the plate examination., A total of 338 real objects were listed from the plate examination. + Catalogs were consulted for these objects. and those which were known to be Local Group dwarls. or not. set aside as non-candidates (we provide a list of (hose below).," Catalogs were consulted for these objects, and those which were known to be Local Group dwarfs, or not, set aside as non-candidates (we provide a list of those below)." + Follow-up observations were made of these objects using the 1.511 at Cerro Tololo Observatory. the 2.1m at Witt Peak National Observatory. and the 2.5m Isaac Newton Telescope at Observatorio del Roque de los Muchachos on the islaud of La Palma.," Follow-up observations were made of these objects using the 1.5m at Cerro Tololo Inter-American Observatory, the 2.1m at Kitt Peak National Observatory, and the 2.5m Isaac Newton Telescope at Observatorio del Roque de los Muchachos on the island of La Palma." + Each was imaged in H in sullicient depth to show the tip of the Red Giant Branch at a nominal distace of 1 Alpe., Each was imaged in $R$ in sufficient depth to show the tip of the Red Giant Branch at a nominal distace of 1 Mpc. + Those objects which resolved into stars were also imaged in V and J (o provide a coloranagnilude diagram and (hus a determination of distance., Those objects which resolved into stars were also imaged in $V$ and $I$ to provide a color-magnitude diagram and thus a determination of distance. + Time sometimesallowed images also in narrowhancl Ila. to distinguish LIT regions from stars ancl confirm the icentification of emission nebulae.," Time sometimesallowed images also in narrowband $\alpha$, to distinguish HII regions from stars and confirm the identification of emission nebulae." + In all we had 206 candidates (134 north. 72 south) and 132 non-candidates (92 north. 40 south).," In all we had 206 candidates (134 north, 72 south) and 132 non-candidates (92 north, 40 south)." + Six objects in the north and six in (he south could not be detected in follow-up observations: this fact will be discussed below., Six objects in the north and six in the south could not be detected in follow-up observations; this fact will be discussed below. + There is clearly a strong asvmmetry. amounting to a [actor of two between the north and the south.," There is clearly a strong asymmetry, amounting to a factor of two between the north and the south." + This cannot not be traced. as in much of astronomy. to a matter of historical development or to differences in equipment or techniques.," This cannot not be traced, as in much of astronomy, to a matter of historical development or to differences in equipment or techniques." + We believe it to happen because a large number of Local Group dwarl candidates must actually be larger. more distant galaxies. but not more distant: Chev will be in nearby groups.," We believe it to happen because a large number of Local Group dwarf candidates must actually be larger, more distant galaxies, but not more distant; they will be in nearby groups." + There are simply more of these. and more populous ones. in (he northern sky. plus of course the Virgo Cluster.," There are simply more of these, and more populous ones, in the northern sky, plus of course the Virgo Cluster." + Observational data on Local Group dwarl galaxy. candidates from the POSS-II survey are presented in Table 1 and from the ESO/SRC plates in Table 2..., Observational data on Local Group dwarf galaxy candidates from the POSS-II survey are presented in Table \ref{northcand} and from the ESO/SRC plates in Table \ref{southcand}. . + All data were derived, All data were derived +photometric parallax.,photometric parallax. + Cizis (2000) have calibrated this relation. deriving valid for spectral types later than M6.5.," Gizis (2000) have calibrated this relation, deriving valid for spectral types later than M6.5." + We have used this relation to estimate cdistauces to LTT dwarfs in the current sample with (J-hy)>0.99., We have used this relation to estimate distances to NLTT dwarfs in the current sample with $_S) > 0.99$. + Tables 6 and 7 present the results., Tables 6 and 7 present the results. + Table 6 lists niue dwar(s with previous spectroscopic observations. including LHS 2090. an M6.5 dwarf recently ideutified as LyinD>ο within the &-parsec sample (Scholzal.. 2001): LP 911-20. the nearest isolated. brown dwarf (Tinney. 1998): four cwarfs [rom the ultracool 2MLASS sample selected by Gigis (1999): aud an earlier type dwarf. LP &60-16. which appears coincident with one of the ighter stars in Arclila (2001) U Sco photometric survey.," Table 6 lists nine dwarfs with previous spectroscopic observations, including LHS 2090, an M6.5 dwarf recently identified as lying within the 8-parsec sample (Scholz, 2001); LP 944-20, the nearest isolated brown dwarf (Tinney, 1998); four dwarfs from the ultracool 2MASS sample selected by Gizis (1999); and an earlier type dwarf, LP 860-46, which appears coincident with one of the brighter stars in Ardila (2001) U Sco photometric survey." + Τιible 7 collects data for a further 12 ultracool dwarls selected from our current sample based on the 2MLASS photometry., Table 7 collects data for a further 42 ultracool dwarfs selected from our current sample based on the 2MASS photometry. + We have estimated distances to these chwarls using the (Mg. (J-Ixg)) relation given above.," We have estimated distances to these dwarfs using the $_K$, $_S$ )) relation given above." + While the majority of these stars have uo prior observatious. niue dwarls have jptical photometry.," While the majority of these stars have no prior observations, nine dwarfs have optical photometry." + Photometric parallaxes derived [rom the latter data (usually (V-Ix4)) iudicate larger distances than the (J-Ixs) calibration., Photometric parallaxes derived from the latter data (usually $_S$ )) indicate larger distances than the $_S$ ) calibration. + hideed. the optically-based distances for the three brightest Ciclas stars are a [actor of four higher than the near-infrared calibration.," Indeed, the optically-based distances for the three brightest Giclas stars are a factor of four higher than the near-infrared calibration." + These stars probably have spectral types earlier than M6.5. but have near-infrared colours on the red extreme of the CI-Ixs) distribution.," These stars probably have spectral types earlier than M6.5, but have near-infrared colours on the red extreme of the $_S$ ) distribution." + The agreement between dy and dya is better amongst the [aiuter (apparent maenituce)e stars in Table 7 (whie1 are also likely to have fainter absolute magnitudes). although the near-infrared. colour iudex still tends to give lower distauces by ~30%.," The agreement between $_f$ and $_{J-K}$ is better amongst the fainter (apparent magnitude) stars in Table 7 (which are also likely to have fainter absolute magnitudes), although the near-infrared colour index still tends to give lower distances by $\sim30\%$." + Nonetheless. all of the dwarls listed in Tables 6 ancl 7 have formal distances either of less than 20 parsecs. or within lo of our distance limit.," Nonetheless, all of the dwarfs listed in Tables 6 and 7 have formal distances either of less than 20 parsecs, or within $\sigma$ of our distance limit." + Of the 51 ultracool dwarls in Tables 6 aud 7. only LP 911-20 has a trigonometric parallax meastuement.," Of the 51 ultracool dwarfs in Tables 6 and 7, only LP 944-20 has a trigonometric parallax measurement." + Our NStars survey aims to identify late type stars aud brown dwarls lying within 20 parsecs ol the Sun., Our NStars survey aims to identify late type stars and brown dwarfs lying within 20 parsecs of the Sun. + Iu this first paper. we have conceutratecd on defining au initial sample of uearby-star candidates from the NLTT catalogue by combining Luyteu's red magnitude estimates with photomety [rom the 2N1ASS database.," In this first paper, we have concentrated on defining an initial sample of nearby-star candidates from the NLTT catalogue by combining Luyten's red magnitude estimates with near-infrared photomety from the 2MASS database." + We also describe a nunber of techniques which will be used iu stuubseqtent papers. both to identify other nearby-star candidates aud to estimate their distauces.," We also describe a number of techniques which will be used in subsequent papers, both to identify other nearby-star candidates and to estimate their distances." + C'ross-referenciug our initial sample against the literature. we have located optical photometry for 169 of the 1215 stars.," Cross-referencing our initial sample against the literature, we have located optical photometry for 469 of the 1245 stars." + We have also used the near-iufrared data provided by 2MLASS to identify a further [1 ultracool dwarfs., We have also used the near-infrared data provided by 2MASS to identify a further 41 ultracool dwarfs. + Most of the stars in the former sample were already known to lie within the immediate Solar Neighbourhood. aud are included in the preliminary version of the Third Catalogue of Nearby Stars.," Most of the stars in the former sample were already known to lie within the immediate Solar Neighbourhood, and are included in the preliminary version of the Third Catalogue of Nearby Stars." + Our re-analysis provides improved cdistauce estimates to many ol these objects., Our re-analysis provides improved distance estimates to many of these objects. +" Three πάτος, and fifty-six stars listed in Table 3 have formal distances of less", Three hundred and fifty-six stars listed in Table 3 have formal distances of less +roni wide field imaging survevs.,from wide field imaging surveys. + For CXO. results for tle uost scusitive observations are usually given as total flix in the soft band from kkeV to 2kkeV. For SIRTF. the uost sensitive results for dust reeniüssion from obscurect regions will be flux deusities in the 21502 MIPS band.," For CXO, results for the most sensitive observations are usually given as total flux in the soft band from keV to keV. For SIRTF, the most sensitive results for dust reemission from obscured regions will be flux densities in the $\mu$ m MIPS band." + The ratio of mfrared to XN-rav brightuess which we define iu lis paper to compare SIRTF aud. Claudra mieasuremeuts is the parameter ΤΝ. defined as Πιν = Gufrared fiux density ineasured with MIPS jan in τι)/(total X-ray Bux observed between 0.5 aud 2.0kkeV in units of 1 CresDUDEN locnm 3).," The ratio of infrared to X-ray brightness which we define in this paper to compare SIRTF and Chandra measurements is the parameter IR/X, defined as IR/X = (infrared flux density measured with MIPS $\mu$ m in mJy)/(total X-ray flux observed between 0.5 and keV in units of $^{-16}$ ergs $^{-1}$ $^{-2}$ )." + In order to determine IR/X as would © observed at differcut redshifts. the relevant bandpasses ive to be transformed to the rest frame spectra of the sources usec.," In order to determine IR/X as would be observed at different redshifts, the relevant bandpasses have to be transformed to the rest frame spectra of the sources used." + The objects which we evaluate have N-rav and infrared spectra extending over sutiicicut wavelenetls in the rest frame that IR/N can be determined for redshifts L 10$ . + Since the star formation efficiency is proportional to Q+ in the outer disk. the μαματον between model aud data might be due ο ou incomplete knowledec of Q in these reeious.," Since the star formation efficiency is proportional to $Q^{-1}$ in the outer disk, the mismatch between model and data might be due to our incomplete knowledge of $Q$ in these regions." +fractions For 15 out of the Is sample galaxies'; CO(C observations; are available., For 15 out of the 18 sample galaxies CO observations are available. +; The VB03 star formation prescription reproduces he molecular fractions of alnost all galaxies (except NGC 1736 aud NCC 5190 roughly within he error bars., The VB03 star formation prescription reproduces the molecular fractions of almost all galaxies (except NGC 4736 and NGC 5194) roughly within the error bars. + There are deviations between the IWALO5 star formation prescription and observed nolecular fractions for NGC 5191. NGC3521. NGC 5055.," There are deviations between the KM05 star formation prescription and observed molecular fractions for NGC 5194, NGC3521, NGC 5055." + Ta NGC 3181. NGC 1736. NGC 6916. and NGC 5191. the clecline of the observed nolecular fraction at the outer edee of he CO distribution is much steeper than predicted by the uodel.," In NGC 3184, NGC 4736, NGC 6946, and NGC 5194 the decline of the observed molecular fraction at the outer edge of the CO distribution is much steeper than predicted by the model." + This is mostly due to sensitivity. because he CO data cubes were clipped at given S/N evels.," This is mostly due to sensitivity, because the CO data cubes were clipped at given S/N levels." + Since the VDOS3. model is axisviunetric. 1 does not include nou-axisviuuetrie structures Dil spiral axius and bars.," Since the VB03 model is axisymmetric, it does not include non-axisymmetric structures like spiral arms and bars." + Whereas spiral arms do no change the eiven picture considerablv (aanοal.2009).. the existence of bars do have a strong inpact on racial eas flows.," Whereas spiral arms do not change the given picture considerably \citep{Haan}, the existence of bars do have a strong impact on radial gas flows." + Despite the importance of a bar in the evolution of ealactic disks. the fac that the VBO3 model does not include their effec docs not affect our conclusions.," Despite the importance of a bar in the evolution of galactic disks, the fact that the VB03 model does not include their effect does not affect our conclusions." + Tun the followineC» we discuss aspects related to different radial profiles: Fie., In the following we discuss aspects related to different radial profiles: Fig. + 1 shows the star formation rate per unif area as a function of the total eas surface density Πο) of our model., \ref{fig:hibigiel} shows the star formation rate per unit area as a function of the total gas surface density $_2$ ) of our model. + The distribution agrees well with observed distributions from THINGS aud the literature (Fig.15ofBigicletal.2008)., The distribution agrees well with observed distributions from THINGS and the literature \citep[Fig.~15 of][]{Bigiel}. +. The absolute values and the shape. ie. the kuec' are reproduced by both the IKMO» and VDUS models.," The absolute values and the shape, i.e. the 'knee', are reproduced by both the KM05 and VB03 models." + As shown in Tamburroetal. (2009). he velocity dispersion of spiral ealaxies decreases with increasing galactocentric radius.," As shown in \citet{Tamburro}, the velocity dispersion of spiral galaxies decreases with increasing galactocentric radius." + In the following. We note that the VDU3 uodel for a stellay disk dominated eravitational ootential vields a racially declining velocity dispersion. Whereas a selferavitatiug gas disk leads οà coustaut velocity dispersion iu the iuncer disk GR Riveak) aud a dechuing velocity dispersion in the outer disk ϱ Ru)," In the following, We note that the VB03 model for a stellar disk dominated gravitational potential yields a radially declining velocity dispersion, whereas a selfgravitating gas disk leads toa constant velocity dispersion in the inner disk $R < R_{\rm break}$ ) and a declining velocity dispersion in the outer disk $R > R_{\rm break}$ )." + Thus. it is in xinciple possible to cdetermime these different reeines from the radial behavior of theobserved velocity dispersion.," Thus, it is in principle possible to determine these different regimes from the radial behavior of theobserved velocity dispersion." + fraction: With the model radial profiles we can investigate the dependence of the, With the model radial profiles we can investigate the dependence of the +changing the mass between 0.47 and 0.53 A7. and radius between 0.23 and 0.26 10...,changing the mass between 0.47 and 0.53 $M_\odot$ and radius between 0.23 and 0.26 $R_\odot$. + Using photometric and spectroscopic data for Bal09. we have shown that the method of mode identification. developed by can be successfully applied to Bal09.," Using photometric and spectroscopic data for Bal09, we have shown that the method of mode identification developed by can be successfully applied to Bal09." + We believe that. if simultaneous multicolour photometry and spectroscopy are carried out. the method will also allow mode identification in other sdBV stars.," We believe that, if simultaneous multicolour photometry and spectroscopy are carried out, the method will also allow mode identification in other sdBV stars." + In Bal09. the spherica degree / was unambiguously identified for the two modes with the largest amplitudes.," In Bal09, the spherical degree $\ell$ was unambiguously identified for the two modes with the largest amplitudes." + For several other modes. we limited the number of possible values of / to two or three.," For several other modes, we limited the number of possible values of $\ell$ to two or three." + If we accep that the two observed multiplets are caused by rotational splitting. then the number of identified modes increases to nine: the triple components have (= I. the quintuplet components. ( = 2.," If we accept that the two observed multiplets are caused by rotational splitting, then the number of identified modes increases to nine: the triplet components have $\ell$ = 1, the quintuplet components, $\ell$ = 2." + Itis clear from our considerations that photometry itself is no sufficient to identify mode satisfactorily for sdBV stars. and tha adding spectroscopic observations greatly improves the situation.," It is clear from our considerations that photometry itself is not sufficient to identify mode satisfactorily for sdBV stars, and that adding spectroscopic observations greatly improves the situation." +" For Bal09., it is certainly worth carrying out another photometric and spectroscopic campaign to identify modes with even lower amplitudes."," For Bal09, it is certainly worth carrying out another photometric and spectroscopic campaign to identify modes with even lower amplitudes." + However. our identification is probably sufficient to go a step further and attempt asteroseismology of this star.," However, our identification is probably sufficient to go a step further and attempt asteroseismology of this star." + However. for this purpose. an appropriate set of models is required.," However, for this purpose, an appropriate set of models is required." + A first attempt was presented in Paper I using the models of(2002)., A first attempt was presented in Paper I using the models of. +. While we had no modes identified at that time. the assumption that the main mode is radial now appears to be correct.," While we had no modes identified at that time, the assumption that the main mode is radial now appears to be correct." + With reliable identification of modes from the 2.8 mHz group. a good seismic model that fits the identified modes might be used to match (and. identify) remaining modes.," With reliable identification of modes from the 2.8 mHz group, a good seismic model that fits the identified modes might be used to match (and identify) remaining modes." + In order to carry out a thorough asteroseismological analysis and potentially learn new physics. it is important that more modes are identified independent of pulsation models in sdBV stars.," In order to carry out a thorough asteroseismological analysis and potentially learn new physics, it is important that more modes are identified independent of pulsation models in sdBV stars." + We have provided a erucial piece of the puzzle. and the challenge is now for pulsation theorists to find models that mateh both the pulsation frequencies and mode identifications derived here.," We have provided a crucial piece of the puzzle, and the challenge is now for pulsation theorists to find models that match both the pulsation frequencies and mode identifications derived here." + This project was partially supported by grant no., This project was partially supported by grant no. + IPO3D 013 29 kindly provided by Polish MNiSW., 1P03D 013 29 kindly provided by Polish MNiSW. + Constructive criticism from the anonymous referee 1s also acknowledged., Constructive criticism from the anonymous referee is also acknowledged. +impose as additional validation: is the variability status based on individual stars are consistent with one another or not?,impose as additional validation: is the variability status based on individual stars are consistent with one another or not? +" In these pairs of variable status indicators using a cquasar-star DLC. the quasar is marked as variable CV) for a C'-value z:2.576 or F-value ο£,(0.99). which corresponds to a confidence level z00.99."," In these pairs of variable status indicators using a quasar-star DLC, the quasar is marked as variable (`V') for a $C$ -value $\ge 2.576$ or $F$ -value $\ge +F_{c}(0.99)$, which corresponds to a confidence level $\ge 0.99$." + ‘Phe quasar is marked. as ‘probably variable’ (Py) if the Co value of quasar-star DLC is in the range 1.950 to 2.576 or if the £-value is between £00.95) and £00.99)., The quasar is marked as `probably variable' (Pv) if the $C$ value of quasar-star DLC is in the range 1.950 to 2.576 or if the $F$ -value is between $F_{c}(0.95)$ and $F_{c}(0.99)$. + Those sources for which the C-values are less than 1.95. or the f-value are less than £;(0.95) are marked Non-variable CNv.," Those sources for which the $C$ -values are less than 1.95, or the $F$ -value are less than $F_{c}(0.95)$ are marked Non-variable (`Nv')." + Column 12 lists the square root of scaling factor. να. where it is computed by &=oYsp/ta?(s].—525 (as in Eq. 3)).," Column 12 lists the square root of scaling factor, $\sqrt\kappa$, where it is computed by $\kappa=\langle\sigma^2(q-s)\rangle/\langle\sigma^2(s1-s2)\rangle$ (as in Eq. \ref{eq:kappa}) )," +" and has been used to scale the variance of the star-star DLCs while computing the {ναιο in the scaled-£""-test.", and has been used to scale the variance of the star-star DLCs while computing the $F$ -value in the $F$ -test. + Ehe last column gives our ACCULACY.. yy in the quasar-star DLCs. which typically are between07 As can be seen from Columns. 9 1 of Table 3 the variability status indicators based on quasar-starl and uasar-siar2 are often not consistent with one another.," The last column gives our photometric accuracy, in the quasar-star DLCs, which typically are between $-$ As can be seen from Columns 9 – 11 of Table \ref{tab:res} the variability status indicators based on quasar-star1 and quasar-star2 are often not consistent with one another." + The importance of our choice to mark the variable status separately based. on individual star vs quasar DLCs can be --Iustrated by taking the example of J004941.10|295519.2., The importance of our choice to mark the variable status separately based on individual star vs quasar DLCs can be illustrated by taking the example of J094941.10+295519.2. + Dased on the C-test its DLC with respect to start shows it as a probable variable but with star2 as non-variable., Based on the $C$ -test its DLC with respect to star1 shows it as a probable variable but with star2 as non-variable. + The standard. £-test. terms it as variable based. on both gatarl and star2 DLCs., The standard $F$ -test terms it as variable based on both star1 and star2 DLCs. + However. this QSO's status using 10 scaled P-test is variable based. on the first star and probably variable using the second star.," However, this QSO's status using the scaled $F$ -test is variable based on the first star and probably variable using the second star." + The average of the scaled. £-valuc for this source comes out to be 2.25. which is just above 11e critical F-value of 2.23 for 0.99 confidence. and hence it would be classified as a variable source. if we used that average criterion.," The average of the scaled $F$ -value for this source comes out to be 2.25, which is just above the critical $F$ -value of 2.23 for 0.99 confidence, and hence it would be classified as a variable source if we used that average criterion." + However. an examination the DLC of this source in top right panel of Fig.," However, an examination the DLC of this source in top right panel of Fig." + 2. hy eve indicates that there is no variation that can celine! coherently by more than 2 points., \ref{fig:s05to10} by eye indicates that there is no variation that can defined coherently by more than 2 points. +" Therefore. to exclude such questionable variability and to be on the conservative side for unambiguous microvariable detection. only those sources should be termed as variable lor which both quasar-starl and quasar-star2 DLCs mark the source as variable (1.6 VV"" in Table 3))."," Therefore, to exclude such questionable variability and to be on the conservative side for unambiguous microvariable detection, only those sources should be termed as variable for which both quasar-star1 and quasar-star2 DLCs mark the source as variable (i.e `V,V' in Table \ref{tab:res}) )." + Probably variable sources are taken as those for which either both the status are of probable variable (i.c. VP in Table 3)) or one quasar-star DLC marks it as a probable variable and the other as a variable (i.e. Dv.V or VW in Table 3)).," Probably variable sources are taken as those for which either both the status are of probable variable (i.e., `Pv,Pv' in Table \ref{tab:res}) ) or one quasar-star DLC marks it as a probable variable and the other as a variable (i.e., `Pv,V' or `Pv,V' in Table \ref{tab:res}) )." + Sources termed. as non-variable (Nw) re those for which at least one of the status based on quasar- and quasar-star2 DLC marked them as non-variable (Le. at least one “Nw status in Table 3)).," Sources termed as non-variable (`Nv') are those for which at least one of the status based on quasar-star1 and quasar-star2 DLC marked them as non-variable (i.e., at least one `Nv' status in Table \ref{tab:res}) )." + Column (9) of Table 3. indicates that the C'-statistics shows two sources as variable and four as probably variable., Column (9) of Table \ref{tab:res} indicates that the $C$ -statistics shows two sources as variable and four as probably variable. + The scaled. f-test shows two sources as variable ancl six sources as probably variable., The scaled $F$ -test shows two sources as variable and six sources as probably variable. +" As we have discussed. above (in section 4.2.3)). that scaled F""-test is better for our work (and probably also better in many observations made by others) than the standard £-test due to differences between the magnitudes of the quasars and their comparison stars."," As we have discussed above (in section \ref{subsubs:fscaled}) ), that scaled $F$ -test is better for our work (and probably also better in many observations made by others) than the standard $F$ -test due to differences between the magnitudes of the quasars and their comparison stars." + This is also evident from column (10) of Table 3 which shows that the standard. {τος would give 13 sources as variable and two as a probably variable. indicating that this test certainly sulfers from the problem related to small variances of the brighter star-star DLCs. at least. for our sample of BALQSOs.," This is also evident from column (10) of Table \ref{tab:res} which shows that the standard $F$ -test would give 13 sources as variable and two as a probably variable, indicating that this test certainly suffers from the problem related to small variances of the brighter star-star DLCs, at least for our sample of BALQSOs." + Although the C-test and thesealed F-test both give two sources as variable. it is not cillicult to appreciate the scaled f-test merits over the C-test by taking specific examples.," Although the $C$ -test and the $F$ -test both give two sources as variable, it is not difficult to appreciate the scaled $F$ -test merits over the $C$ -test by taking specific examples." + For instance. J120051.52| 350831.6 is a DALQSOs with a C-value of 3.25 from quasar-starl DLC and. 3.24. from uasar-star2 DLC. which seems to make it a clear case of —OV detection. particularly since the C'-statistie is usually 'onservalive.," For instance, $+$ 350831.6 is a BALQSOs with a $C$ -value of 3.25 from quasar-star1 DLC and 3.24 from quasar-star2 DLC, which seems to make it a clear case of INOV detection, particularly since the $C$ -statistic is usually conservative." + However. bv looking at the DLCs for this source in the top left panel of Fig. 3..," However, by looking at the DLCs for this source in the top left panel of Fig. \ref{fig:s11to19}," + it is clear even by eve ja: (1) there is likely to have been a random Iuctuation (not a coherent one) for the last 9 points of the DLCs: and (ii) its comparison stars are about 1.5 mag brighter than this uasar. which makes the variance of the star-star DLC very gamall (due to small photon noise).," it is clear even by eye that: (i) there is likely to have been a random fluctuation (not a coherent one) for the last 9 points of the DLCs; and (ii) its comparison stars are about 1.5 mag brighter than this quasar, which makes the variance of the star-star DLC very small (due to small photon noise)." + As a result the C-value will be artificially very high. leading to false detections.," As a result the $C$ -value will be artificially very high, leading to false detections." + This Haw also crops up in the standard. A-test. but is eliminated in the sealed £-test which termed. this BALQSO as a non-variable source (not even probably variable).," This flaw also crops up in the standard $F$ -test, but is eliminated in the scaled $F$ -test which termed this BALQSO as a non-variable source (not even probably variable)." +" Another source. J120024.07| 103612.0. has a C'-value of 3.37 from the quasarcstarl DLC and 3.06 from the quasar-star2 DLC bu these are probably so high because of the ~1.2 mag brighter comparison stars: however. this BALQSO also shows a coherent variability trend (even by eve). and is also terme as variable by the scaled. τον,"," Another source, $+$ 103612.0, has a $C$ -value of 3.37 from the quasar-star1 DLC and 3.06 from the quasar-star2 DLC but these are probably so high because of the $\sim$ 1.2 mag brighter comparison stars; however, this BALQSO also shows a coherent variability trend (even by eye), and is also termed as variable by the scaled $F$ -test." + Phese empirical examples. and the fact that the scaled {του detects two cases of unambiguous variability in comparison to the C-test which makes only one unambiguous detections (after eliminating the false positive case mentioned above) clearly shows tha the scaled. {τοπ beside being more sensitive than the C'- to small ampliude variability. is also sulicientlv robus locliminate nearly any false alarm cetections.," These empirical examples, and the fact that the scaled $F$ -test detects two cases of unambiguous variability in comparison to the $C$ -test which makes only one unambiguous detections (after eliminating the false positive case mentioned above) clearly shows that the scaled $F$ -test, beside being more sensitive than the $C$ -test to small amplitude variability, is also sufficiently robust to eliminate nearly any false alarm detections." + VPherclore. παν. we rely on the result. given. by the scaled. £-test. by which we find two unambiguous detections of microvariability in our sample of 19 BALOQSOs up to an accuracy of 0.01-0.02mag (see columns 9.10. 11 and 13 of ‘Table 3)).," Therefore, finally, we rely on the result given by the scaled $F$ -test, by which we find two unambiguous detections of microvariability in our sample of 19 BALQSOs up to an accuracy of 0.01-0.02mag (see columns 9,10, 11 and 13 of Table \ref{tab:res}) )." + As à result. our sample shows that about 10-11 per cent of BALQSOs ια. 2 out of 19 sources) certainly showed microvariabilitv (at à confidence level of 0.99).," As a result, our sample shows that about 10-11 per cent of BALQSOs (i.e., 2 out of 19 sources) certainly showed microvariability (at a confidence level of 0.99)." + As noted in the introduction. there have been rather extensive examinations of the frequency of optical microvariabilitv for. RQQSOs as well as blazars and other RLOQSOs.," As noted in the introduction, there have been rather extensive examinations of the frequency of optical microvariability for RQQSOs as well as blazars and other RLQSOs." + The typical duty evele (DC) for blazars is 60.65 per cent (c.g@.. Gupta et 22005). while for normal quasars it has been found to be around 2025 per cent (c.g. Carini et 22007).," The typical duty cycle (DC) for blazars is 60–65 per cent (e.g., Gupta et 2005), while for normal quasars it has been found to be around 20–25 per cent (e.g., Carini et 2007)." + For both these classes the number of sources in each total sample was quite larec. so these values should be reasonably reliable. and support the hypothesis that most of these rapid. variations arise. or at least are amplified. in the relativistic jets (e.g.. Jang Miller 1995: Gopal-Ixrishna et 22003).," For both these classes the number of sources in each total sample was quite large, so these values should be reasonably reliable, and support the hypothesis that most of these rapid variations arise, or at least are amplified, in the relativistic jets (e.g., Jang Miller 1995; Gopal-Krishna et 2003)." + The interesting class of radio-quiet. BALOQSOs =vas reported to have a 50 per cent DC but this sample had only 6 members (Carini et 22007)., The interesting class of radio-quiet BALQSOs was reported to have a 50 per cent DC but this sample had only 6 members (Carini et 2007). + Therefore. one of 10 reasons for the difference in DC results could be poor μαatisties in the previous study and better statistics now with a sample about a factor of three larger.," Therefore, one of the reasons for the difference in DC results could be poor statistics in the previous study and better statistics now with a sample about a factor of three larger." + Apart from sample size. some of the dillerence might be due to dilferences in the typical length of the observation.," Apart from sample size, some of the difference might be due to differences in the typical length of the observation." + As long known. lengthier observations of blazars are more likelv to reveal variability," As long known, lengthier observations of blazars are more likely to reveal variability" +A kev problemi in studies of objects ciitting most of their energv in the ΕΠκανα is to establish the relative importance of hiehlv obscured Active Galactic Nuclei (AGN) ancl starburst activity.,A key problem in studies of objects emitting most of their energy in the FIR/submm is to establish the relative importance of highly obscured Active Galactic Nuclei (AGN) and starburst activity. + In particular. it is iuportaut to kuow if it is still possible o hide an ACN. contributing siguificantly to the bolometric enission. when optical to nud-IR spectroscopy and inagius revea oulv a starburst component.," In particular, it is important to know if it is still possible to hide an AGN, contributing significantly to the bolometric emission, when optical to mid-IR spectroscopy and imaging reveal only a starburst component." + Several pieces of evidence sugeestsige that most cosmic AGN activity is obscured., Several pieces of evidence suggest that most cosmic AGN activity is obscured. + Most. aud possibly all. cores of large galaxies host a supermassive black holeAMo:: e.g.àY Richstoue et al. 1998).," Most, and possibly all, cores of large galaxies host a supermassive black hole; e.g. Richstone et al. \cite{richstone}) )." + To complete tlic formation process dn a IIubble time. accretion nius proceed at high rates. producing quasar Iuninosities CL~ LoL).," To complete the formation process in a Hubble time, accretion must proceed at high rates, producing quasar luminosities $L\sim\ten{12}\Lo$ )." + However the observed black hole density is an order of magnitude ereater than that expected from the observed quasar ight. assumune accretion cfiicicucy of sugeesting that most of the accretion listory is obscured (e.g. Fabian Iwasawa 1999.. and references therein).," However the observed black hole density is an order of magnitude greater than that expected from the observed quasar light, assuming accretion efficiency of, suggesting that most of the accretion history is obscured (e.g. Fabian Iwasawa \cite{fabian99}, and references therein)." + It is estimated either that of all ACUNS are obscured (type 2) or that of the accretion history of an object is hidden from view., It is estimated either that of all AGNs are obscured (type 2) or that of the accretion history of an object is hidden from view. + Tn addition. the hard N-vav background (2] keV) requires a huee population of obscured ACNs at higher redshifts {2~ d) since the observed spectral energv distribution cannot be explained with the coutinua of Quasars. be. uuobscured (type 1) ACGNs (Comastri et al. 1995..," In addition, the hard X-ray background $>1\KEV$ ) requires a large population of obscured AGNs at higher redshifts $z\sim1$ ) since the observed spectral energy distribution cannot be explained with the continua of Quasars, i.e. un–obscured (type 1) AGNs (Comastri et al. \cite{comastri}," + Galli et al. 1999))., Gilli et al. \cite{gilli99}) ). +" Despite the above evidence. detections of obscured ACNs at cosmological distances are still sparse (c.g, Akiviuna et al. 1999})."," Despite the above evidence, detections of obscured AGNs at cosmological distances are still sparse (e.g. Akiyama et al. \cite{akiyama}) )." + Ultra. Luniünous Infrared Cralaxies αρα see Sanders Mirabel 1996 for a review) and the sources detected. iu recent far-infrared ando subi surveys, Ultra Luminous Infrared Galaxies (ULIRGs; see Sanders Mirabel \cite{sanders96} for a review) and the sources detected in recent far-infrared and submm surveys +The Vovager l ancl 2 spacecraft. which flew past Saturn in 1980 and 1981. revolutionized! our understanding of the Saturn. system.,"The Voyager 1 and 2 spacecraft, which flew past Saturn in 1980 and 1981, revolutionized our understanding of the Saturn system." + One of the remarkable features discovered. by Vovager was rich radial structure in Saturn's rings., One of the remarkable features discovered by Voyager was rich radial structure in Saturn's rings. + Although some of this structure. mostly in the outer or A ring. is known to arise [rom density or bending waves generated by discrete resonances with the inner satellites. most of (he radial structure remains unexplained. parücularly in the main or D ring.," Although some of this structure, mostly in the outer or A ring, is known to arise from density or bending waves generated by discrete resonances with the inner satellites, most of the radial structure remains unexplained, particularly in the main or B ring." + Horn&Cuzz(1996) point out that wavetrains associated wilh known resonances cover less than of the radial extent of the A and D rings., \citet{hc96} point out that wavetrains associated with known resonances cover less than of the radial extent of the A and B rings. + The remaining vast majority of the structure is often called “irregular” since the bright and dark features show little or no long-range coherence., The remaining vast majority of the structure is often called “irregular” since the bright and dark features show little or no long-range coherence. + The purpose of this paper is to suggest and examine a novel explanation for irregular structure in Saturns rings., The purpose of this paper is to suggest and examine a novel explanation for irregular structure in Saturn's rings. + Rine particles are likely to have (weak) cohesive forces. anc," Ring particles are likely to have (weak) cohesive forces, and" + Rine particles are likely to have (weak) cohesive forces. ancl," Ring particles are likely to have (weak) cohesive forces, and" +deviales [rom (his law (Zwaanetal.1999).,deviates from this law \citep{zwa99}. +". This is not surprising since il is qgCV;,) which should eventually scale as Αμ lor disk like svstems. and we have shown that lor model («) the present data are compatible with this law."," This is not surprising since it is $g(N_{H})$ which should eventually scale as $N_{H}^{-3}$ for disk like systems, and we have shown that for model $(a)$ the present data are compatible with this law." +" For model (5) the best fit gives a=1.47zE0.1. logJj/1,=—1.85d1. and logδνοι7=19.13d:0.4."," For model $(b)$ the best fit gives $\alpha=1.47\pm0.1$, $\log +J_L/\eta_0=-1.85\pm 1 $, and $\log N_*/{\hbox{cm}}^{-2}= {19.4\pm 0.4}$." + This model fits the data better than model (a) with 0.5 being the mininmun 4? value., This model fits the data better than model $(a)$ with 0.5 being the minimum $\chi^2$ value. + The resulting ΓΑ) are shown in Figure 2 together with the data used for the 4? minimization., The resulting $f(N_{HI})$ are shown in Figure 2 together with the data used for the $\chi^2$ minimization. + Both best fitting models reproduce rather well also the high and low column density QSO's absorption data. not used for the fit. but shown in the Figure as well.," Both best fitting models reproduce rather well also the high and low column density QSO's absorption data, not used for the fit, but shown in the Figure as well." + A purepower law wilh no ionization corrections [ails since il gives a minimum 4?~10., A purepower law with no ionization corrections fails since it gives a minimum $\chi^2\sim10$. + Unfortunately the present data are not sulficient to discriminate between (0) and (5) tvpe of model., Unfortunately the present data are not sufficient to discriminate between $(a)$ and $(b)$ type of model. + This is mostly due to the lack of data around Ng;cLOS ? and to the uncertainties on the conversion of atomic hydrogen gas into other barvonie forms al very hieh column densities.," This is mostly due to the lack of data around $N_{HI}\simeq +10^{18}$ $^{-2}$ and to the uncertainties on the conversion of atomic hydrogen gas into other baryonic forms at very high column densities." + In (hese (wo regions (0) and (5) model predictions lor μι) differ substantially., In these two regions $(a)$ and $(b)$ model predictions for $f(N_{HI})$ differ substantially. + The two best fitting power laws for αμ] imply a quite different degree of ionization and therefore different total eas densities in the local Universe., The two best fitting power laws for $g(N_{H})$ imply a quite different degree of ionization and therefore different total gas densities in the local Universe. +" For model (e) most of the eas resides in low column density absorbers: I1 neutral Iractions are of order 0.002 for ? and are as low as 10? for Ny,cLOM 7.", For model $(a)$ most of the gas resides in low column density absorbers; H neutral fractions are of order 0.002 for $N_{HI}\simeq 10^{17}$ $^{-2}$ and are as low as $10^{-5}$ for $N_{HI}\simeq 10^{14}$ $^{-2}$. + The total gas densitv(IL--IHe) predicted by this distribution for 1011 10$ ) corrected by +0.018 mag, (3) the TMASS/IRC value, transformed to the 2MASS system as described above." + If no Juzc: is available a mean colour for RC stars of 1.55 is used in the transformation., If no $I_{\rm IRC}$ is available a mean colour for RC stars of $(I-K)_{\rm IRC} = 1.55$ is used in the transformation. + Of all Hippareos stars that have a /-magnitude assigned. 3116 are based on TMSS. 17 on Dents and 103827 on 2MASS.," Of all Hipparcos stars that have a $K$ -magnitude assigned, 3116 are based on TMSS, 17 on Denis and 103827 on 2MASS." + In this section a model is deseribed to construct synthetic samples of stars and apply various selection criteria in order to generate samples of stars that closely resemble in nature the observed data., In this section a model is described to construct synthetic samples of stars and apply various selection criteria in order to generate samples of stars that closely resemble in nature the observed data. + The model is follows largely Groenewegen Oudmaijer (2000) but is based on the properties of the revised Hipparcos catalogue., The model is follows largely Groenewegen Oudmaijer (2000) but is based on the properties of the revised Hipparcos catalogue. + The coordinate system used is cylindrical coordinates centred on the Galactic centre., The coordinate system used is cylindrical coordinates centred on the Galactic centre. + The galactic distribution ts assumed to be a double exponential disk with a scale height /7 in the τ- (the coordinate perpendicular to the galactic plane). and a seale length Rec: in the galacto-centrie. direction.," The galactic distribution is assumed to be a double exponential disk with a scale height $H$ in the $z$ -direction (the coordinate perpendicular to the galactic plane), and a scale length $R_{\rm GC}$ in the galacto-centric direction." + The distance to the Galactic centre is taken to be 7800 pe (Zucker et al., The distance to the Galactic centre is taken to be 7800 pc (Zucker et al. + 2006)., 2006). + The luminosity function can be arbitrary but. in the case of simulating RC stars. is assumed to be a Gaussian.," The luminosity function can be arbitrary but, in the case of simulating RC stars, is assumed to be a Gaussian." +" In J with a mean Af,—0.27 and ce of 0.20.", In $I$ with a mean $M_{\rm I} = -0.27$ and $\sigma$ of 0.20. + The (VI) colours is assumed to be a Gaussian with mean 0.98 and & = 0.085., The $(V-I)$ colours is assumed to be a Gaussian with mean 0.98 and $\sigma$ = 0.085. + In A the Gaussian has a mean My=——1.60 and σ of 0.22. while the (VoA) colours is taken as a Gaussian with mean 2.32 and a of 0.21.," In $K$ the Gaussian has a mean $M_{\rm K} = -1.60$ and $\sigma$ of 0.22, while the $(V-K)$ colours is taken as a Gaussian with mean 2.32 and $\sigma$ of 0.21." + Visual. extinction in the simulation and to de-redden the observations is based on several 3-dimensional reddening models available in the literature., Visual extinction in the simulation and to de-redden the observations is based on several 3-dimensional reddening models available in the literature. + Marshall et al. (, Marshall et al. ( +2006) presents reddening in the A-band with 15’ sampling along 64 000 lines-of-sight in the direction |/|<100dee and |b|<1üdeg based on 2MASS data.,2006) presents reddening in the $K$ -band with $\arcmin$ sampling along 64 000 lines-of-sight in the direction $\mid l \mid \le 100\deg$ and $\mid b \mid \le 10\deg$ based on 2MASS data. + Drimmel et al. (, Drimmel et al. ( +2003) presents a reddening model based on the dust distribution model of Drimmel Spergel (2001). which is based on COBE/DIRBE data.,"2003) presents a reddening model based on the dust distribution model of Drimmel Spergel (2001), which is based on COBE/DIRBE data." + Arenou et al. (, Arenou et al. ( +1992) presents a reddening model based on à comparison of observed 0.V. photometry with predicted photometry from a star's spectral type.,"1992) presents a reddening model based on a comparison of observed $B,V$ photometry with predicted photometry from a star's spectral type." + Finally. a simple law following Parenago (1940) was considered: The Marshall et al.," Finally, a simple law following Parenago (1940) was considered: The Marshall et al." + results have been taken as reference model. and their reddenings were transformed to iy as Ag0.13.," results have been taken as reference model, and their reddenings were transformed to $A_{\rm V}$ as $A_{\rm K}/0.12$." + However. this model is only available over a limited range in galactic coordinates. therefore a Monte Carlo simulatior made to randomly generate galactie coordinates and distances assuming a constant number density of stars within 3 kpe distance of the Sun.," However, this model is only available over a limited range in galactic coordinates, therefore a Monte Carlo simulation was made to randomly generate galactic coordinates and distances assuming a constant number density of stars within 3 kpc distance of the Sun." + If the galactic coordinates were within the range of applicability of the Marshall et al., If the galactic coordinates were within the range of applicability of the Marshall et al. + model. the visual extinction from the other models was determined.," model, the visual extinction from the other models was determined." + In the end. using several 1000 positions. the average and dispersion in the various ratios between extinction models were calculated. and the results are in Table |.. in the sense model listed in the row divided by model listed in the column.," In the end, using several 1000 positions, the average and dispersion in the various ratios between extinction models were calculated, and the results are in Table \ref{Tab-red}, in the sense model listed in the row divided by model listed in the column." + Although the dispersion in all the ratios is quite large. they mostly agree in the mean.," Although the dispersion in all the ratios is quite large, they mostly agree in the mean." + It only seems that the Arenou et al., It only seems that the Arenou et al. + model gives higher extinction than the Drimmel et al., model gives higher extinction than the Drimmel et al. + and Parenago model., and Parenago model. + The finally adopted visual extinction was the average of the models by Parenago. Drimmel et al..," The finally adopted visual extinction was the average of the models by Parenago, Drimmel et al.," + and Arenou et al., and Arenou et al. + multiplied by 0.84., multiplied by 0.84. + The adopted completeness function in /7j magnitude ts This was derived by comparing the observed magnitude distribution to that predicted with the TRILEGAL Galactic model (Girardi et al., The adopted completeness function in $Hp$ magnitude is This was derived by comparing the observed magnitude distribution to that predicted with the TRILEGAL Galactic model (Girardi et al. + 2005)., 2005). + The completeness functions quoted below are derived by inspecting the ratio of stars that fulfil a particular selection to all stars. as a function of /7p magnitude.," The completeness functions quoted below are derived by inspecting the ratio of stars that fulfil a particular selection to all stars, as a function of $Hp$ magnitude." + The completeness, The completeness +We have performed some test computations using Klimchuk-Raymond's fit for the radiative loss function in order to compare with the results obtained using Hildner's fit (discussed in the previous Subsections).,We have performed some test computations using Klimchuk-Raymond's fit for the radiative loss function in order to compare with the results obtained using Hildner's fit (discussed in the previous Subsections). +" Regarding the form of the temperature perturbations, we find no significant differences."," Regarding the form of the temperature perturbations, we find no significant differences." + The maximum of the temperature perturbation 1s shifted toward slightly larger values of r for Klimchuk-Raymond's fit., The maximum of the temperature perturbation is shifted toward slightly larger values of $r$ for Klimchuk-Raymond's fit. +" For the fundamental mode, the maximum of 7, takes place at"," For the fundamental mode, the maximum of $T_1$ takes place at" +"A second major point made by VME ts that estimates of BH mass are unreliable if the BH radius of influence +; is not ""well-resolved"" by the kinematic data.",A second major point made by VME is that estimates of BH mass are unreliable if the BH radius of influence $r_i$ is not “well-resolved” by the kinematic data. + This ts one facet of the rich question of what different kinds of kinematic data reveal about the gravitational field of the galaxy., This is one facet of the rich question of what different kinds of kinematic data reveal about the gravitational field of the galaxy. + The geometry of the kinematic data can be characterized by: (1) the spatial resolution compared to +;: (2) the radial extent of the data (how far out the data extend): (3) the angular coverage (how many position angles. or whether there is integral-field data): and (4) the sparseness of the data (in radius and angle).," The geometry of the kinematic data can be characterized by: (1) the spatial resolution compared to $r_i$; (2) the radial extent of the data (how far out the data extend); (3) the angular coverage (how many position angles, or whether there is integral-field data); and (4) the sparseness of the data (in radius and angle)." + In addition to these geometrical characteristics. the quality of the data (signal-to-noise and systematic errors such as template mismatches) also determines what one can measure.," In addition to these geometrical characteristics, the quality of the data (signal-to-noise and systematic errors such as template mismatches) also determines what one can measure." + A complete investigation of all these issues is beyond the scope of this paper., A complete investigation of all these issues is beyond the scope of this paper. + We emphasize the distinction between (are the error bars small?), We emphasize the distinction between (are the error bars small?) + and (are the error bars accurately estimated, and (are the error bars accurately estimated?). +" We shall argue that geometric limitations to the quality of the ?).kinematic data of the four kinds listed above reduce the precision of estimates of M,. but the range of acceptable masses can still be judged from the 47 profile. and therefore the mass determination ts reliable."," We shall argue that geometric limitations to the quality of the kinematic data of the four kinds listed above reduce the precision of estimates of $\mbh$, but the range of acceptable masses can still be judged from the $\chi^2$ profile, and therefore the mass determination is reliable." + We parameterize the resolution of the kinematic data near the center in terms of N27/0D. where r; is the BH radius of influence defined earlier. D is the distance. and 0 is the full-width-half-maximum telescope resolution.," We parameterize the resolution of the kinematic data near the center in terms of $\aleph = r_i/\theta D$, where $r_i$ is the BH radius of influence defined earlier, $D$ is the distance, and $\theta$ is the full-width-half-maximum telescope resolution." + VME argue that the resolution N must be much greater than unity for accurate BH mass determinations. although they do not give a clear numerical criterion.," VME argue that the resolution $\aleph$ must be much greater than unity for accurate BH mass determinations, although they do not give a clear numerical criterion." + A number of the BH mass determinations have & only slightly larger than unity., A number of the BH mass determinations have $\aleph$ only slightly larger than unity. + In the example of NGC 821 discussed below. ()~0708 (the observations were made at wwith a 0 71 slit). D=24.1pe and r;~Spe. so N~0.9.," In the example of NGC 821 discussed below, $\theta \sim 0 \farcs 08$ (the observations were made at with a 0 1 slit), $D=24.1 pc$ and $r_i \sim 8 pc$, so $\aleph \sim 0.9$." +" VME's argument that observations with this. resolution cannot determine M, is made without regard to the noise of the data available.", VME's argument that observations with this resolution cannot determine $\mbh$ is made without regard to the signal-to-noise of the data available. + Even in the limit 8= 0. excellent S/N data can reveal the presence of a BH.," Even in the limit $\aleph = 0$ , excellent S/N data can reveal the presence of a BH." +" Given a model with constant mass-to-light ratio Y. a central mass M, and a perfect LOSVD measured with 8«|. the shape of the LOSVD at low velocities (comparable to velocity dispersion of the galaxy as a whole) determines Y. and the shape and extent of the high- wings of the LOSVD determines the mass of a central BH."," Given a model with constant mass-to-light ratio $\Upsilon$, a central mass $\mbh$ and a perfect LOSVD measured with $\aleph \ll 1$, the shape of the LOSVD at low velocities (comparable to velocity dispersion of the galaxy as a whole) determines $\Upsilon$, and the shape and extent of the high-velocity wings of the LOSVD determines the mass of a central BH." +" We have investigated the effect of varying the resolution ® on our determinations of M, by comparing our masses determined using both high-resolution HST data and low-resolution ground-based data to masses determined using the same method with ground-based data alone.", We have investigated the effect of varying the resolution $\aleph$ on our determinations of $\mbh$ by comparing our masses determined using both high-resolution HST data and low-resolution ground-based data to masses determined using the same method with ground-based data alone. + The addition of HST data generally improves & by a factor of 5. from less than unity to greater than unity.," The addition of HST data generally improves $\aleph$ by a factor of 5, from less than unity to greater than unity." + The results of these experiments are shown in Figure 8 in Gebhardtetαἰ.(2005) and Figure 4 in Kormendy(2004)., The results of these experiments are shown in Figure 8 in \citet{geb03} and Figure 4 in \citet{korm04}. +". We find that improved resolution generally improves the precision of the measured M, by narrowing the v profile. but the improved best-fit M, always lies within the range given by the estimated errors from the low-resolution data."," We find that improved resolution generally improves the precision of the measured $\mbh$ by narrowing the $\chi^2$ profile, but the improved best-fit $\mbh$ always lies within the range given by the estimated errors from the low-resolution data." +" This experiment is evidence that the \7 profiles do exactly what they are supposed to—they provide an estimate of M, and of its uncertainty.", This experiment is evidence that the $\chi^2$ profiles do exactly what they are supposed to—they provide an estimate of $\mbh$ and of its uncertainty. +" Lower resolution data yield less precise values of M,. but not unreliable ones."," Lower resolution data yield less precise values of $\mbh$, but not unreliable ones." + We next investigate the influence of kinematic data at larger radii on the precision of the BH measurement (points 2 and 3 above). using data from NGC 821 (see Figure 2).," We next investigate the influence of kinematic data at larger radii on the precision of the BH measurement (points 2 and 3 above), using data from NGC 821 (see Figure 2)." + This example shows that the 47 profile broadens and flattens as data at large radii and along the minor axis are discarded., This example shows that the $\chi^2$ profile broadens and flattens as data at large radii and along the minor axis are discarded. +" The changes in the v. profile imply a decrease in the precision of the measurement of M, and indicate the increased errors.", The changes in the $\chi^2$ profile imply a decrease in the precision of the measurement of $\mbh$ and indicate the increased errors. +" If only HST data is used then models with and without a BH are both acceptable. because of the degeneracy between M, and Y when only data inside and near the radius of influence are used."," If only HST data is used then models with and without a BH are both acceptable, because of the degeneracy between $\mbh$ and $\Upsilon$ when only data inside and near the radius of influence are used." +" Note that the one model with only major axis data (the dashed line) yields a flat-bottomed 4 profile and a very uncertain estimate of M, compared to the model with additional data along the minor axis.", Note that the one model with only major axis data (the dashed line) yields a flat-bottomed $\chi^2$ profile and a very uncertain estimate of $\mbh$ compared to the model with additional data along the minor axis. + We conclude that inadequate spatial coverage of kinematies far from the BH can lead to a poorly defined BH mass and a flat-bottomed 4 just as readily as can poorly resolved data (X>1) in the galaxy center)., We conclude that inadequate spatial coverage of kinematics far from the BH can lead to a poorly defined BH mass and a flat-bottomed $\chi^2$ just as readily as can poorly resolved data $\aleph > 1$ ) in the galaxy center). + Again. inadequate spatial coverage leads to imprecise BH mass estimates. but not unreliable ones.," Again, inadequate spatial coverage leads to imprecise BH mass estimates, but not unreliable ones." + IOpt IOpt Turning to point 4. sparse radial sampling of the kinematic data (which we never do) can also produce a flat bottomed v profile [as illustrated in Figure 3 in Richstone&Tremaine (19855)]] by pushingup or down velocity moments at unobserved radit to maximize or minimize model parameters.," 10pt 10pt Turning to point 4, sparse radial sampling of the kinematic data (which we never do) can also produce a flat bottomed $\chi^2$ profile [as illustrated in Figure 3 in \citet{rt85}] ] by pushingup or down velocity moments at unobserved radii to maximize or minimize model parameters." + Kinematic data with better geometry (both resolution and spatial coverage) leads to smaller uncertainties in the BH mass., Kinematic data with better geometry (both resolution and spatial coverage) leads to smaller uncertainties in the BH mass. +are sensitive to the details of the barvonic svsteimi one is looking at. such as the asstmimed iiass-to-light ratios. eas dvnaniües. or orbital anisotropy of stars. most of which play a marginal role when in the deep MOND regne.,"are sensitive to the details of the baryonic system one is looking at, such as the assumed mass-to-light ratios, gas dynamics, or orbital anisotropy of stars, most of which play a marginal role when in the deep MOND regime." + As pointed out already. this ill-defined transition is cunbersome to haudle i attempts to reproduce the MOND phenomenology through simple GR extensions e.g. Sobouti (2007) or Capozzicllo et al. (," As pointed out already, this ill-defined transition is cumbersome to handle in attempts to reproduce the MOND phenomenology through simple GR extensions e.g. Sobouti (2007) or Capozziello et al. (" +2007).,2007). + Bekeustein (2001) shows that lis relativistic extension of TeVeS in the appropriate non-relativistic limits viclds the interpolating function This particular interpolating function converges to the vieht hits ase 20. aud has a very peculiar property.," Bekenstein (2004) shows that his relativistic extension of $e$ $e$ S in the appropriate non-relativistic limits yields the interpolating function This particular interpolating function converges to the right limits as x 0, and has a very peculiar property." + Direct substitution of equation iuto the absolute value of relation ντο] This equation can be thought of as a eeneralised eravity recipe described by the addition of two terms. the first a standard Newtonian acceleration term and the second the MOND Init acceleration term.," Direct substitution of equation into the absolute value of relation yields This equation can be thought of as a generalised gravity recipe described by the addition of two terms, the first a standard Newtonian acceleration term and the second the MOND limit acceleration term." + Secu iu this way. equation changes its acceleration beliaviour limiting cases to a scale limiting behaviour.," Seen in this way, equation changes its acceleration behaviour limiting cases to a scale limiting behaviour." + Indeed. for the case of a test particle ou a eravitational field produced by a ceutral mass M... located at a distance distance P from it. equation can be written as where G ds Newtou's constant of eravity.," Indeed, for the case of a test particle on a gravitational field produced by a central mass M, located at a distance distance R from it, equation can be written as where G is Newton's constant of gravity." +" Seen iu this wav, equation couverges to Nowtoniui gravity for sufficiently small Αν and reproduces the MOND strong lianit for sufficiently huge πλ Rs, and so the acceleration liits are now “scaleweighted” DDnuits."," Seen in this way, equation converges to Newtonian gravity for sufficiently small R / 's and reproduces the MOND strong limit for sufficiently large R / 's, and so the acceleration limits are now “scale–weighted” limits." + It is worth noting that equation is certainly the simplest modification to Newtonian eravity once the weak acceleration MOND regine is known., It is worth noting that equation is certainly the simplest modification to Newtonian gravity once the weak acceleration MOND regime is known. + Let us now rewrite equation in such a way that the scale weighting becomes clearer., Let us now rewrite equation in such a way that the scale weighting becomes clearer. + To do so. recall that gy=Vox. where . represcuts the standard Noewtouian potential aud gy=Vo. where is the scalar potential of the gravitational field.," To do so, recall that $g_{N}=-\nabla \phi_{N}$, where _N represents the standard Newtonian potential and $g=-\nabla \phi$, where is the scalar potential of the gravitational field." + With this. equation can be written as where \=(my(GY)?(R/ALU?).," With this, equation can be written as where $\chi := (a_0 / G )^{1/2} \, (R/M^{1/2})$." + Tu what follows we use the standard values of ay=1«10Sems7 (\Glerom 2008a) and G=στMarty2kpe?. in units suitable for galactic applications.," In what follows we use the standard values of $a_{0}=1\times 10^{-8} \, \mathrm{cm}\, +\mathrm{s}^{-2}$ (Milgrom 2008a) and $G = 4.5 \times 10^{-39} +M_{\odot}^{-1} \, \mathrm{s}^{-2} \, \mathrm{kpc}^{3}$, in units suitable for galactic applications." + As already mentioned. we are iterested iu the form of pr) at scales of the local dSph galaxies.," As already mentioned, we are interested in the form of $\mu(x)$ at scales of the local dSph galaxies." +" That the articular poe) we are testing is incompatible with solar pAvestem dwnandes implies that a complete gore) MOND ""uetioun is probably couples. that is. if one wants to reat the MOND foriialisii as mere than just an empirical phenomenological description of gravitational plysics on ealactic scales."," That the particular $\mu(x)$ we are testing is incompatible with solar system dynamics implies that a complete $\mu(x)$ MOND function is probably complex, that is, if one wants to treat the MOND formalism as more than just an empirical phenomenological description of gravitational physics on galactic scales." + On the other hand. some researchers (see e.g. Bekeustein 2006 and references therein) οἰα that he Pioneer anomaly can be explained bv the MOND wpothesis.," On the other hand, some researchers (see e.g. Bekenstein 2006 and references therein) claim that the Pioneer anomaly can be explained by the MOND hypothesis." + This assunption can prove wrong if uneven hermal radiation in the spacecrafts is found (Toth Turvshev 2009). which could possibly come frou the fivbw anomaly (Turvshey 2009).," This assumption can prove wrong if uneven thermal radiation in the spacecrafts is found (Toth Turyshev 2009), which could possibly come from the flyby anomaly (Turyshev 2009)." + Tn other words. the MOND ornalisui does not appear to be relevant ou solar svsteii scales. where Ceneral Relativity aud Newtonian Cravitv wave proven correct (c.g. Turvshiev Toth 2009. Aucdersou et al.," In other words, the MOND formalism does not appear to be relevant on solar system scales, where General Relativity and Newtonian Gravity have proven correct (e.g. Turyshev Toth 2009, Anderson et al." + 2002)., 2002). +" Still. as discussed bv MGlerom (2009). it is xossible that currenu tests on solar svsteni scales cannot reach definitive couclusions on the MOND interpolating ""nction."," Still, as discussed by Milgrom (2009), it is possible that current tests on solar system scales cannot reach definitive conclusions on the MOND interpolating function." + For elobular clusters. with Af=105SAL. R=21010 Fkpe. we get values for y of between 0.1 and 01. and the correction becomes sinaller than the errors and uncertainties iu the observational determinations for he values of radii aud masses for elobular clusters.," For globular clusters, with $M=10^{5-6} M_{\odot}$, $R=2-10 +\times 10^{-3} \, \mathrm{kpc}$ , we get values for $\chi$ of between $0.1$ and $0.01$, and the correction becomes smaller than the errors and uncertainties in the observational determinations for the values of radii and masses for globular clusters." +" For eliptical galaxies aud bulges. with masses going from about LO? to 101:AJ, and radi of between 0.5 aud 10 sper \ is about 0.1."," For elliptical galaxies and bulges, with masses going from about $10^{9}$ to $10^{11} M_{\odot}$ and radii of between 0.5 and 10 kpc, $\chi$ is about 0.1." + We thus see that the correction o gravitational dynamics due to the proposed. inclusion of a second terii iu equation is small enough to lave remained undetected in galactic svstems where no eravitational anomaly is found and where clwnamics are consistent with Newtonian eravity. in the absence of any dark matter.," We thus see that the correction to gravitational dynamics due to the proposed inclusion of a second term in equation is small enough to have remained undetected in galactic systems where no gravitational anomaly is found and where dynamics are consistent with Newtonian gravity, in the absence of any dark matter." + Ou the other haud. for svstems where the presence of dark matter is inferred. eiven that this is always required to be dominant. adding the Newtonian term onto the MOND proposal gcucrally provides a neeligible contribution.," On the other hand, for systems where the presence of dark matter is inferred, given that this is always required to be dominant, adding the Newtonian term onto the MOND proposal generally provides a negligible contribution." +" For example. for the Galactic disk at the solar radius. AL=5«101911, and R=SAHkpc give \=2. consistent with an inference of about 50% dark uatter within the solar circle."," For example, for the Galactic disk at the solar radius, $M=5 \times 10^{10} M_{\odot}$ and $R=8.5 \, \textrm{kpc}$ give $\chi=2$, consistent with an inference of about $50\%$ dark matter within the solar circle." + In going to the outskirts of he Milk Wax. we go to R=LO0kpe. hence ν=20.," In going to the outskirts of the Milk Way, we go to $R=100 \textrm{kpc}$, hence $\chi=20$." + The system is either totally dominated by dark matter. or it is iu a regine where the second term in equation almost tly determunes the cvuamics.," The system is either totally dominated by dark matter, or it is in a regime where the second term in equation almost fully determines the dynamics." + We see that the cdistiuct sower-law dependences eusure that the Newtonian term colpletely dominates at small values of 4. while the opposite holds for large values of 4. with a necessarily jurow transition region.," We see that the distinct power-law dependences ensure that the Newtonian term completely dominates at small values of $\chi$, while the opposite holds for large values of $\chi$, with a necessarily narrow transition region." + Froiun the orn of equation (5).. it would be tempting o add the following term of the 1/R series; a further (perhaps positive) constaut term. which would result iu an u additive fermi in equation(6).," From the form of equation , it would be tempting to add the following term of the 1 / R series, a further (perhaps positive) constant term, which would result in an $\chi^{2}$ additive term in equation." +. If chosen suitably xnall. for the sene reasons as eiven above. it would have no measurable effects ou all but the largest scales. perhaps as a tool to model thecostuological constant.," If chosen suitably small, for the same reasons as given above, it would have no measurable effects on all but the largest scales, perhaps as a tool to model thecosmological constant." +As shown in Figure Ibb. the density structure at high latitudes >0) is more complicated because of the partial overlaps of overdense areas closed by arcs with different radii.,"As shown in Figure \ref{fig:ptm}b b, the density structure at high latitudes $|z|>0$ ) is more complicated because of the partial overlaps of overdense areas closed by arcs with different radii." +" The overdeuse regious induced by a slower object (1L6). the regions of interest exhibit eubauced densities because they swallow the perturbations of each crescent-shaped structures."," However, once overlapped $\mach\geq4.6$ ), the regions of interest exhibit enhanced densities because they swallow the perturbations of each crescent-shaped structures." + For iustauce. the case in Figure 1. (LM=10) experiences 3 steps of deusity enbaucement (corresponding to the number of perturbations Av= 7) within the discernible spiral arm in the orbital plane.," For instance, the case in Figure \ref{fig:ptm} $\mach=10$ ) experiences 3 steps of density enhancement (corresponding to the number of perturbations $\pert=7$ ) within the discernible spiral arm in the orbital plane." + But ihe uumber of perturbations decreases at high latitude where the overlapping events are reduced (see also Fig., But the number of perturbations decreases at high latitude where the overlapping events are reduced (see also Fig. + 2bb)., \ref{fig:num}b b). + Eventually above the extension limit (Eq. [9].," Eventually above the extension limit (Eq. \ref{equ:hyp}] ])," + the gas flow experiences only one perturbation so that the deusity euliauceiment has the value of QuinGr.z) (see evan line in Figure Lee along the dotted line. a=aQyinfr0. z)).," the gas flow experiences only one perturbation so that the density enhancement has the value of $\amin(r,z)$ (see cyan line in Figure \ref{fig:ptm}c c along the dotted line, $\alpha=\amin(r=0,\,z)$ )." + Iu order to understaud the clistribution of the peak deusities aloug clistauce. it is preferable to 'efer to the simpler case of the perturbing object moving on a linear trajectory. whose respective yerturbatious equally contribute to the density enhancement of the induced. wake. Ostriker," In order to understand the distribution of the peak densities along distance, it is preferable to refer to the simpler case of the perturbing object moving on a linear trajectory, whose respective perturbations equally contribute to the density enhancement of the induced wake. \citeauthor{ost99}'" + s ormula for the linear motion of a perturber (eq. [2]]), 's formula for the linear motion of a perturber (eq. \ref{equ:ost}] ]) + has roughly an anticorrelation with respect to he clistauce from the perturbing object with the amplitude of rg;M-1|!/? per each contribution.," has roughly an anticorrelation with respect to the distance from the perturbing object with the amplitude of $r_B\,|\mach^2-1|^{-1/2}$ per each contribution." + loclifving Ostrikers formula. for circular orbit cases we hypothlesize a deusity enhancement due o oue perturbation. in the orbital plane.," Modifying \citeauthor{ost99}' 's formula, for circular orbit cases we hypothesize a density enhancement due to one perturbation, in the orbital plane." +" However. in reality. the circular motion modilies the density euliaucemenut [rom a simple collection of ay, by the uunuber of perturbatious."," However, in reality, the circular motion modifies the density enhancement from a simple collection of $\alpha_1$ by the number of perturbations." + Particularly. gas pressure at the central region prevents the propagation of Mach waves. forming instead an equilibrium state with the central value à=rg/rg.," Particularly, gas pressure at the central region prevents the propagation of Mach waves, forming instead an equilibrium state with the central value $\alpha=r_B/r_p$." + A rough guess of ay can be used in an empirical formula for the peak density enhancement in the spiral arm patteru. which shows fairly good fits in Figures lec aud 3. (see black solid curve). except at tlie exact locatious of the arm boundaries where infinite values are introduced by the poiut mass perturber (see below).," A rough guess of $\alpha_1$ can be used in an empirical formula for the peak density enhancement in the spiral arm pattern, which shows fairly good fits in Figures \ref{fig:ptm}c c and \ref{fig:cmp} (see black solid curve), except at the exact locations of the arm boundaries where infinite values are introduced by the point mass perturber (see below)." +Llowever. we will concentrate on the evolution of haloes modeled as a collisionless spherical distribution for application in Paper 2 and adopt the traditional ££... or E.&Sfdines(LH).cos3—JefJ phase-space variables for computational purposes.,"However, we will concentrate on the evolution of haloes modeled as a collisionless spherical distribution for application in Paper 2 and adopt the traditional $E, J, J_z$ or $E, \kappa\equiv J/J_{max}(E), +\cos\beta\equiv J_z/J$ phase-space variables for computational purposes." + In addition. we will not consider any processes with a preferred axis so we can average equation (7)) over J with no loss of information.," In addition, we will not consider any processes with a preferred axis so we can average equation \ref{eq:FP}) ) over $\beta$ with no loss of information." + Lowe are willing to restrict ourselves to an isotropic distribution. we can average over & to vield a l|1 dimensional Fokker-Planck equation in time and energy. ££: this is described in below.," If we are willing to restrict ourselves to an isotropic distribution, we can average over $\kappa$ to yield a $1+1$ dimensional Fokker-Planck equation in time and energy, $E$; this is described in \\ref{sec:fpavg} below." + Because the dillusion coellicients depend on the distribution function. the Fokker-Planck equation in (7)) is non-linear. just as for globular cluster evolution.," Because the diffusion coefficients depend on the distribution function, the Fokker-Planck equation in \ref{eq:FP}) ) is non-linear, just as for globular cluster evolution." + However. it is straightforward to solve this numerically by iteration.," However, it is straightforward to solve this numerically by iteration." + To derive the coellicients 3 and 7. we will use the method described in Weinberg (1998. hereafter Paper 1).," To derive the coefficients $D^{(1)}$ and $D^{(2)}$, we will use the method described in Weinberg (1998, hereafter Paper 1)." + To summarize. we represent distortions in the structure of halo in a biorthogonal basis.," To summarize, we represent distortions in the structure of halo in a biorthogonal basis." + Any distortion can be summarized then by à set of cocllicicnts in three indices., Any distortion can be summarized then by a set of coefficients in three indices. + Because large spatial scales are most important in understanding elobal evolution. we can truncate this expansion and still recover most of the power.," Because large spatial scales are most important in understanding global evolution, we can truncate this expansion and still recover most of the power." + Moreover. we can analytically compute the scll-egravitating response of the halo to some arbitrary perturbation as previously described.," Moreover, we can analytically compute the self-gravitating response of the halo to some arbitrary perturbation as previously described." + This development gives us £(/) for all phase-space variables (cf., This development gives us $\xi(t)$ for all phase-space variables (cf. + eq. 4)), eq. \ref{eq:kramers}) ) + and the appropriate ensemble averages give us the required diffusion coefficients., and the appropriate ensemble averages give us the required diffusion coefficients. + For example. if one uses the same biorthogonal basis in an n-body simulation of a desired. transient process. the time series of coellicients can be used clireethy to derive the cocllicients D! and D'7* after removing the time-invariant (DC) component which corresponds to the equilibrium background.," For example, if one uses the same biorthogonal basis in an n-body simulation of a desired transient process, the time series of coefficients can be used directly to derive the coefficients $D^{(1)}$ and $D^{(2)}$ after removing the time-invariant (DC) component which corresponds to the equilibrium background." + We will consider point mass perturbers in refsec:pointmass and transient perturbers (ebwarf galaxies. decaving substructure. spreading debris trails) in refsecishrapnel..," We will consider point mass perturbers in \\ref{sec:pointmass} and transient perturbers (dwarf galaxies, decaying substructure, spreading debris trails) in \\ref{sec:shrapnel}." + A number of authors have described transformation of the multivariate Fokker-Planck equation. (Itosenbluth et al., A number of authors have described transformation of the multivariate Fokker-Planck equation (Rosenbluth et al. + 1957. lüsken 1989).," 1957, Risken 1989)." + The approach is the familiar one: write the equation in terms of scalars. covariant ancl contravariant vectors and tensors and covariant derivatives only.," The approach is the familiar one: write the equation in terms of scalars, covariant and contravariant vectors and tensors and covariant derivatives only." + In the first case. the authors use the Jacobian of the coordinate transformation as a metric and in the second. the authors use the diffusion matrix.," In the first case, the authors use the Jacobian of the coordinate transformation as a metric and in the second, the authors use the diffusion matrix." + We will use the first case here., We will use the first case here. + Denote the Jacobian of the coordinate transformation as J., Denote the Jacobian of the coordinate transformation as $J$. + Under à change of coordinates. one can show after a fair bit of algebra that the advection and dilfusion terms transform as The phase-space distribution function transforms as /(I)=/f(D) (ef," Under a change of coordinates, one can show after a fair bit of algebra that the advection and diffusion terms transform as The phase-space distribution function transforms as $f^\prime(\bI) += J f(\bI)$ (cf." + Risken 1989) and in the new variables. the equation takes the standard bokker-Planck form: ↓∖⊽∪∖∖⊽↓∢⊾↿↕↙∶↿∖∆⋅⊳∣⋅⋅⋡≼∙⇜∩⋡⇀∖⊳∖⊳∖⊔⊔↓⊲↓⊔⋏∙≟↿⇂↥," Risken 1989) and in the new variables, the equation takes the standard Fokker-Planck form: Now let $\bI^\prime = (E, \kappa, \cos\beta)$." +⋜∐⇂↓↥⋖⋅∠∐⊳∖⇂↓⋰↓∣⋡⋯⊲↓∪⊔⇂⋅⋯⊔∼⇂⊲↓∪⊔⇠∕↔↓⊳∖⇂⊲↓⊔↓⋖⋅−⊲↓⊔∠⇂⋖⋅↓≻∢⊾⊔∠⇂∢⋅⊔↿⋜⋯∠⇂⊔∪⊔−∠⋖⋅↓⋅∪⊳∖∖⋎∢⋅⊔↓⋜↧∙∖⇁⊲↓↓∐∢⋅⋏∙≟↓⋅⋜⋯⋅ ∢⊾⊏↥⇂⇂⋜↧↿↕⋖≱↓↕↿∖⊔∩∪∖⇁∢⊾↓⋅∣⋅⋅⋜⋯∠⇂≼∙⇜⊰⋡∺⊀↓⊔⊓⋅∣⋡∪↿↓⊔⋟," Assuming that the distribution function $f$ is time-independent and non-zero, we may integrate equation \ref{eq:fptrans}) ) over $\kappa$ and $\cos\beta$." +⇂∎↥↓∐⊾⊳∖∢⋅∖⇁⋜⊔⋰↓⋜↧∣⋡↓∢⋅≱∖↓⋯∖⇁∢⊾⋜↧∣⋯⊔⊔∠⇂⋯⇂∠⇂∩⊔⋯⊲↓⊔⊳↿↓⊔⋅∐⇂∟∖↿↓⊔⋅∪⊔⋏∙≟∐∣↓↕⋖⊾↕↓⋅∣⋡∩⊔⊔∠⇂⋜⊔⋰⊓⊾⊳∖⊔↓⊔⊳∖↿ vanish. leaving a single lux term: where the angle brackets denote integration over & and cos? and sum over j denote the sum over all three variables.," Since both of these variables have a bounded domain, the flux through their boundaries must vanish, leaving a single flux term: where the angle brackets denote integration over $\kappa$ and $\cos\beta$ and sum over $j$ denote the sum over all three variables." + The isotropically averaged Fokker-Planck equation is then where (Dppiso and (Deedic. are the isotropically averaged cilfusion coelIicients: Note that the standard notation in the globular cluster literature is fll)=f(E/ PE)., The isotropically averaged Fokker-Planck equation is then where $\langle D_E\rangle_{iso}$ and $\langle D_{EE}\rangle_{iso}$ are the isotropically averaged diffusion coefficients: Note that the standard notation in the globular cluster literature is $f(E)={\bar f}(E)/P(E)$ . +discussed in Sect. 5.1..,"discussed in Sect. \ref{sec:univar_analytic}," +" the first V—| derivatives of p(£) with respect to £ yreld the equations Then. we can consider the N factors a, as the components of a vector d=(di.σιιν. ax)."," the first $N-1$ derivatives of $p(\xi)$ with respect to $\xi$ yield the equations Then, we can consider the $N$ factors $a_n$ as the components of a vector $\vec{a} = (a_1,a_2,\dots,a_N)$ ." + Combining this with another vector b2(0.0.0.....O0) with N entries and with the NN coetficient matrix M of the above equations. we obtain the LSE We can then solve this LSE by any of the usual methods.," Combining this with another vector $\vec{b}=(1,0,0,\dots,0)$ with $N$ entries and with the $N \times N$ coefficient matrix $\tens{M}$ of the above equations, we obtain the LSE We can then solve this LSE by any of the usual methods." + In particular. we applied the Singular Value Decomposition as implemented in the GNU Scientific Library (GSL. .," In particular, we applied the Singular Value Decomposition (SVD) as implemented in the GNU Scientific Library \citep[GSL, ][]{Galassi2009}." +" ""nThis implementation has limited precision. and therefore runs into the same numerical problems described in Sect. 4..", This implementation has limited precision and therefore runs into the same numerical problems described in Sect. \ref{sec:numerical}. + However. SVD solutions for many numerically challenging problems exist. and therefore the general approach seems promising.," However, SVD solutions for many numerically challenging problems exist, and therefore the general approach seems promising." + Since the moments have simpler expressions (Eqs., Since the moments have simpler expressions (Eqs. + 25 and 28 to 32)) than the probability distribution function itself. it seems promising to express the distribution in terms of its moments.," \ref{eq:moments_mean} and \ref{eq:moments_momc2} to \ref{eq:moments_momc6}) ) than the probability distribution function itself, it seems promising to express the distribution in terms of its moments." + One way to do so is the Edgeworth asymptotic expansion. described in ?..," One way to do so is the Edgeworth asymptotic expansion, described in \cite{Blinnikov1998}." +" It has the form with the (probabilist's) Hermite polynomials He,. and ἕ and σ as given in Sect. 2.2.."," It has the form with the (probabilist's) Hermite polynomials $\operatorname{He}_n$, and $\overline{\xi}$ and $\sigma$ as given in Sect. \ref{sec:univar_moments}." +" The inner sum runs over all sets [4 of non-negative integers solving the Diophantine equation and we also defined. for each such set. We calculate the [&,,] and r with the algorithm presented in Appendix C of ?.."," The inner sum runs over all sets $\{k_m\}$ of non-negative integers solving the Diophantine equation and we also defined, for each such set, We calculate the $\{k_m\}$ and $r$ with the algorithm presented in Appendix C of \cite{Blinnikov1998}." +" The first term in the Edgeworth expansion is a simple Gaussian. and the higher order terms are given by the cumulants «, of the distribution 1n. question. which we can derive from the central moments M, as In Fig. 4."," The first term in the Edgeworth expansion is a simple Gaussian, and the higher order terms are given by the cumulants $\kappa_n$ of the distribution in question, which we can derive from the central moments $M_{\mathrm{c},n}$ as In Fig. \ref{fig:pxi_edge}," + we demonstrate the performance of the Edgeworth expansion in two examples. both for Gaussian power spectra.," we demonstrate the performance of the Edgeworth expansion in two examples, both for Gaussian power spectra." + The left panel shows a distribution at zero lag. with Lop=20 and 16 modes.," The left panel shows a distribution at zero lag, with $L \, \sigma_P=20$ and 16 modes." + The Edgeworth term of order zero. a Gaussian with the same mean and variance as the full distribution. is a very bad fit in this case.," The Edgeworth term of order zero, a Gaussian with the same mean and variance as the full distribution, is a very bad fit in this case." + The third- Edgeworth expansion is the best fit. fitting the peak of the distribution almost perfectly and the tail decently well. while also producing negative probabilities for some €<0.," The third-order Edgeworth expansion is the best fit, fitting the peak of the distribution almost perfectly and the tail decently well, while also producing negative probabilities for some $\xi<0$." + Adding additional terms only makes the approximation worse. distorting 1t in the high probability region.," Adding additional terms only makes the approximation worse, distorting it in the high probability region." + For the right panel. we used v/L=0.5. Lop=100 and N=32.," For the right panel, we used $x/L=0.5$, $L \, \sigma_P=100$ and $N=32$." + For this more symmetric distribution. the Gaussian is already abetter fit: still. the third order Edgeworth expansion fits even better at the peak.," For this more symmetric distribution, the Gaussian is already abetter fit; still, the third order Edgeworth expansion fits even better at the peak." + Higher orders again begin to deviate. as evidenced by the strongly two-peaked sixth-order expansion.," Higher orders again begin to deviate, as evidenced by the strongly two-peaked sixth-order expansion." +Photometry and astrometry in crowded fields is usually performed with a PSF fitting algorithm.,Photometry and astrometry in crowded fields is usually performed with a PSF fitting algorithm. +" Perhaps the most widely used software of this kind is DAOPHOT (e.g.,??),, which is also integrated in theIRAF software package."," Perhaps the most widely used software of this kind is DAOPHOT \citep[e.g.,][]{Stetson:1987nx,Stetson:1992eu}, which is also integrated in the software package." + Another popular package is SExtractor (?).., Another popular package is SExtractor \citep{Bertin:1996oq}. +" In this work, I use the StarFinder algorithm (?),, which was specifically developed for images obtained by AO assisted observations and is fairly popular in the AO community."," In this work, I use the algorithm \citep{Diolaiti:2000qo}, which was specifically developed for images obtained by AO assisted observations and is fairly popular in the AO community." +" It has been shown to obtain comparable results to those of DAOPHOT (intheisoplanaticcase,see ??).."," It has been shown to obtain comparable results to those of DAOPHOT \citep[in the +isoplanatic case, see][]{Diolaiti:2000qo,Diolaiti:2000rz}." + I also experimented with DAOPHOT (see refsec:daophot))., I also experimented with DAOPHOT (see \\ref{sec:daophot}) ). +" In theStarFinder algorithm, an empirical point spread function (PSF) is extracted by using one or several stars in the image."," In the algorithm, an empirical point spread function (PSF) is extracted by using one or several stars in the image." + Cross correlation on potential stars is performed., Cross correlation on potential stars is performed. + A correlation threshold is set to accept/reject potential stars., A correlation threshold is set to accept/reject potential stars. + Gaussian readout noise and Poissonian photon noise are determined by the algorithm and taken into account in the fitting process to determine formal uncertainties., Gaussian readout noise and Poissonian photon noise are determined by the algorithm and taken into account in the fitting process to determine formal uncertainties. + A smooth diffuse background emission is fit for the image simultaneously to the point source photometry and astrometry., A smooth diffuse background emission is fit for the image simultaneously to the point source photometry and astrometry. + The PSF extraction can be iteratively improved by using the measured positions and fluxes of detected stars for removal of secondary sources near the PSF reference stars., The PSF extraction can be iteratively improved by using the measured positions and fluxes of detected stars for removal of secondary sources near the PSF reference stars. + There are many parameters that can be modified in theStarFinder algorithm., There are many parameters that can be modified in the algorithm. +" The most important ones are the number of iterations and the point source detection threshold applied at each iteration, the size of the box for background estimation, and the correlation threshold."," The most important ones are the number of iterations and the point source detection threshold applied at each iteration, the size of the box for background estimation, and the correlation threshold." +" The parameter thresh gives both the number of iterations and the threshold in terms of standard deviations from the noise, e.g., thresh[3.,3.] means two iterations with a 3c threshold for each one."," The parameter $thresh$ gives both the number of iterations and the threshold in terms of standard deviations from the noise, e.g., $thresh=[3.,3.]$ means two iterations with a $3\,\sigma$ threshold for each one." + The parameter backbox is given in pixels and designates a box size., The parameter $back\_box$ is given in pixels and designates a box size. +StarFinder estimates the sky background in boxes of size back.boxxback_box and then computes a smooth background by means of interpolation between the background grid points., estimates the sky background in boxes of size $back\_box\times back\_box$ and then computes a smooth background by means of interpolation between the background grid points. +" By default,StarFinder applies bilinear interpolation."," By default, applies bilinear interpolation." + We found that this tends to overestimate the background close to bright point sources and therefore chose cubic interpolation., We found that this tends to overestimate the background close to bright point sources and therefore chose cubic interpolation. + The minimum required value for a correlation to exist between a point source and the PSF is given by min.corr., The minimum required value for a correlation to exist between a point source and the PSF is given by $min\_corr$. +" In this work, the following values of these parameters were applied: thresh[5.] for a first detection of sources that are subsequently used to iteratively improve the PSF; thresh—[5.,5.] for point source extraction; backbox=60 (back.box=30 on deconvolved images); and min.corr=0.8 (min.corr=0.9 on deconvolved images)."," In this work, the following values of these parameters were applied: $thresh=[5.]$ for a first detection of sources that are subsequently used to iteratively improve the PSF; $thresh=[5.,5.]$ for point source extraction; $back\_box=60$ $back\_box=30$ on deconvolved images); and $min\_corr=0.8$ $min\_corr=0.9$ on deconvolved images)." +" For accurate photometry and astrometry, a number of effects must be taken into account in addition to this basic methodology."," For accurate photometry and astrometry, a number of effects must be taken into account in addition to this basic methodology." + We identified the following points as being particularly important: The last point is in part a consequence of the first two points and the desire to improve the accuracy of the applied methodology., We identified the following points as being particularly important: The last point is in part a consequence of the first two points and the desire to improve the accuracy of the applied methodology. + In the following subsections different aspects of the PSFfitting method are addressed in detail., In the following subsections different aspects of the PSFfitting method are addressed in detail. +eternuned values is the scaling factor.,determined values is the scaling factor. + The R-baud image was divided by that value aud then subtracted from the Πα image., The R-band image was divided by that value and then subtracted from the $\alpha$ image. + By that procedure a coutiuuun free Ta nuage is created., By that procedure a continuum free $\alpha$ ] image is created. + Finally the two Πα images have becu ubined to eaim a better S/N ratio., Finally the two $\alpha$ images have been combined to gain a better S/N ratio. + Some cosmics hav been removed manually., Some cosmics have been removed manually. + The detection of cosmiics was4. straight forward since we had two Πα images for each ealaxy. which can be easily compared.," The detection of cosmics was straight forward since we had two $\alpha$ images for each galaxy, which can be easily compared." + Finally a fux calibration has been performed., Finally a flux calibration has been performed. + The uecasured Robaud. photometry data of our edgeou galaxies have been taken fromNED?., The measured R–band photometry data of our edge–on galaxies have been taken from. + These Rband naenitudes represent measured magnitudes in a certain aperture., These R–band magnitudes represent measured magnitudes in a certain aperture. + Therefore we determined the flux (couutrates) inour Rbaud image for the same aperture size as were the photometry data. applving the flux of the standard Vega as a calibrator.," Therefore we determined the flux (countrates) in our R–band image for the same aperture size as were the photometry data, applying the flux of the standard Vega as a calibrator." + We then divided the calculated fux by he value of the nieasured ουνατος n o ταbaud filter. correcting for the integration time and tlic scaling factor of our passhand exposures.," We then divided the calculated flux by the value of the measured countrates in our R–band filter, correcting for the integration time and the scaling factor of our passband exposures." + Finally we altiied this factor with the measured countrate in our Πα ex)osure aud thus ect the relation between the countrates and the flux., Finally we multiplied this factor with the measured countrate in our $\alpha$ exposure and thus get the relation between the countrates and the flux. + The uncertainties with this method are of the order of, The uncertainties with this method are of the order of. + With the transformed flux units it is also possible to couvert the flux values to another commonly used unit. namely the emission measure (EM) which is defined by The emission measure can be calculated according5 to with Z(IIn) the intensity of the Πα cussion. iu Bavleigh (B). and with T the eas teniperature in units of 10 KK. (Reynolds 19903). assuniue case D plotionisation (Osterbrock 1989)).," With the transformed flux units it is also possible to convert the flux values to another commonly used unit, namely the emission measure (EM) which is defined by The emission measure can be calculated according to with $I$ $\alpha$ ) the intensity of the $\alpha$ emission, in Rayleigh (R), and with $T$ the gas temperature in units of $10^4$ K. (Reynolds \cite{Re90}) ), assuming case B photionisation (Osterbrock \cite{Os89}) )." + Usually a conversion is derived at Ia where ήLempe22.06E⋅.10eresNtemZaxesec.7.," Usually a conversion is derived at $\alpha$ where $\rm{1\,cm^ +{-6}\,pc = 2.06 \times 10^{-18} erg\,s^{-1}\,cm^{-2}\,arcsec^{-2}}$." + Although the continmu has been subtracted fromm the images. there is still sole contaniuatio1 of the Ta line from the nearby doublet. which also coutributes to the liue enüssion.," Although the continuum has been subtracted from the images, there is still some contamination of the $\alpha$ line from the nearby ] doublet, which also contributes to the line emission." + This is due to the eiveu filter passband., This is due to the given filter passband. + With knowledee of line ratios. cerived from spectroscopical investigations. the mean ratio of Ila to r1] can in principle bedetermined. which in turn can be used to correct for the r1] emission.," With knowledge of line ratios, derived from spectroscopical investigations, the mean ratio of $\alpha$ to ] can in principle bedetermined, which in turn can be used to correct for the ] emission." + From the measured IIo line fis the total Wa huninosity can be computed bx where D is the distance to the galaxy., From the measured $\alpha$ line flux the total $\alpha$ luminosity can be computed by where $D$ is the distance to the galaxy. + It is now possible to derive the star formation rate (SFR) using the calibration of Madau ctal. (1998)), It is now possible to derive the star formation rate $SFR$ ) using the calibration of Madau etal. \cite{Mad98}) ) + to a Salpeter initial mass functiou (AIF) with mass limits 0.1 aud 100 AD: (Salpeter 19553) which after Kemucutt (199853) vields The results cau be compared with SF Rs derived by far-yared (FIR) fluxes from e.g.. measurenieuts with the IRAS satellite.," to a Salpeter initial mass function (IMF) with mass limits 0.1 and 100 $\rm{M}_{\sun}$ (Salpeter \cite{Sal55}) ) which after Kennicutt \cite{Ke98b}) ) yields The results can be compared with $SFR$ s derived by far--infrared (FIR) fluxes from e.g., measurements with the IRAS satellite." + The SFR. as derived from the FIR flus. are expected to be higher uuless a correcion of the Πα ínxes is performed for internal dust absorption (since many οσοon galaxies bear a more or less promunent dust --10).," The $SFR$, as derived from the FIR flux, are expected to be higher unless a correction of the $\alpha$ fluxes is performed for internal dust absorption (since many edge–on galaxies bear a more or less prominent dust lane)." + The SFR from the FIR Inuinositv cau be caleulated 1ο- a sinilar manner according to νοσα! (1998b)). and reerences therein. takiis muto account the timescales for lxists of SE. which vieds which 19 actually valid for starburst galaxies.," The $SFR$ from the FIR luminosity can be calculated in a similar manner according to Kennicutt \cite{Ke98b}) ), and references therein, taking into account the timescales for bursts of SF, which yields which is actually valid for starburst galaxies." +" The seusitivitv of our observatious is 7.20« O1 average. which corresponds to au emissiou measure (EM) of 3.5ci σος, "," The sensitivity of our observations is $7.2 \times 10^{-18}\,\rm{erg\,s^{-1}\,cm^{-2}\,arcsec^{ +-2}}$ on average, which corresponds to an emission measure (EM) of $3.5\, +\rm{cm^{-6}\,pc}$ ." +Basic paramcters for our sample of 9 edgeon galaxies aro given in Table 2.., Basic parameters for our sample of 9 edge–on galaxies are given in Table \ref{T2}. . + Here the coordinates for the, Here the coordinates for the +We then discuss a possibility of non-thermal origin.,We then discuss a possibility of non-thermal origin. + The most likely case is SNRs with non-thermal X-ravs. like SN 1006 and the Crab Nebula.," The most likely case is SNRs with non-thermal X-rays, like SN 1006 and the Crab Nebula." + In Table 3.. we also list ihe physical parameters of a newly established ον 1006-like SNR. ΑΝ J1343.3—0352 = G28.6—0.1 (Bambaetal.2001a).. for comparison.," In Table \ref{phys_para}, we also list the physical parameters of a newly established SN 1006-like SNR, AX $-$ 0352 = $-$ 0.1 \citep{bamba2001a}, for comparison." + First. we discuss the possibility (hat thev are SN LOOG-like SNRs.," First, we discuss the possibility that they are SN 1006-like SNRs." + Photon indices of G11.0+0.0 and G25.5+0.0 ave ~2. which are smaller (han those of twpical SN. LOOG-like ONRs. SN 1006 μοι. G347.3-0.5. and G266.6—1.2. but are similar to that of G28.6—0.1.," Photon indices of G11.0+0.0 and G25.5+0.0 are $\sim 2$, which are smaller than those of typical SN 1006-like SNRs, SN 1006 itself, $-$ 0.5, and $-$ 1.2, but are similar to that of $-$ 0.1." + This mav indicate that the svnchrotron. X-ravs are due to the electrons with higher energy than (hat of (he acceleration cut-off. which is expected fom the first-order Fermi acceleration (expected D = 1.5: Wentzel 1974).," This may indicate that the synchrotron X-rays are due to the electrons with higher energy than that of the acceleration cut-off, which is expected from the first-order Fermi acceleration (expected $\Gamma$ = 1.5; Wentzel 1974)." + The diameters ancl total Iuminosities also resemble (hose of G28.6—0.1., The diameters and total luminosities also resemble those of $-$ 0.1. + These [acts strongly. support that at least G11.0+0.0 and. G25.5+0.0 are SN 1006-like SNRs., These facts strongly support that at least G11.0+0.0 and G25.5+0.0 are SN 1006-like SNRs. + To establish (he SN 1006-like SNRs. the presence of svnchrotron radio emission is essential.," To establish the SN 1006-like SNRs, the presence of synchrotron radio emission is essential." + Llowever no cataloged radio source is found in the NRAO VLA Skv Survey 20 em survey archivaldatal., However no cataloged radio source is found in the NRAO VLA Sky Survey 20 cm survey archival. +. If the magnetic field is weaker than the other SN 1006-like SNRs. the radio surface brightness would be below the current detection limit.," If the magnetic field is weaker than the other SN 1006-like SNRs, the radio surface brightness would be below the current detection limit." + In order (o estimate the radio flux baud for the SN 1006-like SNRs. we tried the spectral fillings with a sreut model (Reynoldsetal.1998:Reynolds&Keohane1999).," In order to estimate the radio flux band for the SN 1006-like SNRs, we tried the spectral fittings with a $srcut$ model \citep{reynolds1998,reynolds1999}." +. The spectral index at 1 GlIlz was Irozen to a=—0.5. expected value by [ist-order Fermi acceleration.," The spectral index at 1 GHz was frozen to $\alpha = -0.5$, expected value by first-order Fermi acceleration." + The fittings were statistically accepted and the best-lit parameters are listed in Table 2.., The fittings were statistically accepted and the best-fit parameters are listed in Table \ref{bestfit_para}. + We also tried the same fittings with a=—0.6 and found no essential difference in the parameters., We also tried the same fittings with $\alpha = -0.6$ and found no essential difference in the best-fit parameters. + The best-fit ας density for each source suggests that the expected surface brightness at 1 GIIz is 9.8x1071. 7x10.7. and 9.8x10.7! W Τρ tsr ! for G11.0+0.0. G25.5+0.0. and G26.6—0.1. respectively.," The best-fit flux density for each source suggests that the expected surface brightness at 1 GHz is $\times 10^{-24}$, $\times 10^{-23}$, and $\times 10^{-24}$ W $^{-2}$ $^{-1}$ $^{-1}$ for G11.0+0.0, G25.5+0.0, and $-$ 0.1, respectively." + On the other hand. (he minimum surface brightness of the cataloged radio SNRs in our survev field is 2x1074 W ?Iz !ar ! (for G3.8-+0.3: Case Bhattacharva 1998). which is similar to SN. 1006 (3x10.7! Wom Ην !sr |: Long. Blair. van den Bergh 1988: Winkler Long 1997) and G347.3—0.5 (4xLO 2W Iz !ar. 1: Ellison. Slane. Gaensler 2001: assuming a = —0.5). but is two or three orders of magnitude larger than our new sources.," On the other hand, the minimum surface brightness of the cataloged radio SNRs in our survey field is $2\times 10^{-21}$ W $^{-2}$ $^{-1}$ $^{-1}$ (for G3.8+0.3; Case Bhattacharya 1998), which is similar to SN 1006 $\times 10^{-21}$ W $^{-2}$ $^{-1}$ $^{-1}$; Long, Blair, van den Bergh 1988; Winkler Long 1997) and $-$ 0.5 $4\times 10^{-21}$ W $^{-2}$ $^{-1}$ $^{-1}$ ; Ellison, Slane, Gaensler 2001; assuming $\alpha$ = $-0.5$ ), but is two or three orders of magnitude larger than our new sources." +" Even the minimum surface brightness of the all cataloged radio− SNRs- is. larger (han our sample. 6.2""Mx10237? W- >?IHz !sr |! (for. G156.24-5.7:-""A— Case- Bhattacharva 1993)."," Even the minimum surface brightness of the all cataloged radio SNRs is larger than our sample, $6.2\times 10^{-23}$ W $^{-2}$ $^{-1}$ $^{-1}$ (for G156.2+5.7; Case Bhattacharya 1998)." + Therefore. no radio counterpart [or our new X-ray sources would be simple dueto limited detection threshold of the current radio observations.," Therefore, no radio counterpart for our new X-ray sources would be simple dueto limited detection threshold of the current radio observations." +where vl is à constant and {νε is the rigid value of 7;.,where $A$ is a constant and $T_{vr}$ is the rigid value of $T_v$. + Το influence of c4 is very small., The influence of $\epsilon_4$ is very small. + In the same way as Z5. ας is decreasing when es is growing.," In the same way as $T_v$, $T_z$ is decreasing when $\epsilon_3$ is growing." + It confirms that the resonance between the proper rotation of the core and the period of the spin Is reached for e;=0., It confirms that the resonance between the proper rotation of the core and the period of the spin is reached for $\epsilon_3=0$. + Phe third column of Table 3. is more because It significantrepresents the distance of this [requeney w. from the exact resonance., The third column of Table \ref{tab:periodnum} is more significant because it represents the distance of this frequency $\omega_z$ from the exact resonance. + Our canonical variables are very convenient to describe the dynamics of the system. unfortunately they are not observable," Our canonical variables are very convenient to describe the dynamics of the system, unfortunately they are not observable" +ormation rate of long GRBs by fitting the observed. BATSLE differential peak flux number counts in three cilferent scenarios: i) GRBs follow the cosmic star formation and nave a redshiftindependent LE: ii) the GRB LE varies with redshift: iii) GRBs are associated with star formation in lowmetallicity environments.,formation rate of long GRBs by fitting the observed BATSE differential peak flux number counts in three different scenarios: i) GRBs follow the cosmic star formation and have a redshift–independent LF; ii) the GRB LF varies with redshift; iii) GRBs are associated with star formation in low–metallicity environments. + In all cases. it is possible o obtain a good fit to the data hy adjusting the mocel ree parameters.," In all cases, it is possible to obtain a good fit to the data by adjusting the model free parameters." + Using the same LE and formation rate. the models reproduce both BATSE and dilferential counts. showing that the two satellites are observing the same GIUS »opulation.," Using the same LF and formation rate, the models reproduce both BATSE and differential counts, showing that the two satellites are observing the same GRB population." + Finally. SCOT have tested: the burst. recshil distribution obtained in the dilferent scenarios against the number ofSwiff detections at 2=2.5 and z>3.5.," Finally, SC07 have tested the burst redshift distribution obtained in the different scenarios against the number of detections at $z\ge 2.5$ and $z\ge 3.5$." + This procedure allows to constrain moclel results withou any assumption on the redshift distribution of bursts tha lack redshift: determination anc on the elfect of selection biases (see Fiore et al., This procedure allows to constrain model results without any assumption on the redshift distribution of bursts that lack redshift determination and on the effect of selection biases (see Fiore et al. + 2007 for a detailed discussion abou this important. issue)., 2007 for a detailed discussion about this important issue). + Models where GRBs trace the star formation rate (SER) and are described by a constan LE ore robustly rule out by available data., Models where GRBs trace the star formation rate (SFR) and are described by a constant LF are robustly rule out by available data. + 2 detection can be explained. assumine that the LE is evolving in redshift., $z$ detection can be explained assuming that the LF is evolving in redshift. + lo particular. SCOT found. that the typical GRB luminosity should. increases. with (1|z)? with àl.4.," In particular, SC07 found that the typical GRB luminosity should increases with $(1+z)^\delta$ with $\delta> 1.4$." + Alternatively. the large number of = identifications may indicate that GRBs are biased tracer of the star formation. forming preferentially in lowmetallicity environment.," Alternatively, the large number of $z$ identifications may indicate that GRBs are biased tracer of the star formation, forming preferentially in low–metallicity environment." + Assuming that the LE does not evolve in redshift. the number of z burst identifications imply a metallicity threshold for GRBs formation lower than 0.32. (SCOT). consistently with the predictions of collapsar models (Alackadven Woosley 1999: Izzard. RamirezRuiz Tou 2004).," Assuming that the LF does not evolve in redshift, the number of $z$ burst identifications imply a metallicity threshold for GRBs formation lower than $0.3\;\Zsun$ (SC07), consistently with the predictions of collapsar models (MacFadyen Woosley 1999; Izzard, Ramirez–Ruiz Tout 2004)." + Available studies of GRB host galaxies (Sollerman et al., Available studies of GRB host galaxies (Sollerman et al. + 2005. Stanek et al.," 2005, Stanek et al." + 2005. Evnbo et al.," 2005, Fynbo et al." + 2006b) seem o confirm this metallicitybias., 2006b) seem to confirm this metallicitybias. + The large majority of hos galaxies has Z«0.3Z. although two bursts are detecte in galaxies with higher metallicitv., The large majority of host galaxies has $Z<0.3\;\Zsun$ although two bursts are detected in galaxies with higher metallicity. + We want to note here hat many absorption lines detected in optical spectroscopy are possibly not. probing rw nearby GRB environmen (Jakobsson et al., We want to note here that many absorption lines detected in optical spectroscopy are possibly not probing the nearby GRB environment (Jakobsson et al. + 2006b. LYIlia et al.," 2006b, D'Elia et al." + 2007. Watson et al.," 2007, Watson et al." + 2007. Prochaska et al.," 2007, Prochaska et al." + 2007. Vreeswijk et al.," 2007, Vreeswijk et al." + 2007)., 2007). + So. any conclusion about the metallicity of the GAB progenitors inferred by these studies should be taken with some caution.," So, any conclusion about the metallicity of the GRB progenitors inferred by these studies should be taken with some caution." + We limit our analysis here to models in which GRBs form preferentially in lowmetallicity environments and are described. by a constant LE. but. similar results can be obtained assuming evolution in the LE.," We limit our analysis here to models in which GRBs form preferentially in low–metallicity environments and are described by a constant LF, but similar results can be obtained assuming evolution in the LF." +" Phe GRB formation rate is then given by where &cpg is the GRB formation elliciencv. ζην.z) eives the fraction of galaxies at redshift z with metallicity below Z,, (Langer Norman 2006) anc W,(z) is the observed star. formation rate."," The GRB formation rate is then given by where $k_{GRB}$ is the GRB formation efficiency, $\Sigma(Z_{th},z)$ gives the fraction of galaxies at redshift $z$ with metallicity below $Z_{th}$ (Langer Norman 2006) and $\Psi_\star(z)$ is the observed star formation rate." + We adopt the recent determination. of the elobal star formation rate obtained by Hopkins Beacom (2006). slightly moclifiecl in order to match the decline with (1|z)3.8 ab zon 5.2as suggested by recent deep.field. data (see Stark et al.," We adopt the recent determination of the global star formation rate obtained by Hopkins Beacom (2006), slightly modified in order to match the decline with $(1+z)^{-3.3}$ at $z\ge 5$, as suggested by recent deep–field data (see Stark et al." + 2007 and references therein)., 2007 and references therein). +" In the following we explore a wide range of mocel with 0.02Z.Z,,<0.5Z.. computing the expected probability to detect a GRB at z=5 withο"," In the following we explore a wide range of model with $0.02\;\Zsun\le Z_{th}\le 0.3\;\Zsun$, computing the expected probability to detect a GRB at $z\ge 5$ with." +τί For all the details of the moclel computation we refer the interested reader to SCOT., For all the details of the model computation we refer the interested reader to SC07. + We compute the probability for a GRB of observed. peak Whoton flux 7? in the 15150 keV band of BAT to moat 25 as the ratio between the expected. number of GRBs at zc55 and the total number of bursts detectable at peak photon Εαν P., We compute the probability for a GRB of observed peak photon flux $P$ in the 15–150 keV band of /BAT to be at $z\ge 5$ as the ratio between the expected number of GRBs at $z\ge 5$ and the total number of bursts detectable at peak photon flux $P$. + The results are shown in the top xiiel of Fie., The results are shown in the top panel of Fig. + 1. for 0.02Z..€Ziy&0.3Z. (shaded area. ower bound refers to the higher threshold. value).," \ref{fig:zge5} for $0.02\;\Zsun\le Z_{th}\le 0.3\;\Zsun$ (shaded area, lower bound refers to the higher threshold value)." +" Dottedine refers to the model with Z),—0.1Z..", Dottedline refers to the model with $Z_{th}=0.1\;\Zsun$. + The probability o find a burst at >25 increases rapidly with decreasing P and becomes larger than for P«I phs ! 7., The probability to find a burst at $z\ge 5$ increases rapidly with decreasing $P$ and becomes larger than for $P<1$ ph $^{-1}$ $^{-2}$. + Indeed. four out of five bursts confirmed to be at zz5 have ohoton Iluxes in the range 0.60.8 phis. 7.," Indeed, four out of five bursts confirmed to be at $z\gsim 5$ have photon fluxes in the range 0.6–0.8 ph $^{-1}$ $^{-2}$." + Llorizontal xws refer to lower limits derived. from the available GRB detections at 2zz5 in the corresponding lux bin., Horizontal bars refer to lower limits derived from the available GRB detections at $z\gsim 5$ in the corresponding flux bin. +" We ind that the model with Zi,=0.1Z. is consistent with lower limits.", We find that the model with $Z_{th}=0.1\;\Zsun$ is consistent with lower limits. + Models with higher metallicity thresholds, Models with higher metallicity thresholds +considerably modified by the effects of virialisation.,considerably modified by the effects of virialisation. +" To account for them (and for deviations from spherical symmetry), Shaw&Mota(2008) constructed an (extended) semi-analytical spherical collapse model."," To account for them (and for deviations from spherical symmetry), \citet{ShMo} constructed an (extended) semi-analytical spherical collapse model." +" For ó up to about δια (which equals to ~4.6, as the background assumed in the discussed paper is of the Einstein-de Sitter type) their model coincides with the standard spherical model (studied here), while for larger density contrasts it deviates from the latter and under some additional assumptions matches well the results of N-body simulations presented by Hamiltonetal.(1991)."," For $\delta$ up to about $\delta_\mathrm{ta}$ (which equals to $\sim4.6$, as the background assumed in the discussed paper is of the Einstein–de Sitter type) their model coincides with the standard spherical model (studied here), while for larger density contrasts it deviates from the latter and under some additional assumptions matches well the results of N-body simulations presented by \citet{Hami}." +". Indeed, formula (20) of Shaw&Mota (2008), for T'—τ (the limit of the standard model), reduces to our Equation (18)) (their hsc.= 0/3)."," Indeed, formula (20) of \citet{ShMo}, for $T = \tau$ (the limit of the standard model), reduces to our Equation \ref{form:teta closed}) ) (their $h_\mathrm{SC} = \theta/3$ )." + The authors argue that for background universes with dark energy their formula is valid only for 6=100., The authors argue that for background universes with dark energy their formula is valid only for $\delta \ga 100$. +" They claim that for smaller values of 6, their results are not accurate."," They claim that for smaller values of $\delta$, their results are not accurate." + We disagree with these statements., We disagree with these statements. +" As already stated, the weak ( A dependence of the scaled velocity—density relation has been shown on the level of the equations of motion (NuCo98),, so independently of the level of non-linearity."," As already stated, the weak $\Omega$ $\Lambda$ dependence of the scaled velocity–density relation has been shown on the level of the equations of motion \citep{NuCo}, so independently of the level of non-linearity." +" Since for small redshifts dark energy behaves similarly to the cosmological constant (e.g. Riessetal. 2007)), and since only for such redshifts the weak dependence of equations of motion on cosmological parameters starts to play any role (because earlier we had Ω<1; NuCo98)), the velocity-density relations for cosmological models with and without dark energy must be similar."," Since for small redshifts dark energy behaves similarly to the cosmological constant (e.g. \citealt{Riess}) ), and since only for such redshifts the weak dependence of equations of motion on cosmological parameters starts to play any role (because earlier we had $\Omega \la 1$; \citealt{NuCo}) ), the velocity–density relations for cosmological models with and without dark energy must be similar." + KaCPeROO studied the mildly non-linear velocity—density relation using the Cosmological Pressureless Parabolic Advection (CPPA) hydrodynamical code., \citet{KaCPeR} studied the mildly non-linear velocity–density relation using the Cosmological Pressureless Parabolic Advection (CPPA) hydrodynamical code. +" They found that the mean relation between the scaled velocity divergence and the density contrast can be very well described by the so-called ‘y-formula’, with ;1.9."," They found that the mean relation between the scaled velocity divergence and the density contrast can be very well described by the so-called $\gamma$ -formula', with $\gamma \simeq 1.9$." + This formula is a modification of the B92 formula with y instead of 3/2.," This formula is a modification of the \citet{B92} + formula with $\gamma$ instead of $3/2$." +" The offset ε>0 is introduced to account for an effect of a finite variance of the density field: the value of ε is such that the global mean of © is zero, as required. ("," The offset $\eps > 0$ is introduced to account for an effect of a finite variance of the density field: the value of $\eps$ is such that the global mean of $\Theta$ is zero, as required. (" +Another effect of a finite variance is to modify the degree of non- of the relation.),Another effect of a finite variance is to modify the degree of non-linearity of the relation.) +" Without the offset, the above formula yields Θ(--1)=—y—1.9 for —1.9, in significant difference with the value —1.5, obtained neglecting the weak of the exact limit, Eq. (35))."," Without the offset, the above formula yields $\Theta(-1) += -\gamma = -1.9$ for $\gamma = 1.9$, in significant difference with the value $-1.5$ , obtained neglecting the weak of the exact limit, Eq. \ref{form:Teta min}) )." +" However, for Gaussian smoothing scales of a few Mpc, employed in KaCPeROO., the offset shifts the value of O(—1) much closer to —1.5."," However, for Gaussian smoothing scales of a few Mpc, employed in \citet{KaCPeR}, the offset shifts the value of $\Theta(-1)$ much closer to $-1.5$." + B99 analysed the velocity-density relation using N-body simmullattions performed for various background cosmologies., \citet{B99} analysed the velocity–density relation using N-body tions performed for various background cosmologies. + They noticed a weak dependence of the relation on €? and A., They noticed a weak dependence of the relation on $\Omega$ and $\Lambda$. +" B99 invented a somewhat more elaborate fit to the extracted mean relation, presented in the form of density in terms of velocity divergence, Here, 6, slightly smaller than unity, plays a role of the offset € in Equation (53)): it assures that the global mean of 6 is zero, as required."," \citet{B99} invented a somewhat more elaborate fit to the extracted mean relation, presented in the form of density in terms of velocity divergence, Here, $\beta$, slightly smaller than unity, plays a role of the offset $\eps$ in Equation \ref{eq:Theta_gamma}) ): it assures that the global mean of $\delta$ is zero, as required." +" In Equation (54)) + is not a constant, but is approximated as a following function of O: The above equation quantifies the fact that for larger values of velocity divergence, the observed relation becomes more non-linear."," In Equation \ref{eq:delta_B99}) ) $\gamma$ is not a constant, but is approximated as a following function of $\Theta$: The above equation quantifies the fact that for larger values of velocity divergence, the observed relation becomes more non-linear." +" Indeed, y grows with growing © (we recall that y=1 corresponds to the linear theory)."," Indeed, $\gamma$ grows with growing $\Theta$ (we recall that $\gamma = 1$ corresponds to the linear theory)." +" Moreover, for Θ=—3/2, we have 7=3/2, so then 6=—1, as it was intended. ["," Moreover, for $\Theta = - 3/2$, we have $\gamma = 3/2$, so then $\delta = -1$, as it was intended. [" +Note a typo in eq. (,Note a typo in eq. ( +"20) of B99:: instead of 6 (in our notation, ©), there should be 6]","20) of \citet{B99}: instead of $\tilde\theta$ (in our notation, $\Theta$ ), there should be $\theta$ .]" +" How do these findings, based on fully non-linear simulations, relate to our results?"," How do these findings, based on fully non-linear simulations, relate to our results?" +" In overdensities, our Formula (51)) follows closer to the exact relation in the SCM than the formula of B92.."," In overdensities, our Formula \ref{form:fit pot}) ) follows closer to the exact relation in the SCM than the formula of \citet{B92}." +" Moreover, our approximation is a formula with increasing effective index Ύομ.."," Moreover, our approximation is a formula with increasing effective index $\gamma_{\rm eff}$." +" Its second order expansion is the same as that of B92,, so for small 6, yes=3/2."," Its second order expansion is the same as that of \citet{B92}, , so for small $\delta$, $\gamma_{\rm eff} = 3/2$." +" For large density contrasts, the second term in Equation (51)) becomes negligible, so asymptotically yer=2 (for 6> 1)."," For large density contrasts, the second term in Equation \ref{form:fit + pot}) ) becomes negligible, so asymptotically $\gamma_{\rm eff} = 2$ (for $\delta \gg 1$ )." +" Therefore, qualitatively our formula is consistent with the fit of B99,, in a sense that ""y, as a function of © or 6, is growing."," Therefore, qualitatively our formula is consistent with the fit of \citet{B99}, in a sense that $\gamma$, as a function of $\Theta$ or $\delta$, is growing." +" It is also consistent with the fit of KaCPeROO,, in a sense that the average y is slightly larger than 3/2."," It is also consistent with the fit of \citet{KaCPeR}, in a sense that the average $\gamma$ is slightly larger than $3/2$." +" Clearly, our formula is a better fit to the results of numerical simulations than the formula of B92.."," Clearly, our formula is a better fit to the results of numerical simulations than the formula of \citet{B92}." +" Of course, quantitatively there are discrepancies."," Of course, quantitatively there are discrepancies." +" First of all, it is strictly impossible to satisfy simultaneously the features of both fits: iseither constant increasing."," First of all, it is strictly impossible to satisfy simultaneously the features of both fits: $\gamma$ is constant increasing." + This discrepancy between the results of the two groups is not necessarily a sign of a major flaw in any of their analyses., This discrepancy between the results of the two groups is not necessarily a sign of a major flaw in any of their analyses. + The two groups used different codes: N-body versus hydro., The two groups used different codes: N-body versus hydro. +" The first one follows accurately non-linear evolution, but provides naturally a mass-, not volume-, weighted velocity field, while the latter is needed."," The first one follows accurately non-linear evolution, but provides naturally a mass-, not volume-, weighted velocity field, while the latter is needed." +" CPPA, as any hydrodynamical code, provides naturally a volume- velocity field, but follows the non-linear evolution after shell crossings only approximately."," CPPA, as any hydrodynamical code, provides naturally a volume-weighted velocity field, but follows the non-linear evolution after shell crossings only approximately." +" Moreover, the density power spectra used in both simulations were different."," Moreover, the density power spectra used in both simulations were different." +" Also, fit (54)) of B99 was found for top-hat smoothed fields, while fit (53)) ofKaCPeROO was elaborated for fields smoothed with a Gaussian filter (more appropriate for velocity-density comparisons)."," Also, fit \ref{eq:delta_B99}) ) of \citet{B99} was found for top-hat smoothed fields, while fit \ref{eq:Theta_gamma}) ) of\citet{KaCPeR} was elaborated for fields smoothed with a Gaussian filter (more appropriate for velocity–density comparisons)." +" The effectsof smoothing, though small, are different for these two filters (see TTable 1 of KaCPeROO))."," The effectsof smoothing, though small, are different for these two filters (see Table 1 of \citealt{KaCPeR}) )." +" Finally, an inverse of the"," Finally, an inverse of the" +We have used the set of 3D hydrodynamic model atmospheres of red giants by ?? to perform spectral line formation calculations for the [S 1] line and the triplet.,"We have used the set of 3D hydrodynamic model atmospheres of red giants by \citet{Collet2007,Collet2009} to perform spectral line formation calculations for the $\ion{S}{i}$ ] line and the triplet." + These calculations were compared to analogous 1D calculations based on MARCS models to estimate the 3D—1D LTE corrections to the sulphur abundance for giants with different stellar parameters in order to check the effects of our neglect of convective, These calculations were compared to analogous 1D calculations based on MARCS models to estimate the $-$ 1D LTE corrections to the sulphur abundance for giants with different stellar parameters in order to check the effects of our neglect of convective +It has been known for some decades that some radio sources vary in intensity over time (Dent 1965)).,It has been known for some decades that some radio sources vary in intensity over time (Dent \cite{dent}) ). + The range of time scales detected so far. roughly from minutes to decades. is set by the practicalities of measurement rather than by any intrinsic properties of the source populations.," The range of time scales detected so far, roughly from minutes to decades, is set by the practicalities of measurement rather than by any intrinsic properties of the source populations." + The present paper is concerned with sources which exhibit significant variation 1n flux density on time scales of less than 24 hours (so-called Intra-Day Variables or IDVs) and which are also associated with extended structure of a size resolvable by present-day radio interferometers., The present paper is concerned with sources which exhibit significant variation in flux density on time scales of less than 24 hours (so-called Intra-Day Variables or IDVs) and which are also associated with extended structure of a size resolvable by present-day radio interferometers. + The structure makes it of interest to image such sources. but the rapid variability can hinder attempts to do so.," The structure makes it of interest to image such sources, but the rapid variability can hinder attempts to do so." + It is these difficulties in the interferometric imaging of IDV sources which the present paper is designed to address., It is these difficulties in the interferometric imaging of IDV sources which the present paper is designed to address. + How many such sources are there. and of what types?," How many such sources are there, and of what types?" + Any estimation of the incidence of variability among. the radio source population is complicated by the extra degrees of freedom implicit in a non-flat light curve., Any estimation of the incidence of variability among the radio source population is complicated by the extra degrees of freedom implicit in a non-flat light curve. + It is also inevitable that there will be selection effects due to the inability of the instrument to detect modulation depths below a certain cutoff. or the insensitivity of the observing regime to time scales outside a certain range.," It is also inevitable that there will be selection effects due to the inability of the instrument to detect modulation depths below a certain cutoff, or the insensitivity of the observing regime to time scales outside a certain range." + The difference between the population of objects observable in our galaxy and those which are extra-galactic introduces a dependence of incidence on galactic latitude (further complicated by the greater propensity of compact. extragalactic sources to scintillate at low galactic latitudes).," The difference between the population of objects observable in our galaxy and those which are extra-galactic introduces a dependence of incidence on galactic latitude (further complicated by the greater propensity of compact, extragalactic sources to scintillate at low galactic latitudes)." + It is even more difficult to estimate the fraction of variable sources which are IDV. since surveys of the depth and cadence necessary to determine this quantity demand extravagant amounts of observing time.," It is even more difficult to estimate the fraction of variable sources which are IDV, since surveys of the depth and cadence necessary to determine this quantity demand extravagant amounts of observing time." + Of presently-available survey results. De Vries et al (2004)). 1n a two-epoch comparison of a high latitude field. found only ~0.2 deg at 1.4 GHz flux densities of >2 mly.," Of presently-available survey results, De Vries et al \cite{devries}) ), in a two-epoch comparison of a high latitude field, found only $\sim 0.2$ $^{-2}$ at 1.4 GHz flux densities of $\ge 2$ mJy." + Bower et al (2007)) have processed a large amount of VLA 5 and 8.4 GHz archival data and find a ‘snapshot’ incidence of 1.5 deg radio transients at flux densities greater than 350 ply., Bower et al \cite{bower}) ) have processed a large amount of VLA 5 and 8.4 GHz archival data and find a `snapshot' incidence of $1.5$ $^{-2}$ radio transients at flux densities greater than 350 $\mu$ Jy. + Becker et al (2010)) compared 3 epochs of VLA observations of the galactic plane at 6 em and found ~1.6 deg sources between ] and 100 mJy which had a modulation depth greater than505c., Becker et al \cite{becker}) ) compared 3 epochs of VLA observations of the galactic plane at 6 cm and found $\sim 1.6$ $^{-2}$ sources between 1 and 100 mJy which had a modulation depth greater than. +. Regarding the IDV fraction. Kedziora-Chudezer et al (2001)) found. in their multi-frequency study (between 1.4 and 8.6 GHz). that about half of their 13 BL Lac objects. and a smaller fraction of quasars. exhibited IDV up to about modulation: more recently Lovell et al (2008)). in a more comprehensive survey at 5 GHz. report that of their 443 flat-spectrum sources showed significant variability on a 2-day time scale.," Regarding the IDV fraction, Kedziora-Chudczer et al \cite{kedziora}) ) found, in their multi-frequency study (between 1.4 and 8.6 GHz), that about half of their 13 BL Lac objects, and a smaller fraction of quasars, exhibited IDV up to about modulation; more recently Lovell et al \cite{lovell}) ), in a more comprehensive survey at 5 GHz, report that of their 443 flat-spectrum sources showed significant variability on a 2-day time scale." + Sources which exhibit a combination of IDV plus some resolved structure fall into several classes. which are briefly reviewed in the following paragraphs.," Sources which exhibit a combination of IDV plus some resolved structure fall into several classes, which are briefly reviewed in the following paragraphs." + Novae are expected to exhibit significant changes in radio flux density at intraday time scales., Novae are expected to exhibit significant changes in radio flux density at intraday time scales. + In the standard model. the flux density from an expanding isothermal shell is expected initially to increase proportional to the square of time since the outburst (Hjellming 1996)). although some recent VLBA observations appear to be inconsistent with that picture (Krauss et al 2011)).," In the standard model, the flux density from an expanding isothermal shell is expected initially to increase proportional to the square of time since the outburst (Hjellming \cite{hjellming}) ), although some recent VLBA observations appear to be inconsistent with that picture (Krauss et al \cite{krauss}) )." + However. most novae at least in the past decade have not been resolved by radio interferometry until of order 100 days after the outburst. by which time the fractional change in flux density has fallen to about a percent or two per day (see e.g. Eyres et al 2000.. Eyres et al 2005.. Heywood O’Brien 2007)).," However, most novae at least in the past decade have not been resolved by radio interferometry until of order 100 days after the outburst, by which time the fractional change in flux density has fallen to about a percent or two per day (see e.g. Eyres et al \cite{eyres_2000}, Eyres et al \cite{eyres_2005}, Heywood O'Brien \cite{heywood}) )." + A recent exception is the 2006 outburst of the recurrent nova RS Ophiuchi (O’Brien et al 2006a))., A recent exception is the 2006 outburst of the recurrent nova RS Ophiuchi (O'Brien et al \cite{obrien_2006a}) ). + This was observed with the VLBA first on day I4 after the outburst. and the European VLBI Network (EVN) from day 20 (O’Brien et al 2006b)).," This was observed with the VLBA first on day 14 after the outburst, and the European VLBI Network (EVN) from day 20 (O'Brien et al \cite{obrien_2006b}) )." + The size of the source at 6 em wavelength grew from approximately 20 to 35 mas between these observations., The size of the source at 6 cm wavelength grew from approximately 20 to 35 mas between these observations. + The flux density was no longer varying rapidly by that time. but the earliest observations with MERLIN on day 4 after the outburst show it then varying by a factor of 2 over less than a day.," The flux density was no longer varying rapidly by that time, but the earliest observations with MERLIN on day 4 after the outburst show it then varying by a factor of 2 over less than a day." + Model calculations indicate that RS Oph would have been resolvable by the EVN at that time., Model calculations indicate that RS Oph would have been resolvable by the EVN at that time. +vortices merece to form larger vortices mstead ofbreaking up iuto sinaller vortices as in the 3D case.,vortices merge to form larger vortices instead of breaking up into smaller vortices as in the 3D case. + Thus. the turbulent dynamo is expected to behave (f at allpresent) very differeutlv from the 3D case studied here.," Thus, the turbulent dynamo is expected to behave (if at all present) very differently from the 3D case studied here." +" The evolution of the solenoidal ratio toward iore solenoidal turbulence for72 explains that the growth rates in Fieure 9 inerease after 7=7. showing a steepening of 44,077 with time for τσε7. 11. which correlates with the increase in the solenoidal ratio."," The evolution of the solenoidal ratio toward more solenoidal turbulence for$\tau\gtrsim7$ explains that the growth rates in Figure \ref{fig:time_evol_growth_rates} increase after $\tau=7$, showing a steepening of $B_\mathrm{rms}/\rho^{2/3}$ with time for $\tau\approx7$ –11, which correlates with the increase in the solenoidal ratio." + This is because the dwuaime feeds from the solenoidal modes of the turbulence. which increase between 7= aud 11.," This is because the dynamo feeds from the solenoidal modes of the turbulence, which increase between $\tau=7$ and 11." + Since the solenoidal ratio varies stronely with time in the early phases of the collapse. we had to choose a rather late time within the collapse regime to mnieasure ιο erowth rates of the maguctic field. 1.0. we estimated 1ο growth rates in the interval 7=[8.τα) in Figure 9..," Since the solenoidal ratio varies strongly with time in the early phases of the collapse, we had to choose a rather late time within the collapse regime to measure the growth rates of the magnetic field, i.e., we estimated the growth rates in the interval $\tau=[8,\tau_\mathrm{end}]$ in Figure \ref{fig:time_evol_growth_rates}." + Ideally. we would like to measure the erowth rates after ie solenoidal ratio has couverged to 4=2/3. but lue to the computational expense. we could uot follow ie hieh resolutiou simuulatious (61 and 128 cells) far iuto this regime.," Ideally, we would like to measure the growth rates after the solenoidal ratio has converged to $\chi=2/3$, but due to the computational expense, we could not follow the high resolution simulations (64 and 128 cells) far into this regime." + The 32 cell run. however. does show a convergence of \ toward 2/3," The 32 cell run, however, does show a convergence of $\chi$ toward 2/3." + Both the solenoidalratio aud the absolute specific sinctic energv in rotational motions. £L. shown iu Figure 12.. indicate couvergence for a Jeans resolution of 32 cells and higher.," Both the solenoidalratio and the absolute specific kinetic energy in rotational motions, $E_\mathrm{sol}$, shown in Figure \ref{fig:rot_ratio}, indicate convergence for a Jeans resolution of 32 cells and higher." + Using & aud 16 cells to resolve the Jeans length is clearly iusufficieut to resolve rotational motions., Using 8 and 16 cells to resolve the Jeans length is clearly insufficient to resolve rotational motions. + We conclude that at least 20 erid cells per Jeans leugth ust be used in (M)ITD simalatious of selferavitating eas to resolve the turbulent encrey. aud thus the turbulent pressure. aud to obtain minimal dynamo wuplification of the magnetic ficld ou the Jeans scale.," We conclude that at least 30 grid cells per Jeans length must be used in (M)HD simulations of self-gravitating gas to resolve the turbulent energy, and thus the turbulent pressure, and to obtain minimal dynamo amplification of the magnetic field on the Jeans scale." + We presented high-resolution maguctolydrodvuamical siuulatious of the collapse of a dense. maguctized eas cloud. (seealso.Suretal.2010.paperD.," We presented high-resolution magnetohydrodynamical simulations of the collapse of a dense, magnetized gas cloud \citep[see also,][paper I]{SurEtAl2010}." +. During the collapse of the cloud. exevitational. poteutial euergv is converted into turbulent motions. which iu turni amplify the magnetic field exponcutially fast bv the turbulent dynamo process.," During the collapse of the cloud, gravitational, potential energy is converted into turbulent motions, which in turn amplify the magnetic field exponentially fast by the turbulent dynamo process." + The expoueutial amplification is driveu bv the stretching. twisting. and folding of the siuall-scale magnetic field lines (Fig. 3)).," The exponential amplification is driven by the stretching, twisting, and folding of the small-scale magnetic field lines (Fig. \ref{fig:snapshots}) )." + At sufficiently. high Revuolds nuunibers. even extremely small initial seeds of the magnetic Ποια are expected to be amplified o dvmunicallv miportant magnetic Ποια streneths ou nnescales nich shorter than the collapse timescales.," At sufficiently high Reynolds numbers, even extremely small initial seeds of the magnetic field are expected to be amplified to dynamically important magnetic field strengths on timescales much shorter than the collapse timescales." + We conclude that magnetic fields should not be neglected in both primordial aud conteniporary studies of star ornmation., We conclude that magnetic fields should not be neglected in both primordial and contemporary studies of star formation. + We investigated the scale-cdependence of the turbulence and inagnetie field by means of Fourier analysis iu he collapsing frame of reference (Fie. 1)).," We investigated the scale-dependence of the turbulence and magnetic field by means of Fourier analysis in the collapsing frame of reference (Fig. \ref{fig:spect_jeans}) )," + showing sole indication of the Nazautsey spectrum of turbulent οσαο amplification. aud in the fixed frame of reference over more than four orders of magnitude in spatial scale (Fig. 5)).," showing some indication of the Kazantsev spectrum of turbulent dynamo amplification, and in the fixed frame of reference over more than four orders of magnitude in spatial scale (Fig. \ref{fig:spect_fixed}) )." + We fiud that the effective kinetic energy oeijection scale of eravity-diiven turbulence is close to the Jeans leugth (Fig. 7))., We find that the effective kinetic energy injection scale of gravity-driven turbulence is close to the Jeans length (Fig. \ref{fig:vel_spect}) ). + Our Fourier analysis of the maeuctic field shows that the dynamo is only excited. if the Jeans leugth is sufficieutlv resolved (Fig. 8)).," Our Fourier analysis of the magnetic field shows that the dynamo is only excited, if the Jeans length is sufficiently resolved (Fig. \ref{fig:spect_resol}) )." + The radial dependence of the magnetic field is significantly steeper than what is expected from purely dragecd-inOO magnetic field lines. 1e.. Bux-freeziug (Bay.xor6°).," The radial dependence of the magnetic field is significantly steeper than what is expected from purely dragged-in magnetic field lines, i.e., flux-freezing $B_\mathrm{rms}\propto r^{-4/3}$ )." + For a Jeaus resolution of 128 cells. we obtained BaysXrZU. which is expected to steepen further with increasing Jeans resolution (Fig. 2)).," For a Jeans resolution of 128 cells, we obtained $B_\mathrm{rms}\propto r^{-2.0}$, which is expected to steepen further with increasing Jeans resolution (Fig. \ref{fig:resradprofiles}) )." + We find that at least 30 erid cells per Jeans leusth are required for mununmuu dynamo action fo occur iu collapse simulations.a. a resolution requirement. which is not achieved in most current simulations.," We find that at least 30 grid cells per Jeans length are required for minimum dynamo action to occur in collapse simulations, a resolution requirement, which is not achieved in most current simulations." + Here. we studied: dyaiuno amplification with a resolution up to 128 cells per Jeans length. while usually less than 16 cells are used.," Here, we studied dynamo amplification with a resolution up to 128 cells per Jeans length, while usually less than 16 cells are used." + The amplification rate increases with resolution (Fig. 9)).," The amplification rate increases with resolution (Fig. \ref{fig:time_evol_growth_rates}) )," + which renders any existing simulation of dynamo amplification of a lighly turbulent iuecdiunm iusufficieutlv resolved to determine the physical growth rate of the maeguetic field. and can at best provide lower Iunits on the plavsical erowth rates.," which renders any existing simulation of dynamo amplification of a highly turbulent medium insufficiently resolved to determine the physical growth rate of the magnetic field, and can at best provide lower limits on the physical growth rates." + We fud that the probability distribution fiction of the gas density inside the eravityv-driven. turbulent Jeans voluue follows a log-uormal distribution (Fie. 6)).," We find that the probability distribution function of the gas density inside the gravity-driven, turbulent Jeans volume follows a log-normal distribution (Fig. \ref{fig:pdfs}) )." + The standard deviations and Mach numbers inside the core indicate that eravitv-driven turbulence approaches a natural mixture of solenoidal aud compressible modes. LfEroc2/3. after a phase of more compressively driven turbulence. caused by the elobal collapse of the system (Fie. 121).," The standard deviations and Mach numbers inside the core indicate that gravity-driven turbulence approaches a natural mixture of solenoidal and compressible modes, $\solratio\approx2/3$, after a phase of more compressively driven turbulence, caused by the global collapse of the system (Fig. \ref{fig:rot_ratio}) )." + The turbulent cnerey (or turbulent xessure) couverges oulv for a Jeans resolution exceeding 30 exid cells., The turbulent energy (or turbulent pressure) converges only for a Jeans resolution exceeding 30 grid cells. + Iu coutrast. the solenoidal component of the urbuleut euergy is severely uuder-estinated. if the Jeaus cneth is resolved with 16 cells or less.," In contrast, the solenoidal component of the turbulent energy is severely under-estimated, if the Jeans length is resolved with 16 cells or less." + Thus. we sugecst anew Jeans resolution criterion of 30 exid cells per Jeans cheth to obtain couverecd results of the turbulent energy ou the Jeans scale. aud to capture minim magnetic ficld amplification by the turbulent dynamo process.," Thus, we suggest a new Jeans resolution criterion of 30 grid cells per Jeans length to obtain converged results of the turbulent energy on the Jeans scale, and to capture minimum magnetic field amplification by the turbulent dynamo process." + The importance of magnetic fields im prescut-day accretion disks is generally accepted., The importance of magnetic fields in present-day accretion disks is generally accepted. + However. since even sanall initial seeds of the maguetie field are cficicutly aupli&ed by turbulent dvnaimo action. it cannot be excluded that maenetic fields also play an important role in primordial accretion disks.," However, since even small initial seeds of the magnetic field are efficiently amplified by turbulent dynamo action, it cannot be excluded that magnetic fields also play an important role in primordial accretion disks." +" Simulations of primordial eas show that it is highly turbulent (0.5...Abeletal.etal.2008:Cireif 2008).. which sugeests that there is sufficient kinetic energev in rotational modes of the turbuleuce (οιοι,vorticity:seeinparticular.Wise&Abel2007:Greifetal.2008) to dive the small-scale dyuiauuo also iu primordial eas clouds and accretion disks (seealso.Puditz&Silk 1989)."," Simulations of primordial gas show that it is highly turbulent \citep[e.g.,][]{AbelBryanNorman2002,OSheaNorman2007,WiseAbel2007,ClarkGloverKlessen2008,GreifEtAl2008}, which suggests that there is sufficient kinetic energy in rotational modes of the turbulence \citep[e.g., vorticity; see in particular,][]{WiseAbel2007,GreifEtAl2008} to drive the small-scale dynamo also in primordial gas clouds and accretion disks \citep[see also,][]{PudritzSilk1989}." +. Observed turbulent Mach iuuboers iu e.g. preseut-dav xoto-planetary disks are of the order of 0.10.5 (IIushlesetal. 2011).," Observed turbulent Mach numbers in e.g., present-day proto-planetary disks are of the order of 0.1–0.5 \citep[][]{HughesEtAl2011}." + It is typically believed that this disk urbuleuce is driven by the maeueto-rotatioual instability CMRIBalbus&Iawley1991).," It is typically believed that this disk turbulence is driven by the magneto-rotational instability \citep[MRI,][]{BalbusHawley1991}." +. However. in particular in the carly phases of star formation. disk turbulence is xossiblv driven by the eravitational iufall aud accretion of eas from the envelope onto the disk Uslessen&IIen-jiebelle 2010).," However, in particular in the early phases of star formation, disk turbulence is possibly driven by the gravitational infall and accretion of gas from the envelope onto the disk \citep{KlessenHennebelle2010}." +.. The interaction of the AMIRI with selt- instabilitics may effectively decrease the accretion rate aud chanee the disk morphology etal. 2001).. also iu the primordial case (Silk&Langer 2006)..," The interaction of the MRI with self-gravitational instabilities may effectively decrease the accretion rate and change the disk morphology \citep{FromangEtAl2004}, , also in the primordial case \citep{SilkLanger2006}. ." + A spectacular example of dvnamically importaut magnetic fields in the accretion disks of voung stars is the eeneration of high-speed. bipolar jets. which are launched by a tower of magnetic pressure αποον bv a centrifugal magnetic field," A spectacular example of dynamically important magnetic fields in the accretion disks of young stars is the generation of high-speed, bipolar jets, which are launched by a tower of magnetic pressure and/or by a centrifugal magnetic field" +The exceptionally close proximity of the type Hpec supernova SN 1987A in the Large. Alagellanic Cloud. has provided a unique opportunity to observe a core-collapse supernova with all the resources of modern. observational astronomy anc over a very long period. of time.,The exceptionally close proximity of the type IIpec supernova SN 1987A in the Large Magellanic Cloud has provided a unique opportunity to observe a core-collapse supernova with all the resources of modern observational astronomy and over a very long period of time. + Near-infrared (ποσαΗΝ) spectroscopy has plaved a vital role in the determination of the physical conditions in the debris and the investigation of the clement synthesis. providing a valuable complement to optical spectra.," Near-infrared (near-IR) spectroscopy has played a vital role in the determination of the physical conditions in the debris and the investigation of the element synthesis, providing a valuable complement to optical spectra." + In. particular. in the nebular phase (when the lines are mostly. optically thin) the line profiles produced. in the high velocity. homologous expansion have cnabled us to examine. the ejecta abundances and theirspeafied distribution.," In particular, in the nebular phase (when the lines are mostly optically thin) the line profiles produced in the high velocity, homologous expansion have enabled us to examine the ejecta abundances and their distribution." + During the first few vears. all the major southern observatories obtained near-Lh spectra of SN. 1987... Observations at the Anelo-Australian Telescope (AAT) covering the first 3 years post-explosion were described in Meikle et al. (," During the first few years, all the major southern observatories obtained near-IR spectra of SN 1987A. Observations at the Anglo-Australian Telescope (AAT) covering the first 3 years post-explosion were described in Meikle et al. (" +1989. 1993) (hereinafter Papers I. 11).,"1989, 1993) (hereinafter Papers I, II)." + In this paper we describe spectra obtained at the AAT for a further 8 epochs from 1990. November 2 (cay 1348 = 3.7 vears) to 1995 October 17 (day 3158 = 8.6 vears)., In this paper we describe spectra obtained at the AAT for a further 8 epochs from 1990 November 2 (day 1348 = 3.7 years) to 1995 October 17 (day 3158 = 8.6 years). + Epochs are with respect to the explosion date 1987 February 23., Epochs are with respect to the explosion date 1987 February 23. + Our day 1348 spectrum was the last observation of SN. 1987. obtained with the near-H1 spectrometer FLGS (Bailey et al., Our day 1348 spectrum was the last observation of SN 1987A obtained with the near-IR spectrometer FIGS (Bailey et al. + Loss., 1988. + Also see Papers E. ID., Also see Papers I II). + ALL the subsequent spectra were obtained with the more sensitive spectrograph. HUS (Allen et al.," All the subsequent spectra were obtained with the more sensitive spectrograph, IRIS (Allen et al." + 1993). which allowed the acquisition of high resolution near-H3 spectra to a later phase than was achieved at any other observatory.," 1993), which allowed the acquisition of high resolution near-IR spectra to a later phase than was achieved at any other observatory." + Preliminary reports of these data iwe been given in Fassia (1999) and Aleikle (2001)., Preliminary reports of these data have been given in Fassia (1999) and Meikle (2001). + Ehe only other post-3 vear Hi spectra reported are. those of Bautista ct al. (, The only other post-3 year IR spectra reported are those of Bautista et al. ( +1995) which reached. dav 1445. but at a ower resolution than those described. here.,"1995) which reached day 1445, but at a lower resolution than those described here." + In. a future yaper (Fassia ct al..," In a future paper (Fassia et al.," + in preparation) we shall present {1 A-xd spectra of SN LOSTA taken with the MPI imaging, in preparation) we shall present $HK$ -band spectra of SN 1987A taken with the MPE imaging +the extraction aperture: as expected (see 55) we are not able to detect mass segregation in these clusters.,the extraction aperture; as expected (see 5) we are not able to detect mass segregation in these clusters. + The spectra of the four most luminous. globular clusters were de-blueshifted to restframe wavelengths. normalized. and averaged in order to increase| the S/N ratio and diminish the effects of any remaining systematic detector or night sky residuals.," The spectra of the four most luminous globular clusters were de-blueshifted to restframe wavelengths, normalized, and averaged in order to increase the S/N ratio and diminish the effects of any remaining systematic detector or night sky residuals." + The averaging of these four clusters is justified as their ages and metallicities are nearly identical (see refselect.plot))., The averaging of these four clusters is justified as their ages and metallicities are nearly identical (see\\ref{select.plot}) ). + In the following the cluster B189 will be discussed separately. although we note here that including this cluster in the average spectrum has no impact on our analysis or conclusions.," In the following the cluster B189 will be discussed separately, although we note here that including this cluster in the average spectrum has no impact on our analysis or conclusions." + refelobs.plot shows the averaged spectrum of the M31 globular clusters in the wavelength regions near the Il doublet (eft panel) and the Wing-Ford band (right panel)., \\ref{globs.plot} shows the averaged spectrum of the M31 globular clusters in the wavelength regions near the I doublet (left panel) and the Wing-Ford band (right panel). + Note that the Nall doublet is resolved and not blended with TIO. as globular clusters have much lower velocity dispersions than the elliptical galaxies discussed in.," Note that the I doublet is resolved and not blended with TiO, as globular clusters have much lower velocity dispersions than the elliptical galaxies discussed in." +vDC.. Following tthe spectrum was normalized by fitting. second-order polynomials in the top panels (excluding the regions around the features of interest) and first-order polynomials in the bottom panels., Following the spectrum was normalized by fitting second-order polynomials in the top panels (excluding the regions around the features of interest) and first-order polynomials in the bottom panels. + The typical uncertainty inthe averaged spectrum ts AA. as judged from the median scatter among the four globular clusters over the wavelength range -—AA.," The typical uncertainty inthe averaged spectrum is $^{-1}$, as judged from the median scatter among the four globular clusters over the wavelength range –." +. All the easily visible absorption lines are stellar features. not noise.," All the easily visible absorption lines are stellar features, not noise." + We smoothed the spectra slightly to approximate the resolution of the IRTF spectral library (see below)., We smoothed the spectra slightly to approximate the resolution of the IRTF spectral library (see below). + Colored Imes are stellar population synthesis models., Colored lines are stellar population synthesis models. + The models are the same as those invDC:: they are 10 Gyr old. Solar metallicity models based on empirical stellar spectra from the (2009) IRTF library.," The models are the same as those in: they are 10 Gyr old, Solar metallicity models based on empirical stellar spectra from the (2009) IRTF library." +to decline as some of the initially-present SPH disk particles are accreted by orbit 450.,to decline as some of the initially-present SPH disk particles are accreted by orbit 450. +" Our second test was to restart the simulation a third time at orbit 400, but this time to enhance the injection rate of SPH particles at L1 by roughly a factor of 2 over that required(mass to flow)keep the disk particle count constant (Figure 4))."," Our second test was to restart the simulation a third time at orbit 400, but this time to enhance the injection rate of SPH particles (mass flow) at L1 by roughly a factor of 2 over that required to keep the disk particle count constant (Figure \ref{fig: en400420burst}) )." + This enhanced mass flux again dramatically changes the character of the light curve., This enhanced mass flux again dramatically changes the character of the light curve. +" Here the mean pulse shape as shown in the inset is saw-toothed, but with the substructure near the peak from the interaction of the stream with the periodic motion of the spiral features in the disk as viewed in the co-rotating frame."," Here the mean pulse shape as shown in the inset is saw-toothed, but with the substructure near the peak from the interaction of the stream with the periodic motion of the spiral features in the disk as viewed in the co-rotating frame." + Careful comparison of the times of maximum in these two runs (Figures 3 and 4)) reveals that they are antiphased with each other., Careful comparison of the times of maximum in these two runs (Figures \ref{fig: en400420ns} and \ref{fig: en400420burst}) ) reveals that they are antiphased with each other. +" For example, the simulation light curve in Figure 3 shows maxima at times of 403.0 and 404.0 orbits, whereas the simulation light curve in Figure 4. shows minima at these same times."," For example, the simulation light curve in Figure \ref{fig: en400420ns} shows maxima at times of 403.0 and 404.0 orbits, whereas the simulation light curve in Figure \ref{fig: en400420burst} shows minima at these same times." +" Our third experiment was more crude, but still effective."," Our third experiment was more crude, but still effective." +" We began with a disk from a q=0.2 viscosity SPH simulation run that was in a stable, state."," We began with a disk from a $q=0.2$ low-viscosity SPH simulation run that was in a stable, state." +" We offset all of the the SPH particles an amount 0.03a along the line of centers [i.e., >(a:4-0.03a,y, z)], scaled the SPH particle speeds(x,y,z) (but not directions) using theviva equation and restarted the simulation."," We offset all of the the SPH particles an amount $0.03a$ along the line of centers [i.e., $(x,y,z)\rightarrow (x+0.03a,y,z)$ ], scaled the SPH particle speeds (but not directions) using the equation and restarted the simulation." + This technique gives us disk which is non-axisymmetric but not undergoing the superhump oscillation., This technique gives us disk which is non-axisymmetric but not undergoing the superhump oscillation. + The results were as expected: we find maxima in the simulation light curves at the phases where the accretion stream impacts the disk edge deepest in the potential well of the primary., The results were as expected: we find maxima in the simulation light curves at the phases where the accretion stream impacts the disk edge deepest in the potential well of the primary. +" In summary, numerical simulations reproduce the source model for positive superhumps."," In summary, numerical simulations reproduce the two-source model for positive superhumps." +" Photometric signals with periods a few percent shorter than [ον have also been observed in several DN, novalikes, and AM CVn systems - in some cases simultaneously with positive superhumps (see,e.g.,Ta-ble2ofWoodetal.2009,andWoudt 2009)."," Photometric signals with periods a few percent shorter than $\Porb$ have also been observed in several DN, novalikes, and AM CVn systems – in some cases simultaneously with positive superhumps \citep[see, +e.g., Table 2 of][and Woudt et al. 2009]{wts09}." + These oscillations have been termednegative superhumps owing to the sign of the period “excess” obtained using Equation 1.., These oscillations have been termed superhumps owing to the sign of the period “excess” obtained using Equation \ref{eq: eps+}. +" The system TV Col was the first system to show this signal, and Bonnet-Bidaudetal. suggested that the periods were consistent with (1985)what would be expected for a disk that was tilted out of the orbital plane and freely precessing with a period of ~4 d. Barrettetal. expanded on this and suggested what is now the (1988)accepted model for the origin of negative superhumps: the transit of the accretion"," The system TV Col was the first system to show this signal, and \citet{bbmm85} + suggested that the periods were consistent with what would be expected for a disk that was tilted out of the orbital plane and freely precessing with a period of $\sim$ 4 d. \citet{bow88} expanded on this and suggested what is now the accepted model for the origin of negative superhumps: the transit of the accretion" +"and where S,;(Z.g) and νο τμ) ave the critical [Iuxes at the inner and outer boundaries in units of the solar constant.","and where $S_{b,i}$ $T_{\rm eff}$ ) and $S_{b,o}$ $T_{\rm eff}$ ) are the critical fluxes at the inner and outer boundaries in units of the solar constant." + The inner and outer physical boundaries ο in AU were then caleulated using We obtained habitable zone boundaries of 6.8 AU and 13.5 AU.," The inner and outer physical boundaries $r_{i,o}$ in AU were then calculated using We obtained habitable zone boundaries of 6.8 AU and 13.5 AU." + + Dra's planet has a semimajor axis of 1.34 AU (205). so there is no chance the planet orbits anywhere near the habitable zone.," $\iota$ Dra's planet has a semimajor axis of 1.34 AU (Z08), so there is no chance the planet orbits anywhere near the habitable zone." + The CIARA Array is funded by the National Science Foundation through NSF erant AST-0606958 and bv Georgia State University through the College of Arts and. Sciences. and bv the W.M. eek Foundation.," The CHARA Array is funded by the National Science Foundation through NSF grant AST-0606958 and by Georgia State University through the College of Arts and Sciences, and by the W.M. Keck Foundation." + STR. acknowledges partial support by NASA erant NNIIOOAINT21., STR acknowledges partial support by NASA grant NNH09AK731. + This research has made use of the SIMDAD database. operated at CDS. Strasbourg. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France." + This publication makes use of data products from the Two Micron. All sky Survey. which is a joint project of the University. of Massachusetts and the. Infrared Processing and Analvsis Center/California Institute of Technology. Παπάος by the National Aeronautics aud Space Administration and the National Science Foundation.," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation." +uncertainty is estimated from cross-correlation with the single integration and the S/N is measured by calculation of the off-peak RMS.,uncertainty is estimated from cross-correlation with the single integration and the S/N is measured by calculation of the off-peak RMS. +" As the profile has a large on-pulse duty cycle, only ~15% of the pulse period can be used to calculate the noise RMS, which results in a ~10% uncertainty of both the measured S/N and the sharpness estimates."," As the profile has a large on-pulse duty cycle, only $\sim15\%$ of the pulse period can be used to calculate the noise RMS, which results in a $\sim10\%$ uncertainty of both the measured S/N and the sharpness estimates." + The 2-bit distortion is calculated by following the stages laid out in Section 4.5.1.., The 2-bit distortion is calculated by following the stages laid out in Section \ref{sssec:2bittheory}. + As shown in Fig., As shown in Fig. + 6 the 2-bit distortion levels were consistently low during the 2005-09-07 observation and the sharpness was close to normally distributed., \ref{tsharp t2bit} the 2-bit distortion levels were consistently low during the 2005-09-07 observation and the sharpness was close to normally distributed. +" The observation of 2006-12-31, however, shows significantly larger levels of 2-bit distortion as well as correlated, non-Gaussian variations in the sharpness parameter."," The observation of 2006-12-31, however, shows significantly larger levels of 2-bit distortion as well as correlated, non-Gaussian variations in the sharpness parameter." +" Furthermore, the 2-bit distortion has a high degree of correlation with the sharpness levels."," Furthermore, the 2-bit distortion has a high degree of correlation with the sharpness levels." +" The correlation coefficient of the two time series is —0.73, suggesting that the profile distortion is related to the digitisation."," The correlation coefficient of the two time series is $-0.73$, suggesting that the profile distortion is related to the digitisation." +" To illustrate the effect these digitisation-induced shape changes may have on TOA precision, we provide the oroa plot for the data analysed in Fig. 7.."," To illustrate the effect these digitisation-induced shape changes may have on TOA precision, we provide the ${\rm S/N}-\sigma_{\rm +TOA}$ plot for the data analysed in Fig. \ref{snrsigmas}." + Clearly the 2005- data behave as expected: they follow the theoretical inverse relationship and worsen slightly for S/N»1000., Clearly the 2005-09-07 data behave as expected: they follow the theoretical inverse relationship and worsen slightly for $>1000$. +" This worsening is caused by noise in the template profile, which was constructed from the 2005-07-24 dataset."," This worsening is caused by noise in the template profile, which was constructed from the 2005-07-24 dataset." +" To demonstrate this, we created the S/N--oroa curve for simulated data, based on a (simulated) template profile with a S/N identical to that of the 2005-07-24 standard profile."," To demonstrate this, we created the ${\rm S/N}-\sigma_{\rm TOA}$ curve for simulated data, based on a (simulated) template profile with a S/N identical to that of the 2005-07-24 standard profile." + This simulated result is shown as the dotted line in Fig., This simulated result is shown as the dotted line in Fig. + 7 and follows the 2005-09-07 curve well., \ref{snrsigmas} and follows the 2005-09-07 curve well. +" Ideally, therefore, a noise-free analytic template profile would be used (asin ?),, but the small-scale features present in the profile of PSR J0437—4715 require advanced modelling that goes beyond the scope of this paper."," Ideally, therefore, a noise-free analytic template profile would be used \citep[as in][]{kxc+99}, but the small-scale features present in the profile of PSR $-$ 4715 require advanced modelling that goes beyond the scope of this paper." + This may also explain the flattening of the oroa-S/N curve in ?.., This may also explain the flattening of the $\sigma_{\rm TOA}$ -S/N curve in \cite{vbb+10}. + The S/N—oroa curve for the 2006-12-31 data displays much larger deviations: for equal S/N its TOA uncertainty (oroa) is several factors higher than for the 2005-09-07 data and limits the calculated precision to the ~50 nns level.," The ${\rm S/N}-\sigma_{\rm TOA}$ curve for the 2006-12-31 data displays much larger deviations: for equal S/N its TOA uncertainty $\sigma_{\rm TOA}$ ) is several factors higher than for the 2005-09-07 data and limits the calculated precision to the $\sim +50$ ns level." +" The other datasets in our investigation (2005-07- 2007-05-06 and 2008-02-24) also yield well-behaved S/N-oroa curves like that of 2005-09-07, which shows that the majority of our data is not affected by this digitisation artefact."," The other datasets in our investigation (2005-07-24, 2007-05-06 and 2008-02-24) also yield well-behaved $-\sigma_{\rm TOA}$ curves like that of 2005-09-07, which shows that the majority of our data is not affected by this digitisation artefact." +" It must be noted that the only objective statistic that we found to clearly identify the 2006-12-31 data as corrupted, was the 2-bit distortion statistic defined by Eq. (8))"," It must be noted that the only objective statistic that we found to clearly identify the 2006-12-31 data as corrupted, was the 2-bit distortion statistic defined by Eq. \ref{eq:2bitStat}) )" + and that this corruption cannot be corrected post-, and that this corruption cannot be corrected post-detection. + This demonstrates the need to investigate the digitisation distortion in any 2-bit pulsar timing data and to exclude any distorted data from future pulsar timing, This demonstrates the need to investigate the digitisation distortion in any 2-bit pulsar timing data and to exclude any distorted data from future pulsar timing +in low mass halos as compared to bright galaxies in massive halos.,in low mass halos as compared to bright galaxies in massive halos. +" We also find that the satellite fraction or average number of satellite galaxies appears to slowly increase over the redshift interval [0.5,1.0], but a stronger increase by a factor of ~3 over z=[0.1,0.5] is seen."," We also find that the satellite fraction or average number of satellite galaxies appears to slowly increase over the redshift interval [0.5,1.0], but a stronger increase by a factor of $\sim$ 3 over z=[0.1,0.5] is seen." + This can be understood in terms of the dynamical friction that subhalos hosting satellite galaxies encounter within their host halos., This can be understood in terms of the dynamical friction that subhalos hosting satellite galaxies encounter within their host halos. + The efficiency of dynamical friction depends on the relative subhalo to halo mass., The efficiency of dynamical friction depends on the relative subhalo to halo mass. +" Subhalos experience more efficient dynamical friction in low mass halos, which can be thought of as progenitor halos at high redshift."," Subhalos experience more efficient dynamical friction in low mass halos, which can be thought of as progenitor halos at high redshift." + The subhalos are continuously subjected to tidal stripping and gravitational heating within the dense environments and get eroded if not completely., The subhalos are continuously subjected to tidal stripping and gravitational heating within the dense environments and get eroded if not completely. + As time evolves the halo accretes mass and undergoes mergers with other halos., As time evolves the halo accretes mass and undergoes mergers with other halos. +" The subhalos that form as remnants of halo mergers are now more likely to remain intact within the higher mass halo, in turn leading to a larger number of satellite galaxies in present-day halos."," The subhalos that form as remnants of halo mergers are now more likely to remain intact within the higher mass halo, in turn leading to a larger number of satellite galaxies in present-day halos." + A comparison with the SDSS results shows a few interesting features., A comparison with the SDSS results shows a few interesting features. +" The value for Mmin, which is the mass of a halo hosting at least one central galaxy on average, in 40% of the luminosity threshold VVDS samples is similar to values for local SDSS galaxies."," The value for $M_{min}$, which is the mass of a halo hosting at least one central galaxy on average, in $40 \%$ of the luminosity threshold VVDS samples is similar to values for local SDSS galaxies." +" Whereas, M; is generally higher for VVDS galaxies as compared to what is seen locally."," Whereas, $M_1$ is generally higher for VVDS galaxies as compared to what is seen locally." + The ratio of Mi/Mmin is found to be considerably higher (almost a factor of 2) in the VVDS as compared to the SDSS results., The ratio of $M_1/M_{min}$ is found to be considerably higher (almost a factor of 2) in the VVDS as compared to the SDSS results. +" This shows that in order to begin hosting satellite galaxies, halos at high redshift need to accrete a larger amount of mass than is seen locally."," This shows that in order to begin hosting satellite galaxies, halos at high redshift need to accrete a larger amount of mass than is seen locally." + Hence one would observe roughly twice as many local satellite galaxies than high redshift ones within the same evolved halo mass., Hence one would observe roughly twice as many local satellite galaxies than high redshift ones within the same evolved halo mass. + This is another line of evidence in favor of the lower observed satellite fraction at high redshift and high local satellite, This is another line of evidence in favor of the lower observed satellite fraction at high redshift and high local satellite +where aEpκnj is the degenerate clectrou pressure.,where $P_{id}^{(e)} \propto n_e E_F \propto n_e^\gamma$ is the degenerate electron pressure. + Ta analogy with the thermal correction to the electric field. the correction to the electric field duc to Coulomb plivsics scales as nj;EcoErp. where Ec is the Coulomb cuerey of the ious.," In analogy with the thermal correction to the electric field, the correction to the electric field due to Coulomb physics scales as $n_i +E_{\rm C}/n_e E_F$ , where $E_{\rm C}$ is the Coulomb energy of the ions." + Equation (324) is the ceutral result of this section and we now bricfiy discuss its essential plovsics., Equation \ref{eq:full E-field}) ) is the central result of this section and we now briefly discuss its essential physics. +" Whenu Ay/Z,xAe/Zo. ic. dissimilar jns the don scale height is determined by &pT/m,9 which is much simaller than he clectron (pressure) scale height !.—Er/im,g in he stronely degenerate part of the atinosphere."," When $A_1/Z_1 \ne +A_2/Z_2$, i.e., dissimilar $\mu_e$, the ion scale height is determined by $k_BT/m_p g$ which is much smaller than the electron (pressure) scale height $l_e = E_F/m_p g$ in the strongly degenerate part of the atmosphere." +" When AyfZ,cxodo/Zo. he. similar ο. then the zeroth order field produces no differentiating force (uodulo hermal/mass defect corrections)."," When $A_1/Z_1 \approx A_2/Z_2$, i.e., similar $\mu_e$, then the zeroth order field produces no differentiating force (modulo thermal/mass defect corrections)." + Moreover. the thermal correction to the electric feld produces au ion scale weight zz7. as shown earlier.," Moreover, the thermal correction to the electric field produces an ion scale height $\approx l_e$ as shown earlier." + Mass defections corrections xoduce jon scale heights that are similarly large., Mass defections corrections produce ion scale heights that are similarly large. + While lis results iu a decreasing fraction for the lighter ion eoiung deeper into the envelope. the cola of this lighter lon Increases as discussed earlier (aud increase really fast if we include mass defect corrections).," While this results in a decreasing fraction for the lighter ion going deeper into the envelope, the column of this lighter ion increases as discussed earlier (and increase really fast if we include mass defect corrections)." + Inchiding Coulom physics causes the ion scale height to become /./T;. mmcLT sanaller than ἐς for lavee DP. but is still lareer than the jon scale height for dissimilar A/Z bv Leaf.," Including Coulomb physics causes the ion scale height to become $l_e/\Gamma_i$, much smaller than $l_e$ for large $\Gamma$, but is still larger than the ion scale height for dissimilar $A/Z$ by $E_{\rm C}/E_F$." + Dot[um concentration and umuber density for the lighter io- decrease withincreasing depth., Both concentration and number density for the lighter ion decrease with increasing depth. + We now utilize the discussion above to estimate Jeu.," We now utilize the discussion above to estimate $y_{\rm + cut}$." +" Plugeine equation (33)) into livdrostatie balance (13) for a trace. 2. and a backeround. 1. we fud for relativistic degenerate electrous (5= 1/3) that ≋↿∏⋝⊓⋅⋜↧↸⊳⊓∐∶↴⋁⋖∶≩⊔⋝↕⋟↥⋅∪⋯≺∶≩⋅↱⊐⊔⋜⋯≼↧∐∪↑↕∐∶↴⋁↑∐⋜↧↑ fiud | Plugeing in values for a He/C envelope appropriate for Figure b withbase temperature Tj=1«105 K (sec rofsecilleDNB for a discussion of the base temperature). we find that dlu(po/nj)/dlug= Lat p—pags35105ecm? for relativistic degenerate electrons. which GIVES Yourστὸν10?ecu3,"," Plugging equation \ref{eq:simple E-field}) ) into hydrostatic balance \ref{eq:hb ions}) ) for a trace, 2, and a background, 1, we find for relativistic degenerate electrons $\gamma = 4/3$ ) that Subtracting \ref{eq:background}) ) from \ref{eq:trace}) ) and noting that $\partial\ln P/\partial r = \partial\ln y/\partial r = -\rho g/P = - 4Am_pg/ZE_F$ we find Plugging in values for a He/C envelope appropriate for Figure \ref{fig:HeCstructure} with base temperature $T_b = 1\times 10^8$ K (see \\ref{sec:He DNB} for a discussion of the base temperature), we find that ${d\ln (n_2/n_1)}/{d\ln y} = -1$ at $\rho = \rho_{\rm cut} \approx 5 +\times 10^6\,{\rm g\,cm}^{-3}$ for relativistic degenerate electrons, which gives $y_{\rm cut} \approx 2 \times 10^9\,{\rm g\,cm}^{-2}$." + The results of this section show that stratification occurs even for clements with the same yr., The results of this section show that stratification occurs even for elements with the same $\mu_e$. + This has iuportant duplications in high eravity cavirouuents like white cavarfs aud NSs bevoud the problem of Te DNB., This has important implications in high gravity environments like white dwarfs and NSs beyond the problem of He DNB. + Combining the results of 877.. the thermal profile of the envelope. rates of Πο burning. aud rates of diffusion. we now calculate the rate of nuclear burning of Ile in NS envelopes.," Combining the results of \ref{sec:efield}, the thermal profile of the envelope, rates of He burning, and rates of diffusion, we now calculate the rate of nuclear burning of He in NS envelopes." + For the thermal profile. we solve the heat diffusion equation for a constant flux envelope in radiative equilibrium: where & is the opacity.," For the thermal profile, we solve the heat diffusion equation for a constant flux envelope in radiative equilibrium: where $\kappa$ is the opacity." + Starting from the photosphere (with optical depth. 7=2/3). we inteerate the plane-parallel envelope iuward assmuius constant flux to a depth of y=ym—l0theeum7. which we call the base of the euvelope.," Starting from the photosphere (with optical depth, $\tau = 2/3$ ), we integrate the plane-parallel envelope inward assuming constant flux to a depth of $y=y_b \equiv 10^{14}\,{\rm g\,cm}^{-2}$, which we call the base of the envelope." + As in paper IL we use the tabulated couductivities of Potekhiu et al. (," As in paper II, we use the tabulated conductivities of Potekhin et al. (" +1999) and the radiative opacitics and the equation of state of Poteklin Yakovlev (2001). which is applicable to all maeuetic field streneths (see paper II for more details).,"1999) and the radiative opacities and the equation of state of Potekhin Yakovlev (2001), which is applicable to all magnetic field strengths (see paper II for more details)." + Potekhin ct al. (, Potekhin et al. ( +"1997) performed a similar calculation down to a deusity of p=p,10eon7. which they referred to as the base of the envelope.","1997) performed a similar calculation down to a density of $\rho=\rho_b\equiv 10^{10}\,{\rm g\,cm}^{-3}$, which they referred to as the base of the envelope." + These two definitions are roughly equivalent to cach other. namely that ply)510Meen72 ," These two definitions are roughly equivalent to each other, namely that $\rho(y_b) \approx 10^{10}\,{\rm g\,cm}^{-3}$." +We define the temperature af gy as the base teniperature. Z5.," We define the temperature at $y_b$ as the base temperature, $T_b$." + For a NS in thermal equilibrium. the base temperature and the core temperature. Z5 are equal to cach other as the temperature profile is nearly isothermal due to the larec conductivities.," For a NS in thermal equilibrium, the base temperature and the core temperature, $T_c$ are equal to each other as the temperature profile is nearly isothermal due to the large conductivities." + For the most part. Z5 aud T; cuni be use iuterchaugable. except for the very early cooling history of the NS (age =100 yis). when the NS is not in thermal equilibrimu and Z54T...," For the most part, $T_b$ and $T_c$ can be use interchangable, except for the very early cooling history of the NS (age $\lesssim 100$ yrs), when the NS is not in thermal equilibrium and $T_b\neq T_c$." + This poiut will be iuportaut in our discussion of Fieure 5.., This point will be important in our discussion of Figure \ref{fig:He burning lifetime}. . + For the diffusion coefficient of the trace He. we use the results of paper II (also see Brown. Bildsten Chane 2002). where we fouud: where TyT/10K aud p;=p/lQean?.," For the diffusion coefficient of the trace He, we use the results of paper II (also see Brown, Bildsten Chang 2002), where we found: where $T_6 = T/10^6\,{\rm K}$ and $\rho_5 = \rho/10^5 \,{\rm + g\,cm}^{-3}$." + As discussed i paper Ἡ. equation (38)) 19 reasonably accurate in the liquid regine of the background C. 1:Ta;. the material is a crystalline anc we assmue that there is no diffusion. though we never reach this poiut in our parameter reeime.," For $\Gamma > \Gamma_M$, the material is a crystalline and we assume that there is no diffusion, though we never reach this point in our parameter regime." + We now discuss the nuclear processes that coustune Io., We now discuss the nuclear processes that consume He. + For our unclear reaction rates. we have utilized both the NACRE?((Aneulo et al.," For our nuclear reaction rates, we have utilized both the (Angulo et al." + 1999) and compilation of unclear reaction rates aud experimental values (see nucastro.org)., 1999) and compilation of nuclear reaction rates and experimental values (see nucastro.org). + We have not included electron screening in our calculations. though the effect of serecning would be to increase the rate of burning.," We have not included electron screening in our calculations, though the effect of screening would be to increase the rate of burning." + For tiiple-a we use the fit in Nomoto. Thiclemann. Mivaji ull(1985). INQUEbut have found this rate to be typically vorv for the parameters of interest because of the reduced τήν density of He iu the burning region (note the reduced umuuber fraction of Te in FigureE 1)).," For $\alpha$ reactions, we use the fit in Nomoto, Thielemann, Miyaji (1985), but have found this rate to be typically verysmall for the parameters of interest because of the reduced number density of He in the burning region (note the reduced number fraction of He in Figure \ref{fig:HeCstructure}) )." + Hence. we no longer discusstriple-o reactious.," Hence, we no longer discuss$\alpha$ reactions." +" The local rate of We πας is where iod the depth aud i,exp is the deusity of a Ie-captunrnug substrate.", The local rate of He burning is where $z$ is the depth and $n_{\rm \alpha-cap}$ is the density of a He-capturing substrate. +The most elaborated models to calculate the shear viscosity have been considered by Goldreich Tremaine (1978) aud Stewart Ἱναπία (1980). hereinafter referred to as GT and Sly. correspoudinely.,"The most elaborated models to calculate the shear viscosity have been considered by Goldreich Tremaine (1978) and Stewart Kaula (1980), hereinafter referred to as GT and SK, correspondingly." + GT considered inelastic collixious of spherical particles obeving an anisotropic distribution fiction. whereas SK considered (clastic) encounters of particles oheving a Maxwellian distribution.," GT considered inelastic collisions of spherical particles obeying an anisotropic distribution function, whereas SK considered (elastic) encounters of particles obeying a Maxwellian distribution." +" In the both cases. as shown in Appendix A. the viscosity coefficient. can be represcuted iu the form. Tere σι is the ouc-dimensional velocity dispersion. © is the orbital angular velocity in the disk. 7=Of; is the ""optical depth to cloud-cloud interactions (see below). f; is the free path time (iudex /=ο, Gs e stands for collisional. or contact. interactions. G stands for gravitational ones). aud d;D; are the coustaut cocfficieuts defined below."," In the both cases, as shown in Appendix A, the viscosity coefficient can be represented in the form Here $\sigma _v$ is the one-dimensional velocity dispersion, $\Omega$ is the orbital angular velocity in the disk, $\tau = \Omega t_i$ is the `optical depth' to cloud-cloud interactions (see below), $t_i$ is the free path time (index $i=c,~ G$ ; $c$ stands for $c$ ollisional, or $c$ ontact, interactions, $G$ stands for $g$ ravitational ones), and $A_i,~B_i$ are the constant coefficients defined below." + Collisions between the clouds result iu dimiuisliug 7. whereas eravitational eucounters tend to merease it.," Collisions between the clouds result in diminishing $\sigma _v$ , whereas gravitational encounters tend to increase it." + For clouc-cloud collisions. where 6 and s are the typical size of a cloud aud the spatial umber deusitv of the clouds. respectively.," For cloud-cloud collisions, where $a$ and $n$ are the typical size of a cloud and the spatial number density of the clouds, respectively." + For eravitational cucounters between the clouds (Braginskii 1965). where a ids the typical mass of. a cloud.," For gravitational encounters between the clouds (Braginskii 1965), where $m$ is the typical mass of a cloud." + Evideuth.. ας=og.2(344)—162Ginpyfon> calbe considered as an effective size of the domain for eravitational influence of the cloud.," Evidently, $a_G= +2\left(3\sqrt\pi\right)^{-1/2}Gm/\sigma_v^2$ canbe considered as an effective size of the domain for gravitational influence of the cloud." + Coefficients A; aud B; in Eq. (, Coefficients $A_i$ and $B_i$ in Eq. ( +2.1) take the following values: The optical depth r of the disk is a convenieut paraueter describing how effective are the interactions between the clouds.,2.1) take the following values: The optical depth $\tau$ of the disk is a convenient parameter describing how effective are the interactions between the clouds. + By order of mmaguitude. it is nothing but the mean ΓΕΕς of iuteractious suffered by a cloud in passing through the disk.," By order of magnitude, it is nothing but the mean number of interactions suffered by a cloud in passing through the disk." + More accurately. assundue e to be the largest of seoimoetrical and eravitational iuflueuce sizes.," More accurately, assuming $a$ to be the largest of geometrical and gravitational influence sizes." + Hore fis the thickness of the disk given by Since i2ΤΗ. where X is the surface deusitv of the disk. Eq. (," Here $h$ is the thickness of the disk given by Since $h\simeq\Sigma/mn$, where $\Sigma$ is the surface density of the disk, Eq. (" +2.2) can be rewritten as which muplies one more interpretation for 7: it is the covering factor. C. or the fraction of disk area covered by clouds when they are placed as a monolaver.,"2.2) can be rewritten as which implies one more interpretation for $\tau$: it is the covering factor, $C$, or the fraction of disk area covered by clouds when they are placed as a monolayer." + The fillme factor of the system of clouds. the fractional volue filled bv the clouds is Eqs. (," The filling factor of the system of clouds, the fractional volume filled by the clouds is Eqs. (" +2.5). (2.6). aud (2.8) vield oue more expression for 7 coutainius £F: LEvideutlv. Fl for anv cloudy disk with e5% Eddington with peaks exceeding37%,, it is not unreasonable to assume that radiation pressure plays a role in determining the inner disk structure."," Since is accreting at least at $\dot{M}>5\%$ Eddington with peaks exceeding, it is not unreasonable to assume that radiation pressure plays a role in determining the inner disk structure." +" The disk-magnetosphere interaction region is also more complex than usually assumed (see e.g., Rappaportetal.2004,, D’Angelo&Spruit 2010,, Kajavaetal. 2011,, Patrunoetal. 2012)), and v might have a weaker dependence on the bolometric flux than usually assumed."," The disk-magnetosphere interaction region is also more complex than usually assumed (see e.g., \citealt{rap04}, \citealt{dan10}, \citealt{kaj11}, \citealt{pat12}) ), and $\dot{\nu}$ might have a weaker dependence on the bolometric flux than usually assumed." +" We conclude therefore that the interpretation of the long term P as being the spin frequency derivative of is supported by the observations, with the outlier most likely explained by unmodeled timing noise and the lack of correlation between the short term v and fx, which is not surprising, since the expectation of such correlations is based on assumptionsabout the accretion process which may not be valid."," We conclude therefore that the interpretation of the long term $\dot{\nu}$ as being the spin frequency derivative of is supported by the observations, with the outlier most likely explained by unmodeled timing noise and the lack of correlation between the short term $\dot{\nu}$ and $f_{X}$ , which is not surprising, since the expectation of such correlations is based on assumptionsabout the accretion process which may not be valid." +also given in Table 7..,also given in Table \ref{observing_map}. + Note that © represents a typical formal error in any given pixel. whereas the rms. which is lower. is measured directly from the image and represents pixel-to-pixel variations in noise across the map.," Note that $\overline\sigma$ represents a typical formal error in any given pixel, whereas the rms, which is lower, is measured directly from the image and represents pixel-to-pixel variations in noise across the map." + The latter value has beer significantly reduced by combining the three data sets into one., The latter value has been significantly reduced by combining the three data sets into one. + The averaged map and its error map were then interpolatec onto a 1 square pixel grid and rotated to the correct orientation on the sky., The averaged map and its error map were then interpolated onto a $^{\prime\prime}$ square pixel grid and rotated to the correct orientation on the sky. + The resulting ISO and error maps are shown t Fig. 2.., The resulting ISO and error maps are shown in Fig. \ref{iso_map}. + A final positional shift of less than a pixel of the original data (3.47 in RA and 5.1” in DEC) was then applied to these maps to align the ISO map with the SDSS r-banc 1mage., A final positional shift of less than a pixel of the original data $^{\prime\prime}$ in RA and $^{\prime\prime}$ in DEC) was then applied to these maps to align the ISO map with the SDSS r-band image. + The fine adjustment in astrometry was possible because of two sources. shown with crosses in the overlay of Fig. 6..," The fine adjustment in astrometry was possible because of two sources, shown with crosses in the overlay of Fig. \ref{iso_optical}," + that are visible in both the ISO and optical images., that are visible in both the ISO and optical images. + Characteristic map errors are also listed in Table 7.., Characteristic map errors are also listed in Table \ref{observing_map}. + In addition. there is an absolute calibration error of order. +15—20% (e.g. Cola et al.," In addition, there is an absolute calibration error of order, $\pm\,15\,-\,20$ (e.g. Coia et al." + 2005. Pagani et al.," 2005, Pagani et al." + 2003). that will affect comparisons with images at other wavelengths. but shouldnot affect point comparisons on the ISO map itself.," 2003), that will affect comparisons with images at other wavelengths, but shouldnot affect point-to-point comparisons on the ISO map itself." + Fig., Fig. + 2. shows the final ISO 26.75 pm emission along with its error map. and an overlay of the emission on the SDSS image is shown in Fig. 6..," \ref{iso_map} shows the final ISO $\lambda\,6.75$ $\mu$ m emission along with its error map, and an overlay of the emission on the SDSS r-band image is shown in Fig. \ref{iso_optical}." + Before studying these data in detail. however. it is important to establish whether there might be other significant contributors to the 160.75 jm emission. besides PAHs.," Before studying these data in detail, however, it is important to establish whether there might be other significant contributors to the $\lambda\,6.75$ $\mu$ m emission, besides PAHs." + These might include an underlying dusttinuuny.. and a stellar continuum from cool stars.," These might include an underlying dust, and a stellar continuum from cool stars." + Previous observations and spectral modeling indicate that the MIR spectrum of spiral galaxies is overwhelmingly dominated by PAH emission (e.g. Smith et al., Previous observations and spectral modeling indicate that the MIR spectrum of spiral galaxies is overwhelmingly dominated by PAH emission (e.g. Smith et al. + 2007. Draine Li 2007. Vogler et al.," 2007, Draine Li 2007, Vogler et al." + 2005. Lu et al.," 2005, Lu et al." + 2003. Genzel Cesarksky 2000 and references therein) and. as indicated in Sect. 1..," 2003, Genzel Cesarksky 2000 and references therein) and, as indicated in Sect. \ref{introduction}," + the 26.75 jm ISO band is no exception.," the $\lambda\,6.75$ $\mu$ m ISO band is no exception." + Within this band fall the 16.2 pm. 27.7 um. and the short wavelength wing of the 28.6 jm PAH emission features.," Within this band fall the $\lambda\,6.2$ $\mu$ m, $\lambda\,7.7$ $\mu$ m, and the short wavelength wing of the $\lambda\,8.6$ $\mu$ m PAH emission features." + Of these. the 07.7 jim feature is the strongest (see Fig.," Of these, the $\lambda\,7.7$ $\mu$ m feature is the strongest (see Fig." + 7 of Irwin Madden 2006) and can be modeled as a blend of three spectral features at 07.42 jum. 27.60 µπι. and 27.85 jim (Smith et al.," 7 of Irwin Madden 2006) and can be modeled as a blend of three spectral features at $\lambda\,7.42$ $\mu$ m, $\lambda\,7.60$ $\mu$ m, and $\lambda\,7.85$$\mu$ m (Smith et al." + 2007)., 2007). + The 27.7 um PAH complex. alone. can contribute nearly one-half of the total PAH luminosity and up to of the total infrared luminosity (Smith et al.," The $\lambda\,7.7~\mu$ m PAH complex, alone, can contribute nearly one-half of the total PAH luminosity and up to of the total infrared luminosity (Smith et al." + 2007)., 2007). +" Indeed. photometry of the 16.75 jm ISO band is normally taken as a direct proxy for the presence of PAH emission,"," Indeed, photometry of the $\lambda\,6.75~\mu$ m ISO band is normally taken as a direct proxy for the presence of PAH emission." + It has also become clear that galaxies show qualitatively little difference in their MIR spectra and that spectral shape is largely independent of star formation rate (Vogler et al., It has also become clear that galaxies show qualitatively little difference in their MIR spectra and that spectral shape is largely independent of star formation rate (Vogler et al. + 2005. Lu et al.," 2005, Lu et al." + 2003. Genzel Cesarsky 2000 and references therein).," 2003, Genzel Cesarsky 2000 and references therein)." + Lu et al. (, Lu et al. ( +2003). for example. found band-to-band variations of. at most. in the mid-IR spectrum out to ALLym. It is now apparent. however. that some variations in PAH line ratios can exist. depending on their environment.,"2003), for example, found band-to-band variations of, at most, in the mid-IR spectrum out to $\lambda\,11~\mu$ m. It is now apparent, however, that some variations in PAH line ratios can exist, depending on their environment." +" The ratios between the ,16.2. 17.7. and οἱδ.6μπι PAHs do not seem to show much variation within galaxies and between galaxies (Galliano et al."," The ratios between the $\lambda\,6.2$, $\lambda\,7.7$, and $\lambda\,8.6~\mu$ m PAHs do not seem to show much variation within galaxies and between galaxies (Galliano et al." + 2007). but the 26.2/.011.3 and 27.7/.011.3 ratios can. vary by up to an order of magnitude (Lu et al.," 2007), but the $\lambda\,6.2/\lambda\,11.3$ and $\lambda\,7.7/\lambda\,11.3$ ratios can vary by up to an order of magnitude (Lu et al." + 2003: Vogler et al., 2003; Vogler et al. + 2005; Draine Li 2007; Smith et al., 2005; Draine Li 2007; Smith et al. + 2007: Galliano et al., 2007; Galliano et al. + 2007)., 2007). +" This variation can be controlled by the fraction of ionized PAHs. which has been demonstrated to be linked to Go/5, (the ratio of the intensity of the UV radiation field to the electron density. Galliano et al."," This variation can be controlled by the fraction of ionized PAHs, which has been demonstrated to be linked to $G_0/n_e$ (the ratio of the intensity of the UV radiation field to the electron density, Galliano et al." + 2007) or to the modification of the grain size distribution (Smith et al., 2007) or to the modification of the grain size distribution (Smith et al. + 2007)., 2007). +" For this study. since we are dealing only with the 06.75jum ISOCAM band. we can assume constant band ratios between the 06.2. 417.7 and 448.6 uim PAH features. although some variation will not affect our conclusions,"," For this study, since we are dealing only with the $\lambda\,6.75~\mu$ m ISOCAM band, we can assume constant band ratios between the $\lambda\,6.2$ , $\lambda\,7.7$ and $\lambda\,8.6$ $\mu$ m PAH features, although some variation will not affect our conclusions." + As for an underlying hot dust continuum. such a contribution has been shown to be negligible in normal star forming galaxies (e.g. Galliano et al.," As for an underlying hot dust continuum, such a contribution has been shown to be negligible in normal star forming galaxies (e.g. Galliano et al." + 2007)., 2007). + For example. the three PAH features at .06.2..07.7. and 08.6 jm in M 82 can be fit without any significant underlying continuum at all (Laurent et al.," For example, the three PAH features at $\lambda\,6.2$, $\lambda\,7.7$, and $\lambda\,8.6$ $\mu$ m in M 82 can be fit without any significant underlying continuum at all (Laurent et al." + 2000)., 2000). + Vogler et al. (, Vogler et al. ( +2005) also find that a continuum contributes only ~ for M 83 in the ISO bands that trace PAH emission.,2005) also find that a continuum contributes only $\sim$ for M 83 in the ISO bands that trace PAH emission. + Depending on the assumption of PAH line profile. recent models of MIR spectral energy distributions (SEDs. e.g. Draine Li 2007. Galliano et al.," Depending on the assumption of PAH line profile, recent models of MIR spectral energy distributions (SEDs, e.g. Draine Li 2007, Galliano et al." + 2007) typically show an underlying continuum that is at least an order of magnitude lower than the PAH spectral features., 2007) typically show an underlying continuum that is at least an order of magnitude lower than the PAH spectral features. + A stellar component. on the other hand. may be a somewhat larger contributor to the observed emission.," A stellar component, on the other hand, may be a somewhat larger contributor to the observed emission." + Spitzer Space Telescope observations. for example. are typically corrected for a stellar component based on the 13.6 gam image which is assumed to contain only stellar emission.," Spitzer Space Telescope observations, for example, are typically corrected for a stellar component based on the $\lambda\,3.6~\mu$ m image which is assumed to contain only stellar emission." + The correction is based on an extrapolation of the stellar flux to the relevant wavebands according to the prescription of Helou et al. (, The correction is based on an extrapolation of the stellar flux to the relevant wavebands according to the prescription of Helou et al. ( +2004) who have used stellar population models and model photospheric SEDs derived from Starburst99 (Leitherer et al.,2004) who have used stellar population models and model photospheric SEDs derived from Starburst99 (Leitherer et al. + 1999)., 1999). + For NGC 5529. the 2MASS Ks band (2.16 μπι) image is available and we can also assume that this band contains only stellar emission.," For NGC 5529, the 2MASS Ks band $\lambda\,2.16~\mu$ m) image is available and we can also assume that this band contains only stellar emission." + Using the same relation of Helou et al..," Using the same relation of Helou et al.," + we estimate that the global flux of NGC 5529 in the 16.75 um band contains a contribution of stellar flux that amounts to of the 2MASS 2.16 jm fluxt.," we estimate that the global flux of NGC 5529 in the $\lambda \,6.75~\mu$ m band contains a contribution of stellar flux that amounts to of the 2MASS $\lambda\,2.16~\mu$ m ." +. The 2MASS Ks band image. smoothed to the resolution of the ISO 26.75 ummband and multiplied by 1s shown in the Inset to Fig. 6..," The 2MASS Ks band image, smoothed to the resolution of the ISO $\lambda \,6.75~\mu$ mband and multiplied by is shown in the Inset to Fig. \ref{iso_optical}. ." + An integration of this map over the, An integration of this map over the +When the equatious (1.2.7-10) are compared with (11-17). their correlation coefficients and riis show that the accuracy of deteruination of metallicity aud color excesses through ον R) diagrams is not worse than through Wes.WW) diagrams.,"When the equations (1,2,7-10) are compared with (11-17), their correlation coefficients and rms show that the accuracy of determination of metallicity and color excesses through $V vs. +(B-R)$ diagrams is not worse than through $V vs.(B-V)$ diagrams." + Below. we cousider the application of the equations (11-17) to siuultaueous determination for the metallicity [Fe/TI| aud color excesses Epyy for the globular chister 77006.," Below, we consider the application of the equations (11-17) to simultaneous determination for the metallicity [Fe/H] and color excesses $E_{B-R}$ for the globular cluster 7006." + This approximation is good enough for our purposes. since the widths of 9.7 jjm and 15 jm silicate absorption features each cover a relatively small wavelength range (~4 and ~13 pm. respectively).," This approximation is good enough for our purposes, since the widths of 9.7 $\mu$ m and 18 $\mu$ m silicate absorption features each cover a relatively small wavelength range $\sim$ 4 and $\sim$ 13 $\mu$ m, respectively)." + The 9.7 jm silicate feature is 7.5 12.3 jm. where the first continuum point (at 7.5 jim) is chosen because photospheric gas phase SiO bands that might be present in the spectra.," The 9.7 $\mu$ m silicate feature is 7.5 12.3 $\mu$ m, where the first continuum point (at 7.5 $\mu$ m) is chosen because photospheric gas phase SiO bands that might be present in the spectra." + The 18 jm silicate feature 14.2 and 27.0 um. the long wavelength module of Spitzer.," The 18 $\mu$ m silicate feature 14.2 and 27.0 $\mu$ m, the long wavelength module of Spitzer." +" Subsequently. the optical depth profiles are calculated using: where Fy.op, is the observed flux and F,4 1s the flux of the continuum."," Subsequently, the optical depth profiles are calculated using: where $F_{\nu,\mathrm{obs}}$ is the observed flux and $F_{\nu,\mathrm{cont}}$ is the flux of the continuum." + The resulting optical depth profiles are shown in Figs., The resulting optical depth profiles are shown in Figs. + + and 5.. Chiaretal.(2007) investigated the relationshipbetween the strength. of the 9.7 jm silicate feature. το. and the colour excess. E(J-K).," \ref{fig:10feats2} and \ref{fig:18feats2}, \citet{Chiar07} investigated the relationshipbetween the strength of the 9.7 $\mu$ m silicate feature, $\tau_{9.7}$, and the colour excess, $E$ $-$ K)." + For diffuse sightlines there is a tight linear correlation between these two parameters with To 7/E(J-K)=0.34 (Roche&Aitken.1984;Whittet.2003).. but for the molecular sightlines this correlation fails," For diffuse sightlines there is a tight linear correlation between these two parameters with $\tau_{9.7}$ $E$ $-$ K)=0.34 \citep{Roche84,Whittet03},, but for the molecular sightlines this correlation fails" +the auenlar distribution of all the IIDF objects. most of which are ~071.,"the angular distribution of all the HDF objects, most of which are $\sim +0\farcs 1$." + As the left panel of the figure shows. this correspouds to a size <1kpc. aud au Inspection of the TIDF images shows that most of them are blue.," As the left panel of the figure shows, this corresponds to a size $\la 1 \kpc$, and an inspection of the HDF images shows that most of them are blue." + Tence. the excess fait blue ealaxies are dwarfs. not large. high-redshift. elliptical galaxies.," Hence, the excess faint blue galaxies are dwarfs, not large, high-redshift, elliptical galaxies." +" Adone the TDF galaxies are a handful of galaxies at photometric redshitts snl the xiehtest of which are not much fainter than those observed spectroscopically,."," Among the HDF galaxies are a handful of galaxies at photometric redshifts $z +\ga 5$ \cite{lanzetta96,lanzetta98b} the brightest of which are not much fainter than those observed spectroscopically." + shows an example of the spectral energy distribution of such a galaxy wili no detection shortward of the PalWW baud. clear detection in the FstiW and I& bands aud a probable one iu the IE baud.," shows an example of the spectral energy distribution of such a galaxy with no detection shortward of the F814W band, clear detection in the F814W and K bands and a probable one in the H band." + Notice the small sizes of the error bars of the TST observations. which are alinost imperceptible ou the scale ploted.," Notice the small sizes of the error bars of the HST observations, which are almost imperceptible on the scale plotted." + They severely constrain the spectral energy distributions that can be fitted to the data., They severely constrain the spectral energy distributions that can be fitted to the data. + The lower Tit on the EFSL1N/F606W flux ratio can also not be due to dust (in extraordinarily large amounts) because the, The lower limit on the F814W/F606W flux ratio can also not be due to dust (in extraordinarily large amounts) because the +of which is a result of the necessary assuniptious.,of which is a result of the necessary assumptions. + There is one significant improvement that cau be made aud that is the direct observation of the stellar velocity dispersion in these cisks., There is one significant improvement that can be made and that is the direct observation of the stellar velocity dispersion in these disks. + That this is fcsible in practice for edge-on systems las 3001) SLOW] DV Bottema ct al. (, That this is feasible in practice for edge-on systems has been shown by Bottema et al. ( +1987. 1991).,"1987, 1991)." + The observed velocity profiles can be corrected for the line-of-sight effects. giving the anecutial velocity dispersion. which through the observed shape of the rotation curve can be turuec iuto the radial velocity dispersion.," The observed velocity profiles can be corrected for the line-of-sight effects, giving the tangential velocity dispersion, which through the observed shape of the rotation curve can be turned into the radial velocity dispersion." + Although a time cousuniug programiuc. we believe that it is worth doing for two reasous: (1) 1 will sct both versions of the Bottema relation ou a firmer footing. (," Although a time consuming programme, we believe that it is worth doing for two reasons: (1) It will set both versions of the Bottema relation on a firmer footing. (" +2) The uncertainties in the analysis abovecan likely be sieuificantly diuiuished by direct measurement of the radial velocity dispersion rather than having to infer it from the rotation velocity or the disk absolute magnitude.,2) The uncertainties in the analysis above can likely be significantly diminished by direct measurement of the radial velocity dispersion rather than having to infer it from the rotation velocity or the disk absolute magnitude. + PCydly thanks Jerenw Alould for hospitality at the Mount Stromlo and Siding Spring Observatories. where most of this work was done. and Wen Freecniui for discussious. the Space Telescope Scicuce Institute. and Ron Allen for hospitality. when the final version of this paper was prepared. aud the Facultv of. Mathematics and Natural Sciences of the University of Groningen for financial support that mace these visits possible.," PCvdK thanks Jeremy Mould for hospitality at the Mount Stromlo and Siding Spring Observatories, where most of this work was done, and Ken Freeman for discussions, the Space Telescope Science Institute and Ron Allen for hospitality, when the final version of this paper was prepared, and the Faculty of Mathematics and Natural Sciences of the University of Groningen for financial support that made these visits possible." + RdC was supported by NASA erauts NAC 5-3128 and NAC5-6103., RdG was supported by NASA grants NAG 5-3428 and NAG 5-6403. +region al the GC.,region at the GC. +" For (his scenario to account for the observational data. the sterile neutrino resi lass is required to be i,zz16—19 keV (ChanandChu2003)."," For this scenario to account for the observational data, the sterile neutrino rest mass is required to be $m_s \approx 16-19$ keV \citep{Chan}. ." +. Recently. Suzaku X-ray mission has started to observe emission lines above 6 keV near the GC (IxXovamaetal.2007:2010).," Recently, $Suzaku$ X-ray mission has started to observe emission lines above 6 keV near the GC \citep{Koyama,Nobukawa}." +". The observed intensities of the emission lines. including Lya (7.0 keV). Lv? (8.2 keV) andLy5 (8.7 keV). from Fe XXVI are 1.66vx10phem ?s ! "" 5 : ——(uS Ve . 1 ↽⋅ ∃⋃∩⊤⋝⋅⋅∐≀↧↪∖⇁≼↲≺⇂∪∐⊔∐↲⊳∖⊽≼↲↕⋅≼↲⋟∖⊽∏∐⊳∖⇁"," The observed intensities of the emission lines, including $\alpha$ (7.0 keV), $\beta$ (8.2 keV) and$\gamma$ (8.7 keV), from Fe XXVI are $1.66^{+0.09}_{-0.11} \times 10^{-4}$ ph $^{-2}$ $^{-1}$, $2.29^{+1.35}_{-1.31} \times 10^{-5}$ ph $^{-2}$ $^{-1}$ and $1.77^{+0.62}_{-0.56} \times 10^{-5}$ ph $^{-2}$ $^{-1}$ respectively \citep{Koyama}." +⋅↕↴↕⋅∪↳↽∐∪↕⋅∪∖↽≀↧↴∐≼⇂⊳↔⊲↕∐≶⊔∩∐⊔↓∎↓∐≺⇂≀↧↴∐≼↲⇀↸≺∢≼↲⊳∖⇁⊳∖⊽∪↓≯∟∖⇁↶⇩↴↕∐∥↲∐⊳∖⇁∐∡∖↽∪↓⋟ ⊔⋅⊥∶∶∩⋅≺≨⇄⋝⋗⋖⊥∪⊽↴↕↽≻∐≺∢∐↓⇉⊳∖⊽↓⋅∖∖↽∐↕≺∢∐≺∢≀↧↴∐∐∪↥∣↽≻≼↲≼↲⇀↸↕↽≻↥≀↧↴↥∐≼↲≼⇂∣↽≻∡∖⇁↥∪∐↕∠≀↧↴∐∪∐≀↧↴∐≼⇂↕⋅≼↲≺∢∪∐↓∣↽≻↕∐≀↧↴↥↕∪∐," Based on these results, \citet{Prokhorov} find an excess of $\gamma$ intensity of $(1.1 \pm 0.6) \times 10^{-5}$ ph $^{-2}$ $^{-1}$, which cannot be explained by ionization and recombination processes." + ↕↽≻↕⋅∪≺∢≼↲⋟∖⇁⋟∖⇁≼↲⋟∖⊽⋅↥↴↕⋅∪↳↽∐∪↕⋅∪∖↽≀↧↴∐≺⇂⊳↔⊲↕∐↘↽⊔∩∐⊔↕↽≻↕⋅∪↕↽≻∪⊳∖⊽≼↲≼⇂⊔⋯↥≼⇂≼↲≺∢≀↧∶∖⇁↕∐≸≟⊳∖⇁∩↲↕, \citet{Prokhorov} proposed that decaying sterile neutrinos can provide the excess 8.7 keV photons. +⋅∐≼↲∐≼↲∏↥∏∐∪⊳∖⊽≺∢≀↧↴∐↕↽≻↕⋅∪∖↽↕≺⇂≼↲ ≀↧↴∣↽≻∪⋯⊥⊤↳↽≼↲∖⊽⋅∖∖⊽∐↕≺∢∐≀↧∖≺≟↕⋅≼↲≼↲⊳∖⇁∖∖⊽↕⊔↥≼↕⊲∐≀↧↴∐≀↧↴∐≼⇂≼↕⊲∐∏⋅⋟∖⊽↕↽≻↕⋅≼↲≺∐≺∢∐∪∐⊔∩∪⋖⋨⋟⋮⋝⋅ ," As the emitted photon energy $E_s \approx m_s/2$, the required $m_s$ is about 17 keV, which agrees with Chan and Chu's prediction (2008)." +By using the observed excess intensity of 8.7 keV photons and (he Navarro-Frenk-While (NFW) density profile with 21.5 kpe scaled length to model the sterile neutrino halo. which means (hal the sterile neutrinos are the dominant dark matter component. (2010). ealeulated the sterile neutrino decay rate and mixing angle with active neutrinos to be P—(9.0£48)x107 ! and sin?20=(4142.2)x10P respectively.," By using the observed excess intensity of 8.7 keV photons and the Navarro-Frenk-White (NFW) density profile with 21.5 kpc scaled length to model the sterile neutrino halo, which means that the sterile neutrinos are the dominant dark matter component, \citet{Prokhorov} calculated the sterile neutrino decay rate and mixing angle with active neutrinos to be $\Gamma=(9.0 \pm 4.8) \times 10^{-28}$ $^{-1}$ and $\sin^22 \theta=(4.1 \pm 2.2) \times 10^{-12}$ respectively." + However. there is no evidence (hat the density profile of the sterile neutrino halo behaves like the NEW profile.," However, there is no evidence that the density profile of the sterile neutrino halo behaves like the NFW profile." + If the sterile neutrinos are degenerate. the size of the halo can be very. small (radius Ro5x10D7"" !and mixing. angle sin?.L720—10?M1 . whichn are consistent. with. a low reheating temperature and suggest that sterile - active neutrino oscillation may be visible in near future experiments."," In this scenario, the sterile neutrino decay rate $\Gamma \ge 5 \times 10^{-20}$ $^{-1}$and mixing angle $\sin^22 \theta \sim 10^{-3}-10^{-4}$ , which are consistent with a low reheating temperature and suggest that sterile - active neutrino oscillation may be visible in near future experiments." +" Sterile neutrinos max decay into active neutrinos and photons (7,4 v,+3)."," Sterile neutrinos may decay into active neutrinos and photons $\nu_s +\rightarrow \nu_a + \gamma$ )." + The energy, The energy +By extrapolation. it also does not secu uulikely that even lugher multipoles should be included.,"By extrapolation, it also does not seem unlikely that even higher multipoles should be included." + This issuc will be revisited i a future publication., This issue will be revisited in a future publication. + Our second main conclusion is that we find a spectral index. only 1.96 away frou unity. namely 54=0.973+0.01 1.," Our second main conclusion is that we find a spectral index only $1.9\sigma$ away from unity, namely $n_{\textrm{s}} = +0.973\pm0.014$ ." +" To ux. it therefore seem premature to make strong claius concerning n,41: the statistical significance of this is rather low. aud there are likely still uuknuow- systematic errors i this nuiuber."," To us, it therefore seem premature to make strong claims concerning $n_{\textrm{s}}\ne 1$; the statistical significance of this is rather low, and there are likely still unknown systematic errors in this number." + Iu a future publication we will ecueralize the GBR estimator to polarization., In a future publication we will generalize the GBR estimator to polarization. + Once completed. this will enable a fully Cabbs-based ΑΠΟ likelihood analysis at low (Cs. and remove the need for likelihood techniques based on matrix operations. ie. inversion and deternunant evaluation.," Once completed, this will enable a fully Gibbs-based CMB likelihood analysis at low $\ell$ 's, and remove the need for likelihood techniques based on matrix operations, i.e., inversion and determinant evaluation." + The computational cost of a standard: cosmological parameter MICAIC analysis (e.g... CosmoMC) will then once again be driven by the required Boltzimaun codes (e.g... CAMDB or CABFast) and not by the Likelihood evaluation.," The computational cost of a standard cosmological parameter MCMC analysis (e.g., CosmoMC) will then once again be driven by the required Boltzmann codes (e.g., CAMB or CMBFast) and not by the likelihood evaluation." + In turn. this will increase the importance of fast interpolation codes sucli as Pico (Fendt&Wandelt2007) or COSMONET (Auldetal.2007).," In turn, this will increase the importance of fast interpolation codes such as Pico \citep{fendt:2007} or COSMONET \citep{auld:2007}." +. With such fast algorithius for both spectrum aud likehhood evaluations ready at hand. the CPU requirenieuts for cosmological parameter estimation may possibly be reduced by orders of maenitiucde.," With such fast algorithms for both spectrum and likelihood evaluations ready at hand, the CPU requirements for cosmological parameter estimation may possibly be reduced by orders of magnitude." +This paper was inspired by the work of Daddi et al. (,This paper was inspired by the work of Daddi et al. ( +2002. 2001). Blain et al. (,"2002, 2004), Blain et al. (" +2001). and others who lave estimated the spatial clustering streugth of a galaxy population [rom tle observed positious of a simall number of its members.,"2004), and others who have estimated the spatial clustering strength of a galaxy population from the observed positions of a small number of its members." + Unable to fit a correlation function to the biuned uumbers of pair couuts at different spatial separatious. these authors counted the uunber nj; of ealaxy palrs with redshift separation 1—X9«OS and compared to tbe expected number nop for an assumed correlation [function £(r). which Blain et al. (," Unable to fit a correlation function to the binned numbers of pair counts at different spatial separations, these authors counted the number $n_{\rm obs}$ of galaxy pairs with redshift separation $|z_1-z_2|<\Delta z$ and compared to the expected number $n_{\rm exp}$ for an assumed correlation function $\xi(r)$, which Blain et al. (" +2001) calculated to be where N is the number of galaxies with measured redshilts. P(z) is the survey selection H ⊔∩∐⋅−≤≥↥⊳∖↕∐↩⊳∖∩∐≺⇂⋜↕∐∑∸↥≺↵∩⊓∐≺↵⊳∖⋯⋅∖⊽≺↵⊽∖⊽⋅∣↝↓⊇↥⊳∖↕∐≺↵∢∙∩⊔∩∖⊽⋯∑≟≺∐⊳∖↕⋜↕∐∢∙≺↵∣⋈↲↕∖∖↽≺↵≺↵∐↕∐≺↵↥↽≻∩∐∐⊳∖⊳∖↥↽≻≺↵∢∙↓∐≺↵≺⇂H H H H H H ⋅⋅ ∣≻⊽∖⊽⋖∫⊝↕⋅∶↓⋟⋜↕∐≺⊔⋮⊝⊒⋅∶⊇⋝⋅⋜↕∐≺⇂⊝↥⊳∖↕↕≺↵⋜↕∐∑∸⋃↥⋜∐⋅↥↽≻∩⊳∖∐↥∩∐∩↥∎⋜↕∑≟⋜↕↥⋜∟∖⊽∖⇁∖∖↽∐∐↥∐≤≥⋅⋮⊰ ⊺∐≺↵⊽∖⊽↕∐≺↵∐↕⋅↩⊳∖⋃⋅↥∢∙↕≺↵≺⇂↕∐≺↵∐⋅⋜↕⊓≺↵∐↥∩∐↕∩⋜↕↥∎⋜⋃∐∐⊽∖⇁∩∎∢∙∩↕⋅↓⋅≺↲↥⋜↕∏∩∐↥∎⋯∐∙⋃∩∐⊳∖⋚⋜⋮∣⊲⋝∶⋖∫∣↝↙∕∕∣∣⊲∣∣⋝ L5 that could be specified by a single parameter. ry. and estimated ro for their galaxy. population by finding the value that made nex=nop;,"2004) calculated to be where $N$ is the number of galaxies with measured redshifts, $P(z)$ is the survey selection $\Omega$ is the solid angle of the survey, $r_{12}$ is the comoving distance between the points specified by $({\bf\Theta_1},z_1)$ and $({\bf\Theta_2},z_2)$ , and ${\bf\Theta}$ is the angular position of a galaxy within $\Omega$ They then restricted their attention to a family of correlationfunctions $\xi(r)=(r/r_0)^{-1.8}$ that could be specified by a single parameter, $r_0$, and estimated $r_0$ for their galaxy population by finding the value that made $n_{\rm exp}=n_{\rm obs}$." + aspired by Poisson statistics. Blain et al. (," Inspired by Poisson statistics, Blain et al. (" +2001) took as a lo confidence interval the set of ry that satisfied The approach can provide useful coustraints on ry when other methods fail. but the implementation described above is imperfect.,"2004) took as a $1\sigma$ confidence interval the set of $r_0$ that satisfied The approach can provide useful constraints on $r_0$ when other methods fail, but the implementation described above is imperfect." + Equation 1 is uuuecessarily noisy aud is more seusitive to the asstumect selection fuuctiou than to the clustering strength £: equation 2 almost always unclerestimates the true uncertainty dn rp., Equation \ref{eq:blain} is unnecessarily noisy and is more sensitive to the assumed selection function than to the clustering strength $\bar\xi$; equation \ref{eq:blainuncertainty} almost always underestimates the true uncertainty in $r_0$. + The goal of this paper is to draw attentiou to these shortcomiugs and to suggestMOD modifications that make tle analysis less subject to them., The goal of this paper is to draw attention to these shortcomings and to suggest modifications that make the analysis less subject to them. + Section 3.1. discusses the effect of Uncertainties in the selection function. showing that a error in the assumed width of a Caussian selection [uuction cau easily chauge the inferred value of rg by a factor of 2 or more.," Section \ref{sec:selfn} discusses the effect of uncertainties in the selection function, showing that a error in the assumed width of a Gaussian selection function can easily change the inferred value of $r_0$ by a factor of 2 or more." + Sectious aud 3.3. point out two additional sources of uoise in equation 1. that are easily removed.," Sections \ref{sec:angnoise} and \ref{sec:znoise} + point out two additional sources of noise in equation \ref{eq:blain} that are easily removed." + My suggested revisions to tlie method are put forward in { aud tested with a cosmological N-body simulation iu 5.., My suggested revisions to the method are put forward in \ref{sec:alternatives} and tested with a cosmological $N$ -body simulation in \ref{sec:gif}. + Section 6 cousiders the uucertainty iu the best-fit values of ro. showing that equation 2 is a poor approximation aud suggesting a modification that leads to more realistic error bars.," Section \ref{sec:uncertainties} considers the uncertainty in the best-fit values of $r_0$, showing that equation \ref{eq:blainuncertainty} + is a poor approximation and suggesting a modification that leads to more realistic error bars." + The main couclusious are summarized aid discussedin 7.., The main conclusions are summarized and discussedin \ref{sec:summary}. . + To motivate the discussion. I υδρία in 2 with au example that shows tlie staucard aualysis of redshift palr-couuts going badly awry.," To motivate the discussion, I begin in \ref{sec:awry} with an example that shows the standard analysis of redshift pair-counts going badly awry." +‘Turbulent convection occurs frequently in. stellar interiors and other astrophiysical [uid Dows.,Turbulent convection occurs frequently in stellar interiors and other astrophysical fluid flows. + While convective motion naturally transports heat anc chemical elements. the transport of angular momentum by convection in rotating bodies is à more subtle issue.," While convective motion naturally transports heat and chemical elements, the transport of angular momentum by convection in rotating bodies is a more subtle issue." + Lt is of particular interest. in the case of the Sun. where the internal pattern of rotation has been measured but remains incompletely understood.," It is of particular interest in the case of the Sun, where the internal pattern of rotation has been measured but remains incompletely understood." + It may also play an significant role in accretion Lows., It may also play an significant role in accretion flows. + Numerical simulations of astrophysical convection are becoming increasingly powerful and capable of resolving a widening range of leneth and time scales., Numerical simulations of astrophysical convection are becoming increasingly powerful and capable of resolving a widening range of length and time scales. + Nevertheless. a simpler. statistical description of turbulent. transport is desirable in order to treat the elfects of convection on the structure and evolution of stars.," Nevertheless, a simpler, statistical description of turbulent transport is desirable in order to treat the effects of convection on the structure and evolution of stars." + It almost. goes. without saving that such a ceseription cannot be derived: strictly from the equations of [uid dynamics but must involve some mocelling or parametrization., It almost goes without saying that such a description cannot be derived strictly from the equations of fluid dynamics but must involve some modelling or parametrization. + The mixing-length theory of turbulent transport was developed bx. Prandtl (1925) and applied (ο stellar convection by Biermann (1932)., The mixing-length theory of turbulent transport was developed by Prandtl (1925) and applied to stellar convection by Biermann (1932). + It is still the basic mociel used in most calculations of stellar structure and evolution. usually in the form devised. by Dóhhm-Vitense. (1958).," It is still the basic model used in most calculations of stellar structure and evolution, usually in the form devised by Böhhm-Vitense (1958)." + The main purpose of mixine-leneth theory is to relate the convective heat flux to the superadiabatie graclient: in this context Ἡ does not usually deal with the transport of (angular) momentum that arises in the presence of shear or rotation., The main purpose of mixing-length theory is to relate the convective heat flux to the superadiabatic gradient; in this context it does not usually deal with the transport of (angular) momentum that arises in the presence of shear or rotation. + A standard. theoretical approach to convection in differentially rotating stars is set out in the monograph by Rüddiger (1989)., A standard theoretical approach to convection in differentially rotating stars is set out in the monograph by Rüddiger (1989). + Angular momentum transport is deseribed by a Ievnolds stress tensor whose components can be related to the large-scale mean Wows and thermocvnamical gradients., Angular momentum transport is described by a Reynolds stress tensor whose components can be related to the large-scale mean flows and thermodynamical gradients. + X first. contribution to the ltevnolds stress is typically proportional to the angular velocity gradient through a turbulent viscosity coellicient., A first contribution to the Reynolds stress is typically proportional to the angular velocity gradient through a turbulent viscosity coefficient. + An important additional contribution comes from the A-elect. (named after. Lebedinsky). whereby even uniformly rotating convection transports angular momentum by virtue of its anisotropy.," An important additional contribution comes from the $\Lambda$ -effect (named after Lebedinsky), whereby even uniformly rotating convection transports angular momentum by virtue of its anisotropy." + Attempts to constrain or parameterize these quantities have been made through local numerical simulations Whappvla.. Ixorpi Tuominen 2004) or theoretical models. IxIxitchatinov Riieleliger 1993).," Attempts to constrain or parameterize these quantities have been made through local numerical simulations Käppylä,, Korpi Tuominen 2004) or theoretical models Kitchatinov Rüddiger 1993)." + Alean-field. modols of stellar rotation (e.g. Witehatinoy ltüdcdiger 1999. Rempel 2005) have been developed: which use such parameterizecl expressions for the Iteynolds stress and heat Εις.," Mean-field models of stellar rotation (e.g. Kitchatinov Rüddiger 1999, Rempel 2005) have been developed which use such parameterized expressions for the Reynolds stress and heat flux." + Revnolds-stress models of turbulent. flows have been, Reynolds-stress models of turbulent flows have been +Iu this section. we show the outline of the linear stability analysis of a disk when the surface deusity structure is not Πην,"In this section, we show the outline of the linear stability analysis of a disk when the surface density structure is not uniform." + We consider a disk without a planet for simplicity., We consider a disk without a planet for simplicity. + The equations we consider are equations and without cy., The equations we consider are equations and without $\psi_{\rm p}$. + We asiune that the background disk is axisvunmetric with deusity profile Xo(e)., We assume that the background disk is axisymmetric with density profile $\Sigma_0(x)$. +" We denote the backerouud values with subscript ""07.", We denote the background values with subscript “0”. + In the backeround state. the pressure eradieut mst be balanced by Coriolis force aud therefore. aud We now consider linear perturbation.," In the background state, the pressure gradient must be balanced by Coriolis force and therefore, and We now consider linear perturbation." + Perturbed values are denoted by à and consider the solution proportional to exp|fet|Hyg]., Perturbed values are denoted by $\delta$ and consider the solution proportional to $\exp[-i\omega t + ik_y y]$. + Linear perturbation is then where cGe)SweWUCe)., Linear perturbation is then where $\tilde{\omega}(x) \equiv \omega - k_y U(x)$. +" Frou these equatious. we can derive a single second-order ordinary differential equation for @=Nyde,. where and / denotes the derivative with respect tow."," From these equations, we can derive a single second-order ordinary differential equation for $\Phi \equiv \Sigma_0 \delta v_x$, where and $\prime$ denotes the derivative with respect to $x$." + Equation with au appropriate boundary. condition constructs an cigenvalue problem for w., Equation with an appropriate boundary condition constructs an eigenvalue problem for $\omega$. + Since full analyses of equation is not the scope of this paper. we bricty outline the qualitative results about the instability of eap profile that can be derived from equation.," Since full analyses of equation is not the scope of this paper, we briefly outline the qualitative results about the instability of gap profile that can be derived from equation." +(D6).. For an axisvuuetric mode (ky= 0). equation beconies We iuultiply 9 to this equation and imtegrate over c.," For an axisymmetric mode $k_y=0$ ), equation becomes We multiply $\Phi^{\ast}$ to this equation and integrate over $x$." + Assunüng that the perturbation vanishes at e|»x and integratiug bv part. we obtain We first note that from this equation. the eigenvalue το must be real.," Assuming that the perturbation vanishes at $|x|\to\infty$ and integrating by part, we obtain We first note that from this equation, the eigenvalue $\omega^2$ must be real." + For iustabilitv. ο umst be negative aud therefore. #7 must be negative at some point iurc.," For instability, $\omega^2$ must be negative and therefore, $\kappa^2$ must be negative at some point in $x$." + This necessary condition for instability is the well-known Ravleigh criterion., This necessary condition for instability is the well-known Rayleigh criterion. + We can further proceed by using the independent variable Equation now becomes Defining aud, We can further proceed by using the independent variable Equation now becomes Defining and +maenituces and colors from the th‘ee linage sets agreed to 0.01 mae. incicating that coucditious were clear.,"magnitudes and colors from the three image sets agreed to $\sim 0.01$ mag, indicating that conditions were clear." + Fig., Fig. + 1 shows the stars 1reasurecl aud their maguitucles., 1 shows the stars measured and their magnitudes. + Ii acdcitjou to the standardized photometry. we took 28 f-baud siipshots over two nights in oreer salupe tlie light curve aud establis ithe relationship between yhotometric and spectroscopic plase.," In addition to the standardized photometry, we took 28 $I$ -band `snapshots' over two nights in order sample the light curve and establish the relationship between photometric and spectroscopic phase." + ΤΙese were reduced usiug the IRAF implementation of DAOPHOT in a semi-automated mo«ce., These were reduced using the IRAF implementation of DAOPHOT in a semi-automated mode. + The ciffereutial magnitudes were converted to approximate staidard £ magnitudes using the plotometriC secuence., The differential magnitudes were converted to approximate standard $I$ magnitudes using the photometric sequence. + We obtalned 1lore extensive {1uje-series photometry of the οject on tlree nights tn 2001 May sine tl el. Sin Nc‘Craw-Hill elesc‘ope aid a thinned SITe 10212 CCD., We obtained more extensive time-series photometry of the object on three nights in 2004 May using the 1.3 m McGraw-Hill telescope and a thinned SITe $1024^2$ CCD. + To 1iiuiuize dead time we junued le readou 2x2 aud cropped the a‘ea to viel a pepo2005 1uage with a scale of 1.018 arcsec yer (bii1ed) pixel., To minimize dead time we binned the readout $2\times2$ and cropped the area to yield a $256^2$ image with a scale of 1.018 arcsec per (binned) pixel. + We cycled tΙrough 120 s exposures in the B filter. aud 60 s exposures in V and 4 fiΙers.," We cycled through 120 s exposures in the $B$ filter, and 60 s exposures in $V$ and $I$ filters." + Alte* bias subtαςion and [lat fielding ising twilight sky exposures. we measurect uagnitt(es in La'Csec diameter apertures sing IRAF.," After bias subtraction and flat fielding using twilight sky exposures, we measured magnitudes in 4-arcsec diameter apertures using IRAF." + Dillereial magnitudes were computed 'elative t« ytheV=LLS6 comparison star west of tlie variable (see Fig., Differential magnitudes were computed relative to the $V = 14.86$ comparison star west of the variable (see Fig. + 1)., 1). + The V=17.10 mag star ο the soibeast served as a cheek: typical p'ecislons wrere <0.02 mae (after we discarded a few images taken through intermitte| heavy cloud)., The $V = 17.40$ mag star to the southeast served as a check; typical precisions were $< 0.02$ mag (after we discarded a few images taken through intermittent heavy cloud). + Hour aigle coustraints prevented us (rom covering he entire orbit iu one night. but we were abe to plece together coverage of the whole orbit from he three nielits’ data.," Hour angle constraints prevented us from covering the entire orbit in one night, but we were able to piece together coverage of the whole orbit from the three nights' data." + When plase recltuudalcy was obtained the dillerent nights agreed closely — here was no trace of secular vaability., When phase redundancy was obtained the different nights agreed closely – there was no trace of secular variability. + The differential maguitudes and colors were standardized nine the sequence ti Table 2., The differential magnitudes and colors were standardized using the sequence in Table 2. + Fig., Fig. + 2 shows the mean spectrum. shifted to the rest [rame of the secondary using the ephemeris described later.," 2 shows the mean spectrum, shifted to the rest frame of the secondary using the ephemeris described later." + It is essentially that of a late-type star. with uo emission lines.," It is essentially that of a late-type star, with no emission lines." + The flux level implies V—17.5. in good agreement with the filter photometry.," The flux level implies $V = 17.5$, in good agreement with the filter photometry." + Table 3 lists the cross-correlation radial velocities., Table 3 lists the cross-correlation radial velocities. + A search of these vields a strong periodicity near L75 hr. but with several possible precise periods correspoudiug to cdillerent choices of cycle couut over the 50-day interval between 2001 January auc March.," A search of these yields a strong periodicity near 4.75 hr, but with several possible precise periods corresponding to different choices of cycle count over the 50-day interval between 2004 January and March." + Fortunately. the photometric period published by Woudt.Warner.&Pretorius(2001) is cousistent with ouly one of the precise periods.," Fortunately, the photometric period published by \citet{woudtwarner} is consistent with only one of the precise periods." + Once the 50-day cycle cout is decided. the ephieiueris exteuds unambiguosly back to the single 2003 January poiut. πιer lightening the period.," Once the 50-day cycle count is decided, the ephemeris extends unambiguously back to the single 2003 January point, further tightening the period." + To help us verily the ephemeris.ot P. Woidt kindly sent the time-series potometry data usec by Wouet.Warner.&Preto‘ius(200L):: combining this with our own time-series photometry again vielded the same period. coiirinine the eplemeris.," To help us verify the ephemeris, P. Woudt kindly sent the time-series photometry data used by \citet{woudtwarner}; combining this with our own time-series photometry again yielded the same period, confirming the ephemeris." + The period fouud here cli[ers slightly from tlat found wy Woudt. [rom their photometric data alone: our period supersedes tlieirs. since it is base ola longer time span and has greater reduudacy.," The period found here differs slightly from that found by \citet{woudtwarner} from their photometric data alone; our period supersedes theirs, since it is based on a longer time span and has greater redundancy." + Table | gives the paraineers of the best-fitting sinusoicl. aud Fie.," Table 4 gives the parameters of the best-fitting sinusoid, and Fig." + 3 shows the folded velocities with the situsoid superposed., 3 shows the folded velocities with the sinusoid superposed. + Fig., Fig. + I shows the 1.212 time series photometry Lolclec ou tlie spectroscopic ephemeris. in which," 4 shows the 1.3m time series photometry folded on the spectroscopic ephemeris, in which" +founcl cooler temperatures arose when a single power-LIaw spectrum reionized both hydrogen and helium. so that the temperatures are sensitive to the amount of rreionization during the hwdrogen reionization epoch.,"found cooler temperatures arose when a single power-law spectrum reionized both hydrogen and helium, so that the temperatures are sensitive to the amount of reionization during the hydrogen reionization epoch." + Clearly. simulations allowing for a more complex rreionization history involving a range of source histories and spectra are required to fully match the data., Clearly simulations allowing for a more complex reionization history involving a range of source histories and spectra are required to fully match the data. + ‘The simulation matches the median Doppler width of the optically thick absorbers in the radiative transfer simulation to an accuracy of 2kms al z24 and better than O.5kms+ at 2<2oX2.5. but underprediets the widths by as much as 3.5kms.+ at intermediate redshifts.," The simulation matches the median Doppler width of the optically thick absorbers in the radiative transfer simulation to an accuracy of $2\kms$ at $z\ge 4$ and better than $0.5\kms$ at $2\le z \le 2.5$, but underpredicts the widths by as much as $3.5\kms$ at intermediate redshifts." + For the absorbers optically thin at line centre. the agreement isto better than 2knis.+ for 3.0τς 5. but underprecdicts the widths by ~5kms by 2=2.0.," For the absorbers optically thin at line centre, the agreement is to better than $2\kms$ for $3.0\le z \le 5$ , but underpredicts the widths by $\sim5\kms$ by $z=2.0$." + Doubling the hheating rate in an optically thin simulation produces a close match to the median. Doppler parameter of the optically thin absorbers from the simulation with radiative transfer over 3.0<23.5. agrecing to within O.6kms +. Bat by z=2.0. the median Doppler parameter is overpredicted by ~I5kms.+.," Doubling the heating rate in an optically thin simulation produces a close match to the median Doppler parameter of the optically thin absorbers from the simulation with radiative transfer over $3.0\le z \le 3.5$, agreeing to within $0.6\kms$ But by $z=2.0$, the median Doppler parameter is overpredicted by $\sim15\kms$." + The Doppler parameters of the absorption svstems optically thick at line centre are overpredictecd by. 2-6kms [oovep 2.0.2X3.5., The Doppler parameters of the absorption systems optically thick at line centre are overpredicted by $6\kms$ over $2.0\le z \le 3.5$. + The approximate methods are thus unable to. reproduce. the correct amount of broadening to the accuracy with which it is measured over the full range of redshifts for which the forest may be observed in high resolution. high signal-to-nolse ratio spectra.," The approximate methods are thus unable to reproduce the correct amount of broadening to the accuracy with which it is measured over the full range of redshifts for which the forest may be observed in high resolution, high signal-to-noise ratio spectra." + Just as absorption features may fully account for the pixel flux distribution inLya.. a line blanketing moclel accounts well for the evolution in the mean transparency of the LGAL in higher order Lyman series lines.," Just as absorption features may fully account for the pixel flux distribution in, a line blanketing model accounts well for the evolution in the mean transparency of the IGM in higher order Lyman series lines." +" Effective optical depth ratios for the ool ellTpsfTp,yell00.36⋅⋅ and τν.∣⊽⊔∣⊽⊔7520.21− are predicted: at >—40 from theEnzo radiative transfer simulation."," Effective optical depth ratios for the of $\tau_{\rm Ly\beta}^{\rm eff}/ \tau_{\rm Ly\alpha}^{\rm + eff}\simeq0.36$ and $\tau_{\rm Ly\gamma}^{\rm eff}/ \tau_{\rm + Ly\alpha}^{\rm eff}\simeq0.21$ are predicted at $z=3.0$ from the radiative transfer simulation." + Racliative transfer through density inhomogeneities in the IM results in à wide spread of ooptical depths compared with ceven after rreionization has completed inthe simulation at z=3., Radiative transfer through density inhomogeneities in the IGM results in a wide spread of optical depths compared with even after reionization has completed inthe simulation at $z=3$. + A broad. peak centred at THe/THz105 is found at z=3.0. diminishing to NO at z—2.5 and το at z—2.0.," A broad peak centred at $\tau_{\rm HeII}/\tau_{\rm + HI}\simeq105$ is found at $z=3.0$, diminishing to 80 at $z=2.5$ and 75 at $z=2.0$." + As for theHa. the pixel Dux distribution for mmav be Lully accounted. for by absorption lines for 240xο22.5.," As for the, the pixel flux distribution for may be fully accounted for by absorption lines for $2.0\le z \le 2.5$." + At 2.=3.0. however. the mean transmission is too low for meanineful absorption line fitting to be performed.," At $z=3.0$, however, the mean transmission is too low for meaningful absorption line fitting to be performed." + Matching to the corresponding aabsorption features results in a broad. distribution of the column density ratio 7= INgoair£Ngi. with a peak of η2130 ab 2=2.5. well matching. though somewhat narrower than. the distribution measured in the ultraviolet spectra of high redshilts QSOs.," Matching to the corresponding absorption features results in a broad distribution of the column density ratio $\eta=N_{\rm HeII}/ N_{\rm HI}$ , with a peak of $\eta\simeq130$ at $z=2.5$, well matching, though somewhat narrower than, the distribution measured in the ultraviolet spectra of high redshifts QSOs." + While the value for a at the distribution peak results from the rescaling of the relative aanel iionization rates required to mateh the measured. effective aanel ooplical depths. the distribution width is produced by the simulation and suggests that much of the observed. spread may arise naturally from the radiative transfer through an inhomogeneous IGM.," While the value for $\eta$ at the distribution peak results from the rescaling of the relative and ionization rates required to match the measured effective and optical depths, the distribution width is produced by the simulation and suggests that much of the observed spread may arise naturally from the radiative transfer through an inhomogeneous IGM." +" Comparison between the column density. and. optical depth ratios indicates a tvpical Doppler parameter ratio of =byeu/fba,20.4. close to the thermally broadened limit£ of £=0.5."," Comparison between the column density and optical depth ratios indicates a typical Doppler parameter ratio of $\xi=b_{\rm HeII}/ +b_{\rm HI}\simeq0.4$, close to the thermally broadened limit of $\xi=0.5$." + X comparison based on well deblencded. unsaturated svstems with line centre ooplical depths 0.01«τι0.1 shows a range in Doppler parameter ratios peaking between 0.5<£«LO. the latter corresponding to the limit of velocitv-broadened features.," A comparison based on well deblended, unsaturated systems with line centre optical depths $0.01<\tau_0<0.1$ shows a range in Doppler parameter ratios peaking between $0.5<\xi<1.0$, the latter corresponding to the limit of velocity-broadened features." + Line blanketing accounts well for the higher order LLvman transmission through the ICM. as well., Line blanketing accounts well for the higher order Lyman transmission through the IGM as well. +" The simulations predict cllective optical depth ratios of Tpes/Tpeuell00336⋅⋅ at 2=−25. in; agreement with; the measured value. aud πι,qn.c0.20 (currently unmeasured)."," The simulations predict effective optical depth ratios of $\tau_{\rm Ly\beta}^{\rm eff}/ +\tau_{\rm Ly\alpha}^{\rm eff}\simeq0.36$ at $z=2.5$, in agreement with the measured value, and $\tau_{\rm Ly\gamma}^{\rm eff}/ \tau_{\rm + Ly\alpha}^{\rm eff}\simeq0.20$ (currently unmeasured)." +" A range of models. allowing for multiple QSO sources turning on over a range of redshifts with à variety of luminosities. spectral shapes and lifetimes. would be required to accurately match the aand aabsorption data as measured. in the spectra. olf high redshift, background QSOs."," A range of models, allowing for multiple QSO sources turning on over a range of redshifts with a variety of luminosities, spectral shapes and lifetimes, would be required to accurately match the and absorption data as measured in the spectra of high redshift background QSOs." + Theo simulations presented here demonstrate that rreionization simulations including radiative transfer are required to fully exploit the growing body of high quality IGM cata at both optical and ultraviolet wavelengths., The simulations presented here demonstrate that reionization simulations including radiative transfer are required to fully exploit the growing body of high quality IGM data at both optical and ultraviolet wavelengths. + The computations reported here were performed using the SUPA Astrophysical IPC facility and facilities funded by an STEC Rolling-Grant., The computations reported here were performed using the SUPA Astrophysical HPC facility and facilities funded by an STFC Rolling-Grant. + EP. is supported byan STEC Rolline-, E.T. is supported byan STFC Rolling-Grant. + Computations described in this work were performed using the code developed by the Laboratory forComputational Astrophysics at the University of California in San Diego (http://Ica.ucsd.edu)., Computations described in this work were performed using the code developed by the Laboratory forComputational Astrophysics at the University of California in San Diego (http://lca.ucsd.edu). +textscii.,. +. Phe spectrum is reminiscent of 1162316 with similar peculiarities., The spectrum is reminiscent of 162316 with similar peculiarities. + Even the lines ofAA. which are heavily blended in both stars. show similar blending and splitting.," Even the lines of, which are heavily blended in both stars, show similar blending and splitting." + Phe splitting in this line is partial. so it requires a synthetic caleulation to estimate the magnetic field strength.," The splitting in this line is partial, so it requires a synthetic calculation to estimate the magnetic field strength." + refsv179902. shows the profile of this iron line in comparison with a synthetic spectrum., \\ref{sy179902} shows the profile of this iron line in comparison with a synthetic spectrum. + Phe magnetic field also. is confirmed by partial doublet splitting of the line., The magnetic field also is confirmed by partial doublet splitting of the line. + “Phis star was observed twice with FEROS with a 6-d gap. but no significant spectral variability was detected.," This star was observed twice with FEROS with a 6-d gap, but no significant spectral variability was detected." + The magnetic field also did not change within the errors for hese two spectra., The magnetic field also did not change within the errors for these two spectra. + In contrast with 1162316. we did not ind any significant variability for 1179902. using ASAS yhotometry.," In contrast with 162316, we did not find any significant variability for 179902 using ASAS photometry." + This peculiar star shows rather moderate or weak lines ofextscili.. and some other rare earth elements in the spectrum.," This peculiar star shows rather moderate or weak lines of, and some other rare earth elements in the spectrum." + The magnetic field is strong and Zeeman components of the line are split. as can be seen in refsv 184120..," The magnetic field is strong and Zeeman components of the line are split, as can be seen in \\ref{sy184120}." +. Some other lines with large Landé factors also show Zeeman splitting. mostly partial.," Some other lines with large Landé factors also show Zeeman splitting, mostly partial." + Many lines demonstrate magnetic broadening., Many lines demonstrate magnetic broadening. + This star was observed with FEROS twice and. both spectra are similar with no significant spectral variability., This star was observed with FEROS twice and both spectra are similar with no significant spectral variability. + Martinez&Kurtz(1994). clic not find any rapid photometric variability. even though the spectrum ancl physical parameters of this star are similar to roAp stars.," \citet{Mart94} did not find any rapid photometric variability, even though the spectrum and physical parameters of this star are similar to roAp stars." + This magnetic star has a peculiar. spectrum. with very strong lines of ancl &ood lines ofMEDI and some other rare earth. elements.," This magnetic star has a peculiar spectrum with very strong lines of and good lines of, and some other rare earth elements." + This. peculiar star was observed. twice: both spectra are similar., This peculiar star was observed twice; both spectra are similar. + Zeeman splitting is visible in the line. as can be seen in refsv 185204..," Zeeman splitting is visible in the line, as can be seen in \\ref{sy185204}." +. Ehe line of also shows partial doublet splitting and partial splitting is also visible for many other lines across the spectrum., The line of also shows partial doublet splitting and partial splitting is also visible for many other lines across the spectrum. + This star is a promising target for searching for rapid oscillations., This star is a promising target for searching for rapid oscillations. + Martinez&Wurtz(19904)— observed. it twice photometrically. but pulsations were not found.," \citet{Mart94} observed it twice photometrically, but pulsations were not found." + Additional, Additional + z-directious.,$ z $ -directions. + Consequently each cell is rectangular and may have different side leugthis., Consequently each cell is rectangular and may have different side lengths. + Each cell has a neighboring cell in each direction aud faces 6 ueighiboriug cells in total except lor a cell located ou the eric., Each cell has a neighboring cell in each direction and faces 6 neighboring cells in total except for a cell located on the grid. + They evaluated the gravity ou the cell surface using tlie second. order interpolation., They evaluated the gravity on the cell surface using the second order interpolation. + Thetr Poissou equation can be rewritten as wliere yj. and Az; denote the side length of each cell.," Their Poisson equation can be rewritten as where The symbols, $ \Delta x _i $, $ \Delta y _j $, and $ \Delta z _j $ denote the side length of each cell." +" We omitted the interpolation formula for g, and g. to save space.", We omitted the interpolation formula for $ g _y $ and $ g _z $ to save space. + Integrating Equation (21)) over the whole volue. we obtain S pia MM where H;; does 100. vanish in a nonuniforii grid.," Integrating Equation \ref{ricker}) ) over the whole volume, we obtain where $ H _{i,j,k} $ does not vanish in a nonuniform grid." +" This means that ὅτε is not necessary to vanish even when pijj, = 0."," This means that $ \phi _{i,j,k} $ is not necessary to vanish even when $ \rho _{i,j,k} $ = 0." + In other words Equaticu (21)) bas multiple solutious for a given deusity distribution aud bouncary conditious., In other words Equation \ref{ricker}) ) has multiple solutions for a given density distribution and boundary conditions. + This is aserious problei., This is a serious problem. + As shown above. tle approach based on a higler order interpolation formula has some fuucamental problems.," As shown above, the approach based on a higher order interpolation formula has some fundamental problems." + Although our scheme is only the lirst order accurate at the grid bouudaries. it give a quautitativelv οοος soliion.," Although our scheme is only the first order accurate at the grid boundaries, it give a quantitatively good solution." + This is likely to be ¢ue to the fact that our difference scheme satisfies elobal coucditious for the proper Poisson equation ο satisfy., This is likely to be due to the fact that our difference scheme satisfies global conditions for the proper Poisson equation to satisfy. + First our scheme satisfy the Catuss’s theorem as iueutioned repeatedly., First our scheme satisfy the Gauss's theorem as mentioned repeatedly. + Second our scheme eusures the Stokes’ theorem.," Second our scheme ensures the Stokes' theorem, Equation \ref{interpolation1}) ) is equivalent to" +where o4 is the spectral energy index between 2500 tto2 keV (2). and boys ane ory are respectively 2 keV and 2500 iin units of Hz.,"where $\alpha_{\rm ox}$ is the spectral energy index between 2500 to 2 keV \citep{ste06}, , and $\nu_{\rm 2 keV}$ and $\nu_{\rm 2500}$ are respectively 2 keV and 2500 in units of Hz." + Finally.we convert from luminosity Losoy to magnitude AJ;2=2] as (?).. where d=10pe3.08«107em.," Finally,we convert from luminosity $L_{\rm 2500}$ to magnitude $M_i[z=2]$ as \citep{oke83}, where $d=10 \ {\rm pc}=3.08\times10^{19} \ {\rm cm}$." + Thus the U03 XLE can be combined with the ROG OLE., Thus the U03 XLF can be combined with the R06 OLF. + The power-law index po in the U03 ALE characterizes the density. evolution as a function of z at high recshilt., The power-law index $p_2$ in the U03 XLF characterizes the density evolution as a function of $z$ at high redshift. + Although p»=1.5 was used in EPMIO. here we change this to p»=3.5 in order to be consistent with the high-redshift ROG OLE data.," Although $p_2=1.5$ was used in ITM10, here we change this to $p_2=3.5$ in order to be consistent with the high-redshift R06 OLF data." + Since po does not allect the Iow-redshift evolution. the XLE is not significantly altered below z~3.," Since $p_2$ does not affect the low-redshift evolution, the XLF is not significantly altered below $z\sim3$." + Fig., Fig. + 1 shows the AGN ΟΙ at each redshift in terms of Az= 2]in comparison with the ROG OLE. data., \ref{fig:olf} shows the AGN OLF at each redshift in terms of $M_i [z=2]$ in comparison with the R06 OLF data. + With this AGN ALE. we reconstruct the blazar GLE with the ILUMIO blazar sequence SED mocel. following the procedures of LLO9.," With this AGN XLF, we reconstruct the blazar GLF with the ITM10 blazar sequence SED model, following the procedures of IT09." + Note that there are some discrepancies between the OLF cata and our OLE model at the brightest luminosities or low redshifts., Note that there are some discrepancies between the OLF data and our OLF model at the brightest luminosities for low redshifts. +" Vhis might be due to insullicient accuracy in our method. of converting Iuminosities and. luminosity ""unctions.", This might be due to insufficient accuracy in our method of converting luminosities and luminosity functions. + Phe correlation of Eqs.6 and τ is derived [rom a sample of 203 ACGNs (?).. and the conversion. between he NLP to ΟΙ is based on a sample of only 247 objects (?)..," The correlation of \ref{eq:alpha_ox} and \ref{eq:lum_ox} is derived from a sample of 293 AGNs \citep{ste06}, and the conversion between the XLF to OLF is based on a sample of only 247 objects \citep{ued03}." + In order to reliably apply our model to wider ranges of uminosities ancl redshifts. the statistical uncertainties must »e decreased through more data from deeper. larger X-ray and optical ACN surveys.," In order to reliably apply our model to wider ranges of luminosities and redshifts, the statistical uncertainties must be decreased through more data from deeper, larger X-ray and optical AGN surveys." +" The key parameters of our new blazar GLE model are (q.51.8)=(442.1.07.1.9210.""). where q is the ratio )etween the bolometric jet. luminosity— ancl nuclear X-ray uminositv. 7, is the faint-end slope index of the GLE. and Ais à normalization [actor for the GLE (see Section."," The key parameters of our new blazar GLF model are $(q,\ \gamma_1, \kappa)=(4.42, 1.07, 1.92\times10^{-6})$, where $q$ is the ratio between the bolometric jet luminosity and nuclear X-ray luminosity, $\gamma_1$ is the faint-end slope index of the GLF, and $\kappa$ is a normalization factor for the GLF (see Section." + 3 of 100 for details)., 3 of IT09 for details). + Dased on this model. we now cliscuss the prospects for observing high-redshift blazars withF," Based on this model, we now discuss the prospects for observing high-redshift blazars with." +ermi., Fig. + Fig. 2 shows the expected cumulative redshift distribution ofFermimi blazars above LOO MeV. in the entire sky for a ~5- survey [ux sensitivity limit of f(s100MeV)=1 photons/em?/s., \ref{fig:z_dist} shows the expected cumulative redshift distribution of blazars above 100 MeV in the entire sky for a $\sim$ 5-year survey flux sensitivity limit of $F(>100{\rm MeV})=1\times 10^{-9} \rm \ photons/cm^2/s$ . + Phe ellects of intergalactic absorption due to 55 interactions with οσο background. radiation fields are not included here. as they are not expected to be important below 1 GeV (e.g.2?7)..," The effects of intergalactic absorption due to $\gamma\gamma$ interactions with diffuse background radiation fields are not included here, as they are not expected to be important below 1 GeV \citep[e.g.][]{gil09,sin09}." + Neglecting high-redshift optical constraints. may be able to detect blazars up to.10.," Neglecting high-redshift optical constraints, may be able to detect blazars up to $z\sim10$." + Taking into account their high-redshift evolution implied from the AGN OLE. we expect that. will find some blazars up to z6 with the ~5-vear survey sensitivity.," Taking into account their high-redshift evolution implied from the AGN OLF, we expect that will find some blazars up to $z\sim6$ with the $\sim$ 5-year survey sensitivity." + Lt is expected that.Perm will find more than 1.000 blazars in total (222)...," It is expected that will find more than 1,000 blazars in total \citep{nar06,der07,it09}." + Although ~70% of the blazars have confirmed. redshifts. the other ~30% still clo not. (7)..," Although $\sim 70$ of the blazars have confirmed redshifts, the other $\sim 30$ still do not \citep{abd10_catalog}." + Furthermore. of the high-latitude sources remain unidentified (7)..," Furthermore, of the high-latitude sources remain unidentified\citep{abd10}. ." + This implies that the highest. redshift blazars must be searched. for among a large. number of sources and distinguished. [rom numerous unrelated: ones., This implies that the highest redshift blazars must be searched for among a large number of sources and distinguished from numerous unrelated ones. + The following methods for their observational selection should be elective for this purpose., The following methods for their observational selection should be effective for this purpose. +molecular viscosity in the degenerate WD.,molecular viscosity in the degenerate WD. + Substituting the viscosity from Nandkumar&Pethick(1984)— into equation (11)) results in a shear in which Ri<1/4. and thus Kelvin-Helmholtz instability is expected.," Substituting the viscosity from \citet{np84} + into equation \ref{eq:angularmomentum}) ) results in a shear in which $Ri\ll1/4$, and thus Kelvin-Helmholtz instability is expected." + This confirms the result of Yoon&Langer(2004) that in the absence of other instabilities. Kelvin-Helmholtz instability is dominant. so that we view its associated shear as an upper limit.," This confirms the result of \citet{yl04} that in the absence of other instabilities, Kelvin-Helmholtz instability is dominant, so that we view its associated shear as an upper limit." + Kelvin-Helmholtz instability causes a turbulent. eddy diffusivity given by (Fujimoto1993) (1S)SinceLo it. only acts for| Ri.<1/4. it: causes the UTDshearing to evolve until Ri=1/4 is marginally satisfied.," Kelvin-Helmholtz instability causes a turbulent eddy diffusivity given by \citep{fuj93} + Since it only acts for $Ri<1/4$, it causes the shearing to evolve until $Ri=1/4$ is marginally satisfied." + Thus it is à good approximation to estimate the shear to be egyz2N when secular instabilities due to thermal diffusion can be neglected (e.g..Zahn1992). as is the case for the conductive WD core.," Thus it is a good approximation to estimate the shear to be $\sigma_{\rm KH}\approx2N$ when secular instabilities due to thermal diffusion can be neglected \citep[e.g.,][]{zah92}, as is the case for the conductive WD core." + Since electron degeneracy provides the dominant pressure. we approximate the Brunt-Váusállá frequency àsστις where ky is Boltzmann's constant. Z is the charge per ion. and £j is the Fermi energy for a degenerate. relativistic electron gas.," Since electron degeneracy provides the dominant pressure, we approximate the Brunt-Väiisällä frequency as, where $k_{\rm B}$ is Boltzmann's constant, $Z$ is the charge per ion, and $E_{\rm F}$ is the Fermi energy for a degenerate, relativistic electron gas." + We estimate for Kelvin-Helmholtz driven shear. where gio=πω... He Is the mean molecular weight per electron. py=p/10?een. and T;=T/10%Κ.," We estimate for Kelvin-Helmholtz driven shear, where $g_{10}=g/10^{10}\ {\rm cm\ s^{-2}}$, $\mu_e$ is the mean molecular weight per electron, $\rho_9=\rho/10^9\ {\rm g\ cm^{-3}}$, and $T_8=T/10^8\ {\rm K}$." + This result is in reasonable agreement to the detailed. time dependent simulations by Yoon&Langer(2004).," This result is in reasonable agreement to the detailed, time dependent simulations by \citet{yl04}." +. Another hydrodynamic instability that may be important is the baroclinic instability (Fujimoto 1987. 1988: also see Cumming Bildsten 2000).," Another hydrodynamic instability that may be important is the baroclinic instability (Fujimoto 1987, 1988; also see Cumming Bildsten 2000)." + This instability arises because surfaces of constant pressure and density no longer coincide when hydrostatic balance is maintained under differential rotation., This instability arises because surfaces of constant pressure and density no longer coincide when hydrostatic balance is maintained under differential rotation. + In such a configuration. fluid. perturbations along nearly horizontal directions are unstable. though with a sufficient radial component to allow mixing of angular momentum and material.," In such a configuration, fluid perturbations along nearly horizontal directions are unstable, though with a sufficient radial component to allow mixing of angular momentum and material." +" When Ai is greater than the eritical baroclinic Richardson number (Fujimoto1987).. fracQN17"" Coriolis effects limit the horizontal scale of perturbations and the associated turbulent viscosity is approximated from linear theory to be (Fujimoto1993) "," When $Ri$ is greater than the critical baroclinic Richardson number \citep{fuj87}, ^2, Coriolis effects limit the horizontal scale of perturbations and the associated turbulent viscosity is approximated from linear theory to be \citep{fuj93} + =." +In the WD interior Rize~10. whereas the Richardson number found for »=rgc (using eqs. [11]]," In the WD interior $Ri_{\rm BC}\sim10$, whereas the Richardson number found for $\nu=\nu_{\rm BC}$ (using eqs. \ref{eq:angularmomentum}] ]" + and [12]]) is Ri~10°. thus the limit Ri2»Rie is clearly satisfied.," and \ref{eq:richardson}] ]) is $Ri\sim10^6$, thus the limit $Ri\gg Ri_{\rm BC}$ is clearly satisfied." +" The Richardson number can be estimated by combining equations (11)). (12)). and (26)). giving To illustrate2ος how the shear depends on the properties of the interior we take where f,..=M/M ts the accretion timescale and ta,=ou is the dynamical time."," The Richardson number can be estimated by combining equations \ref{eq:angularmomentum}) ), \ref{eq:richardson}) ), and \ref{eq:nubc}) ), giving To illustrate how the shear depends on the properties of the interior we take ^3, where $\tacc=M/\dot{M}$ is the accretion timescale and $t_{\rm dyn}=\wk^{-1}$ is the dynamical time." +" Using ope=N/Ri""7 and (r/R). we estimate"," Using $\sigma_{\rm BC}=N/Ri^{1/2}$ and $I(r)/I_{\rm tot}\sim(r/R)^5$ , we estimate." +1/4((306).. In $2.2.0 we show that the timescale for viscous diffusion from the baroclinie. instability is much shorter than. the timescale over which accretion takes place., In \ref{sec:timescale} we show that the timescale for viscous diffusion from the baroclinic instability is much shorter than the timescale over which accretion takes place. + This means that this instability is able to quickly redistribute angular momentum as it aceretes and the steady-state limit will be reached., This means that this instability is able to quickly redistribute angular momentum as it accretes and the steady-state limit will be reached. + Coupling this fact to the inequality ope~Ckg/GR&—ogy as demonstrated above. we conclude that the baroclinic instability will limit the growth of shear long before the Kelvin-Helmholtz instability can become active.," Coupling this fact to the inequality $\sigma_{\rm BC}\approx\sigma_{\rm KH}/(2Ri)\ll\sigma_{\rm KH}$ as demonstrated above, we conclude that the baroclinic instability will limit the growth of shear long before the Kelvin-Helmholtz instability can become active." + This is consistent with the results of Saio&Nomoto(2004)who included both the Kelvin-Helmholtz instability and the baroclinic instability and found nearly solid body rotation the WD. even for accretion rates as high as throughoutΙΟ. yr.," This is consistent with the results of \citet{sn04} who included both the Kelvin-Helmholtz instability and the baroclinic instability and found nearly solid body rotation throughout the WD, even for accretion rates as high as $10^{-5}\ {M_\odot\rm\ yr^{-1}}$ ." +all of these effects are somewhat less important when dealing with the complete imaging catalogue of SDSS. for which the galaxies typically lie at higher redshifts.,"all of these effects are somewhat less important when dealing with the complete imaging catalogue of SDSS, for which the galaxies typically lie at higher redshifts." + Details of the final SDSS radio sample of 2712 sources are given in Table 2.., Details of the final SDSS radio sample of 2712 sources are given in Table \ref{cattable}. + This table provides the identification details of each source so that they can be matched against either the original spectra or against the catalogues of derived optical properties released by Brinchmann shorteitebri04b.., This table provides the identification details of each source so that they can be matched against either the original spectra or against the catalogues of derived optical properties released by Brinchmann \\shortcite{bri04b}. +. Also provided are the RA and Dee of each source. the host galaxy redshift. the integrated NVSS flux density and. where there is a central FIRST counterpart. the integrated flux density. radio size and offset from the optical galaxy of the central FIRST component.," Also provided are the RA and Dec of each source, the host galaxy redshift, the integrated NVSS flux density and, where there is a central FIRST counterpart, the integrated flux density, radio size and offset from the optical galaxy of the central FIRST component." + Each radio source is also given a classification to identify its radio properties., Each radio source is also given a classification to identify its radio properties. + Class | sources are single-component NVSS sources with a single FIRST counterpart., Class 1 sources are single–component NVSS sources with a single FIRST counterpart. + Class 2 sources have a single NVSS match which is resolved into multiple components by FIRST., Class 2 sources have a single NVSS match which is resolved into multiple components by FIRST. + Class 3 sources have a single—component NVSS source. but no FIRST counterpart.," Class 3 sources have a single--component NVSS source, but no FIRST counterpart." + Class + sources have multiple NVSS components., Class 4 sources have multiple NVSS components. +" The tinal column of the table classifies each radio source as a star-forming galaxy or a radio-loud AGN, according to the criteria described in Section 4.."," The final column of the table classifies each radio source as a star–forming galaxy or a radio–loud AGN, according to the criteria described in Section \ref{radloudagn}." + The sample of radio-emitting galaxies contains both radio—loud AGN and a population of star forming galaxies., The sample of radio–emitting galaxies contains both radio–loud AGN and a population of star forming galaxies. + The latter emit at radio wavelengths mostly as a result of the synchrotron emission of particles accelerated in supernova shocks. and their radio luminosity is therefore roughly correlated. with their star formation rate: a GGHz radio luminosity of 1077 ! corresponds to a star formation. rate of. order SAL. vyrl (e.g. Condon 1992 and references therein: Carilli 20013..," The latter emit at radio wavelengths mostly as a result of the synchrotron emission of particles accelerated in supernova shocks, and their radio luminosity is therefore roughly correlated with their star formation rate: a GHz radio luminosity of $10^{22}$ $^{-1}$ corresponds to a star formation rate of order $5 +M_{\odot}$ $^{-1}$ (e.g. Condon 1992 and references therein; Carilli \nocite{con92,car01b}." + In order to investigate the host galaxies of these two populations. it is first necessary to separate the radio-loud AGN from the star-forming gulaxies.," In order to investigate the host galaxies of these two populations, it is first necessary to separate the radio–loud AGN from the star–forming galaxies." + Star-forming galaxies and AGN are often. separated using optical emission-line properties., Star–forming galaxies and AGN are often separated using optical emission–line properties. + Sadler shortcitesadO2 used a visual emission-line classification in their study of radio sources in the 2dFGRS: radio—emitting galaxies without detectable emission lines were classified as radio-loud AGN., Sadler \\shortcite{sad02} used a visual emission–line classification in their study of radio sources in the 2dFGRS: radio–emitting galaxies without detectable emission lines were classified as radio–loud AGN. + Kauffmann shorteitekau03e used the location of a galaxy in the [ONT] 5007 / H.5 versus [NIT] 6583 / Ha emission line diagnostic diagram (Baldwin. Phillips Terlevich 1981: hereafter to separate optical AGN from normal star forming galaxies.," Kauffmann \\shortcite{kau03c} used the location of a galaxy in the [OIII] 5007 / $\beta$ versus [NII] 6583 / $\alpha$ emission line diagnostic diagram (Baldwin, Phillips Terlevich 1981; hereafter \nocite{bal81} to separate optical AGN from normal star forming galaxies." + À key result of the Kauffmann sstudy was that a significant fraction of emission-line selected AGN also have associated star formation., A key result of the Kauffmann study was that a significant fraction of emission-line selected AGN also have associated star formation. + This result means that optical line ratio diagnostics should not be used to identify radio-loud AGN. because star formation activity in galaxies with a radio-quiet active nucleus would give rise to radio emission (and hence a radio— classification).," This result means that optical line ratio diagnostics should not be used to identify radio–loud AGN, because star formation activity in galaxies with a radio–quiet active nucleus would give rise to radio emission (and hence a radio--loud classification)." + In addition. for galaxies which do contain a genuine radio-loud AGN. the radio luminosity associated with the active nucleus will be overestimated if there is a signitican contribution of star formation to the radio emission.," In addition, for galaxies which do contain a genuine radio–loud AGN, the radio luminosity associated with the active nucleus will be overestimated if there is a significant contribution of star formation to the radio emission." + Machalski Condon (2). studied radio galaxies in the LCRS and used far-infrared to radio flux density ratios and far-infrarec spectral indices to separate the radio-loud AGN and star forming populations., Machalski Condon \shortcite{mac99} studied radio galaxies in the LCRS and used far–infrared to radio flux density ratios and far–infrared spectral indices to separate the radio–loud AGN and star forming populations. + The far-infrared radio correlation for star-forming galaxies (e.g. Yun. Reddy Condon could also be used to correct for the contribution of star formation to the radio luminosities of these systems.," The far–infrared radio correlation for star–forming galaxies (e.g. Yun, Reddy Condon \nocite{yun01} could also be used to correct for the contribution of star formation to the radio luminosities of these systems." + This is perhaps the ideal method. but unfortunately the Infrared Astronomical Satellite (RAS) Fain Source Catalogue is not quite deep enough to allow this to be used for the SDSS galaxies in thispaper.," This is perhaps the ideal method, but unfortunately the Infrared Astronomical Satellite (IRAS) Faint Source Catalogue is not quite deep enough to allow this to be used for the SDSS galaxies in this." +". A variety of alternative methods were therefore considered. and a procedure based on the location of a galaxy in the plane of 2,,(4000) versus Litony1: was adopted."," A variety of alternative methods were therefore considered, and a procedure based on the location of a galaxy in the plane of $D_n(4000)$ versus $L_{\rm 1.4GHz} / M_*$ was adopted." +" The £1cH,/M. ratio provides the radio luminosity per stellar mass of the galaxy and 2,(4000) is a fairly accurate indicator of mean stellar age for ages below about a Gyr (at higher ages it Is also sensitive to metallicity: cf.", The $L_{\rm 1.4GHz} / M_*$ ratio provides the radio luminosity per stellar mass of the galaxy and $D_n(4000)$ is a fairly accurate indicator of mean stellar age for ages below about a Gyr (at higher ages it is also sensitive to metallicity; cf. + Kauffmann Thus. star forming galaxies would be expected to occupy a well-defined locus in this plane. while radio-loud AGN would be offset to higher radio luminosities.," Kauffmann \nocite{kau03a} + Thus, star forming galaxies would be expected to occupy a well–defined locus in this plane, while radio–loud AGN would be offset to higher radio luminosities." + This is demonstrated in the first two panels of Figure 9.., This is demonstrated in the first two panels of Figure \ref{sfagncut}. +" The top panel of Figure 9— shows £,,(4000) versus LjacaMs for radio-emitting galaxies that are classified as star forming galaxies using the [OTN] 5007 / versus [NIH] 6583 / Ha emission line diagnostic diagram."," \nocite{kau03c,bru03} + The top panel of Figure \ref{sfagncut} shows $D_n(4000)$ versus $L_{\rm +1.4GHz} / M_*$ for radio–emitting galaxies that are classified as star forming galaxies using the [OIII] 5007 / $\beta$ versus [NII] 6583 / $\alpha$ emission line diagnostic diagram." + The criteria of Kauffmann, The criteria of Kauffmann +We have now identified our target sample of stars with potential brown-dwarf companions and have obtained the orbital parameters accessible through radial-velocity measurements.,We have now identified our target sample of stars with potential brown-dwarf companions and have obtained the orbital parameters accessible through radial-velocity measurements. +" As the next step, we will search the intermediate astrometric data of the new Hipparcos reduction for signatures of the orbital motion corresponding to the radial-velocity orbit."," As the next step, we will search the intermediate astrometric data of the new Hipparcos reduction for signatures of the orbital motion corresponding to the radial-velocity orbit." +" We describe a method to search the Intermediate Astrometric Data (IAD) of the new Hipparcos reduction for the orbital signatures of stars, whose spectroscopic elements are known from a reliable radial-velocity solution."," We describe a method to search the Intermediate Astrometric Data (IAD) of the new Hipparcos reduction for the orbital signatures of stars, whose spectroscopic elements are known from a reliable radial-velocity solution." + The significance of the derived orbit is determined through the distribution-freepermutation test (??)..," The significance of the derived orbit is determined through the distribution-freepermutation test \citep{Good:1994,Zucker:2001ve}." + Techniques to perform the simultaneous fitting to radial-velocity and Hipparcos astrometry data for substellar companions and to verify the statistical confidence of the solution have been developed by ????..," Techniques to perform the simultaneous fitting to radial-velocity and Hipparcos astrometry data for substellar companions and to verify the statistical confidence of the solution have been developed by \cite{Zucker:2000vn, Pourbaix:2001qe, Halbwachs:2000rt, Zucker:2001ve}. ." +" More recently, ? and"," More recently, \cite{Reffert:2006ly} and" +Telescope... which is operated bv the Jet Propulsion Laboratory. California Institute of Technology. under NASA contract L407.,", which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under NASA contract 1407." +of the high frequency variability in this band by binning the light curve in 1 clay bins.,of the high frequency variability in this band by binning the light curve in 1 day bins. + In this way. the correlation between Iluctuations on time-scales longer than a dav in both bands becomes clearer.," In this way, the correlation between fluctuations on time-scales longer than a day in both bands becomes clearer." + We caleulated the DCE between the 1-day binned. X-rays and the V and B band intensive [ieht curves., We calculated the DCF between the 1-day binned X-rays and the V and B band intensive light curves. + The significance of the correlation was estimated as above and the central peak of the DCE was higher than of the 2000 simulated DCEs for all light curve pairs., The significance of the correlation was estimated as above and the central peak of the DCF was higher than of the 2000 simulated DCFs for all light curve pairs. + The intensive-sampling DCE is shown in Fig., The intensive-sampling DCF is shown in Fig. + 7. together with the significance level curves. in this case we show the X-ray vs V band but note that the X-ray vs D band DCE is virtually. identical.," \ref{ccf_V_int} together with the significance level curves, in this case we show the X-ray vs V band but note that the X-ray vs B band DCF is virtually identical." + We note that the X-ravs retain much more short time-scale variability power than the optica bands even after binning the X-ray data in 1-dav bins., We note that the X-rays retain much more short time-scale variability power than the optical bands even after binning the X-ray data in 1-day bins. + Although the light curves are significantly: correlated. the CCE peak only reaches values 70.7. indicating that par of the variability in X-ray and optical bands is incoherent. which makes the delay harder to see directly from the leh curves.," Although the light curves are significantly correlated, the CCF peak only reaches values $\sim$ 0.7, indicating that part of the variability in X-ray and optical bands is incoherent, which makes the delay harder to see directly from the light curves." + A first elance at Fig., A first glance at Fig. + 3. seems to indicate that the optical bands are leacing the N-ravs by ~10 days because of the sharp drop in Lux in both bands around the middle of 1e light. curve., \ref{intensive} seems to indicate that the optical bands are leading the X-rays by $\sim 10$ days because of the sharp drop in flux in both bands around the middle of the light curve. + Phe CCE analysis. however. reveals that the correlation at that lag only reaches a value of ~0.5 and tha it is not significant.," The CCF analysis, however, reveals that the correlation at that lag only reaches a value of $\sim 0.5$ and that it is not significant." + The only significant peak in the CCE is at positive lag values. with optical bands lageing. which make the overall intensive light. curves match better.," The only significant peak in the CCF is at positive lag values, with optical bands lagging, which make the overall intensive light curves match better." + We note that the significant peak in the CCE at very small lag comes from the low amplitude X-ray/optical Luctuations. as shown in Fig. S.," We note that the significant peak in the CCF at very small lag comes from the low amplitude X-ray/optical fluctuations, as shown in Fig. \ref{norm_lcs}." + ‘Time delays between the different light cures were estimated from the centroid of the central peak in the respective correlation functions., Time delays between the different light cures were estimated from the centroid of the central peak in the respective correlation functions. + The centroid was calculated: as the weighted average of DCE values above of the DCE maximum., The centroid was calculated as the weighted average of DCF values above of the DCF maximum. + The errors were calculated using the bootstrap method. of Petersonctal.(1998). by selecting randomly of the points in each light curve and recording the lag centroid of the resulting DCE., The errors were calculated using the bootstrap method of \cite{bootstrap} by selecting randomly of the points in each light curve and recording the lag centroid of the resulting DCF. + We repeated this procedure 2000 times for cach pair of light curves to measure the mecian and spread of centroid. values., We repeated this procedure 2000 times for each pair of light curves to measure the median and spread of centroid values. + “Phe errors. quoted correspond to the limits of the distribution of centroid values on either side of the median., The errors quoted correspond to the limits of the distribution of centroid values on either side of the median. + The time lags from the long term light curves are Tm6.6(5 days between X-ray and B. 7=5.855 between X-ray and V and 7=0.3i between D ancl V. short. intensively sampled data produced lags of 7=5. tween. N-ravs and D. 726.3275m between N-ravs and V. and 70.4Ll75 between D and. V.; All the lag measurements are summarised in Table 4.1.. positive lag values indicate ügher energy. band Leading.," The time lags from the long term light curves are $\tau=6.6^{+7.2}_{-6.0}$ days between X-ray and B, $\tau=5.8^{+6.2}_{-3.9}$ between X-ray and V and $\tau=0.3^{+3.5}_{-2.4}$ between B and V. The short, intensively sampled data produced lags of $\tau=5.7^{+2.6}_{-2.5}$ between X-rays and B, $\tau=6.3^{+2.7}_{-3.1}$ between X-rays and V, and $\tau=0.4^{+1.1}_{-1.2}$ between B and V. All the lag measurements are summarised in Table \ref{T1}, positive lag values indicate higher energy band leading." + In all cases the lags from the ong and short term light curves are consistent., In all cases the lags from the long and short term light curves are consistent. + Both. V and D bands lag the N-ravs significantlv. from the intensively sampled light curves we measure these lags to be at least 3 and not more than 9 cays long.," Both, V and B bands lag the X-rays significantly, from the intensively sampled light curves we measure these lags to be at least 3 and not more than 9 days long." + The V and D band luctuations are simultaneous within our tinie-resolution. with a delay of V behind B between -0.8 and. 1.5 clays.," The V and B band fluctuations are simultaneous within our time-resolution, with a delay of V behind B between -0.8 and 1.5 days." +to the Local Standard of Rest.,to the Local Standard of Rest. + Errors are formal lo value for the model of the Gaussian line shape., Errors are formal $\sigma$ value for the model of the Gaussian line shape. + AIL the lines were well Lt with more than one Gaussian function. which very likely indicates the. presence of several components or/anc spectral wings. usually signatures of outllows.," All the lines were well fit with more than one Gaussian function, which very likely indicates the presence of several components or/and spectral wings, usually signatures of outflows." +" In Table 2 we present Via. and V,,;,. indicating the respective tota widths of the spectra considering all the components. anc {νο, the intensity integrated over the whole profile."," In Table \ref{lines2} we present $_{max}$ and $_{min}$, indicating the respective total widths of the spectra considering all the components, and $\int{T_{mb} dv}$, the intensity integrated over the whole profile." + The J=32 spectrum presented in Fig., The J=3–2 spectrum presented in Fig. + 4 shows a double peak structure like with a main component centerec at ~54.2 and a loss intense component centerec at ~48.7, \ref{spec00} shows a double peak structure like with a main component centered at $\sim$ 54.2 and a less intense component centered at $\sim$ 48.7. + rpPhe J=8B.2 spectrum presents similar features., The J=3–2 spectrum presents similar features. + We conclude that these lines present an absorption dip at ~51.5 which separates both mentioned velocity components. showing that the lines are self-absorbed as it is usually found towards star-forming regions (Johnstoneetal.2003:Buckle2010:Or-οσαetal. 2010).," We conclude that these lines present an absorption dip at $\sim$ 51.5 which separates both mentioned velocity components, showing that the lines are self-absorbed as it is usually found towards star-forming regions \citep{johnstone03,buckle10,ortega10}." +. Phe velocity of the mentioned and dip is coineident (within the errors) with the central velocities of the SiO (54). HECO (382). and. CIL;OLL (52.3 41.3) lines observed towards the center of EGOg35 by Cyganowskietal.(2009) and with the CS J=76 main component reported. in this work.," The velocity of the mentioned and dip is coincident (within the errors) with the central velocities of the SiO (5–4), $^{13}$ $^{+}$ (3–2), and $_{3}$ OH $_{2,3}$ $_{1,3}$ ) lines observed towards the center of EGOg35 by \citet{cyga09} and with the CS J=7–6 main component reported in this work." + “Pherelore. we conclude hat v 251.5 is the velocity of the ambient gas. and he other reported components (see Table 1)) may be related to outllows or/and high velocity material.," Therefore, we conclude that v $\sim$ 51.5 is the velocity of the ambient gas, and the other reported components (see Table \ref{lines}) ) may be related to outflows or/and high velocity material." + In Section 3.2 we analyse this contention., In Section \ref{secoutflow} we analyse this contention. + ltegardüing the J=43 emission. the profiles towards the center of the surveyed region present a dip at v —54 (seo Fig.," Regarding the $^{+}$ J=4–3 emission, the profiles towards the center of the surveyed region present a dip at v $\sim54$ (see Fig." + 2 bottom. and Fig. 4)).," \ref{obs1} bottom, and Fig. \ref{spec00}) )." + Cvganowski presented a single point observation of LLCO J=43 towards EGOg35., \citet{cyga09} presented a single point observation of $^{13}$ $^{+}$ J=4–3 towards EGOg35. + hey. report. that the LECO , They report that the $^{13}$ $^{+}$ +This explains the extremely high infrared luminosity implied by its detection in the44.15 Paint Source Catalogue.,This explains the extremely high infrared luminosity implied by its detection in the Faint Source Catalogue. + We stress thatcorreeHions For lensing have. been ⋜↧↓≻↓≻∐⋖⋅∠⇂⊲↓⊔↿↓⊔⋅≼∼⊔↓⋅↓⋅∢⊾⊔↿∖∖⋎∪↓⋅↳⊳⇂⋅∪↓⋅⇂↓∏⊳∖↕⊳∖≼↛∪⊔↓↓≻↓⋖⋅⇀∖⋜⋯∠⇂⊔↓⋯⇂⋖⋅↓− dependent.," We stress that for lensing have been applied in the current work, for this is complex and model-dependent." + However. this important. issue. will be tackled in quantitative detail in a future paper (Prickles et al.," However, this important issue will be tackled in quantitative detail in a future paper (Priddey et al.," + in prep.).," in prep.)," + where we present a detailed statistical analysis of all recent JCMT/SCUDA. and LRAAL/MAMBO. high-redshift⋅ sar ο...at, where we present a detailed statistical analysis of all recent JCMT/SCUBA and IRAM/MAMBO high-redshift quasar data. +i In this paper. we have presented the first results from a targetted SCUBAup survey of⋅ optically-Iuminous. (Mg« 27.5). radio-quict quasars at z~2.," In this paper, we have presented the first results from a targetted SCUBA survey of optically-luminous $M_B<-27.5$ ), radio-quiet quasars at $z\sim2$." + This is à continuation of the SCUBA Bright Quasar Survey whose preliminary results. at z9d. were reported by bsaak et al. (," This is a continuation of the SCUBA Bright Quasar Survey whose preliminary results, at $z>4$, were reported by Isaak et al. (" +2002).,2002). + The present data confirm the presence of a larec scatter in the correlation between submim ancl optica ο... despite having minimized the errors in measurement of the latter.," The present data confirm the presence of a large scatter in the correlation between submm and optical luminosity, despite having minimized the errors in measurement of the latter." + Comparing the z>4 and z«3 datasets shows tha there is no evidence for a variation of submm properties of luminous quasars across this redshift range. once one has allowed for a A-correction appropriate for cool. isotherma dust.," Comparing the $z>4$ and $z<3$ datasets shows that there is no evidence for a variation of submm properties of luminous quasars across this redshift range, once one has allowed for a $K$ -correction appropriate for cool, isothermal dust." + However. there is a suggestion that the characteristic subnim luminosity increases with redshift between 2=1.5 and z=3.," However, there is a suggestion that the characteristic submm luminosity increases with redshift between $z=1.5$ and $z=3$." + We note that a companion survey. carried out a 1.2mm with the ALAAIBO array on the HUAM 30m telescope. reaches similar conclusions (Omont et al.," We note that a companion survey, carried out at 1.2mm with the MAMBO array on the IRAM 30m telescope, reaches similar conclusions (Omont et al." + 2002)., 2002). + In forthcoming papers. we shall presen multiwavelength follow-up of bright sources. from. the present sample. results of comparative studies to improve the redshift coverage. detailed: statistical analysis of 7200 high-redshift’ quasars observed. at (sub)mm. wavelengths. and astrophysical interpretation of the findings.," In forthcoming papers, we shall present multiwavelength follow-up of bright sources from the present sample, results of comparative studies to improve the redshift coverage, detailed statistical analysis of $>$ 200 high-redshift quasars observed at (sub)mm wavelengths, and astrophysical interpretation of the findings." + For support through the period during which the bulk of his work was carried. out. RSP and WO thank PPARC and ROM thanks the Roval Society.," For support through the period during which the bulk of this work was carried out, RSP and KGI thank PPARC and RGM thanks the Royal Society." + We are grateful to he JACI stalf anc those JCAIL observers. their projects displaced. by poor weather. who gathered. data for us in allback mode.," We are grateful to the JACH staff and those JCMT observers, their projects displaced by poor weather, who gathered data for us in fallback mode." + The JCMT is operated by JAC. Lilo. on »half of the parent organisations of the Particle Physics and Astronomy Research Council in the Ulx. the National tescarch Council in Canada and the Scientific Rescarch Organisation of the Netherlands.," The JCMT is operated by JAC, Hilo, on behalf of the parent organisations of the Particle Physics and Astronomy Research Council in the UK, the National Research Council in Canada and the Scientific Research Organisation of the Netherlands." + We thank the anonymous referee for constructive comments., We thank the anonymous referee for constructive comments. +and the location of rich groups with at least 30 member galaxies.,and the location of rich groups with at least 30 member galaxies. + The middle panels show the clumpiness Vs vs. the mass fraction mf for a whole mass fraction interval from 0 to 1. and the right panels the shapefinder’s (A).K>) curve (the morphological signature) for a supercluster.," The middle panels show the clumpiness $V_3$ vs. the mass fraction $mf$ for a whole mass fraction interval from 0 to 1, and the right panels the shapefinder's $(K_1,K_2)$ curve (the morphological signature) for a supercluster." + The mass fraction increases anti-clockwise along the curves., The mass fraction increases anti-clockwise along the curves. + In these panels the value of mass fraction mf=0.7 is marked — at this value the morphological signature of rich superclusters changes., In these panels the value of mass fraction $mf =0.7$ is marked – at this value the morphological signature of rich superclusters changes. + We will classify our superclusters as spiders. multispiders. filaments. and multibranching filaments on the basis of their morphological information and visual appearance.," We will classify our superclusters as spiders, multispiders, filaments, and multibranching filaments on the basis of their morphological information and visual appearance." + Often superclusters are of intermediate type between these main types. hence for some superclusters our classification is a suggestion only.," Often superclusters are of intermediate type between these main types, hence for some superclusters our classification is a suggestion only." + We begin with the two richest superclusters from our sample (Fig. 9))., We begin with the two richest superclusters from our sample (Fig. \ref{fig:scl12694}) ). + For these two superclusters the morphological signature (Fig. 9..," For these two superclusters the morphological signature (Fig. \ref{fig:scl12694}," + right panels) is plotted with symbols of the size proportional to the value of the fourth Minkowski functional Vi at a given mass fraction. to show how the morphological signature changes together with the changes in clumpiness. as described in Sect. 3.1..," right panels) is plotted with symbols of the size proportional to the value of the fourth Minkowski functional $V_3$ at a given mass fraction, to show how the morphological signature changes together with the changes in clumpiness, as described in Sect. \ref{sect:mink}." + Here we do not mark the value of mass fraction if.=0.7. for clarity.," Here we do not mark the value of mass fraction $mf=0.7$, for clarity." + at a distance of 256 us the richest member of the SGW(??)., at a distance of 256 is the richest member of the SGW. +. This supercluster contains nme Abell clusters. the largest number in our sample.," This supercluster contains nine Abell clusters, the largest number in our sample." + Five of these are also X-ray clusters(?)., Five of these are also X-ray clusters. +. The richest. of them. A1750. is a merging X-ray cluster(?).," The richest of them, A1750, is a merging X-ray cluster." +. The morphology of SCI 061 resembles a multibranching filament with the maximum value of the fourth Minkowski functional 13. and the ratio of the shapefinders Kj/K»=0.28. one of the lowest in our catalogue (Fig. 9..," The morphology of SCl 061 resembles a multibranching filament with the maximum value of the fourth Minkowski functional $V_{3,\mathrm{max}} = +13$ , and the ratio of the shapefinders $K_1$ $K_2 = 0.28$, one of the lowest in our catalogue (Fig. \ref{fig:scl12694}," + upper row. and Table 1)). (," upper row, and Table \ref{tab:scldata}) ). (" +the Corona Borealis supercluster) at a distance of 215 us the second in richness among our sample.,the Corona Borealis supercluster) at a distance of 215 is the second in richness among our sample. + This system contains three Abell clusters (42067. A2065. and A2089). and is a member of the dominant supercluster plane (?).," This system contains three Abell clusters (A2067, A2065, and A2089), and is a member of the dominant supercluster plane ." +. The distribution of galaxies in the sky in SCI 094 is plotted in Fig., The distribution of galaxies in the sky in SCl 094 is plotted in Fig. + 9. (lower row. left panel).," \ref{fig:scl12694} (lower row, left panel)." + The maximum value of the fourth Minkowski functional of the Corona Borealis supercluster Vi;=10. and the ratio of the shapefinders Kj/K» =0.28 (Fig. 9..," The maximum value of the fourth Minkowski functional of the Corona Borealis supercluster $V_{3,\mathrm{max}} = 10$, and the ratio of the shapefinders $K_1$ $K_2 = +0.28$ (Fig. \ref{fig:scl12694}," + the middle and right panels of the lower row. and Table 1).," the middle and right panels of the lower row, and Table \ref{tab:scldata}) )." + Morphologically SCI 094 is a multispider with a number of clusters connected by low density filaments. with ar overall very elongated shape that resembles a horse-shoe. with the merging X-ray cluster A2065 at the top(2).," Morphologically SCl 094 is a multispider with a number of clusters connected by low density filaments, with an overall very elongated shape that resembles a horse-shoe, with the merging X-ray cluster A2065 at the top." +. SC] 094 has been studied by?.. who found that the core of this system probably has started to collapse.," SCl 094 has been studied by, who found that the core of this system probably has started to collapse." + Numerical simulations show that such collapsing cores in superclusters are rare(?)., Numerical simulations show that such collapsing cores in superclusters are rare. +. proposed that SCI 094 may merge with several surrounding superclusters in the future., proposed that SCl 094 may merge with several surrounding superclusters in the future. + In last years interest in the Corona Borealis supercluster region has grown because of the discovery of the CMB cold spot in its direction., In last years interest in the Corona Borealis supercluster region has grown because of the discovery of the CMB cold spot in it's direction. + This may be partly caused by the warm-hot diffuse gas in the supercluster filaments between the clusters. or by some undiscovered distant clustertherein).," This may be partly caused by the warm-hot diffuse gas in the supercluster filaments between the clusters, or by some undiscovered distant cluster." +.. are also members of the Corona Borealis supercluster., are also members of the Corona Borealis supercluster. +" The morphology of SCI 362 resembles a simple spider with the ratio of the shapefinders Kj/K» =1.0. while that of SCI 366 resembles a multibranching filament with the maximum value of the fourth Minkowski functional V3,4,=4. and the ratio of the shapefinders K\/K> =0.38 (Fig. D2))."," The morphology of SCl 362 resembles a simple spider with the ratio of the shapefinders $K_1$ $K_2 = 1.0$, while that of SCl 366 resembles a multibranching filament with the maximum value of the fourth Minkowski functional $V_{3,\mathrm{max}} = 4$, and the ratio of the shapefinders $K_1$ $K_2 = 0.38$ (Fig. \ref{fig:sclapp2}) )." + contains two rich Abell clusters. A2142 and A2149. both of them are X-ray sources (Table 2)).," contains two rich Abell clusters, A2142 and A2149, both of them are X-ray sources (Table \ref{tab:sclabell}) )." + Chandra observations have revealed that A2142 is probably still merging(?)., Chandra observations have revealed that A2142 is probably still merging. +. SCL 001 is located in a region with a dense concentration of superclusters. close to SCI O11 and SCI 094.," SCl 001 is located in a region with a dense concentration of superclusters, close to SCl 011 and SCl 094." + All these systems form a part of the dominant supercluster plane., All these systems form a part of the dominant supercluster plane. + At the location of SCI 001 the luminosity density ts the highest in the whole SDSS survey: this ts probably at least partly because of the rich X-ray cluster A2142., At the location of SCl 001 the luminosity density is the highest in the whole SDSS survey; this is probably at least partly because of the rich X-ray cluster A2142. + The morphology of SCI 001 resembles a filament where clusters are located almost along a straight line (the 3D model on our web pages shows this best)., The morphology of SCl 001 resembles a filament where clusters are located almost along a straight line (the 3D model on our web pages shows this best). +" The maximum value of the fourth Minkowski functional for SC] 001. Vi,44,=2 and the ratio of the shapefinders ΚΙΝ.=0.48 (Fig."," The maximum value of the fourth Minkowski functional for SCl 001 $V_{3,\mathrm{max}} = 2$ and the ratio of the shapefinders $K_1$ $K_2 = 0.48$ (Fig." + 10. and Table 1))., \ref{fig:scl001} and Table \ref{tab:scldata}) ). + at a distance of 234 ccontams two Abell clusters. A2040 and A2028. which are members of different superclusters in EO].," at a distance of 234 contains two Abell clusters, A2040 and A2028, which are members of different superclusters in E01." + The maximum value of the fourth Minkowski functional Vi;=3 (Fig. 10.," The maximum value of the fourth Minkowski functional $V_{3,\mathrm{max}} = 3$ (Fig. \ref{fig:scl001}," + middle row). the ratio of the shapefinders Kj/K»=0.92.," middle row), the ratio of the shapefinders $K_1$ $K_2 = 0.92$." + The morphology of SCI 011 resembles a sparse multispideror multibranching filament with a quite uniform density (as suggested by the low values of the fourth Minkowski functional Vi for a wide mass fraction interval)., The morphology of SCl 011 resembles a sparse multispideror multibranching filament with a quite uniform density (as suggested by the low values of the fourth Minkowski functional $V_3$ for a wide mass fraction interval). + SC] 011 belongs to the same supercluster complex as SCI 001 (Fig. 3))., SCl 011 belongs to the same supercluster complex as SCl 001 (Fig. \ref{fig:sclid}) ). + at a distance of 230 iis the second richest member of the SGW., at a distance of 230 is the second richest member of the SGW. + SCI 024 contains two Abell clusters. Al424 and AISI6.," SCl 024 contains two Abell clusters, A1424 and A1516." +" Its morphology resembles a multispider with the maximum value of the fourth Minkowski functional Vi,=5 and the ratioof the shapefinders ΚΚ.=0.48 (Fig. 10.."," Its morphology resembles a multispider with the maximum value of the fourth Minkowski functional $V_{3,\mathrm{max}} = 5$ and the ratioof the shapefinders $K_1$ $K_2 = 0.48$ (Fig. \ref{fig:scl001}, ," + lower row)., lower row). + The, The +1998: the mechanism is named. svnchro-curvature radiation by the authors) suggest that the curvature of magnetic field lines plavs an important role in the spectral slope of the svnchrotron spectrum. ie. at the high-cnerey portion of the SED.,"; the mechanism is named 'synchro-curvature radiation' by the authors) suggest that the curvature of magnetic field lines plays an important role in the spectral slope of the synchrotron spectrum, i.e. at the high-energy portion of the SED." + Reeenth. such a new mechanism was used to explain. successfully the high-cnerey excess of several gamma-ray bursts (CiliDs: Deng.Nia&Liu 2005)) the broad-band. emission of which may also originate from relativistic jets.," Recently, such a new mechanism was used to explain successfully the high-energy excess of several gamma-ray bursts (GRBs; \citealt{Deng05}) ) the broad-band emission of which may also originate from relativistic jets." + Since standard svnchrotron models. show systematic deviation from. the observed. X-ray spectra. of AINT jet knots. it would. be interesting also to explore the ellect of curvature of magnetic field lines on the broad-band SED of the AIST jet and other objects in. possible future work.," Since standard synchrotron models show systematic deviation from the observed X-ray spectra of M87 jet knots, it would be interesting also to explore the effect of curvature of magnetic field lines on the broad-band SED of the M87 jet and other objects in possible future work." + We are grateful to Dr. ES. Perlman for fruitfuldiscussions and for supplying data of AIST jet as well as synchrotron model fitting code written by Dr. ¢ απ., We are grateful to Dr. E.S. Perlman for fruitful discussions and for supplying data of M87 jet as well as synchrotron model fitting code written by Dr. C. Carilli. + The authors thank a lot the referee. for very careful reading and valuable comments and suggestions., The authors thank a lot the referee for very careful reading and valuable comments and suggestions. + Phe authors also thank Dr. LL. Marshall. YoY. Zhou. J.M. Bai and D.M. Meng for helpful discussions.," The authors also thank Dr. H.L. Marshall, Y.Y. Zhou, J.M. Bai and D.M. Meng for helpful discussions." + οος Wang acknowledges Dr. J. Ixataoka for continuous help on jet. physics., C.C. Wang acknowledges Dr. J. Kataoka for continuous help on jet physics. + This work is supported by Natural Science Foundation of China (NSEC) through erant. NSEC 10673010. and NSEC 10473013., This work is supported by Natural Science Foundation of China (NSFC) through grant NSFC 10673010 and NSFC 10473013. + CLC. Wang acknowledges also support from Start-up Func of USTC., C.C. Wang acknowledges also support from Start-up Fund of USTC. + This research has made use of NASA's Astrophysics Data Systen.., This research has made use of NASA's Astrophysics Data System. +While the spectroscopicallv identified: galaxy DELP? 41013534 has the smallest angular separation [rom this quasar sightline. eight other likely ealaxies are identified in the DEEP2 photometric catalogue within 100 h.tkpe of the same absorber. and three of these are detected within a projected separation of GO tkpce.,"While the spectroscopically identified galaxy DEEP2 41013534 has the smallest angular separation from this quasar sightline, eight other likely galaxies are identified in the DEEP2 photometric catalogue within 100 $^{-1}$ kpc of the same absorber, and three of these are detected within a projected separation of 60 $^{-1}$ kpc." + Due to the detection of more than one object within this radius. we cannot sav with complete certainty that the spectroscopically observed ealaxy is sinely related. to this absorber.," Due to the detection of more than one object within this radius, we cannot say with complete certainty that the spectroscopically observed galaxy is singly related to this absorber." + However. the nearly exact. match in redshift ancl small projected separation makes a strong argument for a physical link between the spectroscopic galaxy and absorption complex.," However, the nearly exact match in redshift and small projected separation makes a strong argument for a physical link between the spectroscopic galaxy and absorption complex." + Η we assume that this absorber and galaxy are associated. the physical characteristics of the galaxy spectrum can provide insight into the origin of the strong absorption complex.," If we assume that this absorber and galaxy are associated, the physical characteristics of the galaxy spectrum can provide insight into the origin of the strong absorption complex." + The spectrum of galaxy. ΟΙ 41013534 exhibits typical earlv-type characteristics., The spectrum of galaxy DEEP2 41013534 exhibits typical early-type characteristics. + We find no observable emission lines in this spectrum that may be attributed to active star formation., We find no observable emission lines in this spectrum that may be attributed to active star formation. + Aceditionally. the rest frame U-B color of this galaxy is 1.5. placing it firmly on the red sequence.," Additionally, the rest frame U-B color of this galaxy is 1.5, placing it firmly on the red sequence." + Due to the redshift’ of this galaxy and the spectral coverage of the DEEP2 survey. we are unable to determine whether this galaxy exhibits evidence of intrinsic. bluc-shiltecl absorption. which has been observed in many star-forming DIZEDP2 galaxies (Weineretal. 2009).," Due to the redshift of this galaxy and the spectral coverage of the DEEP2 survey, we are unable to determine whether this galaxy exhibits evidence of intrinsic, blue-shifted absorption, which has been observed in many star-forming DEEP2 galaxies \citep{Weiner09}." +". Llowever. the absence of any other clear star-formation indicators in this galaxy implies that we cannot clirecthy link the strong coincident absorption with a measurable rate of ongoing star formation activity in this Case,"," However, the absence of any other clear star-formation indicators in this galaxy implies that we cannot directly link the strong coincident absorption with a measurable rate of ongoing star formation activity in this case." + If we consider a scenario in which the absorbing gas originated. in this ealaxy during an earlier. period of star formation activity. we can roughly constrain the time since the original burst.," If we consider a scenario in which the absorbing gas originated in this galaxy during an earlier period of star formation activity, we can roughly constrain the time since the original burst." + Assuming that it is emitted isotropically. gas with an outllow velocity of 400 km st. which is typical for the star-forming galaxies measured. by Weineretal.(2009).. would take ~100 Myr to travel the comoving distance of 37 *kpe to the quasar sightline.," Assuming that it is emitted isotropically, gas with an outflow velocity of 400 km $^{-1}$, which is typical for the star-forming galaxies measured by \citet{Weiner09}, would take $\sim$ 100 Myr to travel the comoving distance of 37 $^{-1}$ kpc to the quasar sightline." + Stellar absorption features in the stacked spectra of similar quiescent galaxies in. DEEP2 with 0.7zzz1l indicate that these galaxies have an average age of —1 Gyr (Schiavonetal. 2006)., Stellar absorption features in the stacked spectra of similar quiescent galaxies in DEEP2 with $\la$ $\la$ 1 indicate that these galaxies have an average age of $\sim$ 1 Gyr \citep{Schiavon06}. +. Considering that we are unable to constrain the specific velocity of outlows from such a star formation event in this galaxy. the estimated age of the galaxy. appears to be roughly consistent with the time required for the gas to reach the separation at which it is observed.," Considering that we are unable to constrain the specific velocity of outflows from such a star formation event in this galaxy, the estimated age of the galaxy appears to be roughly consistent with the time required for the gas to reach the separation at which it is observed." + So. while we are unable to directly connect the observed. absorption in this close pair to ongoing star formation. we also cannot rule out a scenario in which the eas was emitted curing an earlier period of star formation activity 1 Cyr in the past.," So, while we are unable to directly connect the observed absorption in this close pair to ongoing star formation, we also cannot rule out a scenario in which the gas was emitted during an earlier period of star formation activity $\sim$ 1 Gyr in the past." + We emphasize that this single absorber-galaxy pair is a perilously small sample from which to draw. conclusions regarding the average star-formation properties of host galaxies., We emphasize that this single absorber-galaxy pair is a perilously small sample from which to draw conclusions regarding the average star-formation properties of host galaxies. + However. givenn the growing collection of literature linking strong absorbers with active star formation. particularly at higher redshifts. we found. the contradiction presented by this absorber-galaxy pair to be at least somewhat provocative and worthy of discussion.," However, given the growing collection of literature linking strong absorbers with active star formation, particularly at higher redshifts, we found the contradiction presented by this absorber-galaxy pair to be at least somewhat provocative and worthy of discussion." + The incidence of Mell absorption in close proximity to galaxies provides an estimate of the cold. gas covering fraction. f.. of galaxy haloes.," The incidence of absorption in close proximity to galaxies provides an estimate of the cold gas covering fraction, $f_{c}$, of galaxy haloes." +" Measurements. of f, determined for a range of comoving separations allow us to constrain the elfective gas radius. &,. which is critical for unclerstancling the gas physics in galaxy evolution as well as for properly parameterizing hvdrodynamic simulations."," Measurements of $f_{c}$ determined for a range of comoving separations allow us to constrain the effective gas radius, $R_{g}$, which is critical for understanding the gas physics in galaxy evolution as well as for properly parameterizing hydrodynamic simulations." + Among the full galaxy sample of DIZIEEP2. 63 galaxies are detected within a projected distance of 200 !pe [rom a SDSS quasar sightline in which at the redshift: of the galaxy would. be observable outside of the Lyman-a forest.," Among the full galaxy sample of DEEP2, 63 galaxies are detected within a projected distance of 200 $^{-1}$ kpc from a SDSS quasar sightline in which at the redshift of the galaxy would be observable outside of the $\alpha$ forest." + I£ we restrict this number to quasars having observed magnitudes of m; x20. the approximate SNR. limit to which we can reliably detect with WW)???LOGAN at the mecian redshift of our sample. 41 galaxies remain.," If we restrict this number to quasars having observed magnitudes of $_{i}\leq$ 20, the approximate SNR limit to which we can reliably detect with $_{r}^{\lambda2796}\ga$ at the median redshift of our sample, 41 galaxies remain." + For cach incluclecl quasar-galaxy pair we search for in our List of 21 absorbers presented in Table 1., For each included quasar-galaxy pair we search for in our list of 21 absorbers presented in Table 1. + Allowing for a redshift separation of [syaZub«0.008. we count the number of absorber-galaxy. pairs and compare to the total number of observable quasar-ealaxy pairs available in order to compute ο as a function of impact parameter in the rest frame of the absorbers.," Allowing for a redshift separation of $|z_{gal}-z_{abs}|<$ 0.008, we count the number of absorber-galaxy pairs and compare to the total number of observable quasar-galaxy pairs available in order to compute $f_{c}$ as a function of impact parameter in the rest frame of the absorbers." + The width of the redshift bin in this calculation is equivalent to the scale of the maximum outflow. velocities detected. in Weineretal.(2009) (1000. km +) at the maximum redshift of galaxies in DEEP2. z-1.4.," The width of the redshift bin in this calculation is equivalent to the scale of the maximum outflow velocities detected in \citet{Weiner09} (1000 km $^{-1}$ ) at the maximum redshift of galaxies in DEEP2, z=1.4." +" We measure the WAZ?Z0.6(Tl covering fraction for DIZIZP2 galaxies to he f, —0.5 (1 detected absorber in a sample of 2 quasar-galaxy pairs) on scales of 2060 hi.! pe. which decreases rapidly with increasing impact parameter."," We measure the $_{r}^{\lambda2796}\ga$ covering fraction for DEEP2 galaxies to be $f_{c}$ =0.5 (1 detected absorber in a sample of 2 quasar-galaxy pairs) on scales of 20–60 $^{-1}$ kpc, which decreases rapidly with increasing impact parameter." + In the range 20100 tkpe. we find a covering fraction of f.—0.125z:154 (1 absorber detected. among S possible quasar-galaxy pairs). and. between 100 and 200 tkpe. f. drops to zero (measured from a ssumple of 33 possible quasar-galaxy pairs).," In the range 20–100 $^{-1}$ kpc, we find a covering fraction of $f_{c}$ $\pm^{0.17}_{0.103}$ (1 absorber detected among 8 possible quasar-galaxy pairs), and between 100 and 200 $^{-1}$ kpc, $f_{c}$ drops to zero (measured from a sample of 33 possible quasar-galaxy pairs)." + Due to the small size of our statistical sample. we estimate the Le errors on these measurements using the prescriptions of Helene(1984).. which assumes data with a Poisson distribution.," Due to the small size of our statistical sample, we estimate the $\sigma$ errors on these measurements using the prescriptions of \citet{Helene84}, which assumes data with a Poisson distribution." + Lt is important to emphasize that our covering fraction estimates are driven by the detection of the single absorber. which is discussed in the previous section.," It is important to emphasize that our covering fraction estimates are driven by the detection of the single absorber, which is discussed in the previous section." + Because we co not detect any. galaxyv-absorber pairs with larger projected separations. it is fair to speculate that the typical effective eas radius of the DELP? sample may be as small as —40 h tkpe.," Because we do not detect any galaxy-absorber pairs with larger projected separations, it is fair to speculate that the typical effective gas radius of the DEEP2 sample may be as small as $\sim$ 40 $^{-1}$ kpc." + The sample we examine is. however. undesirably small and. limited. by our conservative cuts on the SNR. οἱ the SDSS quasar spectra.," The sample we examine is, however, undesirably small and limited by our conservative cuts on the SNR of the SDSS quasar spectra." + The obscuration of foreground. galaxies by the brighter background quasar is commonly evoked to. explain. the lack of detected. absorber-galaxy pairs with small angular separations., The obscuration of foreground galaxies by the brighter background quasar is commonly evoked to explain the lack of detected absorber-galaxy pairs with small angular separations. + Investigating the angular incidence of DELP? galaxiesaround SDSS quasars with detected: absorption. we found no galaxies within (equivalent to a comoving distance of 30 προ abo z=1).," Investigating the angular incidence of DEEP2 galaxiesaround SDSS quasars with detected absorption, we found no galaxies within (equivalent to a comoving distance of 30 $^{-1}$ kpc at z=1)." + This finding indicates that the photometrie DEEP2 catalogues. are incomplete, This finding indicates that the photometric DEEP2 catalogues are incomplete +will certainly. provide grounds for extensive studies based on CLE/CON.,will certainly provide grounds for extensive studies based on CLF/CON. +" The dillerent. parameters were allowed to vary within the ollowing ranges: 10x/og(M,: 15. 10fog(Mi)< 15. 10xlogMeus):15. 0.51.4$ ). + Artificially: high values have been noticed in fits to simulations as well (Conroyetal.2006). and occur for galaxy. samples at. high redshifts., Artificially high values have been noticed in fits to simulations as well \citep{con06} and occur for galaxy samples at high redshifts. + Phe lee error bars on the parameters are obtained with the MPELTE algorithm., The $\sigma$ error bars on the parameters are obtained with the MPFIT algorithm. + Figure 3 shows the number-weighted average halo mass. $, versus the redshift." + The svmbols with error. bars represent the various sub-samples selected from the VVDS., The symbols with error bars represent the various sub-samples selected from the VVDS. + The error. bars are obtained based on error. propagation formulas., The error bars are obtained based on error propagation formulas. + The point at the lowest redshift (2~0.1) is obtained from the SDSS using the best-fit HOD parameters from Zehavi et al. (, The point at the lowest redshift $z \sim 0.1$ ) is obtained from the SDSS using the best-fit HOD parameters from Zehavi et al. ( +2005).,2005). + The mass in this case was calculated using the Z model for the luminosity threshold sample having the same AZ clillerenee as the samples at higher redshift in the VWDS (where the dillerence in the r-band. for the SDSS has been converted to the band. Ubert et al.," The mass in this case was calculated using the Z model for the luminosity threshold sample having the same $M - M^*$ difference as the samples at higher redshift in the VVDS (where the difference in the r-band for the SDSS has been converted to the B-band, Ilbert et al." + 2005)., 2005). + Ht can be seen that the halo mass evolves and increases as one goes to lower redshifts., It can be seen that the halo mass evolves and increases as one goes to lower redshifts. + This is an indication of the halo mass growth due to the hierarchical aggregation of matter., This is an indication of the halo mass growth due to the hierarchical aggregation of matter. + We find that on average increases by 90% [rom redshift ~1 to ~0.5. showing that massive halos have a rapid accretion phase quite late on. similar to what is expected. (rom. N-body simulations (Wechsler et al.," We find that on average $$ increases by $~90\%$ from redshift $\sim 1$ to $\sim 0.5$, showing that massive halos have a rapid accretion phase quite late on, similar to what is expected from N-body simulations (Wechsler et al." + 2002)., 2002). + As shown in Wechsler ot al. (, As shown in Wechsler et al. ( +2002) the mass growth can be easily characterized bv the form M(z)=Moe ,2002) the mass growth can be easily characterized by the form $M(z) = M_0 e^{-\beta z}$. +The interesting coniparison with the addition of low redshift SDSS points gives a linear nüninium X7 fit o£; —1.9400.10 for the Z Model and 1.2.0920.04 for the PWZZ model., The interesting comparison with the addition of low redshift SDSS points gives a linear minimum $\chi^2$ fit of $\beta \sim 1.94 \pm 0.10$ for the Z Model and $\beta \sim 2.09 \pm 0.04$ for the TWZZ model. + This is to be compared o the predictions of the mass accretion history of halos in N-xdv. simulations and halos generated through PINOCCLIO (Monacoetal.2002:WechslerLi2007).. where 7ον0.62.," This is to be compared to the predictions of the mass accretion history of halos in N-body simulations and halos generated through PINOCCHIO \citep{mon02, wec02, li07}, where $\beta \sim 0.62$." + One can argue that the direct. comparison xtween data obtained from cillerent. rest-frame bands can x»: tricky and could in part lead to a slight boost in 2. even though necessary care has been taken in converting oa common rest-frame band.," One can argue that the direct comparison between data obtained from different rest-frame bands can be tricky and could in part lead to a slight boost in $\beta$, even though necessary care has been taken in converting to a common rest-frame band." + The latter is reflected in the value obtained for 3. using only the VVDS points loads to a smaller value (~—1.54(1.07)€0.13(0.57) for TWZZ (Z) model) albeit with larger error than that obtained [rom the extrapolation to smaller. redshifts. but. slightly more consistent with the results from simulations.," The latter is reflected in the value obtained for $\beta$, using only the VVDS points leads to a smaller value $\sim 1.54 (1.07)\pm 0.13 (0.57)$ for TWZZ (Z) model) albeit with larger error than that obtained from the extrapolation to smaller redshifts, but slightly more consistent with the results from simulations." + For samples at similar redshifts we can see that the number-weighted average halo mass increases with the luminosity threshold. of the sample reinforcing the notion that luminous galaxies occupy massive halos., For samples at similar redshifts we can see that the number-weighted average halo mass increases with the luminosity threshold of the sample reinforcing the notion that luminous galaxies occupy massive halos. + This is in agreement with results obtained [rom simulations etal.2006). and for LBGs (Ouchietal.2005:Lee 2006).," This is in agreement with results obtained from simulations \citep{con06} and for LBGs \citep{ouc05, lee06}." +. ligure 4. presents the evolution of the galaxy. satellite fraction. or the average number of satellite galaxies.," Figure \ref{Fig_Nvsz} presents the evolution of the galaxy satellite fraction, or the average number of satellite galaxies." + The illustrative reciprocal power law behaviour of the dataset shows relatively little change in the satellite fraction (always close to ~0.1 within 1.0) over the redshift range of z—0.5-, The illustrative reciprocal power law behaviour of the dataset shows relatively little change in the satellite fraction (always close to $\sim0.1$ within 1 $\sigma$ ) over the redshift range of z=[0.5-1.0]. + Over z=0.1-0.5] there is a sharper increase by a factor ~3 to the local SDSS value of 70.3., Over z=[0.1-0.5] there is a sharper increase by a factor $\sim$ 3 to the local SDSS value of $\sim$ 0.3. + The evolution is mainly accentuated bythe SDSSpoints. although the two lowest redshift VWDS points for the case of the Z model do hint towards an increase with lower recshifts.," The evolution is mainly accentuated bythe SDSSpoints, although the two lowest redshift VVDS points for the case of the Z model do hint towards an increase with lower redshifts." + LO is possible that the sharper upturn is once again caused by the complicated comparison between two different data surveys., It is possible that the sharper upturn is once again caused by the complicated comparison between two different data surveys. +Llowever. here again care has been taken to convert to the appropriate rest-frame band when making these comparisons and should,"However, here again care has been taken to convert to the appropriate rest-frame band when making these comparisons and should" +but the largest change in the line bisectors occurred for the intermediate nm = 4 or 5 modes.,but the largest change in the line bisectors occurred for the intermediate $m$ = 4 or 5 modes. + Particularly for emocdes the magnitude of the bisector variations peakecl sharply at m = 4-5 and declined toward lower and higher m-number., Particularly for g-modes the magnitude of the bisector variations peaked sharply at $m$ = 4-5 and declined toward lower and higher $m$ -number. + To investigate whether nonradial pulsations can account for the spectral variations of Aldcharan. theoretical spectral line profiles from a nonraclially pulsating star were calculated using a disk integration on a svnthetic star that was divided into 120 cells.," To investigate whether nonradial pulsations can account for the spectral variations of Aldebaran, theoretical spectral line profiles from a nonradially pulsating star were calculated using a disk integration on a synthetic star that was divided into $\times$ 120 cells." + Local line profiles for cach cell consisted of the Ti 16304. generated using 20 limb angles and a model atmosphere for a WI HE star tabulatecd in Bell et al. (, Local line profiles for each cell consisted of the Ti I generated using 20 limb angles and a model atmosphere for a K1 III star tabulated in Bell et al. ( +1976).,1976). + A stellar inclination of and a projected. rotational velocity of 3 were adopted in the modeling., A stellar inclination of and a projected rotational velocity of 3 were adopted in the modeling. + The latter is comparable to the projected. rotational velocity measured for this star (L1C93)., The latter is comparable to the projected rotational velocity measured for this star (HC93). + X macroturbulent velocity of 3 was also included in the calculation., A macroturbulent velocity of 3 was also included in the calculation. + The dispersion. ancl resolution for this synthetic data was the same as the actual data., The dispersion and resolution for this synthetic data was the same as the actual data. + Only sectoral modes (/ = m) were calculated as these should produce the largest RY and spectral variations., Only sectoral modes $l$ = $m$ ) were calculated as these should produce the largest RV and spectral variations. + In cach stellar cell the combined Doppler shift. due to stellar rotation. the macroturbulent velocity. aid. the pulsational velocity. was applied to a local Line profile prior to computing the integrated profile.," In each stellar cell the combined Doppler shift due to stellar rotation, the macroturbulent velocity, and the pulsational velocity was applied to a local line profile prior to computing the integrated profile." +" Phe contribution. in spherical coordinates. due to nonradial pulsations. of nonracdial pulsations with an amplitude V, is given by where 47"" is the associated. Legendre function. and k ds a constant of proportionality between the horizontal and vertical velocities."," The contribution, in spherical coordinates, due to nonradial pulsations, of nonradial pulsations with an amplitude $V_p$ is given by where $P_{\ell}^m$ is the associated Legendre function and $k$ is a constant of proportionality between the horizontal and vertical velocities." + This horizontal sealer is not a [ree parameter but is related to the frequcney of oscillations by: where AZ and & are the stellar mass and radius and σ is the pulsational frequency., This horizontal scaler is not a free parameter but is related to the frequency of oscillations by: where $M$ and $R$ are the stellar mass and radius and $\sigma$ is the pulsational frequency. + For p-miocles & is less than one. but is greater than unity for gmocdes.," For p-modes $k$ is less than one, but is greater than unity for g-modes." + In. 10908 a mass of 2.5 ÀJ. and a radius of 42 2. were used to calculate the period of the fundamental radial mode., In HC93 a mass of 2.5 $M_\odot$ and a radius of 42 $R_\odot$ were used to calculate the period of the fundamental radial mode. + These values along with a pulsation period of 50 davs vielc & & 6., These values along with a pulsation period of 50 days yield $k$ $\approx$ 6. + Figure 7 shows the predicted radial velocity. variation. as a function of m-number for nonradial pulsations that will also produce a peak-to-peak change in the velocity span of the bisector of 100. as required by Figure 4..," Figure \ref{fig:rvamp} shows the predicted radial velocity variation, as a function of $m$ -number for nonradial pulsations that will also produce a peak-to-peak change in the velocity span of the bisector of 100, as required by Figure \ref{fig:phase}." + The velocity span points for simulations were taken at the same flux level as the Alcdeharan measurements., The velocity span points for simulations were taken at the same flux level as the Aldebaran measurements. + Since the phase diagram of the velocity residuals shows no clear sinusoical variations at a 50-cay period. we have adopted the ris scatter of velocity residuals (after removal of the 643-clay component) as an upper limit to RW-amplituce for such a »eriod.," Since the phase diagram of the velocity residuals shows no clear sinusoidal variations at a 50-day period, we have adopted the rms scatter of velocity residuals (after removal of the 643-day component) as an upper limit to RV-amplitude for such a period." +" ""his rms scatter of about 651. which is marked with a horizontal dashed line in Figure. 7.. is significantly weer than the error of the racial velocity measurement which is about 15r20."," This rms scatter of about 65, which is marked with a horizontal dashed line in Figure \ref{fig:rvamp}, is significantly larger than the error of the radial velocity measurement which is about 15–20." + lt is not known whether the scatter in the RV residuals is due to the 50-day component of he variability of Aldebaran or other short-term variability. xu presently we shall assume the former. ," It is not known whether the scatter in the RV residuals is due to the 50-day component of the variability of Aldebaran or other short-term variability, but presently we shall assume the former. [" +Larson (1996) ound evidence for a L.s-day in her RV measurements for Aldebaran which may contribute to the scatter of our RV residuals.,Larson (1996) found evidence for a 1.8-day in her RV measurements for Aldebaran which may contribute to the scatter of our RV residuals. + There is no evidence for this period in either our jusector or RV measurements. but this is most likely due to he sparse sampling of our data]," There is no evidence for this period in either our bisector or RV measurements, but this is most likely due to the sparse sampling of our data.]" + It scems that the observed changes in the Esspectral line bisectors and the rms scatter of he racial velocity residuals are consistent with an mn = + nonracdial sectoral mode., It seems that the observed changes in the spectral line bisectors and the rms scatter of the radial velocity residuals are consistent with an $m$ = 4 nonradial sectoral mode. + Clearly. for an m = 2 or 3 mode o produce the observed. bisector variations this would also xoduce a large radial velocity which should be seen in the UN. resicuals.," Clearly, for an $m$ = 2 or 3 mode to produce the observed bisector variations this would also produce a large radial velocity which should be seen in the RV residuals." + In fact. the amplitude of such a mode would," In fact, the amplitude of such a mode would" +similar time span has also generated two bubbles.,similar time span has also generated two bubbles. + At z=0.6 this smaller halo reaches ~1/3 of the central cluster mass and merges with it violently., At $z=0.6$ this smaller halo reaches $\sim 1/3$ of the central cluster mass and merges with it violently. + The central Bills of these halos meree as well. increasing the mass of the most massive DII by 10b.TALL.," The central BHs of these halos merge as well, increasing the mass of the most massive BH by $\sim 10^9 \,h^{-1} +{\rm M}_\odot$." + FH can be seen that during this merger event the relie CR bubbles are significantlv. ρουος and displaced towards the right. in the direction from which the smaller halo was falling in.," It can be seen that during this merger event the relic CR bubbles are significantly perturbed and displaced towards the right, in the direction from which the smaller halo was falling in." + Finally. by comparing the left-hand panels to the hand panels in Fig. 4.0," Finally, by comparing the left-hand panels to the right-hand panels in Fig. \ref{Emaps}," + it can be seen that CR bubbles with a steeper power-law spectrum have in general similar morphologies to the à=2.1 case. but they show a somewhat smaller size ancl shorter survival time. as expected. given that Coulomb losses become more important [or a steeper spectrum.," it can be seen that CR bubbles with a steeper power-law spectrum have in general similar morphologies to the $\alpha=2.1$ case, but they show a somewhat smaller size and shorter survival time, as expected given that Coulomb losses become more important for a steeper spectrum." + In Figure 5.. we show radial profiles of gas density (first row) mass-weightoc tomperature (second. row). entropy (third LOW). and thermal pressure (last row) at. three cillerent epochs. 2=0.5. 0.2 and 0.0.," In Figure \ref{g676_profiles}, we show radial profiles of gas density (first row), mass-weighted temperature (second row), entropy (third row), and thermal pressure (last row) at three different epochs, $z=0.5$, $0.2$ and $0.0$." + The black continuous lines ave for the run with cooling anc star formation only. blue dashed. lines denote the run with thermal bubbles (asin2).. while the green. dot-daslwel (a= 2.4) and red triple dot-dashed lines (a= 2.1) show the case with CR bubbles.," The black continuous lines are for the run with cooling and star formation only, blue dashed lines denote the run with thermal bubbles \citep[as in][]{Sijacki2007}, while the green dot-dashed $\alpha=2.4$ ) and red triple dot-dashed lines $\alpha=2.1$ ) show the case with CR bubbles." + lt can be seen that the gas density is alfected by the presence of relativistic particles in the bubbles. being roughly comparable to the simulation. where the bubbles are purely thermal.," It can be seen that the gas density is affected by the presence of relativistic particles in the bubbles, being roughly comparable to the simulation where the bubbles are purely thermal." + Llowever. the gas temperature is altered substantially and in general is always reduced in central regions. as we have also found for our isolated: cluster simulations.," However, the gas temperature is altered substantially and in general is always reduced in central regions, as we have also found for our isolated cluster simulations." + This is simply caused by the fact that significant oressure support in the central cluster regions is in a non-hermal form. which decreases the thermal pressure needd o counteract the gravity exerted by the eluster's potential.," This is simply caused by the fact that significant pressure support in the central cluster regions is in a non-thermal form, which decreases the thermal pressure needed to counteract the gravity exerted by the cluster's potential." + In ?) we have already. shown that a self-regulated CIN eedback mechanism is required in order to obtain realistic emperature profiles that can reproduce the decline towards he innermost regions that has been observed in a number of cool core clusters., In \citet{Sijacki2007} we have already shown that a self-regulated AGN feedback mechanism is required in order to obtain realistic temperature profiles that can reproduce the decline towards the innermost regions that has been observed in a number of cool core clusters. + Having a significant. population of non-thermal particles in the central bubbles further helps in this respect. and provides a natural explanation for he observe gamape of the temperature profiles.," Having a significant population of non-thermal particles in the central bubbles further helps in this respect, and provides a natural explanation for the observed shape of the temperature profiles." + Thus. the oesence of a relativistic particle population inside jACGN-inflated) bubbles is not only. essential for reproducing the observed: morphologies of bubbles and X-ray. cavities in the 100 ICM. but it also improves the temperature distribution of the simulated galaxy clusters.," Thus, the presence of a relativistic particle population inside AGN-inflated bubbles is not only essential for reproducing the observed morphologies of bubbles and X-ray cavities in the hot ICM, but it also improves the temperature distribution of the simulated galaxy clusters." + However. our results also show that the AGN feedback clliciency ancl the assumed raction of the energv in high energy Cl protons are to a certain extent degenerate. suggesting that a detailed comparison with observations is needed to constrain both of these parameters individually.," However, our results also show that the AGN feedback efficiency and the assumed fraction of the energy in high energy CR protons are to a certain extent degenerate, suggesting that a detailed comparison with observations is needed to constrain both of these parameters individually." + The CR. bubble feedback also steepens the entropy profile anc brings it into closer agreement with rav observations. especially at. intermediate radii from. ~20hlkpe to ~300.κροι ," The CR bubble feedback also steepens the entropy profile and brings it into closer agreement with X-ray observations, especially at intermediate radii from $\sim 20 \,h^{-1}{\rm kpc}$ to $\sim 300 \,h^{-1}{\rm kpc}$." +Further information about the role of Cl bubbles can be obtained. from the last row of panels in Figure 5.. where we plot radial profiles of the mass- thermal pressure for all the runs we performed.," Further information about the role of CR bubbles can be obtained from the last row of panels in Figure \ref{g676_profiles}, where we plot radial profiles of the mass-weighted thermal pressure for all the runs we performed." + ‘The symbols give the mean ratio of CR-to-total pressure in each spherical bin., The symbols give the mean ratio of CR-to-total pressure in each spherical bin. +" Lt can be seen that the Cl pressure is most relevant in the central regions. being comparable to 16 thermal pressure for kr«505.""kpe at all threeepochs considered."," It can be seen that the CR pressure is most relevant in the central regions, being comparable to the thermal pressure for $r < 50 h^{-1}{\rm kpc}$ at all threeepochs considered." + At +=0 and inside 1007.tkpe. the mean CR oessure contributes about 37% he total pressure for a μα»ectral slope of a=2.1 (for the case of a=2.4 this =j;unber is 234). while at the virial radius. the non-ermal pressure support crops to 14% (or 1054 fora =2.4).," At $z=0$ and inside $100 h^{-1}{\rm kpc}$ , the mean CR pressure contributes about $37\%$ of the total pressure for a spectral slope of $\alpha=2.1$ (for the case of $\alpha=2.4$ this number is $\sim 23\%$ ), while at the virial radius, the non-thermal pressure support drops to $14\%$ (or $10\%$ for $\alpha=2.4$ )." + vecall however that in this study we have excluded: other potential sources of Clis. namely supernovac anc cosmic structure formation shocks.," Recall however that in this study we have excluded other potential sources of CRs, namely supernovae and cosmic structure formation shocks." + They are expected to further --nerease the overall CR pressure content. and may also allect 1o relative contributions of non-thermal to thermal pressure as à function of radius (forfurtherdetailsontheseissuessee ?)..," They are expected to further increase the overall CR pressure content, and may also affect the relative contributions of non-thermal to thermal pressure as a function of radius \citep[for further +details on these issues see][]{Pfrommer2007a}." + Interestingly. given that the CR pressure contribution is comparable to the thermal pressure ancl that the CR pressure eraclicnt is negative. the central cluster gas might be convectively unstable as proposed by 2) ancl explored in the case of SNe injected. CRs by. 7)..).," Interestingly, given that the CR pressure contribution is comparable to the thermal pressure and that the CR pressure gradient is negative, the central cluster gas might be convectively unstable as proposed by \citet{Chandran2006} and explored in the case of SNe injected CRs by \citet{Pfrommer2007a}." + Actually. since most of the CR pressure is due to Clts residing in the buovantlv rising. bubbles. once can argue that tjo svsben indeed exhibits a Cli-driven convection.," Actually, since most of the CR pressure is due to CRs residing in the buoyantly rising bubbles, one can argue that the system indeed exhibits a CR-driven convection." + An instability did not need to develop. since the Clts in the ICM are directly injected into an unstable configuration of a bubh," An instability did not need to develop, since the CRs in the ICM are directly injected into an unstable configuration of a bubble." + Vhe total N-ray. luminosity within the virial radius in the case of Cl bubbles with a=2.4 lies in between the simulations performed. without AGN feedback and the run with thermal bubbles., The total X-ray luminosity within the virial radius in the case of CR bubbles with $\alpha=2.4$ lies in between the simulations performed without AGN feedback and the run with thermal bubbles. + This increase of the X-ray. emission is à result. of the substantial Coulomb losses of the Ch population combined with the softer equation state of the gas supported by non-thermal pressure., This increase of the X-ray emission is a result of the substantial Coulomb losses of the CR population combined with the softer equation state of the gas supported by non-thermal pressure. + In. the run with a=2.1. Coulomb losses are less important and the total X-rav luminosity is ποσος from a value of ~1.61077ore/s for the case without AGN feedback to ~9.2107orgfs.," In the run with $\alpha=2.1$, Coulomb losses are less important and the total X-ray luminosity is reduced from a value of $\sim 1.6\times10^{43}\,{\rm erg/s}$ for the case without AGN feedback to $\sim 9.2\times10^{42}\,{\rm erg/s}$." + Also. in the simulation with a=2.1. the mean mass-weighted gas temperature is. reduced. from 1.20keV. to 0.97keV. indicating that CR bubbles may significantly inlluence galaxy cluster scaling relations such as the Ly7 relationship. especially at the low mass end.," Also, in the simulation with $\alpha=2.1$, the mean mass-weighted gas temperature is reduced, from $1.20\,{\rm keV}$ to $0.97\,{\rm keV}$, indicating that CR bubbles may significantly influence galaxy cluster scaling relations such as the $L_{\rm X}-T$ relationship, especially at the low mass end." + We plan to analyze this question in more detail in a forthcoming study., We plan to analyze this question in more detail in a forthcoming study. + Finally. we note that the bulk of the DII growth is not allected much by the presence of a non-thermal component in the bubbles: the DII growth is moderately reduced. for 2 2.so that the most massive DIT in the simulated volume has its mass reduced. by less than 204 at z= 0.," Finally, we note that the bulk of the BH growth is not affected much by the presence of a non-thermal component in the bubbles: the BH growth is moderately reduced for $z < 2$, so that the most massive BH in the simulated volume has its mass reduced by less than $20\%$ at $z=0$ ." +" We also note that in our mocel the central star formation rate and the total stellar mass within Ja, (see below) are not. very sensitive to whether the bubbles are filled with thermalor non-thermal energy. indicating that feedback by CTt bubbles"," We also note that in our model the central star formation rate and the total stellar mass within $R_{\rm vir}$ (see below) are not very sensitive to whether the bubbles are filled with thermalor non-thermal energy, indicating that feedback by CR bubbles" +observed jitter of subeliauts makes them uniquely. stable Doppler targets :unoug massive. evolved stars (?7?)..,"observed jitter of subgiants makes them uniquely stable Doppler targets among massive, evolved stars \citep{fischer03,hekker06}. ." + 7T fouudthat t16 1iniuiun niasses and seiminiajor axes ¢ planets around A stars are very different from those of planets around FCR stars., \citet{bowler10} found that the minimum masses and semimajor axes of planets around A stars are very different from those of planets around FGK stars. + Their findings suggest that the formation and migration mechanisms of plauets changes dramaticalvo with increasing stellar mass., Their findings suggest that the formation and migration mechanisms of planets changes dramatically with increasing stellar mass. + The pancts reported m lis work strenethen that conchision., The planets reported in this work strengthen that conclusion. +" The five new planets we have discovered around stars with AZ,>1.5 aall orbit bevoud 1 AU aud have minima, masses >dAny."," The five new planets we have discovered around stars with $M_\star > +1.5$ all orbit beyond 1 AU and have minimum masses $> +1$." + These properties contrast with those of planets orbiting less massive stars. which have a nearly flat distribution iu loge from ο=0.05 AU to a—|] AU (?).. and a steeply rising mass function with dluNfdludAtp-1.4.," These properties contrast with those of planets orbiting less massive stars, which have a nearly flat distribution in $\log{a}$ from $a = 0.05$ AU to $a = 1$ AU \citep{cumming08}, , and a steeply rising mass function with $d\ln{N}/d\ln{M_P} = -1.4$." + Successful theories of the origin and orbital evolution of giaut planets will need to account for the discontiuuitv between the distributious of orbital piu:uueters for plancts around Suu-like and A-type stars (nm.," Successful theories of the origin and orbital evolution of giant planets will need to account for the discontinuity between the distributions of orbital parameters for planets around Sun-like and A-type stars \citep{kennedy08,currie09,kretke09}." + The abundance of super-Jupiters >L Αμ) detected around massive stars bodes well for πιαο cirectmaging surveys., The abundance of super-Jupiters $ > 1$ ) detected around massive stars bodes well for future direct-imaging surveys. + In addition to harboring he massive planets that are predicted to be the most easilv detectable iu high-courast nuages. A-type diwvaurfa rave the added benefit of bei1ο naturally vouig.," In addition to harboring the massive planets that are predicted to be the most easily detectable in high-contrast images, A-type dwarfs have the added benefit of being naturally young." + ÀA 2 sstar has a 11ain-sequence Iffime of only ~1 Cyr. which ueans that Jovian planets iji wide orbits wi] be voune and thermally briehlt.," A 2 star has a main-sequence lifetime of only $\sim1$ Gyr, which means that Jovian planets in wide orbits will be young and thermally bright." + Three of the planets in Table 10 show linear velocity trends 1idicative of addiional lone-01ος. companions., Three of the planets in Table \ref{tab:planets} show linear velocity trends indicative of additional long-period companions. + These inear trends provide clear narkers of massive objects i1 wide orbits arouud uearby stars. and therefore warraut additional scrutiiv from RV. uonitoring and ligh-coutras Huagine.," These linear trends provide clear markers of massive objects in wide orbits around nearby stars, and therefore warrant additional scrutiny from RV monitoring and high-contrast imaging." + We thank the many observers who contributed to the observations reported here., We thank the many observers who contributed to the observations reported here. + Weeratefiully acknowledge the effortsand dedication of the Neck Observatory, Wegratefully acknowledge the effortsand dedication of the Keck Observatory +rns at around 200 kin above the silicon one.,forms at around 200 km above the silicon one. + The same vchavior was fouud for the chromospheric line aud the line core. which peak at around 6 mlz. correspoucing to he 3 munute baud.," The same behavior was found for the chromospheric line and the line core, which peak at around 6 mHz, corresponding to the 3 minute band." + The maxima of the power spectra is rot shifted eradually from 3.5he willz at the photosphere to ueher frequencies at larger iehts.Shon but the photospheric and chromospheric group of lines a discontiuuous chavior.," The maximum of the power spectra is not shifted gradually from 3.5 mHz at the photosphere to higher frequencies at larger heights, but the photospheric and chromospheric group of lines show a discontinuous behavior." + Waves at frequencies above the cut-off merease heir amplitude with height faster than evanesccut Waves low the cut-off. resulting iu larger powerfollows of 3-muuiute Waves i BUM heights.," Waves at frequencies above the cut-off increase their amplitude with height faster than evanescent waves below the cut-off, resulting in larger power of 3-minute waves at chromospheric heights." + Yet. as from Fig.," Yet, as follows from Fig." + sb he LOS velocity power at frequencies above 1 memeasured frou of the line is higher than the one from the Ine: it means that already in the upper photosphere the lugh-frequency power becomes important.," \ref{fig:power_spectra}b b, the LOS velocity power at frequencies above 4 mHz measured from of the line is higher than the one from the line; it means that already in the upper photosphere the high-frequency power becomes important." + This fiudiug sugeests that hieh-frequency waves prominent iu the chromosphere have to be generated in the plotosphere or below and their dominance at the chromospheric height is the result of their large amplitude increase., This finding suggests that high-frequency waves prominent in the chromosphere have to be generated in the photosphere or below and their dominance at the chromospheric height is the result of their large amplitude increase. + These results are cousistent with those obtained from observations by Centenoetal.(2006) using two aand limes. and from numerical simulations by Felipeetal.(2010).," These results are consistent with those obtained from observations by \citet{Centeno+etal2006} using two and lines, and from numerical simulations by \citet{Felipe+etal2010a}." + From the compatibility between our observations aud a simple wave model. we conclude that we observe a continuous feld-aligned propagation of slow magucto-acoustic waves in the upper atmosphere of sunspot.," From the compatibility between our observations and a simple wave model, we conclude that we observe a continuous field-aligned propagation of slow magneto-acoustic waves in the upper atmosphere of sunspot." + These waves first reach the formation height ofSir. then he formation height of the ines from the ine wine located in the upper photosphere. then the orluation height of the iue core and finally that of the ine.," These waves first reach the formation height of, then the formation height of the lines from the line wing located in the upper photosphere, then the formation height of the line core and finally that of the line." + The propagation becomes non-linear at heights vetween the formation of ines and oc10 cOIOC., The propagation becomes non-linear at heights between the formation of lines and line core. + This research las been funded by the Spanish MICTNN through projects AYA2007-63881 and AYA2007-66502., This research has been funded by the Spanish MICINN through projects AYA2007-63881 and AYA2007-66502. +and CCIH based on their observational results in TAIC-1.,and CCH based on their observational results in TMC-1. + They pointed out two possibilities: (i) the formation pathways of the species ancl (ii) the exchange of the FC position after formation of molecules by isolopomer-exchange reactions., They pointed out two possibilities: (i) the formation pathways of the species and (ii) the exchange of the $^{13}$ C position after formation of molecules by isotopomer-exchange reactions. + Specilically they proposed the reactions in Table 1., Specifically they proposed the reactions in Table 1. + If the observed fractionation is due to the formation paths. the following neutral-neutral reaction (e.g. Turner et al.," If the observed fractionation is due to the formation paths, the following neutral-neutral reaction (e.g. Turner et al." + 2000) could significantly contribute to the CCII formation: Two carbon atoms are not equivalent in (his neutral-neutral reaction: If the isotope ratios of the carbon atom and CI» are different. the isotopomer ratio of CCI deviates [rom unitv.," 2000) could significantly contribute to the CCH formation: Two carbon atoms are not equivalent in this neutral-neutral reaction: If the isotope ratios of the carbon atom and $_2$ are different, the isotopomer ratio of CCH deviates from unity." + sinilhulv. the observed isolopomer fractionation of CCS could be due to the neultral-neutral reaction: in which two carbon atoms are not equivalent:," Similarly, the observed isotopomer fractionation of CCS could be due to the neutral-neutral reaction: in which two carbon atoms are not equivalent:" +Presented in Figures 3.. L. and 5 are the credible regions of the fits to the FOSD sample.,"Presented in Figures \ref{fig:a1ap}, \ref{fig:a1N}, and \ref{fig:a2Db} are the credible regions of the fits to the F08b sample." + The function given by Equation | is derived from a size-distribution similar to that expected from accretion calculatious. aud thus provides a proper interpretation of the under-Iying size-distribution.," The function given by Equation \ref{eq:Fraser2008} is derived from a size-distribution similar to that expected from accretion calculations, and thus provides a proper interpretation of the under-lying size-distribution." + We find that the LF is cousistent with a broken power-law size-cdistribution with large aud small object slopes qq=L82:3 and qo=242. and a break diuneter.Dy=62+LO kin assuming albedos.," We find that the LF is consistent with a broken power-law size-distribution with large and small object slopes $q_1=4.8\pm3$ and $q_2=2\pm2$, and a break diameter,$D_b=62\pm 40$ km assuming albedos." + Presented in Figure 6. is a histogram of the FOSb sample. the best-fit LEs for the tluee functional forms we consider. the best-fit power-law LE. [rom ?.. and the best-fit LF presented by ?..," Presented in Figure \ref{fig:diff} is a histogram of the F08b sample, the best-fit LFs for the three functional forms we consider, the best-fit power-law LF from \citet{Fraser2008}, and the best-fit LF presented by \citet{Fuentes2008}." + As can be seen. power-laws do not provide acceptable fits to the data with ΤΗ(11)28. and a more complicated fuuction is required.," As can be seen, power-laws do not provide acceptable fits to the data with $m(R)\sim28$, and a more complicated function is required." + Equatious 3.) aud L both provide reasonable descriptious of the observations., Equations \ref{eq:rolling} and \ref{eq:Fraser2008} both provide reasonable descriptions of the observations. + The user is cautioned from drawing any further couclusious from Figure 6.., The user is cautioned from drawing any further conclusions from Figure \ref{fig:diff}. + The FOsb sample contaius data from many cifferent surveys., The F08b sample contains data from many different surveys. + Thus the sample includes auy calibration errors aud sky-ceusity variatious between surveys which might lead the reader to a false conclusion about the structure of the LF (see ?. lor a discussion of the magnitude aud siguilicauce of these efTects).The best-fit LF presented by ?/— is a harmonic mean of two power-laws with bright-eud slope ap=).7 and faint-encd slope ao=0.3 with a break magnituce of Rog»213., Thus the sample includes any calibration errors and sky-density variations between surveys which might lead the reader to a false conclusion about the structure of the LF (see \citet{Fraser2008} for a discussion of the magnitude and significance of these effects).The best-fit LF presented by \citet{Fuentes2008} is a harmonic mean of two power-laws with bright-end slope $\alpha_1=0.7$ and faint-end slope $\alpha_2=0.3$ with a break magnitude of $R_{eq}\sim 24.3$. + These parameters are consistent with the slopes aud break maguitucde of our best-fit uou-power-law LEs., These parameters are consistent with the slopes and break magnitude of our best-fit non-power-law LFs. + They fiud however. a factor of 3 higher sky-deusity which is iucousisteut at greater than the 3-siema level with the range of sky deusities we find for similar bright-eud slopes (see Figure 1)).," They find however, a factor of 3 higher sky-density which is inconsistent at greater than the 3-sigma level with the range of sky densities we find for similar bright-end slopes (see Figure \ref{fig:a1N}) )." + The source ol the increased number of detections compared to that expected from fits to the FOSb sample is unknown., The source of the increased number of detections compared to that expected from fits to the F08b sample is unknown. + When we cousider the FOSb;.5 sample. we find that the best-fit power-law has slope a=0.5:t with P(A>Apps)<0.0L. aud is a poor description of the data.," When we consider the $_{i>5}$ sample, we find that the best-fit power-law has slope $\alpha=0.55$ with $P(\Delta>\Delta_{obs})<0.04$, and is a poor description of the data." + The sample has uo objects fainter than (1)~25.8., The sample has no objects fainter than $m(R)\sim 25.8$. + The lack of faint objects requires a break near this point., The lack of faint objects requires a break near this point. + The best-fit rolling power-law with parameters (a.a.Moy)=(0.7L.—0.06.0.16) is an acceptable fit to the data with P(A>Aggy)= OL.," The best-fit rolling power-law with parameters $(\alpha,\alpha',\Sigma_{23}) = (0.74,-0.06,0.46)$ is an acceptable fit to the data with $P(\Delta>\Delta_{obs})=0.1$ ." + The best-fit broken power-law model is an acceptable description of the data with P(A>.Nops)=0.1., The best-fit broken power-law model is an acceptable description of the data with $P(\Delta>\Delta_{OBS})=0.1$. + The log-likelihood ratio implies that the broken power-law model of Equation L is preferred over the rolling power-law at the sienilicauce level., The log-likelihood ratio implies that the broken power-law model of Equation \ref{eq:Fraser2008} is preferred over the rolling power-law at the significance level. +" The best-fit has a,=0.7 and breaks at D,=36 kin.", The best-fit has $\alpha_1=0.7$ and breaks at $D_b=36$ km. + Because the FOSb;.5 sample has uo detections faint-ward of the break. both the break diameter aud simall-object slope of this sample are poorly coustrainec.," Because the $_{i>5}$ sample has no detections faint-ward of the break, both the break diameter and small-object slope of this sample are poorly constrained." + The manxiuuun likelihood is found with a break at m(2)=25.8 with uo objects faint-ward of this poiut., The maximum likelihood is found with a break at $m(R)=25.8$ with no objects faint-ward of this point. + ie., ie. + a»=— x. Note: we cousider slopes. a»>—6 to avoid nunerical errors in the likelihood calculations.," $\alpha_2=-\infty$ Note: we consider slopes, $\alpha_2>-6$ to avoid numerical errors in the likelihood calculations." + Presented in Figures 7.. 8.. and 9 are the likelihoodcontours of the best-fit of Equation L to," Presented in Figures \ref{fig:a1N_highi},\ref{fig:a2Db_highi}, and \ref{fig:diff_highi} are the likelihoodcontours of the best-fit of Equation \ref{eq:Fraser2008} to" +Consequently. a simple explanation in terms of a Fourier series (e.g. of a nonsinusoidal light curve) is not applicable.,"Consequently, a simple explanation in terms of a Fourier series (e.g., of a nonsinusoidal light curve) is not applicable." + refechelle shows the Echelle diagram using 2.7763d 4. which demonstrates the presence of remarkable patterns.," \\ref{echelle} shows the Echelle diagram using $\,$ $^{-1}$, which demonstrates the presence of remarkable patterns." +" Investigation of these patterns reveals that they originate in very simple frequency combinations and that the ! is only a marker of the true explanation: combinations of the two dominant modes f, and fo. as shown in refTablel.."," Investigation of these patterns reveals that they originate in very simple frequency combinations and that the $\,$ $^{-1}$ is only a marker of the true explanation: combinations of the two dominant modes $f_1$ and $f_2$ , as shown in \\ref{Table1}." + In fact. 763dd.4 = (fofi).," In fact, $^{-1}$ = $f_2-f_1)$." +" The frequencies shown in the top panel of can be expressed in as very simple way through the equation f.=mf,xnfo. where m and η are small integers."," The frequencies shown in the top panel of \\ref{pattern} can be expressed in as very simple way through the equation $f= m f_1\pm nf_2$, where $m$ and $n$ are small integers." + The fact that { and. f» are the two modes with the highest zimplitudes makes this approach also physically reasonable (see below)., The fact that $f_1$ and $f_2$ are the two modes with the highest amplitudes makes this approach also physically reasonable (see below). + We also detect a frequency at + (σα[ος fs)., We also detect a frequency at $^{-1}$ (called $f_3$ ). + This frequency. is important. since additional patterns are also seen: a number of peaks are separated by exactly the value of fy (see middle panel of refpattern)).," This frequency is important, since additional patterns are also seen: a number of peaks are separated by exactly the value of $f_3$ (see middle panel of \\ref{pattern}) )." + Altogether. 57 frequencies can be identified as numerical combinations and multiples involving fj. f» and fy bw comparing the observed to the predicted frequencies.," Altogether, 57 frequencies can be identified as numerical combinations and multiples involving $f_1$, $f_2$ and $f_3$ by comparing the observed to the predicted frequencies." + We can essentially rule out accidental agreements., We can essentially rule out accidental agreements. + Let us consider the combination [requencies at frequencies. larger than 3ddὃν where the noise figures in the amplitude spectrum are reliable.," Let us consider the combination frequencies at frequencies larger than $^{-1}$, where the noise figures in the amplitude spectrum are reliable." + For our identifications the average deviation between the observed and predicted frequeney. value is only ., For our identifications the average deviation between the observed and predicted frequency value is only $^{-1}$. + Such agreement is remarkable if one considers that themeasurements used a time base of only ck and that 1/7=0.03dd. + where Tis the time span between the last ancl first observation.," Such agreement is remarkable if one considers that the measurements used a time base of only d and that $1/T = +0.03$ $^{-1}$ where $T$ is the time span between the last and first observation." + The present result. is twpica [orNepler satellite data., The present result is typical for satellite data. + [Powe use the least-squares frequency uncertainties calculated byPERIODOA. on average the observed agreemen is 44% than predieted.," If we use the least-squares frequency uncertainties calculated by, on average the observed agreement is $\%$ than predicted." + However. such caleulations assume white noise. which is not warranted.," However, such calculations assume white noise, which is not warranted." + We can adop the formulae given in ο for the upper limit. of the frequeney uncertainty to include frequeney-dependent noise., We can adopt the formulae given in \cite{KallingerReegenWeiss2008} for the upper limit of the frequency uncertainty to include frequency-dependent noise. + We calculated signal/noise ratios in 5 bins centre on each frequency withPERTODO4 using the prewhitenec spectrum., We calculated signal/noise ratios in $^{-1}$ bins centred on each frequency with using the prewhitened spectrum. + With this more realistic approach. the observec deviation of 4 is exactly a factor of two lower than the statistical upper Limit.," With this more realistic approach, the observed deviation of $^{-1}$ is exactly a factor of two lower than the statistical upper limit." + This supports our identifications., This supports our identifications. +" Five almost equidistant frequencies inthe LLl2de ! range are also present together with various combinations of these frequencies with f, and f».", Five almost equidistant frequencies in the $11-12$ $^{-1}$ range are also present together with various combinations of these frequencies with $f_1$ and $f_2$. + This is shown in the bottom panel of refpattern.., This is shown in the bottom panel of \\ref{pattern}. . + We can now explain the patterns seen in the Echelle diagram refechelle)) in à simple manner., We can now explain the patterns seen in the Echelle diagram \\ref{echelle}) ) in a simple manner. + The vertical structures are the combination frequencies involving { and/or f»., The vertical structures are the combination frequencies involving $f_1$ and/or $f_2$. +" They are displaced from each other because dillerent low integers of m and n» (in the equation f.=mf,dX nf») ave involved.", They are displaced from each other because different low integers of $m$ and $n$ (in the equation $f = m f_1\pm nf_2$ ) are involved. + The horizontal structures with a slight incline correspond to the [requencies separated by —0.13 and . which are connected with the rotational frequency. of dd through rotational splitting ancl modulation.," The horizontal structures with a slight incline correspond to the frequencies separated by $\sim$ 0.13 and $^{-1}$, which are connected with the rotational frequency of $^{-1}$ through rotational splitting and modulation." + The incline occurs because the small frequency differences between adjacent frequency values must. show up in both the .r ane y directions of the diagram., The incline occurs because the small frequency differences between adjacent frequency values must show up in both the $x$ and $y$ directions of the diagram. + Details on the values and identifications of the individual frequencies are Listed in retFablel.., Details on the values and identifications of the individual frequencies are listed in \\ref{Table1}. + A few additional peaks have been identified. which are not related to fifs in an obvious or unique manner.," A few additional peaks have been identified, which are not related to $f_1 - f_8$ in an obvious or unique manner." + Phe Lowest [requencies were already. discussed earlier as probable zero-point drift and their values were dependent on how the data were reduced., The lowest frequencies were already discussed earlier as probable zero-point drift and their values were dependent on how the data were reduced. + The non-combination frequency atdeb+ has an amplitude of only pppm., The non-combination frequency at$^{-1}$ has an amplitude of only ppm. + Calculation of the noise around the frequency gives a signal/noise ratio of 3.6. which makes it a very marginal detection.," Calculation of the noise around the frequency gives a signal/noise ratio of 3.6, which makes it a very marginal detection." + shows the amplitude spectrum of the residuals after prewhitening of the 76 frequencies., \\ref{prew} shows the amplitude spectrum of the residuals after prewhitening of the 76 frequencies. + No peak is statistically significant and the overall. distribution. of amplitudes: is, No peak is statistically significant and the overall distribution of amplitudes is +them.,them. +" USTphlot considers the two objects at the western circle edge. A aud D. to be stellar. with V=2L3740.09 and 25.01-50.20 mae. respectively, whereas tle two caster objects. C aud D. are likely extended. with V—23.7540.01 and 23.5340.01 mae. respectively."," HSTphot considers the two objects at the western circle edge, A and B, to be stellar, with $V=24.37{\pm}0.09$ and $25.01{\pm}0.20$ mag, respectively, whereas the two eastern objects, C and D, are likely extended, with $V=23.75{\pm}0.01$ and $23.53{\pm}0.01$ mag, respectively." +" Assuiue a distance of about Fl Mpce aud Calactic extinction Ay=O.Ll anas. the two western objects. A aud B. have AAlO dando 9.8 mae. respectively. certainly at the upper eud of possible stellar buuinosities. while the two eastern objects. C aud D. have AA=110 and =11.5 lage. respectively, BUM certainly too bright to be single stars."," Assuming a distance of about 74 Mpc and Galactic extinction $A_V=0.44$ mag, the two western objects, A and B, have $M_V=-10.4$ and $-9.8$ mag, respectively, certainly at the upper end of possible stellar luminosities, while the two eastern objects, C and D, have $M_V=-11.0$ and $-11.3$ mag, respectively, almost certainly too bright to be single stars." +" Additiouallv. majects A and D are quite blue: for A. the reddeniue-d colors are (f°Dp= (38, ο ο I=019. and VW1)?=0.20 mae: aud. for Object BoVj9--(56. (V.RY?=0.60. QW|I)=020. and (V.T)=(80 nag."," Additionally, Objects A and B are quite blue: for A, the reddening-corrected colors are $(U-V)^0=-0.38$ , $(V-R)^0=0.01$ , $(R-I)^0=0.19$, and $(V-I)^0=0.20$ mag; and, for Object B, $(U-V)^0= -0.56$, $(V-R)^0=0.60$, $(R-I)^0=0.20$, and $(V-I)^0=0.80$ mag." + Colors for Object D iudicate that if mav be a composite of blue aud red olοjects., Colors for Object B indicate that it may be a composite of blue and red objects. + It is heacfoxe likely that the detected objects are too huninous and too blue to be the possible progenitor of SN 1999bx. since as à SN IL we might expect the progenitor to have been a red supergiaut.," It is therefore likely that the detected objects are too luminous and too blue to be the possible progenitor of SN 1999bx, since as a SN II, we might expect the progenitor to have been a red supergiant." + We cannot rule out that the progenitor was either an uuresolved meniber of likely clusters € and D. or was blended with bhlunumous stellar Objects A or D. However. if it is uudetected. nuits onu theabsolute magnitude and color of the progenitor are Ake 7aως26.2. V.Pa2.0 imag. (," It is undetected in either band of the second set of Snapshot images, to $V +\gtrsim 26.2$, $V-I \lesssim 2.0$ mag. (" +Two 300-8 P300W iuages were also obtained by CO-9121 on 2001 August 3. but the SN had most likely faded well below detection iu these damages. aud so we do not further consider tle.),"Two 300-s F300W images were also obtained by GO-9124 on 2001 August 3, but the SN had most likely faded well below detection in these images, and so we do not further consider them.)" + The site is also in a single 500-4 FG06W exposure obtained by GO-5L179 on 1996 May 15 aud in four FE380W images (total exposure time 1800 3) obtained by 6O-6672 on 1998 Aueust 20., The site is also in a single 500-s F606W exposure obtained by GO-5479 on 1996 May 15 and in four F380W images (total exposure time 1800 s) obtained by GO-6672 on 1998 August 29. + We show in Figure 7 the SN site iu the F6OGW image (on the PC chip: again. we have applied to make the image more cosmetically appealing in the figure).," We show in Figure 7 the SN site in the F606W image (on the PC chip; again, we have applied to make the image more cosmetically appealing in the figure)." + Nothing is detected at the SN site to impoggw=26.0 mae., Nothing is detected at the SN site to $m_{\rm F606W} \gtrsim 26.0$ mag. + Additionally. nothing is detected in the F3soWw inage to mgisowz2L7 mag.," Additionally, nothing is detected in the F380W image to $m_{\rm F380W} \gtrsim +24.7$ mag." + For a distance of about 13 Mpc aud Galactic dy=0.17 mag [Turatto et al. (, For a distance of about 43 Mpc and Galactic $A_V=0.17$ mag [Turatto et al. ( +1999) indicate no extinction to the SN]. the corrected magnitude and color correspond to AR.moAMI py<2.45 mag for the progenitor.,"1999) indicate no extinction to the SN], the corrected magnitude and color correspond to $M^0_V \gtrsim -7.3$, $(U-V)^0 \lesssim 2.5$ mag for the progenitor." + SN 19990ec was discovered using WAIT bx Modjaz Li (1999)., SN 1999ec was discovered using KAIT by Modjaz Li (1999). + The SN owas classified as à SN Ib by Jha et al. (, The SN was classified as a SN Ib by Jha et al. ( +19000). although Mathesou et al. (,"1999c), although Matheson et al. (" +2001a) consider it a peculiar SN TL. without a welbdefined. type. simular to SN 1993R (cf.,"2001a) consider it a peculiar SN I, without a well-defined type, similar to SN 1993R (cf." + Filippeuko Matheson 1995)., Filippenko Matheson 1993). +" We measure ona WAITimage the SN position as a = 06? 16"" 16:18. 6 — 21°22/1071. with uncertainty £072. ["," We measure on a KAIT image the SN position as $\alpha$ = $^h$ $^m$ ${\fs}$ 18, $\delta$ = $-$ ${\farcs}$ 1, with uncertainty ${\pm}0{\farcs}2$. [" +This position is discrepant by at least wwith that referred to by Elnegreen et al. (,This position is discrepant by at least with that referred to by Elmegreen et al. ( +2001).],2001).] + The host ealaxy is part of an interacting svsteni. extensively y.udied by Ehucercen et al.," The host galaxy is part of an interacting system, extensively studied by Elmegreen et al." +" with HST (6O-6183): ouly their ""NCGC2207-NW"". F336W (2000 s). FI39W (2000 3). F555WN(660 3). and PalWW (720 8) mages from 1996 λίαν 25 are use here."," with (GO-6483); only their “NGC2207-NW” F336W (2000 s), F439W (2000 s), F555W (660 s), and F814W (720 s) images from 1996 May 25 are of use here." + We apply the 2MAÀSS astrometric grid irectlv to the WEPC2 E555W inosaic. with uucertaimty +012.," We apply the 2MASS astrometric grid directly to the WFPC2 F555W mosaic, with uncertainty ${\pm}0{\farcs}2$." + Figure 8 shows the SN site ou the F555W WE? chip. with total uucertainty 073.," Figure 8 shows the SN site on the F555W WF2 chip, with total uncertainty ${\pm}0{\farcs}3$." + A hint of an object is possibly seen within the circle. but nothing is detected there by IISTphot to V.z25.9 mae.," A hint of an object is possibly seen within the circle, but nothing is detected there by HSTphot to $V \gtrsim 25.9$ mag." + The Galactic extinction is Ay=0.29 mae., The Galactic extinction is $A_V=0.29$ mag. + To derive possibly more accurate lits ou the brielitucss aud color of a progenitor star. we exploit the color iuformation available to us for objects in the SN’s cuviromment. to yossibly estimate the local extinction.," To derive possibly more accurate limits on the brightness and color of a progenitor star, we exploit the color information available to us for objects in the SN's environment, to possibly estimate the local extinction." + As cau be seen from he color-color diagram in Fieure 9. IISTphot considers uost of the objects around the error circle to be exteuded: hey are likely star clusters.," As can be seen from the color-color diagram in Figure 9, HSTphot considers most of the objects around the error circle to be extended; they are likely star clusters." + Howewer. two objects are considered stellar. aud theoue(Star 1) closest to the SN position implies that Az1.6 mag (though the C- photometry may be the least certain. the extinction. even for the clusters. appears to range from —1to ~3 nae}.," However, two objects are considered stellar, and theone(Star 1) closest to the SN position implies that $A_V \approx 1.6$ mag (though the $U$ -band photometry may be the least certain, the extinction, even for the clusters, appears to range from $\sim$ 1to $\sim$ 3 mag)." + Although it is at the οσο of the error circle. it is," Although it is at the edge of the error circle, it is" +continu emission must be small.,continuum emission must be small. +" Assuuiug optically thin emission. the mass can be estimated by where FL is the flux density. D is the distance to the source. and B, is the Planck "," Assuming optically thin emission, the mass can be estimated by where $F_\nu$ is the flux density, $D$ is the distance to the source, and $B_\nu$ is the Planck function." +Assuming D = 100 pe. the total mass is 11512 AL... function.which is cousistent with the mass estimate of Chandler et al. (," Assuming $D$ = 400 pc, the total mass is $^{+1.5}_{-0.7}$ $M_{\odot}$, which is consistent with the mass estimate of Chandler et al. (" +1995).,1995). + This mass inelides both the accretion disk(s) aud the inner protostellar euvelopo., This mass includes both the accretion disk(s) and the inner protostellar envelope. + At the first elance of the 6.9 mun maps. the TIT 21 AIMS svsteuir appears like a combination of a protostar (source 1) aud au outflow (source 2).," At the first glance of the 6.9 mm maps, the HH 24 MMS system appears like a combination of a protostar (source 1) and an outflow (source 2)." + However. the SED shows that. for both sources 1 aud 2. the 6.9 nuu flux is mostly from dust.," However, the SED shows that, for both sources 1 and 2, the 6.9 mm flux is mostly from dust." + Especially. the 6.9 nuu dux of source 2 iust be eutirelv from dust because the 3.6 cur source is uot associated with source 2 (Fig.," Especially, the 6.9 mm flux of source 2 must be entirely from dust because the 3.6 cm source is not associated with source 2 (Fig." + 15)., $b$ ). + That is. it is very uulikely that source 2 is a thermal jet.," That is, it is very unlikely that source 2 is a thermal jet." + Since both sources are extended aud partiallv overlapping. a simple two-compoucut fitting to the image was done to decompose the system.," Since both sources are extended and partially overlapping, a simple two-component fitting to the image was done to decompose the system." + The tage was fitted with a sui of two elliptical Gaussian distributions., The image was fitted with a sum of two elliptical Gaussian distributions. + Ouly the pixels around source 1 aud 2 with intcusitics above 0.3 mJy | were considered for the fit. aud source 3 was ignored.," Only the pixels around source 1 and 2 with intensities above 0.3 mJy $^{-1}$ were considered for the fit, and source 3 was ignored." + Table 1 lists the parameters of the best-fit Gaussian profiles. aud Figure le shows the best-fit intensity distribution. which agrees with the observed nuage within three times the ruis noise.," Table 1 lists the parameters of the best-fit Gaussian profiles, and Figure $c$ shows the best-fit intensity distribution, which agrees with the observed image within three times the rms noise." + The total fiux of the two-component Caussian profile also agrees witli that of the real umage within 0.1 mJy., The total flux of the two-component Gaussian profile also agrees with that of the real image within 0.1 mJy. + There is a bipolar jet seeu iu I ciission iu the ITIT 21 MAIS region with the axis in the northeast-soutlwest direction (Boutemps ct al., There is a bipolar jet seen in $_2$ emission in the HH 24 MMS region with the axis in the northeast-southwest direction (Bontemps et al. + 1996)., 1996). + The uear-IR IT» map of Davis ct al. (, The near-IR $_2$ map of Davis et al. ( +1997) shows that TMT 214 MMS is almost certainly the driving source of this outflow.,1997) shows that HH 24 MMS is almost certainly the driving source of this outflow. +" The position anele of these Πο knots (NE 1. NE 2. aud SW 2) with respect to ΠΠ 214 MMS is +οὖν, which is perpendicular to the clongation of source 1."," The position angle of these $_2$ knots (NE 1, NE 2, and SW 2) with respect to HH 24 MMS is $\pm$, which is perpendicular to the elongation of source 1." + Therefore. source 1l sees to be the driving source of the bipolar outflow.," Therefore, source 1 seems to be the driving source of the bipolar outflow." + The peak position of the 3.6 cm source (Reipurth et al., The peak position of the 3.6 cm source (Reipurth et al. + 2002) does not exactly coincide with the position of source 1 (Fig., 2002) does not exactly coincide with the position of source 1 (Fig. + 10)., $b$ ). + The position displacement is about, The position displacement is about +absorption from 73347543 and from 7851-7973 (then becomes a more reliable indicator of spectral (wpe.,absorption from 7334-7543 and from 7851-7973 then becomes a more reliable indicator of spectral type. + spectral classification in (his temperature range was accomplished through a combination of visual classification and quantitative analvsis of TiO and VO indices which we now describe., Spectral classification in this temperature range was accomplished through a combination of visual classification and quantitative analysis of TiO and VO indices which we now describe. + The indices were computed bv taking the ratio of the average flux in a ~50 wwide band of the continuum to the average in an absorption band., The indices were computed by taking the ratio of the average flux in a $\sim$ 50 wide band of the continuum to the average in an absorption band. + Following Allen (1996). we plotted the TiO index of vvs. the TiO index of aalong with their one sigma errors for each [vera field as well as our dwarf standards.," Following Allen (1996), we plotted the TiO index of vs. the TiO index of along with their one sigma errors for each Hydra field as well as our dwarf standards." + Fig., Fig. + Pa shows a plot of the TiO indices for the cdwarl standards., 2a shows a plot of the TiO indices for the dwarf standards. + There is à general trend. Lor TiO index to increase with later spectral (wpe until MT. where (the trend reverses and the index decreases lor stars cooler (han MT.," There is a general trend for TiO index to increase with later spectral type until M7, where the trend reverses and the index decreases for stars cooler than M7." + To resolve the ambiguity caused by (his reversal. we developed (wo narrow band VO indices for spectral classification of (he coolest stars in our sample.," To resolve the ambiguity caused by this reversal, we developed two narrow band VO indices for spectral classification of the coolest stars in our sample." + A plot of these indices is shown in Fig., A plot of these indices is shown in Fig. + 2b lor M dwar! standards., 2b for M dwarf standards. + The first index is the ratio of the continuum averaged over (wo bands which bracket the VO band centered ab 7485 {to the average flux in the VO band., The first index is the ratio of the continuum averaged over two bands which bracket the VO band centered at 7485 to the average flux in the VO band. + The second index is the ratio of the continuum in a band centered on 8120 {to the flux in the VO band centered at 7979., The second index is the ratio of the continuum in a band centered on 8120 to the flux in the VO band centered at 7979. +Α.. As shown in Fig., As shown in Fig. + 2b. there is a general tvencl for the indices to increase [rom spectral (vpes AIS to M9.," 2b, there is a general trend for the indices to increase from spectral types M3 to M9." + While the use of these indices allowed us (o sort objects by temperature. (he final spectral classifications were made by direct. comparisons of the streneths of the TiO and VO bands with standard star spectra.," While the use of these indices allowed us to sort objects by temperature, the final spectral classifications were made by direct comparisons of the strengths of the TiO and VO bands with standard star spectra." + The sensitivity of these absorption bands (to spectral class allowed us in most cases lo estimate M spectral types to within a subclass., The sensitivity of these absorption bands to spectral class allowed us in most cases to estimate M spectral types to within a subclass. + A rough5 estimate of the surface 5gravity of an object is important in determining5 its native and in estimating accuratelv its effective temperature [ον a given spectral (vpe., A rough estimate of the surface gravity of an object is important in determining its nature and in estimating accurately its effective temperature for a given spectral type. + In parüceular. surface gravity indicators can help identüfv background giants and field clwarls that might contaminate our sample.," In particular, surface gravity indicators can help identify background giants and field dwarfs that might contaminate our sample." + Gravitv-sensitive absorption features available for analysis in our spectra include the Call band centered at 6975 and the Na I doublet at 8183/8195 ((both strongest in dwarls) and absorption from the Ca II triplet αἱ 8660, Gravity-sensitive absorption features available for analysis in our spectra include the CaH band centered at 6975 and the Na I doublet at 8183/8195 (both strongest in dwarfs) and absorption from the Ca II triplet at 8660 +and eventually fill in. (he missing faint red sequence of galaxies seen al z0.75 (de Lucia οἱ al.,"and eventually fill in, the missing faint red sequence of galaxies seen at $z\sim0.75$ (de Lucia et al." + 2004. Goto et al.," 2004, Goto et al." + 2005)., 2005). + However. the high masses (P97). high metallicities (INobulnicky Zaritsky 1999). large extinctions (ILammer et al.," However, the high masses (P97), high metallicities (Kobulnicky Zaritsky 1999), large extinctions (Hammer et al." + 2001). and centrally concentrated (Barton and van Zee 2001) seen in some LCDGs make (hem plausible candidates to be a burst phase of more massive spiral galaxies.," 2001), and centrally concentrated star-bursts (Barton and van Zee 2001) seen in some LCBGs make them plausible candidates to be a burst phase of more massive spiral galaxies." + Both dE’s and more massive bulges are accreted populations in local clusters (Conselice et al., Both dE's and more massive bulges are accreted populations in local clusters (Conselice et al. + 2001: Biviano et al., 2001; Biviano et al.