diff --git "a/batch_s000004.csv" "b/batch_s000004.csv" new file mode 100644--- /dev/null +++ "b/batch_s000004.csv" @@ -0,0 +1,10325 @@ +source,target + Identifications were made using likelihood ratio tests aud by comparing optical aud near-IR nuages with the morphology of the N-rav source., Identifications were made using likelihood ratio tests and by comparing optical and near-IR images with the morphology of the X-ray source. + 27 of the stars were identified morphologically or through positional aligmiment of an N-ray source with a bright star., 27 of the stars were identified morphologically or through positional alignment of an X-ray source with a bright star. + A further 21 stellar identifications were made by fitting multi-waveleusthi photometry to the spectral energy. distributions (SEDs) of templates taken from ?).. while the remaining 13 were identified spectroscopically frou dedicated COSMOS spectroscopic campaigns (see Section 2.2. for more details).," A further 21 stellar identifications were made by fitting multi-wavelength photometry to the spectral energy distributions (SEDs) of templates taken from \citet{salv09}, while the remaining 13 were identified spectroscopically from dedicated COSMOS spectroscopic campaigns (see Section \ref{s-spectra} for more details)." +" In many cases these sources were identified as stars by multiple methods (ο,ο, photometrically identified and then coufirmmed spectroscopicallv).", In many cases these sources were identified as stars by multiple methods (e.g. photometrically identified and then confirmed spectroscopically). + The majority of the remaining Chandra-COSMOS sources were identified as galaxies based on the above methods. with oulv 11 sources reaming unidenti&ed bv ?7): 2 of these have uo ideuti&able counterpart aud 9 either have imultiple possible counterparts or are either associated with fait optical sources in close augular proximity to bright stars or galaxies. such that their properties cannot be studied.," The majority of the remaining -COSMOS sources were identified as galaxies based on the above methods, with only 11 sources remaining unidentified by \citet{civa10}: 2 of these have no identifiable counterpart and 9 either have multiple possible counterparts or are either associated with faint optical sources in close angular proximity to bright stars or galaxies, such that their properties cannot be studied." + Statistically. based ou the 1750 ideutificatious iade. of which only are stars. the 11 nnideutified sources are likely to be ealaxies.," Statistically, based on the 1750 identifications made, of which only are stars, the 11 unidentified sources are likely to be galaxies." + Since the extraction and characterization of COSAIOS sources performed by tle survey collaboration has been conducted on the basis that they are extragalactic sources (which have different morphological and spectral properties to stellar sources) we have re-analyzed the observations of the stellar sources assuiuing that they are stellar., Since the extraction and characterization of COSMOS sources performed by the survey collaboration has been conducted on the basis that they are extragalactic sources (which have different morphological and spectral properties to stellar sources) we have re-analyzed the observations of the stellar sources assuming that they are stellar. + Thiswas done using 1.2 (2).. CALDB 1.2.2. aud the ACIS code (AE.7) usine the method outlined in ?)..," Thiswas done using 4.2 \citep{frus06}, CALDB 4.2.2, and the ACIS code \citep[AE,][]{broo02} using the method outlined in \citet{wrig09a}." + To stuumarize. AE uses a variety of point spread fictions (PSFs) appropriate for the off-axis anele of cach observation of cach source to extract photons m a set fraction of the PSF (typically 90543).," To summarize, AE uses a variety of point spread functions (PSFs) appropriate for the off-axis angle of each observation of each source to extract photons in a set fraction of the PSF (typically )." + The backeround is estimated from a region surroundius this PSF that excludes tlhe PSFs of other sources., The background is estimated from a region surrounding this PSF that excludes the PSFs of other sources. +" From these extractions. AE calculates a source significance aud the Poisson probability. D,,4. hat the source counts are a superposition of backeround ohotous."," From these extractions, AE calculates a source significance and the Poisson probability, $P_{not}$, that the source counts are a superposition of background photons." + At this point all sources were inspected visually and compared to the position of their designated optical counterpart to confini their association., At this point all sources were inspected visually and compared to the position of their designated optical counterpart to confirm their association. +" We then applied a cut to the sample. discarding auv sources that had a ugher probability of being a false source than of being a real source (Le. D,,;20.5). which resulted in oue source vcing discarded aud reduced our sample to GO sources."," We then applied a cut to the sample, discarding any sources that had a higher probability of being a false source than of being a real source (i.e. $P_{not} > 0.5$ ), which resulted in one source being discarded and reduced our sample to 60 sources." + This rather liberal cut level was chosen to maintain a Hel level of completeness with respect to the existingChandra COSMOS catalog., This rather liberal cut level was chosen to maintain a high level of completeness with respect to the existing COSMOS catalog. +" Spectral fitting was performed for the 27 sources with 220 net counts using version 12.6.0 91,", Spectral fitting was performed for the 27 sources with $>20$ net counts using version 12.6.0 \citep{arna96}. + The spectra were compared to (7) spectra corresponding to sinele-temperature thermal plasma nodels (7) in collisional ionization equilibrium aud absorbed by a hydrogen column density using the model (2)., The spectra were compared to \citep{smit01} spectra corresponding to single-temperature thermal plasma models \citep{raym77} in collisional ionization equilibrium and absorbed by a hydrogen column density using the model \citep{balu92}. +. Due to the low Galactic extinetion iu he COSMOS sieht-line the hydrogen column density was allowed to vary ouly up to the maxiuun value for the field of ~2«1029 2 (?2).. while the thermal plasma cluperature was allowed to vary freely.," Due to the low Galactic extinction in the COSMOS sight-line the hydrogen column density was allowed to vary only up to the maximum value for the field of $\sim 2 \times 10^{20}$ $^{-2}$ \citep{kalb05}, while the thermal plasma temperature was allowed to vary freely." + A exid of initial hermal plasma temperatures covering AL=0.7—2.6 was used to prevent fitting local minima and the model with the lowest C-statistic (?) was then used for each source., A grid of initial thermal plasma temperatures covering $kT = 0.7-2.6$ was used to prevent fitting local minima and the model with the lowest C-statistic \citep{cash79} was then used for each source. + Two-temperature thermal plasma models were also tested for these sources. but only the brisehtest source. 516. had sufficient couuts to produce a joticeably better fit using a two-component model.," Two-temperature thermal plasma models were also tested for these sources, but only the brightest source, 546, had sufficient counts to produce a noticeably better fit using a two-component model." + For he 33 sources with less than 20 net counts we used he method outlined iu 7?) to calculate N-rav. fluxes roni count rates and median photon energies, For the 33 sources with less than 20 net counts we used the method outlined in \citet{getm10} to calculate X-ray fluxes from count rates and median photon energies. +" Since he hydrogen colui density in our field of view (FoV) is neelieible. we use apparent X-ray fluxes as intrinsic Ηχος,"," Since the hydrogen column density in our field of view (FoV) is negligible, we use apparent X-ray fluxes as intrinsic fluxes." +" Uncertainties on these fluxes are not specified individually, but were determüued statistically bv. 2).."," Uncertainties on these fluxes are not specified individually, but were determined statistically by \citet{getm10}." + They are an approxinate function of the net counts of he source and range from for sources with ~20 net counts to >TO% forsources with «5 net counts., They are an approximate function of the net counts of the source and range from for sources with $\sim$ 20 net counts to $> 70$ forsources with $< 5$ net counts. + The X-ray properties of the 60 retained sources are isted iu Table 1.., The X-ray properties of the 60 retained sources are listed in Table \ref{xstars_cosmos}. + With the exception of a single very xieht source (CID 516). the majority of sources have count rates of 107—7. appropriate for a sample owed on observations of 100-200. ks and a source detectiono procedure that has extracted sources down/ to ~3 net counts.," With the exception of a single very bright source (CID 546), the majority of sources have count rates of $10^{-5} - 10^{-3}$, appropriate for a sample based on observations of 100-200 ks and a source detection procedure that has extracted sources down to $\sim$ 3 net counts." + Optical aud ucar-IR photometry was taken from the COSMOS optical that include data from the Sloan Digital Sky Survey (SDSS. ?).. the Subaru photometric catalog (?).. aud the CFUT*//Meeacam catalog (?)..," Optical and near-IR photometry was taken from the COSMOS optical that include data from the Sloan Digital Sky Survey \citep[SDSS,][]{york00}, , the Subaru photometric catalog \citep{capa07}, , and the /Megacam catalog \citep{mccr10}. ." + For the brightest sources that saturate im the deep COSMOS catalogs we complemented this data, For the brightest sources that saturate in the deep COSMOS catalogs we complemented this data +predictions of the unmodified SCM prior to turnaround ὃ«5.6.,predictions of the unmodified SCM prior to turnaround $\bar{\delta} < 5.6$. +" We found a best fit value of Ryir/Rta=0.5896, which is fairly close to the value of 0.5 that is generally used in the spherical collapse model, despite the fact that we did not constrained it to be so."," We found a best fit value of $R_{vir}/R_{ta} = 0.5896$, which is fairly close to the value of $0.5$ that is generally used in the spherical collapse model, despite the fact that we did not constrained it to be so." +" For comparison, the improved spherical collapsedeveloped by Engineeretal. gave Ryir/Rta©0.65, and N-body simulations(2000) have been found to support Roir/Rta70.56 (Hamiltonetal."," For comparison, the improved spherical collapsedeveloped by \citet{Engineer:2000} gave $R_{vir}/R_{ta} \approx 0.65$, and N-body simulations have been found to support $R_{vir}/R_{ta} \approx 0.56$ \citep{Hamilton:1991}." + Our value of Ryir/Rta is therefore a better approximation1991).. to the value found from simulations than that generally used in the unmodified SCM and that found in the model developed by Engineeretal.(2000)., Our value of $R_{vir}/R_{ta}$ is therefore a better approximation to the value found from simulations than that generally used in the unmodified SCM and that found in the model developed by \citet{Engineer:2000}. +". In our improved SCM the linear density contrast is given by: When ój;,=1.6865, which corresponds to the instant of collapse in the unmodified SCM, we find 6=54.65 rather than the SCM’s value of 178."," In our improved SCM the linear density contrast is given by: When $\delta_{lin} = 1.6865$, which corresponds to the instant of collapse in the unmodified SCM, we find $\bar{\delta} = 54.65$ rather than the SCM's value of $178$." + We find that 6=200 corresponds to 6jin=2.286., We find that $\bar{\delta} = 200$ corresponds to $\delta_{lin} = 2.286$. +" We compare the form of found in our model to that predicted by the unmodifiedO(dum) SCM model, with virialisation put in by hand, in FIG. 3.."," We compare the form of $\bar{\delta}(\bar{\delta}_{lin})$ found in our model to that predicted by the unmodified SCM model, with virialisation put in by hand, in FIG. \ref{fig3}." +" We also show the divergent behaviour of 6(duin) in the standard SCM without virialisation, and the asymptotic behaviour of if Ria=1.8Ryir as suggested by simulations (Hamiltonó(0j;4)etal. 1991).."," We also show the divergent behaviour of $\bar{\delta}(\bar{\delta}_{lin})$ in the standard SCM without virialisation, and the asymptotic behaviour of $\bar{\delta}(\bar{\delta}_{lin})$ if $R_{ta} = 1.8 R_{vir}$ as suggested by simulations \citep{Hamilton:1991}. ." + The two major advantages of our improved SCM over the unmodified version are clearly visible in this plot:, The two major advantages of our improved SCM over the unmodified version are clearly visible in this plot: +540.,. +5. The contours of wo and wa are plotted in Fig. 1((, The contours of $w_0$ and $w_a$ are plotted in Fig. \ref{u2cont}( ( +"a), andthe contours of Q, and £2; are plotted in Fig. 4((","a), andthe contours of $\Omega_m$ and $\Omega_k$ are plotted in Fig. \ref{u2omkcont}( (" +b).,b). +" For the flat CPL model, Om(z) becomes where Cpz(z) is defined in equation (27)) with Q,=0."," For the flat CPL model, $Om(z)$ becomes where $\Omega_{DE}(z)$ is defined in equation \ref{cplde}) ) with $\Omega_k=0$." +" By fitting the combined data to the flat CPL model, we get the marginalized 1σ constraints, Qm=0,26Τ 10013, wo= —1.05*0-17, and wa=0.077032 with x?=541.1."," By fitting the combined data to the flat CPL model, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.267^{+0.019}_{-0.01}$ , $w_0=-1.05^{+0.17}_{-0.1}$ , and $w_a=0.07^{+0.32}_{-0.88}$ with $\chi^2=541.1$." +" Using this result, we reconstruct Om(z) with equation (28)) and the result is shown in Fig. 2(("," Using this result, we reconstruct $Om(z)$ with equation \ref{cplomz}) ) and the result is shown in Fig. \ref{u2omz}( (" +a).,a). +" For the Jassal-Bagla-Padmanabhan (JBP) parametrization (Jassal,Bagla&Padmanabhan 2005),, the equation of state parameter is so w(z=0)wo and w(z)~wo when z>1."," For the Jassal-Bagla-Padmanabhan (JBP) parametrization \citep{jbp}, the equation of state parameter is so $w(z=0)=w_0$ and $w(z)\sim w_0$ when $z\gg 1$." +" In this model, the parameter wo determines the property of the equation of state parameter w(z) at both low and high redshifts."," In this model, the parameter $w_0$ determines the property of the equation of state parameter $w(z)$ at both low and high redshifts." +" The corresponding dimensionless dark energy density is then where Q,=1—O4, Ωμ.", The corresponding dimensionless dark energy density is then where $\Omega_x=1-\Omega_{m}-\Omega_r-\Omega_{k}$ . +" In thismodel, we also have four parameters p=(Qm,Qe,Wo, Wa)."," In thismodel, we also have four parameters $\mathbf{p}=(\Omega_{m},\ \Omega_{k}, \ w_0, \ w_a)$ ." +" Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and H(z) data, we get the marginalized 1c constraints, (2,=0651001, Qu,=0.004+ 0.006, wo= —1.21*075. and wa=1.297533 with x?=540.6."," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.263^{+0.02}_{-0.01}$, $\Omega_k=0.004\pm 0.006$ , $w_0=-1.21^{+0.32}_{-0.18}$ , and $w_a=1.29^{+1.35}_{-2.33}$ with $\chi^2=540.6$." +" The contours of Ωμ, and CQ; are plotted in Fig. 4((", The contours of $\Omega_m$ and $\Omega_k$ are plotted in Fig. \ref{u2omkcont}( ( +"c), and the contours of wo and wa are plotted in Fig. 1((","c), and the contours of $w_0$ and $w_a$ are plotted in Fig. \ref{u2cont}( (" +b).,b). +" For the flat JBP model, Om(z) becomes where Qpg(z) is defined in equation (30)) with 0."," For the flat JBP model, $Om(z)$ becomes where $\Omega_{DE}(z)$ is defined in equation \ref{jbpde}) ) with $\Omega_k=0$ ." +" By fitting the combined data to the flat JBP model, we get the marginalized 1c constraints, Qm=0.26570017. wo= 1.087376, and wa=0.32*12 with x?=541.0."," By fitting the combined data to the flat JBP model, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.265^{+0.019}_{-0.011}$, $w_0=-1.08^{+0.24}_{-0.19}$ , and $w_a=0.32^{+1.01}_{-1.72}$ with $\chi^2=541.0$." +" Using this result, we reconstruct Om(z) with equation (31)) and the result is shown in Fig. 2(("," Using this result, we reconstruct $Om(z)$ with equation \ref{jbpomz}) ) and the result is shown in Fig. \ref{u2omz}( (" +b).,b). +" Now we consider the parametrization proposed by Wetterich (2004)., For this model, w(z=0)wo and w(z)~0 when z> 1, so the behaviour of w(z) at high redshift is limited."," Now we consider the parametrization proposed by \cite{wetterich}, For this model, $w(z=0)=w_0$ and $w(z)\sim 0$ when $z\gg 1$ , so the behaviour of $w(z)$ at high redshift is limited." +" The dark energy density is In thismodel, the model parameters are p=(Qu,Qk,Wo, Wa)."," The dark energy density is In thismodel, the model parameters are $\mathbf{p}=(\Omega_{m},\ \Omega_{k}, \ w_0, \ w_a)$ ." +" Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and H(z) data, we get the marginalized lo constraints, Qn=0.264+0.013, Q,=0.00910005, wo=—117*025, and wa=0.327946 with x?=540.4."," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.264\pm 0.013$, $\Omega_k=0.009^{+0.014}_{-0.005}$, $w_0=-1.17^{+0.09}_{-0.23}$, and $w_a=0.32^{+0.46}_{-0.16}$ with $\chi^2=540.4$." + The contours of wo and we are plotted in Fig. 1((, The contours of $w_0$ and $w_a$ are plotted in Fig. \ref{u2cont}( ( +"c), and the contours of Qm and €), are plotted in Fig. 4((","c), and the contours of $\Omega_m$ and $\Omega_k$ are plotted in Fig. \ref{u2omkcont}( (" +d).,d). +" For the flat Wetterich model, Om(z) becomes where Qpz(z) is defined in equation (33)) with Q,=0."," For the flat Wetterich model, $Om(z)$ becomes where $\Omega_{DE}(z)$ is defined in equation \ref{wetde}) ) with $\Omega_k=0$." +" By fitting the combined data to the flat Wetterich model, we get the marginalized 1σ constraints, Qn=0.26675015, wo= —1.05*005, and wa=0.14+0.1 with X?=541.1."," By fitting the combined data to the flat Wetterich model, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.266^{+0.01}_{-0.015}$, $w_0=-1.05^{+0.02}_{-0.16}$ , and $w_a=0.14\pm 0.1$ with $\chi^2=541.1$." +" Using this result, we reconstruct Om(z) with equation (34)) and the result is shown in Fig. 2(("," Using this result, we reconstruct $Om(z)$ with equation \ref{wetomz}) ) and the result is shown in Fig. \ref{u2omz}( (" +c).,c). +" Finally, we consider a more model-independent parametrization of w(z), the piecewise parametrization of w(z)."," Finally, we consider a more model-independent parametrization of $w(z)$, the piecewise parametrization of $w(z)$." +" In this parametrization, the equation of state parameter is a constant, w(z)=wi; for the redshift in the range z;-1«z1.8)=-1$ . +" Forflat Universe, if zi4€z< zi, Again, the four parameters w; are correlated and we follow Huterer&Cooray(2005) to transform these parameters to decorrelated parameters W;."," For a flat Universe, if $z_{i-1}\le zO in the redshift range"," For the piecewise parametrization of $q(z)$ , we find that $q(z)<0$ in the redshift range $0\le z\la 0.6$ , and $q(z)>0$ in the redshift range" +The realization that X-ray binaries are. 100-1000. times overabundant in Galactic elobular clusters relative to the rest of the \lilky Way. (Clark1975:Katz1975). was crucial in understanding that intimate and Gehtly coupled relationships exist between stellar evolution and stellar dynamics.,"The realization that X-ray binaries are 100-1000 times overabundant in Galactic globular clusters relative to the rest of the Milky Way \citep{cla75,kat75} was crucial in understanding that intimate and tightly coupled relationships exist between stellar evolution and stellar dynamics." + Among the predictions of this theory is (he expectation that many white chwarl/red cwarf binaries should form via two-body tidal capture (Fabian1975). and/or three-body exchange captures (Int1983:Hut.&Paczvuski1984).," Among the predictions of this theory is the expectation that many white dwarf/red dwarf binaries should form via two-body tidal capture \citep{fab75} and/or three-body exchange captures \citep{hut83,hut84}." +. some of these binary svstems will be in very. close orbits. such that the red dwarl fills its Roche lobe.," Some of these binary systems will be in very close orbits, such that the red dwarf fills its Roche lobe." + This leads to the transfer of mass. via an aceretion disk. from the red dwarl to the white dwarf component in other words. to cataclvsmic variables (CVs).," This leads to the transfer of mass, via an accretion disk, from the red dwarf to the white dwarf component – in other words, to cataclysmic variables (CVs)." + Yel searclies for the many dozens of expected erupting CVs have tvpically found zero to (vo cwarf novae in clusters searched [rom the ground (Sharaοἱal.1994:ÓTuairisg2003). and with," Yet searches for the many dozens of expected erupting CVs have typically found zero to two dwarf novae in clusters searched from the ground \citep{sha94,tua03} and with" +It is important to note a new result evident in Fig. 3::15.,It is important to note a new result evident in Fig. \ref{fig:delta}:. + This is true regardless of the strength of the UVB., This is true regardless of the strength of the UVB. + We will< examine this interesting result furtherin §4.., We will examine this interesting result furtherin \ref{sec:pos}. +" Next, we investigate how the combination of transient UV heating and a persistent LW background impact star formation."," Next, we investigate how the combination of transient UV heating and a persistent LW background impact star formation." +" This is a more physically-relevant scenario, since a LW background is likely established before a large fraction of the Universe has been reionized (?).."," This is a more physically-relevant scenario, since a LW background is likely established before a large fraction of the Universe has been reionized \citep{HAR00}." +" Photons in the LW band dissociate H2 molecules; thus by definition they provide additional negative feedback, undercutting some of the enhancement in the Hz abundances in relic HII regions."," Photons in the LW band dissociate $_2$ molecules; thus by definition they provide additional negative feedback, undercutting some of the enhancement in the $_2$ abundances in relic HII regions." + Negative feedback from a LW background kicks in when the He dissociation timescale becomes shorter than the Ἡο formation timescale., Negative feedback from a LW background kicks in when the $_2$ dissociation timescale becomes shorter than the $_2$ formation timescale. +" Since the formation timescale is inversely proportional to gas density, whereas the dissociation timescale is independent of density, the density decrease caused by UV heating should make halos more susceptible to the negative feedback of a LW background (?)?.."," Since the formation timescale is inversely proportional to gas density, whereas the dissociation timescale is independent of density, the density decrease caused by UV heating should make halos more susceptible to the negative feedback of a LW background \citep{OH03} ." + We investigate these processes further below., We investigate these processes further below. +" Specifically, in Fig. 4,,"," Specifically, in Fig. \ref{fig:LW_delta}," +" we plot values of dy7,ca(z) panel) and ów,ca(z) panel) for our runs including a LW background.", we plot values of $\delM$ ) and $\delN$ ) for our runs including a LW background. + The LW background turns on at z—24.62 and remains on., The LW background turns on at $z=24.62$ and remains on. +" At the simplest level, we can see the suppression of molecular hydrogen (and hence cooling)due to the LW background by the more negative values of both daz,ca(z) and 6n,ca(z) at fixed redshift."," At the simplest level, we can see the suppression of molecular hydrogen (and hence cooling)due to the LW background by the more negative values of both $\delM$ and $\delN$ at fixed redshift." + Does this panel show evidence for theadditional negative impact of the transient UVB discussed above?, Does this panel show evidence for the negative impact of the transient UVB discussed above? +" Without UV heating, a LW background with a specific intensity of Ji]=0.01 is needed for notable negative feedback (see the blue empty triangles at z<14 in the lower panel)."," Without UV heating, a LW background with a specific intensity of $\Jlwb=0.01$ is needed for notable negative feedback (see the blue empty triangles at $z\leq14$ in the lower panel)." +" This value is similar to the one found in MBHO06, where we showed that by equating H5-cooling and H»5-photodissociation one expects this critical LW background to scale as JI""xngfua/T.* When the UV heating is added, this critical value of ή. causing negative feedback decreases by a factor of ~10 to Jay”1073 (see the green solid circles in lower panel at z< 14)."," This value is similar to the one found in MBH06, where we showed that by equating ${\rm H_2}$ –cooling and ${\rm H_2}$ –photodissociation one expects this critical LW background to scale as $\Jlwb \propto n_g f_{\rm H2}/T$ When the UV heating is added, this critical value of $\Jlwb$ causing negative feedback decreases by a factor of $\sim10$ to $\Jlwb\sim10^{-3}$ (see the green solid circles in lower panel at $z\leq14$ )." + This decrease seems to confirm the above arguments., This decrease seems to confirm the above arguments. +" However, such an interpretation is too simplistic and the negative impact of the LWB can be ameliorated by positive feedback inside the HII region at lower redshifts, as we shall see in §4.."," However, such an interpretation is too simplistic and the negative impact of the LWB can be ameliorated by positive feedback inside the HII region at lower redshifts, as we shall see in \ref{sec:pos}." + From Fig., From Fig. +" 4 one can also note that a value of JI""~10”5-- 107? separates feedback regimes dominated by a LW background from those dominated by our transient UVB.", \ref{fig:LW_delta} one can also note that a value of $\Jlwb\sim 10^{-3}$ $10^{-2}$ separates feedback regimes dominated by a LW background from those dominated by our transient UVB. +" This can be seen by the fact that the amount of suppression differs between the NoUVB and Heat0.8 cases at low values of the LW background (Le. for JI""< 1073), while at large values of JL"", the amount of suppression is independent of the UVB."," This can be seen by the fact that the amount of suppression differs between the NoUVB and Heat0.8 cases at low values of the LW background (i.e. for $\Jlwb < 10^{-3}$ ), while at large values of $\Jlwb$ , the amount of suppression is independent of the UVB." +" Near the threshold value of JI?"" , negative feedback transitions from being UV heating"," Near the threshold value of $\Jlwb$ , negative feedback transitions from being UV heating" +superdisks must be drawn mostly. [rom closer objects for which radio maps with adequate resolution ancl dynamic range are available. and for which the actual conditions are often more similar to those of the ICM at lower redshifts.,"superdisks must be drawn mostly from closer objects for which radio maps with adequate resolution and dynamic range are available, and for which the actual conditions are often more similar to those of the ICM at lower redshifts." + Under those circumstances the typical sizes for wind inllated xibbles would be compressed to a few kpe., Under those circumstances the typical sizes for wind inflated bubbles would be compressed to a few kpc. + We now summarize some salient features of our moclel. (, We now summarize some salient features of our model. ( +1) Superdisks (at. least the wider ones) markgian! λαας conduits along which the AGN's non-relativistic wind is able to escape preferentiallv. ic. in directions roughly »rpendicular to the radio axis along which svnachrotron asma is transported.,"1) Superdisks (at least the wider ones) mark planar conduits along which the AGN's non-relativistic wind is able to escape preferentially, i.e., in directions roughly perpendicular to the radio axis along which synchrotron plasma is transported." + We suggest that the surface. of dvnamical interaction between the wind bubble and the radio lobe pair can offen give rise to well-defined. planar »oundaries between the two media. which we identify asinferfaces and which may be manifested. in. the ts as central emission gaps or superdisks. (," We suggest that the surface of dynamical interaction between the wind bubble and the radio lobe pair can often give rise to well-defined, planar boundaries between the two media, which we identify as and which may be manifested in the RGs as central emission gaps or superdisks. (" +In most RCs. rowever. the viewing angle would. work against the sharp edges. Le. a superdisk morphology. being observed).,"In most RGs, however, the viewing angle would work against the sharp edges, i.e., a superdisk morphology, being observed)." + The metal enriched. gas swept out of the host galaxy is thus ransported to great. distances. not only by being dragged along bv the jets. but in the perpendicular. direction. as well (through the superdisk).," The metal enriched gas swept out of the host galaxy is thus transported to great distances, not only by being dragged along by the jets, but in the perpendicular direction as well (through the superdisk)." + Phus. the AGN activity would end to isotropize the metal enrichment process. as is indeed iound Crom measurements (de Grandi et 22004). ," Thus, the AGN activity would tend to isotropize the metal enrichment process, as is indeed found from measurements (de Grandi et 2004). (" +"E) Phis scenario provokes us to revisit the question radsed three decades ago by Jenkins Seheuer (1976): ""what docks the tails of radio source components?""","2) This scenario provokes us to revisit the question raised three decades ago by Jenkins Scheuer (1976): “what docks the tails of radio source components?""" + They concluded that the cause is other than svnchrotron Losses., They concluded that the cause is other than synchrotron losses. + Later. an explanation was proposed in terms of blocking of the radio lobe plasma by the LSAL of the host galaxy (e.g. Leahy Williams 1984).," Later, an explanation was proposed in terms of blocking of the radio lobe plasma by the ISM of the host galaxy (e.g., Leahy Williams 1984)." + In our picture. on the other hand. the sharp ancl straight edges of the strip-like central gaps in the radio bridge signify where the thermal wind outflowing from the AGN is actually countered and redirected. by. the lobe overpressure assisted. by. the dynamic pressure of the back-owing relativistic plasma inside the radio lobes.," In our picture, on the other hand, the sharp and straight edges of the strip-like central gaps in the radio bridge signify where the thermal wind outflowing from the AGN is actually countered and redirected by the lobe overpressure assisted by the dynamic pressure of the back-flowing relativistic plasma inside the radio lobes." + Eventually. when the pressure of this back-Llow has declined sulliciently. it could even mix with and be dragged: along the thermal wind. escaping in the perpendicular direction. (," Eventually, when the pressure of this back-flow has declined sufficiently, it could even mix with and be dragged along the thermal wind escaping in the perpendicular direction. (" +"3) J£ indeed the “wind” outflow precedes the radio jet ejection. the pancake or superdisk resulting from the Iobe-wind interaction can become ""frozen"" in space quite early in the active phase of the galaxy.","3) If indeed the “wind"" outflow precedes the radio jet ejection, the pancake or superdisk resulting from the lobe-wind interaction can become “frozen"" in space quite early in the active phase of the galaxy." + Now. if the galaxy has a large enough component of motion normal to the superclisk (sav. 500 km 1 or more). LE. may even move out of the Latter into. the lobe during its active lifetime.," Now, if the galaxy has a large enough component of motion normal to the superdisk (say, 500 km $^{-1}$ or more), it may even move out of the latter into the lobe during its active lifetime." + Two RCs exemplifving such a situation are 3€ 16 and 3€ 19. where the host galaxy is seen the radio gap (Llarvanck Llarcdeastle 1998: Leahy Perley 19901: Gilbert et 22004).," Two RGs exemplifying such a situation are 3C 16 and 3C 19, where the host galaxy is seen the radio gap (Harvanek Hardcastle 1998; Leahy Perley 1991; Gilbert et 2004)." + While such a morphology is expected only in extreme cases. it is quite conceivable in our picture but hard to understand within the usual interpretation of the radio gaps invoking a buovaney led outward squeezing of the radio lobes by the denser LSAL of the parent galaxy. (," While such a morphology is expected only in extreme cases, it is quite conceivable in our picture but hard to understand within the usual interpretation of the radio gaps invoking a buoyancy led outward squeezing of the radio lobes by the denser ISM of the parent galaxy. (" +4) Notwithstanding the sharp. quasi-planar boundaries of the radio gap. the present model does allow for some fainter radio emission seen within the gap (being remnant of the carly phase when the radio jets were still boring their wav through the bubble).,"4) Notwithstanding the sharp, quasi-planar boundaries of the radio gap, the present model does allow for some fainter radio emission seen within the gap (being remnant of the early phase when the radio jets were still boring their way through the bubble)." + Examples of this can be found in the radio sources J11371613 (Lara οἱ 22001) and J1628| 3932 (de Dreuck οἱ 2004)., Examples of this can be found in the radio sources $+$ 613 (Lara et 2001) and $+$ 3932 (de Breuck et 2004). + Otherpossible manifestations of this situation are 3€ 63 (Llarvanek Llarcleastle 1998). 3€ 136.1 (Leahy Williams. 1984). and 3€ 300 (Leahy Williams. 1984: Llardeastle et 11997).," Otherpossible manifestations of this situation are 3C 63 (Harvanek Hardcastle 1998), 3C 136.1 (Leahy Williams 1984), and 3C 300 (Leahy Williams 1984; Hardcastle et 1997)." + However. such remnant emission usually will be cillicult to see without high dvnamic range observations and will not last. very long compared. to the total lifetime of the radio source.," However, such remnant emission usually will be difficult to see without high dynamic range observations and will not last very long compared to the total lifetime of the radio source." + This is because this inner racio emitting plasma will be cut olf [rom a continued supply of the baekllow from the lobes and. will be mixed. up and dispersed with the the thermal outflow through the chimney (i.e... superclisk).," This is because this inner radio emitting plasma will be cut off from a continued supply of the backflow from the lobes and will be mixed up and dispersed with the the thermal outflow through the chimney (i.e., superdisk)." +" Finally. although the scenario. sketehed here has been quantified in a highly simplified. analytical form. the possibility. of the. sharp-ccged radio gaps being wind-lobe interfaces. Le. ""active surfaces of dynamical interaction between the thermal anc nonthermal outllows. may have other interesting observational ancl theoretical consequences."," Finally, although the scenario sketched here has been quantified in a highly simplified analytical form, the possibility of the sharp-edged radio gaps being wind-lobe interfaces, i.e., “active"" surfaces of dynamical interaction between the thermal and nonthermal outflows, may have other interesting observational and theoretical consequences." + dence. this general picture needs. to. be explored further.," Hence, this general picture needs to be explored further." + Full hyelrodyvnamic simulations of this situation are worth pursuing., Full hydrodynamic simulations of this situation are worth pursuing. + On the observational side. detailed radio imaging of high= radio galaxies would provide useful input and constraints on the basic moclel presented here.," On the observational side, detailed radio imaging of $-z$ radio galaxies would provide useful input and constraints on the basic model presented here." + We thank the referee. Martin. Hardcastle. for criticisms which significantly focussed. the arguments of this paper.," We thank the referee, Martin Hardcastle, for criticisms which significantly focussed the arguments of this paper." + This research— has mace use of the NASA/IPAC Extragalactic Database (NIED) which is operated by the Jet Propulsion Laboratory. under contract with the National Acronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, under contract with the National Aeronautics and Space Administration." + iis erateful [or continuing hospitality at. the Princeton University Department of Astrophysical Sciences. and acknowledges support from a sub-contract to GSU from National Science. Foundation. grant. AST-0507529 to the University of Washington., is grateful for continuing hospitality at the Princeton University Department of Astrophysical Sciences and acknowledges support from a sub-contract to GSU from National Science Foundation grant AST-0507529 to the University of Washington. +,. + Tudeed. Sclavineger(1919) followed this path in deriving an analytic expression for the svuchrotron chussivity.," Indeed, \citet{schwinger49} followed this path in deriving an analytic expression for the synchrotron emissivity." + Tlowever. because the integrands are oscillatory. it is instead preferable to group them together.," However, because the integrands are oscillatory, it is instead preferable to group them together." + Transforming the integration variable from 7 to the phase-lag g defined iu (13)). iu the case of the first τν in (10)). aud as g=wr(l|3(f)) iu the case of the second tei. leads to Eu |.," Transforming the integration variable from $\tau$ to the phase-lag $g$ defined in \ref{phaselagdef}) ), in the case of the first term in \ref{firstorderint}) ), and as $g=\omega\tau(1+\beta(t))$ in the case of the second term, leads to ,t) = ] ]." + where cTA(t.7)/|r|(52) As required. P vanishes to zeroth order in the deviations from a ballistic orbit. (299). (313) and. (33)).," where - - As required, $P$ vanishes to zeroth order in the deviations from a ballistic orbit, \ref{devposition}) ), \ref{devvelocity}) ) and \ref{devdisplacement}) )." +" The erouping of the terms in Equation (51)) in this manner Is especially portant at high frequencies. where the higher order terms in P? aud P, are simall."," The grouping of the terms in Equation \ref{instpower}) ) in this manner is especially important at high frequencies, where the higher order terms in $P_1$ and $P_2$ are small." + Iu this laut. the two terms cau be expressed as = and cancel exactly whensuuuned.," In this limit, the two terms can be expressed as = and cancel exactly whensummed." + In a mmucrical evaluation. a small error remains. which erows linearly with w.," In a numerical evaluation, a small error remains, which grows linearly with $\omega$." + Grouping the terms together prevents the erowtli of this error., Grouping the terms together prevents the growth of this error. + Under the assuniptious that the clectromaguetic fields varyslowly ou the timescale of a photonformatio- leugth. aud that linear acceleration cussion (e.g.Sclwinecr1919) ds unimüportant. we demonstrate 1- appendix A that (51)) reduces to a local ciissivity.," Under the assumptions that the electromagnetic fields varyslowly on the timescale of a photonformation length, and that linear acceleration emission \citep[e.g.][]{schwinger49} is unimportant, we demonstrate in appendix \ref{appendix_synchrotron} that \ref{instpower}) ) reduces to a local emissivity." + This is au obvious ecucralization of standard svuchrotrou Cluission. Which takes account of acceleration iu both magnetic and electric fields by forumlating it iu ters of the local curvature of the trajectory: where woc—oujf2(51) aud the curvature & is defined. locally in terms of the particle velocityaud acceleration 3 aud 3: -- A perturbative approach thatincludes linear acceleration cluission as a first order— correction— to (56))has been preseuted by Melrose(1978).," This is an obvious generalization of standard synchrotron emission, which takes account of acceleration in both magnetic and electric fields by formulating it in terms of the local curvature of the trajectory: ,t) = (x) where /2 and the curvature $\kappa$ is defined locally in terms of the particle velocityand acceleration $\bm{\beta}$ and $\dot{\bm{\beta}}$ : = A perturbative approach thatincludes linear acceleration emission as a first order correction to \ref{instsyncheq}) )has been presented by \citet{melrose78}." +. To perform the imteeration in (51)) ποαν. we first split it at the points where sing= 0. Le.Ίσα g=nz. (n—0.1. x2...). and write it as an infinite sui wt)= |," To perform the integration in \ref{instpower}) ) numerically, we first split it at the points where $\sin g=0$ , i.e., $g=n\pi$ , $(n=0,\pm1,\pm2\dots)$ , and write it as an infinite sum ,t) = ] ]." +majority of satellites reionize later than the mean.,majority of satellites reionize later than the mean. +" In practice, the difference between the patchy and instantaneous case in Fig."," In practice, the difference between the patchy and instantaneous case in Fig." +" 7 is due to a combination of two effects: that the global mean is not necessarily the best instantaneous redshift to choose for a given halo, as well as not capturing the spread in reionization times."," \ref{fig:sat_cand} is due to a combination of two effects: that the global mean is not necessarily the best instantaneous redshift to choose for a given halo, as well as not capturing the spread in reionization times." +" However, we do not find that using e.g. the host halo reionization redshift, or the median satellite reionization redshift, leads to better agreement in each case."," However, we do not find that using e.g. the host halo reionization redshift, or the median satellite reionization redshift, leads to better agreement in each case." +" While we could recover the number of satellites in each case by tuning the instantaneous reionization redshift, the value of such an exercise is limited: the only way to determine that appropriate redshift would be to already know the result from the patchy model."," While we could recover the number of satellites in each case by tuning the instantaneous reionization redshift, the value of such an exercise is limited: the only way to determine that appropriate redshift would be to already know the result from the patchy model." +" As such, this illustrates the main problem with using instantaneous spatially homogeneous reionization models."," As such, this illustrates the main problem with using instantaneous and/or spatially homogeneous reionization models." +" Depending and/oron the application, the fact that there is a distribution of satellite reionization redshifts may be important to the results — and this distribution cannot be captured in a homogeneous model, nor can the appropriate instantaneous approximation be recovered without knowing the patchy result."," Depending on the application, the fact that there is a distribution of satellite reionization redshifts may be important to the results – and this distribution cannot be captured in a homogeneous model, nor can the appropriate instantaneous approximation be recovered without knowing the patchy result." +some of the differences in interpretation of UV spectra of VW νὰ in quiescence.,some of the differences in interpretation of UV spectra of VW Hyi in quiescence. + The first component has a photospheric temperature of 23.000. a rotation rate of 400 kins | and chemical abundances (hat are reasonably consistent wilh previous HIST FOS. GIIRS and OTIS results.," The first component has a photospheric temperature of 23,000K, a rotation rate of 400 km $^{-1}$ and chemical abundances that are reasonably consistent with previous HST FOS, GHRS and STIS results." + This seems to indicate a cooling of the WD 11 days after a normal 3 cay outburst., This seems to indicate a cooling of the WD 11 days after a normal 3 day outburst. + The second component has an effective temperature higher than that of the WD. and a featureless (rather flat) spectrum.," The second component has an effective temperature higher than that of the WD, and a featureless (rather flat) spectrum." + Our numerical modeling is unable to account in detail for some of the features such as: (1) large discrepancies between our theoretical spectrum and (he present FUSE data around 925 and 1100À: (2) the aceretion belt model does not account for the upturn in flux at the Lyiman limit. where (he variability. is strongest. which is also (he region of the spectrum where the WD does not contribute to the flux. and consequently. neither the WD nor the accretion belt model can possibly be the source of the variabili: (3) the OVI emission lines in theFUSE spectrum indicate the possible presence of an optically (hin source in the svslenm.," Our numerical modeling is unable to account in detail for some of the features such as: (1) large discrepancies between our theoretical spectrum and the present FUSE data around 925 and 1100; (2) the accretion belt model does not account for the upturn in flux at the Lyman limit, where the variability is strongest, which is also the region of the spectrum where the WD does not contribute to the flux, and consequently, neither the WD nor the accretion belt model can possibly be the source of the variability; (3) the OVI emission lines in the spectrum indicate the possible presence of an optically thin source in the system." + Therefore. (he exact nature of the second component is still relatively uncertain. due to the lack of better models for spectra of the inner disk in a quiescent. dwarf nova.," Therefore, the exact nature of the second component is still relatively uncertain, due to the lack of better models for spectra of the inner disk in a quiescent dwarf nova." + As we mentioned in 81 the possible candidates for a second component (1) an accretion belt. ie. a fast rotating heated laver of the surface of the WD. possibly created in the outburst and which remains hot primarily because of the effective viscosity of ihe WD. (," As we mentioned in 1 the possible candidates for a second component (1) an accretion belt, i.e. a fast rotating heated layer of the surface of the WD, possibly created in the outburst and which remains hot primarily because of the effective viscosity of the WD. (" +2) the boundary laver. i.e. the region between the inner edge of the disk and the stellar surface where the remaining kinetic energy of (he accreting flow is released.,"2) the boundary layer, i.e. the region between the inner edge of the disk and the stellar surface where the remaining kinetic energy of the accreting flow is released." +" This optically (hin reeion rellects the instantaneous accretion rate ancl is expected to emit X-ray, ", This optically thin region reflects the instantaneous accretion rate and is expected to emit X-ray. ( +3) an optically thick disk. however physically. unjustified in the accretion disk limit evcle nodel (Cannizzo1993).. is what we are numerically able to moclel. (,"3) an optically thick disk, however physically unjustified in the accretion disk limit cycle model \citep{can93}, is what we are numerically able to model. (" +4) ox a corona/chromosphere above a cool disk.,4) or a corona/chromosphere above a cool disk. + Ai the present time. only the optically thick accretion belt ancl accretion disk can be nunerically modeled. while no detailed modeling exists lor the optically thin components spectra).," At the present time, only the optically thick accretion belt and accretion disk can be numerically modeled, while no detailed modeling exists for the optically thin components (spectra)." + The results we obtained here indicate that the [ast rotating belt is the best candidate for the source of the second FUY component., The results we obtained here indicate that the fast rotating belt is the best candidate for the source of the second FUV component. +of the seismic QBO alone cannot be extracted.,of the seismic QBO alone cannot be extracted. + To determine the latitudinal dependence of the seismic QBO we must look at solar minimum., To determine the latitudinal dependence of the seismic QBO we must look at solar minimum. +" However, as we have shown, at this time the signal is not strong enough to constrain the / dependence."," However, as we have shown, at this time the signal is not strong enough to constrain the $l$ dependence." + The amplitude of the QBO in the low-frequency-range /=3 residuals is noticeably larger than for the other / (see Fig., The amplitude of the QBO in the low-frequency-range $l=3$ residuals is noticeably larger than for the other $l$ (see Fig. + 3 and Table 1))., \ref{figure[residuals]} and Table \ref{table[abs dev]}) ). +" This could be a genuine effect: As noted in the previous section, there is a well-known dependence on in the size of the 11-yr solar cycle frequency shifts."," This could be a genuine effect: As noted in the previous section, there is a well-known dependence on $l$ in the size of the 11-yr solar cycle frequency shifts." +" However, we note/ that the estimates of the /=3 mode frequencies are more noisy than the frequencies estimated for the other /."," However, we note that the estimates of the $l=3$ mode frequencies are more noisy than the frequencies estimated for the other $l$." +" Furthermore, estimates of the /=3 mode frequencies are also influenced by the nearby, much stronger, /21 modes."," Furthermore, estimates of the $l=3$ mode frequencies are also influenced by the nearby, much stronger, $l=1$ modes." + This is partially reflected in the size of the error bars associated with the fitted frequencies (see also Figs., This is partially reflected in the size of the error bars associated with the fitted frequencies (see also Figs. +" 1 and 3)), but, as seen in Section ?? it is still possible that the uncertainties are underestimated."," \ref{figure[freq shifts]} and \ref{figure[residuals]}) ), but, as seen in Section \ref{subsection[significance of QBO]} it is still possible that the uncertainties are underestimated." + Fig., Fig. +" 3 shows that the seismic QBO is more evident at high frequencies and it could be argued that the ""signal"" in the low-frequency range is just noise."," \ref{figure[residuals]} + shows that the seismic QBO is more evident at high frequencies and it could be argued that the “signal” in the low-frequency range is just noise." + This implies that the seismic QBO signal shows some frequency dependence., This implies that the seismic QBO signal shows some frequency dependence. + We have used the 182.5dd frequencies to determine the frequency at which the seismic QBO stops being significant., We have used the d frequencies to determine the frequency at which the seismic QBO stops being significant. +" To do this the weighted average frequency shifts were generated for each subset in time, in the manner described in Section ??.."," To do this the weighted average frequency shifts were generated for each subset in time, in the manner described in Section \ref{section[data]}." +" However, here we averaged the frequency shifts of the modes over four overtones only."," However, here we averaged the frequency shifts of the modes over four overtones only." +" The lowest frequency range for which the mean shifts were calculated was mmHz, i.e. the lower limit of the frequency ranges described -in Section ??.."," The lowest frequency range for which the mean shifts were calculated was mHz, i.e. the lower limit of the frequency ranges described in Section \ref{section[data]}." + The next frequency range was positioned so that it overlapped this range by 3 overtones i.e. mmHz., The next frequency range was positioned so that it overlapped this range by 3 overtones i.e. mHz. + This process was repeated until the upper limit on the frequency ranges described in Section ?? was reached., This process was repeated until the upper limit on the frequency ranges described in Section \ref{section[data]} was reached. + In total the mean frequency shift was determined for 11 frequency ranges., In total the mean frequency shift was determined for 11 frequency ranges. +" We have considered the /=2 frequency shifts only, because over the entire epoch considered here, the seismic QBO is strongest in the /=2 frequencies (see Fig. 2))."," We have considered the $l=2$ frequency shifts only, because over the entire epoch considered here, the seismic QBO is strongest in the $l=2$ frequencies (see Fig. \ref{figure[periodograms]}) )." + A periodogram of the /=2 frequency shifts was then determined in the manner described in Section ??.., A periodogram of the $l=2$ frequency shifts was then determined in the manner described in Section \ref{subsection[significance of QBO]}. + We found that the lowest frequency band at which the seismic QBO was still significant at a pper cent false alarm level was mmHz., We found that the lowest frequency band at which the seismic QBO was still significant at a per cent false alarm level was mHz. + Residuals of the /=2 frequency shifts were then determined for the frequency bands in which the seismic QBO was significant., Residuals of the $l=2$ frequency shifts were then determined for the frequency bands in which the seismic QBO was significant. + The maximum absolute deviations of the residuals at times of high- and low-surface activity are shown in Fig. 5..," The maximum absolute deviations of the residuals at times of high- and low-surface activity are shown in Fig. \ref{figure[frequency +dependence]}." +" For comparison purposes the maximum absolute deviation of the raw frequency shifts was also calculated, as this reflects the amplitude of the seismic 11-yr solar cycle."," For comparison purposes the maximum absolute deviation of the raw frequency shifts was also calculated, as this reflects the amplitude of the seismic 11-yr solar cycle." + Fig., Fig. + 5 shows that the frequency dependence of the seismic QBO is weaker than the frequency dependence of the 11-yr solar cycle., \ref{figure[frequency dependence]} shows that the frequency dependence of the seismic QBO is weaker than the frequency dependence of the 11-yr solar cycle. + Although the 11-yr solar cycle magnetic flux is believed to be generated at the base of the convection zone the main influence of the 11-yr signal on the p-mode frequencies occurs in the upper few kkm of the convection zone., Although the 11-yr solar cycle magnetic flux is believed to be generated at the base of the convection zone the main influence of the 11-yr signal on the p-mode frequencies occurs in the upper few km of the convection zone. + This is above the upper turning point of the lowest frequency modes examined here and so explains the, This is above the upper turning point of the lowest frequency modes examined here and so explains the +convection zone: an interlace dvnamo. in which all the action is concentrated at the base of the convection zone ancl in the tachocline: and a {lis transport dynamo. which might be envisaged as having an w-ellect arising from the velocity shear in the tachocline and an a-ellect located close to the solar surlace. with the two linked by some large-scale flow.,"convection zone; an interface dynamo, in which all the action is concentrated at the base of the convection zone and in the tachocline; and a flux transport dynamo, which might be envisaged as having an $\omega$ -effect arising from the velocity shear in the tachocline and an $\alpha$ -effect located close to the solar surface, with the two linked by some large-scale flow." + There are certainly problems with all three types of dvnamo., There are certainly problems with all three types of dynamo. + A distributed dvnamo relies on a coherent a-effect throughout the convection zone: (his is not supported by theoretical argumentis (Cattaneo&Hughes2009) or numerical simulations (Brinetal.2004)., A distributed dynamo relies on a coherent $\alpha$ -effect throughout the convection zone; this is not supported by theoretical arguments \citep{CH09} or numerical simulations \citep{BMT04}. +.. A [Iux transport dvnamo relies crucially on the migration of surface magnetic features and a large-scale flow to return the field to the base of the convection zone. essentially ignoring all the turbulent. dynamics of the convection zone.," A flux transport dynamo relies crucially on the migration of surface magnetic features and a large-scale flow to return the field to the base of the convection zone, essentially ignoring all the turbulent dynamics of the convection zone." + An interlace dvnamo is more appealing in (hat the different aspects of the dvnanmo process are nol widely spatially separated., An interface dynamo is more appealing in that the different aspects of the dynamo process are not widely spatially separated. + Toroidal field would be amplified from the poloidal component bv the differential rotation in the tachocline: the diflicully though is in closing the dvnamo evele., Toroidal field would be amplified from the poloidal component by the differential rotation in the tachocline; the difficulty though is in closing the dynamo cycle. + One possibility is from helical overshooting convection. though this would then still rely on the traditional a-ellect working at hieh magnetic Revnolds numbers.," One possibility is from helical overshooting convection, though this would then still rely on the traditional $\alpha$ -effect working at high magnetic Reynolds numbers." + An emf resulting from magnetic buovancy instability provides a natural possible alternative solution to this problem., An emf resulting from magnetic buoyancy instability provides a natural possible alternative solution to this problem. + Clearly. further. more involved. investigations are needed in order (o examine the viability of Chis idea.," Clearly, further, more involved, investigations are needed in order to examine the viability of this idea." + wwas supported by a studentship Irom (the Science and Technologies Facilities Council., was supported by a studentship from the Science and Technologies Facilities Council. + wwas supported by STFC and by a Roval Society Leverhulme Trust senior Research Fellowship., was supported by STFC and by a Royal Society Leverhulme Trust Senior Research Fellowship. + in the measured ionization potential of 153.1 eV. We found. that this charge is Z=3.3544., in the measured ionization potential of 153.1 eV. We found that this charge is $Z=3.3544$. + We then repeated the calculation of the plasma οσο on the bound states assuming this charge., We then repeated the calculation of the plasma effect on the bound states assuming this charge. + The results are shown in fig. 2.., The results are shown in fig. \ref{fig:hi12-diff}. + We then used the new values for the ionization potential in the Saha equation to find the revised f; ον, We then used the new values for the ionization potential in the Saha equation to find the revised $f_{1}$ $f_{2}$. + The comparison between the values used with and without the plasma correction are shown in fig. 23..," The comparison between the values used with and without the plasma correction are shown in fig. \ref{fig:Be7-sun}," + where the actual run of the occupation numbers in the Sun is given., where the actual run of the occupation numbers in the Sun is given. + lt ijs surprising that (the dillerences in the ionization come out to be quite small., It is surprising that the differences in the ionization come out to be quite small. + The particular results for the binding energy (calculated for a DIL potential) as a function. of the density are shown again in figure 4. along with the run of the ratios RofRelZ=4) and Grof/Rel(Z=4)., The particular results for the binding energy (calculated for a DH potential) as a function of the density are shown again in figure \ref{fig:Be-Debye} along with the run of the ratios $R_{D}/R_{B}(Z=4)$ and $\langle r_{s} \rangle /R_{B}(Z=4)$. + The Debve radius and the mean interparticle distance are caleulated assuming N=034.Y—0.68 and Z=0.02. a composition which is close to the one at the solar core today.," The Debye radius and the mean interparticle distance are calculated assuming $X=0.34, Y=0.68$ and $Z=0.02$, a composition which is close to the one at the solar core today." + We notice that when the density approaches the density in the solar core. namely abou 150οem (a) the Debve radius becomes of the order of the mean interparticle distance and hence the approximation of a smooth Dehve screened. potential loses its validity. emphasizing once more the conclusion reached in section 2.. (," We notice that when the density approaches the density in the solar core, namely about $150~{\rm g~cm^{-3}}$, (a) the Debye radius becomes of the order of the mean interparticle distance and hence the approximation of a smooth Debye screened potential loses its validity, emphasizing once more the conclusion reached in section \ref{sec:whatp}. (" +b) In the solar core. we find that Ry=Re(Z—4) and therefore the probability for complete ionization of the De is very high.,"b) In the solar core, we find that $R_{D} \approx R_{B}(Z=4)$ and therefore the probability for complete ionization of the ${\rm Be}$ is very high." + Llowever. the more important question here is the ratio of the mean interparticle distance to the Bohr radius since we are interested in the possibility that the ions of Bervlium still have bound electrons.," However, the more important question here is the ratio of the mean interparticle distance to the Bohr radius since we are interested in the possibility that the ions of Beryllium still have bound electrons." + Fig. 4..," Fig. \ref{fig:Be-Debye}," + which depicts a graph for the value of £r;. indicates that this value at the center of rw Sun it is close to Z?g(Z=4).," which depicts a graph for the value of $\langle r_{s} \rangle $, indicates that this value at the center of the Sun it is close to $R_{B}(Z=4)$." + Therefore. it is a delicate question whether the Bervilium ions possess any bound electrons.," Therefore, it is a delicate question whether the Beryllium ions possess any bound electrons." + Finally. we point out that Ge). which is depicted in the figure. is the mean interparticle distance irrespective of their type.," Finally, we point out that $\langle r_{s} \rangle$, which is depicted in the figure, is the mean interparticle distance irrespective of their type." + As we shall show. it is an underestimate in the case of a Bervilium ion embedded in Livedrogen and Helium ions.," As we shall show, it is an underestimate in the case of a Beryllium ion embedded in Hydrogen and Helium ions." +Dark Encrey has challenged our knowledge οἱ fundamental plysics since the direct evidence for its existence was discovered using Type Ia supernovae (Riessetal.1998:Perhuutteret 1999)..,"Dark Energy has challenged our knowledge of fundamental physics since the direct evidence for its existence was discovered using Type Ia supernovae \citep{Riess98AJ, Perlmutter99ApJ}." + Because there are currently no compcling theoretical expanatious for Darl Eucrex. the correct cluplasis. as poiuted outby the Darl Encrev Task Force (DETF.Albrechtettal.2006).. is on refining our observations of the accecrated expansion of the universe.," Because there are currently no compelling theoretical explanations for Dark Energy, the correct emphasis, as pointed out by the Dark Energy Task Force \citep[DETF,][]{Albrecht06}, is on refining our observations of the accelerated expansion of the universe." + Decornmendatiou V from the DETF Report (Albrechtμιαςetal.2006) calls for an exploration of the ο effects that could iupair the needed observational refinemieuts., Recommendation V from the DETF Report \citep{Albrecht06} calls for an exploration of the systematic effects that could impair the needed observational refinements. + Acouple of recent studies (Il&Greene2006:Coorav&Caldwell200€j) point out that the redshift every armi ueeded to accurately measure the uuiversa expansion requires the use of a local sample. but that coherent large-scale local 0.2) peculiar velocities add additional uncertaüutv to the Iblde diagran ae rence to the derived cosmological parameters.," Acouple of recent studies \citep{Hui06PhRvD, Cooray06PhRvD} point out that the redshift lever arm needed to accurately measure the universal expansion requires the use of a local sample, but that coherent large-scale local $z < 0.2$ ) peculiar velocities add additional uncertainty to the Hubble diagram and hence to the derived cosmological parameters." + Current analyses (6.8e.Astieretal.2006:RiesseHal.2007:Wood-Vascyvct2007) of the cosmological waralucters do not attempt to correct for the effec 6X local peculiar. velocities.," Current analyses \citep[e.g.,][]{Astier06A&A,Riess07ApJ,Wood-Vasey07astroph} of the cosmological parameters do not attempt to correct for the effect of local peculiar velocities." + As briefly noted bv and Coorav&Calelwell(2006).. it is possible to use local data to measure the local veoocitv fied aud hence liit the impact ou the derived COsinologic:d parameters.," As briefly noted by and \citet{Cooray06PhRvD}, it is possible to use local data to measure the local velocity field and hence limit the impact on the derived cosmological parameters." + Moeasurenienuts of the local veoocitv fieId have improved to the point where there Is consiste1CY ÓdLOlg νους and methods (IIndson 06)...," Measurements of the local velocity field have improved to the point where there is consistency among surveys and methods \citep{Hud03, +HudSmiLuc04, Radburn04MNRAS, PikHud05, Sarkar06}." + Type Ia SI)uova peculiar velocities have been sucdied recently by Radburn-Sinithetal.(2001):Pike&IIudsou(2005):FeclaE and others.," Type Ia supernova peculiar velocities have been studied recently by \cite{Radburn04MNRAS, +PikHud05, JhaRieKir06, HauHanTho06,Watkins07astroph} and others." + Their cnls ceiuonstrate thiHi the local flows derived froin SNe are in agreement wih those derived from other distauce 1xdicators. such as the Tullv-Fisher relation aud the Fuidaimental Plane.," Their results demonstrate that the local flows derived from SNe are in agreement with those derived from other distance indicators, such as the Tully-Fisher relation and the Fundamental Plane." + Οιr alui ds to use the current kuowkdee of the loca pcculiar notions to correct locul SNeaxc. together with a i0niogeneous set of distaun SNe. fit for cosmologica paralucters and measure the effect o tfie corrections on the cosmological fits.," Our aim is to use the current knowledge of the local peculiar motions to correct local SNe and, together with a homogeneous set of distant SNe, fit for cosmological parameters and measure the effect of the corrections on the cosmological fits." +" To produce this 1ieasureiment. we analyze the local anc distant SN Ia sample used in the firs-vear cosmology results from the Supernova Legacy 8rvey (SNLS.Αμα Αθ, "," To produce this measurement, we analyze the local and distant SN Ia sample used in the first-year cosmology results from the Supernova Legacy Survey \citep[SNLS,][hence A06]{Astier06A&A}. ." +This sampl ds οςxuposed of 1 local SNe(AOG.Table8:Wamuctal.1996Riesset are," This sample is composed of 44 local SNe \citep[A06, Table~8:][]{Hamuy96AJ, Riess99AJ, Krisciunas01AJ, +Jha02PhDT, Strolger02AJ, Altavilla04MNRAS, Krisciunas04AJa, +Krisciunas04AJb} and" + Ou June 30th. 1908. something exploded over Tuneuska. in central Siheria.," On June 30th, 1908, something exploded over Tunguska, in central Siberia." + Over the last nineotv vears this catastrophic event has inspired a plethora of scieutific investigations., Over the last ninety years this catastrophic event has inspired a plethora of scientific investigations. + Despite many interesting findiugs. there are still substantial open questions and. iuconsistencies zione the theories aud the available data (for a review see Vasilvey 1998)).," Despite many interesting findings, there are still substantial open questions and inconsistencies among the theories and the available data (for a review see Vasilyev \cite{VASILYEV}) )." + Among many different effects. the Tuuguska explosion produced shock waves. which were recorded by seiunographns at several sites.," Among many different effects, the Tunguska explosion produced shock waves, which were recorded by seismographs at several sites." + DenMonah (1975)) made a cletailed analysis of these seismic records aid derived. an explosive energv of 12.5+2.5 AMtou., Ben–Menahem \cite{MENAHEM}) ) made a detailed analysis of these seismic records and derived an explosive energy of $12.5\pm 2.5$ Mton. + Πο also concluded: tha the data ou the energv source are consistent with an airburst at a height of about 8.5 kin., He also concluded that the data on the energy source are consistent with an airburst at a height of about 8.5 km. + Tn a previous etter (1998)). we have shown that seine data can be used to characterize the very bright 1993 Lugo bolide. obtaining a good match between the derived solution aud the observations.," In a previous letter \cite{FOSCHINI}) ), we have shown that seismic data can be used to characterize the very bright 1993 Lugo bolide, obtaining a good match between the derived solution and the observations." + Tere the Sale methodology is applied to analyze the Tuuguska eveut. musing BenMenalieurs analysis as a starting point.," Here the same methodology is applied to analyze the Tunguska event, using Ben–Menahem's analysis as a starting point." + Several different models have been developed in order to fit all the available data on the Tuneuska event (0.5. Chyba et al. 1993.. ," Several different models have been developed in order to fit all the available data on the Tunguska event (e.g. Chyba et al. \cite{CHYBA}, ," +Grigorian 1998.. ills Coda 1993.. Lyne et al. 1996)).," Grigorian \cite{GRIGORIAN}, Hills Goda \cite{HILLS}, Lyne et al. \cite{LYNE}) )." + All these models have contributed significantly to a general nuprovenient dn. our understanding of the atimospheric disruptiou of meteoroils., All these models have contributed significantly to a general improvement in our understanding of the atmospheric disruption of meteoroids. + They usually assunie that the fraeiieutation process starts when the acrodvuaic pressure is equal to the mechanical strength S of the cosmic body., They usually assume that the fragmentation process starts when the aerodynamic pressure is equal to the mechanical strength $S$ of the cosmic body. + Relating air deusitv to aimburst height. this allows oue to derive the 1neteoroid speed(V): where py is the atinospherie deusity at sea level. fis the height of first fragmentation and Π is the atmospheric scale height (about 8 kia).," Relating air density to airburst height, this allows one to derive the meteoroid speed$V$ ): where $\rho_{\mathrm{sl}}$ is the atmospheric density at sea level, $h$ is the height of first fragmentation and $H$ is the atmospheric scale height (about 8 km)." + From BenMenalieimis analysis we infer that there was a single fragmentation eveut: there is no evidence of multiple explosions. as it should occur diving iuultiple fragmentation events (DenMoenalieia 1975)).," From Ben–Menahem's analysis we infer that there was a single fragmentation event; there is no evidence of multiple explosions, as it should occur during multiple fragmentation events (Ben–Menahem \cite{MENAHEM}) )." + Thus Eq. (1 )), Thus Eq. \ref{e:velo}) ) + can be used to derive V. provided one assumes that the first fragmentation coimcided with the zirburst occurred at f=8.5 kan.," can be used to derive $V$, provided one assumes that the first fragmentation coincided with the airburst occurred at $h += 8.5$ km." + For different types of cosunic body. correspoucding to clifferenut assuinied values for ο (taken from Ilills Cocla. 1993)). we obtain the results listed in Table 1..," For different types of cosmic body, corresponding to different assumed values for $S$ (taken from Hills Goda, \cite{HILLS}) ), we obtain the results listed in Table \ref{speed-actual}." + Now. sncee before exploding large meteoroids undergo a limited mass loss diame their atmospheric path. the preexplosion speed must be close to the (gcoceutric) orbital speed. aud thus must be greater than the Earth's escape velocity (11.2 kms).," Now, since before exploding large meteoroids undergo a limited mass loss during their atmospheric path, the pre--explosion speed must be close to the (geocentric) orbital speed, and thus must be greater than the Earth's escape velocity $11.2$ km/s)." + Therefore. according to the results derived from Eq. (," Therefore, according to the results derived from Eq. (" +1). the most plausible solution would be that of an iron body.,"1), the most plausible solution would be that of an iron body." +" However. the iron body hypothesis is not consistent with the recent onsite recovery of nücroreninants frou, a stouv object (Longo et al. 199 L.. "," However, the iron body hypothesis is not consistent with the recent on–site recovery of microremnants from a stony object (Longo et al. \cite{LONGO}, ," +Serra et al. 1991)., Serra et al. \cite{SERRA}) ). + Actually. taking iuto account the wncertainty in the valueof $ aud the different measurement errors," Actually, taking into account the uncertainty in the valueof $S$ and the different measurement errors" +Alodeling the observed properties of the Galactic population of radio pulsars. with the purpose of inferring their intrinsic properties. has been the subject of extensive investigation for several decades (c.g. Gunn Ostriker 1970: Phinney Dlandford 1981: Lyne et al.,"Modeling the observed properties of the Galactic population of radio pulsars, with the purpose of inferring their intrinsic properties, has been the subject of extensive investigation for several decades (e.g. Gunn Ostriker 1970; Phinney Blandford 1981; Lyne et al." + 1985: Stollman LOST: Emunering Chevalier 1980: Naravan Ostriker 1990: Lorimer et al., 1985; Stollman 1987; Emmering Chevalier 1989; Narayan Ostriker 1990; Lorimer et al. + 1993: Hartman et al., 1993; Hartman et al. + 1997: Cordes Chernoll 1998: Arzoumanian. Cordes Chernoll 2002: Vranesevic ct al 2004: Faucher-Ciguere. Ixaspi: 2006: Ferrario Wickramasinghe 2006).," 1997; Cordes Chernoff 1998; Arzoumanian, Cordes Chernoff 2002; Vranesevic et al 2004; Faucher-Giguere Kaspi 2006; Ferrario Wickramasinghe 2006)." + Since the fraction of »ulsars that can be detected elose to their birth constitutes a negligible fraction. of the total sample. these. studies eencrally use thedey observed. properties of pulsars (namely their period. P ancl period derivative P). together with some assumptions about their time evolution. to reconstruct the birth distribution of periods and magnetic ields for the pulsar population.," Since the fraction of pulsars that can be detected close to their birth constitutes a negligible fraction of the total sample, these studies generally use the observed properties of pulsars (namely their period $P$ and period derivative $\dot{P}$ ), together with some assumptions about their time evolution, to reconstruct the birth distribution of periods and magnetic fields for the pulsar population." + These analyses also need o make assumptions about pulsar properties ancl their evolution (such as. for example. the exact shape of the radio beam and its dependence on the period). as well as overcome a number of selection. effects.," These analyses also need to make assumptions about pulsar properties and their evolution (such as, for example, the exact shape of the radio beam and its dependence on the period), as well as overcome a number of selection effects." + Results from various investigations have often been conflicting. with some studies favoring initial periods in the millisecond range (e.g. Arzoumanian et al.," Results from various investigations have often been conflicting, with some studies favoring initial periods in the millisecond range (e.g. Arzoumanian et al." + 2002). and others instead finding more ikely periods in the range of several tens to several hundreds of milliseconds (c.g. Faucher-Giguere Ixaspi 2006).," 2002), and others instead finding more likely periods in the range of several tens to several hundreds of milliseconds (e.g. Faucher-Giguere Kaspi 2006)." + The ellorts put over the vears into this area of research stem from he fact that the birth properties of neutron stars (NSs) are intimately related to the physical processes occurring during he supernova (SN) explosion and in the proto-neutron star., The efforts put over the years into this area of research stem from the fact that the birth properties of neutron stars (NSs) are intimately related to the physical processes occurring during the supernova (SN) explosion and in the proto-neutron star. + As such. they bear crucial information on the physics of core-collapse SNe. in which most are thought to be formed.," As such, they bear crucial information on the physics of core-collapse SNe, in which most are thought to be formed." + Besides the inferences on the birth parameters. from the radio population discussed. above. we show here that constraints can be derived. also from the X-rays.," Besides the inferences on the birth parameters from the radio population discussed above, we show here that constraints can be derived also from the X-rays." + Young. fast rotating neutron stars are indeed expected to be very bright in the NX-ravs.," Young, fast rotating neutron stars are indeed expected to be very bright in the X-rays." +" In fact. observationally there appears to be a correlation between the rotational energy. loss of the star. Ey. and its X-ray luminosity. £,."," In fact, observationally there appears to be a correlation between the rotational energy loss of the star, $\dot{E}_{\rm rot}$, and its X-ray luminosity, $L_x$." + Phis correlation was noticed by Verbunt et al. (, This correlation was noticed by Verbunt et al. ( +1996). Becker Trumper (1997). Seward Wane (1988). Saito (1998) for a small saniple of objects. and later studied by Possentiet al. (,"1996), Becker Trumper (1997), Seward Wang (1988), Saito (1998) for a small sample of objects, and later studied by Possenti et al. (" +2002: P02 in the following) for the largest sample of pulsars known to date.,2002; P02 in the following) for the largest sample of pulsars known to date. +" ο.‘Combining the birth parameters derived from the radio (which determine the birth distribution. of Ly, for the pulsars). with the empirical L,ο correlation. the distribution of X-ray luminosity can be predicted. for a sample of pulsars with a certain age distribution."," Combining the birth parameters derived from the radio (which determine the birth distribution of $\dot{E}_{\rm rot}$ for the pulsars), with the empirical $L_x - \dot{E}_{\rm rot}$ correlation, the distribution of X-ray luminosity can be predicted for a sample of pulsars with a certain age distribution." + The above calculation was »erformed by Perna Stella (2004)., The above calculation was performed by Perna Stella (2004). + They foune that the ρε parameters derived by Arzoumanian et al. (, They found that the birth parameters derived by Arzoumanian et al. ( +"2002). oecther with the L,La correlation","2002), together with the $L_x - \dot{E}_{\rm +rot}$ correlation" +stellar contributions were included in the SEDs.,stellar contributions were included in the SEDs. + Nebular emission lines have been shown to be important in the first 10 yr (AndersFritze-v.Alvensleben2003) and should be considered when studying unresolved stellar populations (see $55.3)., Nebular emission lines have been shown to be important in the first $10^7$ yr \citep{and03} and should be considered when studying unresolved stellar populations (see 5.3). + Figure | plots the V) (UB) colour-colour diagram., Figure 1 plots the $-$ V) $-$ B) colour-colour diagram. + The black curves are our SB99 models with solar abundances and varying V)., The black curves are our SB99 models with solar abundances and varying $-$ V). + From the bottom to the top. V)20.0. 0.5. 1.0. and. 1.5 mags.," From the bottom to the top, $-$ V)=0.0, 0.5, 1.0, and 1.5 mags." + The filled squares are the observed colours of the standard set of open clusters in the WEBDA sample., The filled squares are the observed colours of the standard set of open clusters in the WEBDA sample. + For each curve. age increases to the right from | Myr to 20 Gyr.," For each curve, age increases to the right from 1 Myr to 20 Gyr." + Note that we have assumed the maximum uncertainty in colour for each OC., Note that we have assumed the maximum uncertainty in colour for each OC. + This study is not intended as a test of the SB99 model's ability to reproduce the colours of young clusters., This study is not intended as a test of the SB99 model's ability to reproduce the colours of young clusters. + This has already been demonstrated (see for e.g.. Vázquez&Leitherer 2005)).," This has already been demonstrated (see for e.g., \citealp{vaz05}) )." + We intend to test how well various colours and initial model assumptions ean recover the ages of well studied Galactie open clusters., We intend to test how well various colours and initial model assumptions can recover the ages of well studied Galactic open clusters. + In addition to using the observed colours to estimate ages. we compared the published colours with the model colours calculated assuming the published ages to look for evidence of stochastic sampling effects.," In addition to using the observed colours to estimate ages, we compared the published colours with the model colours calculated assuming the published ages to look for evidence of stochastic sampling effects." + To determine the model predicted ages of the OCs we compared the observed integrated colours to each of the reddened (and unreddened) SB99 model colours. for a single assumed metallicity.," To determine the model predicted ages of the OCs we compared the observed integrated colours to each of the reddened (and unreddened) SB99 model colours, for a single assumed metallicity." + We used a 47 minimization calculation (e.g.. Pasquali.deGrijs.&Gallagher2003:Grijsetal. 20051) to determine the best match of the observed colours to the models and hence the ages of the open clusters: where N is the number of colours (1-4) used in the analysis. obs; is the observed colour. model; is the corresponding model colour. and c; is the uncertainty in the obs; colour.," We used a $\chi^2$ minimization calculation (e.g., \citealp{pas03,deg05}) ) to determine the best match of the observed colours to the models and hence the ages of the open clusters: where N is the number of colours (1-4) used in the analysis, $_i$ is the observed colour, $_i$ is the corresponding model colour, and $\sigma_i$ is the uncertainty in the $_i$ colour." + All ages with a fit of OX Ν were considered good fits., All ages with a fit of $\chi^2\leq$ N were considered good fits. + For each colour set there was therefore a range of predicted ages for each OC., For each colour set there was therefore a range of predicted ages for each OC. + The age associated with the minimum X? is taken as the best-fit age., The age associated with the minimum $\chi^2$ is taken as the best-fit age. + To determine the uncertainties in the predicted age we find the minimum and maximum ages within a X7 defined to give a confidence level te.g.. Pressetal.19925).," To determine the uncertainties in the predicted age we find the minimum and maximum ages within a $\Delta\chi^2$ defined to give a confidence level (e.g., \citealp{pre92}) )." + Additionally. we add the model step size to the age uncertainty.," Additionally, we add the model step size to the age uncertainty." + We have also predicted the amount of extinction in each case., We have also predicted the amount of extinction in each case. + The amount of extinction applied to the model associated with the best-fit age is the best-titV)., The amount of extinction applied to the model associated with the best-fit age is the best-fit. +. The uncertainty in the predicted iis determined from the minimum and maximum wwithin the same 4? mentioned above., The uncertainty in the predicted is determined from the minimum and maximum within the same $\Delta\chi^2$ mentioned above. + Additionally. we add the model step size to the uuncertainty.," Additionally, we add the model step size to the uncertainty." + In Table |. we list the subset of our sample that has theU.B. andV magnitudes available.," In Table 1, we list the subset of our sample that has the, and magnitudes available." + Column one is the name of the OC. column two is the published age. column three is the predicted age determined from the (UB) and V). column four is My-. columns five and six are the reddening-corrected measured and zero reddened model (UB) colours respectively. column seven is the difference of the measured and model (UB). and columns eight. nine and ten are the same but for the — V) colour.," Column one is the name of the OC, column two is the published age, column three is the predicted age determined from the $-$ B) and $-$ V), column four is $_{V}$, columns five and six are the reddening-corrected measured and zero reddened model $-$ B) colours respectively, column seven is the difference of the measured and model $-$ B), and columns eight, nine and ten are the same but for the $-$ V) colour." + It can be seen from Table | that for of the OCs. the (UB) differences are Z0.141. the assumed maximum measurement uncertainty in measured colour. while of the (BV) differences are =0.14.," It can be seen from Table 1 that for of the OCs, the $-$ B) differences are $\la0.14$, the assumed maximum measurement uncertainty in measured colour, while of the $-$ V) differences are $\la0.14$." + In Figure 2. we plot the predicted ages against the published ages. if only (UB) and V) are used to estimate the ages.," In Figure 2, we plot the predicted ages against the published ages, if only $-$ B) and $-$ V) are used to estimate the ages." + We also provide a histogram showing the distribution of the differences between the predicted and published ages. a plot of the predicted V)s against the published Vos. and a histogram showing the distribution of the differences between the predicted and published Vis.," We also provide a histogram showing the distribution of the differences between the predicted and published ages, a plot of the predicted $-$ V)s against the published $-$ V)s, and a histogram showing the distribution of the differences between the predicted and published $-$ V)s." + In this Figure. we used the solar abundance models.," In this Figure, we used the solar abundance models." + Plots of the predictions determined with the other colour combinations and at other assumed metallicities are similar so are not shown., Plots of the predictions determined with the other colour combinations and at other assumed metallicities are similar so are not shown. + We see from this figure that with the combination of (UB) and V) the ages of the OCs can be predicted with reasonable accuracy., We see from this figure that with the combination of $-$ B) and $-$ V) the ages of the OCs can be predicted with reasonable accuracy. + We present Table 2 to discuss both the accuracy and precision of various colours as age indicators., We present Table 2 to discuss both the accuracy and precision of various colours as age indicators. + Column one is the colour combination. column two is the number of OCs in the sample with those colours available. and column three is the number of good fits for the solar. 0.2 solar and 2.5 solar models. where the number of good fits is the number of models in our grid that give Vox N. Column four is the percentage of recovered ages. which deseribes how often the predicted age uncertainties overlapped with he uncertainties in the measured ages when solar metallicity is assumed.," Column one is the colour combination, column two is the number of OCs in the sample with those colours available, and column three is the number of good fits for the solar, 0.2 solar and 2.5 solar models, where the number of good fits is the number of models in our grid that give $\chi^2\leq$ N. Column four is the percentage of recovered ages, which describes how often the predicted age uncertainties overlapped with the uncertainties in the measured ages when solar metallicity is assumed." + The results from comparisons to models of 0.2 solar and 2.5 solar abundances are similar so are not shown., The results from comparisons to models of 0.2 solar and 2.5 solar abundances are similar so are not shown. + Column tive lists the average uncertainty in predicted logtt) in the negative direction for all the OCs. column six lists the average uncertainty in wedicted logit) in the positive direction for all the OCs. and column seven lists the average of the positive and negative uncertainties or all the OCs.," Column five lists the average uncertainty in predicted log(t) in the negative direction for all the OCs, column six lists the average uncertainty in predicted log(t) in the positive direction for all the OCs, and column seven lists the average of the positive and negative uncertainties for all the OCs." + It should be noted that the model ages range rom a logtt) of 6 to 10.3. therefore 2.15 is the maximum mean xositive and negative uncertainty in log(t).," It should be noted that the model ages range from a log(t) of 6 to 10.3, therefore 2.15 is the maximum mean positive and negative uncertainty in log(t)." + Columns eight. nine.," Columns eight, nine," +A survey of 24 circumstellar disks by Andrews&Wiliams found p~ 0.0-1.0 with an average of p~0.5. while the hydrodynamical simulations of Vorobyov&Basu(2009) found p~ 1.0-2.0 with an average around pz1.5.,"A survey of 24 circumstellar disks by \citet{andrews07} found $p\approx$ 0.0–1.0 with an average of $p\approx0.5$, while the hydrodynamical simulations of \citet{vorobyov09b} found $p\approx$ 1.0–2.0 with an average around $p\approx1.5$." +" Disk mass limits M, for p20.0. 0.5. 1.0 and 1.5. along with the more fundamental surface density limits are given in Table 2.."," Disk mass limits $M_{d}$ for $p=0.0$, 0.5, 1.0 and 1.5, along with the more fundamental surface density limits are given in Table \ref{tab:Mass-Limits}." +" We also provide the characteristic fragment mass (approximate planet mass) M, from eq. (17))", We also provide the characteristic fragment mass (approximate planet mass) $M_{f}$ from eq. \ref{eq:mass}) ) + that we would expect from the disk fragmentation mechanism., that we would expect from the disk fragmentation mechanism. + Also note that. in order to be conservative. we are using the smallest radius found by Chiangetal.(2008) for Fomalhaut b. Using one of their better fits 1115 AU) will deerease our lower disk mass limit by a few percent. increase our upper disk mass limit by —30% (which would make fragmentation slightly easier). and increase the characteristic fragment mass by ~50%.," Also note that, in order to be conservative, we are using the smallest radius found by \citet{chiang08} for Fomalhaut b. Using one of their better fits 115 AU) will decrease our lower disk mass limit by a few percent, increase our upper disk mass limit by $\approx30\%$ (which would make fragmentation slightly easier), and increase the characteristic fragment mass by $\approx50\%$." + We have refined the calculations of Rafikov(2005) and found cooling times over an order of magnitude shorter., We have refined the calculations of \citet{rafikov05} and found cooling times over an order of magnitude shorter. +" We have used these cooling times. along with the observed stellar parameters of Fomalhaut. HR 8799, and HL Tau. to test the viability of the disk. fragmentation mechanism."," We have used these cooling times, along with the observed stellar parameters of Fomalhaut, HR 8799, and HL Tau, to test the viability of the disk fragmentation mechanism." + We found that in each of these systems. at least one planet could have formed as the result of fragmentation. assuming the disk mass interior to those planets fell within a particular range as indicated in Table 2..," We found that in each of these systems, at least one planet could have formed as the result of fragmentation, assuming the disk mass interior to those planets fell within a particular range as indicated in Table \ref{tab:Mass-Limits}." + While the ranges in Table 2 only span a factor of a few. this is not by itself a significant limitation.," While the ranges in Table \ref{tab:Mass-Limits} only span a factor of a few, this is not by itself a significant limitation." + Even if the local surface density is above the upper instability limit. fragmentation may still occur since the surface density must eventually drop through the unstable regime as the disk evolves and dissipates.," Even if the local surface density is above the upper instability limit, fragmentation may still occur since the surface density must eventually drop through the unstable regime as the disk evolves and dissipates." + The caveat is that the surface density needs to evolve on a timescale longer than an orbital period. so that there can be sufficient time to fragment., The caveat is that the surface density needs to evolve on a timescale longer than an orbital period so that there can be sufficient time to fragment. + Our minimum disk masses for Fomalhaut b. HR bb. and HL Tau b are about an order of magnitude larger than those inferred from observations (Andrews&Wiliams 2007).," Our minimum disk masses for Fomalhaut b, HR b, and HL Tau b are about an order of magnitude larger than those inferred from observations \citep{andrews07}." + Note. however. that this is a problem for all planet formation models m general.," Note, however, that this is a problem for all planet formation models in general." + Even core aceretion models require an enhanced surface density (although to a somewhat lesser extent) (Pollacketal.1996:Inaba2003).," Even core accretion models require an enhanced surface density (although to a somewhat lesser extent) \citep{pollack96,inaba03}." +. One possible mechanism for increasing the surface density is mass loading from an infalling envelope (Vorobyov&Basu2006)., One possible mechanism for increasing the surface density is mass loading from an infalling envelope \citep{vorobyov06}. + Conversely. current estimates of disk masses may be too low because they depend on: I) the extrapolation of surface densities in. the outermost regions of the disk to the inner disk. and 2) the rather uncertain dust opacity.," Conversely, current estimates of disk masses may be too low because they depend on: 1) the extrapolation of surface densities in the outermost regions of the disk to the inner disk, and 2) the rather uncertain dust opacity." + For example. larger dust grains would require larger disk masses to fit the observed SEDs (Andrews&Wiliams2007).," For example, larger dust grains would require larger disk masses to fit the observed SEDs \citep{andrews07}." +. As further evidence for underestimated disk masses. numerical hydrodynamical simulations by Vorobyov(2009) found disk masses much higher than those of Andrews&Wil-iams(200," As further evidence for underestimated disk masses, numerical hydrodynamical simulations by \citet{vorobyov09a} found disk masses much higher than those of \citet{andrews07}." +7 In particular. stars like Fomalhaut and HR 8799 can support )..disks as large as 0.5 M... while HL Tau could have a disk as massive as 0.1 M... all of which are within our limits for disk fragmentation.," In particular, stars like Fomalhaut and HR 8799 can support disks as large as 0.5 $M_{\sun}$, while HL Tau could have a disk as massive as 0.1 $M_{\sun}$, all of which are within our limits for disk fragmentation." + We caution. however. that our choice of opacity model can have a major effect on our results.," We caution, however, that our choice of opacity model can have a major effect on our results." + For example. decreasing the dust opacity raises the temperature and decreases the cooling time in the outer disk. resulting in disk fragmentation at smaller radii.," For example, decreasing the dust opacity raises the temperature and decreases the cooling time in the outer disk, resulting in disk fragmentation at smaller radii." + On the other hand. increasing the opacity would have the opposite effect.," On the other hand, increasing the opacity would have the opposite effect." + Regardless of the above considerations. HR 8799 c and d are too close to their parent star to have formed via fragmentation under the conditions modeled here.," Regardless of the above considerations, HR 8799 c and d are too close to their parent star to have formed via fragmentation under the conditions modeled here." + Appealing to chronically overestimated dust opacity can only get us so, Appealing to chronically overestimated dust opacity can only get us so +{he input energy.,the input energy. + The reprocessing optical depth is thus given by the condition To define the quantity Ly.) iis useful conceptually to divide the emergent radiation into stellar photons aud envelope photons., The reprocessing optical depth is thus given by the condition To define the quantity $L_{\rm rep}$ it is useful conceptually to divide the emergent radiation into stellar photons and envelope photons. + In a Monte Carlo simulation. the stellar luminosity is divided into N equal energy photon packets (note that packets with different Irequencies contain a dilferent number of plvsical photons).," In a Monte Carlo simulation, the stellar luminosity is divided into $N$ equal energy photon packets (note that packets with different frequencies contain a different number of physical photons)." +" The energy per packet is given bv where L, is the stellar luminosity anc M is an arbitrary simulation time.", The energy per packet is given by where $L_\star$ is the stellar luminosity and $\Delta t$ is an arbitrary simulation time. + Stellar photons are emitted from the star ancl (μον propagate through the envelope. where (μον may be scatlerecl or absorbed.," Stellar photons are emitted from the star and they propagate through the envelope, where they may be scattered or absorbed." + If a stellar photon is absorbed. radiative equilibrium requires (hat il be reemittec as an envelope photon.," If a stellar photon is absorbed, radiative equilibrium requires that it be reemitted as an envelope photon." + Note (hat scattering does not change the photon ivpe (stellar vs. envelope)., Note that scattering does not change the photon type (stellar vs. envelope). +" The fraction of the stellar Iuminositv reprocessed (absorbed) by the envelope max easily be determined by counting the number of stellar photon packets absorbed by the envelope. *absVi""."," The fraction of the stellar luminosity reprocessed (absorbed) by the envelope may easily be determined by counting the number of stellar photon packets absorbed by the envelope, $N_\star^{\rm abs}$." +" This is equivalent to counting the number of stellar photons that emerge Irom the envelope without absorption. VE""."," This is equivalent to counting the number of stellar photons that emerge from the envelope without absorption, $N_\star^{\rm em}$." +" Thus (he Iuminosity. reprocessed bv the envelope is where L7"" is the emergent stellar huninosity.", Thus the luminosity reprocessed by the envelope is where $L_\star^{\rm em}$ is the emergent stellar luminosity. + This is the method we use to measure Lees in this paper., This is the method we use to measure $L_{\rm rep}$ in this paper. +" Note that scattering affects Ly, because a photon packet that is scattered can be absorbed subsequently.", Note that scattering affects $L_{\rm rep}$ because a photon packet that is scattered can be absorbed subsequently. +" Owing to (hese scattering effects. it is not straiehtlorwarel {ο obtain Z4, from standard radiative transfer quantities."," Owing to these scattering effects, it is not straightforward to obtain $L_{\rm rep}$ from standard radiative transfer quantities." + The reprocessed luminosity is given bv the emergent Iuminosityv of (he envelope. so where da/dQ is the dilferential scattering cross section. which is a function of both incoming and outgoing directions (n and n. respectively). and 72 is the envelope contribution (Monte Carlo envelope photons) to the specific intensitv (this includes scattered. envelope photons but does not include scattered stellar photons).," The reprocessed luminosity is given by the emergent luminosity of the envelope, so where $d \sigma/d\Omega$ is the differential scattering cross section, which is a function of both incoming and outgoing directions $\hat{\rm{n}}^\prime$ and $\hat{\rm{n}}$, respectively), and $I_{\lambda}^{\rm{env}}$ is the envelope contribution (Monte Carlo envelope photons) to the specific intensity (this includes scattered envelope photons but does not include scattered stellar photons)." +" Energy conservation requires (hat Loveyre equals the οποιονS. absorbed in the envelope. so L..,re can also be written as"," Energy conservation requires that $L_{\rm rep}$ equals the energy absorbed in the envelope, so $L_{\rm rep}$ can also be written as" +had la‘ee lit residuas.,had large fit residuals. + For this reason. few data are iicluded from. images with seeing worse than L.5 aresec FWHML. aud the majority of the data are fiom Πάθος with « 1l arcsec seeing.," For this reason, few data are included from images with seeing worse than 1.5 arcsec FWHM, and the majority of the data are from images with $<$ 1 arcsec seeing." + The very best lnages include are around 0.6 arcsec. still not cuite ΕπΠρος," The very best images included are around $0.6$ arcsec, still not quite undersampled." + When the sky was suitably. cloudless. exposures in the CBVRI filters (or sometimes only V aud J) were added to the program. together with sandard star fieds from Landolt(1992) to allow transformation to standard magnitudes.," When the sky was suitably cloudless, exposures in the $UBVRI$ filters (or sometimes only $V$ and $I$ ) were added to the program, together with standard star fields from \citet{landolt92} to allow transformation to standard magnitudes." + Photometric exposures were obtained on at least two nights. aud the results were averaged after aualysis.," Photometric exposures were obtained on at least two nights, and the results were averaged after analysis." + The consistency was generally better than 0.05 mae., The consistency was generally better than 0.05 mag. + The data were reduced using staudard routines for bias subtraction aud flat field correction., The data were reduced using standard routines for bias subtraction and flat field correction. + The flat fields were constructed from offset. mediaued images of the twilight sky.," The flat fields were constructed from offset, medianed images of the twilight sky." + Star centers were measured with the IRAF implenentation of DAOPHOT (originally written Nw Stetson LOST)). which constructs a model »oiut-sp'ead function (PSF) from selected stars and its these to the program stars.," Star centers were measured with the IRAF implementation of DAOPHOT (originally written by \citealt{stetsondao}) ), which constructs a model point-spread function (PSF) from selected stars and fits these to the program stars." + Because he centroid iformation is contained in the steep sides of he PSF. a small fitting radius was used. generally 0.8 arcsec.," Because the centroid information is contained in the steep sides of the PSF, a small fitting radius was used, generally 0.8 arcsec." + For some of the later measurements. he fittiug radius was adapted to the seeing ou the Individual pictures.," For some of the later measurements, the fitting radius was adapted to the seeing on the individual pictures." + The measurement procedure was automated as follows., The measurement procedure was automated as follows. + First. the average of several of the yest pictues (the fiducial frame) was examined to select a set of stars to measure aud a set of suitable PSF stars.," First, the average of several of the best pictures (the `fiducial' frame) was examined to select a set of stars to measure and a set of suitable PSF stars." + Next. lists of stars on all the piettwes frames were generated usingοι orSEvtractor (Bertin&Arnouts19060).," Next, lists of stars on all the pictures frames were generated using or \citep{bertin96}." +.. A computer program matched objects on these lists to the correspouding objects on the fiducial frame. and the matches were used to transform the program and PSF star coordinates to the system of each picture.," A computer program matched objects on these lists to the corresponding objects on the fiducial frame, and the matches were used to transform the program and PSF star coordinates to the system of each picture." + The DAOPHOT measturements proceeded automatically., The DAOPHOT measurements proceeded automatically. + To determiue tlie true scale aud orientation of the fiducial frame. the star images were matched to the USNO A2.0 catalog (Monetοἱal.1996).. which is aligned with the ICRS (essentially J2000).," To determine the true scale and orientation of the fiducial frame, the star images were matched to the USNO A2.0 catalog \citep{mon96}, which is aligned with the ICRS (essentially J2000)." + In most fields several dozen stars were ma(ολους. with plate solutious typically having RMS residuals of 0.2)3. mostly from the centeringD>oO unce‘tainty ο ‘the USNO A2.0 and. proper motious since the USNO A2.0 plate epoch.," In most fields several dozen stars were matched, with plate solutions typically having RMS residuals of $0.''3$, mostly from the centering uncertainty of the USNO A2.0 and proper motions since the USNO A2.0 plate epoch." +" Civen the number of stars in the solutions aud the size of the field. the ünage scales clerivecl from these fits shotId be accurate to a few parts in 101, and the orientation should be accurate to a 0.03) degree."," Given the number of stars in the solutions and the size of the field, the image scales derived from these fits should be accurate to a few parts in $10^4$, and the orientation should be accurate to a $\sim 0.03$ degree." + Using the scale aud orientation. the pixel coordinates of the fictucial stars were transformed to taugeu plane coordinates μα aud αμα. with the program object at the origin.," Using the scale and orientation, the pixel coordinates of the fiducial stars were transformed to tangent plane coordinates $X_{\rm fid}$ and $Y_{\rm fid}$ , with the program object at the origin." + These coordinates correspoud closely to Aa and Adover a siuall field., These coordinates correspond closely to $\Delta \alpha$ and $\Delta \delta$over a small field. +For the eccentricities of our sample of 931 main belt asteroids. the best fit parameters are: We also fit the data to a double-Gaussian distribution. The eumulative distribution function for equation (A3)) is For the eccentricities of our sample of 931 main belt asteroids. we performed a least squares fit to equation CÀ4)) ancl obtained the following best-fit parameters: We evaluated the goodness of fit using the IxXolimogorov-Smirnov (Ix-5) test.,"For the eccentricities of our sample of 931 main belt asteroids, the best fit parameters are: We also fit the data to a double-Gaussian distribution, The cumulative distribution function for equation \ref{e:doublegaussian}) ) is For the eccentricities of our sample of 931 main belt asteroids, we performed a least squares fit to equation \ref{e:doublecdf}) ) and obtained the following best-fit parameters: We evaluated the goodness of fit using the Kolmogorov-Smirnov (K-S) test." + The [νο test determines the probability (iat. two distributions ave (he same. or in our case how well our model distributions fit the observed data (Pressοἱal.1992).," The K-S test determines the probability that two distributions are the same, or in our case how well our model distributions fit the observed data \citep{Press:1992p1610}." +. The Ix-9 test compares the cumulative distribution of the data against the model cumulative distribution function., The K-S test compares the cumulative distribution of the data against the model cumulative distribution function. + We found that our asteroid sample has a probability of 4.5x107 that it comes from the best fit sinele Gaussian (equation (A2))). but a probability of 0.73 that it comes from the (equation (&4))).," We found that our asteroid sample has a probability of $4.5\times10^{-2}$ that it comes from the best fit single Gaussian (equation \ref{e:cdf}) )), but a probability of $0.73$ that it comes from the double-Gaussian (equation \ref{e:doublecdf}) ))." + Therefore. the K-S tests indieate that the double-Gaussian is a better fit to the data than the single-Gaussian.," Therefore, the K-S tests indicate that the double-Gaussian is a better fit to the data than the single-Gaussian." + We performed Hartigan’s dip test (Ilartigan&Hartigan1985) (o test whether the observational data is consistent wilh a multi-peaked distribution., We performed Hartigan's dip test \citep{Hartigan:1985p3924} to test whether the observational data is consistent with a multi-peaked distribution. + Hartigans dip test calculates the probability that the distribution being tested has a single peak., Hartigan's dip test calculates the probability that the distribution being tested has a single peak. + Applving Hartigan's dip test lo a given distribution vields in a test statistic: together with the sample size. the test statistic is matelied to a p-value range in à precomputed table provided bv (1985)..," Applying Hartigan's dip test to a given distribution yields in a test statistic; together with the sample size, the test statistic is matched to a p-value range in a precomputed table provided by \cite{Hartigan:1985p3924}." + The p-value is a measure of the probability that the distribution actually has only one peak (the null-hvpothesis. for this problem).," The p-value is a measure of the probability that the distribution actually has only one peak (the null-hypothesis, for this problem)." + The smaller (he caleulated p-value.," The smaller the calculated p-value," +"there is a level, deep enough in the atmosphere/interior at which the temperature is independent of latitude/longitude. (","there is a level, deep enough in the atmosphere/interior at which the temperature is independent of latitude/longitude. (" +"Note that this should be deeper, peharps considerably, than the level at which the irradiation flux has been completely absorbed).","Note that this should be deeper, peharps considerably, than the level at which the irradiation flux has been completely absorbed)." + I hereafter turn to the derivation of the temperature profile in an atmosphere that advects heat horizontally., I hereafter turn to the derivation of the temperature profile in an atmosphere that advects heat horizontally. +" I now consider that for each atmospheric location (6,9) defined from the substellar point, mixing tables place by horizontal advection and transports heat with a flux gVT."," I now consider that for each atmospheric location $(\theta,\phi)$ defined from the substellar point, mixing tables place by horizontal advection and transports heat with a flux $\qnab$." +" The radiative equilibrium equation becomes: or, The first moment of the radiative transfer equation (eq. 4))"," The radiative equilibrium equation becomes: or, The first moment of the radiative transfer equation (eq. \ref{eq:H}) )" +" becomes by integration and hence Note that since we envision that VT—0 when m—co, this implies H(co)=στά,/(4n)."," becomes by integration and hence Note that since we envision that $\nabla T\rightarrow 0$ when $m\rightarrow\infty$, this implies $H(\infty)=\sigma\tint^4/(4\pi)$." +" Now, the equation for Hi, becomes: and by integration Hqa(0)=H(0)—H,(0) and therefore Inserting this relation into eq. (36))"," Now, the equation for $\Hth$ becomes: and by integration $\Hth(0)=H(0)-\Hv(0)$ and therefore Inserting this relation into eq. \ref{eq:Hth-q}) )" +" yields We now integrate the equation for the second moment of the radiation field: and by integrating by parts: The relation for Ji, can then be found simply from the first Eddington coefficient fxin= Kin/Jin.", yields We now integrate the equation for the second moment of the radiation field: and by integrating by parts: The relation for $\Jth$ can then be found simply from the first Eddington coefficient $\fKth=\Kth/\Jth$ . +" Then, using eq. (32))"," Then, using eq. \ref{eq:B-q}) )" +" yields We use the relations fin= Hq(0)/Jq(0), H,(0)= and H(co)=στὰ, H,(0)=μ.στῄ, to find an expression for the temperature profile at each location (τ,μ.Φ) in the atmosphere: The relation is a complex one and its resolution goes beyond the scope of the present article."," yields We use the relations $\fHth\equiv \Hth(0)/\Jth(0)$, $\Hv(0)=-\mu_*\Jv(0)$ , and $H(\infty)=\sigma\tint^4$, $\Hv(0)=\mu_*\sigma\tirr^4$ to find an expression for the temperature profile at each location $(\tau,\mu,\phi)$ in the atmosphere: The relation is a complex one and its resolution goes beyond the scope of the present article." + We are mostly interested in the deep atmospheric temperature., We are mostly interested in the deep atmospheric temperature. +" As discussed, in the presence of an efficient-enough advection process, the temperature at deep levels should become latitudinally and longitudinally homogeneous."," As discussed, in the presence of an efficient-enough advection process, the temperature at deep levels should become latitudinally and longitudinally homogeneous." +" I therefore average over latitudes and longitudes (defined from the substellar point) to obtain a global mean temperature that depends only on depth r: For a conservative advection scheme (in particular if q does not depend on yp, ¢ or T), $qVTdw=0."," I therefore average over latitudes and longitudes (defined from the substellar point) to obtain a global mean temperature that depends only on depth $\tau$: For a conservative advection scheme (in particular if $q$ does not depend on $\mu$, $\phi$ or $T$ ), $\oint\qnab d\omega=0$." + This leads to a great simplification of eq. (43)), This leads to a great simplification of eq. \ref{eq:T4-adv}) ) +" which becomes after integration over all latitudes and longitudes isha(using µ.= 4): Note that we integrated the intrinsic flux over the entireplanet, whereas the irradiation flux is of course integrated only over the dayside hemisphere."," which becomes after integration over all latitudes and longitudes (using $\mu_*=\mu$ ): Note that we integrated the intrinsic flux over the entireplanet, whereas the irradiation flux is of course integrated only over the dayside hemisphere." +" The integral term can be rewritten or, in terms of exponential integrals E,(z)=ft""e “dt, The E, functions— have a recursive property(?)::"," The integral term can be rewritten or, in terms of exponential integrals $E_n(z)\equiv\int_1^\infty t^{-n}e^{-zt}dt$ , The $E_n$ functions have a recursive property:" +"We develop here a simple geometrical model to estimate the accretion rate onto a massive black hole in a stellar system, fueled by mass loss from stars (Quataertetal. 1999).","We develop here a simple geometrical model to estimate the accretion rate onto a massive black hole in a stellar system, fueled by mass loss from stars \citep{Quataert1999}." +". If a star is located at a distance r from the massive black hole, and if it produces an isotropic wind, with velocity Uwing, only the fraction of gas which passes within the accretion radius of the massive black hole, +¢2),(6) be accreted gravitational focusing)."," If a star is located at a distance $r$ from the massive black hole, and if it produces an isotropic wind, with velocity $v_{\rm wind}$, only the fraction of gas which passes within the accretion radius of the massive black hole, ^2+c^2_s), can be accreted (ignoring gravitational focusing)." +" Here c?scan= is (ignoringthe velocity dispersion of the stellar system at the GMetetar/(2.66r},)half-mass radius.", Here $\sigma^2=GM_{\rm stellar}/(2.66r_h)$ is the velocity dispersion of the stellar system at the half-mass radius. +" For a Hernquist profile, where the density in the inner region pοςr7!, the velocity dispersion decreases towards the center."," For a Hernquist profile, where the density in the inner region $\rho \propto r^{-1}$, the velocity dispersion decreases towards the center." +" Estimating c at the half mass radius gives a conservative lower limit to the accretion radius, and hence the accretion rate."," Estimating $\sigma$ at the half mass radius gives a conservative lower limit to the accretion radius, and hence the accretion rate." +" Following Miller&Hamilton(2002), we assume that in equation 6 the sound speed c,— 10kms~!, and, vying=50kms-!as reference values, although we study the effect that a different vwing has on our model (see Figure "," Following \cite{Miller2002}, we assume that in equation 6 the sound speed $c_s= 10 \kms$ , and, $v_{\rm wind} = 50 \kms$as reference values, although we study the effect that a different $v_{\rm wind}$ has on our model (see Figure \ref{vw}) )." +"If σ>vwinad, Race depends2)). only on the properties of the potential well of the stellar distribution, not on the wind properties."," If $\sigma \gg v_{\rm wind}$, $R_{\rm acc}$ depends only on the properties of the potential well of the stellar distribution, not on the wind properties." +" In particular, Race~ if Mstellar=10°Meu."," In particular, $R_{\rm acc} \simeq M_{\rm BH}R_{\rm + eff}/M_{\rm stellar} \simeq 10^{-3}R_{\rm eff}$ if $M_{\rm + stellar}=10^3 M_{BH}$." +" Note that, at fixed black hole mass, the more massive the galaxy, the smaller Race is, as the scaling of Reg with Megtellar is à power law with exponent less than one (see, e.g., equation 3)."," Note that, at fixed black hole mass, the more massive the galaxy, the smaller $R_{\rm acc}$ is, as the scaling of $R_{\rm eff}$ with $M_{\rm stellar}$ is a power law with exponent less than one (see, e.g., equation 3)." +" On the other hand, if σRace: where M, is the mass loss rate from the star."," Geometrical considerations suggest that, for $r>R_{\rm + acc}$: ], where $\dot M_*$ is the mass loss rate from the star." +" If the star lies within Racc, we consider Macc,x=M..."," If the star lies within $R_{\rm acc}$, we consider $\dot M_{{\rm acc},*}=\dot +M_*$." + Eq. (7)), Eq. \ref{eq:geom}) ) +" implicitly assumes that the stars have a spherically simmetric distribution and that their velocity field (and, as a consequence, the velocity field of the wind) is isotropic."," implicitly assumes that the stars have a spherically simmetric distribution and that their velocity field (and, as a consequence, the velocity field of the wind) is isotropic." +" In a rotating stellar system, the presence of net angular momentum of the gas can change the accretion rate onto the black hole (e.g.,Cuadraetal.2008).."," In a rotating stellar system, the presence of net angular momentum of the gas can change the accretion rate onto the black hole \citep[e.g.,][]{Cuadra2008}." + A study of the dependence of the accretion rate on the degree of rotational support of the stellar distribution is beyond the scope of this paper., A study of the dependence of the accretion rate on the degree of rotational support of the stellar distribution is beyond the scope of this paper. +" The total contribution from all stars is found by integrating over the density profile of the stellar system:≺≺−⊮∂∁∁⊽∗∁⊈⊺⋅↿ where (m,.) is the mean stellar mass and p is given by eq. (2.1))"," The total contribution from all stars is found by integrating over the density profile of the stellar system:, where $\langle m_*\rangle$ is the mean stellar mass and $\rho$ is given by eq. \ref{eq:plummer}) )" + and (2.1))., and \ref{eq:hernquist}) ). + The normalization in eq. (2.2)), The normalization in eq. \ref{eq:mdot}) ) +" is given by the cumulative mass loss rate of all the stars in the stellar structure, that we estimate following Ciottietal.(1991):: 13. where t, is the age of the stellar population, and Lg is the(9) total luminosity of the stellar system."," is given by the cumulative mass loss rate of all the stars in the stellar structure, that we estimate following \cite{Ciotti1991}: , where $t_*$ is the age of the stellar population, and $L_B$ is the total luminosity of the stellar system." +" We set t,=5 Gyr for dSphs and nuclear star clusters, and ἐς=12 Gyr for early type galaxies and globular clusters."," We set $t_*=5$ Gyr for dSphs and nuclear star clusters, and $t_*=12$ Gyr for early type galaxies and globular clusters." + We derive band luminosities from stellar masses assuming a to-light ratio of 5 in the B-band., We derive B-band luminosities from stellar masses assuming a mass-to-light ratio of 5 in the B-band. + We obtain an upper limit of the luminosity of the massive black hole by assuming that the whole Macc is indeed accreted by the massive black hole., We obtain an upper limit of the luminosity of the massive black hole by assuming that the whole $\dot M_{\rm acc}$ is indeed accreted by the massive black hole. +" Figure 2 shows the resulting accretion rate for a central massive black hole in different stellar systems, where we assume that the massive black hole mass scales with the mass of stellar component, Mpy=107?Maia; (Marconi&Hunt2003;HaringRix2004),, and we have considered vying a free parameter."," Figure \ref{vw} shows the resulting accretion rate for a central massive black hole in different stellar systems, where we assume that the massive black hole mass scales with the mass of stellar component, $M_{\rm BH}=10^{-3} M_{\rm + stellar}$ \citep{MarconiHunt2003,Haring2004}, and we have considered $v_{\rm wind}$ a free parameter." +" We have assumed that Reg scales exactly with Maca, following the relationships discussed above."," We have assumed that $R_{\rm + eff}$ scales exactly with $M_{\rm stellar}$ following the relationships discussed above." +" Note that for high values of the stellar masses in early-type galaxies and nuclear star clusters, the accretion rate and Race do not depend on the wind velocities."," Note that for high values of the stellar masses in early-type galaxies and nuclear star clusters, the accretion rate and $R_{\rm acc}$ do not depend on the wind velocities." +" In these cases σ>vwina, and the accretion rate depends only on the properties of the host stellar structure and on the black hole mass (see the discussion of Equation 6 above)."," In these cases $\sigma\gg v_{\rm wind}$, and the accretion rate depends only on the properties of the host stellar structure and on the black hole mass (see the discussion of Equation 6 above)." +" In Figure3 we instead fix vying, and allow for a scatter in the mass-size relationship."," In Figure \ref{size} we instead fix $v_{\rm wind}$ , and allow for a scatter in the mass-size relationship." + For globular clusters we assume Reg=1 pc; Reg=2 pc and Reg=4 pc., For globular clusters we assume $R_{\rm eff}=1$ pc; $R_{\rm eff}=2$ pc and $R_{\rm eff}=4$ pc. +" For galaxies, the middle curve shows the best fit Reg for a given stellar mass value (Equations 1, 2 and 3), thetop curves assume that Reg is half the best fit value, and the"," For galaxies, the middle curve shows the best fit $R_{\rm eff}$ for a given stellar mass value (Equations 1, 2 and 3), thetop curves assume that $R_{\rm + eff}$ is half the best fit value, and the" +The high angular resolution of the SALA allows us to trace the thermal emission of dust grains al physical scales of few hunedrecd astronomical (for objects in the Orion molecular cloud complex) and. therefore. is able to spatially resolve compact dust cores.,"The high angular resolution of the SMA allows us to trace the thermal emission of dust grains at physical scales of few hundred astronomical (for objects in the Orion molecular cloud complex) and, therefore, is able to spatially resolve compact dust cores." + A detailed description of SALA is given in Hoetal.(2004)., A detailed description of SMA is given in \cite{Ho04}. +. The observations were carried oul in 2007 November 24 and December 19 with the SALA in its compact configuration., The observations were carried out in 2007 November 24 and December 19 with the SMA in its compact configuration. + The number of antennas available for the observations were 7 and 6. respectively.," The number of antennas available for the observations were 7 and 6, respectively." + The abmospheric opacityv al 225 Gllz was 0.11 and 0.07 for the first and second dav. respectively (values measured by the Caltech Submillimeter Observatory tau meter).," The atmospheric opacity at 225 GHz was 0.11 and 0.07 for the first and second day, respectively (values measured by the Caltech Submillimeter Observatory tau meter)." + Observations were done in the 345 GlIIz atmospheric window. what corresponds to a wavelength of 870 jn. The SALA receivers operate in (wo sidebands separated by ~10 GlIz.," Observations were done in the 345 GHz atmospheric window, what corresponds to a wavelength of 870 $\mu$ m. The SMA receivers operate in two sidebands separated by $\sim 10$ GHz." + The central observed frequencies for the lower and upper side bands were 336.5 Gllz and 346.5 Gllz. respectively.," The central observed frequencies for the lower and upper side bands were 336.5 GHz and 346.5 GHz, respectively." + The SMA correlator had a bandwidth of 1.9 GIz (for each sideband) divided in 24 “chunks” of 128 channels each., The SMA correlator had a bandwidth of 1.9 GHz (for each sideband) divided in 24 “chunks” of 128 channels each. + In total. the full-band spectrum contains 3072 channels for each sideband and a spectral resolution of 0.62 MlIIz. which corresponds (ο a velocity resolution of 0.7 km t.," In total, the full-band spectrum contains 3072 channels for each sideband and a spectral resolution of 0.62 MHz, which corresponds to a velocity resolution of 0.7 km $^{-1}$." + SMA receivers are single linearly polarized., SMA receivers are single linearly polarized. + By using a quarter-wave plate in front of each receiver. (he incoming radiation is converted into circular polarization (L. R).," By using a quarter-wave plate in front of each receiver, the incoming radiation is converted into circular polarization (L, R)." + The SMA correlator combines the signal into circular polarization vectors: RR. LL. RL. LR.," The SMA correlator combines the signal into circular polarization vectors: RR, LL, RL, LR." + In order to obtain the full four Stokes parameters for all the baselines. (he visibilities have to be averaged on a time scale of 5 minutes.," In order to obtain the full four Stokes parameters for all the baselines, the visibilities have to be averaged on a time scale of 5 minutes." + A description of the SALA polarimeter and (he discussion of the methodology. (both hardware and software aspects)are available in Marroneetal.(2006) and Marrone&Rao (2003).., A description of the SMA polarimeter and the discussion of the methodology (both hardware and software aspects)are available in \citet{Marrone06} and \citet{Marrone08}. . +to roughly the same level at all radii aud for all cases. regardless of initial amplitudes.,"to roughly the same level at all radii and for all cases, regardless of initial amplitudes." + The saturation level appears comparable to the initial field amplitudes in the 3500 case: field amplitudes in cases initially ereater than 3500 are dissipated through bydrodvuamic processes: field amplitudes in cases initially less than D500 are amplified until they reach D500 levels before leveling off., The saturation level appears comparable to the initial field amplitudes in the B500 case: field amplitudes in cases initially greater than B500 are dissipated through hydrodynamic processes; field amplitudes in cases initially less than B500 are amplified until they reach B500 levels before leveling off. + Qur calculations sugecst no mechanism exists which cau drive field amplitudes above B500 levels. implying that we are safely modeling the upper Πιτ of sclbecuerated field streneths.," Our calculations suggest no mechanism exists which can drive field amplitudes above B500 levels, implying that we are safely modeling the upper limit of self-generated field strengths." + Although field amplification does indeed take place in all magnetized ruus we have performed (medium and lieh resolution). it falls well short of. thermal equipartitiou so it cannot casily affect the ανασα] evolution of the star.," Although field amplification does indeed take place in all magnetized runs we have performed (medium and high resolution), it falls well short of thermal equipartition so it cannot easily affect the dynamical evolution of the star." + This is demonstrated iu Figure 6 which shows the mass deusitv weighted average of the inverse plasmabeta (1/op) inside the star., This is demonstrated in Figure \ref{fig:betainv53} which shows the mass density weighted average of the inverse plasmabeta $1/\beta_B$ ) inside the star. + In al cases the increase of magnetic pressure saturates at a level that is significautlv less than of the thermal pressure averaged across the star (with maxinuun peak values of about for the 62 ruus. aud forthe high resolution 96° case).," In all cases the increase of magnetic pressure saturates at a level that is significantly less than of the thermal pressure averaged across the star (with maximum peak values of about for the $64^3$ runs, and forthe high resolution $96^3$ case)." + It appears that field saturation is cleternuned by universal behavior in the partitioning of thermal and maguctic enerev. independent of initial auplitude.," It appears that field saturation is determined by universal behavior in the partitioning of thermal and magnetic energy, independent of initial amplitude." + This is true also for the P—2 aud 3 cases. both of which result iu mean 1/p profiles similar to the Τ=5/3 results shown in Figure 6..," This is true also for the $\Gamma=2$ and $3$ cases, both of which result in mean $1/\beta_B$ profiles similar to the $\Gamma=5/3$ results shown in Figure \ref{fig:betainv53}." + Consequently. we do net expect eravitational waveforms to be affected appreciably by toroidal magnetic fields. as we demoustrate in Figure 7 for the D=5/3 cases. Figure δ for D=2. aud Figure 9. for TP=3.," Consequently, we do not expect gravitational waveforms to be affected appreciably by toroidal magnetic fields, as we demonstrate in Figure \ref{fig:gw53} + for the $\Gamma=5/3$ cases, Figure \ref{fig:gw20} for $\Gamma=2$, and Figure \ref{fig:gw30} for $\Gamma=3$." + Fiewres 7 through 9 plot the quantity rf| normalized by the scale factor (GAZ/cECy., Figures \ref{fig:gw53} through \ref{fig:gw30} plot the quantity $r h+$ normalized by the scale factor $(GM/\varpi_E c^2)^2$ . + Figure 9 also includes results from a poloidal initial field configuration (run PCS30BLO0) for comparison., Figure \ref{fig:gw30} also includes results from a poloidal initial field configuration (run PG30B100) for comparison. +" Figure 7 (corresponding to the DP—5/3 cases) closely rescubles Figure 9 of Newetal.(2000): we match the amplitude and frequency of oscillations and find that our results are intermediate between the ""D1 aud “LI” displays in duration and pattern of the wave signal.", Figure \ref{fig:gw53} (corresponding to the $\Gamma=5/3$ cases) closely resembles Figure 9 of \citet{new00}: we match the amplitude and frequency of oscillations and find that our results are intermediate between the “D1” and “L1” displays in duration and pattern of the wave signal. + It is uot uutil the field streneth is increased to L/opiningl with locally comparable thermal and maguctic pressures that we observe amplitude deviations of order in Figure 1," It is not until the field strength is increased to $1/\beta_{B,min} \sim 1$ with locally comparable thermal and magnetic pressures that we observe amplitude deviations of order in Figure \ref{fig:gw53}." + The first evidence of oscillations in Figure 7?/ occurs at time f—6 which corresponds to the instant when the wm=2 mode fixst begius to dominate the spectral signal in Figure 2.., The first evidence of oscillations in Figure \ref{fig:gw53} occurs at time $t\sim6$ which corresponds to the instant when the $m=2$ mode first begins to dominate the spectral signal in Figure \ref{fig:mode53}. + The global cuvelope shape (essentially the overall amplitude) of the gravitational wave emission tracks uicely the erowth and eventual decay of the m=2 mode curve in Figure2.., The global envelope shape (essentially the overall amplitude) of the gravitational wave emission tracks nicely the growth and eventual decay of the $m=2$ mode curve in Figure\ref{fig:mode53}. . + Maxim peaks in both wave signals and spectral mode profiles correlate preciselv at time f£~16. ane both exhibit comparable rise and decav times.," Maximum peaks in both wave signals and spectral mode profiles correlate precisely at time $t\sim16$, and both exhibit comparable rise and decay times." + Another point of interest iu comparing Figures 7 9 is the appareit trend for tie start of the wave signals to be delayed with Πιοσα]m adiabatic iudex D (evident also iu the spectral mole ots).," Another point of interest in comparing Figures \ref{fig:gw53} – \ref{fig:gw30} + is the apparent trend for the start of the wave signals to be delayed with increasing adiabatic index $\Gamma$ (evident also in the spectral mode plots)." + However. we have found that tιο onset of tie lustability is seusitive to a nuuber of uiuucrical factoTS (e.g... grid resolution. Courant factor). aid it is ciffiaIt ο lnake quantitative conclusions regmlingC» this effec," However, we have found that the onset of the instability is sensitive to a number of numerical factors (e.g., grid resolution, Courant factor), and it is difficult to make quantitative conclusions regarding this effect." + For example. the magnetized aud παςjetized DP--Ὁ üeh-resolution cases reseiible Figure 7 but for a slig delay of about 1.5 ανασα. times. effectively a eniporal shift in the waveform.," For example, the magnetized and unmagnetized $\Gamma=5/3$ high-resolution cases resemble Figure \ref{fig:gw53} but for a slight delay of about 1.5 dynamical times, effectively a temporal shift in the waveform." + However. other aspects of he waveforms are similar between the higher aud lower resolution cases: the magnetized results are essentially identical to the uninagnetized waveforms. aud the wave auplitudes agree nicely.," However, other aspects of the waveforms are similar between the higher and lower resolution cases: the magnetized results are essentially identical to the unmagnetized waveforms, and the wave amplitudes agree nicely." +" Even though the eravitational wave amplitudes are fairly consistent with no obvious correlation with D (approximately 0.15. 0:35.aud 0.11 for E= 5/3. 2 uud jJ. respectively). the wavelength of perturlvations betweeenr] the two biggest wave crests and the burst duratkn (between leading aud trailing wave crestswith amplitiucle larecr than 0.1) do appear to increase 1ionotouicalls ""with D."," Even though the gravitational wave amplitudes are fairly consistent with no obvious correlation with $\Gamma$ (approximately 0.45, 0.35,and 0.44 for $\Gamma=$ 5/3, 2 and 3, respectively), the wavelength of perturbations between the two biggest wave crests and the burst duration (between leading and trailing wave crestswith amplitude larger than 0.1) do appear to increase monotonically with $\Gamma$." + Iu particular. we find wavelengths of approximatelv Af Lot and Lat for D— 5/3. 2. and 3. a fractionalincrease (in wavelength) of about between P2 aud DP2 5/3. aud abhorut betwec‘ll TC=3 and P— 5/5.," In particular, we find wavelengths of approximately $\tilde t$ , $\tilde t$ , and $\tilde t$ for $\Gamma=$ 5/3, 2, and 3, a fractionalincrease (in wavelength) of about between $\Gamma=2$ and $\Gamma=5/3$ and about between $\Gamma=3$ and $\Gamma=5/3$ ." + Trends iu both amplitudes aud wavelengths are consistent with hose of Houser&Cen- (1996).. whofind the amplitude is independent of," Trends in both amplitudes and wavelengths are consistent with those of \citet{houser96}, , whofind the amplitude is independent of" +We note that our analysis is limited to objects in circular motion in a static uniform isothermal £&aseous medium.,We note that our analysis is limited to objects in circular motion in a static uniform isothermal gaseous medium. + For comparison with detailed observatious. our assumptions for the backgrouud uiecdium aud the object motion may 1eed to be relaxed.," For comparison with detailed observations, our assumptions for the background medium and the object motion may need to be relaxed." + However. tlie wake features described iu this paper may sulice to provide a zerothi order approximation of the primary features expected [rom the gravitational wakes clue to stch objects.," However, the wake features described in this paper may suffice to provide a zeroth order approximation of the primary features expected from the gravitational wakes due to such objects." + TIe author is grateful to Ronal« E. Tan for continuous discussion on this topic through reacling the manscript. aud Oscar Morata auc Wooug-Tae iim for euncouragiug and helpful Connieus.," The author is grateful to Ronald E. Taam for continuous discussion on this topic through reading the manuscript, and Oscar Morata and Woong-Tae Kim for encouraging and helpful comments." + The aitlior also acknowledges a stitmulating report from the anonymous referee. which iucreased the sigülicance aud potential of this work.," The author also acknowledges a stimulating report from the anonymous referee, which increased the significance and potential of this work." + This researcl is supported by the Theoretical Institute for Advanced Resea‘cl iu Astrophysics (TIARA) in the Acaclelia Sinica Insitute of Astronomy ancl Astrophysies (ASIAA)., This research is supported by the Theoretical Institute for Advanced Research in Astrophysics (TIARA) in the Academia Sinica Institute of Astronomy and Astrophysics (ASIAA). + The nunerical simulations preseited here are perfoined using FLASH2.0 code developed by the DOE-supported ASC/Alliauce Ceuer for Astropliysical Thermonuclear Flashes at the University of Chicago., The numerical simulations presented here are performed using FLASH3.0 code developed by the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. +should retain the triaxiality predicted by cosmological siuulatiouns.,should retain the triaxiality predicted by cosmological simulations. + This iav help to explain the rather clongated shapes of the ultra-faint MW. satellites (? (although these cau also be attributed to tidal effects im the gravitational feld of the NW) and oddities iu the Kinematics of some dwarf spheroidal galaxies (see.c.g“Se. 7).," This may help to explain the rather elongated shapes of the ultra-faint MW satellites \citep{Martin_etal08} (although these can also be attributed to tidal effects in the gravitational field of the MW) and oddities in the kinematics of some dwarf spheroidal galaxies \citep[see, e.g.,][]{Penarrubia_etal10}." + Many dwarf galaxies are also in the regime 5Z0.5 where they are unable to modity their surrounding halos., Many dwarf galaxies are also in the regime $\eta \simlt 0.5$ where they are unable to modify their surrounding halos. + CGascous disks iu such galaxies should exhibit departures from axisvaiuuetry. unless the halos are either prolate or oblate aud the disk plane comcides with that where the 2D potential is axisvuuuectric.," Gaseous disks in such galaxies should exhibit departures from axisymmetry, unless the halos are either prolate or oblate and the disk plane coincides with that where the 2D potential is axisymmetric." + This could indeed be the case in uearly oblate halos. eiven the preference of the angular moment to align with the nmünor axis (7).," This could indeed be the case in nearly oblate halos, given the preference of the angular momentum to align with the minor axis \citep{Bett_etal07}." +. However. iu nearly prolate idos (a iore conmuuon occurence according to 2V- ον siuimlations) disks whose augular moment aligus with the minor axis would feel a noun-axisviuinetric 2D gravitational potential.," However, in nearly prolate halos (a more common occurrence according to $N$ -body simulations) disks whose angular momentum aligns with the minor axis would feel a non-axisymmetric 2D gravitational potential." + Nou-circular| motions should herefore be fairly conuuon iu the saseous disks of dwarts. aud they could iu principle be used to gauge the raxialitv of their surrounding hialos.," Non-circular motions should therefore be fairly common in the gaseous disks of dwarfs, and they could in principle be used to gauge the triaxiality of their surrounding halos." + To first order. a gaseous disk iu the uou-axisviunietric x»teutial of a triaxial halo would behave just like gas ij a barred potential where the patteru speed of the uw ds zero.," To first order, a gaseous disk in the non-axisymmetric potential of a triaxial halo would behave just like gas in a barred potential where the pattern speed of the bar is zero." + A subdominant disk iu a triaxial potential would thus exhibit the nou-circular ανασα. signature of a (slow) bar but with no obvious bar in the Iuminous distribution., A subdominant disk in a triaxial potential would thus exhibit the non-circular dynamical signature of a (slow) bar but with no obvious bar in the luminous distribution. + Tutercstinely. there is one system where all these conditions are niet.," Interestingly, there is one system where all these conditions are met." + NGC 2976 is a nearby dwarf spiral ealaxy whose barvouic disk is subdominanut. as shown iu the bottom-rielt paucl of Figure 1..," NGC 2976 is a nearby dwarf spiral galaxy whose baryonic disk is subdominant, as shown in the bottom-right panel of Figure \ref{fig1}." + This Ποσο shows that the contribution of the barvonic component peaks at about one-half of the circular velocity at 7=2:284 and therefore 5gz0.5., This figure shows that the contribution of the baryonic component peaks at about one-half of the circular velocity at $r=2.2 R_d$ and therefore $\eta\approx 0.5$. + 2 show that the kinematics of the gaseous disk iu NGC 2976 is hniehlv complex. exlibiting large non-circular motions near the ceuter.," \citet{Simon_etal03} show that the kinematics of the gaseous disk in NGC 2976 is highly complex, exhibiting large non-circular motions near the center." + These. according to 7.. are best understood as the characteristic kinematic asviuunuetries miposed by awa=2 bar inode in the eravitatioual potential (scealso ?)..," These, according to \citet{Spekkens_Sellwood07}, are best understood as the characteristic kinematic asymmetries imposed by an $m=2$ bar mode in the gravitational potential \citep[see also][]{Hayashi_Navarro06}. ." + Ou the other haud. NCC 2976 has uo obvious bar. at least in the optical (butsce?).. so ascribing the origin of the nou-cireular motions to halo triaxiality is clearly tempting.," On the other hand, NGC 2976 has no obvious bar, at least in the optical \citep[but see][]{Menendez_etal07}, so ascribing the origin of the non-circular motions to halo triaxiality is clearly tempting." + If this interpretation is correct. then it would be surprising if other galaxies with subdonüuaut barvouic conrponeuts did not also show sigus of beiug embedded in triaxial potentials.," If this interpretation is correct, then it would be surprising if other galaxies with subdominant baryonic components did not also show signs of being embedded in triaxial potentials." + Dudeed. oue nav even argue that he absence of such signatures m a significant fraction of unbarred LSB aud chwart galaxies would be quite difücult to accommodate within the standard CDAI xwadieumi.," Indeed, one may even argue that the absence of such signatures in a significant fraction of unbarred LSB and dwarf galaxies would be quite difficult to accommodate within the standard CDM paradigm." + Definitive conchisions ou these issues require nore sophisticated theoretical modeling of the formation of subdominant disks iu triaxial halos., Definitive conclusions on these issues require more sophisticated theoretical modeling of the formation of subdominant disks in triaxial halos. + Note that our uodels neglect. for example. the response of the disk o the triaxial forcing of the halo. as well as a realistic accounting of the distribution of disk oricutatious relative o the principal axes of the halo.," Note that our models neglect, for example, the response of the disk to the triaxial forcing of the halo, as well as a realistic accounting of the distribution of disk orientations relative to the principal axes of the halo." + Nevertheless. our results sugeest that a careful search for signatures of wo traniality in a statistically significant sample of dwarf and LSB ealaxies would be warranted.," Nevertheless, our results suggest that a careful search for signatures of halo triaxiality in a statistically significant sample of dwarf and LSB galaxies would be warranted." + Steps iu hisdirection such as those taken by ? , Steps in thisdirection such as those taken by \citet{Trachternach_etal09} +"distribution can be very well described by Equation (7)) introduced by(1996),, where Const, zo=πο and f are free parameters with «z> being the first moment of the distribution and I' the Gamma function.","distribution can be very well described by Equation \ref{eqn:brainerd}) ) introduced by, where $Const$ , $z_0=\frac{\Gamma (3/\beta)}{\Gamma (4/\beta)}$ and $\beta$ are free parameters with $$ being the first moment of the distribution and $\Gamma$ the Gamma function." +" The best fitting values are: Const=6206, zo=0.107, and 6=0.611."," The best fitting values are: $Const=6206$, $z_0=0.107$, and $\beta=0.611$." +" Please note that if we analyse the galaxy photometric redshift histogram with a binning of Az=0.1 there are three clearly visible peaks below redshift of z=2: one at Zpnot=[0.6,0.7], one at Zpnoe=[0.9,1.0], and one at Zpnot= [1.7,1.8]. Interestingly, we also find peaks in the spectroscopic redshift histogram (see also Fig. 9))"," Please note that if we analyse the galaxy photometric redshift histogram with a binning of $\Delta z=0.1$ there are three clearly visible peaks below redshift of $z=2$: one at $z_{phot}=[0.6, 0.7]$, one at $z_{phot}=[0.9, 1.0]$, and one at $z_{phot}=[1.7, 1.8]$ Interestingly, we also find peaks in the spectroscopic redshift histogram (see also Fig. \ref{fig_tz}) )" +" with at least 10 galaxies at Zspec=[0.657,0.669], [0.672, 0.683], and Zspec=[0.926,0.941]."," with at least 10 galaxies at $z_{spec}=[0.657, 0.669]$, $z_{spec}=[0.672, 0.683]$ , and $z_{spec}=[0.926, 0.941]$." + In this section we show the UV luminosity function (LF) at 1500 aas derived from our deep i-selected catalogue and compare it to the LFs in the FDF2004a)., In this section we show the UV luminosity function (LF) at 1500 as derived from our deep i-selected catalogue and compare it to the LFs in the FDF. +. 'To derive the absolute UV band magnitude we use the best fitting SED as determined by the photometric redshift code., To derive the absolute UV band magnitude we use the best fitting SED as determined by the photometric redshift code. +" Since the photometric redshift code works with aperture fluxes, we only need to correct to total luminosities by applying an object dependent scale factor."," Since the photometric redshift code works with aperture fluxes, we only need to correct to total luminosities by applying an object dependent scale factor." + For this scale factor we used the ratio of the I-band aperture flux to the total flux as provided by SExtractor (MAG.AAPER and MAG.AAUTO)., For this scale factor we used the ratio of the I-band aperture flux to the total flux as provided by SExtractor APER and AUTO). +" As the SED fits all observed-frame passbands simultaneously, possible systematic errors which could be introduced by using K-corrections applied to a single observed magnitude are reduceddetails)."," As the SED fits all observed-frame passbands simultaneously, possible systematic errors which could be introduced by using K-corrections applied to a single observed magnitude are reduced." +" As an example, we plot in Fig."," As an example, we plot in Fig." + 14 the absolute UV-band magnitudes against the photometric redshifts of the objects in the COSMOS patch 06a., \ref{fig:absmag_1500} the absolute UV-band magnitudes against the photometric redshifts of the objects in the COSMOS patch 06a. + Moreover we also show the absolute UV-band magnitudes as derived in the FDF., Moreover we also show the absolute UV-band magnitudes as derived in the FDF. +" Both fields agree very well in their magnitude distribution, although there are a few relatively bright objects in the COSMOS patch (about 5 times the area of the FDF) not seen in the FDF distribution."," Both fields agree very well in their magnitude distribution, although there are a few relatively bright objects in the COSMOS patch (about 5 times the area of the FDF) not seen in the FDF distribution." +" To check if those objects could be stars misclassified as galaxies by our star-galaxy separation criterion, we decided to use a more conservative criterion for separating stars from galaxies."," To check if those objects could be stars misclassified as galaxies by our star-galaxy separation criterion, we decided to use a more conservative criterion for separating stars from galaxies." + We changed our criterion from 2Xstar~2 SMGs. which could be explored with high-resolution imaging of the gas distribution (e.g. Greveetal.2005: Carilli&Wang 20061).," However, the line width differences could also indicate that J033229.4 is at a later stage of a merger or has a different galaxy mass or size than typical $z\sim2$ SMGs, which could be explored with high-resolution imaging of the gas distribution (e.g. \citealt{Greve05}; \citealt{Carilli06}) )." + If instead we assume that the gas configuration is spherical (with a uniform distibution) rather than disk-like. then the implied enclosed dynamical mass would be Μωνμίς2kpe)=(1.110 MM...," If instead we assume that the gas configuration is spherical (with a uniform distibution) rather than disk-like, then the implied enclosed dynamical mass would be $_\mathrm{dyn}(<2\,\mathrm{kpc})=(1.1\pm0.6)\times10^{10}$ $_\odot$." + The combination of the gas and stellar mass estimates for JJ033229.4 can be used to calculate the total baryonic mass of the system., The combination of the gas and stellar mass estimates for J033229.4 can be used to calculate the total baryonic mass of the system. + The stellar mass of the system from Coppinetal. has been recontirmed by Wardlowetal.(2010) to be 21b1017 MM... Wa, The stellar mass of the system from \citet{Coppin09} has been reconfirmed by \citet{Wardlow10} to be $\lsim 1 \times 10^{11}$ $_\odot$. +rdlowetal.(2010) has included the new HAWK-I J and A -band photometry. and adjusted the derived mass for a Salpeter(1955) IMF for compatibility with the IMF assumed in deriving the SFR in ??..," \citet{Wardlow10} has included the new HAWK-I $J$ and $K$ -band photometry, and adjusted the derived mass for a \citet{Salpeter55} IMF for compatibility with the IMF assumed in deriving the SFR in \ref{compare}." + We caution that this quantity has an uncertainty of a factor of &5 even before considering a potential AGN contribution to the rest-frame near-infrared emission and so should be considered an approximate upper limit., We caution that this quantity has an uncertainty of a factor of $\lesssim 5$ even before considering a potential AGN contribution to the rest-frame near-infrared emission and so should be considered an approximate upper limit. + Taken together. these estimates imply a total baryonic mass within 2kkpe of Μω MinasΜον=12ὧν100 MM.~1.101 MM.. which is consistent with the dynamical mass estimated above from the CO emission given the considerable uncertainties.," Taken together, these estimates imply a total baryonic mass within kpc of $_\mathrm{bary}$ $_\mathrm{gas}$ $_\mathrm{stars}=1.2^{+4.0}_{-0.8} \times 10^{11}$ $_{\odot}\, \simeq 1 \times 10^{11}$ $_\odot$, which is consistent with the dynamical mass estimated above from the CO emission given the considerable uncertainties." + How representative is JJ033229.4 of the few known >~ 4-5 submillimetre-selected sources and the more abundant >~2 SMG population?, How representative is J033229.4 of the few known $z\sim4$ –5 submillimetre-selected sources and the more abundant $z\sim2$ SMG population? +" Based on the photometric constraints for JJ033229.4 which trace an SED consistent with local star formation dominated ULIRGs. Coppinetal.(2009). derive a dust mass estimate of AL,~510 MM. and a infrared luminosity of Lisc6©107 LL... implying a of c 1000MM. yyr7. close to the median luminosity of the 2o2 and >4 SMG populations (e.g. Kováesetal. 20065)."," Based on the photometric constraints for J033229.4 which trace an SED consistent with local star formation dominated ULIRGs, \citet{Coppin09} derive a dust mass estimate of $M_\mathrm{d}\sim 5 \times 10^{8}$ $_{\odot}$ and a far-infrared luminosity of $_\mathrm{IR}\simeq 6\times10^{12}$ $_\odot$, implying a of $\simeq1000$ $_\odot$ $^{-1}$, close to the median luminosity of the $z\sim2$ and $z>4$ SMG populations (e.g. \citealt{Kovacs06}) )." + When combined with our gas mass estimate above it follows that JJ033229.4 has a star formation efficiency (SFE) of « 250LL. kkmss !ppe?) toa gas-to-dynamical mass fraction of /ZM Mas~0.3(in77/0.25). and a gas-to-dust mass ratio of ~ 30.," When combined with our gas mass estimate above it follows that J033229.4 has a star formation efficiency (SFE) of $\approx 250$ $_\odot$ $^{-1}$ $^{2})^{-1}$, a gas-to-dynamical mass fraction of $f$ $_\mathrm{gas}$ $_\mathrm{dyn}\sim0.3 (\mathrm{sin}^{2}i/0.25)$, and a gas-to-dust mass ratio of $\sim30$ ." + Assumingthat the star formation follows the A -band light. we estimate a star formation surface density of “spur 100MM. 7. which is similar to the intense central starburst mode inferred for SMGs at 2— (e.g. Smailetal. 2003).," Assumingthat the star formation follows the $K$ -band light, we estimate a star formation surface density of $\Sigma_\mathrm{SFR}\sim100$ $_\odot$ $^{-1}$ $^{-2}$, which is similar to the intense central starburst mode inferred for SMGs at $z\sim2$ (e.g. \citealt{Smail03}) )." +" The source properties of JJ033229.4 derived from the CO line emission are very similar to those of the numerous SMGs at. o2 (MM, D38107 MM.. 1210 MM.. fc025. with SFEs of ~TOLL. + ppe)+ ond Ma Masi60: Greve Kováesetal.20062) and also the rarer emerging tail Z74 SMOs (Schinnereretal.2008: Daddietal.2009a.b))."," The source properties of J033229.4 derived from the CO line emission are very similar to those of the numerous SMGs at $z\sim2$ $<\!$ $_\mathrm{gas}\!>\sim3.0\times10^{10}$ $_\odot$, $<\!$ $_\mathrm{dyn}\!>\sim1.2 \times 10^{11}$ $_\odot$, $f\simeq0.25$, with SFEs of $\sim450\pm170$ $_\odot$ $^{-1}$ $^{2})^{-1}$ and $_\mathrm{gas}$ $_\mathrm{dust}\sim60$; \citealt{Greve05}; ; \citealt{Kovacs06}) ) and also the rarer emerging high-redshift tail $z>4$ SMGs \citealt{Schinnerer08}; \citealt{Daddi09a,Daddi09b}) )." + Combining the samples of CO-detected 2>4 SMGs. it follows that they lie within the scatter of the Έ Γκο relation from Greveetal.(2005) Τους —2SMGs (assuming a constant line brightness ratio). with +4-5 SMGs spanning a range of Li—0.6—3 LP LL. and Li~2-6 «101 ! ppc?.," Combining the samples of CO-detected $z>4$ SMGs, it follows that they lie within the scatter of the $_\mathrm{IR}$ $'_\mathrm{CO}$ relation from \citet{Greve05} for $z\sim2$ SMGs (assuming a constant line brightness ratio), with $z\sim4$ –5 SMGs spanning a range of $_\mathrm{IR}\sim0.6$ $3\times10^{13}$ $_\odot$ and $'_\mathrm{CO}\sim2$ $6\times10^{10}$ $^{-1}$ $^{2}$." + It thus appears that within the 2.~1-5 SMG population. πα Ίο is constant with redshift. indicating that SMGs at 2~4-5 are consistent with being higher-redshift analogues of SMGs at 2~2. forming stars with similar efficiencies.," It thus appears that within the $z\sim1$ –5 SMG population, $_\mathrm{IR}$ $'_\mathrm{CO}$ is constant with redshift, indicating that SMGs at $z\sim4$ –5 are consistent with being higher-redshift analogues of SMGs at $z\sim2$, forming stars with similar efficiencies." +" Overall this comparison suggests that SMGs at 2— and 2>d are equally evolved. have similar reservoirs of gas. similar star formation efficiencies. and similar fractions of baryons in cold gus as stars,"," Overall this comparison suggests that SMGs at $z\sim2$ and $z>4$ are equally evolved, have similar reservoirs of gas, similar star formation efficiencies, and similar fractions of baryons in cold gas as stars." + JJ033229.4 appears to be a luminous massive starburst. forming stars at a rate of ~LOOOMM. +. with a total baryonic mass of c1.10!4 MM... with properties representative of SMGs üt ο 2—4.," J033229.4 appears to be a luminous massive starburst, forming stars at a rate of $\sim1000$ $_\odot$ $^{-1}$, with a total baryonic mass of $\simeq 1\times 10^{11}$ $_\odot$, with properties representative of SMGs at $z\sim2$ –4." + The combination of its compact morphology and high SFR is potentially consistent with the small sizes of =:1-2 kkpe claimed for a population of massive extremely dense old quiescent 2~ galaxies (e.g. Daddietal.2005:: Toftetal.2007.2009:: Zirmetal. 2007:: Buitragoetal. 2008:: Cimattietal.20083).," The combination of its compact morphology and high SFR is potentially consistent with the small sizes of $\lsim1$ kpc claimed for a population of massive extremely dense old quiescent $z\sim2$ galaxies (e.g. \citealt{Daddi05}; \citealt{Toft07,Toft09}; \citealt{Zirm07}; \citealt{Buitrago08}; \citealt{Cimatti08}) )." + Such compact dense galaxies at 2 have implied formation redshifts of 2~ 4-5 and are consistent with being the descendents of a population of gas-rich. highly dissipative mergers. such as 27d SMGs.," Such compact dense galaxies at $z\sim2$ have implied formation redshifts of $z\sim4$ –5 and are consistent with being the descendents of a population of gas-rich, highly dissipative mergers, such as $z>4$ SMGs." +" A critical question we can now address is whether JJ033229.4 (assumed to be representative of +4 SMOs) has the baryonic mass and gas consumption timescale necessary to be a ‘prototypical’ progenitor of the luminous ""red and dead galaxy population found at 2~3?", A critical question we can now address is whether J033229.4 (assumed to be representative of $z>4$ SMGs) has the baryonic mass and gas consumption timescale necessary to be a `prototypical' progenitor of the luminous `red and dead' galaxy population found at $z\sim3$? + The baryonic content of JJ033229.4 is roughly equivalent to the typical stellar mass of a giant elliptical galaxy (110'4 MM. Marchesinietal. 2009)). given the large uncertainties in some of our mass estimates.," The baryonic content of J033229.4 is roughly equivalent to the typical stellar mass of a giant elliptical galaxy $1\times 10^{11}$ $_\odot$; \citealt{Marchesini09}) ), given the large uncertainties in some of our mass estimates." + Assuming that the molecular gas reservoir is fueling the star formation within JJ033229.4. then it will have enough gas to sustain the current star formation episode for Tdopletion ~Maa/SFR~L6«1027 MM. /1000MM. vyr5— MMvr. assuming efficiency.," Assuming that the molecular gas reservoir is fueling the star formation within J033229.4, then it will have enough gas to sustain the current star formation episode for $\tau_\mathrm{depletion}\sim$ $_\mathrm{gas}$ $\sim 1.6 \times 10^{10}$ $_\odot$ $_\odot$ $^{-1}\sim 16$ Myr, assuming efficiency." + We also compare Tilepletion with the time to form the current stellar mass of the system., We also compare $\tau_\mathrm{depletion}$ with the time to form the current stellar mass of the system. + At the current SFR. we estimate @ Τιμ ~Meuu./SFR~1 MM. /1000MM. vyr|~LOO MMyr. which is comparable to the assumed age of the stellar population and burst inthe model used in Coppinetal.(2009).," At the current SFR, we estimate a $\tau_\mathrm{formation}\sim$ $_\mathrm{stars}$ $\sim 1\times 10^{11}$ $_\odot$ $_\odot$ $^{-1} \sim 100$ Myr, which is comparable to the assumed age of the stellar population and burst inthe model used in \citet{Coppin09}." +. Although the gas consumption timescale appears to be relatively short. it is similar to thegas depletion timescales of ~100 MMyr for SMGs (e.g. Tacconiet 2008).," Although the gas consumption timescale appears to be relatively short, it is similar to thegas depletion timescales of $\sim100$ Myr for SMGs (e.g. \citealt{Tacconi08}) )." + It follows that we are catching this SMG approximately half way through its current star formation episode. with the majority of thegalaxy mass already in the form of stars. representative of a major stage in galaxy formation.," It follows that we are catching this SMG approximately half way through its current star formation episode, with the majority of thegalaxy mass already in the form of stars, representative of a major stage in galaxy formation." +" It thus seems plausible that JJ033229.4 would display the observed properties of being ""red and dead! by ο3 since the current stellar population would age another71 GGyr between +=4.76 and 2= 3. assuming that no further star formation occurs."," It thus seems plausible that J033229.4 would display the observed properties of being `red and dead' by $z\sim3$ since the current stellar population would age another $>1$ Gyr between $z=4.76$ and $z=3$ , assuming that no further star formation occurs." +Nucleodisruptiot has been found to be a significant producer of D and *He nuclei (?) within the standard evolution of the scale factor.,Nucleodisruption has been found to be a significant producer of D and $^3$ He nuclei \citep{Sihvola01} within the standard evolution of the scale factor. + However. with the slow evolution of the expansion rate in the Dirac-Milne universe and the hypothesis we made about the spatial repartition of the matter and antimatter domains. this situation changes.," However, with the slow evolution of the expansion rate in the Dirac-Milne universe and the hypothesis we made about the spatial repartition of the matter and antimatter domains, this situation changes." + Nuclet produced by nucleodisruption possess a kinetic energy ranging from a few MeV for nuclei to a few of MeV for nucleons (?).., Nuclei produced by nucleodisruption possess a kinetic energy ranging from a few MeV for nuclei to a few of MeV for nucleons \citep{Balestra88}. + These newly produced nuclei thermalize by Coulomb scattering on ambient protons and electrons., These newly produced nuclei thermalize by Coulomb scattering on ambient protons and electrons. + The thermalization length for D nuclei produced with an energy Ey=10MeV is presented in Fig., The thermalization length for D nuclei produced with an energy $E_0=10\;\rm{MeV}$ is presented in Fig. + 6 (blue dotted line)., \ref{diff_length} (blue dotted line). + This distance is always much smaller than the diffusion length. implying that any D nucleus produced by nucleodisruption will finally return towards the annihilation zone and be destroyed there.," This distance is always much smaller than the diffusion length, implying that any D nucleus produced by nucleodisruption will finally return towards the annihilation zone and be destroyed there." +" A possible way to produce a higher fraction of deutertum by nucleodisruption would be to consider small domains of (antiymatter within a larger ""Somain of antimatter (matter).", A possible way to produce a higher fraction of deuterium by nucleodisruption would be to consider small domains of (anti)matter within a larger domain of antimatter (matter). +" This situation occurs continually | an emulsion. which suffers a redistribution of ""domains? when bridges in the emulsion disappear by annihilation."," This situation occurs continually in an emulsion, which suffers a redistribution of “domains"" when bridges in the emulsion disappear by annihilation." + If the nx—imension of the larger domain is larger than the diffusion ength. then an important fraction of the D and *He produced by Seucleodisruption could survive.," If the dimension of the larger domain is larger than the diffusion length, then an important fraction of the D and $^3$ He produced by nucleodisruption could survive." +" However. precise calculations of this production require the. knowledge of the statistical properties of the spatial distribution of domains. which strongly ""Sepends of the separation mechanism."," However, precise calculations of this production require the knowledge of the statistical properties of the spatial distribution of domains, which strongly depends of the separation mechanism." + This point should be estigated in future studies of nucleosynthesis in the Milne universe., This point should be investigated in future studies of nucleosynthesis in the Dirac-Milne universe. + In 1998 (??).. distance measurements for type la ((SNe Ia) revealed that these objects are dimmer than expected if our Universe was correctly described by a decelerating Einstein-de Sitter model.," In 1998 \citep{Riess98, Perlmutter99}, distance measurements for type Ia (SNe Ia) revealed that these objects are dimmer than expected if our Universe was correctly described by a decelerating Einstein-de Sitter model." + The introduction of a cosmological constant A in the field equations of general relativity. which is apt to produce an accelerating expansion. provided an impressive fit to the observational data.," The introduction of a cosmological constant $\Lambda$ in the field equations of general relativity, which is apt to produce an accelerating expansion, provided an impressive fit to the observational data." + Today. SNe Ia are one of the nost important cosmological tests and are considered as prime evidence of an acceleration of the expansion.," Today, SNe Ia are one of the most important cosmological tests and are considered as prime evidence of an acceleration of the expansion." + We recall however that the strong evidence of a recent transition between a decelerating phase and an accelerating phase of expansion heavily relies on the prior hypothesis of spatial flatness., We recall however that the strong evidence of a recent transition between a decelerating phase and an accelerating phase of expansion heavily relies on the prior hypothesis of spatial flatness. + Without this hypothesis. the evidence ts less clear (?)..," Without this hypothesis, the evidence is less clear \citep{Seikel2008}." + The Dirac-Milne universe has neither acceleration nor deceleration and is therefore equivalent to an open empty universe., The Dirac-Milne universe has neither acceleration nor deceleration and is therefore equivalent to an open empty universe. +" In terms of the usual cosmological parameters. this universe corresponds to the combination left,o0."," In terms of the usual cosmological parameters, this universe corresponds to the combination _M=0, )." +" ""EN In this context. the luminosity distance in the Dirac-Milne universe follows the simple expression(?)."," In this context, the luminosity distance in the Dirac-Milne universe follows the simple expression." +. The SNLS data consist of two distinct datasets., The SNLS data consist of two distinct datasets. + The high-redshift sample. from the SNLS. comprises 71 SNe Ia. with redshifts between 0.2€z1.01.," The high-redshift sample, from the SNLS, comprises 71 SNe Ia with redshifts between $0.2\leq z\leq 1.01$." + The second sample is a low-redshift set. consisting of 44 SNe Ia taken from the literature with redshifts 2<0.15.," The second sample is a low-redshift set, consisting of 44 SNe Ia taken from the literature with redshifts $z\leq 0.15$." + These data come from different experiments and are therefore possibly subject to different sources of systematic errors., These data come from different experiments and are therefore possibly subject to different sources of systematic errors. +" Following the definition given in ?.. the distance modulus is where M is the absolute magnitude of SNe la. e and ϱ are global parameters that link the stretch s and the color c to the distance modulus. and 7, is the apparent magnitude of the supernova."," Following the definition given in \citet{Astier06}, the distance modulus is c, where $M$ is the absolute magnitude of SNe Ia, $\alpha $ and $\beta$ are global parameters that link the stretch $s$ and the color $c$ to the distance modulus, and $m^*_B$ is the apparent magnitude of the supernova." + It should be emphasized that. in. contrast to the ACDM cosmology. there is no cosmological parameter dependence in the Dirac-Milne luminosity distance.," It should be emphasized that, in contrast to the $\Lambda$ CDM cosmology, there is no cosmological parameter dependence in the Dirac-Milne luminosity distance." + The only degrees of freedom are the nuisance parameters. M. a. and P.," The only degrees of freedom are the nuisance parameters, $M$, $\alpha$, and $\beta$." + Following the procedure described in 2.. we minimize the expressioni," Following the procedure described in \citet{Astier06}, , we minimize the expression." +"nt Here. c(ug) takes into account measurement errors in the apparent magnitude m,. stretch. and color parameters derived by the analysis of light curves (?).. Gig, Is the so- “intrinsic” dispersion. which is a parameter introduced to account for SNe Ia being astrophysical objects that naturally have some intrinsic dispersion in their absolute magnitude."," Here, $\sigma(\mu_B)$ takes into account measurement errors in the apparent magnitude $m_B^*$, stretch, and color parameters derived by the analysis of light curves \citep{Guy2005}, $\sigma_{\rm{int}}$ is the so-called ""intrinsic"" dispersion, which is a parameter introduced to account for SNe Ia being astrophysical objects that naturally have some intrinsic dispersion in their absolute magnitude." +" However. the valueof this parameter is unknown. and in the fitting procedure. c, 1s adjusted to ensure that the reduced squared is unity."," However, the valueof this parameter is unknown, and in the fitting procedure, $\sigma_{\rm{int}}$ is adjusted to ensure that the reduced chi-squared is unity." + We first performed our analysis on the high-z sample without including any low-z SN Ia. Without this low-z anchoring. the analysis does not permit us to discriminate between the ACDM and the Dirac-Milne universes.," We first performed our analysis on the $z$ sample without including any low-z SN Ia. Without this $z$ anchoring, the analysis does not permit us to discriminate between the $\Lambda$ CDM and the Dirac-Milne universes." + In this respect. we note that the three-year analysis of SNLS using their data alone (?) is consistent to a better than CL with the Dirac-Milne universe. while the Einstein-de Sitter (EdS) model is clearly excluded.," In this respect, we note that the three-year analysis of SNLS using their data alone \citep{Guy10} is consistent to a better than CL with the Dirac-Milne universe, while the Einstein-de Sitter (EdS) model is clearly excluded." + The evidence of an expansion acceleration therefore relies on a comparison between low-z and high-z SNe la. We also present the results for the EdS model., The evidence of an expansion acceleration therefore relies on a comparison between $z$ and $z$ SNe Ia. We also present the results for the EdS model. + The results of the analysis of the 71 SNe la are presented in Tables | and 2.., The results of the analysis of the 71 SNe Ia are presented in Tables \ref{tab:sn5} and \ref{tab:sn4}. + In Table |.. the intrinsic dispersion ts fixed to a null value.," In Table \ref{tab:sn5}, the intrinsic dispersion is fixed to a null value." + The analysis is therefore performed using only the measurement errors. thereby giving a stronger weight to SNe la withredshifts 0.2.€zx 0.4. which have smaller errors.," The analysis is therefore performed using only the measurement errors, thereby giving a stronger weight to SNe Ia withredshifts $0.2 \leq z\leq 0.4$ , which have smaller errors." + (Ehe total and reduced y- of the EdS model are much larger than those of the ACDM and Dirac-Milne models. which are in," The total and reduced $\chi^2$ of the EdS model are much larger than those of the $\Lambda$ CDM and Dirac-Milne models, which are in" +the field lines (Mouschovias&Ciolek.1999).. and the second will have it along the axis. due to entrainment of the field at the shock front.,"the field lines \citep{Mo1999b}, and the second will have it along the axis, due to entrainment of the field at the shock front." + Therefore measuring the field directions could distinguish between these two models., Therefore measuring the field directions could distinguish between these two models. + Detailed studies (Watson.1994;Elitzur. of the polarisation properties of OH. and SiO masers have been made. but there has been relatively little investigation of the polarisation. properties of methanol masers.," Detailed studies \citep{watson_94,elitzur_96c,gray_03} of the polarisation properties of OH, and SiO masers have been made, but there has been relatively little investigation of the polarisation properties of methanol masers." + Single dish observations of polarisation in methanol masers are all from the strongest sources: Kooetal.(1988) observed W3(OH) and NGC 6334F at 12 GHz. while Caswelletal.(1995) determined that the level of circular polarisation for a number of strong 6.7 GHz methanol maser features was less than," Single dish observations of polarisation in methanol masers are all from the strongest sources: \cite{Ko1988} observed W3(OH) and NGC 6334F at 12 GHz, while \cite{Ca1995a} determined that the level of circular polarisation for a number of strong 6.7 GHz methanol maser features was less than." +[σοι Ellingsen(2002) reported on 6.7 GHz polarisation observations with the ATCA of NGC 6334F where he found linear polarisation fractions of up to10%.," \cite{ellingsen_02} reported on 6.7 GHz polarisation observations with the ATCA of NGC 6334F, where he found linear polarisation fractions of up to." +. The first high resolution polarisation images were made with MERLIN at a resolution of 50 mas (Vlemmingsetal..2006). of W3(OH). where polarisation fractions of upto but typically were found.," The first high resolution polarisation images were made with MERLIN at a resolution of 50 mas \citep{vlemmings_06}, of W3(OH), where polarisation fractions of upto but typically were found." + Those polarisation angles were consistent with those of the OH-masers. and furthermore lie along the methanol maser emission as expected for shock excited regions.," Those polarisation angles were consistent with those of the OH-masers, and furthermore lie along the methanol maser emission as expected for shock excited regions." + The maser G339.88-1.26 was discovered at 12 GHz by Norrisetal. (1987).. and at 6.7 GHz by MacLeodetal.(1992).," The maser G339.88-1.26 was discovered at 12 GHz by \cite{norris_87}, and at 6.7 GHz by \cite{macleod_92}." + Follow-up at arcsecond resolution by the Australia Telescope Compact Array (ATCA) showed strong emission with a roughly linear morphology and a monotonie velocity gradient (Norrisetal., Follow-up at arcsecond resolution by the Australia Telescope Compact Array (ATCA) showed strong emission with a roughly linear morphology and a monotonic velocity gradient \citep{norris_93}. +.1993).. Ellingsenetal.(1996) detected weak radio continuum emission which peaks at the same position as the maser emission., \cite{ellingsen_96_cont} detected weak radio continuum emission which peaks at the same position as the maser emission. + The Mid Infra-Red (MIR) observations at 10 jm of Stecklum(1998) detected elongated emission along the same position angle as the disk inferred by the methanol masers., The Mid Infra-Red (MIR) observations at $10~\mu$ m of \cite{St1998a} detected elongated emission along the same position angle as the disk inferred by the methanol masers. + These combined to make this one of the best candidates for the disk model for methanol masers. with the masers formed in the dusty disk hiding αἱ embedded massive. forming. star.," These combined to make this one of the best candidates for the disk model for methanol masers, with the masers formed in the dusty disk hiding an embedded massive, forming, star." + However higher resolution. 10 and 18 jm MIR observations. at the Keck Observatory (DeBuizeretal..2002) resolved the IR source into three components.," However higher resolution, 10 and $18~\mu$ m MIR observations, at the Keck Observatory \citep{debuizer_02} + resolved the IR source into three components." + VLBI observations from 1996. included in the same paper. showed that the masers formed an inverted Y shape and lay between IB and IC. See Figure 2b in that paper.," VLBI observations from 1996, included in the same paper, showed that the masers formed an inverted Y shape and lay between 1B and 1C. See Figure 2b in that paper." + That is they do not mark the disk. indeed there was no disk. nor do they have a Keplerian velocity distribution.," That is they do not mark the disk, indeed there was no disk, nor do they have a Keplerian velocity distribution." + As a telescope tracks à source across the sky the angle of the source on the sky to that of the telescope feed changes., As a telescope tracks a source across the sky the angle of the source on the sky to that of the telescope feed changes. + When observing with Left Circular and Right Circular Polarisations (LCP and RCP) this has the effect of introducing a phase shift between the two recorded data-streams., When observing with Left Circular and Right Circular Polarisations (LCP and RCP) this has the effect of introducing a phase shift between the two recorded data-streams. + To post-process these data these phases need to be removed. and the feed impurities need to be solved for and included in the calibration.," To post-process these data these phases need to be removed, and the feed impurities need to be solved for and included in the calibration." + A good summary of the steps needed to make polarisation VLBI images can be found in Aaron(1997)., A good summary of the steps needed to make polarisation VLBI images can be found in \cite{aaron_97}. +. In this study. and indeed all other sources on VLBI polarisation. the feed mounts are assumed to be Cassegrain or Equatorial.," In this study, and indeed all other sources on VLBI polarisation, the feed mounts are assumed to be Cassegrain or Equatorial." + Different mounts rotate the feeds in different fashions on the sky as the telescope tracks a source., Different mounts rotate the feeds in different fashions on the sky as the telescope tracks a source. + Two new mount types to those supported have been added., Two new mount types to those supported have been added. + For VLBI observations AIPS (Greisen.1988) remains the only tool for data calibration. therefore this has been our target for the extension of mount types.," For VLBI observations AIPS \citep{aips} remains the only tool for data calibration, therefore this has been our target for the extension of mount types." + The code to support the Nasmyth mount type and the E-W mount type have been developed., The code to support the Nasmyth mount type and the E-W mount type have been developed. + The latter is a subset of the X-Y mount (traditionally for Low Earth Orbit satellite tracking stations) where the second axis les East-West., The latter is a subset of the X-Y mount (traditionally for Low Earth Orbit satellite tracking stations) where the second axis lies East-West. + The only example known to the author is the Hobart telescope which is part of the Australian Long Baseline Array (LBA)., The only example known to the author is the Hobart telescope which is part of the Australian Long Baseline Array (LBA). + The alternative configuration is the N-S mount. where the second axis lies orth-South.," The alternative configuration is the N-S mount, where the second axis lies North-South." +" The ""keyhole'. where large angular changes are required for small movements on the sky. falls on the second axis."," The `keyhole', where large angular changes are required for small movements on the sky, falls on the second axis." + Compared the Alt-Az mount. the X-Y mounts move the keyhole from the Zenith to the horizon. where observations are not normally made.," Compared the Alt-Az mount, the X-Y mounts move the keyhole from the Zenith to the horizon, where observations are not normally made." + The second mount type added. which is not used in the data presented here. 1s for the Nasmyth type.," The second mount type added, which is not used in the data presented here, is for the Nasmyth type." + The asmyth mount is more normally used on optical instruments. as it allows space for very large instrumentation packages.," The Nasmyth mount is more normally used on optical instruments, as it allows space for very large instrumentation packages." + Until now this has not been needed for Radio Telescopes. but hew quasi-optical systems allow the siting of multiple feeds for different bands at the Nasmyth foci.," Until now this has not been needed for Radio Telescopes, but new quasi-optical systems allow the siting of multiple feeds for different bands at the Nasmyth foci." + This configuration allows the co-observing of widely separated observing bands. which is particularly useful for the calibration of mm-VLBI (Dodson&Rioja.2008).," This configuration allows the co-observing of widely separated observing bands, which is particularly useful for the calibration of mm-VLBI \citep{fpt_report}." +. The new code is for the new mm-VLBI telescope being constructed at Yebes. Spain. which will cover frequencies from GGHz to GGHz. anc also the IRAM telescope at Pico Veleta (Spain).," The new code is for the new mm-VLBI telescope being constructed at Yebes, Spain, which will cover frequencies from GHz to GHz, and also the IRAM telescope at Pico Veleta (Spain)." + Left handed and Right handed Nasmyth foci are also included in the new AIPS code. as required for the Left or Right optical branch.," Left handed and Right handed Nasmyth foci are also included in the new AIPS code, as required for the Left or Right optical branch." + Full details can be found in Dodson(2007).., Full details can be found in \cite{pol_report}. + These observations with the LBA were used to test EW-mount portion of these new subroutines., These observations with the LBA were used to test EW-mount portion of these new subroutines. + When the LBA results on G339.88-1.26 are compared to those of ATCA observations (Ellingsen. Priv.," When the LBA results on G339.88-1.26 are compared to those of ATCA observations (Ellingsen, Priv." + Comms.).," Comms.)," +" made in Sept 1999, an excellent match in the linear polarised fluxes and angles is found. after including the absolute polarisation angle offset between the brightest polarised component (at —38.7 )."," made in Sept 1999, an excellent match in the linear polarised fluxes and angles is found, after including the absolute polarisation angle offset between the brightest polarised component (at $-38.7$ )." + See Figure | where the position angles. linear polarised and total flux are compared for the two instruments.," See Figure \ref{fig:pa} where the position angles, linear polarised and total flux are compared for the two instruments." + ATCA values are plotted with red closed circles. and the LBA values with blue open boxes.," ATCA values are plotted with red closed circles, and the LBA values with blue open boxes." + The values are extracted from à sum across the Q and U images (with miriad’s imspec) which allows the comparison of these two datasets with very different resolutions., The values are extracted from a sum across the Q and U images (with miriad's ) which allows the comparison of these two datasets with very different resolutions. + The errors are absolute errors from the confidence in the polarisation calibration. the relative errors are much less.," The errors are absolute errors from the confidence in the polarisation calibration, the relative errors are much less." +" Note that Goedhartetal.(2004) report this source as ""not significantly variable. with one component falling (-32.39 )andone rising (-33.19"," Note that \cite{goe_04} report this source as `not significantly variable', with one component falling (-32.39 ) and one rising (-33.19" +"that Ly, requires a distauce estimate to the source.",that $E_{gw}$ requires a distance estimate to the source. + Iu practice. this may require statistical analysis on a sample of detections.," In practice, this may require statistical analysis on a sample of detections." + The author thanks the Norean Institute for Advanced Study for their hospitality aud for hosting a very stimulating mecting., The author thanks the Korean Institute for Advanced Study for their hospitality and for hosting a very stimulating meeting. + Te also thanks G.E. Brown. CAV. Lee and A. Leviuson for continuing couversations.," He also thanks G.E. Brown, C.W. Lee and A. Levinson for continuing conversations." + This work is partially supported by NASA Crant No., This work is partially supported by NASA Grant No. + 5-7012 and au MIT CLE. Reed Award., 5-7012 and an MIT C.E. Reed Award. +education and advocacy.,education and advocacy. + We also thank the Tohono O'odham National for being helpful in their choices for outdoor lighting. the International Dark Sky Association for spreading the word and surrounding governments for their continued willingness to consider the impact of their choices on the conduct of astronomy in southern Arizona.," We also thank the Tohono O'odham National for being helpful in their choices for outdoor lighting, the International Dark Sky Association for spreading the word and surrounding governments for their continued willingness to consider the impact of their choices on the conduct of astronomy in southern Arizona." + Our study shows that these and other efforts have paid off., Our study shows that these and other efforts have paid off. + But. constant vigilance is essential.," But, constant vigilance is essential." + We would also like to thank Di Larmer lor her strong support and advice. Dill Binkert for helping set up the spectrograph on occasion. Jeff Hall for helping us analvze the effects of the solar evele on the night skv brightness. the Friends of Lowell Observatory [or publication costs. and the anonvmous referee for their suggestions that helped improve the paper.," We would also like to thank Di Harmer for her strong support and advice, Bill Binkert for helping set up the spectrograph on occasion, Jeff Hall for helping us analyze the effects of the solar cycle on the night sky brightness, the Friends of Lowell Observatory for publication costs, and the anonymous referee for their suggestions that helped improve the paper." +intervening e10 νου time span.,intervening $\sim10$ -year time span. +" There remains a significant discrepancy will the value Iv.=19.14x0.2 estimated by AlvesdeOliveiraοἱal.(2010).. but we suspect that the difference can be attributed to the smaller elfective beamsize (0.4—0.8"") in the latter observations. which could lead to flux underestimation for an extended source."," There remains a significant discrepancy with the value $K_s=19.14\pm0.2$ estimated by \citet{alv10}, but we suspect that the difference can be attributed to the smaller effective beamsize $0.4''-0.8''$ ) in the latter observations, which could lead to flux underestimation for an extended source." + Object #44450 is not unique in this regardwe have found. a number of other cases in which our sources are slightly extended. aud hypothesize that we may be seeing the effects οἱ scaltering from remnant infalling dust envelopes surrounding the brown dwarl candidates.," Object 4450 is not unique in this regard—we have found a number of other cases in which our sources are slightly extended, and hypothesize that we may be seeing the effects of scattering from remnant infalling dust envelopes surrounding the brown dwarf candidates." + It is not clear what. if any. effect such cases would have on our temperature estimates. but we note that our SED fit for 444450 vielded an effective temperature in complete agreement wilh the spectroscopic value from Marshetal.(2010).," It is not clear what, if any, effect such cases would have on our temperature estimates, but we note that our SED fit for 4450 yielded an effective temperature in complete agreement with the spectroscopic value from \citet{mar10}." +. Our conclusions are based on fits to broad-band SEDs which are subject to the uncertainties (hat we have discussed., Our conclusions are based on fits to broad-band SEDs which are subject to the uncertainties that we have discussed. + Verification must await spectroscopic observations in order to confirm (he nature of individual objects and to better constrain (heir parameters., Verification must await spectroscopic observations in order to confirm the nature of individual objects and to better constrain their parameters. + Nevertheless. SED fitting can play an important role in gathering statistics over wiler areas of (he sky. which is important to do because the mass function is known to vary from region to regionbetween different star-Forming clouds (Evans&Lada1991). and even within the same cloud (Barsonyetal.1997).," Nevertheless, SED fitting can play an important role in gathering statistics over wider areas of the sky, which is important to do because the mass function is known to vary from region to region—between different star-forming clouds \citep{evans91} and even within the same cloud \citep{bar97}." +. Such studies will be aided by upcoming survevs. particularly the Wide-Field Infrared Survey. Explorer (WISE) in conjunction with shorter-waveleneth data from the UIXKIRT Infrared Deep Sky Survey (ΕΝΤΟΣ) and the Visible and Infrared Survey Telescope for Astronomy (VISTA).," Such studies will be aided by upcoming surveys, particularly the Wide-Field Infrared Survey Explorer (WISE) in conjunction with shorter-wavelength data from the UKIRT Infrared Deep Sky Survey (UKIDSS) and the Visible and Infrared Survey Telescope for Astronomy (VISTA)." +" Additional complementary data. consisting of optical and [u-red photometry. will soon be available [rom the Pan-STARRS-1 and Sky-Mapper survey telescopes. and will cover a larger area of skv than UNIDSS and VISTA,"," Additional complementary data, consisting of optical and far-red photometry, will soon be available from the Pan-STARRS-1 and Sky-Mapper survey telescopes, and will cover a larger area of sky than UKIDSS and VISTA." + We (thank (he referee for helpful comments and suggestions., We thank the referee for helpful comments and suggestions. + We also thank Tim Thompson for making the IRAC mosaic images. and John Stauffer and Luisa. Rebull for," We also thank Tim Thompson for making the IRAC mosaic images, and John Stauffer and Luisa Rebull for" + lt ds difficult to. clillerentiate between absorption and emission at —1.2 keV in ‘Ton 5150, It is difficult to differentiate between absorption and emission at $\sim$ 1.2 keV in Ton S180. + A single. absorption edge at. a rest. οποιον of E=1.09+0.03 keV with an optical depth 7=0.17£0.03. vields νοfv=1072/986.," A single absorption edge at a rest energy of $=1.09\pm0.03$ keV with an optical depth $\tau=0.17\pm0.03$, yields $\chi^{2}/{\nu}=1072/986$." + A second. edge in the spectrum (at E=1.42+0.06 keV with τξ 0.130.038) improves the fit further (\7v= 1059/985)., A second edge in the spectrum (at $=1.42\pm0.06$ keV with $\tau=0.13\pm0.03$ ) improves the fit further $\chi^{2}/{\nu}=1059/985$ ). + ‘There is some evidence for an additional edge at ~0.73 keV (v/v= 1048/983) presumably corresponding toOvi., There is some evidence for an additional edge at $\sim$ 0.73 keV $\chi^{2}/{\nu}=1048/983$ ) presumably corresponding to. + Llowever SIS-1 seems to underestimate the flux compared o SIS-0 below 0.8 keV. so any features in the spectrum odow 0.8 keV. need to considered with caution.," However SIS-1 seems to underestimate the flux compared to SIS-0 below 0.8 keV, so any features in the spectrum below 0.8 keV need to considered with caution." + A significant improvement over the soft. excess [it is given when a broad Gaussian emission component is added o the model near 1 keV. The best-fit parameters are line EW=20δ eV. energy E=0.94d:0.03 keV and intrinsic width 0=0.062+0.025 keV. for whieh X7/&=the1055/985.," A significant improvement over the soft excess fit is given when a broad Gaussian emission component is added to the model near 1 keV. The best-fit parameters are line $=20\pm8$ eV, energy $=0.94\pm0.03$ keV and intrinsic width $\sigma=0.062\pm0.025$ keV, for which $\chi^{2}/{\nu}=1055/985$." +MN A model also gives an acceptable fit to vielding a plasma temperature of kP=0.89+0.11 keV (Af= 1050/986).," A model also gives an acceptable fit to the data, yielding a plasma temperature of $=0.89\pm0.11$ keV $\chi^{2}/{\nu}=1050/986$ )." + An absorption [feature definitely gives the best. fit. in ll] 0707495, An absorption feature definitely gives the best fit in 1H 0707–495. + A broad. absorption line improves the fit significantIy. (Xv= 404/335). as per Table 4.," A broad absorption line improves the fit significantly $\chi^{2}/{\nu}=404/335$ ), as per Table 4." + An equally good x7 can be obtained. but for 1 additional free parameter. using twoP instead of a single Gaussian: the first edge is at 1.0020.03 keV with 7=0.632:0.27 and the second at 105-000£0.03edene keV with 7=0540.2.," An equally good $\chi^{2}$ can be obtained, but for 1 additional free parameter, using two edges instead of a single Gaussian; the first edge is at $1.09\pm0.03$ keV with $\tau=0.63\pm0.27$ and the second at $0.90\pm0.03$ keV with $\tau=0.5\pm0.2$." + Leighlv C1997b) also find for one or more absorption features near 1 keV. Ehe addition of a Gaussian emission line in the range 63 keV. instead of an absorption feature. does not provide any improvement in the fit.," Leighly (1997b) also find evidence for one or more absorption features near 1 keV. The addition of a Gaussian emission line in the range 0.6–3 keV, instead of an absorption feature, does not provide any improvement in the fit." + Previous investigations of the N-rav spectrum of NGC 4051 have suggested the existence. of a warm absorber., Previous investigations of the X-ray spectrum of NGC 4051 have suggested the existence of a warm absorber. + There is no evidence for additional spectral features in the first observation (taken during the PV phase of the mission) but the second. CXO2) observation. which has much better signal/noise ratio. does show significant features in the residuals between 0.7 and 0.9 keV. In this case we have modelled this apparent warm absorber with 2 absorption edges. for the first. edge E=0.73+0.02 keV and τ0.33£0.05. for the second. edge L=0.93+0.03 keV and τς0.19+ 0.04.," There is no evidence for additional spectral features in the first observation (taken during the PV phase of the mission) but the second (AO2) observation, which has much better signal/noise ratio, does show significant features in the residuals between 0.7 and 0.9 keV. In this case we have modelled this apparent warm absorber with 2 absorption edges, for the first edge $=0.73\pm0.02$ keV and $\tau=0.33\pm0.05$ , for the second edge $0.93\pm0.03$ keV and $\tau=0.19\pm0.04$ ." + The resulting fit statistic is yofu=2010/1842. an improvement. of Ay?⊳↘=−−77 over the model without. absorption.," The resulting fit statistic is $\chi^{2}/{\nu}=2010/1842$, an improvement of $\Delta\chi^{2}=77$ over the model without absorption." + The results suggest a normal warn absorber in NGC 4051. with the edges probably originating from andOvi.," The results suggest a normal warm absorber in NGC 4051, with the edges probably originating from and." + Our results are broadly consistent with those of CGuainazzi (1996). who consider the fitting of this observation in much greater detail.," Our results are broadly consistent with those of Guainazzi (1996), who consider the fitting of this observation in much greater detail." + Emission and absorption components give comparable fits in PC 12441026., Emission and absorption components give comparable fits in PG 1244+026. + The addition of a broad Gaussian absorption line significantlv> improves the fit (Apoc 601/532). as per Table 4.," The addition of a broad Gaussian absorption line significantly improves the fit $\chi^{2}/{\nu}=601/532$ ), as per Table 4." + A single. edge at an. energy. of 1.18d3 keV. gives a better [it (7/6= 591/533).," A single edge at an energy of $1.18\pm0.03$ keV, gives a better fit $\chi^{2}/{\nu}=591/533$ )." + Adding another edge further improves the fit: with two edges (at E=1.16£0.04 keV and E=0.63n keV) the fit obtained is Vp=SSBΣΙ., Adding another edge further improves the fit; with two edges (at $1.16\pm0.04$ keV and $0.63^{+0.04}_{-0.45}$ keV) the fit obtained is $\chi^{2}/{\nu}=583/531$. + A broad. Gaussian emission. line at an enerev of E=0.97+004 keV also significantly improves the fit ονfr= 589/532). with an equivalent width of EW=36+11 eV. A slightly better fit QCvo= 586/533) is obtained. wit-— the model. with a plasma temperature of kK'T—1.040.1 keV. Fiore (1998) also find evidence for either an absorption feature at ~1.2 keV or an emission feature at 0.9 keV. Absorption components give a slightly. better fit. than emission components.," A broad Gaussian emission line at an energy of $0.97\pm0.04$ keV also significantly improves the fit $\chi^{2}/{\nu}=589/532$ ), with an equivalent width of $36\pm11$ eV. A slightly better fit $\chi^{2}/{\nu}=586/533$ ) is obtained with the model, with a plasma temperature of $1.0\pm0.1$ keV. Fiore (1998) also find evidence for either an absorption feature at $\sim$ 1.2 keV or an emission feature at 0.9 keV. Absorption components give a slightly better fit than emission components." + The addition of a single absorption edge to the model improves the fit. significantly (4c/e= 478/424)., The addition of a single absorption edge to the model improves the fit significantly $\chi^{2}/{\nu}=478/424$ ). + The best fit edge energy is E—1.11+0.04 keV. A second edge improves the further (x7fe= 467/422). with edge energies at 1.0ÜzE0.04 and 1.150.09 keV and optical depths of 7=0.73 and 1.15 respectively.," The best fit edge energy is $1.11\pm0.04$ keV. A second edge improves the fit further $\chi^{2}/{\nu}=467/422$ ), with edge energies at $1.00\pm0.04$ and $1.18\pm0.03$ keV and optical depths of $\tau=0.73$ and 1.15 respectively." + This fit also, This fit also +»edieted due to the TDU. when LBB takes place the C/O ratio is expected either to decrease. as long as C is converted into N by the CN evele. or even to increase if O is ellicientlv int in favour of N bv the ON evecle (see Sect. 4.3)).,"predicted due to the TDU, when HBB takes place the C/O ratio is expected either to decrease, as long as C is converted into N by the CN cycle, or even to increase if O is efficiently burnt in favour of N by the ON cycle (see Sect. \ref{ssec_nucleos}) )." + Variations in. CNO abundances allect the Iow-enmperature opacities essentially in two wavs. Le. i) for Zs3000 K by mocifving the equilibrium molecular pattern depending on the C/O ratio and. to a less extent. ii) for arecr temperatures by changing the contributions of the CNO atoms to both the continuum ancl line opacity.," Variations in CNO abundances affect the low-temperature opacities essentially in two ways, i.e. i) for $T\la 3\,000$ K by modifying the equilibrium molecular pattern depending on the C/O ratio and, to a less extent, ii) for larger temperatures by changing the contributions of the CNO atoms to both the continuum and line opacity." + A detailed discussion can be found in Marigo Aringer (2009: see their section 4.2) anc Ventura Alarigo (2009)., A detailed discussion can be found in Marigo Aringer (2009; see their section 4.2) and Ventura Marigo (2009). + The nuclear network included in the code is described in details in Ventura&D'Antona(2005a)., The nuclear network included in the code is described in details in \citet{paolo4}. +. The cross-sections of the 64 reactions considered. are taken from the NACRE compilation (Anguloctal.1999)... with the exception of HN(p.« O. taken from Formicolactal.(2004)... and. the three proton-capture reactions of the Ne-Na evele. taken from Llaleetal.(2002) for the ??Ne(p.* J Na reaction. and from Llaleetal.(2004). for the two p-captures by sodium nuclei.," The cross-sections of the 64 reactions considered are taken from the NACRE compilation \citep{angulo}, with the exception of $^{14}$ $\gamma$ $^{15}$ O, taken from \citet{luna}, and the three proton-capture reactions of the Ne-Na cycle, taken from \citet{hale1} + for the $^{22}$ $\gamma$ $^{23}$ Na reaction, and from \citet{hale2} for the two p-captures by sodium nuclei." + The stellar models discussed here were followed from the pre-AIS phase to almost the complete ejection of the external envelope., The stellar models discussed here were followed from the pre-MS phase to almost the complete ejection of the external envelope. + The initial chemical composition of the gas is assigned a total metallicity (mass fraction) Z=0.001 and a degree ofa enhancement aο=10.4. with the reference solar mixture taken from Crevesse&Sauval(1998).," The initial chemical composition of the gas is assigned a total metallicity (mass fraction) $Z=0.001$ and a degree of $\alpha-$ enhancement $[\alpha/{\rm Fe}]=+0.4$, with the reference solar mixture taken from \citet{gs98}." +. ‘To investigate how much the results are allected by the the interplay between the use of the opacitics accounting for the CNO variations and the mass-loss description. we calculated 4 sets of evolutionary mociels. designated with SOGLL. SOGC. DII. and. DC. which dilfer in the adopted prescriptions as outlined in Table 1..," To investigate how much the results are affected by the the interplay between the use of the opacities accounting for the CNO variations and the mass-loss description we calculated 4 sets of evolutionary models, designated with S06H, S06C, BH, and BC, which differ in the adopted prescriptions as outlined in Table \ref{tab_mod}." + Specifically. we consider two [ormalisms for the mass Loss. ie. Straniero et al. (," Specifically, we consider two formalisms for the mass loss, i.e. Straniero et al. (" +2006) and Bloecker (1995). and two treatments of the. low-Z* opacities. depending on whether the underlying. chemical mixture is kept fixed or accounts for changes in the CNO abundances.,"2006) and Blöccker (1995), and two treatments of the $T$ opacities, depending on whether the underlying chemical mixture is kept fixed or accounts for changes in the CNO abundances." + In order to better disentangle the ellects of each prescription. the models cover all four combinations of the two parameters. opacity and mass loss.," In order to better disentangle the effects of each prescription, the models cover all four combinations of the two parameters, opacity and mass loss." + The resulting physical ancl chemical. properties of the TP-AGB moclels described above are presented in Table 2.., The resulting physical and chemical properties of the TP-AGB models described above are presented in Table \ref{yields}. +" bor each stellar mass we show the number of thermal pulses experienced by the star. the final core-mass. the maximum temperature reached at the bottom of the external envelope. plus further information concerning the average content of the ejecta, namely the helium mass fraction. and the € Ν. O and Na enhancement/depletion factors. in terms of the quantities N/Ee]. ολ ολ..."," For each stellar mass we show the number of thermal pulses experienced by the star, the final core-mass, the maximum temperature reached at the bottom of the external envelope, plus further information concerning the average content of the ejecta, namely the helium mass fraction, and the C, N, O and Na enhancement/depletion factors, in terms of the quantities [X/Fe], where $\log$ $\log$ $_{\odot}$." + The last column shows the ratio between the average CINIOabundance in the ejecta and the initial value. which is assumed to represent the chemical mixture at the epoch of the stars formation.," The last column shows the ratio between the average C+N+O abundance in the ejecta and the initial value, which is assumed to represent the chemical mixture at the epoch of the star's formation." + We can appreciate the qualitative cllects of the dillerent descriptions of mass loss and molecular opacities from Fig. Ll.," We can appreciate the qualitative effects of the different descriptions of mass loss and molecular opacities from Fig. \ref{3msun}," + where we show the evolution of a BAL. model calculated according to the prescriptions listed in Table 1.. to which we refer for the meaning of the various symbols.," where we show the evolution of a $_{\odot}$ model calculated according to the prescriptions listed in Table \ref{tab_mod}, to which we refer for the meaning of the various symbols." + Core Le ancl He-burning phases are not included. in this plot. that starts from the beginning of the PP-AGB phase.," Core H- and He-burning phases are not included in this plot, that starts from the beginning of the TP-AGB phase." + Each point marks the quiescent stage of pre-EP luminosity maximum., Each point marks the quiescent stage of pre-TP luminosity maximum. + The solid lines are iso-mass locii. and. connect the four evolutionary sequences at the stages when the total mass of the star has been reduced to 2.9. 2.7. 2.5 and 2A1..," The solid lines are iso-mass locii, and connect the four evolutionary sequences at the stages when the total mass of the star has been reduced to 2.9, 2.7, 2.5 and $_{\odot}$." + lo all four cases considered here the 3M. models share a [ew common features. namelv: i) they experience LBL. which is usually associated to an ellect. and ii) they enter the domain of C-stars. as the surface. C/O ratio increases above unity due to the Ελ," In all four cases considered here the $_{\odot}$ models share a few common features, namely: i) they experience HBB, which is usually associated to an effect, and ii) they enter the domain of C-stars, as the surface C/O ratio increases above unity due to the TDU." + At the same time significant dillerences arise., At the same time significant differences arise. + The SOGLL and 806€ models experience a much weaker mass loss at the beginning. evolving at approximately constant mass for many VPs: this is at odes with the behaviour of BLE and BC models. where an cllicient mass loss determines an earlier extinction. of LBB and its overluminosity (following a rapid cooling of the envelope structure).," The S06H and S06C models experience a much weaker mass loss at the beginning, evolving at approximately constant mass for many TPs; this is at odds with the behaviour of BH and BC models, where an efficient mass loss determines an earlier extinction of HBB and its overluminosity (following a rapid cooling of the envelope structure)." + This circumstance is seen in the maximum luminosity attained. which is 0.2 dex fainter than in SO6LL and. SOGC sequences.," This circumstance is seen in the maximum luminosity attained, which is $\sim 0.2$ dex fainter than in S06H and S06C sequences." + The vole plaved by the opacity treatment can be understood by examining the evolution of models sharing 1e same description of mass loss. e.g. the SOGLE ancl SOGC models.," The role played by the opacity treatment can be understood by examining the evolution of models sharing the same description of mass loss, e.g. the S06H and S06C models." + In the latter. the rapid increase in the mass loss rale as soon as the surface ο exceeds unity (clearly etectable as a jump in Al) favours an earlier. reduction of the mass of the external mantle. which again causes an earlier drop in the luminosity £ (we have à ~0.1 dex dilference in the maximum luminosity in this case).," In the latter, the rapid increase in the mass loss rate as soon as the surface C/O exceeds unity (clearly detectable as a jump in $\dot M$ ) favours an earlier reduction of the mass of the external mantle, which again causes an earlier drop in the luminosity $L$ (we have a $\sim 0.1$ dex difference in the maximum luminosity in this case)." + The drop in L is associated to a lower temperature at the bottom of the convective envelope. Le. less favourable conditions for LBB.," The drop in $L$ is associated to a lower temperature at the bottom of the convective envelope, i.e. less favourable conditions for HBB." + As à consequence. we may conclude that. in general. using a mass loss description only mildly dependent on the luminosity. and/or neglecting the changes in the molecular hemistryv. in the opacity computations when C/O 1," As a consequence, we may conclude that, in general, using a mass loss description only mildly dependent on the luminosity, and/or neglecting the changes in the molecular chemistry in the opacity computations when $>1$ ," + As à consequence. we may conclude that. in general. using a mass loss description only mildly dependent on the luminosity. and/or neglecting the changes in the molecular hemistryv. in the opacity computations when C/O 1.," As a consequence, we may conclude that, in general, using a mass loss description only mildly dependent on the luminosity, and/or neglecting the changes in the molecular chemistry in the opacity computations when $>1$ ," +" ppc/"". Αν. Ay~10"". Ενx7’? ~1 Εαν 0.330.88. |0.31. sm. "," $^{\prime\prime}$ ${\rm A_V}$ ${\rm A_V} \sim 10^{\rm m}$ $F_\nu \propto \nu^{1/3}$ $\sim 1$ $\sim 100$ ${\rm d} F_\nu / {\rm d} +\nu$ $-0.33$$-0.88$ $+0.31$ $\mu$ " +galaxies at the distance to the Virgo cluster.,galaxies at the distance to the Virgo cluster. + TFhis region contains the majority of LIL deficient. A better insight into the structure of the cluster. is obtained with Fig., This region contains the majority of HI deficient A better insight into the structure of the cluster is obtained with Fig. + 5. which reports the same data as Fig.," 5, which reports the same data as Fig." + 4. but with symbols whose size decreases with increasing distance. and. whose shape refers to 7 regions of the Virgo cluster. represented. in Fig.," 4, but with symbols whose size decreases with increasing distance, and whose shape refers to 7 regions of the Virgo cluster, represented in Fig." + 6 with clotted lines. (galaxies with o«100Ams1 are omitted)., 6 with dotted lines (galaxies with $\sigma<100~km~s^{-1}$ are omitted). +"; Galaxies'. are assigned. to these regions with a criterion that combines their position on the skv with their distance ancl Distant (p,2 31.5) galaxies with Vie.71900 belong almost exclusively to the regions marked M and: W. These correspond to the. M and. Wo clouds. which thus are found o be in Hubble Distant (4, 31.5) objects with Vee,«1900 mostly xilong to the region marked D. Εις corresponds to Cluster D of Binggeli et al. ("," Galaxies are assigned to these regions with a criterion that combines their position on the sky with their distance and Distant $\mu_o>31.5$ ) galaxies with $V_{LG}>1900$ belong almost exclusively to the regions marked M and W. These correspond to the M and W clouds, which thus are found to be in Hubble Distant $\mu_o>31.5$ ) objects with $V_{LG}<1900$ mostly belong to the region marked B. This corresponds to Cluster B of Binggeli et al. (" +1993). but with a smaller extent than in the original definition.,"1993), but with a smaller extent than in the original definition." + The mean distance moclulus [ου his structure is found to be 31.854. in good agreement with he determination by Federspiel et al. (," The mean distance modulus for this structure is found to be 31.84, in good agreement with the determination by Federspiel et al. (" +1998). (a.= 31.8).,1998) $\mu_o=31.8$ ). +" To the East of approx à=]1225'""' (ALL9) all galaxies iàve distances not cdissimülar [rom those of Cluster A (us0 343).", To the East of approx $\alpha=12^h25^m$ (M49) all galaxies have distances not dissimilar from those of Cluster A $\mu_o~\sim31$ ). + For example 4 spiral galaxies (NGC 4519. 4332. and 4535. and IC 3521) which are assigned to Cluster D bx Bingecli et al. (," For example 4 spiral galaxies (NGC 4519, 4332, and 4535, and IC 3521) which are assigned to Cluster B by Binggeli et al. (" +"1985) are not confirmed. to lie at significantly larger distance than Cluster A. since they are ound at (4,230.2-31.3.","1985) are not confirmed to lie at significantly larger distance than Cluster A, since they are found at $\mu_o$ =30.2-31.3." + For these objects our TE. distance determinations are in agreement with those of Yasuda et al. (, For these objects our TF distance determinations are in agreement with those of Yasuda et al. ( +1997).,1997). + Another 3 E/SO Cluster D candidates according o Binggeli et al. (, Another 3 E/S0 Cluster B candidates according to Binggeli et al. ( +NGC 4472 (M49). 4526. and 4570) have fiex31.2. as determined. using the FP relation.,"NGC 4472 (M49), 4526, and 4570) have $\mu_o<31.2$, as determined using the FP relation." + Our low distance estimate of MAO agrees with independent estimates obtained using all methods quoted above., Our low distance estimate of M49 agrees with independent estimates obtained using all methods quoted above. + Unfortunately this is the only galaxy with independent. distance estimate among this group of carly-twpe objects., Unfortunately this is the only galaxy with independent distance estimate among this group of early-type objects. +" We propose that MA9 belongs to cloud S. Ls redshift (Vee,=1200£ms. 1) is 400 Arnos lower than the mean. but it is well within he distribution of Vie. in this region."," We propose that M49 belongs to cloud S. Its redshift $V_{LG}=1200~km~s^{-1}$ ) is 400 $km~s^{-1}$ lower than the mean, but it is well within the distribution of $V_{LG}$ in this region." +" The remaining galaxies have 4,<31.5.", The remaining galaxies have $\mu_o<31.5$. + They form he main body of the cluster. indicated here with region A (AIST). N. to the NW. E. to the East and S. to the Region A coincides with Cluster A and with the X-ray ;»osition (see Fig.," They form the main body of the cluster, indicated here with region A (M87), N, to the NW, E, to the East and S, to the Region A coincides with Cluster A and with the X-ray position (see Fig." + 7 adapted from Bóhhringer et al., 7 adapted from Böhhringer et al. + 1994. reproduced. on the same scale as Fig.," 1994, reproduced on the same scale as Fig." + 6)., 6). + As expected. most HE deficient. galaxies belong to this region (see Fig.," As expected, most HI deficient galaxies belong to this region (see Fig." + S)., 8). + Two exceptions are surprisingly found at the southern edge of the cluster in the region of NGC 4636. a strong and extended N-ray source (Vrinehieri et al.," Two exceptions are surprisingly found at the southern edge of the cluster in the region of NGC 4636, a strong and extended X-ray source (Trinchieri et al." + L994)., 1994). + We argue that a significant quantity of extended. gas must. be associated with this galaxy., We argue that a significant quantity of extended gas must be associated with this galaxy. +" The distribution of ji. in the cluster A itself is centered ab qn,=30.84 with a dispersion of 0.45 mag.", The distribution of $\mu_o$ in the cluster A itself is centered at $\mu_o=30.84$ with a dispersion of 0.45 mag. + This is comparable to the nominal uncertainty of the. distance determination. methods (0.35 and. 0.45. mae for TE. and FP). thus the depth along the line of sight of this aggregate cannot be determined.," This is comparable to the nominal uncertainty of the distance determination methods (0.35 and 0.45 mag for TF and FP), thus the depth along the line of sight of this aggregate cannot be determined." + One of the most interesting results of the present analysis is that. among galaxies at the main cluster distance. those belonging to clouds N anc S show a significant velocity segregation.," One of the most interesting results of the present analysis is that, among galaxies at the main cluster distance, those belonging to clouds N and S show a significant velocity segregation." + This is illustrated in Fig., This is illustrated in Fig. + 9., 9. + The two rightmost panels of this figure give histograms of Vics and of pi; derived from this work for the 7 considered regions., The two rightmost panels of this figure give histograms of $V_{LG}$ and of $\mu_o$ derived from this work for the 7 considered regions. + While the distances of cluster A and. clouds S. N. and E are in agreement (μμ=30.8431.23) the only significantly more distant structures are cluster D and clouds Wand M. Clusters A and B ancl cloud E have similar velocity distributions peaked at the standard Έτ~1350Amosf.," While the distances of cluster A and clouds S, N, and E are in agreement $\mu_o=30.84-31.23$ ) the only significantly more distant structures are cluster B and clouds W and M. Clusters A and B and cloud E have similar velocity distributions peaked at the standard $V_{LG} \sim 1350~km~s^{-1}$." + Clouds. Wane AL have instead a higher velocity., Clouds W and M have instead a higher velocity. + Clouds S and N have significantly cillerent distributions., Clouds S and N have significantly different distributions. + The N one contains galaxies with Έντο«1300fins+. thus. blueshifted with respect to Virgo.," The N one contains galaxies with $V_{LG}<1300~km~s^{-1}$, thus blueshifted with respect to Virgo." + Similar evidence was pointec out by Llolfmann et al. (, Similar evidence was pointed out by Hoffmann et al. ( +LOS9b) and was extensively analyzed by Tully Shava. (1984) to model the infall of galaxies on the Virgo cluster.,"1989b) and was extensively analyzed by Tully Shaya, (1984) to model the infall of galaxies on the Virgo cluster." + On the contrary. cloud S contains mainly redshifted galaxies. with 750«Vee.2700kims+.," On the contrary, cloud S contains mainly redshifted galaxies, with $750 < V_{LG} < 2700~km~s^{-1}$." + To check if the latter result is not due to the limited statistics of the sample used in this work. and since the velocity distribution can be derived from. a larger body of velocity measurements than the one represented in our sample of galaxies with distance estimates. we determine the velocity. distributions in the 7 studied regions using the whole VCC (which contains over 400 galaxies with redshift estimates) (see left. panel of Fig.," To check if the latter result is not due to the limited statistics of the sample used in this work, and since the velocity distribution can be derived from a larger body of velocity measurements than the one represented in our sample of galaxies with distance estimates, we determine the velocity distributions in the 7 studied regions using the whole VCC (which contains over 400 galaxies with redshift estimates) (see left panel of Fig." + 9)., 9). + The dillerence between regions S and N. noticed in our smaller sample with distance estimates. is equally present in the larger VOC sample. ancl we conclude it represents a real ¢illerence between the two A summary of the mean velocity. velocity. dispersion. ancl distance modulus determinations for all seven regions is presented in Tab.," The difference between regions S and N, noticed in our smaller sample with distance estimates, is equally present in the larger VCC sample, and we conclude it represents a real difference between the two A summary of the mean velocity, velocity dispersion, and distance modulus determinations for all seven regions is presented in Tab." + 3. and is also shown in Fig.," 3, and is also shown in Fig." + 10. where the average velocities and distance. moduli are. plotted with error bars indicating the statistical uncertainties on the determination. of the two quantities (galaxies with a«100kms are exeluded).," 10, where the average velocities and distance moduli are plotted with error bars indicating the statistical uncertainties on the determination of the two quantities (galaxies with $\sigma<100~km~s^{-1}$ are excluded)." + Estimates of cluster A are also given separately for earlv-tvpe. and. latc-type ealaxies. subclividecl into LL deficient anc IL normal.," Estimates of cluster A are also given separately for early-type and late-type galaxies, subdivided into HI deficient and HI normal." + Alean quantities ancl the associatecl uncertainties were computed. using the so-called. biweight estimators (sec Beers et al., Mean quantities and the associated uncertainties were computed using the so-called biweight estimators (see Beers et al. + 1990 for details). that are known to provide a robust parameter estimation for samples covering a wide interval in size.," 1990 for details), that are known to provide a robust parameter estimation for samples covering a wide interval in size." + Statistical uncertainties on the, Statistical uncertainties on the +ligehteurves. accounting as usal for the typical error bars in the data aud in the models.,"lightcurves, accounting as usual for the typical error bars in the data and in the models." + We derive the distributiou of colors or both true and simulated data., We derive the distribution of colors for both true and simulated data. + The distributious are plotted in Figure &.., The distributions are plotted in Figure \ref{fig:BmV}. + The top pane shows the distribution for true data., The top panel shows the distribution for true data. +" There is 10 blue excess in flux iu the true color: iu fact the clistribution has a ueanofg ὃν1ὃν ἃ median ~0.002, anda staudard deviation σ0.051: statistically consistent with a raneol distribution around 0."," There is no blue excess in flux in the true color: in fact the distribution has a mean of $\mu~\sim ~-8 \times 10^{-4}$, a median $\sim 0.002$, and a standard deviation $\sigma \sim 0.054$: statistically consistent with a random distribution around 0." + The distributions eencrated from simulated hehteurves— are shown below the= distribution for tine data in yo (M. ROG contributions RGgareTM664and9€. plotted from the top to the bottom.," The distributions generated from simulated lightcurves are shown below the distribution for true data in Figure \ref{fig:BmV}, for RG contributions $\RGf~=~ 0\%,~33\%,~ 66\%,~ \mathrm{and}~ 99\%$, plotted from the top to the bottom." + Each distribution is generated from a factor of LOO more poiits than the true color distribution ancl is thus Ιαν joisv., Each distribution is generated from a factor of 100 more points than the true color distribution and is thus minimally noisy. + The mean of the cistributiou Increases as we increase aud the distributions eot inercasingly asvnunetric. weighted toward positive values of (bluer color).," The mean of the distribution increases as we increase and the distributions get increasingly asymmetric, weighted toward positive values of (bluer color)." +" The svuthetic distributions generated with no RCis 43) has moments that are extremely siular to frose of the true color distribution: p2«10""7.m median ~0.001. and ac0.077."," The synthetic distributions generated with no RGs ) has moments that are extremely similar to those of the true color distribution: $\mu~\sim~2\times 10^{-3}$, median $\sim 0.001$ and $\sigma \sim 0.077$." + Ouce/— again. this shows hat the distribution of colors iu the SNLS data is compatible with minimal Or no contributiπι of RC to progenitors. confrniug the results obtained from the IN-S tests.," Once again, this shows that the distribution of colors in the SNLS data is compatible with minimal – or no – contribution of RG to progenitors, confirming the results obtained from the K-S tests." + The excess due to shocking of t16 SN ejecta affects the carly time domain plicXtonietrie ancl spectral behavior of the explosions., The excess due to shocking of the SN ejecta affects the early time domain photometric and spectral behavior of the explosions. + Since in surveys such as SNLS aud SDSS are ideutified by heir early lghteurves. and thus an explosio ids followed wp spectroscopically oulv ifit is thought to be a SN explosion. au interesting question is whether this carly effect might have lead to the rejcction of plenonena that indeed wereB. but deviate from the exrected early behavior ou account of shocsine.," Since in surveys such as SNLS and SDSS are identified by their early lightcurves, and thus an explosion is followed up spectroscopically only if it is thought to be a SN explosion, an interesting question is whether this early effect might have lead to the rejection of phenomena that indeed were, but deviated from the expected early behavior on account of shocking." + Iu Uavdenetal.(2010a).. a subset of πιοσο. is visually inspected and no such is found.," In \citet{2010sdss}, a subset of unconfirmed is visually inspected and no such effect is found." + We 1uvestigate 905 SNLS liebhteurves with some redshift iuormation. either spectroscopic or photometric.," We investigate 905 SNLS lightcurves with some redshift information, either spectroscopic or photometric." + We exchde likely or known ACN. variable stars. and core-collapse (CC) SNe.," We exclude likely or known AGN, variable stars, and core-collapse (CC) SNe." + Iu order to avoid contamination frou. 1widentified SNe IL. Ib. or Ic. we aso ayply cuts in stretch aud color space.," In order to avoid contamination from unidentified SNe II, Ib, or Ic, we also apply cuts in stretch and color space." + Iu. particular. CC SNe show a different average color than SNe Ia. ad color constraints eliminate them frou the sample.," In particular, CC SNe show a different average color than SNe Ia, and color constraints eliminate them from the sample." + A detailed discussion of ]photometric selection of iu the SNLS data cau he found in Bazinetal.(2011)., A detailed discussion of photometric selection of in the SNLS data can be found in \citet{Bazin10}. +". We thus believe our new dataset has minimal contamination from, non events.", We thus believe our new dataset has minimal contamination from non events. + Our new dataset contains 336 hehtcurves before our cuts are applied (see Section ??)). and 110 after.," Our new dataset contains 336 lightcurves before our cuts are applied (see Section \ref{sec:data}) ), and 110 after." + Our iw composite liehteurves. contain 25] poiuts iu rest-frarue aud 270 in rest-frame 1- the region of iuterest: =-l7.1 to -7.1 davs to pea- (Figure 9))., Our new composite lightcurves contain 251 points in rest-frame and 270 in rest-frame in the region of interest: -17.4 to -7.4 days to peak (Figure \ref{fig:complc_uncf}) ). + We repeat the I-5 tcts applied eurlier to the extended set aud fud theut the statistics coufinn the upper limits set to the contiibution of RCo binary svstenis to explosious (Figures 10 and 11)), We repeat the K-S tests applied earlier to the extended set and find that the statistics confirm the upper limits set to the contribution of RG binary systems to explosions (Figures \ref{fig:ks_unconf} and \ref{fig:ks_color_unconf}) ). + The K-S test of the composite lighteurve in cach B aud V. with the respective svuthetic lighteurves is entirely consistent with the test for the spectroscopically confirmed subset.," The K-S test of the composite lightcurve in each B and V with the respective synthetic lightcurves is entirely consistent with the test for the spectroscopically confirmed subset," +The abundances of neutron())-capture elements (atomic number Z> 30) are sensitive probes of the nucleosynthetic histories of stellar populations and the chemical evolution of the Universe (???)..,"The abundances of )-capture elements (atomic number $Z>30$ ) are sensitive probes of the nucleosynthetic histories of stellar populations and the chemical evolution of the Universe \citep{wally97, busso99, sneden08}." + Our knowledge of the production of these elements is largely based on the interpretation of abundances derived from stellar spectroscopy (e.g..2222?.andrefer-ences therein)..," Our knowledge of the production of these elements is largely based on the interpretation of abundances derived from stellar spectroscopy \citep[e.g.,][and references therein]{smith90, busso99, travaglio04, sneden08, roederer10}." + However. only a limited number of trans-iron elements can be detected in stellar spectra.," However, only a limited number of trans-iron elements can be detected in stellar spectra." + Moreover. some classes of stars or stages of evolution with high mass-loss rates are very difficult to study spectroscopically due to photospheric obscuration.," Moreover, some classes of stars or stages of evolution with high mass-loss rates are very difficult to study spectroscopically due to photospheric obscuration." +" The recent detection of emission lines from. /--capture elements in a large number of planetary nebulae (PNe) (222?)., as well as other astrophysical objects including H II regions (e.g..90999999*220222222)2222222?).. starburst galaxies (2).. and active galactic nuclei (?).. has demonstrated that nebular spectroscopy is a potentially powerful tool for investigating the nucleosynthesis and chemical evolution of trans-iron species."," The recent detection of emission lines from -capture elements in a large number of planetary nebulae (PNe) \citep{sterling07, sharpee07, sterling08, sterling09}, as well as other astrophysical objects including H II regions \citep[e.g.,][]{aspin94, lumsden96, luhman98, baldwin00, puxley00, okumura01, blum08, roman-lopes09}, starburst galaxies \citep{vanzi08}, and active galactic nuclei \citep{thompson78}, has demonstrated that nebular spectroscopy is a potentially powerful tool for investigating the nucleosynthesis and chemical evolution of trans-iron species." +" The abundances of n--capture elements are of particular interest in PNe. since these species can be produced in PN progenitor stars via slow z--capture nucleosynthesis (the ""s--process"") during the asymptotic giant branch (AGB) stage of evolution."," The abundances of -capture elements are of particular interest in PNe, since these species can be produced in PN progenitor stars via slow -capture nucleosynthesis (the -process”) during the asymptotic giant branch (AGB) stage of evolution." + Nebular spectroscopy provides access to many elements that cannot be detected in cool giant stars. such as the lightest n--capture elements (Z= 31-36) and noble gases.," Nebular spectroscopy provides access to many elements that cannot be detected in cool giant stars, such as the lightest -capture elements $Z=31$ –36) and noble gases." + Due to the difficulty in detecting these species in stellar spectra or supernova remnants (?).. the origins of light -capture elements are based predominantly on theoretical considerations that lack empirical validation.," Due to the difficulty in detecting these species in stellar spectra or supernova remnants \citep{wally95}, the origins of light -capture elements are based predominantly on theoretical considerations that lack empirical validation." +" In. addition, nebular spectroscopy enables investigations of nucleosynthesis in classes or evolutionary stages of stars obscured by optically thick circumstellar envelopes."," In addition, nebular spectroscopy enables investigations of nucleosynthesis in classes or evolutionary stages of stars obscured by optically thick circumstellar envelopes." + For example. intermediate-mass AGB stars (4-8 M4) experience heavy mass loss. shielding their photospheres in a cocoon of circumstellar material that hinders spectroscopic investigations in the wavelength regimes of many useful z--capture element transitions.," For example, intermediate-mass AGB stars (4–8 $_{\odot}$ ) experience heavy mass loss, shielding their photospheres in a cocoon of circumstellar material that hinders spectroscopic investigations in the wavelength regimes of many useful -capture element transitions." + As a result. the contribution of these stars to the Galactic inventory of heavy element nuclei is poorly understood (e.g..?)..," As a result, the contribution of these stars to the Galactic inventory of heavy element nuclei is poorly understood \citep[e.g.,][]{karakas09}." + However. these intermediate-mass stars produce PNe in which z--capture element emission lines are readily detected (??)..," However, these intermediate-mass stars produce PNe in which -capture element emission lines are readily detected \citep{sharpee07, sterling08}. ." + Likewise. AGB stars that become carbon-rich as a result of convective dredge-up (see?) are characterized by high opacities (?) that substantially increase their mass-loss rates. and hence -process enrichments engendered by the final stages of AGB evolution are not well-constrained.," Likewise, AGB stars that become carbon-rich as a result of convective dredge-up \citep[see][]{busso99} are characterized by high opacities \citep{marigo02} that substantially increase their mass-loss rates, and hence -process enrichments engendered by the final stages of AGB evolution are not well-constrained." + PNe are composed of material from the stellar envelope at the end of the AGB phase. and hence are useful probes of s--process enrichments during late AGB evolution.," PNe are composed of material from the stellar envelope at the end of the AGB phase, and hence are useful probes of -process enrichments during late AGB evolution." + However. the accuracy of nebular n--capture element abundances is hindered by the poorly known atomic data for these species. thereby limiting the usefulness of nebular spectroscopy for studying the origins of these elements.," However, the accuracy of nebular -capture element abundances is hindered by the poorly known atomic data for these species, thereby limiting the usefulness of nebular spectroscopy for studying the origins of these elements." + The reason for this is that generally only one or two tons of n-- elements have been detected in individual nebulae. and hence the abundances of unobserved tons must be estimated in order to derive elemental abundances.," The reason for this is that generally only one or two ions of -capture elements have been detected in individual nebulae, and hence the abundances of unobserved ions must be estimated in order to derive elemental abundances." + This ts most robustly achieved by numerically simulating the thermal and ionization structure ofnebulae with phototonization codes such as Cloudy (?).. but the reliability of these models strongly depends on the availability of accurate atomic data for processes that control the tonization balance.," This is most robustly achieved by numerically simulating the thermal and ionization structure of nebulae with photoionization codes such as Cloudy \citep{ferland98}, but the reliability of these models strongly depends on the availability of accurate atomic data for processes that control the ionization balance." + For photoionized nebulae such as PNe. these data include photoionization (PI) cross sections and rate coefficients for radiative recombination (RR). dielectronic recombination (DR). and charge transfer (CT).," For photoionized nebulae such as PNe, these data include photoionization (PI) cross sections and rate coefficients for radiative recombination (RR), dielectronic recombination (DR), and charge transfer (CT)." + Unfortunately. such data have not been determined for the vast majority of trans-iron element tons.," Unfortunately, such data have not been determined for the vast majority of trans-iron element ions." + To address this need. we have computed multi-configuration Breit-Pauli (MCBP) distorted-wave PI cross sections and RR and DR rate coefficients for the first six Se ions. using the atomic structure code AUTOSTRUCTURE (??)..," To address this need, we have computed multi-configuration Breit-Pauli (MCBP) distorted-wave PI cross sections and RR and DR rate coefficients for the first six Se ions, using the atomic structure code AUTOSTRUCTURE \citep{badnell86, badnell97}." + Along with. Kr and. Xe. Se is one of the most widely observed --capture elements in ionized nebulae (??)..," Along with Kr and Xe, Se is one of the most widely observed -capture elements in ionized nebulae \citep{sharpee07, sterling08}." + In fact. Se has been identified in nearly twice as many PNe às any other trans-iron element. and hence is the initial target for our study.," In fact, Se has been identified in nearly twice as many PNe as any other trans-iron element, and hence is the initial target for our study." + In subsequent papers. we will present similar data for low-charge Kr and Xe tons. as well as CT ratecoefficients for several --capture elements.," In subsequent papers, we will present similar data for low-charge Kr and Xe ions, as well as CT ratecoefficients for several -capture elements." + These data will be suitable, These data will be suitable +"In reffig:dlogs,, all aand dderivativeP5,, terms are tied together at zero at small scales.","In \\ref{fig:dlogs}, all and derivative terms are tied together at zero at small scales." +" This is because for each, the variance is unity in 1300/256 Mpc z ccells."," This is because for each, the variance is unity in $1300/256$ Mpc $\approx$ cells." +" The derivative terms are generally smaller in absolute value for these power spectra, which translates into poorer parameter constraints below than for aandPj(145),, with the exception of the parameter ns."," The derivative terms are generally smaller in absolute value for these power spectra, which translates into poorer parameter constraints below than for and, with the exception of the parameter $n_s$ ." +" Curiously, at this resolution, Dj,oz(k) is of comparable absolute magnitude for aand ffor small P5)k."," Curiously, at this resolution, $D_{\lses}(k)$ is of comparable absolute magnitude for and for small $k$." +" Naively, one might expect all information about the amplitude to be destroyed inP5,,,, in which one divides the power spectrum by the variance in cell densities (here, of ssize, but this holds to some degree for "," Naively, one might expect all information about the amplitude to be destroyed in, in which one divides the power spectrum by the variance in grid-cell densities (here, of size, but this holds to some degree for cells)." +"However, recall that the amplitude c2 is the ccells).variance in vvolumes in the linearly, not nonlinearly, evolved density field; the nonzero Dj, at small scales is apparently from the rise in the nonlinearoz(k) power spectrum in aandP"," However, recall that the amplitude $\sigma_8^2$ is the variance in volumes in the linearly, not nonlinearly, evolved density field; the nonzero $D_{\lses}(k)$ at small scales is apparently from the rise in the nonlinear power spectrum in and." +"5,,.. reffig:ellipsesyplogshowserrorbarsoverthesetof aandPj(.5).."," \\ref{fig:ellipses_pplog} shows error bars over the set of five cosmological parameters, for and." + The effective volume for these results is (1.8 Gpc)?/2z1.1 Gpce?z.5 Gpc))?., The effective volume for these results is (1.3 $^3/2\approx 1.1$ $^3\approx .5$ $^3$. +" The factor of two is from the sinusoidal weightings used for the covariance matrices, which effectively halve the volume."," The factor of two is from the sinusoidal weightings used for the covariance matrices, which effectively halve the volume." +" Along the diagonal, the curves are unmarginalized error bars over single parameters, holding all else fixed."," Along the diagonal, the curves are unmarginalized error bars over single parameters, holding all else fixed." +" Off the diagonal, we examine error bars allowing sets of two parameters to vary at a time."," Off the diagonal, we examine error bars allowing sets of two parameters to vary at a time." +" The upper plots show how error ellipses contract as ἆγμακ increases, while the lower plots show how marginalized error bars shrink."," The upper plots show how error ellipses contract as $k_{\rm + max}$ increases, while the lower plots show how marginalized error bars shrink." +" Constraints obtained analyzing aare substantially smaller than forP5,,(1..5) for all parameters, typically by a factor of 2 or 3 if the analysis is pushed to the smallest scales shown."," Constraints obtained analyzing are substantially smaller than for, for all parameters, typically by a factor of 2 or 3 if the analysis is pushed to the smallest scales shown." +" The difference is particularly large for n,, where the error bar is reduced by a factor of 5."," The difference is particularly large for $n_s$, where the error bar is reduced by a factor of 5." + Another parameter whose behavior is simple to understand is Ino2., Another parameter whose behavior is simple to understand is $\lses$. +" As discussed above, Diyo2(k) is smaller for tthan forP(1..5)P5, at all k."," As discussed above, $D_{\lses}(k)$ is smaller for than for, at all $k$." +" Looking at the diagonal, unmarginalized plots, this is why the error bars are degraded in wwhen only Pjlinear (1,5)scales are included."," Looking at the diagonal, unmarginalized plots, this is why the error bars are degraded in when only linear scales are included." +" However, when pushing into translinear scales, the penalty from the decreased derivative term is quickly overcome because of drastically reduced cosmic variance, resulting in tighter constraints from aat sufficiently small Py(1+5)scales."," However, when pushing into translinear scales, the penalty from the decreased derivative term is quickly overcome because of drastically reduced cosmic variance, resulting in tighter constraints from at sufficiently small scales." +" reffig:ellipses, vpgshowsthesame figure forP aand", \\ref{fig:ellipses_pvpg} shows the same figure for and. +" Except for the case of the stilt/> n,, the constraints Pg(sj.from aare weaker than Pas)from and often even weaker than fromP;."," Except for the case of the tilt $n_s$, the constraints from are weaker than from, and often even weaker than from." +". This could be P,(.5),,surprising given that the covariance matrix of hhas the smallest non-GaussianPa; component, and the highest diagonality, of any of the power spectra considered here."," This could be surprising given that the covariance matrix of has the smallest non-Gaussian component, and the highest diagonality, of any of the power spectra considered here." +" The performance of fivecosmologiiàlplsFaflieephoinóye, given the high P5,diagonality of its covariance matrix; the performance is also degraded for ccompared/o to ffor some parameters.", The performance of is also disappointing given the high diagonality of its covariance matrix; the performance is also degraded for compared to for some parameters. +" For aandP5/,,, this behavior is Pas)from small derivative terms D(k)."," For and, this behavior is from small derivative terms $\bD(k)$." +" As discussed above, this is largely from the unitvariance enforced in cell densities for these density fields."," As discussed above, this is largely from the unitvariance enforced in cell densities for these density fields." + Other analysis procedures are certainly possible., Other analysis procedures are certainly possible. + It would be convenient to use, It would be convenient to use +large accretion rates at carlicy stages unexplained.,large accretion rates at earlier stages unexplained. +" There Is no reason to expect MRI turbulence in the outer disk to ""shut off when a eapis opened. so while our observatiou of a sinall turbuleut linewidth in the TW να system is consistent with the 7T. hwpothesis. if is still surprising that the turdlent Lnewidth in WD 163296 should be sO mich larger."," There is no reason to expect MRI turbulence in the outer disk to “shut off” when a gap is opened, so while our observation of a small turbulent linewidth in the TW Hya system is consistent with the \citet{chi07} hypothesis, it is still surprising that the turbulent linewidth in HD 163296 should be so much larger." + Another oossibilitv wnrelatcc to the AIRT is that ΠΟ 163296 is still expericucing iufal outo the disk from a relait envelope., Another possibility unrelated to the MRI is that HD 163296 is still experiencing infall onto the disk from a remnant envelope. + Since he high optical depth of the CO(3-2) line iuples that most of the enüssion arises from the up]xY lavers of the disk. such a scenario could nuuc tje signature of a tfirbuleut Hnewidth that we observe: however» there is no observational evidence for anu envelope iu this system.," Since the high optical depth of the CO(3-2) line implies that most of the emission arises from the upper layers of the disk, such a scenario could mimic the signature of a turbulent linewidth that we observe; however, there is no observational evidence for an envelope in this system." + We plan to address this possibility more thoroughly iu a follow-up paper modeling 1nultiple lines with lower optical depths tlat probe deeper toxs the disk midplane., We plan to address this possibility more thoroughly in a follow-up paper modeling multiple lines with lower optical depths that probe deeper towards the disk midplane. + The presence of 3bsonic turbulence in protoplanetary accretion disks likely substautially subsonic iu the uilpluie — is consiseut with the observations xeseuted in this) study., The presence of subsonic turbulence in protoplanetary accretion disks – likely substantially subsonic in the midplane – is consistent with the observations presented in this study. + Susonic turbulence has inportaut iuplications for the formation aud evolution of vouug anetarv svstenis., Subsonic turbulence has important implications for the formation and evolution of young planetary systems. + Oue SCTICS of papers (2272) explores im detail tιο effects of turbulence oi planct-ormune disks.," One series of papers \citep{pap03,pap04,nel03,nel04} explores in detail the effects of turbulence on planet-forming disks." + Thei evlindrical models of urbuleut disks⋅ have au average o iu⋅ the range of 10 ⊳↽⋅≻↽7-1052a mt they demonstrae that the realistic iuplemoenutatiou of turbulence results dn differeut effects than are secu i luuinur disk siuulatious with comparable values of a incorporated as an anomalous Navicer-Sto|SOS viscosity.," Their cylindrical models of turbulent disks have an average $\alpha$ in the range of $10^{-2}$ $10^{-3}$, but they demonstrate that the realistic implementation of turbulence results in different effects than are seen in laminar disk simulations with comparable values of $\alpha$ incorporated as an anomalous Navier-Stokes viscosity." + They show that for massive planets. turbulence can widen and deepen the eap « Ες protoplauets; and may reduce the accretion rate oito the protoplanet.," They show that for massive planets, turbulence can widen and deepen the gap opened by massive protoplanets, and may reduce the accretion rate onto the protoplanet." + Εςx the case of nüerating low-niass planet cores. the picποσο of turbulence iu the disk can slow or even reversc» the uueration rate. converting the mionotonic inward uotion of the plaiet into a random walk.," For the case of migrating low-mass planet cores, the presence of turbulence in the disk can slow or even reverse the migration rate, converting the monotonic inward motion of the planet into a random walk." + The presence of dead zones im he racial direction may also act to walt migration axl encourage the survival and erowth of protoplancts (c.g.?7).., The presence of dead zones in the radial direction may also act to halt migration and encourage the survival and growth of protoplanets \citep[e.g.][]{mat09}. + Ànotlor inportant propose effect of subsonic turbulence is to aid du concenutratiuο plauetesuunals to allow them to collapse gravitation:uly (2).., Another important proposed effect of subsonic turbulence is to aid in concentrating planetesimals to allow them to collapse gravitationally \citep{joh07}. + AMID turbuleuce on these scales can also redice the streneth of the eravitational iustabilitv aud redice disk fragmentation (?).., MHD turbulence on these scales can also reduce the strength of the gravitational instability and reduce disk fragmentation \citep{fro05}. + There is also subsautial literature on the effects of turbule100 Oll dust settling and ex:un erowth (e.c.727??7)..," There is also substantial literature on the effects of turbulence on dust settling and grain growth \citep[e.g.][]{joh05,car06, +cie07,bal09,fro09}." + Although it i« difheult to compare the properties of the siulations directle with our observations. the generic features of tlvese models (610. 2-10.7. subsonic turbulence even i the upper disk lavers) are globally consistent with the derived. properties of turbulence iu the disks around ΠΟ 163296 and TW Iva. indicating that these effects are likely to play a role in dlanet formation.," Although it is difficult to compare the properties of the simulations directly with our observations, the generic features of these models $\alpha$ $10^{-2}$ $10^{-3}$, subsonic turbulence even in the upper disk layers) are globally consistent with the derived properties of turbulence in the disks around HD 163296 and TW Hya, indicating that these effects are likely to play a role in planet formation." + The most obvious iuprovenient to our method would be to include additional spectral lines frou different transitions or dsofcypologues of the CO molecule. iu order to provide iilependenut constraints ou the gas teiiperature., The most obvious improvement to our method would be to include additional spectral lines from different transitions or isotopologues of the CO molecule in order to provide independent constraints on the gas temperature. + While this would necessarily iutroduce additional parameters iuto the model G.c.. to describe the vertical distribution of temperature aud turbuence. as well as a consistent density disribution to properly account for the line opacity). the acdition of severa lies that are resoved in the spectral and spatial dowads would more fxiulv constraiu he models.," While this would necessarily introduce additional parameters into the model (i.e., to describe the vertical distribution of temperature and turbulence, as well as a consistent density distribution to properly account for the line opacity), the addition of several lines that are resolved in the spectral and spatial domains would more firmly constrain the models." + It might also provide direc nueasurenmentas of t1ο vertical profile of the turbuleut VC‘locity. structure., It might also provide direct measurements of the vertical profile of the turbulent velocity structure. + ? and ? provide exanples of sudies that use multiale molecular liles to study the verlcd structure of deusity and tempcrature in circiuustellar disks: these tecudques could be extended ο constrain the turbulent lineidti dn snuilar svstenis., \citet{dar03} and \citet{pan08} provide examples of studies that use multiple molecular lines to study the vertical structure of density and temperature in circumstellar disks; these techniques could be extended to constrain the turbulent linewidths in similar systems. + Another possibility is to observe 10is rather than jeutral species., Another possibility is to observe ions rather than neutral species. + This would clinunate colplicatious introduced by the interaction between 10is and neutrals. ancl would more cürectlv xobe the turlulent motions of he charged gas.," This would eliminate complications introduced by the interaction between ions and neutrals, and would more directly probe the turbulent motions of the charged gas." + Even with he curren set of observations. greater sensitivitv wolId be extremely valuable iu conustraining he turbulent luevidth. since the distinctions between urbuleut arc thermal broadening are subtle (sec Section L.1)).," Even with the current set of observations, greater sensitivity would be extremely valuable in constraining the turbulent linewidth, since the distinctions between turbulent and thermal broadening are subtle (see Section \ref{sec:degen}) )." + The vast improvements i seusitivitv xovided bw tιο Atacama Large Millimeter Array will vert sienificautly better inodelius of the velocity stcture of voung disks., The vast improvements in sensitivity provided by the Atacama Large Millimeter Array will permit significantly better modeling of the velocity structure of young disks. + Such data will also allow us to filv nle out deviations from perfect Keplerian rotation hat could complicate the derivation of turbulent linewidth., Such data will also allow us to firmly rule out deviations from perfect Keplerian rotation that could complicate the derivation of turbulent linewidth. + m accditiou. hieher sensitivitv combined with a ereater spatial dynamic range will allow for he investigation of radial variations 1ji the turbuleut inewidth.," In addition, higher sensitivity combined with a greater spatial dynamic range will allow for the investigation of radial variations in the turbulent linewidth." + We have obtaijid. the. first spatially resolved observations of molecala line emissiou from two nearby cireunistellar disks witji spectral rexution finer than the expected turinlew luewidth., We have obtained the first spatially resolved observations of molecular line emission from two nearby circumstellar disks with spectral resolution finer than the expected turbulent linewidth. + We ft these high spectral resoution observations of he CO(3-2) line enudsson using tWO woLtested models of circtuustelar disk structure. and derive a turbueut Lnewidth of ~ he disk around IID 163296 aud = ," We fit these high spectral resolution observations of the CO(3-2) line emission using two well-tested models of circumstellar disk structure, and derive a turbulent linewidth of $\sim$ $^{-1}$ for the disk around HD 163296 and $\lesssim$ " +area in that energy range (see Figure 1)).,area in that energy range (see Figure \ref{spectra}) ). +" At energies below 300 eV. we find that the PN and MOS counts numbers are smaller than expected from what we see in ACIS-S. This might be explained by statistical fluctuations. errors in. the effective area determination or energy redistribution effects in the CCD detectors (EPIC “low-energy shoulder"")."," At energies below 300 eV, we find that the PN and MOS counts numbers are smaller than expected from what we see in ACIS-S. This might be explained by statistical fluctuations, errors in the effective area determination or energy redistribution effects in the CCD detectors (EPIC ""low-energy shoulder"")." + Given these uncertainties for very low energies. we use only the counts (0.45-0.65 keV) of PN and MOS for our flux calculations and then extrapolate the flux to à common energy range of 11 keV for comparison.," Given these uncertainties for very low energies, we use only the counts (0.45-0.65 keV) of PN and MOS for our flux calculations and then extrapolate the flux to a common energy range of 1 keV for comparison." + For the other instruments. we use 0.65 keV as the upper bound of the energy range and their low-energy sensitivity limits as the lower bound (0.15 keV for ACIS-S/HRC. 0.1 keV for PSPC) and then extrapolate to the common energy range.," For the other instruments, we use 0.65 keV as the upper bound of the energy range and their low-energy sensitivity limits as the lower bound (0.15 keV for ACIS-S/HRC, 0.1 keV for PSPC) and then extrapolate to the common energy range." + The fluxes normalized to the 11 keV energy band and the corresponding X-ray luminosities are consistent within lo errors except for the HRC-I flux. which seems to be larger.," The fluxes normalized to the 1 keV energy band and the corresponding X-ray luminosities are consistent within $1\sigma$ errors except for the HRC-I flux, which seems to be larger." + The count rate measured by the HRC instrument is higher by a factor of ca., The count rate measured by the HRC instrument is higher by a factor of ca. + 2.5 compared to the ACIS-S count rate., 2.5 compared to the ACIS-S count rate. + The nominal effective areas of the two instruments are very similar at low energies. with the HRC having somewhat larger effective area below 200 eV (AA=10em? or at 200 eV. at 150 eV).," The nominal effective areas of the two instruments are very similar at low energies, with the HRC having somewhat larger effective area below 200 eV $\Delta A \approx 10\ \mbox{cm$ $}$ or at 200 eV, at 150 eV)." + The additional counts might arise from photons at these energies. but considering the small difference in effective areas. it does not seem likely that this is the case for all excess HRC photons.," The additional counts might arise from photons at these energies, but considering the small difference in effective areas, it does not seem likely that this is the case for all excess HRC photons." + This mismatch is further validated by comparing ACIS-S and HRC count rates with WebPIMMS: assuming a thermal plasma with solar abundances and 7=1 MK. 8 counts in the 0.1500.65 keV energy band in ACIS-S translate into 9 expected counts in the same energy band in HRC-I. which is obviously inconsistent with the 21 recorded HRC photons only 15 minutes after the ACIS-S observation.," This mismatch is further validated by comparing ACIS-S and HRC count rates with WebPIMMS: assuming a thermal plasma with solar abundances and $T=1$ MK, 8 counts in the 0.65 keV energy band in ACIS-S translate into 9 expected counts in the same energy band in HRC-I, which is obviously inconsistent with the 21 recorded HRC photons only 15 minutes after the ACIS-S observation." + Thephoton count estimate changes by <20% if one assumes a plasma temperature of 0.8 or 1.25 MK. so a slightly different plasma2 temperature does not cure the substantial mismatch in the cour=a rates.," Thephoton count estimate changes by $<20\%$ if one assumes a plasma temperature of 0.8 or 1.25 MK, so a slightly different plasma temperature does not cure the substantial mismatch in the count rates." + Mismatches between HRC and count rates have been reported before for « Cen (??)..," Mismatches between HRC and count rates have been reported before for $\alpha$ Cen \citep{robradeschmittfavata2005, ayresjudgesaar2008}." + This mismatch between almost simultaneous HRC and ACIS-S count rates can be explained reasonably by two possibilities: either the effective area of the HRC at low energies is underestimated in the current calibration or the effective areas ofXMM MOS and PN (while using the thick filter) as well as S are overestimated in that energy range., This mismatch between almost simultaneous HRC and ACIS-S count rates can be explained reasonably by two possibilities: either the effective area of the HRC at low energies is underestimated in the current calibration or the effective areas of MOS and PN (while using the thick filter) as well as ACIS-S are overestimated in that energy range. + A detailed cross-calibration effort. preferably with a soft coronal source. could help to resolve any systematic errors in the effective areas of the instruments.," A detailed cross-calibration effort, preferably with a soft coronal source, could help to resolve any systematic errors in the effective areas of the instruments." + We found 51 Peg to be a rather constant. weak and soft source over the last 15 years.," We found 51 Peg to be a rather constant, weak and soft X-ray source over the last 15 years." + Another available activity indicator isCan., Another available long-term activity indicator is. + In the H and K line flux monitoring programs carried out at the Mount Wilson and Lowell Observatories (??).. 5] Peg was found to have a very low chromospheric activity level GR)=-S.01. 0.16).," In the H and K line flux monitoring programs carried out at the Mount Wilson and Lowell Observatories \citep{baliunasdonahuesoon1995, halllockwoodskiff2007}, , 51 Peg was found to have a very low chromospheric activity level $\langle R^{'}_{HK}\rangle=-5.01$, $S_{MW}\approx 0.16$ )." + In Figure 3. we plot the stars Mount Wilson S index measured since 1996 together with the average of older data., In Figure \ref{calcium} we plot the star's Mount Wilson S index measured since 1996 together with the average of older data. + Clearly. the overall chromospherte activity is low. with some variations in the older set of data which is also seen in the more recent observations.," Clearly, the overall chromospheric activity is low, with some variations in the older set of data which is also seen in the more recent observations." + Apart from one data point which is derived from a very small number of observations. 51 Peg's S indices are at the lower end of or even below the Sun's respective data during a solar minimum (data taken from ?)).," Apart from one data point which is derived from a very small number of observations, 51 Peg's S indices are at the lower end of or even below the Sun's respective data during a solar minimum (data taken from \cite{baliunasdonahuesoon1995}) )." + Other stellar properties like radius. mass. age and effective temperature are similar to the Sun's respective parameters.," Other stellar properties like radius, mass, age and effective temperature are similar to the Sun's respective parameters." + The steady low-activity behavior of 51 Peg's H and K line fluxes is also reflected by its X-ray properties., The steady low-activity behavior of 51 Peg's H and K line fluxes is also reflected by its X-ray properties. + Compared to estimates for the solar X-ray luminosity in theROSAT RASS band (0.122.4 keV) during a solar cycle (2).. 51 Peg's luminosity is also at the lower end of the Sun’s values.," Compared to estimates for the solar X-ray luminosity in the RASS band 2.4 keV) during a solar cycle \citep{judgesolomonayres2003}, 51 Peg's luminosity is also at the lower end of the Sun's values." + The ratio of the star’s X-ray to bolometric luminosity is also rather low with Ly/Lp.=1x1077., The ratio of the star's X-ray to bolometric luminosity is also rather low with $L_X/L_{bol}=1\times10^{-7}$. + The X-ray surface flux of F to M stars was shown to be constrained at the lower end by the surface flux level of a solar coronal hole: Fy¢holey*107 erg s7| em7El for theROSAT and energy band. which translates to =[099 ere sv! em? for XMM's 112 keV band (?)..," The X-ray surface flux of F to M stars was shown to be constrained at the lower end by the surface flux level of a solar coronal hole; $F_{X\,\mbox{(hole)}}\approx10^{4}$ erg $^{-1}$ $^{-2}$ for the and energy band, which translates to $\approx10^{3.8}$ erg $^{-1}$ $^{-2}$ for 's 12 keV band \citep{schmitt1997}." + 5] Peg's surface flux. calculated from the ACIS-S data. is one of the lowest so far detected with logFy=10 erg s! em: the coronal hole surface flux seems to be a good deseription of this star’s X-ray flux. with regards to the flux level as well as the plasma temperature.," 51 Peg's surface flux, calculated from the ACIS-S data, is one of the lowest so far detected with $\log F_{X}=10^{3.7}$ erg $^{-1}$ $^{-2}$; the coronal hole surface flux seems to be a good description of this star's X-ray flux, with regards to the flux level as well as the plasma temperature." + There has been some discussion on how to identify a Maunder minimum (MM) star over the last years., There has been some discussion on how to identify a Maunder minimum (MM) star over the last years. + The original criterion of chromospheric activity levels (RWR=-5.] was derived by ?.. but relied on a stellar sample contaminated with evolved stars. which have significantly lower chromosphericactivity levels compared to main sequence stars.," The original criterion of chromospheric activity levels $\langle R^{'}_{HK}\rangle=-5.1$ was derived by \cite{henrysoderblomdonahue1996}, , but relied on a stellar sample contaminated with evolved stars, which have significantly lower chromosphericactivity levels compared to main sequence stars." + ? reanalyzed these data. excluding evolved stars with luminosities more," \cite{wright2004} reanalyzed these data, excluding evolved stars with luminosities more" +the fainter side. without changing its shape.,"the fainter side, without changing its shape." +" The black short-dashed. line included in the figure gives the observational estimate of the rest-frame V-bancl luminosity function. by Shapleyetal.(2001) with a faint-end slope of a=1.85. normalisation P=0.18.10.7h?Alpe"". and characteristic magnitude Al=2221|5logh—22.98. for h=07."," The black short-dashed line included in the figure gives the observational estimate of the rest-frame V-band luminosity function by \citet{Sha01} with a faint-end slope of $\alpha=-1.85$, normalisation $\Phi^*=0.18\times 10^{-2} +h^3\mpc^{-3}$, and characteristic magnitude $M*=-22.21+5\log h = +-22.98$, for $h=0.7$." + ‘The observational magnitude limit of Ady=20.5r is shown bv the arrows., The observational magnitude limit of $M_V= -20.5$ is shown by the arrows. + The most prominent feature seen in all panels is that the luminosity functions of the simulated. galaxies are all very steep. with a faint-end slope comparable toa~2. which is the slope of the dark matter halo mass function.," The most prominent feature seen in all panels is that the luminosity functions of the simulated galaxies are all very steep, with a faint-end slope comparable to $\alpha \sim -2$, which is the slope of the dark matter halo mass function." +— “Phis suggests that the strong feedback included in the simulations has not been able to reduce the luminosities of low-mass ealaxies much more strongly than those of more massive systems: if such a cilferential elect existed. it should. have manifested. itself as a flattening of the faint-end compared to the halo mass function.," This suggests that the strong feedback included in the simulations has not been able to reduce the luminosities of low-mass galaxies much more strongly than those of more massive systems; if such a differential effect existed, it should have manifested itself as a flattening of the faint-end compared to the halo mass function." + t face value. however. the observational data actually support a rather steep end slope at 2=3. quite close to that of the halo mass function.," At face value, however, the observational data actually support a rather steep faint-end slope at $z=3$, quite close to that of the halo mass function." + One should note. however. that the observational estimate of the slope à ats=3 is very uncertain because 1ο observations can only reach down to a magnitude of Ad~20.5. even with S-meter class telescopes.," One should note, however, that the observational estimate of the slope $\alpha$ at $z=3$ is very uncertain because the observations can only reach down to a magnitude of $M_V\sim -20.5$, even with 8-meter class telescopes." +" When compared. with the observational fit of Shapleyal. (2001)... it is clear that the ""OQr-eries. are. deficient in the brightest galaxies at the high. Iuminositv-end. of the uminositv function."," When compared with the observational fit of \citet{Sha01}, it is clear that the `Q'-series are deficient in the brightest galaxies at the high luminosity-end of the luminosity function." +" This can be understood as a result of ye small box size (Li,=10h.+ Alpe) of these runs. which do not have large enough volume to allow a faithful sampling of rare. bright objects."," This can be understood as a result of the small box size $\Lbox = 10\,\himpc$ ) of these runs, which do not have large enough volume to allow a faithful sampling of rare, bright objects." +" As the box size becomes larger from Ίο QU-series to the D'-series (Ling=33.75ht Alpe). and ren to the ""C-series (Li=1005.+ Alpe). this situation improves however."," As the box size becomes larger from the `Q'-series to the `D'-series $\Lbox=33.75\,\himpc$ ), and then to the `G'-series $\Lbox=100\,\himpc$ ), this situation improves however." + More and more of the luminous objects can then be found. and the agreement with the observation xcomes better at the bright-end of the luminosity function.," More and more of the luminous objects can then be found, and the agreement with the observation becomes better at the bright-end of the luminosity function." + On the other extreme of the luminosity distribution. we see that increasing the resolution from (Q3 to Q4. and hen to Q5. allows inclusion of ever. fainter objects. as expected.," On the other extreme of the luminosity distribution, we see that increasing the resolution from Q3 to Q4, and then to Q5, allows inclusion of ever fainter objects, as expected." +" Therefore the luminosity function becomes wider owards the fainter end,", Therefore the luminosity function becomes wider towards the fainter end. + Note. however. that the bright-end hardly changes. suggesting good. convergence in the simulation results for the massive galaxies.," Note, however, that the bright-end hardly changes, suggesting good convergence in the simulation results for the massive galaxies." + The run :O. (no wind run) slightly. overpredicts the number of galaxies compared to observations. arguing for," The run `O3' (no wind run) slightly overpredicts the number of galaxies compared to observations, arguing for" +When 5c€min- ρμ1) is determined bv electrons with 5=nine,"When $\gamma_{\rm c}<\gamma_{\rm min}$ , $U_{\rm ph}(\nu)$ is determined by electrons with $\gamma=\gamma_{\rm min}$." +" However. in contrast with the previous case. electrons with 5=s,yin lose all the energy. ancl. hence. the factor (min/c) Is substituted by unity. which leads to Physically. Che factor (αμος) accounts lor the decrease in the column density. of electrons with 5—,4, Causecl by cooling."," However, in contrast with the previous case, electrons with $\gamma=\gamma_{\rm min}$ lose all the energy and, hence, the factor $\left(\gamma_{\rm min}/\gamma_{\rm c}\right)^{\alpha}$ is substituted by unity, which leads to Physically, the factor $\left(\gamma_{\rm min}/\gamma_{\rm c}\right)^{\alpha}$ accounts for the decrease in the column density of electrons with $\gamma = \gamma_{\rm min}$ caused by cooling." +" The value of a describes the upper envelope connecting (he dillerent Compton orders and is determined by electrons of a given energy (1.6.. , OF 4.) ."," The value of $\alpha$ describes the upper envelope connecting the different Compton orders and is determined by electrons of a given energy (i.e., $\gamma_{\rm min}$ or $\gamma_{\rm c}$ ) ." +" Hence. the local spectral index can deviate substantially from o. in particular. for large values of 5,44 or ον."," Hence, the local spectral index can deviate substantially from $\alpha$, in particular, for large values of $\gamma_{\rm min}$ or $\gamma_{\rm c}$." + However. as discussed in D.AO0. a power-law distribution of electron energies considerably smoothens the spectrum as compared to a thermal/mono-energetic distribution.," However, as discussed in BA00, a power-law distribution of electron energies considerably smoothens the spectrum as compared to a thermal/mono-energetic distribution." +" A distinct feature of a power-law distribution is that the energy of the electrons determining the value of a changes rapidly from . to y, (or vice versa) as the value of τι goes through unity.", A distinct feature of a power-law distribution is that the energy of the electrons determining the value of $\alpha$ changes rapidly from $\gamma_{\rm c}$ to $\gamma_{\rm min}$ (or vice versa) as the value of $\tau_{\rm o}$ goes through unity. +" Although the value of a changes smoothly in this transition. the local spectral index can change rapidly. in particular for cases will +.X44, al this instance."," Although the value of $\alpha$ changes smoothly in this transition, the local spectral index can change rapidly, in particular for cases with $\gamma_{\rm c} \gg\gamma_{\rm min}$ at this instance." +" This change in spectral character from a bumpw to a smooth spectvim as , is replaced by5,44, as the main contributor to the inverse Compton emission is evident in the spectra presented in DAOO."," This change in spectral character from a ""bumpy"" to a smooth spectrum as $\gamma_{\rm c}$ is replaced by$\gamma_{\rm min}$ as the main contributor to the inverse Compton emission is evident in the spectra presented in BA00." +" These expressions for a and 5, for a given value of 7, depend only on (he assumption ol cooling in the IxXlein-Nishina limit.", These expressions for $\alpha$ and $\gamma_{\rm c}$ for a given value of $\tau_{\rm o}$ depend only on the assumption of cooling in the Klein-Nishina limit. +" In order (o relate the values for a and 5, to the source properties. the origin of the seed photons needs to be considered."," In order to relate the values for $\alpha$ and $\gamma_{\rm c}$ to the source properties, the origin of the seed photons needs to be considered." + Two different scenarios are usually envisaged: external photons. whose properties are unrelated to those of the relativistic electrons. and svnchrotron photons produced by the relativistic electrons themselves models).," Two different scenarios are usually envisaged; external photons, whose properties are unrelated to those of the relativistic electrons, and synchrotron photons produced by the relativistic electrons themselves (SSC-models)." + When the seed photons are due (ο svuchrotron radiation from the same electrons producing the inverse Compton flix. a particular simple description is possible.," When the seed photons are due to synchrotron radiation from the same electrons producing the inverse Compton flux, a particular simple description is possible." + This is due to the fact that svuehrotron radiation can be regarded as inverse Compton scattering of (he virtual photons associated with the magneticfield., This is due to the fact that synchrotron radiation can be regarded as inverse Compton scattering of the virtual photons associated with the magneticfield. +" Hence. the second equation needed to obtain separatevalues for a and >, is straightforward to derive."," Hence, the second equation needed to obtain separatevalues for $\alpha$ and $\gamma_{\rm c}$ is straightforward to derive." + a> (p—1)/2: The expression relating the svnchrotron and inverse Compton components, $\alpha>(p-1)/2$ : The expression relating the synchrotron and inverse Compton components +Therefore. it is difficult to make a statement on the probable cause for the changing orbital period of NTE J1710-251.,"Therefore, it is difficult to make a statement on the probable cause for the changing orbital period of XTE J1710-281." + We cmphasise that if magnetic evcling of the binary components is indeed a reason behind the observed epochs of orbital period. then long term monitoring of N'TIS J1710-351. is required. to determine the timescales of magnetic evcling of the secondary star.," We emphasise that if magnetic cycling of the binary components is indeed a reason behind the observed epochs of orbital period, then long term monitoring of XTE J1710-281, is required to determine the timescales of magnetic cycling of the secondary star." + It may also be useful to foretell the cistinet orbital period epochs of NTE JIT10-281. if any.," It may also be useful to foretell the distinct orbital period epochs of XTE J1710-281, if any." + Lastly. the forthcoming Inclan-satcllite. ASTROSAL with a very large area. X-ray proportional counter (Paul2009) could be a boon in determining the orbital parameters of the system.," Lastly, the forthcoming Indian-satellite, $ASTROSAT$ with a very large area X-ray proportional counter \citep{Paul09} could be a boon in determining the orbital parameters of the system." + This research has made use of cata obtained: from the Ligh Enerev Astrophysics Science Archive Research Center (IIEASARC). provided by NASA's Goddard Space Flight Center.," This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center." +"results in any sensible way, given the flatness of the spectrum in this short wavelength range.","results in any sensible way, given the flatness of the spectrum in this short wavelength range." + The LF of galaxies at any redshift z is obtained by counting the galaxies with a given absolute magnitude in each magnitude bin and dividing the final result by the total volume of the simulation and bin size (0.5 mag)., The LF of galaxies at any redshift $z$ is obtained by counting the galaxies with a given absolute magnitude in each magnitude bin and dividing the final result by the total volume of the simulation and bin size (0.5 mag). +" We perform this procedure for the following six redshifts z=(5,6,7,8,9,10)."," We perform this procedure for the following six redshifts $z=(5, 6, 7, 8, 9, 10)$." + The results are shown in Fig., The results are shown in Fig. +" 1 as solid histograms, where the error bars represent the Poisson error on the number of galaxies in each magnitude bin."," \ref{fig:LF} as solid histograms, where the error bars represent the Poisson error on the number of galaxies in each magnitude bin." + These theoretical LFs are then compared to the experimental ones collected from the various analyses of the HUDF., These theoretical LFs are then compared to the experimental ones collected from the various analyses of the HUDF. + For z—10 we show the upper limits on the LF obtained from the three available candidates identified by Bouwens et al. (, For $z=10$ we show the upper limits on the LF obtained from the three available candidates identified by Bouwens et al. ( +2009).,2009). + Let us now analyze the results shown in Fig., Let us now analyze the results shown in Fig. + 1 in more detail., \ref{fig:LF} in more detail. + It is clear that the luminosity range sampled by the observations and our predictions is only partially overlapping., It is clear that the luminosity range sampled by the observations and our predictions is only partially overlapping. +" This is because on one hand, even the exquisite sensitivity of WFC3 is not sufficient to properly sample the faint-end of the LF (Μυνρω2 —18); on the other hand, our simulations, which are specifically designed to properly resolve the very first galactic units in a relatively small volume, lack the most massive, rare objects which comprise the bright end of the LF."," This is because on one hand, even the exquisite sensitivity of WFC3 is not sufficient to properly sample the faint-end of the LF $M_{UV}\simgt -18$ ); on the other hand, our simulations, which are specifically designed to properly resolve the very first galactic units in a relatively small volume, lack the most massive, rare objects which comprise the bright end of the LF." +" In spite of these shortcomings, we consider it a rewarding success that the amplitudes of the theoretical and experimental LFs match almost perfectly, and at the same time, have quite similar slopes at all redshifts for which data are available."," In spite of these shortcomings, we consider it a rewarding success that the amplitudes of the theoretical and experimental LFs match almost perfectly, and at the same time, have quite similar slopes at all redshifts for which data are available." +" This is even more striking as no attempts have been made to fit or adjust the theoretical curves to the observed LF, i.e. they have been computed directly from the simulation output with no free extra parameters."," This is even more striking as no attempts have been made to fit or adjust the theoretical curves to the observed LF, i.e. they have been computed directly from the simulation output with no free extra parameters." + Our results suggest two clear trends., Our results suggest two clear trends. +" First, the LFs shift towards fainter luminosities with increasing redshift, mimicking a pure luminosity or density evolution."," First, the LFs shift towards fainter luminosities with increasing redshift, mimicking a pure luminosity or density evolution." +" This is quite consistent with the trend of an increasing My with redshift, found in the data by several groups (see the extended discussion in Ouchi et al."," This is quite consistent with the trend of an increasing $M^*_{UV}$ with redshift, found in the data by several groups (see the extended discussion in Ouchi et al." +" 2009), preferring a pure luminosity evolution."," 2009), preferring a pure luminosity evolution." +" Second, the faint-end slope of the simulated LF does not vary (within errors) from z—5 to"," Second, the faint-end slope of the simulated LF does not vary (within errors) from $z=5$ to" +distribution resenibles à noded network. with filancuts converging and cuding at vertices iu the uetwork. the filaments in the CGaussimu raudom field appear more randomly orieuted and show no apparent correlations with one another.,"distribution resembles a noded network, with filaments converging and ending at vertices in the network, the `filaments' in the Gaussian random field appear more randomly oriented and show no apparent correlations with one another." + Using 5 siuoothliug. the Blunent leugth distributions for the Gaussian random Held aud dark matter distribution are shown in the centre xuel of Fig. 6..," Using $5$ smoothing, the filament length distributions for the Gaussian random field and dark matter distribution are shown in the centre panel of Fig. \ref{fig:FilsGRFCompare_all}." + The distributions are very sinilar aud clearly exponential above a leugth of ~LOAlpe. with ΔΟΕ)~1077. sugecsting that filaments lave rot collapsed πιο aloug their longest axis since their ormation. but have chaneed their aliguiment in relation o nearby structures.," The distributions are very similar and clearly exponential above a length of $\sim 10$, with $N(L) \sim 10^{\frac{-0.1L}{\rm Mpc}}$, suggesting that filaments have not collapsed much along their longest axis since their formation, but have changed their alignment in relation to nearby structures." + We will define the width ofa flament clement. IH. to be he root mean squared perpendicular offset of particles within a sinoothing leugth: that is. where Ry is defined in Equation 5 aud the sum is over all of the NV particles within oue smoothing leneth of the filament element.," We will define the widthof a filament element, $W$, to be the root mean squared perpendicular offset of particles within a smoothing length; that is, where $\mathbf{R_i}$ is defined in Equation \ref{eq:PerpDisplace} and the sum is over all of the $N$ particles within one smoothing length of the filament element." + In the bottom pancl of Fie. 6..," In the bottom panel of Fig. \ref{fig:FilsGRFCompare_all}," + we plot he width distributions for the two fields. again using P=5Nope.," we plot the width distributions for the two fields, again using $l=5$." + The dark matter width distributions are broader aud are peaked at simaller widths. sugeesting hat the flaments have collapsed significantly along wo of their principal axes. despite having a similar eueth distribution.," The dark matter width distributions are broader and are peaked at smaller widths, suggesting that the filaments have collapsed significantly along two of their principal axes, despite having a similar length distribution." + As oue would expect with bottomsup structure formation. the width distribution in the Gaussian raudonm field auc dark matter distribution are nore discrepant at siialler smoothing scales (other scales rot show).," As one would expect with bottom-up structure formation, the width distribution in the Gaussian random field and dark matter distribution are more discrepant at smaller smoothing scales (other scales not shown)." + Tn Paper 1. we showed that on a given comoving snoothing scale. there was evidence for ai wallto-filament-to-chunp evolution with cosiic finc.," In Paper $1$, we showed that on a given comoving smoothing scale, there was evidence for a wall-to-filament-to-clump evolution with cosmic time." + Furthermore. we showed that the axis of structure— aligns with the filamentary backbone in two-dimensional slices frou cosmological simulations as carly απ 2—3 (sce fleure Ll in Paper 1)," Furthermore, we showed that the axis of structure aligns with the filamentary backbone in two-dimensional slices from cosmological simulations as early as $z=3$ (see figure 14 in Paper 1)." + Fig., Fig. + 7 shows the filament distribution at ;= Qand:=3. now with?=157 sso as to test the largest and least-evolved structures in the simulation box.," \ref{fig:EvolveAll} shows the filament distribution at $z=0$ and $z=3$, now with $l=15$ so as to test the largest and least-evolved structures in the simulation box." + We used a smaller removal width. N=0.6. for the 2=3 filament distribution because the filaments are of lower contrast than at 2.=0. causing Equation 3. to overestimate their sizes.," We used a smaller removal width, $K=0.6$, for the $z=3$ filament distribution because the filaments are of lower contrast than at $z=0$, causing Equation \ref{eq:RemoveWidth} to overestimate their sizes." + The :=3 and :=0 filament distributious are very sinular to the eve. sugeesting that the basic flamenut framework for |=15 is almost entirely in place at 2=3 (here 15 fluctuations have CAMAyNE 0.1).," The $z=3$ and $z=0$ filament distributions are very similar to the eye, suggesting that the basic filament framework for $l=15$ is almost entirely in place at $z=3$ (where $15$ fluctuations have $\left<\left(\Delta M/M\right)^2\right>^{1/2}\sim 0.1$ )." + The righthaud paucl of Fig., The righthand panel of Fig. + 7 shows the flament clement width distributions as a function of redshift., \ref{fig:EvolveAll} shows the filament element width distributions as a function of redshift. + As non-linear evolution proceeds. the fBluueut width distributions broaden and peak at stnaller widths.," As non-linear evolution proceeds, the filament width distributions broaden and peak at smaller widths." + Before we proceed to ideutifv filameuts in the SDSS data. we run the filament finder ou the mock galaxy saluples iu redshift space (see Paper 1) aud compare he resulting filaments to those identified iu the space +=0 dark matter distribution.," Before we proceed to identify filaments in the SDSS data, we run the filament finder on the mock galaxy samples in redshift space (see Paper 1) and compare the resulting filaments to those identified in the real-space $z=0$ dark matter distribution." + The 7!=Sh filament distribution is vorv stronglv affected we redshift distortions the contamination rates are vpicallv ~LO per cent. about double the contamination of the fllamcut samples without redshift distortions.," The $l=5$ filament distribution is very strongly affected by redshift distortions – the contamination rates are typically $\sim 40$ per cent, about double the contamination of the filament samples without redshift distortions." + This is due primarily to the Ππσα-οἱσος effect. which causes ealaxv clusters to extend iuto narrow. sharp flunenut-like features alone the Lue of sight.," This is due primarily to the `finger-of-god' effect, which causes galaxy clusters to extend into narrow, sharp filament-like features along the line of sight." + Fortunately. the filament finder is insensitive to these distortions on 107 aud lsh scales because the fingers-6-eod are typically Z inwidth.," Fortunately, the filament finder is insensitive to these distortions on $10$ and $15$ scales because the fingers-of-god are typically $\lesssim 1$ in width." + Nevertheless. we ean improve our results if we first remove the fingers-ofgod.," Nevertheless, we can improve our results if we first remove the fingers-of-god." + Fingers-ofeod from galaxy clusters are extended aloug the observers Lue of sight. while real flameutary structure have no preferred direction.," Fingers-of-god from galaxy clusters are extended along the observer's line of sight, while real filamentary structure have no preferred direction." + Iu order to separate the fiugers-of-god from the real filaments. we will use a fricuds-offricuds aleorithii with two linking leneths. where fis the unit vector along the observers line of sight (7)..," In order to separate the fingers-of-god from the real filaments, we will use a friends-of-friends algorithm with two linking lengths, where $\mathbf{\hat{r}}$ is the unit vector along the observer's line of sight \citep{FOF}. ." + With these two parameters defined. the aleorithni searches for cylindrical structures with a iamietorto-leugth ratio of bj ," With these two parameters defined, the algorithm searches for cylindrical structures with a diameter-to-length ratio of $b_\perp/b_\parallel$ ." +"?.hereafterDOG. did an exhaustive study of this two-paranueter/bj. space and found that bj,=00.ll aud bj=0.75 gave unbiased estimates of theeroup multiplicity function. so we adopt these values in our study."," \citet[e.g.][hereafter B06]{ZClusterFind2} did an exhaustive study of this two-parameter space and found that $b_\perp=0.14$ and $b_\parallel=0.75$ gave unbiased estimates of thegroup multiplicity function, so we adopt these values in our study." +"light curve, Fig. [I],","light curve, Fig. \ref{fig:LATGBMlight curve}," + consisted of a single pulse with Του of 2042 s (8-1000 keV)., consisted of a single pulse with $_{90}$ of $\pm$ 2 s (8-1000 keV). +" The time-averaged, combined GBM/LAT spectrum from TO to T0+20.7 s, where TO is the trigger time, is best fit by a Band function (Band et al."," The time-averaged, combined GBM/LAT spectrum from T0 to T0+20.7 s, where T0 is the trigger time, is best fit by a Band function (Band et al." +" 1993), with Eyeak = 26844 keV, a = -0.69340.009 and 8 = -2.342+0.011."," 1993), with $E_{peak}$ = $\pm$ 4 keV, $\alpha$ = $\pm0.009$ and $\beta$ = $\pm 0.011$." +" The fluence (10 keV - 10 GeV) during this interval is (2.474-0.03)x10-7* ergs cm7?, bright enough to result in a repointing."," The fluence (10 keV - 10 GeV) during this interval is $\pm$ $\times10^{-4}$ ergs $^{-2}$, bright enough to result in a repointing." +" In the first 300 s, LAT observed 150 and 20 photons above 100 MeV and 1 GeV, respectively."," In the first 300 s, LAT observed 150 and 20 photons above 100 MeV and 1 GeV, respectively." + Possible extended emission continued out to a few kilo-seconds., Possible extended emission continued out to a few kilo-seconds. +" The highest energy photon, 19.6 GeV, was observed 26 s after the trigger."," The highest energy photon, 19.6 GeV, was observed 26 s after the trigger." +" The LAT light curve, Fig. [I],"," The LAT light curve, Fig. \ref{fig:LATGBMlight curve}," + is fit by a power-law of a = -2.17+0.14., is fit by a power-law of $\alpha$ = $\pm0.14$ . +" We fit the LAT spectrum, from 100 - 1000 s, with a power-law of 6=—1.26*025."," We fit the LAT spectrum, from 100 - 1000 s, with a power-law of $\beta = -1.26^{+0.24}_{-0.22}$." +" XRT began observing GRB 0909264 ~46.6 ks after the trigger, in Photon Counting (PC) mode."," XRT began observing GRB 090926A $\sim$ 46.6 ks after the trigger, in Photon Counting (PC) mode." +" The light curve, Fig."," The light curve, Fig." + (taken from the XRT light curve repository; Evans et al., \ref{fig:lightcurves} (taken from the XRT light curve repository; Evans et al. +" 2|2007, Evans et al."," 2007, Evans et al." +" 2009), shows a decaying behavior with some evidence of variability, and is fit with a single power-law, decaying with a = -1.404-0.05 confidence level)."," 2009), shows a decaying behavior with some evidence of variability, and is fit with a single power-law, decaying with $\alpha$ = $\pm$ 0.05 confidence level)." + The average spectrum from 46.6(90% ks — 149 ks is best fit by an absorbed power-law model with @=—1.6*03 and an absorption column density of 1.0°9°3x107+ cm? in excess of the Galactic value of 2.7x10?? cm-? (Kalberla et al., The average spectrum from 46.6 ks – 149 ks is best fit by an absorbed power-law model with $\beta = -1.6^{+0.3}_{-0.2}$ and an absorption column density of $1.0^{+0.5}_{-0.3}\times10^{21}$ $^{-2}$ in excess of the Galactic value of $\times10^{20}$ $^{-2}$ (Kalberla et al. + 2005)., 2005). + The counts to observed flux conversion factor deduced from this spectrum is 3.5x107!! ergs cm? count~!., The counts to observed flux conversion factor deduced from this spectrum is $\times10^{-11}$ ergs $^{-2}$ $^{-1}$. + The average (unabsorbed) fluxes are 1.3(1.9)x10~! ergs cm observeds, The average observed (unabsorbed) fluxes are $\times10^{-12}$ ergs $^{-2}$ $^{-1}$. +" UVOT began settled observations of GRB 0909264 at T0+~47 ks, and the optical afterglow was immediately detected (Gronwall et al."," UVOT began settled observations of GRB 090926A at $\sim$ 47 ks, and the optical afterglow was immediately detected (Gronwall et al." + , 2009). +The resulting optical afterglow light curve is shown in 2009).Fig. 2}., The resulting optical afterglow light curve is shown in Fig. \ref{fig:lightcurves}. +" Removing these flares, the underlying optical light curve is well fit (x2, = 0.92/82 d.o.f)"," Removing these flares, the underlying optical light curve is well fit $\chi^{2}_{red}$ = 0.92/82 d.o.f.)" + by a broken powerlaw., by a broken powerlaw. +" The best fit parameters are: QOpt.1=—1.01*007, toreak=351*102, ks, GOpt2=—1."," The best fit parameters are: $\alpha_{Opt,1} = -1.01^{+0.07}_{-0.03}$, $t_{break} = 351^{+70.2}_{-141.9}$ ks, $\alpha_{Opt,2} = -1.77^{+0.21}_{-0.26}$." +" X-shooter, mounted on the Very Large Telescope UT2, 713025.found a spectroscopic redshift of z — 2.1062 (Malesani et al."," X-shooter, mounted on the Very Large Telescope UT2, found a spectroscopic redshift of $z$ = 2.1062 (Malesani et al." + 2009)., 2009). + The variability in the X-ray is not statistically strong (peaking ~2.80 above the underlying fit) but is temporally coincident with stronger flaring in the UVOT., The variability in the X-ray is not statistically strong (peaking $\sim$ $\sigma$ above the underlying fit) but is temporally coincident with stronger flaring in the UVOT. +" The first flare, at ~70 ks — 95ks, is well defined in the UVOT lightcurve with At/t z 0.35, but is only seen in the X-ray as minor variability, with individual points varying from the underlying fit."," The first flare, at $\sim$ 70 ks – 95ks, is well defined in the UVOT lightcurve with $\Delta t$ $t$ $\approx$ 0.35, but is only seen in the X-ray as minor variability, with individual points varying from the underlying fit." +" The second flare, at 195 ks — 260 ks, is better defined in the X-ray (though only peaking at ~1c) but is matched by a similarly shaped, stronger feature in the UVOT 5’ "," The second flare, at 195 ks – 260 ks, is better defined in the X-ray (though only peaking at $\sim$ $\sigma$ ) but is matched by a similarly shaped, stronger feature in the UVOT $\Delta t$ $t$ $\approx$ 0.28)." +"Due to an observing gap, we may not have (At/tobserved 0.28).the peak of the UVOT feature, but it appears to lag the peak of the X-ray feature by at least 6 ks, which is consistent with lower energy emission from flares laging the higher energy (Margutti 2010)."," Due to an observing gap, we may not have observed the peak of the UVOT feature, but it appears to lag the peak of the X-ray feature by at least 6 ks, which is consistent with lower energy emission from flares laging the higher energy (Margutti 2010)." +" GRB 090926A was a long burst with more than 20 photons in the GeV range, that was also easily detected by the XRT and UVOT nearly 13 hrs after the initial trigger and has late time flares in the UVOT afterglow."," GRB 090926A was a long burst with more than 20 photons in the GeV range, that was also easily detected by the XRT and UVOT nearly 13 hrs after the initial trigger and has late time flares in the UVOT afterglow." +" The overall brightness and behavior of the optical afterglow are more reminiscent of afterglows observed immediately after the trigger, as opposed to observations starting at 47 ks after the trigger (Oates et al."," The overall brightness and behavior of the optical afterglow are more reminiscent of afterglows observed immediately after the trigger, as opposed to observations starting at 47 ks after the trigger (Oates et al." + 2009; Roming et al., 2009; Roming et al. + 2009; Roming et al., 2009; Roming et al. +" 2010, in "," 2010, in preparation)." +"The late time light curve could be due to preparation).late time energy injection, supported by the presence of flares in the light curve, or could be a LAT selection effect."," The late time light curve could be due to late time energy injection, supported by the presence of flares in the light curve, or could be a LAT selection effect." + We explore both of these possibilities., We explore both of these possibilities. + X-ray flares at late times have been attributed to two different sources (Wu et al., X-ray flares at late times have been attributed to two different sources (Wu et al. +" 2005): central engine powered internal emission, or features of the external shock."," 2005): central engine powered internal emission, or features of the external shock." + There is evidence suggesting that the GRB prompt emission and X-ray flares originate from similar physical processes (see Burrows et al., There is evidence suggesting that the GRB prompt emission and X-ray flares originate from similar physical processes (see Burrows et al. + 2005b; Zhang et al., 2005b; Zhang et al. + 2006; Chincarini et al., 2006; Chincarini et al. + 2007; Krimm et al., 2007; Krimm et al. +" 2007), including a lower energy budget and ‘spiky’ flares more like those actually seen in X-ray light curves."," 2007), including a lower energy budget and `spiky' flares more like those actually seen in X-ray light curves." +" If the central engine is the source of GRB flares, the X-ray flare spectrum should be similar to that of the prompt spectrum."," If the central engine is the source of GRB flares, the X-ray flare spectrum should be similar to that of the prompt spectrum." +" In the case of GRB 0909264, the prompt emission was seen to have a Band-function spectrum."," In the case of GRB 090926A, the prompt emission was seen to have a Band-function spectrum." +" Assuming the optical behaves similarly to the X-ray and that the flares are caused by central engine activity, we would expect a Band-function spectrum during the flares."," Assuming the optical behaves similarly to the X-ray and that the flares are caused by central engine activity, we would expect a Band-function spectrum during the flares." + A Band-function spectrum is not observed during the X-ray variability or optical flares., A Band-function spectrum is not observed during the X-ray variability or optical flares. +" The flares are both well fit by a power-law, with no indication of a break in the spectrum or sign of spectral evolution in the X-ray."," The flares are both well fit by a power-law, with no indication of a break in the spectrum or sign of spectral evolution in the X-ray." +" It should be stated, however, that the statistics of the X-ray light curve are low enough that detecting a Band spectrum may not be possible, even if it exists."," It should be stated, however, that the statistics of the X-ray light curve are low enough that detecting a Band spectrum may not be possible, even if it exists." +" Combining the poor statistics with the dominate underlying continuum, it is not surprising that a power-law is the best fit."," Combining the poor statistics with the dominate underlying continuum, it is not surprising that a power-law is the best fit." + We also find no evidence of change in the spectral shape after creating a spectral energy distribution using optical/UV photometry before and during the first flare., We also find no evidence of change in the spectral shape after creating a spectral energy distribution using optical/UV photometry before and during the first flare. +" A non Band-like spectrum for the flares does not expressly prohibit central engine activity from being the source of the flares, but it does allow for alternate explanations."," A non Band-like spectrum for the flares does not expressly prohibit central engine activity from being the source of the flares, but it does allow for alternate explanations." + Code for modeling X-ray flares in GRBs developed by Maxham and Zhang (2009) can produce optical flares through the collision of low energy shells or wide shells., Code for modeling X-ray flares in GRBs developed by Maxham and Zhang (2009) can produce optical flares through the collision of low energy shells or wide shells. +" If the two flares are indeed due to internal shocks, then this code can put constraints on the time of ejection and maximum energy (Lorentz factor) of the matter shells that could produce such flares."," If the two flares are indeed due to internal shocks, then this code can put constraints on the time of ejection and maximum energy (Lorentz factor) of the matter shells that could produce such flares." +" Since ejection time in the GRB rest frame is highly correlated to the collision time of shells in the observer frame, this means that the central engine is active around 70 ks and 197 ks."," Since ejection time in the GRB rest frame is highly correlated to the collision time of shells in the observer frame, this means that the central engine is active around 70 ks and 197 ks." +" Using the prompt emission fluence to constrain the total energy contained in the blastwave, the internal shock model requires that Lorentz factors of the shells causing flares must be less than the Lorentz factorof the blastwave when the shells are ejected."," Using the prompt emission fluence to constrain the total energy contained in the blastwave, the internal shock model requires that Lorentz factors of the shells causing flares must be less than the Lorentz factorof the blastwave when the shells are ejected." +" Fast moving shells will simply collide onto the blastwave giving small, undetectable glitches, whereas slow moving shells will be allowed to collide internally, releasing the energy required"," Fast moving shells will simply collide onto the blastwave giving small, undetectable glitches, whereas slow moving shells will be allowed to collide internally, releasing the energy required" +times for GRB 050724. CRB 050709. GRB 051221 are 22d).(14.. 10d). ο 5d) respectively with corresponding power law indices of ay and αν (1.5. 2).(1.25.2.83) andí1.2),"times for GRB 050724, GRB 050709, GRB 051221 are, 22d), 10d), 5d) respectively with corresponding power law indices of $\alpha_1$ and $\alpha_2$ $(-1.5,-2)$, $(-1.25,-2.83)$ and $(-1,-2)$." + Table 1 shows the derived. parameters with the extrapolated A-banc magnitude at 1 hr post burst at. 300 Alpe., Table 1 shows the derived parameters with the extrapolated $R$ -band magnitude at 1 hr post burst at 300 Mpc. + We point out that the optical data. used. in. the references to derive the beaming angle and break times is uncertain. and we do not account for optical bumps. and Hares that can be significant. especially at early. times.," We point out that the optical data used in the references to derive the beaming angle and break times is uncertain, and we do not account for optical bumps and flares that can be significant, especially at early times." + Nonetheless. it is clear from Table 1 that if one of the well localised SCGItBs occurred. within M.. ancl was on-axis. it would be bright at early times and easily detected by moclest aperture telescopes.," Nonetheless, it is clear from Table 1 that if one of the well localised SGRBs occurred within $D_s$, and was on-axis, it would be bright at early times and easily detected by modest aperture telescopes." + To calculate the rate of triggered. detection of on-axis alterelows requires accounting for the beaming angle 6;., To calculate the rate of triggered detection of on-axis afterglows requires accounting for the beaming angle $\thjet$. + Equation (3)) caleulates the number of afterglows seen. per ve for a certain €; assuming a LIGO/Vireo detection rate of Rao~ d35vr (see section ??)) The rate of off-axis bursts dis. determined. bv the nmiaximum angle. urs. away from the jet center that an olf- observer could see the afterglow.," Equation \ref{eq3}) ) calculates the number of afterglows seen per yr for a certain $\thjet$ assuming a LIGO/Virgo detection rate of $R_{\mathrm{det}}\sim135$ $^{-1}$ (see section \ref{rates}) ) The rate of off-axis bursts is determined by the maximum angle, $ \thmax$, away from the jet center that an off-axis observer could see the afterglow." + This angle depends critically on the Dux limit of the telescope Plu. £; and 6.," This angle depends critically on the flux limit of the telescope $ F_{\rm lim}$, $F_j$ and $\thjet$." + For olf-axis detection. the main constraint is the off-axis emission only becomes visible after the jet-break time. which may be days after the prompt burst. Totani&Panaitescu (2002).," For off-axis detection, the main constraint is the off-axis emission only becomes visible after the jet-break time, which may be days after the prompt burst. \cite{tot02}," +". assuming the uniform jet model. show that £,,,; can be expressed. as where à» is the post-break optical decay index and 9 is a numerical factor 1."," assuming the uniform jet model, show that $ \thmax$ can be expressed as where $\alpha_2$ is the post-break optical decay index and $\delta$ is a numerical factor $\sim 1$." +" 6; can be replaced with μμ in equation (4)) to estimate the SGRB oll-axis detection rate: We note that if 6,4,:€; only on-axis afterglows will be visible at any time. and the rate is determined by 0."," $\thjet$ can be replaced with $\thmax$ in equation \ref{eq:theta-max}) ) to estimate the SGRB off-axis detection rate; We note that if $\thmax \le \thjet $ only on-axis afterglows will be visible at any time, and the rate is determined by $\thjet$." + Using the above relations and light curve characteristics for GARB 050724. απο 050709 and GRB 051221. we extrapolate the light curves bevond the jet-break times to constrain detection limits. rates and cadence times using the sensitivities of TAROT. Zadko and an (8/— 10)m class telescope.," Using the above relations and light curve characteristics for GRB 050724, GRB 050709 and GRB 051221, we extrapolate the light curves beyond the jet-break times to constrain detection limits, rates and cadence times using the sensitivities of TAROT, Zadko and an $(8-10)$ m class telescope." + Figure 1 shows the temporal evolution of the three HOband light curves using equations (1) and (2) at à source distance of 300 Alpe. and. published: values for the decay indices.," Figure 1 shows the temporal evolution of the three $R-band$ light curves using equations (1) and (2) at a source distance of 300 Mpc, and published values for the decay indices." + The three curves are quite dilferent. GRB 050724 and GRB 051221. are relatively bright at carly times. and can be seen from days to some tens of days by meter class telescopes.," The three curves are quite different, GRB 050724 and GRB 051221, are relatively bright at early times, and can be seen from days to some tens of days by meter class telescopes." +" Table 2 shows μας. the detection rates Ze, ancl eur. and the maximum. possible times that an on-axis burst would be visible for the three telescopes."," Table 2 shows $\thmax$, the detection rates $R_{\mathrm {on}}$ and $R_{\mathrm {off}}$, and the maximum possible times that an on-axis burst would be visible for the three telescopes." + We find that CRB 050724 like bursts are detectable at a relatively high rate., We find that GRB 050724 like bursts are detectable at a relatively high rate. + ‘This is because the initial beaming angle is large 25. so more of the afterglows can be seen on-axis.," This is because the initial beaming angle is large $>25\degr$, so more of the afterglows can be seen on-axis." + Conversely. the brightest afterglow at the post break time. CRB 051221. is the least likely to be deteetec because of the small 0;—7°.," Conversely, the brightest afterglow at the post break time, GRB 051221, is the least likely to be detected because of the small $\thjet \sim 7\degr$." + Wis apparent that both TAROT and Zadko are unlikely to detect oll-axis altcreglows from these SGRBs. but a telescope capable of deep imaging to m=26 could detect an additional 5 afterelows ! for GRB 051221 like events.," It is apparent that both TAROT and Zadko are unlikely to detect off-axis afterglows from these SGRBs, but a telescope capable of deep imaging to $m=26$ could detect an additional 5 afterglows $^{-1}$ for GRB 051221 like events." + ‘Table 2 also shows the maximum time. μμ. that the elescopes could detect the SGIUD afterglows.," Table 2 also shows the maximum time, $t_{\mathrm {max}}$, that the telescopes could detect the SGRB afterglows." + TFhis sets the imit on the cadence times for imaging., This sets the limit on the cadence times for imaging. + GRB 051221 has the xiehtest afterglow and is potentially detectable the longest ime: Fas~ Lld for Zadko., GRB 051221 has the brightest afterglow and is potentially detectable the longest time; $t_{\mathrm {max}}\sim11$ d for Zadko. + Given that the GW error ellipse is of order degrees in size. identification of a transient is more easible for this afterglow type.," Given that the GW error ellipse is of order degrees in size, identification of a transient is more feasible for this afterglow type." + Unfortunately. they occur aba rate of lve Land given optical selection cllects (see section ?? fora cliscussion) may be missed altogether.," Unfortunately, they occur at a rate of 1 $^{-1}$, and given optical selection effects (see section \ref{disc} for a discussion) may be missed altogether." + CRB 50724 like events. occurring at an optimistic rate of 13 ! would be detectable up to 5d by Zadko.," GRB 050724 like events, occurring at an optimistic rate of 13 $^{-1}$, would be detectable up to 5d by Zadko." + This would. allow ime for surveving degree size fields and multiple telescopes at diferent longitudes to perform follow-up imaging., This would allow time for surveying degree size fields and multiple telescopes at different longitudes to perform follow-up imaging. + Our results in Table 2. based on a broad. distribution of beaming angles. suggest that the optimal strategy [or identifving the optical emissions triggered by gravitational wave detectors is through initial rapid response searches with robotic telescopes. followed by deeper imaging at later times if an afterglow is not detected within several days of the trigger.," Our results in Table 2, based on a broad distribution of beaming angles, suggest that the optimal strategy for identifying the optical emissions triggered by gravitational wave detectors is through initial rapid response searches with robotic telescopes, followed by deeper imaging at later times if an afterglow is not detected within several days of the trigger." + The first attempts for a triggered search of the optical counterparts of NS-NS coalescences using CI. detectors are just commencing., The first attempts for a triggered search of the optical counterparts of NS-NS coalescences using GW detectors are just commencing. + There are many uncertainties. ancl issues that will need. careful consideration for these types of searches., There are many uncertainties and issues that will need careful consideration for these types of searches. + Firstly. our results show that the coincident detection rate depends. eritically on the beaming angle distribution.," Firstly, our results show that the coincident detection rate depends critically on the beaming angle distribution." + For nearky isotropic optical emission. similar to GRB O507124. the coincident rates are very promising ancl will improve the confidence of the CAV detection. aud provide much needed: localisation.," For nearly isotropic optical emission, similar to GRB 050724, the coincident rates are very promising and will improve the confidence of the GW detection and provide much needed localisation." + Even non-detections of optical emissions for high signal-to-noise ratio NS-NS CAV candidates is interesting., Even non-detections of optical emissions for high signal-to-noise ratio NS-NS GW candidates is interesting. + Non-detections of a statistically significant sample would constrain the SGRB beaming angle distribution. or show that SGRBs are not linked to NS-NS coalescences.," Non-detections of a statistically significant sample would constrain the SGRB beaming angle distribution, or show that SGRBs are not linked to NS-NS coalescences." + Both implications are critical to our unclerstancling of the progenitors of SCRBs., Both implications are critical to our understanding of the progenitors of SGRBs. + ‘To fully use joint optical and GW observations requires understanding and accounting for selection ellects that have historically plaguecl SGRB optical observations., To fully use joint optical and GW observations requires understanding and accounting for selection effects that have historically plagued SGRB optical observations. + Typical, Typical +LLF measurements at z~6.5 from Iuetal.(2010).. Iwashikawaetal. (2011).. and Ouchietal.(2010)..,"LF measurements at $z\sim6.5$ from \citet{hu10}, \citet{kas11}, and \citet{ouc10}. ." + The results of Iashikawactal.(2011). and Ouchictal.(2010) agree with cach other in a wide luninosity rauge covered., The results of \citet{kas11} and \citet{ouc10} agree with each other in a wide luminosity range covered. + The result of IIuetal.(2010) also agrees with them in the bright eud of the LE. but show a significaut discrepancy in the faint eud. where the deusitv of Thietal.(2010). is about three times lower.," The result of \citet{hu10} also agrees with them in the bright end of the LF, but show a significant discrepancy in the faint end, where the density of \citet{hu10} is about three times lower." + The reason is still unclear., The reason is still unclear. + Our LF in the faint cud is slieltly hieher thau that of IIuetal.(2010).. but is lower than the Iashikwaetal.(2011). and Ouchietal.(2010) LEs.," Our LF in the faint end is slightly higher than that of \citet{hu10}, but is lower than the \citet{kas11} and \citet{ouc10} + LFs." + Given the laree uncertainties our result is generally iu agreement with these previous LAE surveys., Given the large uncertainties our result is generally in agreement with these previous LAE surveys. + The most distant galaxy in our sample is at 5~6.1. and we did not find απ. galaxies at :>6.6.," The most distant galaxy in our sample is at $z\sim6.4$, and we did not find any galaxies at $z>6.6$." + The reason is colplicated., The reason is complicated. + The deep zbaud image used in this paper has securely detected one of the most distant LAEs known at 2=6.96 (Iveetal.2006)., The deep $z'$ -band image used in this paper has securely detected one of the most distant LAEs known at $z=6.96$ \citep{iye06}. +. We successfully recovered this object during our candidate selection. and we also have six good:>6.6 candidates that have been observed.," We successfully recovered this object during our candidate selection, and we also have six good $z>6.6$ candidates that have been observed." + If they were galaxies like the >=6.96 LAE. we should have identified them in the DEIMOS aask images.," If they were galaxies like the $z=6.96$ LAE, we should have identified them in the DEIMOS mask images." + This is illustrated in Figures | and 6., This is illustrated in Figures 4 and 6. + The detection probability of the :=6.96 LAE is higher than those for a half of the LBCs or LAEs in our sample., The detection probability of the $z=6.96$ LAE is higher than those for a half of the LBGs or LAEs in our sample. + However. the throughput of DEIMOS drops steadily from 9000 towards higher wavelength. and im this range the skv background is brighter and the OTD lines are denser.," However, the throughput of DEIMOS drops steadily from 9000 towards higher wavelength, and in this range the sky background is brighter and the OH lines are denser." + These issues result in significantly lower signal-to-noise ratios in the DEIMOS images. but they were not considered in Figures [ and 6.," These issues result in significantly lower signal-to-noise ratios in the DEIMOS images, but they were not considered in Figures 4 and 6." + Therefore it is likely that our spectra at >9000 aare not deep enough to ideutify eenisson lines., Therefore it is likely that our spectra at $>9000$ are not deep enough to identify emisson lines. + On the other haud. we cannot rule out the possibility that there are uo :>6.6 LDCs with strong eniüssion in the covered region.," On the other hand, we cannot rule out the possibility that there are no $z>6.6$ LBGs with strong emission in the covered region." +Due to the increasing ueutral fraction of IGM at z>6. the deusity of LAEs at the bright cud may decline rapidly towards higher redshifts (e.g.Iashikawaetal.2011:Peutericcict2011:Scheukeretal. 2011).,"Due to the increasing neutral fraction of IGM at $z>6$, the density of LAEs at the bright end may decline rapidly towards higher redshifts \citep[e.g.][]{kas11,pen11,sch11}." +. Iu this paper we have reported the discovery of 19 LBGs from our deep spectroscopic observations of a saluple of 2>6 LBG candidates in SDF., In this paper we have reported the discovery of 19 LBGs from our deep spectroscopic observations of a sample of $z>6$ LBG candidates in SDF. + The candidates were selected using the traditional dropout technique from an ultra-deep z/baud image., The candidates were selected using the traditional dropout technique from an ultra-deep $z'$ -band image. + This image. with a total iuteeration time of 29 hours. enables us to select ealaxics down to :/=27 mag over a wide field.," This image, with a total integration time of 29 hours, enables us to select galaxies down to $z'=27$ mag over a wide field." + The follow-up spectroscopy was made with Keck DEIMOS., The follow-up spectroscopy was made with Keck DEIMOS. + The 19 LBGs span a redshift range of 6€:x6.1 and a inaenitude range of 25.1<το27., The 19 LBGs span a redshift range of $6 \le z \le 6.4$ and a magnitude range of $25.1 \le z' \le 27$. + They have moderate eenission line «οποίας compared to those in LAEs at simular redshifts., They have moderate emission line strengths compared to those in LAEs at similar redshifts. + The median value of rest-frame EEWs is ~50À.. aud four LBCs have EWs 7100À.," The median value of rest-frame EWs is $\sim50$, and four LBGs have EWs $>100$." +". This well-defined spectroscopic LBC sample spans a UV hnuninositv range of 0.6~5Li across the UV characteristic huninositv Li aud a llinniuosity range of 0.3~3£p, across the ccharacteristie Inninositv Zj,,.", This well-defined spectroscopic LBG sample spans a UV luminosity range of $0.6\sim5\ L^{\ast}_{\rm UV}$ across the UV characteristic luminosity $L^{\ast}_{\rm UV}$ and a luminosity range of $0.3\sim3\ L^{\ast}_{\rm Ly\alpha}$ across the characteristic luminosity $L^{\ast}_{\rm Ly\alpha}$. + It thus provides uique constraints on both the UV. aud LLFs at :>6., It thus provides unique constraints on both the UV and LFs at $z>6$. + We correct for sample iuconipleteuess from) source detection. galaxy candidate selection. aud spectroscopic identification.," We correct for sample incompleteness from source detection, galaxy candidate selection, and spectroscopic identification." + In particular. for the UV LF we asstune that the distribution of EEWsat: ~6 is the same as that at 2~3.," In particular, for the UV LF we assume that the distribution of EWs at $z\sim6$ is the same as that at $z\sim3$." + We then calculate the volume deusitv of the galaxies aud estimate the LFs at (2)~6.2 using a Schechter function., We then calculate the volume density of the galaxies and estimate the LFs at $\langle z\rangle \sim6.2$ using a Schechter function. + We fiud that our measurement of the UV. LF is consistent with the results of previous studies based on photometric LBC saluples at 5«iocτν including samples from: TDF aud URIDSS UDF.," We find that our measurement of the UV LF is consistent with the results of previous studies based on photometric LBG samples at $5 50%) of the infrared Iuninositv is eencrated in reeions of sizes raneing frou, ppc to a Lkkpe. with the imclear starbursts often dominating the iuid- lainesity.","2001) have obtained high resolution mid-infrared observations of LIRGs and reported that a substantial fraction $>50\,\%$ ) of the infrared luminosity is generated in regions of sizes ranging from pc to a kpc, with the nuclear starbursts often dominating the mid-infrared luminosity." + They also concluded. that the 12pan chussion traces the current sites ofdusty hnuuinous star formation.," They also concluded that the $12\,\mu$ m emission traces the current sites of luminous star formation." + This can be confirmed by the good COLTCSPOleence between the mid-infrared aud the Pana Cluission morphologies of the galaxies in common with our study: Arp 299. VV ας NGC 1611.," This can be confirmed by the good correspondence between the mid-infrared and the $\alpha$ emission morphologies of the galaxies in common with our study: Arp 299, VV 114 and NGC 1614." + Tn Table 2 we list the otal Πα Iunuinositv from the detected reeions. along with the percentage of the Pan cussion «ποιαπιο in the nuclei of galaxies.," In Table 2 we list the total $\alpha$ luminosity from the detected regions, along with the percentage of the $\alpha$ emission originating in the nuclei of galaxies." +" These fractious shou«4 be considered onlv as lower hits as the compact nuclear regions are usually iore reddened than the regiois where the more diffuse regions are located (see ο, AAIIO0: Lippari et al."," These fractions should be considered only as lower limits as the compact nuclear regions are usually more reddened than the regions where the more diffuse regions are located (see e.g., AAH00; pari et al." + 2000: Scoville et al., 2000; Scoville et al. + 2000: see also Murphy et al., 2000; see also Murphy et al. + 2001 for ULIRCs)., 2001 for ULIRGs). + Nevertheless. 1 is apparent that the nuclear to total ων ratios vary significantly from system to svsteni. aud show simuiaritics with the same ratios computed for the infrared Iuminosities (Soifer et al.," Nevertheless it is apparent that the nuclear to total emission ratios vary significantly from system to system, and show similarities with the same ratios computed for the infrared luminosities (Soifer et al." + 2001)., 2001). + In the isolated svstenis most of the star formation is occurring in the disks of the galaxies. whereas in the interacting/mereine," In the isolated systems most of the star formation is occurring in the disks of the galaxies, whereas in the interacting/merging" +Clearly. since the compact object continuously accretes matter from its companion. the svslenm is never precisely in equilibrium.,"Clearly, since the compact object continuously accretes matter from its companion, the system is never precisely in equilibrium." + However. (he accretion timescale is longer than that of most of the relevant physical processes. so (he steady-state approximation is acceptable.," However, the accretion timescale is longer than that of most of the relevant physical processes, so the steady-state approximation is acceptable." + In (liis case. X becomes a good Lagrangian variable. and so the use of X as our independent variable is justified.," In this case, $\Sigma$ becomes a good Lagrangian variable, and so the use of $\Sigma$ as our independent variable is justified." + Stable and/or unstable hydrogen and helium burning produces most of the carbon that ultimately triggers a superburst., Stable and/or unstable hydrogen and helium burning produces most of the carbon that ultimately triggers a superburst. + As of this writing. each svstem with an observed superburst also undergoes normal Type I X-ray. bursts (Ixuulkers2004:intZaneetal.2004a).," As of this writing, each system with an observed superburst also undergoes normal Type I X-ray bursts \citep{K04,intZCC04}." +. The carbon vield resulting from both stable helium burning and unstable burning curing normal bursts is uncertain (see 844)., The carbon yield resulting from both stable helium burning and unstable burning during normal bursts is uncertain (see 4). + To account for (his uncertainty. we introduce a [ree parameter Ct. the fraction of hydrogen and helium that ultimately burns to carbon.," To account for this uncertainty, we introduce a free parameter $C_{\mathrm{f}}$, the fraction of hydrogen and helium that ultimately burns to carbon." + Equation (19) thus beconies so al the base of the accreted aver. ΖονοseCy.," Equation (19) thus becomes so at the base of the accreted layer, $Z_{\mathrm{CNO}} \approx C_{\mathrm{f}}$." + Clearly this is an approximation., Clearly this is an approximation. + llowever. it enables us to model the composition of the accreted laver as well as possible.," However, it enables us to model the composition of the accreted layer as well as possible." + Specifically. we can model the composition of both the hyvdrogen- and. helium-rich. upper region of the outer crust and the carbon-rich lower region to high accuracy.," Specifically, we can model the composition of both the hydrogen- and helium-rich upper region of the outer crust and the carbon-rich lower region to high accuracy." + Additionally. the laver in which the hvedrogen and helium burn to carbon is most likely very narrow in the column density X. so (his transition region is inconsequential to (he thermal and lvcrostatic profiles of the outer crust.," Additionally, the layer in which the hydrogen and helium burn to carbon is most likely very narrow in the column density $\Sigma$, so this transition region is inconsequential to the thermal and hydrostatic profiles of the outer crust." +where the polarization goes to zero between the top two regions.,where the polarization goes to zero between the top two regions. + Lhe highest levels of fractional polarization occur at the bottom and. top. while the lowest one occurs in he middle.," The highest levels of fractional polarization occur at the bottom and top, while the lowest one occurs in the middle." + The polarization structure at 5 Cllz shows hat the magnetic fields appear alternately orthogonal and aligned down the jet. with a signature of bifurcating to he opposite sides from the local jet spine.," The polarization structure at 5 GHz shows that the magnetic fields appear alternately orthogonal and aligned down the jet, with a signature of bifurcating to the opposite sides from the local jet spine." + ALL these racliative features can be explained either with a large scale of helical magnetic field. present within the jet. or with angled. magnetic fields compressed. ancl shearecl down the jet.," All these radiative features can be explained either with a large scale of helical magnetic field present within the jet, or with tangled magnetic fields compressed and sheared down the jet." + Further polarimetric VLBI observations are required with sullicient high resolution and sensitivity at. multiple wavelengths to further determine if the magnetic field. is velical or not., Further polarimetric VLBI observations are required with sufficient high resolution and sensitivity at multiple wavelengths to further determine if the magnetic field is helical or not. +" The authors co appreciate the anonymous referee. for insightful. comments anc constructive suggestions. which were ereatIv helpful in improving our paper. we also thank ""pof. Jiang for helpful discussions."," The authors do appreciate the anonymous referee for insightful comments and constructive suggestions, which were greatly helpful in improving our paper, we also thank Prof. Jiang for helpful discussions." + This work was supported »w the National Natural Science. Foundation of China (orants 10573029. 10625314. 10633010 and 10821302) and he Ixnowledge Innovation Program of the Chinese Academy of Sciences (Grant No.," This work was supported by the National Natural Science Foundation of China (grants 10573029, 10625314, 10633010 and 10821302) and the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No." + IXJOCN2-YW-T03). by the Science and ‘Technology Commission. of Shanghai Municipality 09Z111437400) ancl the Scientific Research Foundation or Returned Scholars. Ministry of Eclucation of China (9020090306). bv the Program of Shanghai Subject Chief Scientist (06ND14024) and the Na Basic ne Development Program of China m(No.," KJCX2-YW-T03), by the Science and Technology Commission of Shanghai Municipality (09ZR1437400) and the Scientific Research Foundation for Returned Scholars, Ministry of Education of China (9020090306), by the Program of Shanghai Subject Chief Scientist (06XD14024) and the National Key Basic Research Development Program of China (No." + unNe2007€D815405)., 2007CB815405). + MihiThis vaper mace use of data. Cron ;niversity. of tadio Astronomy Observatory. supported by the University of Michigan and the National Science. Foundation.," This paper made use of data from the University of Michigan Radio Astronomy Observatory, supported by the University of Michigan and the National Science Foundation." + ZOS acknowledges the support by the One-HEundred-Talent Program of Chinese Academy of Sciences., ZQS acknowledges the support by the One-Hundred-Talent Program of Chinese Academy of Sciences. +"where Ax, is the linear Eulerian separation. as eiven by Eq.(1)).","where $\Delta \vx_L$ is the linear Eulerian separation, as given by \ref{Zeldef}) )." + Thus. this second model oulv differs frou the Zeldovich αναος when the parallel linear Euleriau separation. Awery. is negative. in which case we set it equal to zero.," Thus, this second model only differs from the Zeldovich dynamics when the parallel linear Eulerian separation, $\Delta x_{L1}$, is negative, in which case we set it equal to zero." +" This is thus a simplified version of the ""adhesion model”. as once Aer reaches zero. it remaius equal to zero forever."," This is thus a simplified version of the “adhesion model”, as once $\Delta x_{L1}$ reaches zero, it remains equal to zero forever." +" However. the model (16)) cannot ο explicitly derived from the ""adhesion model. since we ake ucither transverse directions nor larger scales iuto account."," However, the model \ref{Deltax-def}) ) cannot be explicitly derived from the “adhesion model”, since we take neither transverse directions nor larger scales into account." + Therefore. we use the more generic name “sticky nodel”. to refer to this sticking along one direction for the dr separatiou.," Therefore, we use the more generic name “sticky model”, to refer to this sticking along one direction for the pair separation." +" Itis clear that the condition Avy<) where the wo models differ. is oulv a sufficient condition for shell crossing. but it is uot necessary,"," Itis clear that the condition $\Delta x_{L1}<0$, where the two models differ, is only a sufficient condition for shell crossing, but it is not necessary." + Thus. it is a local condition that does not take the “cloud-in-cloud” problem into account: even though wo shell crossing seenis to have appeared on scale g vet. it may happen that his reeddn Iswih enclosed within a larger domain of size L tha has greatly collapsed. so that particles in the smaller domain have actually experienced. shell crossing (?)..," Thus, it is a local condition that does not take the “cloud-in-cloud” problem into account: even though no shell crossing seems to have appeared on scale $q$ yet, it may happen that this region is enclosed within a larger domain of size $L$ that has already collapsed, so that particles in the smaller domain have actually experienced shell crossing \citep{Bond1991}." + Iu erus of the Lagrangian potential gp. which chues the Lagrangian uappiug. q»x. through Eq.(39)). the absence of shell crossing on a small domain of size q means that qr is equal ο its convex hull iu this domain (777)..," In terms of the Lagrangian potential $\varphi_L$, which defines the Lagrangian mapping, $\vq\mapsto\vx$, through \ref{xq}) ), the absence of shell crossing on a small domain of size $q$ means that $\varphi_L$ is equal to its convex hull in this domain \citep{Vergassola1994,Bec2007,BernardeauVal2010b}." +" However. he coustruction of the couvex hull is a elobal problem. as one must cousider the behavior of z5(q) over all the space. thereby taking into accouu the ""cloud-du-cloud xoblemi. while in the definition of the inodel (16)) we oulv check a weaker coudition. since we onlv consider he two poiuts O aud q."," However, the construction of the convex hull is a global problem, as one must consider the behavior of $\varphi_L(\vq)$ over all the space, thereby taking into account the “cloud-in-cloud” problem, while in the definition of the model \ref{Deltax-def}) ) we only check a weaker condition, since we only consider the two points $0$ and $\vq$." + This means that we somewhat underestimate the effects of she] crossing. but we cau expect to obtain a reasonable estimate of their amplitude IO‘vause the probability of collaoe decreases on larger scales and we perform a statisticalintegration over the aneles of qin Eq.(7)).," This means that we somewhat underestimate the effects of shell crossing, but we can expect to obtain a reasonable estimate of their amplitude because the probability of collapse decreases on larger scales and we perform a statisticalintegration over the angles of $\vq$ in \ref{Pkxq}) )." + From the previous discussiows. the csfiekv model” (16)) and the Zeldovich dvuaiiics (1)) coincide before shell crossing. since then we have Avy41270.," From the previous discussions, the “sticky model” \ref{Deltax-def}) ) and the Zeldovich dynamics \ref{Zeldef}) ) coincide before shell crossing, since then we have $\Delta x_{L1}>0$." + This implics that both theories coicide at all oxers of the perturbation theory: that is. they show the same expansions (31)) aud (36)) over powers of P.," This implies that both theories coincide at all orders of the perturbation theory; that is, they show the same expansions \ref{Pnstd}) ) and \ref{Pn-sigv}) ) over powers of $P_L$ ." + Towever. hev differ through uonperturbative terms. which arise youn them different behaviors after shell crossing.," However, they differ through nonperturbative terms, which arise from their different behaviors after shell crossing." +" From Eq.C16)) we obtain AW,=max(AW;;.q). for q=4e,. and Ae)dn where we factorized the result associated with the usual Zeldovich dyvuamics (8)) iu the first two terms and we introduced the variance of the linear longitudinal displacement. PrGn)(1) = 205 244043] Matqi."," From \ref{Deltax-def}) ) we obtain $\Delta\Psi_1=\max(\Delta\Psi_{L1},-q)$, for $\vq=q \, \ve_1$, and , where we factorized the result associated with the usual Zeldovich dynamics \ref{Pksq}) ) in the first two terms and we introduced the variance of the linear longitudinal displacement, = = 2 P_L(w) = _v^2 -2 I_0(q) + 4 I_2(q)." + Separating the coutribution fom AWr4 we obtain for the last two terms of Eq.(17)). —qq . qordtu cM) yu rieht)) -lg rieht)). where erfe(:) is the complementary error fiction (extended to the complex plane). orte((z) Then. substituting iuto Eqs.(17)) aud (7)). we can see that the density power spectrum of the ‘sticky model. Pieick (kh). is equal| to the usual Zeldovich power spectrum obtained in Sect.," Separating the contribution from $\Delta\Psi_{L1}<-q$, we obtain for the last two terms of \ref{mean-kx}) ), = 1+ ( - ) = 1 + ) - ), where $\erfc(z)$ is the complementary error function (extended to the complex plane), (z) = t.Then, substituting into \ref{mean-kx}) ) and \ref{Pkxq}) ), we can see that the density power spectrum of the “sticky model”, $\Psticky(k)$ , is equal to the usual Zeldovich power spectrum obtained in Sect." + 2.1. plus a correction terii Po. (A). (tk," \ref{Non-linear-Zeldovich} + plus a correction term $\Psc(k)$ , (k) = (k) + (k) , with (k) = ) - ) ." +dwarfs within this distance would require a similar amount of time to the existing observations of ultracool dwarfs. but it will significantly increase the chance of detecting rare flaring objects.,"dwarfs within this distance would require a similar amount of time to the existing observations of ultracool dwarfs, but it will significantly increase the chance of detecting rare flaring objects." +" Coupled with simultaneous radio observations. this survey will also allow us to better assess the radio/X-ray correlation and its breakdown,"," Coupled with simultaneous radio observations, this survey will also allow us to better assess the radio/X-ray correlation and its breakdown." + Beyond additional observations. progress in. our understanding of the decline in X-ray emission and the breakdown of the radio/X-ray correlation requires detailed theoretical studies of coronal conditions in ultracool dwarfs.," Beyond additional observations, progress in our understanding of the decline in X-ray emission and the breakdown of the radio/X-ray correlation requires detailed theoretical studies of coronal conditions in ultracool dwarfs." + The existing work (Mohantyetal.2002) investigated atmospheric conditions that are only applicable to the stellar chromosphere. and led to the conclusion that dissipation of the magnetic field 1s suppressed by the increasing neutrality of the stellar atmospheres.," The existing work \citep{mbs+02} + investigated atmospheric conditions that are only applicable to the stellar chromosphere, and led to the conclusion that dissipation of the magnetic field is suppressed by the increasing neutrality of the stellar atmospheres." + However. particle. acceleration in the magnetic fields appears to remain efficient at least to mid-L dwarfs as evidenced by radio observations. suggesting that in the corona the magnetic fields may couple effectively to the tenuous atmosphere.," However, particle acceleration in the magnetic fields appears to remain efficient at least to mid-L dwarfs as evidenced by radio observations, suggesting that in the corona the magnetic fields may couple effectively to the tenuous atmosphere." + We thank the Chandra. Gemini. and VLA. schedulers for their invaluable help in coordinating these observations.," We thank the Chandra, Gemini, and VLA schedulers for their invaluable help in coordinating these observations." + This work has made use of the SIMBAD database. operated at CDS. Strasbourg. France.," This work has made use of the SIMBAD database, operated at CDS, Strasbourg, France." + It is based in part on observations obtained at the Gemini Observatory. which is operated by the Association of Universities for Research in Astronomy. Inc.. under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science. Foundation. (United. States). the Science and Technology Facilities Council (United Kingdom). the National Research Council (Canada). CONICYT (Chile). the Australian Research Council (Australia). CNPq (Brazil) and CONICET (Argentina).," It is based in part on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil) and CONICET (Argentina)." + Data from the UVOT instrument on Swift were used in this work., Data from the UVOT instrument on Swift were used in this work. + Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number G08-9013A issued by the Chandra X-ray Observatory Center. which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics. Space Administration under contract NAS8-03060.," Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number G08-9013A issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060." + In addition to the observations presented in this paper. we retrieved from the archive observations of the M8 dwarf 4412-31 that were obtained as part of program 09200198 (PI: Stelzer) on 2007 December 22.95 UT for a total of 40.6 ks.," In addition to the observations presented in this paper, we retrieved from the archive observations of the M8 dwarf 412-31 that were obtained as part of program 09200198 (PI: Stelzer) on 2007 December 22.95 UT for a total of 40.6 ks." + This object is located at a distance of 14.6370.1 pe (Reid&Cruz2002). and has a bolometrie luminosity of Lu;10779 L....," This object is located at a distance of $14.6\pm 0.1$ pc \citep{rc02}, and has a bolometric luminosity of $L_{\rm bol}\approx 10^{-3.26}$ $_\odot$." + It was previously detected with with a quiescent luminosity of Lyz1.6«107 erg s. and a flare that peaked at Lyz4.6<1077 ere s! (Stelzeretal.2006b).," It was previously detected with with a quiescent luminosity of $L_X\approx 1.6\times 10^{27}$ erg $^{-1}$ , and a flare that peaked at $L_X\approx 4.6\times 10^{29}$ erg $^{-1}$ \citep{ssm+06}." +. We analyzed the data using CLAO version 3.4. and extracted counts in a 3” radius circle centered on the position of 4412-3," We analyzed the data using CIAO version 3.4, and extracted counts in a $3''$ radius circle centered on the position of 412-31." + The source ts clearly detected. with a total of 239 counts in the 0.2—5 keV range. compared to about | count expected from the background.," The source is clearly detected, with a total of 239 counts in the $0.2-5$ keV range, compared to about 1 count expected from the background." + To determine the X-ray flux we fit the spectrum using VIT., To determine the X-ray flux we fit the spectrum using V11. + We restrict the fit to the energy range 0.3—3 keV over which most of the counts are detected., We restrict the fit to the energy range $0.3-3$ keV over which most of the counts are detected. + Using a single-temperature Raymond-Smith model with the abundance set to 0.3. we find a poor fit to the data (47—22 for 15 degrees of freedom) with a temperature of kTz0.8 keV (Figure Aaa).," Using a single-temperature Raymond-Smith model with the abundance set to 0.3, we find a poor fit to the data $\chi^2=22$ for 15 degrees of freedom) with a temperature of $kT\approx 0.8$ keV (Figure \ref{fig:lp412-31_x}a a)." + A significantly improved fit (425.5 for 13 degrees of freedom) is obtained with a two-temperature Raymond-Smith model. with temperatures of ATτε0.3 and =I keV (Figure Abb).," A significantly improved fit $\chi^2=5.5$ for 13 degrees of freedom) is obtained with a two-temperature Raymond-Smith model, with temperatures of $kT\approx +0.3$ and $\approx 1$ keV (Figure \ref{fig:lp412-31_x}b b)." + The resulting flux of 4412-31 for this model is 2.0«1077 erg em s! in the 0.3-3 keV energy range (and about 15% lower for the 0.5— keV energy range)., The resulting flux of 412-31 for this model is $2.0\times 10^{-14}$ erg $^{-2}$ $^{-1}$ in the $0.3-3$ keV energy range (and about $15\%$ lower for the $0.5-3$ keV energy range). + Thus. the X-ray luminosity is 5.1«107 erg s7!. and the ratio relative to the bolometric luminosity ts Ly/Loop371075.," Thus, the X-ray luminosity is $5.1\times 10^{26}$ erg $^{-1}$ , and the ratio relative to the bolometric luminosity is $L_X/L_{\rm bol}\approx 10^{-3.6}$." + This value is about a factor of 3 times lower than the quiescent luminosity measured with (Stelzeretal.2006b)., This value is about a factor of 3 times lower than the quiescent luminosity measured with \citep{ssm+06}. +. 4412-31 was also observed with the VLA at 8.46 GHz as part of program AS879 on four separate occasions (2006 October 31 and 2006 November 5. 7. and 9 for a total of about 13.4 hours). and as part of program S90198 simultaneously with the observation.," 412-31 was also observed with the VLA at 8.46 GHz as part of program AS879 on four separate occasions (2006 October 31 and 2006 November 5, 7, and 9 for a total of about 13.4 hours), and as part of program S90198 simultaneously with the observation." + We obtained the publie data from the archive and processed the observations in the manner described in refsec:rad.., We obtained the public data from the archive and processed the observations in the manner described in \\ref{sec:rad}. +" The combined 2006 observations reveal a possible weak source coincident with the position of 4412-31. with a flux of E,237ΤΙ gy (using only the two longest observations. which account for 75% of the data. we find F,,245+12 ji y)."," The combined 2006 observations reveal a possible weak source coincident with the position of 412-31, with a flux of $F_\nu=37\pm 11$ $\mu$ Jy (using only the two longest observations, which account for $75\%$ of the data, we find $F_\nu=45\pm 12$ $\mu$ Jy)." +" In the subsequent simultaneous observation we do not detect any emission at the position of 4412-31. with a 30 upper limit of F,=25 jy."," In the subsequent simultaneous observation we do not detect any emission at the position of 412-31, with a $3\sigma$ upper limit of $F_\nu\lesssim 25$ $\mu$ Jy." + This indicates that the source either fluctuated in brightness by at least a factor of 2. or that the initial weak source Was spurious.," This indicates that the source either fluctuated in brightness by at least a factor of 2, or that the initial weak source was spurious." + Theresulting limit on the radio luminosity is ματ6.4«1077 erg s! Hz.," Theresulting limit on the radio luminosity is $L_{\rm +\nu,rad}\lesssim 6.4\times 10^{12}$ erg $^{-1}$ $^{-1}$." + Combining the X-ray and radio results. we find a limit of LiμιαωνX10777 Hz!. about a factor of 40 times higher than the expected value (Equation 3)).," Combining the X-ray and radio results, we find a limit of $L_{\rm +\nu,rad}/L_X\lesssim 10^{-14.4}$ $^{-1}$, about a factor of 40 times higher than the expected value (Equation\ref{eqn:lxlr}) )." +In January 2004 a new reflection nebula (MeNeil's Nebula) appeared in the 11640 dark cloud of the BB molecular cloud complex (McNeiletal. 2004)).,In January 2004 a new reflection nebula (McNeil's Nebula) appeared in the 1640 dark cloud of the B molecular cloud complex \cite{McNeil}) ). + OOri. whose outburst (—4mmag in the I-band) caused the appearance of MecNeil’s Nebula. is a low-mass pre-main sequence object (Bricefioetal.2004.. Abrahametal. 2004a)).," Ori, whose outburst $\sim$ mag in the I-band) caused the appearance of McNeil's Nebula, is a low-mass pre-main sequence object \cite{Briceno}, \cite{abraham04a}) )." + Its eruptive behaviour suggests that OOri 1s. either an FU Orionis (FUor) or an EX Lupi (EXor) type object. or maybe an intermediate-type object between FUors and EXors (Muzerolleetal.2005.. Kóspáletal. 2005)).," Its eruptive behaviour suggests that Ori is either an FU Orionis (FUor) or an EX Lupi (EXor) type object, or maybe an intermediate-type object between FUors and EXors \cite{Muzerolle}, \cite{kospal}) )." + Near-infrared colour maps show that the source is embedded in an elongated disk-like structure. whose size is approximately 7000 AU. and its inclination (the angle between the normal of the disk and the line of sight) is about 60° (Acosta-Pulido et al..," Near-infrared colour maps show that the source is embedded in an elongated disk-like structure, whose size is approximately 7000 AU, and its inclination (the angle between the normal of the disk and the line of sight) is about $^{\circ}$ (Acosta-Pulido et al.," + in prep.)., in prep.). + The object had been gradually fading until October 2005. when the eruption rapidly ended (Kóspáletal. 2005)).," The object had been gradually fading until October 2005, when the eruption rapidly ended \cite{kospal}) )." + Both FUors and EXors are low-mass pre-main sequence stars which exhibit optical brightening of several magnitudes., Both FUors and EXors are low-mass pre-main sequence stars which exhibit optical brightening of several magnitudes. + FUors are characterised by outbursts of several decades. while EXors exhibit repetitive outbursts on monthly timescale.," FUors are characterised by outbursts of several decades, while EXors exhibit repetitive outbursts on monthly timescale." + The eruptive mechanism of both types is thought to be a rapid temporal increase of the disk accretion rate (Hartmann&Kenyon1996 and references therein)., The eruptive mechanism of both types is thought to be a rapid temporal increase of the disk accretion rate \cite{HK96} and references therein). + In this model the young star is accreting a substantial amount of material from the parent molecular cloud core (10.° ./yr) via a circumstellar disk., In this model the young star is accreting a substantial amount of material from the parent molecular cloud core $10^{-6}$ $_{\odot}$ /yr) via a circumstellar disk. + The infalling matter piles up in the inner disk until its surface density — and thus opacity — becomes high enough to switch on a thermal instability leading to the dramatically increased aceretion rate (10.! — 10? ./yr)., The infalling matter piles up in the inner disk until its surface density – and thus opacity – becomes high enough to switch on a thermal instability leading to the dramatically increased accretion rate $10^{-4}$ – $10^{-3}$ $_{\odot}$ /yr). + It is still debated whether perturbation due to a close companion is needed to trigger the outburst. and it is also an open question whether all eruptive stars have companions (e.g. Wangetal.2004.. Reipurth&Aspin 2004b)).," It is still debated whether perturbation due to a close companion is needed to trigger the outburst, and it is also an open question whether all eruptive stars have companions (e.g. \cite{wang04}, \cite{RA04b}) )." + The geometrical structure of the inner part of the circumstellar material in. eruptive systems — though it is probably closely related to the outburst mechanism — is still unclear., The geometrical structure of the inner part of the circumstellar material in eruptive systems – though it is probably closely related to the outburst mechanism – is still unclear. + Most models assume that apart from. the circumstellar disk. there is an infalling remnant envelope of the molecular cloud core. whose inner radius 1s of the order of a few AU (Kenyon&Hartmann1991.. Turneretal.1997)).," Most models assume that apart from the circumstellar disk, there is an infalling remnant envelope of the molecular cloud core, whose inner radius is of the order of a few AU \cite{KH91}, \cite{Turner}) )." + This envelope supplies the disk with the material needed for the strong eruptions., This envelope supplies the disk with the material needed for the strong eruptions. + In the case of OOri. Muzerolle et al. (," In the case of Ori, Muzerolle et al. (" +2005) proposed that an optically thin envelope would be necessary to explain the flat infrared spectral energy distribution.,2005) proposed that an optically thin envelope would be necessary to explain the flat infrared spectral energy distribution. + However. a direct detection of such envelopes around eruptive stars has not been attempted so far.," However, a direct detection of such envelopes around eruptive stars has not been attempted so far." + In this paper we report on AU-scale observations of VI647OO0rn at 1θμῃπι with MIDI. the mid-infrared interferometric instrument mounted at the Very Large Telescope Interferometer (VLTI) of ESO's Paranal Observatory (Leinertetal. 2003)).," In this paper we report on AU-scale observations of Ori at $\mu$ m with MIDI, the mid-infrared interferometric instrument mounted at the Very Large Telescope Interferometer (VLTI) of ESO's Paranal Observatory \cite{Leinert03}) )." + We present. spectrally resolved interferometric visibility points. and analyse the data with special emphasis on the structure of the circumstellar material and on the signature of a nearby companion.," We present spectrally resolved interferometric visibility points, and analyse the data with special emphasis on the structure of the circumstellar material and on the signature of a nearby companion." + V1647 Ort was succesfully observed with MIDI on the UT3-UT4 baseline of the VLTI on March 2. 2005.," V1647 Ori was succesfully observed with MIDI on the UT3-UT4 baseline of the VLTI on March 2, 2005." +" The projected baseline length was 56mm with a PÁZII2"".", The projected baseline length was m with a $^{\circ}$. +" Due to the lack of adequate guide star.MACAO!.. could not support the observation. which was thus affected by the seeing 1.0"" at the time of the observation)."," Due to the lack of adequate guide star, could not support the observation, which was thus affected by the seeing $''$ at the time of the observation)." + Single telescope N-band spectra were also taken with both UT3 and UT4., Single telescope N-band spectra were also taken with both UT3 and UT4. + Additional N-band spectra were obtained on December 31. 2004 (then the interferometrie part of the observation failed).," Additional N-band spectra were obtained on December 31, 2004 (then the interferometric part of the observation failed)." + On March 2. 337160 was observed as a calibrator. while on December 31 observations of 550778. performed 2 hours later. were used.," On March 2, 37160 was observed as a calibrator, while on December 31 observations of 50778, performed 2 hours later, were used." + The obtained data set consists of acquisition images with the N8.7 filter. sm low resolution spectra (R=30). and interferometric measurements.," The obtained data set consists of acquisition images with the N8.7 filter, $\mu$ m low resolution spectra (R=30), and interferometric measurements." + In. the data reduction we followed the general processing scheme as described by Leinert et al. (, In the data reduction we followed the general processing scheme as described by Leinert et al. ( +2004).,2004). + The measured raw visibilities of OOri were divided by raw visibilities obtained from the 337160 data., The measured raw visibilities of Ori were divided by raw visibilities obtained from the 37160 data. + The observations were reduced 1n two, The observations were reduced in two +"Low SFR systems are easier to observe locally, while their detection efficiency decreases rapidly at larger distances.","Low SFR systems are easier to observe locally, while their detection efficiency decreases rapidly at larger distances." +" On the other hand, high SFR hosts are easily observed at larger distances because of their high luminosities."," On the other hand, high SFR hosts are easily observed at larger distances because of their high luminosities." + Another element that needs to be considered is that environments with SFRs comparable to the BCG ones are rare in the local volume (< 20 Mpc)., Another element that needs to be considered is that environments with SFRs comparable to the BCG ones are rare in the local volume $<$ 20 Mpc). +" In this case, the position of the M83 starburst nucleus at about 5 Mpc and [>20 gives evidence that high star formation efficiency are also observed in systems where blending and crowding are not an issue."," In this case, the position of the M83 starburst nucleus at about 5 Mpc and $\Gamma > 20$ gives evidence that high star formation efficiency are also observed in systems where blending and crowding are not an issue." +" If we restrict the comparison to the BCG sample, we do not see any difference between the distant and nearby systems, supporting the idea that blending is not severe in either of the 3 most distant galaxies."," If we restrict the comparison to the BCG sample, we do not see any difference between the distant and nearby systems, supporting the idea that blending is not severe in either of the 3 most distant galaxies." + LROO introduced the specific luminosity for young star clusters defined as TL=100Lectusters/Znost., LR00 introduced the specific luminosity for young star clusters defined as $_{\textnormal{L}}=100L_{\textnormal{clusters}}/L_{\textnormal{host}}$. + TL gives an estimate of the fraction of the total galaxy light that is produced by stars in clustered regions., $_{\textnormal{L}}$ gives an estimate of the fraction of the total galaxy light that is produced by stars in clustered regions. +" Using a sample of galaxies which includes quiescent spirals and star-forming dwarf systems, LROO found that the specific luminosity in the U band, Τι (U) and the SFR of the hosts were positively correlated."," Using a sample of galaxies which includes quiescent spirals and star-forming dwarf systems, LR00 found that the specific luminosity in the $U$ band, $_{\textnormal{L}}$ (U) and the SFR of the hosts were positively correlated." +" We present the same sample in Figure 5,, including the BCG data points."," We present the same sample in Figure \ref{tlu-sfr}, including the BCG data points." + We estimate Lclusters using only clusters for which a SED fit has been performed., We estimate $L_{\textnormal{clusters}}$ using only clusters for which a SED fit has been performed. +" The values of Τι (U), and for two other filters, FUV and B, are listed in Table 2.."," The values of $_{\textnormal{L}}$ (U), and for two other filters, $FUV$ and $B$, are listed in Table \ref{table-obs2}." + The TL(U) and the Usgrr are higher in BCGs., The $_{\textnormal{L}}$ (U) and the $\Sigma_\mathrm{SFR}$ are higher in BCGs. +" In general, the trend suggests that the fraction of star formation happening in clusters is important and increases as function of the SFR."," In general, the trend suggests that the fraction of star formation happening in clusters is important and increases as function of the SFR." +" To understand why we observe a much higher fraction of TL(U) in BCGs than in spiral galaxies, we need to look at the different star formation histories in these two classes of hosts and not only at the SFRs."," To understand why we observe a much higher fraction of $_{\textnormal{L}}$ (U) in BCGs than in spiral galaxies, we need to look at the different star formation histories in these two classes of hosts and not only at the SFRs." +" In general, we observe that the young star clusters in BCGs are preferentially clustered in clumps, in agreement with observations of high correlations in position as function of the age among young systems."," In general, we observe that the young star clusters in BCGs are preferentially clustered in clumps, in agreement with observations of high correlations in position as function of the age among young systems." +" Studies of spatial correlation among field stars, associations, and clusters show a higher clustering for younger samples, and a clear smoothing of the older structures (Gielesetal.2008;Bastian2009,2011).."," Studies of spatial correlation among field stars, associations, and clusters show a higher clustering for younger samples, and a clear smoothing of the older structures \citep{2008MNRAS.391L..93G, 2009MNRAS.392..868B, 2010arXiv1010.1837B}." + 'The star formation in spiral systems has proceeded more or less constantly for a long lapse of time., The star formation in spiral systems has proceeded more or less constantly for a long lapse of time. + Therefore cluster disruption has worked in favour of populating the stellar fields which form the bulk of the optical luminosity in these systems., Therefore cluster disruption has worked in favour of populating the stellar fields which form the bulk of the optical luminosity in these systems. +" In BCGs, the starburst has been acting for rather short timescales (~40 Myr), suggesting that cluster disruption (mostly infant mortality) has not been effective."," In BCGs, the starburst has been acting for rather short timescales $\sim 40$ Myr), suggesting that cluster disruption (mostly infant mortality) has not been effective." +" Looking at the values listed in Table 2,, we see that the fraction of light produced by the star clusters increases at shorter wavelengths and contributes significantly to the UV and U luminosities of the BCGs."," Looking at the values listed in Table \ref{table-obs2}, we see that the fraction of light produced by the star clusters increases at shorter wavelengths and contributes significantly to the UV and U luminosities of the BCGs." +" Therefore, it suggests that clustered regions in galaxies at redshift ~2- 3, with metallicities similar to the BCGs, contribute to a considerable fraction of the UV-rest frame light."," Therefore, it suggests that clustered regions in galaxies at redshift $\sim$ 2-3, with metallicities similar to the BCGs, contribute to a considerable fraction of the UV-rest frame light." +" In studies of Lyman break galaxy analogs at redshift between ~0.1 and 0.2, Overzieretal.(2008) observed super starburst compact regions which dominate the UV light of these targets."," In studies of Lyman break galaxy analogs at redshift between $\sim$ 0.1 and 0.2, \citet{2008ApJ...677...37O} observed super starburst compact regions which dominate the UV light of these targets." + Similarly compact clumps are also observed at redshift >1 galaxies (Elmegreenetal.2009;ForsterSchreiber 2011)..," Similarly compact clumps are also observed at redshift $>$ 1 galaxies \citep{2009ApJ...692...12E, 2011arXiv1104.0248F}." +" In our analysis, we find some evidence that those bright areas are probably unresolved star cluster knots recently formed and not dispersed yet by the interaction with the galactic environment, e.g. similarly to what is observed in BCGs and in spiral arms (Bastianetal.2005;Elmegreenetal. 2006).."," In our analysis, we find some evidence that those bright areas are probably unresolved star cluster knots recently formed and not dispersed yet by the interaction with the galactic environment, e.g. similarly to what is observed in BCGs and in spiral arms \citep{2005A&A...443...79B, 2006ApJ...644..879E}." +" The Mprshtest_gpR relation was first noticed by L02, who suggested that the visual magnitude of the most luminous cluster and the total galaxy SFR where correlated."," The $_V^{\textnormal{brightest}}$ -SFR relation was first noticed by L02, who suggested that the visual magnitude of the most luminous cluster and the total galaxy SFR where correlated." + By means, By means +tracks of Siess (2000) for this luminosity ancl spectral (wpe.,tracks of Siess (2000) for this luminosity and spectral type. + The 2MASS photometry of AIWC 480 shows an infrared SED rising well above the stellar photosphere: the A-band excess is 4 times the stellar photospheric continuum., The 2MASS photometry of MWC 480 shows an infrared SED rising well above the stellar photosphere; the $K$ -band excess is $\simeq 4$ times the stellar photospheric continuum. + A continuum veiling of (his magnitude is consistent with the absence of stellar photospheric features in the NIRSPEC spectra., A continuum veiling of this magnitude is consistent with the absence of stellar photospheric features in the NIRSPEC spectra. + To estimate the stellar contribution to the spectrum. we eeneraled stellar svithetic spectra using the program MOOG (Sneclen 1973) and Iauschildit et ((1999) model atmospheres.," To estimate the stellar contribution to the spectrum, we generated stellar synthetic spectra using the program MOOG (Sneden 1973) and Hauschildt et (1999) model atmospheres." + The initial line list was taken from Ixurucz (1993). and individual line parameters were adjusted (o fit the observed disk-center solar spectrum of Livingston Wallace (1991).," The initial line list was taken from Kurucz (1993), and individual line parameters were adjusted to fit the observed disk-center solar spectrum of Livingston Wallace (1991)." + A synthetic stellar photosphere with Zi;=8400 IWIN. logg=4.5. and esin;=τοκιν! predicts weak (<2.7% deep) stellar absorption lines in the A'-band (e.g. Meg I at 2.28148jan).," A synthetic stellar photosphere with $T_{\rm eff} = 8400$ K, $\log g = 4.5,$ and $v \sin i = 75\kms$ predicts weak $< 2.7$ deep) stellar absorption lines in the $K$ -band (e.g. Mg I at $2.28143\micron$ )." + A stellar rotation velocity of esiní=T5kms! is (vpical. or even conservative. for a MMvwvr old. A-type star. based on rotation statistics found for the Orion OB association (Wolff. Strom. Ilillenbrand 2004).," A stellar rotation velocity of $v\sin i = 75\kms$ is typical, or even conservative, for a $\sim 1$ Myr old A-type star, based on rotation statistics found for the Orion OB association (Wolff, Strom, Hillenbrand 2004)." + With a continuum. veiling of ry=d. the ratio of the continuum excess to the stellar photospheric flux at A. (hese leatures would be hidden within (he noise of our observations (S/N~ 400). consistent with the absence of absorption leatures in our spectira of NWC. 480.," With a continuum veiling of $r_K = 4$, the ratio of the continuum excess to the stellar photospheric flux at $K$, these features would be hidden within the noise of our observations $S/N \sim 400$ ), consistent with the absence of absorption features in our spectra of MWC 480." + In the V1331 (νο spectrum. the (vo strongest features blueward of the r=2 0 CO bandhead have a FWILM of 18—22kms.+.," In the V1331 Cyg spectrum, the two strongest features blueward of the $v$ =2–0 CO bandhead have a FWHM of $18-22\kms$." + These lines are blended with weaker water lines. although each feature is dominated by a single strong water line.," These lines are blended with weaker water lines, although each feature is dominated by a single strong water line." + Isolated CO lines recdward of the bandhead have FWILM z29—35kms.!., Isolated CO lines redward of the bandhead have FWHM $\approx 29-35\kms$. + Thus. the water emission lines are narrower ihan the CO lines. similar (o the situation found lor other sources such as SVS-13 and DG Tau (Carr et al.," Thus, the water emission lines are narrower than the CO lines, similar to the situation found for other sources such as SVS-13 and DG Tau (Carr et al." + 2004: Najita et 22000)., 2004; Najita et 2000). + CO and water emission [rom the voung star SVS-13 was previously studied by Carr el ((2004) in the region near the e—20 CO bandhead at 2.3pam., CO and water emission from the young star SVS-13 was previously studied by Carr et (2004) in the region near the $v$ =2–0 CO bandhead at $2.3\micron$. + As discussed in Carr et ((2004). a major clilficulty in modeling near-infrarecl water emission is the need for a complete and accurate line list.," As discussed in Carr et (2004), a major difficulty in modeling near-infrared water emission is the need for a complete and accurate line list." + In their study. Carr et ((2004) developed a water line list for the 2.3an region.," In their study, Carr et (2004) developed a water line list for the $2.3\micron$ region." + Thev started with the Partridge Sehwenke (1997) theoretical line list and improved (he accuracy of both Che line positions ancl strengtlis., They started with the Partridge Schwenke (1997) theoretical line list and improved the accuracy of both the line positions and strengths. + Using the derived line list. thev fit (he spectrum of SVS-13 with a simple model of a differentiallv rotating disk.," Using the derived line list, they fit the spectrum of SVS-13 with a simple model of a differentially rotating disk." +" llere. we adopt (he water linelist ancl disk model used by. Carr et ((2004) to moclel ihe spectrum of VI331 (νο,"," Here, we adopt the water linelist and disk model used by Carr et (2004) to model the spectrum of V1331 Cyg." + As in Carr et ((2004). the observed spectrum is modeled," As in Carr et (2004), the observed spectrum is modeled" +CRED.,. +.. The inteusities within a 3- pixclavide aperture were Μαιος] and this aperture was slid along the dispersion axis taking iuto account the tilt of the spectu.," The intensities within a 3-4 pixel-wide aperture were summed and this aperture was slid along the dispersion axis, taking into account the tilt of the spectrum." + The remaining backerouik helt was subtracted after a low-order polynomial fit., The remaining background light was subtracted after a low-order polynomial fit. + The wavelength calibration was performed using the ines in the προςτι of Vega taken with the same instruuoeut and setup., The wavelength calibration was performed using the lines in the spectrum of Vega taken with the same instrument and setup. + The Vosa spectruni was also used for the flux calibration., The Vega spectrum was also used for the flux calibration. +" Fist. the telescope response fiction was determined bv matehiug the iueasured σωμα fluxes of the Vosa spectrun with the tabulated ones (given iu e.g.àY Cray, 1992))."," First, the telescope response function was determined by matching the measured continuum fluxes of the Vega spectrum with the tabulated ones (given in e.g. \cite{gray}) )." + Then. the SN. spectrum was imultiplied bv the response function producing a. fiux-calibrated spectrin.," Then, the SN spectrum was multiplied by the response function producing a flux-calibrated spectrum." + The resulting spectra of SN. 2000E are plotted together iu Fie.h. where an arbitrary vertical shift was applied for better visibility.," The resulting spectra of SN 2000E are plotted together in Fig.5, where an arbitrary vertical shift was applied for better visibility." + Information for line identification was collected from Filippeuko.1997., Information for line identification was collected from \cite{filip1}. +. It is apparent from Fie.5 that SN 2000E shows the standard spectral features of a Type Ia SN at oue mouth after naxinunm light., It is apparent from Fig.5 that SN 2000E shows the standard spectral features of a Type Ia SN at one month after maximum light. + A closer inspection of the features arouud 6000. with those of SN 1998aq taken at the same phase (Vinkoetal.. 1999)). showed &ooc agreement. despite of the iumchl lower resolution of the preseut spectra.," A closer inspection of the features around 6000 with those of SN 1998aq taken at the same phase \cite{vinko}) ) showed good agreement, despite of the much lower resolution of the present spectra." + This confirms the classification of Type Ia. although a slisbtlv confusing description of the presence of the 776 line was also reported in TAUC 7353 by Polcaroetal..2000.," This confirms the classification of Type Ia, although a slightly confusing description of the presence of the $H\alpha$ line was also reported in IAUC 7353 by \cite{polc}." +. This was then revised in TAUC 7359., This was then revised in IAUC 7359. +" There is continuously erowiug amount of evidence that SNe. Ia show considerable diversity in peal brightuess, decline rate. spectral features. etc. ("," There is continuously growing amount of evidence that SNe Ia show considerable diversity in peak brightness, decline rate, spectral features, etc. (" +seo e.g. Filippeuko.1997.Phillipsetal.1999.Nugeutetal..1995.IHatanoab.2000/— and references herein).,"see e.g. \cite{filip1, phil, nugent, hat} and references therein)." +" The similarity between the spectra of SN 20001. and SN 1998aq may mean that SN 20001 is close to he ""normal SNe Ia beiug neither SN 1991T-like. nor SN 19911gSOuike event."," The similarity between the spectra of SN 2000E and SN 1998aq may mean that SN 2000E is close to the “normal” SNe Ia being neither SN 1991T-like, nor SN 1991bg-like event." + It should be noted. however. that he spectroscopic diversity between these subclasses of SNe Ta is usually studied at earlier epochs. between —£10 days around maximum.," It should be noted, however, that the spectroscopic diversity between these subclasses of SNe Ia is usually studied at earlier epochs, between $\pm 10$ days around maximum." + Therefore. the spectra preseuted rere are too late for such a distinction.," Therefore, the spectra presented here are too late for such a distinction." + This issue will be studied in more detail using the shape of the light curve in the next section., This issue will be studied in more detail using the shape of the light curve in the next section. + Iu this) section. first. we estimate the reddening of SN 20005. then its distance is determined from the analysis of the lieht curve.," In this section, first, we estimate the reddening of SN 2000E, then its distance is determined from the analysis of the light curve." + Finally. the discussion of the errors of distance measurement is presented.," Finally, the discussion of the errors of distance measurement is presented." + The presence of Na D was reported in the very first spectimun of SN 2000E (see Sect.1) indicating siguificaut reddening., The presence of Na D was reported in the very first spectrum of SN 2000E (see Sect.1) indicating significant reddening. + This feature night also be visible in the spectra in Fie.5. although it is quite difficult to identity the heavily blended lines at the eud of the photospheric phase.," This feature might also be visible in the spectra in Fig.5, although it is quite difficult to identify the heavily blended lines at the end of the photospheric phase." + Nevertheless. the determination of reddening is esseutial if SN Ww2000E is to be used for distance neasureimoeut.," Nevertheless, the determination of reddening is essential if SN 2000E is to be used for distance measurement." +" The reddening map of Durustein&Πα]ος.1982 indicates E(BV)=0.20 at the position of SN 200010, while the more recent map of Schlegeletal..1998 ooOVCs 1.36 nae."," The reddening map of \cite{buhe} indicates $E(B-V)=0.20$ at the position of SN 2000E, while the more recent map of \cite{sfd} gives 0.36 mag." + This is referred as the ealactic component of ie reddening. originating mostly from the interstellar nedimm (ISM) within the A\filky Way.," This is referred as the galactic component of the reddening, originating mostly from the interstellar medium (ISM) within the Milky Way." + The nap of Schlegel et al., The map of Schlegel et al. + is thought to be a better represcutative of the true amount of reddenine. but it has been o)mted out that this map svstematically overestimates he reddening at directions where £(DV)>015 nae (Arce&(οςαμα. 1999)).," is thought to be a better representative of the true amount of reddening, but it has been pointed out that this map systematically overestimates the reddening at directions where $E(B-V) \geq 0.15$ mag \cite{arce}) )." + Since several ealactic clus clouds are visible ou the long-exposure frames of NGC 6951. substantial reddenius due to the Milky Wavy ISM is expected.," Since several galactic cirrus clouds are visible on the long-exposure frames of NGC 6951, substantial reddening due to the Milky Way ISM is expected." + Taking iuto account the possible overestimate in the map of Schlegel et al.," Taking into account the possible overestimate in the map of Schlegel et al.," + the ealactic coniponeut of £(BV) max be somewhere between the two values given above (0.2 - 0.36 mag)., the galactic component of $E(B-V)$ may be somewhere between the two values given above (0.2 - 0.36 mag). + The total reddening of SN 2000E was estimated by colmparing the observed (BVW) index with its expected value at the given epoch., The total reddening of SN 2000E was estimated by comparing the observed $(B-V)$ index with its expected value at the given epoch. + This may give reasonable results. because SNe Ia are thought to show some lind of homogeneity i them (2BV) colours at epochs later than 60 davs post-masximain (Phillipsetal... 1999)).," This may give reasonable results, because SNe Ia are thought to show some kind of homogeneity in their $(B-V)$ colours at epochs later than 60 days post-maximum \cite{phil}) )." + Using JD 51578 as the epoch of the πιαπα (sec LON section). the phase of the B-data in Table 3 is between 7 = SO and 86 davs.," Using JD 51578 as the epoch of the $B$ -maximum (see next section), the phase of the $B$ -data in Table 3 is between $\tau$ = 80 and 86 days." + The empirical formmla of Phillipsctal.1999. results in ου=0.19.0.05 , The empirical formula of \cite{phil} results in $(B-V)_0 = 0.49 ~\pm~ 0.05$ +ias been observed.,has been observed. + Chatterjee.Heruquist&Naravau(1999) proposed a scenario in which the ANPs are formed as single neutron stars with fossil disks uade from fallback material from the supernovae explosions.," \cite{chat99} + proposed a scenario in which the AXPs are formed as single neutron stars with fossil disks made from fallback material from the supernovae explosions." + In this model. the spin-down from au initial period of a few ms to ~ο sis due to stroneo xopeller effect. at some period when the accretio1 rate is very low.," In this model, the spin-down from an initial period of a few ms to $\sim$ 6 s is due to strong propeller effect at some period when the accretion rate is very low." + But. if accretion is the correct phenomenon in the ANPs. as high spin-down ουςμα onu iu presence of substantial accretion. spin-cowu due to wind outflow secs to be more plausible tlau accretion imduced aneular momentum loss.," But, if accretion is the correct phenomenon in the AXPs, as high spin-down goes on in presence of substantial accretion, spin-down due to wind outflow seems to be more plausible than accretion induced angular momentum loss." + However. it should be remembered that the classical equilibrium disk picture asstuned here is often found uot to be the most appropriate description for the N-rayv pulsars (Bildstenetal. 1997)).," However, it should be remembered that the classical equilibrium disk picture assumed here is often found not to be the most appropriate description for the X-ray pulsars \cite{bild97}) )." + Iu view of a very narrow mass aud type allowed for any binary companion. and several areuients against 16 conimnon envelope evolution model. the maguetar uodel secius to be the most likely one for the ANPs.," In view of a very narrow mass and type allowed for any binary companion, and several arguments against the common envelope evolution model, the magnetar model seems to be the most likely one for the AXPs." + If 16 spin-down is due to magnetic braking. dipole field streneth of the order of 1053 gauss is estimated for aese sources.," If the spin-down is due to magnetic braking, dipole field strength of the order of $10^{14}$ gauss is estimated for these sources." + A nearly coustant spiu-dowu property was thought to favour the magnetar model over a juarv scenario., A nearly constant spin-down property was thought to favour the magnetar model over a binary scenario. + In two ANDPs. IE 015 (Cotthelf et al. 1999)).," In two AXPs, 1E $-$ 045 (Gotthelf et al. \cite{gott99}) )," + and IRNS 100910 (Ixaspi. Chakrabarty Steiubereer 1999)). there is very strong evidence for constant spiu-down. whereas iv deviation from a linear trend is clear.," and 1RXS $-$ 400910 (Kaspi, Chakrabarty Steinberger \cite{kasp99}) ), there is very strong evidence for constant spin-down, whereas in, deviation from a linear trend is clear." + Beceutlv. a deviation has also Όσοι detected from (Woods et al. 1999)).," Recently, a deviation has also been detected from (Woods et al. \cite{wood99}) )." + 1E 2259|586. the most frequently observed ANP. has provided an interesting pulse period jstoryv.," 1E 2259+586, the most frequently observed AXP, has provided an interesting pulse period history." + Observations made for about 15 vears with uaznyv mstrunenuts preceding sshowed considerable variation iu the spiu-down rate (Bavkal&Swauk 1996))., Observations made for about 15 years with many instruments preceding showed considerable variation in the spin-down rate \cite{bayk96}) ). + But. the. pulse-cohere-t iuueg observations with yproved it tobe otherwise. at east for a period of last 2.6 vy (Ixaspi et al. 1999)).," But, the pulse-coherent timing observations with proved it to be otherwise, at least for a period of last 2.6 yr (Kaspi et al. \cite{kasp99}) )." + Two scenarios have been proposed wlich cau explain he chaugiug spin-down rate even when the overall raking is due to the ultrastroug maeuetic feld., Two scenarios have been proposed which can explain the changing spin-down rate even when the overall braking is due to the ultrastrong magnetic field. + Alelatos(1999) showed that for reasonable neutron star parameters. a radiative precession effect may ake place which can give the observed spin-down variations with time scale of about 10 vears.," \cite{mela99} showed that for reasonable neutron star parameters, a radiative precession effect may take place which can give the observed spin-down variations with time scale of about 10 years." + It will be xossible to verity this scenario when more pulse period ueasuremeuts become available in the next few vears., It will be possible to verify this scenario when more pulse period measurements become available in the next few years. + Woods et al. (19993) , Woods et al. \cite{wood99}) ) +have identified a possible in cclose to the time when SCR activity was very stroug., have identified a possible in close to the time when SGR activity was very strong. + But if the spin-down variation is related to the SCR activity. sinulay activities should have been observed from aand LE 2259|586.," But if the spin-down variation is related to the SGR activity, similar activities should have been observed from and 1E 2259+586." + We have found that all the gama rav bursts observed with the BATSE for which the estimated positious are within 26 of these AXDPs (about 30 CRBs around each ANP). have strong lugh enerey cussion uulike SCR musts.," We have found that all the gamma ray bursts observed with the BATSE for which the estimated positions are within $2\sigma$ of these AXPs (about 30 GRBs around each AXP), have strong high energy emission unlike the SGR bursts." + evIleruquist(1999) have proposed that the spiu- Variations can be explained as elitches (similar to radio pulsars) superposed on constant spin-down., \cite{heyl99} have proposed that the spin-down variations can be explained as glitches (similar to radio pulsars) superposed on constant spin-down. + But. with recent pulse period measurements of aand|11£.. this will require too many elitches. one before almost every observation unless there areglitches. wever observed iu radio pulsars.," But, with recent pulse period measurements of and, this will require too many glitches, one before almost every observation unless there are, never observed in radio pulsars." + Iu the magnetar model. the X-ray ciission is due to decay of the magnetic field.," In the magnetar model, the X-ray emission is due to decay of the magnetic field." + The energy generated at the core is transported to the crust alone the magnetic feld direction., The energy generated at the core is transported to the crust along the magnetic field direction. + The black body. component of the spectrum is thermal cussion from the hot spots at the magnetic polar regions aud the power-law conriponenut is part of the thermal cussion reprocessed by the magnetic field and the cuviromment., The black body component of the spectrum is thermal emission from the hot spots at the magnetic polar regions and the power-law component is part of the thermal emission reprocessed by the magnetic field and the environment. + Investigation is required about the expected. pulse profile anc its euerev dependence., Investigation is required about the expected pulse profile and its energy dependence. + Time and/or energy dependence of the pulse profile as has been observed iun (I&ouveliotouctal. 1998)) and (IDulevetal.1999: Ilxouveliotou.οἳal. 1999:: Afurakaunietal. 19993) also requires to be addressed., Time and/or energy dependence of the pulse profile as has been observed in \cite{kouv98}) ) and \cite{hurl99}; \cite{kouv99}; \cite{mura99}) ) also requires to be addressed. + A double peaked pulse profile at low energv aud single peaked profile at high euergv are observed iu (Figure 1)., A double peaked pulse profile at low energy and single peaked profile at high energy are observed in (Figure 1). + The pulsation is very weak iu some sources (only 1054 in aand 61)). and E in," The pulsation is very weak in some sources (only $\%$ in and ), and $\%$ in." + If the pulsation is due to confinement of the heat iu the magnetic polar regious by the magnetic feld. correlation between magnetic field streneth aud pulse fraction should be observed.," If the pulsation is due to confinement of the heat in the magnetic polar regions by the magnetic field, a correlation between magnetic field strength and pulse fraction should be observed." + But. it is likely to be sancared by the geometric effect of individual sources. ic. the orientation of the spin and magnetic axes with respect to the line of sieht.," But, it is likely to be smeared by the geometric effect of individual sources, i.e. the orientation of the spin and magnetic axes with respect to the line of sight." + Tn the magnetar model. there are two mechanisms bv which X-rays can be generated.," In the magnetar model, there are two mechanisms by which X-rays can be generated." + If the X-ray cussion is powered by decaving maenetic field. the ποπτν is a very strong function of the maguctic field strength. L.xD! (Thompson&Duncan 1996)).," If the X-ray emission is powered by decaying magnetic field, the luminosity is a very strong function of the magnetic field strength, ${\rm L_x \propto B^4}$ \cite{thom96}) )." + Alternate process of, Alternate process of +process.,process. + Furthermore. only data in the range kkeV were fitted: below kkeV. the calibration becomes uncertain whereas above tkkeV spectral complexities due to the Fe ke line become relevant.," Furthermore, only data in the range keV were fitted: below keV the calibration becomes uncertain whereas above keV spectral complexities due to the Fe $\alpha$ line become relevant." + In detail our spectral mocel has three components.," In detail, our spectral model has three components." + First. the primary power-law and theover warm absorber are modeled: using as described above.," First, the primary power-law and the warm absorber are modeled using as described above." + Secondly. the elect of thefener warnt absorber was modeled as a absorption celero with (rest-frame) threshold energy kkeV ancl optical depth at threshold of ros=0.18 (Otaniet al.," Secondly, the effect of the warm absorber was modeled as a absorption edge with (rest-frame) threshold energy keV and optical depth at threshold of $\tau_{\rm O8}=0.18$ (Otani et al." +"L99G)"".. Lastly. Galactic absorption bv a cold column of Ny=4.06I020cm2 Ws included."," Lastly, Galactic absorption by a cold column of $N_{\rm H}=4.06\times 10^{20}\pcmsq$ was included." + Phe spectral fitting results are shown in Table 4., The spectral fitting results are shown in Table 4. + Table 4 shows that the assumed dust composition has a significant cllect on the goodness of fit., Table 4 shows that the assumed dust composition has a significant effect on the goodness of fit. + The mocel which assumes graphite grains only is a much better Lit than the model with a standard: dust. mixture (Αν=68 for the same number of dof)., The model which assumes graphite grains only is a much better fit than the model with a standard dust mixture $\Delta\chi^2=68$ for the same number of dof). + The reason for this dilference is illustrated in Fig., The reason for this difference is illustrated in Fig. + 6 which shows the best-fit unfolded model and the kkeV SISO data for cach ofthe two assumed dust compositions., 6 which shows the best-fit unfolded model and the keV SIS0 data for each of the two assumed dust compositions. + The standard dust. model predicts a large photoelectrie Ix-edge due to neutral oxygen (threshold energy 0.533 keV)., The standard dust model predicts a large photoelectric K-edge due to neutral oxygen (threshold energy $0.533\keV$ ). + Such an edge is not observed., Such an edge is not observed. + The graphite grain model predicts a significanth smaller neutral oxvecn edge which is much more consistent with observations., The graphite grain model predicts a significantly smaller neutral oxygen edge which is much more consistent with observations. + Note that the neutral oxvgen edge in the latter model originates purely. from the Galactic column and not from the cust’ warm. absorber., Note that the neutral oxygen edge in the latter model originates purely from the Galactic column and not from the dusty warm absorber. + Thus. the graphite erain niodel seems to be preferred over the standard dust mixture niocel.," Thus, the graphite grain model seems to be preferred over the standard dust mixture model." + The signatures of dust in a dusty warm absorber only become significant at X-ray energies below theAL band., The signatures of dust in a dusty warm absorber only become significant at X-ray energies below the band. +" ""Thus. we must check that the dusty warm absorber mociel is consistent with the soft. X-ray spectrum as determined by theROSAL PSPC."," Thus, we must check that the dusty warm absorber model is consistent with the soft X-ray spectrum as determined by the PSPC." + In detail. we compared theROSAL PSPC data with a spectral model consisting of a power-law form (photon index E) absorbed by three components: a) a dusty warm absorber model as computed by (column density Wy and ionization parameter £). b) an absorption edge at the threshold energy of to mimic the effect. of the dust-free. inner warm. absorber (optical depth at threshold. 70). c) neutral absorption to account for Galactic. and intrinsic cold gas absorption (column density Αμ}.," In detail, we compared the PSPC data with a spectral model consisting of a power-law form (photon index $\Gamma$ ) absorbed by three components: a) a dusty warm absorber model as computed by (column density $N_{\rm W}$ and ionization parameter $\xi$ ), b) an absorption edge at the threshold energy of to mimic the effect of the dust-free inner warm absorber (optical depth at threshold $\tau_{\rm O8}$ ), c) neutral absorption to account for Galactic and intrinsic cold gas absorption (column density $N_{\rm H}$ )." + This 6 parameter scheme over-mocdels theOSAT PSPC spectrum (which has ~5 independent energy channels)., This 6 parameter scheme over-models the PSPC spectrum (which has $\sim 5$ independent energy channels). + Thus. we do not formally fit the data since any such [it is very. poorly constrained we merely seek to demonstrate consistency. with the fit parameters. derived from the data.," Thus, we do not formally fit the data since any such fit is very poorly constrained – we merely seek to demonstrate consistency with the fit parameters derived from the data." + Both the standard. dust. and. the eraphite clust warm. absorber models. are. found. to. be consistent with the PSPC data for the following parameters: b=28. Nw=4.5↓∪≼∼⊔↓⊳⋚∶−≽∪⋖⋅↓⋅⋏∙≟≼⇍⊔↓⊳∖212o; −i Tox=LS. Ny=6.910720em2p .," Both the standard dust and the graphite dust warm absorber models are found to be consistent with the PSPC data for the following parameters: $\Gamma=2.8$, $N_{\rm W}=4.5\times 10^{21}\pcmsq$, $\xi=20\erg\cm\ps$, $\tau_{\rm O8}=0.83$, $N_{\rm H}=6.9\times 10^{20}\pcmsq$ ." + These parameters are roughly consistent with those derived from the data with the exception of D and. τος., These parameters are roughly consistent with those derived from the data with the exception of $\Gamma$ and $\tau_{\rm O8}$. + We will brictly address these in turn., We will briefly address these in turn. + First. the photon index E is inferred to be significantly steeper in theROSA observation than the observation.," First, the photon index $\Gamma$ is inferred to be significantly steeper in the observation than the observation." + At least some of this cliscrepaney (AL~0.5) max be due to previously noted errors in the cross-calibration., At least some of this discrepancy $\Delta\Gamma\sim 0.5$ ) may be due to previously noted errors in the cross-calibration. + However. there may be a true softening of the N-ray spectrum in theROSAT band due to the onset of ἃ soft excess.," However, there may be a true softening of the X-ray spectrum in the band due to the onset of a soft excess." + It must be noted that the data do not show any evidence of a soft excess above 0.6keV. (ονnolcds 1997)., It must be noted that the data do not show any evidence of a soft excess above $0.6\keV$ (Reynolds 1997). + Temporal variations of FL may. also explain such a discrepancy (note that theZO0SAT and observations are separated by over 2 vears), Temporal variations of $\Gamma$ may also explain such a discrepancy (note that the and observations are separated by over 2 years). + Secondly. the edge depth tox is inferred to be significantly deeper in theSAT observation than. in observation.," Secondly, the edge depth $\tau_{\rm O8}$ is inferred to be significantly deeper in the observation than in observation." + This can be understood as a real (ic. physical) change.," This can be understood as a real (i.e., physical) change." + Otani ct al. (, Otani et al. ( +1996) ancl Revnolels (1996) have found a relationship between the instantaneous value of τος (as measured by LSC) and the luminosity of this source.,1996) and Reynolds (1996) have found a relationship between the instantaneous value of $\tau_{\rm O8}$ (as measured by ) and the luminosity of this source. + From the analysis of Revnolds (1996). this relation takes the form where Loyy is the kkeV. luminosity of the source.," From the analysis of Reynolds (1996), this relation takes the form where $L_{2-10}$ is the keV luminosity of the source." + This can be understood physically in terms of a highly-ionizecL warm absorber in which most of the oxvgen atoms are fully stripped of all electrons (1.0. is the dominant state)., This can be understood physically in terms of a highly-ionized warm absorber in which most of the oxygen atoms are fully stripped of all electrons (i.e. is the dominant state). + A drop in ionizing luminosity results in an increased number of ions due to recombination of the ions., A drop in ionizing luminosity results in an increased number of ions due to recombination of the ions. + ‘This produces the observed anti-correlation between Tox aud Lsio., This produces the observed anti-correlation between $\tau_{\rm O8}$ and $L_{2-10}$. + During the observation. the average kkeV luminosity is in the range £o.40=+8.107eres+.," During the observation, the average keV luminosity is in the range $L_{2-10}=4-8\times 10^{42}\ergps$." + The large uncertainty in luminosity is due to the uncertainty in the extrapolation from theROSAY band to the LokkeV band., The large uncertainty in luminosity is due to the uncertainty in the extrapolation from the band to the keV band. + Vhe corresponding range of edge depth is Tox=0.24., The corresponding range of edge depth is $\tau_{\rm O8}=0.2-1.4$. + Thus. the value needed to agree with the spectrum. τος=0.83. is completely consistent with this relationship.," Thus, the value needed to agree with the spectrum, $\tau_{\rm O8}=0.83$, is completely consistent with this relationship." + ‘Yo summarize these X-ray. results. we have shown tha a warm absorber containing sullicient. dust to explain the optical redcdening is also compatible with the aneROSAT data.," To summarize these X-ray results, we have shown that a warm absorber containing sufficient dust to explain the optical reddening is also compatible with the and data." + In. principle. a detailed examination of the neutral [Ix-edges. of the various clust-phase metals allows the composition of the dust. to be probed.," In principle, a detailed examination of the neutral K-edges of the various dust-phase metals allows the composition of the dust to be probed." + Although 1 is extremely hard. to make definitive statements vet due to the lack of high-quality soft N-rayv spectra. there. is evidence that the dust grain composition is non-stancare in so far as it contains[ον silicate grains.," Although it is extremely hard to make definitive statements yet due to the lack of high-quality soft X-ray spectra, there is evidence that the dust grain composition is non-standard in so far as it containsfew silicate grains." + We note tha cue to the tentative nature of this conclusion. we have no," We note that due to the tentative nature of this conclusion, we have not" +carbon excitation temperature of 29.16.35 for our siuuple.,carbon excitation temperature of $\pm$ K for our sample. + This temperature is lower than what is IKIK.typically found iu starformung regions idu the local universe despite the fact that the sample galaxies have star formation rate surface densitics ον kpe scales of 1008 of M Hkkpe 7? (comparable to the most extreme starbursts in the local universe. but ou larger spatial scales}.," This temperature is lower than what is typically found in starforming regions in the local universe despite the fact that the sample galaxies have star formation rate surface densities on kpc scales of 100's of $_\odot$ $^{-1}$ $^{-2}$ (comparable to the most extreme starbursts in the local universe, but on larger spatial scales)." + However. the temperatures are roughly consistent with published dust temperatures of highredshift) starforming galaxies (Beelen ct 22006. I&ováces et al.," However, the temperatures are roughly consistent with published dust temperatures of high--redshift starforming galaxies (Beelen et 2006, Kováccs et al.," + 2006. 2010).," 2006, 2010)." + Low carbou excitation as well as dust temperatures could iudicate that the nieasurenients mcelude a significant amount of eas/dust unaffected by. star formation., Low carbon excitation as well as dust temperatures could indicate that the measurements include a significant amount of gas/dust unaffected by star formation. + Towever one should also keep in nünd that the couversion of excitation temperature to kinetic temperature may be complicated by non.LTE excitation of atomic carbon., However one should also keep in mind that the conversion of excitation temperature to kinetic temperature may be complicated by non–LTE excitation of atomic carbon. +" The aalbundauces n our siuuple ealaxies (S.143.5)<10 7) are colparable, withinCN[C| the ΠΟ:uncertainties. to what is found in local starforming cuvirommenuts (Section 1.6)."," The abundances in our sample galaxies $_2$ $\pm3.5)\times$ $^{-5}$ ) are comparable, within the uncertainties, to what is found in local starforming environments (Section 4.6)." + This πράος hat the highz galaxies studied here are siguificautly enriched in carbon on galactic scales. even though the ookback times are considerable (our average redshift of χ.ο corresponds to an age of the wniverse of ~2 CO).," This implies that the high–z galaxies studied here are significantly enriched in carbon on galactic scales, even though the look–back times are considerable (our average redshift of $\sim$ 3 corresponds to an age of the universe of $\sim$ Gyr)." + Iu terms of the cooling budget the lines are a negligible coolaut (average Logq/Lgpug=(7.74L6)«10 ©)., In terms of the cooling budget the lines are a negligible coolant (average $L_\ci$ $L_{\rm FIR}=(7.7\pm4.6)\times10^{-6}$ ). + We find tentative evidence that this ratio may be elevated in the SMCs bv a factor of a few compared to the QSOs. but a larger sample will be receded to beat down the current lowumber statistics.," We find tentative evidence that this ratio may be elevated in the SMGs by a factor of a few compared to the QSOs, but a larger sample will be needed to beat down the current low–number statistics." + The increase in sensitivity afforded bv ALMA will be critical to increase the sample size auc push sstudies at hieh redshift bevoud the brightest svstenis that are accessible todav., The increase in sensitivity afforded by ALMA will be critical to increase the sample size and push studies at high redshift beyond the brightest systems that are accessible today. + We thank the referee for comments that helped to iuprove the paper and thank Rowin \eijerink for useful discussions., We thank the referee for comments that helped to improve the paper and thank Rowin Meijerink for useful discussions. + This work is based ou observations witli the IRAM. Plateau de. Bure Tuterferometer., This work is based on observations with the IRAM Plateau de Bure Interferometer. + IRAM. is supported by INSU/SCNRS (France). MPG. (Germany)," IRAM is supported by INSU/CNRS (France), MPG (Germany)" +Small-amplitude oscillations and propagating waves are commonly observed in. both quiescent and active region prominences/filaments.,Small-amplitude oscillations and propagating waves are commonly observed in both quiescent and active region prominences/filaments. + They have been interpreted in terms of magnetohydrodynamic (MHD) eigenmodes of the magnetic structure and/or propagating MHD waves., They have been interpreted in terms of magnetohydrodynamic (MHD) eigenmodes of the magnetic structure and/or propagating MHD waves. + The reader is referred to some recent reviews for more information about the observational and theoretical backgrounds (Oliver&Ballester2002:Engvold2004:etal.2007:Engvold2008) Prominence oscillations are known to be quickly damped. with damping times corresponding to a few oscillatory periods (thistopichasbeenreviewedbyOliver2009:Mackayetal.," The reader is referred to some recent reviews for more information about the observational and theoretical backgrounds \citep{oliverballester02,engvold04,ballester,banerjee,engvold08} + Prominence oscillations are known to be quickly damped, with damping times corresponding to a few oscillatory periods \citep[this topic has been reviewed by][]{oliver, mackay}." +2009).. Several damping mechanisms of MHD waves have been proposed. non-adiabatic effects and collisions being the more extensively investigated.," Several damping mechanisms of MHD waves have been proposed, non-adiabatic effects and ion-neutral collisions being the more extensively investigated." + In order to understand in detail these effects. they have been studied in simple configurations such as unbounded and homogeneous media.," In order to understand in detail these effects, they have been studied in simple configurations such as unbounded and homogeneous media." + Carbonelletal.(2004) investigated the time damping in à homogeneous prominence medium taking non-adiabatie effects (optically thin radiation losses and thermal conduction) into account., \citet{carbonell04} investigated the time damping in a homogeneous prominence medium taking non-adiabatic effects (optically thin radiation losses and thermal conduction) into account. + Later on. the spatial damping was studied by Carbonelletal.(2006) and the effect of à background mass flow was analyzed by Carbonelletal.(2009).," Later on, the spatial damping was studied by \citet{carbonell06} and the effect of a background mass flow was analyzed by \citet{carbonell09}." +. Subsequently. some works have extended these previous results by considering the presence of the coronal medium 2009a)..," Subsequently, some works have extended these previous results by considering the presence of the coronal medium \citep{soler07,soler08,soler09NA}." + The common conclusion of these investigations is that only slow and thermal waves are efficiently damped by non-adiabatic effects. while fast waves are very slightly damped and Alfvénn waves are completely unaffected.," The common conclusion of these investigations is that only slow and thermal waves are efficiently damped by non-adiabatic effects, while fast waves are very slightly damped and Alfvénn waves are completely unaffected." + On the other hand. the influence of partial ionization on the propagation and time damping of MHD waves has been also investigated in an unbounded medium.," On the other hand, the influence of partial ionization on the propagation and time damping of MHD waves has been also investigated in an unbounded medium." + Fortezaetal.(2007) followed the treatment by Braginskii(1965) and derived the full set of MHD equations along, \citet{forteza07} followed the treatment by \citet{brag} and derived the full set of MHD equations along +"imply a very high efficiency of dlogR./dlogM~2.6 for growing spheroids, just consistent with the upper end of estimates determined from merger simulations (e.g.,?)..","imply a very high efficiency of $d\log R_e / d \log M \simeq 2.6$ for growing spheroids, just consistent with the upper end of estimates determined from merger simulations \citep[e.g.,][]{Hopkins2010}." + Also striking is the different trend seen in less massive 10«logMayn/Mo11 galaxies (open diamonds in Figure , Also striking is the different trend seen in less massive $10 < \log M_{\rm dyn}/\msol < 11$ galaxies (open diamonds in Figure \ref{fig:size}) ). +"Although the high-z samples are small and include 3)).some compact examples, we find no evidence for mean size evolution over 010'! Mo sample, where we are complete for any reasonable mass-to-light ratio."," This is not a concern for the $>$ $^{11}$ $_{\odot}$ sample, where we are complete for any reasonable mass-to-light ratio." +" A characterization of the bias requires a self-consistent model with Monte Carlo simulations, which is beyond the scope of this Letter and is left for future work when larger samples will be available."," A characterization of the bias requires a self-consistent model with Monte Carlo simulations, which is beyond the scope of this Letter and is left for future work when larger samples will be available." +" Comparisons at fixed mass may be affected by “progenitor bias.""", Comparisons at fixed mass may be affected by “progenitor bias.” +" A preferred approach, when dynamical data are available, is to examine galaxies of the samedispersion."," A preferred approach, when dynamical data are available, is to examine galaxies of the same." +. 'This offers the two advantages discussed in 1 and is illustrated in Figure 4.., This offers the two advantages discussed in 1 and is illustrated in Figure \ref{fig:sigmaRe}. + A cut in iincludesMayn only the largest galaxies at a fixed σ., A cut in includes only the largest galaxies at a fixed $\sigma$. +" Therefore, if galaxies below some threshold opp are missing from the high-redshift samples, this could mimic an evolutionary trend in mass-selected samples."," Therefore, if galaxies below some threshold $\sigma_{\rm ET}$ are missing from the high-redshift samples, this could mimic an evolutionary trend in mass-selected samples." +" According to the preferred prescription of ?,, σετ=233 km s! at z=1.3."," According to the preferred prescription of \citet{vanderWel2009}, $\sigma_{\rm ET}=233$ km $^{-1}$ at $z=1.3$." +" Therefore we should expect to see some effect for our sample, even though the presence of lower c objects in our sample already suggests that the progenitor bias is not as strong."," Therefore we should expect to see some effect for our sample, even though the presence of lower $\sigma$ objects in our sample already suggests that the progenitor bias is not as strong." + Figure 4 shows this comparison in terms of the c—R plane., Figure \ref{fig:sigmaRe} shows this comparison in terms of the $\sigma-R_e$ plane. +" To avoid luminosity selection biases, we consider only galaxies with o>200 km s~!, where we are complete, based on the SDSS distribution of luminosity at fixed o and a conservative estimate of luminosity evolution, consistent with passive evolution of an old stellar population formed at 2/=3."," To avoid luminosity selection biases, we consider only galaxies with $\sigma > 200$ km ${}^{-1}$, where we are complete, based on the SDSS distribution of luminosity at fixed $\sigma$ and a conservative estimate of luminosity evolution, consistent with passive evolution of an old stellar population formed at $z_f=3$." + The SDSS galaxies are weighted so as to match the o distribution of the (grayscale)0.9«z1.6 sample (top , The SDSS galaxies (grayscale) are weighted so as to match the $\sigma$ distribution of the $0.9 < z < 1.6$ sample (top panel). +The right panel of Figure 4 then compares the size panel).distributions of the localand 0.9«z1.6 samples at matching, The right panel of Figure \ref{fig:sigmaRe} then compares the size distributions of the localand $0.9 < z < 1.6$ samples at matching +This investigation has been supported by the Austrian Fonds zur F'orrderung der wissenschaftlichen Forschung.,This investigation has been supported by the Austrian Fonds zur Förrderung der wissenschaftlichen Forschung. +Alter more than a decade of searching. the direct exoplanet imaging «quest was finally successful in 2008 with the discovery of three planetary svstems (Alaroisοἱal. 2009).,"After more than a decade of searching, the direct exoplanet imaging quest was finally successful in 2008 with the discovery of three planetary systems \citep{marois08,kalas08,lagrange09}." +. One Κον advantage of this technique is the detection of the planets thermal emission., One key advantage of this technique is the detection of the planet's thermal emission. + Detailed multi-band photometry aud spectrometry can be acquired that can then be compared with atmospheric models (o derive (he planets physical characteristies and study the effect of dust and molecular chemistry., Detailed multi-band photometry and spectrometry can be acquired that can then be compared with atmospheric models to derive the planet's physical characteristics and study the effect of dust and molecular chemistry. + With its multiple co-eval Jovian planets. the svstem is an ideal laboratory to study voung planets will low temperature/surface gravity almospheres and bridge the gap between massive field brown clwarls and (the cold solar svstem planets.," With its multiple co-eval Jovian planets, the system is an ideal laboratory to study young planets with low temperature/surface gravity atmospheres and bridge the gap between massive field brown dwarfs and the cold Solar system planets." + is à 30Mvr old (Alaroisοἱal.2010:Zuckermanetal.2011) ASV star located 39.4pc away (Leeuwenetal.2007) in the Pegasus constellation.," is a 30Myr old \citep{marois10,zuckerman11} A5V star located 39.4pc away \citep{leeuwen07} in the Pegasus constellation." + It is classified as à Doradus and à A Bootis star (Gravetal. 1999)., It is classified as a $\gamma$ Doradus and a $\lambda$ Bootis star \citep{gray99}. +. It also shows an Ii excess (Vega- star) consistent. with a debris disk composed of a warm dust disk (6 to 15ÀU). a massive cold dust disk (90 up to 300AU) and a small dust. particle halo extending up to a 1.000AU (Rheeetal.2007:Sual. 2009).," It also shows an IR excess (Vega-like star) consistent with a debris disk composed of a warm dust disk (6 to 15AU), a massive cold dust disk (90 up to 300AU) and a small dust particle halo extending up to a 1,000AU \citep{rhee07,su09}." +. Photometry aud some spectroscopy of the planets are available in several bands from 1 to 3.8ym (Maroisοἱelal.2011:Barmanet 2011)..," Photometry and some spectroscopy of the planets are available in several bands from 1 to $\mu$ m \citep{marois08, lafreniere09,metchev09,janson10,marois10, hinz10,currie11,barman11}." + An initial characterization has been achieved using the available data and state-of-the-art atmospheric: models developed for Ποια brown dwarf analvsis., An initial characterization has been achieved using the available data and state-of-the-art atmospheric models developed for field brown dwarf analysis. + It is clear that these planets are cuite different than most. [field brown clwarls. showing verv dustw aünospheres while being cool («—1.000I) with no sign of methane molecular absorption.," It is clear that these planets are quite different than most field brown dwarfs, showing very dusty atmospheres while being cool $\sim $ 1,000K) with no sign of methane molecular absorption." +" L- and Al-band detections/upper limits suggest (his lack of methane is due toa CO/CII, non-equilibrium chemistry (Saumonelal.Ciurieetal.2011:Barman 2011)."," L- and M-band detections/upper limits suggest this lack of methane is due to a $_4$ non-equilibrium chemistry \citep{saumon03,cushing06,leggett07,hinz10,bowler10,currie11,barman11}." +. Other teams have been able to [it the available photometry with patchy clouds and equilibrium chemistyy atinosphieres (Maroisetal.2008:Currieοἱ2011).," Other teams have been able to fit the available photometry with patchy clouds and equilibrium chemistry atmospheres \citep{marois08,currie11}." +. Accurate M-band. photometry can help disentangle the various models. but it is hard on a ground-based telescope cue io the bright thermal background. mainly from the telescope and the adaptive optics svstem (Llovel2000).," Accurate M-band photometry can help disentangle the various models, but it is hard on a ground-based telescope due to the bright thermal background mainly from the telescope and the adaptive optics system \citep{Lloyd00}." +. This background is parüeularly hard {ο remove al Ixeck. as il varies with time as the instrument image rotator (which is located very near focus) moves and as the AO cdeformable mirror modulates the rotator-induced background pattern as seen bv the detector.," This background is particularly hard to remove at Keck, as it varies with time as the instrument image rotator (which is located very near focus) moves and as the AO deformable mirror modulates the rotator-induced background pattern as seen by the detector." + As a result. conventional skv/backeround subtraction routines leaves a spatially variable residual that limits final sensitivity.," As a result, conventional sky/background subtraction routines leaves a spatially variable residual that limits final sensitivity." + In this letter. we present (he first M-band (4.67050) detecGons of three of the currently four known planets. the longest wavelength at which these planets have been imaged.," In this letter, we present the first M-band $4.670 \mu$ m) detections of three of the currently four known planets, the longest wavelength at which these planets have been imaged." + The observations are discussed in, The observations are discussed in +"Then the well-known dispersion relation of axisvmmetric 2D density waves in the thin dise is (e.g.?) where we have used the same normalization as before and because of that ου=cs,O0/26No.","Then the well-known dispersion relation of axisymmetric 2D density waves in the thin disc is \cite[e.g.,][]{GT78} + where we have used the same normalization as before and because of that $Q_{2D}=c_{sm}\Omega/\pi G \Sigma_0$." + This dispersion relation is a parabola with a minimum at the Jeans waventunber Ay)=L/Qop., This dispersion relation is a parabola with a minimum at the Jeans wavenumber $k_J=1/Q_{2D}$. + This is the wavenumber. at which the etfect of sclberavity is most prominent. and if Qop<1 it gives the characteristic scale of gravitational instability.," This is the wavenumber, at which the effect of self-gravity is most prominent, and if $Q_{2D}<1$ it gives the characteristic scale of gravitational instability." + At small &«fy. 2D density waves are dominated by seli-gravitv ancl inertial forces. while at Large &Aj. pressure/compressibilitv dominates over self-gravitv and density waves appear as an acoustic mode.," At small $k\ll k_J$, 2D density waves are dominated by self-gravity and inertial forces, while at large $k\gg +k_J$, pressure/compressibility dominates over self-gravity and density waves appear as an acoustic mode." + At Kk—Αι all three factors can be important., At $k\sim k_J$ all three factors can be important. + Let us now look a the dispersion curves of the basic branches of the even r- and convectively unstable even. e-moces in. Figs., Let us now look at the dispersion curves of the basic branches of the even r- and convectively unstable even g-modes in Figs. +" 3c.5c.5g. They have similar parabolic shape in the self-eravityv. anc compressibility dominated regime at &Ay, with the linear phase at smaller &«x&,,. where only self-gravity and inertia forces play a role."," 3c,5c,5g. They have similar parabolic shape in the self-gravity and compressibility dominated regime at $k \sim k_m$ with the linear phase at smaller $k\ll k_m$, where only self-gravity and inertial forces play a role." + This linear phase at long wavelengths is well reproduced. by the 2D dispersion. relation., This linear phase at long wavelengths is well reproduced by the 2D dispersion relation. +" Therefore. we can identify the wavenumber 4&,. at which the elfec of sell-eravity on the 3D modes is largest. with the Jeans wavenumber Avy."," Therefore, we can identify the wavenumber $k_m$, at which the effect of self-gravity on the 3D modes is largest, with the Jeans wavenumber $k_J$ ." +" In some sense. in the case of instability when Q«(Qu. hin, gives a more accurate value for the raclia scale. Αι. of the eravitationally most. unstable mode than that given by the Jeans wavenumber A; in the 2D model."," In some sense, in the case of instability when $Q100$, we sum to $z_{est}=0.15$." + The error bars on these measurements were estimated using the same methodology as discussed above for the EDCCITI cluster surface cleusitics., The error bars on these measurements were estimated using the same methodology as discussed above for the EDCCII cluster surface densities. +" Receutly, Holden et al. ("," Recently, Holden et al. (" +1999) published 81 redshift uecasureineuts towards 16 low redshiff PDCS clusters.,1999) published $84$ redshift measurements towards $16$ low redshift PDCS clusters. + From these data. Holden et al. (," From these data, Holden et al. (" +1999) showed that the uatehed filter redshift estimate for i4;«0.5 PDCS clusters had au error of ouly 62~0.07: much simaller tla xeviouslw quoted. by Postinan ct al. (,1999) showed that the matched filter redshift estimate for $z_{est}<0.5$ PDCS clusters had an error of only $\delta z\simeq0.07$; much smaller than previously quoted by Postman et al. ( +1999).,1999). +" Therefore. n1 Table 5.. we present our estimates of the PDCS space aenusitv of low redshift clusters (0.2«—iu;<< 0.6) using 1ο PDCS :,., measurements and the data eiven in Table lof Postinan et al. ("," Therefore, in Table \ref{space}, we present our estimates of the PDCS space density of low redshift clusters $0.2200$, in the ${\rm V_4}$ data, to minimize the effects of spurious detections (see Postman et al." + 1996)., 1996). + Therefore. these space deusities may be lower iun expected since we have poteutially excluded some real clusters as well.," Therefore, these space densities may be lower than expected since we have potentially excluded some real clusters as well." + This approach is valid as the true error ou La IN now significantly simaller than our redshift slice a substantial nuniber of clusters will not be scattered iu. or out. of our sample because of the error in i54.," This approach is valid as the true error on $z_{est}$ is now significantly smaller than our redshift slice a substantial number of clusters will not be scattered in, or out, of our sample because of the error in $z_{est}$." + For the lO16imag. where the interior of the cores becomes predominantly heated by tjo dust enission from the filaments.," Independent of the assumed external pressure, the variation in the heating rate decreases for highly embedded cores within filaments with $A_V\gg 16~{\rm mag}$, where the interior of the cores becomes predominantly heated by the dust emission from the filaments." + Tn the model. the SEDs of the cores are produced by the ΗΕ of individal erains of different siz and compositions that have unique teniperature and CLUISSI1Oji behaviors.," In the model, the SEDs of the cores are produced by the re-emission of individual grains of different sizes and compositions that have unique temperature and emission behaviors." + The temperature of the individual eyalls as a function of radius is shown in Fig. 6.., The temperature of the individual grains as a function of radius is shown in Fig. \ref{fig_grtemp}. + The gram sizes are Luge eroueh for their temperature ΠΠtion to be close to a narrow distribution around he equilibrium temperature., The grain sizes are large enough for their temperature distribution to be close to a narrow distribution around the equilibrium temperature. +" The radial variation iu the cluperature is nios visible or the siunallest eyalis, Which are heaed predomiiantlv by the stronely «nuinished UV ancl optical ight."," The radial variation in the temperature is most visible for the smallest grains, which are heated predominantly by the strongly diminished UV and optical light." + T1ο figure also shows the depeideuce of he dust toiuperatire ou composition., The figure also shows the dependence of the dust temperature on composition. + Sinall iron. grains are considerably warmer than silicate or graphite graius )ecause of he higji absorption in the UV. and optical and the low enudsskn probability in the infrared (?).., Small iron grains are considerably warmer than silicate or graphite grains because of the high absorption in the UV and optical and the low emission probability in the infrared \citep{Fischera2004b}. + Iu cores enbecded iu filaments with Ay-=Simae that are uessurized w the nean ISAL pressure. the temperatures of large eraius lie between 8 I aud 15 Ik. I note that the clupcerature variation for «ifereut erain types is smaller in both the core interior ai more opaque filaments where he eraius are heated by a nore reddened radiation field.," In cores embedded in filaments with $A_V=8\,{\rm mag}$ that are pressurized by the mean ISM pressure, the temperatures of large grains lie between 8 K and 15 K. I note that the temperature variation for different grain types is smaller in both the core interior and more opaque filaments where the grains are heated by a more reddened radiation field." + The physical explanation is the simular absorption aud cluission behavior of the erains at loug waveleueths. which for uost eraius is closcly described by a power law with OvsalesUUferxa/AT2 where a is: the grain: size.," The physical explanation is the similar absorption and emission behavior of the grains at long wavelengths, which for most grains is closely described by a power law with $Q^{\rm abs/em}_{\lambda}\propto a/\lambda^2$ where $a$ is the grain size." +. Iu this. limit.⋅⋅ the ratk» of the cooling to the heating rates aud therefore the evalji temperatures become the same.," In this limit, the ratio of the cooling to the heating rates and therefore the grain temperatures become the same." +" Fiero T shows the otained SEDs of cores. which axe αποσα, in spwerical Glameuts with Ay=&mae and AGlnag."," Figure \ref{fig_sedfit} shows the obtained SEDs of cores, which are embedded in spherical filaments with $A_V=8~{\rm mag}$ and $A_V=64~{\rm mag}$." + The SEDs of cores eiibedded im evlindrical filaments have he saue properties but slightly lower PAII emission axd ower dust temperatures for the same extinction values., The SEDs of cores embedded in cylindrical filaments have the same properties but slightly lower PAH emission and lower dust temperatures for the same extinction values. + The SEDs xfectt ie dependence of the opaqueuess of he coros Oll ot1 extiuctioji aud external prCSSHIOC as ciscussed in the previous sectious., The SEDs reflect the dependence of the opaqueness of the cores on both extinction and external pressure as discussed in the previous sections. +" For highly eiibedded cores, the SEDs deud to ukot parts on the extinction of he filament aud is largely independent of the external pressure (Sect. 2.1.2))."," For highly embedded cores, the SEDs depend to most parts on the extinction of the filament and is largely independent of the external pressure (Sect. \ref{sect_pressextrel}) )." + The cores are highly opaque aud are hoeatecL almost 1ji equal part by the attenuated stellar raciation field ancl the PAII ewission from the filaments (Seo Appendix. AppeudixAs. Fie. Al)).," The cores are highly opaque and are heated almost in equal part by the attenuated stellar radiation field and the PAH emission from the filaments (see Appendix \ref{sect_modelapprox}, Fig. \ref{fig_heatapprox}) )." + The minuiunuu arolud 10gan is cnranced by siicate absorption., The minimum around $10~\mu{\rm m}$ is enhanced by silicate absorption. + At the blue sice of the spectrum. the emission is οπαΤο:| by lisht scattered wihin the core.," At the blue side of the spectrum, the emission is dominated by light scattered within the core." + For a given extiwction zd. the scattered radiation is ouly wildly dependent «m the pressure since nost of the scattcved liebt οποιατος in a laver close to the surface of the Care (νους Fie. D).," For a given extinction $A_V$, the scattered radiation is only mildly dependent on the pressure since most of the scattered light originates in a layer close to the surface of the core (see Fig. \ref{fig_heating}) )." + Muliple scattered leh ouly becomes important at wavelengths À«23jan., Multiple scattered light only becomes important at wavelengths $\lambda< 3~\mu{\rm m}$. + The Jnik of the dust re-eiuissionisc oscly clescribec by a 1nodifiecl ack-bodv unction., The bulk of the dust re-emission is closely described by a modified black-body function. + At shorter wavelenelis. t1ο spectra shape is donunated by the enission from stochastic dust emission. s1anall eraius. avd PAILu jolecules.," At shorter wavelengths, the spectral shape is dominated by the emission from stochastic dust emission, small grains, and PAH molecules." + The effect of he dust ateuuation iMside he core is clearly visible in the PAT eiission., The effect of the dust attenuation inside the core is clearly visible in the PAH emission. + Because of the low inensitv of tιο UVοtical. theraio of the PAIL cussion to the «ust enisslon Jveals is lower than iu the dittse ISM or inside tιο filaments (Sect. 3.1.1))," Because of the low intensity of the UV/optical, theratio of the PAH emission to the dust emission peak is lower than in the diffuse ISM or inside the filaments (Sect. \ref{sect_sed_jmean}) )" + and. decreases svstenatically with extiition (Fie. 8))., and decreases systematically with extinction (Fig. \ref{fig_sedcores}) ). +" For highly embedded: cores. the reddeied radiatiou affects the specral share of the PATI enission spectra as the photons are not sfhcieutlv arerectic o heat the molecules to high temperaures,"," For highly embedded cores, the reddened radiation affects the spectral shape of the PAH emission spectrum as the photons are not sufficiently energetic to heat the molecules to high temperatures." + For a given extinction «ντ. the PAID emission of (uhedded cores is not strongly depeudoeut ou the external Moessure ew the heating flux for the PAIT 120ecules ds arecly absorbed iu the core.," For a given extinction $A_V$, the PAH emission of embedded cores is not strongly dependent on the external pressure as the heating flux for the PAH molecules is largely absorbed in the core." + The dust emisso1 on the 6her hand. appears to be colder auc strouger in ligher oessure regions as tle erains in the core’s center are jeated by a more strongly attenuated radiation field with a larecr fraction of the radiation being absorbed insicle he core.," The dust emission, on the other hand, appears to be colder and stronger in higher pressure regions as the grains in the core's center are heated by a more strongly attenuated radiation field with a larger fraction of the radiation being absorbed inside the core." + There is. however. a limit to the total hnunositv eiven by the ZS/2F heating the filameuts (see Sect. 3.2.2))," There is, however, a limit to the total luminosity given by the $ISRF$ heating the filaments (see Sect. \ref{sect_mbb_lum}) )" + The effect of the extinction for a given external Xessure pas on the dust ciuission from cores is shown in Fie. 8. ," The effect of the extinction for a given external pressure $p_{\rm ext}/k$ on the dust emission from cores is shown in Fig. \ref{fig_sedcores}, ," +which covers the range from noun-enibedded, which covers the range from non-embedded +shell of 5127. !Mpe size.,shell of $h^{-1}$ Mpc size. + The dashed line is for the quarter cube., The dashed line is for the quarter cube. + The top panel shows how the error iu he potential varies as one moves mto the subceubes., The top panel shows how the error in the potential varies as one moves into the subcubes. + Lines and error bars are the mean aud RAIS differences obtained from eieht subcube results., Lines and error bars are the mean and RMS differences obtained from eight subcube results. + The difference nonotouically decreases as the distance from boundaries Increases., The difference monotonically decreases as the distance from boundaries increases. + Since potentials cau be added by a coustaut without altering physics. the difference of about log rear the center can be ignored in the case of half cubo.," Since potentials can be added by a constant without altering physics, the difference of about $\sigma_{\Phi}$ near the center can be ignored in the case of half cube." + The figure tells that. if the potential field is to be obtained with error less than sav of its RAIS value. one should stay more than 515 HMpe from all sample undaries.," The figure tells that, if the potential field is to be obtained with error less than say of its RMS value, one should stay more than $54h^{-1}$ Mpc from all sample boundaries." + The quarter cube results show a much larecr variance that the half cube results., The quarter cube results show a much larger variance that the half cube results. + A similar trend is secu for the potential gradient as shown in the middle panel of Figure 2., A similar trend is seen for the potential gradient as shown in the middle panel of Figure 2. + The «c-componeut of the potential eradicut nminmics the linear racial peculiar velocity field very far from an observer., The $x$ -component of the potential gradient mimics the linear radial peculiar velocity field very far from an observer. + Due to lack of data outside subcubes the error in eracieut is large near boundaries but monotonically decreases as d increases., Due to lack of data outside subcubes the error in gradient is large near boundaries but monotonically decreases as $d$ increases. + The difference is snaller if one ignores the large-scale eracdieut ou the scale of the subceube., The difference is smaller if one ignores the large-scale gradient on the scale of the subcube. + The bottom panel of Figure 2 compares among the shear cllipticity from the full. half. aud quarter cubes.," The bottom panel of Figure 2 compares among the shear ellipticity from the full, half, and quarter cubes." + It is important to note that the error drops as the distance from boundaries duiereases essentiadlv in the une wav for the half aud quarter cube cases;, It is important to note that the error drops as the distance from boundaries increases essentially in the same way for the half and quarter cube cases. + The error reaches of the RAMS shear ellipticitv at the distance of d=33h ‘Mpc., The error reaches of the RMS shear ellipticity at the distance of $d=33 h^{-1}$ Mpc. + The depth of this buffer reeion must be a function ofthe amplitude aud shape of the power spectrum., The depth of this buffer region must be a function of the amplitude and shape of the power spectrum. + We conclude that one uceds to have an observational sample imch larger than 60% +\Ipe to secure the reeious where the shear field has error less than of its RAIS fluctuation., We conclude that one needs to have an observational sample much larger than $h^{-1}$ Mpc to secure the regions where the shear field has error less than of its RMS fluctuation. + Iu the previous section we used the προς deusitv of dark halos to calculate the potential field as it is cohbunon to use the ealaxv nuunber denusitv to define environment of galaxies., In the previous section we used the number density of dark halos to calculate the potential field as it is common to use the galaxy number density to define environment of galaxies. + However. it is the matter field that determines the true eravitational potential feld.," However, it is the matter field that determines the true gravitational potential field," +phases of recent star formation activity in PIxXS1345-—12: one occuring less (han 6 Myr ago that is associated with the SSCs and perhaps also linked to current the AGN and ULIRG activitv: the other occuring more than 40 Myr ago and associated with the diffuse light.,phases of recent star formation activity in PKS1345+12: one occuring less than 6 Myr ago that is associated with the SSCs and perhaps also linked to current the AGN and ULIRG activity; the other occuring more than 40 Myr ago and associated with the diffuse light. + This is consistent wilh previous LST imaging studies which have shown evidence for more than one episode of star formation activity in other merging svstems including the Antennae (?).. NGC7252 (??).. and Arp220 (?)..," This is consistent with previous HST imaging studies which have shown evidence for more than one episode of star formation activity in other merging systems including the Antennae \citep{Whitmore99}, NGC7252 \citep{Miller97,Maraston01}, and Arp220 \citep{Wilson06}." + Therefore our results fit in with the emerging trend that the star formation in merging svslenis is complex and multianocdal., Therefore our results fit in with the emerging trend that the star formation in merging systems is complex and multi-modal. +apparent.,apparent. + For M3. a small number of possible AGB stars are noted in the figure with black svinbols.," For M3, a small number of possible AGB stars are noted in the figure with black symbols." + The majority of these stars appear CN-weak. with only one CN-strong AGB stor.," The majority of these stars appear CN-weak, with only one CN-strong AGB star." + This result is similar to the observations reported by (2010).. who found that. in a sample of nine Galactie GCs. all showed either a total lack of CN-strong AGB stars or a significant depletion of CN-strong AGB stars compared to those present on the RGB.," This result is similar to the observations reported by , who found that, in a sample of nine Galactic GCs, all showed either a total lack of CN-strong AGB stars or a significant depletion of CN-strong AGB stars compared to those present on the RGB." + These authors noted (that no current explanation exists in standard stellar evolution theory as to why stars on the AGB should have reduced CN abundances compared to the RGB. particularly because the low effective temperatures should be suitable for similarly efficient molecular CN formation.," These authors noted that no current explanation exists in standard stellar evolution theory as to why stars on the AGB should have reduced CN abundances compared to the RGB, particularly because the low effective temperatures should be suitable for similarly efficient molecular CN formation." + In principle. increased mixing both on the RGB and al the beginning of AGB ascent should contribute more N (and thus stronger CN) to the stellar envelope. which should be apparent in surface abundance measurements.," In principle, increased mixing both on the RGB and at the beginning of AGB ascent should contribute more N (and thus stronger CN) to the stellar envelope, which should be apparent in surface abundance measurements." + Such a discrepancy. has been noted for a long lime: (wo possible explanations were proposed bv (1981)., Such a discrepancy has been noted for a long time; two possible explanations were proposed by . + First. if (vo chemically disünet populations in the cluster existed after star formation ceased. one of which was helium-rich and evolved to populate the blue end of the horizontal branch (HB). but never ascended to the AGB. this might lead to the delicieney of CN-strong stars.," First, if two chemically distinct populations in the cluster existed after star formation ceased, one of which was helium-rich and evolved to populate the blue end of the horizontal branch (HB), but never ascended to the AGB, this might lead to the deficiency of CN-strong stars." + The second explanation hypothesized (hat increased mixing in some stars produced increased. CN abundaices. but also led to increased mass loss at the RGB tip. producing stars populating the blue end of the WB that never ascended the ACD.," The second explanation hypothesized that increased mixing in some stars produced increased CN abundances, but also led to increased mass loss at the RGB tip, producing stars populating the blue end of the HB that never ascended the AGB." + The problem remains unsolved. and requires additional work.," The problem remains unsolved, and requires additional work." + Adopting the corrected values obtained [rom the above procedure. we produced a generalized histogram of the 0$(3839). distribution for each cluster. shown in Figure 4..," Adopting the corrected values obtained from the above procedure, we produced a generalized histogram of the $\delta$ $_{\rm N}$ distribution for each cluster, shown in Figure \ref{figdcngenhist}." + This was accomplished by representing each point as a Gaussian. centered on d5(3839). with a EWIIM equal to the uncertainty of that particular 09(2839) measurement. aud then adding the individual Gaussians together.," This was accomplished by representing each point as a Gaussian, centered on $\delta$ $_{\rm N}$ with a FWHM equal to the uncertainty of that particular $\delta$ $_{\rm N}$ measurement, and then adding the individual Gaussians together." + The uncertainty lor each $8(3839) measurement, The uncertainty for each $_{\rm N}$ measurement +The Tully-Fisher relation is also controlled by disk surface density.,The Tully-Fisher relation is also controlled by disk surface density. +" We use the empirical L-band Tully-Fisher TF) relation: L,=Crrv%,T?with az4 in the K-band (Mastersetal||2008) and v, the maximum rotation velocity, and where the virial theorem requires that Cry=(3/41)G?Y/ (LeMio)."," We use the empirical I-band Tully-Fisher (TF) relation: $L_\ast=C_{TF}v_r^\alpha,$with $\alpha\approx 4$ in the K-band \citep{mas08} + and $v_r$ the maximum rotation velocity, and where the virial theorem requires that $C_{TF}=(3/{4 \pi})G^{-2}\Sigma_{tot}^{-1}(L_\ast/M_{tot})$ ." + We find using equation (6)) that We infer that the Schmidt-Kennicutt law residuals should anti-correlate with the Tully-Fisher law residuals., We find using equation \ref{eq:AA}) ) that We infer that the Schmidt-Kennicutt law residuals should anti-correlate with the Tully-Fisher law residuals. +" The Tully-Fisher normalization is correct, by assumption: what is new is the predicted inverse correlation between SK and TF law residuals."," The Tully-Fisher normalization is correct, by assumption: what is new is the predicted inverse correlation between SK and TF law residuals." + The global star formation law can be applied to regions that are gas-dominated., The global star formation law can be applied to regions that are gas-dominated. +" When gas dominates the self-gravity, the cloud collision model suggests that X.xx22y,,,U?A and the KS law steepens."," When gas dominates the self-gravity, the cloud collision model suggests that $\dot\Sigma_\ast \propto { \Sigma_g}^{3/2}{\Sigma_{tot} }^{1/2}\simpropto {\Sigma_{gas} }^2, $ and the KS law steepens." +" There are indications of Xoas,such a steepening in several environments.", There are indications of such a steepening in several environments. + Steepening in a cloud collision model is not a unique explanation for any of these phenomena., Steepening in a cloud collision model is not a unique explanation for any of these phenomena. +" For example, the outer parts of disks are more thermally stable and the star formation rate in DLAs could be [2004),,suppressed because of the low Hz content due to a combination of a low dust content plus a high radiation field."," For example, the outer parts of disks are more thermally stable \citep{sch04}, and the star formation rate in DLAs could be suppressed because of the low $_2$ content due to a combination of a low dust content plus a high radiation field." + Turbulent pressure-regulated star formation is especially likely to be important in starbursts., Turbulent pressure-regulated star formation is especially likely to be important in starbursts. +" In disks, atomic cooling provides an effective thermostat for the turbulent velocity dispersion."," In disks, atomic cooling provides an effective thermostat for the turbulent velocity dispersion." + Feedback operates via the hot phase venting into the halo., Feedback operates via the hot phase venting into the halo. +" Gas may cool and fall back into the disk, as in the galactic fountain model, or escape in a wind, as happens for dwarf starburst galaxies."," Gas may cool and fall back into the disk, as in the galactic fountain model, or escape in a wind, as happens for dwarf starburst galaxies." +" The simple porosity description of supernova feedback in a multi-phase ISM provides an expression for the star formation rate in which porosity-driven turbulence is the controlling factor: px=Qmgsx(4n/3R3t,)-!, where the shell reaches a final size R4 before break-up, determined by the ambient pressure at expansion time t,."," The simple porosity description of supernova feedback in a multi-phase ISM \citep{sil01} provides an expression for the star formation rate in which porosity-driven turbulence is the controlling factor: $\dot\rho_\ast=Q m_{SN}({4\pi/ 3}R_a^3t_a)^{-1},$ where the shell reaches a final size $R_a$ before break-up, determined by the ambient pressure at expansion time $t_a$." +" The shell evolution is generally described by (Cioffietal.]1988]) and where v9=413km/s,Ro14pc,to1.3x104yr. Here cooling becomes significant at shell velocity Ve=38kms where the cooling time-scale within413E1n1/ a SN-driven shell moving at velocity v. is te=ve/Ap, and Aejf(T) is the effective cooling rate 5t-1/? over the relevant temperature range 10* = 0.86 \pm +0.21$." + This corresponds to ~4c detection of non Gaussianity from the cleaned maps., This corresponds to $\sim 4\sigma$ detection of non Gaussianity from the cleaned maps. + We interpret the non-vanishing (K) in terms of residual foreground contamination originating from the galactic plane., We interpret the non-vanishing $\left < \mathcal K \right>$ in terms of residual foreground contamination originating from the galactic plane. +" After flagging of the pixels determined by the G20 mask we obtain, (K)=—0.02+0.06, which is consistent with zero."," After flagging of the pixels determined by the G20 mask we obtain, $\left < \mathcal K \right> = -0.02 \pm 0.06$, which is consistent with zero." +" Henceforth, we use G20 mask as the basic mask to remove pixels contaminated by the residual foreground while analyzing cleaned maps from Monte-Carlo simulations as well as WMAP data."," Henceforth, we use G20 mask as the basic mask to remove pixels contaminated by the residual foreground while analyzing cleaned maps from Monte-Carlo simulations as well as WMAP data." +" The mean weights for 5 frequency bands satisfy, (W)=(0.049+0.021,—0.4190.063,—0.213+0.027,1.6430.063,—0.059 0.029)."," The mean weights for $5$ frequency bands satisfy, $\left <{\bf W}\right> = (0.049 \pm 0.021, -0.419 \pm 0.063, +-0.213 \pm 0.027, 1.643 \pm 0.063, -0.059 \pm 0.029)$ ." + Using the Monte-Carlo simulations we verify that the pixel temperature of cleaned maps outside the G20 mask follows a Gaussian distribution., Using the Monte-Carlo simulations we verify that the pixel temperature of cleaned maps outside the G20 mask follows a Gaussian distribution. + For this we apply G20 mask both to a randomly chosen CMB realization and its foreground cleaned counterpart., For this we apply G20 mask both to a randomly chosen CMB realization and its foreground cleaned counterpart. +" To verify the Gaussian nature of these distributions we fit the histogram of input CMB map (after G20 mask is applied) by a normalized Gaussian probability distribution, g(T)=exp-(T—a/(252))//Qs?), where a and s denote respectively mean and standard deviation of the distribution."," To verify the Gaussian nature of these distributions we fit the histogram of input CMB map (after G20 mask is applied) by a normalized Gaussian probability distribution, $g(T) = +exp(-(T-a)^2/(2s^2))/\sqrt{(2 \pi s^2)}$, where $a$ and $s$ denote respectively mean and standard deviation of the distribution." +" From the fit we find that, s=69.95+0.09uK and 0.11uK ?."," From the fit we find that, $s = 69.95 \pm 0.09 \mu K$ and $a = 2.12 \pm 0.11 \mu K$ ." + We apply G20 mask on each of the 200 foreground cleaned CMB maps and estimate full sky estimate of CMB power spectrum using MASTER method (Hivonetal. (2002)))., We apply G20 mask on each of the $200$ foreground cleaned CMB maps and estimate full sky estimate of CMB power spectrum using MASTER method \cite{Hivon02}) ). + The average of 200 power spectra obtained from the foreground removed maps matches excellently with the average of the input CMB power spectra., The average of $200$ power spectra obtained from the foreground removed maps matches excellently with the average of the input CMB power spectra. + We show both spectra in Fig., We show both spectra in Fig. + 2 along with the cosmic variance., \ref{NoBiasCl} along with the cosmic variance. + This verifies that no significant foreground contamination exists outside the G20 mask and the method outlined in this paper can be used to estimate CMB power spectrum to extract cosmological information., This verifies that no significant foreground contamination exists outside the G20 mask and the method outlined in this paper can be used to estimate CMB power spectrum to extract cosmological information. + In some of the earlier publications (Sahaetal.(2006);(2010))) the authors reported that the harmonic space based ILC method gives rise to a negative bias in its power spectrum at the low multipoles.," In some of the earlier publications \cite{Saha06,Tarun06,Saha08,Samal10}) ) the authors reported that the harmonic space based ILC method gives rise to a negative bias in its power spectrum at the low multipoles." + The bias appears due to a mere chance correlation between CMB and foregrounds at large angles due to availability of only small number of modes in the large scales on the sky., The bias appears due to a mere chance correlation between CMB and foregrounds at large angles due to availability of only small number of modes in the large scales on the sky. +" In principle, the negative bias in the power spectrum can be present in both pixel based and multipole based ILC algorithms which rely upon minimization of net foreground variance from the cleaned map, since in these cases the finite correlation between CMB and foregrounds arises due to certain degree of overlap between hot spots and cold spots of CMB and foregrounds and the algorithm creates a negative bias due to nonlinear dependence of weights on the empirical covariance matrix (Sahaetal. (2008)))."," In principle, the negative bias in the power spectrum can be present in both pixel based and multipole based ILC algorithms which rely upon minimization of net foreground variance from the cleaned map, since in these cases the finite correlation between CMB and foregrounds arises due to certain degree of overlap between hot spots and cold spots of CMB and foregrounds and the algorithm creates a negative bias due to nonlinear dependence of weights on the empirical covariance matrix \cite{Saha08}) )." +" However, the foreground removal method described in this paper relies upon the Gaussian nature of the final distribution, without explicitly minimizing the variance of the data."," However, the foreground removal method described in this paper relies upon the Gaussian nature of the final distribution, without explicitly minimizing the variance of the data." + This leads to the advantage that the power spectrum obtained from the cleaned map does not have any negative bias., This leads to the advantage that the power spectrum obtained from the cleaned map does not have any negative bias. + Before the analysis we mask out the positions of known point sources from each of WMAP's 5 frequency maps using the point source mask., Before the analysis we mask out the positions of known point sources from each of WMAP's $5$ frequency maps using the point source mask. + After masking each map contains 3054273 pixels comprising 97% of the full sky area., After masking each map contains $3054273$ pixels comprising $97\%$ of the full sky area. + The discovery and characterization of extrasolar terrestrial planets in the habitable zone (HZ) of their central star ts one of the most exciting prospects of exoplanetary science., The discovery and characterization of extrasolar terrestrial planets in the habitable zone (HZ) of their central star is one of the most exciting prospects of exoplanetary science. + Such planets are extremely good candidates for the search for extraterrestrial life., Such planets are extremely good candidates for the search for extraterrestrial life. + The HZ is usually defined as the shell around a star where a planet could retain liquid water on the surface (2).., The HZ is usually defined as the shell around a star where a planet could retain liquid water on the surface \citep{kasting1993}. + This definition is motivated because liquid water seems to be the fundamental requirement for life as we know it on Earth., This definition is motivated because liquid water seems to be the fundamental requirement for life as we know it on Earth. + Being located inside the HZ as defined by ? for an Earth-like planet. however. not necessarily implies habitability for à specific planetary scenario (see. e.g.. Mars in our own solar system).," Being located inside the HZ as defined by \citet{kasting1993} for an Earth-like planet, however, not necessarily implies habitability for a specific planetary scenario (see, e.g., Mars in our own solar system)." + The potential habitability of a planet depends eritically on atmospheric composition and surface pressure., The potential habitability of a planet depends critically on atmospheric composition and surface pressure. + Still. for a planet located well inside this classical HZ. habitability is achievable for a much broader range of atmospheric conditions (greenhouse effect etc.)," Still, for a planet located well inside this classical HZ, habitability is achievable for a much broader range of atmospheric conditions (greenhouse effect etc.)" + than for a planet near one of the boundaries., than for a planet near one of the boundaries. + Among the more than 500 extrasolar planets discovered so far. some orbit their central star inside or near the HZ (e.g.. 2... 2. 2.. 2).," Among the more than 500 extrasolar planets discovered so far, some orbit their central star inside or near the HZ (e.g., \citealp{mayor2004}, , \citealp{lovis2006}, \citealp{fischer2008}, \citealp{haghighipour2010}) )." + Most of these planets are Neptune- or gas planets., Most of these planets are Neptune- or Jupiter-like gas planets. + The planetary system (GL 581). however. contains at least four planets (?.. 2.. 2)). one of which is a potentially habitable Super-Earth. GL 581 d. This was shown by ?.. 2.. ? and ? who presented 1D modeling studies of different atmospheric scenarios of GL 58] d. They found habitable surface conditions (1.e.. surface temperatures above 273 K) with CO» partial pressures as low as | bar. depending on CO» concentration.," The planetary system (GL 581), however, contains at least four planets \citealp{bonfils2005}, \citealp{udry2007}, \citealp{mayor2009gliese}) ), one of which is a potentially habitable Super-Earth, GL 581 d. This was shown by \citet{wordsworth2010}, \citet{vparis2010gliese}, \citet{hu2011} and \citet{kaltenegger2011} who presented 1D modeling studies of different atmospheric scenarios of GL 581 d. They found habitable surface conditions (i.e., surface temperatures above 273 K) with $_2$ partial pressures as low as 1 bar, depending on $_2$ concentration." + These results imply that the GL 581 planetary system contains indeed at least one potentially habitable. possibly terrestrial planet.," These results imply that the GL 581 planetary system contains indeed at least one potentially habitable, possibly terrestrial planet." + Orbital simulations presented by ?./ showed that between the orbits of GL 581 ο and d (re. inside the classical HZ). another Super-Earth planet would be dynamically stable.," Orbital simulations presented by \citet{zollinger2009} + showed that between the orbits of GL 581 c and d (i.e., inside the classical HZ), another Super-Earth planet would be dynamically stable." + Specifically. they stated a stability range for a low-eccentricity planet of not more than 2.6 Earth masses (m.) ranging from 0.126 AU to 0.17 AU.," Specifically, they stated a stability range for a low-eccentricity planet of not more than 2.6 Earth masses $_{\oplus}$ ) ranging from 0.126 AU to 0.17 AU." + Recently. ? claimed the detection of two more planets in the GL 581 system. one of them (called GL 581 gin ?)) with a minimum mass of 3.1 ma and an orbital distance of 0.146 AU. hence inside the stability range calculated by ?..," Recently, \citet{vogt2010gliese} claimed the detection of two more planets in the GL 581 system, one of them (called GL 581 gin \citealp{vogt2010gliese}) ) with a minimum mass of 3.1 $_{\oplus}$ and an orbital distance of 0.146 AU, hence inside the stability range calculated by \citet{zollinger2009}." + These detections are controversial and disputed by further analysis of the radial velocity data (?).., These detections are controversial and disputed by further analysis of the radial velocity data \citep{tuomi2011}. + Nevertheless. we use this claimed discovery as a starting point to investigate the habitability of planets in the GL 58] system.," Nevertheless, we use this claimed discovery as a starting point to investigate the habitability of planets in the GL 581 system." + Such model calculations aim at supporting the selection of future targets for detailed observational programs of habitable planets which 1s probably needed in the future (?).. given the expected number of targets.," Such model calculations aim at supporting the selection of future targets for detailed observational programs of habitable planets which is probably needed in the future \citep{horner2010}, , given the expected number of targets." + Such potentially habitable planets are expected to be discovered in the near future by on-going ground-based programs such as MEarth (2) or space missions like Kepler (see. e.g.. ? foran overview of Kepler candidates) and the planned PlaTO mission (?)..," Such potentially habitable planets are expected to be discovered in the near future by on-going ground-based programs such as MEarth \citep{nutzman2008} or space missions like Kepler (see, e.g., \citealp{borucki2011} for an overview of Kepler candidates) and the planned PlaTO mission \citep{catala2009}." + First attempts at characterizing the atmospheres of transiting Super-Earth planets have already been made(CoRoT-7 b. ?.. and GJ 1214 b. 2.. 2. 25).," First attempts at characterizing the atmospheres of transiting Super-Earth planets have already been made(CoRoT-7 b, \citealp{guenther2011}, and GJ 1214 b, \citealp{bean2010}, \citealp{desert2011}, \citealp{croll2011_gj1214}) )." + For the claimed planet in the HZ of GL 581. dedicated modeling studies have been performed by ?.. ? and ?..," For the claimed planet in the HZ of GL 581, dedicated modeling studies have been performed by \citet{pierrehumbert2011}, \citet{heng2011} and \citet{bloh2011}." + ? presented several possible atmospheric scenarios. (airless planet. pure N». mixed CO>/H2O atmospheres) and discussec potential implications for surface conditions. without detailec calculations of the atmospheric structure for the mixed CO;/H;O cases.," \citet{pierrehumbert2011} presented several possible atmospheric scenarios (airless planet, pure $_2$, mixed $_2$ $_2$ O atmospheres) and discussed potential implications for surface conditions, without detailed calculations of the atmospheric structure for the mixed $_2$ $_2$ O cases." + On the other hand. ? used à general circulation model of Earth to simulate the dynamics and circulation on GL 581 σ. however did not investigate surface conditions and habitability in. detail.," On the other hand, \citet{heng2011} used a general circulation model of Earth to simulate the dynamics and circulation on GL 581 g, however did not investigate surface conditions and habitability in detail." + The. study of ? used a geodynamie box model to assess planetary habitability. coupling geophysical and atmospheric processes in à simplified approach.," The study of \citet{bloh2011} used a geodynamic box model to assess planetary habitability, coupling geophysical and atmospheric processes in a simplified approach." + Previous modeling studies of habitability in the GL 581 system either focused on the existing planets GL... 581 c and d (e.g.. 2.. 2)). used a very simple model to simulate atmospheric. processes and surface conditions (e.g.. 2)) or investigated only à very small subset of potential atmospheric scenarios in. terms ofCO» level and surface pressure when varying orbital distance (?)..," Previous modeling studies of habitability in the GL 581 system either focused on the existing planets GL 581 c and d (e.g., \citealp{selsis2007gliese}, \citealp{bloh2007}) ), used a very simple model to simulate atmospheric processes and surface conditions (e.g., \citealp{bloh2011}) ) or investigated only a very small subset of potential atmospheric scenarios in terms of$_2$ level and surface pressure when varying orbital distance \citep{kaltenegger2011}. ." + We present heremodel calculations for possible terrestrial planets in the GL 581 system along the same line of reasoning as in 2. using," We present heremodel calculations for possible terrestrial planets in the GL 581 system along the same line of reasoning as in \citet{vparis2010gliese}, , using" +which are entities of interest (see. e.g. Negi Durgapal 1999: and references therein).,"which are entities of interest (see, e.g. Negi Durgapal 1999; and references therein)." + For the lower limit of the ‘central’ weighted mean value of Q20.05. the Vela mass can reduce upto a value of about 2.05241...," For the lower limit of the `central' weighted mean value of $Q \simeq 0.05$, the Vela mass can reduce upto a value of about $2.052 M_\odot$." + The corresponding values of surface redshift and core mass turn out to be 0.6066 and O4SOAL. respectively., The corresponding values of surface redshift and core mass turn out to be 0.6066 and $0.489M_\odot$ respectively. + Thus. the core mass of the structure varies between 23.8 % to 47.6% of the total mass. for the lower limit of Qo20.05 to the upper limit of Q20.19 respectively.," Thus, the core mass of the structure varies between 23.8 $\%$ to $\%$ of the total mass, for the lower limit of $Q \simeq 0.05$ to the upper limit of $Q \simeq 0.19$ respectively." + For (2 values larger than about 0.197 (io... the point of maximum mass Adj.=2.2.M.). the structures become pulsationally unstable. whereas the minimumstable Vela mass corresponds to a value about 1.758 M. as(Q 0.," For $Q$ values larger than about 0.197 (i.e., the point of maximum mass $M_{max} = 2.2 M_\odot$ ), the structures become pulsationally unstable, whereas the minimumstable Vela mass corresponds to a value about 1.758 $M_\odot$ as $Q \rightarrow 0$ ." +" In the previous study. we considered the values of constan E, = (4/3). (5/3). and 2 respectively for the density range below the fiduciary transition density £y on the basis of ‘compatibility criterion’ in order to construct the starquake models for Crab pulsar (Negi 2005)."," In the previous study, we considered the values of constant $\Gamma_1$ = (4/3), (5/3), and 2 respectively for the density range below the fiduciary transition density $E_b$ on the basis of `compatibility criterion' in order to construct the starquake models for Crab pulsar (Negi 2005)." + LE (1) the observationa constraint of the στο healing parameter. ancl (i) the observational constraint of the recently evaluated: value of the moment of inertia for the Crab pulsar were combine together with the ‘compatibility criterion’ mentioned above. the model with Py=(5/3) envelope itself. vielded: the value of transitions density. 22.7.10!οem7. the nuclear matter saturation clensity at the core-envelope boundary.," If (i) the observational constraint of the glitch healing parameter, and (ii) the observational constraint of the recently evaluated value of the moment of inertia for the Crab pulsar were combined together with the `compatibility criterion' mentioned above, the model with $\Gamma_1 = (5/3)$ envelope itself yielded the value of transitions density, $ \simeq 2.7 \times + 10^{14}\,{\rm g\, cm}^{-3}$, the nuclear matter saturation density at the core-envelope boundary." + This value of ££ vields the upper bound. on NS masses MaascΛιν. of the EOS of the envelope (Negi 2005).," This value of $E_b $ yields the upper bound on NS masses $M_{\rm max} \simeq 4.1 M_\odot$, of the EOS of the envelope (Negi 2005)." +" Not only this value is found. Lully consistent with the upper bound on NS masses obtained by. using modern I08s for NS matter. fitted to experimental nucleon-nucleon scattering data and the properties of light nuclei. consistent with causality and dynamical stability (see. Fig.2 of Ixalogera Bavin 1996. for a fiduciary. transition density ky=2.710gem.5 7). the upper bound on compactness ratio of these mocels. Cia.2 0.34) was also found. Lully consistent with the ""absolute"" upper bound on compactness ratio of NSs consistent with causality ancl pulsational stability (Neei 2004b)."," Not only this value is found fully consistent with the upper bound on NS masses obtained by using modern EOSs for NS matter, fitted to experimental nucleon-nucleon scattering data and the properties of light nuclei, consistent with causality and dynamical stability (see, Fig.2 of Kalogera Baym 1996, for a fiduciary transition density $E_b = 2.7 \times 10^{14}\,{\rm g\, cm}^{-3}$ ), the upper bound on compactness ratio of these models $u_{max} \simeq 0.34$ ) was also found fully consistent with the `absolute' upper bound on compactness ratio of NSs consistent with causality and pulsational stability (Negi 2004b)." + Phe results of this study are also supported by observations. since the existed. value of the upper bound on the energy. of a eravitationally recishifted 5-ray line at about O40 MeV from the Crab pulsar is found consistent with the predicted. value in the energy range of about 0.4214 - 418 MeV. (see. Negi 2005: and references therein).," The results of this study are also supported by observations, since the existed value of the upper bound on the energy of a gravitationally redshifted $\gamma$ -ray line at about 0.40 MeV from the Crab pulsar is found consistent with the predicted value in the energy range of about 0.414 - 418 MeV (see, Negi 2005; and references therein)." +" 1n the previous study. the value of the ratio of pressure to density at the core-envelope. boundary. P,/Es. on the basis of ‘compatibility criterion! was caleulatecd as 1.06510. 7. which represents the region very close to the surface of the star (thin crust). and does not require the necessary continuity of the speed of sound. (together. with other variables) at this boundary which (obviously) corresponds to a region of relatively low density."," In the previous study, the value of the ratio of pressure to density at the core-envelope boundary, $P_b/E_b$, on the basis of `compatibility criterion' was calculated as $\sim 1.065 \times 10^{-2}$ , which represents the region very close to the surface of the star (thin crust), and does not require the necessary continuity of the speed of sound (together with other variables) at this boundary which (obviously) corresponds to a region of relatively low density." + Since. we were concerned with the larger values of the elitch healing parameter. €> 0.70. for the Crab pulsar which demanded that more than τον of the moment of inertia should remain attached to the core component.," Since, we were concerned with the larger values of the glitch healing parameter, $Q \geq 0.70$ , for the Crab pulsar which demanded that more than $\%$ of the moment of inertia should remain attached to the core component." + Llowever. the much smaller. values of the elitch healing parameter for Vela pulsar. Q 0.20. require thatmore than SOC of the moment of inertia should remain confined to the envelope region which obviously require," However, the much smaller values of the glitch healing parameter for Vela pulsar, $Q \leq 0.20$ , require thatmore than $\%$ of the moment of inertia should remain confined to the envelope region which obviously require" +ες200 correspond to angular scales 0ο17.. to which the WSRT is not seusitive.,"$\ell \la 200$ correspond to angular scales $\theta \ga +1$, to which the WSRT is not sensitive." +" The visibilities from which a map is iade are Voaplttο)=ωμάeyPac), where Vins are 1C observed visibilities. aud ανο) is the taper function."," The visibilities from which a map is made are $V_{map}(u,v) = +V_{obs}(u,v)\, T(u,v)$, where $V_{obs}$ are the observed visibilities, and $T(u,v)$ is the taper function." +"ue The calculated intensity of the tapered data is (15,,4,)=FO«© FL). where F is a Fourier transform and the asterisk denotes convolution."," The calculated intensity of the tapered data is ${\cal F}(V_{map}) = {\cal F}(V_{obs})*{\cal F}(T)$ , where ${\cal F}$ is a Fourier transform and the asterisk denotes convolution." + The power spectrum of the Stokes parameter NV. PS(X). is then: where X is Stokes Q or C.," The power spectrum of the Stokes parameter $X$, $PS(X)$, is then: where $X$ is Stokes $Q$ or $U$." + Although polarized intensity P is derived from Q aud C and thus not directly observed. correction for the taper in the same wav as for Q aud {ὁ power spectra is a good approximation.," Although polarized intensity $P$ is derived from $Q$ and $U$ and thus not directly observed, correction for the taper in the same way as for $Q$ and $U$ power spectra is a good approximation." + As an illustratio- Fig.," As an illustration, Fig." + E shows the power spectrum of P of the tapered data in the Auriga region at 311 MIIz (solid line)., \ref{f9:ps_corr} shows the power spectrum of $P$ of the tapered data in the Auriga region at 341 MHz (solid line). + The dotted line is the samme spectrum. but corrected for the tapering according to Eq. (1)).," The dotted line is the same spectrum, but corrected for the tapering according to Eq. \ref{e:taper}) )." + The power law behavior exteuds to loe(()zz3.6., The power law behavior extends to $\log(\ell) \approx 3.6$. + In Fig. 5.," In Fig. \ref{f9:ps_p_obs}," + we show the power spectra of P iu the Auriga and Horologium regions at 5 frequencies. both for the tapered (upper curve) aud uutapered data (ower curve) in the same plot.," we show the power spectra of $P$ in the Auriga and Horologium regions at 5 frequencies, both for the tapered (upper curve) and untapered data (lower curve) in the same plot." + The amplitudes of the power spectra of the tapered data are lower than those of the untapered data ouly because the iuteusities are expressed iu mJv/beauu., The amplitudes of the power spectra of the tapered data are lower than those of the untapered data only because the intensities are expressed in mJy/beam. + Because the beam widths are cüffereut for the two datasets. this gives a difference in the magnitude of P in tapered aud uutapered data.," Because the beam widths are different for the two datasets, this gives a difference in the magnitude of $P$ in tapered and untapered data." + The power spectra of RAL in the Auriga and Worologimm field are e¢iven in Fie 6.., The power spectra of $RM$ in the Auriga and Horologium field are given in Fig \ref{f9:ps_rm_obs}. + Ouly tapered data give reliable enough RAL determinations to produce power spectra for thoi., Only tapered data give reliable enough $RM$ determinations to produce power spectra for them. + Fies., Figs. +" 7 and & show power spectra for the Stokes piriüueters Q aud Ü in the Auriga aud Worologimm region respectively, again for tapered and uutapered data."," \ref{f9:ps_qu_aur} and \ref{f9:ps_qu_hor} show power spectra for the Stokes parameters $Q$ and $U$ in the Auriga and Horologium region respectively, again for tapered and untapered data." + The correspouding multipole spectral indices à. derived for a iultipole range of 100«(6«z1500. are eiven in Table 1..," The corresponding multipole spectral indices $\alpha$, derived for a multipole range of $400 < \ell < 1500$, are given in Table \ref{t9:a_obs}. ." + At small scales aree (). the power spectra of the uutapered data flatten out due to the noise in the maps. while the low-resolution data steepen due to the taperiug. as illustrated in Fig. L.," At small scales (large $\ell$ ), the power spectra of the untapered data flatten out due to the noise in the maps, while the low-resolution data steepen due to the tapering, as illustrated in Fig. \ref{f9:ps_corr}." +" At luge scales. the Q and CU power spectra of the apered data show a decrease,"," At large scales, the $Q$ and $U$ power spectra of the tapered data show a decrease." + This decrease could be due to the lack of large-scale structure (see Sect. 2.1)).," This decrease could be due to the lack of large-scale structure (see Sect. \ref{s9:wsrtdata}) )," + but then it is hard to explain why there is no such decline in 2., but then it is hard to explain why there is no such decline in $P$. + The nower spectra of Q and Uo are steeper and have a larecr auplitude than the power spectra of P., The power spectra of $Q$ and $U$ are steeper and have a larger amplitude than the power spectra of $P$. + This could be caused by the preseuce of a Faraday screen in frout of he ciuittinec» region., This could be caused by the presence of a Faraday screen in front of the emitting region. +Oo A Faraday screen will rotate the polarization angle. aux so induce extra structure in Q and (. while leaving P unaltered.," A Faraday screen will rotate the polarization angle, and so induce extra structure in $Q$ and $U$, while leaving $P$ unaltered." + This results i a higher amplitude of the power spectrmu., This results in a higher amplitude of the power spectrum. + As the Faraday screcu consists of foreground. immaterial. its angular size is large. steepeniug the spectrum.," As the Faraday screen consists of foreground material, its angular size is large, steepening the spectrum." + This effect was also noticed. by Tucci et (02002)., This effect was also noticed by Tucci et (2002). + The logarithnuc slope of the power spectra of polarized intensity is apz 2.1 - 2.3(Table 13). which," The logarithmic slope of the power spectrum of polarized intensity is $\alpha_P \approx$ 2.1 - 2.3(Table \ref{t9:a_obs}) ), which" +A reasonable match with the MIR to UV datapoints could be obtained with a reddened QSO template with Ay0.7—0.8 the extinction curve of Gaskell&Benker 2007)).,A reasonable match with the MIR to UV datapoints could be obtained with a reddened QSO template with $A_V\sim0.7-0.8$ (adopting the extinction curve of \citealt{gb07}) ). +"(adopting When converting the measured optical extinction into an equivalent hydrogen column density by applying the relation valid for the Milky Way ISM (Ng~1.8x10?! Ay), we find Ny~1.3x1031 cm-?, which is three dex smaller than what is estimated from the X-ray spectral fit."," When converting the measured optical extinction into an equivalent hydrogen column density by applying the relation valid for the Milky Way ISM $N_H\sim1.8\times10^{21}A_V$ ), we find $N_H\sim 1.3\times10^{21}$ $^{-2}$, which is three dex smaller than what is estimated from the X-ray spectral fit." +" A mismatch between the X-ray and the optically estimated column density, in the range of ~3—100, is observed in local AGN, calling for a number of interpretations (e.g.,lowdust-to-gasratio;Maiolinoetal. 2001)."," A mismatch between the X-ray and the optically estimated column density, in the range of $\sim3-100$, is observed in local AGN, calling for a number of interpretations \citep[e.g., low dust-to-gas ratio;][]{maiolino01powder}." +". The mismatch observed in XID403 is ~1000, which would make this object extreme."," The mismatch observed in XID403 is $\sim$ 1000, which would make this object extreme." +" In their SED analysis Coppinetal. suggest a different, stellar origin for the optical/UV (2009)rest frame emission."," In their SED analysis \citet{coppin09} suggest a different, stellar origin for the optical/UV rest frame emission." +" Following the parameterization used by Vignalietal. and Pozzietal. for obscured AGN, we (2009)fitted the SED of XID403(2010) with a stellar component, an AGN torus component, and a dusty starburst component."," Following the parameterization used by \citet{vignali09} and \citet{pozzi10} for obscured AGN, we fitted the SED of XID403 with a stellar component, an AGN torus component, and a dusty starburst component." +" 'The dusty starburst is responsible for the bulk of the FIR to radio emission, while the AGN torus produces the entire emission at 244m (4ym rest-"," The dusty starburst is responsible for the bulk of the FIR to radio emission, while the AGN torus produces the entire emission at $\mu$ m $\mu$ m rest-frame)." +" A galaxy template with M,~1.2x10!! Mo, frame).Ay~1 and a 1-Gyr-old constant star formation rate nicely fits the optical/UV.,,, data."," A galaxy template with $M_\star\sim1.2\times10^{11}\,M_{\odot}$ , $A_V\sim1$ and a $\sim$ 1-Gyr-old constant star formation rate nicely fits the $_{rest}$ data." +" However, a possible problem in interpreting the optical/UV,cs¢ emission as stellar light is that XID403 is pointlike in the deep HST/ACS images (CLASS_SSTAR=0.99 in i775 and which would imply half-light radius of <0.3 kpc."," However, a possible problem in interpreting the $_{rest}$ emission as stellar light is that XID403 is pointlike in the deep HST/ACS images STAR=0.99 in $i_{775}$ and $z_{850}$ ), which would imply a half-light radius of $<0.3$ kpc." +" Although2850). very compact morphologiesa have been observed in a fraction of distant sub-mm galaxies (Ricciardellietal. 2010), the pointlike nature of XID403, coupled to the presence of broad NV suggest that the light has a emission,nuclear mightorigin."," Although very compact morphologies have been observed in a fraction of distant sub-mm galaxies \citep{ricciardelli10}, the pointlike nature of XID403, coupled to the presence of broad NV emission, might suggest that the $_{rest}$ light has a nuclear origin." +" In particular, we could be optical/UV;yes¢looking at a fraction of nuclear radiation that leaks out without being (cabsorbed10%) or is scattered towards us and thus would be polarized."," In particular, we could be looking at a fraction $\sim10\%$ ) of nuclear radiation that leaks out without being absorbed or is scattered towards us and thus would be polarized." +" If true, the effective extinction to the nucleus would be much higher than that estimatedby fitting the whole MIR to UV emission with a reddened QSO template, being more in line with the large X-ray column density."," If true, the effective extinction to the nucleus would be much higher than that estimatedby fitting the whole MIR to UV emission with a reddened QSO template, being more in line with the large X-ray column density." +" This interpretation has been already proposed by Pollettaetal.(2008) to explain the relatively blue optical/UV emission and broad line components of two sub-mm galaxies at z~3.5 hosting heavily obscured AGN, similar to XID403."," This interpretation has been already proposed by \citet{polletta08} to explain the relatively blue optical/UV emission and broad line components of two sub-mm galaxies at $z\sim3.5$ hosting heavily obscured AGN, similar to XID403." +" Also, although the stellarity parameter is uncertain for the faint K-band detection, the decrease of CLASS.SSTAR from 0.95 in Y to 0.74 in K may also suggest that the host galaxy contributes significantly only at Arest>4000À."," Also, although the stellarity parameter is uncertain for the faint $K$ -band detection, the decrease of STAR from 0.95 in $Y$ to 0.74 in $K$ may also suggest that the host galaxy contributes significantly only at $\lambda_{rest}>4000$." +. In Fig.2 we show a possible SED decomposition for XID403 obtained by adding an AGN torus component and a scattering component (corresponding to ~10% of the AGN intrinsic UV emission!9)) to the SED of Arp220., In Fig.2 we show a possible SED decomposition for XID403 obtained by adding an AGN torus component and a scattering component (corresponding to $\sim10\%$ of the AGN intrinsic UV ) to the SED of Arp220. +" In summary, the full SED analysis shows that XID403 is not a classic, type-2 QSO (i.e., a narrow-line, X-ray obscured AGN whose physical properties can be explained within the standard, geometry-based Unified Model; Normanetal. 2002)), but points to a complex physical picture likely related to its active assembly phase."," In summary, the full SED analysis shows that XID403 is not a classic, type-2 QSO (i.e., a narrow-line, X-ray obscured AGN whose physical properties can be explained within the standard, geometry-based Unified Model; \citealt{norman02}) ), but points to a complex physical picture likely related to its active assembly phase." +" The IR emission from the AGN torus and the measured X-ray emission are used (see e.g., Vignalietal.2009;Pozzietal. 2010)) to derive an AGN bolometric power of 7x10* erg s~!."," The IR emission from the AGN torus and the measured X-ray emission are used (see e.g., \citealt{vignali09,pozzi10}) ) to derive an AGN bolometric power of $7\times10^{45}$ erg $^{-1}$." +" Assuming that the BH is at the Eddington limit, as might be expectedradiating during these active BH and galaxy build-up phases, would imply Mpy=5x10’Mo."," Assuming that the BH is radiating at the Eddington limit, as might be expected during these active BH and galaxy build-up phases, would imply $M_{BH}=5\times10^7\,M_{\odot}$." +" This in turn gives ΛΜΙΗΗ/Μι 10-4, which is a factor of 5 smaller than the local value."," This in turn gives $M_{BH}/M_{\star} \sim 4\times10^{-4}$ , which is a factor of 5 smaller than the local value." +" It would then seem that both BH and stellar mass are rapidly growing towards their final values, but the BH is lagging behind as seen in sub-mm galaxies at z~2 (Alexanderetal.2008b) and expected by recent analytic models of formation (Lamastraetal. 2010)."," It would then seem that both BH and stellar mass are rapidly growing towards their final values, but the BH is lagging behind as seen in sub-mm galaxies at $z\sim2$ \citep{alex08submm} and expected by recent semi-analytic models of BH/galaxy formation \citep{lamastra10}." +". However, since the BH/galaxyestimated BH mass is a lower limit (accretion might be sub-Eddington) and the stellar mass derived in the previous section might be an upper limit (the AGN likely contributes to the es: light), this ratio might well be equal to the optical/UV;local value."," However, since the estimated BH mass is a lower limit (accretion might be sub-Eddington) and the stellar mass derived in the previous section might be an upper limit (the AGN likely contributes to the $_{rest}$ light), this ratio might well be equal to the local value." +" While the space density of luminous, unobscured and moderately obscured QSOs declines exponentially at zZ3 (eg.Brusaetal.2009;Civano2011),, the behaviour of heavily obscured objects has still to be properly determined."," While the space density of luminous, unobscured and moderately obscured QSOs declines exponentially at $z\gtrsim3$ \citep[e.g.,][]{brusa09,civano11}, the behaviour of heavily obscured objects has still to be properly determined." +" Semi-analytic modelsof BH/galaxy evolution linking the obscuration on nuclear scales to the gas availability in the host galaxy (e.g.,Menci 2008), would predict an increasing abundance of obscured AGN towards high redshifts, and some observational evidence of this trend has been reported (Treisteretal.2009 and references therein)."," Semi-analytic modelsof BH/galaxy evolution linking the obscuration on nuclear scales to the gas availability in the host galaxy \citep[e.g.,][]{menci08}, , would predict an increasing abundance of obscured AGN towards high redshifts, and some observational evidence of this trend has been reported \citealt{tuv09} and references therein)." +We should stress that. as proved iu an earlier paper (Lombardi Bertin 100δυ). the three formulations are nathematically equivalent.,"We should stress that, as proved in an earlier paper (Lombardi Bertin 1998b), the three formulations are mathematically equivalent." + Thus it would not be surprising to find that proper nunerical implementations orforiu. for large values of the exid nmuuber AN. in a simular iuanner as far as accuracy and reliability are concerned.," Thus it would not be surprising to find that proper numerical implementations perform, for large values of the grid number $N$, in a similar manner as far as accuracy and reliability are concerned." + Iu practice. for finite values of EI. the third nethod turus out to be characterized by small errors. often παος. than those associated with the other two οςσος.," In practice, for finite values of $N$, the third method turns out to be characterized by small errors, often smaller than those associated with the other two procedures." + Direct methods im variational problems are well-known especially in applied mathematics (sec. e.g. Colfand. Fomin 1963).," Direct methods in variational problems are well-known especially in applied mathematics (see, e.g., Gelfand Fomin 1963)." +" Suppose that oue can find a sot of functions (f£,] on the domain 9 (the full definition of “complete” will be given below). so that auy function on Q can be represcuted as a linear combination of the form More precisely. we assume that for any. function &(0). there is a choice for the coefficients {ce} such that Let us now introduce a sequence of trial mass maps We further require that the function η qninimizes the functional.H S:+ iuH other words. clte|d“1([η] are chosen so that the fictional S has minima value."," Suppose that one can find a set of functions $\{ f_\alpha \}$ on the domain $\Omega$ (the full definition of “complete” will be given below), so that any function on $\Omega$ can be represented as a linear combination of the form More precisely, we assume that for any function $\tilde +\kappa(\vec\theta)$, there is a choice for the coefficients $\{ +c_\alpha \}$ such that Let us now introduce a sequence of trial mass maps We further require that the function $\tilde\kappa^{[n]}$ minimizes the functional $S$: in other words, $c^{[n]}_1, c^{[n]}_2, \dots, +c^{[n]}_n$ are chosen so that the functional $S$ has minimum value." + This obviously happens when Solving this set of » equations. we obtain the η cocficicuts zu aud thus the function αἱ].," This obviously happens when Solving this set of $n$ equations, we obtain the $n$ coefficients $c^{[n]}_\alpha$, and thus the function $\tilde\kappa^{[n]}$." + By repeating this operation for a sequence of values of ». we fiud a sequence of functions &*J.," By repeating this operation for a sequence of values of $n$, we find a sequence of functions $\tilde\kappa^{[n]}$." +" These functions. under suitable assuniptious (verified in our problem). have the following properties (see Gelfand Fomin 1963 for a detailed discussion): (i) Let us call Sl] the value of S when & is replaced bv the function gl, Then. obviously. the sequence SUI is not increasing. G"," These functions, under suitable assumptions (verified in our problem), have the following properties (see Gelfand Fomin 1963 for a detailed discussion): (i) Let us call $S^{[n]}$ the value of $S$ when $\tilde\kappa$ is replaced by the function $\tilde\kappa^{[n]}$ Then, obviously, the sequence $S^{[n]}$ is not increasing. (" +"i) If the set {1,1 is complete. then the fictions ΟΠ] converge to the solution & of the problem.","ii) If the set $\{ f_\alpha \}$ is complete, then the functions $\tilde\kappa^{[n]}$ converge to the solution $\tilde\kappa$ of the problem." + This method thus provides a way to obtain the function &(8) with desired accuracy., This method thus provides a way to obtain the function $\tilde\kappa(\vec\theta)$ with desired accuracy. + The method described here can be casily applied. to our problem., The method described here can be easily applied to our problem. + In fact. by expanding gli as in Eq.(," In fact, by expanding $\tilde\kappa^{[n]}(\vec\theta)$ as in Eq.," +8).. we find The previous equation. for a=1.2.....0. represeuts a linear svstein of 7 equatious for the ο variables nu\ ," we find The previous equation, for $\alpha = 1, 2, \dots, n$, represents a linear system of $n$ equations for the $n$ variables $\bigl\{ +c^{[n]}_\alpha \bigr\}$." +Its solution is thus the set of cocficients to be used iu Eq. (8)., Its solution is thus the set of coefficients to be used in Eq. . +. Uowever. we note that care must be taken im the choice of a sot of functions.," However, we note that care must be taken in the choice of a set of functions." + Let us define. for the purpose. the product (6.0 between two genericvector ποια» e(8) and 20(0) as As our problem involves Vee. the completeness has to be referred to the set of the eradicuts.," Let us define, for the purpose, the product $\langle \vec v, \vec w \rangle$ between two genericvector fields $\vec v(\vec\theta)$ and $\vec w(\vec\theta)$ as As our problem involves $\nabla \tilde\kappa$, the completeness has to be referred to the set of the gradients." + In other words. the set {fa| is complete if for every o iuplies £(0)= coustaut.It is easy to slow that this condition isequivalent to Eq. (7)..," In other words, the set $\bigl\{ f_\alpha \bigr\}$ is complete if for every $\alpha$ implies $\tilde\kappa(\vec\theta) = +\mbox{constant}$ .It is easy to show that this condition isequivalent to Eq. ." +We have used state-of-the-art Bivdrodynamic: simulations of structure formation. to investigate the abundance. of DLAs in a ACDAL universe.,We have used state-of-the-art hydrodynamic simulations of structure formation to investigate the abundance of DLAs in a $\Lam$ CDM universe. + Our study represents a first attempt to apply a large series of simulations to. this problem. probing an unprecedented range in both mass and spatial scales. enabling us to quantify systematic effects due to numerical resolution.," Our study represents a first attempt to apply a large series of simulations to this problem, probing an unprecedented range in both mass and spatial scales, enabling us to quantify systematic effects due to numerical resolution." + Furthermore. we improved the simulation. methodology. by adopting a novel formulation of SPIL (seeSpringel&LHoernqui:4.|2002) that minimises systematic inaccuracies in simulations with cooling. and by using an improved model for the treatment of the multiphase structure of the ISM in the context of star formation and feedback (Springel&Lcrnquist2003a).," Furthermore, we improved the simulation methodology by adopting a novel formulation of SPH \citep[see][]{SH02a} that minimises systematic inaccuracies in simulations with cooling, and by using an improved model for the treatment of the multiphase structure of the ISM in the context of star formation and feedback \citep{SH02b}." +. ὃν comparing our results for DLA abundance in a series of runs as a function of resolution and feedback strength. we were able to demonstrate that insullicient resolution. or a lack of a proper treatment of effective feedback. processes. leads to an incorrect estimate of the relation between the DLA cross-section and the halo mass.," By comparing our results for DLA abundance in a series of runs as a function of resolution and feedback strength, we were able to demonstrate that insufficient resolution, or a lack of a proper treatment of effective feedback processes, leads to an incorrect estimate of the relation between the DLA cross-section and the halo mass." + This likely led to an overestimate of the DLA abundance in earlier studies. for the reasons we discussed in detail in Section 4.1.. Prochaska," This likely led to an overestimate of the DLA abundance in earlier studies, for the reasons we discussed in detail in Section \ref{section:z3_area}." +&Wolfe(2001) pointed out. that. the observed. velocity width distribution cannot be reproduced if the relation between the DLA cross-section and the halo mass derived [rom these earlier. SPL simulations is used., \citet{Pro01} pointed out that the observed velocity width distribution cannot be reproduced if the relation between the DLA cross-section and the halo mass derived from these earlier SPH simulations is used. + They also suggested. that one possibility to. remedy. this inconsistency was to suppose that the relationship between the DLA cross-section and the halo mass was incorrectly determined., They also suggested that one possibility to remedy this inconsistency was to suppose that the relationship between the DLA cross-section and the halo mass was incorrectly determined. + This is exactly what we find in our current study., This is exactly what we find in our current study. + LD owe use the new relation found. in our highest resolution simulation. we obtain a DLA abundance that is consistent with observations. which is very encouraging.," If we use the new relation found in our highest resolution simulation, we obtain a DLA abundance that is consistent with observations, which is very encouraging." + The slope of the relation that we infer from our simulations ab ο=3 ds in the range of OF— LO. which coincides with the range that Llachnelt.Steinmetz.&Rauch(2000) derived by requiring their model prediction of velocity width distribution to match the observed one.," The slope of the relation that we infer from our simulations at $z=3$ is in the range of $0.7 - 1.0$ , which coincides with the range that \citet{Hae00} derived by requiring their model prediction of velocity width distribution to match the observed one." + Llowever. while our simulations reproduce the DLA abundance at ο=3 very well. our predictions at 2x are not equally. reliable because they are based on simulations with larger box-sizes and lower resolution.," However, while our simulations reproduce the DLA abundance at $z=3$ very well, our predictions at $z\leq 2$ are not equally reliable because they are based on simulations with larger box-sizes and lower resolution." + This is also evident from the poor agreement between the simulated and the observed cobumn density clistribution function at low redshift., This is also evident from the poor agreement between the simulated and the observed column density distribution function at low redshift. + To make the predictions at. low-redshift more, To make the predictions at low-redshift more +"background is limited by natural radiation sources (Galactic. extragalactic. CMB): this allows a wider coverage (including high frequencies) without the risk of a high background on the detectors,","background is limited by natural radiation sources (Galactic, extragalactic, CMB): this allows a wider coverage (including high frequencies) without the risk of a high background on the detectors." + For a summary see fig.l.. where the coverage of the different configurations 1s compared to the SZ and foreground spectra.," For a summary see \ref{fig1}, where the coverage of the different configurations is compared to the SZ and foreground spectra." +" In. order to evaluate the performance of different experimental configurations. we have considered the following benchmark situation: the observation of a line of sight that crosses a rich cluster of galaxies. with 7,=0.005. 7,= SkeV. ΑΤΟΜΗΞ22K (corresponding to v=480km/s. if the intrinsic anisotropy of the CMB along the line of sight is negligible). Ty20.0001. a@=-2.7. pj=2.75xSMke V/c)."," In order to evaluate the performance of different experimental configurations, we have considered the following benchmark situation: the observation of a line of sight that crosses a rich cluster of galaxies, with $\tau_t = 0.005$ , $T_e = 5 keV$ , $\Delta +T_{CMB} = 22 \mu K$ (corresponding to $ \rm{v}=480 km/s $, if the intrinsic anisotropy of the CMB along the line of sight is negligible), $\tau_{nt} = 0.0001$, $\alpha=-2.7$, $p_1 = 2.75 +\times 511 keV/c$ )." + We assumed that the angular resolution of all channels of all experimental configurations is sufficient to resolve the source., We assumed that the angular resolution of all channels of all experimental configurations is sufficient to resolve the source. + Otherwise we would have needed to take into account dilution and shape factors: in this LOS approach we avoided these complications., Otherwise we would have needed to take into account dilution and shape factors: in this LOS approach we avoided these complications. + We believe that this approach is adequate for the purpose of this paper. which 15 to compare the performance of different experimental configurations.," We believe that this approach is adequate for the purpose of this paper, which is to compare the performance of different experimental configurations." + The integration time on the same line of sight is assumed to be3 hours for all cases but EC4., The integration time on the same line of sight is assumed to be 3 hours for all cases but EC4. +" For EC4 (a space-borne whole-sky survey d-la-Planck) the integration time on the considered sky pixel is 30 s. The signal power on the detectors was computed as where A is the collecting area. 1s the solid angle sampled by each detector. E(v) is the efficiency of the detection system. €,Cv) is the total emissivity of the optical system at room temperature and of the atmosphere in the measurement band."," For EC4 (a space-borne whole-sky survey ) the integration time on the considered sky pixel is 30 s. The signal power on the detectors was computed as where $A$ is the collecting area, $\Omega$ is the solid angle sampled by each detector, $E(\nu)$ is the efficiency of the detection system, $\epsilon_m(\nu)$ is the total emissivity of the optical system at room temperature and of the atmosphere in the measurement band." +" We have neglected A/;; and A/, because they are negligible with respect to AZ; in the frequency range and for the observations at high galactic latitudes of interest here.", We have neglected $\Delta I_{ff}$ and $\Delta I_{sy}$ because they are negligible with respect to $\Delta I_d$ in the frequency range and for the observations at high galactic latitudes of interest here. +" We modelled typical Galactic cirrus anisotropy at the angular scale of a cluster (a few aremin) as AZj(v)=A(v/v,)! with A=600Jv/sr and v,2150GHz: a value typical of very clean high-latitude regions (see e.g. Masi et al. 2006))"," We modelled typical Galactic cirrus anisotropy at the angular scale of a cluster (a few arcmin) as $\Delta I_d (\nu) += A (\nu / \nu_o)^4 $ with $A = 600 \ Jy/sr$ and $\nu_o = 150 \ +GHz$: a value typical of very clean high-latitude regions (see e.g. Masi et al. \cite{Masi06}) )." + We assumed that the detector array is optimized to be limited by the photon noise of the radiative background that is produced by the instrument and the atmosphere (if present)., We assumed that the detector array is optimized to be limited by the photon noise of the radiative background that is produced by the instrument and the atmosphere (if present). + Cryogenic bolometers reach this performance level even in the extremely low background achievable in space. 1f properly designed (see e.g. Holmes et al. 2008))," Cryogenic bolometers reach this performance level even in the extremely low background achievable in space, if properly designed (see e.g. Holmes et al. \cite{Holm08}) )." +" The background power on the detectors was computed as where x4,=fiv/kT,,. Ty, 1s the temperature of the optical system and of the atmosphere. x= Av/KT. T is the temperatureof the cosmic microwave background."," The background power on the detectors was computed as where $x_m = h\nu / kT_m$, $T_m$ is the temperature of the optical system and of the atmosphere, $x = h\nu / kT$ , $T$ is the temperatureof the cosmic microwave background." + The fluctuations of the background were computed as For the photometric measurements we integrated equations 6 and 8 over the detection bandwidth BW to obtain the error on the signal for each band: where 7 1s the total integration time., The fluctuations of the background were computed as For the photometric measurements we integrated equations \ref{theory} and \ref{noise} over the detection bandwidth $BW$ to obtain the error on the signal for each band: where $T$ is the total integration time. +" In the case of spectroscopic measurements. the error on the measurement of each spectral bin was computed as follows,"," In the case of spectroscopic measurements, the error on the measurement of each spectral bin was computed as follows." + In the FTS the input power ts splitted in the two arms of the interferometer. and a variable delay is introduced in one of the two beams. before recombining them on the detector.," In the FTS the input power is splitted in the two arms of the interferometer, and a variable delay is introduced in one of the two beams, before recombining them on the detector." + The variable delay is introduced by a moving mirror. which can be offset by x with respect to the corresponding steady mirror in the other arm of the interferometer.," The variable delay is introduced by a moving mirror, which can be offset by $x$ with respect to the corresponding steady mirror in the other arm of the interferometer." + In this way a 2cv delay is introduced., In this way a $2cx$ delay is introduced. + The power measured in position x of the moving mirror is PCv) (the interferogram). and the spectrum is estimated as the Fourier transform of the interferogram: where «c is the wavenumber (in em!)," The power measured in position $x$ of the moving mirror is $P(x)$ (the interferogram), and the spectrum is estimated as the Fourier transform of the interferogram: where $\sigma$ is the wavenumber (in $^{-1}$ )." + The spectral resolution of the measurement ts (see e.g. Chantry 1971))., The spectral resolution of the measurement is (see e.g. Chantry \cite{Chan71}) ). +" In a real instrument. the interferogram is sampled at the positions v;=‘Av. (/2.1..N). with N=x4,,/Ax."," In a real instrument the interferogram is sampled at the positions $x_i=i\Delta x$, $(i=1..N)$, with $N=x_{max}/\Delta x$." + The integral isthenestimated as a discrete sum Since each sample of the interferogram has an integration time 7/N. and photons from the whole observed frequency 7)bandwidth contribute to the noise. theerror in the measurement Is therefore," The integral isthenestimated as a discrete sum Since each sample of the interferogram has an integration time $T/N$ , and photons from the whole observed frequency bandwidth contribute to the noise, theerror in the measurement is therefore" +published on these tests and we just refer in the following to a few recent papers.,published on these tests and we just refer in the following to a few recent papers. +" Some recent tests try to use the cosmuc evolution of condeusatious of mass on large scales that can be studied with gravitational arcs or weals lensing modeling. or to probe directly the curvature parameter of the Universe. O,.."," Some recent tests try to use the cosmic evolution of condensations of mass on large scales that can be studied with gravitational arcs or weak lensing modeling, or to probe directly the curvature parameter of the Universe $\Omega_k$." + These tests use the measurements of deviations of helt ravs passing through sale lenses but connue frou distant sources at different redshifts., These tests use the measurements of deviations of light rays passing through same lenses but coming from distant sources at different redshifts. +" Deflexiou aneles induced by lenses are proportional to the effective angular distance D—DiyDisDi, (sce Meller et al.", Deflexion angles induced by lenses are proportional to the effective angular distance $D = D_{ol}.D_{ls}/D_{os}$ (see Mellier et al. + this coufereuce)., this conference). +" The Dj; are respectively the angular distauce/ between the observer. the lenses aud the sources. aud Dj; is defined by IT, — [out>| (20,3 lay. ⋯∐↖⇁↸∖↥⋅↴∖↴↸∖⋜⋯≼↧⇁≀⋅↕⋟∪↥⋅⋜↧∏⋜↧↑∏∐↕↖⇁↸∖↥⋅↴∖↴↸∖∙⋜⋯≼↧ SH,das TEES sies."," The $D_{ij}$ are respectively the angular distance between the observer, the lenses and the sources, and $D_{ij}$ is defined by H_0 = _0 (2 _0 _0 y^2 + dy, where $sinn(x)$ is respectively $sin (x)$ for close universe, $sinh (x)$ for an open universe and $x$ for a flat universe, and, _0-q_0, _0, _0." + Hence. deviation aveles. iupact paraüueter like Eisteiu radius or location of critical lines depend on the existence of O4.," Hence, deviation angles, impact parameter like Einstein radius or location of critical lines depend on the existence of $\Omega_{\Lambda}$." + Iu practice direct. geometrical lensing tests with D. in particular for fat muiverses as predicted bv inflation. work ouly when the cosmological constaut )econmies larger than about 0.6 because it is only above this value that the A effect becomes observable at large z.," In practice direct geometrical lensing tests with $D$, in particular for flat universes as predicted by inflation, work only when the cosmological constant becomes larger than about 0.6 because it is only above this value that the $\Lambda$ effect becomes observable at large $z$." + The observational difficulty. comes from he sinall excess of deviation. which is never larger than of the deviation expected for the O4=0 case having the same O9.," The observational difficulty comes from the small excess of deviation, which is never larger than of the deviation expected for the $\Omega_{\Lambda}=0$ case having the same $\Omega_0$." + This is why this new class of tests are only relevant for lcusine-clusters with large augular scales., This is why this new class of tests are only relevant for lensing-clusters with large angular scales. + In the ollowing we sunmuuize the results and new trends for all the class of lensing osts., In the following we summarize the results and new trends for all the class of lensing tests. + The volume per unit redshift at large distance and consequently the relative uber of leused sources for a fixed co-moving deusity mereases with increasing, The volume per unit redshift at large distance and consequently the relative number of lensed sources for a fixed co-moving density increases with increasing +"We are now in a position to correct the n(z) estimates [rom to iuclude the coutributiou from halos with AZ$ 7." +Table 2 shows details of different. at searchescareful 0601 ., Table 2 shows details of different searches at $z>$ 7. + After aud sclectiocliofLya possible. sources of. ccandidates we have ford WITSfour ecuutter contannation.candidates im a survey of Lya28& NM with a limiting fux of ος10.areaerestanaroun’.7.," After careful selection of candidates and eliminating possible sources of contamination, we have found four emitter candidates in a survey area of $28 \times 28$ $^{2}$, with a limiting flux of $\rm 6 \times 10^{-18} erg \;s^{-1} \; cm^{-2}$." + The xes of these four candidates are 1.1. 0.91. 0.81 and (0.72 in units of 10.1eres+em7.," The fluxes of these four candidates are 1.1, 0.91, 0.84 and 0.72 in units of $\rm 10^{-17} \; erg \;s^{-1} \; cm^{-2}$." + 33 shows the resulting cuumlative Thuninosity fiction., 3 shows the resulting cumulative luminosity function. + Solid filled circles show the LLF derived from our candidates. while open circles represent LF trom IHübouetal.(2009).," Solid filled circles show the LF derived from our candidates, while open circles represent LF from \citet{hib09}." +.. Arrows oexdicate that this is the upper luit ou the LLF. aud upper error bars are the Poisson errors.," Arrows indicate that this is the upper limit on the LF, and upper error bars are the Poisson errors." + The otted aud dashed lines show LLFs from Ouchiotal.(2008) and. Washikawa respectively., The dotted and dashed lines show LFs from \citet{ouc08} and \citet{kas06} respectively. + The open square is the LLF at :26.96 (Iveetal.2006)., The open square is the LF at $z$ =6.96 \citep{iye06}. +. If all of our. candidates are :—fad ealaxies. the LF derived from our sample shows moderate evolution compared to LF at :26.5 (Nashikawactal.2006).," If all of our candidates are $z$ =7.7 galaxies, the LF derived from our sample shows moderate evolution compared to LF at $z$ =6.5 \citep{kas06}." +. On the other haud. conservatively if ouly one of the candidates isa.=7.7 galaxy. then the LLF does not show any evolution compared to the 2=6.6 LLF.," On the other hand, conservatively if only one of the candidates is a $z=7.7$ galaxy, then the LF does not show any evolution compared to the $z=6.6$ LF." + Ilibonetal.(2009) conclude that the observed LLF at :=7.7 does not evolve siguificautlv. compared o LLF at -=6.5 (Ixashikiwactal.2006).. if hey cousider hat all of their cauclidates are real.," \citet{hib09} conclude that the observed LF at $z=7.7$ does not evolve significantly compared to LF at $z$ =6.5 \citep{kas06}, if they consider that all of their candidates are real." + Finalv. while our LLF lies above the LF obtained by ITibouetal.(2009).. he counts are consistent with the uuuber of star-forming ealaxies iu the IITUDE with interred line fuxes >6«10Dogs!on7 20095b).. and also cousisteut with the LLF at :—5.7 (Ouchietal.2008).," Finally, while our LF lies above the LF obtained by \citet{hib09}, the counts are consistent with the number of star-forming galaxies in the HUDF with inferred line fluxes $\rm > 6\times 10^{-18} erg \;s^{-1} \; cm^{-2}$ \citep{fin09b}, and also consistent with the LF at $z$ =5.7 \citep{ouc08}." +. As described iu Section 5. all surveys for. eeuitters at 2>6 μια from cosmic variance.," As described in Section 5, all surveys for emitters at $z > 6$ suffer from cosmic variance." + We do CXect to see field-to-field variation in number counts evel at the same redshitt., We do expect to see field-to-field variation in number counts even at the same redshift. + Therefore it is duportaut to ect statistics from more than one field for cach redshift., Therefore it is important to get statistics from more than one field for each redshift. + The feld-to-field variation is expected to be stronger for brighter sources., The field-to-field variation is expected to be stronger for brighter sources. + Therefore the higher redshift s1rvers. which are more sensitivity lauited. are lit the hardest.," Therefore the higher redshift surveys, which are more sensitivity limited, are hit the hardest." +" Several studies have found muuerous emitters having laree rest-frame equivalent widths. EW,>2[0A (Malhotra&Rhoads2002:Shimasalkuetal.2006:2008)."," Several studies have found numerous emitters having large rest-frame equivalent widths, $\rm EW_{rest} > 240 \AA$ \citep{mr02, shi06, daw07, gro07,ouc08}." + These exceed theoretical predietious for noriial star formineDA ealaxies1, These exceed theoretical predictions for normal star forming galaxies. + Since the J-baud filter does not include the Ilinc. we have used the following relation to calculate the rest-frame LEWs for our four ccandidates: Hore fx aud £y3p are the UND line flux (ergs.feu). and J-band flux (ere | cu? At) respectively.," Since the J-band filter does not include the line, we have used the following relation to calculate the rest-frame EWs for our four candidates: Here $\rm f_{ {NB}}$ and $\rm f_{ \lambda,{BB}}$ are the UNB line flux $\rm erg \; s^{-1} cm^{2}$ ), and J-band flux (erg $^{-1}$ $^{2}$ $^{-1}$ ) respectively." + Since none of the four candidates are detected i J-baud. we used J-band laniting magnitude to calculate a lower Iit ou the EEWs.," Since none of the four candidates are detected in J-band, we used J-band limiting magnitude to calculate a lower limit on the EWs." + We note that the EW will depeud on the exact redshift. shape. aud precise position of the line in the UND filter.," We note that the EW will depend on the exact redshift, shape, and precise position of the line in the UNB filter." + However. forsimplicity aud because we oulv put lower lits ou EWs. we assume that the UND filter encloses all the. line dux in calculating EWs.," However, forsimplicity and because we only put lower limits on EWs, we assume that the UNB filter encloses all the line flux in calculating EWs." + For our ccandidates. with liue flux estimates from 7 to 10Perge?5s À and our broad band limit 25.5 mae. we find. EWyor23A.," For our candidates, with line flux estimates from $7$ to $11 \times 10^{-18} \ergcm2s$ , and our broad band limit $J_{NF} \ge 23.5$ mag, we find $\rm EW_{rest} \gtrsim 3 \AA$." +" This EW limit is considerably smaller than the EW,>DA obtained bv Iibonetal.(2009) for their candidates at 2=7.7.", This EW limit is considerably smaller than the $\rm EW_{rest} > 9 \AA$ obtained by \citet{hib09} for their candidates at $z$ =7.7. + This difference arises due to the sanaller bandwidth of our UND filter. and our somewhat shallower J baud imagine.," This difference arises due to the smaller bandwidth of our UNB filter, and our somewhat shallower J band imaging." + Deep «ας observations will help in getting either nieasuremieuts or stricter lower liuüts on the line EWs. but will also be observationallv challenging.," Deep J-band observations will help in getting either measurements or stricter lower limits on the line EWs, but will also be observationally challenging." + We have performed a deep. wide field search for τιν eenitters on the NEWFIRAL camera at the KPNO bu Alavall telescope.," We have performed a deep, wide field search for $z=$ 7.7 emitters on the NEWFIRM camera at the KPNO 4m Mayall telescope." + We used an ultranarrowbaud filter with width 9A and central wavelength of 1.063440. vielding high seusitivity to narrow cluission lines.," We used an ultra-narrowband filter with width $\rm \AA$ and central wavelength of $\mu m$ , yielding high sensitivity to narrow emission lines." +paraueters were chosen using the procedure described im Lemoine et al. (1995)).,parameters were chosen using the procedure described in Lemoine et al. \cite{lemoine}) ). + The photospheric ccoutinua of Sinus D was non-trivial aud its normalization will be described in L.., The photospheric continua of Sirius B was non-trivial and its normalization will be described in \ref{Study_of_the_lya_lines_toward_Sirius_A_and_Sirius_B}. + The thigh resolution spectra of Sirius A obtained using Echelle-A was unusable. probably because of the very high diffision of adjacent order in the spectrograph by this xieht star.," The high resolution spectra of Sirius A obtained using Echelle-A was unusable, probably because of the very high diffusion of adjacent order in the spectrograph by this bright star." + The thigh resolution spectra of Sirius Bo obtained using Echelle-A presented a very low S/N (~ 5)., The high resolution spectra of Sirius B obtained using Echelle-A presented a very low $S/N$ $\sim5$ ). + We did not use them iu our fits of the lues £9). which are mace only on the medi spectal resolution data obtained using C110M. We just use then in order to check that the eeocoronal ccluission diving our observations was at the bottom of the saturated aabsorptious.," We did not use them in our fits of the lines \ref{Study_of_the_lya_lines_toward_Sirius_A_and_Sirius_B}) ), which are made only on the medium spectal resolution data obtained using G140M. We just use them in order to check that the geocoronal emission during our observations was at the bottom of the saturated absorptions." + Iudeed. this ciission is detected in the Sirius D EEchelle-À spectra. but not in the GLLOM spectra.," Indeed, this emission is detected in the Sirius B Echelle-A spectra, but not in the G140M spectra." + The eeocoronal cussion thus did not deteriorate the wines of the aabsorptiou lines., The geocoronal emission thus did not deteriorate the wings of the absorption lines. + As it can be seen in L.the Hines are not obvious.," As it can be seen in \ref{Study_of_the_lya_lines_toward_Sirius_A_and_Sirius_B}, the lines are not obvious." + We thus used oulv the interstellar metal lines aall but 0) to study the structure of the line of sieht toward the binary Sivius A / Sivius D. We assume in all our study that the iuterstellar absorbers are the sale toward Sirius A aud Sidus D. the two stars being separated by less than lt aresec on the kv at the time of our observations. which corresponds to ~10 AU at the Sinus distance of 2.6 pc.," We thus used only the interstellar metal lines all but ) to study the structure of the line of sight toward the binary Sirius A / Sirius B. We assume in all our study that the interstellar absorbers are the same toward Sirius A and Sirius B, the two stars being separated by less than 4 arcsec on the sky at the time of our observations, which corresponds to $\sim10$ AU at the Sirius distance of 2.6 pc." +" For a eiven transition of a given clement. cach conrponeut in the sightline produces am absorption line modeled by a Voigt profile. which is defined. iu addition to atonic parameters. by four cloud parameters: the radial velocity. e Gu.7) of. the cloud. the colin cleusity. N. Guo 7) of element ce. the temperature T (in IS) of the gas. aud its turbulent velocity 0 (m ly, "," For a given transition of a given element, each component in the sightline produces an absorption line modeled by a Voigt profile, which is defined, in addition to atomic parameters, by four cloud parameters: the radial velocity $v$ (in) of the cloud, the column density $N_e$ (in $^{-2}$ ) of element $e$, the temperature $T$ (in K) of the gas, and its turbulent velocity $\sigma$ (in )." +Iu order to determine the muuber of clouds. their velocity. temperature. turbulence aud coluuus deusitv for each clement. we used a new fitting program developed by AL. Lemoine. which permits to fit Voigt profiles to several Ines in different spectral ranges sinmltaucouslv.," In order to determine the number of clouds, their velocity, temperature, turbulence and columns density for each element, we used a new fitting program developed by M. Lemoine, which permits to fit Voigt profiles to several lines in different spectral ranges simultaneously." + This new o»ogran Works in the same spirit as the code preseuted iu Lemoine⋅ et al. ↽ (1995)).," This new program works in the same spirit as the code presented in Lemoine et al. \cite{lemoine}) )," + which obtains the vost fit⋅ by 479 sinulated annealing optimization., which obtains the best fit by $\chi^2$ simulated annealing optimization. + This allows us to find he best sohition compatible with differcut spectral ranges vased on the basic assimnption that all the considered ines give the same values for c. T and 6 for a given component. aud all the lines for a given clement € aud a even conrponeut eive the same value for Αι," This allows us to find the best solution compatible with different spectral ranges based on the basic assumption that all the considered lines give the same values for $v$, $T$ and $\sigma$ for a given component, and all the lines for a given element $e$ and a given component give the same value for $N_e$." + The spread of the lines combines both paramcters ἆ and o. which can only be separately deteriined if several clements with different masses are simultaneously fitted.," The spread of the lines combines both parameters $T$ and $\sigma$, which can only be separately determined if several elements with different masses are simultaneously fitted." + This procedure was used to solve the structure of the line of sight toward the white dwart C191-B2B (Vidal-Aladjar et al. 1998))., This procedure was used to solve the structure of the line of sight toward the white dwarf G191-B2B (Vidal-Madjar et al. \cite{avm98}) ). + The previous study of the line of sight toward Sirius A (Lallemenut et al. 19913) , The previous study of the line of sight toward Sirius A (Lallement et al. \cite{lalle}) ) +clearly showed two distinct interstellar clouds with a projected velocity shift equal to 5.7£0.2+., clearly showed two distinct interstellar clouds with a projected velocity shift equal to $5.7\pm0.2$. + The red conrponeut was identified as the Local Interstellar Cloud (LIC). detected i laa directions with projected velocities corresponding to the coleren motion of a cloud in which the solar svstem ds embedded: (Lallemen Bertin 1992)).," The red component was identified as the Local Interstellar Cloud (LIC), detected in many directions with projected velocities corresponding to the coherent motion of a cloud in which the solar system is embedded (Lallement Bertin \cite{lall_bert_lic}) )." + To improve the precision of our study. we decided to fit the 10 lines of our new observation ogether with the 2311A.. 2600A. 2796 aud 2803 lines from Lallement et al. (1991)).," To improve the precision of our study, we decided to fit the 10 lines of our new observation together with the 2344, 2600, 2796 and 2803 lines from Lallement et al. \cite{lalle}) )," + which present very lüeh S/N (see Table 2))., which present very high $S/N$ (see Table \ref{detect}) ). + Our fitting program is suitable for a simultaneous study of several lines with the restriction that their wavelengths are precisely determined., Our fitting program is suitable for a simultaneous study of several lines with the restriction that their wavelengths are precisely determined. + If there exist sieuificant velocity shifts between different lines caused for instance. by instrumental effects. the program then becomes unable to find the right solution coherent with all the fittec lines.," If there exist significant velocity shifts between different lines caused for instance, by instrumental effects, the program then becomes unable to find the right solution coherent with all the fitted lines." + Therefore. on a first iteration. we have corrected for any possible justrmuental velocity shifts.," Therefore, on a first iteration, we have corrected for any possible instrumental velocity shifts." + Tn order to estimate the values of these iustraucutal shifts. we decided to beein our study by fitting oue by one all the lines. asinus that there were two compoucuts. the blue one (BC) aud the red one (LIC). with the following constraiuts: These values were the result of the Lallemieut et al. (1991))," In order to estimate the values of these instrumental shifts, we decided to begin our study by fitting one by one all the lines, assuming that there were two components, the blue one (BC) and the red one (LIC), with the following constraints: These values were the result of the Lallement et al. \cite{lalle}) )" + paper., paper. + The stroug constraints were the projected velocity shift Acpie:pe=5.7 Loxactly which is the Lallement et al. (19913) ," The strong constraints were the projected velocity shift $\Delta v_{\mathrm{LIC-BC}}=5.7$ exactly, which is the Lallement et al. \cite{lalle}) )" +result without the reported errors. and Tig:=TOOO I&. which is the stancdare value assumed for the LIC [see for example Liusky. ct al. (1995))].," result without the reported errors, and $T_{\mathrm{LIC}}=7000$ K, which is the standard value assumed for the LIC [see for example Linsky et al. \cite{linsky95}) )]." + Each fit gives a pair of volocies. one for the DC ane oue for the LIC. separated by 5.7 ," Each fit gives a pair of velocies, one for the BC and one for the LIC, separated by 5.7 ." +We did not find the same pairs of velocitics for al the lines. aud we interpreted these shifts as sigus of iustrumental errors in the absolute waveleugth calibration.," We did not find the same pairs of velocities for all the lines, and we interpreted these shifts as signs of instrumental errors in the absolute wavelength calibration." +There were 2440 candidates spread (throughout the M32 halo: that is. in the region outside of the central MeeaCam image.,"There were 2440 candidates spread throughout the M33 halo; that is, in the region outside of the central MegaCam image." + 87 (5) highest-confidence cluster candidates ancl 2294 (54) possible clusters were found by (he automated (visual) search method., 87 (5) highest-confidence cluster candidates and 2294 (54) possible clusters were found by the automated (visual) search method. + The nmunbers of all classified objects from both the automated and visual inspection searches are shown in Table 2.., The numbers of all classified objects from both the automated and visual inspection searches are shown in Table \ref{objects}. + Results of the above searches were plotted within (he original selection criteria. and are shown in Figure 6..," Results of the above searches were plotted within the original selection criteria, and are shown in Figure \ref{where}." + We wanted to exclude the maximum amount of parameter space so that we could increase (he efficiency of (he automated search. aud it is not obvious from this figure (hat more space could have been excluded.," We wanted to exclude the maximum amount of parameter space so that we could increase the efficiency of the automated search, and it is not obvious from this figure that more space could have been excluded." + Raclial density plots for the categories 1 (high confidence cluster). 2 (possible cluster). 3 (background galaxy) are also shown in Figure 7..," Radial density plots for the categories 1 (high confidence cluster), 2 (possible cluster), 3 (background galaxy) are also shown in Figure \ref{rad_density}." + We compared (hese number densities at large radii to control fields. also taken with MegaCanm and with verv similar image quality. from the M31. outer halo ancl the field near the Draco dwarl spheroidal.," We compared these number densities at large radii to control fields, also taken with MegaCam and with very similar image quality, from the M31 outer halo and the field near the Draco dwarf spheroidal." + The M31 fields are (wo scquare-degree fields selected. directly from the PAndAS data. at a similar Qalactie latitude to M33 of -31.33 degrees. al the edge of the PAncdAS footprint around M31 (1.6... at a projected racius of 72150 kpe) and did not contain any. clusters - either previously-known clusters. or clusters detected in the PAncdAS images.," The M31 fields are two square-degree fields selected directly from the PAndAS data, at a similar Galactic latitude to M33 of -31.33 degrees, at the edge of the PAndAS footprint around M31 (i.e., at a projected radius of $\sim$ 150 kpc) and did not contain any clusters - either previously-known clusters, or clusters detected in the PAndAS images." + The Draco fields are seven square-degree fields ab a Galactic latitude of 34.72 degrees (2).., The Draco fields are seven square-degree fields at a Galactic latitude of 34.72 degrees \citep{2007MNRAS.375..831S}. + Our searches were again applied to the control fields following exactly the same selection criteria. and we obtained an average densitv of each category of objects in the control fields.," Our searches were again applied to the control fields following exactly the same selection criteria, and we obtained an average density of each category of objects in the control fields." + The radial distribution plots indicate (hat few if any of the category 3 objects are genuine clusters since they show little detectable central concentration to the galaxy outside the crowcled disk region., The radial distribution plots indicate that few if any of the category 3 objects are genuine clusters since they show little detectable central concentration to the galaxy outside the crowded disk region. + For all three categories plotted. the number density settles down to a virtually constant level similar to that of the M31 control fields for rZ1 degree. consistent with the conclusion (that there are few Clusters left to be found in the M33 halo down to the PAndAS limiting magnitudes. (," For all three categories plotted, the number density settles down to a virtually constant level similar to that of the M31 control fields for $r \gtrsim 1$ degree, consistent with the conclusion that there are few clusters left to be found in the M33 halo down to the PAndAS limiting magnitudes. (" +The number densitv of all objects in the Draco fields is much lower (han that in either the AI33 or M21 fields. highlighting that it was appropriate to compare M32 with the M31,"The number density of all objects in the Draco fields is much lower than that in either the M33 or M31 fields, highlighting that it was appropriate to compare M33 with the M31" +aand aaccount for more than of CFHT papers.,and account for more than of CFHT papers. + ApJ has the most publications with of all CFHT publications. while rreceives of the publications.," ApJ has the most publications with of all CFHT publications, while receives of the publications." + The breakdown of publications by journal for different. years shows au interesting change., The breakdown of publications by journal for different years shows an interesting change. + In. 1996/1907 and of papers were published in aand rrespectively. while for 1998/1990 the numbers were audν," In 1996/1997 and of papers were published in and respectively, while for 1998/1999 the numbers were and." +ι One explanation for this change is that the French are publishing more aud the Canadians/UH. less in recent years.," One explanation for this change is that the French are publishing more and the Canadians/UH, less in recent years." + Only 75 )) of the French papers appeared in American journals while only 23 (9.7%)) Canadian papers. at| 6 UH papers (5.1%)). appeared iu non-North American journals.," Only 75 ) of the French papers appeared in American journals while only 53 ) Canadian papers, and 6 UH papers ), appeared in non-North American journals." + There is a very strong trend for European authors to publish in European journals and North American :hors to publish in North American journals., There is a very strong trend for European authors to publish in European journals and North American authors to publish in North American journals. + This may be a result of the fact that hhas no page charges aud subsequently the French do not have a large budget for page charges., This may be a result of the fact that has no page charges and subsequently the French do not have a large budget for page charges. +" This tendency for authors to publish ou their side of the ""Atlantic Ocean"" is particularly meaningful for any Comparison of publication activity levels between North American (only) aud multinational observatories.", This tendency for authors to publish on their side of the “Atlantic Ocean” is particularly meaningful for any comparison of publication activity levels between North American (only) and multinational observatories. + The distribution of citatious per paper (CPP) across the jouruals is shown in Table 2., The distribution of citations per paper (CPP) across the journals is shown in Table 2. + The three major journals. ((inelucling the Letters). aandAJ.. account lor of the citations to CFHT papers.," The three major journals, (including the Letters), and, account for of the citations to CFHT papers." + While ApJ papers account for of the CFHT total. these papers received almost half )) of the citations.A," While ApJ papers account for of the CFHT total, these papers received almost half ) of the citations.," +CA...ACAS..AJ.. aand aall have a citation rate lower than the average CPP of 20.35., and all have a citation rate lower than the average CPP of 20.35. + Nature has the highest CPP of any journal (2.8%)): and yet these represeut ouly of CFHT papers., Nature has the highest CPP of any journal ); and yet these represent only of CFHT papers. + The primary instrument used to acquire the data was kleutified for each publication., The primary instrument used to acquire the data was identified for each publication. +" In a few Cases, several instruments were grouped together into a siugle category."," In a few cases, several instruments were grouped together into a single category." +" For example. FP refers to several different. “Fabry-Perot” instruments. Couclé refers to the two Couclé spectrographis that have jeen used at CEHT. and “Direct Imaging"" combines several different direct inagiug Cameras that iive been used at CEHT over the years."," For example, FP refers to several different “Fabry-Perot” instruments, Coudé refers to the two Coudé spectrographs that have been used at CFHT, and “Direct Imaging” combines several different direct imaging cameras that have been used at CFHT over the years." + HRCam (MeClureetal.1950). which incorporated fast ip-tilt correction. and. MOCANL (Cuillaudreetal.1996) aud. UHSI (Metzger.M...Luppino.CLA.&Miyazaki.S.1995) two mosaic cameras are identified separately [rom other direct cameras jecause they represent new technologies. aud we wish to track their impact directly.," HRCam \citep{mcl89}, which incorporated fast tip-tilt correction, and, MOCAM \citep{jcc96} and UH8K \citep{met95} two mosaic cameras are identified separately from other direct cameras because they represent new technologies, and we wish to track their impact directly." + A total of 39 distinct instruimeut or instrument categories were identified: however. a large number of instruments oroduced a very few papers and approximately o£ CFHT papers were produced by the top five instrument/instrument categories.," A total of 39 distinct instrument or instrument categories were identified; however, a large number of instruments produced a very few papers and approximately of CFHT papers were produced by the top five instrument/instrument categories." + Table 2 shows the number of papers. the FCC per paper aud he FCC per night of scheduled telescope time for the top-ten paper producing instruments.," Table 2 shows the number of papers, the FCC per paper and the FCC per night of scheduled telescope time for the top-ten paper producing instruments." + The, The +he NT06 PLE model of the CLF. and Figure 2. preseuts he calculation assuuine the NTOG LDDE model of heGLE.,"the NT06 PLE model of the GLF, and Figure \ref{fig-BlazarEGRBLDDE} presents the calculation assuming the NT06 LDDE model of the." +.. The top panels present the calculations asstuning the ? EBL model. while the bottom paucls xeseut the calculations assuming the ? EBL model.," The top panels present the calculations assuming the \citet{ste06} EBL model, while the bottom panels present the calculations assuming the \citet{gil09} EBL model." + All calculations are made asstuing the parameters of je. SID calculated based on the LBAS (sce Section ??))!4.., All calculations are made assuming the parameters of the SID calculated based on the LBAS (see Section \ref{subsec-blsp}). + For conrparison. we have also plotted re? deterinination of the ECGRD as measured by the EGRET (square data poiuts with statistical error bars). re? determination of the EGRET ECGRD (circular data points with statistical error bars}. a grav band represcuting the preluminary EGRD (iucliding statistical and instrumental systematic uncertainties) from the first 9 mouths ofdata!?.. the collective intensity of blazar spectra assunine no absorption (dotted nes). the collective teusitv of blazar spectra includius oulv absorption of the highest energy photons (dashed. lines). aud the cascade radiation (dot-ashed dines)," For comparison, we have also plotted the \citet{sre98} determination of the EGRB as measured by the EGRET (square data points with statistical error bars), the \citet{str04} determination of the EGRET EGRB (circular data points with statistical error bars), a gray band representing the preliminary EGRB (including statistical and instrumental systematic uncertainties) from the first 9 months of, the collective intensity of blazar spectra assuming no absorption (dotted lines), the collective intensity of blazar spectra including only absorption of the highest energy photons (dashed lines), and the cascade radiation (dot-dashed lines)." + Iu this analysis. we include intrinsic quisson up to 100 TeV. As evident. the amount of cascade radiation created. 1i the propagation of VIIE photons cau be substantial. anepeudiug on the shape of the collective iuteusitv of woetrinsic blazar spectra (for examples of cascade radiation οκπιο frou other shapes. sce below).," In this analysis, we include intrinsic emission up to $100$ TeV. As evident, the amount of cascade radiation created in the propagation of VHE photons can be substantial, depending on the shape of the collective intensity of intrinsic blazar spectra (for examples of cascade radiation resulting from other shapes, see below)." + For the shape eteruiued by the SID indicated by data. the cascade radiation significantly alters both the amount and the spectral shape of the overall intensity.," For the shape determined by the SID indicated by data, the cascade radiation significantly alters both the amount and the spectral shape of the overall intensity." + Iu fact. for model GLEs that predict the contribution of intrinsic blazar spectra to comprise onlv ~50 of the ECRB. the addition of cascade radiation ereatly increases the overall contribution from blazars. at least at the highest energies.," In fact, for model GLFs that predict the contribution of intrinsic blazar spectra to comprise only $\sim 50$ of the EGRB, the addition of cascade radiation greatly increases the overall contribution from blazars, at least at the highest energies." + At lower cucreics. the cascade radiation drops off slowly over several decades in energy. aud the collective intensity of mtriusie blazar spectra ries quickly: thus. the coutributiou of the cascade radiatiou to the overall collective blazar iutensity is much ess at lower energies.," At lower energies, the cascade radiation drops off slowly over several decades in energy, and the collective intensity of intrinsic blazar spectra rises quickly; thus, the contribution of the cascade radiation to the overall collective blazar intensity is much less at lower energies." + Also seen in the figure is the contrast iu appearance )otwoeen the PLE model of blazars aud the LDDE model. nost notably at the highest energies.," Also seen in the figure is the contrast in appearance between the PLE model of blazars and the LDDE model, most notably at the highest energies." + As noted iu ?.. the collective blazar mteusitv is much more distributed with respect to redshift in the PLE model than in the LDDE uodel. in which the radiation teuds to be concentrated at lower redshifts (see their Figure 2).," As noted in \citet{ven09}, the collective blazar intensity is much more distributed with respect to redshift in the PLE model than in the LDDE model, in which the radiation tends to be concentrated at lower redshifts (see their Figure 2)." + Hence. just as the absorption feature in the collective inteusitv of iutriusic dazar spectra is imuch more prominent in the PLE nodel. so is it in the cascade radiation calculated from lis model.," Hence, just as the absorption feature in the collective intensity of intrinsic blazar spectra is much more prominent in the PLE model, so is it in the cascade radiation calculated from this model." + Thus. not surprisingly. while there is more cascade radiation below 10 CeW iu the PLE iuodel than iu the LDDE model. above 10 GeV. the cascade radiation in the LDDE 1uodel overtakes that of the PLE model.," Thus, not surprisingly, while there is more cascade radiation below $10$ GeV in the PLE model than in the LDDE model, above $10$ GeV, the cascade radiation in the LDDE model overtakes that of the PLE model." + Since there is more high-energy absorption of the collective iuteusitv from iutriusic blazar spectra in the PLE model. the cascade radiation in the PLE uodel dominates the intensity at enereijes bevond the EGRET cucreyv range. contributing nearlv 1 times as uuch radiation as the contribution from intrinsic blazar spectra at LOO GeV. Not so for the LDDE model. in which he cascade radiation contributes at most 50% more thaw hat of the intrinsic blazar spectra at 100 GeV. Iu addition to considering various blazar GLP models. we also investigate the impact of the EBL model.," Since there is more high-energy absorption of the collective intensity from intrinsic blazar spectra in the PLE model, the cascade radiation in the PLE model dominates the intensity at energies beyond the EGRET energy range, contributing nearly 4 times as much radiation as the contribution from intrinsic blazar spectra at $100$ GeV. Not so for the LDDE model, in which the cascade radiation contributes at most $50$ more than that of the intrinsic blazar spectra at $100$ GeV. In addition to considering various blazar GLF models, we also investigate the impact of the EBL model." + Iu botcor uodels. the effect of the cascade radiation is to fatte he overall collective iutensity from blazars.," In both models, the effect of the cascade radiation is to flatten the overall collective intensity from blazars." + However. at the highest energies. there is less absorption iu the Cihuore model than in the Stecker model.," However, at the highest energies, there is less absorption in the Gilmore model than in the Stecker model." + Below 1 , Below $10$ +on the southern side we are looking into the inside of a spiral arn.,on the southern side we are looking into the inside of a spiral arm. + We thank Piet van der Ixruit. for stimulating cliscussions and acknowledge useful suggestions by the referee. M. Pohlen.," We thank Piet van der Kruit for stimulating discussions and acknowledge useful suggestions by the referee, M. Pohlen." + MNThis work is. partially. based on the undergraduate senior thesis of INKIIN at the University of Virginia., This work is partially based on the undergraduate senior thesis of KHW at the University of Virginia. + Hide acknowledges partial funding [rom NASA grants NAG 5-3428 and NAC 5-6403 and hospitality at the University of Groningen., RdeG acknowledges partial funding from NASA grants NAG 5-3428 and NAG 5-6403 and hospitality at the University of Groningen. + This research. has made use of NASA Astrophysics Data System Abstract Service and. of. the NASA/IPAC Extragalactic Database (NED)., This research has made use of NASA's Astrophysics Data System Abstract Service and of the NASA/IPAC Extragalactic Database (NED). +~Rooy.,"$\simeq +\rm{R}_{200}$." + Phe scatter shown in Fig., The scatter shown in Fig. + S is rather large but in the very centre of the clusters. where clliptical galaxies are all very old. (212 Gyr) they have about solar metallicity. and have very red BOY colour (5- 0.95).," \ref{fig:ell_cluster} is rather large but in the very centre of the clusters, where elliptical galaxies are all very old $\simeq 12\,{\rm Gyr}$ ), they have about solar metallicity, and have very red $-$ V colour $\simeq 0.95$ )." + In the hierarchical galaxy formation scenario. elliptical ealaxies form through mergers of smaller units. anc larger systems are expected to be mace up by a larger number of progenitor galaxies.," In the hierarchical galaxy formation scenario, elliptical galaxies form through mergers of smaller units, and larger systems are expected to be made up by a larger number of progenitor galaxies." + A very interesting question is therefore how large the number of progenitor svstems of galaxies is. and how this number varies as a function of final mass.," A very interesting question is therefore how large the number of progenitor systems of galaxies is, and how this number varies as a function of final mass." +" To get a quantitative handle on this question. we celine for each galaxy an by computing the quantity where m; denotes the masses of all the stars that make up a galaxy of final mass Mi=SM,m;."," To get a quantitative handle on this question, we define for each galaxy an by computing the quantity where $m_i$ denotes the masses of all the stars that make up a galaxy of final mass $M_{\rm final} = \sum_i m_i$." + The quantity Δον gives the stellar mass of the galaxy. within which the star 7 formed. at the time of formation of the star.," The quantity $M_{i, \rm form}$ gives the stellar mass of the galaxy within which the star $i$ formed, at the time of formation of the star." + In the case where all stars form in a single object that grows to the final stellar mass without experiencing any merger. Ίσα. (3))," In the case where all stars form in a single object that grows to the final stellar mass without experiencing any merger, Eq. \ref{eq:neff}) )" + can be viewed as a discretised form of the integral which evaluates to Nar=1 independent of the detailed star formation history., can be viewed as a discretised form of the integral which evaluates to $N_{\rm eff}= 1$ independent of the detailed star formation history. + However. if a galaxy is assembled [rom several pieces we expect a larger value of Nor. because then the values of AM that enter the sum in. the denominator of Eq. (3))," However, if a galaxy is assembled from several pieces we expect a larger value of $N_{\rm eff}$, because then the values of $M_{i, \rm form}$ that enter the sum in the denominator of Eq. \ref{eq:neff}) )" + beeome lower., become lower. + For example. if the stars of a galaxy. were formed. in two progenitors of equal final size. which then merged into a single object. without any further star formation. we obtain Ni=2.," For example, if the stars of a galaxy were formed in two progenitors of equal final size, which then merged into a single object without any further star formation, we obtain $N_{\rm eff}= 2$." + Note that in more general cases we will obtain fractional values for Nya due to the mass-weighting of the progenitors. which is built into the definition of Mar.," Note that in more general cases we will obtain fractional values for $N_{\rm eff}$ due to the mass-weighting of the progenitors, which is built into the definition of $N_{\rm eff}$." + For example. if à galaxy is made up of three pieces that contain one half. one quarter and one quarter of the final stellar mass. respectively. one ects jar=8/3. which is less than the absolute number of progenitors.," For example, if a galaxy is made up of three pieces that contain one half, one quarter and one quarter of the final stellar mass, respectively, one gets $N_{\rm eff} = +8/3$ , which is less than the absolute number of progenitors." + This reflects the fact that the majority of the stars formed in a single object., This reflects the fact that the majority of the stars formed in a single object. + The mass-weighting hence delivers an ellective count of the progenitors by giving weight only to those progenitor svstems that contribute significantly to the final stellar mass of the galaxy., The mass-weighting hence delivers an effective count of the progenitors by giving weight only to those progenitor systems that contribute significantly to the final stellar mass of the galaxy. + In. contrast. a count of the total number of progenitors would be dominated. by the large number of negligibly small satellites that fall into a galaxy during its growth in a hierarchical universe.," In contrast, a count of the total number of progenitors would be dominated by the large number of negligibly small satellites that fall into a galaxy during its growth in a hierarchical universe." + We therefore. argue that Mar is a more useful proxy for the number of significant mergers required to assemble a galaxy., We therefore argue that $N_{\rm eff}$ is a more useful proxy for the number of significant mergers required to assemble a galaxy. + We caution however that a straightforward interpretation of Noy in the context of spheroid formation is complicated by the fact that bulges can also grow in our model without mergers. through clisk instabilities.," We caution however that a straightforward interpretation of $N_{\rm eff}$ in the context of spheroid formation is complicated by the fact that bulges can also grow in our model without mergers, through disk instabilities." + In Fig. 9..," In Fig. \ref{fig:mergers}," + we show the οσσνο number of progenitors as a function of galaxy stellar mass., we show the effective number of progenitors as a function of galaxy stellar mass. + Filled circles represent the median of the distributions in our default. model while empty circles. represent the median of the. distributions in a model where bulge growth through disk. instability is switched. olf., Filled circles represent the median of the distributions in our default model while empty circles represent the median of the distributions in a model where bulge growth through disk instability is switched off. + Interestinely. bulge growth. through disk instability seems to be an ellicient process for intermediate mass ellipticals but rather inellective for the most massive ellipticals in our sample.," Interestingly, bulge growth through disk instability seems to be an efficient process for intermediate mass ellipticals but rather ineffective for the most massive ellipticals in our sample." + As expected. more massive galaxies are mace up of more pieces.," As expected, more massive galaxies are made up of more pieces." + Fig., Fig. + 9 shows that the number of elfective progenitors is less than 2 up to stellar masses of ~IAL:. indicating that the formation of these systems typically involves only a small number of major mergers.," \ref{fig:mergers} shows that the number of effective progenitors is less than $2$ up to stellar masses of $\simeq 10^{11}\,{\rm M}_{\sun}$, indicating that the formation of these systems typically involves only a small number of major mergers." + Only galaxies more massive than cLOMML; are built up through a larger number of mergers. reaching up to Nap£95 for the most massive galaxies.," Only galaxies more massive than $\simeq 10^{11}\,{\rm M}_{\sun}$ are built up through a larger number of mergers, reaching up to $N_{\rm eff}\simeq 5$ for the most massive galaxies." + We recall that these most massive elliptical galaxies are. however. also the ones with the oldest stellar populations.," We recall that these most massive elliptical galaxies are, however, also the ones with the oldest stellar populations." + We note that the monolithic collapse scenario would prediet Na;=1 for these large ellipticals. in marked. dillerence to our hierarchical prediction.," We note that the monolithic collapse scenario would predict $N_{\rm eff}=1$ for these large ellipticals, in marked difference to our hierarchical prediction." +al... i UM,", in preparation)." + Columns are taken [rom Zhang 31 objects. except io (ef.Guainazzietal.2005): this work 5 objects: Guainazziefal.(2005) — 11. and 5591: Reevesefal(2004) 33783: Maiolinoefal.(1998) 33081: and Poundsefal(2003) 414253.," Columns are taken from Zhang – 31 objects, except 5256 \citep[cf.][]{gua05}; this work – 5 objects; \citet{gua05} – 1, 17, and 591; \cite{ree04} – 3783; \citet{mai98} – 3081; and \cite{pounds03} – 4253." + In order of precedence. we adopt results from SAX. AMAL Chandra and ASCA. except for 33079. where we judged the XMM lower limit (Cappie£al2006). to be more consistent vith SAX data than larger limits based on SAX data alone (Ivomotoefa£.2001).," In order of precedence, we adopt results from SAX, XMM, Chandra and ASCA, except for 3079, where we judged the XMM lower limit \citep{cappi06} to be more consistent with SAX data than larger limits based on SAX data alone \citep{iyo01}." +. Of the 42 AGN. (25) ave Compton thick abu: relfig2)).," Of the 42 AGN, (25) are Compton thick \\ref{tabnh}; \\ref{fig2}) )." + This fraction is consistent with that obtained for the smaller sample of (2006).. (18 of 31).," This fraction is consistent with that obtained for the smaller sample of \citet{zha06}, (18 of 31)." + Within the current sample of 42. a greater fraction of recognized disk-maser galaxies are Compton thick. (16 of 21).," Within the current sample of 42, a greater fraction of recognized disk-maser galaxies are Compton thick, (16 of 21)." + The distribution of columns for disk masers is significantly skewed and non-Gaussian rellig2))., The distribution of columns for disk masers is significantly skewed and non-Gaussian \\ref{fig2}) ). + Substitution (over time) of Ny estimates for lower limits will exagerrate this., Substitution (over time) of $_{\rm H}$ estimates for lower limits will exagerrate this. + In contrast. the distribution for. AGN masers without evidence of origins in edge-on disks includes a larger proportion of Compton-thin sources.," In contrast, the distribution for AGN masers without evidence of origins in edge-on disks includes a larger proportion of Compton-thin sources." + A Nolmogorov-Smirnoy (INS) test indicates a <3.2% probability that the two distributions are drawn from a single parent., A Kolmogorov-Smirnov (KS) test indicates a $< 3.2\%$ probability that the two distributions are drawn from a single parent. + To account for lower limits in our test. we constructed a Monte Carlo simulation of 1000 trials. sampled a uniformly distributed random variable of 107! and 1075 ? for each galaxy. with a limit. and compiled a distribution of INS statistics.," To account for lower limits in our test, we constructed a Monte Carlo simulation of 1000 trials, sampled a uniformly distributed random variable of $10^{24}$ and $10^{26}$ $^{-2}$ for each galaxy with a limit, and compiled a distribution of KS statistics." + Boundaries of 107? and 1075 vielded probabilities of <3% as well., Boundaries of $10^{25.5}$ and $10^{28}$ yielded probabilities of $\la3\%$ as well. + Distinelions between δι distributions for AGN that host acknowledged. disk masers and those that do not may be still greater than estimated., Distinctions between $_{\rm H}$ distributions for AGN that host acknowledged disk masers and those that do not may be still greater than estimated. + Maser classifications depend on identification of spectroscopic markers: highly red. and blue-shilted emission bracketing the svslemic velocity., Maser classifications depend on identification of spectroscopic markers: highly red and blue-shifted emission bracketing the systemic velocity. + Disks may be oriented close to edge-on. resulting in large columns toward the central engine. while (hese spectroscopic markers may nonetheless be absent (e... masers may be beamed! away Irom the observer due (to warping: cL.," Disks may be oriented close to edge-on, resulting in large columns toward the central engine, while these spectroscopic markers may nonetheless be absent (e.g., high-velocity masers may be beamed away from the observer due to warping; cf." + Mivoshi 11995)., Miyoshi 1995). +" Zhangetal,(2006) discussed an alternate sub-sample. selected. based. on apparent maser luminosity (i.e.. megamasers)."," \citet{zha06} discussed an alternate sub-sample, selected based on apparent maser luminosity (i.e., megamasers)." + Within the current sample of 42 AGN with masers. we count (18 of 31) of recognized megamaser hosts are Compton thick (13 from Zhange/ (2006).. plus 11194. 66926. 11. 11419. ancl 334). matching the incidence among maser AGN broadly reftabnh)).," Within the current sample of 42 AGN with masers, we count (18 of 31) of recognized megamaser hosts are Compton thick (13 from \citet{zha06}, plus 1194, 6926, 1, 1419, and 34), matching the incidence among maser AGN broadly \\ref{tabnh}) )." + We link the larger incidence of columns >107 7 among disk-masers to a simple model geometry (edge-on orientation) aud contrast this with selection based on maser Iuninosityv. which is nearly always estimated with the convenient but inaccurate assumption," We link the larger incidence of columns $>10^{24}$ $^{-2}$ among disk-masers to a simple model geometry (edge-on orientation) and contrast this with selection based on maser luminosity, which is nearly always estimated with the convenient but inaccurate assumption" +ksec.,ksec. + For each observation we used the position of the detectedsources?.. excluding the nuclear source M81. N-5. to check for possible misalignements of the astrometric [rames ancl to correct for small spacecraft errors: no further alignment was needed.," For each observation we used the position of the detected, excluding the nuclear source M81 X-5, to check for possible misalignements of the astrometric frames and to correct for small spacecraft errors; no further alignment was needed." +" The PSPC and IBI position determinations are consistent with each other and from now on we will use the more accurate IRI centroid coordinates: RA 95754.320.1 and Dec 6970346.4+0.5"" (J2000)."," The PSPC and HRI position determinations are consistent with each other and from now on we will use the more accurate HRI centroid coordinates: RA $9^h 57^m 54.3\pm 0.1^s$ and Dec $69^{\circ}03'46.4\pm 0.5""$ (J2000)." + For each WRI observation. source counts were extracted from a circular region with 1.3 radius. as found with the IRAF/PROS algorithun (S. Dyson. 1999. private comnminieation).," For each HRI observation, source counts were extracted from a circular region with 1.3' radius, as found with the IRAF/PROS algorithm (S. Dyson 1999, private communication)." + The 21 available ASCA observations of M81 (ÀA1-A21) were also used to estimate the flux of the nucleus (see Table 1:5: for a detailed analvsis of these data see Ishisakiοἱ and Ivomoto&Makishima 2001))., The 21 available ASCA observations of M81 (A1-A21) were also used to estimate the flux of the nucleus (see Table \ref{log}; for a detailed analysis of these data see \citealp{ishi} and \citealp{iyo}) ). + The ASCA/SIS data are less contaminated by the $N1993J emission than the ASCA/GIS ones., The ASCA/SIS data are less contaminated by the SN1993J emission than the ASCA/GIS ones. + We extracted ASCA/SIS spectra [rom a Jt’ circular region centered on the apparent centroid of the M81. N-5 emission. excluding a 2 circular region centered on the supernova (that lies 2.8 [rom M81. N-5).," We extracted ASCA/SIS spectra from a 4' circular region centered on the apparent centroid of the M81 X-5 emission, excluding a 2' circular region centered on the supernova (that lies 2.8' from M81 X-5)." + The background was extracted from the portion of the SIS chip not contained in the above regions., The background was extracted from the portion of the SIS chip not contained in the above regions. + BeppoSAX observed M81 on June 4 1998., BeppoSAX observed M81 on June 4 1998. + This observation was studied in detail by Pellegrinietal.(2000)., This observation was studied in detail by \citet{pelle}. +. Here. we compare the SAN/LECS (Low ποιον Concentrator Spectrometer) spectrum and ROSAT/PSPC spectra in order to check for spectral variability.," Here, we compare the SAX/LECS (Low Energy Concentrator Spectrometer) spectrum and ROSAT/PSPC spectra in order to check for spectral variability." + For the BeppoSAX data. we used the standard source and background spectra provided by the Narrow Field Instruments publicarchive*.. extracted [rom a 6 radius region centered on the source centroid position.," For the BeppoSAX data, we used the standard source and background spectra provided by the Narrow Field Instruments public, extracted from a 6' radius region centered on the source centroid position." + //ACIS has observed. MIS] twice (loetal.2001.. Swartzetal. 2003)).," /ACIS has observed M81 twice \citealp{ho4}, \citealp{swa}) )." + We used the observation with the longest exposure time (50 ksec. Table 1)).," We used the observation with the longest exposure time (50 ksec, Table \ref{log}) )." + The high flux of the nucleus produces > of pile-up fraction. making the direct study of the properties ol the nucleus unreliable.," The high flux of the nucleus produces $>$ of pile-up fraction, making the direct study of the properties of the nucleus unreliable." + We therefore used the read-out trailed image of the nucleus to extract a spectrum unaffected by pile-up. using a narrow box region (5) running alone the read-out direction of the chip containing (he nuclear trailed image and excluding the direct image.," We therefore used the read-out trailed image of the nucleus to extract a spectrum unaffected by pile-up, using a narrow box region (5”) running along the read-out direction of the chip containing the nuclear trailed image and excluding the direct image." + The background was extracted [rom (wo similar regions adjacent to the source region. each 5 wide.," The background was extracted from two similar regions adjacent to the source region, each 5” wide." + In the following. this spectrum will be referred to as --T. The PSF allows the study of the circum-aimclear region. and in particular of its contribution to the ROSAT and BeppoSAX spectra.," In the following, this spectrum will be referred to as -T. The sub-arcsecond PSF allows the study of the circum-nuclear region, and in particular of its contribution to the ROSAT and BeppoSAX spectra." + To this aim we extracted separately the spectra of the point-like sources (spectrum a) and of the unresolved emission (spectrum b). using the same extraction radius as for the on-axis ROSAT spectra (3°).," To this aim we extracted separately the spectra of the point-like sources (spectrum ) and of the unresolved emission (spectrum ), using the same extraction radius as for the on-axis ROSAT spectra (3')." + The coordinates, The coordinates +Currently. measurements of Doppler shifted winds via (transmission spectroscopy require that (he transmission spectra be integrated over the full transit just to attain the necessary for making a 1 km ! measurement.,"Currently, measurements of Doppler shifted winds via transmission spectroscopy require that the transmission spectra be integrated over the full transit just to attain the signal-to-noise necessary for making a 1 km $^{-1}$ measurement." + However. future observations that can measure Doppler shifts as a function of orbital phase throughout transit will be a very powerful tool for resolving the spatial structure of the winds across a planets terminator.," However, future observations that can measure Doppler shifts as a function of orbital phase throughout transit will be a very powerful tool for resolving the spatial structure of the winds across a planet's terminator." + These tvpes of measurements will likely necessitate next generation eground-based 30-11 class telescopes to attain high signal-to-noise over shorter exposure times., These types of measurements will likely necessitate next generation ground-based 30-m class telescopes to attain high signal-to-noise over shorter exposure times. + Of particular interest is (he measurement of Doppler shifts during transit ingress and egress when only one limb of the planet is in front of the star. which will allow for a straightforward mapping of the eastward and westward flows on either limb of the planet.," Of particular interest is the measurement of Doppler shifts during transit ingress and egress when only one limb of the planet is in front of the star, which will allow for a straightforward mapping of the eastward and westward flows on either limb of the planet." + We calculate Doppler shifts as a function of orbital phase throughout transit for each of the four model atmospheres in Figure 3.., We calculate Doppler shifts as a function of orbital phase throughout transit for each of the four model atmospheres in Figure \ref{phase_shift}. + We separately show the cumulative effects of rotation. winds. and orbital motion.," We separately show the cumulative effects of rotation, winds, and orbital motion." + Generally. the orbital motion is the dominant effect on the Doppler-shilted signal.," Generally, the orbital motion is the dominant effect on the Doppler-shifted signal." + When (hat motion is subtracted off. as in 2.. the effects of winds become apparent.," When that motion is subtracted off, as in \citet{sne10}, the effects of winds become apparent." + some details of the calculation resulüng in Figure δ are as lollows., Some details of the calculation resulting in Figure \ref{phase_shift} are as follows. + Throughout the analvsis we use a single snapshot from each model. safely assuming that the amount of temporal variation is negligible and its effect is small compared to our other simplifving assumptions.," Throughout the analysis we use a single snapshot from each model, safely assuming that the amount of temporal variation is negligible and its effect is small compared to our other simplifying assumptions." + We account for rotation of the planet away [rom phase 4?=0 by shifting the longitudes in our model by an angle equivalent to the orbital phase., We account for rotation of the planet away from phase $\varphi = 0$ by shifting the longitudes in our model by an angle equivalent to the orbital phase. + This step is important because the planet rotates by an angle of 16° over the duration of the transit relative {ο an observer on Earth. whereas the frame of reference of the model atmosphere ealeulations always has the 0° line of longitude al planets substellar point.," This step is important because the planet rotates by an angle of $^{\circ}$ over the duration of the transit relative to an observer on Earth, whereas the frame of reference of the model atmosphere calculations always has the $^{\circ}$ line of longitude at planet's substellar point." + The planets rotation relative to the observer has only a small effect on the caleulatecl velocities. but the effects of the slow eastward motion of both the hottest aud coldest points on the planet does induce small velocily shifts throughout transit.," The planet's rotation relative to the observer has only a small effect on the calculated velocities, but the effects of the slow eastward motion of both the hottest and coldest points on the planet does induce small velocity shifts throughout transit." + For simplicity. we assume that the planet transits exactly across the middle of the star at an orbital inclination of 90°.," For simplicity, we assume that the planet transits exactly across the middle of the star at an orbital inclination of $^{\circ}$." + We do not include anv effects ol limb darkening., We do not include any effects of limb darkening. + We also ignore the geometric effects of curvature on the limb of the star. in effect treating the edge of (he star as a straight line. tangential to the orbital direction of the planet.," We also ignore the geometric effects of curvature on the limb of the star, in effect treating the edge of the star as a straight line, tangential to the orbital direction of the planet." + These last three effects should minimally impact (he results shown in Figure 8.. but the qualitative results are still instructive.," These last three effects should minimally impact the results shown in Figure \ref{phase_shift}, but the qualitative results are still instructive." + During [ull transit. between (he 2nd and 3rd contact points when (he planet is completely in front of the star. (he wind and rotation RVs are fairly constant. despite a very small effect from the rotation of the planet relative to the observer. which can cause shifts of up to 200 ms f.," During full transit, between the 2nd and 3rd contact points when the planet is completely in front of the star, the wind and rotation RVs are fairly constant, despite a very small effect from the rotation of the planet relative to the observer, which can cause shifts of up to 200 m $^{-1}$." + In contrast. the orbital RV signature varies considerably during transit as it sweeps," In contrast, the orbital RV signature varies considerably during transit as it sweeps" +"Mach number x and temperature y, there is z amount of radio emission per comoving Mpc/h per AlogMAlogT.”","Mach number $x$ and temperature $y$, there is $z$ amount of radio emission per comoving Mpc/h per $\Delta +log\Mach \Delta log T$ .”" +" The utility of these diagrams is demonstrated in Figure 4,, where it is immediately clear that the bulk of the radio emission in both simulations originates from hot gas with T=106—5x10""K, and Mach number M=3—10."," The utility of these diagrams is demonstrated in Figure \ref{fig:mach-temp-radio}, where it is immediately clear that the bulk of the radio emission in both simulations originates from hot gas with $T=10^6-5\times10^7\mathrm{K}$, and Mach number $\Mach=3-10$." +" This reinforces our earlier hypothesis that the radio features are generated from interior shocks associated with merging subclusters that have low Mach numbers but high mass and energy flux due to the high relative density, and therefore shock velocity, of cluster cores."," This reinforces our earlier hypothesis that the radio features are generated from interior shocks associated with merging subclusters that have low Mach numbers but high mass and energy flux due to the high relative density, and therefore shock velocity, of cluster cores." +"Second, it points out that shocks with M=20—100 have little role at z—0 in producing appreciable radio emission.","Second, it points out that shocks with $\Mach=20-100$ have little role at $z=0$ in producing appreciable radio emission." +" In fact, their integrated luminosity is a factor of 500—1000 less than their low-Mach number counterparts."," In fact, their integrated luminosity is a factor of $500-1000$ less than their low-Mach number counterparts." +" At first glance, one also picks out a diagonal structure in the phase diagram that seems to be an upper limit on the temperature for a given Mach number."," At first glance, one also picks out a diagonal structure in the phase diagram that seems to be an upper limit on the temperature for a given Mach number." + This is à very interesting feature that has a simple explanation., This is a very interesting feature that has a simple explanation. + We calculate our Mach number using a minimum pre-shock temperature of 10*K., We calculate our Mach number using a minimum pre-shock temperature of $10^4\ \mathrm{K}$. +" Now, while the gas at the location of the shock is not necessarily the pre- or post-shock temperature, it is bounded by those two values."," Now, while the gas at the location of the shock is not necessarily the pre- or post-shock temperature, it is bounded by those two values." +" This is because the shock location is based on the cell with the most convergent flow, not the location of the pre- or post-shock gas."," This is because the shock location is based on the cell with the most convergent flow, not the location of the pre- or post-shock gas." +" Because of this, if gas with pre-shock temperature Τι<10K is being accreted, the gas at the location of the shock will have a maximum temperature of Tj,441$, Comptonization of external soft photons from a cold accretion disk) can dominate electron cooling (see, Ghisellini et 1998)." + Thus. sau<οι is a likely condition in those sources.," Thus, $\gamma_{\rm nth}<\gamma_{\rm t}$ is a likely condition in those sources." + Let go(5) be the synchrotron emission. coefficient. of a single electron. averaged. both over the electron. velocity direction and thedirection of emission., Let $\bar{\eta}_\nu(\gamma)$ be the synchrotron emission coefficient of a single electron averaged both over the electron velocity direction and the direction of emission. + Then. the absorption coclicient for an isotropic distribution of electrons in a chaotic magnetic field is GCGhisellini Svensson 1991) is We assume a homogenous spherical source of the radius. H. and the Thomson optical depth. rrp. where rp=poophR and op is the Thomson cross section.," Then, the absorption coefficient for an isotropic distribution of electrons in a chaotic magnetic field is Ghisellini Svensson 1991) is We assume a homogenous spherical source of the radius, $R$, and the Thomson optical depth, $\tau_{\rm T}$, where $\tau_{\rm T}\equiv n_{\rm e}\sigma_{\rm +T}R$ and $\sigma_{\rm T}$ is the Thomson cross section." +" Then. we can numerically calculate the absorption cocllicicnt with equation for the distribution of equation ancl then. solve equation for the turnover frequency. απ,"," Then, we can numerically calculate the absorption coefficient with equation for the distribution of equation and then solve equation for the turnover frequency, $\nnth$." +" ""phis can be compared with the turnover Crequeney.whieh for plasma parameters tvpical for accreting black holes can he approximated as (WZ00)"," This can be compared with the turnover frequency,which for plasma parameters typical for accreting black holes can be approximated as (WZ00)" +an assumed distribution of Ruse. the assumption of random axial inclination and taking account of the selection effects and measurement. errors.,"an assumed distribution of $R_{\rm true}$, the assumption of random axial inclination and taking account of the selection effects and measurement errors." + If we accept that Pss is related. to Lise. the true rotation period in the absence of measurement uncertainties. according to a normal error distribution characterised by a fractional measurement uncertainty 077. then where C is a random number drawn from a Caussian distribution with mean of zero and unit standard deviation.," If we accept that $P_{\rm obs}$ is related to $P_{\rm true}$, the true rotation period in the absence of measurement uncertainties, according to a normal error distribution characterised by a fractional measurement uncertainty $\delta P$, then = ( 1 + _P, where $U$ is a random number drawn from a Gaussian distribution with mean of zero and unit standard deviation." + The precision of the periods is generally very. goock and we assume dp=0:01 in all cases., The precision of the periods is generally very good and we assume $\delta_P=0.01$ in all cases. +" Similarly. there is a relationship between the true ancl observed projected equatorial velocity = (1 | 9,175. where de is the fractional observational uncertainty in ΠΕΜΕ (taken from the papers where the measurement was presented)."," Similarly, there is a relationship between the true and observed projected equatorial velocity (v = (1 + _v , where $\delta v$ is the fractional observational uncertainty in $(v +\sin i)_{\rm obs}$ (taken from the papers where the measurement was presented)." + In this case (ga and sin; are split into separate factors in order to properly model the observational lower limits to esin and any selection elfect on the possible values of/ (see below)., In this case $v_{\rm true}$ and $\sin i$ are split into separate factors in order to properly model the observational lower limits to $v \sin i$ and any selection effect on the possible values of $i$ (see below). +"£ Equations 13 can be combined to give = (1 | 1108,ini. where sin’ can be generated assuming random. axial orientation and C4, and C» ave dilferent. random numbers taken [from a unit Gaussian distribution."," Equations 1–3 can be combined to give (R = (1 + _v, where $\sin i$ can be generated assuming random axial orientation and $U_1$ and $U_2$ are different random numbers taken from a unit Gaussian distribution." + Note that in this formulation (2sino5 is independent of the assumed P. OF Pune Values. but that this is not the case once selection elfects are considered (see below).," Note that in this formulation $(R \sin i)_{\rm obs}$ is independent of the assumed $P_{\rm true}$ or $v_{\rm true}$ values, but that this is not the case once selection effects are considered (see below)." + For a given observational sample. 101 randomised values of (RsinAan. are generated. for cach star.," For a given observational sample, $10^{4}$ randomised values of $(R \sin i)_{\rm obs}$ are generated for each star." + The initial Rose distribution is taken [rom model isochrones at the Zi; corresponding to cach star in the observed. sample., The initial $R_{\rm true}$ distribution is taken from model isochrones at the $T_{\rm eff}$ corresponding to each star in the observed sample. + As a further refinement Zeus can be drawn randomly. from a distribution. either in terms of a spread about the isochronal racius. or specified as a distribution of age (see section 3.2)).," As a further refinement $R_{\rm true}$ can be drawn randomly from a distribution, either in terms of a spread about the isochronal radius, or specified as a distribution of age (see section \ref{agedist}) )." + There are some further complications which are dealt with in the model., There are some further complications which are dealt with in the model. + First. because the isochrones have a significant slope in the LI-1t diagram. then an uncertainty in Tir leads to additional dispersion in the expected Zi.," First, because the isochrones have a significant slope in the H-R diagram, then an uncertainty in $T_{\rm eff}$ leads to additional dispersion in the expected $R_{\rm true}$." + This is accounted for with a £150 KW Gaussian perturbation in Tor when Aya is calculatect from the evolutionary models., This is accounted for with a $\pm 150$ K Gaussian perturbation in $T_{\rm eff}$ when $R_{\rm true}$ is calculated from the evolutionary models. + Second. the observational sample will be incomplete for objects which have a low inclination angle because starspot moclulation may be dillieult to observe in these stars (see Jelfries 2007 for a discussion).," Second, the observational sample will be incomplete for objects which have a low inclination angle because starspot modulation may be difficult to observe in these stars (see Jeffries 2007 for a discussion)." + This is dealt with by adopting a threshold inclination angle jy. below which randomised trials will be rejected from the model distribution.," This is dealt with by adopting a threshold inclination angle $i_{\rm th}$, below which randomised trials will be rejected from the model distribution." + This free parameter principally alfects the low end of the Z?sin distribution., This free parameter principally affects the low end of the $R \sin i$ distribution. + It is assumed that 4 is independent of rotation period., It is assumed that $i_{\rm th}$ is independent of rotation period. + There is also the issue of limits imposed. by. spectral resolution on the values of (esind)... that can be recorded., There is also the issue of limits imposed by spectral resolution on the values of $(v \sin i)_{\rm obs}$ that can be recorded. + This is dealt with by cdiscarding randonmiüsed trials which have a esin£ lower than the threshold appropriate for the dataset in question., This is dealt with by discarding randomised trials which have a $v \sin i$ lower than the threshold appropriate for the dataset in question. + “Phe minimum measurable value. of (esin/)on. is well defined. but the rejection process requires that an initial ere distribution is also specified.," The minimum measurable value of $(v \sin i)_{\rm obs}$ is well defined, but the rejection process requires that an initial $v_{\rm true}$ distribution is also specified." + Here L follow the example in Jelfries (2007) ancl hypothesise a simple roe distribution. which after multiplying hy the projection factor ancl accounting for observational uncertainties. provides a good match (measured with a Ίντο test) to the observed. eosin?’ distribution.," Here I follow the example in Jeffries (2007) and hypothesise a simple $v_{\rm true}$ distribution, which after multiplying by the projection factor and accounting for observational uncertainties, provides a good match (measured with a K-S test) to the observed $v\sin i$ distribution." + The exact choice “ol rue distribution has very little οοσί on the simulated In; distributions (see also Jellrics 2007)., The exact choice of $v_{\rm true}$ distribution has very little effect on the simulated $R\sin i$ distributions (see also Jeffries 2007). + A number of possible radius or age distributions can be tested to see whether they provide a reasonable description of any particular sample., A number of possible radius or age distributions can be tested to see whether they provide a reasonable description of any particular sample. +" Ehe scenarios investigated are: (1) à co-eval population: (2) a Gaussian distribution of log,2 around an isochronal locus: (3) a racius calculated according to a Gaussian distribution in log), age: (4) a radius calculated. from an age distribution. which exponentially decavs bevond an initial starting age: and (5) a radius calculated: according to the age distributions inferred [rom the traditional LI-R. diagram (see Figs.", The scenarios investigated are: (1) a co-eval population; (2) a Gaussian distribution of $\log_{10} R$ around an isochronal locus; (3) a radius calculated according to a Gaussian distribution in $\log_{10}$ age; (4) a radius calculated from an age distribution which exponentially decays beyond an initial starting age; and (5) a radius calculated according to the age distributions inferred from the traditional H-R diagram (see Figs. + 2. and 3))., \ref{age} and \ref{age2}) ). + Because Aus is expected to vary with Liye at à given age then the distributions of Z should. be specified as a function of Z;r., Because $R_{\rm true}$ is expected to vary with $T_{\rm eff}$ at a given age then the distributions of $R_{\rm true}$ should be specified as a function of $T_{\rm eff}$. + Phis problem is finessecl by normalising Rone by its value at an age of MMyr and at the Zigp of a given star (for the observations) or trial (for the models)., This problem is finessed by normalising $R_{\rm true}$ by its value at an age of Myr and at the $T_{\rm eff}$ of a given star (for the observations) or trial (for the models). + This cllectively collapses the two-dimensional. clistribution along the isochrones. reducing the observed. distribution to one-dimensional form and will be termed the distribution of normalised projected racii. 2sinssi.," This effectively collapses the two-dimensional distribution along the isochrones, reducing the observed distribution to one-dimensional form and will be termed the distribution of normalised projected radii, $R\sin i/R_{\rm 3Myr}$." + The results from. scenarios £/| and 2 will be largely independent of the choice of evolutionary model as they rely only on normalising the Zhi values with an appropriate isochrone of £2 vs Liar., The results from scenarios 1 and 2 will be largely independent of the choice of evolutionary model as they rely only on normalising the $R_{\rm true}$ values with an appropriate isochrone of $R$ vs $T_{\rm eff}$. + However. the absolute ages ancl age spreads in scenarios 3.5 could be very dependent on choice of evolutionary model.," However, the absolute ages and age spreads in scenarios 3–5 could be very dependent on choice of evolutionary model." + With this in mind the evolutionary models of D'Xntona Mazzitelli (L997 hereafter DAALOT) and the solar metallicitv models of Siess. Dufour Forestini (2000. hereafter SOO) have both been tested.," With this in mind the evolutionary models of D'Antona Mazzitelli (1997 – hereafter DAM97) and the solar metallicity models of Siess, Dufour Forestini (2000, hereafter S00) have both been tested." + Vhere are too many [ree parameters and too. few data points in the binned distribution of (AsinAon. (sec section 4)) to attempt an inversion to a true. radius distribution or to perform chi-squared fitting — although this may be possible in future with more numerous data points., There are too many free parameters and too few data points in the binned distribution of $(R \sin i)_{\rm obs}$ (see section \ref{results}) ) to attempt an inversion to a true radius distribution or to perform chi-squared fitting – although this may be possible in future with more numerous data points. + Instead. Ίντο tests are usec to. determine whether a model is capable of providing a satisfactory description ol the observed (cumulative) (2sino.use distributionand to show which models can be ruled out by the data.," Instead, K-S tests are used to determine whether a model is capable of providing a satisfactory description of the observed (cumulative) $(R \sin i)_{\rm +obs}/R_{\rm 3Myr}$ distributionand to show which models can be ruled out by the data." + In each scenario the parameter which determines the mean Hsniffss values Les. the central isochronal age. has been adjusted to minimise the Ix-S statistic ancl maximise consistency. between data ancl model.," In each scenario the parameter which determines the mean $R \sin i/R_{\rm 3Myr}$ value, i.e. the central isochronal age, has been adjusted to minimise the K-S statistic and maximise consistency between data and model." + The main goals are to answer the following questions:, The main goals are to answer the following questions: +see that ὁ approaches a constant.,see that $\delta$ approaches a constant. + Another general point is that 9 is independent of 1 while depencing linearly on the mass of the lens (OsisxθεM. where we are considering the mass within some fixed physical radius: )).," Another general point is that $\delta$ is independent of $\beta$, while depending linearly on the mass of the lens $\delta_{\rm SIS} \propto \theta_E \propto M$, where we are considering the mass within some fixed physical radius; \\ref{sec:PL1}) )." + Profiles shallower than isothermal (5.=1) show a qualitatively dillerent behaviour: as σι increases. the angular beam separation 9 initially rises but then reaches a peak before turning over and returning to zero as τιtn.," Profiles shallower than isothermal $\gamma>1$) show a qualitatively different behaviour: as $z_{\rm l}$ increases, the angular beam separation $\delta$ initially rises but then reaches a peak before turning over and returning to zero as $z_{\rm l} \to z_{\rm s}$." + While there is no simple. general expression for 9 as a function of both the power law slope + and source position 7. we can find an enlightening analytic result for the limit πμfe.," While there is no simple, general expression for $\delta$ as a function of both the power law slope $\gamma$ and source position $\beta$, we can find an enlightening analytic result for the limit $\beta \ll \theta_E$." +" in this casethe images are near the Einstein racius. 81,»7 Op. so the two cdellections angles are A,2{2 1218. and we"," In this casethe images are near the Einstein radius, $\theta_{1,2}\approx\theta_E$ , so the two deflections angles are $\hat{\alpha}_{1,2}\approx D_{\rm s}/D_{\rm ls}\theta_E$ , and we" +cilference.,difference. + In addition. the Le LEE -front mostly lags the LI L-front but in some cases the Lle LL front almost catches up to the LE -lront.," In addition, the He III I-front mostly lags the H I-front but in some cases the He III front almost catches up to the H I-front." + Thus. it appears that these species’ fronts can be coincident for sullicientlv hard radiation.," Thus, it appears that these species' I-fronts can be coincident for sufficiently hard radiation." + The He Ll ionization fraction exceeds that of LL I by a small margin. particularly bevond the edge of the UV. I-front.," The He II ionization fraction exceeds that of H I by a small margin, particularly beyond the edge of the UV I-front." + We recognize this as the characteristic tail of added secondary ionizations from X-ravs. which manifest more stronely at larger physical scales where the UV photons do not penetrate as [ar.," We recognize this as the characteristic tail of added secondary ionizations from X-rays, which manifest more strongly at larger physical scales where the UV photons do not penetrate as far." + This can be seen best by comparing the no-N-rays and X-ravs-only. panels of all the figures in this section. where the He HL front lags or is similar to the 1l E front when X-rays are absent but leads the LD E front when only X-ravs are present.," This can be seen best by comparing the no-X-rays and X-rays-only panels of all the figures in this section, where the He II front lags or is similar to the H I front when X-rays are absent but leads the H I front when only X-rays are present." + Thisinterplay between X-rav secondary ionization and the ionization balance of II and Le in the presence of hard radiation leads to ionization boundaries that are less sharp than in the UV-ionization case alone (see also ? ο this point in relation to the morphology of helium reionization at. lower redshifts. z~ 3).," Thisinterplay between X-ray secondary ionization and the ionization balance of H and He in the presence of hard radiation leads to ionization boundaries that are less sharp than in the UV-ionization case alone (see also \citealt{furlanetto08a} on this point in relation to the morphology of helium reionization at lower redshifts, $z \sim$ 3)." + Last. in the case with only a LO? AL. starburst (Figure 5)). we see that there is little dillerence between these two panels. as this case has low X-ray. production.," Last, in the case with only a $10^6$ $_\odot$ starburst (Figure \ref{fig:stars}) ), we see that there is little difference between these two panels, as this case has low X-ray production." + To test the variation with redshift. we perform the same calculations for our standard. case assumptions at 2=20.," To test the variation with redshift, we perform the same calculations for our standard case assumptions at $z=20$." + Exploring redshifts lower than z 10 marks the era of overlapping I-fronts as reionization clraws to an end. which our current treatment cannot model well.," Exploring redshifts lower than $z \sim$ 10 marks the era of overlapping I-fronts as reionization draws to an end, which our current treatment cannot model well." + Accditionally. there is not much LH Lremoaining outside of galaxy halos to generate an interesting 21 cm signal at the enc of. reionization. whereas the 21 cm signal is expected. to be significant a >=10 20.," Additionally, there is not much H I remaining outside of galaxy halos to generate an interesting 21 cm signal at the end of reionization, whereas the 21 cm signal is expected to be significant at $z = 10$ –20." + The calculations at z=20 for our stancdare case are displaved in Figure 7 with the same three panels as in the ionization and temperature figures., The calculations at $z=20$ for our standard case are displayed in Figure \ref{fig:ionz20} with the same three panels as in the ionization and temperature figures. + As the IG is denser and the recombination timescales are shorter. we garow Curves for times at 1: Myr and LO Myr (rather than 10 p»Ive and 100 Myr) after the source turns on.," As the IGM is denser and the recombination timescales are shorter, we show curves for times at 1 Myr and 10 Myr (rather than 10 Myr and 100 Myr) after the source turns on." + We see tha w ionization curves at 10 Myr between the z=20 case anc our standard case at 2=LO have very similar shapes. with 1 2=20 curves lageing the >=10 curves. expected [rom 1e higher IGM densities at earlier times.," We see that the ionization curves at 10 Myr between the $z=20$ case and our standard case at $z=10$ have very similar shapes, with the $z=20$ curves lagging the $z=10$ curves, expected from the higher IGM densities at earlier times." + Note however tha 10 peak temperatures achieved in all of these cases remain Lgimilar. around. 107 Ix. We perform a simple estimate of the tradeolf between 1e local X-ray. [lux from a single galaxy versus the X-rays rom a number of distant sources.," Note however that the peak temperatures achieved in all of these cases remain similar, around $10^5$ K. We perform a simple estimate of the tradeoff between the local X-ray flux from a single galaxy versus the X-rays from a number of distant sources." + The comoving number density of halos in our work with masses 107 AL. is. n= 1.147 (6.443 10.1) at z =10 (20).," The comoving number density of halos in our work with masses $\ga 10^8$ $M_\odot$ is, $n =$ 1.147 (6.443 $\times 10^{-4})$ $^{-3}$ at $z=$ 10 (20)." + his translates to an average spacing between such halos of ~ 0.95 (11.5) Alpe at ο= 10 (20)., This translates to an average spacing between such halos of $\sim$ 0.95 (11.5) Mpc at $z=$ 10 (20). + The emission rate of H-ionizing photons for a ld’ M. starburst with a LO? AL. DIE (our typical is S—13.10 photons +., The emission rate of H-ionizing photons for a $10^5$ $_\odot$ starburst with a $10^6$ $_\odot$ BH (our typical is $S \sim 1.3 \times 10^{51}$ photons $^{-1}$. +" Ehe associated X-ray photon production rate is 1.3107"" (2.1 107) photons + at 300 eV. and 1 keV respectively.", The associated X-ray photon production rate is $\sim 1.3 \times 10^{49}$ $2.1 \times 10^{48}$ ) photons $^{-1}$ at 300 eV and 1 keV respectively. + Lowe assume a uniform IGM with no attenuation and that the visibility sphere for sources can go out to a maximum radius given by the MEP derived for X-rays as a function of energy in Fig. 2..," If we assume a uniform IGM with no attenuation and that the visibility sphere for sources can go out to a maximum radius given by the MFP derived for X-rays as a function of energy in Fig. \ref{fig:mfp}," + then the critical distance from an individual galaxy source at which the flux of the source become equal to the background. [ux from sources of similar individual Ηχος is 0.10.5 Mpe at z=10 for 300 eV to 1 keV N-ravs., then the critical distance from an individual galaxy source at which the flux of the source become equal to the background flux from sources of similar individual fluxes is 0.1–0.5 Mpc at $z=10$ for 300 eV to 1 keV X-rays. + Thus. our results at z=I0. e.g. in Figure. 3.. could have additional contributions to X-ray ionization from neighboring galaxy halos at radii 0.1.1 Alpe. although this will be less of an issue at 2=20.," Thus, our results at $z=10$, e.g. in Figure \ref{fig:ionstd}, could have additional contributions to X-ray ionization from neighboring galaxy halos at radii 0.1–1 Mpc, although this will be less of an issue at $z=20$." + In reality. we need to factor in realistic density profiles for the galaxies and the IGM. as well as the time variability of individua sources.," In reality, we need to factor in realistic density profiles for the galaxies and the IGM, as well as the time variability of individual sources." + We will pursue this in future work involving a ful cosmological calculation through extensions to the curren Calacticus code (see £4)., We will pursue this in future work involving a full cosmological calculation through extensions to the current Galacticus code (see 4). + Last. we note the oscillations in the He LE fraction au temperature profiles in some of our models.," Last, we note the oscillations in the He II fraction and temperature profiles in some of our models." + We perform a number of checks to make sure these were not mere numerical clleets., We performed a number of checks to make sure these were not mere numerical effects. + We found that these oscillations are robus to increases in the time resolution. ODE solver accuracy aux number of racial shells used in our code.," We found that these oscillations are robust to increases in the time resolution, ODE solver accuracy and number of radial shells used in our code." + These oscillations are also welbresolved racüallv. ancl have a near-constan wavelength. despite the logarithmicallv-spaced. grid spacing in radius.," These oscillations are also well-resolved radially, and have a near-constant wavelength, despite the logarithmically-spaced grid spacing in radius." + What may be occurring is similar to the physics of the instability strip in stellar atmospheres., What may be occurring is similar to the physics of the instability strip in stellar atmospheres. + Inside the ionize region. the optical depth is very small. so the incident [ux drops as Le.," Inside the ionized region, the optical depth is very small, so the incident flux drops as $1/r^2$." + The small HE L. Ho L ancl He. HE fractions are determined by the balance. between photoionization. collisional ionization ancl recombination rates. while the empoerature is controlled by the balance of photoheating and cooling rates.," The small H I, He I and He II fractions are determined by the balance between photoionization, collisional ionization and recombination rates, while the temperature is controlled by the balance of photoheating and cooling rates." + As we move outward. in radius. this cads to a complex interplay between the photoheating rate. emperature and the Le LE fraction in the region of the ο 111 o He HE transition. leading to the temperature and. He 11 raction oscillating with radius.," As we move outward in radius, this leads to a complex interplay between the photoheating rate, temperature and the He II fraction in the region of the He III to He II transition, leading to the temperature and He II fraction oscillating with radius." + “Phis arises from our solving he time-dependent ionization and heating equations rather han adopting the equilibrium solution., This arises from our solving the time-dependent ionization and heating equations rather than adopting the equilibrium solution. + Civen several of our idealized approximations here such as spherical svmmetry. we do not expect this elfect to have a significant. impact. xwticularlv on the 21 em signal whieh we discuss next.," Given several of our idealized approximations here such as spherical symmetry, we do not expect this effect to have a significant impact, particularly on the 21 cm signal which we discuss next." + Over the last. decade. there has been a growing literature on the 21 em radio signals arising [rom the percolation of reionization. ie. the erowth of ionized bubbles around the first lumünous sources and the associated heating (7?7?77777727?7?7)..," Over the last decade, there has been a growing literature on the 21 cm radio signals arising from the percolation of reionization, i.e., the growth of ionized bubbles around the first luminous sources and the associated heating \citep{zaldarriaga04,chen04,chen08,kuhlen06,McQuinn:06,furlanetto04,furlanetto06,furlanetto06a,pritchard07,Thomas:08,Ripamonti:08,santos08,morales10}." + “Phe signature is expected. to. be absorption (emission) against the CAIB if. the ionized region ids colder (warmer) than the CAIB 80 those epochs., The signature is expected to be absorption (emission) against the CMB if the ionized region is colder (warmer) than the CMB at those epochs. + Forthcoming interferometric experiments at. racio wavelengths. such as LOPAR and SKA. ave predicted. to » able to resolve ionized. bubbles of size 100 kpe up to a lew Alpe.," Forthcoming interferometric experiments at radio wavelengths, such as LOFAR and SKA, are predicted to be able to resolve ionized bubbles of size $\sim$ 100 kpc up to a few Mpc." + The dominant signal arises from. the coupling of the spin temperature of neutral hydrogen with 1 kinetic temperature of the background: LGAL eas., The dominant signal arises from the coupling of the spin temperature of neutral hydrogen with the kinetic temperature of the background IGM gas. + After recombination. the IGM cools as (| z)? whereas the CMD ‘ools as (1 | z). leading to a 21 em absorption signal from. re neutral LGAL gas.," After recombination, the IGM cools as (1 + $z$ $^2$ whereas the CMB cools as (1 + $z$ ), leading to a 21 cm absorption signal from the neutral IGM gas." + At later epochs. the spin states of ivdrogen come into equilibrium with the CMD. leading to a ecreasing 21 em signal.," At later epochs, the spin states of hydrogen come into equilibrium with the CMB, leading to a decreasing 21 cm signal." + As the first stars and quasars turn on. a 21 em emission signal is generated. through coupling 16 spin states with the scattering of Lvo photons and other DOCOCSSCS.," As the first stars and quasars turn on, a 21 cm emission signal is generated through coupling the spin states with the scattering of $\alpha$ photons and other processes." + llere. we follow the formalism. outlined in. ?..," Here, we follow the formalism outlined in \citet{chen08}. ." + As, As +easily. explained.,easily explained. + The characteristic progression of velocity οι with period is caused by the 2:1 resonance between the first overtone and the fourth overtone (Ixienzlectal.1999:Feuchtingeretal. 2000).," The characteristic progression of velocity $\phi_{21}$ with period is caused by the 2:1 resonance between the first overtone and the fourth overtone \citep{kie99, FEU00}." +. Phe center of this resonance is located at 2=4.2 l.6dayv., The center of this resonance is located at $P=4.2-4.6$ day. + The exact location οἱ the resonance in hvdrodsnamic models depends mostly on the chosen mass-Iuminositv relation., The exact location of the resonance in hydrodynamic models depends mostly on the chosen mass-luminosity relation. +" This relation was not adjusted. in our calculations to match the observed resonance progression”... As shown in το ρε, the resonance center (displayed. with the dashed line) crosses the center of the first overtone LS for periods shorter than 4days. which explains the horizontal shift in refltSfourier.."," This relation was not adjusted in our calculations to match the observed resonance As shown in \\ref{RShr}, the resonance center (displayed with the dashed line) crosses the center of the first overtone IS for periods shorter than days, which explains the horizontal shift in \\ref{RSfourier}." +" Taking into account this shift. amplitudes. amplitude ratios ancl Fourier. phases. agree: satisfactorily with observations. although at the short. periods theoretical Oo, values are slightly too high."," Taking into account this shift, amplitudes, amplitude ratios and Fourier phases agree satisfactorily with observations, although at the short periods theoretical $\phi_{21}$ values are slightly too high." + Considering. V440. Per. we see the very good agreement. with the model sequence closest to the blue edge of the overtone instability: strip (NT= 258).," Considering V440 Per, we see the very good agreement with the model sequence closest to the blue edge of the overtone instability strip $\Delta T\! =\! 25$ K)." + An exact match can be easily obtained. for the model sequence located: slightly closer to the blue edge., An exact match can be easily obtained for the model sequence located slightly closer to the blue edge. + We note. that the progression of the overtone O21 at long periods is insensitive to the choice of AY.," We note, that the progression of the overtone $\phi_{21}$ at long periods is insensitive to the choice of $\Delta T$." + The models predict slightly. higher o»; than actually observed in V440 Per. but the two values are consistent within the error bar.," The models predict slightly higher $\phi_{21}$ than actually observed in V440 Per, but the two values are consistent within the error bar." + Using our newTelescope we obtained 155 high precision. radial velocity. observations of a low amplitude Cepheicl V440 Per., Using our new we obtained 158 high precision radial velocity observations of a low amplitude Cepheid V440 Per. +" We constructed the pulsation velocity. curve of V440. Per and we were able to reliably detect its Ist harmonic. with amplitude of only 1H03:15 m/s. The measured Fourier phase O2,=2.76+0.12 rad. dilfers [rom the values observed in fundamental mode Cepheids of a similar period by 7.250."," We constructed the pulsation velocity curve of V440 Per and we were able to reliably detect its 1st harmonic, with amplitude of only $140\pm +15$ m/s. The measured Fourier phase $\phi_{21}=2.76\pm +0.12$ rad differs from the values observed in fundamental mode Cepheids of a similar period by $\sigma$." + Thus. we demonstrated on purely morphological ground that V440 Per does not pulsate in the fundamental mode.," Thus, we demonstrated on purely morphological ground that V440 Per does not pulsate in the fundamental mode." + This settles the dispute between Szaboetal.(2007) and Ixienzleetal.(1999) and allows to classify V440 Per as an overtone pulsator. the one with the longest period identified so far (2?=7.57 day).," This settles the dispute between \citet{SZ07} and \citet{kie99} and allows to classify V440 Per as an overtone pulsator, the one with the longest period identified so far $P=7.57$ day)." + Our results. demonstrate. that with suitable care. our inexpensive instrument. featuring MUSICOS Echelle Es»ectrograph and a small robotic telescope can achieve gaability and precision. stwpassed only in the extrasolar planet searches.," Our results demonstrate that with suitable care, our inexpensive instrument featuring MUSICOS Echelle spectrograph and a small robotic telescope can achieve stability and precision surpassed only in the extrasolar planet searches." + Note. that we cmiplovect neither the iodine coll nor environment. control.," Note, that we employed neither the iodine cell nor environment control." + Yet. our observations prove ju the secure mode identification is feasible even for the Pcory Low amplitude Galactic Cepheids.," Yet, our observations prove that the secure mode identification is feasible even for the very low amplitude Galactic Cepheids." + The overtone pulsation of ΕΜ) Per has interesting jceoretical consequences., The overtone pulsation of V440 Per has interesting theoretical consequences. + To investigate them we emploved our convective linear and nonlinear pulsation codes (Smolec 2008).., To investigate them we employed our convective linear and nonlinear pulsation codes \citep{SM08}. . +" The first overtone linear mocdels are already. constrained by. the value of the pulsation period at the center of the Pu,=wy, resonance (hienzleetal.1999:Feuchtingeret2000)."," The first overtone linear models are already constrained by the value of the pulsation period at the center of the $2\omega_1=\omega_4$ resonance \citep{kie99, FEU00}." +. The very existence of ΕΜ) Per imposes additional constraints., The very existence of V440 Per imposes additional constraints. + Namely. to inearlv excite the first overtone anc then to obtain a overtone pulsation of such a long »wiod. one has to [fine tune the cynamical convection model used. in the pulsation caleulations.," Namely, to linearly excite the first overtone and then to obtain a overtone pulsation of such a long period, one has to fine tune the dynamical convection model used in the pulsation calculations." + Our numerical experiments demonstrate that in the convective cnerey ransport radiative losses must be properly accounted or to maintain consistency with the observations., Our numerical experiments demonstrate that in the convective energy transport radiative losses must be properly accounted for to maintain consistency with the observations. + With his οσο taken into account. the nonlinear overtone Cepheicl models not only reproduce the exceptionally long »viod of V440 Per. but they also reproduce neatly all Fourier parameters of its pulsation velocity curve.," With this effect taken into account, the nonlinear overtone Cepheid models not only reproduce the exceptionally long period of V440 Per, but they also reproduce neatly all Fourier parameters of its pulsation velocity curve." +" No such agreement can be achieved with models. pulsating in the ""undamental mode.", No such agreement can be achieved with models pulsating in the fundamental mode. + Phese results of the hvdrodvnamical modeling provide additional. support for our empirical classification of V440 Per as a first overtone pulsator., These results of the hydrodynamical modeling provide additional support for our empirical classification of V440 Per as a first overtone pulsator. + This publication is based on the first. results fromTelescope. ai large instrumental project developed: at A. Mickiewicz University in Poznan in the course of many vears.," This publication is based on the first results from, a large instrumental project developed at A. Mickiewicz University in Poznań in the course of many years." + Recent work by RB. ME. and ASC was supported from the Polish MNil grant N N203 3020 35.," Recent work by RB, MF and ASC was supported from the Polish MNiI grant N N203 3020 35." + We acknowledge with gratitude permission to use facilities of- and help from- the Borowiec Geodynamical Observatory of Centre for Space Research (CBI PAN. Borowiec). in eencral. and encouragement [rom Prof. Stanislaw Schillak. in particular.," We acknowledge with gratitude permission to use facilities of- and help from- the Borowiec Geodynamical Observatory of Centre for Space Research (CBK PAN, Borowiec), in general, and encouragement from Prof. aw Schillak, in particular." + RS and PM work on the pulsation codes is supported by the MNiISW Grant 1: DP03D 011 30., RS and PM work on the pulsation codes is supported by the MNiSW Grant 1 P03D 011 30. + We would like to acknowledge inspiration and support by. late Prof. 3ohdan Paczvnski., We would like to acknowledge inspiration and support by late Prof. Bohdan Paczynski. +Dr. Jacques. Baudrand. kindly. supplied us with the blueprints ofMUSICOS.,Dr. Jacques Baudrand kindly supplied us with the blueprints ofMUSICOS. +"We investigated the LF and spatial distribution of LMXBs in the Milky Way, M31 and Cen A. These galaxies are the only massive galaxies in which the LF of LMXBs can be studied at the faint end («10°° erg s71).","We investigated the LF and spatial distribution of LMXBs in the Milky Way, M31 and Cen A. These galaxies are the only massive galaxies in which the LF of LMXBs can be studied at the faint end $<10^{36}$ erg $^{-1}$ )." +" We have shown that the LF flattens significantly at luminosities below few times 10?"" erg s~!.", We have shown that the LF flattens significantly at luminosities below few times $10^{37}$ erg $^{-1}$. + We have also found that the LF of field sources is different from the LF of the LMXBs found in GCs., We have also found that the LF of field sources is different from the LF of the LMXBs found in GCs. +" This indicates that the two populations are formed differently, and is à strong argument against the idea that all LMXBs are formed in GCs (?).."," This indicates that the two populations are formed differently, and is a strong argument against the idea that all LMXBs are formed in GCs \citep{White2002}." +" Furthermore the difference provides an additional constraint that can be important for modelling the formation and evolution of the LMXBs, and indicates that the bright and faint systems are not simply different evolutionary states of the same type of We have also found a new population of LMXBs, formed dynamically in the central bulge of M31."," Furthermore the difference provides an additional constraint that can be important for modelling the formation and evolution of the LMXBs, and indicates that the bright and faint systems are not simply different evolutionary states of the same type of We have also found a new population of LMXBs, formed dynamically in the central bulge of M31." +" This population shows up as a surplus of X-ray sources in the central 1 arcmin of M31, and the spatial distribution is in agreement with our theoretical model."," This population shows up as a surplus of X-ray sources in the central 1 arcmin of M31, and the spatial distribution is in agreement with our theoretical model." + The LF displays the same dearth of faint sources as the LF of dynamically formed LMXBs in, The LF displays the same dearth of faint sources as the LF of dynamically formed LMXBs in +By repeating this procedureVo=12.764 (times. I created one realization of the 465. σ.. fi. 0 parameter set.,"By repeating this procedure$N_{\rm gal} = 12{,}764$ times, I created one realization of the $\mu_\gamma$ , $\sigma_\gamma$, $\mu$, $\sigma$ parameter set." + After creating 16.000 realizations. I computed the mean and standard deviation of the expected number of galaxies in each of the 40 bins in Figure L.. and computed a A7 probability for that particular set of parameters.," After creating 000 realizations, I computed the mean and standard deviation of the expected number of galaxies in each of the 40 bins in Figure \ref{fig:q_sdss}, and computed a $\chi^2$ probability for that particular set of parameters." +" A search through four-dimensional parameter space revealed that the best fit for gay, in the / band was provided by the set of parameters qt,=0.222. σ.=0.057. ji=—1.85. and σ=0.89."," A search through four-dimensional parameter space revealed that the best fit for $q_{\rm am}$ in the $i$ band was provided by the set of parameters $\mu_\gamma = 0.222$, $\sigma_\gamma = 0.057$, $\mu = -1.85$, and $\sigma = 0.89$." + The resulting 47 probability was P=3x10H1.," The resulting $\chi^2$ probability was $P = 3 +\times 10^{-4}$." + Formally. this is not a good fit to the data. but more than half the contribution to 47 comes from the bins on the far left. with gan<0.3.," Formally, this is not a good fit to the data, but more than half the contribution to $\chi^2$ comes from the bins on the far left, with $q_{\rm am} < 0.3$." + As emphasized by Fasanoefaf.(1993).. the distributions of 5 and 7 for spiral galaxies are almost. completely decoupled. im that (he distribution of 5 determines the left. hand side of (ο) while the distribution of 5 determines the right hand side.," As emphasized by \citet{fa93}, the distributions of $\gamma$ and $\varepsilon$ for spiral galaxies are almost completely decoupled, in that the distribution of $\gamma$ determines the left hand side of $f(q)$ while the distribution of $\varepsilon$ determines the right hand side." + The models relatively poor fit at gay«0.3 indicates that the galaxies in the sample have a distribution of thicknesses which is nol well fit by a Gaussian., The model's relatively poor fit at $q_{\rm am} < 0.3$ indicates that the galaxies in the sample have a distribution of thicknesses which is not well fit by a Gaussian. + In any case. the distribution of disk (hickuesses in my sample is nol the same as the true distribution of disk thicknesses.," In any case, the distribution of disk thicknesses in my sample is not the same as the true distribution of disk thicknesses." + As shown bv (1992).. a maenitude-Imited sample of galaxies such as the SDSS DII spectroscopic galaxy sample. which has a limiting (Petrosian) magnitude r<17.77. will show a deficit of low-q spiral galaxies.," As shown by \citet{hu92}, , a magnitude-limited sample of galaxies such as the SDSS DR1 spectroscopic galaxy sample, which has a limiting (Petrosian) magnitude $r < 17.77$, will show a deficit of high-inclination, $q$ spiral galaxies." + This deficit is due to exünction by dust., This deficit is due to extinction by dust. + In (he D band. for instance. an Se galaxy is 100 1.5 magnitudes fainter when seen edge-on than when seen [face- (Iluizinga&vanAlbada1992).," In the $B$ band, for instance, an Sc galaxy is 1 to 1.5 magnitudes fainter when seen edge-on than when seen face-on \citep{hu92}." +. Although the inclinalion-dependent dimming is smaller al longer wavelengths ancl for earlier (wpe spirals. the fitted disk thickness should be regarded wilh skepticism.," Although the inclination-dependent dimming is smaller at longer wavelengths and for earlier type spirals, the fitted disk thickness should be regarded with skepticism." + Fortunately for (he purposes of this paper. spiral galaxies Chat appear nearly circular (qZ 0.8) are nearly [ace-0n. and hence their thickness isalmost totally irrelevant: its (he distribution of disk ellipticity 7 that determines the shape of f/(q) al large q.," Fortunately for the purposes of this paper, spiral galaxies that appear nearly circular $q \gtrsim 0.8$ ) are nearly face-on, and hence their thickness isalmost totally irrelevant; it's the distribution of disk ellipticity $\varepsilon$ that determines the shape of $f(q)$ at large $q$ ." + Table 1. shows the best filling model parameters. ων σοι ji. and 5. for the two different shape measures. Gam aud dos. and for the three different bancs. gy. 7. ancl 7.," Table \ref{tab:models} shows the best fitting model parameters, $\mu_\gamma$, $\sigma_\gamma$, $\mu$ , and $\gamma$ , for the two different shape measures, $q_{\rm am}$ and $q_{25}$, and for the three different bands, $g$ , $r$, and $i$." + In addition. the best values of jp and are plotted as points in Figure 2..," In addition, the best values of $\mu$ and $\gamma$ are plotted as points in Figure \ref{fig:prob_sdss}." + Note that going from g band (triangles) to r band (squares) to 7 band (circles) results in a smaller spread. of disk elliptidities (that is. 3mnaller values of 6).," Note that going from $g$ band (triangles) to $r$ band (squares) to $i$ band (circles) results in a smaller spread of disk ellipticities (that is, smaller values of $\sigma$ )." + Going [rom qa (fillel sviubols) to ds; (open sviubols) results in a V.naller cisk ellipticity (hat is. smaller values of jp().," Going from $q_{\rm am}$ (filled symbols) to $q_{25}$ (open symbols) results in a smaller disk ellipticity (that is, smaller values of $\mu$ )." + In the 7 band. for instance. using gam for ye shape measure results in a best fit log-normal distribution with j(=—1.85 and a=0.39: 1e modal ellipticity for Chis distribution is 0.071. the median is 2eez0.16. and the mean is 0.21.," In the $i$ band, for instance, using $q_{\rm am}$ for the shape measure results in a best fit log-normal distribution with $\mu = -1.85$ and $\sigma = 0.89$; the modal ellipticity for this distribution is 0.071, the median is $\approx e^\mu \approx 0.16$, and the mean is 0.21." + Using qs for the shape measure resulis in po=—2.06 and στ0.83: the modal ellipticity is 0.064. the median is zeπό 0.13. and the meanis 0.17.," Using $q_{25}$ for the shape measure results in $\mu = -2.06$ and $\sigma = 0.83$; the modal ellipticity is 0.064, the median is $\approx e^\mu \approx 0.13$ , and the meanis 0.17." + Although the clisks are rounder. on average. in the outer regions. {μον sill have a significant. ellipticitv.," Although the disks are rounder, on average, in the outer regions, they still have a significant ellipticity." + Notealso the color dependence of the mean thickness 6: galactic disks are thicker. on average.al longerwavelengths.," Notealso the color dependence of the mean thickness $\mu_\gamma$ ; galactic disks are thicker, on average,at longerwavelengths." +This dependencereflects the fact that older stellar populations. which have redder colors. have a greater vertical velocity dispersion ancl hence a greater disk scale,"This dependencereflects the fact that older stellar populations, which have redder colors, have a greater vertical velocity dispersion and hence a greater disk scale" +about à super-massive black hole (e.g. Rees 1984: Rauch Blandford 1991: Agol Ixrolik. 1999).,about a super-massive black hole (e.g. Rees 1984; Rauch Blandford 1991; Agol Krolik 1999). + Conversely. if a source size of ~LOMem is assumed. then the our limits on microlens mass corresponding to the short light-curve peak and large microlens variation are respectively Go»0.25M. (09'4)) and £n>0.002534. (9543).," Conversely, if a source size of $\sim 10^{15}cm$ is assumed, then the our limits on microlens mass corresponding to the short light-curve peak and large microlens variation are respectively $\langle m\rangle>0.25M_{\odot}$ ) and $\langle m\rangle>0.0025M_{\odot}$ )." + Note that for a source having a ciameter of ~LOem we have explicitly checked masses down to £m)~10A4.., Note that for a source having a diameter of $ \sim 10^{15}cm$ we have explicitly checked masses down to $\langle m\rangle\sim 10^{-5}M_{\odot}$. + A much smaller source must therefore be assumed if sub-stellar masses were to forni the bulk of the galactic bulge in Q2237|0305., A much smaller source must therefore be assumed if sub-stellar masses were to form the bulk of the galactic bulge in Q2237+0305. + Our calculations assume hat the dominant contribution to optical depth comes from a population of microlenses having a range smaller than two orders of magnitude., Our calculations assume that the dominant contribution to optical depth comes from a population of microlenses having a range smaller than two orders of magnitude. + We note that our model therefore. does. not account for the possibility suggested by Refsdal Stabell (1993) in which a population of stars and another of very low-mass objects both contribute significantly to the optical depth., We note that our model therefore does not account for the possibility suggested by Refsdal Stabell (1993) in which a population of stars and another of very low-mass objects both contribute significantly to the optical depth. + In this case. the rapid. variation due to the small masses. and the slower variation due to the large masses should. be approximately superimposed: (Itefscdal Stabell 1993).," In this case, the rapid variation due to the small masses, and the slower variation due to the large masses should be approximately superimposed (Refsdal Stabell 1993)." + However our results can be (qualitatively interpreted for this scenario., However our results can be qualitatively interpreted for this scenario. + There are two possibilities., There are two possibilities. +" Firstly. if the source has dimensions Sxapa, (where nas ds the Einstein radius of the mean microlens mass of the low mass population). then our results hold. since mo ds quite insensitive to the value of the heavy. masses."," Firstly, if the source has dimensions $S\ll\eta_{sm}$ (where $\eta_{sm}$ is the Einstein radius of the mean microlens mass of the low mass population), then our results hold since $\langle m\rangle$ is quite insensitive to the value of the heavy masses." +" Secondlv. WS22ape, then the light-curves will be like those resulting from microlensing by the Large masses only (with a continuous component of mass densitv). combined with a continuous low amplitude ticker."," Secondly, if $S\gg\eta_{sm}$ then the light-curves will be like those resulting from microlensing by the large masses only (with a continuous component of mass density), combined with a continuous low amplitude flicker." + In this case. the results we have presented can be interpreted as the ratio of source size to the Einstein radius of the mean microlens mass of the large population.," In this case, the results we have presented can be interpreted as the ratio of source size to the Einstein radius of the mean microlens mass of the large population." + We therefore conclude that a significant contribution to the optical depth comes from objects with Einstein radius larger than the source size. regardless of the mass function.," We therefore conclude that a significant contribution to the optical depth comes from objects with Einstein radius larger than the source size, regardless of the mass function." + The conclusion that the source is small with respect to the microlens Einstein radius is important because it means that caustic crossing light-curves can be inverted to obtain extremely high resolution information on the continuum SOULCE slructure., The conclusion that the source is small with respect to the microlens Einstein radius is important because it means that caustic crossing light-curves can be inverted to obtain extremely high resolution information on the continuum source structure. + The authors would like to thank Sjur Itefsdal and Joachim Wanmbseganss for enlightening discussions. as well as the anonvmous referee for suggestions which have enhanced the presentation of this work.," The authors would like to thank Sjur Refsdal and Joachim Wambsganss for enlightening discussions, as well as the anonymous referee for suggestions which have enhanced the presentation of this work." + We would. also. like to acknowledge the OGLE collaboration for making their monitoring cata publically available in real time., We would also like to acknowledge the OGLE collaboration for making their monitoring data publically available in real time. + “Phis work was supported by NSE erant. ASTOS-02802.., This work was supported by NSF grant AST98-02802. + JSBW acknowledges the support of an Australian Postgraduate Award and a Melbourne University Postgraduate Overseas Research Experience Award., JSBW acknowledges the support of an Australian Postgraduate Award and a Melbourne University Postgraduate Overseas Research Experience Award. +slower than the Pop.,slower than the Pop. + II one. as a result the Pop.," II one, as a result the Pop." + I star has a smaller II-exhausted core aud hieher-mass envelope than the Pop., I star has a smaller H-exhausted core and higher-mass envelope than the Pop. + II star when (μον have (he same radii. (hus higher A values.," II star when they have the same radii, thus higher $\lambda$ values." + We used the II abundance laver as the stellar core-envelope boundary to caleulate the binding energy ancl A. since the core mass from such definition increases in most of the time and is suitable for caleulating the binding οποιον (Eggleton 2009).," We used the H abundance layer as the stellar core-envelope boundary to calculate the binding energy and $\lambda$, since the core mass from such definition increases in most of the time and is suitable for calculating the binding energy (Eggleton 2009)." + Note that Dewi(2000) used the IL abundance laver as the core-envelope boundary. and in our caleulation we found that the two definitions give similar results.," Note that \citet{dew00} used the H abundance layer as the core-envelope boundary, and in our calculation we found that the two definitions give similar results." + There are other criteria to define this boundary. such as the maximum energy generation laver or the density gradient criteria (lanetal.1994:Dewi&Tauris2000).," There are other criteria to define this boundary, such as the maximum energy generation layer or the density gradient criteria \citep{han94, dew00}." +. According to Tauris&Dewi(2001). and Dewi&Tauris(2001).. most of these criteria give outer core boundary and higher core mass.," According to \citet{tau01} and \citet{dew01}, most of these criteria give outer core boundary and higher core mass." + In general. if (he total stellar mass is a constant. a more massive core will decrease the total binding enerey of the envelope ancl result in a larger A-value (Dewi&Tauris2000:Dewi&Tauris 2001).," In general, if the total stellar mass is a constant, a more massive core will decrease the total binding energy of the envelope and result in a larger $\lambda$ -value \citep{dew00, tau01,dew01}." +. In other words. the A-values we calculated may be regarded as the lower limit of the actual ones.," In other words, the $\lambda$ -values we calculated may be regarded as the lower limit of the actual ones." + Stars more massive (han LOAL. lose LO% to 30% of its total mass curing its evolution. which can affect the stellar structure and the values of A (Dewi&Tauris2000.2001:Poclsiadlowskietal.2003).," Stars more massive than $10 M_\odot$ lose $10\%$ to $30\%$ of its total mass during its evolution, which can affect the stellar structure and the values of $\lambda$ \citep{dew00, dew01, pod03}." +. Dewi&Tauris(2001) anc Podsiacdlowskietal.(2003) have also found that A is sensitive to the wind mass loss for massive stars. and including stellar wind leads to higherbinding energy (absolute value) and lower value of A.," \citet{dew01} and \citet{pod03} have also found that $\lambda$ is sensitive to the wind mass loss for massive stars, and including stellar wind leads to higherbinding energy (absolute value) and lower value of $\lambda$ ." +" Our results suggest that Aj, can take values significantly larger than 0.5 during the late-stage evolution of stars with mass between ~2 and LOAL.. which will significantly increase (he efficiency of envelope ejection."," Our results suggest that $\lambda_{\rm b}$ can take values significantly larger than $0.5$ during the late-stage evolution of stars with mass between $\sim 2$ and $10 M_\odot$ , which will significantly increase the efficiency of envelope ejection." + If we consider an evolved giant or AGB star in (his mass range wilh A>>0.5. the envelope binding energy may be much smaller compared to (hat with A= 0.5.," If we consider an evolved giant or AGB star in this mass range with $\lambda>>0.5$, the envelope binding energy may be much smaller compared to that with $\lambda = 0.5$ ." + Itis thenmuch easier lor its companion to eject the CE. and to," Itis thenmuch easier for its companion to eject the CE, and to" +The final result of this sectiou is really Theorem 5 of Markushevich [11]: we iuclude a slight simplification of his proof. which avoids calculations iu loca coordinates.,"The final result of this section is really Theorem 5 of Markushevich \cite{markushevich95}; we include a slight simplification of his proof, which avoids calculations in local coordinates." +"ttrausuission ina pixelis 7j],=expt0.025reas.) (cf","transmission in a pixel is $\Trans_{\rm HeI, i}^{\rm est} = \exp(-0.025 \,\tau_{{\rm HI, 1216}, {\it i}})$ (cf." + equations 2 aud 2))., equations \ref{eqn:584GP2}~ and \ref{eqn:tauNHI}) ). + Towever. in the lit τιοκι l. the SNR of the cross correlation is uot affected bv what we asstune for the proportionality between ΤΙπει and nzunisioó.," However, in the limit $\tau_{\rm HeI, 584} \ll 1$ , the SNR of the cross correlation is not affected by what we assume for the proportionality between $\tau_{\rm HeI, 584}$ and $\tau_{\rm HI, 1216}$." + In fact. we find that it is onlv mareinally sensitive to this proportionality in realistic cases because the aabsorption is weak and because the SNR idu cross correlation depends more on the phase of modes thau ou their amplitude.," In fact, we find that it is only marginally sensitive to this proportionality in realistic cases because the absorption is weak and because the SNR in cross correlation depends more on the phase of modes than on their amplitude." + We discuss in Sec., We discuss in Sec. + L2.0. how au iuperfeet estimate for affects our estimates., \ref{sssec:imperfecttemplate} how an imperfect estimate for $\Trans_{\rm HeI}^{\rm est}$ affects our estimates. + An estimator for ΠΡΙdetecting this signal 1 cross correlation is where D represeuts the data. tildes denote a quantitv ij Fourier space (a convenieut basis because the covariance matrix of the noise is diagonal). Py is the power spectrum of the foreground aabsorptiou. and P4 is the power spectrum of the instrumental noise (which we assunie is white).," An estimator for detecting this signal in cross correlation is where ${D}$ represents the data, tildes denote a quantity in Fourier space (a convenient basis because the covariance matrix of the noise is diagonal), $P_{\rm HI}$ is the power spectrum of the foreground absorption, and $P_{\rm inst}$ is the power spectrum of the instrumental noise (which we assume is white)." +" Convenicutly. the variauce ou this estimator owine to nolse is its average, making it an estimate for the square of the SNR."," Conveniently, the variance on this estimator owing to noise is its average, making it an estimate for the square of the SNR." + This estimator is unbiased im the scuse hat compoucuts that do not correlate with ΠΡΙ do iof contribute., This estimator is unbiased in the sense that components that do not correlate with $\tilde{\Trans}_{\rm HeI}^{\rm est}$ do not contribute. + This estimator asses that the signal is known since it requires πιω as input., This estimator assumes that the signal is known since it requires $\tilde{\Trans}_{\rm HeI}$ as input. +" In practice. his asstunption can be avoided because for interesting cases we fud that ΤμxTig (aud the normalization actor can be determined iu a measurement to fractional srecision eO.5SSNR +),"," In practice, this assumption can be avoided because for interesting cases we find that $\tilde{\Trans}_{\rm HeI}^{\rm est} \propto \tilde{\Trans}_{\rm HeI}$ (and the normalization factor can be determined in a measurement to fractional precision $\approx 0.5$ $^{-1}$ )." + The ensemble average of this estimator over the nolse and foreground absorption vields The cross correlation coefficient rh) is bounded such that /—dο<1 ancl is defined as The approximate equality given by equation (7)) is à rough estimate for the SNR of detection ifσε1 aud if the information is comiue from modesnear the resolution limit (which roughly holds for Ro=20.000).," The ensemble average of this estimator over the noise and foreground absorption yields The cross correlation coefficient $r(k)$ is bounded such that $-1 < r(k) < 1$ and is defined as The approximate equality given by equation \ref{eqn:stonapprox}) ) is a rough estimate for the SNR of detection if$r \approx 1$ and if the information is coming from modesnear the resolution limit (which roughly holds for ${\cal R}\lesssim 20,000$ )." + Iu this equality. Vy. is the προ of resolution elements. aud Tha2 Ty2 Md e$2 are respectivelyH the variance- of. the SEA fransimissiontnorimalizedsuchthatzya ss|0 ds transmission of unitv). the foreground ttrausunission. aud the instriuuoeutal noise in a resolution clement.," In this equality, $N_{\rm res}$ is the number of resolution elements, and $\sigma_{\rm HeI}^2$, $\sigma_{\rm HI}^2$ and $\sigma_{\rm inst}^2$ are respectively the variance of the $584~$ transmission (normalized such that $\tau_{\rm HeI, 584} =0$ is transmission of unity), the foreground transmission, and the instrumental noise in a resolution element." +" This approximate relation shows that. for AR.=Φον10! and N44,=105 (Aszm (0,2). such a cross correlation can be used to detectthe signal even if the fluctuations in the signal are more than aun order of magnitude smaller than the fluctuations iu the Figure L plots the expected average SNR as a function! of Jing at which the aabsorption can be detected in cross correlation. assunüue JN10* aud Ro=2«107."," This approximate relation shows that, for ${\cal R} = 2\times 10^4$ and $N_{\rm res} = 10^3$ $\Delta z \approx 0.2$ ), such a cross correlation can be used to detectthe signal even if the fluctuations in the signal are more than an order of magnitude smaller than the fluctuations in the Figure \ref{fig:matched} plots the expected average SNR as a function of $\sigma_{\rm inst}$ at which the absorption can be detected in cross correlation, assuming $N_{\rm res} = 10^3$ and ${\cal R} = 2\times 10^4$." +" To calculate this quantity, we substitute terius of the form 77T. with their euseiible-average in equation (6))."," To calculate this quantity, we substitute terms of the form $\tilde{\Trans}^\dag \tilde{\Trans}$ with their ensemble-average in equation \ref{eqn:ston}) )." + The red curves are this SNR for observations of aabsorptiou at +—3 (thin) aud :—1 (thick)., The red curves are this SNR for observations of absorption at $z=3$ (thin) and $z=4$ (thick). + aabsorption can be detected statistically using this technique even with an extremely poor SNR per resolution clement (at z10σ for σι= 0.3).," absorption can be detected statistically using this technique even with an extremely poor SNR per resolution element (at $\approx 10\,\sigma$ for $\sigma_{\rm inst} = 0.3$ )." + In the case of COS. Ni.2500. 1000. and 1500. depending ou whether 1.2. or 3 of the ~LO A baudpasses (that cach COS NUV erating cau simultaucousIy observe) cover the forest for a giveu target.," In the case of COS, $N_{\rm res} \approx 500, 1000$ , and $1500$ , depending on whether $1,2$ , or $3$ of the $\approx 40$ A bandpasses (that each COS NUV grating can simultaneously observe) cover the forest for a given target." +The dashed lines delineate second sequences where stars with nucleosvnthetic signatures in common with the Lyman a [orest gas lie.,The dashed lines delineate second sequences where stars with nucleosynthetic signatures in common with the Lyman $\alpha$ forest gas lie. + In every figure. (he Cavrel οἱ sstars labelled 5. 30. 32. and 34 are offset [rom the Pop II sequence and straddle (he dashed line.," In every figure, the Cayrel et stars labelled 5, 30, 32, and 34 are offset from the Pop II sequence and straddle the dashed line." + Other stars may also belong (o this group. but either one or both of carbon. oxvgen or silicon abundances are not available to confirm (his possibility or they ave masked by observational uncertainty especially near the observational limit.," Other stars may also belong to this group, but either one or both of carbon, oxygen or silicon abundances are not available to confirm this possibility or they are masked by observational uncertainty especially near the observational limit." + The [C-O/1I] abundances of these 4 stars are plotted as a histogram in the right hand panel of 44., The [C-O/H] abundances of these 4 stars are plotted as a histogram in the right hand panel of 4. + Note that compared to Pop ll stars. these stars have reduced carbon and oxveen but enhanced silicon with respect to iron.," Note that compared to Pop II stars, these stars have reduced carbon and oxygen but enhanced silicon with respect to iron." + In particular. we note that the C and O independent ratio [Si/Fe] differs by 0.2 dex between the two groups.," In particular, we note that the C and O independent ratio [Si/Fe] differs by 0.2 dex between the two groups." + From Fig.2 the enhanced [Si/C] ratio is ~0.6., From Fig.2 the enhanced [Si/C] ratio is $\sim0.6$. + Note also that the (O/C) ratio for these stars is ~0.4. similar to that of the Pop IH star sequence.," Note also that the [O/C] ratio for these stars is $\sim0.4$, similar to that of the Pop II star sequence." + Dased on the similarity of the observed ΟΠΗ) distribution and [Si/C] ratio with that of the diffuse gas. ilis suggested (hat these 4 stars. and possibly several others. are first generation stars.," Based on the similarity of the observed [C-O/H] distribution and [Si/C] ratio with that of the diffuse gas, it is suggested that these 4 stars, and possibly several others, are first generation stars." + Note that because the model distributions in Figure 4 begin with an assumed oxvgen abundance of zero and end when the Pop I stars start to dominate. the distributions aud the appropriate abundance ratios define what is referred to as first generation.," Note that because the model distributions in Figure 4 begin with an assumed oxygen abundance of zero and end when the Pop II stars start to dominate, the distributions and the appropriate abundance ratios define what is referred to as first generation." + From Figs., From Figs. + 13 the first stellar generation nuclear vields [C'/Mg]. |O/Meg]. [51/Mg]. and Fe/Me| are —0.4. 0.0. 0.2. and —0.35 respectively.I will an estimated uncertainty in each of 0.1.," 1–3 the first stellar generation nuclear yields [C/Mg], [O/Mg], [Si/Mg], and [Fe/Mg] are $-0.4$ , 0.0, 0.2, and $-0.35$ respectively, with an estimated uncertainty in each of $\pm0.1$." + These vields can be compared to those caleulated by Heger Woosley (2002) for a variety of Population HI enrichment scenarios (hat are shown graphically in their Fies., These yields can be compared to those calculated by Heger Woosley (2002) for a variety of Population III enrichment scenarios that are shown graphically in their Figs. + 35., 3–5. + The closest fit to the first tree observed ratios above is the model represented by (the solid line in their Fig., The closest fit to the first three observed ratios above is the model represented by the solid line in their Fig. + 5 (i.e. high energy explosions of 1240 M. stars including exploding very nassive stars (ου140—260 AL.) modelled with a Salpeter-like IME., 5 (i.e. high energy explosions of 12–40 $_{\odot}$ stars including exploding very massive stars $\sim140-260$ $_{\odot}$ ) modelled with a Salpeter-like IMF. + The predicted ratios (CO.Si/Mg] are —0.31. 0.03. and 0.48.," The predicted ratios [C,O,Si/Mg] are $-0.31$, 0.03, and 0.48." + Both carbon and especially silicon are over produced. but a very massive star contribution appears to be required.," Both carbon and especially silicon are over produced, but a very massive star contribution appears to be required." + The model emploved here is similar to the one used to describe the global star formation history (1104). and it is based on the simple mass loss model (e.g. Hartwick 1976. also see Pagel 1997. and Binney Merrifield 1993).," The model employed here is similar to the one used to describe the global star formation history (H04), and it is based on the simple mass loss model (e.g. Hartwick 1976, also see Pagel 1997, and Binney Merrifield 1998)." + Its novelty is a premature halüng of the chemical evolution in a distributed but physically. motivated way., Its novelty is a premature halting of the chemical evolution in a distributed but physically motivated way. + Consider (the standard one zone mass loss model of chemical evolution., Consider the standard one zone mass loss model of chemical evolution. + Gas is slowly turned into stars while being gradually enriched in heavy. elements according to a specified chemical viekl. p. Similtineously. as a result of supernova driven winds. gas with the same abundance as (he gas currently forming stars is also being lost to further star formation at a ratewhich is proportional to the," Gas is slowly turned into stars while being gradually enriched in heavy elements according to a specified chemical yield, p. Similtaneously, as a result of supernova driven winds, gas with the same abundance as the gas currently forming stars is also being lost to further star formation at a ratewhich is proportional to the" +calculate [reeze-out nucleosyntliesis vields in relativistic fireballs using the code developed by Kawano lor BBN (xawano1992).,calculate freeze-out nucleosynthesis yields in relativistic fireballs using the code developed by Kawano for BBN \citep{kawano}. +. First. however. we illustrate some of the salient aspects of nucleosyntliesis in these relativistic fireballs by. using a simplified tov reaction network.," First, however, we illustrate some of the salient aspects of nucleosynthesis in these relativistic fireballs by using a simplified toy reaction network." + Suppose for a moment that deuterium were the only possible bound nuclear species (i.e. [low to heavier nuclei is prevented)., Suppose for a moment that deuterium were the only possible bound nuclear species (i.e. flow to heavier nuclei is prevented). + In (liis case the evolution of the deuterium number fraction Y (Vy is defined as the number density of nucleus X divided by (he number density of barvous) is given bv Ilere (70)pup«x47105em?/(smol) is the reaction rate for n(p.>)d. Ta is the temperature in units of 10A. and (Qz2.2 MeV is the binding οποιον of the deuteron.," In this case the evolution of the deuterium number fraction $Y_D$ $Y_X$ is defined as the number density of nucleus $X$ divided by the number density of baryons) is given by Here $\langle \sigma v \rangle_{\rm pnD\gamma}\approx 4.7\cdot10^{4} +{\, \rm cm^3/(s mol)}$ is the reaction rate for ${\rm +n(p,\gamma)\dd}$, $T_9$ is the temperature in units of $10^9K$, and $Q\approx 2.2$ MeV is the binding energy of the deuteron." +" To a first approximation.Yp tracks the equilibrium ο until the destruction rate AJ,zzerp(-Q/Ty)(or)pup, falls below the expansion rate. ("," To a first approximation,$Y_D$ tracks the equilibrium value, $Y_D^{\rm NSE}$, until the destruction rate $\lambda_\gamma Y_\gamma \approx 5\cdot +10^9 exp(-Q/T_9)\langle \sigma v \rangle_{\rm pnD\gamma} $ falls below the expansion rate. (" +The expression for the reverse rale follows from theformalism developed by Fowler.Canghlan.&Zimmerman (1967)..),The expression for the reverse rate follows from theformalism developed by \cite{fcz}. .) +" At this time. Y [reezes out at approximately Y595:YoY,Ltr5/ss)."," At this time, $Y_D$ freezes out at approximately $Y_D^{\rm FO}\approx Y_p Y_n T_9^3 +(\tau_{-5}/s_5)$." + llere 7.5 is the dynamic timescale in units of 10s and s; is the entropy per barvon in units of 10°., Here $\tau_{-5}$ is the dynamic timescale in units of $10^{-5}s$ and $s_5$ is the entropy per baryon in units of $10^5$. + This result implies that [or (75/55)>10+. ie. for essentially all reasonable fireball parameters. there is (ime to form interesting abundances of ?IL.," This result implies that for $(\tau_{-5}/s_5)> 10^{-1}$, i.e. for essentially all reasonable fireball parameters, there is time to form interesting abundances of $\hh$." + In this case the final ?II abundance is limited by the flow to heavier nuclei., In this case the final $\hh$ abundance is limited by the flow to heavier nuclei. + To estimate the effects of [low to heavier nuclei we emplov the code developed by Wagoner (WEIL) and subsequently modified by Kawano., To estimate the effects of flow to heavier nuclei we employ the code developed by Wagoner (WFH) and subsequently modified by Kawano. + This code contains a reaction network for 26 light nuclei anc rates for the relevant weak processes., This code contains a reaction network for 26 light nuclei and rates for the relevant weak processes. +" The parameters of the ""Universe"" relevant for BBN are: Hubble constant =r. a lreely chosen initial n/p (in contrast to BBN where n/p is initially determined by weak reactions and assumed lepton numbers/spectra). and a final barvon to photon ratio y23.6/(s/hy,)."," The parameters of the “Universe” relevant for BBN are: Hubble constant $\tau_{\rm +dyn}^{-1}$, a freely chosen initial n/p (in contrast to BBN where n/p is initially determined by weak reactions and assumed lepton numbers/spectra), and a final baryon to photon ratio $\eta\approx +3.6/(s/k_b)$." + Note that the η relevant for these relativistic winds is some five orders of magnitude larger (han the primordial value (jo6-10. 1). and that the dynamic timescale for relativistic winds can be seven orders of magnitude smaller (han the dvnamic timescale of 1005 characterizing the epoch of BLN.," Note that the $\eta$ relevant for these relativistic winds is some five orders of magnitude larger than the primordial value $\eta\sim 6\cdot 10^{-10}$ ), and that the dynamic timescale for relativistic winds can be seven orders of magnitude smaller than the dynamic timescale of $\sim 100 s$ characterizing the epoch of BBN." +" In Figure5 1 we show the evolution with time of the mass Iractions of 4 light5 nuclei lor winds with an entropy per baryon s/h,=10? and differing dynamic tmescales Taya7.10110and s."," In Figure \ref{allfig} we show the evolution with time of the mass fractions of 4 light nuclei for winds with an entropy per baryon $s/k_b= 10^{5}$ and differing dynamic timescales $\tau_{\rm +dyn}=10^{-3},10^{-4},10^{-5}{\rm and\,\,\,} 10^{-6} s$ ." + This figure5 illustrates the effects of the competition between production and photo-dissociation of Η for fast outflows. and the flow to heavier nuclei for slow outflows.," This figure illustrates the effects of the competition between production and photo-dissociation of $\hh$ for fast outflows, and the flow to heavier nuclei for slow outflows." +" For Ti=10 ""s. the particle capture reactions out of deuterium are too slow to influence ?IL/II. and jy freezes out at approximately Y?z 1/80."," For $\tau_{\rm dyn} =10^{-6}s$ , the particle capture reactions out of deuterium are too slow to influence $\hh$ /H, and $Y_{\rm D}$ freezes out at approximately $Y_D^{\rm FO}\approx +1/80$ ." + For τιν—10. s.," For $\tau_{\rm dyn}=10^{-5}s$ ," +the lisht curve.,the light curve. + Phe parameters of the 9 Caussians are given in Table 1.., The parameters of the 9 Gaussians are given in Table \ref{3c345_flares}. + The columns of this table give the (1) component designation. (2) observing frequency. (3) epoch of maximum flux. (4) maximum amplitude. (5) full width at half maximum. (WIAD of the Gaussian. component corresponding to the outburst O. (6) time delay between he epoch of maximum flux for the outbursts at the given requency and the corresponding epoch at the highest available frequency. AY. (7) caleulated spectral indexes and (5) caleulated αν values (the A. values will be. discussed οσον).," The columns of this table give the (1) component designation, (2) observing frequency, (3) epoch of maximum flux, (4) maximum amplitude, (5) full width at half maximum (FWHM) of the Gaussian component corresponding to the outburst $\Theta$, (6) time delay between the epoch of maximum flux for the outbursts at the given frequency and the corresponding epoch at the highest available frequency $\Delta T$, (7) calculated spectral indexes and (8) calculated $k_{r}$ values (the $k_r$ values will be discussed below)." +" We use a positive spectral index convention 57""", We use a positive spectral index convention $S \sim \nu^\alpha$. + We measured. the spectral index for each flare. fitting a inear regression into log(?) vs. log(S) plots. where S is an amplitude of a flare. obtained. as the maximum of fitted Gaussian function.," We measured the spectral index for each flare, fitting a linear regression into $\nu$ ) vs. log(S) plots, where S is an amplitude of a flare, obtained as the maximum of fitted Gaussian function." + Spectral index was calculated. only. for hose outbursts that have been detected at three or more TOequencies., Spectral index was calculated only for those outbursts that have been detected at three or more frequencies. + We were able to calculate time-delay core shifts. for he epochs of three outbursts associated with the ejection of components for which superluminal speeds have been xublished: C2. C4 and CT. marked. in Fig. 2," We were able to calculate time-delay core shifts for the epochs of three outbursts associated with the ejection of components for which superluminal speeds have been published: C2, C4 and C7, marked in Fig. \ref{3c345_lcurve}." + Core-shilt measurements based on a direct comparison of VLBI images at dillerent. frequencies are available for epochs near our measured time delavs., Core-shift measurements based on a direct comparison of VLBI images at different frequencies are available for epochs near our measured time delays. + Table 20 summarizes ancl compares the core shifts directly measured from the VLBI images and our calculated. core shifts derived. [rom time lags obtained with single dish observations., Table \ref{3C345_shifts} summarizes and compares the core shifts directly measured from the VLBI images and our calculated core shifts derived from time lags obtained with single dish observations. + The epoch of the VLBI observations and name of the ejected jet components. used for the analvsis are listed in this table as well., The epoch of the VLBI observations and name of the ejected jet components used for the analysis are listed in this table as well. + Aretta.Moore.&Cohen(1986). measured core shifts for 3€ 345 of 0.0540.18 mas between 10.7 112 and 5 Gllz in 1982 ancl 0.11120.007 mas between 22.2 Cllz and 10.7 Giz in 1983.5. during two powerful flares that were associated with the ejection of the new jet components C2 and C4 (Fig. 2)).," \citet*{Biretta_1986} measured core shifts for 3C 345 of $0.05 \pm 0.13$ mas between 10.7 GHz and 5 GHz in 1982 and $0.111 \pm 0.007$ mas between 22.2 GHz and 10.7 GHz in 1983.5, during two powerful flares that were associated with the ejection of the new jet components C2 and C4 (Fig. \ref{3c345_lcurve}) )." + Component C2 displayed an apparent speed. of 0.48+0.02 mas/vr. (Diretta.et.al.1986): similar speeds were detected for this component by Zensusetal.(1995). Gap = 0.4:0.53 mas/vr.," Component C2 displayed an apparent speed of $0.48 \pm 0.02$ mas/yr \citep{Biretta_1986}; similar speeds were detected for this component by \citet{Zensus_1995}, $\beta_{app}$ = 0.4–0.53 mas/yr." + The measured time lag between 5 Cillz and S Cllz for the 1982 outburst corresponding to the ejection of C2 is 0.12£0.04 ves., The measured time lag between 5 GHz and 8 GHz for the 1982 outburst corresponding to the ejection of C2 is $0.12 \pm 0.04$ yrs. + Following our method of calculating the core shifts from the time lags νο = AMMane NES) opp mas/vsr]. this corresponds to a core shift of 0.06=0.02 mas.," Following our method of calculating the core shifts from the time lags as $\Delta R_{proj}$ [mas] = $\Delta t(\nu)_{obs}$ [yrs] $\cdot {\beta_{app}}$ [mas/yr], this corresponds to a core shift of $0.06 \pm 0.02$ mas." + This “time-lag” core shift coincides well with the core shift of 0.05£0.13 measured directly by aligning VLBI images (Direttactal.1986)., This “time-lag” core shift coincides well with the core shift of $0.05 \pm 0.13$ measured directly by aligning VLBI images \citep{Biretta_1986}. +. The jet component C4 displayed an apparent speed of WeweMΗTO15 mas/vr (Caproni&Abraham2," The jet component C4 displayed an apparent speed of $0.225 \pm +0.015$ mas/yr \citep{Caproni_2004a}." +004a).. Zensusetal.(1995). ancl Direttactal.(1986) detected: similar speeds of 0.32z50.15 mas/vr and 0.295+0.009 masvr for this jet component., \citet{Zensus_1995} and \citet{Biretta_1986} detected similar speeds of $\pm$ 0.15 mas/yr and $\pm$ 0.009 mas/yr for this jet component. + The calculated. time lag between 22. Cillz and S CGllz for the 1984 [are is 0.45d0.08 ves., The calculated time lag between 22 GHz and 8 GHz for the 1984 flare is $0.45 \pm 0.08$ yrs. + Lowe use an average of the three speed estimates. this vields a time-delay core shift of 0.1240.02. which is very close to the core shift olf 0.111dE0.007 clireetly measured by Direttaetal. (1986)..," If we use an average of the three speed estimates, this yields a time-delay core shift of $\pm$ 0.02, which is very close to the core shift of $0.111 \pm 0.007$ directly measured by \citet{Biretta_1986}. ." + Lobanov(1998). measured core shifts of Ar=0.05d mas (5.0δε Cllz). Ar=0.21£0.06 mas (8.4 CGllz). and Ar=0.33£0.10 mas (522.2 CGllz) in 93 (see Table 2)).," \citet{Lobanov_1998} measured core shifts of $\Delta r = 0.05 \pm 0.03$ mas (5.0–8.4 GHz), $\Delta r = 0.21 \pm 0.06$ mas (8.4 --22.2 GHz), and $\Delta r = 0.33 \pm 0.10$ mas (5–22.2 GHz) in $\sim 1993$ (see Table \ref{3C345_shifts}) )." + We calculated core shifts using our measured time lags for the flare in 1992: 0.43+0.01 ves (4.88.0 12). 0.89c0.03 ves (8.022.2 111). and 1.32+0.03 ves (4.822.0 Gllz).," We calculated core shifts using our measured time lags for the flare in 1992: $0.43 \pm 0.01$ yrs (4.8–8.0 GHz), $0.89 \pm 0.03$ yrs (8.0–22.2 GHz), and $1.32 \pm 0.03$ yrs (4.8–22.0 GHz)." + The speed. of the jet. component CT «οσο during the 1992 [lare has been estimated. to e 0.208+0.025 mas/vr (Caproni&Abraham2004). and )30d:0.16 mas/vr (Rosetal.2000)., The speed of the jet component C7 ejected during the 1992 flare has been estimated to be $0.208 \pm 0.025$ mas/yr \citep{Caproni_2004} and $0.30 \pm 0.16$ mas/yr \citep{Ros_2000}. +. Taking this speed for he newly ejected jet component C7 and using the measured ime lags. we can calculate the frequencey-dependent: core shifts. shown in Table 2..," Taking this speed for the newly ejected jet component C7 and using the measured time lags, we can calculate the frequency-dependent core shifts, shown in Table \ref{3C345_shifts}." + ‘Table 2. clearly shows that the core shifts. measured rom the VLBI observations and calculated: using our requenev-dependent time lags and the measured jet-component speeds coincide very well., Table \ref{3C345_shifts} clearly shows that the core shifts measured from the VLBI observations and calculated using our frequency-dependent time lags and the measured jet-component speeds coincide very well. + This provides a clirect est of the proposed. method. and suggests that it can be used to reliably calculate core shifts from total [ux-density ight curves.," This provides a direct test of the proposed method, and suggests that it can be used to reliably calculate core shifts from total flux-density light curves." + Moreover. this provides direct evidence that the jet component speed is the actual physical speed of a knot or à shock. rather than a pattern speed.," Moreover, this provides direct evidence that the jet component speed is the actual physical speed of a knot or a shock, rather than a pattern speed." + Looking at Eq. (, Looking at Eq. ( +"3). we expect a plot of the time lags versus frequeney to have the form The plots of time lags versus frequency for ὃς 345 show tha rese do. indeed. follow such a power law. enabling us to fit je time lags and derive Zl, values from the fits.","3), we expect a plot of the time lags versus frequency to have the form The plots of time lags versus frequency for 3C 345 show that these do, indeed, follow such a power law, enabling us to fit the time lags and derive $k_{r}$ values from the fits." + Figuree 4. shows the fit for Ware £ as an example., Figure \ref{3c345_eflare} shows the fit for flare $E$ as an example. + The estimated αρ value from this plot is 1.91-E0.04., The estimated $k_r$ value from this plot is $\pm$ 0.04. + We used the highest frequency. 37 Giz. as the reference Frequency for all measured time lags.," We used the highest frequency, 37 GHz, as the reference frequency for all measured time lags." +" Measuring &, can tell us about the jet gcometry. since the distance from the VLBI core to the base of the jet scales with Ay às rasot (leq. 9))."," Measuring $k_r$ can tell us about the jet geometry, since the distance from the VLBI core to the base of the jet scales with $k_r$ as $r_{core} \sim \nu^{-1/k_{r}}$ (Eq. \ref{eq:rcore}) )." + The Ay values contain information about the distributions of the magnetic field and electron number density. since Αν depends on the indices m and n» (Iq. 5)).," The $k_r$ values contain information about the distributions of the magnetic field and electron number density, since $k_r$ depends on the indices $m$ and $n$ (Eq. \ref{k_r}) )," + whieh indicate how the electron. number density ancl magnetic field decrease along the jet (Eq. SJ)., which indicate how the electron number density and magnetic field decrease along the jet (Eq. \ref{nm}) ). +" Phe caleulatecl A, values for each. llave. of 3€ 345 are listed in the last column of Table 1..", The calculated $k_r$ values for each flare of 3C 345 are listed in the last column of Table \ref{3c345_flares}. +" Phe range of our &, values encompasses the average value Ay=0.96 derived for 3€ 345 by Lobanov(1998).", The range of our $k_r$ values encompasses the average value $k_r = 0.96$ derived for 3C 345 by \citet{Lobanov_1998}. +". We can also use A, to calculate the core-region magnetic fields using Lqs. 7.. 10."," We can also use $k_r$ to calculate the core-region magnetic fields using Eqs. \ref{eq:omega}, \ref{eq:b1}," +. and Ll..., and \ref{eq:bcore}. +" Our Αν values imply magnetic fields in the core of 3€ 345 20.1 Ci. The measured A, values for ος 345 suggest a significant time evolution.", Our $k_r$ values imply magnetic fields in the core of 3C 345 $\simeq 0.1$ G. The measured $k_r$ values for 3C 345 suggest a significant time evolution. + “Phe time delavs versus frequency are evolving with time., The time delays versus frequency are evolving with time. + Figure 5. shows time lags for individual lares., Figure \ref{3c345_tdel} shows time lags for individual flares. + Phe maximum time lag is changing between 0.4 ves and LS ves., The maximum time lag is changing between 0.4 yrs and 1.8 yrs. +" Figure 6 shows that the &Á, values are almost at the same level in the period [rom 1982 to 1992. about 1.8. then begin to decrease to f,~0.4 in 1999."," Figure \ref{3c345kr} shows that the $k_r$ values are almost at the same level in the period from 1982 to 1992, about 1.8, then begin to decrease to $k_r \sim 0.4$ in 1999." + In this same period. 1982.1990. 3€ 345 experienced a major lare. reaching llux-density levels of about19 Jy (Fig. 2)).," In this same period, 1982–1990, 3C 345 experienced a major flare, reaching flux-density levels of about19 Jy (Fig. \ref{3c345_lcurve}) )." +" The lower Ay values seem to correspond. to. Lares with less cramatic amplitudes. suggesting a possible connection between &, and the Iux-density level."," The lower $k_r$ values seem to correspond to flares with less dramatic amplitudes, suggesting a possible connection between $k_r$ and the flux-density level." +" Figure 7 shows £, versus the [lux at 14.5 CGllz: there is a clear tendeney for brighter Hares to have higher &, values. reaching a kind. of saturation level of about A,~1.8 for Hluxes higher than 6 Jv at 14.5 Cillz."," Figure \ref{3c345_kr_flux} shows $k_r$ versus the flux at 14.5 GHz; there is a clear tendency for brighter flares to have higher $k_r$ values, reaching a kind of saturation level of about $k_r \sim 1.8$ for fluxes higher than 6 Jy at 14.5 GHz." +Gas dynamics is modeled. using a second-order unsplit Godunov scheme (7???) based on the LILLC Riemann solver and the MinAlod slope limiter (?)..,"Gas dynamics is modeled using a second-order unsplit Godunov scheme \citep{Teyssier:2002p451, Teyssier:2006p413, Fromang:2006p400} based on the HLLC Riemann solver and the MinMod slope limiter \citep{Toro:1994p1151}." + We assume a perfect gas equation of state (EOS) with 5=5/3., We assume a perfect gas equation of state (EOS) with $\gamma=5/3$. + Part of the galaxy formation process has been caleulated using sub-erid moclels. since a correct modeling of the turbulent and multiphase interstellar medium (LSAT) is beyond the reach of present-day cluster simulations.," Part of the galaxy formation process has been calculated using sub-grid models, since a correct modeling of the turbulent and multiphase interstellar medium (ISM) is beyond the reach of present-day cluster simulations." + In both simulations: lt has been shown that these galaxy. formation recipes are able to successfully. reproduce the properties of spiral galaxies in the field (72777) as well as other observed galaxy properties like the WKennieutt-Schmiicltt law. star ormation rates. galactic winds (???)..," In both simulations: It has been shown that these galaxy formation recipes are able to successfully reproduce the properties of spiral galaxies in the field \citep{Mayer:2008p1478, Governato:2009p1455, Governato:2010p1442, 2011MNRAS.410.1391A} as well as other observed galaxy properties like the Kennicutt-Schmidt law, star formation rates, galactic winds \citep{Dubois:2008p393, Devriendt:2010p5266, 2011MNRAS.410.1391A}." + On galaxy group scales the same recipes are less successful in. reproducing he observed. properties (2).. while on galaxy. cluster scales hev fail (277)..," On galaxy group scales the same recipes are less successful in reproducing the observed properties \citep{Feldmann:2010p1516}, while on galaxy cluster scales they fail \citep{Borgani:2004p1066, Kravtsov:2005p702, Borgani:2009p728}." + 1n simulated galaxy clusters similar sets of xhenomenological models. produce overcooling of gas that ceads to the formation of a higher fraction of stars than observed in real systems (2)..., In simulated galaxy clusters similar sets of phenomenological models produce overcooling of gas that leads to the formation of a higher fraction of stars than observed in real systems \citep{Borgani:2009p728}. + AGN feedback is expected. to provide enough energv to heat up gas in halos ancl partially blow it away. thus preventing further star formation.," AGN feedback is expected to provide enough energy to heat up gas in halos and partially blow it away, thus preventing further star formation." + The analysis of cosmological simulations of galaxy groups and clusters including ACN feedback like the ones of 7. support this scenario., The analysis of cosmological simulations of galaxy groups and clusters including AGN feedback like the ones of \cite{Puchwein:2008p767} support this scenario. + The two simulations of the Virgolike cluster we are considering cliller substantially., The two simulations of the Virgo–like cluster we are considering differ substantially. + “Phe first run has been performed using only the galaxy formation recipes described above. without considering the presence of SMDIIS. and neglecting ACN feedback. therefore after much thought of a clever acronvmn. we call it the ACGN-OLETE. run.," The first run has been performed using only the galaxy formation recipes described above, without considering the presence of SMBHs and neglecting AGN feedback, therefore after much thought of a clever acronymn, we call it the AGN-OFF run." + In the second run we include SMDBlIS and we take into account AGN feedback: we call it the AGN-ON run., In the second run we include SMBHs and we take into account AGN feedback; we call it the AGN-ON run. + The seeds for SMBlII formation are thought to be either Pop I stars (2)... or à result direct. collapse of barvonic material within low angular momentum halos (2?7)..," The seeds for SMBHs formation are thought to be either Pop III stars \citep{Madau:2001p3493}, or a result direct collapse of baryonic material within low angular momentum halos \citep{Bromm:2003p3495, Begelman:2006p3499}." + In both cases the seed SMBlIS are expected to grow relatively quickly to Mig.=10” when thev will start to interact. with the environment. anc selt-regulate their gas accretion rate.," In both cases the seed SMBHs are expected to grow relatively quickly to $M_{\rm BH,s}=10^5$ $_\odot$ when they will start to interact with the environment and self-regulate their gas accretion rate." + The fact that this black hole mass is at least one order ofmagnitude lower than the minimum SAIBL mass observed in the AJpy @ relation (ο) allows us to consider Apg.. as the prototypical seed SMDBII mass.," The fact that this black hole mass is at least one order ofmagnitude lower than the minimum SMBH mass observed in the $M_{\rm BH}-\sigma$ relation \citep{Gebhardt:2000p1011, Gultekin:2009p475} allows us to consider $M_{\rm BH,s}$ as the prototypical seed SMBH mass." + In our model we use sink particles to. simulate SAIBLIs. following the prescription of ?..," In our model, we use sink particles to simulate SMBHs, following the prescription of \cite{Krumholz:2004p1079}. ." + When the following conditions are met.we create a new SMDLIL in the simulation:," When the following conditions are met,we create a new SMBH in the simulation:" +simultaneously calculating the mass-loss rate terminal velocity.,simultaneously calculating the mass-loss rate terminal velocity. + Model A has a iiass-loss rate of log == -6.95., Model A has a mass-loss rate of log = -6.95. + The behaviour of the line acceleration as a function of the distance from the stellay surface. gp6r) is shown in Fig. 5..," The behaviour of the line acceleration as a function of the distance from the stellar surface, $g_{\rm L}(r)$ is shown in Fig. \ref{f_modelA}." + The sonic point is reached at a distance of 1.025 R.., The sonic point is reached at a distance of 1.025 $R_*$. + Tt is clear that most of the line driving is produced far bevoud the sonic point., It is clear that most of the line driving is produced far beyond the sonic point. + But. as was explained in Sect.," But, as was explained in Sect." + 2 the important region that determines the mass-loss rate is below the sonic poiut., \ref{sec:simple} the important region that determines the mass-loss rate is $below$ the sonic point. + Therefore. the part of the atmosphere around the sonic poiut is eularged in Fig. 5((," Therefore, the part of the atmosphere around the sonic point is enlarged in Fig. \ref{f_modelA}( (" +h).,b). + To investigate the origin of the jump. it is useful to know which clemeuts are effective line drivers in which part of the stellar wind.," To investigate the origin of the jump, it is useful to know which elements are effective line drivers in which part of the stellar wind." + Therefore. extra Moute-C'arlo calculations were performed.," Therefore, extra Monte-Carlo calculations were performed." + The first extra Monte-C'arlo «αμαπο was performed with a line list coutainime ouly Fe lines., The first extra Monte-Carlo simulation was performed with a line list containing only Fe lines. + The second one was performed with a line list containing the lines of the clements C. N aud OQ. Figure 5((b) shows that Fe is the main line driver below the sonic point.," The second one was performed with a line list containing the lines of the elements C, N and O. Figure \ref{f_modelA}( (b) shows that Fe is the main line driver below the sonic point." + C. N and O. are important line divers in the supersonic part of the wind. which can be seen in 5((a).," C, N and O, are important line drivers in the supersonic part of the wind, which can be seen in \ref{f_modelA}( (a)." + C. N and ο contribute roughly 50 of the liue acceleration in the supersonic part of the wind.," C, N and O contribute roughly 50 of the line acceleration in the supersonic part of the wind." + Not indicated here. but relevant to mention is that Si. Cl. P and S are other miportaut line drivers iu the supersonic," Not indicated here, but relevant to mention is that Si, Cl, P and S are other important line drivers in the supersonic" +of NGC 7009 is taken as an example. but the emphasis is not in the construction of a detailed model for this object in particular.,"of NGC 7009 is taken as an example, but the emphasis is not in the construction of a detailed model for this object in particular." + With this in mind we described the nebula by an ellipsoidal rim. with a II number density. Ng. peaking to 9000 in the short axis direction. exponentially decreasing to a minimuni value of 4000 in the Long axis direction.," With this in mind we described the nebula by an ellipsoidal rim with a H number density, $_H$, peaking to 9000 $^{-3}$ in the short axis direction exponentially decreasing to a minimum value of 4000 $^{-3}$ in the long axis direction." + The short and long axes of the inner and outer ellipsoids measure 3.84. 107 em and 1075. ena. and 7.06 101 em and. 107 eni respectively. at the distance assumed for NCC τοῦ.," The short and long axes of the inner and outer ellipsoids measure $\times$ $^{16}$ cm and $\times$ $^{16}$ cm, and $\times$ $^{16}$ cm and $\times$ $^{17}$ cm, respectively, at the distance assumed for NGC 7009." + “Phe rim is surrounded bv a spherical shell of less opaque. homogeneous density gas. with Ny = .," The rim is surrounded by a spherical shell of less opaque, homogeneous density gas, with $_H$ = $^{-3}$." + The diameter of the sphere is equal to the long axis of the outer ellipsoid defining the rim., The diameter of the sphere is equal to the long axis of the outer ellipsoid defining the rim. + Cylindrical jets. 1.75. 102 em in diameter. connect the rim to à pair of clisk-shaped knots aligned at a distance of 3.49.- 104 em from the central star. along the long axis of the ellipsoid.," Cylindrical jets, $\times$ $^{16}$ cm in diameter, connect the rim to a pair of disk-shaped knots aligned at a distance of $\times$ $^{17}$ cm from the central star, along the long axis of the ellipsoid." + The evlindrical jets widen into cone-shapes a the knot ends in order to simulate the effect of materia accumulating at the knots. as suggested by the £87 images (particularly for knot WA. as seen. in the right. panels of ligure 2).," The cylindrical jets widen into cone-shapes at the knot ends in order to simulate the effect of material accumulating at the knots, as suggested by the $HST$ images (particularly for knot K4, as seen in the right panels of Figure 2)." + Phe diameter of the base of the cones equals tha of the disk-shaped knots., The diameter of the base of the cones equals that of the disk-shaped knots. + The centres of the 107° em diameter circular disks representing the knots are alignec with the centres of the exlindrical jets (hence they are seen almost edge on)., The centres of the $\times$ $^{16}$ cm diameter circular disks representing the knots are aligned with the centres of the cylindrical jets (hence they are seen almost edge on). + Phe width of the disks is assumed to be 3.88. 104 em in our model. although only a fraction of these is ionised. as is clear from the right. panels of Figure 2.," The width of the disks is assumed to be $\times$ $^{16}$ cm in our model, although only a fraction of these is ionised, as is clear from the right panels of Figure 2." + The Lo number density in the jets and knots is taken to be homogeneous and. equal to 1250 cm and 1500 respectively. consistently with the values derived in1.," The H number density in the jets and knots is taken to be homogeneous and equal to 1250 $^{-3}$ and 1500 $^{-3}$, respectively, consistently with the values derived in." + ltesults from the ellipsoidal rim and the spherical outer shell are combined into a single to enable us to carry out a direct comparison with the slit spectra fromL. as we show in Table 1.," Results from the ellipsoidal rim and the spherical outer shell are combined into a single to enable us to carry out a direct comparison with the slit spectra from, as we show in Table 1." + The jets (CJ-componen!) are included in our simulation as the radiation field has to be transferred. through. them before reaching the outer ansac (A-componenb)., The jets ) are included in our simulation as the radiation field has to be transferred through them before reaching the outer ansae ). + However. eiven that the emission detected. from this region is very faint and that such structures may not be in equilibrium. we take our results for theJ-componenh as very uncertain and omit them from any further discussion.," However, given that the emission detected from this region is very faint and that such structures may not be in equilibrium, we take our results for the as very uncertain and omit them from any further discussion." + Finally. neither the inner caps nor the tenuous halo were included in our model.," Finally, neither the inner caps nor the tenuous halo were included in our model." + Phe former because they do not lie on the same axis as the (Reavy&Atherton1985).. and ave therefore not expected to have a major inlluence on the ionization structure of the outer knots.," The former because they do not lie on the same axis as the \citep{b037}, and are therefore not expected to have a major influence on the ionization structure of the outer knots." + And the latter because it is very faint. and therefore it is not. expected to contribute significantly to the integrated. emission. line spectrum.," And the latter because it is very faint, and therefore it is not expected to contribute significantly to the integrated emission line spectrum." + Figure 1 shows model profiles along the major axis. in agreement with our assumed density. as No. /Ng ratio is correlated. to. the level of ionisation of the gas (see Section 3.4)," Figure 1 shows model profiles along the major axis, in agreement with our assumed density, as $_e$ $_H$ ratio is correlated to the level of ionisation of the gas (see Section 3.4)." + The best fit to the observed spectra was obtained assuming the parameters given in Table 2. as discussed in Section 2.3..," The best fit to the observed spectra was obtained assuming the parameters given in Table 2, as discussed in Section \ref{subsec:input}." + Table 3 shows the predicted: ancl observed. intensities of some important collisionally excited. lines. in which values are given relative to that of H12((100). for each nebular component (lt and It) and integrated over. the nebula (NEB).," Table 3 shows the predicted and observed intensities of some important collisionally excited lines, in which values are given relative to that of (=100) for each nebular component (R and K) and integrated over the nebula (NEB)." + Phe model fluxes are given in the first row of the table., The model fluxes are given in the first row of the table. + The dereddened line intensities quoted in the column of Table 3 were obtained. from. the spectroscopic data presented in Table 1 ofr. bv using a logarithmic extinction. constant 500.16 (Goncalvesetal.2003). and the reddening law of Cardellietal.(1989).," The dereddened line intensities quoted in the column of Table 3 were obtained from the spectroscopic data presented in Table 1 of, by using a logarithmic extinction constant 0.16 \citep{b017} and the reddening law of \citet{b09}." +.. For cach line intensity. in each component. the upper row (of the column) shows the values for the North-East (111 and Wd) regions of NCC 7009. while those for the South-Western H2 and KA components are given in the lower row (see Figure |. and Table | οἱ 1)).," For each line intensity, in each component, the upper row (of the column) shows the values for the North-East (R1 and K1) regions of NGC 7009, while those for the South-Western R2 and K4 components are given in the lower row (see Figure 1 and Table 1 of )." + The line intensities predicted. by our model were convolved with a lone-slit profile (assumed {ο be rectangular) aligned along the long axis of the PN., The line intensities predicted by our model were convolved with a long-slit profile (assumed to be rectangular) aligned along the long axis of the PN. + This is a necessary correction for an extended object with a complex ecometry. such as that of NGC του. if any meaningful conclusions regarding the ionisation and. temperature structures are to be gained from the comparison of the model with the observations.," This is a necessary correction for an extended object with a complex geometry, such as that of NGC 7009, if any meaningful conclusions regarding the ionisation and temperature structures are to be gained from the comparison of the model with the observations." + The dimensions of vvs. aat a distance of 0.86 kpe were assumed. in order to be consistent withαι., The dimensions of vs. at a distance of 0.86 kpc were assumed in order to be consistent with. + For cach nebular component listed in Table 3 we give the ancl line intensities in adjacent columns., For each nebular component listed in Table 3 we give the and line intensities in adjacent columns. +" Vhe absolute value for the observed στ lux. o£ NGC 7009 of 3.197 1I"" ere em st. quoted in Table 3. was obtained from the VLA radio recombination line [lux (Garayetal.1989)."," The absolute value for the observed $\beta$ flux of NGC 7009 of 3.197 $\times$ $^{-10}$ erg $^{-2}$ $^{-1}$, quoted in Table 3, was obtained from the VLA radio recombination line flux \citep{b015}." +.. Ehis flux should be compared to the nebula-integrated: value (NEB) predicted by our model for the case., This flux should be compared to the nebula-integrated value (NEB) predicted by our model for the case. + A very good agreement (better than 24)) is louncl., A very good agreement (better than ) is found. + From the comparison of the models6/ ancl columns it appears that some emission lines are more alfected than others., From the comparison of the model and columns it appears that some emission lines are more affected than others. + This is verv easy to understand if one considers the electron temperature cistribution and the physical extension of the various regions where each of the relevant ionic species are most abundant., This is very easy to understand if one considers the electron temperature distribution and the physical extension of the various regions where each of the relevant ionic species are most abundant. + 11ο 1144686. for example. is enhanced by —31 in thesl results for the It component and ~29% overall.," He $\lambda$ 4686, for example, is enhanced by $\sim$ in the results for the R component and $\sim$ overall." + The opposite xhiaviour is shown by the Le lines for which the results show a —5'4 depletion for He 1A5876 and He 1A6678 in both he It component. and NEB component., The opposite behaviour is shown by the He lines for which the results show a $\sim$ depletion for He $\lambda$ 5876 and He $\lambda$ 6678 in both the R component and NEB component. + Similar beaviours are observed for other species as well. particularly we note he enhancement of intensities in the column for N uj. Sj and S uiu] lines.," Similar beaviours are observed for other species as well, particularly we note the enhancement of intensities in the column for [N ], [S ] and [S ] lines." + We also note that different lines from he same ionic species appear to be enhanceddepleted. by different amounts. like S 1144069. A4076. enhanced by —10- and A6717.A6731 enhanced by —15-18'4.," We also note that different lines from the same ionic species appear to be enhanced/depleted by different amounts, like [S $\lambda$ 4069, $\lambda$ 4076, enhanced by $\sim$ and $\lambda$ $\lambda$ 6731 enhanced by $\sim$." +. This is due o the different sensitivities of the various transitions to changes in the electron tempcratures., This is due to the different sensitivities of the various transitions to changes in the electron temperatures. + We show in the last three columns of Table 3 a comparison of our model with the observations integrated. over the whole, We show in the last three columns of Table 3 a comparison of our model with the observations integrated over the whole +"wave (activity over an extended area of the field-of-view), and from the SOHO/EIT instrument a concomitant EIT wave is visible (Wills-Davey&Thompson1999).","wave (activity over an extended area of the field-of-view), and from the SOHO/EIT instrument a concomitant EIT wave is visible \citep{wills-davey1999}." +. The TRACE data also reveal how the EIT wave front causes the positioning of some coronal loops to be disturbed., The TRACE data also reveal how the EIT wave front causes the positioning of some coronal loops to be disturbed. +" The particular loop under investigation is situated in the south-eastern part of1,, with a zoom into the region of interest in2."," The particular loop under investigation is situated in the south-eastern part of, with a zoom into the region of interest in." +". Using the standard calibration/correction packages available in theSolarSoft library, the TRACE data was processed in the usual way: spikes from cosmic ray hits were removed, data frames were normalized to a constant exposure time, and the image sequence was de-rotated."," Using the standard calibration/correction packages available in the library, the TRACE data was processed in the usual way: spikes from cosmic ray hits were removed, data frames were normalized to a constant exposure time, and the image sequence was de-rotated." +" The TRACE satellite entered the Southern Atlantic Anomaly at approximately 15:50 UT, and images up to this point clearly display a propagating wave front."," The TRACE satellite entered the Southern Atlantic Anomaly at approximately 15:50 UT, and images up to this point clearly display a propagating wave front." +" The characteristics of a global EIT wave were studied in detail by Ballaietal.(2005),, who demonstrated that the global disturbance is a wave with an average periodicity of approximately 400 s. To accurately probe the effects of this wave front on more rigidly fixed coronal loop structures, the loop edge was tracked spatially and temporally using a wavelet modulus maxima technique described by Jessetal.(2008)."," The characteristics of a global EIT wave were studied in detail by \citet{ballai2005}, who demonstrated that the global disturbance is a wave with an average periodicity of approximately 400 s. To accurately probe the effects of this wave front on more rigidly fixed coronal loop structures, the loop edge was tracked spatially and temporally using a wavelet modulus maxima technique described by \citet{Jess08}." +". Since the 195 response function is somewhat lower than that of the 171 passband, longer exposure times are required to provide the same signal as the 171 channel (a s average exposure time at 195À, versus 24s at 171 images)."," Since the 195 response function is somewhat lower than that of the 171 passband, longer exposure times are required to provide the same signal as the 171 channel (a s average exposure time at 195, versus s at 171 images)." +" As a result, rapidly moving structures may be blurred in the 195 passband because of their substantially longer exposure times."," As a result, rapidly moving structures may be blurred in the 195 passband because of their substantially longer exposure times." +" Furthermore, the 171 images are at full resolution (1 pixel = 0.499”), whereas the195 data are 2x2 binned, resulting in a pixel size of 0.998""."," Furthermore, the 171 images are at full resolution (1 pixel = $''$ ), whereas the195 data are $2{\times}2$ binned, resulting in a pixel size of $''$." +" Through use of blind iterative deconvolution techniques, Golubetal.(1999) and Linetal.(2001) determined the absolute spatial resolution of the TRACE instrument to be 1.25""."," Through use of blind iterative deconvolution techniques, \citet{Gol99} and \citet{Lin01} determined the absolute spatial resolution of the TRACE instrument to be $''$." +" Since the 171 data is not degraded by spatial binning, it enables us to monitor small-scale disturbances more clearly in coronal loop structures."," Since the 171 data is not degraded by spatial binning, it enables us to monitor small-scale disturbances more clearly in coronal loop structures." +" As a result, only images taken in the 171 bandpass could be tracked with an average cadence of 90 s. First, a segment of the loop edge, between the loop footpoint and apex, was passed through a Laplacian filter to sharpen the images and make the edge of the structure more pronounced."," As a result, only images taken in the 171 bandpass could be tracked with an average cadence of 90 s. First, a segment of the loop edge, between the loop footpoint and apex, was passed through a Laplacian filter to sharpen the images and make the edge of the structure more pronounced." +" Next, a lower intensity threshold was applied to the data to remove contributions from the underlying quiet Sun."," Next, a lower intensity threshold was applied to the data to remove contributions from the underlying quiet Sun." +" A threshold of the background mean flux plus 4.5 σ was used, which produces the image displayed in the upper-left panel of2."," A threshold of the background mean flux plus 4.5 $\sigma$ was used, which produces the image displayed in the upper-left panel of." +". To emphasize feature edges and remove shallow intensity gradients, we used a binary format for the feature mapping."," To emphasize feature edges and remove shallow intensity gradients, we used a binary format for the feature mapping." + All pixels of values above the lower flux intensity threshold defined above were assigned a value of ‘1’., All pixels of values above the lower flux intensity threshold defined above were assigned a value of `1'. +" Those pixels which lie below the threshold are assigned a value of ‘0’, producing the binary map shown in the upper-right panel of2."," Those pixels which lie below the threshold are assigned a value of `0', producing the binary map shown in the upper-right panel of." +". To assist the analysis, each image was rotated by 45? clockwise until the southern edge of the loop structure was parallel with the x-axis."," To assist the analysis, each image was rotated by $^{\circ}$ clockwise until the southern edge of the loop structure was parallel with the x-axis." +" This caused loop displacements to be confined to the direction of the y-axis, as a function of the loop length (x-axis)."," This caused loop displacements to be confined to the direction of the y-axis, as a function of the loop length (x-axis)." +" TRACE images acquired between the initiation of oscillatory behaviour at 15:29 UT, and 15:50 UT when the instrument entered the Southern Atlantic Anomoly, were binary mapped for edge detection and tracking using the methodology described by Jessetal.(2008)."," TRACE images acquired between the initiation of oscillatory behaviour at 15:29 UT, and 15:50 UT when the instrument entered the Southern Atlantic Anomoly, were binary mapped for edge detection and tracking using the methodology described by \citet{Jess08}." +". Utilizing the resulting loop-edge positions, the displacement of the loop segment as a function of time from its quiescent state was established for 30 pixels («11000 km; see dashed lines in 2)) along the loop edge between the footpoint and apex."," Utilizing the resulting loop-edge positions, the displacement of the loop segment as a function of time from its quiescent state was established for 30 pixels ${\approx}11000$ km; see dashed lines in ) along the loop edge between the footpoint and apex." +" Owing to the minimal shifts in the loop equilibrium position with time, and the need to minimise the number of free fitting parameters, no long-term trends were subtracted from the original time series."," Owing to the minimal shifts in the loop equilibrium position with time, and the need to minimise the number of free fitting parameters, no long-term trends were subtracted from the original time series." + The loop-edge displacement curve was then fitted using sinusoids of varying frequency and amplitude., The loop-edge displacement curve was then fitted using sinusoids of varying frequency and amplitude. + The best fit sinusoid was then subtracted from the original data to produce a residual time series., The best fit sinusoid was then subtracted from the original data to produce a residual time series. +" The residual data, again, was modelled with the best-fit sinusoid function."," The residual data, again, was modelled with the best-fit sinusoid function." +" To determine the success of the fitting process, Kolmogorov-Smirnov and cross-correlation statistics (Pressetal.1992;Christian1998;Jess2007a,b) were determined for each stage of the sinusoid fitting process, as well as for the combined fit with respect to the original time series."," To determine the success of the fitting process, Kolmogorov-Smirnov and cross-correlation statistics \citep{Press92, Christian98, Jess07a, Jess07b} were determined for each stage of the sinusoid fitting process, as well as for the combined fit with respect to the original time series." +" An example of this process is displayed in3,, where Kolmogorov-Smirnov statistics for the s, s, and combined fits are88%,,91%,, and 92%,, respectively."," An example of this process is displayed in, where Kolmogorov-Smirnov statistics for the s, s, and combined fits are, and , respectively." +" Cross-correlation statistics for the same fitting functions are90%,,74%,, and 98%,, respectively, indicating that these sinusoid functions recreate the observed data with a high degree of precision."," Cross-correlation statistics for the same fitting functions are, and , respectively, indicating that these sinusoid functions recreate the observed data with a high degree of precision." +appear to be slightly brighter.,appear to be slightly brighter. + The dispersion about the 1:1 relation (red solid lines) for all clusters in common is oy = 0.28 (SMC) and 0.22 (LMC)., The dispersion about the 1:1 relation (red solid lines) for all clusters in common is $\sigma_V$ = 0.28 (SMC) and 0.22 (LMC). +" The younger the star clusters the brighter they are because young clusters still contain very massive hot stars (e.g, supergiants), which contribute most of the light."," The younger the star clusters the brighter they are because young clusters still contain very massive hot stars (e.g, supergiants), which contribute most of the light." + T'he older a cluster gets the more of these massive stars are in their end stage of evolution and no longer contribute to the cluster light., The older a cluster gets the more of these massive stars are in their end stage of evolution and no longer contribute to the cluster light. +" Therefore, clusters become fainter and redder with increasing age."," Therefore, clusters become fainter and redder with increasing age." + This effect can be seen in the upper panels of Figs., This effect can be seen in the upper panels of Figs. +" 13 and 14 (LMO), in which cluster age is plotted versus (SMC)luminosity."," \ref{fig:smcraf_Vager} (SMC) and \ref{fig:lmcraf_Vager} (LMC), in which cluster age is plotted versus luminosity." + 'The red dots represent the mean of the age distribution in magnitude bins of 0.3 mag., The red dots represent the mean of the age distribution in magnitude bins of 0.3 mag. +" We overplotted three GALEV models (Kotullaetal.2009) for the total cluster masses of 10?M, (blue dash-dotted line), 10?Mc (blue dotted line), and 10Mg (blue solid line) using a Salpeter initial mass function."," We overplotted three GALEV models \citep{Kotulla09} for the total cluster masses of $10^2M_{\odot}$ (blue dash-dotted line), $10^3M_{\odot}$ (blue dotted line), and $10^4M_{\odot}$ (blue solid line) using a Salpeter initial mass function." + GALEV is a model for computing the spectral evolution of single stellar populations and galaxies., GALEV is a model for computing the spectral evolution of single stellar populations and galaxies. + The GALEV models give an overview of the cluster mass range., The GALEV models give an overview of the cluster mass range. + The lower plots of Figs., The lower plots of Figs. +" 13 and 14 show that star clusters of the SMC and LMC become brighter with increasing radius, which is expected assuming a larger number of stars within the cluster radius, contributing to the total cluster luminosity."," \ref{fig:smcraf_Vager} and \ref{fig:lmcraf_Vager} show that star clusters of the SMC and LMC become brighter with increasing radius, which is expected assuming a larger number of stars within the cluster radius, contributing to the total cluster luminosity." +" We have presented ages and luminosities of 324 and 1193 populous SMC and LMC star clusters, respectively."," We have presented ages and luminosities of 324 and 1193 populous SMC and LMC star clusters, respectively." + An age range of ~9 Myr to 1 Gyr was covered based on isochrone fitting to resolved color-magnitude diagrams in both galaxies., An age range of $\sim$ 9 Myr to 1 Gyr was covered based on isochrone fitting to resolved color-magnitude diagrams in both galaxies. +" Using only cluster ages derived in this study, we find two maxima of enhanced cluster formation for both galaxies which appear to be correlated."," Using only cluster ages derived in this study, we find two maxima of enhanced cluster formation for both galaxies which appear to be correlated." +" In the SMC, the peaks are found at ~160 Myr and ~630 Myr, and in the LMC at ~125 Myr and ~800 Myr."," In the SMC, the peaks are found at $\sim$ 160 Myr and $\sim$ 630 Myr, and in the LMC at $\sim$ 125 Myr and $\sim$ 800 Myr." + Model calculations predict that the last close encounter between LMC and SMC occurred around 100-200 Myr ago., Model calculations predict that the last close encounter between LMC and SMC occurred around 100-200 Myr ago. +" During a close encounter, the star formation is expected to be enhanced."," During a close encounter, the star formation is expected to be enhanced." +" Therefore, the first peaks in the cluster age distributions could have been triggered by this tidal interaction."," Therefore, the first peaks in the cluster age distributions could have been triggered by this tidal interaction." + Extending our samples with cluster ages derived by C06 we find a third pronounced period of enhanced cluster formation in the SMC at around 8 Myr., Extending our samples with cluster ages derived by C06 we find a third pronounced period of enhanced cluster formation in the SMC at around 8 Myr. + We find the same in the LMC combining our sample with the one of PUOO., We find the same in the LMC combining our sample with the one of PU00. +" These peaks are only visible if we extend our sample with objects classified as associations, objects which did not or could not reach higher ages because they dissolve too quickly."," These peaks are only visible if we extend our sample with objects classified as associations, objects which did not or could not reach higher ages because they dissolve too quickly." +" The youngest objects in both galaxies are associated with super giant shells, giant shells, the inter-shell region, and with HII regions."," The youngest objects in both galaxies are associated with super giant shells, giant shells, the inter-shell region, and with HII regions." + Their formation is probably related to shell expansion and shell interaction., Their formation is probably related to shell expansion and shell interaction. + In the spatial distribution of the clusters younger than ~16 Myr the two SMC shells are clearly visible., In the spatial distribution of the clusters younger than $\sim$ 16 Myr the two SMC shells are clearly visible. +" The older objects are widely spread across the entire SMC main body, but show a concentration in the western part of the galaxy."," The older objects are widely spread across the entire SMC main body, but show a concentration in the western part of the galaxy." +" In the LMC, the youngest objects are concentrated in 30 Doradus, SGS 11 (LMC 4), and in the giant shells located in the western part and in the bar region."," In the LMC, the youngest objects are concentrated in 30 Doradus, SGS 11 (LMC 4), and in the giant shells located in the western part and in the bar region." + The older LMC clusters are mostly distributed along the bar and along the rim., The older LMC clusters are mostly distributed along the bar and along the rim. + One can see nicely how star cluster formation propagated along the LMC bar., One can see nicely how star cluster formation propagated along the LMC bar. + We find no indication for propagating star cluster formation in the SGSs in either LMC or SMC., We find no indication for propagating star cluster formation in the SGSs in either LMC or SMC. +" Most of the LMC star clusters are older than the dynamical ages of the SGSs and therefore may have formed in shells, which already have dissolved and cannot be detected at the present day."," Most of the LMC star clusters are older than the dynamical ages of the SGSs and therefore may have formed in shells, which already have dissolved and cannot be detected at the present day." + No obvious dissolution effects were found for MCs star clusters younger than ~1 Gyr., No obvious dissolution effects were found for MCs star clusters younger than $\sim$ 1 Gyr. + It is quite difficult to ascertain a real absence of cluster dissolution using this study., It is quite difficult to ascertain a real absence of cluster dissolution using this study. + Two biases may play a major role: 1., Two biases may play a major role: 1. +" Infant mortality cannot be accounted for, because very young star clusters and OB-associations are not included in our sample; and 2."," Infant mortality cannot be accounted for, because very young star clusters and OB-associations are not included in our sample; and 2." +" Cluster dissolution processes for clusters older than ~1 Gyr, because we did not age-date clusters"," Cluster dissolution processes for clusters older than $\sim$ 1 Gyr, because we did not age-date clusters" +"""conical morphology (Colinaetal.1991)... associated with a eiat elliptical or SO host galaxy.","“conical” morphology \citep{Col91}, associated with a giant elliptical or S0 host galaxy." + The black hole uass is estinated to be 1095/5 AL. (Vasudevanetal. 2010)., The black hole mass is estimated to be $10^{7.41}$ $M_{\odot}$ \citep{Vas10}. +. IKovainactal.(1992). observed this object with heGinga satellite aud found that the energy spectiun in the 318 keV band is described by a power-law with a photon iudex of 1.5 aud au absorption column deusitv of 2«41077.. Vi," \citet{Koy92} observed this object with the satellite and found that the energy spectrum in the 3–18 keV band is described by a power-law with a photon index of 1.5 and an absorption column density of $2 \times +10^{23}$." +enalietal.(1997). report the results of observations withSCA pudROSAT., \citet{Vig97} report the results of observations with and. +" Frou the 0.1LO keV spectrum of IC 5062. indicthey detect two power-law colmponcuts (with photou es of L.7+0.2 and 2.20.3. where the former is absorbed with Ny~2«107? 7)). iid a narrow mon-Ie line at Ey,& 6.1 keV (with an equivalent width of ~200 eV)."," From the 0.1--10 keV spectrum of IC 5063, they detect two power-law components (with photon indices of $ +1.7\pm0.2$ and $2.2\pm0.3$, where the former is absorbed with $\sim 2 +\times 10^{23}$ ), and a narrow $\alpha$ line at $E_{\rm +K\alpha} \approx$ 6.4 keV (with an equivalent width of $\sim$ 200 eV)." + The organization of this paper is as follows., The organization of this paper is as follows. + Section 2 sunmaerizes the observations., Section 2 summarizes the observations. + Data analysis aud results are presented in Section 3., Data analysis and results are presented in Section 3. + We discuss the implication of our results in Section [., We discuss the implication of our results in Section 4. +" The cosmological parameters Ον-- (TO Ian t ft. 0.3. 0,7: Nomatsn 2009)) are adopted im calculating the Iuniinosities."," The cosmological parameters = (70 km $^{-1}$ $^{-1}$, 0.3, 0.7; \citealt{Kom09}) ) are adopted in calculating the luminosities." + The errors attached to spectral parameters correspond to those at confidence Bits for a sinele parameter.ο," The errors attached to spectral parameters correspond to those at confidence limits for a single parameter.," +σα the fifth Japauese Nav satellite (Alitsuda 2007).. carries a set of X-ray CCD cameras called the N-rav huagiug Spectrometer (NIS) aud non-inuaegiueginstrumeut called the Tard Nav. Detector (IIXND) composed of $i PIN photodiodes aud Cadolinimui Silicon Oxide (CSO) scintillation counters.," the fifth Japanese X-ray satellite \citep{Mit07}, carries a set of X-ray CCD cameras called the X-ray Imaging Spectrometer (XIS) and a non-imaging instrument called the Hard X-ray Detector (HXD) composed of Si PIN photodiodes and Gadolinium Silicon Oxide (GSO) scintillation counters." +" In this paper. we analyze the data of three NISs aud IND/PIN. which cover the euecrgv baud of 0.210 keV aud 1060 keV. respectively,"," In this paper, we analyze the data of three XISs and HXD/PIN, which cover the energy band of 0.2–10 keV and 10–60 keV, respectively." + The data of IIND/GSO covering energies above 50 keV are not utilized because the fluxes of our targets are too faint to be detected., The data of HXD/GSO covering energies above 50 keV are not utilized because the fluxes of our targets are too faint to be detected. + Iu the spectral analvsis. we also use the spectra of Swift/BAT iu the Lt195 keV band averaged for 58-2nouths (Bawugartueretal. 2011).," In the spectral analysis, we also use the spectra of /BAT in the 14–195 keV band averaged for 58-months \citep{Bau11}." +. The two NLRGs 3€ 103 aud IC 5063. cataloged iu the Susift/DAT 9-2nouths survey (Tucllsetal.2008).. were observed with in 2000 April.," The two NLRGs 3C 403 and IC 5063, cataloged in the /BAT 9-months survey \citep{Tue08}, were observed with in 2009 April." + The basic information of our targets and observation log are sununarized in Table , The basic information of our targets and observation log are summarized in Table \ref{targets}. +"Each object was observed at the ""IIXND nominal” pointing position for a net exposure of 50 ks after data screeniug.", Each object was observed at the “HXD nominal” pointing position for a net exposure of $\sim$ 50 ks after data screening. + The data reduction was performed according to standard procedures from the cleaned eveut Hes provided bv the team (processing version 2.3.12.25)., The data reduction was performed according to standard procedures from the cleaned event files provided by the team (processing version 2.3.12.25). + We used FTOOLS (heasoft version 6.8) for extraction of helt curves and spectra. aud NSPEC (version 12.5.1) for spectral fitting.," We used FTOOLS (heasoft version 6.8) for extraction of light curves and spectra, and XSPEC (version 12.5.1n) for spectral fitting." + The NIS events of the source were extracted from circular regious centered. on the source peak with a radius of 27 (060 103) and 2.5 (IC 5063). in which and of the total source photons are accunmlated bv the XN-rav telescopes. respectively.," The XIS events of the source were extracted from circular regions centered on the source peak with a radius of 2' (3C 403) and 2'.5 (IC 5063), in which and of the total source photons are accumulated by the X-ray telescopes, respectively." + The background data were taken fron) aunulus regions centered. at the averaged optical axis of the N-rav telescopes with radii between 2.86.7 for 3€ 103 aud 1.276.3. for Το 5063. bv excluding regious where the target aud other bright sources ave located.," The background data were taken from annulus regions centered at the averaged optical axis of the X-ray telescopes with radii between 2.8'–6.7' for 3C 403 and 1.2'–6.3' for IC 5063, by excluding regions where the target and other bright sources are located." + We generatec the RAIF files of the NIS. withοὐκομ. and the ARF files with Ushisakietal.2007).," We generated the RMF files of the XIS with, and the ARF files with \citep{Ish07}." +. The “tuned NNB event files provided bv the IIND tea were utilized to produce the backeround spectra. to which that of the cosumic N-rav backeround (CNB) was added based ou the formula of Gruberetal.(1999).," The “tuned” NXB event files provided by the HXD team were utilized to produce the background spectra, to which that of the cosmic X-ray background (CXB) was added based on the formula of \citet{Gru99}." + The source fiux of IIND/PIN iu the 15LO keV baud corresponds to 26% (3C 103) and z21% (IC 5063) of the backeround (NND|CNB) rate., The source flux of HXD/PIN in the 15–40 keV band corresponds to $\simeq 6$ (3C 403) and $\simeq 24$ (IC 5063) of the background (NXB+CXB) rate. + The sigual-to-roise ratio calculated as the source photon counts divided bv the square root of the total (source plus vackeround) counts in this baud is 5.3 for 3€ 1023 aud 26.7 for IC 5063., The signal-to-noise ratio calculated as the source photon counts divided by the square root of the total (source plus background) counts in this band is 5.3 for 3C 403 and 26.7 for IC 5063. + The statistical error is larger than he systematic uncertaiutv of ~0.30 (lo) in the vackeround inodel for a LO Xs exposure (Fukazawaotal. 2009)., The statistical error is larger than the systematic uncertainty of $\simeq 0.34\%$ $\sigma$ ) in the background model for a 40 ks exposure \citep{Fuk09}. +. We used ac_hhsxcl_ppinhsnomed_220080716.28 or the IIND/PIN respousc., We used 20080716.rsp for the HXD/PIN response. + Figure l shows the light curves of 3€ 103 and IC 5063 in the 210 keV baud combined from XIS-0 aud. XIS-5 (upper). those in the 15.10 keV.baud from IIND/PIN (mdddle). aud their harduess ratio between the two bands.," Figure \ref{Suzaku_LC} shows the light curves of 3C 403 and IC 5063 in the 2–10 keV band combined from XIS-0 and XIS-3 (upper), those in the 15–40 keV band from HXD/PIN (middle), and their hardness ratio between the two bands." + A bin width of 5760of s. the orbital periodof (ποΠιοµας periods data gap that are excluded to calculate the count rate). is chosen to eliminate auv systematics caused by the orbital change of the satellite.," A bin width of 5760 s, the orbital period of (including periods of data gap that are excluded to calculate the count rate), is chosen to eliminate any systematics caused by the orbital change of the satellite." + There is no MN time variabilitv in the light curves of 3C. 103. while from210 keV flux of IC 5063 increases after ~6« Lots the thebegimuiug of the observation.," There is no evident time variability in the light curves of 3C 403, while the 2–10 keV flux of IC 5063 increases after $\sim 6 \times 10^4$ s from the beginning of the observation." + The coustant flux model is rejected by with reduced 4? of 6.31 with 15 degrees of freedom., The constant flux model is rejected by with reduced $\chi^2$ of 6.34 with 15 degrees of freedom. + Due to the limited, Due to the limited +High Mass X-Ray Binaries (HMXBs) are systems composed of an early-type massive star and an accreting compact object.,High Mass X-Ray Binaries (HMXBs) are systems composed of an early-type massive star and an accreting compact object. + All sub-groups of HMXBs involve OB type stars and are commonly found in the galactie plane and in the Magellanic Clouds. among their OB The majority of the known systems are Be/X-ray Binaries (BeXRBs). consisting of a neutron star accreting matter from the circumstellar equatorial dise of a Be star.," All sub-groups of HMXBs involve OB type stars and are commonly found in the galactic plane and in the Magellanic Clouds, among their OB The majority of the known systems are Be/X-ray Binaries (BeXRBs), consisting of a neutron star accreting matter from the circumstellar equatorial disc of a Be star." + Most of them are transient. exhibiting short and bright outbursts (Ly~ erg s! in the case of Type I outbursts. generally close to the periastron passage of the neutron star; Ly>10 eres! in the case of Type II outbursts).," Most of them are transient, exhibiting short and bright outbursts $L_{X}\sim 10^{36} - 10^{37}$ erg $^{-1}$ in the case of Type I outbursts, generally close to the periastron passage of the neutron star; $L_{X} \ge 10^{37}$ erg $^{-1}$ in the case of Type II outbursts)." + In the second major class of HMXBs. the Supergiant X-ray Binaries (SGXRBs). the counterpart is an early supergiar= star. feeding the compact object with its radially outflowinisi stellar wind.," In the second major class of HMXBs, the Supergiant X-ray Binaries (SGXRBs), the counterpart is an early supergiant star, feeding the compact object with its radially outflowing stellar wind." + As a result. the SGXRBs are. generally. persister= systems (Ly~107 ere κ).," As a result, the SGXRBs are, generally, persistent systems $L_{X}\sim 10^{36}$ erg $^{-1}$ )." + The five-year INTEGRAL data possibly reveal a differer= scenario., The five-year INTEGRAL data possibly reveal a different scenario. + A recent subgroup has been proposed by ?.. named Supergiant Fast X-ray Transients (SFXTs): these objects. associated with a supergiant companion. occasionally undergo a short period of X-ray activity lasting less then a day. typically a few hours (2).. with a very different behavior from those observed in other X-ray biaries.," A recent subgroup has been proposed by \citet{negue06}, named Supergiant Fast X-ray Transients (SFXTs): these objects, associated with a supergiant companion, occasionally undergo a short period of X-ray activity lasting less then a day, typically a few hours \citep{sguera05}, with a very different behavior from those observed in other X-ray binaries." + These outbursts show very sharp rises. reaching the peak of the flare in <1 hour.," These outbursts show very sharp rises, reaching the peak of the flare in $\lesssim$ 1 hour." + The decay is generally of a complex kind. with two or three further flares.," The decay is generally of a complex kind, with two or three further flares." + The physical reason for these fast outbursts is still unknown. although theoretical speculations would connect them to some sort of discrete mass ejection from the supergiant donor (?) or to wind variability (2).. or to the possible presence of a second. equatorial. wind component (?)..," The physical reason for these fast outbursts is still unknown, although theoretical speculations would connect them to some sort of discrete mass ejection from the supergiant donor \citep{gol03} or to wind variability \citep{int05}, , or to the possible presence of a second, equatorial, wind component \citep{sid07} ." + Due to high interstellar absorption and to the transient nature of these sources. SFEXTs are difficult to detect. and 1 most cases. the sources had not been detected by previous missions.," Due to high interstellar absorption and to the transient nature of these sources, SFXTs are difficult to detect, and in most cases, the sources had not been detected by previous missions." + To date. six objects have been firmly characterized as SFXTs. but many other systems are likely candidates. and their number has grown rapidly since the launch of INTEGRAL (?).. so that they could actually constitute a major class of X-ray binaries.," To date, six objects have been firmly characterized as SFXTs, but many other systems are likely candidates, and their number has grown rapidly since the launch of INTEGRAL \citep{wink03}, so that they could actually constitute a major class of X-ray binaries." + Up to now. the INTEGRAL survey of the Galactic Plane and central regions has revealed the existence of more than 200 sources (??) in the energy range 20-100 keV. with à position accuracy of 2’—3’.ο depending on count rate. position in the FOV and exposure.," Up to now, the INTEGRAL survey of the Galactic Plane and central regions has revealed the existence of more than 200 sources \citep{bird07,bodag07} in the energy range 20–100 keV, with a position accuracy of $2'-3'$, depending on count rate, position in the FOV and exposure." + A large fraction of the newly discovered sources are found to be heavily obscured. displaying much larger column densities (Nj=107? emo?) than would be expected along the line of sight (see?)..," A large fraction of the newly discovered sources are found to be heavily obscured, displaying much larger column densities $N_{H}\gtrsim 10^{23}$ $^{-2}$ ) than would be expected along the line of sight \citep[see][]{kuulkers05}." + These sources were missed by previous high-energy missions. whose onboard instruments were sensitive to a softer energy range.," These sources were missed by previous high-energy missions, whose onboard instruments were sensitive to a softer energy range." + Moreover. optical counterparts to these obscured sources are poorly observable due to the high interstellar extinction. with Ay i excess of up to ~20 In this context. the recent availability of infrarec spectroscopy has emerged as a strong tool to characterize these systems and. together with high-energy data. reveal the HMXB sub-class they belong to.," Moreover, optical counterparts to these obscured sources are poorly observable due to the high interstellar extinction, with $A_{V}$ in excess of up to $\sim20$ In this context, the recent availability of infrared spectroscopy has emerged as a strong tool to characterize these systems and, together with high-energy data, reveal the HMXB sub-class they belong to." + This results in the identification of the mass transfer process of the system. with information about the intrinsic physics of the X-ray binary.," This results in the identification of the mass transfer process of the system, with information about the intrinsic physics of the X-ray binary." + The need for low energy data is particularly urgent in the case of SFXTs. which show X-ray properties common to other objects (such as RS CVs binaries and Low Mass X-ray binaries) and thus crucially require the spectral classificatior of their counterpart in order to be properly In this paper we present spectral analysis and classification of six HMXBs discovered (or re-descovered) by INTEGRAL.," The need for low energy data is particularly urgent in the case of SFXTs, which show X-ray properties common to other objects (such as RS CVs binaries and Low Mass X-ray binaries) and thus crucially require the spectral classification of their counterpart in order to be properly In this paper we present spectral analysis and classification of six HMXBs discovered (or re-descovered) by INTEGRAL." + The selected IGR sources are the following: IGR J16207-5129. IGR J16465-4507. IGR J16479-4514. AX J1841.0-0536 anc IGR 1191400051.," The selected IGR sources are the following: IGR J16207–5129, IGR J16465–4507, IGR J16479–4514, AX J1841.0–0536 and IGR J19140+0951." + We also included the well known system 4U 1907+09 since the spectral classification of its counterpart has been a matter of debate in the past. and no infrared spectra have been published up to now.," We also included the well known system 4U 1907+09 since the spectral classification of its counterpart has been a matter of debate in the past, and no infrared spectra have been published up to now." + The first three sources are located in the direction of the Norma-arm tangent region. the fourth in the Scutum-arm tangent region. the fifth and the last one in the Sagittarius arm tangent.," The first three sources are located in the direction of the Norma-arm tangent region, the fourth in the Scutum-arm tangent region, the fifth and the last one in the Sagittarius arm tangent." + In the next section we describe the observations and data reduction: in Section 3. we report the obtained spectra. analyze their features and propose a classification; wecalculate the interstellar hydrogen column," In the next section we describe the observations and data reduction; in Section \ref{results} we report the obtained spectra, analyze their features and propose a classification; wecalculate the interstellar hydrogen column" +For calculating the dise spectrum in full general relativity including light bending elfect. for rapid. rotation we adopt the following procedure.,For calculating the disc spectrum in full general relativity including light bending effect for rapid rotation we adopt the following procedure. +" The observed spectrum from the accretion disc is given by where the subseript ""ob denotes the quantity in observers frame. £ is expressed in. /em? /keV. EL is photon energy in keV. / is specific intensity and LL is the solid angle subtended by the source at the observer."," The observed spectrum from the accretion disc is given by where the subscript `ob' denotes the quantity in observer's frame, $F$ is expressed in $^2$ /keV, $E$ is photon energy in keV, $I$ is specific intensity and $\Pi$ is the solid angle subtended by the source at the observer." + As L/E remains unchanged along the path of a photon (Misner et al., As $I/E^3$ remains unchanged along the path of a photon (Misner et al. +" 1973). it is possible to calculate fon. if Lous is known (we use the subscript ""em to denote the quantities in the emitter's frame)."," 1973), it is possible to calculate $I_{\rm ob}$, if $I_{\rm em}$ is known (we use the subscript `em' to denote the quantities in the emitter's frame)." + We assume the accretion disc to raciate like a cüluted blackbocly (see Shimura Lakahara. 1995).," We assume the accretion disc to radiate like a diluted blackbody (see Shimura Takahara, 1995)." +" So £L, is given by where f isthe colour factor of the disc. D is Planck function and 7; — fir."," So $I_{\rm em}$ is given by where $f$ isthe colour factor of the disc, $B$ is Planck function and $T_{\rm c}$ = $f T_{\rm eff}$." +" The quantities ZZ, and dea, are related. by f = μιά.| 2). where (1 | z) contains the elects of both eravitational redshift ancl Doppler shift. ("," The quantities $E_{\rm ob}$ and $E_{\rm em}$ are related by $E_{\rm em}$ = $E_{\rm ob} (1 + z)$ , where (1 + $z$ ) contains the effects of both gravitational redshift and Doppler shift. (" +1 |) 2) is given bv (Luminet 1979) where 7 is the inclination angle of the disc with respect to an observer at. infinity. b is the impact parameter of the photon relative to the line joining the source ancl the observer and à is the polar angle of the position of the photon on the observers photographic plate.,"1 + $z$ ) is given by (Luminet 1979) where $i$ is the inclination angle of the disc with respect to an observer at infinity, $b$ is the impact parameter of the photon relative to the line joining the source and the observer and $\alpha$ is the polar angle of the position of the photon on the observer's photographic plate." + Pherefore bebda is the apparent area of a disc clement at observer's sky and the corresponding solid angle is given by where D is the distance of the source from the observer.," Therefore $b\,db\,d\alpha$ is the apparent area of a disc element at observer's sky and the corresponding solid angle is given by where $D$ is the distance of the source from the observer." + For a configuration. described by AZ and © (and thus specified by a set of gu). we obtain Oy.," For a configuration, described by $M$ and $\Omega$ (and thus specified by a set of $g_{\mu \nu}$ ), we obtain $\Omega_{\rm K}$." + To calculate the spectrum for a given. value of / with light bending effects. we backtrack the photons path from the observer to the disc. using standard rav tracing techniques (e.g. Chandrasekhar 1983) and the relevant boundary conditions.," To calculate the spectrum for a given value of $i$ with light bending effects, we backtrack the photons path from the observer to the disc, using standard ray tracing techniques (e.g. Chandrasekhar 1983) and the relevant boundary conditions." + For the metric (1)) that we use. the equations of motion for photons are provided in the Appendix.," For the metric \ref{eq:metric}) ) that we use, the equations of motion for photons are provided in the Appendix." +" We cover the dise between radii rn and rua=100064 rin being the radius of the inner edge of the disc and ry, the Schwarzschild radius (increasing Fui has no significant effect. on the spectrum).", We cover the disc between radii $r_{\rm in}$ and $r_{\rm mid}=1000 r_{\rm g}$; $r_{\rm in}$ being the radius of the inner edge of the disc and $r_{\rm g}$ the Schwarzschild radius (increasing $r_{\rm mid}$ has no significant effect on the spectrum). + Devond Mudge we ignore the effect. of light-bending Le. we take bsina=rsine (ois the azimuthal angle on disc plane) aud dla. — (rdrdécosi)/D? (Bhattacharyya et al.," Beyond $r_{\rm mid}$, we ignore the effect of light-bending i.e., we take $b \sin\alpha = r \sin\phi$ $\phi$ is the azimuthal angle on disc plane) and $d\Pi_{\rm ob}$ = $(r\;dr\;d\phi\;\cos i)\;/\;D^2$ (Bhattacharyya et al." + 2001)., 2001). + We have performed. several consistency. checks on our results: (1) by switching olf the light bending ellect. ιο. by considering Hat space-time while backtracking the photon's path). we see that the spectrum matches very well with that computed by ignoring light bending elfects (caleulated by an independent code Bhattacharyya ct al.," We have performed several consistency checks on our results: (1) by switching off the light bending effect (i.e. by considering flat space-time while backtracking the photon's path), we see that the spectrum matches very well with that computed by ignoring light bending effects (calculated by an independent code – Bhattacharyya et al." + 2001)., 2001). + Also. in this case. the analytically caleulated values of several quantities on the disc plane (e.g. i. o. dofdt. dé/dl ete.)," Also, in this case, the analytically calculated values of several quantities on the disc plane (e.g. $r$, $\phi$, $d\phi/dt$, $d\theta/dt$ etc.)" + are reproduced satisfactorily by our numerical method. (2) an increase in the number of grid. points on the (5.0) plane do not have any significant effect. on the computed. spectrum. (3) the spectrum matches very well with the Newtonian spectrum (Mitsuda et al.," are reproduced satisfactorily by our numerical method, (2) an increase in the number of grid points on the $b$ $\alpha$ ) plane do not have any significant effect on the computed spectrum, (3) the spectrum matches very well with the Newtonian spectrum (Mitsuda et al." + 1984) at low energy limit., 1984) at low energy limit. + This would imply that for higher frequencies. our spectrum is correct to within to 0.," This would imply that for higher frequencies, our spectrum is correct to within to ." +354.. We calculate the general relativistic spectrum. from. the accretion disc around rapidly rotating neutron star. taking into account the light bending effect.," We calculate the general relativistic spectrum from the accretion disc around rapidly rotating neutron star, taking into account the light bending effect." +" “Phe spectrum. is calculated: as a function of 6 parameters: M. OQ. distance of the source (CD). inclination angle (7) (for facc-on. 7=0""). accretion rate (Al ) and colour factor f. for each of the chosen EOS."," The spectrum is calculated as a function of 6 parameters: $M$, $\Omega$, distance of the source $D$ ), inclination angle $i$ ) (for face-on, $i = 0\degr$ ), accretion rate $\dot M$ ) and colour factor $f$, for each of the chosen EOS." + Our results are displayed in Figs., Our results are displayed in Figs. + 1 to 5., 1 to 5. + In all the displayed spectra. we have assumed AZ=14A. (canonical mass for neutron stars) D—5 kpe and f=2.0.," In all the displayed spectra, we have assumed $M = 1.4 M_{\odot}$ (canonical mass for neutron stars), $D = 5$ kpc and $f = 2.0$." + In Fig., In Fig. + l. we have plotted the Newtonian spectrum. and GIR spectra with (LBGIU and without (NLIGID) light bending effect. keeping the values of all the parameters same.," 1, we have plotted the Newtonian spectrum and GR spectra with (LBGR) and without (NLBGR) light bending effect, keeping the values of all the parameters same." + At 10 keV. the Newtonian lux is almost 2.5 times the LBGR Hux.," At 10 keV, the Newtonian flux is almost 2.5 times the LBGR flux." + This is quite expected. because in the inner parts of the disc. Newtonian temperature is considerably higher than the GR temperature (see Fig.," This is quite expected, because in the inner parts of the disc, Newtonian temperature is considerably higher than the GR temperature (see Fig." + 2 of Bhattacharyya et al..," 2 of Bhattacharyya et al.," + 2000)., 2000). + LBGR tus is about higher than NLBOR tux at 10 keV. ‘This is because light bending causes the disc to subtend a larger solid angle at the observer than otherwise., LBGR flux is about higher than NLBGR flux at 10 keV. This is because light bending causes the disc to subtend a larger solid angle at the observer than otherwise. + Thus the general οσοι of light bending is to increase the observec Hux., Thus the general effect of light bending is to increase the observed flux. + According to Shimura Vakahara (1995). the thin blackbody description. of the accretion disc. as adopte in this paper. is valid for OIAMe21 for any given color in the observed range., Note that in the outer Regions (0-5) the $CF=0.50$ level occurs at $m_{F814W}>24$ for any given color in the observed range. + La particular. the TRGB (at ΠΠ~21.5 aud ΠΠσσΗν.ov 1.6) les 1.51jag above this level.," In particular, the TRGB (at $m_{F814W}\sim 24.5$ and $m_{F555W}-m_{F814W}\sim 1.6$ ) lies $\sim 1.5$ mag above this level." + An evenly spaced [n]«)rid of blending vectos ds also superimposed to the CALDs (thin lines with slack dots in Fig. 22.., An evenly spaced grid of blending vectors is also superimposed to the CMDs (thin lines with black dots) in Fig. \ref{cm_corr_vi}. + The amplitude of hese vectors is tlie average Ar described above. the dots indicate the direction of the vectors.," The amplitude of these vectors is the average $\Delta m$ described above, the dots indicate the direction of the vectors." + The effect of such vectors become appreciable ouly [or HLs]IM.>21 in BRegious 5 aud 6. aud iiyuy>26 for Regions 0-I and only at extreme colors.," The effect of such vectors become appreciable only for $m_{F814W}\ge 24$ in Regions 5 and 6, and $m_{F814W}\ge 26$ for Regions 0-4 and only at extreme colors." + ΤΙe analogous plot for the infrared aux inlrared/optical CMDs is presented in Fig. 23.., The analogous plot for the infrared and infrared/optical CMDs is presented in Fig. \ref{cm_corr_jhv}. . + In the outer Regions (1-6) the CF=0.50 level occurs al metuv22—22.5 in both the CALDs and the effect of blending becomes significant over tie whole observed color range ouly [or 25460.2723.5., In the outer Regions (4-6) the $CF=0.50$ level occurs at $m_{F160W}\sim 22-22.5$ in both the CMDs and the effect of blending becomes significant over the whole observed color range only for $m_{F160W}\ge 23.5$. + While he use of the TRGB luminosity as a standard caucdle dates back to 1930 (see Maclore Preediuiia1 1998. ancl yeerences therein). the developineut of the method as a sale aud viable techuique is relatively receit (Lee. Freedman. Maclore 1993).," While the use of the TRGB luminosity as a standard candle dates back to 1930 (see Madore Freedman 1998, and references therein), the development of the method as a safe and viable technique is relatively recent (Lee, Freedman, Madore 1993)." + In the last few vears it has become a widely acopted techuique (see. for instaice. Ferrarese et al.," In the last few years it has become a widely adopted technique (see, for instance, Ferrarese et al." + 2000). with all the possible biases well characerized aud cuiied (Madore Freedman 1995. hereafter NLE925).," 2000), with all the possible biases well characterized and quantified (Madore Freedman 1995, hereafter MF95)." + The key observable is the magiitude of the LF sharp cut-off it he Cousius E passband. usually identified by applying au edge-detection algori nto the LE of he upper RGB (see Sakai. Madore. Freediuau. 1996. hereafter 51F96. for a staucdard application[un).," The key observable is the magnitude of the LF sharp cut-off in the Cousins I passband, usually identified by applying an edge-detection algorithm to the LF of the upper RGB (see Sakai, Madore, Freedman 1996, hereafter SMF96, for a standard application)." + As apparent from te CNDs shown iu he previous sections. our data allow for a goodsaimpliug olthe RGB.," As apparent from the CMDs shown in the previous sections, our data allow for a goodsampling ofthe RGB." + Iu particiar. dje. WE cameras sample exclusively the outer halo of the galaxy. a relatively. uncrowded region. dominated by ow-luass RGB starsaud uegligibly contamiuated by," In particular, the WF cameras sample exclusively the outer halo of the galaxy, a relatively uncrowded region dominated by low-mass RGB starsand negligibly contaminated by" +that the for the larger scales. the map containing CMD has larger variance whereas for the smaller scales the dillerence map containing only noise has largest variance.,"that the for the larger scales, the map containing CMB has larger variance whereas for the smaller scales the difference map containing only noise has largest variance." + We have used the galaxy density [field obtained from the PSC: galaxy. survey and hyedrodynamical simulations based. on the observed. distribution of LRAS 1.2Jy. galaxies to make a full-sky. prediction of the SZ ellect from diffuse hot eas in the local universe (<80h. Mpe)., We have used the galaxy density field obtained from the $z$ galaxy survey and hydrodynamical simulations based on the observed distribution of IRAS 1.2Jy galaxies to make a full-sky prediction of the SZ effect from diffuse hot gas in the local universe $<80 \hmpc$ ). + We have studied whether this elect could be observed and studied by the CMD observations performed by the WALADP satellite and if it could be a contaminating factor in the study of the CM at large angular scales., We have studied whether this effect could be observed and studied by the CMB observations performed by the WMAP satellite and if it could be a contaminating factor in the study of the CMB at large angular scales. + We have cross-correlated our map of the predicted local SZ-ellect with the WALAP data at cilferent frequencies taking into account the frequeney dependence of the SZ elfect., We have cross-correlated our map of the predicted local SZ-effect with the WMAP data at different frequencies taking into account the frequency dependence of the SZ effect. + We have performed the cross-correlation test in three spaces. enabling us to test certain parts of the sky (pixel space test). certain multipole ranges (harmonic space test) ancl certain wavelet," We have performed the cross-correlation test in three spaces, enabling us to test certain parts of the sky (pixel space test), certain multipole ranges (harmonic space test) and certain wavelet" +CD Tau € (bv means of e.g. high-accuracy LU measurements of the visual component alone) may provide a more stringent test to the quality of the evolutionary models.,CD Tau C (by means of e.g. high-accuracy IR measurements of the visual component alone) may provide a more stringent test to the quality of the evolutionary models. + What scenis clear at this point. is that the systematies that Popper (1997) and Clausen et al. (," What seems clear at this point, is that the systematics that Popper (1997) and Clausen et al. (" +1999) pointed out are not observed in CD Tau €. Indeed. the stellar. parameters. are very accurately described by the isochrone that fits the more MASSIVE ccnponents.,"1999) pointed out are not observed in CD Tau C. Indeed, the stellar parameters are very accurately described by the isochrone that fits the more massive components." + LE. Masana. E. Comerónn. E. Oblak and 8S. ανν are thank for their kind collaboration in performing and reducing the observations at Carlos Sánnchez Telescope. Mount Stromlo Observatory and Observatoire cHaute Provence.," E. Masana, F. Comerónn, E. Oblak and S. Udry are thanked for their kind collaboration in performing and reducing the observations at Carlos Sánnchez Telescope, Mount Stromlo Observatory and Observatoire d'Haute Provence." + A. Clare is acknowledged for making stellar evolutionary. mocels for low-mass stars available to us., A. Claret is acknowledged for making stellar evolutionary models for low-mass stars available to us. + We also thank J.D. Pritchare for providing the latest version of the WD program usec for light. curve modelling. as well as several algorithms and routines.," We also thank J.D. Pritchard for providing the latest version of the WD program used for light curve modelling, as well as several algorithms and routines." + This work was supported by the Spanish CICYT under contract ESDP97-1803., This work was supported by the Spanish CICYT under contract ESP97-1803. + L1t. also acknowledges the grant of theievestigador by the CIRIT. (Generalitat de Catalunva)(re., I.R. also acknowledges the grant of the by the CIRIT (Generalitat de Catalunya)(ref. + FLPG/95-1111)., FI-PG/95-1111). +The Ca He Fs line region is included in most of the spectra but the ellicienev of the spectrograph and the CCD decreases very rapidly due to the position of these lines at he end of the echellogram.,The Ca H K line region is included in most of the spectra but the efficiency of the spectrograph and the CCD decreases very rapidly due to the position of these lines at the end of the echellogram. + Therefore. the obtained S/N ratio is very low. and the normalization of the spectra is very difficult.," Therefore, the obtained S/N ratio is very low, and the normalization of the spectra is very difficult." + In many cases we could not measure the £M(o ines and in other we measured them in the observed spectra as ib was not possible to apply the spectral subtraction for his region (sce Tables 10. and. 11))., In many cases we could not measure the $EW$ lines and in other we measured them in the observed spectra as it was not possible to apply the spectral subtraction for this region (see Tables \ref{tab:ew} and \ref{tab:fl}) ). + Strong emission in the Ca Η [y is seen despite the ow s/h. The three lines of the Ca11 (ART) are included in all our echelle spectra., Strong emission in the Ca H K is seen despite the low S/N. The three lines of the Ca (IRT) are included in all our echelle spectra. + In all of them a clear emission arising in the corethe absorption lines is seen (see Fig. 12)), In all of them a clear emission arising in the core of the absorption lines is seen (see Fig. \ref{fig:hairt}) ). + Averagedof of valuesemission £M are £M (Cai) = 0.74. 0.93 and 0.81 flor AASAO8S. 8542. and 8662 in FOCESO4 run.," Averaged values of emission $EW$ are $EW$ (Ca ) = 0.74, 0.93 and 0.81 for $\lambda\lambda$ 8498, 8542, and 8662 in FOCES04 run." + £M(Ca i) 0.49. 0.72 and 0.61 iin FOCESOG run.," $EW$ (Ca ) = 0.49, 0.72 and 0.61 in FOCES06 run." + LM ‘all) = 266. 0.86 and 0.70 iin FOCESOTa.," $EW$ (Ca ) = 0.66, 0.86 and 0.70 in FOCES07a." + £M (Ca 11) = -0 and 0.77 iin F'OCESOTb and m(Ca 11) = 0.71. i0.89 and 0.79 iin FUESOSs.," $EW$ (Ca ) = 0.79, 1.03 and 0.77 in FOCES07b and $EW$ (Ca ) = 0.71, 0.89 and 0.79 in FIES08." + The variation of the emission in these lines is significant although not as strong as in Hla(see Table 10))., The variation of the emission in these lines is significant although not as strong as in $\alpha$ (see Table \ref{tab:ew}) ). + Only for the FOCESO4+-run we have enough data points to compare variations between Io. £Ms and Cau fs. Lo other active stars a clear anticorrelation is usually seen (as their emissions come from cillerent features in the stellar surface). see e.g. stars in Arévalo&Lázaro (1999).. Montesetal. (2000)... Gálvezetal. (2002)..Gálvezetal.lie.(2009) etc.," Only for the FOCES04-run we have enough data points to compare variations between $\alpha$ $EW$ s and Ca $EW$ s. In other active stars a clear anticorrelation is usually seen (as their emissions come from different features in the stellar surface), see e.g. stars in \citet{arevalo99}, , \citet{Montes00b}, \citet{Galvez02}, \citet{Galvez09} etc.," + but it is very weak in the case of FR 6πό (see 16))., but it is very weak in the case of FR Cnc (see Fig. \ref{fig:hairtfec11}) ). + ln addition. we have calculated the ratio of excess emission £M. which is also an indicator of the tvpe of chromospheric TUR.structure. which produces the observed emission.," In addition, we have calculated the ratio of excess emission $EW$ , $\frac{E_{8542}}{E_{8498}}$, which is also an indicator of the type of chromospheric structure, which produces the observed emission." + In solar plage values. of = 13 are measured. while in solar prominence the imvalues are zz 9. the limit of an optically thin emitting plasma (Chester 1991)).," In solar plage values of $\frac{E_{8542}}{E_{8498}}$ $\approx$ 1.5–3 are measured, while in solar prominence the values are $\approx$ 9, the limit of an optically thin emitting plasma \citeauthor{chester} \citeyear{chester}) )." + We have found a Iia. indicating that Ca ICE emission comes from plage-like regions.," We have found a $\frac{E_{8542}}{E_{8498}}$$\approx$ 1.3, indicating that Ca IRT emission comes from plage-like regions." + Since FR Cne is a rapid. rotator with considerable broadeninge of spectral lines. we ὃνgenerated an indirect starspot map using the Doppler Tomography of Stars (Do'TS) imaging code (Cameron 2001)).," Since FR Cnc is a rapid rotator with considerable broadening of spectral lines, we generated an indirect starspot map using the Doppler Tomography of Stars (DoTS) imaging code \citeauthor{cameron01mapping} \citeyear{cameron01mapping}) )." + In order to detect the line distortion due to starspots in the high resolution spectra. we have appliccd least-squares deconvolution (Donatietal. 1997: Barnesetal. 1998)) to the 43626845 wavelength region of FOCTSO4 spectra (obtained 2004 March. April).," In order to detect the line distortion due to starspots in the high resolution spectra, we have applied least-squares deconvolution \citeauthor{donati97zdi} \citeyear{donati97zdi}; \citeauthor{barnes98aper} \citeyear{barnes98aper}) ) to the 4362--6845 wavelength region of FOCES04 spectra (obtained at 2004 March – April)." + A single line. free of the effects of rotational line blending and with high S/N is thus derived.," A single line, free of the effects of rotational line blending and with high S/N is thus derived." + ⊥≻∢⋅≼∙∢≱↓↥∖⇁⋖≱↓⇂⇂↥↕⋖≱↓↥⊲↓⊳∖≼∼⋜⊔⋅↓⋰↓∢⊾∠⇂⋯∐⊔⊳∖⊀↓⊔⋏∙≟⋜↧⊻⊽∶⇉∔↱≻∪↓∖⋡⊔↓⋯⇂⋖⊾↓ ∐⊔∢⋅∐⊳∖⇂↿∖∖↾⇀∖∟∐∶≱∖⋖⋅⋖⋅↓∖⋡⊔↓≻↳⋜⊔⊾↿⋜↧↓⊳↓≤⋗≤⋗≤⋗⊾∖↽⇉∪∪∪∩∖∖⊽↓↥⊀⊔⇍∐ indicates that there are 8345 lines in the selected wavelength region with normalized depths of 0.051.0., Deconvolution is carried out using a $T$ = 2450 K model line list (VALD; see \citeauthor{Kupka1} \citeyear{Kupka2} \citeyear{Kupka1}) ) which indicates that there are 8345 lines in the selected wavelength region with normalized depths of 0.05–1.0. + Regions around hyelrogen Balmer lines. the Mg triplet and Na doublet. are excluded from the deconvolution.," Regions around hydrogen Balmer lines, the Mg triplet and Na doublet are excluded from the deconvolution." + A single line profile with a mean of A = 5460.4 iis derived for each observed spectrum., A single line profile with a mean of $\lambda$ = 5460.4 is derived for each observed spectrum. + ‘The mean S/N of the input spectra over the entire wwavelength region was 21.8. while the mean deconvolved line profiles possess S/N = 1008 (indicating a gain of 46.2).," The mean S/N of the input spectra over the entire - wavelength region was 21.8, while the mean deconvolved line profiles possess S/N = 1008 (indicating a gain of 46.2)." + should be noted that while the profile shown in Fig., It should be noted that while the profile shown in Fig. + 9 (upper panel) represents the broadening Lunction of ER. Cne (i.c. rotational velocity. plus starspot distortions). the LSD profiles in Section 7 are deconvolved. using a linelist rather than a template.," \ref{fig:perfil} (upper panel) represents the broadening function of FR Cnc (i.e. rotational velocity plus starspot distortions), the LSD profiles in Section 7 are deconvolved using a linelist rather than a template." + As such. the LSD profiles still contain the intrinsic stellar profile. and any distortions due to starspots will appear to possess a lower amplitude when compared with à templatesderived CCE.," As such, the LSD profiles still contain the intrinsic stellar profile, and any distortions due to starspots will appear to possess a lower amplitude when compared with a template-derived CCF." + For the imaging procedure. we used the standard star. LID 151877. to represent. the local intensity profile of a slowly rotating star.," For the imaging procedure, we used the standard star, HD 151877, to represent the local intensity profile of a slowly rotating star." + A two temperature model with Tasa = 4250 dx and doa = 3000 [dX was used., A two temperature model with $T_{\rm phot}$ = 4250 K and $T_{\rm spot}$ = 3000 K was used. + The starspot image therefore represents the spot filling factor., The starspot image therefore represents the spot filling factor. + Details of the Doppler imaging technique can be found in Cameron(2001)..., Details of the Doppler imaging technique can be found in \citet{cameron01mapping}. +" We optimized the goodness of Lit to the 10. deconvolved profiles for. heliocentric RW. axial inclination. equivalent width and essini. findingV,,g = 18.6 d 0.6. essini — 46.27 0ὅ kis. landi — 55 d55.."," We optimized the goodness of fit to the 10 deconvolved profiles for heliocentric RV, axial inclination, equivalent width and $v$ $i$, finding $V_{hel}$ = 18.6 $\pm$ 0.6, $v$ $i$ = 46.2 $\pm$ 0.8 km $^{-1}$ and i = 55 $\pm$." + The essiniecaltucishigherlhan.bulstilleonsistentwilh.ourmcanvy ssini value derived. in Section 5.3.," The $v$ $i$ value is higher than, but still consistent with, our mean $v$ $i$ value derived in Section 5.3." + Since we here use al rotation phases to derive our best fit Doppler image. 1 is likely that the result. is less biased. than the previous results in Section. 5.3 that co πο take account of the presence. of. starspots. which alfect the profile shape.," Since we here use all rotation phases to derive our best fit Doppler image, it is likely that the result is less biased than the previous results in Section 5.3 that do not take account of the presence of starspots, which affect the profile shape." + Starspot distortions in the wings of the profiles for instance. are likely to lead to underestimations of essin uehenmuisingasinglespeclbrum.leadingloasystemealicallglowermoeanesti ," Starspot distortions in the wings of the profiles for instance, are likely to lead to underestimations of $v$ $i$ when using a single spectrum, leading to a systematically lower mean estimation of $v$ $i$." +"We note however that our result for the 2004 observations is Ho with the value tabulatecd in Table 9 (i.e. 44. +1.9""km 4).", We note however that our result for the 2004 observations is consistent with the value tabulated in Table 9 (i.e. 44.1 $\pm$ 1.9km $^{-1}$ ). + Fig., Fig. + l8. shows the deconvolved profiles phases of observation) while Fig., \ref{fig:xxx} shows the deconvolved profiles (and phases of observation) while Fig. + 19. shows mercator projections of the starspot image of FR Cne., \ref{fig:yyy} shows mercator projections of the starspot image of FR Cnc. + The surface inFig., The surface map inFig. + 19. (upper panel) indicates that ER €ne. possesses mapconsiderable spot. coverage as suggested by the time varying distortions in the deconvolved. profiles, \ref{fig:yyy} (upper panel) indicates that FR Cnc possesses considerable spot coverage as suggested by the time varying distortions in the deconvolved profiles +In our picture of a radiation-reaction limited acceleration of the primary beam it follows that the Lorentz factor of the secondary plasma is given bv This Lorentz factor is above the minimum 5;;v.,In our picture of a radiation-reaction limited acceleration of the primary beam it follows that the Lorentz factor of the secondary plasma is given by _p = 3 10^5 This Lorentz factor is above the minimum $\gamma_{KN}$. + Therefore. IC scattering bv the secondary plasma (takes place in the INN regime and we can use the same relations (hal we have derived in (he previous section for (he emission produced by (he primary. beam. (," Therefore, IC scattering by the secondary plasma takes place in the KN regime and we can use the same relations that we have derived in the previous section for the emission produced by the primary beam. (" +For multiplicities mush higher (han (he assumed AsLOO the scattering by UV photons occurs in the Thompson reeime.,For multiplicities mush higher than the assumed $\lambda \approx 100$ the scattering by UV photons occurs in the Thompson regime. + Overall. (he convolution of the electron and the soft photon spectrum requires detailed radiative calculations which include global magnetospheric models ancl anisotropic angular clistrvibutions of the photons.)," Overall, the convolution of the electron and the soft photon spectrum requires detailed radiative calculations which include global magnetospheric models and anisotropic angular distributions of the photons.)" + The maximum energy of IC photons produced by the secondary. plasma is EEq. (3.2))) , The maximum energy of IC photons produced by the secondary plasma is Eq. \ref{gg}) )) _ +ο ο.- and the peak Iuminosity of the IC scattered UV photons is LEEq. (3.2)),p m_e c^2 = 150 and the peak luminosity of the IC scattered UV photons is Eq. \ref{OK}) ) + is Ευ Both the energy (3.3)) and the peak luminosity (3.3)) are consistent with the VERITAS detection., is = _ Both the energy \ref{22}) ) and the peak luminosity \ref{OK1}) ) are consistent with the VERITAS detection. + Thus. IC up-scattering of UV. photons by the secondary. plasmacan explain the," Thus, IC up-scattering of UV photons by the secondary plasmacan explain the" +Surveys such as the Sloan Digital Sky Survey (SDSS) (Yorketal.2000). and the Digitized Palomar Sky Survey (Djorgovskiοἱal.1999). have revealed large samples of quasi-stellar objects (QSOs) out (o z7 6.,"Surveys such as the Sloan Digital Sky Survey (SDSS) \citep{YOR00} and the Digitized Palomar Sky Survey \citep{DJO99} have revealed large samples of quasi-stellar objects (QSOs) out to $z \sim +6$ ." +" Studies by Fanetal.(2002) have shown that ad such a high redshift we are approaching the epoch of reionization. the edge of the ""dark ages. when the first stars and massive black holes were formed."," Studies by \citet{FAN02} have shown that at such a high redshift we are approaching the epoch of reionization, the edge of the “dark ages”, when the first stars and massive black holes were formed." + Edclington-limit arguments sugeest (hat (he supermassive black holes at the center of (hese QSOs are on (he order of 10?M..., Eddington-limit arguments suggest that the supermassive black holes at the center of these QSOs are on the order of $10^9~M{_\odot}$. + If the correlation between bulge and black-hole masses (Gebhardtetal.2000:Ferrarese&Merritt.2000) also holds at these high redshifts. then these sources have associated spheroids with masses on the order of ~LO’AA...," If the correlation between bulge and black-hole masses \citep{GEB00,FEME00} + also holds at these high redshifts, then these sources have associated spheroids with masses on the order of $\sim 10^{12}~M_\odot$." + It is challenging to explain the formation of such massive structures on relatively short timescalesGyr)., It is challenging to explain the formation of such massive structures on relatively short timescales. + However. Writhe&Loeb(2002) estimate that almost one third of known quasars al z~6 ought to be lensed by galaxies along the line of sight.," However, \citet{WL02} estimate that almost one third of known quasars at $z\sim6$ ought to be lensed by galaxies along the line of sight." + If these quasars are indeed gravitationally lensed. the estimated masses of their associated spheroids could be siler by up to an order of magnitude: this would allow a less efficient assembly. process.," If these quasars are indeed gravitationally lensed, the estimated masses of their associated spheroids could be smaller by up to an order of magnitude; this would allow a less efficient assembly process." + lligh resolution radio observations of high-redshift radio-Ioud quasars can be used to test for strong gravitational lensine by looking for multiple imaging onscales [rom tens, High resolution radio observations of high-redshift radio-loud quasars can be used to test for strong gravitational lensing by looking for multiple imaging onscales from tens +with the assumption kt«jmDNE ,with the assumption $k_{\parallel} ^0 \ll k_\parallel ^{min} \ll k_\parallel ^{max}$. +We consider first the transverse drift in Eq.(23))., We consider first the transverse drift in \ref{Fmu2}) ). + We average FU?) over an isotropic pitch angle distribution., We average $F(\mu^2)$ over an isotropic pitch angle distribution. +"Using evlindrical coordinate (d'/=dhjkdbdvi) we have In units of the Bohm coefficient diffusion (a,=(1/3)ry0) and approximating Fa]""/epoQ1ὃν we obtain where the time-dependence iscontained in the new variable yrIrteg~werOl (and ""n=Keyl~ Fino) and we used where ία.2) is the incomplete gamma function (see Gradshtevn&Ryzhik(1973).. I2q.(3.761.2)).","Using cylindrical coordinate $d^3 k = dk_\parallel k_\perp dk_\perp d\psi$ ) we have In units of the Bohm coefficient diffusion $\kappa_B = (1/3)r_g v$ ) and approximating $r_g/v_\parallel \simeq \Omega^{-1}$, we obtain where we defined where the time-dependence iscontained in the new variable $y_\parallel ^{m} = k_\parallel ^{min} v_\parallel t \simeq k_\parallel ^{min} r_g \Omega t$ (and $y_\parallel ^{0} = k_\parallel ^{0} v_\parallel t \simeq k_\parallel ^{0} r_g \Omega t$ ) and we used where $\Gamma (a, z)$ is the incomplete gamma function (see \citet{gr73}, Eq.(3.761.2))." +" The time evolution of the drift coellicient dj, is depicted in Fig.l.", The time evolution of the drift coefficient $d^s_D$ is depicted in \ref{drift}. +. The first term in Eq. 2 (33)).," The first term in Eq. \ref{F1}) )," + corresponding to scales smaller than. coherence scale at (hmDUM ). dominates over (he second term. corresponding to scales larger than 2gUU (hk«x km).," corresponding to scales smaller than coherence scale $2\pi/k_\parallel^{min}$ $ k > k_\parallel^{min}$ ), dominates over the second term, corresponding to scales larger than $2\pi/k_\parallel^{min}$ $ k < k_\parallel^{min}$ )." +" The diffusive behaviour can be found by using the approximation of D(a.z) [or =y""meu<] (see Gradshtevn&Byzhik (1973). Eq.(8.354.2)). because yv< l: since we assume a weak magnetic [huctuation. it is reasonable to assume that the"," The diffusive behaviour can be found by using the approximation of $\Gamma(a,z)$ for $|z| = y_\parallel ^{m} = k_\parallel ^{min} v_\parallel t \ll 1$ (see \citet{gr73}, , Eq.(8.354.2)), because $y_\parallel ^{m} \ll 1$ ; since we assume a weak magnetic fluctuation, it is reasonable to assume that the" +defined piecemeal.,defined piecemeal. + This is a particularly interesting projection since the euomonic is locally but it is clear that geodesies will trace out straight lines in the enomonic cube cube map because they beud when they cross an edge between faces.," This is a particularly interesting projection since the gnomonic is locally flexion-free, but it is clear that geodesics will trace out straight lines in the gnomonic cube cube map because they bend when they cross an edge between faces." + The gnomonic cube is presented as a Cross. so 2 edges are included in the map proper.," The gnomonic cube is presented as a cross, so 5 edges are included in the map proper." +— CGeoclesics beud when they cross au edge in this laid out Cross configuration., Geodesics bend when they cross an edge in this laid out cross configuration. + The above comparisous do not depend ou how iuportant each of the criteria are (Le. what weighting to give each measure)., The above comparisons do not depend on how important each of the criteria are (i.e. what weighting to give each measure). + Laskowski (1997ab) suggested a meaus of ranking very disparate maps., Laskowski (1997ab) suggested a means of ranking very disparate maps. +" Though his weighting scheme is not unique. as a simple illustration of how this cau be done. we will minimize the sum of the squares of all 6 parameters. normalized to their values iu the equirectangular projection: Following Laskowksi (1997ab) we set the normalization constants equal to the values of these errors in the Equirectangular projection Cr= À. y= o) JN;=0.51. Na=0.11. Np0.0. Ne=0.60. Ng= 0.119. Ny,=0.25."," Though his weighting scheme is not unique, as a simple illustration of how this can be done, we will minimize the sum of the squares of all 6 parameters, normalized to their values in the equirectangular projection: Following Laskowksi (1997ab) we set the normalization constants equal to the values of these errors in the Equirectangular projection $x=\lambda$ , $y=\phi$ ): $N_i= 0.51$ , $N_a = 0.41$, $N_f = +0.64$, $N_s = 0.60$, $N_d = 0.449$ , $N_b = 0.25$." + The projections with the lowest values of X are: This approach is certainly not unique., The projections with the lowest values of $\Sigma_\varepsilon$ are: This approach is certainly not unique. + One may take issue with the weighting of the individual j»arameters. the domain over which they are applied (the whole earth. as opposed to contineuts ouly. for exaiuple). or even how the parameters are computed. we preseut it as a simple example of low our results may be combiued with previous studies of map projectious.," One may take issue with the weighting of the individual parameters, the domain over which they are applied (the whole earth, as opposed to continents only, for example), or even how the parameters are computed, we present it as a simple example of how our results may be combined with previous studies of map projections." +" It is interesting tliat he ""best map. as selected by this criterion is the one already. used by the Natioual Geographic or its whole world projection."," It is interesting that the “best” map, as selected by this criterion is the one already used by the National Geographic for it's whole world projection." + It is also interesting to note that the Winkel-Tripel has especially OW SIKEWLLESS., It is also interesting to note that the Winkel-Tripel has especially low skewness. + Another nice property of this weighting scheme is that it gives a low score to pathologica srojectious., Another nice property of this weighting scheme is that it gives a low score to pathological projections. + For example. a series ofu gores (made using the polycouic projection) arranged ina sunflower pattern would approximate the Avimuthal equidistaut projection iu distance errors as 1 jecame large but would have arbitrarily low values o£ LÀ. Ε and S. But ifa boundary eut term B is included this term would blow up and save us from picking the bad subcdivided map as better thar he more visually pleasing projections described above.," For example, a series of n gores (made using the polyconic projection) arranged in a sunflower pattern would approximate the Azimuthal equidistant projection in distance errors as n became large but would have arbitrarily low values of I, A, F, and S. But if a boundary cut term B is included this term would blow up and save us from picking the bad subdivided map as better than the more visually pleasing projections described above." + Stretching individual pixels at the edges of he gores to fill the gaps between them would eliminate the boundary cuts., Stretching individual pixels at the edges of the gores to fill the gaps between them would eliminate the boundary cuts. + However. it would also cause the skewness to blow up. preventing us from giving a good score to a bad projection.," However, it would also cause the skewness to blow up, preventing us from giving a good score to a bad projection." + Interested readers may visit to cdownloac a free IDL code to measure the flexion. area. aud other measures discussed in this paper.," Interested readers may visit to download a free IDL code to measure the flexion, area, and other measures discussed in this paper." + We have uot done all known projectious. but have covered ones that have available mathematical formulasaud we thought likelytodo well.," We have not done all known projections, but have covered ones that have available mathematical formulasand we thought likelytodo well." +KI 15D is a unique eclipsing pre-miain sequence (PAIS) system near the Cone nebula in NGC 2264 (Ixearnsetal.1997:KearnsandHerbst1993).,"KH 15D is a unique eclipsing pre-main sequence (PMS) system near the Cone nebula in NGC 2264 \citep{kehm,kh98}." +. The visible star is of ING or Ix spectral class (lamilionetal.2001:Agol2004). and has an Ha equivalent width of ~ 2A. typical of a weak-lined T Tauri star (WTTS).," The visible star is of K6 or K7 spectral class \citep{ham01,agol} and has an $\alpha$ equivalent width of $\sim$ 2, typical of a weak-lined T Tauri star (WTTS)." + Its mass ancl age are ~0.6 M. and 2 Alv. respectively (lamiltonetal.2001).," Its mass and age are $\sim$ 0.6 $M_\odot$ and 2 My, respectively \citep{ham01}." +. At high spectral resolution the star reveals broad wines on its hydrogen emission lines ancl during eclipse one clearly sees forbidden emission lines (Hamiltonοἱal.2003)., At high spectral resolution the star reveals broad wings on its hydrogen emission lines and during eclipse one clearly sees forbidden emission lines \citep{ham03}. +. These features signiflv that accretion and outflow are still active, These features signify that accretion and outflow are still active +where 44=2+0.001 Ix (lo error) is the current value of the CAIBR. temperature as determined. from the instrument (Alatheretal1999:Smoot& 2000).,"where $T_0=2.725\pm 0.001$ K $1\sigma$ error) is the current value of the CMBR temperature as determined from the instrument \cite{Mather99,Smoot}." +. We caution. however. that. this relation. remains vet observationally unprooven.," We caution, however, that this relation remains yet observationally unprooven." + In section 3.3. we review the currently available pieces of evidence., In section \ref{section:CMBR} we review the currently available pieces of evidence. + Equation (2)) is the system. of statistical equilibrium equations that must. be solved. in order to compute the population ratios of the fine-structure levels., Equation \ref{eq:sum}) ) is the system of statistical equilibrium equations that must be solved in order to compute the population ratios of the fine-structure levels. + LE we mocel the atom/ion as becing composed of m levels. then we must deal with a system of mi1 equations.," If we model the atom/ion as beeing composed of $m$ levels, then we must deal with a system of $m-1$ equations." + 1n order to numerically solve this svstem we have built a Fortran 90 code - (Silva&Viceas 2000)-- that reads in the basic atomic physics parameters and automatically computes the rates for all the processes becing considered., In order to numerically solve this system we have built a Fortran 90 code - \cite{SV2000}- - that reads in the basic atomic physics parameters and automatically computes the rates for all the processes beeing considered. + The code is very. Uexible. allowing the user to account for an arbitrary number of levels ancl processes.," The code is very flexible, allowing the user to account for an arbitrary number of levels and processes." + The code. as well as the input files for the atoms/ions considered. in this paper. are available upon request from one of the authorsCAISY.," The code, as well as the input files for the atoms/ions considered in this paper, are available upon request from one of the authors." +. Le may. also be used. in other astronomical applications. such as calculating intensity ratios of collisionally excited emission. lines (such as coronal emission lines) ancl computing cooling rates due to collisional excitation.," It may also be used in other astronomical applications, such as calculating intensity ratios of collisionally excited emission lines (such as coronal emission lines) and computing cooling rates due to collisional excitation." + Next. we describe the computations for each atom/ion considered. in greater detail.," Next, we describe the computations for each atom/ion considered in greater detail." + As the population ratios of the fine-structure levels will be strongly. dependent: upon several atomic physics parameters. it is essential to search the literature for the most up to date values.," As the population ratios of the fine-structure levels will be strongly dependent upon several atomic physics parameters, it is essential to search the literature for the most up to date values." + In this work. we give precedence to results obtained recently by two large international collaborations: the Opacity Project (Seatonal.1994). and the Iron Project (Hummeretal.1993).," In this work, we give precedence to results obtained recently by two large international collaborations: the Opacity Project \cite{Opacity} + and the Iron Project \cite{Iron}." +. For reasons of space. we illustrate the results obtained for the population ratios of the fine-structure levels under a limited range of physical conditions only.," For reasons of space, we illustrate the results obtained for the population ratios of the fine-structure levels under a limited range of physical conditions only." + We urge the user to make use of the numerical code in order to get accurate predictions in his/her applications., We urge the user to make use of the numerical code in order to get accurate predictions in his/her applications. +" The ground state of the C"" atom is comprised of the 222p? ιο triplet levels."," The ground state of the $^0$ atom is comprised of the $^2$ $^2$ $^3\mathrm{P}^e_{0,1,2}$ triplet levels." + The. energies. of the. [ine-structure excited. levels relatively to the ground. state are 16.40 em! and 43.40 |., The energies of the fine-structure excited levels relatively to the ground state are 16.40 $^{-1}$ and 43.40 $^{-1}$. + The transition. probabilities are Alyy=7.9821078ὃν chy=2.0541075s4 anc ela=2.65410os*.," The transition probabilities are $A_{10}=7.932\ 10^{-8}\ \mathrm{s}^{-1}$, $A_{20}=2.054\ 10^{-14}\ \mathrm{s}^{-1}$ and $A_{21}=2.654\ 10^{-7}\ \mathrm{s}^{-1}$." + Our mocel atom includes the five lowest energy levels: 222p?E pipo. 222p? FDS and 272p? 185.," Our model atom includes the five lowest energy levels: $^2$ $^2$ $^3\mathrm{P}^e_{0,1,2}$, $^2$ $^2$ $^1\mathrm{D}^e_2$ and $^2$ $^2$ $^1\mathrm{S}^e_0$ ." +" ""he energies were taken from Moore (1970). and the transition probabilities from the Iron Project calculation of is. Mendoza and Zeippen (1997).."," The energies were taken from Moore \shortcite{MooreCI} and the transition probabilities from the Iron Project calculation of s, Mendoza and Zeippen \shortcite{AijCI}." + The CAMIBR will be an important excitation mechanism for the first excited P level. since it is so closely separated from the ground level.," The CMBR will be an important excitation mechanism for the first excited $^3\mathrm{P}^e_1$ level, since it is so closely separated from the ground level." + Assuming the temperature-recshilt relation as given by equation (6)). the CMDI spectrum will peak at the first-exeited level frequeney at a redshift 2o2.," Assuming the temperature-redshift relation as given by equation \ref{eq:Tlaw}) ), the CMBR spectrum will peak at the first-excited level frequency at a redshift $z\sim 2$." + ‘Vable lo gives the excitation rates of the ο fine-structure levels as a function of redshift. again assuming the temperature-redshift relation (6)).," Table \ref{table:Kij} gives the excitation rates of the $^0$ fine-structure levels as a function of redshift, again assuming the temperature-redshift relation \ref{eq:Tlaw}) )." + The line-structure transitions may also be induced. by collisions., The fine-structure transitions may also be induced by collisions. + Fig., Fig. + 1. shows the collision rates for the most important collision particles., \ref{figure:qijCI} shows the collision rates for the most important collision particles. + The rates for collisions bv protons were taken from Roucll Le DBourlot. (1990).. bv neutral hydrogen from Launay Ποιο (1977a).. by molecular hydrogen from. Schródder et al.," The rates for collisions by protons were taken from Roueff Le Bourlot \shortcite{q_proton_CI}, by neutral hydrogen from Launay Roueff \shortcite{q_H0_CI}, by molecular hydrogen from Schrödder et al." + (1991). and. by neutral helium from Staemmler Flower (1991).., \shortcite{q_H2_CI} and by neutral helium from Staemmler Flower \shortcite{q_He_CI}. + For the rates bv collisions with electrons we have employed. the analytic fits given by Johnson. Burke Ixingston (1987)..," For the rates by collisions with electrons we have employed the analytic fits given by Johnson, Burke Kingston \shortcite{q_electron_CI}." + We point out that the similar plot in Ποιο Le Bourlot’s paper comparing collision rates bv. protons ancl electrons is incorrect. since an error has crept in their figure. and they compare excitation and de-exceitation rates (Roucll private conum.J.," We point out that the similar plot in Roueff Le Bourlot's paper comparing collision rates by protons and electrons is incorrect, since an error has crept in their figure, and they compare excitation and de-excitation rates (Roueff, private comm.)." + We have also considered the ellect of excitation of the upper TDS and 485 levels by. collisions with electrons., We have also considered the effect of excitation of the upper $^1\mathrm{D}^e_2$ and $^1\mathrm{S}^e_0$ levels by collisions with electrons. +" We took the analytic fits to the Alaxwellian-averaged collision strengths 5 for transitions involving these levels given by Péqquignot Aldrovanci (1976).. and. transformed them from LS coupling to the fine-structure levels according to their statistical weights: llowever. the inclusion of these levels can hardly influence the population of the I"". fine-structure levels at temperatures prevailing in ionization regions where the atom C"" is likely to be found."," We took the analytic fits to the Maxwellian-averaged collision strengths $\gamma$ for transitions involving these levels given by Péqquignot Aldrovandi \shortcite{high_e_CI}, and transformed them from LS coupling to the fine-structure levels according to their statistical weights: However, the inclusion of these levels can hardly influence the population of the $^3\mathrm{P}^e$ fine-structure levels at temperatures prevailing in ionization regions where the atom $^0$ is likely to be found." + For example. even for temperatures as high as Z=10*A the population ratio of the ΤΙ level relatively to the ground state will increase by no more than 5 percent (10 percent for the δν level).," For example, even for temperatures as high as $T=10^4\ K$ the population ratio of the $^3\mathrm{P}^e_1$ level relatively to the ground state will increase by no more than 5 percent (10 percent for the $^3\mathrm{P}^e_2$ level)." + The test calculations were done taking into account onlycollisions by electrons (and spontaneous decays): if this is not the main excitation mechanism. then the error will be significantly smaller.," The test calculations were done taking into account onlycollisions by electrons (and spontaneous decays); if this is not the main excitation mechanism, then the error will be significantly smaller." + Excitation of the fine-structure levels by Duorescence was also investigated., Excitation of the fine-structure levels by fluorescence was also investigated. + We considerLOS allowed UY, We consider108 allowed UV +projected diameter) with resolving powers of Ae46.000 and 67.000. respectively. giving a wavelength coverage of ~3600—7400AA.,"projected diameter) with resolving powers of $R \approx 46,\!000$ and $67,\!000$, respectively, giving a wavelength coverage of $\sim 3600-7400$." +.. We used the wavelength range from approximately ~4100—5600 (ο determine the RVs following the procedures described in Buchhave et al. (, We used the wavelength range from approximately $\sim 4100-5600$ to determine the RVs following the procedures described in Buchhave et al. ( +2010).,2010). + The exposure lime was between 2400 ancl 3600 seconds. vielding a S/N [rom 22 (to 30 per pixel in the wavelength range used.," The exposure time was between 2400 and 3600 seconds, yielding a S/N from 22 to 30 per pixel in the wavelength range used." + The FIES RV results are also given in refrvstab.., The FIES RV results are also given in \\ref{rvstab}. + We also determined the line bisectors for the 6 FIES spectra., We also determined the line bisectors for the 6 FIES spectra. + They have a hieher precision than (the IRS results since we could use the entire spectrum for the analvsis (FIES does not use an I;-cell)., They have a higher precision than the HRS results since we could use the entire spectrum for the analysis (FIES does not use an $_2$ -cell). + The FIES bisector data are listed in and shown as a function of orbital phase in refbvs2.., The FIES bisector data are listed in \\ref{bisector} and shown as a function of orbital phase in \\ref{bvs2}. + The average uncertainty of the FIES bisector measurements is 13.8+2.31m ! and their total scatter is 12.5 |., The average uncertainty of the FIES bisector measurements is $13.8\pm2.3$ $^{-1}$ and their total scatter is $12.5$ $^{-1}$. + They appear to be constant within the measurement uncertainties., They appear to be constant within the measurement uncertainties. + We determined stellar parameters using the local thermodynamic equilibrium (LTE) line analvsis and spectral svnthesis code (Sneden 1973). together with a grid of ήπιο (1993) ATLASS mocdel atmospheres.," We determined stellar parameters using the local thermodynamic equilibrium (LTE) line analysis and spectral synthesis code (Sneden 1973), together with a grid of Kurucz (1993) ATLAS9 model atmospheres." + The method used is virtually identical to that described in Brugamver et ((2011)., The method used is virtually identical to that described in Brugamyer et (2011). + To check (his method. we first measured (he equivalent widths of a carefullv selected list of 48 neutral iron lines ancl 11 sinelyv-ionizecl iron lines in a spectrum of (he clayGime sky. taken using (he same instrumental setup and configuration as (hat used for ]xepler-15.," To check this method, we first measured the equivalent widths of a carefully selected list of 48 neutral iron lines and 11 singly-ionized iron lines in a spectrum of the daytime sky, taken using the same instrumental setup and configuration as that used for Kepler-15." + MOOG [orce-fits abundances to match (hese measured equivalent widths. using declared atomic line parameters.," MOOG force-fits abundances to match these measured equivalent widths, using declared atomic line parameters." + By assuming excitation equilibrium. we constrained the stellar temperature by eliminating anv trends will excitation potential: assuming ionization equilibrium. we constrained the stellar surface eravily by forcing the derived iron abundance using neutral lines to match that of singlv-ionized lines.," By assuming excitation equilibrium, we constrained the stellar temperature by eliminating any trends with excitation potential; assuming ionization equilibrium, we constrained the stellar surface gravity by forcing the derived iron abundance using neutral lines to match that of singly-ionized lines." + The microturbulent velocity was constrained bv eliminating any trend with reduced equivalent width (2EW/A)., The microturbulent velocity was constrained by eliminating any trend with reduced equivalent width $\lambda$ ). + Our derived stellar parameters for the Sun (using our cayvGme skv spectrum) are as lollows: Tur 5755+ TOKK. log ο = 448£0.09 dex. Vmie = 1.07£0.06 |. and log (Fe) = -IVTwn3c0.05 dex.," Our derived stellar parameters for the Sun (using our daytime sky spectrum) are as follows: $_{\rm eff}$ = $5755 \pm 70$ K, log g = $4.48 \pm 0.09$ dex, Vmic = $1.07 \pm 0.06$ $^{-1}$, and log (Fe) = $7.53 \pm 0.05$ dex." +timing analysis using the LAT software. and the different tests used to validate this process.,"timing analysis using the LAT software, and the different tests used to validate this process." + Topocentric photon arrival times recorded at the observatory at finite frequency have to be transfered to solar system baryeenter (SSB) times at infinite frequency. mainly by correcting times for the motion of the earth and the observatory in the solar system frame.," Topocentric photon arrival times recorded at the observatory at finite frequency have to be transfered to solar system barycenter (SSB) times at infinite frequency, mainly by correcting times for the motion of the earth and the observatory in the solar system frame." + Then one folds the barycenter times. using the truncated Taylor series expansion for P(r): where Το is the reference epoch of the pulsar ephemeris. fiis the frequency derivative of order /. and Dp ts the absolute phase. an arbitrary pulsar phase at t=Το. We have tested both and tools.," Then one folds the barycenter times, using the truncated Taylor series expansion for $\Phi(t)$: where $T_0$ is the reference epoch of the pulsar ephemeris, $f_i$ is the frequency derivative of order $i$, and $\Phi _0$ is the absolute phase, an arbitrary pulsar phase at $t = T_0$ We have tested both and tools." + The procedure ts: To test the barycenter software alone. we have simulated arrival times at Nangaay observatory and compared LAT barycenter software with andTEMPO?2.," The procedure is: To test the barycenter software alone, we have simulated arrival times at Nançaay observatory and compared LAT barycenter software with and." +. Some time and coordinate definition differences. exist between these different codes., Some time and coordinate definition differences exist between these different codes. + Most pulsar timing solutions have been published using the JPL DE200 planetary ephemerides (?).., Most pulsar timing solutions have been published using the JPL DE200 planetary ephemerides \citep{ST90}. +" forms barycentric times in ""Barycentrie Dynamic Time"" (TDB).", forms barycentric times in “Barycentric Dynamic Time” (TDB). +" uses the JPL DE405 (?) solar system ephemerides and computes baryeentric time in. ""Barycentrie. Coordinate Time"". (TCB) units. taking into account the time dilation results from ?.."," uses the JPL DE405 \citep{ST98} solar system ephemerides and computes barycentric time in “Barycentric Coordinate Time” (TCB) units, taking into account the time dilation results from \citet{IF99}." + The LAT barycenter tool handles both the DE200 ephemerides and the recommended DE405 model. also forming TDB times.," The LAT barycenter tool handles both the DE200 ephemerides and the recommended DE405 model, also forming TDB times." +" The relation between TDB and TCB times is given by: where Ly=1.550519767x1075+2107 and (date — 1977 January 1. 00:00) TAI x86400 s. TAI times refer to ""International Atomic Time""."," The relation between TDB and TCB times is given by: where $ L_B = 1.550519767 \times 10^{-8} \pm 2 \times 10^{-17} $ and $ \Delta T = ($ date $-$ 1977 January 1, 00:00) TAI $ \times 86400$ s. TAI times refer to “International Atomic Time”." + has a emulation mode. settingthe barycentric time to TDB.)," has a emulation mode, settingthe barycentric time to TDB.)" + More details on time-coordinate definitions can be found in 2.. ?. and 9," More details on time-coordinate definitions can be found in \citet{AN99}, \citet{RI01} and \citet{MP04}." + In the simulation. 10000 arrival times are recorded on the ground. beginning on MJD 54100 (arbitrary). with a constant step size (no assumption of periodic emission is made). over I year.," In the simulation, $10000$ arrival times are recorded on the ground, beginning on MJD 54100 (arbitrary), with a constant step size (no assumption of periodic emission is made), over 1 year." + Nangaay times are expressed in Modified Julian Days (MJD) UTC. at finite frequency.," Nançaay times are expressed in Modified Julian Days (MJD) UTC, at finite frequency." + They first have to be moved to the LAT time format. at infinite frequency.," They first have to be moved to the LAT time format, at infinite frequency." +" The dispersion delay in the propagation of a signal at a frequency at the solar system barycenter fs5, through the interstellar medium is the following: where K22.410x107+ MHz7? em™ pe s! is the (seee.g.2?) and DM is the dispersion measure.", The dispersion delay in the propagation of a signal at a frequency at the solar system barycenter $f_{SSB}$ through the interstellar medium is the following: where $K \equiv 2.410 \times 10^{-4}$ $^{-2}$ $^{-3}$ pc $^{-1}$ is the \citep[see e.g.][]{MT77} and $DM$ is the dispersion measure. + Note that the frequency at the barycenter fssp 1s different from the frequency at the observatory. due to the Doppler shift resulting from the motion of the observatory with respect to the pulsar (?)..," Note that the frequency at the barycenter $f_{SSB}$ is different from the frequency at the observatory, due to the Doppler shift resulting from the motion of the observatory with respect to the pulsar \citep{ED06}." + Higher order relativistic corrections are neglected here., Higher order relativistic corrections are neglected here. + The simulated values for the pulsar position at J2000 epoch and dispersion measure are (4.6)=(20.757.45?). and DM=0 cm pe.," The simulated values for the pulsar position at J2000 epoch and dispersion measure are $(\alpha,\delta) = (20.75^{\circ},45^{\circ})$, and $DM = 0$ $^{-3}$ pc." + The position of the radio telescope with respect to the solar system barycenter for each time of arrival was calculated using the DE200 model in the comparison. and using the DE405 model with in TDB mode for the comparison.," The position of the radio telescope with respect to the solar system barycenter for each time of arrival was calculated using the DE200 model in the comparison, and using the DE405 model with in TDB mode for the comparison." + The topocentric times are then transfered to the SSB., The topocentric times are then transfered to the SSB. + The resulting differences as a function of time are shown in Figure 3.., The resulting differences as a function of time are shown in Figure \ref{comps_fig}. + In both cases. time differences are below 0.7 ys. better than the instrumental precision.," In both cases, time differences are below 0.7 $\mu$ s, better than the instrumental precision." + We conclude that there is agreement between the LAT barycenter code and the other standard tools., We conclude that there is agreement between the LAT barycenter code and the other standard tools. + Giant pulses are known only from a handful of young and millisecond pulsars. and occupy very small windows of pulsar phase (seee.g. 22)..," Giant pulses are known only from a handful of young and millisecond pulsars, and occupy very small windows of pulsar phase \citep[see e.g.][]{JR04,KNI06}. ." + Times of arrival for 3498 main component, Times of arrival for 3498 main component +Tu the spirit of making as a direct comparison as possibl with observations. we shows the σπανο distributio- of the observed (steps) and predicted (curves) GRD rates. normalized to the total uuuber of bursts between 2=0 and zo= Lin Figure 3. following Iistler (2007).,"In the spirit of making as a direct comparison as possible with observations, we shows the cumulative distribution of the observed (steps) and predicted (curves) GRB rates, normalized to the total number of bursts between $z=0$ and $z=4$ in Figure 3, following Kistler (2007)." + Tere. in order to make a direct comparison with Ixistler (2007) and to remove uncertaimties in the overall star ornmation rate in our saüulation. we normalize the star ormation rate of the al-ealaxy sample in our simulation o the analytic values of Hopkius Beacom (2006). as did EKistler (2007).," Here, in order to make a direct comparison with Kistler (2007) and to remove uncertainties in the overall star formation rate in our simulation, we normalize the star formation rate of the all-galaxy sample in our simulation to the analytic values of Hopkins Beacom (2006), as did Kistler (2007)." + Then. the star formation rates or the other two (lower metallicity) samples are adjusted uultiplicatively by the same factor.," Then, the star formation rates for the other two (lower metallicity) samples are adjusted multiplicatively by the same factor." + It is seen that. if one siuplv assumes that the total CRB rate is proportional o the star formation rate of metallicity less than 0.LZ... he observed evolution of CRB rate frou 2=0 to:=| is reproduced to a hieh degree. clearly visible in the good agreement between the solid curve aud the step curve in Figure 3.," It is seen that, if one simply assumes that the total GRB rate is proportional to the star formation rate of metallicity less than $0.1\zsun$, the observed evolution of GRB rate from $z=0$ to $z=4$ is reproduced to a high degree, clearly visible in the good agreement between the solid curve and the step curve in Figure 3." + Taken all the observational facts together along with our theoretical results. a broadly cousisteut picture appears to emieree: Evideuth. the observed evolution of GRB vate from 2.=0 to : locui be explained.0.," Taken all the observational facts together along with our theoretical results, a broadly consistent picture appears to emerge: Evidently, the observed evolution of GRB rate from $z=0$ to $z=4$ can be explained,." +1Z.. Iucludiug higher metallicity stars would produce GRD rate evolution frou +=0 to:=1 that is inconsistent with observations., Including higher metallicity stars would produce GRB rate evolution from $z=0$ to $z=4$ that is inconsistent with observations. + Nevertheless. this overall picture would also be consistent with a theoretical preference or possibly requirement of low metallicity for GRB progenitors iu the context of “collapsar” models (AlacFavden Woosley 1999: Woosley Ποσο 2006).," Nevertheless, this overall picture would also be consistent with a theoretical preference or possibly requirement of low metallicity for GRB progenitors in the context of “collapsar"" models (MacFayden Woosley 1999; Woosley Heger 2006)." + What is implicitly assumed is that the stellar initial mass fuuction (IME) las remained the same over the redshift range considered., What is implicitly assumed is that the stellar initial mass function (IMF) has remained the same over the redshift range considered. + Iu other words. whatever mictallicity dependence of CRB rate may have. this dependence is assuined not to evolve with redshift.," In other words, whatever metallicity dependence of GRB rate may have, this dependence is assumed not to evolve with redshift." + One should note that it is not fully known observationally or understood theoretically how the IAIF evolves with time., One should note that it is not fully known observationally or understood theoretically how the IMF evolves with time. + Therefore. additional possible evolutionary effect of IMP would add another laver of complexity to this issue.," Therefore, additional possible evolutionary effect of IMF would add another layer of complexity to this issue." + It is often thought that lower metallicity cuvirommeut uuelt favor formation of more massive stars., It is often thought that lower metallicity environment might favor formation of more massive stars. + If CRB progenitors are massive stars. this would then trauslate to the expectation that additional effect duc to an evolving IMP may further steepen the evolution of the GRD rate with redshift.," If GRB progenitors are massive stars, this would then translate to the expectation that additional effect due to an evolving IMF may further steepen the evolution of the GRB rate with redshift." + This. however. is not required or borue out in our analvsis," This, however, is not required or borne out in our analysis." + Our results thus imply that the evolution of IME from +=E to 20. if au. appears to be weak.," Our results thus imply that the evolution of IMF from $z=4$ to $z=0$, if any, appears to be weak." +" If we place this result iu a larger context of star formation over the eutire cosnüuc historv. one might come to the couclusion that. while there may be a cramatic transition of IMF from Population III metal-free stars ποια, M. 2002: Abel. Bryan Novia 2002: Dronuu. Coppi. Larson 2002) to Population II stars at some hieh redshift (6.9.. Con 2003: Trac Cen 2007). further evolution of IME at lower redshift may be modest. in the sense that the mass fraction of high mass stars that are prestunably CRB progenitors of the total stellar maass remains relatively constant."," If we place this result in a larger context of star formation over the entire cosmic history, one might come to the conclusion that, while there may be a dramatic transition of IMF from Population III metal-free stars Umemura, M. 2002; Abel, Bryan Norman 2002; Bromm, Coppi, Larson 2002) to Population II stars at some high redshift (e.g., Cen 2003; Trac Cen 2007), further evolution of IMF at lower redshift may be modest, in the sense that the mass fraction of high mass stars that are presumably GRB progenitors of the total stellar mass remains relatively constant." + We utilize a simulation of galaxw formation in the standard cosmological model that has Όσοι shown to produce results consistent with extant observations of ealaxy formation (c.g.. Nagamine 2006) to shed light ou the relation between CRB rate aud star formation rate.," We utilize a simulation of galaxy formation in the standard cosmological model that has been shown to produce results consistent with extant observations of galaxy formation (e.g., Nagamine 2006) to shed light on the relation between GRB rate and star formation rate." + We fud that a consistent picture for Counnmna-Bax Bursts and star formation that is in broad agreecimeut with observations would emerge. Because of the merease of ietallicitv with cosmic time. CRB rate consequently evolves iore stronely with redshift than the overall star formation rate.," We find that a consistent picture for Gamma-Ray Bursts and star formation that is in broad agreement with observations would emerge, Because of the increase of metallicity with cosmic time, GRB rate consequently evolves more strongly with redshift than the overall star formation rate." + We find that the observed evolution of GRB rate from 2=0 to += can be explained... whereas au inclusion of stars with metallicity as high as 0.3Z.. vields CRB rate evolution from 2—0 to += Liucousisteut with observations.," We find that the observed evolution of GRB rate from $z=0$ to $z=4$ can be explained, whereas an inclusion of stars with metallicity as high as $0.3\zsun$ yields GRB rate evolution from $z=0$ to $z=4$ inconsistent with observations." + Therefore. we reach the couchision that CRBs may not be a good tracer of cosmic star formation. especially over a long timeline.," Therefore, we reach the conclusion that GRBs may not be a good tracer of cosmic star formation, especially over a long timeline." + As a result. a simple inference of star formation rate or its derived quantities such as the ionizing photon production rate at high redshifts. based ou the observed GRD rate. should be dome with caution aud may require careful calibrations.," As a result, a simple inference of star formation rate or its derived quantities such as the ionizing photon production rate at high redshifts, based on the observed GRB rate, should be done with caution and may require careful calibrations." +"kinetic energy, K.E.—IPwv-dV, is converted to thermal energy.","kinetic energy, $\mathrm{K.E.}=\onehalf \rho_w v_s^2 dV$, is converted to thermal energy." +" Putting this in terms of the mass-loss rate, M, we can express the CSM density as and we can calculate the energy available to be converted to luminosity, L, as The luminosity dependence on R, drops out and we have A key missing ingredient is a more detailed modeling of the kinetic energy tooptical luminosity conversion term, α(λ,t)."," Putting this in terms of the mass-loss rate, $\dot{M}$, we can express the CSM density as and we can calculate the energy available to be converted to luminosity, $L$, as The luminosity dependence on $R_s$ drops out and we have A key missing ingredient is a more detailed modeling of the kinetic energy tooptical luminosity conversion term, $\alpha(\lambda, t)$." +" We note that the available kinetic energy is on the order of 1.6x10“ erg s! for M=10-°Mz yr-!, v,=104 km s~!, and v,=10 km s-!."," We note that the available kinetic energy is on the order of $1.6\times +10^{44}$ erg $^{-1}$ for $\dot{M} = 10^{-5}~M_\sun$ $^{-1}$, $v_s = +10^4$ km $^{-1}$, and $v_w = 10$ km $^{-1}$." +" This implies a conversion efficiency from shock interaction Κ.Ε. to luminosity of50%,, given the luminosity, 1.6x1074 erg s, of SN 2002ic and the typical luminosity of a SN Ia near maximum of 0.8x104 erg s~t."," This implies a conversion efficiency from shock interaction K.E. to luminosity of, given the luminosity, $1.6\times10^{44}$ erg $^{-1}$ , of SN 2002ic and the typical luminosity of a SN Ia near maximum of $0.8\times10^{44}$ erg $^{-1}$." +" Assuming this constant conversion produces reasonable agreement with the data, so we proceed with this simple assumption."," Assuming this constant conversion produces reasonable agreement with the data, so we proceed with this simple assumption." + Using Eq., Using Eq. +" 4 to give the time dependence of v,, we obtain the time dependence of the luminosity, which can be expressed in magnitude units as where C is a constant that incorporates M, PSN, Vw, , and the appropriate units for those parameters."," \ref{eq:vs_time} to give the time dependence of $v_s$, we obtain the time dependence of the luminosity, which can be expressed in magnitude units as where $C$ is a constant that incorporates $\dot{M}$, $\rho_{\mathrm{SN}}$, $v_w$, $n$, and the appropriate units for those parameters." +" The difference in magnitude between two times, t, and t», then becomes We obtain a date of B-maximum for the supernova component of 2452606 JD from our SN curve analysis."," The difference in magnitude between two times, $t_1$ and $t_2$, then becomes We obtain a date of B-maximum for the supernova component of $2452606$ JD from our SN Ia-light curve analysis." +" Our fit yields an a=0.16—n8.5 for any fixed M and v,,.", Our fit yields an $\alpha=0.16 \Rightarrow n = 8.5$ for any fixed $\dot{M}$ and $v_w$ . + This n is squarely in the range of values suggested byChevalier&Fransson(1994) as being typical for SN ejecta., This $n$ is squarely in the range of values suggested by\citet{chevalier94} as being typical for SN ejecta. +" While Chevalier&Fransson(1994) is framed in the context of SNe II, their formalism"," While \citet{chevalier94} is framed in the context of SNe II, their formalism" +The final velocity resolution is 0.161.,The final velocity resolution is 0.16. +.. The final ruis noise level in the absorption spectra is 5&10.| over ο channels (or 3410.Lover channel)., The final rms noise level in the absorption spectra is $5\times10^{-4}$ over 0.5 channels (or $3\times10^{-4}$ over 1 channels). + After the data reduction. for both sources. 3€286 and SC287. we have au II absorption (ο55) aud aud an II Cluission spectrum (Zp(e): note that this is the enission spectrum that would be observed in the absence of the continuuu source).," After the data reduction, for both sources, 3C286 and 3C287, we have an HI absorption $e^{-\tau(v)}$ ) and and an HI emission spectrum $T_{\rm B}(v)$; note that this is the emission spectrum that would be observed in the absence of the continuum source)." + We next ciploved the techuique bv Ieiles&Trolaud(2003a) to estimate the spin teiiperature for the CNM clouds., We next employed the technique by \cite{Heiles03a} to estimate the spin temperature for the CNM clouds. + This technique assumes that the CNAL coutributes to both ΤΗ absorption and enmuüssiou spectra. while the warm neutral medium (WNAL) contributes only to the II enuüsson spectimm.," This technique assumes that the CNM contributes to both HI absorption and emission spectra, while the warm neutral medium (WNM) contributes only to the HI emission spectrum." + The technique is based ou the Gaussian decomposition of both absorption aud emission spectra. and it takes into account the fact that a certain raction of the WNAL eas may be located in frout of the CNAL clouds resulting iu only a portion of the WNM cine absorbed by the CNAL," The technique is based on the Gaussian decomposition of both absorption and emission spectra, and it takes into account the fact that a certain fraction of the WNM gas may be located in front of the CNM clouds resulting in only a portion of the WNM being absorbed by the CNM." + We note though that this echuique may not be applicable for the case when CNM occupies a solid angle significautly sinaller than that of the Arecibo telescope beam (FWIIN23.5 arcmin). as is most ikelv the case with some CNAL compouents we find im Section L3.," We note though that this technique may not be applicable for the case when CNM occupies a solid angle significantly smaller than that of the Arecibo telescope beam (FWHM=3.5 arcmin), as is most likely the case with some CNM components we find in Section 4.3." + In this case the observed absorption spectrin nav not correspond to the absorption that would be see- youn all eas included in the euissiou spectrum. aud hence a direct comparison of the TT absorption and enüssion spectra nav not be a valid approach.," In this case the observed absorption spectrum may not correspond to the absorption that would be seen from all gas included in the emission spectrum, and hence a direct comparison of the HI absorption and emission spectra may not be a valid approach." + For those very siuall clouds that do not fill the beam our emission iutenusitv 1ρα nuderestimated. resulting in the derived spin tempcratur being too low.," For those very small clouds that do not fill the beam our emission intensity is underestimated, resulting in the derived spin temperature being too low." + Thus. we should regard our derived spi- temperatures as lower limits.," Thus, we should regard our derived spin temperatures as lower limits." + Another issue rcearding this technique is the use of Caussiau functions to represcut the CNM absorption profiles., Another issue regarding this technique is the use of Gaussian functions to represent the CNM absorption profiles. + IHTeiles&Trolaud.(20034) discussed pros and cons of this approach in some detail., \cite{Heiles03a} discussed pros and cons of this approach in some detail. + Iu Fig., In Fig. + d we show IIT e1uissiou aud absorption spectra for 3C286 (on the loft side) aud 3C287 (on the right side)., \ref{f:3c286} we show HI emission and absorption spectra for 3C286 (on the left side) and 3C287 (on the right side). + Three panels are shown for 3€286: (Top:) the TT enuüson spectrüni (a main beam efficiency of κ. was used to convert this spectrum from the antenna telmperature units to the brightuess teniperature scale) and separate contributions frou the CNAL aud WNAL to the III brightuess temperature are shown with cliffercut lines: the final (simultancous) fit to the spectrum is also overlaid. (AMiddle:), Three panels are shown for 3C286: ) the HI emission spectrum (a main beam efficiency of 0.9 was used to convert this spectrum from the antenna temperature units to the brightness temperature scale) and separate contributions from the CNM and WNM to the HI brightness temperature are shown with different lines; the final (simultaneous) fit to the spectrum is also overlaid. ) + the II absorption spectrum with fitted individual Gaussian componcuts., the HI absorption spectrum with fitted individual Gaussian components. + We detect three CNM conrponeuts towards 3C286. (BDoftom:), We detect three CNM components towards 3C286. ) + the residuals of the absorption προςπια for 3C286 after the fitting process., the residuals of the absorption spectrum for 3C286 after the fitting process. +" These ranucdomu-looking residuals demonstrate that the fit is perfect at the present level of signal/noise, aud that the Gaussian represeuntatiou of CNAL comiponeuts is valid iu this case."," These random-looking residuals demonstrate that the fit is perfect at the present level of signal/noise, and that the Gaussian representation of CNM components is valid in this case." + In the case of 3C287 we have ouly a mareinal detection at this stage., In the case of 3C287 we have only a marginal detection at this stage. + The UL absorption spectrum shows three distinct features. in good agreement with BINOS.," The HI absorption spectrum shows three distinct features, in good agreement with BK05." + We have fitted them with three Caussian functious centered at LSR velocities Bas. 123. and 7.1 (Table 1).," We have fitted them with three Gaussian functions centered at LSR velocities $-28.8$, $-14.3$, and $-7.4$ (Table 1)." + The spin temperature is well-coustrained at the 1054 level for the first two Catssian coniponenuts., The spin temperature is well-constrained at the $10\%$ level for the first two Gaussian components. + The contribution to the III cnussion profile from the last CNM component appears to be very πα]. resulting im its spin temperature not beime well coustrained (60% level).," The contribution to the HI emission profile from the last CNM component appears to be very small, resulting in its spin temperature not being well constrained $60\%$ level)." + The resultant HI coluun densities are directly proportional to these temperatures and are eiven in Table 1 (column 7)., The resultant HI column densities are directly proportional to these temperatures and are given in Table 1 (column 7). + They are all very low. 5{\sigma}$ significance. + The A2515 detection is within the forest. aud caunot be coufirmed by other transitions.," The $\lambda$ 2515 detection is within the forest, and cannot be confirmed by other transitions." + However. we expect that it is valid because of the precise aligumeut with the ο-- 00 cloud.," However, we expect that it is valid because of the precise alignment with the $v$ =-69 cloud." + We thus conclude that there is more than sufficient evidence that absorption in neutral species is detected. makine Cloud 1 in this svstem unique among other weak systems (Naravananetal.2008).," We thus conclude that there is more than sufficient evidence that absorption in neutral species is detected, making Cloud 1 in this system unique among other weak systems \citep{Anand08}." +. The ratio of the A 2803 to α 2796 equivalent width iu Cloud 1 of the VLT spectro (Fig. 1)), The ratio of the $\lambda$ 2803 to $\lambda$ 2796 equivalent width in Cloud 1 of the VLT spectrum (Fig. \ref{fig:clouds_labeled}) ) + is not 0.5(LF as expected (Naravanuau 2008). and as seen idu Clouds 2-[. but ijs (SL: the weaker member is cousiderably stronger than would be expected.," is not $0.5-0.7$ as expected \citep{Anand08}, and as seen in Clouds 2-4, but is $0.84$; the weaker member is considerably stronger than would be expected." + This ratio implies either unresolved saturation of the line profile. or partial coverius of the quasar broad emission line region (DELR).," This ratio implies either unresolved saturation of the line profile, or partial covering of the quasar broad emission line region (BELR)." + If the profile were unresolved and saturated. profile fits to2803 would severcly underestimate the cohuun density and overestimate the Doppler parameters of to the lines.," If the profile were unresolved and saturated, profile fits to would severely underestimate the column density and overestimate the Doppler parameters of fits to the lines." + We consider this possibility iu defining araneefits of models to be considered., We consider this possibility in defining a range of models to be considered. + We initially perform Voiet profile fitting on the2803 using MINFEFIT (Churchilletal. 2003)., We initially perform Voigt profile fitting on the using MINFIT \citep{Churchill03}. +. We choose to optimize ouMet (to require Cloudy models to reproduce exactly the observed value) because it is the only ion detected in all four clouds. aud is the strongest ion detected for this 2=0.1521 absorber outside of the forest.," We choose to optimize on (to require Cloudy models to reproduce exactly the observed value) because it is the only ion detected in all four clouds, and is the strongest ion detected for this $z=0.4524$ absorber outside of the forest." + The Doppler parameters (5) and column densitics CV) eiven from the fit for Clouds 2-| ave in Table 2.. along with the redshifts of each cloud.," The Doppler parameters $b$ ) and column densities $N$ ) given from the fit for Clouds 2-4 are in Table \ref{tab:Nb}, along with the redshifts of each cloud." + The profile for Cloud 2 is asvnuunetric. aud we find that a two colmponcnt fit provides a significautly better fit than does oue component.," The profile for Cloud 2 is asymmetric, and we find that a two component fit provides a significantly better fit than does one component." + These components are denoted as 2a and 2b in Table 2.., These components are denoted as 2a and 2b in Table \ref{tab:Nb}. +" We note that the resolution of the spectrum. ~6.6ο, is ereater than the value of b for our out of the five Voiet profile components. implying hat the clouds may not be fully resolved."," We note that the resolution of the spectrum, $\sim 6.6$, is greater than the value of $b$ for four out of the five Voigt profile components, implying that the clouds may not be fully resolved." + The best ft to the Cloud Lo VLT spectra is. provided bv a model with cobhuuu deusity QOeN(Meu)=12.4fem7) and Doppler parameter h3.[o however this fit ovorproduces A2796 and uniderproduces A2803. as expected w the difference iu WOMgliIN2796) aud the ratio of the oscillator streneths of the two πωtransitions.," The best fit to the Cloud 1 VLT spectrum is provided by a model with column density $\log N({\MgII}) = 12.1~[{\rm cm}^{-2}]$ and Doppler parameter $b=3.1 $, however this fit overproduces $\lambda$ 2796 and underproduces $\lambda$ 2803, as expected by the difference in $\frac{W_r({\MgII}\lambda + 2796)}{W_r({\MgII}\lambda 2803)}$ and the ratio of the oscillator strengths of the two transitions." + Fits to the other clouds were adequate., Fits to the other clouds were adequate. + Because of the likelihood of unresolved saturation. we mnerease No until the ratio of equivalent widths of the svuthetic profile matches that of the observed profile.," Because of the likelihood of unresolved saturation, we increase $N$ until the ratio of equivalent widths of the synthetic profile matches that of the observed profile." +" We also consider stualler Doppler parameters iu our modeling process, and for these values we adjust Vo accordingly."," We also consider smaller Doppler parameters in our modeling process, and for these values we adjust $N$ accordingly." + We also consider the possibility. of partial coverimg of the BELR of TE0001-2310 to explain the observed equivalent widths., We also consider the possibility of partial covering of the BELR of HE0001-2340 to explain the observed equivalent widths. + The size of the broad cussion line region of IIEO001-2310. camnot be calculated directly. as the spectruiu is uot ux calibrated.," The size of the broad emission line region of HE0001-2340 cannot be calculated directly, as the spectrum is not flux calibrated." +" However, via comparison to a quasar of similarredshift and magnitude with a flux calibrated spectra. we may approximate the BELR size."," However, via comparison to a quasar of similarredshift and magnitude with a flux calibrated spectrum, we may approximate the BELR size." + With :=2.28 aud V= IIEEX0001-23LO may be compared to 85 0836|71 with 2=2.172 aud V=16.5.," With $z=2.28$ and $V=16.7$ , HE0001-2340 may be compared to S5 0836+71 with $z=2.172$ and $V=16.5$." +" Deutzetal.(2007). gives the following relation for BELR size: With logAL,~17. we estimate that the BELR size of IIEOQ001-2310 is ~1.0 pe."," \citet{Benz07} gives the following relation for BELR size: With $\log \lambda L_{\lambda} \sim 47$, we estimate that the BELR size of HE0001-2340 is $\sim 1.0$ pc." + Therefore. partial coverage of the BELR requires a very small cloud size.," Therefore, partial coverage of the BELR requires a very small cloud size." + We explore this possibility as an alternative to unresolved saturation. and perform VP fitting to the doublet for Clou L. using a modified version of MINFIT (Churchilletal.2003) in which the coveringfactor. C'(Mgli). is allowed to vary along with NV aud b.," We explore this possibility as an alternative to unresolved saturation, and perform VP fitting to the doublet for Cloud 1, using a modified version of MINFIT \citep{Churchill03} in which the coveringfactor, $C_f({\MgII})$, is allowed to vary along with $N$ and $b$." + A covering factor of CetMg)=0.60+0.10 best fits the profile. as determine by the 4? minimization technique described in Gaugulyetal.(1999).. and applied to a large doublet sample iu Misawaetal.(2007).," A covering factor of $C_f({\MgII})=0.60\pm 0.10$ best fits the profile, as determined by the $\chi^2$ minimization technique described in \citet{Ganguly99}, and applied to a large doublet sample in \citet{Misawa07}." +". The INN(Mgir) aud b(Mg) values for this C, are 10223 and 3.1+. respectively."," The $N({\MgII})$ and $b({\rm Mg})$ values for this $C_f$ are $10^{12.1}$ and 3.1, respectively." + Since we would not expect to find evidence for partial covering in au absorber that is uot intrinsic fo a quasar. we examine how significant an improvement C'a(Mg)~0.6 provides as compared to other possible values of the covering factor.," Since we would not expect to find evidence for partial covering in an absorber that is not intrinsic to a quasar, we examine how significant an improvement $C_f({\MgII}) \sim 0.6$ provides as compared to other possible values of the covering factor." +" We force C, to have various other values and in each case find the best No aud b aud compute the (P comparing the best model to the data.", We force $C_f$ to have various other values and in each case find the best $N$ and $b$ and compute the $\chi^2$ comparing the best model to the data. + Figure 3. shows hat a clear mininuunm iu u occurs at οκο)~0.6., Figure \ref{fig:cf} shows that a clear minimum in $\chi^2$ occurs at $C_f({\MgII}) \sim 0.6$. +" The C, measured from VP fitting is an ""effective covering factor”. represcuting the absorption of the total Hux at that waveleugth. which is a combination of fiux roni the quasar continuum source aud BELR (CGaueulyetal.1999)."," The $C_f$ measured from VP fitting is an ""effective covering factor"", representing the absorption of the total flux at that wavelength, which is a combination of flux from the quasar continuum source and BELR \citep{Ganguly99}." +. The different transitions for the iterveniug >=(0.1521 system fall at different positions relative o the quasar enuiüssion lines. and will therefore absorb different relative fractious of coutimmun aud BELR &ux.," The different transitions for the intervening $z=0.4524$ system fall at different positions relative to the quasar emission lines, and will therefore absorb different relative fractions of continuum and BELR flux." +" Iu geueral. C,CONI where C. djs the covering ‘factor of the coutimmun. C4, is the covering factor of tle BELR. aud Cy is the total covering factor (Ganguly 1999)."," In general, $C_f = \frac{C_c+{\rm W}C_{elr}}{1+{\rm W}}$, where $C_c$ is the covering factor of the continuum, $C_{elr}$ is the covering factor of the BELR, and $C_f$ is the total covering factor \citep{Ganguly99}." +. The value of W. the ratio of the broad eimissiou- flux to the contimmun flux at the waveleneth of he narrow mtervenimg absorption line (δνΕν} cau be determined for each transition usine a low resolution spectrum (Tytleretal.2001).," The value of W, the ratio of the broad emission-line flux to the continuum flux at the wavelength of the narrow intervening absorption line $F_{elr}/F_c$ ), can be determined for each transition using a low resolution spectrum \citep{Tytler04}." + However. in order to calculate the effective covering factor. Cy. we must make an asstuuption about the relative covering factors of the continu aud BELR.," However, in order to calculate the effective covering factor, $C_f$, we must make an assumption about the relative covering factors of the continuum and BELR." + For Meu. the value Cy=0.6 can correspond to a range of possible C. Cj. pairs.," For , the value $C_f = 0.6$ can correspond to a range of possible $C_c$, $C_{elr}$ pairs." + However. we know hat €. cannot be verv snall as we see detectious of inv transitions that are not superimposed on au Cluission line.," However, we know that $C_c$ cannot be very small, as we see detections of many transitions that are not superimposed on an emission line." + Since the σολμαι source is likely to ο considerably simaller than the BELR. it is most straightforward to assuue that itis fully covered aud hat the BELR is partially covered.," Since the continuum source is likely to be considerably smaller than the BELR, it is most straightforward to assume that itis fully covered and that the BELR is partially covered." +" For the W value ucasured for AV= 1.0). aud C.=1. we then Gud €,=0.2."," For the W value measured for ${\rm W}=1.0$ ), and $C_c=1$, we then find $C_{elr}=0.2$." +" Cj, values should be the same foTR all transitions.if their absorptionarises from the sam cloud."," $C_{elr}$ values should be the same for all transitions,if their absorptionarises from the same cloud." +" With this asstuuption. using the W values of each ranstiou. we can compte the effective covering factorpA as C, LEN. "," With this assumption, using the W values of each transition, we can compute the effective covering factors as $C_f = \frac{1+0.2{\rm W}}{1+{\rm W}}$ ." +"Table 3. lists the C, values for all ransitious detected from Cloud 1.", Table \ref{tab:ew2} lists the $C_{f}$ values for all transitions detected from Cloud 1. +" Maux of the detected jeutral transitions have valuesthat are close to 1. rendering their absorption C,stronger relative to the Met. which only partially absorbs a siguificaut fraction of the incident flux due to its position ou a broad emission linc."," Many of the detected neutral transitions have $C_{f}$ valuesthat are close to $1$ , rendering their absorption stronger relative to the , which only partially absorbs a significant fraction of the incident flux due to its position on a broad emission line." +"Besides these basic capabilities for regular observing modes, there are a number of speciality modes, including: The WIDAR correlator is Canada’s contribution to the EVLA project, and was designed and built to meet or exceed the requirements of the EVLA by the HIA correlator group, located at DRAO near Penticton, BC, Canada.","Besides these basic capabilities for regular observing modes, there are a number of speciality modes, including: The WIDAR correlator is Canada's contribution to the EVLA project, and was designed and built to meet or exceed the requirements of the EVLA by the HIA correlator group, located at DRAO near Penticton, BC, Canada." +" A more thorough description of the EVLA's design, including that of its correlator, is found in Perleyetal. (2009)."," A more thorough description of the EVLA's design, including that of its correlator, is found in \cite{per09}." +. A compact summary of the expansion in capabilities of the EVLA in comparison to those of the VLA is provided in Table 2 The conversion of the VLA into the EVLA was scheduled to take more than a decade.," A compact summary of the expansion in capabilities of the EVLA in comparison to those of the VLA is provided in Table \ref{tab:EVLA} + The conversion of the VLA into the EVLA was scheduled to take more than a decade." + It was therefore considered vital to maintain operation as a productive scientific facility throughout the conversion process., It was therefore considered vital to maintain operation as a productive scientific facility throughout the conversion process. + This required designing in a backward compatibility between the newly-converted antennas and the original correlator., This required designing in a backward compatibility between the newly-converted antennas and the original correlator. +" This process has been very successful, enabling nearly seamless continuing observing, with the array only shut down for a single 7-week period between January and March 2010 in order to move hardware from the old VLA correlator to the WIDAR correlator upon the latter’s implementation."," This process has been very successful, enabling nearly seamless continuing observing, with the array only shut down for a single 7-week period between January and March 2010 in order to move hardware from the old VLA correlator to the WIDAR correlator upon the latter's implementation." + This has enabled the NRAO to offer steadily increasing scientific capabilities to the user community ahead of the completion of the construction project., This has enabled the NRAO to offer steadily increasing scientific capabilities to the user community ahead of the completion of the construction project. +" The growth in capabilities can be separated into two parts: that provided by the antennas, including the receivers and the data transmission system, and that provided by the correlator."," The growth in capabilities can be separated into two parts: that provided by the antennas, including the receivers and the data transmission system, and that provided by the correlator." + Figure 2 shows the current and anticipated availability of the eight receiver bands., Figure \ref{fig:RcvrAvail} shows the current and anticipated availability of the eight receiver bands. +" Full outfitting of four receiver bands are now complete — these are the 4 — 8 GHz band, and the three highest frequency bands, spanning 18 through 50 GHz."," Full outfitting of four receiver bands are now complete – these are the 4 – 8 GHz band, and the three highest frequency bands, spanning 18 through 50 GHz." +" A critical component, not illustrated in the figure, is the growth in data transmission capabilities."," A critical component, not illustrated in the figure, is the growth in data transmission capabilities." +" The current maximum total bandwidth which can be transferred from antenna to correlator is 4 GHz, available in two pairs of oppositely polarized signals of bandwidth 1 GHz each."," The current maximum total bandwidth which can be transferred from antenna to correlator is 4 GHz, available in two pairs of oppositely polarized signals of bandwidth 1 GHz each." + Implementation of the full 16 GHz capability will not be available for science observing until at least mid-2012., Implementation of the full 16 GHz capability will not be available for science observing until at least mid-2012. +"We will not study. the non generic case where {ΑΝ/xU, is an integer.",We will not study the non generic case where $HN^{}/ \pi \bar {U}_0$ is an integer. +" We introduce the subcritical modes corresponding to 1n, For the (n«n.) we prescribe the folowing boundary conditions: And [or the (n> n.) we prescribe a slightly different sel of boundary conditions: The well-posedness of the linearized svstem associated with has been studied in [?] (see also |?]))."," We introduce the subcritical modes corresponding to $1 \le n < n_c$, and the supercritical modes corresponding to $n > n_c$ For the $n < n_c$ ) we prescribe the following boundary conditions: And for the $n>n_c$ ) we prescribe a slightly different set of boundary conditions: The well-posedness of the linearized system associated with has been studied in \cite{RTT08} (see also \cite{RTT09}) )." + The boundary conditions are different from those proposed in |?) and [?].., The boundary conditions are different from those proposed in \cite{RTT08} and \cite{RTT09}. + We believe that the well-posecuess of the linearized svstem corresponding; to and supplemented with the foregoing boundary conditions can be established in the same way as in [?) and ολα this problem will be studied. elsewhere., We believe that the well-posedness of the linearized system corresponding to and supplemented with the foregoing boundary conditions can be established in the same way as in \cite{RTT08} and \cite{RTT09}; this problem will be studied elsewhere. + We remark here that there are several sets of boundary conditions which make the linearized svstem It is also a conjecture that the boundary conditions of [2] or ο) or the conditions are suitable for the nonlinear equations for a certain lime al least., We remark here that there are several sets of boundary conditions which make the linearized system It is also a conjecture that the boundary conditions of \cite{RTT08} or \cite{RTT09} or the conditions are suitable for the nonlinear equations for a certain time at least. +transfer rate play an important role. m. at least. some types of dwarf uova outbursts (Suneiς 1996: Lasota 1996: Canuizzo Wing 1998).,"transfer rate play an important role, in, at least, some types of dwarf nova outbursts (Smak 1996; Lasota 1996; Cannizzo King 1998)." + The DIM rexoduces rather well the basic properties of ‘typical’ dwarf uova outbursts (see ILuueury et al., The DIM reproduces rather well the basic properties of `typical' dwarf nova outbursts (see Hameury et al. + 1998 for the most recent version of he model)., 1998 for the most recent version of the model). +" When it comes o the description of the variety of outburst propertiss, however. the range of reCmrence times and the emission properties of dwarf 1rova cycles. the DIM is less successful."," When it comes to the description of the variety of outburst properties, however, the range of recurrence times and the emission properties of dwarf nova cycles, the DIM is less successful." + Very long recurrence times in WZ Sectv20 SVSTCLUS. are obtained ou vbyv: istudie either very low values of tje Viscosity parameter (Sunals 1998). or iuncr disc radii larger than tlicelite dwarf radius audinereased Lass rausfor diving the ottburst (Lasota et al.," Very long recurrence times in WZ Sge–type systems, are obtained only by assuming either very low values of the viscosity parameter (Smak 1998), or inner disc radii larger than the white dwarf radius and increased mass transfer during the outburst (Lasota et al." + 1995: Ibuueurv e al., 1995; Hameury et al. + 1997)., 1997). + Clearly. these problems are due. at least in part. ο our poor knowedge of the VISCOs processes operating mu accretio1 disces.," Clearly, these problems are due, at least in part, to our poor knowledge of the viscous processes operating in accretion discs." + Aditional difficulties apyear When one tric to obtain accretion disc spectra., Additional difficulties appear when one tries to obtain accretion disc spectra. +" Tn the sinplest case, it is assiued that each xine of an optically thick disc cuits like a lack body."," In the simplest case, it is assumed that each ring of an optically thick disc emits like a black body." + Another ayproach conists 1u usiug atinosphere models TOSrounding to the dise effective temperature a eravity at optica depth one., Another approach consists in using atmosphere models corresponding to the disc effective temperature and gravity at optical depth one. + s shown by Wade (1988) aud Shaviv Welrse (199]) such models provide i inadequate description of accretion disc specra., As shown by Wade (1988) and Shaviv Wehrse (1991) such models provide an inadequate description of accretion disc spectra. + Ii the case of optically imn disces. various approximate schemes have been used to describe continua vl line radiation (Williams 1980: Tvleuda 1981: Maius1 1987: Lin et al.," In the case of optically thin discs, various approximate schemes have been used to describe continuum and line radiation (Williams 1980; Tylenda 1981; Marsh 1987; Lin et al." + 1988: ineshiee Wood 1990. Duinont et al.," 1988; Mineshige Wood 1990, Dumont et al." + 1991: Williams 1991: Wood et al., 1991; Williams 1991; Wood et al. + 1992) mt these uodels are not self-consisteut: iu particular μον often require very uch 1) values of the viscosity parameter (see below)., 1992) but these models are not self-consistent; in particular they often require very high $>> 1$ ) values of the viscosity parameter (see below). + Quiesccut dwarf nova discs present a rather surprising puzzle. which results. xobablv. roni two weaknesses of accretion disc models: the ignorance of the mature of viscosity which drives accretion (see e.g. Camunic Moenou 1997) aud t1ο inadequate description of the disc emission.," Quiescent dwarf nova discs present a rather surprising puzzle, which results, probably, from two weaknesses of accretion disc models: the ignorance of the nature of viscosity which drives accretion (see e.g. Gammie Menou 1997) and the inadequate description of the disc emission." + These two features are not independent. sluce lie dise temperature straications depeud on the vertical cistrition of the xdscous heating.," These two features are not independent, since the disc temperature stratifications depend on the vertical distribution of the viscous heating." +" T disc iustabiitv model in its ""stadiC forma predicts an optically thick. quiescit accifion (isc.", The disc instability model in its `standard' form predicts an optically thick quiescent accretion disc. + In several cases. however. the observed. contiuuuuau radian of such diSC wowsupgeests rather an opically thin disc emission because of tlie rescence. of lie Bahuer jump in enission and. at lounger waveleneths. οi douπατος o» the Pascheu coutimtun (sec e.g. Wood et al.," In several cases, however, the observed continuum radiation of such discs suggests rather an optically thin disc emission because of the presence of the Balmer jump in emission and, at longer wavelengths, emission dominated by the Paschen continuum (see e.g. Wood et al." + 1989: Wor 1990: Wfood ct al., 1989; Wood 1990; Wood et al. + 1992)., 1992). + The simple Gsothermal slab) models of such discs. however. require. enornious values (qu 107) of. the viscosity. parameter which. accordiis tofre5 model. should be s11.aller than unitv aud whose value 1n quiescence. :recordic to the DIM. should ↽⋅≻ ↴⋝↸∖∿∐∣−∙↕∐↑↸∖↥," The simple (isothermal slab) models of such discs, however, require enormous values $ \sim 10^2$ ) of the viscosity parameter which, according to the model, should be smaller than unity and whose value in quiescence, according to the DIM, should be $\sim 10^{-2}$." +⋅↸∖↴∖↴⊓∐∶↴⋁↕⋅↖↽∙↕⊔∪≼∐∖∐∐∶↴⋁⋅ ⋅ Bahuer cussion lines in such disces also requix ∖↴∖↴↖↽↸∖↥⋅⋅↖↽↕⋜∐⋅∶↴∙⊾↸∖↖⇁⋜↧↕⋯∖↴∖↴∪↕≯↑∐↸∖↖⇁↕↴∖↴↸⊳∪↴∖↴↕↑⋅↖↽ parameter. bu in thIs case endsson can Ὡς ∖⋜↧↑⊓⋅∏⋝∏↑↸∖≺↧↑∪⋜⋯∪↻↑↕↸⊳⋜↧∐⋅↖↽↑↕∐∐ ↸⊳↕∐⋅∪↕⊔∪↴∖↴↻∐↸∖↥⋅↸∖⋖⋀∖∐∐↸∖↴∖↴∐↕∶↴⋁," Interestingly, modeling Balmer emission lines in such discs also requires very large values of the viscosity parameter, but in this case emission can be attributed to an optically thin chromosphere (Mineshige Wood 1990)." +↸∖∙∖↽↖↖⊽∪∪≺↧↕∩⋂↭∙⊀≚↴∖↴↻∪↕∐↑↸∖≼↧∪, As pointed out by Wood et al. ( +∏↑↴⋝∙↖⇁∖↖⊽∪∪≺⊓∖↑⋜↧↕∙∐∩≝⊔∶ ↴∖↴↸∖↸∖⋜↧↕↴∖↴∪∖⊽↥⋅↕↸∖∐⊔⋜⋯∐↕∩⋂⊤⋝↑↕∐∖↖⇁↸∖↥⋅⋅↖⇁↕∐∶↴∙⊾∐↖↽⋜↧↕↿ es of the viscosity parameter most ↻↥⋅∪↴⋝⋜∏⋝↕∙↖↽↥⋅↸∖↴∖↴↿∏↑↕≯↥⋅∪↕⊔↑↕∐∖↴∖↴↕∐∏≻∐∖↴↑↕↸⊳⊓⋅↸∖⋜↧↑⋯↸∖∐ 6f radiation from an optically thin discs.,1992; see also Vrielmann 1997) the very high values of the viscosity parameter most probably result from the simplistic treatment of radiation from an optically thin discs. + There exists. however. a description of the disc vertical structure developed by Shaviv Welirse (1991: hereafter SW) and successfully applied to novalike cataclvsnic variables (Idan," There exists, however, a description of the disc vertical structure developed by Shaviv Wehrse (1991; hereafter SW) and successfully applied to nova–like cataclysmic variables (Idan" +Tere we discuss the relationship between coufideuce intervals aud hypothesis tests aud in particular how a hypothesis test can be used to construct a confuence interval.,Here we discuss the relationship between confidence intervals and hypothesis tests and in particular how a hypothesis test can be used to construct a confidence interval. + A confidence interval reports he set of valies oft le paraiuetcY that are consistent with the data., A confidence interval reports the set of values of the parameter that are consistent with the data. + When this set ineTides Ay=0 it incsus that the «ata are consistent with no source and we expect the uull hypothesis not to |)o rejected and i0 source to be deteced., When this set includes $\lamS=0$ it means that the data are consistent with no source and we expect the null hypothesis not to be rejected and no source to be detected. + There is a amore formal relationship betwoeeu confidence intervals and hypothesis testing and we can use a detection method to generate a comficdence interval., There is a more formal relationship between confidence intervals and hypothesis testing and we can use a detection method to generate a confidence interval. + Suppose that rather than esting the null hypotresis that Ay=0. we are interested in testing the more general uull hypothesis that AsAv. where At is any non-negative nunber.," Suppose that rather than testing the null hypothesis that $\lamS=0$, we are interested in testing the more general null hypothesis that $\lamS\leq\lamS^\star$, where $\lamS^\star$ is any non-negative number." + That is. we are interested iu detecting onlv sources of at least a certain brightuess.," That is, we are interested in detecting only sources of at least a certain brightness." +" In this case. the detection threshold. S*(AZ). is defined as the sialest value such tlat Cüven au observed value of S. we can coustruct the set of values AZ, for which we cannot reject the null hypothesis that Ag< AS."," In this case, the detection threshold, $\thresh(\lamS^\star)$, is defined as the smallest value such that Given an observed value of $\thrtest$, we can construct the set of values $\lamS^\star$ for which we cannot reject the null hypothesis that $\lamS\leq\lamS^\star$ ." + This is a set of vaues of Ay that are consistent with the data aud they form a 100(1ανά confidence interval., This is a set of values of $\lamS$ that are consistent with the data and they form a $100(1-\alpha)$ confidence interval. + This particular. couticence interval. however is of the form ον|ox For auy observed count there is a AZ laree enough so that we cannot reject the null lwpothesis that As2«10 K during the outbursts in., The companion is heated to $>2\times 10^4$ K during the outbursts in. +. We presume that this transient external heating has little effect on the interior of the BD: rather we focus on the continuous heating in quiescence from the hot NS., We presume that this transient external heating has little effect on the interior of the BD; rather we focus on the continuous heating in quiescence from the hot NS. + Bildsten and Brown (1997) showed that the quiescent heating of the outer disk was insufficient to suppress the disk instability responsible for the outbursts., Bildsten and Brown (1997) showed that the quiescent heating of the outer disk was insufficient to suppress the disk instability responsible for the outbursts. + However. 1t appears sufficient to dramatically alter the entropy evolution of the low-mass stellar companion once nuclear burning has ceased.," However, it appears sufficient to dramatically alter the entropy evolution of the low-mass stellar companion once nuclear burning has ceased." + Transiently accreting NSs are always detected in quiescence at an X-ray luminosity >107 erg s (see Bildsten and Rutledge 2000 for an overview)., Transiently accreting NSs are always detected in quiescence at an X-ray luminosity $>10^{32}$ erg $^{-1}$ (see Bildsten and Rutledge 2000 for an overview). + This emission has two components: a soft thermal component from the NS surface (Brown. Bildsten Rutledge 1998: Rutledge et al.," This emission has two components: a soft thermal component from the NS surface (Brown, Bildsten Rutledge 1998; Rutledge et al." + 1999. 2000. 2001) and a hard power-law tail of unknown origin (see Campana Stella 2000 for a discussion).," 1999, 2000, 2001) and a hard power-law tail of unknown origin (see Campana Stella 2000 for a discussion)." + The thermal emission level is well predicted by the relation of Brown et al. (, The thermal emission level is well predicted by the relation of Brown et al. ( +1998) which arises from the deep nuclear heating that the NS receives every outburst.,1998) which arises from the deep nuclear heating that the NS receives every outburst. + For the time-averaged flux derived above. equation (4)) predicts thermal emission at 4.5«I07ereenv?s.," For the time-averaged flux derived above, equation \ref{eq:lq}) ) predicts thermal emission at $4.5\times 10^{-13} {\rm erg \ cm^{-2} \ +s^{-1}}$." + There are two weak detections of the quiescent X-ray emission fromJ1808., There are two weak detections of the quiescent X-ray emission from. +4—3658.. Stella et al. (, Stella et al. ( +2000) report (1-2)«107ergems! (0.5210 keV) withBeppoSAX (in excellent agreement once the spectral corrections are applied; see Table 4 of Rutledge et al.,"2000) report $(1-2)\times 10^{-13} +{\rm erg \ cm^{-2} \ s^{-1}}$ (0.5–10 keV) with (in excellent agreement once the spectral corrections are applied; see Table 4 of Rutledge et al." + 2000) while Dotant. Asai Wijnands (2000) report a value about a factor of 3 lower fromASCA.," 2000) while Dotani, Asai Wijnands (2000) report a value about a factor of 3 lower from." + We use the quiescent luminosity from equation (4)) as a lower-limit to the heating and find the temperature. 7y. of the companion on the side facing the NS. σομΤῃΞ{μιππία-- Ry. as a function of (Mj.," We use the quiescent luminosity from equation \ref{eq:lq}) ) as a lower-limit to the heating and find the temperature, $T_{\rm H}$, of the companion on the side facing the NS, $\sigma_{SB}T_{\rm +H}^4=L_{\rm th}/4\pi(a-R)^2$ , as a function of $\langle \dot +M\rangle$." + For plausible inclinations of. Tyz—38004800K. far above the expected value for a BD that has cooled after passing through the period minimum.," For plausible inclinations of, $T_{\rm H}\approx +3800-4800 {\rm K}$, far above the expected value for a BD that has cooled after passing through the period minimum." + We conjecture that this continuous heating fixes the entropy of the BD ata value higher than would occur in the absence of heating. where the entropy is free to decrease once nuclear burning has halted.," We conjecture that this continuous heating fixes the entropy of the BD at a value higher than would occur in the absence of heating, where the entropy is free to decrease once nuclear burning has halted." + This would also increase the minimum orbital period of such binaries., This would also increase the minimum orbital period of such binaries. + There are no appropriate calculations that allow us to accurately. estimate the slowing of contraction from partial irradiation at these levels., There are no appropriate calculations that allow us to accurately estimate the slowing of contraction from partial irradiation at these levels. + However. the effects of less irradiation of smaller mass objects. the irradiated. extrasolar giant planets. lead to radit larger than expected (Burrows et al.," However, the effects of less irradiation of smaller mass objects, the irradiated extrasolar giant planets, lead to radii larger than expected (Burrows et al." + 2000). as has been observed for the transiting planet around HD 209458 (Brown et al.," 2000), as has been observed for the transiting planet around HD 209458 (Brown et al." + 2001)., 2001). +" In addition to making the case that the companion to iis a brown dwarf. our work also places it in relation to the short orbital period. (<6hr) fast (P,«5ms) MRPs both in the field (PSR J2051—0827. Stappers et."," In addition to making the case that the companion to is a brown dwarf, our work also places it in relation to the short orbital period $<6 \ {\rm hr}$ ) fast $P_s< 5 \ {\rm ms}$ ) MRPs both in the field (PSR $-$ 0827, Stappers et." + al., al. + 1999) and in globular clusters (47 Tuc L J. O. P and R. Camilo et al.," 1999) and in globular clusters (47 Tuc I, J, O, P and R, Camilo et al." + 2000: PSR J1807—2459 in NGC 6544. Ransom et.," 2000; PSR $-$ 2459 in NGC 6544, Ransom et." + al., al. + 2001: PSR 1908+00 in NGC 6760. Deich et al.," 2001; PSR 1908+00 in NGC 6760, Deich et al." + 1993)., 1993). + The longer orbital period for PSR 1957420 places it far outside of this group., The longer orbital period for PSR 1957+20 places it far outside of this group. + The top panel in Figure 3 shows M. for cosi=0.5 for the field pulsar PSR J2051—0827 (open triangle) and globular cluster pulsars (solid squares)., The top panel in Figure 3 shows $M_c$ for $\cos i=0.5$ for the field pulsar PSR $-$ 0827 (open triangle) and globular cluster pulsars (solid squares). + All have lower mass companions than (Casterisk)., All have lower mass companions than (asterisk). + We plot two other related quantities in Figure 3., We plot two other related quantities in Figure 3. + We use the measured orbital parameters and presume that the companion was. in the past. Roche lobe filling at the current orbital period and transferring mass at the rate set by GR losses with 2—1/3.," We use the measured orbital parameters and presume that the companion was, in the past, Roche lobe filling at the current orbital period and transferring mass at the rate set by GR losses with $n=-1/3$." + The mass transfer rate (shown as a time scale in the bottom panel) and the heated companion temperature. 74 (middle panel) are shown for cos;20.5.," The mass transfer rate (shown as a time scale in the bottom panel) and the heated companion temperature, $T_{\rm H}$ (middle panel) are shown for $\cos i=0.5$." + hhas the most heated companion and nearly the shortest accretion time scale (47 Tuc R ts just barely shorter). consistent with it being a progenitor to the pulsars.," has the most heated companion and nearly the shortest accretion time scale (47 Tuc R is just barely shorter), consistent with it being a progenitor to the pulsars." + If the heating maintains a constant entropy in the BD of.. further mass transfer will evolve it along the solid line.," If the heating maintains a constant entropy in the BD of, further mass transfer will evolve it along the solid line." + Since the heating is clearly dropping. we also plot (dashed line) a constant radius evolution (7=0. or decreasing entropy).," Since the heating is clearly dropping, we also plot (dashed line) a constant radius evolution $n=0$, or decreasing entropy)." + These clearly bracket many of the observed systems at longer orbital periods., These clearly bracket many of the observed systems at longer orbital periods. +" For 20. it will take 6.6 Gyrs for to reach a system like PSR J2051-0827 (M,=0.03M ..)."," For $n=0$, it will take 6.6 Gyrs for to reach a system like PSR J2051-0827 $M_c=0.03M_\odot$ )." + Something eventually allows the BD to contract and fall within the Roche lobe. halting mass transfer and allowing the NS to become a MRP.," Something eventually allows the BD to contract and fall within the Roche lobe, halting mass transfer and allowing the NS to become a MRP." + In this respect. it is important that most of the 7u's for the MRPs are comparable to a BD in the contraction phase (Chabrier et al.," In this respect, it is important that most of the $T_{\rm H}$ 's for the MRPs are comparable to a BD in the contraction phase (Chabrier et al." + 2000). implying that the reduced heating at larger orbital periods might well allow the BD to finally fall within the Roche radius.," 2000), implying that the reduced heating at larger orbital periods might well allow the BD to finally fall within the Roche radius." + iis clearly a long-lived (~ Gyr) X-ray source that undergoes mass transfer at a rate of ~1071M... yr!.," is clearly a long-lived $\sim {\rm Gyr}$ ) X-ray source that undergoes mass transfer at a rate of $\approx 10^{-11} +M_\odot$ $^{-1}$." + If this long-lived system is the progenitor type to the short-orbital-period MRPs in 47 Tuc. then we expect to see faint X-ray transients in 47 Tue comparable in number to the MRP binaries.," If this long-lived system is the progenitor type to the short–orbital-period MRPs in 47 Tuc, then we expect to see faint X-ray transients in 47 Tuc comparable in number to the MRP binaries." + The infrequent sampling and long recurrence times would make their detection in outburst unlikely., The infrequent sampling and long recurrence times would make their detection in outburst unlikely. + However. they should easily be detected in quiescence with at the levels implied by equation (4).," However, they should easily be detected in quiescence with at the levels implied by equation \ref{eq:lq}) )." + Discovery of such a plethora of quiescent. short-orbital-period LMXBs would confirm this connection.," Discovery of such a plethora of quiescent, short–orbital-period LMXBs would confirm this connection." + We thank D. Chernoff. A. Cumming. S. Phinney. R. Rutledge. H. Spruit. S. Thorsett. and M. van Kerkwijk for conversations and comments on this work. which was partially supported by NASA via grants NAG 5-8658 and NAG 5-9184 and by the NSF under grant PHY99-07949.," We thank D. Chernoff, A. Cumming, S. Phinney, R. Rutledge, H. Spruit, S. Thorsett, and M. van Kerkwijk for conversations and comments on this work, which was partially supported by NASA via grants NAG 5-8658 and NAG 5-9184 and by the NSF under grant PHY99-07949." + L. B. is a Cottrell Scholar of the Research Corporation., L. B. is a Cottrell Scholar of the Research Corporation. +Alter describing the different fringe patterns due to the parasitic interference. we hiehlieht the resulting interferometric observables that have been degraded.,"After describing the different fringe patterns due to the parasitic interference, we highlight the resulting interferometric observables that have been degraded." + From the general correlation term. . we extract the resulting parasitized coherent [ux pe; andparasitized phase vo :," From the general correlation term $<{\rm X}_1{\rm X}^*_2>$, we extract the resulting parasitized coherent flux $\rho_{\rm ext}$ andparasitized phase $\chi_{\rm ext}$ :" +be related to the preferential accretion of haloes along the filaments of the cosmic web.,be related to the preferential accretion of haloes along the filaments of the cosmic web. +" Haloes tend to fall along the central spines of filaments, so that the range of trajectories, and thus orbits, that they acquire when they enter a halo is restricted (Libeskindetal. 2009).. Shawetal. (2006),,"," Haloes tend to fall along the central spines of filaments, so that the range of trajectories, and thus orbits, that they acquire when they enter a halo is restricted \citep{li09}. . \cite{sh06}, ," + Warnick&Knebe(2006) and Libeskindetal.(2009) confirmed the conclusion of Libeskindetal.(2005) that satellite accretion is a highly anisotropic process and found in their simulations a significant population of subhaloes that co-rotated with the spin of their hosts., \cite{wa06} and \cite{li09} confirmed the conclusion of \cite{li05} that satellite accretion is a highly anisotropic process and found in their simulations a significant population of subhaloes that co-rotated with the spin of their hosts. +" However, Shawetal.(2006) simulated galaxy cluster haloes, not galactic haloes; Warnick&Knebe(2006) also focused on cluster haloes except for one example of a galaxy halo which, however, had only moderate resolution (a minimum subhalo mass of main=5.7x 10'Ms)."," However, \cite{sh06} + simulated galaxy cluster haloes, not galactic haloes; \cite{wa06} also focused on cluster haloes except for one example of a galaxy halo which, however, had only moderate resolution (a minimum subhalo mass of $m_{\mathrm{min}}=5.7\times10^{7}\mathrm{M}_{\odot}$ )." + The largest sample of galaxy halo simulations so far is that of Libeskindetal.(2009)., The largest sample of galaxy halo simulations so far is that of \cite{li09}. + They analysed 436 haloes but were only able to resolve subhaloes of mass Mmin>2.76x10°Mo., They analysed 436 haloes but were only able to resolve subhaloes of mass $m_{\mathrm{min}}\geq 2.76\times10^{9}\mathrm{M}_{\odot}$. +" In this study, we analyse the state-of-the-art, high resolution simulations of six galactic haloes of mass ~1x10’°Mo of the Aquarius project (Springeletal.2008b)."," In this study, we analyse the state-of-the-art, high resolution simulations of six galactic haloes of mass $\sim1\times10^{12}\mathrm{M}_{\odot}$ of the Aquarius project \citep{sp08b}." +. These simulations resolve subhaloes of mass exceeding ~ 10°Mo., These simulations resolve subhaloes of mass exceeding $\sim10^{5}\mathrm{M}_{\odot}$ . +" We calculate the angular momentum of subhaloes, and use the results to interpret the Milky Way data."," We calculate the angular momentum of subhaloes, and use the results to interpret the Milky Way data." + The paper is organised as follows., The paper is organised as follows. + In Section 2 we briefly describe the Aquarius project and the analysis performed for this paper., In Section \ref{SC} we briefly describe the Aquarius project and the analysis performed for this paper. + The results follow in Section 3 and our conclusions in Section 4.., The results follow in Section \ref{Re} and our conclusions in Section \ref{Co}. + The Aquarius project is a set of dark matter simulations containing haloes similar in size and environment to those of the Milky Way; each one has been run from z—127 to z=0., The Aquarius project is a set of dark matter simulations containing haloes similar in size and environment to those of the Milky Way; each one has been run from $z=127$ to $z=0$. +" There are six different haloes (Aq-A - Aq-F), each of which has been resimulated at at least two levels of resolution (L1, the highest, down to L5, the lowest)."," There are six different haloes (Aq-A - Aq-F), each of which has been resimulated at at least two levels of resolution (L1, the highest, down to L5, the lowest)." + They were performed using the code (Springeletal.2008b).., They were performed using the code \citep{sp08b}. +" In all cases, the resimulations at different resolutions show remarkable convergence in the positions and internal properties of subhaloes."," In all cases, the resimulations at different resolutions show remarkable convergence in the positions and internal properties of subhaloes." +" This project has already yielded several interesting results, including a study of the near-universality of halo density profiles (Springeletal.2008b;Navarro2010),, predictions for the y-ray signal from annihilating dark matter in the galactic halo (Springeletal.2008a) and for direct dark matter detection experiments (Vogelsbergeretal.2009)."," This project has already yielded several interesting results, including a study of the near-universality of halo density profiles \citep{sp08b,na10}, predictions for the $\gamma$ -ray signal from annihilating dark matter in the galactic halo \citep{sp08a} and for direct dark matter detection experiments \citep{Vogelsberger09}." +. A summary of key parameter values for each simulation is given in Table 1.., A summary of key parameter values for each simulation is given in Table \ref{table1}. + It is important for this study to establish that the sample of six Aquarius haloes can be considered at least approximately representative of the population of Milky-Way mass haloes as à whole., It is important for this study to establish that the sample of six Aquarius haloes can be considered at least approximately representative of the population of Milky-Way mass haloes as a whole. +" The Aquarius haloes are all drawn from the same parent cosmological simulation, and it is possible to address this issue directly for several properties."," The Aquarius haloes are all drawn from the same parent cosmological simulation, and it is possible to address this issue directly for several properties." +" The spins, concentrations and formation histories of the Aquarius haloes are compared to the parent population in Boylan-Kolchinetal.(2010)."," The spins, concentrations and formation histories of the Aquarius haloes are compared to the parent population in \citet{bo10}." +". Broadly speaking, the properties of the Aquarius haloes span the expected range for the population as a whole."," Broadly speaking, the properties of the Aquarius haloes span the expected range for the population as a whole." +" We give the values of the halo spin, concentration and formation redshift, defined as the redshift when half the halo mass is assembled, in Table 1.."," We give the values of the halo spin, concentration and formation redshift, defined as the redshift when half the halo mass is assembled, in Table \ref{table1}." +" Also in the table we list the shape axis ratios for the haloes, approximating them as ellipsoids."," Also in the table we list the shape axis ratios for the haloes, approximating them as ellipsoids." + The axis ratios are taken from Vera-Ciro et al. (, The axis ratios are taken from Vera-Ciro et al. ( +"in preparation) and calculated for ellipsoids which are determined by applying the iterative method of Allgoodetal.(2006) to the haloes with the substructure removed (actually to the ‘main halo’, defined below).","in preparation) and calculated for ellipsoids which are determined by applying the iterative method of \cite{al06} + to the haloes with the substructure removed (actually to the `main halo', defined below)." + The six haloes show a range of shapes and are typical for ACDM haloes (Allgoodetal.2006;Bett 2007)..," The six haloes show a range of shapes and are typical for $\Lambda$ CDM haloes \citep{al06,be07}. ." + The halo membership of each particle is determined using the friends-of-friends (FOF) algorithm (Davisetal. 1985)., The halo membership of each particle is determined using the friends-of-friends (FOF) algorithm \citep{da85}. +". The particles in each FOF group are, in turn, assigned to self-bound structures using the code (Springeletal.2001)."," The particles in each FOF group are, in turn, assigned to self-bound structures using the code \citep{sp01a}." +" We call the largest of these self-bound substructures the main halo, and the remainder we call subhaloes."," We call the largest of these self-bound substructures the main halo, and the remainder we call subhaloes." + A small proportion («1 per cent) of the particles within the FOF group are found to form a ‘fuzz’ that is not gravitationally bound to any other object; they arenot consideredany further., A small proportion $<1$ per cent) of the particles within the FOF group are found to form a `fuzz' that is not gravitationally bound to any other object; they arenot consideredany further. + Our primary aim is to determine the orientations of dark matter subhalo orbits inthe Aquarius simulations and compare the results with data for galactic satellites., Our primary aim is to determine the orientations of dark matter subhalo orbits inthe Aquarius simulations and compare the results with data for galactic satellites. + We, We +Faraday rotation is a physical phenomenon where (he position angle of linearly polarized radiation propagating through a magneto-ionic mecium is rotated as a function of frequency.,Faraday rotation is a physical phenomenon where the position angle of linearly polarized radiation propagating through a magneto-ionic medium is rotated as a function of frequency. + The work on astrophisical Faraday. rotation has been initiated in (Burn1966).. and since (hen several important contributions have been added to (his topic (Gardier&Whiteoak1966:Sokololfetal.1998.1999:Kronbere1994:Vallee1980;Widrow| 2002).," The work on astrophisical Faraday rotation has been initiated in \citep{Burn1966}, and since then several important contributions have been added to this topic \citep{Gardner1966,Sokoloff1998,Sokoloff1999,Kronberg1994,Vallee1980,Widrow2002}." +. Recently. Faraday rotation measure (IM) svuthesis has been re-introduced as ai important method for analyzing mullichannel polarized radio data. where multiple emitting regions are present along the single line of sight of the observations (Drentjens 09).," Recently, Faraday rotation measure (RM) synthesis has been re-introduced as an important method for analyzing multichannel polarized radio data, where multiple emitting regions are present along the single line of sight of the observations \citep{Brentjens2005,Heald2009}." +. In practice. the method requires the recovery. of the Faraday dispersion. hunction," In practice, the method requires the recovery of the Faraday dispersion function" +in Appendix AppendixD: svuchrotron cmissiou and absorption are described. aud Appendix Appendix€: deals with the IC and SSC processes.,"in Appendix \ref{sec:sync} synchrotron emission and absorption are described, and Appendix \ref{sec:IC} deals with the IC and SSC processes." + This formalisin is applied to study the spectral evolution of the SSC emission. aud the IC scattered CAIB and for a set of characteristic radio sources in Sect. bl:," This formalism is applied to study the spectral evolution of the SSC emission, and the IC scattered CMB and for a set of characteristic radio sources in Sect. \ref{sec:asscs}:" + powerful radio galaxies. like Cveuus A (Sect. L1)).," powerful radio galaxies, like Cygnus A (Sect. \ref{sec:CygA}) )," + GPS (Sect. L.2]).," GPS (Sect. \ref{sec:GPS}) )," + ejut radio galaxies (Sect. L3)).," giant radio galaxies (Sect. \ref{sec:grg}) )," + the fossil radio plasma possibly released by our own galaxy (Sect. 1.0).," the fossil radio plasma possibly released by our own galaxy (Sect. \ref{sec:ourghost}) )," + and radio halo coutainiug clusters of galaxies. like the Coma cluster (Sect. 1.5)).," and radio halo containing clusters of galaxies, like the Coma cluster (Sect. \ref{sec:clogl}) )." + Our nuin findines are sunmnmarzed m Sect. 5.., Our main findings are summarized in Sect. \ref{sec:concl}. + We use monochromatic approximations for the calculation of the svuchrotrou aud the inverse Compton radiation., We use monochromatic approximations for the calculation of the synchrotron and the inverse Compton radiation. + This eives accurate results for the power-law reeiues. but surely will be a crude approximation close to spectral cutoffs.," This gives accurate results for the power-law regimes, but surely will be a crude approximation close to spectral cutoffs." + But the uncertainties du the asstumedL inodel paraucters do not require a higher accuracy dn our ---lustrative treatment., But the uncertainties in the assumed model parameters do not require a higher accuracy in our illustrative treatment. + Our treatineut is not affected ly the possible presence of a relativistic proton compoucut in the radio plasima. since the model paraimcters were chosen ou the basis of the observed radio flux.," Our treatment is not affected by the possible presence of a relativistic proton component in the radio plasma, since the model parameters were chosen on the basis of the observed radio flux." + Svuchrotron absorption of internal aud external radiation fields is taken iuto account., Synchrotron absorption of internal and external radiation fields is taken into account. + The effect of the plasma frequency. aud also the Tsvtovich-Razin (Tsvtovich.1951:Razin.1960).. the free-free. aud induced Compton (Suuvaev.1971) absorption low frequency cutoffs of the source internal svuchrotron radiation field are neglected.," The effect of the plasma frequency, and also the Tsytovich-Razin \cite{tsytovich1951,razin1960}, the free-free, and induced Compton \cite{1971SvA....15..190S} absorption low frequency cutoffs of the source internal synchrotron radiation field are neglected." + This is justified due to the very low expected thermal eas density iu racio cocoons., This is justified due to the very low expected thermal gas density in radio cocoons. + And even in the much denser galaxy clusters these effects are only important vclow ~10 kIIz due to the high cluster temperatures (Lang.1999.fortherelevant formulae)...," And even in the much denser galaxy clusters these effects are only important below $\sim 10$ kHz due to the high cluster temperatures \cite[for the relevant +formulae]{1999asfo.book.....L}." + External frece-free absorption of the resulting low frequency enmiüssiou can affect the observed SSC spectra of radio plasima embedded iu the iuterstellar uediuni of galaxies. as the GPS sources.," External free-free absorption of the resulting low frequency emission can affect the observed SSC spectra of radio plasma embedded in the interstellar medium of galaxies, as the GPS sources." + But since we caleulate the iutriusic source spectrum. we do not correct for this.," But since we calculate the intrinsic source spectrum, we do not correct for this." + The details of the caleulatious are laid down iu the Appendix., The details of the calculations are laid down in the Appendix. + Similar and more sophisticated formalisms were derived aud applied dy amauy other authors (Alarscher.1977:Gould.1979:Baud&Cuindlay.1985.for exiauuple)..," Similar and more sophisticated formalisms were derived and applied by many other authors \cite[for +example]{1977ApJ...216..244M,1979A&A....76..306G,1985ApJ...298..128B}." +" But severa details of the calculation preseuted in the Appendix are not το our knowledge vet reported iu the literature: e.gο, formulae for the exact umber density. (Eq. 151) ", But several details of the calculation presented in the Appendix are not – to our knowledge – yet reported in the literature: e.g. formulae for the exact number density (Eq. \ref{eq:nsync}) ) +and total nunuber (Eq. D19)), and total number (Eq. \ref{eq:Nsync}) ) + of svuchrotrou yhotous within a sphericallv homogeneous source. the generality of having several electron populations which can be located iu regions with cifferiue magnetic Ποια streueths. useful asvauptotic correct approximations of the external IC aud SSC fluxes as a function of optical depth. aud the inclusion of the IC. decrement in external radiation fields iuto such a theoretical framework.," of synchrotron photons within a spherically homogeneous source, the generality of having several electron populations which can be located in regions with differing magnetic field strengths, useful asymptotic correct approximations of the external IC and SSC fluxes as a function of optical depth, and the inclusion of the IC decrement in external radiation fields into such a theoretical framework." + Iu the following we eive a qualitative discussion of the properties of the processes involved., In the following we give a qualitative discussion of the properties of the processes involved. + This should clarify. for example. how our model spectra would change if different parameters were assunied.," This should clarify, for example, how our model spectra would change if different parameters were assumed." +centered on the cluster and control regions. as mentioned earlier (see Sect.,"centered on the cluster and control regions, as mentioned earlier (see Sect." + 2.1)., 2.1). + 44 shows the J—H/HN CC diagram for the cluster field., 4 shows the $J-H/H-K$ CC diagram for the cluster field. + The solid (botfom-leff) and broken heavy curves represent the main-sequence clwarl and giant stars. respectively.," The solid ) and broken heavy curves represent the main-sequence dwarf and giant stars, respectively." + The dotted line indicates the locus of T Tauri stars (Meyer.Calvet&Iillenbrand.1997).. while {he dashed-dotted line represents the ILÀeDe locus (Lada&Adams1992).," The dotted line indicates the locus of T Tauri stars \citep{meyer97}, while the dashed-dotted line represents the HAeBe locus \citep{ladadams92}." +. The three dashed parallel lines are (he reddening vectors., The three dashed parallel lines are the reddening vectors. + We adopt a slope consistent with E(J—H)/E(IL—ἐν} — 1.9 (BD svsteni). which is appropriate to an interstellar reddening law of R = 3.12 1980).," We adopt a slope consistent with $E(J-H)/E(H-K)$ = 1.9 (BB system), which is appropriate to an interstellar reddening law of R = 3.12 \citep{whittet80}." +. The CC diagram was used to idenüilv the reddened population that, The CC diagram was used to identify the reddened population that +excesses. compared to of the SWOP sample.,"excesses, compared to of the SWOP sample." + The discrepaney. of these methods is related to the presence of upper limits. which are correctly. handled in our survival analysis.," The discrepancy of these methods is related to the presence of upper limits, which are correctly handled in our survival analysis." + It is an open question whether the orbital parameters of the planets correlate with the presence of debris disks (Chiangetal.2009)., It is an open question whether the orbital parameters of the planets correlate with the presence of debris disks \citep{chiang}. +. We compared stars with. and without excesses within (he 9WP sample., We compared stars with and without excesses within the SWP sample. + The two-sample tests mentioned above show that the planets. semimajor axes follow the same distribution in (he (wo groups. while eccentricities and masses are slightly higher for stars having both planets aud debris disks than (hose without debris disks. although the differences are not statistically significant.," The two-sample tests mentioned above show that the planets' semimajor axes follow the same distribution in the two groups, while eccentricities and masses are slightly higher for stars having both planets and debris disks than those without debris disks, although the differences are not statistically significant." + The mean metallicities for our stars are 2 0.018 and —0.097 + 0.024 [or SWPs and SWOPs. respectively.," The mean metallicities for our stars are $\,\pm\,$ 0.018 and $-$ $\,\pm\,$ 0.024 for SWPs and SWOPs, respectively." + As expected (Santosοἱal.2001;Valenti 2005).. (wo-saniple tests show the metallicity distributions to be significantly different in our saples.," As expected \citep{santos2001, vf}, two-sample tests show the metallicity distributions to be significantly different in our samples." + To check whether there are differences in (he distribution of excesses between metal-rich aud metal-poor stars. we analyzed (he οΑς and SWODs samples separately.," To check whether there are differences in the distribution of excesses between metal-rich and metal-poor stars, we analyzed the SWPs and SWOPs samples separately." + For each sample. we compared Iz; between the bottom and top thirds of the metallicity distributions. using WAL estimators.," For each sample, we compared $_{70}$ between the bottom and top thirds of the metallicity distributions, using KM estimators." + We found that metallicity does not correlate with the inlrared excess in either sample. confirming results obtained for smaller samples (Greaves2006:Beichmanetal.2005:Drvden 2006).," We found that metallicity does not correlate with the infrared excess in either sample, confirming results obtained for smaller samples \citep{greaves2006, beichman2005, bryden2006}." +. While metallicity is one of the strongest. predictors for the presence of eiant. planets (Valenti&Fischer 2005).. it does nol predict the presence of debris disks.," While metallicity is one of the strongest predictors for the presence of giant planets \citep{vf}, , it does not predict the presence of debris disks." + Aloro-Martiietal.(2007) argued (hat the larger metallicity of SWPs implies that more planetesimals were formed early in those svstems but that most were expelled due to the orbital evolution of the giant. planets., \citet{moromartin} argued that the larger metallicity of SWPs implies that more planetesimals were formed early in those systems but that most were expelled due to the orbital evolution of the giant planets. + The planetesimal configurationis then the same, The planetesimal configurationis then the same +"Sodium has established itself as an important tracer of Galactic chemical evolution, and numerous investigations of the Na abundances of late-type stars, residing in different regions of the Galaxy, have been conducted (e.g.2003 ⋅⋅","Sodium has established itself as an important tracer of Galactic chemical evolution, and numerous investigations of the Na abundances of late-type stars, residing in different regions of the Galaxy, have been conducted \citep[e.g.][]{Takeda03,Gehren06,Andrievsky07}." +" Na is mainly synthesised during hydrostatic carbon-burning in massive stars, through the reaction !*C('*C,p)Na."," Na is mainly synthesised during hydrostatic carbon-burning in massive stars, through the reaction $^{12}$ $^{12}$ $^{23}$ Na." +" As pointed out by (1995),, the production is dependent on the available neutron excess through secondary reactions, which implies metal-dependent yields."," As pointed out by \citet{Woosley95}, the production is dependent on the available neutron excess through secondary reactions, which implies metal-dependent yields." +" In addition, there is a production channel via proton-capture reactions, Z2Ne(p.y)?Na ⋅⋅"," In addition, there is a production channel via proton-capture reactions, $^{22}$ $\gamma$ $^{23}$ Na \citep{Denisenkov90}." +" The latter, the so-called NeNa-cycle, occurs when temperatures are high enough for H-burning through the CNO-cycle, e.g. in the cores or H-burning shells of intermediate mass and massive stars."," The latter, the so-called NeNa-cycle, occurs when temperatures are high enough for H-burning through the CNO-cycle, e.g. in the cores or H-burning shells of intermediate mass and massive stars." +" Abundance studies of late-type stars in the thin disk show a steady increase from solar to positive [Na/Fe] ratios at super-solar metallicities, while thin and thick disk stars instead form a decreasing trend [[993)slightly below solar metallicities (e.g.[Ed-] [2004)."," Abundance studies of late-type stars in the thin disk show a steady increase from solar to positive [Na/Fe] ratios at super-solar metallicities, while thin and thick disk stars instead form a decreasing trend slightly below solar metallicities \citep[e.g.][]{Edvardsson93,Reddy03,Bensby03,Shi04}." +". Relying exclusively on weak lines for the analysis, LTE has been proved a reasonable approximation in this metallicity regime."," Relying exclusively on weak lines for the analysis, LTE has been proved a reasonable approximation in this metallicity regime." +" For metal-poor stars the situation is different, especially in cases where the strong Nall D resonance lines nnm) are the only available abundance indicators."," For metal-poor stars the situation is different, especially in cases where the strong I D resonance lines nm) are the only available abundance indicators." +" As shown by (2003) and (2006),, [Na/Fe] ratios are slightly subsolar (—0.1...— 0.5) in metal-poor stars in the thick disk and the halo in the metallicity range [Fe/H]-—3.0...—1.0."," As shown by \citet{Takeda03} and \citet{Gehren06}, [Na/Fe] ratios are slightly subsolar $-0.1...-0.5$ ) in metal-poor stars in the thick disk and the halo in the metallicity range $=-3.0...-1.0$." +" This deficiency is only recovered through non-LTE analysis, because LTE investigations tend to overestimate the abundances, sometimes by as much as ~0.5 ddex (see refsec:deps))"," This deficiency is only recovered through non-LTE analysis, because LTE investigations tend to overestimate the abundances, sometimes by as much as $\sim0.5$ dex (see \\ref{sec:deps}) )." +" Moreover, almost solar values are obtained from non-LTE analysis of extremely metal-poor stars below [Fe/H]«—3.0, where LTE analysis, at least of giants, instead yields positive ratios, [Na/Fe]~0.3 Nissen&Schuster(2010)etal {irievsky2007)."," Moreover, almost solar values are obtained from non-LTE analysis of extremely metal-poor stars below $\rm[Fe/H]<-3.0$, where LTE analysis, at least of giants, instead yields positive ratios, $\approx0.3$ \citep{Cayrel04,Andrievsky07}." +". Interestingly. found evidence for systematic Na abundance differences of the order of ddex between a-poor and a-rich halo stars, with important implications for the presumably separate origin of these two Galactic components."," Interestingly, \citet{Nissen10} found evidence for systematic Na abundance differences of the order of dex between $\alpha$ -poor and $\alpha$ -rich halo stars, with important implications for the presumably separate origin of these two Galactic components." +" To place all Galactic stellar populations on an absolute Na abundance scale to the same and better precision, non-LTE is clearly required."," To place all Galactic stellar populations on an absolute Na abundance scale to the same and better precision, non-LTE is clearly required." +" In globular clusters, Na is of particular interest, because the large overabundances of this element, compared with those of field stars of similar metallicities, imply a chemical evolution scenario that is specific to these dense stellar systems (e.g.Q004)."," In globular clusters, Na is of particular interest, because the large overabundances of this element, compared with those of field stars of similar metallicities, imply a chemical evolution scenario that is specific to these dense stellar systems \citep[e.g.][]{Gratton04}." +". By detailed mapping of the Na abundance and its correlating behaviour with similar-mass and lighter elements we may distinguish between stars formed in different formation episodes in globular clusters and eventually identify the elusive self-enrichment process that so efficiently polluted the star-forming gas with the nucleosynthesis products of hot H-burning through the CNO-cycle and the related NeNa- and MgAl-chains (i.e. enhancement of N, Na, and Al, and depletion of C, O, and Mg, see e.g. and (Carrettaet al.2009))."," By detailed mapping of the Na abundance and its correlating behaviour with similar-mass and lighter elements we may distinguish between stars formed in different formation episodes in globular clusters and eventually identify the elusive self-enrichment process that so efficiently polluted the star-forming gas with the nucleosynthesis products of hot H-burning through the CNO-cycle and the related NeNa- and MgAl-chains (i.e. enhancement of N, Na, and Al, and depletion of C, O, and Mg, see e.g. \citealt{Lind10a} and \citealt{Carretta09b}) )." +" In this study we present 1D, non-LTE calculations for several neutral Na lines for a large stellar grid."," In this study we present 1D, non-LTE calculations for several neutral Na lines for a large stellar grid." + The given non-LTE abundances can be interpolated to arbitrary stellar-parameter combinations and will consequently be useful for Na abundance analyses with a variety of applications., The given non-LTE abundances can be interpolated to arbitrary stellar-parameter combinations and will consequently be useful for Na abundance analyses with a variety of applications. +" In a forthcoming paper we will apply the non-LTE modelling procedure described here to individual stars, and extend it to using 3D hydrodynamical model atmospheres."," In a forthcoming paper we will apply the non-LTE modelling procedure described here to individual stars, and extend it to using 3D hydrodynamical model atmospheres." +" Typically, the largest uncertainties affecting the LTE calculations in stellar atmospheres are collisional cross-sections, especially for collisions with hydrogen atoms (e.g.[Asplund| 2005)."," Typically, the largest uncertainties affecting the non-LTE calculations in stellar atmospheres are collisional cross-sections, especially for collisions with hydrogen atoms \citep[e.g.][]{Asplund05}." +". As described in and D.4], recent quantum mechanical calculations of cross-sections for collisions with both electrons and hydrogen have significantly improved the situation for sodium, and a reliable atom can now be constructed."," As described in \\ref{sec:ecoll} and \ref{sec:hcoll}, recent quantum mechanical calculations of cross-sections for collisions with both electrons and hydrogen have significantly improved the situation for sodium, and a reliable atom can now be constructed." +" In this study, we put extra emphasis on assessing to which extent the remaining uncertainties in collisional rates influence the statistical equilibrium of II."," In this study, we put extra emphasis on assessing to which extent the remaining uncertainties in collisional rates influence the statistical equilibrium of I." +corresponding fractions in per cent are presented in the last column of Table 2..,corresponding fractions in per cent are presented in the last column of Table \ref{tabkinstpop}. +" For 9 our of 14 objects the derived dark matter contents are consistent with zero, while for F-5, F-11, F-34, and F-53 the dynamical masses turn to be lower than the stellar ones resulting in “negative” formally computed dark matter fractions, i.e. —100 per cent corresponding to the stellar M/L ratio being twice as high as the dynamical one."," For 9 our of 14 objects the derived dark matter contents are consistent with zero, while for $F$ $5$, $F$ $11$, $F$ $34$, and $F$ $53$ the dynamical masses turn to be lower than the stellar ones resulting in “negative” formally computed dark matter fractions, i.e. $-$ 100 per cent corresponding to the stellar $M/L$ ratio being twice as high as the dynamical one." + What is the reason for derived negative dark matter fractions?, What is the reason for derived negative dark matter fractions? + We either underestimate the dynamical mass and/or overestimate the stellar one., We either underestimate the dynamical mass and/or overestimate the stellar one. + Underestimatation of dynamical masses may originate from imperfect surface photometry (too small effective radius) or velocity dispersion measurements biased towards lower values., Underestimatation of dynamical masses may originate from imperfect surface photometry (too small effective radius) or velocity dispersion measurements biased towards lower values. +" Although our UCDs have quite small spatial sizes, most of them are sufficiently well resolved to rule out the former possibility."," Although our UCDs have quite small spatial sizes, most of them are sufficiently well resolved to rule out the former possibility." +" The latter option is also hardly possible, because our data have sufficiently high spectral resolution to reliably measure velocity dispersions down to 5km s."," The latter option is also hardly possible, because our data have sufficiently high spectral resolution to reliably measure velocity dispersions down to 5 km $^{-1}$." + Stellar masses may become overestimated if the adopted stellar mass-to-light ratio is too high., Stellar masses may become overestimated if the adopted stellar mass-to-light ratio is too high. +" The only parameter which may strongly affect them at our regime (i.e. old ages, intermediate and low metallicities) is the shape of the stellar mass function at low masses, where stars do not contribute much to the total light, but do change significantly the mass because of strongly non-linear behaviour of the mass-luminosity relation for main sequence stars."," The only parameter which may strongly affect them at our regime (i.e. old ages, intermediate and low metallicities) is the shape of the stellar mass function at low masses, where stars do not contribute much to the total light, but do change significantly the mass because of strongly non-linear behaviour of the mass--luminosity relation for main sequence stars." + Changing the low mass slope power law index from 2.3 to 1.3 (ie. Salpeter to Kroupa) decreases the mass-to-light ratios of old stellar populations by ~50 per cent., Changing the low mass slope power law index from 2.3 to 1.3 (i.e. Salpeter to Kroupa) decreases the mass-to-light ratios of old stellar populations by $\sim$ 50 per cent. + Does this suggest IMF variations in the UCDs of our sample?, Does this suggest IMF variations in the UCDs of our sample? +" We have to keep in mind that CSSs observed today might have experienced dynamical evolution effects on their stellar mass functions, i.e. the observed mass function may differ from the IMF."," We have to keep in mind that CSSs observed today might have experienced dynamical evolution effects on their stellar mass functions, i.e. the observed mass function may differ from the IMF." +" It is known (????) that in globular clusters the dynamical evolution causes mass segregation, ie. massive stars are moving toward the centre while low-mass stars migrate to the cluster outskirts, where they are tidally stripped during the passages close to the centre of a host galaxy or through its disc."," It is known \citep{Spitzer87,BM03, KAS07,KM09} that in globular clusters the dynamical evolution causes mass segregation, i.e. massive stars are moving toward the centre while low-mass stars migrate to the cluster outskirts, where they are tidally stripped during the passages close to the centre of a host galaxy or through its disc." +" This creates a deficit of low mass stars in a cluster, changing the shape of its integrated stellar mass function."," This creates a deficit of low mass stars in a cluster, changing the shape of its integrated stellar mass function." +" The characteristic timescale of this process is related to the dynamical relaxation time, which can be estimated for a CSS (?) as trelax=[οςmvMaynr3/0.0045 Myr, where Mayn is in Solar masses and r. is in pc."," The characteristic timescale of this process is related to the dynamical relaxation time, which can be estimated for a CSS \citep{Mieske+08} as $t_{\mathrm{relax}} = +\frac{0.234}{\log M_{\mathrm{dyn}}} \sqrt{M_{\mathrm{dyn}} r_{e}^3 / +0.0045}$ Myr, where $M_{\mathrm{dyn}}$ is in Solar masses and $r_{e}$ is in pc." + In Fig 6 we present the ratio between dynamical (Mays) and stellar (M.) masses versus the relaxation time., In Fig \ref{mltrel} we present the ratio between dynamical $M_{\mathrm{dyn}}$ ) and stellar $M_{*}$ ) masses versus the relaxation time. + We see, We see +A second question we can answer is: what is the time duration of the LBG phase?,A second question we can answer is: what is the time duration of the LBG phase? + For bright LBGs. we detine this as the time during which Lis>Li in the current LBG phase. while for faint LBGs we detine the duration as the time during which O.LL;7-4-.," For bright LBGs, we define this as the time during which $L_{UV} > L^{*}_{UV}$ in the current LBG phase, while for faint LBGs we define the duration as the time during which $L_{UV} > 0.1 +L^{*}_{UV}$ ." + We show the distribution of LBG durations for LBG samples in Fig. 4..," We show the distribution of LBG durations for volume-limited LBG samples in Fig. \ref{fig:duration}," + where the top panel shows results for bright LBGs identified at +=3 and 6. and the lower panel faint LBGs identified at >=3. 6 and 10.," where the top panel shows results for bright LBGs identified at $z=3$ and $6$, and the lower panel faint LBGs identified at $z=3$, $6$ and $10$." + For bright LBOs. the median duration is around 20 Myr at both 2=3 and 2=6.," For bright LBGs, the median duration is around 20 Myr at both $z=3$ and $z=6$." + For faint LBOs. the durations are generally larger. as expected. decreasing from around 60 Myr at 2=3 to 30 Myr at +=6 and 20 Myr at >=10.," For faint LBGs, the durations are generally larger, as expected, decreasing from around 60 Myr at $z=3$ to 30 Myr at $z=6$ and 20 Myr at $z=10$." + The short durations for bright LBGs reflect the relatively short timescales of the bursts responsible for most of them., The short durations for bright LBGs reflect the relatively short timescales of the bursts responsible for most of them. + Having shown some illustrative examples of galaxy merger trees with LBG progenitors in the previous subsection. we now perform a statistical study and compute the probability that a present-day galaxy had a progenitor that was an LBG or that a present-day halo had a progenitor halo which hosted an LBG.," Having shown some illustrative examples of galaxy merger trees with LBG progenitors in the previous subsection, we now perform a statistical study and compute the probability that a present-day galaxy had a progenitor that was an LBG or that a present-day halo had a progenitor halo which hosted an LBG." + The predictions for the fraction of present-day galaxies that are descendants of LBGs are presented in Fig. 5...," The predictions for the fraction of present-day galaxies that are descendants of LBGs are presented in Fig. \ref{FRACTIONLBG}," + with the top panels showing results for descendants of bright LBGs at 3<2 dtand 6<2«7. and the lower panels results for descendants of faint LBGs at 3«z< 4.6«zT and lO«2II. (," with the top panels showing results for descendants of bright LBGs at $3= 10.),The model does not predict a significant number bright LBGs at $z=10$ .) + Inthe left-hand panels we plot the fraction of present-day galaxies. as a function of their stellar mass. which are predicted to have at least one bright LBG progenitor in the specified redshift range.," In the left-hand panels we plot the fraction of present-day galaxies, as a function of their stellar mass, which are predicted to have at least one bright LBG progenitor in the specified redshift range." + In the right-hand panels we show the fraction of present-day halos having progenitor halos which hosted an LBG in the specitied redshift range., In the right-hand panels we show the fraction of present-day halos having progenitor halos which hosted an LBG in the specified redshift range. + We see that the probability to have an LBG progenitor increases with increasing present-day mass (both stellar and halo}. but decreases with increasing LBG redshift Considering first the bright LBGs. we find that galaxies with stellar masses of 6.310bTAL. 6110hTAL. and LS.I0FAL. are predicted to respectively have 1066... and probabilities of having at least one bright LBG progenitor in the range 3«&z«4.," We see that the probability to have an LBG progenitor increases with increasing present-day mass (both stellar and halo), but decreases with increasing LBG redshift Considering first the bright LBGs, we find that galaxies with stellar masses of $6.3\times 10^{9} h^{-1}M_{\odot}$, $6.1\times 10^{10} +h^{-1}M_{\odot}$ and $1.8\times 10^{11} h^{-1}M_{\odot}$ are predicted to respectively have , and probabilities of having at least one bright LBG progenitor in the range $3=10. the model does not predict a significant population of bright LBGs (see Fig. 1).," Note that at $z=10$, the model does not predict a significant population of bright LBGs (see Fig. \ref{LF}) )." + When we construct the distribution of properties of the descendants of LBOs. each descendant galaxy is counted once (with a weight depending on its abundance). regardless of the number of LBG progenitors it possesses.," When we construct the distribution of properties of the descendants of LBGs, each descendant galaxy is counted once (with a weight depending on its abundance), regardless of the number of LBG progenitors it possesses." + The model predicts that the stellar masses of LBGs identitied at a given UV luminosity decrease with increasing redshift., The model predicts that the stellar masses of LBGs identified at a given UV luminosity decrease with increasing redshift. + On the other hand. the stellar masses of their present-day descendants show the opposite trend. increasing with increasing redshift.," On the other hand, the stellar masses of their present-day descendants show the opposite trend, increasing with increasing redshift." + This behaviour is seen for both bright and faint LBGs. as we now discuss in detail.," This behaviour is seen for both bright and faint LBGs, as we now discuss in detail." + We plot the stellar mass distributions of LBGs and of their present-day descendants in the left and right panels of Fig. 6.., We plot the stellar mass distributions of LBGs and of their present-day descendants in the left and right panels of Fig. \ref{mstdesc}. + The top panels show results for bright LBGs(Loy>Lp )atz =3 and z= 6. while the lower panels show results for faint LBGs Go>Ον ας= 3.2= Gand:=10.," The top panels show results for bright LBGs$L_{UV} > L^{*}_{UV}$ ) at $z=3$ and $z=6$ , while the lower panels show results for faint LBGs $L_{UV} > 0.1 L^{*}_{UV}$ ) at $z=3$, $z=6$ and $z=10$." +" We see that the median stellar mass of bright LBGs at >=3 is Al,—13.10°ΣΑΙ which is 6 times larger than that of their faint counterparts at this redshift. and z2.5 times larger than the median mass of bright LBGs at 2=6."," We see that the median stellar mass of bright LBGs at $z=3$ is $M_{*}=1.3\times10^{9} h^{-1}M_{\odot}$, which is 6 times larger than that of their faint counterparts at this redshift, and $\approx 2.5$ times larger than the median mass of bright LBGs at $z=6$." +" The median stellar mass of the >=0 descendants (right panels) of these two LBG populations (2=3 und >= 6) are predicted to be A4,=5«10275.1AJ. for the bright LBGs at >=3 and Al,=11045ΣΑΙ. for the bright LBGs at >=6.", The median stellar mass of the $z=0$ descendants (right panels) of these two LBG populations $z=3$ and $z=6$ ) are predicted to be $M_{*}=5\times10^{10} h^{-1}M_{\odot}$ for the bright LBGs at $z=3$ and $M_{*}=1\times 10^{11} h^{-1}M_{\odot}$ for the bright LBGs at $z=6$. + We separate the galaxies into bulge-dominated (if the bulge to total stellar mass ratio D/7> 0.5) and disk-dominated galaxies (Le. 5/7< 0.5)., We separate the galaxies into bulge-dominated (if the bulge to total stellar mass ratio $B/T > 0.5$ ) and disk-dominated galaxies (i.e. $B/T < 0.5$ ). + Bright LBGs at ς=3 and 2=6 are predicted to be typically }) disk-dominated., Bright LBGs at $z=3$ and $z=6$ are predicted to be typically ) disk-dominated. + However. while the descendants of bright LBGs at 2=3 are also mainly disk-dominated. descendants of bright LBGs at 2=6 aremainly bulge-dominated.," However, while the descendants of bright LBGs at $z=3$ are also mainly disk-dominated, descendants of bright LBGs at $z=6$ aremainly bulge-dominated." +" The median stellarmass of faint LBGs at >=3 is M,= which is an order of magnitude larger than the median mass of faint LBGs at += 6."," The median stellarmass of faint LBGs at $z=3$ is $M_{*}=2\times10^{8} +h^{-1}M_{\odot}$ , which is an order of magnitude larger than the median mass of faint LBGs at $z=6$ ." + Faint LBGs at +=10 are 25 times less massive than faint LBGs at >= 3., Faint LBGs at $z=10$ are 25 times less massive than faint LBGs at $z=3$ . +" The medianstellar masses of the descendants of the 2=3 and 2=6 populations are predicted to be similar (A,~(3.5)«1075.AL. y.", The medianstellar masses of the descendants of the $z=3$ and $z=6$ populations are predicted to be similar $M_{*} \sim (3-5)\times10^{9} h^{-1}M_{\odot}$ ). + The median descendant mass of a 2=10 faint LBG is an order of magnitude larger than for faint LBGs identified at >= 30r 2= 6., The median descendant mass of a $z=10$ faint LBG is an order of magnitude larger than for faint LBGs identified at $z=3$ or $z=6$ . +Once we will eather enoeh prompt Is observations we will be able to estimate the nature of dist present in host molecular clouds from the fraction of lost I& afterelows.,Once we will gather enough prompt K observations we will be able to estimate the nature of dust present in host molecular clouds from the fraction of lost K afterglows. + We uudoerliue he fact tha with present observational data it is impossible to produce areal statistic for dark burss due to the late and varving nue of observatious aud to the different magnitudes reacied., We underline the fact that with present observational data it is impossible to produce a real statistic for dark bursts due to the late and varying time of observations and to the different magnitudes reached. + Iu the future. from the afterglow results given by Swift ail REM. we will be able to determiue the uaure of dark GRBs.," In the future, from the afterglow results given by Swift and REM, we will be able to determine the nature of dark GRBs." + Indeed with a further refinement of the model aud a good statistics of bursts observed iu various colors we wil certainly be able to know which kind of dust is present in the ονολο! of the burst., Indeed with a further refinement of the model and a good statistics of bursts observed in various colors we will certainly be able to know which kind of dust is present in the environment of the burst. +" jarerespectivelytheeleclrochemicalandchemicalpotentials,",are respectively the electrochemical and chemical potentials. + A gradient of chemical potential could be caused by several reasons., A gradient of chemical potential could be caused by several reasons. + We could obtain a eradient bv changing (he concentration. the pressure and the temperature.," We could obtain a gradient by changing the concentration, the pressure and the temperature." + Dhermodyvnanmically. (he cause of an electric current is the electrochemical gradient.," Thermodynamically, the cause of an electric current is the electrochemical gradient." + If (here is no current present in a material. the gradient of electrochemical potential must be zero.," If there is no current present in a material, the gradient of electrochemical potential must be zero." + If we take into account all these generators in the last relation aud impose the equilibrium condition. we obtain where is the pressure. temperature ancl concentration.," If we take into account all these generators in the last relation and impose the equilibrium condition, we obtain where is the pressure, temperature and concentration." + In the radial direction in the Earth core. the conservation of charge grants that the nel current over sullicient long periods of time must be zero.," In the radial direction in the Earth core, the conservation of charge grants that the net current over sufficient long periods of time must be zero." + This condition leave only the possibility that the radial current is zero or oscillate around (his value., This condition leave only the possibility that the radial current is zero or oscillate around this value. + We start our discussion by taking (he firs possibility., We start our discussion by taking the firs possibility. + The main cause of In (his simple model we assume (wo concentric spherical shells filled with some substance wilh electric permillivily. electric conductivityjJ. andthermalconductivily)," The main cause of In this simple model we assume two concentric spherical shells filled with some substance with electric permittivity, electric conductivity, and thermal conductivity." + HE heseshellscorrespondstotheinnercoreboundarg(4 C D)andlhecoremantleboundarg( CMD)., These shells corresponds to the inner core boundary (ICB) and the core mantle boundary (CMB). + The energv balance equation of the material filling the svstem is. if we consider electrical effects. where Jisthemassdensily. internal energv per unit mass. Jeleetricaleurrentdensily.," The energy balance equation of the material filling the system is, if we consider electrical effects, where is the mass density, internal energy per unit mass, electrical current density," +rather a high Ic/Tboratio of about 2.0 (e.g.Sinartt2009].,rather a high Ic/Ib ratio of about 2.0 \citep[e.g.][]{Smartt09}. + This discrepancy would become even larevwith 10. as iaaplied by Fie. 15..," This discrepancy would become even larger with $f_\mathrm{WR} =10$ , as implied by Fig. \ref{fig:mimf2}." + This raises a question on the nature of SN Ic progenitors. audit should be kept im wind that we still do not fully understand what distinguishes SN Ic progenitors from those of SN Ib.," This raises a question on the nature of SN Ic progenitors, and it should be kept in mind that we still do not fully understand what distinguishes SN Ic progenitors from those of SN Ib." + A recent work bv Dessartetal.(2010) indicates that the mass fraction of heliun in the— outermost lavers (3.). rather than the total mass of helimu. may be more relevant for the presence of helium lines iu supernova spectra.," A recent work by \citet{Dessart10} indicates that the mass fraction of helium in the outermost layers $Y_\mathrm{s}$ ), rather than the total mass of helium, may be more relevant for the presence of helium lines in supernova spectra." + Specifically. it is shown that if helium is well nüxed with CO material such that ὃς becomes less than about 0.5. helium lines are not secu in carly time spectra. despite rather a large total amount of hel (Mqzm1.0 ML.) if non-thenual excitation is absent.," Specifically, it is shown that if helium is well mixed with CO material such that $Y_\mathrm{s}$ becomes less than about 0.5, helium lines are not seen in early time spectra, despite rather a large total amount of helium $M_\mathrm{He} \simeq 1.0$ ), if non-thermal excitation is absent." + Iu our progenitor models. such a sall 3; is realized ouly for Me2 5.5 at solar iietallicitv Gvith fig= 5).," In our progenitor models, such a small $Y_\mathrm{s}$ is realized only for $M_\mathrm{f} \ga$ 5.5 at solar metallicity (with $f_\mathrm{WR} = 5$ )." + This is not different from the above-discussed iass limit for having Ay.X0.5AL... uitorsimplying that the initial mass range for SN Ic proge would not change much even if we adopted ὃς as a criterion. at least for the high mass class;," This is not different from the above-discussed mass limit for having $M_\mathrm{He} \la 0.5$, implying that the initial mass range for SN Ic progenitors would not change much even if we adopted $Y_\mathrm{s}$ as a criterion, at least for the high mass class." + On the other haud. we have ὃς=0.98 in the primary star of Seq.," On the other hand, we have $Y_\mathrm{s} = 0.98$ in the primary star of Seq." + 3 at carbon exhaustion while the total mass of helm is less than 0.2ML., 3 at carbon exhaustion while the total mass of helium is less than 0.2. +.. This iuples that the initial mass range for the low mass class SN Ic progenitors uuelt be affected if the condition of ὃν«(0.5 for SN Ic progenitors were applied., This imples that the initial mass range for the low mass class SN Ic progenitors might be affected if the condition of $Y_\mathrm{s} < 0.5$ for SN Ic progenitors were applied. + But Dessartetal.(2010). did uot vet calculate such a ow mass SN progenitor model (Agz2.0 M). aud heir analyses were limited to carly times of supernovae.," But \citet{Dessart10} did not yet calculate such a low mass SN progenitor model $M_\mathrm{f} \la 2.0$ ), and their analyses were limited to early times of supernovae." + It remains to be an muportant subject of future work ο systematically investigate which types of superunova xoesenitors would lead to the presence or absence of elim lines in the supernova spectra at differeut epochs. including the effect of non-thermal excitation.," It remains to be an important subject of future work to systematically investigate which types of supernova progenitors would lead to the presence or absence of helium lines in the supernova spectra at different epochs, including the effect of non-thermal excitation." + Therefore. he above discussion on Type Ic progenitors based. ou he total amount of helium should ouly be considered indicative at this stage.," Therefore, the above discussion on Type Ic progenitors based on the total amount of helium should only be considered indicative at this stage." + Tt is interesting that. at Z~Z... the presence of a thin hydrogen laver is ouly expected for a limited range of the initial/final mass of SN Ib progenitors. as shown iu Figs νι aud 11..," It is interesting that, at $Z \approx \mathrm{Z_\odot}$, the presence of a thin hydrogen layer is only expected for a limited range of the initial/final mass of SN Ib progenitors, as shown in Figs \ref{fig:dmh}, and \ref{fig:mimf}." + The detection of hydrogen absorptio- ines at high velocity has been indeed reported ii way SNe Ib (e.g.Dengetal.2000:Brauch2002:Ehuliuadiοtal.2006).. iu favor of our model prediction or the presence of a thin hydrogen laver in SNe I xogenitors.," The detection of hydrogen absorption lines at high velocity has been indeed reported in many SNe Ib \citep[e.g.,][]{Deng00, Branch02, +Elmhamdi06}, in favor of our model prediction for the presence of a thin hydrogen layer in SNe Ib progenitors." + This might prowide a strong coustraiut for 16 progenitor masses of Observed SNe Tb. in principle.," This might provide a strong constraint for the progenitor masses of observed SNe Ib, in principle." + Note also that explosions of such helm stars with in hvdyvroseu layers could be recognized as SN IIb rather than Ib. ifhwdrogeu lines were detected short after supernova explosion. e.g.. as in the case of SN 2008ax (Chornockotal.POLO) aud as recently discussed by Speucer&Barou(2010) and Dessartofal.(2010)..," Note also that explosions of such helium stars with thin hydyrogen layers could be recognized as SN IIb rather than Ib, if hydrogen lines were detected short after supernova explosion, e.g., as in the case of SN 2008ax \citep{Chornock10} + and as recently discussed by \citet{Baron10} and \citet{Dessart10}. ." + The radii of these progenitor models rauge from ~lottαμ to ~1012cm., The radii of these progenitor models range from $\sim 10^{11}~\mathrm{cm}$ to $\sim 10^{12}~\mathrm{cm}$. + They may corredpoud to the “compact” category of SN IIo progenitors. which is cliscussed in Chevalier&Soderberg(2010).," They may corredpond to the ”compact” category of SN IIb progenitors, which is discussed in \citet{Chevalier10}." +.. The relatively low ejecta masses of stich SNe Tb are consitcut with our model predictions., The relatively low ejecta masses of such SNe IIb are consitent with our model predictions. + Ou the other hand. Case C mass transfer can also leave helium cores covered with siuall amounts of livdrogen envelope.," On the other hand, Case C mass transfer can also leave helium cores covered with small amounts of hydrogen envelope." + As the life time of such stars made via Case C iuass transfer should be rather short. they cau retain much more hydrogen (Mj20.1 M). than what is predicted from our binary models with Case AB/B ass transfer.," As the life time of such stars made via Case C mass transfer should be rather short, they can retain much more hydrogen $M_\mathrm{H} > 0.1$ ), than what is predicted from our binary models with Case AB/B mass transfer." + Such a star may eventually explode as a SN IIb like SN 19937 (e.g.Podsiacdlowskietal.1993:Maunudetal. 200L).. with a inuch extended envelope (102?1015 cm).," Such a star may eventually explode as a SN IIb like SN 1993J \citep[e.g.][]{Podsiadlowski93, Maund04}, with a much extended envelope $\sim 10^{13} - 10^{14}~\mathrm{cm}$ )." + Therefore. the two categories of SN IIb. progenitors according to their sizes. which has been recently sugeested by Chevalier&Soderberg(2010).. may be understood within the framework of binary evolution: SNe IIb of the compact type may be produced via Case AB/B mass transfer (especially at Z=Z.). aud SNe IIb of the extended type via Case C mass transfer.," Therefore, the two categories of SN IIb progenitors according to their sizes, which has been recently suggested by \citet{Chevalier10}, may be understood within the framework of binary evolution; SNe IIb of the compact type may be produced via Case AB/B mass transfer (especially at $Z \la \mathrm{Z_\odot}$ ), and SNe IIb of the extended type via Case C mass transfer." + This work is supported by the DOE SciDAC Program (DOE DE-FCO2-06ERI1135). the NSF eraut (NSE- AST-0909129). and theNASA Theory Program CNNNOOATI236€).," This work is supported by the DOE SciDAC Program (DOE DE-FC02-06ER41438), the NSF grant (NSF-ARRA AST-0909129), and theNASA Theory Program (NNX09AK36G)." + We are grateful to Luc Dessart for useful diseussious., We are grateful to Luc Dessart for useful discussions. +The detection for most ULX of spectral curvature. in the form of a deficit of photons at energies £22 kkeV (Robertsetal.2005:Stobbartetal.2006:Mivawaki 20099) has led to the suggestion that most ULX have spectral properties that do not correspond to any of the accretion states Known in Black Hole Binaries (BHB). making it unlikely that ULX are powered by sub-Eddington flows onto an IMBH (Robertsetal.2007).,"The detection for most ULX of spectral curvature, in the form of a deficit of photons at energies $E{\ge}2$ keV \citealt{roberts05,stobbart06,miyawaki09}) ) has led to the suggestion that most ULX have spectral properties that do not correspond to any of the accretion states known in Black Hole Binaries (BHB), making it unlikely that ULX are powered by sub-Eddington flows onto an IMBH \citep{roberts07}." +". The application of Comptonization models to the data (Stobbartetal.2006:Gladstoneetal.2009 and references therein) results in strikingly high and low values for the coronal opacity (725) and the electron temperature (AV,=|— 3kkeV). dithcult to explain for the expected physical conditions in a corona surrounding the black hole."," The application of Comptonization models to the data \citealt{stobbart06,gladstone09} + and references therein) results in strikingly high and low values for the coronal opacity ${\tau}{\ge}5$ ) and the electron temperature $kT_{e}=1-3$ keV), difficult to explain for the expected physical conditions in a corona surrounding the black hole." + This is very different to the typical values found for BHB during the/ouhard state. with spectra dominated by Comptonization'.. and appears irreconcilable with the IMBH model. which assumes that they operate as simple scaled-up BHB.," This is very different to the typical values found for BHB during the state, with spectra dominated by Comptonization, and appears irreconcilable with the IMBH model, which assumes that they operate as simple scaled-up BHB." + Here. we present an alternative interpretation of the spectral shape. based on a physically-justified model commonly used on other accreting black holes.," Here, we present an alternative interpretation of the spectral shape, based on a physically-justified model commonly used on other accreting black holes." + The soft part of the spectrum (E<| KkeV)— the soft X-ray excess — and the high-energy curvature are just aspects of a reflection spectrum expected from accretion (Guilbert&Rees1988:GeorgeFabian 19919).," The soft part of the spectrum $E{\le}1$ keV) – the soft X-ray excess – and the high-energy curvature are just aspects of a reflection spectrum expected from accretion \citealt{guilbert88,george91}) )." + Α major component of reflection. the broad iron K line. has been found in many Seyfert galaxies (Tanakaetal.1995:Nandra 20089). accreting stellar-mass black holes (Miller 2009a)) and even accreting neutron stars (Cackettetal.2008:Reisetal. 2009b)).," A major component of reflection, the broad iron K line, has been found in many Seyfert galaxies \citealt{tanaka95,nandra08}) ), accreting stellar-mass black holes \citealt{miller07,reis09a}) ) and even accreting neutron stars \citealt{cackett08,reis09b}) )." + Both the soft excess and the relativistic broad iron K line have recently been demonstrated to be part of the same physical process. Le.. the reaction of the disk to irradiation from a source. in the Seyfert-1 galaxy 1H 0707-495 (Fabianetal. 2009).," Both the soft excess and the relativistic broad iron K line have recently been demonstrated to be part of the same physical process, i.e., the reaction of the disk to irradiation from a high-energy source, in the Seyfert-1 galaxy 1H 0707-495 \citep{fabian09}." +. In this paper we investigate whether reflection models can account for the spectra of these ULX and. if so. we put them in the context of the accreting black holes known so far.," In this paper we investigate whether reflection models can account for the spectra of these ULX and, if so, we put them in the context of the accreting black holes known so far." + For this study. we choose the ULX with the best available data and with the longest exposure time observations (x[00 kks of exposure time) of the satellite.," For this study, we choose the ULX with the best available data and with the longest exposure time observations ${\approx}100$ ks of exposure time) of the satellite." + By using only the highest quality data from the widest band pass. highest sensitivity instruments available we expect to make good statements on the accretion processes in these ULX.," By using only the highest quality data from the widest band pass, highest sensitivity instruments available we expect to make good statements on the accretion processes in these ULX." + In Section 2. we describe the observations and data used. in Section 3. we report on the results of the application of fits with the reflection model to the spectra and in Section 4. discuss the results obtained.," In Section \ref{observ} we describe the observations and data used, in Section \ref{spec_anal} we report on the results of the application of fits with the reflection model to the spectra and in Section \ref{discuss} discuss the results obtained." + In this work. we consider the time averaged EPIC-pn spectra from the longest available observations of sources with a rate 20.5 ccounts/s in the X-ray band.," In this work, we consider the time averaged EPIC-pn spectra from the longest available observations of sources with a rate ${\ge}0.5$ counts/s in the X-ray band." + The datasets were obtained through the public data archive., The datasets were obtained through the public data archive. + The EPIC-pn camera has a higher effective area than the EPIC-MOS cameras. and drives the results of any joint spectral analysis.," The EPIC-pn camera has a higher effective area than the EPIC-MOS cameras, and drives the results of any joint spectral analysis." + The reduction and analysis reported in this work used SAS version 8.0.0., The reduction and analysis reported in this work used SAS version 8.0.0. + We checked for pile-up in all the observations and found that this was not significant (i.e. less than 5 per cent for the high energy channels) for all the observations., We checked for pile-up in all the observations and found that this was not significant (i.e. less than 5 per cent for the high energy channels) for all the observations. + In Table | we present a log of the observations., In Table \ref{log_obs} we present a log of the observations. + We applied the standard time and flare filtering (rejecting high-background periods of rate 20.4 ccounts/s. as recommended for the pn camera 7).," We applied the standard time and flare filtering (rejecting high-background periods of rate ${\ge}0.4$ counts/s, as recommended for the pn camera )." + We filtered the event files. selecting only the best-calibrated events (pattern«4 for the pn). and rejecting flagged events (flag=0).," We filtered the event files, selecting only the best-calibrated events ${\le}4$ for the pn), and rejecting flagged events $=0$ )." + For each exposure. we extracted the flux from a circular region on each source.," For each exposure, we extracted the flux from a circular region on each source." + The background was extracted from a circular region. not far from the sources.," The background was extracted from a circular region, not far from the sources." + Both the coordinates of the centroids and the radius used for the regions were the same as those employed by Gladstoneetal.(2009)., Both the coordinates of the centroids and the radius used for the regions were the same as those employed by \citet{gladstone09}. +. We built response functions with the SAS tasks andarfgen., We built response functions with the SAS tasks and. + We fitted the background-subtracted spectra with standard models in XSPEC 12.5.0 (Arnaud1996)., We fitted the background-subtracted spectra with standard models in XSPEC 12.5.0 \citep{a1}. +. All errors quoted in this work are 90% confidence errors. obtained by allowing all variable parameters to float during the error scan.," All errors quoted in this work are $90\%$ confidence errors, obtained by allowing all variable parameters to float during the error scan." + Owing to the uncertainties in the EPIC calibration. we used only the kKkeV range.," Owing to the uncertainties in the EPIC calibration, we used only the keV range." + The resulting spectra were grouped with the FTOOL0.3-10 to bins with a minimum of 20 counts each., The resulting spectra were grouped with the FTOOL to bins with a minimum of 20 counts each. + In contrast to previous work. where Comptonization models are used to fit the data. we looked at the observations of NGC 1313 X-l. NGC 1313 X. M8! X-6. HOLM IX X-1. NGC 5408 X-| and HOLM II X-1 from the point of view of a broad iron emission line. Le. a reflection spectrum.," In contrast to previous work, where Comptonization models are used to fit the data, we looked at the observations of NGC 1313 X–1, NGC 1313 X–2, M81 X–6, HOLM IX X–1, NGC 5408 X–1 and HOLM II X–1 from the point of view of a broad iron emission line, i.e. a reflection spectrum." + An absorbed powerlaw was titted to the data in the bands 1.2—3 and 8—-lOkke¥V. In the case of GC 1313 X and M81 X—6 we used the energy range 1—2 and kkeV instead., An absorbed powerlaw was fitted to the data in the bands 1.2–3 and keV. In the case of NGC 1313 X–2 and M81 X–6 we used the energy range 1–2 and keV instead. + The ratio of the whole KkeV data set to he absorbed powerlaw is shown in Figure I.., The ratio of the whole keV data set to the absorbed powerlaw is shown in Figure \ref{plots_ratio}. +" The column densities ‘ound are in the range of Ay,=(0.1—0.5)x107 7. thus arger than the corresponding galactic Hydrogen column densities (Dickey&Lockman1990).. indicating the presence of either local extra-absorption to the sources or intrinsic to the host galaxies."," The column densities found are in the range of $N_{\rm H}=(0.1-0.5){\times}10^{22}$ $^{-2}$, thus larger than the corresponding galactic Hydrogen column densities \citep{dickey90}, indicating the presence of either local extra-absorption to the sources or intrinsic to the host galaxies." + A arge skewed emission feature. similar to those found in BHB and AGN (Milleretal.2007:Tanaka1995:Nandra 2008)) is evident about 3 and kkeV. and a soft excess (like those found in AGN) below kkeV. The data between 1.5 and IOKKeV were then modelled with a powerlaw and a relativistic emission line (Laor1991).," A large skewed emission feature, similar to those found in BHB and AGN \citealt{miller07,tanaka95,nandra08}) ) is evident about 3 and keV, and a soft excess (like those found in AGN) below keV. The data between 1.5 and keV were then modelled with a powerlaw and a relativistic emission line \citep{laor91}." +. A good ft is obtained with Fo=1.5—3 (see Table 21)., A good fit is obtained with ${\Gamma}=1.5-3$ (see Table \ref{tparam}) ). + The addition of this line represents an improvement in the statistics of Ay?=60.115.367.103.65.10 (for 5 extra d.o.£.)," The addition of this line represents an improvement in the statistics of ${\Delta}{\chi}^{2}=60,115,367,103,65,10$ (for 5 extra d.o.f.)" + for NGC 1313 X-I. GC 1313 X. Msi X-6. HOLM IX X-1. NGC 5408 X-1 and HOLM II X-1. respectively.," for NGC 1313 X–1, NGC 1313 X–2, M81 X–6, HOLM IX X–1, NGC 5408 X–1 and HOLM II X–1, respectively." + The line was thereafter significant in all the sources with exception of HOLM II X-1., The line was thereafter significant in all the sources with exception of HOLM II X–1. + HOLM II X-1 has he lowest line detection. due to both the short exposure time and steepness of the spectrum (ve will refer to this point later).," HOLM II X–1 has the lowest line detection, due to both the short exposure time and steepness of the spectrum (we will refer to this point later)." + Further longer exposure observations of HOLM II X-1 are needed o fully address this point., Further longer exposure observations of HOLM II X–1 are needed to fully address this point. + Notice that no extreme inclination is required to reproduce the spectral drop (40— 607)., Notice that no extreme inclination is required to reproduce the spectral drop ${\approx}40-60^{\circ}$ ). + The strength of he line (equivalent width). the rest frame energy and the emissivity index of the line are in the range of EW=0.15—I.27 kkeV. E=6.4-6:97 kKkeV and g=6—10 (see Table 2).," The strength of the line (equivalent width), the rest frame energy and the emissivity index of the line are in the range of $EW=0.15-1.27$ keV, $E=6.4-6.97$ keV and $q=6-10$ (see Table \ref{tparam}) )." + For the case of NGC 1313 X-I. NGC 1313 X2. M81 X-6 and HOLM IX X— the rest-frame energies imply that we are dealing with ionized reflectors (the steepness of the powerlaw for the case of NGC 5408 X-1| and HOLM II X-1 did not allow us to obtain reliable values for the line parameters).," For the case of NGC 1313 X–1, NGC 1313 X–2, M81 X–6 and HOLM IX X--1 the rest-frame energies imply that we are dealing with ionized reflectors (the steepness of the powerlaw for the case of NGC 5408 X–1 and HOLM II X–1 did not allow us to obtain reliable values for the line parameters)." + There are remarkable emission line spectral, There are remarkable emission line spectral +"Neither fit gives a satisfactory halo density contrast, and the PDFs look quite different.","Neither fit gives a satisfactory halo density contrast, and the PDFs look quite different." + The right panel shows the same but this time using the third-order fit with all three bias parameters., The right panel shows the same but this time using the third-order fit with all three bias parameters. +" Here, both fits give PDF's which are almost indistinguishable, but the agreement with the simulated halo density contrast is still not perfect."," Here, both fits give PDFs which are almost indistinguishable, but the agreement with the simulated halo density contrast is still not perfect." + This discrepancy can be seen for all mass bins: Fig., This discrepancy can be seen for all mass bins: Fig. + 9 shows the PDFs of the fits for mass bins III and V compared to the simulated density contrast., \ref{fig:pdf_haloesb4} shows the PDFs of the third-order fits for mass bins III and V compared to the simulated density contrast. + This indicates that the local bias model does not capture all the properties of the halo density field., This indicates that the local bias model does not capture all the properties of the halo density field. + Fig., Fig. +" 10 shows again two slices of the simulation along one axis, extending over the box length L=150Mpc/h."," \ref{fig:dhvsfdmdm_lowdens} shows again two slices of the simulation along one axis, extending over the box length $L=150\ \mathrm{Mpc}/h$." +" Overplotted are the fits of different order to ó5, (left panel) and to dgpr (right panel).", Overplotted are the fits of different order to $\delta_{\mathrm{m}}^{\mathrm{s}}$ (left panel) and to $\delta_{\mathrm{SPT}}^{\mathrm{s}}$ (right panel). +" In the former case, the different fits behave very similarly."," In the former case, the different fits behave very similarly." +" In the latter case, the third-order fit (black long-dashed) seems to be closest to the simulation."," In the latter case, the third-order fit (black long-dashed) seems to be closest to the simulation." +" It is clear that in both cases, the local bias model does not resemble the simulated halo density field on small scales."," It is clear that in both cases, the local bias model does not resemble the simulated halo density field on small scales." +" We also show the results for a medium and a high mass bin (III and V) in Fig. 11,,"," We also show the results for a medium and a high mass bin (III and V) in Fig. \ref{fig:dhvsfdmdm_otherbin}," + but here we show only the fits to ὅτι., but here we show only the fits to $\delta_{\mathrm{m}}^{\mathrm{s}}$. +" Also for higher masses and larger smoothing scales, the ELB model is not satisfactory on a point-by-point level, although the PDFs shown before were similar."," Also for higher masses and larger smoothing scales, the ELB model is not satisfactory on a point-by-point level, although the PDFs shown before were similar." +" We also calculate the linear correlation coefficient c and the Spearman ranked correlation coefficient csp which allows for a general, non-linear correlation between the simulated and fitted 6,(x) (Table 3))."," We also calculate the linear correlation coefficient $c$ and the Spearman ranked correlation coefficient $c_{\mathrm{Sp}}$ which allows for a general, non-linear correlation between the simulated and fitted $\delta_{\mathrm{h}}(\mathbf{x})$ (Table \ref{tab:corrsptb1}) )." +" The values are very close to 1, which shows as well that overall, the local bias assumption is not such a bad model for out data."," The values are very close to 1, which shows as well that overall, the local bias assumption is not such a bad model for out data." +" From now on we will use the third-order fit because it is the model preferred by the AIC, the correlations also support this choice and it is consistent with the order of the SPT calculation."," From now on we will use the third-order fit because it is the model preferred by the AIC, the correlations also support this choice and it is consistent with the order of the SPT calculation." + Fig., Fig. +" 12 shows the mass dependence of the bias parameters (fitting ὃς vs. ó5,) for the mass bins defined in Table 1 and R=12 Mpc/h.", \ref{fig:massdep} shows the mass dependence of the bias parameters (fitting $\delta_{\mathrm{h}}^{\mathrm{s}}$ vs. $\delta_{\mathrm{m}}^{\mathrm{s}}$ ) for the mass bins defined in Table \ref{tab:bins} and $R=12\ \mathrm{Mpc}/h$ . +" Different symbols distinguish the different parameters: red squares for bi, green triangles for b and blue crosses for b3."," Different symbols distinguish the different parameters: red squares for $b_1$, green triangles for $b_2$ and blue crosses for $b_3$." + The lines show a theoretical prediction for the bias parameters obtained as follows: The first step is to apply the peak-background-split model to the halo mass function in the simulation (from the fitting formula presented in ?))., The lines show a theoretical prediction for the bias parameters obtained as follows: The first step is to apply the peak-background-split model to the halo mass function in the simulation (from the fitting formula presented in \citealt{Pillepich08}) ). + ''he second step uses the spherical collapse model to relate the Lagrangian and Eulerian bias parameters (?).., The second step uses the spherical collapse model to relate the Lagrangian and Eulerian bias parameters \citep{2010PhRvD..81f3530G}. +" The two sets of bias parameters show the same trend with halo mass, but they are not in a perfect agreement given the jackknife errors bars (see also ?))."," The two sets of bias parameters show the same trend with halo mass, but they are not in a perfect agreement given the jackknife errors bars (see also \citealt{2010MNRAS.402..589M}) )." +" The error in bs is strongly influenced by shot noise, because there are fewer points in the very high and low density regions which determine the shape of the polynomial."," The error in $b_3$ is strongly influenced by shot noise, because there are fewer points in the very high and low density regions which determine the shape of the polynomial." + In this section we test the accuracy of SPT and ELB for the halo power spectrum., In this section we test the accuracy of SPT and ELB for the halo power spectrum. +" In order to calculate the SPT halo power spectra, we have to re-arrange Ony(x) into terms of the same order in ὅ(x), e.g. 'The biased, third-order SPT halo power spectrum then consists of three terms: with Phymn(k)ος(k)) (as in Eq. 8))."," In order to calculate the SPT halo power spectra, we have to re-arrange $\delta_{\mathrm{h},f_i}^{\mathrm{SPT}}(\mathbf{x})$ into terms of the same order in $\delta_{\mathrm{1}}^{\mathrm{s}}(\mathbf{x})$, e.g. The biased, third-order SPT halo power spectrum then consists of three terms: with $P_{\mathrm{h},mn}(k)\propto \langle \tilde{\delta}_{\mathrm{h}}^{(m)}(\mathbf{k})\, \tilde{\delta}_{\mathrm{h}}^{(n)}(\mathbf{k'}) \rangle$ (as in Eq. \ref{pgen}) )." +" In this way we can make sure(60 that(k) also6” the halo power spectrum does not contain terms of order higher than δὲ,", In this way we can make sure that also the halo power spectrum does not contain terms of order higher than $\delta_1^4$. + Fig., Fig. +" 13 shows the ratio of the reconstructed halo power spectrum to the one from the simulation (left panel: large box, right panel: small box), which has been corrected for (Poissonian) shot noise in the following way: where N is the number of halos in each bin and L is the box size."," \ref{fig:ratio_comp_f11_f31_f31spt} shows the ratio of the reconstructed halo power spectrum to the one from the simulation (left panel: large box, right panel: small box), which has been corrected for (Poissonian) shot noise in the following way: where $\overline{N}$ is the number of halos in each bin and $L$ is the box size." + The top panel on each side corresponds to the power spectrum of while the middle panel corresponds to ," The top panel on each side corresponds to the power spectrum of $\delta_{\mathrm{h},\mathrm{f}_1}^{\mathrm{SPT}}$, while the middle panel corresponds to $\delta_{\mathrm{h},\mathrm{f}_3}^{\mathrm{SPT}}$." +"In the lowest Ont.panel we consider ὅμ,ε,."," In the lowest panel we consider $\delta_{\mathrm{h},\mathrm{f}_3}$." +" Two effects can be dj,noticed:- In general, both linear and third-order SPT underestimates the power apart from the largest scales in both boxes."," Two effects can be noticed: In general, both linear and third-order SPT underestimates the power apart from the largest scales in both boxes." +" However, when kRz7, the unsmoothing effect sets in, eventually leading to a diverging ratio."," However, when $kR \approx \pi$, the unsmoothing effect sets in, eventually leading to a diverging ratio." +" The lowest panel shows that this behaviour is not caused by SPT, because Du and dn,s, have very similar power spectra."," The lowest panel shows that this behaviour is not caused by SPT, because $\delta_{\mathrm{h},\mathrm{f}_3}^{\mathrm{SPT}}$ and $\delta_{\mathrm{h},\mathrm{f}_3}$ have very similar power spectra." +" We also tried to reverse the order of smoothing and fitting in the following way: Determining the bias parameters from a scatter plot of the halo and matter densities,then multiplying the (unsmoothed) matter density with these new bias parameters and applying Eq. (13))"," We also tried to reverse the order of smoothing and fitting in the following way: Determining the bias parameters from a scatter plot of the halo and matter densities,then multiplying the (unsmoothed) matter density with these new bias parameters and applying Eq. \ref{smooth}) )" + to the resulting biased halo field., to the resulting biased halo field. + The halo power spectra from, The halo power spectra from +the occurrence of short (71000 s) thermal bursts at early times after supernova explosion has been predicted. albeit at very soft energies. possibly even lower than those observable bv the LECS (Schlegel 1995).,"the occurrence of short $\sim$ 1000 s) thermal bursts at early times after supernova explosion has been predicted, albeit at very soft energies, possibly even lower than those observable by the LECS (Schlegel 1995)." + We fouud no evidence iu the LECS light curves of similar events. but the suupliug is not conducive to that detection.," We found no evidence in the LECS light curves of similar events, but the sampling is not conducive to that detection." + ILlowever. since there is no evidence of variabilitv of the soft component in the long term. it wight not be related to the supernova.," However, since there is no evidence of variability of the soft component in the long term, it might not be related to the supernova." + In fact. its spectrum cau be fitted also with a power-law superimposed on. aud steeper than. the one which describes the spectrum at higher energies.," In fact, its spectrum can be fitted also with a power-law superimposed on, and steeper than, the one which describes the spectrum at higher energies." + This suggests that the component nüght lave a lore conmlex spectrum (possibly extending toward ultraviolet wavelengths). of which a black body or steep power-law are onlv approximations.," This suggests that the component might have a more complex spectrum (possibly extending toward ultraviolet wavelengths), of which a black body or steep power-law are only approximations." + It could rather be a persistent (or slowly variable with a simall amplitude) source of soft N-ravs such as the host ealaxy itself. or just its bulee. or the superposition of unresolved X-rav sources Within that ealaxx. or diffuse hot eas. or the ITT reeion in which SN 1998bw is located (Calhuna ot al.," It could rather be a persistent (or slowly variable with a small amplitude) source of soft X-rays such as the host galaxy itself, or just its bulge, or the superposition of unresolved X-ray sources within that galaxy, or diffuse hot gas, or the HII region in which SN 1998bw is located (Galama et al." + 1998). or the underline cluster DN 1931-529. or more probably. the stun of some or all of these coutributions.," 1998), or the underlying cluster DN 1931-529, or more probably, the sum of some or all of these contributions." +" The limited augular resolution of BeppoSAX does not allow us to ciseutaugle this component from the swpcrnova νο,", The limited angular resolution of BeppoSAX does not allow us to disentangle this component from the supernova itself. + Notwithstanding this possibility. we note that the tmabsorbed huninositv in the 0.1-2 keV rauge. 5«1010 eres ft. eiven by the superposition of the fitted power-law and black body components. is simular to Iuninosities of supernovac observed m soft N-ravs (Canizares et al.," Notwithstanding this possibility, we note that the unabsorbed luminosity in the 0.1-2 keV range, $5 \times 10^{40}$ erg $^{-1}$, given by the superposition of the fitted power-law and black body components, is similar to luminosities of supernovae observed in soft X-rays (Canizares et al." + 1982: Bregman Pildis 1992: Zinuuermaun ct al., 1982; Bregman Pildis 1992; Zimmermann et al. + 1991: Schlegel et al., 1994; Schlegel et al. + 1996: Fabian Torlevich 1996: Duuuler et al., 1996; Fabian Terlevich 1996; Immler et al. + 1998b)., 1998b). + The GRDB9850125 prompt event is relatively weak with respect to other GRBs. aud rather soft.," The GRB980425 prompt event is relatively weak with respect to other GRBs, and rather soft." + ITowever. it has no outstanding features with respect to other BeppoSAX or BATSE CRBs. which wieght suggest a peculiar counterpart at longer wavelengths. such as a bright supernova. mstead of a “classical” power-law fading afterglow.," However, it has no outstanding features with respect to other BeppoSAX or BATSE GRBs, which might suggest a peculiar counterpart at longer wavelengths, such as a bright supernova, instead of a “classical"" power-law fading afterglow." + The ~h-seconds temporal lag between the WFC aud the GRBAL helt curves could be due to a delav of N-rayv cussion during the burst with respect to the 5-ravs. or ascribed to intrinsic absorption iu a 1iediuni becoming mereasinglv transparent (see c.e.. Dóttteher et al.," The $\sim$ 5-seconds temporal lag between the WFC and the GRBM light curves could be due to a delay of X-ray emission during the burst with respect to the $\gamma$ -rays, or ascribed to intrinsic absorption in a medium becoming increasingly transparent (see e.g., Bötttcher et al." + 1999)., 1999). + Simular soft lags from few to —10 seconds are observed also iu other GRBs (Piro ct al., Similar soft lags from few to $\sim$ 10 seconds are observed also in other GRBs (Piro et al. + 19955: Piro et al., 1998b; Piro et al. + 1998c: Froutera ct al., 1998c; Frontera et al. + 1999)., 1999). + If SN 1998lw is the counterpart of GRD9850125. the production of 5-ravs could be accounted for bv the explosion of the 11 M... hoeliu core of à ~35M. star (Woosley et al.," If SN 1998bw is the counterpart of GRB980425, the production of $\gamma$ -rays could be accounted for by the explosion of the 14 $M_{\odot}$ helium core of a $\sim 35 ~ M_{\odot}$ star (Woosley et al." + 19992: MacFacdyeu Woosley 1999) aud bv the subsequent expansion of a relativistic shock. iu which non-thermal electrous are radiatiug photous of ~ 100 keV. provided the explosion is asvinimetric. ie. the CRB is produced in a relativistie jet (Iwamoto et al.," 1999a; MacFadyen Woosley 1999) and by the subsequent expansion of a relativistic shock, in which non-thermal electrons are radiating photons of $\sim$ 100 keV, provided the explosion is asymmetric, i.e. the GRB is produced in a relativistic jet (Iwamoto et al." + 1998: Woosley et al., 1998; Woosley et al. + 1999a: Wotich. Wheeler. Wang 1999: Rej 1998: sce however. πα et al.," 1999a; Höfflich, Wheeler, Wang 1999; Rej 1998; see however, Kulkarni et al." + 1998a)., 1998a). + The presence of zu undetectable. or barely detectable. nou-thermal CRB remnant. uuderlviug the brighter thermal supernova cjecta cannot be excluded (sec e.g.. Iwamoto 1999).," The presence of an undetectable, or barely detectable, non-thermal GRB remnant, underlying the brighter thermal supernova ejecta cannot be excluded (see e.g., Iwamoto 1999)." + Recent speculations have led to the proposal that every long (>1 s) GRB is formed via supernova. or lypernova. explosion (A\lacFacven Woosley 1999).," Recent speculations have led to the proposal that every long $> 1$ s) GRB is formed via supernova, or hypernova, explosion (MacFadyen Woosley 1999)." + The presence of a supernova uuderlving the CRB afterelow has been recently tested for the optical transicuts of some GRBs with suggestive results (GRB9T0228. Reichart 1999: Calama et al.," The presence of a supernova underlying the GRB afterglow has been recently tested for the optical transients of some GRBs with suggestive results (GRB970228, Reichart 1999; Galama et al." + 19990: CRBOTO508. Cormany et al.," 1999c; GRB970508, Germany et al." + 1999: CGRD980326. Bloom et al.," 1999; GRB980326, Bloom et al." + 1999: GBRDB990510. Fruchter et al.," 1999; GRB990510, Fruchter et al." + 1999d: Beuerimanun et al., 1999d; Beuermann et al. + 1999: CRD990712.. IIorth et al.," 1999; GRB990712, Hjorth et al." + 1999)., 1999). + Ludecd. the recent discovery of a GRD optical counterpart at the intermediate redshift ;=0.13 (Galama et al.," Indeed, the recent discovery of a GRB optical counterpart at the intermediate redshift $z = 0.43$ (Galama et al." + 1999d) müsght support a continuity of properties between GRDB980125 and the other precisely localized GRBs. perhaps based on the different iunouut jet collimation (Woosley. MacFadven. Ποσο 19995) or different beaming. depending on the deeree of jet ienment (Eichler Levinsou 1999: Con 1998: Postuov. Prokhorov. Lipunov 1999).," 1999d) might support a continuity of properties between GRB980425 and the other precisely localized GRBs, perhaps based on the different amount of jet collimation (Woosley, MacFadyen, Heger 1999b) or different beaming, depending on the degree of jet alignment (Eichler Levinson 1999; Cen 1998; Postnov, Prokhorov, Lipunov 1999)." + Di highly collimated or lughly beamed GRBs the non-thermal multiwvaveleueth afterglow could overwhelin the underlying superuova enusson., In highly collimated or highly beamed GRBs the non-thermal multiwavelength afterglow could overwhelm the underlying supernova emission. + This should instead be detected more clearly in less collimated or less beamed (i.c.. secu oft-axis) CRBs. like CRBOs0125. which are. or appear. weaker.," This should instead be detected more clearly in less collimated or less beamed (i.e., seen off-axis) GRBs, like GRB980425, which are, or appear, weaker." + Asstunine association with SN L99Sbw and isotropic cussion. the total cnerey of CRD980125 in the ΙΙΤΟ keV. ~5«Lat ere. is at least four orders of magnitude less than that of GRBs with known distance.," Assuming association with SN 1998bw and isotropic emission, the total energy of GRB980425 in the 40-700 keV, $\sim 5 \times 10^{47}$ erg, is at least four orders of magnitude less than that of GRBs with known distance." + Ou the other hand. disregarding the fact that the xobabilitv of a chance coincidence of GCRBOSO125 aud SN 100δν is extremely low. one might consider S2 as he X-ray counterpart candidate ofthe burst.," On the other hand, disregarding the fact that the probability of a chance coincidence of GRB980425 and SN 1998bw is extremely low, one might consider S2 as the X-ray counterpart candidate of the burst." + The possible detection of S2 in 2-3 λίαν 1998. one week after the CRB. iurplies. with respect to the first NFI detection in April. a uuch slower decay than that ποιααν observed for ταν afterelows (c.e@.. Costa et al.," The possible detection of S2 in 2-3 May 1998, one week after the GRB, implies, with respect to the first NFI detection in April, a much slower decay than that normally observed for X-ray afterglows (e.g., Costa et al." + 1997: Nicastro et al., 1997; Nicastro et al. + 1998: Dal Fine et al., 1998; Dal Fiume et al. + 1999: in t Zand ct al., 1999; in 't Zand et al. + 1998: Nicastro ct al., 1998; Nicastro et al. + 1999: Vreeswijk et al., 1999; Vreeswijk et al. + 1999: ITeise et al., 1999; Heise et al. + 1999)., 1999). + Assuming a power-law decay between the ταν fux ucasured by the WEC in the 2-10 keV range in the last ~20 seconds of the CRB aud the fux measured in the first NFI observation (Fie., Assuming a power-law decay between the X-ray flux measured by the WFC in the 2-10 keV range in the last $\sim$ 20 seconds of the GRB and the flux measured in the first NFI observation (Fig. + ra). we derive a power-law oeidex p1.5. which is similar to commonly observed X-rav afterelows.," 7a), we derive a power-law index $p \sim 1.5$, which is similar to commonly observed X-ray afterglows." + If S2 is an afterelow. one would expect at its intraday variability followed this same temporal schavior.," If S2 is an afterglow, one would expect that its intraday variability followed this same temporal behavior." + Therefore. we have binned the light curve of S2 in the first portion of the April 1998 pointing in five intervals of 20000 seconds cach.," Therefore, we have binned the light curve of S2 in the first portion of the April 1998 pointing in five intervals of 20000 seconds each." + We have then comuected with powerlaws the last WFC ieasurement with the first and last of these fluxes and have determined their oexdices to be pz1.6 aud pz1.1 (Fig.," We have then connected with power-laws the last WFC measurement with the first and last of these fluxes and have determined their indices to be $p +\simeq 1.6$ and $p \simeq 1.4$ (Fig." + το respectively.," 7c), respectively." + The reduced 47 values computed for these two powor-laws with respect to the remainder four NFI data poiuts of April are 3 and 30. respectively. corresponding to low probabilities and <1) that the power-laws describe the observed intrapointing Leht curve. (," The reduced $\chi^2$ values computed for these two power-laws with respect to the remainder four NFI data points of April are 3 and 30, respectively, corresponding to low probabilities and $\ll$ 1) that the power-laws describe the observed intrapointing light curve. (" +All points sec rather consistent with a constant ος.),All points seem rather consistent with a constant trend.) + The upper luüt derived for the secoud portion of the April pointing is inconclusive., The upper limit derived for the second portion of the April pointing is inconclusive. + However. the detection of S2 in May L998 sueeests a mareiual deviation from the above power-laws < 2.450).," However, the detection of S2 in May 1998 suggests a marginal deviation from the above power-laws $\simgt 2.5 \sigma$ )." + Therefore. the prescut data exclude at a confidence level of ~99%.. or higher. that $2 is an afterglow. uuless a simall re-burstius. oue week after the CRB. is superimposed to the power- monotonic decline.," Therefore, the present data exclude at a confidence level of $\sim$, or higher, that S2 is an afterglow, unless a small re-bursting, one week after the GRB, is superimposed to the power-law monotonic decline." + This would be reminiscent of GRD970508. although the time scales for re-bursting," This would be reminiscent of GRB970508, although the time scales for re-bursting" +stars.,stars. + Two of the most perplexing arid long standing xoblems concermug galactic cooling flows are (1) o determine where cooine to kv temperatures actually occurs in the galaxies axd (2) to determine he final physical disposition of he' cooled gas., Two of the most perplexing and long standing problems concerning galactic cooling flows are (1) to determine where cooling to low temperatures actually occurs in the galaxies and (2) to determine the final physical disposition of the cooled gas. + The dropout or cooling of inerstellar eas mst occur over a substantial volume of the inucr galaxy. but he radial mass profile of cooed gas cannot be oxedieted. from first principles since dt depends critically on cutropy fluctuations acquired curing a varietv of complex processes (stellar nass loss. superuovae explosious. maenetic feld variations. ete).," The dropout or cooling of interstellar gas must occur over a substantial volume of the inner galaxy, but the radial mass profile of cooled gas cannot be predicted from first principles since it depends critically on entropy fluctuations acquired during a variety of complex processes (stellar mass loss, supernovae explosions, magnetic field variations, etc.)." +" To aceconunodate this micertaiuty. we have considered a variety of cooling droout models i which the hot eas ds assuned to cool at à rate (Opfüf)q,ρω. where faDinKT/2gupX is the ocal (coistait pressure) cooling time aud qr) is an adjustable dropout huction (Brigheuti Mathews 1999)j."," To accommodate this uncertainty, we have considered a variety of cooling dropout models in which the hot gas is assumed to cool at a rate $(\partial \rho / \partial t)_{do} = -q(r) \rho/t_{do}$, where $t_{do} = 5 m_p k T / 2 \mu \rho \Lambda$ is the local (constant pressure) cooling time and $q(r)$ is an adjustable dropout function (Brighenti Mathews 1999b)." +" We conrpar5 computed interstellar xoperties with currently (f,13 Civis) observed imterscllar eas in the luumous elliptical NGC 1172.", We compare computed interstellar properties with currently $t_n = 13$ Gyrs) observed interstellar gas in the luminous elliptical NGC 4472. + Alost of these models are unacceptable because je radial distributions of N-vaysurface brightuess aMry. gas density mr} or temperature Z(r) disaer‘ee with profiles observed iu this ealaxy.," Most of these models are unacceptable because the radial distributions of X-raysurface brightness $\Sigma_x(r)$, gas density $n(r)$ or temperature $T(r)$ disagree with profiles observed in this galaxy." + Ainois the models considered. the simple coustaut qtr)L model eave the best results. although the agreement with observed ορ) was still rot perfect: we consider this model again here o estimate the nass dropout in NGC 1172.," Among the models considered, the simple constant $q(r) = 1$ model gave the best results, although the agreement with observed $\Sigma_x(r)$ was still not perfect; we consider this model again here to estimate the mass dropout in NGC 4472." + Reearding the secouc perplexing aud long standing problem. it has lone been speculaed hat the cud product of the cocded gas are ow nass. non-ununous stars (Falan. Nulseu Canizares 1982: Thomas 1986: C'owie Diu10v 198s: Vedder. Trester Canizares LOSS: Saraziu Ashe 1989: Ferand. Fabian Johustone 1991).," Regarding the second perplexing and long standing problem, it has long been speculated that the end product of the cooled gas are low mass, non-luminous stars (Fabian, Nulsen Canizares 1982; Thomas 1986; Cowie Binney 1988; Vedder, Trester Canizares 1988; Sarazin Ashe 1989; Ferland, Fabian Johnstone 1994)." + We have receutlv recosidered. the star formation process in elliptical eaaxy cooling flows and lave concluded that fjo dnass of stars in the droyout stellar popilation proably extends to ~2 AL... be (Mathews Brigjouti 1999a).," We have recently reconsidered the star formation process in elliptical galaxy cooling flows and have concluded that the mass of stars in the dropout stellar population probably extends to $\sim 2$ $M_{\odot}$, i.e. (Mathews Brighenti 1999a)." +" As cold gas collects at a cool18o site. d] DeCOMCS eravitationally unstable at this liwiting mass, setting a firm uopor mass Buut n, Ol the IME for stars forming in the central regions of massive ellipticals."," As cold gas collects at a cooling site, it becomes gravitationally unstable at this limiting mass, setting a firm upper mass limit $m_u$ on the IMF for stars forming in the central regions of massive ellipticals." + The τιopor mass limit on the (bottoniheavy) ΠΑΤΕ increases ouly modestly with ealactic radius (~1 AL. at ror.) and ds almost iudependent of time during the evolution of the cooling flow for redshifts DEI., The upper mass limit on the (bottom-heavy) IMF increases only modestly with galactic radius $\sim 4$ $M_{\odot}$ at $r \approx r_e$ ) and is almost independent of time during the evolution of the cooling flow for redshifts $z \lta 1$. + Additional support for the formation of optically huninous stars in galactic cooling flows is provided by the thiuness of the fundamental plane., Additional support for the formation of optically luminous stars in galactic cooling flows is provided by the thinness of the fundamental plane. + For agreement with observed X-aax surface brightuess distributious iu elliptieals. most of the mass of cooled. gas Is concentrated we] within r. where 1e relative‘lw snall dropout mass cau contijbute substantially to the central mass aud niaSS fo ight ratio determined frou scellar velocities.," For agreement with observed X-ray surface brightness distributions in ellipticals, most of the mass of cooled gas is concentrated well within $r_e$ where the relatively small dropout mass can contribute substantially to the central mass and mass to light ratio determined from stellar velocities." + Lf 16 dropou stellar population is assume to be ron-huninous. Mathews Brigheuti (19995) have VAj0wn that the variation of dark dropou lius mone ellipicals causes large. undesiralle süfts iu 16 fundamental plane that are meonipatibe with its observe| thiuuess.," If the dropout stellar population is assumed to be non-luminous, Mathews Brighenti (1999b) have shown that the variation of dark dropout mass among ellipticals causes large, undesirable shifts in the fundamental plane that are incompatible with its observed thinness." + However. these perturbations ou the fturdamental pluie may be lesseιο or removed if the dropout stars are luminous.," However, these perturbations on the fundamental plane may be lessened or removed if the dropout stars are luminous." + Star formation in cllipticals is cficient im the sense that the total mass of ITT eas and cold neutral or molecular gas at any timeare both muuch less than the total mass of gas that has cooled., Star formation in ellipticals is efficient in the sense that the total mass of HII gas and cold neutral or molecular gas at any timeare both much less than the total mass of gas that has cooled. +" Therefore. the star formation rate (Very) i| NGC [172 is equal to the imstautaneous rate that hot iuterscllar eas cools by radiative |ΟΡΟ,"," Therefore, the star formation rate $\Psi_{SFR}$ ) in NGC 4472 is equal to the instantaneous rate that hot interstellar gas cools by radiative losses." +" The total acemulated mass that has cooled iu NGC 1172 since f.=2 Cr. AL(4). aud VaFRdM,fdt ave shown in Figure la: these are based on the 4 model that best fits the N-rav observations of NGC 1172 (Brigheuti Alathews 1999b3."," The total accumulated mass that has cooled in NGC 4472 since $t_* = 2$ Gyr, $M_{do}(t)$, and $\Psi_{SFR} = dM_{do}/dt$ are shown in Figure 1a; these are based on the $q = 1$ model that best fits the X-ray observations of NGC 4472 (Brighenti Mathews 1999b)." +" The mass dropou Ανfu) at f,=13 Cars for this model occurs mostly in kÀEX:s and the total «ropout Wass ls Mist)LT«Late AL..."," The mass dropout $M_{do}(r,t_n)$ at $t_n = 13$ Gyrs for this model occurs mostly in $r \lta r_e$ and the total dropout mass is $M_{do}(t_n) = 4.7 \times 10^{10}$ $M_{\odot}$." +" This is much less han the total ciureut stellar miass ia NGC 1172. Alfa736410 Al... determine: with M/Lgy-0.2,"," This is much less than the total current stellar mass in NGC 4472, $M_{*t} = 7.26 \times 10^{11}$ $M_{\odot}$, determined with $M/L_B = 9.2$." + For the »urpose of illusration. We assu| that the old eaactic stars cau be approximate asa sinele burst stellar population having a Sapeter IMF from Hh0.1 to Hh125 AL...," For the purpose of illustration, we assume that the old galactic stars can be approximated as a single burst stellar population having a Salpeter IMF from $m_{\ell} = 0.1$ to $m_u = 125$ $M_{\odot}$ ." +" By contrast. f1c younger dropout stellar popuation with varialΊο SER. Usry(t). js asstumecl to have a Salpeter IME from ii=0.1 to an,2.5 Al..."," By contrast, the younger dropout stellar population with variable SFR, $\Psi_{SFR}(t)$ , is assumed to have a Salpeter IMF from $m_{\ell} = 0.1$ to $m_u = 2.5$ $M_{\odot}$ ." + Bothof these IMF's are available in suele burst, Bothof these IMFs are available in single burst +In next section we will provide an illustrative application of Sturm theorem by applying it to compute the number of critical points for axisymmetric polytropic accretion in Paczynsski and Wiita (1980) pseudo-Schwarzschild potential.,In next section we will provide an illustrative application of Sturm theorem by applying it to compute the number of critical points for axisymmetric polytropic accretion in Paczyńsski and Wiita (1980) pseudo-Schwarzschild potential. + In $2.2.1.. we have shown that the energy first integral of motion polynomial in critical points is a fourth degree equation for this case. and hence analytical solution is possible to explicitly find the roots Qvhich has been performed in $2.3)).," In \ref{subsubsection2.2.1}, we have shown that the energy first integral of motion polynomial in critical points is a fourth degree equation for this case, and hence analytical solution is possible to explicitly find the roots (which has been performed in \ref{subsection2.3a}) )." + We compute the number of roots (for same set of initial boundary condition) as a sanity check against the known (already calculated. both analytically as well as numerically) to show that Sturm theorem can actually provide the exact number of sonic point. before we apply it to tind out the number of roots for relativistic accretion where no such analytical solution exists (since it is a fourteenth degree equation as already been demonstrated in $2.4.29) for cross verification.," We compute the number of roots (for same set of initial boundary condition) as a sanity check against the known (already calculated, both analytically as well as numerically) to show that Sturm theorem can actually provide the exact number of sonic point, before we apply it to find out the number of roots for relativistic accretion where no such analytical solution exists (since it is a fourteenth degree equation as already been demonstrated in \ref{subsubsection2.4.2}) ) for cross verification." +" The energy first integral polynomial for such situation can be expressed as: where Subsequently we obtain the corresponding sequences as: where For the parameter set |£.=0.0001.A1.75.-71>]. one obtains. We now consider the left boundary of the open interval to be the Schwarzschild radius. which is unity in our scaled unit of radial distance used to describe the flow equation for pseudo-Schwarzschild axisymmetric polytropic accretion. and the right boundary to be 10"" (in our scaled unit of radial distance}. which is such a large distance that beyond which practically no critical point is expected to form."," The energy first integral polynomial for such situation can be expressed as: where Subsequently we obtain the corresponding sequences as: where For the parameter set $\left[{\cal E}=0.0001, \lambda =1.75, \gamma =\displaystyle\frac{4}{3}\right]$, one obtains We now consider the left boundary of the open interval to be the Schwarzschild radius, which is unity in our scaled unit of radial distance used to describe the flow equation for pseudo-Schwarzschild axisymmetric polytropic accretion, and the right boundary to be $10^6$ (in our scaled unit of radial distance), which is such a large distance that beyond which practically no critical point is expected to form." + We then calculate the sign changes of the Sturm sequence and show the results in the following table:, We then calculate the sign changes of the Sturm sequence and show the results in the following table: +lt transpires that spectra within areas of this plot appear broadly similar ancl six broad eroupines can be distinguished.,It transpires that spectra within areas of this plot appear broadly similar and six broad groupings can be distinguished. + These are identified by different svmbols in Fie., These are identified by different symbols in Fig. + 4 md some subsequent plots., \ref{slopes} amd some subsequent plots. + Typical examples of each group are shown in Fig. 5.., Typical examples of each group are shown in Fig. \ref{sample}. + These arbitrarily. defined eroups are maintained to aid the following discussion., These arbitrarily defined groups are maintained to aid the following discussion. + Fig., Fig. + 4 also shows the set of N-tvpe comparison stars., \ref{slopes} also shows the set of N-type comparison stars. + Fhese lie below the J stars in the plot. though there is some overlap. particularly towards the lower left-hand corner.," These lie below the J stars in the plot, though there is some overlap, particularly towards the lower left-hand corner." + lt is easy to see the kev features of these groups by inspecting the spectra in Fig. 5.. (, It is easy to see the key features of these groups by inspecting the spectra in Fig. \ref{sample}. ( +Phese are. unsmoothed spectra.),These are unsmoothed spectra.) + The peak is stronger than the peak in Group 1. these two peaks are at about the same level in Groups 23. whilst in Groups 46 the peak is below the other.," The peak is stronger than the peak in Group 1, these two peaks are at about the same level in Groups 2–3, whilst in Groups 4–6 the peak is below the other." + Spectral distinction within Groups 23 and Groups 46 is mace by the level of the flux at the peak at relative to the and 6202 peaks., Spectral distinction within Groups 2–3 and Groups 4–6 is made by the level of the flux at the peak at relative to the and 6202 peaks. + The best examples of these groups in the Galactic J-star spectra plotted by Barnbaum et al., The best examples of these groups in the Galactic J-star spectra plotted by Barnbaum et al. + (1996). are Group 1 WA Cve J6(€3 J4)] (though WX Cvg is peculiar in some respects). Group 2 HO Cas 44.5 (C5 3]. and Group GL Lyr Mp (C5 3.5)].," \shortcite{barnbaum96} are Group 1 – WX Cyg [J6 $^-$ J4)] (though WX Cyg is peculiar in some respects), Group 2 – HO Cas [J4.5 (C5 $^-$ )], and Group 6 – T Lyr [J4:p (C5 J3.5)]." + The terms in the square brackets are the MIS. classifications based. on the revised. sheme of Keenan (1993) as quoted by Barnbaum et al. (1996)., The terms in the square brackets are the MK classifications based on the revised sheme of Keenan \shortcite{keenan93} as quoted by Barnbaum et al. \shortcite{barnbaum96}. +. Phere are no representatives of Groups 3.5., There are no representatives of Groups 3–5. + Near-Infrared. (NUR) photometry of sources in much of the LAIC is available through the Second. Incremental Data Release of the Pwo Micron. All Sky Survey (Skrutskicctal.1997). which. is accessible on-line at http://irsaipac.caltech.edu., Near-Infrared (NIR) photometry of sources in much of the LMC is available through the Second Incremental Data Release of the Two Micron All Sky Survey – \cite{skrutskie97} which is accessible on-line at http://irsa.ipac.caltech.edu. + JEN. measurements were extracted for. most of the carbon stars by matching catalogue coordinates., $JHK$ measurements were extracted for most of the carbon stars by matching catalogue coordinates. + Only two J stars hack ambiguous identifications in the database., Only two J stars had ambiguous identifications in the database. + The (/A) colour is related to the effective temperature — Z;rr; (Bessell et al. (1983).," The $(J-K)$ colour is related to the effective temperature – $T_{eff}$ (Bessell et al. \shortcite{bessell83}," +. Dergeat. Ixnapik Rutily (200122).," Bergeat, Knapik Rutily \shortcite{bergeat01}) )." + IJKk photometry is also available from the Deep Survey of the southern sky DENIS (Cioniοἱal.100) which is available on-line [rom the CDS at Strasbourg (http://cdsweb.u-strasbe.fr/denis.html).," $IJK$ photometry is also available from the Deep Near-Infrared Survey of the southern sky – DENIS \cite{cioni00} + which is available on-line from the CDS at Strasbourg (http://cdsweb.u-strasbg.fr/denis.html)." + Phe J and A data were extracted. for. the stars and. used. for. those stars with no measurements., The $J$ and $K$ data were extracted for the J stars and used for those stars with no measurements. + These magnitudes: were made fainter by mmag and. mmag respectively to bring them into alignment with the data., These magnitudes were made fainter by mag and mag respectively to bring them into alignment with the data. + ποσο corrections were calculated from the cülferences seen for the sample of J stars measured in both surveys., These corrections were calculated from the differences seen for the sample of J stars measured in both surveys. + Phere was no magnitude dependence and the rms values were mamas and mamag., There was no magnitude dependence and the rms values were mag and mag. + Ri photometry of the LAIC stars is available [rom IXDMINSOLT., $RI$ photometry of the LMC stars is available from KDMK01. + Le was derived from measurements of. direct UBST plates made. with the SuperCOSAIOS measuring machine: see IXDMINSOL for details., It was derived from measurements of direct UKST plates made with the SuperCOSMOS measuring machine; see KDMK01 for details. + Phe Af photometry in &eneral sullers more from the blending of the carbon star images with close line-of-sight companions than the infrared photometry because the neighbouring stars are usually bluer than the carbon stars., The $RI$ photometry in general suffers more from the blending of the carbon star images with close line-of-sight companions than the infrared photometry because the neighbouring stars are usually bluer than the carbon stars. + Nevertheless. the extraction software used to obtain the ΠΕ photometry copes with. blended images in all but the severest: situations.," Nevertheless, the extraction software used to obtain the $RI$ photometry copes with blended images in all but the severest situations." + Also. a few stars suller from contamination of 2 due to Ho emission from background. nebulositv.," Also, a few stars suffer from contamination of $R$ due to $\alpha$ emission from background nebulosity." + An infrared. A. (/A) colour-magnitude diagram. is shown in Fig. 6.. ," An infrared $K$, $(J-K)$ colour-magnitude diagram is shown in Fig. \ref{jk_k}, ," +again with the spectral groups as define in Fig., again with the spectral groups as defined in Fig. + 4. indicated., \ref{slopes} indicated. + Superimposecl are lines representing he sequence of LMC N stars (including the Co-weak stars)., Superimposed are lines representing the sequence of LMC N stars (including the $_2$ -weak stars). + This sequence was obtained from the 44A. photometry of he N stars in the 2d sample by contructing histograms in A for each 0.1 mae interval in (/A)., This sequence was obtained from the $JHK$ photometry of the N stars in the 2dF sample by contructing histograms in $K$ for each 0.1 mag interval in $(J-K)$. + The solic ine is the mean and the dotted. [lines show the extents of the region containing SO per cent of the stars in each Xn., The solid line is the mean and the dotted lines show the extents of the region containing 80 per cent of the stars in each bin. + A full. description of the work on the N stars wil » presented. elsewhere., A full description of the work on the N stars will be presented elsewhere. + What is clear is that most. of the J stars form a sequence which lies about 0.6 mag fainter han the N-star sequence., What is clear is that most of the J stars form a sequence which lies about 0.6 mag fainter than the N-star sequence. + This is certainly so for stars redder than (/0A) 11.2. but caution must be appliec ο this statement for the bluer stars which are much fewer in number.," This is certainly so for stars redder than $(J-K)$ 1.2, but caution must be applied to this statement for the bluer stars which are much fewer in number." + Phere are also some exceptions which are much xiehter., There are also some exceptions which are much brighter. + Phese are almost all Group 1 stars: in fact. all bu one of the Group 1 stars lie to the bright side of the mean N- sequence.," These are almost all Group 1 stars; in fact, all but one of the Group 1 stars lie to the bright side of the mean N-star sequence." + The sequence of faint blue stars is almost al rom Group 2 and the reddest stars are predominantly from Group 6., The sequence of faint blue stars is almost all from Group 2 and the reddest stars are predominantly from Group 6. + Thus. there is a clear link between optical spectra characteristics on the one hand. and. temperature. and/or uminosity (às determined. from. the NUR photometry) on he other.," Thus, there is a clear link between optical spectral characteristics on the one hand and temperature and/or luminosity (as determined from the NIR photometry) on the other." + The displacement. of the J stars from the bulk of the μίας in Fig., The displacement of the J stars from the bulk of the N stars in Fig. + G6 has been interpreted here as a change inuminositv. although the effect. could also be due at least in xwt to changes in the spectra. caused by molecular bands in the near-LR.," \ref{jk_k} has been interpreted here as a change inluminosity, although the effect could also be due at least in part to changes in the spectra, caused by molecular bands in the near-IR." + Only. infrared. spectroscopy can settle this xit the luminosity interpretation is favoured since the shifts in (JAK) colour would be very large for many stars. anel »ecause a similar elfect is seen in the £ (21) CMD (sec Fig.," Only infrared spectroscopy can settle this but the luminosity interpretation is favoured since the shifts in $(J-K)$ colour would be very large for many stars, and because a similar effect is seen in the $I$ $(R-I)$ CMD (see Fig." + Y below). where the loci are almost horizontal.," \ref{ri_i} below), where the loci are almost horizontal." + The possible existence of two groups. of JJ. stars with cdillercnt [uminosities arising from stars of cdillerent initial mass and perhaps following different evolutionary mechanisms has alreacy been suggested: (Lorenz-Martins (1996).. Abia Isern (2000))).," The possible existence of two groups of J stars with different luminosities arising from stars of different initial mass and perhaps following different evolutionary mechanisms has already been suggested (Lorenz-Martins \shortcite{lorenz96}, Abia Isern \shortcite{abia00}) )." + The photometric separation of Group 1 stars from the rest lends support to this idea., The photometric separation of Group 1 stars from the rest lends support to this idea. + tt will. be useful in. Section 6 to. consider the dependence of various spectral parameters on the near-infrared photometry., It will be useful in Section 6 to consider the dependence of various spectral parameters on the near-infrared photometry. + Normal J stars will be taken tobe those ocated in the broad. band of stars centred: on a sequence roughly parallel to but. fainter than that of the No stars., Normal J stars will be taken tobe those located in the broad band of stars centred on a sequence roughly parallel to but fainter than that of the N stars. + Bright J stars are taken to be those more than mmag xiehter in A than this sequence., Bright J stars are taken to be those more than mag brighter in $K$ than this sequence. + Vhree colour ranges will wove tobe useful: 7.A)€ 125. 1.25.π(JJ.N)«€1.5 and (JJ/—Αν} 11...," Three colour ranges will prove tobe useful: $(J-K) \leq 1.25$ , $1.25 \leq (J-K) \leq 1.5$ and $(J-K) \geq 1.5$ ." + Some of the carbon stars are likely to be variable. so the Whotometry has this additional uncertainty.," Some of the carbon stars are likely to be variable, so the photometry has this additional uncertainty." + However. with xh. infrared ancl visual observations having been almost," However, with both infrared and visual observations having been almost" +velocity perturbation during the trausit and the transit photometric liehteurve.,velocity perturbation during the transit and the transit photometric lightcurve. + We fully recognize the limitations and approximations inherent in this modoeliug procedure., We fully recognize the limitations and approximations inherent in this modeling procedure. + First. there is no veason to assume that lnb-darkenius should follow any particular lav.," First, there is no reason to assume that limb-darkening should follow any particular law." + Also. the lil darkening iu photospheric absorption lines is quite different frou the hb darkening im the contiuuuu.," Also, the limb darkening in photospheric absorption lines is quite different from the limb darkening in the continuum." + While this iypears to be taken iuto account bv Claret(2000). the lib. darkening paramcterization is based on model atmospheres rather than ou real stars.," While this appears to be taken into account by \citet{Cl00}, the limb darkening parameterization is based on model atmospheres rather than on real stars." + More iiportautly. in our model we compute the specificiutensity weighted apparent Doppler shift of the visible portion of the photosphere.," More importantly, in our model we compute the specific-intensity weighted apparent Doppler shift of the visible portion of the photosphere." + On the other hand. our spectra record transit-perturbed stellar absorption line profile shapes from which we measure au appareut Doppler shift using a computer code that assunes an unperturbed lue-profile shape.," On the other hand, our spectra record transit-perturbed stellar absorption line profile shapes from which we measure an apparent Doppler shift using a computer code that assumes an unperturbed line-profile shape." + In future improvements to our RM model. we will attempt to improve several of these limitations.," In future improvements to our RM model, we will attempt to improve several of these limitations." + We used the model described iu Sec., We used the model described in Sec. +" ?? to analyze siuultazueouslv the data sets from the ILJST cs23. the HET URS. aud the observations published bx Naritaetal.(2008). which we will refer to as the ""OAO/IIIDES"" data set."," \ref{sec:RMModel} to analyze simultaneously the data sets from the HJST cs23, the HET HRS, and the observations published by \citet{NaSaOh08}, which we will refer to as the “OAO/HIDES” data set." + Since cach data set has its own independent velocity zero-point. we allowed the systemic velocity of cach data set to be au independent ree parauneter in the aualvsis.," Since each data set has its own independent velocity zero-point, we allowed the systemic velocity of each data set to be an independent free parameter in the analysis." + The values of the fixed xuwanueters for the analysis are given iu Table 3.., The values of the fixed parameters for the analysis are given in Table \ref{tab:fixedparams}. + The uanetarv orbital clemeuts were taken from bwinetal. (2008)., The planetary orbital elements were taken from \citet{IrChNu08}. +. These elements are essentially indistinguishable roni the single-plauct fit of Shortetal.(2008)., These elements are essentially indistinguishable from the single-planet fit of \citet{ShWeOr08}. +. We rote that the conclusious of this work depeud ou the articular values of these parameters we adopt., We note that the conclusions of this work depend on the particular values of these parameters we adopt. + If anv of these parameters turn out to be in significant error. hose errors will propagate through this analysis.," If any of these parameters turn out to be in significant error, those errors will propagate through this analysis." + Iu modeling the data. we allowed the orbital plane inclination /. the projected angle A between the planetary orbital axis and the stellar rotation axis. the projected stellar rotational velocity οσαἐν as well as the svstenic velocity of cach separate data set to be free parameters.," In modeling the data, we allowed the orbital plane inclination $i$, the projected angle $\lambda$ between the planetary orbital axis and the stellar rotation axis, the projected stellar rotational velocity $v \sin i$, as well as the systemic velocity of each separate data set to be free parameters." + We then uuimimized the chi-squared of the model ft to the data., We then minimized the chi-squared of the model fit to the data. +" For the combined data sets. we obtained A=9.149.3"" at cmn;=6.3+ 11klhuss and ¢=85.97tal’."," For the combined data sets, we obtained $\lambda = 9.4\arcdeg \pm +9.3\arcdeg$ at $v \sin i = 6.3 \pm 1.1$ $^{-1}$ and $i = 85.9\arcdeg \pm 0.4\arcdeg$." + This indicates that the planet is orbiting near the stellar equatorial plane. to within the uncertainty of our determination.," This indicates that the planet is orbiting near the stellar equatorial plane, to within the uncertainty of our determination." + Our derived csiu/ is somewhat larecr than the value of 5| found by (2008) and the + given by Fischer2007)., Our derived $v \sin i$ is somewhat larger than the value of $^{-1}$ found by \citet{NaSaOh08} and the $^{-1}$ given by \citet{FiVoMa07}. +. Our inclination is within oue o of the Naritaetal. value of 85.657.," Our inclination is within one $\sigma$ of the \citeauthor{NaSaOh08} + value of $85.65\arcdeg$." +" However. our value for A from the conibined data differs significantly from that of etal.(2008)... who found A=62°+2h"","," However, our value for $\lambda$ from the combined data differs significantly from that of \citet{NaSaOh08}, who found $\lambda = 62\arcdeg \pm 25\arcdeg$." + Tn order to uuderstaud the reason for this difference. we then modeled each of the three data sets separately.," In order to understand the reason for this difference, we then modeled each of the three data sets separately." + The derived A and ; for the combined fit. as well as for cach individual data set are given in Tab. L.," The derived $\lambda$ and $i$ for the combined fit, as well as for each individual data set are given in Tab. \ref{tab:results}." + We also eive σοι the systemic velocity for cach data set in the combined fit. as well as 5;. the svstemic velocity for eac[um individual data set fit.," We also give $\gamma_c$ , the systemic velocity for each data set in the combined fit, as well as $\gamma_i$, the systemic velocity for each individual data set fit." +" From the OAO/IIIDES data set alone. we computed A=59.1""+19.77 at {=86.2""+mo"". "," From the OAO/HIDES data set alone, we computed $\lambda = 59.4\arcdeg \pm 19.7\arcdeg$ at $i = 86.2\arcdeg \pm +0.8\arcdeg$ ." +"Tf we fix the inclination at the /=85.65"" value of Naritaetal.(2008).. we eet A=61.17+28.57."," If we fix the inclination at the $i = 85.65\arcdeg$ value of \citet{NaSaOh08}, we get $\lambda = 61.4\arcdeg \pm 28.5\arcdeg$." + The surprisinely excellent agreement of all of these value for he OAO/IIIDES data set thus validates the modeling Xocess of Naritactal..., The surprisingly excellent agreement of all of these value for the OAO/HIDES data set thus validates the modeling process of \citeauthor{NaSaOh08}. + We note that the results from he ILJST data alone are iu verv good aereciment with he combined results., We note that the results from the HJST data alone are in very good agreement with the combined results. + Due to the desigu lianitations of he TET. the VET/IIRS data ouly covered the first half of the transit.," Due to the design limitations of the HET, the HET/HRS data only covered the first half of the transit." + Thus. the code could trade-off A vs. the systemic velocity for the data set. aud derived a slisbtly ower v? with A=32.1725.2? for the ITET data alouc.," Thus, the code could trade-off $\lambda$ vs. the systemic velocity for the data set, and derived a slightly lower $\chi^2$ with $\lambda = -32.4\arcdeg \pm 25.2\arcdeg$ for the HET data alone." + The model fit tothe data is shown iu Fie. L., The model fit tothe data is shown in Fig. \ref{fig:rvfit}. + We also computed a model with uo RM effect by setting esin;=0., We also computed a model with no RM effect by setting $v \sin i = 0$. + This removes the stellar rotation. aud thus there is no apparent Doppler shift of the portion of the stellar photosphere eclipsed by the planet.," This removes the stellar rotation, and thus there is no apparent Doppler shift of the portion of the stellar photosphere eclipsed by the planet." + The exin;=0 model gave 47=71.56 (42=1.13) ax opposed to 4?=10.53 (2= 0.83) for the best fittine RM model for the conibined data set., The $v \sin i = 0$ model gave $\chi^2 = 71.56$ $\chi^2_r = 1.43$ ) as opposed to $\chi^2 = 40.53$ $\chi^2_r = 0.83$ ) for the best fitting RM model for the combined data set. + Thus. we conclude that the RM effect was indeed convincingly detected iu spite of the appareut noise in the data.," Thus, we conclude that the RM effect was indeed convincingly detected in spite of the apparent noise in the data." + Examining the 4? of each individual data set in the full mocel aud the esin/=0 model showed that even in the noisiest case of the OAO/IIIDES data. the RM effect reduced the total 47 by 13.1.," Examining the $\chi^2$ of each individual data set in the full model and the $v \sin i = 0$ model showed that even in the noisiest case of the OAO/HIDES data, the RM effect reduced the total $\chi^2$ by 13.1." + Due to the svunuetiic signature of the RM effect iu the ÀzzO case. it is critically important to sample the eutire transit.," Due to the symmetric signature of the RM effect in the $\lambda \approx 0$ case, it is critically important to sample the entire transit." + This is evidenced by the fit to the IIET/IIRS data alone. in which despite the lieh quality of the Chea. onlv the first half of the trausit was observable. and therefore crroncous parameters are derived.," This is evidenced by the fit to the HET/HRS data alone, in which despite the high quality of the data, only the first half of the transit was observable, and therefore erroneous parameters are derived." + In order to successfully calibrate the baseline. radial velocity variation. observations well before aud after the trausit are required.," In order to successfully calibrate the baseline radial velocity variation, observations well before and after the transit are required." + Lf the radial velocity cau be well calibrated by observations before aud after transit. the iuflueuce of nucertaity in the zero-point velocity offset (5) will be uceleible ou the RAL effect parameters.," If the radial velocity can be well calibrated by observations before and after transit, the influence of uncertainty in the zero-point velocity offset $\gamma$ ) will be negligible on the RM effect parameters." + We have reanalyzed the data of Naritactal.(2008) along with our own independent observations of the spectroscopic transit of the eccentric exoplanctIID117156b. aud we find that A=οι+ 9.3.," We have reanalyzed the data of \citet{NaSaOh08} along with our own independent observations of the spectroscopic transit of the eccentric exoplanet17156b, and we find that $\lambda = 9.4\arcdeg \pm 9.3\arcdeg$ ." + We conclude that this exoplanetary svsteni ds simular to almost all of the other short-period transiting exoplauetary svstenis studied using the RM effect so far. in that it shows that the projected planetary orbital," We conclude that this exoplanetary system is similar to almost all of the other short-period transiting exoplanetary systems studied using the RM effect so far, in that it shows that the projected planetary orbital" +A systematic search for new PNe was conducted in a 63x aremin- region near the star forming complex 30 Doradus using publicly available deep ESO WFI B. V. [O III] and He imaging.,"A systematic search for new PNe was conducted in a $63\times63$ $^2$ region near the star forming complex 30 Doradus using publicly available deep ESO WFI $B$, $V$ , [O III] and $\alpha$ imaging." + Two bona-fide PNe (MNCI and MNC2) and one possible PN (MNC3) were identified and their. basic properties presented., Two bona-fide PNe (MNC1 and MNC2) and one possible PN (MNC3) were identified and their basic properties presented. + The [O III] images were calibrated in flux using previously known PNe with literature fluxes., The [O III] images were calibrated in flux using previously known PNe with literature fluxes. + At 6-7 magnitudes fainter than the PNLF cut-off. the new discoveries indicate the PN population in the 30 Doradus region ts relatively complete to this depth.," At 6–7 magnitudes fainter than the PNLF cut-off, the new discoveries indicate the PN population in the 30 Doradus region is relatively complete to this depth." + There may however be some PNe totally embedded in the nebula emission and velocity-sensitive techniques such as cross-dispersed or fabry-perot imaging may be required to detect them (Jacoby De Marco 2002)., There may however be some PNe totally embedded in the nebula emission and velocity-sensitive techniques such as cross-dispersed or fabry-perot imaging may be required to detect them (Jacoby De Marco 2002). + The main result of our survey is that there remains a small population of faint PNe of small angular size awaiting discovery in the LMC., The main result of our survey is that there remains a small population of faint PNe of small angular size awaiting discovery in the LMC. + At 2-3 PN per square degree. with identical observations of the inner 5x5 degrees coinciding with the RP2006a survey footprint. we would expect to reveal 50-75 new PNe 6-7 mag fainter than the bright-end of the PNLF.," At 2–3 PN per square degree, with identical observations of the inner $5\times5$ degrees coinciding with the RP2006a survey footprint, we would expect to reveal 50–75 new PNe 6–7 mag fainter than the bright-end of the PNLF." +" This is a substantial population that should be factored into estimates of the total LMC PN population,", This is a substantial population that should be factored into estimates of the total LMC PN population. + An additional bona-fide PN. MNC4. Was found serendipitously from. visual examination of the deep 8.88 tile from the near-infrared VMC survey.," An additional bona-fide PN, MNC4, was found serendipitously from visual examination of the deep 8 tile from the near-infrared VMC survey." + Spectroscopic observations show the object to be a PN with a rare [WC9]- Wolf-Rayet central star., Spectroscopic observations show the object to be a PN with a rare [WC9]--[WC11] Wolf-Rayet central star. + There are now at least six [WR] central stars in MCPNe (Leisy Dennefeld 2006)., There are now at least six [WR] central stars in MCPNe (Leisy Dennefeld 2006). + This object is located outside the RP2006b survey footprint anc clearly demonstrates that the VMC survey can find new PNe that are underrepresented in the current population., This object is located outside the RP2006b survey footprint and clearly demonstrates that the VMC survey can find new PNe that are underrepresented in the current population. + Estimating the theoretical. or indeed. observed LMC P population is at present highly uncertain.," Estimating the theoretical, or indeed, observed LMC PN population is at present highly uncertain." + The theoretical estimate of 1000250 PNe (Jacoby 1980; Peimbert 1990) contains a large uncertainty that could easily be higher., The theoretical estimate of $1000\pm250$ PNe (Jacoby 1980; Peimbert 1990) contains a large uncertainty that could easily be higher. + Emphasis must therefore instead be placed on producing a robust tally of observed PNe., Emphasis must therefore instead be placed on producing a robust tally of observed PNe. + Our survey of a small regior IS à positive step m this direction. but the VMC survey will have a much larger impact on the tally.," Our survey of a small region is a positive step in this direction, but the VMC survey will have a much larger impact on the tally." + We have demonstratec here with MNC4 that it is possible to find new PNe from the VMC survey alone., We have demonstrated here with MNC4 that it is possible to find new PNe from the VMC survey alone. + The VMC survey 1s also well-suited to the removal of contaminating objects that fall into Ha: selectec samples such as RP2006b(e.g. Frew Parker 2010)., The VMC survey is also well-suited to the removal of contaminating objects that fall into $\alpha$ selected samples such as RP2006b (e.g. Frew Parker 2010). + Initial results indicate a very ‘high contamination fraction of - for 98 previously catalogued PNe that are mostly located near 30 Doradus (Cioni et al., Initial results indicate a very high contamination fraction of $\sim$ for 98 previously catalogued PNe that are mostly located near 30 Doradus (Cioni et al. + 2011: Miszalski et al., 2011; Miszalski et al. + 2011)., 2011). +" It is plausible that up to 170 PNe classified as ""likely"" anc ""possible"" by RP2006b could eventually be removed with the assistance of further VMC observations.", It is plausible that up to 170 PNe classified as `likely' and `possible' by RP2006b could eventually be removed with the assistance of further VMC observations. + This would drop the PN population down to «620 PNewhich includes our potential survey contribution of 50-75 PNe., This would drop the PN population down to $\sim$ 620 PNewhich includes our potential survey contribution of 50–75 PNe. +negligible compared to the masses of their host galaxies.,negligible compared to the masses of their host galaxies. + In that case the critical rate of energy deposition will no longer be independent of mgu and we do not expect Eq., In that case the critical rate of energy deposition will no longer be independent of $\mbh$ and we do not expect Eq. + 2 to hold.," \ref{eq:prop} + to hold." + We have thus confirmed that feedback enables BHs to regulate their growth., We have thus confirmed that feedback enables BHs to regulate their growth. +" Moreover, we demonstrated that this self-regulation takes places on scales over which the gravitational influence of the BHs is negligible, provided that the fraction of the accreted rest mass energy that is coupled back into the interstellar medium is >107°."," Moreover, we demonstrated that this self-regulation takes places on scales over which the gravitational influence of the BHs is negligible, provided that the fraction of the accreted rest mass energy that is coupled back into the interstellar medium is $\gtrsim +10^{-5}$." +" To test whether it is the stellar or the dark matter distribution that determines the mass of BHs, we compare the BH masses in two simulations that are identical except for the assumed efficiency of star formation."," To test whether it is the stellar or the dark matter distribution that determines the mass of BHs, we compare the BH masses in two simulations that are identical except for the assumed efficiency of star formation." +" One uses our fiducial star formation law, but in the other simulation we reduced its amplitude by a factor of 100, making the gas consumption time scale much longer than the age of the Universe."," One uses our fiducial star formation law, but in the other simulation we reduced its amplitude by a factor of 100, making the gas consumption time scale much longer than the age of the Universe." +" Because changing the amount of stars would imply changing the rate of injection of supernova energy, which could affect the efficiency of BH feedback, we neglected feedback from star formation in both runs."," Because changing the amount of stars would imply changing the rate of injection of supernova energy, which could affect the efficiency of BH feedback, we neglected feedback from star formation in both runs." +" In the simulation with sstar formation the central regions of the galaxies are dominated gravitationally by the baryonic component of the galaxy, whereas in the simulation with reduced star formation the DM dominates everywhere."," In the simulation with star formation the central regions of the galaxies are dominated gravitationally by the baryonic component of the galaxy, whereas in the simulation with reduced star formation the DM dominates everywhere." + Fig., Fig. + 2 shows the ΠΙΒΗ—mnaio and mpu—m. relations at redshift 0., \ref{fig:changing_baryons} shows the $\mbh-\mhalo$ and $\mbh-\ms$ relations at redshift 0. +" While the two runs produce nearly identical BH masses for a fixed halo mass, the ΠΙΒΗ—m. relation is shifted to lower stellar masses by more than an order of magnitude in the model with reduced star formation."," While the two runs produce nearly identical BH masses for a fixed halo mass, the $\mbh-\ms$ relation is shifted to lower stellar masses by more than an order of magnitude in the model with reduced star formation." + The insensitivity of the relation between mpy and mma to the assumed star formation efficiency demonstrates that the BH mass is not set by the gravitational potential on the scale of the galaxy., The insensitivity of the relation between $\mbh$ and $\mhalo$ to the assumed star formation efficiency demonstrates that the BH mass is not set by the gravitational potential on the scale of the galaxy. + We have verified that the same result holds at redshift two for the simulations with 64 times better mass resolution., We have verified that the same result holds at redshift two for the simulations with 64 times better mass resolution. +" Clearly, stellar mass does not significantly influence the relation between the mass of the BH and that of its host halo."," Clearly, stellar mass does not significantly influence the relation between the mass of the BH and that of its host halo." + T'his implies that BH self-regulation occurs on the scale of DM haloes., This implies that BH self-regulation occurs on the scale of DM haloes. +" If the rate by which the BHs inject energy is independent of the assumed feedback efficiency, then we expect the same to be true for the factor by which BH feedback suppresses star formation."," If the rate by which the BHs inject energy is independent of the assumed feedback efficiency, then we expect the same to be true for the factor by which BH feedback suppresses star formation." + This is confirmed by comparison of the global SFRs in runs with different values of e¢ (see Fig., This is confirmed by comparison of the global SFRs in runs with different values of $\epsf$ (see Fig. + 6 of BS09)., 6 of BS09). + Fig., Fig. + 3 compares the predicted Ίοδιρmagn—mnaio relation with observation (Bandaraetal.2009)., \ref{fig:mhalombh} compares the predicted $\log_{10}\mbh-\log_{10}\mhalo$ relation with observation \citep{band09}. +10610 The agreement is striking., The agreement is striking. +" The slope and normalization of the observed logy(mpu/Mo)—log,o(mnaio/10P?Μο) relation are 1.55+0.31 and 8.18+0.11 respectively, whereas the simulation predicts 1.55+0.05 and 8.01+0.04."," The slope and normalization of the observed $\log_{10}(\mbh/\msun)-\log_{10}(\mhalo/10^{13}\,\msun)$ relation are $1.55\pm0.31$ and $8.18\pm0.11$ respectively, whereas the simulation predicts $1.55\pm0.05$ and $8.01\pm0.04$." + Note that the simulation was only tuned to match the normalization of the relations between mgu and the galaxy stellar properties., Note that the simulation was only tuned to match the normalization of the relations between $\mbh$ and the galaxy stellar properties. +" If the energy injected by a BH is proportional to the halo gravitational binding energy, then, for isothermal models (Silk&Rees1998),, mauος mj,.."," If the energy injected by a BH is proportional to the halo gravitational binding energy, then, for isothermal models \citep{silk98}, $\mbh\propto\mhalo^{5/3}$ ." +" Here we extend these models to the more realistic universal halo density profile (Navarroetal.1997),, whose shape is specified by a concentration parameter, c (we assumed cοςULax/U2, where Umax and vy are the maximum halo circular velocity and the circular velocity at the virial radius respectively)."," Here we extend these models to the more realistic universal halo density profile \citep{nava97}, whose shape is specified by a concentration parameter, $c$ (we assumed $c\propto v_{\rm max}^2/v_{\rm v}^2$, where $v_{\rm + max}$ and $v_{{\rm v}}$ are the maximum halo circular velocity and the circular velocity at the virial radius respectively)." +" It is known that concentration decreases with increasing halo mass, cοςημ��ς. (Bullocketal.2001;Duffy2008),, which then affects BH mass through the dependence of halo binding energy on concentration."," It is known that concentration decreases with increasing halo mass, $c\propto\mhalo^{-0.1}$ \citep{bulo01,duff08}, which then affects BH mass through the dependence of halo binding energy on concentration." + If the total energy injected by a BH of a given mass is proportional to the energy required to unbind gas from a DM halo, If the total energy injected by a BH of a given mass is proportional to the energy required to unbind gas from a DM halo +galaxies simply contain fewer stars than expected for an observed satellite of the same mass.,galaxies simply contain fewer stars than expected for an observed satellite of the same mass. +" However, the simulation already has comparatively weak feedback, and allowing for brighter satellites by a constant factor would cause the most luminous satellites, which are in good agreement with the Magellanic Clouds, to become too bright."," However, the simulation already has comparatively weak feedback, and allowing for brighter satellites by a constant factor would cause the most luminous satellites, which are in good agreement with the Magellanic Clouds, to become too bright." +" Furthermore, making the star formation more efficient in all satellites would shift the points in Fig."," Furthermore, making the star formation more efficient in all satellites would shift the points in Fig." +" 15 both down and to the right, hence spoiling the good agreement with the location of the break in the observed relation."," \ref{fig:Mateo_Plot} both down and to the right, hence spoiling the good agreement with the location of the break in the observed relation." +" In Figure 16,, we show the relation between photometric surface brightness of all simulated dwarf galaxies inside a sphere of radius 350kpc centred on a fiducial position of the Sun."," In Figure \ref{fig:Satellites_Vmag_phot}, we show the relation between photometric surface brightness of all simulated dwarf galaxies inside a sphere of radius $350\; \mathrm{kpc}$ centred on a fiducial position of the Sun." +" The Sun was assumed to lie 8.5kpc away from the centre of the galaxy, in the central plane of the stellar disc."," The Sun was assumed to lie $8.5\; \mathrm{kpc}$ away from the centre of the galaxy, in the central plane of the stellar disc." +" As can be seen from the relatively large scatter of the plot, the simulation produces also satellites that are well above the SDSS surface brightness detection limit."," As can be seen from the relatively large scatter of the plot, the simulation produces also satellites that are well above the SDSS surface brightness detection limit." +" Counting the galaxies with a photometric magnitude brighter then 30mag/arcsec? (dashed red line) and a distance smaller than 280kpc (dot dashed blue line) results in observable 46 (77, 18, 70) satellites for the(BH,,CR,, WiND)) simulation."," Counting the galaxies with a photometric magnitude brighter then $30\; \mathrm{mag/arcsec^2}$ (dashed red line) and a distance smaller than $280\; \mathrm{kpc}$ (dot dashed blue line) results in observable $46$ $77$, $18$, $70$ ) satellites for the, ) simulation." + This is actually in reasonable agreement with the prediction of 57 satellites for the Milky Way., This is actually in reasonable agreement with the prediction of $57$ satellites for the Milky Way. +" The cutoff radius of 280kpc was chosen as a compromise between the measured distances to allknown satellites, which reach up to &1Mpc, and the virial radius of rooo=238kpc of the simulated host galaxy."," The cutoff radius of $280\; \mathrm{kpc}$ was chosen as a compromise between the measured distances to allknown satellites, which reach up to $\approx 1\;\mathrm{Mpc}$, and the virial radius of $r_{200}= 238\;\mathrm{kpc}$ of the simulated host galaxy." +" This is also the same cut off radius that has been used in previous work (??),, although we note that some studies have adopted a different choice (e.g.?).."," This is also the same cut off radius that has been used in previous work \citep{Koposov08,Maccio10}, although we note that some studies have adopted a different choice \citep[e.g.][]{Via_Lactea_I}." + The rather small number of satellites classified as ‘observable’ for the simulation can easily be explained by the lower luminosity function shown in figure 1.., The rather small number of satellites classified as `observable' for the simulation can easily be explained by the lower luminosity function shown in figure \ref{fig:Satellites_Luminosity_Function}. +" Finally, we consider the relation between the dark matter masses of our simulated satellites with their stellar mass and luminosity, as shown in Figure 17.."," Finally, we consider the relation between the dark matter masses of our simulated satellites with their stellar mass and luminosity, as shown in Figure \ref{fig:maccio_5}." +" For each satellite, we plot the dark matter mass with different symbols, both at the epoch of accretion and at the present epoch."," For each satellite, we plot the dark matter mass with different symbols, both at the epoch of accretion and at the present epoch." +" To simplify a comparison with figure 5 of ?,, we used exactly the same axis range in our plot as they did."," To simplify a comparison with figure 5 of \citet{Maccio10}, , we used exactly the same axis range in our plot as they did." +" Unlike in the results of ?,, we find a clear bend in the relation, meaning that our satellites tend to have higher stellar masses, especially at the low mass end, than the satellites of ?.."," Unlike in the results of \citet{Maccio10}, we find a clear bend in the relation, meaning that our satellites tend to have higher stellar masses, especially at the low mass end, than the satellites of \citet{Maccio10}." + The latter results are based on a semi-analytic model where the orbits of an infalling satellite are estimated based on a random choice of plausible infall parameters., The latter results are based on a semi-analytic model where the orbits of an infalling satellite are estimated based on a random choice of plausible infall parameters. +" It is possible that this explains the discrepancy, or that it originates in approximate treatments of tidal or ram pressure stripping in the semi-analytic model."," It is possible that this explains the discrepancy, or that it originates in approximate treatments of tidal or ram pressure stripping in the semi-analytic model." +" In future work, it will be interesting to inter-compare direct hydrodynamical simulations and the semi-analytic models on a satellite by satellite basis, in order to better understands the origin of these differences in the predictions."," In future work, it will be interesting to inter-compare direct hydrodynamical simulations and the semi-analytic models on a satellite by satellite basis, in order to better understands the origin of these differences in the predictions." +" In this work, we studied a set of high-resolution hydrodynamical simulations of the formation of a Milky Way sized galaxy, starting from cosmological initial conditions."," In this work, we studied a set of high-resolution hydrodynamical simulations of the formation of a Milky Way sized galaxy, starting from cosmological initial conditions." +" Such simulations are now able to reach sufficiently high resolution to directly resolve the formation of the small dwarf galaxies that orbit in the halo, thereby allowing studies of the missing satellite problem and of the properties predicted by simulations for the population of satellite galaxies."," Such simulations are now able to reach sufficiently high resolution to directly resolve the formation of the small dwarf galaxies that orbit in the halo, thereby allowing studies of the missing satellite problem and of the properties predicted by simulations for the population of satellite galaxies." +" These galaxies are especially interesting both because the dark matter substructure abundance is a fundamental challenge for the ACDM cosmology, and because the low star formation efficiencies of the satellites provide crucial information about the physics of feedback."," These galaxies are especially interesting both because the dark matter substructure abundance is a fundamental challenge for the $\Lambda$ CDM cosmology, and because the low star formation efficiencies of the satellites provide crucial information about the physics of feedback." +" We have therefore repeated our simulations using different models for feedback physics, with the goal to test the sensitive of the results for the satellites with respect to these physics assumptions."," We have therefore repeated our simulations using different models for feedback physics, with the goal to test the sensitive of the results for the satellites with respect to these physics assumptions." +" In the model, we considered only star formation and SN feedback, together with instantaneous reionization at z=6."," In the model, we considered only star formation and SN feedback, together with instantaneous reionization at $z=6$." +" The three other models included additional processes like AGN feedback (BH)), wind driven galactic outflows (WIND)) and the generation and decay of cosmic rays (CR))."," The three other models included additional processes like AGN feedback ), wind driven galactic outflows ) and the generation and decay of cosmic rays )." +" Not unexpectedly, the model showed no significant differences compared to the reference model, as most of the satellites are simply too small to grow a large supermassive black hole and are rarely affected by strong quasar feedback in neighbouring galaxies."," Not unexpectedly, the model showed no significant differences compared to the reference model, as most of the satellites are simply too small to grow a large supermassive black hole and are rarely affected by strong quasar feedback in neighbouring galaxies." +" In contrast, the model showed a significant reduction of the number of high mass satellites, but did not give a significantly different abundance of low mass systems."," In contrast, the model showed a significant reduction of the number of high mass satellites, but did not give a significantly different abundance of low mass systems." + The model had exactly the opposite effect as it did not change the high mass satellites but suppressed star formation in low mass satellites., The model had exactly the opposite effect as it did not change the high mass satellites but suppressed star formation in low mass satellites. + This made the cosmic ray model most successful in matching the faint-end of the observed satellite luminosity function., This made the cosmic ray model most successful in matching the faint-end of the observed satellite luminosity function. + Our results further suggest that a combination of the and feedback models should be able to yield a nearly perfect match of the luminosity function., Our results further suggest that a combination of the and feedback models should be able to yield a nearly perfect match of the luminosity function. + The total number of satellites observable with an SDSS- survey covering the whole sky has been estimated to be 57 (?).., The total number of satellites observable with an SDSS-like survey covering the whole sky has been estimated to be $57$ \citep{SatKinematics}. . +" Interestingly, imposing the same surface brightness detection threshold on all ofour simulated systems yields"," Interestingly, imposing the same surface brightness detection threshold on all ofour simulated systems yields" +(AS) al separation ju] <- te = (Παρ)x EEΑθ,", at separation | < x_o = G m_1/ (v_c^2a_n)." +") This means the physical acceleration of particle j caused by MW is ο/η, and the acceleration. ofB MW~ caused by particle. jP is mj/, times. cz/r.L7 which. conserves momentum."," This means the physical acceleration of particle $j$ caused by MW is $v_c^2/r$, and the acceleration of MW caused by particle $j$ is $m_j/m_1$ times $v_c^2/r$ , which conserves momentum." +" Equation (A2)) is simplified bv setting E, E, =f, .— where Γι =Fy follows from the conditions νο—0 and ax17/7 at à—0."," Equation \ref{eq:eofm}) ) is simplified by setting F^+_n=, F^-_n= =, =, where F^-_1 = 0=F^+_0 follows from the conditions $a_{1/2}=0$ and $a\propto t^{2/3}$ at $a\rightarrow 0$." + This brings eq. (A2)), This brings eq. \ref{eq:eofm}) ) +" to — .] +EF, 1): + + TOI224 The coordinates are relaxed toward a solution at ο=0 bv the coordinate shift δη thatsatisfies"," to = ) + ) + + H_o^2 The coordinates are relaxed toward a solution at $S_{i,k,n}=0$ by the coordinate shift $\delta x_{i,k,n}$ thatsatisfies" +"have been studied by many authors (see reviews by, e.g., Leighton 1963, Spruit et al.","have been studied by many authors (see reviews by, e.g., Leighton 1963, Spruit et al." +" 1990, Nordlund et al."," 1990, Nordlund et al." + 2009 and references therein)., 2009 and references therein). +" Through the magnetic field, the convective energy is transported upward to supply the sufficient energy to maintain the 1 MK corona."," Through the magnetic field, the convective energy is transported upward to supply the sufficient energy to maintain the 1 MK corona." +" Therefore, the dynamics of the convective motions plays a key role in the so-called coronal heating problem, one of the most important issues in the solar physics."," Therefore, the dynamics of the convective motions plays a key role in the so-called coronal heating problem, one of the most important issues in the solar physics." +" However, the temporal evolution of convection motion have not been sufficiently elucidated."," However, the temporal evolution of convection motion have not been sufficiently elucidated." + The vertical motion in convection is easily observed by using Doppler analysis., The vertical motion in convection is easily observed by using Doppler analysis. + This motion generates compressible waves such as magnetohydrodynamic slow mode waves or fast mode waves., This motion generates compressible waves such as magnetohydrodynamic slow mode waves or fast mode waves. +" Although a lot of energy can be transported upward by the waves caused by convection, compressible waves are not considered to contribute to coronal heating, because the wave energy will be significantly reduced before reaching the corona by shock dissipation or reflection in the chromosphere (Hollweg1981)."," Although a lot of energy can be transported upward by the waves caused by convection, compressible waves are not considered to contribute to coronal heating, because the wave energy will be significantly reduced before reaching the corona by shock dissipation or reflection in the chromosphere \citep{holl81}." +". On the other hand, the horizontal motion in convection plays an important role in the coronal heating."," On the other hand, the horizontal motion in convection plays an important role in the coronal heating." + The interaction between magnetic field and the convection generates Alfvénn waves (UchidaKaburaki1974) while the stochastic photospheric motion braids the field lines to store the energy in the corona as electric current (Parker1983)., The interaction between magnetic field and the convection generates Alfvénn waves \citep{uchi74} while the stochastic photospheric motion braids the field lines to store the energy in the corona as electric current \citep{park83}. +". Due to the lack of observations, it has been poorly understood what mechanisms contribute to coronal heating."," Due to the lack of observations, it has been poorly understood what mechanisms contribute to coronal heating." + The local correlation tracking (LCT) method commonly is used to derive the horizontal velocity field (November&Simon1988;Bergeretal.1998).," The local correlation tracking (LCT) method commonly is used to derive the horizontal velocity field \citep{nove88,berg98}." +". Since LCT method uses apparent motion of granules to derive the velocity, it is better to use high spatial resolution and seeing-free data sets."," Since LCT method uses apparent motion of granules to derive the velocity, it is better to use high spatial resolution and seeing-free data sets." +" From the horizontal velocity derived by LCT method, mesogranules and supergranules can be observed (e.g. Kitai et al."," From the horizontal velocity derived by LCT method, mesogranules and supergranules can be observed (e.g. Kitai et al." +" 1997, Ueno Kitai 1998, Shine et al."," 1997, Ueno Kitai 1998, Shine et al." + 2000)., 2000). +" Although various studies reveal the frequency distribution (Titleetal.Bergeretal.1998) and the spatial power spectra (Rieutordetal.2000,2008) of horizontal velocity fields, few studies explicitly mention the temporal power spectra"," Although various studies reveal the frequency distribution \citep{titl89,berg98} and the spatial power spectra \citep{rieu00, rieu08} of horizontal velocity fields, few studies explicitly mention the temporal power spectra" +the time is ereater than 750 000 vears. then the orbits of particles in the cust rl1 are eettiue close to the orbits of the planets due o the increase of particles eccentricities.,"the time is greater than 750 000 years, then the orbits of particles in the dust ring are getting close to the orbits of the planets due to the increase of particles eccentricities." + The situation afer 15) 000. vears can be seen in Fie., The situation after 750 000 years can be seen in Fig. + 7., 7. +" The dust particles wih R= 2 yo. ο = 1 g/au? aud Qh, = 0.75 are claracerized by he value J 5 0.216 (sec Eq."," The dust particles with $R$ $=$ 2 $\mu$ m, $\varrho$ $=$ 1 $^{3}$ and $\bar{Q}'_{pr}$ $=$ 0.75 are characterized by the value $\beta$ $\approx$ 0.216 (see Eq." + 15)., 45). + For tus value of 3. one obtains e z 57.7 AU for he location of tlC CXCLIO niea1 motion 2/1 resona1ος with Neptune: it follows froma αρα1/7 (3/1)P°°. where ap is senianajor axis of Neptune.," For this value of $\beta$, one obtains $a$ $\approx$ 57.7 AU for the location of the exterior mean motion 3/1 resonance with Neptune; it follows from $a$ $=$ $a_{P}$ $(1 - \beta)^{1/3}$ $(3/1)^{2/3}$, where $a_{P}$ is semi-major axis of Neptune." + We cau sec. from he evoluion of seniauajor axis 1i Fig.," We can see, from the evolution of semi-major axis in Fig." + T. that the sealar seni-nuajoy axis is a decreasing function of time ching he first 750 000 vears.," 7, that the secular semi-major axis is a decreasing function of time during the first 750 000 years." + Thus the semiauajor axis cau evolve TOM ald 1utial value of GO AU to the location close to the 11011111οjon 3/1 resonance., Thus the semi-major axis can evolve from an initial value of 60 AU to the location close to the mean-motion 3/1 resonance. + Particles are influenced both w the vicinitv of Neptune orbit and the exterior mean motion 3/1 resonance with Neptune., Particles are influenced both by the vicinity of Neptune orbit and the exterior mean motion 3/1 resonance with Neptune. + Evolution during the first 750 O00 vears is influenced mainly bv the neutral interstellar hwdrogen gas and. later on. mainly by the eravitation of planets.," Evolution during the first 750 000 years is influenced mainly by the neutral interstellar hydrogen gas and, later on, mainly by the gravitation of planets." + Tuchision of the P-R effect. the non-radial solar wind and the interstellar gas into the equation of motion of the dust particle without planets can stabilize the particles orbit.," Inclusion of the P-R effect, the non-radial solar wind and the interstellar gas into the equation of motion of the dust particle without planets can stabilize the particle's orbit." + The stabilization is characterized by stable values of orbital elements., The stabilization is characterized by stable values of orbital elements. + This stabilization is discussed in Klackka et al. (, This stabilization is discussed in Klačkka et al. ( +2009a) for sine = 0.05.,2009a) for $\sin \varepsilon$ $=$ 0.05. + The process of stabilization requires about b « 107 vears for the dust particle with i = 0.01., The process of stabilization requires about 1 $\times$ $^{8}$ years for the dust particle with $\beta$ $=$ 0.01. + This time is not very sensitive to the efiiciency factor for radiation pressure ο., This time is not very sensitive to the efficiency factor for radiation pressure $\bar{Q}'_{pr}$. + Towever. for lower values of ο the stabilization occur with larecr probability. because stabilization effect of the non-radial solar wind is stronegcr (see Eq.," However, for lower values of $\bar{Q}'_{pr}$ the stabilization occur with larger probability, because stabilization effect of the non-radial solar wind is stronger (see Eq." + 18)., 48). + Tf also plaucts are cousidered iu, If also planets are considered in +s primary objective is to detect. Earth-size planets in the habitable zone of Main Sequence stars., primary objective is to detect Earth-size planets in the habitable zone of Main Sequence stars. + The large field of view (FOV) targeting the rich star field in Cygnus (~10 degrees olf the galactic plane) was carefully chosen to optimize the science vield, The large field of view (FOV) targeting the rich star field in Cygnus $\sim 10$ degrees off the galactic plane) was carefully chosen to optimize the science yield +Making observational detections in cosmology is hard.,Making observational detections in cosmology is hard. + Two to three sigma evidence lor new plivsies is common in the literature and the community is rightly skeptical of results with marginal statistical significance., Two to three sigma evidence for new physics is common in the literature and the community is rightly skeptical of results with marginal statistical significance. + Even in the case of5o results. detections can be questioned if the results are surprising or conflicting cata is released.," Even in the case of$5\sigma$ results, detections can be questioned if the results are surprising or conflicting data is released." + When detections are expected there is a natural tendency (o accept them more readily., When detections are expected there is a natural tendency to accept them more readily. + Barvon Acoustic Oscillations (BAO) (BAO:e.g...Bassett&Illozek2010) are a good example., Baryon Acoustic Oscillations (BAO) \citep[BAO; \eg][]{bao_review} are a good example. + The original BAO results of the SDSS and 2dF teams (Eisensteinetal.al.2005) were at less than 36. significance.," The original BAO results of the SDSS and 2dF teams \citep{sdss_bao, 2df_bao} were at less than $3\sigma$ significance." + Nevertheless. the detection has been essentially unanimously accepted by the community (althoughseeSvlosLabinietal.2009) despite the diffieultv of localizing the BAO peak. illustrated by the shift in BAO results between 2007 and 2009 in Percivaletal.(2007) and Percivaletal.(2010) and recent studies ol mock catalogs (Ixazinοἱal.2010b) which suggest that the BAO peak would be invisible in at least LOW of SDSS DI-sized samples.," Nevertheless, the detection has been essentially unanimously accepted by the community \citep[although see][]{LVBL} despite the difficulty of localizing the BAO peak, illustrated by the shift in BAO results between 2007 and 2009 in \citet{will} and \citet{dr7} and recent studies of mock catalogs \citep{sim} which suggest that the BAO peak would be invisible in at least $10\%$ of SDSS DR7-sized samples." + such detections are easy to accept since the detected peak is precisely in the place where il was expected to be., Such detections are easy to accept since the detected peak is precisely in the place where it was expected to be. + This willingness to accept marginal detections carries (wo dangers., This willingness to accept marginal detections carries two dangers. + First. (he signal may actually be pure statistical fIuctuation and hence provide precise but inaccurate knowledge.," First, the signal may actually be pure statistical fluctuation and hence provide precise but inaccurate knowledge." + Second. it can actively discourage publication of other studies which are apparently at odds with the *detection.," Second, it can actively discourage publication of other studies which are apparently at odds with the `detection'." + In (his/etfer. we point out that the possibility that the detection is not real. but just a statistical [Inctuation due to noise. has a significant impact on use of the data lor parameter estimation.," In this, we point out that the possibility that the detection is not real, but just a statistical fluctuation due to noise, has a significant impact on use of the data for parameter estimation." + This arises because the full posterior twpically has very non-gaussian tails even if the likelihood is gaussian. as illustrated in Figure (1)).," This arises because the full posterior typically has very non-gaussian tails even if the likelihood is gaussian, as illustrated in Figure \ref{BAO_pdf}) )." + Like a scorpion. the sting is in the tail.," Like a scorpion, the sting is in the tail." + The prototypical example we have in mind is the use of the BAO peak for cosmology. but the principle is valid generally.," The prototypical example we have in mind is the use of the BAO peak for cosmology, but the principle is valid generally." + While the current best BAO combined detection is ad the ~4.90 level from the SDSS. 6df ancl WigeleZ catalogues (Blakeοἱal.2011).. lower significance detections will alwavs mark the fronüer of the subject as we push (o higher redshifts and different samples.," While the current best BAO combined detection is at the $\sim 4.9 \sigma$ level from the SDSS, 6df and WiggleZ catalogues \citep{blake_wigglez}, lower significance detections will always mark the frontier of the subject as we push to higher redshifts and different samples." +The search for BAO with the SDSS. 20Z and 28LACG survey quasars illustrates our point.,"The search for BAO with the SDSS, 2QZ and 2SLAQ survey quasars illustrates our point." + While they show a peak in the expected place (1055.! Mpe. thev also show a (presumably) fake peak near 855.! Mpe (Sawangwitetal.," While they show a peak in the expected place $105 h^{-1}$ Mpc, they also show a (presumably) fake peak near $85 h^{-1}$ Mpc \citep{Sawangwit}." + 2011)... more standard: example is the recent 6d£ survey which found 2.10. evidence for BAO while the WieeleZ detection is 3.26 at z= 0.6., A more standard example is the recent 6df survey which found $2.4 \sigma$ evidence for BAO while the WiggleZ detection is $3.2 \sigma$ at $z = 0.6$ . + This will continue with a munber of BAO first detections still to come in the next lew vears:, This will continue with a number of BAO first detections still to come in the next few years: +figure. the entire neutron star is assumed to be emitting uniforily.,"figure, the entire neutron star is assumed to be emitting uniformly." + The asvinmetry of the line profies Decolue nore »rominen wheu ouly a racion of the stelar surface contributes to the line emission., The asymmetry of the line profiles become more prominent when only a fraction of the stellar surface contributes to the line emission. + Sucl a configuratio ikely in the case of votle neutrO1 stars. which may have lateral compositio1 ας temperature οells owing to heir strong magne fields.," Such a configuration is likely in the case of young neutron stars, which may have lateral composition and temperature gradients owing to their strong magnetic fields." + Nonuniloriu eluission is almost certainly relevart also j e case of burste ‘sas 1dicated the observatious of large aim»litude {lus oscillationsk cdLjug he jiermonuclear διists (Strolunay 2001)., Nonuniform emission is almost certainly relevant also in the case of bursters as indicated by the observations of large amplitude flux oscillations during the thermonuclear bursts (Strohmayer 2001). + As Figure 2 shows. iu he case ofuou-uniformni emission. p€ase-jutegratecL line proiles acquir a coubly peaked character. with a brighter blue wine.," As Figure 2 shows, in the case of non-uniform emission, phase-integrated line profiles acquire a doubly peaked character, with a brighter blue wing." + Iu this figure. the emittiug 'eelon. which 1a an angular radius of 207. is assumed to je at 1the rotational eqtator.," In this figure, the emitting region, which has an angular radius of $20^\circ$, is assumed to be at the rotational equator." + This conlietration vields the largeste separation of the two peaks in the liie profile |)ecallse O ‘the largest. li1le-Osieht velocities., This configuration yields the largest separation of the two peaks in the line profile because of the largest line-of-sight velocities. + Note that due to the strong (0eravitational lensing.Om the two maxina of the dou)ly »eaked profile do uot correspond to the line emission at rotaticmal pliases o=+a 7/2. where o=0 [1euotes tlie phase when the center of the emitting regiou is aliened with tle observer.," Note that due to the strong gravitational lensing, the two maxima of the doubly peaked profile do not correspond to the line emission at rotational phases $\phi = \pm \pi/2$ , where $\phi = 0$ denotes the phase when the center of the emitting region is aligned with the observer." + As a conseqence. the separation ol the peaks is not proportional to 22Ofix/c. where 5 is the Lorentz factor corresponding to the rotational velocity and Q is the augular velocity ofthe neutron star.," As a consequence, the separation of the peaks is not proportional to $2 \gamma \Omega R_{\rm NS} / c$, where $\gamma$ is the Lorentz factor corresponding to the rotational velocity and $\Omega$ is the angular velocity ofthe neutron star." +The middle panels of Fig.,The middle panels of Fig. + 7 show that the faring phase is characterised by three consecutive bursts also of period about 3 niu., \ref{fig7} show that the flaring phase is characterised by three consecutive bursts also of period about 3 min. + The power of the 3-mun oscillations during the fare is two orders of magnitude higher than iu the pre-flare pliase., The power of the 3-min oscillations during the flare is two orders of magnitude higher than in the pre-flare phase. + In the decay phase shown in the bottom panels of Fig. 7..," In the decay phase shown in the bottom panels of Fig. \ref{fig7}," + the 3-anin oscillations are also preseut., the 3-min oscillations are also present. + Their level is of the samme order as in the pre-flare pliasc. anc does not exceed the 30 level.," Their level is of the same order as in the pre-flare phase, and does not exceed the $\sigma$ level." + We consider another flaring event associated with AR 10756. which occurred on 2005 Mav | at 01:5002:10. UT.," We consider another flaring event associated with AR 10756, which occurred on 2005 May 4 at 01:50-02:10 UT." + The visual inspection of the light curve of this event (Fie. 3..," The visual inspection of the light curve of this event (Fig. \ref{burst_lc}," + central panel) muplies that aud1 oscillations are preseut., central panel) implies that 3-min oscillations are present. +" As in the event ou 2005 April 28, we first analyse the time evolution of the polarisatio- signal integrated. over the FOL"," As in the event on 2005 April 28, we first analyse the time evolution of the polarisation signal integrated over the FOI." + The results obtained for the integrated signal are preseuted in Fi, The results obtained for the integrated signal are presented in Fig. +e.o 8 ina similar fashion to Fig. 7.., \ref{fig8} in a similar fashion to Fig. \ref{fig7}. + As on 2005 April 28. 3aniu oscillation traius are present in all phases of the flare.," As on 2005 April 28, 3-min oscillation trains are present in all phases of the flare." + Tn the wavelet spectrum. the fille period of these wave rains is situated iu the 2-1 min band aud is nof seen to change with tine.," In the wavelet spectrum, the filling period of these wave trains is situated in the 2-4 min band and is not seen to change with time." +" Before the flare. iu the time iuterval 1:36 - 01:50 UT one cau see a strong. well over 39. Increase in the power of 2aunin oscillation traius. with a uaxinmni at about 01:10. UT (see Fig. δι,"," Before the flare, in the time interval 01:36 - 01:50 UT one can see a strong, well over $3\sigma$, increase in the power of 3-min oscillation trains, with a maximum at about 01:40 UT (see Fig. \ref{fig8}," + upper row)., upper row). + During the faring phase (01:50-02:10. UT). there were our pronounced enüssion oeaks of period about 3 miu (see Fig. 8..," During the flaring phase (01:50-02:10 UT), there were four pronounced emission peaks of period about 3 min (see Fig. \ref{fig8}," + muddle row)., middle row). + The maxiuun power of anim oscillatious was reached at about 1:57 UT., The maximum power of 3-min oscillations was reached at about 1:57 UT. + In the post-flare jxiase (02:10-03:00. UT. see. Fig. S.," In the post-flare phase (02:10-03:00 UT, see Fig. \ref{fig8}," + bottom row). when he enüssion decreases gradually to the pre-flaring level. radius of Jani oscillations are also present.," bottom row), when the emission decreases gradually to the pre-flaring level, trains of 3-min oscillations are also present." + At this stage. he 3aniu oscillation trains have approximately coustaut )»wer.," At this stage, the 3-min oscillation trains have approximately constant power." + The time intervals between the oscillation trains are iu this case about 10-20 min., The time intervals between the oscillation trains are in this case about 10-20 min. + We emphasize that this behaviour appears to differ from the post-Hare phase of the event on 2005 Apri 28 (Sect. 2.1)).," We emphasize that this behaviour appears to differ from the post-flare phase of the event on 2005 April 28 (Sect. \ref{2804}) )," + when initially the time intervals between the Senda oscillation trains were rather stable with a value of about 12-13 niu., when initially the time intervals between the 3-min oscillation trains were rather stable with a value of about 12-13 min. + Figure 9 shows the spatial location of microwave sources during the flare., Figure \ref{fig9} shows the spatial location of microwave sources during the flare. + There are two istiuct sources. one situated over the sunspot aud another associated with the flare.," There are two distinct sources, one situated over the sunspot and another associated with the flare." + This time. in coutrast to the event on 2005 April 28. the sunspot and the flare-associated burst sources of the microwave enüsson are spatially separated at a distance of about 35 from each other.," This time, in contrast to the event on 2005 April 28, the sunspot and the flare-associated burst sources of the microwave emission are spatially separated at a distance of about 35"" from each other." +" Παισο, this eveut allows us to study αλα oscillations over the sunspot and in the flare site. spatially separately but simultaucous iu ie."," Hence, this event allows us to study 3-min oscillations over the sunspot and in the flare site, spatially separately but simultaneous in time." + As in the previous section. the spatial structure of 3-win oscillations is analysed by the PWF icthod.," As in the previous section, the spatial structure of 3-min oscillations is analysed by the PWF method." + Figure 9 shows he location of the uarrowhaucl σα oscillation naps superimposed ou the EUV image of the active region. Which highlights the structure of the coronal uagnetie feld.," Figure \ref{fig9} shows the location of the narrowband 3-min oscillation maps superimposed on the EUV image of the active region, which highlights the structure of the coronal magnetic field." +" Both the sunspot :mosplere and the faring οποιονOo, release show pronounced 3-11 oscillations.", Both the sunspot atmosphere and the flaring energy release show pronounced 3-min oscillations. + It is c»seen that while the flare source is svuumetric. the sources of ια oscillatious over the sunspot have a wonounced V-shape.," It is seen that while the flare source is symmetric, the sources of 3-min oscillations over the sunspot have a pronounced V-shape." + The iiis of the V-shaped structure are inore pronounced during the maxima of the 3-min oscillation trains., The arms of the V-shaped structure are more pronounced during the maxima of the 3-min oscillation trains. + This is simular to the eveut cliscussed in the previous section. but the arms of the V-shaped structure spread in a different direction.," This is similar to the event discussed in the previous section, but the arms of the V-shaped structure spread in a different direction." + In coutrast to the event on 2005 April 28. the arms are secu to extend in the direction perpendicular to the appareut plasma structures in the maguetic fan extended from the sunspot.," In contrast to the event on 2005 April 28, the arms are seen to extend in the direction perpendicular to the apparent plasma structures in the magnetic fan extended from the sunspot." + Towever. this interpretation is counterintuitive. because Jandu waves radiating frou a sunspot iuto the corona are known to be guided by magnetic field lines (6.8. De Moortel. 2006).," However, this interpretation is counterintuitive, because 3-min waves radiating from a sunspot into the corona are known to be guided by magnetic field lines (e.g., De Moortel, 2006)." + Another option could be fast waves. )t their localisation in the direction perpendicular to heir wave frouts requires the presence of some euiding structures (6.8g.. Van Doorsselaere et al.," Another option could be fast waves, but their localisation in the direction perpendicular to their wave fronts requires the presence of some guiding structures (e.g., Van Doorsselaere et al.," + 2008)., 2008). + On the other haud. the direction of the arnus coincides with he direction of loops in the EUW arcade that spatially coincide with the fare source in the image (see Fig. 9)).," On the other hand, the direction of the arms coincides with the direction of loops in the EUV arcade that spatially coincide with the flare source in the image (see Fig. \ref{fig9}) )." + Since the EUW loops should. be situated under the flare site. it is reasonable to assume tha the arms of he V-shaped structure of narrowbaud 3auin oscillations Hehleht hotter maguetic structures (which are not secu in EUV) situated over the EUV arcade. which may links he flare site to the sunspot.," Since the EUV loops should be situated under the flare site, it is reasonable to assume that the arms of the V-shaped structure of narrowband 3-min oscillations highlight hotter magnetic structures (which are not seen in EUV) situated over the EUV arcade, which may link the flare site to the sunspot." + Hence. as for the event on 2005 Apri 28. the aris may represcut the paths of οαι wave cakage from the sunspot before the flare. aloug the naenetic field Hues towards the flare epiceutre.," Hence, as for the event on 2005 April 28, the arms may represent the paths of 3-min wave leakage from the sunspot before the flare, along the magnetic field lines towards the flare epicentre." + Iu this case. the fingers of he V-shaped structure xovide scisinological evidence οἳ the waveedine structure unseen in EUV.," In this case, the fingers of the V-shaped structure provide seismological evidence of the waveguiding structure unseen in EUV." +" Unfortunately, uo nmuaeiug information corresponding to hotter temperature was available for this event."," Unfortunately, no imaging information corresponding to hotter temperature was available for this event." + Iun particular. the RITESSI," In particular, the RHESSI" +position.,position. + Svsteim temperatures of the final spectra rauged from 200 to 500 I& on the scale., System temperatures of the final spectra ranged from 200 to 500 K on the $^*$ scale. + In Fig., In Fig. + 5. we present the poiutiugs aud the map of relative noise of the suuuaced Spectra., \ref{fig:n4330_co_noisemap} we present the pointings and the map of relative noise of the summed spectra. +" The telescope main-beam aud forward efficiencies are has=OSL aud gg,=0.90.", The telescope main-beam and forward efficiencies are $\eta_{\rm mb}=0.54$ and $\eta_{\rm for}=0.90$. + At the assumed distance of NQC 1330. 17 Mpe. the CO(21) beam corresponds to 0.9 kpe.," At the assumed distance of NGC 4330, 17 Mpc, the CO(2–1) beam corresponds to 0.9 kpc." +" Iu order to couvert CO integrated iuteusities iuto molectlar eas masses. we have assumed a (ο/Zeoio4, ratio: of D.2«--107 IL, mol 5? per K. |"," In order to convert CO integrated intensities into molecular gas masses, we have assumed a $N({\rm H}_2) / I_{\rm CO(2-1)}$ ratio of $2 \times 10^{20}$ $_2$ mol $^{-2}$ per K $^{-1}$." + Our. conclusions. however. do not depend stirly on the IN(Io)/Ze ratio within reasonable variations.," Our conclusions, however, do not depend strongly on the $N({\rm H}_2) / I_{\rm CO}$ ratio within reasonable variations." + We made a first moment map bv interpolating the CO(21) flux density of the poiutiues on a regular erid as we did iu Vollmer et al. (, We made a first moment map by interpolating the CO(2–1) flux density of the pointings on a regular grid as we did in Vollmer et al. ( +2006).,2006). + The distribution of molecular gas is shown im the upper panel of Fie. 6.., The distribution of molecular gas is shown in the upper panel of Fig. \ref{fig:n4330_hi_co}. + The morphology consists of a strong niaxinuni in the ealactic center and an asvnunuetric molecular gas disk., The morphology consists of a strong maximum in the galactic center and an asymmetric molecular gas disk. + The sheht bending of the molecular eas distribution in the ealactic disk is roninisceut of spiral structure., The slight bending of the molecular gas distribution in the galactic disk is reminiscent of spiral structure. + To the soutlivest. the molecular gas disk euds well within the distribution. whereas it exteuds to the edee of the distribution iu the northeast.," To the southwest, the molecular gas disk ends well within the distribution, whereas it extends to the edge of the distribution in the northeast." + We observe a faint extension in the upturn reeion., We observe a faint extension in the upturn region. + We do not detect any extraplanar CO enmissiou iu the tail regiou down to a eas mass of ~6«109 AL. Giuchiding helium)., We do not detect any extraplanar CO emission in the tail region down to a gas mass of $\sim 6 \times 10^{6}$ $_{\odot}$ (including helium). + We also checked for faint CO emission in the gas-free galactic disk ou the leading side of the interaction (northeast)., We also checked for faint CO emission in the gas-free galactic disk on the leading side of the interaction (northeast). + No CO ChUSSION dis fou to a level of ~2«4109 AL. when 15 spectra are averaged., No CO emission is found to a level of $\sim 2 \times 10^{6}$ $_{\odot}$ when 15 spectra are averaged. +" Iu coutrast. we found ~2«109 M, of molecular gas iu the gas-free galactic disk on the leading side of the interaction iu NGC 1522 (Vollmer et al."," In contrast, we found $\sim 2 \times 10^{6}$ $_{\odot}$ of molecular gas in the gas-free galactic disk on the leading side of the interaction in NGC 4522 (Vollmer et al." +" 2006: see Sec. 1010),", 2006; see Sec. \ref{sec:overall}) ). + I£ sucli a gas mass were present in the uptum region of NCC 1330. we should have detected it.," If such a gas mass were present in the upturn region of NGC 4330, we should have detected it." + To obtain the model molecular easdistribution of NGC 1330 we follow Vollmer et al. (, To obtain the model molecular gasdistribution of NGC 4330 we follow Vollmer et al. ( +2006) and weight the particle dass with Lobyp. where p dis the large-scale gas density.,"2006) and weight the particle mass with $1.4 \sqrt{\rho}$, where $\rho$ is the large-scale gas density." + The model molecular gas distribution is shown in the lower panel of Fig. G.., The model molecular gas distribution is shown in the lower panel of Fig. \ref{fig:n4330_hi_co}. . + The model molecular gas, The model molecular gas +about half the sample for which we have Ca IL EM. information (see Figure 12)).,about half the sample for which we have Ca II $EW$ information (see Figure \ref{fig:caii_dist}) ). + As the majority ol stars in the ONC appear to possess a circumstellar accretion disk. judging from both Ca II line aud IR photometric inclicators (Hilleubrandetal.1998:Lada2000:Muench2001).. we reler to stars tn the two selected groups as liaviug audlow circumstellar accretion aud avoid using the terms “classical” or weak-liue T Tauri stars.," As the majority of stars in the ONC appear to possess a circumstellar accretion disk, judging from both Ca II line and IR photometric indicators \citep{hil98a,lad00,mue01}, we refer to stars in the two selected groups as having and circumstellar accretion and avoid using the terms “classical” or “weak-line” T Tauri stars." + In Figuree 13. we present X-ray. luminosity Duuctious for stars in the six lowest mass rauges defined tu 82.2.. computed separately for the two accretiou-dillerentiatecl samples.," In Figure \ref{fig:XLF_CW} we present X-ray luminosity functions for stars in the six lowest mass ranges defined in \ref{sect:LxvsMass}, computed separately for the two accretion-differentiated samples." + Figure 14. slows nedian Log(Ly) vs. LogCM/AL.) depicted in the same format as Figure | and separated into ow- aud high-accretiou subsamples., Figure \ref{fig:LXvsM_CWa} shows median $Log(L_X)$ vs. $Log(M/M_{\odot})$ depicted in the same format as Figure \ref{fig:LXvsMb} and separated into low- and high-accretion subsamples. + For auy mass bin with enough points. it is clear in either 'epresentation that stars with high accretion have lower iuedian Ly than low-accretion stars.," For any mass bin with enough points, it is clear in either representation that stars with high accretion have lower median $L_X$ than low-accretion stars." + The difference ofthe mediaus is about an order of magnitude in the 0.25—2.0AL/AL. mass range., The difference ofthe medians is about an order of magnitude in the $0.25-2.0~M/M_{\odot}$ mass range. + Two- statistical tests coufirui the differeuce with hieh couflideuce (null-Biypothiesis probabilities ess than 10. 5 for Ad=0.25—0.50 AI/AL.).," Two-population statistical tests confirm the difference with high confidence (null-hypothesis probabilities less than $10^{-4}$ , for $M=0.25-0.50~M/M_{\odot}$ )." + Similar plots for Ly/Ly.¢ confirm the same result.," Similar plots for $L_X/L_{bol}$ confirm the same result," +astrophysical capture rate in the \lilky Way and M32 to the LISA rate a (withinfactor of a lew).,astrophysical capture rate in the Milky Way and M32 to the LISA rate (within a factor of a few). +We make the same assumption. but that the cautionfraction of captures LISA can actually detect per galaxy may be small.," We make the same assumption, but caution that the fraction of captures LISA can actually detect per galaxy may be small." + We can estimate the rate of capture for different. compact. object populations fora parücular galaxy by converting the mass density of particles in our simulation into a number density of the compact objects of interest., We can estimate the rate of capture for different compact object populations for a particular galaxy by converting the mass density of particles in our simulation into a number density of the compact objects of interest. + To do (his we assume that the mass densitvoi, To do this we assume that the mass density or +I thank Ina Wasserman. Eaanna Flanagan. Leonidas Moustakas. Jason Rhodes. and the anonvimous referee for (their helpful advice and review of the manuscript.,"I thank Ira Wasserman, Éaanna Flanagan, Leonidas Moustakas, Jason Rhodes, and the anonymous referee for their helpful advice and review of the manuscript." + This work was carried out at the Jet Propulsion Laboratory. California Institute of Technology. under a contract with NASA.," This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA." + The Millennium Rain simulation used in this paper was carried out by the Virgo Supercomputing Consortium al the Computing Centre of the Max-Plauck Society in Garching., The Millennium Run simulation used in this paper was carried out by the Virgo Supercomputing Consortium at the Computing Centre of the Max-Planck Society in Garching. + The semi-analvlic galaxy catalog is publicly available at, The semi-analytic galaxy catalog is publicly available at http://www.mpa-garching.mpg.de/galform/agnpaper. +ends up partly in OIL and mainly in CO.,ends up partly in OH and mainly in CO. + Figure 2 illustrates the detailed budget of carbon: Co and the primary hydrocarbons. CHI. Cllo. Coll quickly decay into Colle. which. in this Giruncated scheme of reactions. is a final product. as is CO.," Figure 2 illustrates the detailed budget of carbon: $_{2}$ and the primary hydrocarbons, CH, $_{2}$, $_{2}$ H quickly decay into $_{2}$ $_{2}$, which, in this truncated scheme of reactions, is a final product, as is CO." + Now. Collis is known to be the seed ol carbonaceous grains (see Frenklach ancl Fiegelson (1989))).," Now, $_{2}$ $_{2}$ is known to be the seed of carbonaceous grains (see Frenklach and Fiegelson \cite{fre}) )." + This justifies the truncation of the reaction chain lor our present purposes., This justifies the truncation of the reaction chain for our present purposes. + several runs with different initial densities of mother atoms showed Chat asymptotic values of products. expressed as fractions of ne(0). vary notably with the ratio ne(0)/no(0). but are quite insensitive to (he absolute values of these (wo densities.," Several runs with different initial densities of mother atoms showed that asymptotic values of products, expressed as fractions of $n_{C}(0)$, vary notably with the ratio $n_{C}(0)/n_{O}(0)$, but are quite insensitive to the absolute values of these two densities." + The asymptotic values of interest. neotf)/ne(0) and neqCf)/ne(0). ave therefore plotted in Fig.," The asymptotic values of interest, $n_{CO}(f)/n_{C}(0)$ and $n_{Cgr}(f)/n_{C}(0)$, are therefore plotted in Fig." + 4d and 5 as a funelion of ne(0)/no(0). Dor a lew cases spanning the relevant range (filled squares: straight lines are drawn between squares to help the eve).," 4 and 5 as a function of $n_{C}(0)/n_{O}(0)$, for a few cases spanning the relevant range (filled squares; straight lines are drawn between squares to help the eye)." + Tt may help to know that a square polynomial fit to the points in Fie., It may help to know that a square polynomial fit to the points in Fig. + 4 gives. to a very eood approximation.," 4 gives, to a very good approximation," +spread in > observed for individual SLACS/LSD lenses is comparable to the range of values founcl in our halo models. so strong conclusions about halo structure from these svstem will depend on averages over the samples rather than the results for individual lenses.,"spread in $\gamma$ observed for individual SLACS/LSD lenses is comparable to the range of values found in our halo models, so strong conclusions about halo structure from these system will depend on averages over the samples rather than the results for individual lenses." + The critical issue for determining (he sample average properties is the degree to which ihe populations are homogeneous., The critical issue for determining the sample average properties is the degree to which the populations are homogeneous. + A heterogeneous sample cannot easily be averaged to determine mean properties., A heterogeneous sample cannot easily be averaged to determine mean properties. + We [ind the probability of homogeneity is very. sensitive to the uncertainties in both the velocity dispersion and (he luminosity., We find the probability of homogeneity is very sensitive to the uncertainties in both the velocity dispersion and the luminosity. +" If Cake the measurement errors al [ace value. there is a low probability of homogeneity in either dvnamical structure (p,< 20%) or evolutionary history (pj,1556)."," If take the measurement errors at face value, there is a low probability of homogeneity in either dynamical structure $p_\sigma\le{20\%}$ ) or evolutionary history $p_L\le{15\%}$ )." + Many. lenses such as SDSS J1250-4-052. 1I15434-535. SDSS JL420+601. SDSS J0912--002. MG20164-112. and ALG1549+305 have low (< 10%) likelihoods of belonging to a homogeneous sample.," Many lenses such as SDSS J1250+052, H1543+535, SDSS J1420+601, SDSS J0912+002, MG2016+112, and MG1549+305 have low $<10\%$ ) likelihoods of belonging to a homogeneous sample." + The primary problem is probably that there are significant svstematic uncertainties that must be included with the nmeasurenient errors., The primary problem is probably that there are significant systematic uncertainties that must be included with the measurement errors. + Simple considerations show that tvpical svstematic errors in interpreting the velocity dispersions should be large compared to the measurement errors. versus5&.. anc adding these estimated svstematic uncertainties greatly increases the likelihood ol dynamical homogeneity.," Simple considerations show that typical systematic errors in interpreting the velocity dispersions should be large compared to the measurement errors, versus, and adding these estimated systematic uncertainties greatly increases the likelihood of dynamical homogeneity." + Sources of svstematic error in the mass-to-light ratio are less amenable to simple arguments. but should certainly. include the dispersion in (he average star formation epoch of earlv-tvpe galaxies found in an earlier analyses of galaxy. evolution with lenses by husin Ixochanek (2005) ancl Trenetal.(2006).," Sources of systematic error in the mass-to-light ratio are less amenable to simple arguments, but should certainly include the dispersion in the average star formation epoch of early-type galaxies found in an earlier analyses of galaxy evolution with lenses by Rusin Kochanek (2005) and \citet{tkbbm06}." +. Η we simply analyze the data to determine the most likely svstematic errors. we find that we must include fractional systematic errors of approximately in the velocity dispersion estimates ancl in the mnass-lo-lelt ratio estimates in order (ο make (he sample consistent with the hypothesis of homogenelilv.," If we simply analyze the data to determine the most likely systematic errors, we find that we must include fractional systematic errors of approximately in the velocity dispersion estimates and in the mass-to-light ratio estimates in order to make the sample consistent with the hypothesis of homogeneity." + Once we account for the inhomogeneity or svstenia(ic errors in the sample. we can evaluate sample averages (hat properly account for these problems.," Once we account for the inhomogeneity or systematic errors in the sample, we can evaluate sample averages that properly account for these problems." +" We find that the halo mass fraction represented by (he barvons in stars is /,=0.056+0.011 if we acliabatically compress (the dark matter and f.=0.0262:0.006 if we do not.", We find that the halo mass fraction represented by the baryons in stars is $f_* = 0.056\pm0.011$ if we adiabatically compress the dark matter and $f_* = 0.026\pm0.006$ if we do not. + These results are comparable to similar the range of estimates (hat relied on stellar population models to estimate the stellar mass., These results are comparable to similar the range of estimates that relied on stellar population models to estimate the stellar mass. + For example. Lintott.Ferreras&Lahaw(2006) obtained a stellar mass [raction of 8% by fitting monolithie collapse models to 2000 SDSS galaxies. Hoekstraetal.(2005) found f.=0.065018 using weak lensing. and Mandelbaim et al. (," For example, \citet{lfl06} obtained a stellar mass fraction of $\backsim 8\%$ by fitting monolithic collapse models to 2000 SDSS galaxies, \citet{hhylg05} found $f_* = 0.065^{+0.010}_{-0.008}$ using weak lensing, and Mandelbaum et al. (" +"2006) found f,=0.03(t using weak lensing.",2006) found $f_*=0.03^{+0.02}_{-0.01}$ using weak lensing. + The results in these studies depend on (he assumed IAIF (the estimate drops to f.=0.035toni if the initial mass fraction of the stars is changed from a standard Salpeter IME to a scaled Salpeter IAIF., The results in these studies depend on the assumed IMF – the \citet{hhylg05} estimate drops to $f_* = 0.035^{+0.005}_{-0.004}$ if the initial mass fraction of the stars is changed from a standard Salpeter IMF to a scaled Salpeter IMF. + Our results probably bound the stellar mass [raction since the Blumenthal et al. (, Our results probably bound the stellar mass fraction since the Blumenthal et al. ( +1986) model we used may overestimate the amount of acliabatic compression (Guedin et al.,1986) model we used may overestimate the amount of adiabatic compression (Gnedin et al. + 2004)., 2004). +" In all our models. the stellar mass fraction]. is. much smaller than the cosmological: barvon mass fraction: Ορ,=0.116.=e0.00615 "," In all our models, the stellar mass fraction is much smaller than the cosmological baryon mass fraction $\Omega_b/\Omega_m=0.176^{+0.006}_{-0.019}$ " +We fit Gaussian profiles to the Lla line. using. the package in (lxriss1094).,"We fit Gaussian profiles to the $\alpha$ line, using the package in \cite{kri94}." +. After normalising each spectrum by a low-order polynomial fit to. the continuum. we fit either two or three gaussians to the [a Ilinc.," After normalising each spectrum by a low-order polynomial fit to the continuum, we fit either two or three gaussians to the $\alpha$ line." + TEje spectrum taken on 1999 Juv 11 cleary showed a clouble-»ealked: profile. in addition to he broad Xdue-shifted component. so we fit three gaussians to this spectrum.," The spectrum taken on 1999 July 11 clearly showed a double-peaked profile, in addition to the broad blue-shifted component, so we fit three gaussians to this spectrum." + T reducec v» flor ν=85 ddegrees of freedom: changes from Ve2=4.9 [for a two-gaussian fit ο X5ο—1. Που three gaussians., The reduced $\chi_{\nu}^2$ for $\nu=85$ degrees of freedom changes from $\chi_{\nu}^2 = 4.9$ for a two-gaussian fit to $\chi_{\nu}^2 = 1.1$ for three gaussians. + “Lhe specrum from 200) Alay 10 aso recquired an extra narrow component to achieve a good fi (yo=1.52 for à two-gaussian fit. v5—1.23 for three gaussians).," The spectrum from 2000 May 16 also required an extra narrow component to achieve a good fit $\chi_{\nu}^2 = 1.52$ for a two-gaussian fit, $\chi_{\nu}^2 = 1.23$ for three gaussians)." + The other spectra were fit with two gaussians., The other spectra were fit with two gaussians. + The details of the its are listed in Table 2.., The details of the fits are listed in Table \ref{tab:fits}. . + The data and the fits are shown in Figure... with he spectra arrangede in order of phase.," The data and the fits are shown in Figure \ref{fig:Halpha-fits}, with the spectra arranged in order of phase." + Despite the spectra waving been taken over a span of more than a vear. there appears to be a clear. trend. of line shape with orbital ohase.," Despite the spectra having been taken over a span of more than a year, there appears to be a clear trend of line shape with orbital phase." + The spectrum taken at. phase 0. (200) Alay 22) is he only completely symmetric profile., The spectrum taken at phase 0 (2000 May 22) is the only completely symmetric profile. + At small phases. the ine profile begins to show asvnimetry in the line.," At small phases, the line profile begins to show asymmetry in the line." + Sometime after phase 0.4. the line shows a second. peak in addition o the broad component (200 May. 16). which persists for he second half of the orbi (1999 July 11).," Sometime after phase 0.4, the line shows a second peak in addition to the broad component (2000 May 16), which persists for the second half of the orbit (1999 July 11)." + We have fit wo narrow components to the line at phase 0. although it is »xossible that the profile is Hat-topped instead of intrinsically double-peaked.," We have fit two narrow components to the line at phase 0, although it is possible that the profile is flat-topped instead of intrinsically double-peaked." + We will discuss the implications of this in Section 4.3.., We will discuss the implications of this in Section \ref{sec:Detection-accretion-disk}. + In Paper LE we presented five archival spectra from the AAT and one from. HIST: we can re-examine these spectra [or evidence of the same pattern in the line profiles., In Paper I we presented five archival spectra from the AAT and one from HST; we can re-examine these spectra for evidence of the same pattern in the line profiles. + Phree spectra (1976 May. 1978 August and 1997 June) were taken near apastron. at phases 0.54. 0.52 and 0.51: none of them shows a double-peaked profile.," Three spectra (1976 May, 1978 August and 1997 June) were taken near apastron, at phases 0.54, 0.52 and 0.51; none of them shows a double-peaked profile." + Phe spectra taken in the first half of the orbit all show an asvmnmetry on the blue wing: no spectra were taken during the second. half of the orbit (phases 0.60.9). so we do not knowwhether the," The spectra taken in the first half of the orbit all show an asymmetry on the blue wing; no spectra were taken during the second half of the orbit (phases 0.6–0.9), so we do not knowwhether the" +Figure lis a plot of the intensity angular correlation funetion (ACF) given bv where the sunm is over all pairs of map pixels. ἐνj. separated by an angle 9. J; is the intensity of the /// pixel. 1 is the mean intensity. and Ny is the number of pairs of pixels separated by 9.,"Figure 1 is a plot of the intensity angular correlation function (ACF) given by where the sum is over all pairs of map pixels, $i,j$, separated by an angle $\theta$, $I_i$ is the intensity of the $ith$ pixel, $\bar{I}$ is the mean intensity, and $N_{\theta}$ is the number of pairs of pixels separated by $\theta$." + Photon shot noise only appears in the 9=0° bin and has been removed., Photon shot noise only appears in the $\theta = 0^\circ$ bin and has been removed. + The hiehlv correlated error bars were determined from 1000 Monte Carlo trials in which the pixel intensity distribution was assumed to be Gaussian with the same AC'F as in the figure., The highly correlated error bars were determined from 1000 Monte Carlo trials in which the pixel intensity distribution was assumed to be Gaussian with the same ACF as in the figure. + The dashed curve represents the expected functional form of the contribution to the ACF due to telescope beam smearing of a random distribution of uncorrelated sources normalized to the ACF(0) point., The dashed curve represents the expected functional form of the contribution to the ACF due to telescope beam smearing of a random distribution of uncorrelated sources normalized to the ACF(0) point. + It represents the profile that is expected if there were no intrinsic correlations in the XRD., It represents the profile that is expected if there were no intrinsic correlations in the XRB. + The point spread function (PSF) of the map is due to pixelization aud to the finile telescope beam and was accurately determined [from the profiles of GO bright. nearby point sources.," The point spread function (PSF) of the map is due to pixelization and to the finite telescope beam and was accurately determined from the profiles of 60 bright, nearby point sources." + It is clear from Figure 1 that the NRB possesses intrinsic (i.e.. not due to beam smearing) correlated structure out to angular scales of ~10°.," It is clear from Figure 1 that the XRB possesses intrinsic (i.e., not due to beam smearing) correlated structure out to angular scales of $\sim 10^{\circ}$." + Full details of the analvsis are discussed in Boughn. Crittenden. IXoehrsen (2002).," Full details of the analysis are discussed in Boughn, Crittenden, Koehrsen (2002)." +" In order to determine the N-rav bias factor 6, from (the measured ACF. it is essential {ο know from which redshifts the X-ray fluctuations originate: the underlying density [Iuctuations erow quickly. so it is important that they be compared to the X-ray [Iuctuations at the same redshifts."," In order to determine the X-ray bias factor $b_x$ from the measured ACF, it is essential to know from which redshifts the X-ray fluctuations originate; the underlying density fluctuations grow quickly, so it is important that they be compared to the X-ray fluctuations at the same redshifts." + This requires understanding the contribution to the 2—10hel X-ray LF as a function of redshift., This requires understanding the contribution to the $2-10~keV$ X-ray LF as a function of redshift. + Llowever. the IEAOL À2 observations are total intensity measurements ol the hard XRDB with no information as to the fluxes or redshifts of individual sources. so we must infer the LF bv other means.," However, the HEAO1 A2 observations are total intensity measurements of the hard XRB with no information as to the fluxes or redshifts of individual sources, so we must infer the LF by other means." + Recently the Chandra satellite has made possible large. [aint hard. X-ray. surveys with measured redshifts.," Recently the $Chandra$ satellite has made possible large, faint hard X-ray surveys with measured redshifts." + Cowie et al. (, Cowie et al. ( +2003) and Stellen et al. (,2003) and Steffen et al. ( +2003) have combined Chandra sources with brighter sources [rom ASCA (Akivama el al.,2003) have combined $Chandra$ sources with brighter sources from $ASCA$ (Akiyama et al. + 2000) and ROSAT (Lehmann et al., 2000) and $ROSAT$ (Lehmann et al. + 2001) to determine the redshift evolution of the 2—8heV LF with few assumptions about the character of the sources., 2001) to determine the redshift evolution of the $2-8~keV$ LF with few assumptions about the character of the sources. + The incompleteness uncertainty in the redshift dependence of the volume X-ray. enissivitv. is estimated (o be a [actor <2 at anv redshift., The incompleteness uncertainty in the redshift dependence of the volume X-ray emissivity is estimated to be a factor $\ls 2$ at any redshift. + The spectroscopicallv identified sources comprise 75% of the total 2—8keV. X-ray intensity: the dominant uncertainties result [rom the unknown recdshift distiibution of the unidentified sources., The spectroscopically identified sources comprise $75\%$ of the total $2-8~keV$ X-ray intensity; the dominant uncertainties result from the unknown redshift distribution of the unidentified sources. +"and p, is the mass density of a planetesimal.",and $\rho_g$ is the mass density of a planetesimal. +" The mass of a merged pair is Af;+M»—AL). where the mass ejected in the collision is M,;=0.5(M4+M3)(Q./Q7)""? "," The mass of a merged pair is $M_1 + M_2 - M_{ej}$, where the mass ejected in the collision is $M_{ej} = 0.5 (M_1 + M_2) (Q_c/Q_d^*)^{9/8}$ \citep{kl99}." +Consistent wilh recent i-body simulations. we consider (wo sets of [ragmentation parameters fj.," Consistent with recent $n$ -body simulations, we consider two sets of fragmentation parameters $f_i$ ." +" Styong planetesimals have fy = (Q,=1.105.or10ergοF9, 2 0. Q, = L5 erg σοι 5, = 1.25: KBOS.1999)."," Strong planetesimals have $f_S$ = \citep[$Q_b$ = 1, $10^3$, or $10^5$ erg g$^{-1}$, $\beta_b \approx$ 0, $Q_g$ = 1.5 erg $^{-1}$ $^{-1.25}$, $\beta_g$ = 1.25; KB08,." +" Weaker planetesimals have fy = 10ergg tem! 3,2 —0.4. Q, = 0.22 erg gbem I, 9, ="," Weaker planetesimals have $f_W$ = \citep[$Q_b$ = $2 \times 10^5$ erg g$^{-1}$ $^{0.4}$, $\beta_b \approx -0.4$ , $Q_g$ = 0.22 erg $^{-1}$ $^{-1.3}$, $\beta_g$ =." + Our initial conditions are appropriate for a disk around a voung star (e.g.Dullemond&Ciesla20072:Garaud2007:Braueretal... 2008b).," Our initial conditions are appropriate for a disk around a young star \citep[e.g.][]{dul05,cie07a,gar07,bra08b}." +". We consider svstems of 32 annuli with a; 2 510 AU and da;/a; = 0.025.The disk is composed of small planetesimals with radii ranging [rom rj,5,=rs£2 0.5 2m (Ralikov2004) to ry = 1 km. 10 km. or 100 kim and an initial mass distribution n;(Mj)xALON, "," We consider systems of 32 annuli with $a_i$ = 5–10 AU and $\delta a_i/a_i$ = 0.025.The disk is composed of small planetesimals with radii ranging from $r_{min} = r_s \approx$ 0.5–2 m \citep{raf04} to $r_0$ = 1 km, 10 km, or 100 km and an initial mass distribution $n_i(M_{ik}) \propto M_{ik}^{-0.17}$." +"The mass ratio between adjacent. bins is 0—Mip4/Mj, = 1.42 (e.g..Ikenvon&Lin1998.INDOS)."," The mass ratio between adjacent bins is $\delta = M_{ik+1}/M_{ik}$ = 1.4–2 \citep[e.g.,][KB08]{kl98}." +. Each bin has the same initial eccenlricily ey=10.1 and inclination 7)=ἐμ/2., Each bin has the same initial eccentricity $e_0 = 10^{-4}$ and inclination $i_0 = e_0/2$. + For each combination of ry. fj. and ορ = 15. we calenlate the growth of oligarchs with two different. approaches (to erain accretion.," For each combination of $r_0$, $f_i$, and $x_m$ = 1–5, we calculate the growth of oligarchs with two different approaches to grain accretion." +" In models without grain accretion. fragments with rSr4, are lost to the grid."," In models without grain accretion, fragments with $r \lesssim r_{min}$ are `lost' to the grid." + Oligarchs cannot accrete these fragments: their masses stall at AV 0.1M..., Oligarchs cannot accrete these fragments; their masses stall at $M \lesssim$ 0.1. +" In models with grain accretion. we track the abundances of fragments with 0.1 mm SrοSryi, which settle to the disk midplane on short timescales."," In models with grain accretion, we track the abundances of fragments with 0.1 mm $ \lesssim r \lesssim r_{min}$ which settle to the disk midplane on short timescales." + Oligarchs can accrete these fragmentis: {μον erow rapidly at rates set by the production of collision fragments., Oligarchs can accrete these fragments; they grow rapidly at rates set by the production of collision fragments. +" For the gaseous disk.. we adopt a=10.1, an initial. surfaceB density.. 4 Moo LOOM. aty,d5L7στ. and a depletion time /, = 3 Myr."," For the gaseous disk, we adopt $\alpha = 10^{-4}$, an initial surface density, $\Sigma_{g,0}$ = 100 $\Sigma_{s,0}~x_m~a^{-3/2}$, and a depletion time $t_g$ = 3 Myr." +" The surface density at later times is X,,=Nyy€""v."," The surface density at later times is $\Sigma_{g,t} = \Sigma_{g,0}~e^{-t/t_g}$." + We ignore the migration of protoplanets from torques between (he gas and the planet (LinWard| 1997).," We ignore the migration of protoplanets from torques between the gas and the planet \citep{lin86,war97}." +. Alibertetal.(2005) show that migration enhances erowth of protoplanets: (hus our approach underestimates the growth (me., \citet{ali05} show that migration enhances growth of protoplanets; thus our approach underestimates the growth time. + We also ignore the racial drift of fragments coupled to the gas., We also ignore the radial drift of fragments coupled to the gas. + Depending on the internal structure of the disk. fragments can drift inward.drift outward. or become concentrated within local pressure maxima or turbulent eddies (Weidenschilline1977:Haghiehipour&Boss2003:Inaba2003).," Depending on the internal structure of the disk, fragments can drift inward,drift outward, or become concentrated within local pressure maxima or turbulent eddies \citep{wei77,hagh2003,inaba06,masset06,cie07b,kret07,kato08}." +. llere. our goal is to provide a reasonable first estimate for (he growth rates of protoplanets.," Here, our goal is to provide a reasonable first estimate for the growth rates of protoplanets." + We plan to explore (he consequences ofradial drift in subsequent papers., We plan to explore the consequences ofradial drift in subsequent papers. +restricted to be less than 8 ... which is a conventional limit that a helium star will become a neutron star instead of a black hole (see. e.g.. Figure | in Belezynski et al.,"restricted to be less than 8 $_{\sun}$, which is a conventional limit that a helium star will become a neutron star instead of a black hole (see, e.g., Figure 1 in Belczynski et al." + 2002; Table 16.4 in Tauris van den Heuvel 2004)., 2002; Table 16.4 in Tauris van den Heuvel 2004). +" The conservation laws of orbital energy and angular momentum allow for real solutions only for Mo;. Vj. 0. o. and values satisfying the orbital dynamics constraints given by A,,,syequation (21)-(27) in Willems et al. ("," The conservation laws of orbital energy and angular momentum allow for real solutions only for $M_{2i}$ , $V_k$, $\theta$, $\phi$, and $A_{preSN}$ values satisfying the orbital dynamics constraints given by equation (21)–(27) in Willems et al. (" +2005).,2005). +" For PSR B1I534+12. PSR B1913+16. and PSR J0737-3039, these constraints are supplemented with the measured NSI spin tilt angle constraints."," For PSR B1534+12, PSR B1913+16, and PSR J0737-3039, these constraints are supplemented with the measured NS1 spin tilt angle constraints." + Applying these constraints together with the constraints imposing stability of any mass transfer taking place right before the second supernova explosion yields a PDF of the natal kick velocity of NS2., Applying these constraints together with the constraints imposing stability of any mass transfer taking place right before the second supernova explosion yields a PDF of the natal kick velocity of NS2. +" A corresponding PDF for the kick velocity V;4, imparted to the binary’s center of mass ts obtained using equations (28)-(32) in Willems et al. ("," A corresponding PDF for the kick velocity $V_{k,sys}$ imparted to the binary's center of mass is obtained using equations (28)–(32) in Willems et al. (" +2005).,2005). + In all past studies. kinematic analyses have either been skipped (Wang et al.," In all past studies, kinematic analyses have either been skipped (Wang et al." + 2006) or simplified to one dimension (Piran Shaviv 2004) or have suffered by ad hoc assumptions about the un-measurable radial velocities., 2006) or simplified to one dimension (Piran Shaviv 2004) or have suffered by ad hoc assumptions about the un-measurable radial velocities. + Willems et al. (, Willems et al. ( +2006) used general DNS population synthesis models to guide this assumption.,2006) used general DNS population synthesis models to guide this assumption. + In this sutdy we employ a new method that still uses forward in time kinematic simulations. but they are tied to each observed system instead of being general.," In this sutdy we employ a new method that still uses forward in time kinematic simulations, but they are tied to each observed system instead of being general." + We perform a Monte Carlo simulation of the motion of DNS in the Galactic potential., We perform a Monte Carlo simulation of the motion of DNS in the Galactic potential. + For this purpose. we adopt a reference frame with origin at the Galactic center. with z- pointing to the northern Galactic pole. and with the - pointing in the direction from the Sun to the Galactic center.," For this purpose, we adopt a reference frame with origin at the Galactic center, with $z$ -axis pointing to the northern Galactic pole, and with the $x$ -axis pointing in the direction from the Sun to the Galactic center." + With respect to this reference frame. the Sun is located at R..=(-8.5.0.0.03) kkpe (Ghez et al.," With respect to this reference frame, the Sun is located at $\vec{R}_\odot = (-8.5, 0, 0.03)$ kpc (Ghez et al." + 2008. Gillessen et al.," 2008, Gillessen et al." + 2009. Reid et al.," 2009, Reid et al." + 2009. Joshi 2007) and has a peculiar velocity of (10.5.7) kknys (Bienaymé 1999).," 2009, Joshi 2007) and has a peculiar velocity of $(10, 5, 7)$ km/s (Bienaymé 1999)." + With the given R. and peculiar velocity. the Sun is moving at a velocity V..=(10.226.7) kknys. To simulate the motion of DNS in the Galaxy. we randomly distribute a population of newly formed DNS in the Galactic disk according to a double exponential distribution function Here R and z are the cylindrical galactic coordinates. /75 and h- ave the Galactic scale length and height respectively.," With the given $\vec{R}_\sun$ and peculiar velocity, the Sun is moving at a velocity $\vec{V}_\odot = (10, 226, 7)$ km/s. To simulate the motion of DNS in the Galaxy, we randomly distribute a population of newly formed DNS in the Galactic disk according to a double exponential distribution function Here R and z are the cylindrical galactic coordinates, $h_R$ and $h_z$ are the Galactic scale length and height respectively." + The distribution is normalized to unity by setting no=LH/(GEz/iA)., The distribution is normalized to unity by setting $n_0 = 1/(4 \pi h_z h_R^2)$. + Since the progenitors of DNS are distributed in the same way as the massive stellar binaries in our galaxy. we choose Jip = 2.8 kpe and /i. = 0.07 kpe (see Joshi 2007).," Since the progenitors of DNS are distributed in the same way as the massive stellar binaries in our galaxy, we choose $h_R$ = 2.8 kpc and $h_z$ = 0.07 kpc (see Joshi 2007)." + For all of the observed DNS except PSR B1534+12. we use a population of ~10° simulated binaries.," For all of the observed DNS except PSR B1534+12, we use a population of $\sim$ $^9$ simulated binaries." + We use a population of —10'7 in the analysis of PSR BIS34+12. due to the limiting chance of kicking it to the currently high Galactic altitude and simultaneously satisfying the constraints derived from the orbital dynamics of supernova explosions.," We use a population of $\sim$ $^{12}$ in the analysis of PSR B1534+12, due to the limiting chance of kicking it to the currently high Galactic altitude and simultaneously satisfying the constraints derived from the orbital dynamics of supernova explosions." + If the scale height /i- were larger than 70 pe. it would reduce the difficulty in satisfying the galactic dynamics constraints of PSR B1534«12.," If the scale height $h_z$ were larger than 70 pc, it would reduce the difficulty in satisfying the galactic dynamics constraints of PSR B1534+12." + A smaller population of simulated binaries would then be needed for the analysis of this system., A smaller population of simulated binaries would then be needed for the analysis of this system. + The initial center-of-mass velocity of the DNS ts obtained by summing up the kickvelocity Vos imparted tothe binary center of mass during the second supernova explosion and the local Galactic rotational velocity V.," The initial center-of-mass velocity of the DNS is obtained by summing up the kickvelocity $\vec{V}_{k,sys}$ imparted tothe binary center of mass during the second supernova explosion and the local Galactic rotational velocity $\vec{V}_{rot}$ ." + Given the unknown, Given the unknown +"be thought of direction-dependent Jones matrices in their own right. and subsumed into the overall sky-Jones term by defining E,-E,W,.","be thought of direction-dependent Jones matrices in their own right, and subsumed into the overall sky-Jones term by defining $\jones{E}{p} = \jones{\bar E}{p}W_p$." + The full-sky RIME (Eq. 17)), The full-sky RIME (Eq. \ref{eq:me-allsky0}) ) + can then be rewritten using a 2D Fourier Transform of the pq.. or By: I shall return to this general formulation in Paper II (?)..," can then be rewritten using a 2D Fourier Transform of the , or $\coh{B}{pq}$: I shall return to this general formulation in Paper II \citep{RRIME2}." +" In the meantime. consider the import of those pg indices in B,,."," In the meantime, consider the import of those $pq$ indices in $\coh{B}{pq}$." +" They are telling us that we're measuring a 2D Fourier Transform of the sky — but the ""sky"" is different for every baseline!", They are telling us that we're measuring a 2D Fourier Transform of the sky – but the “sky” is different for every baseline! + This violates the fundamental premise of traditional selfcal. which assumes that we're measuring the E.T. of one common sky.," This violates the fundamental premise of traditional selfcal, which assumes that we're measuring the F.T. of one common sky." + From the above. it follows that this premise only holds when all DDEs are across all antennas: Ευ=EC) (or at least where B(/)4 0).," From the above, it follows that this premise only holds when all DDEs are across all antennas: $\jones{E}{p}(\vec l) \equiv \jones{E}{}(\vec l)$ (or at least where $\coh{B}{}(\vec l) \ne 0$ )." +" Only under this condition does the apparent sky B,, become the same on all baselines (in the traditional view. this corresponds to the ""true"" sky attenuated by the power beam): If this is met. we can then rewrite the full-sky RIME as: where X,,=Χρ.vj). and the matrix function XQ) is simply the (element-by-element) two-dimensional Fourier of the matrix function Bays()."," Only under this condition does the apparent sky $\coh{B}{pq}$ become the same on all baselines (in the traditional view, this corresponds to the “true” sky attenuated by the power beam): If this is met, we can then rewrite the full-sky RIME as: where $\coh{X}{pq} = \coh{X}{}(u_{pq},v_{pq})$, and the matrix function $\coh{X}{}(\vec u)$ is simply the (element-by-element) two-dimensional Fourier of the matrix function $\coh{B}{\rm app}(\vec l)$ ." + E shall also write this as Bapp., I shall also write this as $\coh{X}{}={\cal F}\coh{B}{\mathrm{app}}$ . + The similarity to Eq. (13)), The similarity to Eq. \ref{eq:me-point-source-corrupted}) ) + of a single point source is readily apparent., of a single point source is readily apparent. + For obvious reasons. I shall call X(z0) thecoherency.," For obvious reasons, I shall call $\coh{X}{}(\vec u)$ the." + Effectively. we have derived the van Cittert-Zernike theorem (VCZ). the cornerstone of radio interferometry Sect.|. 1).. from the basic RIME!," Effectively, we have derived the van Cittert-Zernike theorem (VCZ), the cornerstone of radio interferometry \citep[Sect.~14.1]{tms}, from the basic RIME!" + Such an approach turns the original original coherency matrix formulation of ? on its head., Such an approach turns the original original coherency matrix formulation of \citet{ME4} on its head. + Note that Eq. (19)), Note that Eq. \ref{eq:me-allsky-simple}) ) + here is the same as Eq. (, here is the same as Eq. ( +2) of that work.,2) of that work. + In the RIME papers. Hamaker et al.," In the RIME papers, Hamaker et al." +" defer to VCZ. treating the coherency as a ""given"" (while recasting it to matrix form) to which Jones matrices then apply."," defer to VCZ, treating the coherency as a “given” (while recasting it to matrix form) to which Jones matrices then apply." + Treating phase (K) as a Jones matrix in its own right (2) allows for a natural extension of the Jones formalism into the (/.1) plane. and shows that VCZ is actually a consequence of the RIME rather than being something extrinsic to it.," Treating phase $K$ ) as a Jones matrix in its own right \citep{JEN:note185} allows for a natural extension of the Jones formalism into the $(l,m)$ plane, and shows that VCZ is actually a consequence of the RIME rather than being something extrinsic to it." + This also allows DDEs to be incorporated into the same formalism. in a manner similar to that suggested for w-projection (?)..," This also allows DDEs to be incorporated into the same formalism, in a manner similar to that suggested for $w$ -projection \citep{Cornwell:wproj}." + [shall return to this subject in Paper II (?).., I shall return to this subject in Paper II \citep{RRIME2}. + | have hitherto ignored the time variable., I have hitherto ignored the time variable. + Signal propagation effects. and indeed the sky itself. do vary in time. but the RIME describes an effectively instantaneous measurement (ignoring for the moment the issue of time averaging. which will be considered separately in. Sect. 5.2)).," Signal propagation effects, and indeed the sky itself, do vary in time, but the RIME describes an effectively instantaneous measurement (ignoring for the moment the issue of time averaging, which will be considered separately in Sect. \ref{sec:smearing}) )." + Time begins to play a critical role when we consider DDEs., Time begins to play a critical role when we consider DDEs. + At any point in time. an interferometer given by Eq. (19) ," At any point in time, an interferometer given by Eq. \ref{eq:me-allsky-simple}) )" +measures the coherency function X(zw) at a number of points tjj (i.e. for all baselines pq)., measures the coherency function $\coh{X}{}(\vec u)$ at a number of points $\vec u_{pq}$ (i.e. for all baselines $pq$ ). +" This ""snapshot"" measurement gives a limited samplig of the «v plane.", This “snapshot” measurement gives a limited sampling of the $uv$ plane. +" To sample the «v plane more fully. we usually rely on the Earth's rotation. which over several hours effectively ""swings"" every baseline vector ur, through an arc in the wy plane."," To sample the $uv$ plane more fully, we usually rely on the Earth's rotation, which over several hours effectively “swings” every baseline vector $\vec u_{pq}$ through an arc in the $uv$ plane." + Therefore. for Eq. (19))," Therefore, for Eq. \ref{eq:me-allsky-simple}) )" + to hold throughout an observation. we must additionally assume that the apparent sky Bapp remains constant over the observation time!," to hold throughout an observation, we must additionally assume that the apparent sky $\coh{B}{\rm app}$ remains constant over the observation time!" +" In other words. unless we're dealing with snapshot imaging. the E,=E assumption must be further augmented: This equation captures the fundamental assumption of traditional selfeal."," In other words, unless we're dealing with snapshot imaging, the $\jones{E}{p}\equiv\jones{E}{}$ assumption must be further augmented: This equation captures the fundamental assumption of traditional selfcal." + | shall call DDEs that satisfy Eq. (20)) DDEs.., I shall call DDEs that satisfy Eq. \ref{eq:trivial-ddes}) ). + As shown above. trivial DDEs effectively replace the true sky B by a single apparent sky Bj. and are not usually a problem for calibration. since they can be corrected for entirely in the image For example. the primary beam gain is usually treated as a trivial DDE in 2GC packages (see?.Sect. 2.1).," As shown above, trivial DDEs effectively replace the true sky $\coh{B}{}$ by a single apparent sky $\coh{B}{\mathrm{app}}$, and are not usually a problem for calibration, since they can be corrected for entirely in the image For example, the primary beam gain is usually treated as a trivial DDE in 2GC packages \citep[see Paper II,][Sect.~2.1]{RRIME2}." +" Equation (20)) is most readily met with narrow FoVs (Le. with £, rapidly going to zero away from the field centre. leaving little scope for other variations). small arrays (small Wy. also all stations see through the same atmosphere). higher frequencies (narrow ΕΟΝ. less tonospheric effects). and also with coplanar arrays such as the WSRT 6,=0. thus W,=1)."," Equation \ref{eq:trivial-ddes}) ) is most readily met with narrow FoVs (i.e. with $\jones{E}{p}$ rapidly going to zero away from the field centre, leaving little scope for other variations), small arrays (small $w_p$, also all stations see through the same atmosphere), higher frequencies (narrow FoV, less ionospheric effects), and also with coplanar arrays such as the WSRT $w_p\equiv0$, thus $W_p\equiv1$ )." + The new crop of instruments is. of course. trending in the opposite direction on all these points. and is thus subject to far more severe and non-trivial DDEs.," The new crop of instruments is, of course, trending in the opposite direction on all these points, and is thus subject to far more severe and non-trivial DDEs." + Scalar closure relationships have played an important role in 2GC calibration. both as a diagostic tool. and as an observable.," Scalar closure relationships have played an important role in 2GC calibration, both as a diagnostic tool, and as an observable." +" Traditionally. these are expressed in terms of a three-way phase closure and a four-way amplitude closure (seee.g.?,Sect.10.3)."," Traditionally, these are expressed in terms of a three-way phase closure and a four-way amplitude closure \citep[see e.g.][Sect.~10.3]{tms}." + Since the underlying premise of a closure relationship ts that observed scalar visibilities can be expressed in terms of per-antenna scalar gains. and the RIME is a generalization of the same premise 1 matrix terms. it seems worthwhile to see 1f a general matrix (re.fully polarimetric) closure relationship can be derived.," Since the underlying premise of a closure relationship is that observed scalar visibilities can be expressed in terms of per-antenna scalar gains, and the RIME is a generalization of the same premise in matrix terms, it seems worthwhile to see if a general matrix (i.e.fully polarimetric) closure relationship can be derived." + Indeed. in the case of a single point source. we can write out a four-way closure for antennas mn.p.q as follows: The above equationcan be easily verified by substituting in Eq. (8))," Indeed, in the case of a single point source, we can write out a four-way closure for antennas $m,n,p,q$ as follows: The above equationcan be easily verified by substituting in Eq. \ref{eq:me0}) )" + for each visibility term. and remembering that (ABy!=B UAT.," for each visibility term, and remembering that $(\jones{A}{}\jones{B}{})^{-1}=\jonesinv{B}{}\jonesinv{A}{}$ ." +polarization is larger than 1077. which is about three times of the polarization noise level (Lites οἱ al.,"polarization is larger than $10^{-2}$, which is about three times of the polarization noise level (Lites et al." + 2008)., 2008). +" This is a criteria applied to all helicity parameter calculations, upon all other criteria we apply in following analysis."," This is a criteria applied to all helicity parameter calculations, upon all other criteria we apply in following analysis." +" In calculating a. and ay, we have used two different representations of magnetic field measurement."," In calculating $\alpha_{z}$ and $\alpha_{hc}$, we have used two different representations of magnetic field measurement." +" One is related to “flux density”, where the longitudinal magnetic field B.=f-Bcos(y) and the transverse magnetic field B,=Vf-Bsin(y)."," One is related to “flux density"", where the longitudinal magnetic field $B_z = f \cdot B \cos(\gamma)$ and the transverse magnetic field $B_t = \sqrt{f} \cdot B \sin(\gamma)$." +" The other is the “field strength"" where B.=Bcos(y) and B,=Bsin(y)."," The other is the “field strength"" where $B_z = B \cos(\gamma)$ and $B_t = B \sin(\gamma)$." + Hereafter we present the first type as B. Bl and the second type as B2. B.," Hereafter we present the first type as $B_z^1$, $B_t^1$ and the second type as $B_z^2$ , $B_t^2$ ." +" Correspondingly helicity parameters are also hereafter presented as o. di;l and 5az, az.hc5 respectively."," Correspondingly helicity parameters are also hereafter presented as $\alpha^1_{z}$, $\alpha^1_{hc}$ and $\alpha^2_{z}$, $\alpha^2_{hc}$ respectively." +". In most previous. studies. researchers used the helicity. parameters of> the first type, that is, based on the flux density measurement of magnetic field."," In most previous studies researchers used the helicity parameters of the first type, that is, based on the flux density measurement of magnetic field." +" Due to the precise measurement of SP on boardHinode, an accurate measurement of filling factor and hence of field strength becomes possible."," Due to the precise measurement of SP on board, an accurate measurement of filling factor and hence of field strength becomes possible." +" Thus in this Letter we calculate the helicity parameter of the second type too, in order to check whether our results depend on the type of magnetic field measurement or not."," Thus in this Letter we calculate the helicity parameter of the second type too, in order to check whether our results depend on the type of magnetic field measurement or not." +" Figure | presents the variation of a! (left panels) and a (right panels) with the solar latitude for the 30 ARs in the descending phase of solar cycle 23 (top panels), the 34 ARs in the ascending phase of solar cycle 24 (middle panels) and the total 64 ARs (bottom panels)."," Figure 1 presents the variation of $\alpha_{z}^1$ (left panels) and $\alpha_{z}^2$ (right panels) with the solar latitude for the 30 ARs in the descending phase of solar cycle 23 (top panels), the 34 ARs in the ascending phase of solar cycle 24 (middle panels) and the total 64 ARs (bottom panels)." + Here a! and a2 are calculated only using points with |B!|> 100 G or |B:|> 100 G. The solid lines indicate the results ot least-square linear fits., Here $\alpha_{z}^1$ and $\alpha_{z}^2$ are calculated only using points with $|B_{z}^1| > $ 100 G or $|B_{z}^2| > $ 100 G. The solid lines indicate the results of least-square linear fits. +" Similarly, Figure 2 gives the the variation of qu. (left panels) and o.3 (right panels) with the solar latitude for the 30 ARs in solar cycle 23 (top panels), the 34 ARs in solar cycle 24 (middle panels) and the total 64ARs (bottompanels)."," Similarly, Figure 2 gives the the variation of $\alpha_{hc}^1$ (left panels) and $\alpha_{hc}^2$ (right panels) with the solar latitude for the 30 ARs in solar cycle 23 (top panels), the 34 ARs in solar cycle 24 (middle panels) and the total 64ARs (bottompanels)." + The αι.| and az.5 are also calculated only using. points, The $\alpha_{hc}^1$ and $\alpha_{hc}^2$ are also calculated only using points + The αι.| and az.5 are also calculated only using. points., The $\alpha_{hc}^1$ and $\alpha_{hc}^2$ are also calculated only using points +Cepheids. and (on a preliminary basis) one Iate-type line eclipsing binary as mentioned above.,"Cepheids, and (on a preliminary basis) one late-type double-line eclipsing binary as mentioned above." + In turn the results found here and in other recent papers strengthen the conclusions reached by Bresolin (2011). who found. such a shallow oxvgen abundance gradient in NGC 4258 LIL regions that abundance cdillerences. could not realistically explain the cdillerence in. brightness between Copheids in the outer and inner regions of that galaxy.," In turn the results found here and in other recent papers strengthen the conclusions reached by Bresolin (2011), who found such a shallow oxygen abundance gradient in NGC 4258 HII regions that abundance differences could not realistically explain the difference in brightness between Cepheids in the outer and inner regions of that galaxy." + We would like to thank the South African. Astronomical Observatory lor generous allotments of observing time with what may be the world's last instrument capable of hieh-»ecision Ht observations of bright objects., We would like to thank the South African Astronomical Observatory for generous allotments of observing time with what may be the world's last instrument capable of high-precision IR observations of bright objects. + Travel funding or this project has been provided by the Brigham Young University Department of Physics and Astronomy., Travel funding for this project has been provided by the Brigham Young University Department of Physics and Astronomy. + Support rom the FOCUS and TIAM subsidies of the Foundation for olish Science (END) is also acknowledged., Support from the FOCUS and TEAM subsidies of the Foundation for Polish Science (FNP) is also acknowledged. + We extend our hanks to Dr. Benjamin J. Taylor for his comments on our original manuscript., We extend our thanks to Dr. Benjamin J. Taylor for his comments on our original manuscript. + We also thank Lisa Joner for her careful »oofreading of several different versions of this paper., We also thank Lisa Joner for her careful proofreading of several different versions of this paper. + This research. has made use of the Vizielt catalogue access tool. CDS. Strasbourg. France.," This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France." +Fernandes οἱ al. (,Fernandes et al. ( +2010) in their recent study about the “forgotten” population of weak line galaxies (WLGs).,2010) in their recent study about the “forgotten” population of weak line galaxies (WLGs). + Note also that since our galaxies have N>3 they do not classify as WLGs., Note also that since our galaxies have $\ge3$ they do not classify as WLGs. + In Figure 1 we show the NII diagram for the NELGs with the emission lines missing., In Figure \ref{fig:01} we show the NII diagram for the NELGs with the emission lines missing. + of the galaxies without ΤΟΠ falls on the AGN side of the NII diagram (to the right of separation line at -0.3 in Ha)., of the galaxies without [OIII] falls on the AGN side of the NII diagram (to the right of separation line at -0.3 in $\alpha$ ). + This fraction increases to [or the galaxies without both lines ancl for the galaxies without 19., This fraction increases to for the galaxies without both lines and for the galaxies without $\beta$. + Therelore. most of the NELGs with emission lines missing are AGNs.," Therefore, most of the NELGs with emission lines missing are AGNs." + These results differ significantly from what Cid Fernandes et al. (, These results differ significantly from what Cid Fernandes et al. ( +2010) have obtained.,2010) have obtained. + Thev found very few WLG are AGNs., They found very few WLG are AGNs. + This suggests that the absence of emission lines points to a different nature for the galaxies., This suggests that the absence of emission lines points to a different nature for the galaxies. + Most of the NELGs with emission lines missing have EW below Log(IEW|NII[)—0.6: without JOLL]. without IL? and without both lines.," Most of the NELGs with emission lines missing have EW below $=0.6$: without [OIII], without $\beta$ and without both lines." + By definition. the EW is the ratio between (he flux in (he emission line and the flux in the adjacent. continuum.," By definition, the EW is the ratio between the flux in the emission line and the flux in the adjacent continuum." + This parameter is consequently sensitive to the Iuminosityv of the emission line and (o the underlving stellar population., This parameter is consequently sensitive to the luminosity of the emission line and to the underlying stellar population. + A small value of EW suggests the galaxies have an earlv-tvpe morphology (see the article by Torres-Papaqui et al., A small value of EW suggests the galaxies have an early-type morphology (see the article by Torres-Papaqui et al. + in this proceeding). andor that the emission line has a low Iuminositv.," in this proceeding), and/or that the emission line has a low luminosity." + This is confirmed in Figure 1 where it is seen that the Ia luminosity decreases with the EW., This is confirmed in Figure \ref{fig:01} where it is seen that the $\alpha$ luminosity decreases with the EW. + The median Ho luminosity below Log(IZW][NII[)—0.6 is that of the galaxies without IL2. which is 5.6x 10 erg !.," The median $\alpha$ luminosity below $=0.6$ is that of the galaxies without $\beta$, which is $\times$ $^{39}$ erg $^{-1}$." + This property categorizes these galaxies as Low Linninositv AGNs (LLAGNs)., This property categorizes these galaxies as Low Luminosity AGNs (LLAGNs). + Figure2. shows that the NELGs with emission lines missing have broacl EWIIM. similar to luminous AGNs.," \ref{fig:02} shows that the NELGs with emission lines missing have broad FWHM, similar to luminous AGNs." + After correction for the resolution of the instrument. the FWIIM values fall between 170 up to 700 kins 1.," After correction for the resolution of the instrument, the FWHM values fall between 170 up to 700 km $^{-1}$." + A higher fraction of the galaxies without [OLLI] have lower FWIIAL. which is consistent with the high number of TOs and SEGs in this sample.," A higher fraction of the galaxies without [OIII] have lower FWHM, which is consistent with the high number of TOs and SFGs in this sample." + The EWIIM seems like another good criterion to separate AGNs from SFGs., The FWHM seems like another good criterion to separate AGNs from SFGs. +"The host galaxy of 9980125 was imaged at and with theCRB MIPS instimment as partmnn of "": Cycle 3 General Observer program (PID: 225 AOR kevs 21966656 21966100).","The host galaxy of 980425 was imaged at and with the MIPS instrument as part of a Cycle 3 General Observer program (PID: 251, AOR keys 24966656 24966400)." +" The observations were carried out in 2008 using the MIPS ""Small Scale Photometry” uode.", The observations were carried out in 2008 using the MIPS “Small Scale Photometry” mode. + With this operating mode a set of LO frames is taken for cach observing evele and a dither is automatically performed around the targeted source., With this operating mode a set of 10 frames is taken for each observing cycle and a dither is automatically performed around the targeted source. + We respectively obtained 5 aud 12 cveles at aneΊσθμια. which resulted in a total ou-source integration time of ss at aud ss atμαι.," We respectively obtained 5 and 12 cycles at and, which resulted in a total on-source integration time of s at and s at." + Fora very modest amount of additional requested time we also performed a new observation of the 9980125 host atjan.. with the goal of checking if some fraction of the luminosity of the bright point source detected in our previous data (LeFlochetal.2006) couldbe associated to the enuüsson from a transient object (e.g. supernova).," For a very modest amount of additional requested time we also performed a new observation of the 980425 host at, with the goal of checking if some fraction of the luminosity of the bright point source detected in our previous data \citep{LeFloch06} could be associated to the emission from a transient object (e.g., supernova)." + A siuele evele of 10 ο was obtained. leading to a total inteeratiou time of ss ou SOUrCC.," A single cycle of 10 frames was obtained, leading to a total integration time of s on source." + Each individual image was processed with the most recent version (v.3.1) of the MIPS Data Analysis Tool (DAT.Gordonctal.2005).," Each individual image was processed with the most recent version (v.3.1) of the MIPS Data Analysis Tool \citep[DAT,][]{Gordon05}." + This update includes additional processing steps with respect to the first version of the DAT initially released., This update includes additional processing steps with respect to the first version of the DAT initially released. + Tn particular a pixel«depeudeut backerounc subtraction was applied to each iudividual frame before co-addiug the images., In particular a pixel-dependent background subtraction was applied to each individual frame before co-adding the images. + We used calibration factors of /CADU) and D/CADU) at and. respectively (Cordonetal.2007:Stausherry2007).," We used calibration factors of $^{-1}$ )/(ADU) and $^{-1}$ )/(ADU) at and respectively \citep{Gordon07,Stansberry07}." +. The pixel size of the final miosaics was set to half the pixel size of the MIDPS detectors aud the absolute astrometric registration was fied to the astrometry of the raw data as provided by the Science Center., The pixel size of the final mosaics was set to half the pixel size of the MIPS detectors and the absolute astrometric registration was tied to the astrometry of the raw data as provided by the Science Center. + The nuages obtained at the \OPS waveleugths are presented in 11., The images obtained at the 3 MIPS wavelengths are presented in 1. + For reference3 they are compared with the image of the 9980125 host galaxy obtaimed at from our first observations (LeFlocletal. 2006)., For reference they are compared with the image of the 980425 host galaxy obtained at from our first observations \citep{LeFloch06}. +. .lena The αι] spectroscopic follow-up of the WR recion was performed as part of the IRS Cuarauteed Time Observation (GTO) program ou 19 April 2006 (AOR kev: 12216528)., .4cm The mid-IR spectroscopic follow-up of the WR region was performed as part of the IRS Guaranteed Time Observation (GTO) program on 19 April 2006 (AOR key: 12246528). + The target was first acquired using the red peak-arp (RPU) camera., The target was first acquired using the red peak-up (RPU) camera. + During this acquisition an inage of the source at was obtained iu Double Correlated Sampling (DCS) mode to locate the mid-IR ceutroid of the target. and then offset to the appropriate slit (sce the Spitzer Observers Maunal for more details).," During this acquisition an image of the source at was obtained in Double Correlated Sampling (DCS) mode to locate the mid-IR centroid of the target, and then offset to the appropriate slit (see the Spitzer Observers Manual for more details)." + Using the Short-Low (SL. ;12)) and Long-Low (LL. μα) modules of the IRS. we obtained a S~38 low resolution spectrum of the WR region.," Using the Short-Low (SL, ) and Long-Low (LL, ) modules of the IRS, we obtained a $\sim$ low resolution spectrum of the WR region." + The total ou-source exposure time was 2118 (2 cevcles of 6088) per SL order and 1265s (2 evcles of 3088) per LL order., The total on-source exposure time was s (2 cycles of s) per SL order and s (2 cycles of s) per LL order. + In addition. hieher resolution observations were obtained with the IRS Short-High (SIT. ;an)) for a total on-source time of O75ss (L eveles of 12083).," In addition, higher resolution observations were obtained with the IRS Short-High (SH, ) for a total on-source time of s (4 cycles of s)." + For each mode of our IRS observatious the orientation of the slit aperture with respect to the 9950125 host galaxy is illustrated in 11 (top-right panel)., For each mode of our IRS observations the orientation of the slit aperture with respect to the 980425 host galaxy is illustrated in 1 (top-right panel). + We beeun analyzing the observations by processing the data with theSpitser Science Center pipeline (version 15.5) and the extraction of tle signal was carried. out with the Spectral Modeling. Analysis. Reduction Tool (SMARTVer.5.5.1.Tiedonetal.2001).," We begun analyzing the observations by processing the data with the Science Center pipeline (version 15.5) and the extraction of the signal was carried out with the Spectral Modeling, Analysis, Reduction Tool \citep[SMART Ver. 5.5.1,][]{Higdon04b}." +. In the case of the low-resolution data though. the final reduced spectrum later used in this paper was retrieved from the receutly published (CASSIS.Lebouteilleretal.2011a).. which provided us with an imuiproved aud updated processiug of the data.," In the case of the low-resolution data though, the final reduced spectrum later used in this paper was retrieved from the recently published \citep[CASSIS, ][]{Lebouteiller11b}, which provided us with an improved and updated processing of the data." + Iun bref. the IRS data reduction starts from the intermediate pipeline products (droop files). which oulv lack stray light and fat field correction.," In brief, the IRS data reduction starts from the intermediate pipeline products (droop files), which only lack stray light and flat field correction." + Iudividual pointings to cach nod position of the slit were co-added using median averaging., Individual pointings to each nod position of the slit were co-added using median averaging. + For SL and LL spectra. we considered the difference of the two nod positious to remove the contribution of the backerouud.," For SL and LL spectra, we considered the difference of the two nod positions to remove the contribution of the background." + Then we extracted. the spectra for cach nod. position using a variable width aperture. which scales the extraction aperture with wavelength to recover the same fraction of the diffraction limited iustrunmnieuntal Point Spread Fuuction (PSF).," Then we extracted the spectra for each nod position using a variable width aperture, which scales the extraction aperture with wavelength to recover the same fraction of the diffraction limited instrumental Point Spread Function (PSF)." + The data from SII were extracted using the full slit extraction method from the inediau of the combined- images., The data from SH were extracted using the full slit extraction method from the median of the combined images. + Since no sky (offposition) micasurements were taken for the high resolution module. the contribution of the skv emission was not subtracted frou SII spectra.," Since no sky (off–position) measurements were taken for the high resolution module, the contribution of the sky emission was not subtracted from SH spectra." + Then the spectra were flux calibrated by multiplication with the Relative Spectral Bespouse Function (RSRE). which was created from the IRS standard stars a Lac for SL aud LL aud £& Dra for SII. for which accurate templates were available (Cohen ot al.," Then the spectra were flux calibrated by multiplication with the Relative Spectral Response Function (RSRF), which was created from the IRS standard stars $\alpha$ Lac for SL and LL and $\xi$ Dra for SH, for which accurate templates were available (Cohen et al." + 2003)., 2003). + Webuilt our RSREs by extracting the spectra of thecalibration stars du the exact same wav as the science target. and dividing the stellar templates by the extracted stellar spectra.," We built our RSRFs by extracting the spectra of the calibration stars in the exact same way as the science target, and dividing the stellar templates by the extracted stellar spectra." + We produced one RSRF for cach nod position iu order to avoid svstematic fat field errors., We produced one RSRF for each nod position in order to avoid systematic flat field errors. + The signal difference between the nod positions provide the error estimates., The signal difference between the nod positions provide the error estimates. + Finally. the fiux. calibrated spectra of cach order of the low-resolution modules were sealed to the first order of LL (LELI. 36/11). which was usec to definethe overall continu of the source.," Finally, the flux calibrated spectra of each order of the low-resolution modules were scaled to the first order of LL (LL1, $\mu$ m), which was used to define the overall continuum of the source." + The fnal low-resolution IRS spectrmm of the WR reeiou is shown in Figure 2.., The final low-resolution IRS spectrum of the WR region is shown in Figure \ref{fig:plot_spec}. . + Caven the star-forming nature of GRB host galaxies we compared it with the IRS observations of the starburst ealaxy τπτ (Braudletal.2001). and the super-Iuninous ITIT region 25151 in the spiral galaxv 1101 (Gordonetal. 2008)., Given the star-forming nature of GRB host galaxies we compared it with the IRS observations of the starburst galaxy 7714 \citep{Brandl04} and the super-luminous HII region 5461 in the spiral galaxy 101 \citep{Gordon08}. + The three SEDs exhibit striking simularitics but also noticeable differcuces., The three SEDs exhibit striking similarities but also noticeable differences. + First. they are all characterized by a steeply-visine coutimmiuu of hot dust enüssiou. aud the Polvevche Aromatic Hycdrocarbous (PAT) features conmmonly seen in star-forming galaxies (Laurentetal.2000:Brandl2006:Sunithct2007) are also clearly appareut.," First, they are all characterized by a steeply-rising continuum of hot dust emission, and the Polycyclic Aromatic Hydrocarbons (PAH) features commonly seen in star-forming galaxies \citep{Laurent00,Brandl06,Smith07} are also clearly apparent." + These PAIIs as well as the σοιπαπα eweston originate frou dust eraius stochastically heated by the radiation field’ audby the UV photous from vouug populatious of massive stars., These PAHs as well as the continuum emission originate from dust grains stochastically heated by the radiation field and by the UV photons from young populations of massive stars. + Their Iunünositv correlates verv well with the total IR huninosity measured between and (Braud and they aretherefore considered as a fairly accurate and extinction-free tracer of the activity of star formation iu galaxies (6...ctRousselet 2008)..," Their luminosity correlates very well with the total IR luminosity measured between and \citep{Brandl06} and they aretherefore considered as a fairly accurate and extinction-free tracer of the activity of star formation in galaxies \citep[e.g.,][]{Roussel01,Calzetti07,Diaz_Santos08}. ." +These weak sources appear in the same field as aand4715.,These weak sources appear in the same field as and. +. Thev are also listed as unidentified. EUVE JO437-475 and EUVE J0436472. respectively. in the Second Ssource Catalog (Bowveretal.1996).," They are also listed as unidentified, EUVE J0437-475 and EUVE J0436–472, respectively, in the Second Source Catalog \citep{bll96}." +.. Armed with precise positions from the IWhieh Resolution hnager. we identiliel both of these sources spectroscopically as NLS1s using (he CTIO 1.5m telescope in 1993 October ancl 1999 November.," Armed with precise positions from the High Resolution Imager, we identified both of these sources spectroscopically as NLS1s using the CTIO 1.5m telescope in 1998 October and 1999 November." + Their reshilis are 20.44 for RX JOL387.14731 and =0.361 for RX JO436.4-4714., Their reshifts are $z = 0.144$ for RX J0437.1–4731 and $z = 0.361$ for RX J0436.4-4714. + Ton S180 is a NLSI galaxy., Ton S180 is a NLS1 galaxy. + The 33 dav oobservation of Ton 9180 in late 1999 was coordinated with aand during the last 12 days (Eclelsonetal.2002:Turner2002).," The 33 day observation of Ton S180 in late 1999 was coordinated with and during the last 12 days \citep{etp02,tu02}." +. The light curves during the 12 day period of overlap are well correlated. with no apparent time delays.," The light curves during the 12 day period of overlap are well correlated, with no apparent time delays." + Leighly(1999a) showed that NLS1s are more variable (han ordinary. Sevlert galaxies of similar X-ray luminosity. and the Iheht eurves of Ton S180 (and Mik 478. another NLS1) seem to bear this out.," \cite{l99a} showed that NLS1s are more variable than ordinary Seyfert galaxies of similar X-ray luminosity, and the light curves of Ton S180 (and Mrk 478, another NLS1) seem to bear this out." + The 1999 oobservation of Ton S180 was the only one in our compilation to suffer significantly from imperlect correction of cleac-time ancl Primbsching due to high background., The 1999 observation of Ton S180 was the only one in our compilation to suffer significantly from imperfect correction of dead-time and Primbsching due to high background. + However. the svinplom of (his problem is easily recognized and eliminated.," However, the symptom of this problem is easily recognized and eliminated." + When (he background is hieh and the correction [actor is Z2. the correction becomes inaccurate. possibly nonlinear. and one or two orbits of data per day are clearly discrepant from the others.," When the background is high and the correction factor is $\gsim 2$, the correction becomes inaccurate, possibly nonlinear, and one or two orbits of data per day are clearly discrepant from the others." + These bad points induce a signal in (he perioclogram αἱ 0.99 days (ancl its harmonics). which is the period at which the SAA on the rotating Earth passes through the night side of the slowly precessing satellite orbit. (," These bad points induce a signal in the periodogram at 0.99 days (and its harmonics), which is the period at which the SAA on the rotating Earth passes through the night side of the slowly precessing satellite orbit. (" +Data obtained when the satellite is on the davlight side of the Earth are not used here).,Data obtained when the satellite is on the daylight side of the Earth are not used here). + When the bad. points. in this case less than of the data. are excised. the 0.99 clay signal in the periodogram disappears.," When the bad points, in this case less than of the data, are excised, the 0.99 day signal in the periodogram disappears." + Figure 4. shows the light curve cleaned of bad. points., Figure \ref{lc4} shows the light curve cleaned of bad points. + The periodogram of the cleaned 1999 observation of Ton S180 (Figure 8)) shows several possible periods. the strongest being al 2.03 davs.," The periodogram of the cleaned 1999 observation of Ton S180 (Figure \ref{ps2}) ) shows several possible periods, the strongest being at 2.08 days." + It às important to note that because this observation was so long. the detected period cannot be attributed to a sub-harmonic of the 0.99 dav SAA period. as it is well resolved from it.," It is important to note that because this observation was so long, the detected period cannot be attributed to a sub-harmonic of the 0.99 day SAA period, as it is well resolved from it." + Furthermore. the 2.08 clay signal is much stronger than any weak residual at 0.99 davs (1.18x10.7 Lz). the latter being undetected in (he periodogram of the cleaned light curve.," Furthermore, the 2.08 day signal is much stronger than any weak residual at 0.99 days $1.18 \times 10^{-5}$ Hz), the latter being undetected in the periodogram of the cleaned light curve." + Weaker peaks in Figure 8. are present at 2.81, Weaker peaks in Figure \ref{ps2} are present at 2.81 +and latitude which vary depending on the size of the sunspot and age of the active region (Howardetal. 1986).,and latitude which vary depending on the size of the sunspot and age of the active region \citep{Howard_etal84}. +. For this reason sunspots and their immediate surroundings are masked out., For this reason sunspots and their immediate surroundings are masked out. + We found that this could be done quite effectively by identifying all mapped pixels with field strengths |B|>500 G and all pixels within 5 mapped pixels of those points with |B|>100 G as masked pixels., We found that this could be done quite effectively by identifying all mapped pixels with field strengths $\left|B\right| > 500$ G and all pixels within 5 mapped pixels of those points with $\left|B\right| > 100$ G as masked pixels. + An example of one of these mapped and masked magnetograms is shown in Fig., An example of one of these mapped and masked magnetograms is shown in Fig. + 1., 1. + The axisymmetric motions — differential rotation and meridional flow — of the magnetic elements were determined by cross-correlating strips of pixels from pairs of mapped images separated by 8 hours and finding the shift in longitude and latitude that gave the strongest correlation. (, The axisymmetric motions – differential rotation and meridional flow – of the magnetic elements were determined by cross-correlating strips of pixels from pairs of mapped images separated by 8 hours and finding the shift in longitude and latitude that gave the strongest correlation. ( +Results obtained with image pairs separated by 4.8 hours were substantially the same.),Results obtained with image pairs separated by 4.8 hours were substantially the same.) + Each strip was 11 pixels (~ 2?) high in latitude and 600 pixels (~ 105?) long in longitude., Each strip was 11 pixels $\sim 2\degr$ ) high in latitude and 600 pixels $\sim 105\degr$ ) long in longitude. + The shift in longitude and latitude producing the strongest correlation was calculated to a fraction of a pixel by fitting parabolas in longitude and latitude through the correlation coefficient peaks., The shift in longitude and latitude producing the strongest correlation was calculated to a fraction of a pixel by fitting parabolas in longitude and latitude through the correlation coefficient peaks. + This process was performed at 860 latitude positions from 75°S to 75?N for typically about 400 image pairs over each 27-day rotation of the Sun., This process was performed at 860 latitude positions from $75\degr$ S to $75\degr$ N for typically about 400 image pairs over each 27-day rotation of the Sun. +" In all we obtained measurements from over 60,000 magnetogram pairs."," In all we obtained measurements from over 60,000 magnetogram pairs." + 'The average and the standard deviation of the differential rotation and meridional flow velocities were calculated at each latitude for each solar rotation of 27.25 days., The average and the standard deviation of the differential rotation and meridional flow velocities were calculated at each latitude for each solar rotation of 27.25 days. +" The differential rotation and meridional flow profiles for each rotation were fit with fourth order polynomials in sinA, where A is the heliographic latitude."," The differential rotation and meridional flow profiles for each rotation were fit with fourth order polynomials in $\sin \lambda$, where $\lambda$ is the heliographic latitude." + Errors in the fit coefficients were estimated using a Monte Carlo method with random variations at each latitude characterized by the standard deviations from the measurements., Errors in the fit coefficients were estimated using a Monte Carlo method with random variations at each latitude characterized by the standard deviations from the measurements. + These polynomial coefficients were also recast in terms of associated Legendre polynomials of the first order., These polynomial coefficients were also recast in terms of associated Legendre polynomials of the first order. + The Legendre polynomial coefficients are better suited for studies of time variations based on the orthogonality of the polynomials themselves (Snodgrass1984)., The Legendre polynomial coefficients are better suited for studies of time variations based on the orthogonality of the polynomials themselves \citep{Snodgrass84}. +. 'The latitudinal profiles of differential rotation and meridional flow as measured with these data and this method represent the actual axisymmetric motions of the magnetic elements., The latitudinal profiles of differential rotation and meridional flow as measured with these data and this method represent the actual axisymmetric motions of the magnetic elements. + Since the magnetic elements are fully resolved in these data the effects of supergranule diffusion are seen as random motions of the magnetic elements and these random motions do not introduce any systematic errors in our measurements as will be shown in Section 7., Since the magnetic elements are fully resolved in these data the effects of supergranule diffusion are seen as random motions of the magnetic elements and these random motions do not introduce any systematic errors in our measurements as will be shown in Section 7. + Profiles were obtained for 178 rotations of the Sun from June 1996 to September 2010 with a gap from June 1998 to February 1999 when radio contact with SOHO was lost and not fully recovered., Profiles were obtained for 178 rotations of the Sun from June 1996 to September 2010 with a gap from June 1998 to February 1999 when radio contact with SOHO was lost and not fully recovered. + The average differential rotation profile from the entire dataset is shown in Fig., The average differential rotation profile from the entire dataset is shown in Fig. + 2., 2. + The velocities are taken relative to the Carrington frame of reference which has a sidereal rotation rate of 14.184degday!., The velocities are taken relative to the Carrington frame of reference which has a sidereal rotation rate of $14.184\rm{\ deg\ day}^{-1}$. + The average differential rotation profile is well represented by just the three terms with symmetry across the equator —, The average differential rotation profile is well represented by just the three terms with symmetry across the equator – +The total cluster ass can be inferred by applying a selfsinular relation that links it o the iutegrated coluptonization parameter.,The total cluster mass can be inferred by applying a self-similar relation that links it to the integrated comptonization parameter. + The M;Y scaling law is uxuallv calibrated for a fixed overdcusity value. while in this work we are dealing with masses calculated at different overdeusities.," The $M_{tot}-Y$ scaling law is usually calibrated for a fixed overdensity value, while in this work we are dealing with masses calculated at different overdensities." + For this reasou in the scaling law. we make the dependence ou overdeusity explicit.," For this reason in the scaling law, we make the dependence on overdensity explicit." + Simp5 considerations. based on the assumption that cluster evolution is completely determined by eravitational processes. lead to an easy. scaling relation that connects the total mass of a cluster of ealaxics. Mg. to its temperature. τοι consideriug an isothermal structure for the ICAL," Simple considerations, based on the assumption that cluster evolution is completely determined by gravitational processes, lead to an easy scaling relation that connects the total mass of a cluster of galaxies, $M_{tot}$, to its temperature, $T_e$, considering an isothermal structure for the ICM." + Following Ixravtsov et al. (, Following Kravtsov et al. ( +"2006) and Bryan Norman (1998) aud keeping the overdeusitv depeudence explicit. we lave a spherically inteerated quautity (6.8. total cluster nias) fo one cerived bv a cvliudical iutegration (ο.ο, integrated SZ flux). we consider the spherical analogous to the SZ flux. Ys.","2006) and Bryan Norman (1998) and keeping the overdensity dependence explicit, we have To connect a spherically integrated quantity (e.g. cluster total mass) to one derived by a cylindrical integration (e.g. integrated SZ flux), we consider the spherical analogous to the SZ flux, $Y_{S}$." +" This quantity is directly proportional to the cluster total mass as where Ας is the cluster total mass inside a sphere with radius equal to rj. aud Dy), Is the gas weighted mean temperature."," This quantity is directly proportional to the cluster total mass as where $M_{tot}$ is the cluster total mass inside a sphere with radius equal to $r_{int}$, and $T_{mw}$ is the gas mass-weighted mean temperature." + By combining the previous equations. we ect This πασάς that. by estimating Ys. we can easilv iufer the corresponding total cluster mass.," By combining the previous equations, we get This means that, by estimating $Y_{S}$, we can easily infer the corresponding total cluster mass." + Furthermore. in order to derive the iutegrated SZ flux. we need to solve the equation where 0;MintiDy and. g(0) is extracted by the simulated SZ teuperature decrement profiles Gu the CC case} or calculated directly from Eq. E. ," Furthermore, in order to derive the integrated SZ flux, we need to solve the equation where $\theta_{int}=r_{int}/D_A$ and $y(\theta)$ is extracted by the simulated SZ temperature decrement profiles (in the CC case) or calculated directly from Eq. \ref{eq_ybeta}, ," +by considers he paraiucters as derived from the ΑΙΤΙΟΝΤΟ analysis iu Sect., by considering the parameters as derived from the MCMC analysis in Sect. + ο (in the ISO case).," \ref{sec_MCMC} + (in the ISO case)." + The two defined integrated Comptonization parameters (Ys and Y) are connected by he dineusiouless quantity C=Όσα ος., The two defined integrated Comptonization parameters $Y_S$ and $Y$ ) are connected by the dimensionless quantity $C=D_A^2Y/Y_{S}$ . +" We averaged the C factors. assuming different evliudric depths equal to 2. 5. and 10 7;,;. obtaining C»=1.52€ OT. Cs=L85z2zkO0.LLH. and Cyy=2.0040.19. respectively. conveoreiue to the value in Bonameute et al. ("," We averaged the $C$ factors, assuming different cylindric depths equal to 2, 5, and 10 $r_{int}$, obtaining $C_2=1.52\pm0.07$ , $C_5=1.85\pm0.14$, and $C_{10}=2.00\pm0.19$, respectively, converging to the value in Bonamente et al. (" +2008).,2008). + The scaling law can be rewritten as which ean directly eive an estimation of cluster total mass Msn.," The scaling law can be rewritten as which can directly give an estimation of cluster total mass $M_{tot,SL}$." + All the quantities included in the scaling law are listed in Table 5 The results clearly show that a gcucral interpretation of cluster physics. as asstuced ina pure sclfsimilar scaling law like Ae—Y. can infer a wrong estimate of cluster total mmass.," All the quantities included in the scaling law are listed in Table \ref{table_SL} + The results clearly show that a general interpretation of cluster physics, as assumed in a pure self-similar scaling law like $M_{tot}-Y$, can infer a wrong estimate of cluster total mass." + To emphasize aud to quantity this poiut. we define a nass bias as This quauti&es the difference between the SZ derived mass. as results from the isothermal bete--model asstuuption (ISO) aud the X-ray derived mass (CC). which we deduce from the ITE. POR. aud SL approaches.," To emphasize and to quantify this point, we define a mass bias as This quantifies the difference between the SZ derived mass, as results from the isothermal -model assumption (ISO) and the X-ray derived mass (CC), which we deduce from the HE, FGF, and SL approaches." + We notice no siguificaut yas depeudence on the beam size used to convolve the SZ signals. under the assuuption of the presence of mstrunnental noise alone.," We notice no significant bias dependence on the beam size used to convolve the SZ signals, under the assumption of the presence of instrumental noise alone." + Therefore. all plots refers to results obtained with a of 7 arciuiu FWIIM. considering Py values as in Table 2..," Therefore, all plots refers to results obtained with a of 7 arcmin FWHM, considering $T_X$ values as in Table \ref{table_te}." + We calculate the mass bias for all the analyzed approaches., We calculate the mass bias for all the analyzed approaches. +" Since the ATSszy paramcter does not give us unique oe-ormation on the plivsies of the ICAL. we have to study Lmffereut pairs of the paramcters my and T,."," Since the $\Delta T_{SZ0}$ parameter does not give us unique information on the physics of the ICM, we have to study different pairs of the parameters $n_{e0}$ and $T_x$." + Thus. we select values of T. that describe a reliable range of electro- telperatures (fou 5 keV to 15 keV) aud calculatethe corresponding yg.," Thus, we select values of $T_x$ that describe a reliable range of electron temperatures (from 5 keV to 15 keV) and calculatethe corresponding $n_{e0}$." + The mass biases are plotted im Figur laa. where the three cases (IIE. FOR. and SL) are show- all together in the plots corresponding to clusters CTyyoso. CTyoo). aud Clayisin1115. represcuting a wide spa- in the electron temiperature values.," The mass biases are plotted in Figure \ref{fig_bias}a a, where the three cases (HE, FGF, and SL) are shown all together in the plots corresponding to clusters $Cl_{A1689}$, $Cl_{A2204}$, and $Cl_{RXJ1347.5-1145}$, representing a wide span in the electron temperature values." + Table 6 lists. tlie lnass biases. as estimated at the N-rav derived electro- temperature (Ly in Table 2)).," Table \ref{table_bias} lists the mass biases, as estimated at the X-ray derived electron temperature $T_X$ in Table \ref{table_te}) )." + A check of the eooduess of the procedure was done bv simulating the observation of a cluster having an isothermal bete-iode ATsz(0) profile instead of a CC cluster., A check of the goodness of the procedure was done by simulating the observation of a cluster having an isothermal -model $\Delta T_{SZ}(\theta)$ profile instead of a CC cluster. + For this validation procedure. named.Test... we used the same analytical expression of the SZ signal to extract the parameters.," For this validation procedure, named, we used the same analytical expression of the SZ signal to extract the parameters." + The assumed electron teiiperature is the one obtained bv Bonamente ot al. (, The assumed electron temperature is the one obtained by Bonamente et al. ( +2006) aud reported in the last coluun in Table 2..,2006) and reported in the last column in Table \ref{table_te}. + Iu Figure [bb we represent the cluster total mass bias with these assunuptions., In Figure \ref{fig_bias}b b we represent the cluster total mass bias with these assumptions. + While the bias is always zero in the WE approach. for the FGF aud SL cases; as expocted. we notice a imass bias dependence ou J...," While the bias is always zero in the HE approach, for the FGF and SL cases, as expected, we notice a mass bias dependence on $T_e$." +" Due to the degeneracy between he electron temperature aud uuuber density, the mass bias varies with ης."," Due to the degeneracy between the electron temperature and number density, the mass bias varies with $n_e$." + Iu all cases. it is worth noting that these biases nullifv for elecYOu telperatures equal to Ley values. thus proving that the method is uot affected by svsteiaties.," In all cases, it is worth noting that these biases nullify for electron temperatures equal to $T_{e0}$ values, thus proving that the method is not affected by systematics." +" The degeneracy between the ICM paralegrers, resulting from viclding the same SZ signal. produces ciffereut troeuds on FOR aud SL biases with electron eaperatuve."," The degeneracy between the ICM parameters, resulting from yielding the same SZ signal, produces different trends on FGF and SL biases with electron temperature." + For duereasing. values οἱ. electron temperature it underestimates the Alga., For increasing values of electron temperature it underestimates the $M_{gas}$ . + Cousidoeriug the FOP approach. this implies an underestimationof the total mass. too.," Considering the FGF approach, this implies an underestimationof the total mass, too." + For the SL method thiswould, For the SL method thiswould +The computation of the tilt parameter. Lis straightforward. given (9)): As eyavitational wave perturbations do not directly interact with the iuflaton field. they may be related directly to the expansion rate.,"The computation of the tilt parameter $n_s-1$ is straightforward, given \ref{lphi4deltaH}) ): As gravitational wave perturbations do not directly interact with the inflaton field, they may be related directly to the expansion rate." + The amplitude of eravitational waves is simply: ' All expressions are to be evaluated when the given scale & first crosses the horizon. k—afl.," The amplitude of gravitational waves is simply: \cite{mfb} + All expressions are to be evaluated when the given scale $k$ first crosses the horizon, $k = a H$." + Aun example perturbation «spectruuu is shown in Fie. 2..," An example perturbation spectrum is shown in Fig. \ref{dnd2}," + while Fig., while Fig. + 3 shows the dependence of the spectrum on the initial state for à umuber of possible evolutions., \ref{deltaphi} shows the dependence of the spectrum on the initial state for a number of possible evolutions. + Both of these Heures show distinct regions characterized by a blue spectral tilt., Both of these figures show distinct regions characterized by a blue spectral tilt. + RL. was supported in part by the Departiieut of Encrey Contract, R.H. was supported in part by the Department of Energy Contract DE-FG02-91-ER40682. +radii whereas artificial mass loss from the outer boundary is not negligible with smaller outer boundary radii.,radii whereas artificial mass loss from the outer boundary is not negligible with smaller outer boundary radii. + The temperature is calculated by the Newton-Raphson method., The temperature is calculated by the Newton-Raphson method. +" For all simulations, the mass of the central star is the solar mass, Mo, the initial mass of the disc is 0.1 Mo, and the initial surface density is proportional to r! with the outer edge of 20 AU."," For all simulations, the mass of the central star is the solar mass, $M_{\odot}$, the initial mass of the disc is 0.1 $M_{\odot}$, and the initial surface density is proportional to $r^{-1}$ with the outer edge of 20 AU." + The adopted time step size is 1 yr., The adopted time step size is 1 yr. + A single simulation for ~ 10 Myr takes roughly one cpu day., A single simulation for $\sim$ 10 Myr takes roughly one cpu day. + We conduct 8 runs for discs with radially constant a’s and 18 runs for discs with dead zones., We conduct 8 runs for discs with radially constant $\alpha$ 's and 18 runs for discs with dead zones. + The input parameters are shown in Tables 2 and 3 for simulations of discs without and with dead zones., The input parameters are shown in Tables 2 and 3 for simulations of discs without and with dead zones. + Results for all simulations are summarized in Table 4., Results for all simulations are summarized in Table 4. +" Figure 1 shows time evolution of the surface density X, the temperature T', and the mass accretion rate M for a disc with a radially constant o (run N2)."," Figure 1 shows time evolution of the surface density $\Sigma$, the temperature $T$, and the mass accretion rate $\dot{M}$ for a disc with a radially constant $\alpha$ (run N2)." +" As the disc spreads with time, © and T decrease."," As the disc spreads with time, $\Sigma$ and $T$ decrease." +" The kinks seen in the T profile correspond to the opacity transition temperatures (150 K, 180 K, and 1380 K) and the corresponding kinks are also seen in X."," The kinks seen in the $T$ profile correspond to the opacity transition temperatures (150 K, 180 K, and 1380 K) and the corresponding kinks are also seen in $\Sigma$." +" The direction of the radial gas motion is inward in the inner disc and outward in the outer disc, and the zero radial velocity radius expands with disc expansion."," The direction of the radial gas motion is inward in the inner disc and outward in the outer disc, and the zero radial velocity radius expands with disc expansion." +" The accretion rate M is independent of r in the inner disc and is equivalent to the mass accretion rate onto the central star M., as long as M is sufficiently larger than the mass loss rate due to photoevaporation My."," The accretion rate $\dot{M}$ is independent of $r$ in the inner disc and is equivalent to the mass accretion rate onto the central star $\dot{M}_{*}$, as long as $\dot{M}$ is sufficiently larger than the mass loss rate due to photoevaporation $\dot{M}_{\rm w}$." +" When M. becomes less than M,,, X rapidly decreases and eventually a gap opens at slightly beyond 1 AU, as well as simulations in Owen (2011)."," When $\dot{M}_{*}$ becomes less than $\dot{M}_{\rm w}$, $\Sigma$ rapidly decreases and eventually a gap opens at slightly beyond 1 AU, as well as simulations in \citet{Owe11}." +". Once a gap opens, the inner disc (inside the gap) disperses very quickly and mass accretion onto the central star stops."," Once a gap opens, the inner disc (inside the gap) disperses very quickly and mass accretion onto the central star stops." + The hole size is only 1.3 AU at this time., The hole size is only 1.3 AU at this time. +" The temperature increases when the disc becomes optically thin, but this phase (with a non-zero gas density) is very short."," The temperature increases when the disc becomes optically thin, but this phase (with a non-zero gas density) is very short." +" The gap opening slightly outside rx,i, is explained as follows."," The gap opening slightly outside $r_{\rm X,in}$ is explained as follows." +" Let us assume that the inward mass flux due to viscous accretion at rx,out is Mout."," Let us assume that the inward mass flux due to viscous accretion at $r_{\rm X,out}$ is $\dot{M}_{\rm out}$." +" As gas moves inward by dr, the mass flux is reduced by 27rwdr."," As gas moves inward by $dr$, the mass flux is reduced by $2\pi r \dot{\Sigma}_{\rm w}dr$ ." +" Therefore, the inward mass flux decreases with decreasing r and eventually becomes zero at rxjin if Mou= My."," Therefore, the inward mass flux decreases with decreasing $r$ and eventually becomes zero at $r_{\rm X,in}$ if $\dot{M}_{\rm out} = \dot{M}_{\rm w}$ ." +" Thus, if M is independent of r without photoevaporation, a gap inevitably opens near rx,in."," Thus, if $\dot{M}$ is independent of $r$ without photoevaporation, a gap inevitably opens near $r_{\rm X,in}$." +" Since it takes a time for gas to radially move from rx,out to rx,in (the viscous time scale at rx,out), Mout becomes much less than My at the time of actual gap opening (see the black curve in Fig."," Since it takes a time for gas to radially move from $r_{\rm X,out}$ to $r_{\rm X,in}$ (the viscous time scale at $r_{\rm X,out}$ ), $\dot{M}_{\rm out}$ becomes much less than $\dot{M}_{\rm w}$ at the time of actual gap opening (see the black curve in Fig." + 1)., 1). +" In some runs, large gaps can open (runs N3 and N6; see Table 4)."," In some runs, large gaps can open (runs N3 and N6; see Table 4)." +" This happens because the disc sizes are not sufficiently larger than rx,ou« and the mass accretion rates are not radially constant near the outer edges of the discs."," This happens because the disc sizes are not sufficiently larger than $r_{\rm X,out}$ and the mass accretion rates are not radially constant near the outer edges of the discs." +" Even in these cases, the mass accretion rates onto the central stars at the time of gap opening are much smaller than those seen intransition discs."," Even in these cases, the mass accretion rates onto the central stars at the time of gap opening are much smaller than those seen intransition discs." +" Overall,a large accretion rate and"," Overall,a large accretion rate and" +with other stellar objects in the vicinity. as well as interactions with circumbinary discs (Bate. Bonnell Bromim 2002b).,"with other stellar objects in the vicinity, as well as interactions with circumbinary discs (Bate, Bonnell Bromm 2002b)." + Llowever. this sort of calculation (that fully resolve [fragmentation in a cloud. of e.g. 50 AL. of gas in DIIS case) is very demanding computationally. and a wide range of initial conditions cannot easily be. explored.," However, this sort of calculation (that fully resolve fragmentation in a cloud of e.g. 50 $_\odot$ of gas in BBB's case) is very demanding computationally, and a wide range of initial conditions cannot easily be explored." + In addition. such caleulations remain inconclusive about the ooperties of multiple stars (in. particular the existence of ong lived. multiples ancl the production of wide binaries) since the evolution of the resulting stellar systems is not ollowecd until decay to a stable hierarchical configuration is achieved.," In addition, such calculations remain inconclusive about the properties of multiple stars (in particular the existence of long lived multiples and the production of wide binaries) since the evolution of the resulting stellar systems is not followed until decay to a stable hierarchical configuration is achieved." + For example. out of the 50 objects formed in he BBB simulation. LS are contained in non-hierarchical eroupings containing 11 and 7 members.," For example, out of the 50 objects formed in the BBB simulation, 18 are contained in non-hierarchical groupings containing 11 and 7 members." + Since. in this simulation. onlv the more compact eroupines have had time o decav to a stable configuration. BBB understandably ocused their attention on the implications of their work for binary formation.," Since, in this simulation, only the more compact groupings have had time to decay to a stable configuration, BBB understandably focused their attention on the implications of their work for binary formation." + In this paper we have taken an alternative approach which is a natural complement to the BBB simulations., In this paper we have taken an alternative approach which is a natural complement to the BBB simulations. + VPhrough the modelling of less massive clouds over longer timescales. we have been able to follow wice binary formation and the production of long lived multiple systems.," Through the modelling of less massive clouds over longer timescales, we have been able to follow wide binary formation and the production of long lived multiple systems." + We find that by modelling an ensemble of isolated cores οἱ mass 5 M... we can improve the number of stars formed per CPU hour by a factor 7 compared with the BBB calculation. which comprised a total mass of 50 M..," We find that by modelling an ensemble of isolated cores of mass 5 $_\odot$, we can improve the number of stars formed per CPU hour by a factor 7 compared with the BBB calculation, which comprised a total mass of 50 $_\odot$." + This economwv stems from the fact that by focusing on individual dense cores. we dispense with the computational expense of following the dilfuse gas in the BBB simulation.," This economy stems from the fact that by focusing on individual dense cores, we dispense with the computational expense of following the diffuse gas in the BBB simulation." + We remark. however. as à caveat. that we find that the formation of multiples proceedsfierarchicalty. with structures on any. scale being progressively modified by interactions on larger scales.," We remark, however, as a caveat, that we find that the formation of multiples proceeds, with structures on any scale being progressively modified by interactions on larger scales." + Thus in these models with scale free turbulence.ay upper mass cut-oll (i.c. the finite mass of the system mocelled) may have some influence on the multiple systems produced.," Thus in these models with scale free turbulence, upper mass cut-off (i.e. the finite mass of the system modelled) may have some influence on the multiple systems produced." + By comparing our results with those of BBB. we are able to assess how sensitive our results are to the total mass of the region simulated.," By comparing our results with those of BBB, we are able to assess how sensitive our results are to the total mass of the region simulated." + The computational economies that we gain through the simulation of less massive cores. allows us to instead concentrate our elforts on the longer timescale integration of the multiple systems produced.," The computational economies that we gain through the simulation of less massive cores, allows us to instead concentrate our efforts on the longer timescale integration of the multiple systems produced." + We wish to understand how our results are alfectec if weaway the eas component at a certain evolutionary stage (when of the initial eas has been accreted) ancl thereafter evolve the system as an N-body ensemble., We wish to understand how our results are affected if we the gas component at a certain evolutionary stage (when of the initial gas has been accreted) and thereafter evolve the system as an $N$ -body ensemble. + We follow the stellar dvnaniucal -body problem for 10. Myr (this typically corresponding to 10 orbits of multiple systems at the median separation). using the code. by Aarseth (Aarseth 1963)," We follow the stellar dynamical $N$ -body problem for 10 Myr (this typically corresponding to $10^4$ orbits of multiple systems at the median separation), using the code, by Aarseth (Aarseth 1963)." + Another advantage that we reap from this less computationally. expensive approach is that we eain improved statistics (i.c. we form z150 stars and brown chwarls. compared with the =50 of BBB). ancl from this dataset. are able to extract reasonable statistics. in a manner similar to Sterzik Durisen (1998: 2003) for the purely [IN -body case.," Another advantage that we reap from this less computationally expensive approach is that we gain improved statistics (i.e. we form $\approx 150$ stars and brown dwarfs, compared with the $\approx 50$ of BBB), and from this dataset are able to extract reasonable statistics, in a manner similar to Sterzik Durisen (1998; 2003) for the purely $N$ -body case." + We stress that our simulations share the property of the BBB simulations that they resolve the opacity limit for fragmentation (Low Lyncden-Bell 1976: Rees 1976) and that. assuming that fragmentation does not occur at densities greater than those at which the eas becomes opaque to infrared radiation. these calculations are able to model the formation of all the stars and brown dwarfs that. under the initial conditions imposed. can be produced.," We stress that our simulations share the property of the BBB simulations that they resolve the opacity limit for fragmentation (Low Lynden-Bell 1976; Rees 1976) and that, assuming that fragmentation does not occur at densities greater than those at which the gas becomes opaque to infrared radiation, these calculations are able to model the formation of all the stars and brown dwarfs that, under the initial conditions imposed, can be produced." + Our spatial resolution limit for binaries allows us to study a wide range of separations. and the particle numbers we employ allow us to model accretion dises around the protostars which are as long lived as those modelled by BBB.," Our spatial resolution limit for binaries allows us to study a wide range of separations, and the particle numbers we employ allow us to model accretion discs around the protostars which are as long lived as those modelled by BBB." + Our study has four major findings: The structure of this paper is as follows., Our study has four major findings: The structure of this paper is as follows. + In Section 2 the computational method and initial conditions applied to our models are described., In Section 2 the computational method and initial conditions applied to our models are described. + The results on multiple stars are given in Section 3., The results on multiple stars are given in Section 3. + In Section 4 we perform a detailed comparison of our results with available observational data. and suggest [uture experiments.," In Section 4 we perform a detailed comparison of our results with available observational data, and suggest future experiments." + Our conclusions are given in Section 5., Our conclusions are given in Section 5. + The results presented in this paper were obtained from the same simulations introduced in. Delgado-Donate. Clarke Bate (2004: henceforth DCDBOA).," The results presented in this paper were obtained from the same simulations introduced in Delgado-Donate, Clarke Bate (2004; henceforth DCB04)." + A detailed description of the SPILL code that was used to perform those calculations as well as the initial conditions imposed is given there., A detailed description of the SPH code that was used to perform those calculations as well as the initial conditions imposed is given there. + Here we briellv summarise the computational methocd., Here we briefly summarise the computational method. + The caleulations were performed. using a 3D. hybrid SPLI N-body code. withvariable smoothing lengths.," The calculations were performed using a 3D hybrid SPH $N$ -body code, withvariable smoothing lengths." + The SPIEL equations are solved. using a second order Itunge-]xutta-Fehlberg integrator with individual timesteps for each particle (Bate. Bonnell Price 1995).," The SPH equations are solved using a second order Runge-Kutta-Fehlberg integrator with individual timesteps for each particle (Bate, Bonnell Price 1995)." + We use the standard form of artificial viscosity (Monaghan CGingold 1983) with strength parameters ἂν=1 and 2=2., We use the standard form of artificial viscosity (Monaghan Gingold 1983) with strength parameters $\alpha_{\rm v} = 1$ and $\beta_{\rm v} = 2$. + We have assumed that the gas becomes optically thick when the density p reaches a critical value pe=10.Meem. *.," We have assumed that the gas becomes optically thick when the density $\rho$ reaches a critical value $\rho_{\rm c} = 10^{-13} {\rm +g~cm^{-3}}$ ." + This, This + , +Whereas the halo bias factor can be less than unity. the bias factor of the subclumps is always. greater than unity.,"Whereas the halo bias factor can be less than unity, the bias factor of the subclumps is always greater than unity." + “Phe more accurate model for subclump biasing (equation 20)). which should be accurate on smaller scales. can also be solved analytically: If this ratio is expressed as a Taylor series in 9. then the coefficient of the term which is proportional to 9 is the same as the linear bias factor derived from the counting argument (equation 24)).," The more accurate model for subclump biasing (equation \ref{nsubbias}) ), which should be accurate on smaller scales, can also be solved analytically: If this ratio is expressed as a Taylor series in $\delta$, then the coefficient of the term which is proportional to $\delta$ is the same as the linear bias factor derived from the counting argument (equation \ref{bsubps}) )." + To see this explicitly. consider the limit of large cells. for which As is large simply because V. is large.," To see this explicitly, consider the limit of large cells, for which $M_\delta$ is large simply because $V$ is large." + Then e(Ms)/o(m)+0 and o0(8)~0«δις. so that Numerical simulations show that the spherical collapse based equation (11)) isa good but not perfect description of the number density of parent halos.," Then $\sigma(M_\delta)/\sigma(m)\to 0$ and $\delta_0(\delta)\sim \delta \ll \delta_{\rm sc}$, so that Numerical simulations show that the spherical collapse based equation \ref{nmps}) ) is a good but not perfect description of the number density of parent halos." + A more accurate formula is (Sheth Tormen. 1990). where vo-δι)σημα). aosO71 p=0.3 and cL=0.322 insures that the distribution is normalized to unity.," A more accurate formula is (Sheth Tormen 1999), where $\nu = \delta_{\rm sc}(t)/\sigma(m)$, $a\approx 0.71$, $p=0.3$ and $A=0.322$ insures that the distribution is normalized to unity." + Sheth. Mo Tormen (2001) argue that this expression may be related to models in which halos form [from an ellipsoidal collapse.," Sheth, Mo Tormen (2001) argue that this expression may be related to models in which halos form from an ellipsoidal collapse." + Pereival. Miller Peacock (2000) show that the insertion of equation. (27)) in equation (13)) provides a better description. of halo formation in simulations than does equation (112).," Percival, Miller Peacock (2000) show that the insertion of equation \ref{st99}) ) in equation \ref{form}) ) provides a better description of halo formation in simulations than does equation \ref{nmps}) )." + Therefore. it probably provides a more accurate model. of the subclump abundances ancl bias [actors as well.," Therefore, it probably provides a more accurate model of the subclump abundances and bias factors as well." + To use this requires a model. for the analog of the conditional mass function (equation 5)): Sheth Tormen (2002) argue that simply changing. variables in n(m.b). as is appropriate when equation (11)) is the mass function. while incorrect. is not à bad approximation.," To use this requires a model for the analog of the conditional mass function (equation \ref{NmM}) ); Sheth Tormen (2002) argue that simply changing variables in $n(m,t)$, as is appropriate when equation \ref{nmps}) ) is the mass function, while incorrect, is not a bad approximation." + In this approximation. the analog of equation (21)) is again proportional to ALVESTEG7(M). the subclump mass function (integrated over parent masses AJ) can be written in terms of hypergeometric functions. as can the large-scale bias factor.," In this approximation, the analog of equation \ref{NmMT}) ) is again proportional to $M/\sqrt{\sigma^2(m)-\sigma^2(M)}$, the subclump mass function (integrated over parent masses $M$ ) can be written in terms of hypergeometric functions, as can the large-scale bias factor." + “Phe expressions. are. lengthy. so Ll haven't reproduced. them here.," The expressions are lengthy, so I haven't reproduced them here." + Figure 1. compares the large-scale bias factor of the parent halos (dashed. from Sheth Tormen 1999). with that for the subclumps (solid).," Figure \ref{biassub} compares the large-scale bias factor of the parent halos (dashed, from Sheth Tormen 1999), with that for the subclumps (solid)." + The lower anc upper dotted curves show the parent and subclump bias factors associated. with equations (23)) ancl (24))., The lower and upper dotted curves show the parent and subclump bias factors associated with equations \ref{biasmw}) ) and \ref{bsubps}) ). + L derived a model of the subclump distribution uncer the assumption that there. are no processes by which a subclump can lose mass as it falls in to a larger system., I derived a model of the subclump distribution under the assumption that there are no processes by which a subclump can lose mass as it falls in to a larger system. + Although this idealization is not realistic. it should. be thought of as. providing the initial conditions for more sophisticated: caleulations which do incorporate the effects of tidal stripping and dynamical friction.," Although this idealization is not realistic, it should be thought of as providing the initial conditions for more sophisticated calculations which do incorporate the effects of tidal stripping and dynamical friction." + For instance. the cumulative distribution of subclumps in this model is When mOAL. this scales as Ada(n). which is rather dillerent. from. the m scaling seen in simulations alter tidal stripping.," For instance, the cumulative distribution of subclumps in this model is When $m\ll M$, this scales as $M\,\sigma(m)$, which is rather different from the $m^{-1}$ scaling seen in simulations after tidal stripping." + Nevertheless. the model is useful. because it provides simple. closed-form: expressions for. how the abundances and spatial distributions of the subclumps ciller [rom those of their parent. halos.," Nevertheless, the model is useful because it provides simple closed-form expressions for how the abundances and spatial distributions of the subclumps differ from those of their parent halos." + If mergers are unimportant. then equation (22)) can be turned into an estimate of the luminosity function.," If mergers are unimportant, then equation \ref{nsubmps}) ) can be turned into an estimate of the luminosity function." + This can be done either by assuming a mean mass-to-light ratio. or bv assuming some relation for how the light-curve evolves with time. and then convolving with the formation ime distributions derived. here.," This can be done either by assuming a mean mass-to-light ratio, or by assuming some relation for how the light-curve evolves with time, and then convolving with the formation time distributions derived here." + E: have not. pursued. this urther because this model for the subclump distribution is not sulliciently realistic., I have not pursued this further because this model for the subclump distribution is not sufficiently realistic. + For example. [dmmnagatm)/p is generally ereater than unity.," For example, $\int {\rm d}m\,mn_{\rm sub}(m)/\bar\rho$ is generally greater than unity." + This is a consequence of the act that objects counted as having formed with mass m may xeviouslv have been counted as having formed with mass mb«m., This is a consequence of the fact that objects counted as having formed with mass $m$ may previously have been counted as having formed with mass $m'1/2$." + Comparison with inferred inner holes in. observed accretion disks vieles results consistent with our estimates for the above transition radius. the point where shears in the Low (and hence heating) end.," Comparison with inferred inner holes in observed accretion disks yields results consistent with our estimates for the above transition radius, the point where shears in the flow (and hence heating) end." + Well collimated jets. readily appear. proving the existence of purely hydrodyvnamical mechanisms for the generation of astrophysical jets.," Well collimated jets readily appear, proving the existence of purely hydrodynamical mechanisms for the generation of astrophysical jets." + Xavier Lernancez acknowledges the hospitality of the Observatoire de Paris for the duration of a sabbatical stay during which many of the ideas. presented. here were first developed., Xavier Hernandez acknowledges the hospitality of the Observatoire de Paris for the duration of a sabbatical stay during which many of the ideas presented here were first developed. + Pablo Itendon and Rosa Iocdriguez acknowledge financial support from project DAPIEE INIIO41I. DOAPA UNAM., Pablo Rendon and Rosa Rodriguez acknowledge financial support from project PAPIIT IN110411 DGAPA UNAM. + Antonio Capella. acknowledges financial support [rom project PAPIET INIOI410 DGAPA UNAM., Antonio Capella acknowledges financial support from project PAPIIT IN101410 DGAPA UNAM. +cannot therefore be explained by variations of the ionization parameters. which should first of all affect the [ΟΠ{ΟΠΗ ratio.,"cannot therefore be explained by variations of the ionization parameters, which should first of all affect the [OIII]/[OII] ratio." + A possible explanation for this is discussed in Sect. 4.8.., A possible explanation for this is discussed in Sect. \ref{model_others}. + Temperature and density sensitive line ratios are summarized in Table 3.., Temperature and density sensitive line ratios are summarized in Table \ref{tab_diagnostic}. + Note that only a few values are available on the nucleus because of the strong stellar continuum which prevents the measurement of faint lines., Note that only a few values are available on the nucleus because of the strong stellar continuum which prevents the measurement of faint lines. + The relatively large TOIL). slightly lower (ΗΕ and much cooler NII]. [SII] temperatures are typical of gas phototonized by a “typical AGN”. re. a spectrum characterized by a power law continuum with a super-imposed UV bump peaked at 250-100 eV (e.g. Mathews Ferland 1957).," The relatively large (OIII), slightly lower (SIII) and much cooler [NII], [SII] temperatures are typical of gas photoionized by a “typical AGN”, i.e. a spectrum characterized by a power law continuum with a super–imposed UV bump peaked at $\approx$ 50–100 eV (e.g. Mathews Ferland \cite{mathews87}) )." + As T.((OUL) mainly depends on the average energy of /iv eV ionizing photons. “bumpy” spectra. which are quite flat between 13 and 54 eV. yield hot [OIII].," As (OIII) mainly depends on the average energy of $h\nu\!<\!54$ eV ionizing photons, “bumpy” spectra, which are quite flat between 13 and 54 eV, yield hot [OIII]." + The lower ionization species. such as [NII] and [SII]. mostly form in the partially tonized region. heated by soft X-rays. whose temperature cannot exceed 10! K due to the powerful cooling by collisionally excited Ένα and 22photon. emission.," The lower ionization species, such as [NII] and [SII], mostly form in the partially ionized region, heated by soft X–rays, whose temperature cannot exceed $^4$ K due to the powerful cooling by collisionally excited $\alpha$ and 2–photon emission." + The contrast between the OHI and NII temperatures can be further increased if sub-solar metallicities are adopted. because [ΟΠΗ is a major coolant while [NH] only plays a secondary role in the cooling of the partially tonized region.," The contrast between the OIII and NII temperatures can be further increased if sub–solar metallicities are adopted, because [OIII] is a major coolant while [NII] only plays a secondary role in the cooling of the partially ionized region." + An alternative explanation for the ΟΠΠ. NII ete.," An alternative explanation for the OIII, NII etc." + temperature differences is to assume that part of the line emission arises from density bounded clouds., temperature differences is to assume that part of the line emission arises from density bounded clouds. + In this case there is no need to adopt a “bumpy” AGN spectrum and detailed models. assuming a pure power law ionizing continuum. were developed by Binette et al. (," In this case there is no need to adopt a “bumpy” AGN spectrum and detailed models, assuming a pure power law ionizing continuum, were developed by Binette et al. (" +1996. hereafter B96)).,"1996, hereafter \cite{B96}) )." + However. it should be kept in mind that 7;.((OIL)> Te((NID does not necessarily indicate the presence of density bounded clouds.," However, it should be kept in mind that $>$ (NII) does not necessarily indicate the presence of density bounded clouds." + There ts a clear trend between and excitation of the species used to determine the density., There is a clear trend between and excitation of the species used to determine the density. + The [SII] red doublet yields densities lower than [OIL] which 1$ compatible with à single-density cloud for the following reason., The [SII] red doublet yields densities lower than [OII] which is compatible with a single-density cloud for the following reason. + If the flux of soft X-rays (200-500 eV) is strong enough. then [SII| lines are mostly produced in the X-ray heated region where the average hydrogen ionization fraction is quite low (50.1).," If the flux of soft X-rays (200-500 eV) is strong enough, then [SII] lines are mostly produced in the X-ray heated region where the average hydrogen ionization fraction is quite low $\la$ 0.1)." + The lines of [OH] on the contrary can only be produced in the transition region. where the ionization degree is close to unity. because of the very rapid O- charge exchange reactions.," The lines of [OII] on the contrary can only be produced in the transition region, where the ionization degree is close to unity, because of the very rapid O--H charge exchange reactions." + Hence »((SID-«»(OID most probably indicates the presence of a strong soft-X flux. as one indeed expects to be the case for an AGN spectrum.," Hence $<$ (OII) most probably indicates the presence of a strong soft-X flux, as one indeed expects to be the case for an AGN spectrum." + This is also confirmed by the detailed modelling described below., This is also confirmed by the detailed modelling described below. + The higher densities in the fully tonized region are new results because the blue [ArlV] doublet is usually too weak in AGN spectra and the FIR [NeV] lines are only accessible with the ISO-SWS spectrometer (M96))., The higher densities in the fully ionized region are new results because the blue [ArIV] doublet is usually too weak in AGN spectra and the FIR [NeV] lines are only accessible with the ISO-SWS spectrometer \cite{M96}) ). + The [ArIV| density of knot C is equal. within the errors. to that derived by [OIL] thus indicating that no large variations of densities are present in this cloud.," The [ArIV] density of knot C is equal, within the errors, to that derived by [OII] thus indicating that no large variations of densities are present in this cloud." +probability of 2«10.5 that both distributions are extracted from the same 1parent ΡΟΙpopulation.,probability of $2 \times 10^{-3}$ that both distributions are extracted from the same parent population. + We also performed the same test but comparing CVs with all svmbiotic stars., We also performed the same test but comparing CVs with all symbiotic stars. + The test gives a probability. of 4.10? that both distributions are extracted. from the same parent population., The test gives a probability of $4 \times 10^{-4}$ that both distributions are extracted from the same parent population. + The number of points is not high. but sullicient. as shown in Fasano Franceschini (LOST). and the cdifferenee is significant.," The number of points is not high, but sufficient, as shown in Fasano Franceschini (1987), and the difference is significant." + This result indicates that in this diagram there are clues to the cause of the differences between the flickering of these two classes of accreting white chvarls., This result indicates that in this diagram there are clues to the cause of the differences between the flickering of these two classes of accreting white dwarfs. + 1n the svmbioties of course. the mass donor is a red giant and the orbital periods are >100 d. In the CVs the mass donors are late-tywpe dwarls and the orbital periods are c1000 times shorter.," In the symbiotics of course, the mass donor is a red giant and the orbital periods are $>100$ d. In the CVs the mass donors are late-type dwarfs and the orbital periods are $\sim 1000$ times shorter." + To the best of our knowledge this is the first evidence that Dickering dillers in these types of acercting WDs and the physical cause of this dilference warrants further investigation (see below)., To the best of our knowledge this is the first evidence that flickering differs in these types of accreting WDs and the physical cause of this difference warrants further investigation (see below). + In quiescence RS Oph varies irregulary between V=10.012.2 (Collazzi ct al., In quiescence RS Oph varies irregulary between $V=10.0-12.2$ (Collazzi et al. + 2009. AAVSO light. curves)," 2009, AAVSO light curves)." + This variability is observed. before as well as after the 2006 outburst., This variability is observed before as well as after the 2006 outburst. + Darnley et al.(2008) detected an increase of the brightness in 2 from D—13.5 to B=11.9 mag and from 1—12.0 to V—10.5 for a vear after the 2006 outburst., Darnley et al.(2008) detected an increase of the brightness in $B$ from $B=13.5$ to $B=11.9$ mag and from $V=12.0$ to $V=10.5$ for a year after the 2006 outburst. + Worters et al. (, Worters et al. ( +2007) detected: an increase in V1. [rom V—11.3 to V=119 for 2 weeks.,2007) detected an increase in $V$ from $V=11.3$ to $V=11.9$ for 2 weeks. + The brightness of RS Oph at the time of our Hickering observations is well inside these limits (unfortunately. there does not seem to be any published C light curve).," The brightness of RS Oph at the time of our flickering observations is well inside these limits (unfortunately, there does not seem to be any published $U$ light curve)." + The derived parameters of the Ilickering can be considered as typical for quiescence., The derived parameters of the flickering can be considered as typical for quiescence. + After the 2006 outhurst the flickering of RS Oph disappeared (Zamanov et al., After the 2006 outburst the flickering of RS Oph disappeared (Zamanov et al. + 2006) probably as a result of (1) destruction of the accretion disk [rom the nova explosion or (2) a change in the inner disk associated with jet. production (Sokoloski et al., 2006) probably as a result of (1) destruction of the accretion disk from the nova explosion or (2) a change in the inner disk associated with jet production (Sokoloski et al. + 2008)., 2008). + The Uickering resumed by clay 241 of the outburst (Worters et al., The flickering resumed by day 241 of the outburst (Worters et al. + 2007)., 2007). + For the svmbiotic star CIL €vg. Sokoloski Ixenvon (2003) observed. changes in he HlickeringT in association with the mass cjectionj event.," For the symbiotic star CH Cyg, Sokoloski Kenyon (2003) observed changes in the flickering in association with the mass ejection event." + Observations of CLL €vgaS and RS Oph therefore indicate that a connection does exist between the Dickering behaviour and he ejection of matter from the WD., Observations of CH Cyg and RS Oph therefore indicate that a connection does exist between the flickering behaviour and the ejection of matter from the WD. + Dilferent sites for the origin of the Hlickering have been discussed., Different sites for the origin of the flickering have been discussed. + They are all related to the accretion process: the bright spot (the region of impact of the stream of transferred matter from the mass donor star on the accretion clisk): the boundary layer (between the innermost accretion clisk and the white chvarl surface): inside the accretion disk itself., They are all related to the accretion process: the bright spot (the region of impact of the stream of transferred matter from the mass donor star on the accretion disk); the boundary layer (between the innermost accretion disk and the white dwarf surface); inside the accretion disk itself. + The findings of Bruch (2000) for IUE Cas. V2051 Oph. IP Pee and. UN UAla demonstrated that the llickering in these CVs can originate in both regions and(ii).," The findings of Bruch (2000) for HT Cas, V2051 Oph, IP Peg and UX UMa demonstrated that the flickering in these CVs can originate in both regions and." + The temperature and. the size of the bright. spot are derived. for a number of CVs., The temperature and the size of the bright spot are derived for a number of CVs. + X. few examples. of temperatures are: for OY Car Wood et al (1989) caleulated black bods ZY=13800+1300 Ik. and color temperature ZY=9000 WK: Marsh. (1988) for LP Peg - Z=11200 lx: Zhang Robinson (1987) for U Gem - 2=11600+500 Ex: tobinson et al. (," A few examples of temperatures are: for OY Car Wood et al (1989) calculated black body $T=13800\pm1300$ K, and color temperature $T=9000$ K; Marsh (1988) for IP Peg - $T = 11200$ K; Zhang Robinson (1987) for U Gem - $T=11600\pm500$ K; Robinson et al. (" +1015) give. Fo=16000 Ix. for the bright μαrot in WZ See.,1978) give $T=16000$ K for the bright spot in WZ Sge. +" The temperature of the optical [ickering source of RS Oph Fy,10000 Ix. (see Seet.4.1) is similar to 1e temperature of the bright spot for the CVs.", The temperature of the optical flickering source of RS Oph $T_{fl} \approx 10000$ K (see Sect.4.1) is similar to the temperature of the bright spot for the CVs. + Phe mass ransfer in RS Oph max not be from Roche lobe overllow (as in CVs). but via stellar wine accretion.," The mass transfer in RS Oph may not be from Roche lobe overflow (as in CVs), but via stellar wind accretion." + As a result of 16 supersonic motion of the WD through the red giant wind 1ere should be a shock cone and an accretion wake., As a result of the supersonic motion of the WD through the red giant wind there should be a shock cone and an accretion wake. + Around 10 WD. it is likely that an aceretion disk and/or a cocoon is formed.," Around the WD, it is likely that an accretion disk and/or a cocoon is formed." + In the place where the matter Hlowing through 10 accretion wake encounters the accretion disk/cocoon a xieht spot could. be formed. (analogous to the bright spot ormed in the case of CVs. where the mass flow from the inner Lagrangian point encounters the aecretion disk).," In the place where the matter flowing through the accretion wake encounters the accretion disk/cocoon a bright spot could be formed (analogous to the bright spot formed in the case of CVs, where the mass flow from the inner Lagrangian point encounters the accretion disk)." + Another possible site for the origin of the Ilickering in RS Oph is the boundary [aver between the white dwarf and accretion disk., Another possible site for the origin of the flickering in RS Oph is the boundary layer between the white dwarf and accretion disk. + Bruch Duschl (1993) estimated the size of the boundary laver (ο) in RS Oph as «=2.20., Bruch Duschl (1993) estimated the size of the boundary layer $\epsilon$ ) in RS Oph as $\epsilon = 2.20$. +" In their model τμ is connected with the size of the boundary laver (£, is the the luminosity of the accretion cisk. Ly; is the Iuminosity of the boundary laver: see Fig 1: in Bruch Duschl 1993)."," In their model $L_{d}/L_{bl}$ is connected with the size of the boundary layer $L_{d}$ is the the luminosity of the accretion disk, $L_{bl}$ is the luminosity of the boundary layer; see Fig 1 in Bruch Duschl 1993)." + I£ we assume Ly|Lap&Lace71102000 L...and LuzLyeH150L... then we calculate μή—1.2.12. and the lower value agrees with the size of the boundary laver as estimated by Bruch Duschl (1993).," If we assume $L_d + L_{bl} \approx L_{acc} \approx 110-2000$ , and $L_{bl} \approx L_{fl} \approx 5 - 150$, then we calculate $L_{d}/L_{bl}=1.2-12$, and the lower value agrees with the size of the boundary layer as estimated by Bruch Duschl (1993)." + Llowever. Zr; of RS Oph as derived in Sect.," However, $T_{fl}$ of RS Oph as derived in Sect." + 4.1 is too low for a boundary. laver., 4.1 is too low for a boundary layer. + For UU Aqr. Baptista Bortoletto (2008) found no evidence of Ilickering generated in regions and.," For UU Aqr, Baptista Bortoletto (2008) found no evidence of flickering generated in regions and." +(ii). They suggested that the flickering in UU Jer is generated in the acerction disk. itself ancl a possible reason can be turbulence generated after the collision of disk gas with the densitv-enhanced spiral wave in the accretion disk., They suggested that the flickering in UU Aqr is generated in the accretion disk itself and a possible reason can be turbulence generated after the collision of disk gas with the density-enhanced spiral wave in the accretion disk. + The racial temperature profile of a steady-state accretion clisk is: where @is the Stefan-Boltzmann constant. f is the radial distance from the WD.," The radial temperature profile of a steady-state accretion disk is: where $\sigma$is the Stefan-Boltzmann constant, $R$ is the radial distance from the WD." + Using the parameters for RS Oph. a temperature Z5; ~9500 Ix (the temperature of the Uickering light source as derived in Sect. 4.1))," Using the parameters for RS Oph, a temperature $T_{fl} \sim$ 9500 K (the temperature of the flickering light source as derived in Sect. \ref{Tfl}) )" + should be achieved at a distance /?z20.5.1 [rom the WD., should be achieved at a distance $R\approx 0.5-1$ from the WD. + Lf is the place for the origin of the Uickering of RS Oph. then it comes from δὲ 1 {from the WD.," If is the place for the origin of the flickering of RS Oph, then it comes from $R$ 1 from the WD." + To understand: more fully the nature of the Iickering variability of RS Oph we need to acquire a set of spectra simultaneously. with photometry and with time resolution 30 seconds (see also Sokoloski 2003)., To understand more fully the nature of the flickering variability of RS Oph we need to acquire a set of spectra simultaneously with photometry and with time resolution $\sim 30$ seconds (see also Sokoloski 2003). + Such spectra potentially can clirectly give the spectrum of the Iickering light source., Such spectra potentially can directly give the spectrum of the flickering light source. + We report our CCD observations of the flickering variability of the recurrent nova RS Oph. simultancoush with 4 telescopes in the (BVRL bands.," We report our CCD observations of the flickering variability of the recurrent nova RS Oph, simultaneously with 4 telescopes in the $UBVRI$ bands." +" RS Oph has a Ilickering source with (£.D),= OG2PLO.OT. CD.Vu= 0.190.109. (VoRy—0.25 £0.05."," RS Oph has a flickering source with $(U-B)_0=-0.62 \pm 0.07$ , $(B-V)_0=0.15 \pm 0.10$ , $(V-R)_0=0.25 \pm 0.05$ ." +like the model H II region in Osterbrock. the WINES cooling function is dominated by [O II] ane [N HI].,"like the model H II region in Osterbrock, the WIM's cooling function is dominated by [O II] and [N II]." + An equilibrium temperature for each value of |z can be computed [rom eqtation (3) ane oue of the above heatiug-cooliug; balance equations., An equilibrium temperature for each value of $|$ $|$ can be computed from equation (3) and one of the above heating–cooling balance equations. + The values of Cty aud Gy. or o aud Ci. cai then be adjusted to fit the T; vs |z| distribution in Figuο ].," The values of $_{0}$ and $_{1}$, or $_{0}$ and $_{2}$, can then be adjusted to fit the $_e$ vs $|$ $|$ distribution in Figure 1." +" The best-lit values are listed in Table 1 for four cases: (a) supplemental Ieating Gyn, aud constant f: (b) supplemental heating Go ane constant f: (c supplemental heatiiο Cyne and a variabe f(iz|): and (d) supplemenal heating Ct» ancl variable f (|z).", The best-fit values are listed in Table 1 for four cases: (a) supplemental heating $_{1}$ $_e$ and constant $f$; (b) supplemental heating $_{2}$ and constant $f$ ; (c) supplemental heating $_{1}$ $_e$ and a variable $f(|$ $|$ ); and (d) supplemental heating $_{2}$ and variable $f(|$ $|$ ). + The associated yest-fit curves are also potted on Figure 1 [or comparison witl T. vs [z| inferred from the observed [N Πα ratios iitl e Perseus arin., The associated best-fit curves are also plotted on Figure 1 for comparison with $_e$ vs $|$ $|$ inferred from the observed [N $\alpha$ ratios in the Perseus arm. + Note that the derive values for uic Ci» are proportio malto H2 and !. respectively. where L is the assumed patl leneth thro the Pe‘seus aru.," Note that the derived values for $_{1}$ and $_{2}$ are proportional to $^{-\case{1}{2}}$ and $^{-1}$, respectively, where L is the assumed path length through the Perseus arm." +" Also. Haffuer et al (1999) «iscussed the possible contamination of the [N IH] sp""ira by a weak αἱοςyheric emission liue."," Also, Haffner et al (1999) discussed the possible contamination of the [N II] spectra by a weak atmospheric emission line." + If tus liue is present with the inteusity of their upper iit. (OL R). then the best fit values for Ct atd Ci» would be — lower that those preseitecd in Table 1. while Gy would be less affected.," If this line is present with the intensity of their upper limit (0.1 R), then the best fit values for $_{1}$ and $_{2}$ would be – lower than those presented in Table 1, while $_{0}$ would be less affected." +" Figure 1 shows that al four cases give good fits to the inferred T, vs [z| distribution. within the uncertainty implied by the jaggeduess of the distributio1."," Figure 1 shows that all four cases give good fits to the inferred $_e$ vs $|$ $|$ distribution, within the uncertainty implied by the jaggedness of the distribution." +" Therefore. a supplemental heat source with a heating rate per unit voliue proportional to u;1 x n"" could account for the observed jatious in the line inteusity alios."," Therefore, a supplemental heat source with a heating rate per unit volume proportional to $_{e}^{1}$ or $_{e}^{0}$ could account for the observed variations in the line intensity ratios." +" Moreover. these restilts place tight coustraints on the required es. lImplyiug a photoionization jieating rate coellicielτς q νο.291x104>2! eres yslu . anda yplemental rate coellicient o eit]er Gio1x107 erον€» for a~ [ew"" x10-Ur7! eres 3 1"," Moreover, these results place tight constraints on the required rates, implying a photoionization heating rate coefficient $_0$ $\approx 1 +\times 10^{-24}$ ergs $^{+3}$ $^{-1}$, and a supplemental rate coefficient of either $_1$ $\sim 1 \times 10^{-25}$ ergs $^{-1}$ or $_2$ $\sim$ few $\times 10^{-27}$ ergs $^{-3}$ $^{-1}$." +" ΤΙus [or uy greater πα 1 ""ahe heating rate per uni VC)Une is dominated by photoionizatiol. wlile below ( .1-0.0Lem 7. th eslyplemental beating cloutales."," Thus for $_e$ greater than 1 $^{-3}$, the heating rate per unit volume is dominated by photoionization, while below 0.1 – 0.04 $^{-3}$, the supplemental heating dominates." + This value for Cu correspouds Oo a stellar iouizing spectrtμα with Tyyp 8 30.000 — 35.000 Ix. (Ostersock 1989). Le.. late O to early B. αμα is Consistent witl the οservations of weal He I recoribiuation line emission from the WIl (Tulte 1997. Reynolds Tulte 1995: Heiles et a 1996).," This value for $_0$ corresponds to a stellar ionizing spectrum with $_{eff}$ $\approx$ 30,000 – 35,000 K (Osterbrock 1989), i.e., late O to early B, and is consistent with the observations of weak He I recombination line emission from the WIM (Tufte 1997, Reynolds Tufte 1995; Heiles et al 1996)." + Values of Gy near 1 x10.7? eres + (Tabe 1) have it [act been predicted for the WIM in the Milky Way by iexels of photoelectric grain heating {Revyuolds Cox 1992: Draine 1975) aud by models of the dissipation of iuerstellar turbulence (linter Spangler 1997)., Values of $_1$ near 1 $\times 10^{-25}$ ergs $^{-1}$ (Table 1) have in fact been predicted for the WIM in the Milky Way by models of photoelectric grain heating (Reynolds Cox 1992; Draine 1978) and by models of the dissipation of interstellar turbulence (Minter Spangler 1997). + At electron temperatures above 8000 Ix the net |eallug νοallis decreases sharply due to cooliug vy collisious (Draine LOTS). auc. terefore. tliis process is 100 likely to account for the 0.000 Ix — 11.000 Ix. temperatures at high |z|. uless photoelectric heating in the WIM is comuneed by large molecules (e.e.. PAHs) (Lepp Dalgarno 1985).," At electron temperatures above 8000 K the net heating by grains decreases sharply due to cooling by electron--grain collisions (Draine 1978), and, therefore, this process is not likely to account for the 9,000 K – 11,000 K temperatures at high $|$ $|$, unless photoelectric heating in the WIM is dominated by large molecules (e.g., PAHs) (Lepp Dalgarno 1988)." +" Minter Spaeler (1997). on the oher haud. have predictec an energy cissipatiou rateof approximately 1 x10on -""n.ergscm ""sM Lgie to lon-nettral collisional dampening in the Milky Ways nearly. fully ioilized 104 I WIM."," Minter Spangler (1997), on the other hand, have predicted an energy dissipation rateof approximately 1 $ \times +10^{-25}$ $_e$ ergs $^{-3}$ $^{-1}$ due to ion–neutral collisional dampening in the Milky Way's nearly fully ionized $^4$ K WIM." + Thev concluded that the dissipation of turbulence probably plays a major ‘ole in heating the WII and contributing to the [S IH] aud, They concluded that the dissipation of turbulence probably plays a major role in heating the WIM and contributing to the [S II] and +transitions have the same number of spectral components. and at the same redshifts. (2) the background source morphology is frequency-dependent. implying that the NH; and rotational transitions might arise along slightly different sightlines. (3) the background source flux density (and hence morphology) varies with time. so observations at different epochs might probe different sightlines. (4) the assumption of LTE for the ΝΗ: hyperfine structure. (5) saturation effects if highly-saturated lines [e.g. the HCO! and HCN lines used by Murphyetal. (2008a)]] are used. and (6) local velocity offsets between the species giving rise to the transitions.,"transitions have the same number of spectral components, and at the same redshifts, (2) the background source morphology is frequency-dependent, implying that the $_3$ and rotational transitions might arise along slightly different sightlines, (3) the background source flux density (and hence morphology) varies with time, so observations at different epochs might probe different sightlines, (4) the assumption of LTE for the $_3$ hyperfine structure, (5) saturation effects if highly-saturated lines [e.g. the $^+$ and HCN lines used by \citet{murphy08}] ] are used, and (6) local velocity offsets between the species giving rise to the transitions." + As noted by Murphyetal.(2008a).. all these effects could yield significant contributions to their systematic errors.," As noted by \citet{murphy08}, all these effects could yield significant contributions to their systematic errors." + For example. the inversion. and rotational transitions used by Murphyetal.(2008a) were at very different frequencies. ~1I GHz and ~106 GHz: changes in the background source morphology could thus result in different sightlines in the different transitions.," For example, the inversion and rotational transitions used by \citet{murphy08} were at very different frequencies, $\sim 14$ GHz and $\sim 106$ GHz; changes in the background source morphology could thus result in different sightlines in the different transitions." + The NH; and HCO!/HCN observations were separated by a few years. implying that temporal variability in the source morphology could also be an issue. especially given that saturated transitions were used in the analysis.," The $_3$ and $^+$ /HCN observations were separated by a few years, implying that temporal variability in the source morphology could also be an issue, especially given that saturated transitions were used in the analysis." + Finally. the NH; spectra were of too low signal-to-noise ratio (S/N) to detect the NH; hyperfine structure and to test for non-LTE effects.," Finally, the $_3$ spectra were of too low signal-to-noise ratio (S/N) to detect the $_3$ hyperfine structure and to test for non-LTE effects." + Most of the above issues have been directly addressed in the present work., Most of the above issues have been directly addressed in the present work. + All three transitions used in the analysis are unsaturated and have been observed at high S/N. and with the same telescope.," All three transitions used in the analysis are unsaturated and have been observed at high S/N, and with the same telescope." + The two outlying NH; hyperfine components (at +19.5 km/s relative to the strongest component) in the NH; (1.1) line have also been clearly detected (see Fig. ," The two outlying $_3$ hyperfine components (at $\pm 19.5$ km/s relative to the strongest component) in the $_3$ (1,1) line have also been clearly detected (see Fig. \ref{fig:fig1}[ [" +ΗΑΕ.,A]). +" As noted by Murphyetal.(2008a).. non-LTE effects resulting in hyperfine ""anomalies"" should cause the satellite hyperfine components (with AF,σὲ0. where Fi is the quadrupole quantum number) to have different optical depths."," As noted by \citet{murphy08}, non-LTE effects resulting in hyperfine “anomalies” should cause the satellite hyperfine components (with $\Delta F_1 \ne 0$, where $F_1$ is the quadrupole quantum number) to have different optical depths." + No evidence for such non-LTE conditions is apparent in the +£19.5 kin/s satellite hyperfine components in Fig. I[[, No evidence for such non-LTE conditions is apparent in the $\pm 19.5$ km/s satellite hyperfine components in Fig. \ref{fig:fig1}[ [ +A]: the optical depths are found to agree within the noise.,A]; the optical depths are found to agree within the noise. +" We note. finally. that the systematic error of 7.6«10* in the result of Murphyetal.(2008a) contains two contributions: (1) 7«10* because spectral components detected in the HCO! and HCN spectra may not be detected in the NH: spectra. due either to the large frequency difference between the inversion and rotation lines or to the fact that HCO! and HCN lines are optically thick. and (2) 3ς10.the' due to the possibility of non-LTE effects in the NH, spectra."," We note, finally, that the systematic error of $7.6 \times 10^{-7}$ in the result of \citet{murphy08} contains two contributions: (1) $7 \times 10^{-7}$ because spectral components detected in the $^+$ and HCN spectra may not be detected in the $_3$ spectra, due either to the large frequency difference between the inversion and rotation lines or to the fact that the $^+$ and HCN lines are optically thick, and (2) $3 \times 10^{-7}$ due to the possibility of non-LTE effects in the $_3$ spectra." + Our choice of rotational lines and the higher sensitivity of our NH; spectra implies that neither of these are significant sources of systematic error in the present analysis., Our choice of rotational lines and the higher sensitivity of our $_3$ spectra implies that neither of these are significant sources of systematic error in the present analysis. + Lisztetal.(2006). find that NH: column densities correlate best with CS and H5CO column densities in Galactic diffuse clouds: CS and H2CO are thus likely to be the best rotational transitions for the inversion/rotation comparison. as the correlation in column densities suggests that the three species are likely to arise in the same part of a gas cloud.," \citet{liszt06} find that $_3$ column densities correlate best with CS and $_2$ CO column densities in Galactic diffuse clouds; CS and $_2$ CO are thus likely to be the best rotational transitions for the inversion/rotation comparison, as the correlation in column densities suggests that the three species are likely to arise in the same part of a gas cloud." + Galactic absorption has also been detected in allthree species towards two quasars. BO355+508 and BO415+379 (Liszt&Lucas1995;&Liszt1998:etal. 200601: both sightlines show two components in all species. with line velocities agreeing within 0.2 km/s [see Table | of Liszt&Lucas 1995.. Table 6 of Lucas&Liszt1998 and Table Al of Lisztetal. 2006): local velocity offsets between the species thus appear to be small.," Galactic absorption has also been detected in allthree species towards two quasars, B0355+508 and B0415+379 \citep{liszt95,lucas98,liszt06}; both sightlines show two components in all species, with line velocities agreeing within 0.2 km/s [see Table 1 of \citealt{liszt95}, Table 6 of \citealt{lucas98} and Table A1 of \citealt{liszt06}] ]; local velocity offsets between the species thus appear to be small." + Further. the rotational and inversion line frequencies are much closer here than in the comparison of Murphyetal.(2008a).. with the redshifted NH;. CS. and H»CO lines at ~11 GHz. ~29 GHz and ~13 GHz. respectively.," Further, the rotational and inversion line frequencies are much closer here than in the comparison of \citet{murphy08}, with the redshifted $_3$, CS, and $_2$ CO lines at $\sim 14$ GHz, $\sim 29$ GHz and $\sim 43$ GHz, respectively." + Changes in source morphology with frequency are thus a less important issue here than in the analysis of Murphyetal.(20083)., Changes in source morphology with frequency are thus a less important issue here than in the analysis of \citet{murphy08}. +.. A direct test comes from the comparison between the two rotational lines. whose frequencies differ by a factor of ~1.5. comparable to the ratio of the CS and NH; frequencies (~2).," A direct test comes from the comparison between the two rotational lines, whose frequencies differ by a factor of $\sim 1.5$, comparable to the ratio of the CS and $_3$ frequencies $\sim 2$ )." + The CS-H2CO comparison also provides an estimate of the systematic error due to local velocity offsets between different species in the clouds., The $_2$ CO comparison also provides an estimate of the systematic error due to local velocity offsets between different species in the clouds. + This test found the CS and H»CO line redshifts to agree within the noise: the 1o error in this comparison has been used to quantify the systematic error due to both local velocity offsets and differing background source morphology at the different line. frequencies., This test found the CS and $_2$ CO line redshifts to agree within the noise; the $1\sigma$ error in this comparison has been used to quantify the systematic error due to both local velocity offsets and differing background source morphology at the different line frequencies. + Finally. similar. velocity offsets (consistent. within the errors) were obtained in the independent comparisons between the NH; and CS lines. and the NH; and H»CO lines.," Finally, similar velocity offsets (consistent within the errors) were obtained in the independent comparisons between the $_3$ and CS lines, and the $_3$ and $_2$ CO lines." + A source of systematic effects that could not be directly addressed here is time variability in the background source morphology. which might yield different sightlines through the absorbing clouds at different epochs [Murphyetal.200δα:: see Muller&Guélin(2008) for the 2~0.886 lens towards 210].," A source of systematic effects that could not be directly addressed here is time variability in the background source morphology, which might yield different sightlines through the absorbing clouds at different epochs \citealp{murphy08}; see \citet{muller08} for the $z \sim 0.886$ lens towards $-$ 210]." + Unfortunately. the redshifted NH. CS and H2CO transitions towards BO218+357 require different GBT receivers and cannot be observed simultaneously.," Unfortunately, the redshifted $_3$, CS and $_2$ CO transitions towards B0218+357 require different GBT receivers and cannot be observed simultaneously." + The present NH;. CS and H2CO observations were carried out between January and August 2008: the possibilitythat the weak offset between the inversion and rotational lines arises due to small changes in the sightline thus cannot be ruled out.," The present $_3$ , CS and $_2$ CO observations were carried out between January and August 2008; the possibilitythat the weak offset between the inversion and rotational lines arises due to small changes in the sightline thus cannot be ruled out." + Further. the agreement between CS and H2CO velocities does not ruleout the possibility that nitrogen-bearing species like NH; arise at different velocities than carbon-bearing species like CS and H2CO.," Further, the agreement between CS and $_2$ CO velocities does not ruleout the possibility that nitrogen-bearing species like $_3$ arise at different velocities than carbon-bearing species like CS and $_2$ CO." +" This can only be tested by using rotational transitions of other nitrogen-bearing species (e.g. HC:,N. CH3CN. ete)."," This can only be tested by using rotational transitions of other nitrogen-bearing species (e.g. $_3$ N, $_3$ CN, etc)." + While there are two possible sources of systematic error that we are as yet unable to quantify. the present data show no statistically-significant (7 30) evidence for changes in the proton-electron mass ratio.," While there are two possible sources of systematic error that we are as yet unable to quantify, the present data show no statistically-significant $\ge 3\sigma$ ) evidence for changes in the proton-electron mass ratio." + Our 30 upper limit on changes in eis Αμ<3.6«10.*. between +~0.685 and >= O(a lookbacktime of 6.2 Gyrs).," Our $3\sigma$ upper limit on changes in $\mu$ is $\dmu < 3.6 \times 10^{-7}$, between $z \sim 0.685$ and $z = 0$ (a lookbacktime of 6.2 Gyrs)." +" For comparison. Murphyetal.(2008a) obtained. [Agr/s:|Ls.10* (2o) in the ;~0.685 absorber towards BO2184357. while Henkeletal.(2009) obtained Αμ1.1«108 (3o) in the 0,550 absorber towards 210. with both results based on inversion/rotation comparisons."," For comparison, \citet{murphy08} obtained $\dmu < 1.8 \times 10^{-6}$ $2\sigma$ ) in the $z \sim 0.685$ absorber towards B0218+357, while \citet{henkel09} obtained $\dmu < 1.4 \times 10^{-6}$ $3\sigma$ ) in the $z \sim 0.886$ absorber towards $-$ 210, with both results based on inversion/rotation comparisons." +" Note. however. that Henkeletal.(2009) used single-Gaussian fits for the NH; and HC4N lines towards B1830. 210. although it is clear from the profiles of other unsaturated lines (e.g. CS) that at least three absorbing ""clouds"" are present along the sightline."," Note, however, that \citet{henkel09} used single-Gaussian fits for the $_3$ and $_3$ N lines towards $-$ 210, although it is clear from the profiles of other unsaturated lines (e.g. CS) that at least three absorbing “clouds” are present along the sightline." + Further. the GBT spectra in the strongest [Cl.1). (2.2) and (3.3)] NH; lines towards 210 were severely affected by radio frequency interference (see Fig.," Further, the GBT spectra in the strongest [(1,1), (2,2) and (3,3)] $_3$ lines towards $-$ 210 were severely affected by radio frequency interference (see Fig." + | of Henkel ))., 1 of \citealt{henkel08}) ). + The effect of these issues on the results of Henkelet is unclear.but the error budget is likely to increase.," The effect of these issues on the results of \citet{henkel09} is unclear,but the error budget is likely to increase." +" At higher redshifts. the best published constraint on changes in jt ds that ofKingetal. (2008): [Aqr/pi]<6.0«10. P, using H» lines (but see Wendt&Molaro201 1))."," At higher redshifts, the best published constraint on changes in $\mu$ is that of\citet{king08}: : $\dmu < 6.0 \times 10^{-6}$ , using $_2$ lines (but see \citealt{wendt11}) )." + The present result. [App]<3.6s10* Qo) atc~ 0.685. is thus the most sensitive constraint on temporal changes in µ at any redshift. by à factor z 5.," The present result, $\dmu < 3.6 \times 10^{-7}$ $3\sigma$ ) at $z \sim 0.685$ , is thus the most sensitive constraint on temporal changes in $\mu$ at any redshift, by a factor $\gtrsim 5$ ." + To compare this result with those from laboratory studies. it is necessary to assume a model for the variation of ji with," To compare this result with those from laboratory studies, it is necessary to assume a model for the variation of $\mu$ with" +"passing the shock, the gas looses most of its velocity and does not move further inward, but is accumulated at the outer wings of the profile, leaving the inner part unchanged.","passing the shock, the gas looses most of its velocity and does not move further inward, but is accumulated at the outer wings of the profile, leaving the inner part unchanged." +" With time, a continuously decreasing fraction of matter remains outside of the shocked region."," With time, a continuously decreasing fraction of matter remains outside of the shocked region." + The accretion onto the pancake declines over time., The accretion onto the pancake declines over time. + This results in a slower shock speed and in a declining density profile., This results in a slower shock speed and in a declining density profile. +" The final density profile bound by the shocks covers about 2.5 orders of magnitude, and is proportional to 7-7/3 (?).."," The final density profile bound by the shocks covers about 2.5 orders of magnitude, and is proportional to $r^{-2/3}$ \citep{Shandarin89}." + The pressure profile remains almost constant., The pressure profile remains almost constant. + This is an expected behavior since pressure gradients would be quickly erased by hydrodynamic advection., This is an expected behavior since pressure gradients would be quickly erased by hydrodynamic advection. + The small deviation from uniformity as well as the weak redshift dependence are the imprint of the gravitational potential and the cosmological expansion., The small deviation from uniformity as well as the weak redshift dependence are the imprint of the gravitational potential and the cosmological expansion. + This almost isobaric behavior can be used to explain the shape of the temperature profiles., This almost isobaric behavior can be used to explain the shape of the temperature profiles. +" Given a constant pressure, Eq. (8))"," Given a constant pressure, Eq. \ref{eT}) )" + implies an inverted behavior between temperature and density., implies an inverted behavior between temperature and density. + The temperature is given in physical units implying a cosmic evolution οςa7’., The temperature is given in physical units implying a cosmic evolution $\propto a^{-2}$. +" Without heating and cooling, the physical dimensions can be eliminated from the hydrodynamic equations, and therefore the qualitative outcome of these simulations does not depend on the given length scale L."," Without heating and cooling, the physical dimensions can be eliminated from the hydrodynamic equations, and therefore the qualitative outcome of these simulations does not depend on the given length scale $L$." +" If we impose a reference system given by L, the background density of the Universe p, and the Hubble time 1/Ho, we are able to obtain scaling relations for all quantities."," If we impose a reference system given by $L$, the background density of the Universe $\bar{\rho}$, and the Hubble time $1/H_0$, we are able to obtain scaling relations for all quantities." + For the temperature scale this yields Thus the temperature in the shocked region scales as the square of the length scale of the initial perturbation., For the temperature scale this yields Thus the temperature in the shocked region scales as the square of the length scale of the initial perturbation. +" Besides the length scale of the perturbation, the initial amplitude is set as a parameter."," Besides the length scale of the perturbation, the initial amplitude is set as a parameter." +" Its value determines the time of caustic formation, as shown in ?.."," Its value determines the time of caustic formation, as shown in \citet{Bryan95}." +" The chosen value of A=0.02 corresponds to a shock formation at redshift z~1, which could be a reasonable value for the WHIM."," The chosen value of $A = 0.02$ corresponds to a shock formation at redshift $z \sim 1$, which could be a reasonable value for the WHIM." +" Owing to the cosmological expansion, the temperature declines very fast from its initial value."," Owing to the cosmological expansion, the temperature declines very fast from its initial value." +" Therefore, the initial temperature has a negligible influence on the dynamical evolution and on the resulting profiles."," Therefore, the initial temperature has a negligible influence on the dynamical evolution and on the resulting profiles." +" If cooling and heating are included into the consideration, an intrinsic physical scale is introduced."," If cooling and heating are included into the consideration, an intrinsic physical scale is introduced." +" Unlike before, the physical dimension cannot be eliminated from the dynamical equations."," Unlike before, the physical dimension cannot be eliminated from the dynamical equations." + Simulations using different perturbation scales L differ not only quantitatively but also qualitatively., Simulations using different perturbation scales $L$ differ not only quantitatively but also qualitatively. +" As a consequence, the constraint on the ratio between the spatial resolution Ax and the local Jeans length A, as presented in has to be fulfilled: If this criterion is not fulfilled, the pressure is too weak to even out small scale perturbations, which are caused by the finite numerical resolution."," As a consequence, the constraint on the ratio between the spatial resolution $\Delta x$ and the local Jeans length $\lambda_J$ as presented in \citet{Truelove97} has to be fulfilled: If this criterion is not fulfilled, the pressure is too weak to even out small scale perturbations, which are caused by the finite numerical resolution." +" These perturbations may then grow rapidly, and induce fragmentation for purely numerical reasons."," These perturbations may then grow rapidly, and induce fragmentation for purely numerical reasons." + In one-dimensional simulations this violates the spatial symmetry of the configuration., In one-dimensional simulations this violates the spatial symmetry of the configuration. +" Without the inclusion of either a (formal) heating source or an artificial pressure floor, catastrophic cooling in the center will appear, i.e., the density increases while the pressure decreases."," Without the inclusion of either a (formal) heating source or an artificial pressure floor, catastrophic cooling in the center will appear, i.e., the density increases while the pressure decreases." + This will always result in a Jeans length that violates Eq. (15))., This will always result in a Jeans length that violates Eq. \ref{eTruelove}) ). +" For the one- collapse, the heating due to the UV background is sufficient to prevent such a cooling catastrophe."," For the one-dimensional collapse, the heating due to the UV background is sufficient to prevent such a cooling catastrophe." + In Fig., In Fig. + 2 we present the outcome of our simulations including radiative cooling and heating for different length scales L of the initial perturbation., \ref{fCool} we present the outcome of our simulations including radiative cooling and heating for different length scales $L$ of the initial perturbation. +" For the computation of the chemical network, we assume IE, as described in Sect. ??.."," For the computation of the chemical network, we assume IE, as described in Sect. \ref{sDyn}." + The influence of non-IE will be discussed in Sect. ??.., The influence of non-IE will be discussed in Sect. \ref{sChem}. +" Like before, the initial amplitude is A=0.02."," Like before, the initial amplitude is $A = 0.02$." +" With increasing L the number of grid points increases from 2000 to 64000, thus keeping a constant spatial resolution of 0.5 kpc."," With increasing $L$ the number of grid points increases from $2000$ to $64000$, thus keeping a constant spatial resolution of $0.5$ kpc." +" Displayed are the density, the density flux (instead of the velocity, because it emphasizes the high-density region in the center), and the"," Displayed are the density, the density flux (instead of the velocity, because it emphasizes the high-density region in the center), and the" +"Wicle-area"" surveys for⋅ transiting↔ extra-solar planets such as WASP (Wide Anele Search for Planets. ?)). LINDTnet (?).. XO (7) and ‘Tels (0) provide high cadence photometry for millions of bright stars across a large fraction of the sky.","Wide-area surveys for transiting extra-solar planets such as WASP (Wide Angle Search for Planets,\citealt{2006PASP..118.1407P}) ), HATnet \citep{2004PASP..116..266B}, , XO \citep{2005PASP..117..783M} and TrES \citep{2006AAS...20922602O} provide high cadence photometry for millions of bright stars across a large fraction of the sky." + This provides the opportunity to find and study many new examples of known classes of variable star. e.g.. eclipsing brown chwarl binary systems. (?).. double-mode RR Lyr stars (2)... W UMa stars (2).. voung solar-tvpe stars (7?) and cataclysmic variable stars (2)...," This provides the opportunity to find and study many new examples of known classes of variable star, e.g., eclipsing brown dwarf binary systems \citep{ 2011ApJ...726L..19A}, , double-mode RR Lyr stars \citep{2010IBVS.5955....1W}, W UMa stars \citep{2011A&A...528A..90N}, young solar-type stars \citep{2011arXiv1104.2986M} and cataclysmic variable stars \citep{2011JAVSO.tmp..140W}." + New discoveries. will certainly be made now that much of the cata from these surveys is becoming widely available (2).. , New discoveries will certainly be made now that much of the data from these surveys is becoming widely available \citep{2010A&A...520L..10B}. . +Phe photometricprecision achieved bythese surveys with modest equipment, The photometricprecision achieved bythese surveys with modest equipment +Alternately. Soleretal.(2011b)— have shown that in the presence of flow the damping leugth remains inversely proportional to the frequency. but the factor of proportionality is different for forward aud backward xopasatiug waves to the flow direction aud depends on he characteristics of the flow.,"Alternately, \citet{solerflow} have shown that in the presence of flow the damping length remains inversely proportional to the frequency, but the factor of proportionality is different for forward and backward propagating waves to the flow direction and depends on the characteristics of the flow." +" Ποπονα, noue of these xevious works investigated the effect of longitudinal stratification."," However, none of these previous works investigated the effect of longitudinal stratification." + The analysis of kink MIID waves in longitudinally io0niogeneonus inodecls ake some problems ie6re ractable from an analytical point of view., The analysis of kink MHD waves in longitudinally homogeneous models make some problems more tractable from an analytical point of view. + Realistic nodels of solar waveguides should include longitudinal stratification., Realistic models of solar waveguides should include longitudinal stratification. + E.g.. coronal loops cau exteud out iuto the atmosphere up to heights of the order of several deusity scale heights.," E.g., coronal loops can extend out into the atmosphere up to heights of the order of several density scale heights." + This menus that the differences iu the density at their footpoiuts and apex can be significant., This means that the differences in the density at their footpoints and apex can be significant. +" There is evidence of such stratification iu coronal loops both from emission measure analysis (οιοι,Asclavaudenetal.1090) and coronal magnetoscisimology (seeAu-diiesetal.2009).forreviewofthis topic)."," There is evidence of such stratification in coronal loops both from emission measure analysis \citep[e.g.,][]{aschwanden1999} and coronal magnetoseismology \citep[see][for review of this topic]{andries2009b}." +" Regarding spicules, there lave been spectroscopic line intensity studies to show the plasina densitv is longitudinally strouely stratified (οι,Beckers1968:Makita2003) and nore recently by maguetoscisuoloey (Verthetal. 2011).."," Regarding spicules, there have been spectroscopic line intensity studies to show the plasma density is longitudinally strongly stratified \citep[e.g.,][]{beckers1968, makita2003} and more recently by magnetoseismology \citep[][]{verth2011}. ." +" Tt is also clear from Πα observations (οι,Linetal.2008) at prominence threads too exhibit longitudinal density inhomogeneity."," It is also clear from $\alpha$ observations \citep[e.g.,][]{lin08} that prominence threads too exhibit longitudinal density inhomogeneity." + For these reasons. the main aim of the xeseut paper is to investigate the effect of longitudinal stratification on the properties of resonantly damped xopasatiueg kink waves.," For these reasons, the main aim of the present paper is to investigate the effect of longitudinal stratification on the properties of resonantly damped propagating kink waves." + This is an interesting problem roni a theoretical. as well as observational poiut of view.," This is an interesting problem from a theoretical, as well as observational point of view." + The reason is that a radial variation of density causes damping due to resonant absorption while a longitudiual variation might cause au increase of the amplitude., The reason is that a radial variation of density causes damping due to resonant absorption while a longitudinal variation might cause an increase of the amplitude. +" An increase of the amplitude due to stratification along the naenetic field direction has been obtained by. c.g.. DeAloorteletal.(1999). for phase mixed Alfvén waves and DeMoortel&Hood(2001). for propagating slow uodes,"," An increase of the amplitude due to stratification along the magnetic field direction has been obtained by, e.g., \citet{inekealfven} for phase mixed Alfvénn waves and \citet{inekeslow} for propagating slow modes." + Iu this paper. we investigate the effect of loungitudiua density variation on propagating kink waves by usine voth analytical and umunerical approaches.," In this paper, we investigate the effect of longitudinal density variation on propagating kink waves by using both analytical and numerical approaches." + Analytica heorv is used to the largest possible extent., Analytical theory is used to the largest possible extent. + To do so. we apply standard approximations usually adopte in the preceding literature for tlhe investigation of kiuk waves in magnetic tubes.," To do so, we apply standard approximations usually adopted in the preceding literature for the investigation of kink waves in magnetic tubes." + The approximations used im he analytical part of this paper are brieflv discussec and justified in the next two paragraphs., The approximations used in the analytical part of this paper are briefly discussed and justified in the next two paragraphs. + In addition to he analytical theory. the problem is solved uuuercally )vond the limitations of the analytical approximations.," In addition to the analytical theory, the problem is solved numerically beyond the limitations of the analytical approximations." + The comparison between the analytical results aud those roni the full nuinerical siiulatious will enable us to check the validitv of the analytical theory., The comparison between the analytical results and those from the full numerical simulations will enable us to check the validity of the analytical theory. + Qur waveeuide model is a straight ονΠοσα magnetic Hux tube. inhomogeneous in both the radial and ongitucdinal directions. and embedded in a imuagnetized environment.," Our waveguide model is a straight cylindrical magnetic flux tube, inhomogeneous in both the radial and longitudinal directions, and embedded in a magnetized environment." + To investigate propagating kink waves analytically we adopt the following approximations., To investigate propagating kink waves analytically we adopt the following approximations. + We use the thin tube (TT) approximation. so that the wavelength. A. is much larger than the radius of the tube. R.," We use the thin tube (TT) approximation, so that the wavelength, $\lambda$, is much larger than the radius of the tube, $R$." + This condition is casily fulfilled for propagating waves observed in the solar atmosphere (sce the various references given above)., This condition is easily fulfilled for propagating waves observed in the solar atmosphere (see the various references given above). + The variation of density iu the radial direction is confined to a thin transitional laver. and we adopt the thin boundary (TB) approximation (seedetailsin.e.g..Hollweg&Yaug1988:Sakuralctal.1991:Ctoosseuset1992:Coossens2008).," The variation of density in the radial direction is confined to a thin transitional layer, and we adopt the thin boundary (TB) approximation \citep[see details in, e.g.,][]{hollwegyang,SGH91,goossens92,goossensIAU}." +. The TB approximation has been proved to be very accurate even when radial inhomogeneity is not restricted to a thin laver (see.e.g..VauDoorssclacreetal.2001:Andresetal.2005:Arreeni2005).," The TB approximation has been proved to be very accurate even when radial inhomogeneity is not restricted to a thin layer \citep[see, e.g.,][]{tom3, andries2005, arregui2005}." +. Regarding inhomogencity iu the longitudinal direction. we assune that the lank mode wavelength is shorter than the longitudinal iuhoimoseneitv Ieneth scale. so that the WISB approximation cau be applied.," Regarding inhomogeneity in the longitudinal direction, we assume that the kink mode wavelength is shorter than the longitudinal inhomogeneity length scale, so that the WKB approximation can be applied." + In the uunucrical part of this paper. the problem is solved iu the gencral case where large variations of density in both the radial aud loneitudinal directions are considered aud for arbitrary wavceleusth.," In the numerical part of this paper, the problem is solved in the general case where large variations of density in both the radial and longitudinal directions are considered and for arbitrary wavelength." + Ciurvature is neglected in the model., Curvature is neglected in the model. +The effect of curvature was studied by. e$... VanDoorsselaereetal.(2005). aud Terradasetal.(2006).. and it has beeu reviewed by VanDoorsselacreetal.(2009).,"The effect of curvature was studied by, e.g., \citet{tom1} and \citet{terradascurv}, and it has been reviewed by \citet{tom2}." +.. Analvtically. VanDoorsselacreetal.(2005) VAshowed that curvature has uo first-order effect on the frequency aud the damping of làuk modes in curved cvlndrical models.," Analytically, \citet{tom1} showed that curvature has no first-order effect on the frequency and the damping of kink modes in curved cylindrical models." + The result that curvature has ouly a nuünor effect ou kink MIID waves was also muuerically confirmed by VauDoorsselacreetal.(2005). aud Terradasetal.(2006)., The result that curvature has only a minor effect on kink MHD waves was also numerically confirmed by \citet{tom1} and \citet{terradascurv}. +.. Wave damping due to leakage is not cousidered., Wave damping due to leakage is not considered. + Leaky waves. io. waves damped by ΑΠΟ radiation. were first studied im magnetic flux tubes by Spruit(1982).. whose conclusion was that leakage is only important for waveleugths of the order of the tube radius or sinaller.," Leaky waves, i.e., waves damped by MHD radiation, were first studied in magnetic flux tubes by \citet{spruit}, whose conclusion was that leakage is only important for wavelengths of the order of the tube radius or smaller." + For thin tubes leakage is unimportant., For thin tubes leakage is unimportant. + This result was comfirmec by Goossens&Tolhwee(1993) and Ctoosseusetal.(2009)., This result was confirmed by \citet{goossenshollweg} and \citet{goossens2009}. +. Finalhy. the )=t approxination is also adopted. where } is the ratio of eas pressure to niaguetie pressure.," Finally, the $\beta = 0$ approximation is also adopted, where $\beta$ is the ratio of gas pressure to magnetic pressure." + The assuniption of j=0 implies that waves do not have motious along the equilibrium maguetic field direction., The assumption of $\beta = 0$ implies that waves do not have motions along the equilibrium magnetic field direction. + It has been explained bw. e.g. Spruit(1982) aud Coosseusetal.(2009) that the longitudinal component of the velocity is proportional to the transverse conrponeut. with a factor of proportionality that depeuds of } aud CR/AY?.," It has been explained by, e.g., \citet{spruit} and \citet{goossens2009} that the longitudinal component of the velocity is proportional to the transverse component, with a factor of proportionality that depends of $\beta$ and $(R/\lambda)^2$." + Tn the low-.) case and for thin tubes the longitudinal component of the velocity is much smaller than the transverse component., In the $\beta$ case and for thin tubes the longitudinal component of the velocity is much smaller than the transverse component. + In magnetic structures of the solar atmosphere 3l., In magnetic structures of the solar atmosphere $\beta \ll 1$. + This ineans that the longitudinal component of the velocity can be ueglected aud the +=0 approximation cau be safely adopted., This means that the longitudinal component of the velocity can be neglected and the $\beta = 0$ approximation can be safely adopted. + For the effect of plasma οι the resonant damping of kink waves. Soleretal.(2009) (μουalsoCtoosseusetal.2009). showed that the contribution of the slow coutimain camping. preseut when z0. is nesliejible compared to the Alfvéóuu ΟΕ dampine.," For the effect of plasma $\beta$ on the resonant damping of kink waves, \citet{solerslow} \citep[see also][]{goossens2009} showed that the contribution of the slow continuum damping, present when $\beta \ne 0$, is negligible compared to the Alfvénn continuum damping." + This paper is organized as follows., This paper is organized as follows. + The description of he mocel configuration and basic equations are eiven iu Section 2.., The description of the model configuration and basic equations are given in Section \ref{sec:model}. + Then. we obtain general expressions for the auplitude and wavelength of propagating kink waves m ongitudinally aud transversely inhomoecncous magnetic Hux tubes in Section 3...," Then, we obtain general expressions for the amplitude and wavelength of propagating kink waves in longitudinally and transversely inhomogeneous magnetic flux tubes in Section \ref{sec:general}." + Later. we use these general expressions fo study resonantly damped propagating sinks waves in stratified solar waveguides and compare he analytical predictions with full nuuencal time- sinulatiousiu Section [.," Later, we use these general expressions to study resonantly damped propagating kink waves in stratified solar waveguides and compare the analytical predictions with full numerical time-dependent simulationsin Section \ref{sec:appli}." + The implications or the method of solar atinosphlierie maeuctoscisuioloey are given in Section 5.., The implications for the method of solar atmospheric magnetoseismology are given in Section \ref{sec:seis}. . + Finally. Section 6 contains the discussion of the results aud our conclusions.," Finally, Section \ref{sec:discussion} contains the discussion of the results and our conclusions." +The author wishes to thank Drs.,The author wishes to thank Drs. + Ix. Aoki. Ix. Okoshi. S. Satoh. S. Ixameno. T. Yamamoto and T. Totani. and Mr. Y. Tutui at National Astronomical Observatory of Japan for helpful comments and criticisms.," K. Aoki, K. Okoshi, S. Satoh, S. Kameno, T. Yamamoto and T. Totani, and Mr. Y. Tutui at National Astronomical Observatory of Japan for helpful comments and criticisms." + Phe author also thanks to the anonymous referee for comprehensive comments for improvement., The author also thanks to the anonymous referee for comprehensive comments for improvement. + Phe author also thanks to Mr. S. Abe and Dr. A. Ixawamura for the technical support., The author also thanks to Mr. S. Abe and Dr. A. Kawamura for the technical support. +(scePettersetal.2001.Pheorem9.1)..,\citep[see][Theorem 9.1]{Petters_book}. +" To find the image positions. we expand 0, and 62 in à power series in c."," To find the image positions, we expand $\theta_1$ and $\theta_2$ in a power series in $\epsilon$." + Since the left-hancl sides of equations (12)) and (13)) are accurate to Oc). the right-hand sides must be accurate to the same order.," Since the left-hand sides of equations \ref{eq:lens1-u1}) ) and \ref{eq:lens1-u2}) ) are accurate to $\mathcal{O}(\epsilon)$, the right-hand sides must be accurate to the same order." + Noting that the lowest-order terms on the right-hand side are linear or quadratic in 9. we write Substituting into the lens equation. we obtain Note that these equations are carried to different orders in e. since the leacling-order term in equation (12)) is linear in 0. while the leacing-orcer term in equation (13)) is quadratic in 8.," Noting that the lowest-order terms on the right-hand side are linear or quadratic in $\bt$, we write Substituting into the lens equation, we obtain Note that these equations are carried to different orders in $\epsilon$, since the leading-order term in equation \ref{eq:lens1-u1}) ) is linear in $\bt$ , while the leading-order term in equation \ref{eq:lens1-u2}) ) is quadratic in $\bt$." + Since e is non-zero. equations (16)) and (17)) must be satisfied at each order in c.," Since $\epsilon$ is non-zero, equations \ref{eq:lens2-u1}) ) and \ref{eq:lens2-u2}) ) must be satisfied at each order in $\epsilon$." + We can work term by term to solve for the coellicients à4. 6» and d». and then write the image positions as where the x labels indicate the parities of the images.," We can work term by term to solve for the coefficients $\alpha_1$, $\alpha_2$ and $\beta_2$, and then write the image positions as where the $\pm$ labels indicate the parities of the images." + From these equations. we see that two images form near the point 0— on the critical curve. provided that πο)>0.," From these equations, we see that two images form near the point $\bt=\bmo$ on the critical curve, provided that $(-u_2/3h) > 0$." + Since hx0 for standard lens potentials (e.g... an isothermal ellipsoid or isothermal sphere with shear). we must have πο2Q0.," Since $h \le 0$ for standard lens potentials (e.g., an isothermal ellipsoid or isothermal sphere with shear), we must have $u_2 > 0$." + In other words. the source must lie inside the caustic in order to produce a pair of Fold images.," In other words, the source must lie inside the caustic in order to produce a pair of fold images." + In practice. a more useful quantity is the image separation. given by To find the time delay between the two fold images. we begin with the general expression for the scaled time delay 1992): The scale factor is given by where D.Da and Dis are the angular-diameter distances from the observer to lens. observer to source. and lens to source. respectively.," In practice, a more useful quantity is the image separation, given by To find the time delay between the two fold images, we begin with the general expression for the scaled time delay \citep[e.g.,][]{Schneider_lensing}: The scale factor is given by where $D_L, D_S$ and $D_{LS}$ are the angular-diameter distances from the observer to lens, observer to source, and lens to source, respectively." + The lens redshift is denoted by σεν, The lens redshift is denoted by $z_L$. + Making the substitution τὰ(cuj.Πο). we have for the two fold images which," Making the substitution $\bu \rightarrow (\epsilon u_1, \epsilon u_2)$, we have for the two fold images The time delay between images is then (cf. \citealt{Schneider_lensing}," + is positive. in agreement with the general result that images with negative parity trail those with positive parity.," pp 190 - 191) which is positive, in agreement with the general result that images with negative parity trail those with positive parity." + We find that the only coellicient from the lens potential that enters the expression for the differential time delay is the parameter f=coss(0)/6.," We find that the only coefficient from the lens potential that enters the expression for the differential time delay is the parameter $h +=\psi_{222}(\bmo)/6$." + We also see that to leading order in e. the image separation and the dilferential time delay depend only on the πο component of the source position.," We also see that to leading order in $\epsilon$, the image separation and the differential time delay depend only on the $u_2$ component of the source position." + Unlike the image positions. our expression for the time delay does not involve any of the fourth-order terms in the potential.," Unlike the image positions, our expression for the time delay does not involve any of the fourth-order terms in the potential." +This is because the time delay involves the potential directly. while the image positions depend. on first derivatives ofthe potential.,"This is because the time delay involves the potential directly, while the image positions depend on first derivatives ofthe potential." +" Phis means that all fourth-order terms in the potential enter the time delay. at Q> (0). while. these same terms enter at Q(c)""y7 Bip.in quantitiesMA involving. derivatives.."," This means that all fourth-order terms in the potential enter the time delay at $\order{\epsilon}{2}$ , while these same terms enter at $\order{\epsilon}{3/2}$ in quantities involving derivatives." +mass star formation is unlikelv to occur.,mass star formation is unlikely to occur. + By doing so. we are able to investigate claims of a high-mass biased IME at high redshilts.," By doing so, we are able to investigate claims of a high-mass biased IMF at high redshifts." + In § 2 we list the relevant physical processes and give estimates of (he timescales., In $\S$ \ref{sec:timescales} we list the relevant physical processes and give estimates of the timescales. + The cooling functions ancl ionization fractions are determined from a complex model of interstellar chemistry. described in § 3.., The cooling functions and ionization fractions are determined from a complex model of interstellar chemistry described in $\S$ \ref{sec:model}. + Our results are described in 8$ 4.. and some general conclusions regarding low mass star formation at high redshifts are mace in § 6..," Our results are described in $\S$ \ref{sec:results}, and some general conclusions regarding low mass star formation at high redshifts are made in $\S$ \ref{sec:conclusions}." + Star formation is a complex process., Star formation is a complex process. + While gravity is the main driver. there are many other mechanisms (hat compete to aid and oppose Che collapse of molecular clouds.," While gravity is the main driver, there are many other mechanisms that compete to aid and oppose the collapse of molecular clouds." + Cooling bv molecular radiation leads to thermally induced collapse of a molecular cloud ancl if the limescale associated. with this process is longer than the free-fall time. the collapse will be halted.," Cooling by molecular radiation leads to thermally induced collapse of a molecular cloud and if the timescale associated with this process is longer than the free-fall time, the collapse will be halted." + The rate of cooling in turn is determined by the abunclances of the various different molecular coolants such as CO and so we can see (he role (hat chemistry plavs., The rate of cooling in turn is determined by the abundances of the various different molecular coolants such as CO and so we can see the role that chemistry plays. + The chemistry itself is driven by cosmic ray. ionisation of molecular hydrogen., The chemistry itself is driven by cosmic ray ionisation of molecular hydrogen. + In some circumstances. the surfaces of dust grains can become coated with ice due to the of different species onto the grains.," In some circumstances, the surfaces of dust grains can become coated with ice due to the of different species onto the grains." + This process is effective in removing coolant molecules from the gas phase., This process is effective in removing coolant molecules from the gas phase. + Energy released [rom £/5 formation can liberate the species into their gaseous phase., Energy released from $H_2$ formation can liberate the species into their gaseous phase. + Interstellar magnetic fields (oo can affect the collapse of molecular clouds., Interstellar magnetic fields too can affect the collapse of molecular clouds. + The ions are coupled to field lines and neutral atoms to the ions via collisions., The ions are coupled to field lines and neutral atoms to the ions via collisions. + The fractional ionisation therefore determines the magnetic pressure and the level of jion-neutral friction which in (urn can halt collapse., The fractional ionisation therefore determines the magnetic pressure and the level of ion-neutral friction which in turn can halt collapse. + In the local universe. the timescales associated with these various competing processes are found to be roughly of the same order of magnitude - ~10? vis (7). [or a core density of ~l0tem .," In the local universe, the timescales associated with these various competing processes are found to be roughly of the same order of magnitude - $\sim 10^{5}$ yrs \citep{Williams:astrochem_intro} for a core density of $\sim10^4$ $^{-3}$." + This balance of timescales is clearly conducive to star formation., This balance of timescales is clearly conducive to star formation. + Dv exploring the change in (hese (imescales for a range of initial conditions. we can effectively explore different regions of redshilt space aud hope to learn something about when and how the first low mass stars started to form.," By exploring the change in these timescales for a range of initial conditions, we can effectively explore different regions of redshift space and hope to learn something about when and how the first low mass stars started to form." + Low mass star formation essentially occurs by the collapse of a molecular cloud under iis own weight accompanied by (he dissipation of gravitational potential energv., Low mass star formation essentially occurs by the collapse of a molecular cloud under its own weight accompanied by the dissipation of gravitational potential energy. + In any situation where the star formation is not externally triggered bv a violent event. for example," In any situation where the star formation is not externally triggered by a violent event, for example" +Iu this paper. we consider the solutions of the following first-order ordinary differential equation: where e 2-0. 4; stauds for du!jg; or equivalently Orat. and αμ is à real umber.,"In this paper, we consider the solutions of the following first-order ordinary differential equation: where $\eps>0$ , $u^{\eps}_{t}$ stands for $\frac{du^{\eps}}{dt}$ or equivalently $\partial_{t}u^{\eps}$, and $u_{0}$ is a real number." + We are interested in the rate of convergence of the solution « to its limit in the framework of periodic homogenization., We are interested in the rate of convergence of the solution $u^{\eps}$ to its limit in the framework of periodic homogenization. + We employ the following assumptions on the function f: Let us male short comments on these assuiiptious., We employ the following assumptions on the function $f$: Let us make short comments on these assumptions. + Remark that assumption (AL) eusures the existence aud uniqueness of the solution « of (1.1)) via the Cauchy-Lipschitz theorem., Remark that assumption (A1) ensures the existence and uniqueness of the solution $u^{\eps}$ of \ref{main_eq}) ) via the Cauchy-Lipschitz theorem. + Moreover. the assumed boundeduess of f is nof a restrictive condition while we work on any finite time interval [0.7].," Moreover, the assumed boundedness of $f$ is not a restrictive condition while we work on any finite time interval $[0,T]$." + The monotonicity asstuunption (À3) ay seeni uimnecessaryv at a first glance. but will be indeed useful to euuautee the uniqueness of the solution to the homogenized equation (see Proposition 1.1)).," The monotonicity assumption (A3) may seem unnecessary at a first glance, but will be indeed useful to guarantee the uniqueness of the solution to the homogenized equation (see Proposition \ref{ganaza}) )." + Moreover. assumption (A3) will plav a crucial role to establish the rate of converecuce of ut to its limit a (soo for instance Section ??)).Tn order to define the homogenized equation. we will use the following proposition:," Moreover, assumption (A3) will play a crucial role to establish the rate of convergence of $u^{\eps}$ to its limit $u^{0}$ (see for instance Section \ref{sec4}) ).In order to define the homogenized equation, we will use the following proposition:" +and rey0.1 in this paper (we adopt a cosmological moce with totaldensity parameter Qo=1 and the present Hubble constant Lo=50 km/s/Mpc]).,and $r_{BH}=0.1$ in this paper (we adopt a cosmological model with total density parameter $\Omega_0=1$ and the present Hubble constant $H_0=50$ [km/s/Mpc]). +" In their paper. the DII formation epoch z,;, is obtaine from somewhat complicated: procedure. however. in a DI mass range 10747.«—m<1017A4.. z,;, varies in a very narrow range around 2.7,200. then we neglect the mass dependence for simplicity ancl put. ce;=200 throughou this paper."," In their paper, the BH formation epoch $z_{vir}$ is obtained from somewhat complicated procedure, however, in a BH mass range $10^6 M_\odot \leq m \leq10^{10} M_\odot$, $z_{vir}$ varies in a very narrow range around $z_{vir} \sim 200$, then we neglect the mass dependence for simplicity and put $z_{vir} \equiv 200$ throughout this paper." + The resultant mass functions of 1115 are shown in figure 4.., The resultant mass functions of BHs are shown in figure \ref{fig:IMF}. + We can obtain the luminosity function Φ at the cosmic time /. where ngg(m) is the total number of BlIs having the mass smaller than m.," We can obtain the luminosity function $\Phi$ at the cosmic time $t$, where $n_{BH}(m)$ is the total number of BHs having the mass smaller than $m$." + Usually. evolution of the luminosity function is parametrized by z instead. of {.," Usually, evolution of the luminosity function is parametrized by $z$ instead of $t$ ." + We adopt here the Einstein-de Sitter universe as the cosmological model to relate / with z. where fy 107vr]v is the present time.," We adopt here the Einstein-de Sitter universe as the cosmological model to relate $t$ with $z$, where $t_0 \sim 10^{10}$ [yr] is the present time." + lere. we discuss a. number of examples. of the dependence of the magnetic filed. Bo at the source region on DII mass m., Here we discuss a number of examples of the dependence of the magnetic filed $B_0$ at the source region on BH mass $m$. + The locus of the plasma source is supposed to several times the horizon radius (me4.6m [or «= (0.1) where the pair creation seenis to be effective due to the outer gap mocel (Hirotani Okamoto 1998)., The locus of the plasma source is supposed to several times the horizon radius $\sim m \epsilon^{-2/3} \sim 4.6 m$ for $\epsilon=0.1$ ) where the pair creation seems to be effective due to the outer gap model (Hirotani Okamoto 1998). + The case Dyxm|?(¢=1/2) is so-called the I5ddington value., The case $B_0 \propto m^{-1/2}\ (\zeta=-1/2)$ is so-called the Eddington value. + This formula is derived. as follows., This formula is derived as follows. +" Dased on the spherical accretion with the Eddington accretion rate, we suppose the equipartition condition of energy density between the gravitational one and the magnetic one."," Based on the spherical accretion with the Eddington accretion rate, we suppose the equipartition condition of energy density between the gravitational one and the magnetic one." + Hlowever. in this case. the lifetime of the [Iv-wheel engine is determined. independent of m from equation (3)).," However, in this case, the lifetime of the fly-wheel engine is determined independent of $m$ from equation \ref{eq:LBH}) )." + We can easily imagine the evolution. of the luminosity function of this case., We can easily imagine the evolution of the luminosity function of this case. + The curve moves rightward holding its shape corresponding to the increase of output power. ancl arrives at the explosive stage. and then. all the DIL engines simultaneously cease their activity.," The curve moves rightward holding its shape corresponding to the increase of output power, and arrives at the explosive stage, and then, all the BH engines simultaneously cease their activity." + Vhis is trivially inconsistent with the observation (see figure 2?2)). hence we reject this case.," This is trivially inconsistent with the observation (see figure \ref{fig:LFO}) ), hence we reject this case." + The magnetic field of the inner region of the Shakura-Sunvaev's accretion. disk is evaluated. as follows., The magnetic field of the inner region of the Shakura-Sunyaev's accretion disk is evaluated as follows. + “hey assumed the equipartition between the magnetic energy and the thermal energy., They assumed the equipartition between the magnetic energy and the thermal energy. + For the radiation. pressure. supported case. C=1/2 (similar to the Eddington value).," For the radiation pressure supported case, $\zeta = -1/2$ (similar to the Eddington value)." + This case is also unsuitable as discussed. above., This case is also unsuitable as discussed above. + For the eas pressure supported case. ¢—1/20 assuming that the mass accretion rate is proportional to m (like the Eeleington limit).," For the gas pressure supported case, $\zeta = -1/20$ assuming that the mass accretion rate is proportional to $m$ (like the Eddington limit)." + In our discussion. since the dynamic range of the DII mass m is 10AL.omX107ALL. merely in the dynamic range of the fourth order of magnitude. the dependence ¢=1/20 means almost By~const. Hence we can assume that the mass dependence of the magnetic field. Bo at the source region is presumably very weak. 1/2« ὃν ," In our discussion, since the dynamic range of the BH mass $m$ is $10^6 M_\odot \leq m \leq10^{10} M_\odot$, merely in the dynamic range of the fourth order of magnitude, the dependence $\zeta = -1/20$ means almost $B_0 \sim const.$ Hence we can assume that the mass dependence of the magnetic field $B_0$ at the source region is presumably very weak, $-1/2 < \zeta$ ." +In the following discussion. we assume ¢=0 and set By= 1T] independent ob m.," In the following discussion, we assume $\zeta=0$ and set $B_0=1$ [T] independent of $m$." + Evolution of the luminosity function is shown in figure 5.. 6 for the tvpical case ¢=0.60OLS.," Evolution of the luminosity function is shown in figure \ref{fig:LF1}, \ref{fig:LF2} for the typical case $\zeta=0, n=-0.8$." +" In case ¢=0. the initial luminosity is proportional to n. hence the luminosity function at the formation stage 2ota, remarkably reflects the initial mass function (see ligure 4))."," In case $\zeta=0$, the initial luminosity is proportional to $m^2$, hence the luminosity function at the formation stage $z \sim z_{vir}$ remarkably reflects the initial mass function (see figure \ref{fig:IMF}) )." + The curve of the luminosity function consists of monotonically decreasing power-law slope ancl exponential cut-olL., The curve of the luminosity function consists of monotonically decreasing power-law slope and exponential cut-off. + For ὁ=0. the lifetime of the [lv-wheel engine is a ecreasing function of m (see equation 3)).," For $\zeta=0$, the lifetime of the fly-wheel engine is a decreasing function of $m$ (see equation \ref{eq:LBH}) )." +" When the BlIs of mass. sav. m=my approach to the explosive stage /—fines the luminosity LeyGro.) and dLgg(m:t)fedm]|u-u, uickly increase."," When the BHs of mass, say, $m=m_0$ approach to the explosive stage $t=t_{max}$ , the luminosity $L_{BH}(m_0,t)$ and $dL_{BH}(m; t)/dm|_{m=m_0}$ quickly increase." + Until this time. the BlIs having mass molgno have already died.," Until this time, the BHs having mass $m > m_0$ have already died." + Hence the brighter-end of 1e Luminosity function quickly extended in the lower-righ irection (see eq. 10]., Hence the brighter-end of the luminosity function quickly extended in the lower-right direction (see eq. \ref{eq:Phi}] ]). + Lf the initial luminosity function ws a sullicicntly steep sloop. the evolution results a [if up at the brighter-end.," If the initial luminosity function has a sufficiently steep sloop, the evolution results a lift up at the brighter-end." + On the other hand. if the initia uminosity function has a Dat sloop. at the first. the brightcr- Lifts up. however. the brighter-end. reach the junction roint between the power law partancl the exponential cu olf part of the Luminosity function. the initial curve is bend in ower direction by the evolution (seefigure 5 fora= 0.8).," On the other hand, if the initial luminosity function has a flat sloop, at the first, the brighter-end lifts up, however, the brighter-end reach the junction point between the power law partand the exponential cut off part of the luminosity function, the initial curve is bend in lower direction by the evolution (seefigure \ref{fig:LF1} for $n=-0.8$ )." + This behavior seems to be plausible to explain the observec evolution of the luminosity function shown in figure ?? , This behavior seems to be plausible to explain the observed evolution of the luminosity function shown in figure \ref{fig:LFO} + (Revuoldsetal.2008).. Jouker&Nelemans(2001). 2001)...," \citep{Jon04}. \citep{Rey08}, \citet{Jon04}, ." + Accurate distances are also required to interpret the measured proper motions of black hole X-ray binaries. by converting a measured proper motion into a physical speed. frou which we can derive the peculiar velocity of the source (6.g..Mirabeletal.2001.Aliller-Jouesetal. 2009).," Accurate distances are also required to interpret the measured proper motions of black hole X-ray binaries, by converting a measured proper motion into a physical speed, from which we can derive the peculiar velocity of the source \citep[e.g.,][]{Mir01,Mir02,Mir03,Dha07,Mil09}." +.. This cau be used to place constraints on any velocity kick the black hole might have received im its natal supernova. aud hence on the formation nechanisn of the black hole (Brandtetal.1995:Willemsetal.2005:Fragos 2009).," This can be used to place constraints on any velocity kick the black hole might have received in its natal supernova, and hence on the formation mechanism of the black hole \citep{Bra95,Wil05,Fra09}." + The only direct. inodebliudepeudeut method of ueasurnue distances is via trigonometric parallax. which as hitherto been impossible for black hole X-ray binary systenas. since they Le at distances of several Ipc. aud rence require sub-illiarcsecond astrometry to measure heir parallaxes.," The only direct, model-independent method of measuring distances is via trigonometric parallax, which has hitherto been impossible for black hole X-ray binary systems, since they lie at distances of several kpc, and hence require sub-milliarcsecond astrometry to measure their parallaxes." + Very Lone Baseline Tuterferometiy (VLBI) at radio wavelengths is currently the only echuique available for such high-precision astrometric neasurements., Very Long Baseline Interferometry (VLBI) at radio wavelengths is currently the only technique available for such high-precision astrometric measurements. + However. black hole X-ray binaries sped he majority of their time in a faint quiescent state. where they are often not detected in the radio baud at current sensitivities.," However, black hole X-ray binaries spend the majority of their time in a faint quiescent state, where they are often not detected in the radio band at current sensitivities." + They become bright euough o be detected during outbursts. but such outbursts are typically not sufficicutly loug or frequent and do rotseunplethe Earth's orbit well enough to make a," They become bright enough to be detected during outbursts, but such outbursts are typically not sufficiently long or frequent and do notsamplethe Earth's orbit well enough to make a" +The open cluster 22 lies in a blowout region of the giant complex 449.,The open cluster 2 lies in a blowout region of the giant complex 49. + Interest mn the stellar population of 22 was triggered by two independent observational studies., Interest in the stellar population of 2 was triggered by two independent observational studies. + On. the one hand. 449 Was observed with the Infrared Array Camera aboard in the framework of the GLIMPSE legacy survey (Churchwell et citeChurchwell04)).," On the one hand, 49 was observed with the Infrared Array Camera aboard in the framework of the GLIMPSE legacy survey (Churchwell et \\cite{Churchwell04}) )." + These observations revealed strong evidence of ongoing star formation activity and underlined the need for a detailed study of the properties of the early-type stars in the cluster core and their impact on the surrounding nebula., These observations revealed strong evidence of ongoing star formation activity and underlined the need for a detailed study of the properties of the early-type stars in the cluster core and their impact on the surrounding nebula. + On the other hand. 220a - one of the two stars in 449 - was found to be a very massive eclipsing binary consisting of two WNoOha stars with individual masses of about 80M. (Rauw et citeRauw04.Rauw05:: Bonanos et citebonanos)).," On the other hand, 20a - one of the two Wolf-Rayet stars in 49 - was found to be a very massive eclipsing binary consisting of two WN6ha stars with individual masses of about $80\,M_{\odot}$ (Rauw et \\cite{Rauw04,Rauw05}; Bonanos et \\cite{bonanos}) )." + Since previous spectroscopic studies revealed only one O6: and sixO7: stars. in the cluster core (Moffat. Shara Potter 1991)). the existence of a pair of stars that massive was somewhat unexpected.," Since previous spectroscopic studies revealed only one O6: and sixO7: stars, in the cluster core (Moffat, Shara Potter \cite{MSP}) ), the existence of a pair of stars that massive was somewhat unexpected." + The nature of 22 thus remains to be established: is it à super-cluster maybe harbouring dozens of very massive early O-type stars. or is it “just” a medium-size agglomerate that produced the very massive WN6oha + WNoOha binary system WR220a more or less by chance?," The nature of 2 thus remains to be established: is it a super-cluster maybe harbouring dozens of very massive early O-type stars, or is it ""just"" a medium-size agglomerate that produced the very massive WN6ha + WN6ha binary system 20a more or less by chance?" + This question called for a re-investigation of the population of early-type stars in this cluster., This question called for a re-investigation of the population of early-type stars in this cluster. + A first step in this direction was performed by Rauw et ((2007.. hereafter Paper D. who presented a photometric monitoring of the cluster as well as a spectroscopic snapshot study of its brightest members.," A first step in this direction was performed by Rauw et \cite{GR}, hereafter Paper I), who presented a photometric monitoring of the cluster as well as a spectroscopic snapshot study of its brightest members." + This study allowed us to discover three previously unknown eclipsing binaries among the likely cluster members and to derive spectral types between O3 and O6.5 ssignificantly earlier than previously thought) for the twelve brightest O-stars in the cluster., This study allowed us to discover three previously unknown eclipsing binaries among the likely cluster members and to derive spectral types between O3 and O6.5 significantly earlier than previously thought) for the twelve brightest O-stars in the cluster. + Moreover. we inferred a spectrophotometrie distance of 8.0+1.4 kkpe.," Moreover, we inferred a spectrophotometric distance of $8.0 \pm 1.4$ kpc." + While this distance measurement is in excellent agreement with that of 220a (Rauw et citeRauw05)). it is nevertheless problematic 1n. several ways.," While this distance measurement is in excellent agreement with that of 20a (Rauw et \\cite{Rauw05}) ), it is nevertheless problematic in several ways." + Indeed. despite the much earlier spectral types inferred for the most massive cluster members. the current census of early-type stars Ἡ 22 accounts for only of the ionizing photons required to explain the observed radio emission of the 449 complex.," Indeed, despite the much earlier spectral types inferred for the most massive cluster members, the current census of early-type stars in 2 accounts for only of the ionizing photons required to explain the observed radio emission of the 49 complex." +" Moreover. a near-IR photometric study of the cluster by Ascenso et ((2007)) resulted in a distance estimate of kkpe. inferred from a comparison between their JHK, data with pre-main sequence evolutionary tracks."," Moreover, a near-IR photometric study of the cluster by Ascenso et \cite{Ascenso}) ) resulted in a distance estimate of kpc, inferred from a comparison between their $JHK_s$ data with pre-main sequence evolutionary tracks." + The origin of these discrepancies remains unclear., The origin of these discrepancies remains unclear. + More recently. yet another distance determination. was obtained.," More recently, yet another distance determination was obtained." + From the mean velocity and velocity spread of molecular gas in the molecular cloud associated with 449. Furukawa et ((2009)) inferred a kinematic distance of 54 kkpe.," From the mean velocity and velocity spread of molecular gas in the molecular cloud associated with 49, Furukawa et \cite{Furukawa}) ) inferred a kinematic distance of $5.4^{+1.1}_{-1.4}$ kpc." + These authors further suggested that the collision between two molecular clouds might have triggered the formation of the 22 cluster., These authors further suggested that the collision between two molecular clouds might have triggered the formation of the 2 cluster. + Determining the correct distance of this cluster Is a fundamental issue: if the distance were confirmed to be κκρο. 22 might be one of the most massive clusters of our Galaxy (along with 33603. OOB2. and 11).," Determining the correct distance of this cluster is a fundamental issue: if the distance were confirmed to be kpc, 2 might be one of the most massive clusters of our Galaxy (along with 3603, OB2, and 1)." + Otherwise. if the distance were established to be much shorter than kkpc. 220a would be left in relative isolation. thereby challenging the theories. of competitive accretion (Bonnell. Vine Bate 2004)) and the link between the mass of a cluster and the mass of its most massive member (Weidner et citeWeidner)).," Otherwise, if the distance were established to be much shorter than kpc, 20a would be left in relative isolation, thereby challenging the theories of competitive accretion (Bonnell, Vine Bate \cite{Bonnell}) ) and the link between the mass of a cluster and the mass of its most massive member (Weidner et \\cite{Weidner}) )." + The distance ts also of fundamental importance to understand the link with the TeV source HESS J1023—575 (Aharonian et citeAharonian)). which is spatially consistent with the bright Fermi-LAT pulsar PSR J1023.0—5746 (Abdo et citeAbdo.. Ackermann et citeAckermann)).," The distance is also of fundamental importance to understand the link with the TeV source HESS $-575$ (Aharonian et \\cite{Aharonian}) ), which is spatially consistent with the bright -LAT pulsar PSR $-$ 5746 (Abdo et \\cite{Abdo}, , Ackermann et \\cite{Ackermann}) )." + At much longer wavelengths. a peculiar jet as well as arc-like molecular (0Ο) emission feature were," At much longer wavelengths, a peculiar jet as well as arc-like molecular $^{12}$ CO) emission feature were" +mocel to explain the existence of two supposed. terrestrial planets in the system.,model to explain the existence of two supposed terrestrial planets in the system. + Migaszewskietal.(2009). and Wangetal.(2009). further showed that Earth-size bodies might be formed in the LIZ of the system., \citet{miga09} and \citet{wang09} further showed that Earth-size bodies might be formed in the HZ of the system. + From our simulations. we note that more than (19 out of 46) of the total runs have formed. planets in the LIZ. within 0.25 — 0.36 AU (Alieaszewskietal.2009).," From our simulations, we note that more than (19 out of 46) of the total runs have formed planets in the HZ, within 0.25 $\sim$ 0.36 AU \citep{miga09}." +. In fact. we lind that in certain configurations with a smaller mutual 7 (< 107) may have a great probability. e.g... 16 out of 22 runs formed a terrestrial planet in the HZ.," In fact, we find that in certain configurations with a smaller mutual $i$ $\leq 10^{\circ}$ ) may have a great probability, e.g., 16 out of 22 runs formed a terrestrial planet in the HZ." + Fig., Fig. + 9. shows all final configurations of 19 runs have produced. habitable planets at the end of numerical simulation. where Run 1 ~ 8 are adopted from Croup 2. Run 9 — 16 from Croup 3. and Run 17. IS and 19 from Group 1. 4 and 5. respectively.," \ref{fig9} shows all final configurations of 19 runs have produced habitable planets at the end of numerical simulation, where Run 1 $\sim$ 8 are adopted from Group 2, Run 9 $\sim$ 16 from Group 3, and Run 17, 18 and 19 from Group 1, 4 and 5, respectively." + Obviously. as illustrated in Fig. 9..," Obviously, as illustrated in Fig. \ref{fig9}," + most of the runs are from Group 2 and 3. which have an initial distribution for embryos and planetesimals ranging from 0.3 - 5.2 AU.," most of the runs are from Group 2 and 3, which have an initial distribution for embryos and planetesimals ranging from 0.3 - 5.2 AU." + The common feature in these runs is indicative of the final configuration to consist of two terrestrial planets. with one in the WZ and the other in outer region from 0.4 to 1.0 AU.," The common feature in these runs is indicative of the final configuration to consist of two terrestrial planets, with one in the HZ and the other in outer region from 0.4 to 1.0 AU." + Typically. the planet in the LIZ seems to be more massive (0.75~2.63 4). while the outer body has a smaller mass (0.27~LSLAL) ).," Typically, the planet in the HZ seems to be more massive $0.75 \sim 2.6 +M_{\oplus}$ ), while the outer body has a smaller mass $0.27 \sim +1.81 M_{\oplus}$ )." + In addition. there also exists some configurations (totally 6 runs) that three terrestrial planets formed.," In addition, there also exists some configurations (totally 6 runs) that three terrestrial planets formed." + In these cases. the other two planets do not reside in habitable zone.," In these cases, the other two planets do not reside in habitable zone." + However. no configuration of a single habitable planet has been found. in the final simulations. although. it was considered. to be a. stable. model. under the combinations of a low eccentric orbit ancl some proper orbital parameters of jovian planets. (Migaszewskictal. 2009).," However, no configuration of a single habitable planet has been found in the final simulations, although it was considered to be a stable model under the combinations of a low eccentric orbit and some proper orbital parameters of jovian planets \citep{miga09}." +. The uniform characteristics of the formation of habitable terrestrial planets in our simulations over 400 Myr. could be served as à significant evidence of the stability of the LIZ in the OCGLE-2006-DLC-109L system.," The uniform characteristics of the formation of habitable terrestrial planets in our simulations over 400 Myr, could be served as a significant evidence of the stability of the HZ in the OGLE-2006-BLG-109L system." + The OGLE-2006-BLG-1L09L system has cdirawn many researcher's attention as it is resembling to a rescaled solar system., The OGLE-2006-BLG-109L system has drawn many researcher's attention as it is resembling to a rescaled solar system. + Waneetal.(2009) showed that the stability of the region is within «:1.5 AU and α2.7 in their numerical simulations. and also pointed out the 112 is broader enough [or a stable. Earth-mass planet.," \citet{wang09} + showed that the stability of the region is within $a \leq 1.5$ AU and $a \geq 9.7$ in their numerical simulations, and also pointed out the HZ is broader enough for a stable Earth-mass planet." + From the runs. we find that terrestrial planets could emerge in the regions where Ol 7.5$ AU." + For 1.13«e1.5 AU. there may remain stable for an additional planet. as suggested. by Wangetal.(2009).. where a great. many of initial bodies are ejectecl due to strong stirring of two jovian planets. and they either scatter out of the system or clirectly run into the central star.," For $1.13 < a < 1.5$ AU, there may remain stable for an additional planet as suggested by \citet{wang09}, where a great many of initial bodies are ejected due to strong stirring of two jovian planets, and they either scatter out of the system or directly run into the central star." + As a result. simplyA a few number of objects were left as accretion stuf for further planetary. formation. consequently none of the planets has finally formed. in this region.," As a result, simply a few number of objects were left as accretion stuff for further planetary formation, consequently none of the planets has finally formed in this region." + Herein. we also confirm the stability of the LIZ in this svstem: 19 out of total 46 runs have a final planet locating in 0.25 to 0.36 AU. which is in good agreement with theirs.," Herein we also confirm the stability of the HZ in this system: 19 out of total 46 runs have a final planet locating in 0.25 to 0.36 AU, which is in good agreement with theirs." +" Malhotra&Alinton(2008) founcl that secular resonance arising from the massive planets in the system could drive an LEarth-mass planet. out of the LZ. and an additional inner planet. with mass larger than 0.347, at απθ AU. is required to maintain the habitabilitv of the OCGLIZ-2006-DLCG-109L. svstem."," \citet{malhotra08} found that secular resonance arising from the massive planets in the system could drive an Earth-mass planet out of the HZ, and an additional inner planet, with mass larger than $0.3 M_{\oplus}$ at $a\leq 0.1$ AU, is required to maintain the habitability of the OGLE-2006-BLG-109L system." + Vhercfore. they suggest a," Therefore, they suggest a" +Scherer (2000. p. 332) furthermore states that orbital plane under the effect of the interstellar eas flow will be rotated iuto a plane coplanar to the flow vector wy. independent of imuitial position of the orbital plane.,"Scherer (2000, p. 332) furthermore states that orbital plane under the effect of the interstellar gas flow will be rotated into a plane coplanar to the flow vector $\vec{v}_{H}$, independent of initial position of the orbital plane." + We showed. using merical inteeratious. that the statement of Scherer is not correct.," We showed, using numerical integrations, that the statement of Scherer is not correct." + Retrograde orbits were uot discussed by Scherer., Retrograde orbits were not discussed by Scherer. + We found an intercsting orbit behavior., We found an interesting orbit behavior. + It depends on the orbit orientation with respect to the hydrogeu eas velocity vector Ὁnu., It depends on the orbit orientation with respect to the hydrogen gas velocity vector $\vec{v}_{H}$ . + Tt oy lies in a plane ; = 0 and vg is perpendicular to the vector erp (iu this case $ = Vaud (é/9/dt; = 0). tren the iuerstellar eas flow can change prograde orbit iuto a retrograde one (even more times for oue particle) aud inclination does not approach the value / = 0.," If $\vec{v}_{H}$ lies in a plane $i$ $=$ 0 and $\vec{v}_{H}$ is perpendicular to the vector $\vec{e}_{RP}$ (in this case $S$ $=$ 0 and $\langle dS/dt \rangle$ $=$ 0), then the interstellar gas flow can change prograde orbit into a retrograde one (even more times for one particle) and inclination does not approach the value $i$ $=$ 0." + Wo nmuuericallyv solved Eq. (, We numerically solved Eq. ( +3) aud the system of differential equations represented. by Eqs. (,3) and the system of differential equations represented by Eqs. ( +22)-(26).,22)-(26). + Solutions are compared in Fie., Solutions are compared in Fig. + 1., 4. + We assumed that the direction of the imterstellar eas velocity vector is identical to the direction of the velocity of the iuterstellar dust particles euteriug the Solar System., We assumed that the direction of the interstellar gas velocity vector is identical to the direction of the velocity of the interstellar dust particles entering the Solar System. + The interstellar dust particles cuter the Solar System with a speed of about ος = 26 kms (Laudgraf et al., The interstellar dust particles enter the Solar System with a speed of about $v_{\infty}$ $=$ 26 km/s (Landgraf et al. +" 1999) aud they are arriving from direction of À,,4 = 259"" Chehoceutric eciptic longitude) aud 444 — N (helocentric ecliptic latitude) (Lauderaf 2000).", 1999) and they are arriving from direction of $\lambda_{ecl}$ $=$ $^{\circ}$ (heliocentric ecliptic longitude) and $\beta_{ecl}$ $=$ $^{\circ}$ (heliocentric ecliptic latitude) (Landgraf 2000). +" Thus. colmponcuts ofthe velocity in the ecliptic coordinates with x-axis aligned toward the equinox. AVC Ug = 26 kai/s (σον259"") cos(87). sin(2597)costs?). sin(87))."," Thus, components of the velocity in the ecliptic coordinates with x-axis aligned toward the equinox are $\vec{v}_{H}$ $=$ $-$ 26 km/s $\cos(259^{\circ}) ~\cos(8^{\circ})$ , $\sin(259^{\circ}) ~\cos(8^{\circ})$, $\sin(8^{\circ})$ )." +" As an initial conditions for a dust particle with R = 2 gnu and mass density o = 1 s/cnb we used aj, = 60 AU. ej, = 05. a, = 90° QO, = 90% J), = 20° for Eqs. ("," As an initial conditions for a dust particle with $R$ $=$ 2 $\mu$ m and mass density $\varrho$ $=$ 1 $^{3}$ we used $a_{in}$ $=$ 60 AU, $e_{in}$ $=$ 0.5, $\omega_{in}$ $=$ $^{\circ}$, $\Omega_{in}$ $=$ $^{\circ}$, $i_{in}$ $=$ $^{\circ}$ for Eqs. (" +22)-(26).,22)-(26). +" The initial true anomaly of the dust particle was f;, for Eq. (", The initial true anomaly of the dust particle was $f_{in}$ $=$ $^{\circ}$ for Eq. ( +3).,3). + Fig l., Fig 4. + shows that the obtained evolutions are m a good aerecimeut., shows that the obtained evolutions are in a good agreement. + Evolutious begin separate as the eccentricity approaches 1., Evolutions begin separate as the eccentricity approaches 1. + This is caused by the fact that approximation σ & 1l. νου Eq. (," This is caused by the fact that approximation $\sigma$ $\ll$ 1, see Eq. (" +15). does not hold or large eccentricities.,"15), does not hold for large eccentricities." + Detailed nmmuerical solution of the equation of notion (Eq., Detailed numerical solution of the equation of motion (Eq. + 3) vields that the secular seninajor axis is a decreasing function of tine also when eccentricity approaches 1., 3) yields that the secular semi-major axis is a decreasing function of time also when eccentricity approaches 1. + We can sunumnuarize. on the basis of the previous paragraph.," We can summarize, on the basis of the previous paragraph." + Ifthere is no other force. besides solar eravity and he flux of interstellar gas. then the semi-anajor axis of an interplauctary dust particle decreases aud the particle can lit the Sun.," If there is no other force, besides solar gravity and the flux of interstellar gas, then the semi-major axis of an interplanetary dust particle decreases and the particle can hit the Sun." + Towever. the particle cau hit the Sun also by another possibilitv: particles eccentricity mnereases to 1l.," However, the particle can hit the Sun also by another possibility: particle's eccentricity increases to 1." + These mathematical possibilities probably do not occur in reality. since other forces cau act ou the dust particle aud the interstellar gas is jouized below the helioceutric distance of about | AU.," These mathematical possibilities probably do not occur in reality, since other forces can act on the dust particle and the interstellar gas is ionized below the heliocentric distance of about 4 AU." + Let us return. once again. to the planar case (C = 0) in which S = 0 and the dominant term in the square braces in Eq. (," Let us return, once again, to the planar case $C$ $\equiv$ 0) in which $S$ $=$ 0 and the dominant term in the square braces in Eq. (" +23). the term (3/2) F. is negative.,"23), the term (3/2) $I$, is negative." + Ninerical integration of Eq. (, Numerical integration of Eq. ( +3) shows that if the ecceutricity decreases to 0. then the aremment of perihelion w “shifts” its value to the value w | a.,"3) shows that if the eccentricity decreases to 0, then the argument of perihelion $\omega$ ""shifts"" its value to the value $\omega$ $+$ $\pi$." + This mcans that the negative value of £ changes to positive aud the ecceutricity beeins to increase with the same slope., This means that the negative value of $I$ changes to positive and the eccentricity begins to increase with the same slope. + The approxiuiative solution represented by Eq. (, The approximative solution represented by Eq. ( +38) is in a good agreement with the detailed ummerical solution of Eqs. (,38) is in a good agreement with the detailed numerical solution of Eqs. ( +22)-(26) for the dlanar case with ο z 0.,22)-(26) for the planar case with $S$ $\neq$ 0. + This holds for the whole time interval. also for £ close to zero.," This holds for the whole time interval, also for $I$ close to zero." + Eq. (, Eq. ( +38) holds. approximately. also for the nou-plauar evolution depicted in Fig.,"38) holds, approximately, also for the non-planar evolution depicted in Fig." + l1., 4. +" Tn this case / ds close to zero. eg; cm ey aud Q = 907 at the ecceutricity τα,"," In this case $i$ is close to zero, $v_{H}$ $\approx$ $v_{HY}$ and $\Omega$ $\approx$ $^{\circ}$ at the eccentricity minimum." + Eq. (, Eq. ( +35) eives e m D eycosuw|.,38) gives $e$ $\approx$ $D$ $/$ $\vert v_{H} \cos \omega \vert$. + The evolutionary mini of eccentricity occurs for the case when uz is close ta 1807., The evolutionary minimum of eccentricity occurs for the case when $\omega$ is close to $^{\circ}$. + This is in accordance with Eq. (, This is in accordance with Eq. ( +38).,38). + We have considered oulv the effect of iuterstellar gas flow. up to now.," We have considered only the effect of interstellar gas flow, up to now." + In reality. some other non-eravitational eects play uou-ueelicible role.," In reality, some other non-gravitational effects play non-negligible role." + Thus. we want to compare the ctfect of the interstellar gas flow with the other eects influcucing dvuamics of dust eraius in the Solar Syste.," Thus, we want to compare the effect of the interstellar gas flow with the other effects influencing dynamics of dust grains in the Solar System." + pax this purpose we included the Povutiug-Robertsou effect (P-R effect) and the radial solu wind iuto the equation of motion., For this purpose we included the Poynting-Robertson effect (P-R effect) and the radial solar wind into the equation of motion. + The P-R effect i$ electromagnetic radiation pressure force acting on a spherical particle (Iklackka 2001: arXiviastro-ph/0807.2915:. arXiv:astro-ph/090[.0368)., The P-R effect is electromagnetic radiation pressure force acting on a spherical particle (Klačkka 2004; arXiv:astro-ph/0807.2915; arXiv:astro-ph/0904.0368). + Equation of motion for the P-R effect. the effect of the radial solar wind aud the effect of gas flow has the form (c.g. Ilackka et al.," Equation of motion for the P-R effect, the effect of the radial solar wind and the effect of gas flow has the form (e.g. Klačkka et al." + 200905) where decrease of partielles lass (corpuscular sputtering) and higher orders in w/e are neglected., 2009b) where decrease of particle's mass (corpuscular sputtering) and higher orders in $\vec{v} / c$ are neglected. + e is the speed of light in vacunmn., $c$ is the speed of light in vacuum. + Parameter3 is defined as the ratio of the radial comipoueut of the clectromaguectic radiation pressure force and the eravitational force between the Sun aud the particle iu rest with respect to the Sun: L. ds the solar huninositv. L. = 382 &. 10279W (Baheall 2002). Qi. is the dimensionless efficiency factor for radiation pressure inteerated over the solar spectra. aud calenlated for the radial direction (1epr=l for a pertectly absorbing sphere) aud ο is mass density of the particle.," Parameter$\beta$ is defined as the ratio of the radial component of the electromagnectic radiation pressure force and the gravitational force between the Sun and the particle in rest with respect to the Sun: $L_{\odot}$ is the solar luminosity, $L_{\odot}$ $=$ 3.842 $\times$ $^{26}$W (Bahcall 2002), $\bar{Q}'_{pr}$ is the dimensionless efficiency factor for radiation pressure integrated over the solar spectrum and calculated for the radial direction $\bar{Q}'_{pr}=1$ for a perfectly absorbing sphere) and $\varrho$ is mass density of the particle." + j is the ratio of solar wind cnerey to, $\eta$ is the ratio of solar wind energy to +Maeuetic fields are oJSCYVOX on a wide variety of cosiuical bodies. along which are pplanets. stars and galaxies.,"Magnetic fields are observed on a wide variety of cosmical bodies, among which are planets, stars and galaxies." + With the exception «Mf a few types of objects whose magnetic ficlds are hough o be frozen-in relie. fields. cosunical maenetic fields are :tributed to dvuiuuo action.," With the exception of a few types of objects whose magnetic fields are thought to be frozen-in relic fields, cosmical magnetic fields are attributed to dynamo action." + Dynamo theory coucerus the generation of niaguetic fields iueectrically conducting fhids., Dynamo theory concerns the generation of magnetic fields in electrically conducting fluids. + Iu stars and planets. dynamo action ds fie resul of an interplay between convection and rotation.," In stars and planets, dynamo action is the result of an interplay between convection and rotation." + The resent smiulatious focus on dynamo action in late-type stars. which are characterized. by an outer convective' zone on top of a stably stratified radiative mterior.," The present simulations focus on dynamo action in late-type stars, which are characterized by an outer convective zone on top of a stably stratified radiative interior." + Maiv late-type sars are laguctically active. aud some οκit magnetic evcles. as does the Sun.," Many late-type stars are magnetically active, and some exhibit magnetic cycles, as does the Sun." + A successful solar nodel was first proposed by Parker (1955) who recognize that shear aud helicity cooperate in such a wav that fhe mean magnetic feld oscillates in a nueratory lualincr: later Yoshinmura (1975) lias shown that the fek eencrally propagates along the surfaces of coustaut angular velocity., A successful solar model was first proposed by Parker (1955) who recognized that shear and helicity cooperate in such a way that the mean magnetic field oscillates in a migratory manner; later Yoshimura (1975) has shown that the field generally propagates along the surfaces of constant angular velocity. + Since then. magnetic eveles aud butterflv «liagranis have been produced bv πασάΠο] models using splierical geometry. (Steeubeck Irause 1969). with depli-depeudeut magnetic diffusivity (Roberts Stix 1972) and with the character of an iuterface wave at the |vase of the convection zone (ParSCL 1993. Charbonneau MacCireeor 1997).," Since then, magnetic cycles and butterfly diagrams have been produced by mean-field models using spherical geometry (Steenbeck Krause 1969), with depth-dependent magnetic diffusivity (Roberts Stix 1972), and with the character of an interface wave at the base of the convection zone (Parker 1993, Charbonneau MacGregor 1997)." + Asa1 alternative to the helical effect of convection (the «a offect). he systematic tilt of flux tubes that become 1ustable aud crupt to the solu strface has been cmploved as a regenerative agent for he mean pooidal field (Leighton 1969: Durnev 1995. 1997: Sclunitt et al.," As an alternative to the helical effect of convection (the $\alpha$ effect), the systematic tilt of flux tubes that become unstable and erupt to the solar surface has been employed as a regenerative agent for the mean poloidal field (Leighton 1969; Durney 1995, 1997; Schmitt et al." + 1996: Dikpati Charbouneau 1999)ο with eqal success regarding he existence of Suu-like eveles and pitterfly (lagrais.," 1996; Dikpati Charbonneau 1999), with equal success regarding the existence of Sun-like cycles and butterfly diagrams." + Iu all cases. however. tl peecleraive ferius in the mean-field equations were based either on approsimatious such as fuwt-order smoothing. or on the limited available knowledge about the |vchavior of magnetic flux tubes iu the convection zone: the review o Stix (2001) stmarizes some of the current problems.," In all cases, however, the regenerative terms in the mean-field equations were based either on approximations such as first-order smoothing, or on the limited available knowledge about the behavior of magnetic flux tubes in the convection zone; the review of Stix (2001) summarizes some of the current problems." + Iu principle. the problem cau be attacked by càrect nnmuuierical iuteeratiou of the equations of maenetolivdrodvuamics (ATID) for the stars convection zone (for a review. see e.g.àY Nordlund et al. 1991)).," In principle, the problem can be attacked by direct numerical integration of the equations of magnetohydrodynamics (MHD) for the star's convection zone (for a review, see e.g. Nordlund et al. \cite{nordlund94}) )." + But severe problems are eucouuteree, But severe problems are encountered. +" Fish a stellar convection zone is a higlilv turbulent plasiua (Re>Lot), so that the kinetic enorgv spectrin OlCOLLbpassCS d VOrv wide range of leugth scales."," Firstly, a stellar convection zone is a highly turbulent plasma $\mb{Re}>10^{12}$ ), so that the kinetic energy spectrum encompasses a very wide range of length scales." + If trese were all o be 1050ved. a prolibitive nuniber of mesh poiits woud be required.," If these were all to be resolved, a prohibitive number of mesh points would be required." + Secondly. since the maguetic Reyjolds uber is also huge (Ria> 105). a similar argninent holds for the cheth scales of the maeneic field.," Secondly, since the magnetic Reynolds number is also large $\mb{Rm}>10^8$ ), a similar argument holds for the length scales of the magnetic field." + For hese reaso threc-dinieusiounal ATID siuulations ofteu have been restricted to a rectangular box that represeuts οiv a sla] section of a stellar convection zone., For these reasons three-dimensional MHD simulations often have been restricted to a rectangular box that represents only a small section of a stellar convection zone. + Ii the Xese work we do this. too.," In the present work we do this, too." + Thinelv. the Praxdtl nuuber. the ratio of the làueiatic VISCOSI to he radiative ditmsivity. is very πα d the sol rection zone (Przo!το *). so that the flow can vary ou much Suler scales than the temperature.," Thirdly, the Prandtl number, the ratio of the kinematic viscosity to the radiative diffusivity, is very small in the solar convection zone $\mb{Pr}\approx 10^{-4}-10^{-7}$ ), so that the flow can vary on much smaller scales than the temperature." + This is) kuown to have consequences for the topologv aud teuporal behavior of couvective turbulence {6fattaneco et al. 1991: , This is known to have consequences for the topology and temporal behavior of convective turbulence (Cattaneo et al. \cite{cattaneo91}; ; +Draudeuburg et al. 1996:, Brandenburg et al. \cite{brandenburg96}; + Drulie Let al. 1996)).," Brummell et al. \cite{brummell96}) )," + butin the preseut sunulatious. we legnore suci effects; and set Pr1l.," butin the present simulations, we ignore such effects, and set $\mb{Pr}=1$." +" Fourthly. the Mach. uuuber. Ma=«efe, decreases with depth in the soir convection zoue from about (0.1 iu the phoosphere to less than 0.0Ho near the base."," Fourthly, the Mach number, $\mb{Ma}=u/c_{\rm s}$, decreases with depth in the solar convection zone from about $0.1$ in the photosphere to less than $0.001$ near the base." + The correspowing hieh sound sved iu the lower conveclon zone necessitates the use of very siall time steps in order ο fulhll the CFL coudijon for colpressible lhivdrodyuanes (Atm Ave). while it is often desirabe to continue simations for at cast several convective turnover times.," The corresponding high sound speed in the lower convection zone necessitates the use of very small time steps in order to fulfill the CFL condition for compressible hydrodynamics $\Delta t<\Delta x/c_{\rm s}$ ), while it is often desirable to continue simulations for at least several convective turnover times." + One possibility to circunivenut this problem is to acοX the anclastic apxoxiniation whereby souxd waves are excluded. so that larger time steps can be used (Οσοιra Charney 1962: Lautz Fan 19993).," One possibility to circumvent this problem is to adopt the anelastic approximation whereby sound waves are excluded, so that larger time steps can be used (Ogura Charney \cite{ogura62}; Lantz Fan \cite{lantz99}) )." + Tere we mautai1 full compressibility. aud attain a nean Maci uuuiber of the order 0.1: in a subsequent paper we shall study effects ofà sinallez Mach umuber.," Here we maintain full compressibility, and attain a mean Mach number of the order $0.1$ ; in a subsequent paper we shall study effects ofa smaller Mach number." +Data from LRAS (the Infra-Red Astronomical Satellite) allows unparalleled. uniformity. skv coverage anc depth for mapping the local galaxy density field.,"Data from IRAS (the Infra-Red Astronomical Satellite) allows unparalleled uniformity, sky coverage and depth for mapping the local galaxy density field." + In. 1992. with completion of the QDOT. anc 12 Jv surveys. (Rowan-Robinson 1990a. Lawrence 1999. Strauss 1990. 1992. Fisher 1995). and with other large redshift surveys in progress. it became clear that a complete redshift survey of the LRAS Point Source Catalog (the PSC. scichman 1984. henceforth ES) had become feasible.," In 1992, with completion of the QDOT and 1.2 Jy surveys (Rowan-Robinson 1990a, Lawrence 1999, Strauss 1990, 1992, Fisher 1995), and with other large redshift surveys in progress, it became clear that a complete redshift survey of the IRAS Point Source Catalog (the PSC, Beichman 1984, henceforth ES) had become feasible." + Our specific targets for the PSCz survey were two- (a) we wanted to maximise sky coverage in order to predict the gravity field. and (b) we wanted to obtain the best. possible completeness and flux. uniformity. within well-defined area and redshift ranges. for statistical stuclies of the IAS galaxy population ancl its distribution.," Our specific targets for the PSCz survey were two-fold: (a) we wanted to maximise sky coverage in order to predict the gravity field, and (b) we wanted to obtain the best possible completeness and flux uniformity within well-defined area and redshift ranges, for statistical studies of the IRAS galaxy population and its distribution." + The availability. of cligitisecl optical information allowed: us to relax the ΗΛ selection criteria used in the OICGC (Rowan-Robinson 1990b). ancl use optical identification as an essential part of the selection process.," The availability of digitised optical information allowed us to relax the IRAS selection criteria used in the QIGC (Rowan-Robinson 1990b), and use optical identification as an essential part of the selection process." + This allowed. ercater sky coverage. being essentially limited: only by requiring that optical extinctions be small enough to allow complete identilications.," This allowed greater sky coverage, being essentially limited only by requiring that optical extinctions be small enough to allow complete identifications." + The PSC was used as starting material. because of its superior sky coverage ancl treatment of confused. and extended sources as compared. with the Faint Source Survey (CMoshir 1989).," The PSC was used as starting material, because of its superior sky coverage and treatment of confused and extended sources as compared with the Faint Source Survey (Moshir 1989)." + The depth of the survey (0.6.) derives from the depth to which the PSC is complete over most of the sky., The depth of the survey $0.6\Jy$ ) derives from the depth to which the PSC is complete over most of the sky. + The topology of the survey is analysed. and. presented » Canavezes (1998): the inferred velocity field. by Dranchini (1999): the real-space power spectrum and its distortion in redshift-space by Tadros. (1999): he vedshift-space power spectrum. by Sutherland (1999)., The topology of the survey is analysed and presented by Canavezes (1998); the inferred velocity field by Branchini (1999); the real-space power spectrum and its distortion in redshift-space by Tadros (1999); the redshift-space power spectrum by Sutherland (1999). + “Phe direction. ancl convergeance of the dipole ji been investigated by Rowan-Robinson (1999). and its implications for cosmological models by Schmoldt (1999).," The direction and convergeance of the dipole has been investigated by Rowan-Robinson (1999), and its implications for cosmological models by Schmoldt (1999)." + Sharpe (1999). presented. a. Least- reconstruction of the local velocity field. while an optical/LRAS clustering comparison was presented. by Seaborne (1999).," Sharpe (1999) presented a least-action reconstruction of the local velocity field, while an optical/IRAS clustering comparison was presented by Seaborne (1999)." + Many of these results are summarised in Saunders (1999)., Many of these results are summarised in Saunders (1999). + We aimed to include in the survey all areas of sky with (a) reliable and complete LRAS data. and (b) optical extinction small enough to allow reliable galaxy identifications ancl spectroscopic followup.," We aimed to include in the survey all areas of sky with (a) reliable and complete IRAS data, and (b) optical extinction small enough to allow reliable galaxy identifications and spectroscopic followup." + We defined a mask of those parts, We defined a mask of those parts +population content (e.g.Tayloretal.2010;Paudel2010)..,"population content \citep[e.g.][]{2010ApJ...712.1191T,2010ApJ...724L..64P}." +" Resolving the kinematics of objects with angular half-light radii on the order of 1"", however, takes optical integral field spectroscopy to its limits."," Resolving the kinematics of objects with angular half-light radii on the order of $1\arcsec$, however, takes optical integral field spectroscopy to its limits." +" On the other hand, present day adaptive-optics aided, near infra-red integral field units (IFUs; e.g. Gemini/NIFS, McGregoretal.2003,, VLT/SINFONI, Eisenhaueretal. 2003)), provide only moderate spectral resolution (R=AA/A<4000 or Oins232 kkm s), limiting the ability to accurately sample the velocity distribution of typical UCDs with velocity dispersions of ~25 kkm s."," On the other hand, present day adaptive-optics aided, near infra-red integral field units (IFUs; e.g. Gemini/NIFS, \citealt{2003SPIE.4841.1581M}, VLT/SINFONI, \citealt{2003SPIE.4841.1548E}) ), provide only moderate spectral resolution $\mathrm{R}=\Delta\lambda/\lambda\la4000$ or $\sigma_\mathrm{ins}\ga32$ km $^{-1}$ ), limiting the ability to accurately sample the velocity distribution of typical UCDs with velocity dispersions of $\sim 25$ km $^{-1}$." +" In this Letter we present, for the first time, the spatially resolved kinematics of an UCD."," In this Letter we present, for the first time, the spatially resolved kinematics of an UCD." +" detailed description of the data reduction, of the technical aspectsA involved in the analysis and of the dynamical modelling will be presented in a forthcoming paper."," A detailed description of the data reduction, of the technical aspects involved in the analysis and of the dynamical modelling will be presented in a forthcoming paper." +" The target of our study, UCD3, is one of the originally discovered objects (Hilkeretal.1999), which subsequently led to the definition of the class of UCDs."," The target of our study, UCD3, is one of the originally discovered objects \citep{1999A&AS..134...75H}, which subsequently led to the definition of the class of UCDs." +" Nevertheless, UCD3 is not an average UCD in several ways: With My——13.55 mmag, it is the brightest known UCD in the Fornax cluster, separated by ~0.8 mmag from the rest of the cluster's UCD population."," Nevertheless, UCD3 is not an average UCD in several ways: With $M_{V}=-13.55$ mag, it is the brightest known UCD in the Fornax cluster, separated by $\sim0.8$ mag from the rest of the cluster's UCD population." +" In projection, it is relatively close to the central cluster galaxies NGC 1399 and NGC 1404 (projected distances of kkpc and kkpc, respectively)."," In projection, it is relatively close to the central cluster galaxies NGC 1399 and NGC 1404 (projected distances of kpc and kpc, respectively)." +" It is unusually red, with a spectroscopic metallicity of [Fe/H]~—0.2 ddex (Chilingarianetal.2008).."," It is unusually red, with a spectroscopic metallicity of $\sim-0.2$ dex \citep{2008MNRAS.390..906C}." +" Most importantly, it has a large half-light radius of ry=87 ppc (or ~ 0""95) and is one of the few UCDs where an extended, low surface-brightness envelope has been detected (Evstigneeva 2008),, making it possible to resolve it from the ground with seeing- instruments."," Most importantly, it has a large half-light radius of $r_\mathrm{h}=87$ pc (or $\sim\,0\farcs95$ ) and is one of the few UCDs where an extended, low surface-brightness envelope has been detected \citep{2008AJ....136..461E}, making it possible to resolve it from the ground with seeing-limited instruments." + UCD3 was observed under excellent seeing with the ARGUS IFU (Kauferetal.2003) of the Flames/GIRAFFE (Pasquinietal. spectrograph mounted on UT2 at the VLT., UCD3 was observed under excellent seeing with the ARGUS IFU \citep{2003Msngr.113...15K} of the Flames/GIRAFFE \citep{2002Msngr.110....1P} spectrograph mounted on UT2 at the VLT. +" The IFU was used in the 1:1 scale, yielding a field of view of 11""5x7""3 at a spatial sampling of 0""52x0/52 per lenslet (or spaxel), with the LRO4 grism, providing a spectral resolution of Re«9600 (or ~13kkm s! in terms of Gaussian σ) over the range 5015—5831A."," The IFU was used in the 1:1 scale, yielding a field of view of $11\farcs 5\times 7\farcs 3$ at a spatial sampling of $0\farcs52\times 0\farcs52$ per lenslet (or spaxel), with the LR04 grism, providing a spectral resolution of $\!\sim\!9600$ (or $\sim\!13$ km $^{-1}$ in terms of Gaussian $\sigma$ ) over the range $5015\!-\!5831$." +. The observations were executed in service mode over the period of almost one year and consisted of eight exposures of 2775 seconds each., The observations were executed in service mode over the period of almost one year and consisted of eight exposures of $2775$ seconds each. +" The basic data reduction and the extraction of wavelength calibrated spectra was carried out using the Giraffe Baseline Data Reduction System (Blechaetal.2000),, standard IRAF tasks and custom python routines."," The basic data reduction and the extraction of wavelength calibrated spectra was carried out using the Giraffe Baseline Data Reduction System \citep{2000SPIE.4008..467B}, standard IRAF tasks and custom python routines." + The sky spectrum was estimated from IFU spectra outside an aperture of r27 spaxels around the object's centre and the dedicated sky fibres placed around the IFU., The sky spectrum was estimated from IFU spectra outside an aperture of $r\ge7$ spaxels around the object's centre and the dedicated sky fibres placed around the IFU. + The data were corrected for heliocentric velocities and the observations from all nights were resampled to a common logarithmic wavelength scale and organised into 3d data cubes., The data were corrected for heliocentric velocities and the observations from all nights were resampled to a common logarithmic wavelength scale and organised into 3d data cubes. +" For each data cube, the centre of the UCD and the effective seeing were determined by fitting a model image to the reconstructed image."," For each data cube, the centre of the UCD and the effective seeing were determined by fitting a model image to the reconstructed image." +" The model image consisted of an ACS high resolution channel (HRC) image in the F606W filter (shownintheupperleftpanelofFig.1;; HST programme2007), convolved with a Gaussian PSF and rebinned to the IFU's spatial scale."," The model image consisted of an ACS high resolution channel (HRC) image in the F606W filter \citep[shown in the upper left panel of Fig.~\ref{figmaps}; HST programme, convolved with a Gaussian PSF and rebinned to the IFU's spatial scale." +" The five observations with the best seeing (0/50< PSF FWHM < 0""67, with a mean of 0""60), were then stacked by resampling them to a common coordinate grid, at the same time removing the effect of atmospheric dispersion (Filippenko1982).."," The five observations with the best seeing $0\farcs50\le$ PSF FWHM $\le0\farcs67$ , with a mean of $0\farcs60$ ), were then stacked by resampling them to a common coordinate grid, at the same time removing the effect of atmospheric dispersion \citep{1982PASP...94..715F}." +" The resampling was done using the drizzle algorithm (Fruchter&Hook2002),, treating each spatial slice as an image and masking bad spaxels (cf."," The resampling was done using the drizzle algorithm \citep{2002PASP..114..144F}, treating each spatial slice as an image and masking bad spaxels (cf." + the weight map in Fig. 1)), the weight map in Fig. \ref{figmaps}) ). +" These comprised a hot column on the detector (see the Flames User Manual), as well as spectra that were strongly affected bythe stray light from neighbouring simultaneous"," These comprised a hot column on the detector (see the Flames User Manual), as well as spectra that were strongly affected bythe stray light from neighbouring simultaneous" +noise.,noise. +" To characterize the power spectrum of the D(0,$) maps we introduce the definition If the derived signal is Gaussian, that power represents all the dnstatistical properties of the signal."," To characterize the power spectrum of the $D(\theta,\phi)$ maps we introduce the definition If the derived $d^{\Delta}_{\l,m}$ signal is Gaussian, that power represents all the statistical properties of the signal." +" For non-Gaussian signal, D(£) power characterizes the diagonal elements of the correlation matrix."," For non-Gaussian signal, $D(\l)$ power characterizes the diagonal elements of the correlation matrix." +" From Fig.11 it can be clearly seen that for foregrounds, especially for V and W bands, the power spectra of D(0,9) are significantly smaller than the power of the CMB, for estimation of which we simply use the power of TOH FCM map, transformed by d? estimator as assuming that FCM map is fairly clean from the foreground signal."," From \ref{Psim} it can be clearly seen that for foregrounds, especially for V and W bands, the power spectra of $D(\theta,\phi)$ are significantly smaller than the power of the CMB, for estimation of which we simply use the power of TOH FCM map, transformed by $d^{\Delta}_{\l,m}$ estimator as assuming that FCM map is fairly clean from the foreground signal." +" An important point of analysis of the foregrounds is that for V and W bands d? estimator decreases significantly the amplitude of GF, practically by 1 to 2 order of magnitude below the CMB level."," An important point of analysis of the foregrounds is that for V and W bands $d^{\Delta}_{\l,m}$ estimator decreases significantly the amplitude of GF, practically by 1 to 2 order of magnitude below the CMB level." + 'The most intriguing question related to 4n-correlation of the derived map from the WMAPV and W band signals is what is reproduced by the d? estimator?," The most intriguing question related to $4n$ -correlation of the derived map from the V and W band signals is what is reproduced by the $d^{\Delta}_{\l,m}$ estimator?" +" The next question, which we would like to discuss is why the power spectrum of d? estimation of the V and W bands shown in Fig.12 are practically the same at the range of multipoles £«100, when we can neglect the contribution from instrumental noise to both channels and differences of the antenna beams."," The next question, which we would like to discuss is why the power spectrum of $d^{\Delta}_{\l,m}$ estimation of the V and W bands shown in \ref{fig22} are practically the same at the range of multipoles $\l \le 100$, when we can neglect the contribution from instrumental noise to both channels and differences of the antenna beams." +" The equivalence of the powers for these two signals, shown in Fig.12,, clearly tell us that these derived maps are related with pure CMB signal (which we assume to be frequency independent)."," The equivalence of the powers for these two signals, shown in \ref{fig22}, clearly tell us that these derived maps are related with pure CMB signal (which we assume to be frequency independent)." +1alo of the elliptical is also represented by NEW profile with he scale length the same as the elective radius of the stellar component of NGC 1404 (i.e. 2.5 kpe).,halo of the elliptical is also represented by NFW profile with the scale length the same as the effective radius of the stellar component of NGC 1404 (i.e. 2.5 kpc). + The mass ratio of he dark matter halo to the stellar component is set to be 5., The mass ratio of the dark matter halo to the stellar component is set to be 5. + The elfective radius and the total mass of the stellar components is 2.5 kpe and 4.4 107 AL.. respectively. which are consistent with observational properties of NGC 1404.," The effective radius and the total mass of the stellar components is 2.5 kpc and 4.4 $\times$ $10^{10}$ $M_{\odot}$, respectively, which are consistent with observational properties of NGC 1404." + The projected density profile of the stellar component is represented by Rl [aw and the density prolile is eut olfat {ιτ 585 , The projected density profile of the stellar component is represented by $R^{1/4}$ law and the density profile is cut off at $R$ = $5R_{\rm e}$. +We estimate both the velocities of the dark matter halo particles and those of stellar ones from the gravitational potential at the positions where they are located., We estimate both the velocities of the dark matter halo particles and those of stellar ones from the gravitational potential at the positions where they are located. + In detail. we first calculate the one-dimensional isotropic dispersion according to the (local) virial theorem: where (C(r) is the gravitational potential αἲ the position r.," In detail, we first calculate the one-dimensional isotropic dispersion according to the (local) virial theorem: where $U(r)$ is the gravitational potential at the position $r$." + Then we allocate a velocity to cach collisionless particle. (dark matter halo and. stellar particles) so that the distribution of velocities of these particles can have a Gaussian form with a cispersion equal to στ(1)., Then we allocate a velocity to each collisionless particle (dark matter halo and stellar particles) so that the distribution of velocities of these particles can have a Gaussian form with a dispersion equal to ${\sigma}^{2}(r)$. + lt shoulel be noted here that we use the above, It should be noted here that we use the above +The mass function f(Al|/)dM. gives the distribution of mass in isolated halos at a given epoch. and is related to the number density of halos by pf(AlJ)OdAl=Mn(M)gdA.,"The mass function $f(M|t)\,dM$, gives the distribution of mass in isolated halos at a given epoch, and is related to the number density of halos by $\bar{\rho} f(M|t)\,dM=Mn(M)\,dM$." + The mass function can be calculated analytically for a sharp A-space filter because the trajectories are Brownian random walks and therefore have special svnunetries 1991)..," The mass function can be calculated analytically for a sharp $k$ -space filter because the trajectories are Brownian random walks and therefore have special symmetries \cite{ps,peacock,bond}." + Defining the PS mass function can be written as Note that when the mass function is written in this wav. its [orm ds independent of epoch.," Defining the PS mass function can be written as Note that when the mass function is written in this way, its form is independent of epoch." + It is not. possible to obtain corresponding analytic formulae for top-hat or Gaussian filtering (Bondοἱaf 1991)., It is not possible to obtain corresponding analytic formulae for top-hat or Gaussian filtering \cite{bond}. . +". ὃν creating an ensemble of 10"" trajectories for cach of the filters given by Equations 1.. 2 3/ using the method described in Section 2.. the mass function has been estimated at six epochs."," By creating an ensemble of $10^6$ trajectories for each of the filters given by Equations \ref{eq:fk}, \ref{eq:fth}~ \ref{eq:fg} using the method described in Section \ref{sec:ps}, the mass function has been estimated at six epochs." + These data are presented in Fig., These data are presented in Fig. + as a function of v.," \ref{fig:mf} + as a function of $\nu$." + Recent work analvsing the mass function predicted. by numerical simulations has suggested that. although the mass function has a universal form when written as a function of wv. this form is altered. from that of Equation Ll (Sheth 2001)..," Recent work analysing the mass function predicted by numerical simulations has suggested that, although the mass function has a universal form when written as a function of $\nu$, this form is altered from that of Equation \ref{eq:psmf} + \cite{sheth,ev2,jenkins2000}. ." + Instead. Sheth Vormen (1999). found that à &ood Lit to the N-body cata was given by where ο;=αἲ2τν and a p are parameters.," Instead, Sheth Tormen \shortcite{sheth} found that a good fit to the N-body data was given by where $\nu'=a^{1/2}\nu$ and $a$ $p$ are parameters." + of is determined. by requiring that the probability density Function is correctlynormalized., $A$ is determined by requiring that the probability density function is correctlynormalized. +" Sheth ""Tormoen found best fit parameters e=0.707 and p=0.3 for their simulations ancl &roup finding algorithm.", Sheth Tormen found best fit parameters $a=0.707$ and $p=0.3$ for their simulations and group finding algorithm. + The standard PS multiplicity function has e—1. p—0 and l=1/2.," The standard PS multiplicity function has $a=1$, $p=0$ and $A=1/2$." + In Percival shorteiteev2.. à small tweak was required for theparameters in order to fitthe data giving @—0.774 p= 0.274.," In Percival \\shortcite{ev2}, a small tweak was required for theparameters in order to fitthe data giving $a=0.774$ $p=0.274$ ." + These fits to the mass function are presented in Fig. 3.., These fits to the mass function are presented in Fig. \ref{fig:mf}. . + The mass funetion calculated. from trajectories, The mass function calculated from trajectories +The upper line (labelled M. with e»=20.25. is relevant to the deep. MOND limit. or equivalently the complete dominance of dark matter.,"The upper line (labelled M), with $c_2 = 20.25$, is relevant to the deep MOND limit, or equivalently the complete dominance of dark matter." + The lower curve. with e»=1. applies to highly. Newtonian objects (η= 10) or a Jalfe model with a verv low clark matter content within Z2.," The lower curve, with $c_2 = 1$, applies to highly Newtonian objects $\eta = 10$ ) or a Jaffe model with a very low dark matter content within $\mathit{R_{eff}}$." + Objects with a fixed value of 5g correspond to homologous structures having a fixed mean surface density. X. within an ellective radius.," Objects with a fixed value of $\eta$ correspond to homologous structures having a fixed mean surface density, $\Sigma$, within an effective radius." + Constant surface densitv and the virial heorem vield otx67AIX or a Mxe? relation even for he Newtonian svstems., Constant surface density and the virial theorem yield $\sigma^4\approx G^2M\Sigma$ or a $M\propto \sigma^4$ relation even for the Newtonian systems. + Large internal acceleration (high 7) implies a large X which implies that the Newtonian line. or the FJ relation. lies to the right of the MOND line. opposite to the FP relation.," Large internal acceleration (high $\eta$ ) implies a large $\Sigma$ which implies that the Newtonian line, for the FJ relation, lies to the right of the MOND line, opposite to the FP relation." + Again. the solid. points are the same objects with luminosity multiplied by ML from the »opulation synthesis models.," Again, the solid points are the same objects with luminosity multiplied by M/L from the population synthesis models." + Although the scatter is larger han for the FP relation. most of these points lic near the he relation for Newtonian Jalfe models (low discrepancy).," Although the scatter is larger than for the FP relation, most of these points lie near the the relation for Newtonian Jaffe models (low discrepancy)." + The Faber-Jackson relation for the wider class of objects. elobular. clusters to clusters of galaxies. is shown in Fig.," The Faber-Jackson relation for the wider class of objects, globular clusters to clusters of galaxies, is shown in Fig." + 5., 5. + Most objects. ranging from Newtonian to deep MOND. in so far as they can be approximated by. the isotropic Jalfe model. should lie in the range between the wo parallel lines i£ ML is near unity.," Most objects, ranging from Newtonian to deep MOND, in so far as they can be approximated by the isotropic Jaffe model, should lie in the range between the two parallel lines if M/L is near unity." + Phe predicted scatter. due to à variation of 7 only. is a factor of four larger than or the FP relation.," The predicted scatter, due to a variation of $\eta$ only, is a factor of four larger than for the FP relation." + As in 33. for the clusters of galaxies (open squares). i is the gas mass that is plotted. agains he MOND parameter (at έναν).," As in 3, for the clusters of galaxies (open squares), it is the gas mass that is plotted against the MOND parameter ${\sigma^4}/Ga_0$ )." + As has been pointed ou elsewhere (e.g.. Sanders 2003) the cluster masses calculate with MOND still require about three times more matter han is directly observed in stars and hot eas.," As has been pointed out elsewhere (e.g., Sanders 2003) the cluster masses calculated with MOND still require about three times more matter than is directly observed in stars and hot gas." +" Including this “missing mass"" would move the cluster points up by abou 1.5 in the logarithm in this plot."," Including this “missing mass"" would move the cluster points up by about 0.5 in the logarithm in this plot." + Broaclly speaking. this wide range of objects is consistent with the EJ. relation. implied by MOND: tha is to sav. there exists a Universal. Faber-Jackson: relation applving to all near-isothermal pressure supported objects.," Broadly speaking, this wide range of objects is consistent with the FJ relation implied by MOND; that is to say, there exists a Universal Faber-Jackson relation applying to all near-isothermal pressure supported objects." + In particular. the dwarf spheroidal svstems. deep MOND objects. do not exhibit such a large and systematic oll-set from the mean relation as they do in the case of the EP relation.," In particular, the dwarf spheroidal systems, deep MOND objects, do not exhibit such a large and systematic off-set from the mean relation as they do in the case of the FP relation." + The significance of this oll-set is assessed in final two figures which are alternative representations of the EP and EJ relations over the range of luminosity where chwarf spheroidals overlap the more compact objects., The significance of this off-set is assessed in final two figures which are alternative representations of the FP and FJ relations over the range of luminosity where dwarf spheroidals overlap the more compact objects. +" 66 is a plot of the quantity log(a?R,gAGL) against logCL) for dwarf spheroidals. globular clusters and ultra-compact cwarfs from 10! to 10* L.."," 6 is a plot of the quantity $\log(\sigma^2 \mathit{R_{eff}}/ +GL)$ against $\log(L)$ for dwarf spheroidals, globular clusters and ultra-compact dwarfs from $10^4$ to $10^7$ $_\odot$." + The plotted quantity is proportional to M/L as estimated from the FP (virial theorem)., The plotted quantity is proportional to M/L as estimated from the FP (virial theorem). + Ehe points with, The points with +"sequence for a model of piecewise polytrope (PwPoly30-1345) with masses of MNS\, and MNS,=1.45Mo in Figure 7..",sequence for a model of piecewise polytrope (PwPoly30-1345) with masses of $M_{\rm ADM}^{\rm NS1}=1.25 M_{\odot}$ and $M_{\rm ADM}^{\rm NS2}=1.45 M_{\odot}$ in Figure \ref{fig7}. +" This figure compares the linear momentum of the Y-component, where we assume that the centers of mass of the neutron stars are located on the X-axis (see Figure 6 about the location of each star)."," This figure compares the linear momentum of the $Y$ -component, where we assume that the centers of mass of the neutron stars are located on the $X$ -axis (see Figure \ref{fig6} about the location of each star)." + This shows that the present results give by more than two orders smaller values than those calculated by the old code through the sequence., This shows that the present results give by more than two orders smaller values than those calculated by the old code through the sequence. + This improvement results from the change in the solution method of the center of mass for achieving a convergence., This improvement results from the change in the solution method of the center of mass for achieving a convergence. + Note that the linear momentum of the X- and Z-directions is zero within the machine precision because of the imposed symmetries., Note that the linear momentum of the $X$ - and $Z$ -directions is zero within the machine precision because of the imposed symmetries. + We also compare the relative difference of the binding energy from that obtained by the 3PN approximation in Figure 8.., We also compare the relative difference of the binding energy from that obtained by the 3PN approximation in Figure \ref{fig8}. + The definition of the relative difference is shown in Equation (59))., The definition of the relative difference is shown in Equation \ref{eq:deb}) ). +" The (black) solid curve with the filled circles denotes the results calculated by the new code, and the (red) dashed curve with the open squares is those computed by the old code."," The (black) solid curve with the filled circles denotes the results calculated by the new code, and the (red) dashed curve with the open squares is those computed by the old code." + The error bar is drawn for an estimated error size derived from the virial error., The error bar is drawn for an estimated error size derived from the virial error. + It is found from Figure 8 that the results by the new code have a factor of 2-5 smaller error bar than those by the old code except for very close separations (MoQ> 0.037)., It is found from Figure \ref{fig8} that the results by the new code have a factor of 2--5 smaller error bar than those by the old code except for very close separations $M_0 \Omega > 0.037$ ). +" Additionally, when we used the old code, we could not compute sufficiently converged figures for larger separations (MoQ« 0.017), because the code fails to correctly determine the center of mass during the computational iterations."," Additionally, when we used the old code, we could not compute sufficiently converged figures for larger separations $M_0 \Omega < +0.017$ ), because the code fails to correctly determine the center of mass during the computational iterations." +" For smaller mass ratio than the model shown in Figure 8,, MNS,/MX8%,,c 0.862, the old code also fails to achieve the convergence, because the code crushes at earlier steps of computational iteration."," For smaller mass ratio than the model shown in Figure \ref{fig8}, $M_{\rm ADM}^{\rm NS 1}/M_{\rm +ADM}^{\rm NS 2} \simeq 0.862$ , the old code also fails to achieve the convergence, because the code crushes at earlier steps of computational iteration." + We conclude that our new code gives results as accurate as those obtained by the old code., We conclude that our new code gives results as accurate as those obtained by the old code. +" In addition, it can compute models with smaller mass ratios that the old code cannot."," In addition, it can compute models with smaller mass ratios that the old code cannot." +" Quasi-equilibrium sequences for 18 EOSs are computed, choosing three total masses, Mo= 2.4Mo, 2.7Mo, and 3.0Mo, and three mass ratios for each total mass."," Quasi-equilibrium sequences for 18 EOSs are computed, choosing three total masses, $M_0=2.4 M_{\odot}$ , $2.7 M_{\odot}$, and $3.0 M_{\odot}$, and three mass ratios for each total mass." +" The computation is performed with the collocation points of N,xNeNg=33x2524 for larger separations and 33x1716 for closer ones.", The computation is performed with the collocation points of $N_r \times N_{\theta} \times N_{\phi}=33 \times 25 \times 24$ for larger separations and $33 \times 17 \times 16$ for closer ones. + The number of domains which cover the computational region around each star is six for larger separations and five for closer ones., The number of domains which cover the computational region around each star is six for larger separations and five for closer ones. +with de-evolved luminosity Ly=£/(1H+2) and a maximum cutoff vedshilt of τςTHC—5v,with de-evolved luminosity $L_{0}=L/\left(1+z\right)^{\beta}$ and a maximum cutoff redshift of $z_{max}=5$. +" The energv range of (his integrated. luminosity is £»100 MeV. The best fit found. [or this broken power law is parametrized bv 24 100$ MeV. The best fit found for this broken power law is parametrized by $\gamma_{1}\lesssim1.2$, $L_{B}=1.1\times10^{46}$ erg/s and $\beta=2.7$, with cosmological parameters $\Omega_M=1, \Omega_{\Lambda}=0,$ and $H_0 = 75$ km/s/Mpc." + Each model was separately [it in a sell-consistent. fashion to the EGRET data to produce the Iumninosity functions., Each model was separately fit in a self-consistent fashion to the EGRET data to produce the luminosity functions. + More recent cosmological data suggest a non-zero value lor Oy., More recent cosmological data suggest a non-zero value for $\Omega_{\Lambda}$. + The impact on the huninosity function. however. is small: we therefore retain the original model. along with the fit to the data. for our caleulations.," The impact on the luminosity function, however, is small; we therefore retain the original model, along with the fit to the data, for our calculations." + Of course. one of the important goals of the GLAST mission will be to constrain the luminosity [nnction.," Of course, one of the important goals of the GLAST mission will be to constrain the luminosity function." + The spectra of the blazars observed by EGRET are well characterized in the MeV range bv power laws with an average photon spectral index of —2.15+0.04 (Mukherjee et al., The spectra of the blazars observed by EGRET are well characterized in the $E > 100$ MeV range by power laws with an average photon spectral index of $-2.15\pm0.04$ (Mukherjee et al. + 1997)., 1997). + The spectra of some individual blazars have a measured index sienificantlv different. [rom the mean value. suggesting true scatter in the distribution of blazar spectra. which our simulation takes into account as described below.," The spectra of some individual blazars have a measured index significantly different from the mean value, suggesting true scatter in the distribution of blazar spectra, which our simulation takes into account as described below." + More importantly. most of the EGRET blazars have not been detected by TeV telescopes: for many of these sources. (his implies a spectral break or rollolf at some energy between (he EGRET and TeV enerev ranges.," More importantly, most of the EGRET blazars have not been detected by TeV telescopes; for many of these sources, this implies a spectral break or rolloff at some energy between the EGRET and TeV energy ranges." + Intergalactic attenuation. the very effect explored in this paper. would account for the lack of detection of high-redshift objects. but there are relatively low-recdshift blazars that are bright in the EGRET range and undetected in the TeV range.," Intergalactic attenuation, the very effect explored in this paper, would account for the lack of detection of high-redshift objects, but there are relatively low-redshift blazars that are bright in the EGRET range and undetected in the TeV range." + More tellingly. most ol the TeV blazars belong to the same subset of blazars. (he X-ray selected BL Lac objects (XDLs).," More tellingly, most of the TeV blazars belong to the same subset of blazars, the X-ray selected BL Lac objects (XBLs)." + Since only a small [raction of the EGRET blazars are NDLs. this implies that the non-XDL blazars may. have spectra wilh intrinsic rolloffs independent of anv intergalactic attenuation effects.," Since only a small fraction of the EGRET blazars are XBLs, this implies that the non-XBL blazars may have spectra with intrinsic rolloffs independent of any intergalactic attenuation effects." + Finally. blazars that have been detected in both the GeV and TeV ranges have TeV [Iuxes that are lower than simple extrapolations of the EGRET power laws would suggest.," Finally, blazars that have been detected in both the GeV and TeV ranges have TeV fluxes that are lower than simple extrapolations of the EGRET power laws would suggest." + Of course. such an extrapolation over such a wide range of energies is unreasonable.," Of course, such an extrapolation over such a wide range of energies is unreasonable." + Most of the models for blazar spectra attribute both the GeV and TeV emission to the same inverse Compton component of the emission., Most of the models for blazar spectra attribute both the GeV and TeV emission to the same inverse Compton component of the emission. + However. with little observational data in the 30-300 GeV range. no firm conclusions can be drawn about the precise shape of the spectra.," However, with little observational data in the 30-300 GeV range, no firm conclusions can be drawn about the precise shape of the spectra." + Indeed. (his is one of the motivations for the next eeneration of experiments.," Indeed, this is one of the motivations for the next generation of experiments." + Our technique. as described in Section 3.. is to form (he ratio of the observed fluxes for E 10GeV and E> 1GeV. This ratio is simple. robust. aud insensitive to rollolfs above ~50 GeV[or most EBL models," Our technique, as described in Section \ref{sec-3}, , is to form the ratio of the observed fluxes for $E\,>\,10\,$ GeV and $E\,>\,1\,$ GeV, This ratio is simple, robust, and insensitive to rolloffs above $\sim50$ GeVfor most EBL models" +The discrepancy in the analytical aud numerical values after the MITID shock was <1% for the magnetic field aud <0.5% for the deusity.,The discrepancy in the analytical and numerical values after the MHD shock was $<1\%$ for the magnetic field and $<0.5\%$ for the density. + The same test las been made for the shock. moving along z-axis with simular discrepancy.," The same test has been made for the shock, moving along $z$ -axis with similar discrepancy." +sources (JOI37+331). while (he array phase was monitored by switching between the GRD and the phase calibrators J16372-462 (at 8.46 GlIIz) aud J16582-476 (at 4.86 Gz).,"sources (J0137+331), while the array phase was monitored by switching between the GRB and the phase calibrators J1637+462 (at 8.46 GHz) and J1658+476 (at 4.86 GHz)." + There were three radio sources inside the initial IPN error box (figure 3)., There were three radio sources inside the initial IPN error box (figure 3). + OF these. two were previously known from an earlier survev of this part of the skv (Decker. White ILelfand 1995).," Of these, two were previously known from an earlier survey of this part of the sky (Becker, White Helfand 1995)." +" The third source. located at located at (epoch J2000) a 163353.50* (40.015) à +46°27'20.9"" (40.17) was near (the center of the initial IPN error box."," The third source, located at located at (epoch J2000) $\alpha$ $16^h33^m53.50^s$ $\pm{0.01^s}$ ) $\delta$ $+46^\circ27^\prime20.9^{\prime\prime}$ $\pm{0.1}^{\prime\prime}$ ) was near the center of the initial IPN error box." +" On the basis of its position. compactness (<0.3""). and a rising flux density between 4.86 (Ην and 8.46 Giz (327 4 45 jJ and 107 + 39 jJ respectively). Frail (1999) proposed. that ib was the afterglow ofGRD991208."," On the basis of its position, compactness $<0.8^{\prime\prime}$ ), and a rising flux density between 4.86 GHz and 8.46 GHz (327 $\pm$ 45 $\mu$ J and 707 $\pm$ 39 $\mu$ J respectively), Frail (1999) proposed that it was the afterglow of." +. Despite the proximity of this location to the Sun (~ TO). numerous optical observations were carried out. and this suggestion was quickly confirmed by the independent detection of a coincident optical source. nol visible on the Digital Skv Survey. (Castro-Tirado et al.," Despite the proximity of this location to the Sun $\rm \sim 70 \arcdeg$ ), numerous optical observations were carried out, and this suggestion was quickly confirmed by the independent detection of a coincident optical source, not visible on the Digital Sky Survey (Castro-Tirado et al." + 1999)., 1999). +" In the week following the alterelow discovery. i( was determined (hat the optical flux [aded as a power-law with a rather steep temporal decav index a~2.15 (where F,x17) (Jensen οἱ al."," In the week following the afterglow discovery, it was determined that the optical flux faded as a power-law with a rather steep temporal decay index $\alpha\simeq 2.15$ (where $F_\nu\propto t^\alpha$ ) (Jensen et al." + 1999: Garnavich and Noriega-Crespo 1999: Masetti et al., 1999; Garnavich and Noriega-Crespo 1999; Masetti et al. + 1999)., 1999). + Optical spectroscopy emission lines from a presumed host galaxy. if identified with [OII] and ΟΠΗ features. place al a redshift 2=0.707d:0.002 (Dodonov et al 1999). making this the (third closest GRB with a spectroscopically-measured redshift.," Optical spectroscopy emission lines from a presumed host galaxy, if identified with [OII] and [OIII] features, place at a redshift $z=0.707 \pm 0.002$ (Dodonov et al 1999), making this the third closest GRB with a spectroscopically-measured redshift." + has been no less interesting al radio wavelengths., has been no less interesting at radio wavelengths. + It has the brightest radio afterglow detected to date and consequently it has been detected and is well-studied between | GIIz and 350 Gllz (Poolev 1999: Shepherd et al., It has the brightest radio afterglow detected to date and consequently it has been detected and is well-studied between 1 GHz and 350 GHz (Pooley 1999; Shepherd et al. + 1999: Bremer et al., 1999; Bremer et al. + 1999)., 1999). +The main reason for this is. that the resultant electron distribution below μη becomes Hat and therefore does not show up in the SSC spectrum.,"The main reason for this is, that the resultant electron distribution below $\gamma_{\rm min}$ becomes flat and therefore does not show up in the SSC spectrum." + Interestingly. (his scheme also allows one to relax the very low magnetic field constraints.," Interestingly, this scheme also allows one to relax the very low magnetic field constraints." + We also examined (he relevance of a Maxwellian-like electron distribution that peaks at hieh electron Lorentz [actors ~10°., We also examined the relevance of a Maxwellian-like electron distribution that peaks at high electron Lorentz factors $\sim 10^5$. + Such a distribution represents a simple time-dependent solution that already takes radiative energy losses into account. aud (uris out to be capable of successfully reproducing the hard spectra in the TeV range (with limiting values and a=1. respectively).," Such a distribution represents a simple time-dependent solution that already takes radiative energy losses into account, and turns out to be capable of successfully reproducing the hard spectra in the TeV range (with limiting values $\alpha=1/3$ and $\alpha=1$, respectively)." + Maxwellian distributions can be the outcome of a stochastic acceleration process balanced by svnchrotron or Thomson cooling., Maxwellian distributions can be the outcome of a stochastic acceleration process balanced by synchrotron or Thomson cooling. +" Depending on the phivsieal conditions within a source. e... if particles undergo additional cooling in an area clilferent from the acceleration one (Saugé&Ilenri2006:Giebelsetal. 2007)). or if the medium is clumpy supporting a ""multi-blob scenario in which the observed radiation is (he result of superposition of regions characterized bv different. parameters. (he combination of pile-up distributions may allow a suitable interpretation of different (vpe of sources."," Depending on the physical conditions within a source, e.g., if particles undergo additional cooling in an area different from the acceleration one \citealt{sauge06,giebels07}) ), or if the medium is clumpy supporting a ""multi-blob"" scenario in which the observed radiation is the result of superposition of regions characterized by different parameters, the combination of pile-up distributions may allow a suitable interpretation of different type of sources." + For (the case presented here. they demonstrate a plivsical wav of achieving the high low-enerey cut-olls needed in leptonic svuchrotron-Compton models for the hard spectrum sources.," For the case presented here, they demonstrate a physical way of achieving the high low-energy cut-offs needed in leptonic synchrotron-Compton models for the hard spectrum sources." + Although our main purpose here is not to fit data. Fig.," Although our main purpose here is not to fit data, Fig." + 10. shows that a \laxwellian- electron distribution could also provide a satisfactory explanation for the hard TeV component in 1ES 02294-200., \ref{apply} shows that a Maxwellian-type electron distribution could also provide a satisfactory explanation for the hard TeV component in 1ES 0229+200. + Our results illustrate that even within a leptonic svnchrotron-Conmpton approach relatively hard intrinsic TeV source spectra may be encountered under a variety. of conditions., Our results illustrate that even within a leptonic synchrotron-Compton approach relatively hard intrinsic TeV source spectra may be encountered under a variety of conditions. +" While (his max be reassuring. the possibility of having such hard source spectra within “stanclarel models"" unfortunately constrain the potential of extracting limits on the EBL density based on 5-rav observations of Blazars. one of the hot topics currently discussed in (hie context of next generation VILE"," While this may be reassuring, the possibility of having such hard source spectra within ""standard models"" unfortunately constrain the potential of extracting limits on the EBL density based on $\gamma$ -ray observations of Blazars, one of the hot topics currently discussed in the context of next generation VHE" +PDAIFs. and show the results in Fig.,"PDMFs, and show the results in Fig." +" ltbb. The figure shows that smaller values of to, result in larger values of à for any given 5.", \ref{fig:const_exp}b b. The figure shows that smaller values of $\tau_{exp}$ result in larger values of $\alpha$ for any given $\gamma$. +" The trend can be explained by the fact that since a smaller value of 7,4 results in a steeper fe prolile. and that all profiles must. converge to Relrany) at the present-time. Ae profiles with smaller values of των have had. overall more star formation in the past."," The trend can be explained by the fact that since a smaller value of $\tau_{exp}$ results in a steeper $R_B$ profile, and that all profiles must converge to $R_B(\tau_{MW})$ at the present-time, $R_B$ profiles with smaller values of $\tau_{exp}$ have had overall more star formation in the past." + More overall star formation means that the present-day mass function is comprised of fractionally more lower-niass stars since the ME favors lower-mass stars., More overall star formation means that the present-day mass function is comprised of fractionally more lower-mass stars since the IMF favors lower-mass stars. + Phe constant build-up of ILmass stars results in a steeper PDME. so that for any given ~ 0 should be larger.," The constant build-up of lower-mass stars results in a steeper PDMF, so that for any given $\gamma$, $\alpha$ should be larger." + The figure shows that for exponentially decreasing star formation 7 must be = 0.6. 0.8. 0.9 and 1.0 [or Tarp= 3. 5. Y. and 9€vr respectively.," The figure shows that for exponentially decreasing star formation $\gamma$ must be $\gtrsim$ 0.6, 0.8, 0.9 and 1.0 for $\tau_{exp} = $ 3, 5, 7, and 9Gyr respectively." + The final case we consider is episodic star formation. where each episode lasts for à duration Af. where the ending and beginning of each episode is separated by a time. 7. and where the magnitude of each episode is Z?g(rui).," The final case we consider is episodic star formation, where each episode lasts for a duration $\Delta t$, where the ending and beginning of each episode is separated by a time, $T$, and where the magnitude of each episode is $R_B(\tau_{MW})$." +" For such a star formation history. the solution to equation (34)) is: where nj,=lloor(rineAOS|ΔΕΣ. and where we again solve for nmi4(0) with equation. (33))."," For such a star formation history, the solution to equation \ref{eq:xi_general}) ) is: where $n_{max}=\mathrm{floor}\{ (\tau_{MW}-\Delta t)/(T+\Delta t)\}$, and where we again solve for $n_{tot}(0)$ with equation \ref{eq:no_eqn}) )." +" We consider O cases with Af and TZ=10"". 101. and 10 yrs. and show 1e results in Fig. 15.."," We consider 9 cases with $\Delta t$ and $T = 10^6$, $10^7$ , and $10^8$ yrs, and show the results in Fig. \ref{fig:step}." +" In each panel the lowest line is M vrs and the highest line is Af= I0""vrs.", In each panel the lowest line is $\Delta t = 10^8$ yrs and the highest line is $\Delta t = 10^6$ yrs. +" Por T= I0""vrs. ~> 0.8 and 0.5 for Af=10° and 10 vrs respectively. while the Af=10° yrs case results inconstraints on that are too low to be realistic."," For $T = 10^6$ yrs, $\gamma \gtrsim $ 0.8 and 0.5 for $\Delta t = 10^6$ and $10^7$ yrs respectively, while the $\Delta t = 10^8$ yrs case results inconstraints on $\gamma$ that are too low to be realistic." + For Z=10 yrs. 52 0.5 and 0.4 for A’=10° and 10 vrs respectively. while again. the Af=10 ves ease results in unrealistic constraints.," For $T = 10^7$ yrs, $\gamma \gtrsim $ 0.5 and 0.4 for $\Delta t = 10^6$ and $10^7$ yrs respectively, while again, the $\Delta t = 10^8$ yrs case results in unrealistic constraints." +" Finally. for the T= qv. 1.5 for A’=10"". while the A?=10° and LO? ves case result in unrealistic constraints."," Finally, for the $T = 10^8$ yrs, $\gamma \gtrsim $ 0.5 for $\Delta t = 10^6$, while the $\Delta t = 10^7$ and $10^8$ yrs case result in unrealistic constraints." + We test whetberwhen the last star formation episode occurs relative to the present day allects our solution of £CAZ.zii) by. varving the start time of the star formation episodes.," We test whetherwhen the last star formation episode occurs relative to the present day affects our solution of $\xi(M, \tau_{MW})$ by varying the start time of the star formation episodes." + By varving je start time and testing all the combinations of Af and T ji we consider. we find that the lines in Fig.," By varying the start time and testing all the combinations of $\Delta t$ and $T$ that we consider, we find that the lines in Fig." + 15. vary by at most about5%... so that the main trends in the figure are unallectect.," \ref{fig:step} vary by at most about, so that the main trends in the figure are unaffected." + Spectroscopic observations have revealed that the central xuwsec of the Galaxy harbors a significant population of eint stars (Paumarectal.2006:Maness2007).," Spectroscopic observations have revealed that the central parsec of the Galaxy harbors a significant population of giant stars \citep{paumard:2006, maness:2007}." +. Duc o their [large radii (and hence large cross sections). it is »xossible that they could play an important part in the mass oss rate due to collisions in the Galactic centre.," Due to their large radii (and hence large cross sections), it is possible that they could play an important part in the mass loss rate due to collisions in the Galactic centre." + ln assessing their contribution to the mass loss rate. care must be taken when deriving the collision rates. because heir rac. recs. ave strong Functions of time. /.," In assessing their contribution to the mass loss rate, care must be taken when deriving the collision rates, because their radii, $r_{RG}$, are strong functions of time, $t$." + Dalectal.(2009) have already calculated the probability. ρω). for a red giant (RO) in the Galactic centre to undergo collisions with main sequence impactors.," \citet{dale:2009} have already calculated the probability, $P(r_{gal})$, for a red giant (RG) in the Galactic centre to undergo collisions with main sequence impactors." + They have taken into account hat ree?) by integrating the collision probability over the ime that the star resides on the RC branch., They have taken into account that $r_{RG} (t)$ by integrating the collision probability over the time that the star resides on the RG branch. + We use their results to estimate the mass loss rate due to RO - AIS star collisions., We use their results to estimate the mass loss rate due to RG - MS star collisions. + Yo find the number density of RGs in the Galactic centre. we weight the total stellar density by the fraction of time the star spends on the BG branch: This approximation should be valid given a star formation history thatis approximately constant when averaged: over time periods of order 756.," To find the number density of RGs in the Galactic centre, we weight the total stellar density by the fraction of time the star spends on the RG branch: This approximation should be valid given a star formation history thatis approximately constant when averaged over time periods of order $\tau_{RG}$ ." + Lhe number of collisions per unit time sullereck by any one rec giant. Pru). should of order the collision rate averaged over the," The number of collisions per unit time suffered by any one red giant, $\dot P(r_{gal})$ , should of order the collision rate averaged over the" +"pete By our normalization. e,,;,;7ding.","^5 By our normalization, $a_{p,ini}\approx a_{ini}$." +" Substituting these expressions iuto cq(32)) aud dividing the resulting equation. by the relationH (7,JDH»s.eca""hncPon,2POata we ect: masscouserving∙⋝ condition.m Pye=PinetalGuida Pine.ta—g=&unbita andl. Ph--—Powtalia|BL:i). can change eq(35)) iuto the followine fori:ay where &H[ees 1n Eq(38)} c"," Substituting these expressions into \ref{EConsII}) ) and dividing the resulting equation by the relation $\rho_{mc,c}^2a_{p,c}^6=\rho_{mc,ta}^2a_{p,ta}^6$ we get: ] Using energy conservation law and the approximate massconserving condition, $\rho_{mc,c}=\rho_{mc,ta}[\frac{a_{p,ta}}{a_{p,c}}]^3$, $\rho_{mc,ta}=\zeta\rho_{mb,ta}$ and $\rho_{Qb,c}=\rho_{Qb,ta}[\frac{a_{ta}}{a_c}]^{-3(1+w)}$, we can change \ref{aptaOapc_def_QCDM1}) ) into the following form: where $\xi=\frac{\nu}{\zeta}[\frac{a_{ta}}{a_c}]^{3(1+w)}$ . \ref{aptaOapc_def_QCDM2}) )" +"an be solved analytically. Essen] Using5 the fact that f.=2f4,t and background5 Friccanan+ equationB GMYPX(Pint|pos) We cau set up au integration equation where my—LQua cuu."," can be solved analytically, ] Using the fact that $t_c=2t_{ta}$ and background Friedman equation $(\frac{\dot{a}}{a})^2\propto(\rho_{mb}+\rho_{Qb})$ we can set up an integration equation where $\nu_0=\frac{1-\Omega_{m0}}{\Omega_{m0}}$ ." +" SolveQ 113).: umuerieally.: we can eet the relation eg; v.s. a,."," Solve \ref{QCDMtcandtta}) ) numerically, we can get the relation $a_{ta}$ v.s. $a_c$ ." +" Substitutiug eq(39)) and oedn solved from eqt11)) iuto eq(26)). we will finally ect the quantity A,."," Substituting \ref{aptaOapc}) ) and $\frac{a_{ta}}{a_c}$ solved from \ref{QCDMtcandtta}) ) into \ref{DeltacDefinition2}) ), we will finally get the quantity $\Delta_c$." + We uote that. if wzx—l1. then for verv siall nu. if a cluster is to virialize too later. then at the vinalization point. its radius will be larger than that of the turn around time. ic. a“oo1. see FICS.," We note that, if $w\leq -1$, then for very small $\Omega_{m0}$, if a cluster is to virialize too later, then at the virialization point, its radius will be larger than that of the turn around time, i.e. $\frac{a_{p,ta}}{a_{p,c}}<1$, see \ref{aptaOapcFig}." + Plvsically this meaus that. after the “turn arouud oomt. instead of collapsing. the cluster experience a period of expinusiou to reach virialization status.," Physically this means that, after the ""turn around"" point, instead of collapsing, the cluster experience a period of expansion to reach virialization status." + Mathematically this oulv means that the turi around »oiut is a local ui imsteadof a local maxima of he cluster radius aud has no problemin principle., Mathematically this only means that the turn around point is a local minimum instead of a local maximum of the cluster radius and has no problem in principle. + This nav be new structure which has not Όσσα discovered oeviouxlv. we call it “phantom hole aud leave the detailed discussion of this structure for future works.," This may be new structure which has not been discovered previously, we call it ""phantom hole"" and leave the detailed discussion of this structure for future works." + The formation of “phantom hole” will male the kineticenerev of the mattersvstem in dt less than 0. please see eqt53)). which may be a serious problem.," The formation of ""phantom hole"" will make the kineticenergy of the matter-system in it less than $0$, please see \ref{vMrelation}) ), which may be a serious problem." +" We provide πιοΊσα results for ὃςεν0,9.0.) and Alu.O440.) in FIG.I-5.."," We provide numerical results for $\delta_c(w,\Omega_{m0},a_c)$ and $\Delta_c(w,\Omega_{m0},a_c)$ in \ref{dcFig}- \ref{cpDcFig}. ." +" About this two fieurc.what we would like poiutout is that. as a,> 0. ó.>LGSG aud A.>178 whatever c and O,,9 Is."," About this two figure,what we would like pointout is that, as $a_c\rightarrow0$ , $\delta_c\rightarrow1.686$ and $\Delta_c\rightarrow178$ whatever $w$ and $\Omega_{m0}$ is." + Phnysuueallv. thisis because. the earlier iu over-«deuse," Physically, thisis because, the earlier an over-dense" +"Because of the Moon's small 1.0 kin/s orbital velocity and standard literature values of ος~ lun/s (Shoemaker1983:Chybaefal 1991).. one expects az1/16—1/10 aud thus a crater enhancement on the leacdiug hemisphere in the range 1.1—1.7. in terms of the CIMAACA,","Because of the Moon's small 1.0 km/s orbital velocity and standard literature values of $\bar{v}_{\infty} \sim 10-16$ km/s \citep{shoe83,chyba94}, , one expects $\alpha \approx +1/16-1/10$ and thus a crater enhancement on the leading hemisphere in the range $\sim 1.4-1.7$, in terms of the GMAACA." + Recent studies of young rayed craters (MorotaaudFuriunoto2003:Morotaefal2005) are found to be consistent with these estimates.," Recent studies of young rayed craters \citep{morota03,morota05} are found to be consistent with these estimates." + We will calculate theCMAACA that current NEO impactors, We will calculate theGMAACA that current NEO impactors +he runaway is halted when bard binaries form near the ceuer aud release energy through encouuters.,the runaway is halted when hard binaries form near the center and release energy through three-body encounters. + Observatious of globular clusters. which: cau be siguificantly older than their 'elaxalion times. iive confirmed these expectatious beautiltlly.," Observations of globular clusters, which can be significantly older than their relaxation times, have confirmed these expectations beautifully." + The surface brightness profiles of lilky Way globuar clusters indicae that some 20 percent iarbor collapsed cores (Djorgovski&Chenolf&Djorgovski19809:Trager.Wine. 1993).," The surface brightness profiles of Milky Way globular clusters indicate that some 20 percent harbor collapsed cores \citep{dk86,cd89,t93}." +. Near the centers of lalw systems are X-ray binarles aid blue stragelersMD {Baily11995).. both created at lieh stellar deisity. perlaps «uring the collapse phase.," Near the centers of many systems are X-ray binaries and blue stragglers \citep{b95}, both created at high stellar density, perhaps during the collapse phase." + -lobular clusters have impressive populatious ). but are relaively rare auc distan| erouys.," Globular clusters have impressive populations ), but are relatively rare and distant groups." + 02611 Clusters are sparser Q)). but imich more comiion aud closer at Hald. wit Lover a thousanmd catalogued (Diasetal.20(yo2) the sample is thought o be complete out to 2 kpe (Brown2001).," Open clusters are sparser ), but much more common and closer at hand, with over a thousand catalogued \citep{d02}; the sample is thought to be complete out to 2 kpc \citep{b01}." +. Ironically. their evolutionary status is nuch less clear.," Ironically, their evolutionary status is much less clear." + Half of open cluste5 disintegrate \vithiu after birth (Wielen197T1)..a s)ali οΤΟΣΟing to at most a lew initial 'elaxatio1 tunes.," Half of open clusters disintegrate within after birth \citep{w74}, a span corresponding to at most a few initial relaxation times." + Not surprisingly. there is little observational signature hat relaxation has οςcurred. aside pcsibly [from mass segregation. first ouud[ot by ναιdeuBergh&Sher(1960).," Not surprisingly, there is little observational signature that relaxation has occurred, aside possibly from mass segregation, first found by \citet{vs60}." +. A stall raction of oper clusters. located at the outskirts o(d ie Galaxy. have survived for over 1 Gyr (Friel1995).," A small fraction of open clusters, located at the outskirts of the Galaxy, have survived for over 1 Gyr \citep{f95}." +. Even thlese aucient systems show no sign of core collapse., Even these ancient systems show no sign of core collapse. + À prototypical example. MOT. as a sluooth sulace deusity profile that. unlike pos-collapse systems. is well fi by a ας model (Bica&Bonatio20025): the system appears to be in the last stages of tida disruption (Daveport&Sandqist.2010).," A prototypical example, M67, has a smooth surface density profile that, unlike post-collapse systems, is well fit by a King model \citep{bb05}; the system appears to be in the last stages of tidal disruption \citep{ds10}." +. Huleyetal.(2005) perormed N-body simulations to follow the evolution o. NOT fro infancy to its iuferred. age of | Gyr., \citet{h05} performed $N$ -body simulations to follow the evolution of M67 from infancy to its inferred age of 4 Gyr. + Their preferred model began with |12.000 siugle stars ai an equal number of binaries: ouy about 10 percent of these stars survive to the eic.," Their preferred model began with 12,000 single stars and an equal number of binaries; only about 10 percent of these stars survived to the end." + Eve Over he prOlracted time ¢of the simulaion. the cluster never exhibited classica dynamica relax:iOL.," Even over the protracted time of the simulation, the cluster never exhibited classical dynamical relaxation." + Instead. the central mass cleusity rose slieuly aid then declined.," Instead, the central mass density rose slightly and then declined." + Hurleyeal.(2005) attributed his behavior o the|ανΙΟ i-—itial population., \citet{h05} attributed this behavior to the binary-rich initial population. + Hard binaries uudergo superelastic encotlilers witli other stars and effectively heat the custer (Hegeie19725).. counteracting the outward elergvy ransfer driving dyuainical relaxation.," Hard binaries undergo superelastic encounters with other stars and effectively heat the cluster \citep{he75}, counteracting the outward energy transfer driving dynamical relaxation." + Luceecl. it has loig been appreciated that the presetce of evell a few binaries cal adically alter the evolution of tle sparsest groups (Terlevich1987).," Indeed, it has long been appreciated that the presence of even a few binaries can radically alter the evolution of the sparsest groups \citep{t87}." +. These inclines prowοἱ us to ask a more genera question: Uider what coucitious does binary heatiug »event siguificant co'e collapse?, These findings prompt us to ask a more general question: Under what conditions does binary heating prevent significant core collapse? + In this paper. we »eeln to address tliis larger issue. utilizine our own suite of N-body simualious.," In this paper, we begin to address this larger issue, utilizing our own suite of $N$ -body simulations." + The basic aisSwer to«our question is that is essential., The basic answer to our question is that is essential. + These massive stals οouple wi thothe Ντο [ου pairs that. through tluree-ody interactions. [rustrate core conraction relatively early. so tlat there is little or no rise of the central density.," These massive stars couple with others to form pairs that, through three-body interactions, frustrate core contraction relatively early, so that there is little or no rise of the central density." + The system the'eafter undergoesexpansion., The system thereafter undergoes. + Here. the stellar density falls everywhere.," Here, the stellar density falls everywhere." + However. there a nitigating factor in this scenerio - stellar evolution.," However, there a mitigating factor in this scenerio - stellar evolution." + Iu more populous custers with longer relaxation times. the most massive stars cie out.," In more populous clusters with longer relaxation times, the most massive stars die out." + Binary heating is tuned. aud does uot ellectively oppose core contraction until later in the clusters evolution.," Binary heating is tamed, and does not effectively oppose core contraction until later in the cluster's evolution." + As a result. this contraction," As a result, this contraction" +There are. 1101 stars with {κοΠΠ<0.25. correspouding to the thick disk. which have peaks— at |Z|=1.26 kpe and |Fe/H|-0.51.,"There are 1101 stars with $-1.0 < \feh <-0.25$, corresponding to the thick disk, which have peaks at $|Z|=1.26$ kpc and $\feh=-0.54$." + Iu order to exclude the contribution of the thin disk and the halo. we obtain stumlation data from the Desaucoon Galaxy model (Robinetal.2003) using the selection criteria: 1) 122.3) colors, even when low luminosities (C18«M;—19) are considered.","the luminosity dependence; in fact, in the densest environments (originated from the most biased regions of the primordial field) the distribution is entirely skewed toward red $u-r>2.3$ ) colors, even when low luminosities $-18 2.5; note that such histories are broadly peaked at z&4—5 and sharply decline at z2, while the histories leading to blue local galaxies typically reach their maximum at σα”2—3, since at high-z the star formation is effectively suppressed by Supernovae feedback (see Sect."," 2), with large values of $\dot m_*$ at $z\gtrsim 2.5$ ; note that such histories are broadly peaked at $z\approx 4-5$ and sharply decline at $z\lesssim 2$, while the histories leading to blue local galaxies typically reach their maximum at $z\approx 2-3$, since at $z$ the star formation is effectively suppressed by Supernovae feedback (see Sect." + 5)., 5). + Note that bursts do not seem to constitute the physical origin of the bimodality in the color distribution at z=0., Note that bursts do not seem to constitute the physical origin of the bimodality in the color distribution at $z\approx 0$. +" Indeed, the red side of the population is mostly contributed by galaxies with smoothly evolving rn, (like that represented by the heavy dashed line in the bottom panel of fig."," Indeed, the red side of the population is mostly contributed by galaxies with smoothly evolving $\dot m_*$ (like that represented by the heavy dashed line in the bottom panel of fig." +" 5), although several histories are characterized by major bursts, like the extreme star formation history (marked by the heavy solid line in the bottom panel) which has udergone a major bursts at z72.5."," 5), although several histories are characterized by major bursts, like the extreme star formation history (marked by the heavy solid line in the bottom panel) which has udergone a major bursts at $z\approx 2.5$." +" On the other hand, bursts seem to be crucial in providing extremely red objects (EROS) already at high z>1.5, as shown again by the history marked by the heavy solid line; see also the other history characterized by a major burst at z©2 and by a drop of m, at z>1.3."," On the other hand, bursts seem to be crucial in providing extremely red objects (EROs) already at high $z\gtrsim 1.5$, as shown again by the history marked by the heavy solid line; see also the other history characterized by a major burst at $z\approx 2$ and by a drop of $\dot m_*$ at $z\gtrsim 1.3$." + We checked that switching off starbursts triggered by encounters does not affect appreciably the bimodality of our color distribution at z~ 0; this is consistent with our previous results (Menci et al., We checked that switching off starbursts triggered by encounters does not affect appreciably the bimodality of our color distribution at $z\approx 0$ ; this is consistent with our previous results (Menci et al. + 2004) which showed such events to alter mainly the properties of large-mass galaxies at z1 without affecting the local distributions., 2004) which showed such events to alter mainly the properties of large-mass galaxies at $z\gtrsim 1$ without affecting the local distributions. + The above conclusion is confirmed by the observation that galaxies residingin dense environments are characterized by red colors at z—0 evenif, The above conclusion is confirmed by the observation that galaxies residingin dense environments are characterized by red colors at $z=0$ evenif +would have a C/O ratio larger than unity and a very low neon abundance).,would have a C/O ratio larger than unity and a very low neon abundance). + During the final Dash. the new hvdrogen-deficient giant expands and starts transferring mass to the ONeMg WD primary again.," During the final flash, the new hydrogen-deficient giant expands and starts transferring mass to the ONeMg WD primary again." + This renewed accretion pushes the WD over the limit for a nova detonation., This renewed accretion pushes the WD over the limit for a nova detonation. + Depending on the aceretion rate. the nova can occur relatively quickly.," Depending on the accretion rate, the nova can occur relatively quickly." + The nova ejecta is oxygen and neon rich ancl becomes mixed with the recently. produced. final Dash. ejecta., The nova ejecta is oxygen and neon rich and becomes mixed with the recently produced final flash ejecta. + Ehe. primary WD eventually faces as a typical post-nova WD. while the secondary WD [follows the canonical post-final flash evolution. developing a WC] spectral type.," The primary WD eventually fades as a typical post-nova WD, while the secondary WD follows the canonical post-final flash evolution, developing a [WC] spectral type." + The observed. hydrogen-deficient ejecta are. in this scenario. à mix of the final Dash. and nova ejecta.," The observed hydrogen-deficient ejecta are, in this scenario, a mix of the final flash and nova ejecta." + As we can see from Table 1.. it is not impossible to conceive of a scenario that mixing of these two types of ejecta would result in the observed. abundances. as long as the ejected masses are approximately similar.," As we can see from Table \ref{tab:abundances}, it is not impossible to conceive of a scenario that mixing of these two types of ejecta would result in the observed abundances, as long as the ejected masses are approximately similar." + This is likely to be the case: the hyelrogen-cdelicicnt ejecta mass of A 58 was measured to be 5.25.10.7 (?).. while nova ejecta masses could be in the range 1-10.10? (?)..," This is likely to be the case: the hydrogen-deficient ejecta mass of A 58 was measured to be $\times 10^{-5}$ \citep{Wesson08}, while nova ejecta masses could be in the range $\times 10^{-6}$ \citep{Starrfield1998}." + If today’s WR] central star is the secondary. final ashes can explain the surface temperature change from 50001 in 1919 to 95.000 Ix. now.," If today's [WR] central star is the secondary, final flashes can explain the surface temperature change from 5000K in 1919 to 95,000 K now." + This scenario would also explain the dilference in the ejecta and the stellar abundances: the massive WD primary is responsible for the observed. abundances of the hyedrogen-delicient knot. while the secondary. is responsible for the observed central star abunelances.," This scenario would also explain the difference in the ejecta and the stellar abundances: the massive WD primary is responsible for the observed abundances of the hydrogen-deficient knot, while the secondary is responsible for the observed central star abundances." + The nova explosion would. in this scenario. follow shortly after the final Hash.," The nova explosion would, in this scenario, follow shortly after the final flash." + We therefore wonder whether the nova outburst should. have been detected. as was the case for the outhurst due to the final Wash.," We therefore wonder whether the nova outburst should have been detected, as was the case for the outburst due to the final flash." + As it turns out. monitoring of this star since 1917 has been relatively sparse and ONeMg novae. tend to be relatively dim and return to light minimum in relatively short time scales.," As it turns out, monitoring of this star since 1917 has been relatively sparse and ONeMg novae tend to be relatively dim and return to light minimum in relatively short time scales." + The lowest apparent peak V magnitude of novae observed in the LMC is ~12.5 (7).., The lowest apparent peak $V$ magnitude of novae observed in the LMC is $\sim$ 12.5 \citep{Shida04}. . + Scaling this magnitude to the distance of V605 Aql (3.5 kpe. 22). the apparent. (dereddened) V magnitude of our nova might have been —6.8.," Scaling this magnitude to the distance of V605 Aql $\sim$ 3.5 kpc, \citealt{Clayton97}) ), the apparent (dereddened) $V$ magnitude of our nova might have been $\sim$ 6.8." + LE we take into account an interstellar reddening Ay=1.7 (forafuldiscussionofthereddeningsee2). the apparent magnitude could have been as low as 8.5 mag., If we take into account an interstellar reddening $\rm{A_v} = 1.7$ \citep[for a full discussion of the reddening see][]{Clayton97} the apparent magnitude could have been as low as 8.5 mag. +" The lighteurve reportec by 2. between 1917 ancl 1924 shows that V605 Aq! reache a peak of my,10 but later remained. between 12 ane 14 magnitudes."," The lightcurve reported by \citet{Harrison96}, between 1917 and 1924 shows that V605 Aql reached a peak of $ m_{pg}\sim 10$ but later remained between 12 and 14 magnitudes." + A nova with an apparent magnitude of 9. nmüght have been easily detected. were it not for the fac hat the light curve of V605 Ael was sparsely sanipled anc a nova could have gone olf and returned to minimum lieh αἱοσα observations.," A nova with an apparent magnitude of 9, might have been easily detected, were it not for the fact that the light curve of V605 Aql was sparsely sampled and a nova could have gone off and returned to minimum light between observations." + Lf the accretion rate at the time of he final [ash was hieh enough and the WD was massive. he neon nova decline time could. be as short as 12 days and its luminosity would be a meagre ~ts6107L. 2)," If the accretion rate at the time of the final flash was high enough and the WD was massive, the neon nova decline time could be as short as 12 days and its luminosity would be a meagre $\sim 4.8-6\times10^{4}\rm L_\odot$ \citep{Prialnik95}." + lt is therefore not excluded: that a nova did. indeed ake place but remained undetected., It is therefore not excluded that a nova did indeed take place but remained undetected. + We also note that if we require a dim nova with a fast return to light mininum. other nova explosions must have occurred in the past of this system.," We also note that if we require a dim nova with a fast return to light minimum, other nova explosions must have occurred in the past of this system." + Hence. it is possible that other knots with similar abundances could be found within the PN. though they will be further away [from the central star.," Hence, it is possible that other knots with similar abundances could be found within the PN, though they will be further away from the central star." + Le would. also follow that other outbursts may vet be detected., It would also follow that other outbursts may yet be detected. + Of the two scenarios. the nova one described in 2.2. is the only one where each phase is reasonably well understood and we can therefore apply a stellar population svnthesis mocel to determine its frequeney of occurrence.," Of the two scenarios, the nova one described in \ref{ssec:nova} is the only one where each phase is reasonably well understood and we can therefore apply a stellar population synthesis model to determine its frequency of occurrence." + To determine the frequeney of such systems. we use a rapid binary-evolution algorithm (BSE:?)..," To determine the frequency of such systems, we use a rapid binary-evolution algorithm \citep*[BSE; ][]{Hurley02}." + Using this code. we can generate a binary population and determine which systems can [ead to the formation of A 5s-like svstems.," Using this code, we can generate a binary population and determine which systems can lead to the formation of A 58-like systems." + The code uses the detailed: single-star evolution formulae of 2. to calculate the stellar [uminositv. radius. core mass. core radius and spin frequency for cach of the component. stars as they evolve.," The code uses the detailed single-star evolution formulae of \citet*{Hurley00} to calculate the stellar luminosity, radius, core mass, core radius and spin frequency for each of the component stars as they evolve." + X prescription for common envelope evolution is also included., A prescription for common envelope evolution is also included. + The ace parameter. the efficiency. of the orbital energy transfer to the envelope during the common envelope evolution. is set to be equal to unity.," The $\alpha_{\rm CE}$ parameter, the efficiency of the orbital energy transfer to the envelope during the common envelope evolution, is set to be equal to unity." + This parameter is very uncertain., This parameter is very uncertain. + Details of the binary-cvolution algorithm are described by ?.. Hle, Details of the binary-evolution algorithm are described by \citet{Hurley02}. +re. we want to highlight the treatment of wind accretion.," Here, we want to highlight the treatment of wind accretion." + This is a Κον process for the scenario described in 2.2 because for a moderately wide binary that avoids common envelope phase ancl Roche lobe overllow. mass is transferred. through wind aceretion instead.," This is a key process for the scenario described in \ref{ssec:nova} because for a moderately wide binary that avoids common envelope phase and Roche lobe overflow, mass is transferred through wind accretion instead." + When a star loses mass in a stellar wind. its companion can accrete some of the material as it orbits through it.," When a star loses mass in a stellar wind, its companion can accrete some of the material as it orbits through it." + Moreover. the mass loss may be tidally enhanced. by the presence of the companion if the secondary. is moderately. close.," Moreover, the mass loss may be tidally enhanced by the presence of the companion if the secondary is moderately close." + A descriptive formula given by ? ds used in the code to calculate the enhanced: mass-loss rate., A descriptive formula given by \citet{Tout88} is used in the code to calculate the enhanced mass-loss rate. + “Pvpically. the mass accretion rate onto the secondary will be significantly tically enhanced when the radius of the primary reaches of the Roche Lobe radius.," Typically, the mass accretion rate onto the secondary will be significantly tidally enhanced when the radius of the primary reaches of the Roche Lobe radius." +" The accretion rate is tvpicallv of the order of LO""1ο""M. in the svstems that we are investigating."," The accretion rate is typically of the order of $10^{-6}-10^{-9}\,\rm M_\odot$ $^{-1}$ in the systems that we are investigating." + In our scenario. the primary is already an ONeMg WD and mass is deposited onto it by wind accretion from an AGB secondary.," In our scenario, the primary is already an ONeMg WD and mass is deposited onto it by wind accretion from an AGB secondary." + However. the accretion. stops when the secondary evolves into a WD and its mass loss decreases.," However, the accretion stops when the secondary evolves into a WD and its mass loss decreases." + When the final Hash causes the secondary to expand again as it evolves back to the post-AGB track. wind accretion restarts.," When the final flash causes the secondary to expand again as it evolves back to the post-AGB track, wind accretion restarts." + Renewed mass transfer can take place for only a brief time since the star will soon shrink again. so the amount of mass accreted during this post-final Lash phase cannot be laree.," Renewed mass transfer can take place for only a brief time since the star will soon shrink again, so the amount of mass accreted during this post-final flash phase cannot be large." + The code is unable to predict. exactly when a nova occurs. but it can trace the amount of mass deposited onto the WD.," The code is unable to predict exactly when a nova occurs, but it can trace the amount of mass deposited onto the WD." + A few test models are used to simulate the mass accretion after the final flash. with a subroutine forcing the secondary WD to be reborn from the WD cooling track back onto the ACD.," A few test models are used to simulate the mass accretion after the final flash, with a subroutine forcing the secondary WD to be reborn from the WD cooling track back onto the AGB." + Dased on the test models and nova evolution models by 2.. svstems with mass aceretion rates reaching 10AL. 5 at the end of AGB evolution. will result. in a nova shortly. after the final Hash.," Based on the test models and nova evolution models by \citet{Prialnik95}, systems with mass accretion rates reaching $10^{-7}\rm M_\odot$ $^{-1}$ at the end of AGB evolution will result in a nova shortly after the final flash." + The recurrent. periods of such novae are 0.771.19.6 vears., The recurrent periods of such novae are $0.771-19.6$ years. + The actual required accretion rates could. be slightly. lower because mass may be deposited on the WD primary before the final flash. but it will not significantly alter our estimated frequency.," The actual required accretion rates could be slightly lower because mass may be deposited on the WD primary before the final flash, but it will not significantly alter our estimated frequency." + Our binary system needs to beclose enough so that the accretion rate onto the primary WD is high enough to trigger a nova explosion., Our binary system needs to beclose enough so that the accretion rate onto the primary WD is high enough to trigger a nova explosion. + As an example of a svstem that may. satisfy our, As an example of a system that may satisfy our +where fis the exposure time (in seconds). w is the sht width (in aresec) and p is the projected pixel scale (aresee px !),"where $t$ is the exposure time (in seconds), $w$ is the slit width (in arcsec) and $p$ is the projected pixel scale (arcsec $^{-1}$ )." + An example of flux calibrated spectra obtained with this procedure is presented in Fig. |.., An example of flux calibrated spectra obtained with this procedure is presented in Fig. \ref{fig:skyspectrum}. + The resulting signal-to-noise ratio on the pseudo-continuum changes according to the exposure time of the original frame. but it is always larger than 100.," The resulting signal-to-noise ratio on the pseudo-continuum changes according to the exposure time of the original frame, but it is always larger than 100." + The line flux integration is carried out in a fully automated way within a given wavelength window after subtracting the estimated pseudo-continuum intensity., The line flux integration is carried out in a fully automated way within a given wavelength window after subtracting the estimated pseudo-continuum intensity. + The integration boundaries have been set according to the spectral resolution., The integration boundaries have been set according to the spectral resolution. + For single lines. like the [OIJ5577. the optimal window semi-amplitude has been set to 1.7xFWHM which corresponds to à t4o from the line center.," For single lines, like the [OI]5577, the optimal window semi-amplitude has been set to $\times$ FWHM which corresponds to a $\pm$ $\sigma$ from the line center." + The pseudo-continuum level is estimated in the adjacent emission line-free regions., The pseudo-continuum level is estimated in the adjacent emission line-free regions. + For more complex features (Na ID doublet. OH bands). the integration boundaries and the continuum region/s have been setfoc. and are reported in Table 2..," For more complex features (Na ID doublet, OH bands), the integration boundaries and the continuum region/s have been set, and are reported in Table \ref{tab:flux}." + Following Barbier (1956)). I have also introduced. four bands. indicated as BI. B2. B3 and B4. in the blue spectral domain (see Table 2)).," Following Barbier \cite{barbier}) ), I have also introduced four bands, indicated as B1, B2, B3 and B4, in the blue spectral domain (see Table \ref{tab:flux}) )." + The gap between bands B1 and B2 has been set in order to avoid the strong Ca II H&KK absorptions (Fig. 2))., The gap between bands B1 and B2 has been set in order to avoid the strong Ca II K absorptions (Fig. \ref{fig:bluband}) ). + Finally. a broad band ranging from to has been introduced. with the main aim of giving an overall flux estimate.," Finally, a broad band ranging from to has been introduced, with the main aim of giving an overall flux estimate." + As in the case of the broad-band Measurements. the line fluxes need to be corrected for ülrmass.," As in the case of the broad-band measurements, the line fluxes need to be corrected for airmass." +" Between the two cases. however. there is a difference: in fact. while the integrated flux within a broad-band filter is the result of extra-terrestrial sources (zodiacal light. unresolved stars and galaxies) and emission within the atmosphere. in the case of nightglow emission lines all the radiation is of terrestrial origin,"," Between the two cases, however, there is a difference: in fact, while the integrated flux within a broad-band filter is the result of extra-terrestrial sources (zodiacal light, unresolved stars and galaxies) and emission within the atmosphere, in the case of nightglow emission lines all the radiation is of terrestrial origin." + Practically this coincides with setting f=| in Eq., Practically this coincides with setting $f=1$ in Eq. + C.3 of Paper I. which I have used to correct the observed values.," C.3 of Paper I, which I have used to correct the observed values." + In general. the signal in the measured features is so high that the uncertainty in the line fluxes is by far dominated by the contamination by unresolved OH lines and. to a smaller extent. to the uncertainty on the pseudo-continuum level.," In general, the signal in the measured features is so high that the uncertainty in the line fluxes is by far dominated by the contamination by unresolved OH lines and, to a smaller extent, to the uncertainty on the pseudo-continuum level." + Since the data set includes observations obtained under a wide variety of conditions. in order to estimate the zenith sky brightness during dark time it is necessary to apply some filtering.," Since the data set includes observations obtained under a wide variety of conditions, in order to estimate the zenith sky brightness during dark time it is necessary to apply some filtering." + To this aim [have adopted the same eriteria described in Paper E: photometric conditions. airmass X.€ L4. galactic latitude |b] 10”. helio-echlitpic longitude [1—ο 2907. time distance from the closest twilight Ar;> 1 hour and no moon (fractional lunar illumination FLI=0 or moon elevation hy€ —187).," To this aim I have adopted the same criteria described in Paper I: photometric conditions, airmass $X\leq$ 1.4, galactic latitude $|b|>$ $^\circ$, helio-eclitpic longitude $|\lambda-\lambda_\odot|\geq$ $^\circ$, time distance from the closest twilight $\Delta t_{twi}>$ 1 hour and no moon (fractional lunar illumination FLI=0 or moon elevation $h_M\leq-$ $^\circ$ )." + The results of this selection. which reduced the number of suitable data points to 3736. are summarized in Table 3..," The results of this selection, which reduced the number of suitable data points to 3736, are summarized in Table \ref{tab:dark}." + As one can see. the average values are all within O.] mag from those reported in Paper I (see Table 4).," As one can see, the average values are all within 0.1 mag from those reported in Paper I (see Table 4)." + In all filters there is a systematic shift towards darker values. with the only exception. of the / band.," In all filters there is a systematic shift towards darker values, with the only exception of the $I$ band." + Since the values reported in Paper I were obtained during the sunspot maximum and. given the correlation between solar activity and night sky brightness shown by Walker (1988)). Pilachowski et al. (1989));," Since the values reported in Paper I were obtained during the sunspot maximum and, given the correlation between solar activity and night sky brightness shown by Walker \cite{walker88}) ), Pilachowski et al. \cite{pila}) );" + Krisciunas (1990)). Leinert et al. (1995))," Krisciunas \cite{krisc90}) ), Leinert et al. \cite{leinert95}) )" + and Mattila et al. (1996..," and Mattila et al. \cite{attila}," + Krisciunas (1997)). Krisciunas et al. (2007)).," Krisciunas \cite{krisc97}) ), Krisciunas et al. \cite{krisc07}) )," + this behavior was indeed expected., this behavior was indeed expected. + Given the time distribution of data points (see Fig. 3)).," Given the time distribution of data points (see Fig. \ref{fig:hist}) )," + the average values reported in Table 3 are biased towards the sunspot maximum phase., the average values reported in Table \ref{tab:dark} are biased towards the sunspot maximum phase. + For solar activity corrected data. see next section.," For solar activity corrected data, see next section." +1)) ancl its ellect ou data analysis strategies.,\ref{sec:AMIBA}) ) and its effect on data analysis strategies. + We used a moving mesh lyclrocdyuamics (NIMH) code (Peu1995a)., We used a moving mesh hydrodynamics (MMH) code \citep{Pen98a}. +". It features a [ull «wvilinear total-variation-cdiminishiug (TVD) hydro code with a ""urvilinrear particle mesh (PM) body code ou a moving coordinate system.", It features a full curvilinear total-variation-diminishing (TVD) hydro code with a curvilinear particle mesh (PM) N-body code on a moving coordinate system. + The full Euler equations are solved in an ex[jxlieit. [1x-conservative form usiug a secoud order TVD scheme., The full Euler equations are solved in an explicit flux-conservative form using a second order TVD scheme. + The curvilinear coordiuates used i1 the cexle are derived [rom a eracient of the Cartesian coordiuate system., The curvilinear coordinates used in the code are derived from a gradient of the Cartesian coordinate system. + Lf’ are the Cartesia inates. the curvilinear coordinates are £/=ur!4üro(£).," If $x^i$ are the Cartesian coordinates, the curvilinear coordinates are $\xi^i = x^i + \partial_\xi^i\phi({\bf +\xi})$." + The transformation is completely s by the single potential fied of€./).," The transformation is completely specified by the single potential field $\phi({\bf \xi},t)$." + The potential deformation Μπομας a very regular grid: ‘ein high density ‘eolous., The potential deformation maintains a very regular grid structure in high density regions. + The gravity aud grid deformation equations are solved usiug : jerarcical multigrid algoritlun for linear elliptic equatious., The gravity and grid deformation equations are solved using a hierarchical multigrid algorithm for linear elliptic equations. + These are solved in linear time. aia are asyuptotically faster han the FFT eravity solver.," These are solved in linear time, and are asymptotically faster than the FFT gravity solver." + At the same ine. adaptive dyuamic resolΠο. Is achieved.," At the same time, adaptive dynamic resolution is achieved." + Duriug the evolution any one constraiut can be satisfied by the grid., During the evolution any one constraint can be satisfied by the grid. + In our case. we follow the mass [ield such that the mass per unit grid cell ‘elnalus approximately coustaut.," In our case, we follow the mass field such that the mass per unit grid cell remains approximately constant." + This gives a the ον:uuic rauge advantages of smooth particle dro (SPH) combined with the speed aud biel resoluion of grid algorithms., This gives all the dynamic range advantages of smooth particle hydro (SPH) combined with the speed and high resolution of grid algorithms. + The explicit time integration limits the time step by the Courant condition., The explicit time integration limits the time step by the Courant condition. + To achieve a reasonable rui time. we limit he compression [actor to a factor of 5 in leneth. correspoucding to a factor of 125 in deusity.," To achieve a reasonable run time, we limit the compression factor to a factor of 5 in length, corresponding to a factor of 125 in density." + Most SZ coutributious arise below such densities. eeivingOm a dimiuishiugOm return to eeo to higher[we compression ‘ACLOLS.," Most SZ contributions arise below such densities, giving a diminishing return to go to higher compression factors." + The parameters we aclopted in our 512° simulation are Qy=0.37. O4=0.63. QE=0.05. hi0.7. σε=1.0. power spectrum index (&=1. box size L=1005.! Mpe aud smallest erie spacing LWA+t kpc.," The parameters we adopted in our $512^3$ simulation are $\Omega_0=0.37$, $\Omega_{\Lambda}=0.63$, $\Omega_B=0.05$ , $h=0.7$, $\sigma_8=1.0$, power spectrum index $n=1$ box size $L=100 h^{-1}$ Mpc and smallest grid spacing $40 h^{-1}$ kpc." + The simulation twed 30 GB memory aud took about three weeks (~1500 steps) οι a 32 processor shared memory Apha G$320 at CITA using Open MP parallelization clirectives., The simulation used $30$ GB memory and took about three weeks $\sim 1500$ steps) on a 32 processor shared memory Alpha GS320 at CITA using Open MP parallelization directives. + During the sce.nulation we store 2D projectious through the 3D box at every light crossing time through the box., During the simulation we store 2D projections through the 3D box at every light crossing time through the box. + The projectious are uade alternatively in the x. v. z directions to minimize the repetition of the same structsres lu the projection.," The projections are made alternatively in the x, y, z directions to minimize the repetition of the same structures in the projection." + We store projectious of thermal SZ. kinetic SZ. gas and dark matter densities.," We store projections of thermal SZ, kinetic SZ, gas and dark matter densities." + For the thermal SZ. we store 2Ay=eq=P. as given by equ. (3)).," For the thermal SZ, we store $2 \Delta +y=\frac{2 \sigma_T}{m_ec^2} P_e L$ as given by eqn. \ref{eqn:y}) )." + Our 2D inaps are stored ou 2018? grids., Our 2D maps are stored on $2048^2$ grids. + As tested by Seljak.Burwell&Pen(2001).. this preserves all the information down to the finest grid spacing.," As tested by \citet{Seljak01}, this preserves all the information down to the finest grid spacing." + Alter the simulation. we stack the SZ sectional naps separated by the width of simulation box. randomly choosing the center of each section ancl randomly roating aud flippiug each section.," After the simulation, we stack the SZ sectional maps separated by the width of simulation box, randomly choosing the center of each section and randomly rotating and flipping each section." + The periodic boundary condition euarautees that there are no ¢iscontiuuities in any of the maps., The periodic boundary condition guarantees that there are no discontinuities in any of the maps. + We then add these sectious onto a map of constant angular size., We then add these sections onto a map of constant angular size. +" Usiug clilleομί raucous seeds for the aliguments aud rotations. we make LO maps of width 1.19 degrees to cak""ulate the SZ statistics."," Using different random seeds for the alignments and rotations, we make $40$ maps of width $1.19$ degrees to calculate the SZ statistics." + The mean y parameter in these I0 maps y£x10.9., The mean $y$ parameter in these $40$ maps $\bar{y}\simeq4 \times 10^{-6}$. + The mean y parameer is still below the upper limit 1.5xI0.? from COBE FIRAS (Fixsenetal.1996)., The mean $y$ parameter is still below the upper limit $1.5\times 10^{-5}$ from COBE FIRAS \citep{Fixsen96}. +. One typical hermal SZ sky map aud a kinetic SZ sky map at the same field of view are shown iu fig., One typical thermal SZ sky map and a kinetic SZ sky map at the same field of view are shown in fig. + 2 aud lig.) 3..," \ref{fig:tszmap} and fig.\ref{fig:kszmap}, ," +respectively.,respectively. +" With these maps. we calculate the 54 power spectrum. the SZ nou-Gaussianity. the y PDF and yj, CDF."," With these maps, we calculate the SZ power spectrum, the SZ non-Gaussianity, the $y$ PDF and $y_p$ CDF." +achievable in the standard picture. of 10°! erg.,"achievable in the standard picture, of $10^{51}$ erg." + One may claim that Li. and probably also ?Be (García-Pérez&Primas2005).. in stars max have been depleted from their initial values. since the observed abundances of 'Li/ll ave a few times smaller (han that predicted by standard big-bang nucleosvnthesis. and ?Li is more fragile than ‘Li (Asplundοἱal.2005).," One may claim that $^6$ Li, and probably also $^9$ Be \citep{GPerez05}, in metal-poor stars may have been depleted from their initial values, since the observed abundances of $^7$ Li/H are a few times smaller than that predicted by standard big-bang nucleosynthesis, and $^6$ Li is more fragile than $^7$ Li \citep{Asplund05}." +". The actual survival fraction of ""Li is difficult to evaluate reliably. because the pre-main-sequence Li destruction is sensitive {ο convection. which cannot be modeled without [ree parameters."," The actual survival fraction of $^6$ Li is difficult to evaluate reliably because the pre-main-sequence Li destruction is sensitive to convection, which cannot be modeled without free parameters." + However. depletion factors as arge as LO may still be compatible with our picture.," However, depletion factors as large as 10 may still be compatible with our picture." + The estimates in (he preceding; section is based on an explosion οποίον of the order of 1077 eres., The estimates in the preceding section is based on an explosion energy of the order of $10^{52}$ ergs. +" The mass of ejecta with energy per nucleon above a certain value scales very strongly with the explosion energy. Ei, as E! *Naleunura&Shigevama2004)."," The mass of ejecta with energy per nucleon above a certain value scales very strongly with the explosion energy, $E_{\rm ex}$ as $E_{\rm ex}^{3.4}$ \citep{Nakamura04}." +. Thus à SN with the explosion energv 2 (mes higher than that considered in the preceding section will be able to produce ~10 times larger amounts of ight elements depending on the distribution of He and N. Nevertheless. if such very energetic explosions turn out to be rare. the mechanism proposed here may. play a rather limited role compared to other potential LiBeB production processes.," Thus a SN with the explosion energy 2 times higher than that considered in the preceding section will be able to produce $\sim 10$ times larger amounts of light elements depending on the distribution of He and N. Nevertheless, if such very energetic explosions turn out to be rare, the mechanism proposed here may play a rather limited role compared to other potential LiBeB production processes." + Both the degree of mass loss aud (he amount of N enrichment in (he progenitor star are expected to be sensitive to ils initial rotation speed (Mevnet&Maederetal. 2006).," Both the degree of mass loss and the amount of N enrichment in the progenitor star are expected to be sensitive to its initial rotation speed \citep{Meynet02, Meynet06}." +. The actual rotation speed is presumably distributed: over a wide range. as is (he explosion energv aud the extent of mass loss at the time of the explosion.," The actual rotation speed is presumably distributed over a wide range, as is the explosion energy and the extent of mass loss at the time of the explosion." +" ‘Therefore. dispersions in the ""Li and Be abundances are expected. and current observations suggest that (his may indeed be the case [or ""Li (Aokietal.2004:Asplundοἱ2005:Inoue2005) as well as Be (Boeseaard&Novicki2005)."," Therefore, dispersions in the $^6$ Li and Be abundances are expected, and current observations suggest that this may indeed be the case for $^6$ Li \citep{Aoki04,Asplund05,Inoue05} as well as Be \citep{Boesgaard05}." +. Our scenario predicts a close relation between Be and N. since De arises directly as a consequence of N spallation.," Our scenario predicts a close relation between Be and N, since Be arises directly as a consequence of N spallation." +" A looser correlation between ""Li and N is also expected. as effective ""Li production requires sufficient mass loss. which in turn implies significant N enrichment."," A looser correlation between $^6$ Li and N is also expected, as effective $^6$ Li production requires sufficient mass loss, which in turn implies significant N enrichment." + Further observations of °Li. Be ancl N for a large sample of metal-poor stars should provide definitive tests.," Further observations of $^6$ Li, Be and N for a large sample of metal-poor stars should provide definitive tests." +" Note that such correlations are 100 expected for other scenarios which involve mainly ""Li production only. such as structure omnnalion cosmic ravs (Suzuki&Inoue2002:Rollindeetal.2005).. active galactic nuclei oulllows (Prantzos2006:Nathetal.2006)... and production processes in (he early universe (Jecamziketal.2005)."," Note that such correlations are not expected for other scenarios which involve mainly $^6$ Li production only, such as structure formation cosmic rays \citep{Suzuki02,Rollinde05}, active galactic nuclei outflows \citep{Prantzos06,Nath06}, and production processes in the early universe \citep{Jedamzik05}." +. It is also mentioned that mass loss onto companion stars in binary svslenms may represent an additional palaway (o our scenario. provided that sulliciently thick CSAI is remaining at the time of the explosion.," It is also mentioned that mass loss onto companion stars in binary systems may represent an additional pathway to our scenario, provided that sufficiently thick CSM is remaining at the time of the explosion." + We reiterate that more observational data is necessary (o elucidate what Iraction of the LiBeB abundances seen in halo stars of different nelallicily can be explained by the mechanism proposed here., We reiterate that more observational data is necessary to elucidate what fraction of the LiBeB abundances seen in halo stars of different metallicity can be explained by the mechanism proposed here. + We are grateful to Georges Mevnet. Raphael Hirschi. Takeru Ix. Suzuki and Sean Ryan for valuable discussions.," We are grateful to Georges Meynet, Raphael Hirschi, Takeru K. Suzuki and Sean Ryan for valuable discussions." + We also acknowledge the contributions of an anonvimous referee.," We also acknowledge the contributions of an anonymous referee," +formation mechanism of the jet (BP82 and/or BZ77).,formation mechanism of the jet (BP82 and/or BZ77). + More fundamentally. it provides an important method for detection the spin of the and evaluation of the general theory of relativity.," More fundamentally, it provides an important method for detection the spin of the and evaluation of the general theory of relativity." + Such conjectures will be explored by direct imaging with future submm VLBI experiments., Such conjectures will be explored by direct imaging with future submm VLBI experiments. + We thank M. Inoue. A. Dor. H. Nagai. D. Garofalo and P.T.P. Ho for stimulating discussions and proof reading.," We thank M. Inoue, A. Doi, H. Nagai, D. Garofalo and P.T.P. Ho for stimulating discussions and proof reading." + We would like to sincerely acknowledge R. Craig Walker for his providing the VLBA image at 43 GHz., We would like to sincerely acknowledge R. Craig Walker for his providing the VLBA image at 43 GHz. + M.N. is grateful to D. L. Meier and C. A. Norman for inspiring. discussions., M.N. is grateful to D. L. Meier and C. A. Norman for inspiring discussions. + Μ.Ν. was supported by the Allan C. Davis fellowship jointly awarded by JHU and STScel. The European VLBI Network is a Joint facility of European. Chinese. South African and other radio astronomy institutes funded by their national research councils.," M.N. was supported by the Allan C. Davis fellowship jointly awarded by JHU and STScI. The European VLBI Network is a joint facility of European, Chinese, South African and other radio astronomy institutes funded by their national research councils." + MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of STFC., MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of STFC. + The National Radio Astronomy Observatory is afacility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc.VLBA..," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.." +"and M,=-2EL1z—an[i5| is the power spectra associated with the mask.",and $W_l= {1 \over 2l+1}\sum_m |w_{lm}|^2 $ is the power spectra associated with the mask. +" Note that the transformation matrices AL depends on the of] the weighting. function. w5,7.NOY. whereas the matrix. ALS for. cross-power spectra .is determined. by the cross-power spectra 11i.p of. two weighting functions."," Note that the transformation matrices $M^{X,Y}$ depends on the power-spectrum of the weighting function $w_{lm}^{X,Y}$, whereas the matrix $M^{XY}$ for cross-power spectra is determined by the cross-power spectra $\tilde W_{l_3}^{XY}$ of two weighting functions." + Independent of the choice of weights the estimators C;'un remain unbiased., Independent of the choice of weights the estimators $\cal C_{\ell}^\alpha$ remain unbiased. + The pseudo-C;s are unbiased., The ${\cal C}_{\ell}$ s are unbiased. + The variances of these estimators can be computed analytically for arbitrary sky coverage and a non-uniform Gaussian noise distribution., The variances of these estimators can be computed analytically for arbitrary sky coverage and a non-uniform Gaussian noise distribution. + The deviation of the estimated 6 from the ensemble average £C'i? is denoted by oC‘., The deviation of the estimated $\tilde C_l$ from the ensemble average $\langle \tilde C_l \rangle$ is denoted by $\delta \tilde C_l$. + We ure concerned here with the computation of the covariance of estimated C's., We are concerned here with the computation of the covariance of estimated $C_ls$. + We begin by defining the covariance matrix: The covariance of Cs from individual surveys d** or &? can be expressed as follows (Efstathiou2004)., We begin by defining the covariance matrix: The covariance of ${\cal C}_ls$ from individual surveys $\Phi^{X}$ or $\Phi^{Y}$ can be expressed as follows \citep{Efs1}. + Extending the above results similarly the covariance of C? for the cross-power-spectrum can be expressed as: In our derivation we have assumed that all three power spectra are being estimated from the data simultaneously., Extending the above results similarly the covariance of ${\cal C}^{\chi}_l$ for the cross-power-spectrum can be expressed as: In our derivation we have assumed that all three power spectra are being estimated from the data simultaneously. + The three off-diagonal terms ean be similarly expressed as: Here we have introduced following notations:, The three off-diagonal terms can be similarly expressed as: Here we have introduced following notations: +spectrograph. 8D (Weitzel et al.,"spectrograph, 3D (Weitzel et al." + 1996). at the AAT on 1997 Dee 16 (day 3949 = 10.5 vears) and. 1998 Dee 1 (clay 4299 = 11s vears).," 1996), at the AAT on 1997 Dec 16 (day 3949 = 10.8 years) and 1998 Dec 1 (day 4299 = 11.8 years)." + We also note that the earliest Llubble Space Telescope (LIST) NICALOS spectrum of SN 1987 was taken on 1998 June 15 (clay 4130 = 11.3 vears). but has not vet been published.," We also note that the earliest Hubble Space Telescope (HST) NICMOS spectrum of SN 1987A was taken on 1998 June 15 (day 4130 = 11.3 years), but has not yet been published." + The observations are summarised in Table 1., The observations are summarised in Table 1. + Some of the data. presented. here were obtained in runs of several days., Some of the data presented here were obtained in runs of several days. + lo the text anc diagrams these runs will usually be identified by the epoch of the first day of cach., In the text and diagrams these runs will usually be identified by the epoch of the first day of each. + For further details of the FIGS spectrometer. used to obtain the dav 1348 spectrum. see Bailey οἱ al. (," For further details of the FIGS spectrometer, used to obtain the day 1348 spectrum, see Bailey et al. (" +1988) ancl Papers Lb LL.,1988) and Papers I II. + The LIUS spectrograph was based on a 128.128 pixel 11οςαTe array., The IRIS spectrograph was based on a $128\times128$ pixel HgCdTe array. + All the HUS observations were taken at [/36. vielding a plate seale of 0.79. aresec/pixel.," All the IRIS observations were taken at f/36, yielding a plate scale of 0.79 arcsec/pixel." + Spectra. were acquired. in the cchelle mode for epochs 14692112. days and in the /f-erism mode for the subsequent. epochs., Spectra were acquired in the echelle mode for epochs 1469–2112 days and in the $H$ -grism mode for the subsequent epochs. + In the echelle mocde. 4 orders of cross-clispersed spectra were provided. covering 0.9.1.5 jum (£4 band) and 1.42.4 pam (ILI. band).," In the echelle mode, 4 orders of cross-dispersed spectra were provided, covering 0.9–1.5 $\mu$ m $IJ$ band) and 1.4–2.4 $\mu$ m $HK$ band)." + The slit was usually oriented at a DX. of 90 deg., The slit was usually oriented at a P.A. of 90 deg. + cast-west., east-west. + The slit length was 13 aresee (16 pixels) while in the dispersion direction. 2 pixels corresponded to a spectral. resolution of about 375 (A/4NA) (equivalent to ~s00 kms).," The slit length was 13 arcsec (16 pixels) while in the dispersion direction, 2 pixels corresponded to a spectral resolution of about 375 $\lambda/\Delta\lambda$ ) (equivalent to $\sim$ 800 km/s)." + Llowever. the actual resolution was ecnerally poorer than this (see below).," However, the actual resolution was generally poorer than this (see below)." + To enable skv-subtraction. the telescope was nodcec along the slit by 58 aresec (610 pixels).," To enable sky-subtraction, the telescope was nodded along the slit by 5–8 arcsec (6–10 pixels)." + To improve the flux measurement precision of both the ejecta and the bright ring. the slit width for the 7/4 observations was set at 5.8 aresec.," To improve the flux measurement precision of both the ejecta and the bright ring, the slit width for the $IJ$ observations was set at 5.8 arcsec." + similarly. the 1348 d FIGS spectrum was obtained with a 5.9 aresec aperture.," Similarly, the 1348 d FIGS spectrum was obtained with a 5.9 arcsec aperture." + Thus. the resolution ofthe (point-source) ejecta spectra was cllectively determined by the seeing.," Thus, the resolution of the (point-source) ejecta spectra was effectively determined by the seeing." + For the CSAL spectra. the finite extent of the bright ring (1.661.21 aresec. Plait et al.," For the CSM spectra, the finite extent of the bright ring $1.66\times1.21$ arcsec, Plait et al." + 1995) would have produced. a slightly. lower resolution., 1995) would have produced a slightly lower resolution. + The £./ cchelle resolutions listed in. Table 1. column 4. were obtained. directly from the ENIM of the Le L 1.083 (m line.," The $IJ$ echelle resolutions listed in Table 1, column 4, were obtained directly from the FWHM of the He I 1.083 $\mu$ m line." + They were typically 200400 (A/AA)., They were typically 200–400 $\lambda/\Delta\lambda$ ). + As already mentioned. the resolution of the ejecta spectra was probably slightly higher.," As already mentioned, the resolution of the ejecta spectra was probably slightly higher." + For the {1 observations. we were unable to use the 5.8 aresee slit since it. produced severe degradation of the S/N. We therefore. used a. slit width of 1.4 aresee in this band.," For the $HK$ observations, we were unable to use the 5.8 arcsec slit since it produced severe degradation of the S/N. We therefore used a slit width of 1.4 arcsec in this band." + The £A. resolution was obtained from the EFWIIM. of the He L 2.058 jm CSAIL line., The $HK$ resolution was obtained from the FWHM of the He I 2.058 $\mu$ m CSM line. + Owing to the declining Hux. after day 2112. spectra were taken using the lower resolution /f-grism mode.," Owing to the declining flux, after day 2112, spectra were taken using the lower resolution $H$ -grism mode." + This covered. 1.22.1 jm in a single order., This covered 1.2–2.1 $\mu$ m in a single order. + The slit was usually oriented. at a PLA. of 135 deg., The slit was usually oriented at a P.A. of 135 deg. + in order to maximise the spatial separation of the spectra of the supernova and Stars 2 and 3 (see below), in order to maximise the spatial separation of the spectra of the supernova and Stars 2 and 3 (see below). + The slit length. was 24 arcsec (30 pixels). while in the clispersion direction a 1.6 aresec (2 pixel) wide slit was used. vielding a spectral resolution of 120 (AfAA) (equivalent to 72.500. km/s).," The slit length was 24 arcsec (30 pixels), while in the dispersion direction a 1.6 arcsec (2 pixel) wide slit was used, yielding a spectral resolution of 120 $\lambda/\Delta\lambda$ ) (equivalent to $\sim$ 2,500 km/s)." + The nod throw was 1015 arcsec., The nod throw was 10–15 arcsec. + The dav 1348 FLGS spectrum was reduced. using FLCARO (Shortridge 1995)., The day 1348 FIGS spectrum was reduced using FIGARO (Shortridge 1995). + Final Uuxing was by comparison with contemporary broad-band photometry obtained. with the AAT IR photometer IRPS procedure described. in Paper HL. using the AT dwarf BS 2015 as the local standard.," Final fluxing was by comparison with contemporary broad-band photometry obtained with the AAT IR photometer IRPS procedure described in Paper II), using the A7 dwarf BS 2015 as the local standard." + Llowever. by this epoch. the narrow He L 1.083 jan line from the bright ring had an intensity of about of the Dux within the J/-photometry wavelengt-— window.," However, by this epoch, the narrow He I 1.083 $\mu$ m line from the bright ring had an intensity of about of the flux within the $J$ -photometry wavelength window." + Moreover it lay right at the blue edge. of the J-band filter. making it dillicult to judge the ellect of the bright ring on the J-magnitude. (," Moreover it lay right at the blue edge of the $J$ -band filter, making it difficult to judge the effect of the bright ring on the $J$ -magnitude. (" +Lhe spatial coverage of IPS included. the ring).,The spatial coverage of IRPS included the ring). + Therefore. taking into account other uncertainties. we judge the uncertainty in the Huxing to be of order £25%..," Therefore, taking into account other uncertainties, we judge the uncertainty in the fluxing to be of order $\pm$." + The wavelength scale was calibrated using the narrow He E 1.083 jn and lines. adopting a redshift of |289 km/s (Crotts Lleathcote 1991).," The wavelength scale was calibrated using the narrow He I 1.083 $\mu$ m and $\beta$ lines, adopting a redshift of +289 km/s (Crotts Heathcote 1991)." + The LRIS cata were also reduced using FIGARO., The IRIS data were also reduced using FIGARO. + After bias-subtraction and [at-eld correction the mmage-pair obtained at the two nod. positions were subtracted to remove sky line emission., After bias-subtraction and flat-field correction the image-pair obtained at the two nod positions were subtracted to remove sky line emission. + For the echelle-mode data. cilferent echelle orders were then traced and corrected for echelle distortion.," For the echelle-mode data, different echelle orders were then traced and corrected for echelle distortion." + The positive and negative spectra were extracted: from. the resulting frames using simple extraction., The positive and negative spectra were extracted from the resulting frames using simple extraction. + We extracted over 46 pixel rows (3.24.8 aresec). depending on the seeing.," We extracted over 4–6 pixel rows (3.2–4.8 arcsec), depending on the seeing." +" ""This is discussed. further below.", This is discussed further below. + Cosmic rays. and residual sky-lines were identified and removed by comparing repeat observations of spectra obtained at. dilferent. times during the night., Cosmic rays and residual sky-lines were identified and removed by comparing repeat observations of spectra obtained at different times during the night. + Waveleneth calibration was by means of argon and. xenon. are lamps and the night-skyv emission lines present in the supernova spectra., Wavelength calibration was by means of argon and xenon arc lamps and the night-sky emission lines present in the supernova spectra. + “Phe wavelength uncertainty in the echelle spectra ranges from. —O0.0014 sam in the £J-band spectra to +0.0025 jm in the 4A-band spectra., The wavelength uncertainty in the echelle spectra ranges from $\pm$ 0.0014 $\mu$ m in the $IJ$ -band spectra to $\pm$ 0.0025 $\mu$ m in the $HK$ -band spectra. + Phe wavelength uncertainty in the erism spectra is E0.009 rm. To correct for the atmospheric and instrumental transmission functions and to Dux-calibrate the spectra. we used the €i dwarf spectrophotometric standard BS 1294 (Allen Crage 1983).," The wavelength uncertainty in the grism spectra is $\pm$ 0.009 $\mu$ m. To correct for the atmospheric and instrumental transmission functions and to flux-calibrate the spectra, we used the G dwarf spectrophotometric standard BS 1294 (Allen Cragg 1983)." + The adopted: magnituces were J=15.20. Hl14.90. Ix—|4.54. (," The adopted magnitudes were J=+5.20, H=+4.90, K=+4.84. (" +For the grism. spectrum on day 3158. we used the A+ giant LID 19904. adopting L=16.66).,"For the grism spectrum on day 3158, we used the A4 giant HD 19904, adopting H=+6.66)." + The spectral orders of the echelle spectra were then merged to form single spectra., The spectral orders of the echelle spectra were then merged to form single spectra. + The final Hüxing of the spectra is now described., The final fluxing of the spectra is now described. + Accurate flux calibration of the spectra was cillicult. ancl became increasinely so with time., Accurate flux calibration of the spectra was difficult and became increasingly so with time. + This was due to the combined effects of the declining SN Εκ. variable seeing. variable atmospheric transmission for both supernova ancl standard. (the airmass was inevitably quite high 1.4L8). pointing errors of up to ~2 aresee and. for the echelle spectra. the small number of detector pixels (16) along the slit in a given order.," This was due to the combined effects of the declining SN flux, variable seeing, variable atmospheric transmission for both supernova and standard (the airmass was inevitably quite high 1.4–1.8), pointing errors of up to $\sim$ 2 arcsec and, for the echelle spectra, the small number of detector pixels (16) along the slit in a given order." + Flux measurement uncer poor secing conditions was a particular problem. for the narrow slit spectra due to the greater (but uncertain) vienctting ellects., Flux measurement under poor seeing conditions was a particular problem for the narrow slit spectra due to the greater (but uncertain) vignetting effects. + However. the most dillicult. problem. of," However, the most difficult problem of" +correspond to only a small portion of the mass in the disk.,correspond to only a small portion of the mass in the disk. + This consistently explains why using the empirical relation without including the faint flares can we estimate the hard X-ray peak flux of a bright outburst — the indicator of the disk mass., This consistently explains why using the empirical relation without including the faint flares can we estimate the hard X-ray peak flux of a bright outburst – the indicator of the disk mass. +" In order to get an idea on how good the estimation or prediction is. we also ""predict the hard X-ray peak flux for 2004 and 2007 outbursts with the data before the 2004 and the 2007 outburst respectively. and then compared the ""predictions"" with the observations (Fig 3))."," In order to get an idea on how good the estimation or prediction is, we also “predict” the hard X-ray peak flux for 2004 and 2007 outbursts with the data before the 2004 and the 2007 outburst respectively, and then compared the “predictions” with the observations (Fig \ref{fig_pred}) )." + We then studiec the deviations of the predicted values from the actual observec peak fluxes during the 2004 outburst and the 2007 outburst., We then studied the deviations of the predicted values from the actual observed peak fluxes during the 2004 outburst and the 2007 outburst. + The deviations are -0.012 crab and -0.034 crab. or and6.4%.. respectively.," The deviations are -0.012 crab and -0.034 crab, or and, respectively." + Considering that the 10-day time binning woulc bring uncertainties. these predictions are extraordinarily good.," Considering that the 10-day time binning would bring uncertainties, these predictions are extraordinarily good." + The prediction made for the next bright outburst should have a similar accuracy., The prediction made for the next bright outburst should have a similar accuracy. + The hard X-ray peak of the next outburst should fall on the prediction in Fig 3. with a lower limit around 0.65 crab. which is the predicted hard X-ray peak flux of an outburst 1f it happened at present (around MJD 55074).," The hard X-ray peak of the next outburst should fall on the prediction in Fig \ref{fig_pred} + with a lower limit around 0.65 crab, which is the predicted hard X-ray peak flux of an outburst if it happened at present (around MJD 55074)." + We included recent hard X-ray monitoring observations of GX 339-4 with Swift/BAT in addition to CGRO/BATSE and RXTE/HEXTE observations., We included recent hard X-ray monitoring observations of GX 339-4 with Swift/BAT in addition to CGRO/BATSE and RXTE/HEXTE observations. + We have analyzed the X-ray observations of GX 339-4 in the past 18 years following Yuetal.(2007) and re-examined the empirical relation between the hard X-ray peak flux and the outburst waiting time during bright outbursts found by Yuetal.(2007)., We have analyzed the X-ray observations of GX 339-4 in the past 18 years following \citet{Yu07} and re-examined the empirical relation between the hard X-ray peak flux and the outburst waiting time during bright outbursts found by \citet{Yu07}. +. We found that the hard X-ray peak flux of the 2007 outburst follows the empirical relation determined with observations before 2007 very well., We found that the hard X-ray peak flux of the 2007 outburst follows the empirical relation determined with observations before 2007 very well. + We checked the potential influence of faint flares on the empirical relation., We checked the potential influence of faint flares on the empirical relation. + The empirical relation was determined based on the observations of bright outbursts. not including those faint flares below about 0.12 crab.," The empirical relation was determined based on the observations of bright outbursts, not including those faint flares below about 0.12 crab." + The actually minimal waiting time required for an outburst to occur consistently explains that there exists a lower limit of peak flux for the outburst studied here., The actually minimal waiting time required for an outburst to occur consistently explains that there exists a lower limit of peak flux for the outburst studied here. + A refined relation between the hard ray peak flux and the waiting time in the past 18 years has been obtained., A refined relation between the hard X-ray peak flux and the waiting time in the past 18 years has been obtained. + Based on this relation. we can estimate the hard X-ray peak flux for the next bright outburst as soon as it starts.," Based on this relation, we can estimate the hard X-ray peak flux for the next bright outburst as soon as it starts." + It has been 750 days since the end of the most recent bright outburst., It has been 750 days since the end of the most recent bright outburst. + Based on this. we predict that the hard X-ray peak flux should be no less than 0.65 crab.," Based on this, we predict that the hard X-ray peak flux should be no less than 0.65 crab." + One may think that during different outbursts the properties of the accretion flow are different. such that the radiation efficiencies differ for different. outbursts while the actual mass accreted are about the same.," One may think that during different outbursts the properties of the accretion flow are different, such that the radiation efficiencies differ for different outbursts while the actual mass accreted are about the same." + This is not the case., This is not the case. + The correlation between the hard X-ray peak flux and the peak flux of the corresponding HS state is found to hold for individual black hole binaries and neutron star low mass ray binaries (Yuetal..2004:Yu&Dolence.2007:Yan.2009).," The correlation between the hard X-ray peak flux and the peak flux of the corresponding HS state is found to hold for individual black hole binaries and neutron star low mass X-ray binaries \citep{YKF04,YD07,YY09}." +. Given that the neutron star has a hard surface. the observed X-ray flux from the neutron star system should in general reflect the instantaneous mass accretion rate.," Given that the neutron star has a hard surface, the observed X-ray flux from the neutron star system should in general reflect the instantaneous mass accretion rate." + Therefore outbursts with different flux amplitude in neutror star systems should correspond to different mass accretion rate., Therefore outbursts with different flux amplitude in neutron star systems should correspond to different mass accretion rate. + Because the black hole systems fall on the same correlation track as those. the mass accretion rates should be different when GX 339-4 reaches the hard X-ray peaks during outbursts of different amplitudes.," Because the black hole systems fall on the same correlation track as those, the mass accretion rates should be different when GX 339-4 reaches the hard X-ray peaks during outbursts of different amplitudes." + The empirical relation. confirmed by the BAT observations of the 2007 outburst. provides strong evidence that there is a link between the mass in the accretion disk and. the brightest LH state that GX 339-4 can reach.," The empirical relation, confirmed by the BAT observations of the 2007 outburst, provides strong evidence that there is a link between the mass in the accretion disk and the brightest LH state that GX 339-4 can reach." + The mechanism behind this link is not clear., The mechanism behind this link is not clear. + But if the mass in the accretior disk is directly related to the production of the hard X-ray flux. then a major portion of the disk should be involved i generating the hard X-ray flux.," But if the mass in the accretion disk is directly related to the production of the hard X-ray flux, then a major portion of the disk should be involved in generating the hard X-ray flux." + Independent of such accretior geometry considerations. Yu&Yan(2009) have recently performed a comprehensive study of spectral state transitions in bright Galactic X-ray binaries.," Independent of such accretion geometry considerations, \citet{YY09} have recently performed a comprehensive study of spectral state transitions in bright Galactic X-ray binaries." + The results have confirmed the correlation between LH-to-HS transition luminosity and the peak luminosity of the following soft state shown in previous studies (Yuetal..2004.2007:Yu&Dolence.2007).. ane provided strong evidence for that: a) non-stationary accretior plays a dominant role in generating a bright LH state and b) the rate-of-increase of the mass accretion rate can be the dominant parameter determining spectral state transitions.," The results have confirmed the correlation between LH-to-HS transition luminosity and the peak luminosity of the following soft state shown in previous studies \citep{YKF04,Yu07,YD07}, and provided strong evidence for that: a) non-stationary accretion plays a dominant role in generating a bright LH state and b) the rate-of-increase of the mass accretion rate can be the dominant parameter determining spectral state transitions." + The empirical relation between the LH-to-HS state transition luminosity and the peak luminosity of the following HS state and the empirical relation studied in this paper connect the mass in the accretion disk (the cause and initial condition) and the peak luminosity of the hard state (the result) to the rate-of-increase of the mass, The empirical relation between the LH-to-HS state transition luminosity and the peak luminosity of the following HS state and the empirical relation studied in this paper connect the mass in the accretion disk (the cause and initial condition) and the peak luminosity of the hard state (the result) to the rate-of-increase of the mass +calibrator was observed for about 6 minutes before and after an observation of about 30 to [5 nuinutes ou the field centered on 22008D. The data were analyzed usine AIDS.,calibrator was observed for about 6 minutes before and after an observation of about 30 to 45 minutes on the field centered on 2008D. The data were analyzed using AIPS. + To correct for the diffuse ciission due to the host ealaxv iu the CAIRT observations. we have removed the shortest baselines. using a simular procedure as for the WSRT ineasurements.," To correct for the diffuse emission due to the host galaxy in the GMRT observations, we have removed the shortest baselines, using a similar procedure as for the WSRT measurements." + The GMBT las a random distribution of Ll out of its 30 antennae within the central square. which gives several short basclines.," The GMRT has a random distribution of 14 out of its 30 antennae within the central square, which gives several short baselines." + We used only those baselines louger than 5 kA at 1950 AITIz. 3 kA at GLO MIIz. aud about 2 kA at 325 MIIz.," We used only those baselines longer than 5 $\lambda$ at 1280 MHz, 3 $\lambda$ at 610 MHz, and about 2 $\lambda$ at 325 MHz." + This ensures discarding the short baselines iu the CAIRT central square as well as elsewhere in the array., This ensures discarding the short baselines in the GMRT central square as well as elsewhere in the array. + All the results of our observations are given in Table 1.. aud the helt curves are shown in Figures 1 aud 2..," All the results of our observations are given in Table \ref{table:wsrtgmrtdata}, and the light curves are shown in Figures \ref{fig:SN2008Dlcs} and \ref{fig:SN2007uylcs}." + We organized Tarect of Opportunity slobal VLBI observations on 2008. February 6 aud 2008 March Ls., We organized Target of Opportunity global VLBI observations on 2008 February 6 and 2008 March 18. + The primary target was 22008D. 28 aud 69 davs after the N-vay discovery. but short scaus on SN22007uv were also performed.," The primary target was 2008D, 28 and 69 days after the X-ray discovery, but short scans on 2007uy were also performed." + The participating telescopes were Arccibo. Effelsbere. Jodrell Bauk (MIT). Ihutebeesthoek. Aledicina. Noto. Ousala. Torun aud Westerbork from the Evropeau VLBI Network (EWN). and Hancock and St. Croix from the VLBA.," The participating telescopes were Arecibo, Effelsberg, Jodrell Bank (MkII), Hartebeesthoek, Medicina, Noto, Onsala, Torun and Westerbork from the European VLBI Network (EVN), and Hancock and St. Croix from the VLBA." + The s-hour observations (of which Arecibo could track the source ouly for about 1.5 hours) were carried out at 5 GIIz at 1021 Mbps using 2-bit sampling., The 8-hour observations (of which Arecibo could track the source only for about 1.5 hours) were carried out at 5 GHz at 1024 Mbps using 2-bit sampling. + The VLBA statious recorded at a rate of 512 Mbps with 1-bit siuupling. to obtain the same observing bandwidth.," The VLBA stations recorded at a rate of 512 Mbps with 1-bit sampling, to obtain the same observing bandwidth." + The svuthesis array data from the WSRT were recorded parallel to the VLBI observatious., The synthesis array data from the WSRT were recorded parallel to the VLBI observations. + The target was pliase-referenced to the nearby calibrators J0911|3319 (C1) and J0919|3321 (C2). at an angular distance of 0.8 and 2 deerces from the target (Dj. respectively.," The target was phase-referenced to the nearby calibrators J0911+3349 (C1) and J0919+3324 (C2), at an angular distance of 0.8 and 2 degrees from the target (T), respectively." + The phase reference cycle pattern was T-CI-T-C1-€2 etc., The phase reference cycle pattern was T-C1-T-C1-C2 etc. + with correspouding 3:30-1:30-3:30-1:30-2:30 minute scans: the last scan included a 1 minute gap for slewing aud system temperature measurements at the EVN telescopes., with corresponding 3:30-1:30-3:30-1:30-2:30 minute scans; the last scan included a 1 minute gap for slewing and system temperature measurements at the EVN telescopes. +" The total on source time on 22008D was 200 imiüuutes and 210 minutes at the two epochs. respectively,"," The total on source time on 2008D was 200 minutes and 210 minutes at the two epochs, respectively." +" As a colmparison source, we iucluded scans on 220070 phase-referenced ina simular fashion."," As a comparison source, we included scans on 2007uy phase-referenced in a similar fashion." + The total on-source time on 220070. was 38 minutes at the first epoch. and 19 minutes at the second epoch.," The total on-source time on 2007uy was 38 minutes at the first epoch, and 49 minutes at the second epoch." + The data reduction was carried out in AIPS using standard techniques (ee.7).. aud the calibrated data were exported to Difinap (2)..," The data reduction was carried out in AIPS using standard techniques \citep[e.g.][]{diamond1995}, and the calibrated data were exported to Difmap \citep[][]{shepherd1994baas}." + Because J0911|3319 had a resolved structure. ifs structural phase was removed in the process of phase-reterencing.," Because J0911+3349 had a resolved structure, its structural phase was removed in the process of phase-referencing." + First we plhase-referenced JOOLL|3319 to 00190|3321. and made a map of these nearby calibrators in Difinap.," First we phase-referenced J0911+3349 to J0919+3324, and made a map of these nearby calibrators in Difmap." +. We carried out the structural plase correction in two different wavs., We carried out the structural phase correction in two different ways. + The frinege-fit solutions from J0919|3321 were interpolated to all sources., The fringe-fit solutions from J0919+3324 were interpolated to all sources. + The J0911|3319 data were additionally phase sclfcalibrated aud these solutions. too. were interpolated to the target.," The J0911+3349 data were additionally phase self-calibrated and these solutions, too, were interpolated to the target." + Iu the other method we repeated fringe-fittine frou scratch. usine now JO9LL|3319 as the primary reference source and its imap was used to correct for the structural phase.," In the other method we repeated fringe-fitting from scratch, using now J0911+3349 as the primary reference source and its map was used to correct for the structural phase." + These two methods should ideally eive identical or very simular results., These two methods should ideally give identical or very similar results. + The advantage of the first method is that the compact source JO0919|3320 is expected o produce higher signal-to-noise delay and cdelav-rate solutions. but the phase-refercuce cvele time in lis case is quite long. ie. 1l iminutes.," The advantage of the first method is that the compact source J0919+3324 is expected to produce higher signal-to-noise delay and delay-rate solutions, but the phase-reference cycle time in this case is quite long, i.e. 11 minutes." + However. to determine the target source position independent of xossible remaining structural phase aud positional errors in the nearby calibrator J0911|3319. we directly pliase- the tareet to J0919|3321.," However, to determine the target source position independent of possible remaining structural phase and positional errors in the nearby calibrator J0911+3349, we directly phase-referenced the target to J0919+3324." +" The coordinates of his source were taken from the VLBA Calibrator=: RA=0921908"".787122. LU.9L287 (.J2000)."," The coordinates of this source were taken from the VLBA Calibrator: $09^{\rm h}19^{\rm m}08^{\rm s}.787122$, $^{\circ}$ .94287 (J2000)." + The elobal VLBI nuages of SN22008D appeared uuresolved oat both epochs., The global VLBI images of 2008D appeared unresolved at both epochs. + The observed peak brightuesses were 2.0 mJv aud 0.9 wy ou February 6 and March 18. respectively.," The observed peak brightnesses were 2.0 mJy and 0.9 mJy on February 6 and March 18, respectively." + These values are consistent with the WSRT total flux density measurements of 2.0940.06 indy and O.S86£0.06 indy. taken during the VLBI observations (sec Table 1)).," These values are consistent with the WSRT total flux density measurements of $\pm$ 0.06 mJy and $\pm$ 0.06 mJy, taken during the VLBI observations (see Table \ref{table:wsrtgmrtdata}) )." + The offsource image noise was 20-25 gJv/beam using natural weighting. but it was higher near the target.," The off-source image noise was 20-25 $\mu$ Jy/beam using natural weighting, but it was higher near the target." + We carried out modelfitting of the we-data in Difiuap to eive constraints ou the apparent augular size., We carried out model-fitting of the $uv$ -data in Difmap to give constraints on the apparent angular size. + Both point and circular Caussian components were fitted to the data., Both point and circular Gaussian components were fitted to the data. + At the first epoch. we obtained aneular diauueteyr sizes of 0.36 and 0.10 millearcsecoud (πας) using the two differeut wavs of processing.," At the first epoch, we obtained angular diameter sizes of 0.36 and 0.40 milli-arcsecond (mas) using the two different ways of processing." + The secoud epoch data produced different results., The second epoch data produced different results. + Using the first method the circular Caussian component collapsed to zero radius: in the other case we obtained a size of 0.5 mas. although the ft was poorer.," Using the first method the circular Gaussian component collapsed to zero radius; in the other case we obtained a size of 0.5 mas, although the fit was poorer." + The reason for this difference may be the poor phase stability at the secoud epoch due to bad weather conditions., The reason for this difference may be the poor phase stability at the second epoch due to bad weather conditions. + JO0911|3319. after phase-reterencing to the more compact calibrator. showed phase instabilities on short timescales.," J0911+3349, after phase-referencing to the more compact calibrator, showed phase instabilities on short timescales." + Modcl-fittine of the sparser 22007uy data at the first epoch resulted in a similar. although somewhat smaller size of 0.28 nas and 0.12 mas using the two calibration nethods.," Model-fitting of the sparser 2007uy data at the first epoch resulted in a similar, although somewhat smaller size of 0.28 mas and 0.12 mas using the two calibration methods." + At the second epoch the size of the fitted circular Gaussian componuent collapsed to zero radius imn oth cases., At the second epoch the size of the fitted circular Gaussian component collapsed to zero radius in both cases. + To better understand the significance of the imocdol-fittine results for 22008D. we performed Monte Carlo siauulations.," To better understand the significance of the model-fitting results for 2008D, we performed Monte Carlo simulations." + Using simulated data with we-coveraee and telescope seusitivites identical to the first epoch observations. 2 1aJw circular Caussian sources with a size of 0.33 nias and 0.03 mas (practically a poiut source) were added to the simulated data in £00 trials each.," Using simulated data with $uv$ -coverage and telescope sensitivites identical to the first epoch observations, 2 mJy circular Gaussian sources with a size of 0.33 mas and 0.03 mas (practically a point source) were added to the simulated data in 400 trials each." + Iu the first case the recovered source sizes were typically 0.3 mas aud in all cases less than 0.5 mas., In the first case the recovered source sizes were typically 0.3 mas and in all cases less than 0.5 mas. + In the second case witli he point source model. the recovered size is less than 425 ias.," In the second case with the point source model, the recovered size is less than 0.25 mas." + These simulations incicate that the data are uarginallv consistent with a resolved source of 0.360.LO nas with an error of E0.1 mas., These simulations indicate that the data are marginally consistent with a resolved source of 0.36–0.40 mas with an error of $\pm$ 0.1 mas. + We note. however. that in this analysis we simulated only the effect of thermal jose. aud the error may be somewhat higher due to adverse weather aud other svstematic errors that may ave affected plase-refercucing.," We note, however, that in this analysis we simulated only the effect of thermal noise, and the error may be somewhat higher due to adverse weather and other systematic errors that may have affected phase-referencing." + For the second epoch we simulated a 0.9 πι] source with a size of 0.35 mas to see if it could be consisteut with the previous epoch aud he measured value., For the second epoch we simulated a 0.9 mJy source with a size of 0.35 mas to see if it could be consistent with the previous epoch and the measured value. + The results were very simular to the frst epoch. with recovered sizes less than 0.5 mas.," The results were very similar to the first epoch, with recovered sizes less than 0.5 mas." + We conclude that at the second epoch the sizes obtained, We conclude that at the second epoch the sizes obtained +spaced frequencies. we have the opportunity to test whether C has the same radio continuum spectrum as A and D. Assuming that the flux density of each component obevs ον)xv7 (where a; is the spectral index of component 7). a linear least-squares fit to the data in Table gives ay=—0.2T£0.07. ayn=—0.25£0.07. and ας=0.29£0.18.,"spaced frequencies, we have the opportunity to test whether C has the same radio continuum spectrum as A and B. Assuming that the flux density of each component obeys $S_i(\nu) \propto +\nu_i^{\alpha}$ (where $\alpha_i$ is the spectral index of component $i$ ), a linear least-squares fit to the data in Table \ref{tbl:fluxes} + gives $\alpha_{\rm A} = -0.27\pm 0.07$, $\alpha_{\rm B} = -0.25\pm +0.07$, and $\alpha_{\rm C} = +0.29\pm 0.18$." + The uncertainties in the spectral indices inclicde a contribution from the uncertainties in the absolute flux density scale. which is at least at all frequencies.," The uncertainties in the spectral indices include a contribution from the uncertainties in the absolute flux density scale, which is at least at all frequencies." + The comparison between o4 and oc can be made more precise by examining the [ιν density ratios. because the ratios are independent of the uncertainties in the absolute [lux densitv scale.," The comparison between $\alpha_{\rm A}$ and $\alpha_{\rm C}$ can be made more precise by examining the flux density ratios, because the ratios are independent of the uncertainties in the absolute flux density scale." + The difference in spectral indices. ag—ay. is the logarithimnic slope olSe(v)/S(r).," The difference in spectral indices, $\alpha_{\rm C} - +\alpha_{\rm A}$, is the logarithmic slope of." +. The flux density ratios and are plotted in Fig. 4.., The flux density ratios and are plotted in Fig. \ref{fig:ratios}. + The solid line represents the best-fit power law toSe(v)/S\(v).. which has a slope Qc—0&4=0.51x 0.17. implving the spectral indices of C and A are discrepant at the 30 level.," The solid line represents the best-fit power law to, which has a slope $\alpha_{\rm C} - \alpha_{\rm A} = ++0.51\pm 0.17$ , implying the spectral indices of C and A are discrepant at the $3\sigma$ level." + The dashed line is a fit to the data under the hypothesis that C is a (hired quasar image whose spectrum had been modified by [ree-[ree absorption (see 3))., The dashed line is a fit to the data under the hypothesis that C is a third quasar image whose spectrum had been modified by free-free absorption (see \ref{sec:interpretation}) ). + Also plotted are upper limits on from VLA data at the two highest [requencies., Also plotted are upper limits on from VLA data at the two highest frequencies. + The position angles of the jets in A and D were measured by fitting elliptical components io the VLBA maps withAlps. using a procedure (JAIFIT) that corrects for the ellipticity of the beam.," The position angles of the jets in A and B were measured by fitting elliptical components to the VLBA maps with, using a procedure (JMFIT) that corrects for the ellipticity of the beam." + Formodeling purposes. we adopted the average of the 1.7 Gllz and 8.4 Gllz results. giving ὧν=8° and ὁμ=—697. measured east of north.," Formodeling purposes, we adopted the average of the 1.7 GHz and 8.4 GHz results, giving $\phi_{\rm A} = 8\arcdeg$ and $\phi_{\rm B} = +-69\arcdeg$, measured east of north." + We estimate the uncertainty in each position angle to be zx15. an error range that is approximately twice the difference between the 1.7 Gllz aud 8.4 Gllz results.," We estimate the uncertainty in each position angle to be $\pm 15\arcdeg$, an error range that is approximately twice the difference between the 1.7 GHz and 8.4 GHz results." + These ranges of position angle are illustrated by dotted lines in Figs., These ranges of position angle are illustrated by dotted lines in Figs. + 2. and 3.. although it is diffieult to account for the elliptical beam in a visual inspection.," \ref{fig:vlba-18cm} and \ref{fig:vlba-3.5cm}, although it is difficult to account for the elliptical beam in a visual inspection." + The flux density ratio is nearly independent of observing Ireeuency. as should be the case for gravitationallv lensed images of a single compact source.," The flux density ratio is nearly independent of observing frequency, as should be the case for gravitationally lensed images of a single compact source." + By contrast. the flux density ratio increases significantly with frequency.," By contrast, the flux density ratio increases significantly with frequency." + This immediately suggests that C is not a third image of (he same background source., This immediately suggests that C is not a third image of the same background source. + Given that its position is consistent with the optical position of the lens galaxy. it would be natural to conclude that C represents faint radio emission [rom the lens galaxy. as discussed further in 3.1..," Given that its position is consistent with the optical position of the lens galaxy, it would be natural to conclude that C represents faint radio emission from the lens galaxy, as discussed further in \ref{subsec:emission}." + However. there are several mechanisms (hat might cause a third quasar image (to appear to have a different spectral index than the two brighter images.," However, there are several mechanisms that might cause a third quasar image to appear to have a different spectral index than the two brighter images." + These are discussed in 3.2- 3.5. The only mechanism we cannot rule out is Iree-Iree absorption 3.5))., These are discussed in \ref{subsec:variability}- \ref{subsec:propagation}.. The only mechanism we cannot rule out is free-free absorption \ref{subsec:propagation}) ). +The Princeton pulsar database Clavlor. Manchester Lyne 1993) now contains ~ SOO pulsars. 101 of whom have measured proper motions or upper limits.,"The Princeton pulsar database (Taylor, Manchester Lyne 1993) now contains $\sim$ 800 pulsars, 101 of whom have measured proper motions or upper limits." + The number of surveys responsible for this profusion is also gradually increasing in size (in excess of 15)., The number of surveys responsible for this profusion is also gradually increasing in size (in excess of 15). + To do a proper treatmen of the selection elfects for the full proper motion sample would then require modelling the selection elfects. of a significant number of these surveys., To do a proper treatment of the selection effects for the full proper motion sample would then require modelling the selection effects of a significant number of these surveys. + Luckily. we note tha most of the proper motion pulsars were detected. in the earlier. surveys.," Luckily, we note that most of the proper motion pulsars were detected in the earlier surveys." + By restricting ourselves to those. pulsars detected. in the Molonglo 2 (Manchester et al., By restricting ourselves to those pulsars detected in the Molonglo 2 (Manchester et al. + LOTS) anc Green. Bank/NRAQO 1.2 and 3 surveys (Damashek ct al.," 1978) and Green Bank/NRAO 1,2 and 3 surveys (Damashek et al." + 1978. Dewey et al.," 1978, Dewey et al." + 1985. Stokes et al.," 1985, Stokes et al." + 1985. Stokes ct al.," 1985, Stokes et al." + 1986). we are left with δ out of 101 pulsars.," 1986), we are left with 86 out of 101 pulsars." + We note that 12 of the 15 pulsars left out have P<0.1 s (and only one of our restricted. sample satisfies this criterion). which is not surprising. since many of the later surveys focussed on inding faster spinning pulsars.," We note that 12 of the 15 pulsars left out have $<0.1$ s (and only one of our restricted sample satisfies this criterion), which is not surprising, since many of the later surveys focussed on finding faster spinning pulsars." + In. performing this cut. we ose one voung pulsar and all but one of the pulsars with characteristic ages ereater than 1 Gar.," In performing this cut, we lose one young pulsar and all but one of the pulsars with characteristic ages greater than 1 Gyr." + This also means we are not alfectecl by the possibly different evolutionary uistories of millisecond. pulsars (in particular the inlluence of binaries)., This also means we are not affected by the possibly different evolutionary histories of millisecond pulsars (in particular the influence of binaries). + We shall omit the one old binary pulsar (PSR 1655|64) which does fall into our sample as well., We shall omit the one old binary pulsar (PSR 0655+64) which does fall into our sample as well. + Figure 12 shows the distribution of the included and excluded. pulsars as a function of period and velocity.," Figure \ref{select} + shows the distribution of the included and excluded pulsars as a function of period and velocity." + The observed: pulsar sample sullers from two obvious selection elfects. due to [iux limits and proper motion limits respectively.," The observed pulsar sample suffers from two obvious selection effects, due to flux limits and proper motion limits respectively." + Figure 13. shows the distribution of inferred luminosities and transverse velocities., Figure \ref{Lv} shows the distribution of inferred luminosities and transverse velocities. + The lack of faint. fast pulsars (upper left corner) and. bright. slow pulsars (lower right corner) is evident.," The lack of faint, fast pulsars (upper left corner) and bright, slow pulsars (lower right corner) is evident." + To correct for this bias. we need to weight the pulsars according to the maximum volume in which they could have been detected. Le. using a Ys weighting.," To correct for this bias, we need to weight the pulsars according to the maximum volume in which they could have been detected, i.e. using a $V_{\rm max}$ weighting." + To do this we need to consider the detection ellicieney of the various pulsar surveys., To do this we need to consider the detection efficiency of the various pulsar surveys. + After Naravan (LOST) (see also Dewey et al., After Narayan (1987) (see also Dewey et al. + 1984). the minimum Εις detectable is =54M) where Zi and Zij are the svstem and sky noise temperatures. So is the Dux normalization. anc Wis the measured pulse width.," 1984), the minimum flux detectable is =, where $ T_{\rm rec}$ and $ T_{\rm sky}$ are the system and sky noise temperatures, $ S_{\rm 0}$ is the flux normalization, and W is the measured pulse width." + WW. is the intrinsic pulse width. which is broaclened because of sampling. dispersion and scattering so that οpr qz ir... ‘Thus we calculate the minimum Ilux for a given survey in a particular direction.," $ W_{\rm e}$ is the intrinsic pulse width, which is broadened because of sampling, dispersion and scattering so that W^2 = ^2 + + + Thus we calculate the minimum flux for a given survey in a particular direction." + The parameters describing each survey were taken from Naravan and Stokes et al. (, The parameters describing each survey were taken from Narayan and Stokes et al. ( +1986).,1986). + We used the updated: electron. distribution moclel of Tavlor. and. Cordes. (1993) to calculate the dispersion and scatter broadening along a given line of sight., We used the updated electron distribution model of Taylor and Cordes (1993) to calculate the dispersion and scatter broadening along a given line of sight. + This accounts for the bias due to the flux limits., This accounts for the bias due to the flux limits. + No such simple model exists for treating the proper motion limits., No such simple model exists for treating the proper motion limits. + This is because the accuracy of a given proper motion measurement depends on the vagaries of the distribution of background radio sources near the pulsar position on the sky. (Harrison. Lyne Anderson 093).," This is because the accuracy of a given proper motion measurement depends on the vagaries of the distribution of background radio sources near the pulsar position on the sky (Harrison, Lyne Anderson 1993)." + As a crude model of this. we fit the distribution of proper motion errors in Llarrison et al.," As a crude model of this, we fit the distribution of proper motion errors in Harrison et al." + using the distribution p(i—expt.pr/10.5masvr.1.," using the distribution $\rm p(\mu) = exp(-\mu/10.5\, mas \, +yr^{-1})$." + In the Vias calculations to follow. the proper motion cutolf is randomly selected. from this distribution for each line of sight and," In the $ V_{\rm max}$ calculations to follow, the proper motion cutoff is randomly selected from this distribution for each line of sight and." + We also used. simple limits of 5 and 2 masvr| as à test of the importance of this selection elect.," We also used simple limits of 5 and 2 $\rm mas \, yr^{-1}$ as a test of the importance of this selection effect." + This introduces a variationD. of⋅ ~l0kmsn in the mean velocity. of. the voung sample anc about 30knis in the old sample. indicating that most of the Έα are Hux-limited rather than proper motion limited.," This introduces a variation of $\sim \rm 10 \, km \, s^{-1}$ in the mean velocity of the young sample and about $30 \rm \, km \, s^{-1}$ in the old sample, indicating that most of the $ +V_{max}$ are flux-limited rather than proper motion limited." + Lben ancl Tutukov. (1996) have also taken account of this selection elfect., Iben and Tutukov (1996) have also taken account of this selection effect. + For each pulsar. we randomly place it in cdilferent directions and at dilferent distances with respect το the observer and caleulate whether or not it would be detectable with its known luminosity ancl transverse velocity (uncorrected for the local standard of rest) in any of the surveys we consider.," For each pulsar, we randomly place it in different directions and at different distances with respect to the observer and calculate whether or not it would be detectable with it's known luminosity and transverse velocity (uncorrected for the local standard of rest) in any of the surveys we consider." + Phus. using this Monte. Carlo integration procedure. we determine the volume within which each pulsar could. have been detected.," Thus, using this Monte Carlo integration procedure, we determine the volume within which each pulsar could have been detected." + These Vises values determine the relative weights of cach of the pulsars in the corrected sample., These $V_{\rm max}$ values determine the relative weights of each of the pulsars in the corrected sample. + A possible source of concern with this procedure is illastratecd by Figure I4.., A possible source of concern with this procedure is illustrated by Figure \ref{Slim}. + Phe analytic Dux limits do not describe the complications of the true detection. limits perfectly (interstellar scintillation makes the apparent Εαν vary)., The analytic flux limits do not describe the complications of the true detection limits perfectly (interstellar scintillation makes the apparent flux vary). + In Figure 14. we find. four pulsars detected. by the AMolonelo survey that lic below the analytically describe detection. threshold. for that survey., In Figure \ref{Slim} we find four pulsars detected by the Molonglo survey that lie below the analytically described detection threshold for that survey. + This. will reduce. the weight accorded to these pulsars., This will reduce the weight accorded to these pulsars. + To estimate the impact of this error on our results. we repeated the analysis with these pulsars artificially ‘brightened to meet the Dux Timit expression.," To estimate the impact of this error on our results, we repeated the analysis with these pulsars artificially `brightened' to meet the flux limit expression." + The mean proper motion we infer for the voung pulsar sample increases hy only 7 kms.J|. so this is not à significant source of error for our analysis here.," The mean proper motion we infer for the young pulsar sample increases by only 7 $\rm km \, s^{-1}$, so this is not a significant source of error for our analysis here." + The Vias Correction is not without biases of its own., The $V_{\rm max}$ correction is not without biases of its own. + In particular. weighting pulsars by their Vis presupposes hat the real population is distributed uniformly throughout he ealactic volume.," In particular, weighting pulsars by their $V_{\rm max}$ presupposes that the real population is distributed uniformly throughout the galactic volume." + However. the pulsars are born [rom a disk population with a scale height of about 150-450 xc (Naravan and Ostriker 1990).," However, the pulsars are born from a disk population with a scale height of about 150-450 pc (Narayan and Ostriker 1990)." + Thus. à population born with small velocities will not expand to fill as much of the spherical volume as a fast population.," Thus, a population born with small velocities will not expand to fill as much of the spherical volume as a fast population." + The above analysishen overcorrects [or the slow pulsars (see Lelfancl and ‘Tacemaru 1977: Cordes 1986: Lyne Lorimer 1994)., The above analysisthen overcorrects for the slow pulsars (see Helfand and Tademaru 1977; Cordes 1986; Lyne Lorimer 1994). + In, In +the basis of the scintillation time scales and the time delavs between (he scintillation flix variations as seen by two widely separated radio telescopes.,the basis of the scintillation time scales and the time delays between the scintillation flux variations as seen by two widely separated radio telescopes. + Our analvsis confirms ancl places more sliingent constraints on Che distances to the scattering screens., Our analysis confirms and places more stringent constraints on the distances to the scattering screens. + For example. place the scattering screen toward B1257326 within 10 pc of the Sun. and we argue (hat it is located within 6.7 pe.," For example, \citet{Bignall2006} place the scattering screen toward B1257–326 within 10 pc of the Sun, and we argue that it is located within 6.7 pc." + Dennett-Thorpe&deBruyn(2003) argue that the scaltering screen lor J18194-385 is located between 1 and 12 pe from the Sun. and present (wo models (hat fit their data with the scattering screen located al 2.820.3 pe or 2.02:0.3 pc.," \citet{Dennett2003} + argue that the scattering screen for J1819+385 is located between 1 and 12 pc from the Sun, and \citet{Macquart2007} present two models that fit their data with the scattering screen located at $3.8\pm 0.3$ pc or $2.0\pm 0.3$ pc." + We argue that (he screen toward this source is located at the edee of the Mic cloud within 5.1 pe of the Sun., We argue that the screen toward this source is located at the edge of the Mic cloud within 5.1 pc of the Sun. + If the Mic cloud is indeed compressed aud heated by the LIC and G clouds. then the scattering sereen in (he Mic cloud is located much closer to the Sun than 5.1 pe.," If the Mic cloud is indeed compressed and heated by the LIC and G clouds, then the scattering screen in the Mic cloud is located much closer to the Sun than 5.1 pc." + The scattering screen toward DI519273 near the edge of the G cloud is likely closer than 3 pe from the Sun., The scattering screen toward B1519–273 near the edge of the G cloud is likely closer than 3 pc from the Sun. + An important result is that for each source. the line of sight to the quasar passes through or very near (o at least (wo warm clouds.," An important result is that for each source, the line of sight to the quasar passes through or very near to at least two warm clouds." + Although we know only upper limits to the distances to most of these clouds. (μον are all nearby ancl could interact.," Although we know only upper limits to the distances to most of these clouds, they are all nearby and could interact." + For example. interaction of the LIC and G clouds is likely responsible for the shape and high temperature of the Mic cloud.," For example, interaction of the LIC and G clouds is likely responsible for the shape and high temperature of the Mic cloud." + Since tvpical velocity differences between. clouds along (he three lines of sieht are 1020!|.. the interactions could easily produce turbulence that would be responsible for the scintillation.," Since typical velocity differences between clouds along the three lines of sight are 10–20, the interactions could easily produce turbulence that would be responsible for the scintillation." + Also. cloud edges are regions of high ionization because of the absence ol shielding from the strong UV radiation from hot stars and white dwarls.," Also, cloud edges are regions of high ionization because of the absence of shielding from the strong UV radiation from hot stars and white dwarfs." + Figure 2. shows areas on the sky where the velocity differences between clouds along the line of sight are large aud where cloud-cloud interactions could produce turbulence., Figure \ref{fig:fig2} shows areas on the sky where the velocity differences between clouds along the line of sight are large and where cloud-cloud interactions could produce turbulence. + We predict that these are regions Where large aunplitude IDV sources will be discovered., We predict that these are regions where large amplitude IDV sources will be discovered. + Two examples (hat deserve further study are the two IDV sources located in the southern hemisphere (PINS 0405385 and PSR. JO4374715) that are plotted in Figure 2. but are not analvzed in this paper as hieh quality ISS data are not vet published., Two examples that deserve further study are the two IDV sources located in the southern hemisphere (PKS 0405–385 and PSR J0437–4715) that are plotted in Figure \ref{fig:fig2} but are not analyzed in this paper as high quality ISS data are not yet published. + We thank Dr. Havlev Dignall [ον providing the data on PISS D1257-326 that we have analvzed in this paper., We thank Dr. Hayley Bignall for providing the data on PKS B1257-326 that we have analyzed in this paper. + We also than Dr. Jean-Pierre Macquart lor discussions on this topic and (he referee for his verv useful suggestions., We also than Dr. Jean-Pierre Macquart for discussions on this topic and the referee for his very useful suggestions. + SR. would like to acknowledge support provided by NASA through Ilubble Fellowship grant IIST-IIE-01190.01. awarded. by the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. Inc.. for NASA. under contract NAS 5-26555.," S.R. would like to acknowledge support provided by NASA through Hubble Fellowship grant HST-HF-01190.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555." +Chromospheric-coronal activity is ubiquitous m cool stars possessing subphotospheric convection zones.,Chromospheric-coronal activity is ubiquitous in cool stars possessing subphotospheric convection zones. + Hot coronas result in existence of thermal winds carrying away stellar mass and angular momentum., Hot coronas result in existence of thermal winds carrying away stellar mass and angular momentum. + The precise knowledge of the mass loss rate (MLR) during the stellar life is of crucial importance for modeling evolution of mass. luminosity and rotation of single stars and of orbital parameters of close binary stars.," The precise knowledge of the mass loss rate (MLR) during the stellar life is of crucial importance for modeling evolution of mass, luminosity and rotation of single stars and of orbital parameters of close binary stars." + Mass loss of a central star of a planetary system may also influence evolution of physical parameters of orbiting planets., Mass loss of a central star of a planetary system may also influence evolution of physical parameters of orbiting planets. + Proximity of the Sun made possible direct measurements of solar wind with the use of interplanetary probes., Proximity of the Sun made possible direct measurements of solar wind with the use of interplanetary probes. + The average velocity of the wind near the Earth orbit is of the order of 400 km s! and the average MLR is 2x107 Ma/yr with uncertainty of some 50 (Feldman et al.," The average velocity of the wind near the Earth orbit is of the order of 400 km $^{-1}$ and the average MLR is $2\times 10^{-14} +M_{\sun}$ /yr with uncertainty of some 50 (Feldman et al." + 1977)., 1977). +" The expected MLRs for other cool dwarfs may differ from that at most by a couple of orders of magnitude but even the highest MLRs of such stars are far lower than those occurring in hot. early type stars or red giants,"," The expected MLRs for other cool dwarfs may differ from that at most by a couple of orders of magnitude but even the highest MLRs of such stars are far lower than those occurring in hot, early type stars or red giants." + The present observational capabilities are still insufficient to obtain the data for other dwarfs with comparable to the solar case accuracy., The present observational capabilities are still insufficient to obtain the data for other dwarfs with comparable to the solar case accuracy. + For many years only indirect methods of MLR estimate of such stars existed., For many years only indirect methods of MLR estimate of such stars existed. + Analyzing the infrared and radio observations of M dwarfs Mullan et al. (, Analyzing the infrared and radio observations of M dwarfs Mullan et al. ( +1992) obtained a value of 107 Moj/yr as an upper limit for MLR of these stars.,1992) obtained a value of $10^{-10} M_{\sun}$ /yr as an upper limit for MLR of these stars. + Later. van den Oord Doyle (1997) revised that limit dow1 to 107 Mce/yr.," Later, van den Oord Doyle (1997) revised that limit down to $10^{-12} M_{\sun}$ /yr." + A similar value was obtained by Lim White (1996)., A similar value was obtained by Lim White (1996). + Wargelin Drake (2002) obtained an upper limit of 3x107 Mayr for Cen., Wargelin Drake (2002) obtained an upper limit of $3\times 10^{-13} M_{\sun}$ /yr for Cen. +" In the recent years Wood and coworkers published a number of papers in which they analyzed profiles of L, arising at the collisional front betwee! stellar wind and interstellar matter.", In the recent years Wood and coworkers published a number of papers in which they analyzed profiles of $_{\alpha}$ arising at the collisional front between stellar wind and interstellar matter. + By modeling the collisior process the authors were able to measure MLRs for a dozer stars (Wood et al., By modeling the collision process the authors were able to measure MLRs for a dozen stars (Wood et al. + 2002. 2005).," 2002, 2005)." + The measured rates extend from 2x107 Mojvr for 70 Oph down to 3x107 Ma/yr for DK UMa., The measured rates extend from $2\times 10^{-12} M_{\sun}$ /yr for 70 Oph down to $3\times 10^{-15} M_{\sun}$ /yr for DK UMa. + The authors derived a relation between MLR and age (or X-ray flux)., The authors derived a relation between MLR and age (or X-ray flux). + Their latest results give Mo£77 for t>0.7 Gyr but observations of younger. more active stars suggest a sudden drop of MLR from about 2x107 to ~ 107Myr. e. by more than an order of magnitude.," Their latest results give $\dot M \propto t^{-2.33}$ for $t \ge 0.7$ Gyr but observations of younger, more active stars suggest a sudden drop of MLR from about $2\times +10^{-12}$ to $\sim 10^{-13} M_{\sun}$ /yr, e. by more than an order of magnitude." + This unexpected result is based on seanty data and needs confirmation., This unexpected result is based on scanty data and needs confirmation. + A different. indirect method of estimation an amount of mass lost by the Sun during its past life was suggested by Sackmann Boothroyd (2003).," A different, indirect method of estimation an amount of mass lost by the Sun during its past life was suggested by Sackmann Boothroyd (2003)." + Based on the geological evidence that the terrestrial atmosphere was warm in early life of the Solar System and liquid water was present on Mars. they calculated the minimum initial mass of the Sun needed to produce enough luminosity. for the initial mass of 1.07 Me and MLR decreasing exponentially with time.," Based on the geological evidence that the terrestrial atmosphere was warm in early life of the Solar System and liquid water was present on Mars, they calculated the minimum initial mass of the Sun needed to produce enough luminosity, for the initial mass of 1.07 $M_{\sun}$ and MLR decreasing exponentially with time." + Here we another method of measuring the total amount of mass lost during the stellar life., Here we another method of measuring the total amount of mass lost during the stellar life. + It is based on the analysis of the stellar mass distribution in an open cluster., It is based on the analysis of the stellar mass distribution in an open cluster. + The next section describes details of the method., The next section describes details of the method. + The last section contains discussion of the results and conclusions., The last section contains discussion of the results and conclusions. +" The total energy flux carried away with the stellar wind. Fi. consists of three components (Holzer 1987) where F4, is the energy flux needed to carry the wind matter out of the potential well of the star. Εις 1s the kinetic energy flux of the wind in infinity and F4 is the flux radiated away by the wind."," The total energy flux carried away with the stellar wind, $F_{\mathrm{tot}}$, consists of three components (Holzer 1987) where $F_{\mathrm{grav}}$ is the energy flux needed to carry the wind matter out of the potential well of the star, $F_{\infty}$ is the kinetic energy flux of the wind in infinity and $F_{\mathrm{rad}}$ is the flux radiated away by the wind." + Based on observations of the solar wind Fu can be neglected., Based on observations of the solar wind $F_{\mathrm{rad}}$ can be neglected. +" We thus obtain where v4, is the escape velocity from the stellar surface and va Is the wind velocity in infinity.", We thus obtain where $v_{\mathrm{esc}}$ is the escape velocity from the stellar surface and $v_{\infty}$ is the wind velocity in infinity. + The last approximate equality results from the assumption that both velocities are of the same order., The last approximate equality results from the assumption that both velocities are of the same order. +" With v,=(9GM/R)7. where G is gravitational constant. and M and R are stellar mass and radius. respectively. we have The ultimate source of energy for thermal winds in cool stars is stellar luminosity which drives convection and. via a chain of physical processes. makes a magnetized wind to blow."," With $v_{\mathrm{esc}} = (2GM/R)^{1/2}$, where $G$ is gravitational constant, and $M$ and $R$ are stellar mass and radius, respectively, we have The ultimate source of energy for thermal winds in cool stars is stellar luminosity which drives convection and, via a chain of physical processes, makes a magnetized wind to blow." + Rotational energy. albeit necessary for magnetic field," Rotational energy, albeit necessary for magnetic field" +accretors 1n refsecinmplications..,accretors in \\ref{sec:implications}. + We performed high-time-resolution optical cdiffercutial photometry at D and at ©. using the l-aueter Nickel telescope at Lick Observatory between 1997 and 2000.," We performed high-time-resolution optical differential photometry at $B$ and at $U$, using the 1-meter Nickel telescope at Lick Observatory between 1997 and 2000." + Iu this paper. we focus ou observations from around the time of the 1997 radio jet.," In this paper, we focus on observations from around the time of the 1997 radio jet." + In addition. P. Derliud. AL Calkius. and several other observers acquired low-resolution optical spectra of CTL Cyeui with FAST. a lüeh throughput. slit spectrograph mounted at the Fred L. Whipple Observatory 1.5au telescope on Mount IHopkius. Arizona (Fabricantetal.1998).," In addition, P. Berlind, M. Calkins, and several other observers acquired low-resolution optical spectra of CH Cygni with FAST, a high throughput, slit spectrograph mounted at the Fred L. Whipple Observatory 1.5-m telescope on Mount Hopkins, Arizona \citep{fab98}." +. See Sokoloski. Bildsten. IIo 2001 for description of photometric observing technique and iustimments. aud paper II for details of the CTI Οτο data analysis.," See Sokoloski, Bildsten, Ho 2001 for description of photometric observing technique and instruments, and paper II for details of the CH Cyg data analysis." + Example ligh-time-resolution light curves from 1997 and 1998 are shown in Fiewre 1., Example high-time-resolution light curves from 1997 and 1998 are shown in Figure \ref{fig:alllcs}. + The first two observations. from L997 April aud June. show low-amplitude (Am<0.15 imag) smooth variations. and have power spectra that generally cannot be fit with power-law models (similar light curves were reported bv Rodgersetal.(L997) as carly as 1996 June)," The first two observations, from 1997 April and June, show low-amplitude $\Delta m < 0.15$ mag), smooth variations, and have power spectra that generally cannot be fit with power-law models (similar light curves were reported by \cite{rod97} + as early as 1996 June)." + A few mouths later. in L997 August. the fractional flickering aüuplitude had not changed. but the streneth of the fastest (aninute-tinie-scale) variations increased.," A few months later, in 1997 August, the fractional flickering amplitude had not changed, but the strength of the fastest (minute-time-scale) variations increased." + The lelt curve then had a more jJagged appearance., The light curve then had a more jagged appearance. +" The power spectruu of this observation had the staudard power-law shape fouud in non-magnetic CVs,", The power spectrum of this observation had the standard power-law shape found in non-magnetic CVs. + One vear later. in 1998 July and Aueust. the variability amplitude increased to the typical hieli-state value of Am~0.5 mag while the power spectrum retained its power-law shape.," One year later, in 1998 July and August, the variability amplitude increased to the typical high-state value of $\Delta m \sim +0.5$ mag while the power spectrum retained its power-law shape." + Figure 2 compares a power spectrum frou the post-jet period when oulv sinooth variations were seen with a power spectrum from a few inouths later. when mnünute-tine-sceale variations returned.," Figure \ref{fig:pdss} compares a power spectrum from the post-jet period when only smooth variations were seen with a power spectrum from a few months later, when minute-time-scale variations returned." + Based ou the radio observations reported by Ikarovskaetal. (1998).. CID Cyeui began producing a radio jet sometime before 1997 January. when they first detected extended radio cussion.," Based on the radio observations reported by \cite{kar98}, CH Cygni began producing a radio jet sometime before 1997 January, when they first detected extended radio emission." + The radio fux density began to rise in 1997 April. at the same time as we started our plotometric observing campaign.," The radio flux density began to rise in 1997 April, at the same time as we started our photometric observing campaign." + Radio extension associated with the radio brightening was later confirmed by Rarovska (private communication): Evresetal.(2002) discuss the mass outflow from CT Cvenui diving aud after 1998., Radio extension associated with the radio brightening was later confirmed by Karovska (private communication); \cite{eyres02} discuss the mass outflow from CH Cygni during and after 1998. + Fieure 1 shows the loug-toxiu optical light curve of CTL ονο Usindly provided by the AAVSO). with the times of our fast photometric observations marked. aud the carly development of the radio jet at 22 GIIz al. 1998).," Figure \ref{fig:jet} shows the long-term optical light curve of CH Cygni (kindly provided by the AAVSO), with the times of our fast photometric observations marked, and the early development of the radio jet at 22 GHz \citep{kar98}." +. We cau estimate the speed of the jet material. aud hence the approximate time when the material was expelled. if we assune that the radio cloueation measured in 1999," We can estimate the speed of the jet material, and hence the approximate time when the material was expelled, if we assume that the radio elongation measured in 1999" +Sect.,Sect. + 7., 7. + All the light curves in our catalogue are presented in the Appendix., All the light curves in our catalogue are presented in the Appendix. + The WeCAPP project (7) was a dedicated survey to search for microlensing events towards our neighboring galaxy M31., The WeCAPP project \citep{2001A+A...379..362R} was a dedicated survey to search for microlensing events towards our neighboring galaxy M31. +" We continuously monitored the bulge of M31 (when it was visible, when the weather was cooperative and when there was an observer) between September 1997 and March 2008 using the 0.8 m telescope of the Wendelstein Observatory located in the Bavarian Alps."," We continuously monitored the bulge of M31 (when it was visible, when the weather was cooperative and when there was an observer) between September 1997 and March 2008 using the 0.8 m telescope of the Wendelstein Observatory located in the Bavarian Alps." + The data was taken optimally on a daily basis in both and filters with a field of view of 8/3 x 8/3., The data was taken optimally on a daily basis in both and filters with a field of view of $\farcm$ 3 $\times$ $\farcm$ 3. + From June 1999 to February 2002 we further extended our observations with the 1.23 m (17/2 x 17/2 FOV) telescope of the Calar Alto Observatory in Spain., From June 1999 to February 2002 we further extended our observations with the 1.23 m $\farcm$ 2 $\times$ $\farcm$ 2 FOV) telescope of the Calar Alto Observatory in Spain. + After 2002 we use the Wendelstein telescope solely to mosaic the full Calar Alto field of view with four pointings., After 2002 we use the Wendelstein telescope solely to mosaic the full Calar Alto field of view with four pointings. + The position of these four pointing are indicated in Fig. 1.., The position of these four pointing are indicated in Fig. \ref{fig.m31_farbig}. +" The data volume and quality of the four pointings (F1, F2, F3, F4) drastically differs during the 11 seasons."," The data volume and quality of the four pointings (F1, F2, F3, F4) drastically differs during the 11 seasons." + list of the number of nights observed in each season is shownA in Table 2.., A list of the number of nights observed in each season is shown in Table \ref{tab.nights}. + A detailed overview of the observaions can be found in ? and Riffeser et., A detailed overview of the observaions can be found in \cite{2006A+A...445..423F} and Riffeser et. + al. (, al. ( +in prep.).,in prep.). +" 'To quantify a realistic time sampling of the survey we define “good quality data points"" as data points with PSF fluxes with an error below 0.4x10~5Jy."," To quantify a realistic time sampling of the survey we define “good quality data points” as data points with PSF fluxes with an error below $0.4 + \times 10^{-5}\mathrm{Jy}$." + In Fig., In Fig. + 2 we show for every night the fractional area of pixels with errors below this limit., \ref{fig.lownoise_sampling} we show for every night the fractional area of pixels with errors below this limit. + indicates we have no observations during the night., indicates we have no observations during the night. + Fig., Fig. + 3 shows the spatial variation of the fraction of all data with flux errors below the flux error limit averaged over 11 seasons., \ref{fig.lownoise} shows the spatial variation of the fraction of all data with flux errors below the flux error limit averaged over 11 seasons. +" It demonstrates that we expect most of our novae in field F1 and fewer in the fields F2, F3, and F4."," It demonstrates that we expect most of our novae in field F1 and fewer in the fields F2, F3, and F4." + The field F1 was observed much more frequently than the other one because it is the subfield with highest lensing probability., The field F1 was observed much more frequently than the other one because it is the subfield with highest lensing probability. +" The data was then reduced by our customized pipeline MUPIPE (see ?), which performs CCD reduction, position alignment, photometric alignment, frame stacking and difference imaging following the algorithm of ?.."," The data was then reduced by our customized pipeline MUPIPE \citep[see ][]{2002A+A...381.1095G}, which performs CCD reduction, position alignment, photometric alignment, frame stacking and difference imaging following the algorithm of \cite{1998ApJ...503..325A}." +" After the difference imaging, we perform PSF photometry on each pixel as follows."," After the difference imaging, we perform PSF photometry on each pixel as follows." +" First, we extracted the PSF from several isolated, bright and unsaturated reference stars."," First, we extracted the PSF from several isolated, bright and unsaturated reference stars." + Then we fit this PSF to all variable sources., Then we fit this PSF to all variable sources. +" Finally, we integrate the count rates over the area of the PSF to determine the flux of the source."," Finally, we integrate the count rates over the area of the PSF to determine the flux of the source." + The results of the project are presented in ?? and partially contributed to ?..," The results of the project are presented in \cite{2003ApJ...599L..17R, 2008ApJ...684.1093R} and partially contributed to \cite{2010ApJ...717..987C}." +" In addition to the original microlensing targets, the intensive observations in two bands also yields more than 20,000 variables in the bulge of M31 (?) and the nova candidates presented in this paper."," In addition to the original microlensing targets, the intensive observations in two bands also yields more than 20,000 variables in the bulge of M31 \citep{2006A+A...445..423F} and the nova candidates presented in this paper." +This behaviour can be understood. by considering the corresponding numerical divergence of the magnetic field.,This behaviour can be understood by considering the corresponding numerical divergence of the magnetic field. + Fig., Fig. + 15. shows -[VB[/|B| as a function of time for all simulations., \ref{DIVBwithtime} shows $h\cdot|\nabla\cdot\textbf{B}|/|\textbf{B}|$ as a function of time for all simulations. + In all cases. the growth of -|VB|/|DB| behaves similar to the amplification of the total magnetic field. i.e. the higher the divergence. the stronger the amplification of the Ποια.," In all cases, the growth of $h\cdot|\nabla\cdot\textbf{B}|/|\textbf{B}|$ behaves similar to the amplification of the total magnetic field, i.e. the higher the divergence, the stronger the amplification of the field." + Thoush the numerical divergence in the simulation using IZuler potentials (black) is higher than in the simulation with a smoothing interval of 5. timesteps (ereen). its value does not directly correlate with the field erowth.," Though the numerical divergence in the simulation using Euler potentials (black) is higher than in the simulation with a smoothing interval of 5 timesteps (green), its value does not directly correlate with the field growth." + That is because the (defective) magnetic field itself is not used for calculating the magnetic. field: evolution within the Euler potential formalism as is the case for the direct magnetic field description (compare eqs., That is because the (defective) magnetic field itself is not used for calculating the magnetic field evolution within the Euler potential formalism as is the case for the direct magnetic field description (compare eqs. + 17 and 18))., \ref{IndEqsSPH} and \ref{euler}) ). + Using the smoothing scheme lowers the divergence (in case of smoothing every 5 timesteps even below the numerical divergence of the Euler potential formalism) and lowers also the field: amplification. leading (if applied. not. too. often) to an amplification of the total field much more similar to that using the Euler potentials. which are free [rom divergence by construction.," Using the smoothing scheme lowers the divergence (in case of smoothing every 5 timesteps even below the numerical divergence of the Euler potential formalism) and lowers also the field amplification, leading (if applied not too often) to an amplification of the total field much more similar to that using the Euler potentials, which are free from divergence by construction." + Interestingly. for simulations applving the viscosity. limiter suggested by 2.. the magnetic field: amplification using the direct magnetic field description is in both codes much higher than without applying this limiter (orange lines in Figs.," Interestingly, for simulations applying the viscosity limiter suggested by \cite{Balsara1995}, the magnetic field amplification using the direct magnetic field description is in both codes much higher than without applying this limiter (orange lines in Figs." + 13 and 14))., \ref{Bwithr} and \ref{Bwithtime}) ). + The reason for this higher amplification is the higher velocity dispersion in these simulations., The reason for this higher amplification is the higher velocity dispersion in these simulations. + The viscosity limiter lowers the viscosity in regions of strong shear Hows. thus suppressing velocity diffusion and Leading to higher velocity gradients.," The viscosity limiter lowers the viscosity in regions of strong shear flows, thus suppressing velocity diffusion and leading to higher velocity gradients." + Consistently. also the numerical divergence of the magnetic field is higher (and considerably higher than the unavoidable value of approximately. one) in these simulations (orange lines in Figs.," Consistently, also the numerical divergence of the magnetic field is higher (and considerably higher than the “unavoidable” value of approximately one) in these simulations (orange lines in Figs." + 10. and. 15))., \ref{divergence_radius} and \ref{DIVBwithtime}) ). + Applving the viscosity limiter in simulations using Euler potentials. however. does not change the evolution of the magnetic field significantly (not shown).," Applying the viscosity limiter in simulations using Euler potentials, however, does not change the evolution of the magnetic field significantly (not shown)." + Vherefore. again. itis probable that the higher numerical V-B terms lead via the induction equation (eq. 3))," Therefore, again, it is probable that the higher numerical $\nabla\cdot \mathbf{B}$ terms lead via the induction equation (eq. \ref{induktionsglg}) )" + to an enhanced magnetic ficld growth., to an enhanced magnetic field growth. +"In Fig. 3,","In Fig. \ref{fig_2}," + we plot Lpoiacn against our adopted Manu estimates (the associated 1-σ errors for Mpy measurements are described in section 3) for the 17 AGNs in our volume-limited sample.," we plot $L_{\rm Bol,AGN}$ against our adopted $\Mbh$ estimates (the associated $\sigma$ errors for $\Mbh$ measurements are described in section 3) for the 17 AGNs in our volume-limited sample." +" Lgoi,acn is inferred from either accurate intrinsic high-quality hard X-ray (2-10 keV) constraints (where available) or AGN-produced [OIV] 425.80um emission (see 844.1 and 4.2)."," $L_{\rm Bol,AGN}$ is inferred from either accurate intrinsic high-quality hard X-ray (2–10 keV) constraints (where available) or AGN-produced [OIV] $\lambda 25.80 \um$ emission (see 4.1 and 4.2)." +" The Lgoi,acn 1-o errors for the sources with hard X-ray constraints are the result of combining the uncertainty in the Lx,»10κεν measurement with that of the mean spread in the bolometric correction factor employed from ?.."," The $L_{\rm Bol,AGN}$ $\sigma$ errors for the sources with hard X-ray constraints are the result of combining the uncertainty in the $L_{X,2-10keV}$ measurement with that of the mean spread in the bolometric correction factor employed from \citet{marconi04}." +" For those AGNs with Lmo,AGN derived from Lyorv;, the error is derived from the uncertainty in as quoted in GAOY combined in quadrature with the Ljorvjintrinsic scatter of the empirical [OIV]—Lpoi,acn relation (equation 4)."," For those AGNs with $L_{\rm Bol,AGN}$ derived from $L_{\rm [OIV]}$, the error is derived from the uncertainty in $L_{\rm + [OIV]}$ as quoted in GA09 combined in quadrature with the intrinsic scatter of the empirical $L_{\rm bol,AGN}$ relation (equation 4)." +was instead conducted.,was instead conducted. + Eq., Eq. +" 3 was fit (allowing freedom of a and b which minimised xy?) and transformed back into normal space, giving a function of the form shown in Eq. 4.."," \ref{eq:logf} was fit (allowing freedom of $a$ and $b$ which minimised $\chi^2$ ) and transformed back into normal space, giving a function of the form shown in Eq. \ref{eq:flam}." + where a describes the wavelength power index (approximately 4) while b serves as a scale for the pattern., where $a$ describes the wavelength power index (approximately 4) while $b$ serves as a scale for the pattern. +" Significant differences in the parameters which minimised x? were apparent - for example, ae3.9, bez6.66 provides a good fit for a T = 3500 K, log(g) = 4.5 and [M/H] = 0.0 model spectrum while a=4.03, b=6.94 provides a good fit for a model spectrum with the same parameters."," Significant differences in the parameters which minimised $\chi^2$ were apparent - for example, $a \approx 3.9$, $b \approx 6.66$ provides a good fit for a T = 3500 K, log(g) = 4.5 and [M/H] = 0.0 model spectrum while $a \approx 4.03$, $b \approx 6.94$ provides a good fit for a model spectrum with the same parameters." +" For each model spectrum, such a fit was performed, the spectrum extrapolated out to 24 um and 70 um and the flux integrated over the corresponding Spitzer MIPS passbands which are sensitive to dust emission at 1 AU and outside 10 AU from a solar-like star respectively (?))."," For each model spectrum, such a fit was performed, the spectrum extrapolated out to $24$ $\mu$ m and $70$ $\mu$ m and the flux integrated over the corresponding Spitzer MIPS passbands which are sensitive to dust emission at 1 AU and outside 10 AU from a solar-like star respectively \cite{rieke_multiband_2004}) )." +" For each set of andMARCS or model spectra identical in stellar parameters, the broadband fluxes of these passbands were compared."," For each set of and or model spectra identical in stellar parameters, the broadband fluxes of these passbands were compared." + Fig., Fig. + 3 displays a ratio of these fluxes for each set of synthetic spectra.," \ref{fig:compspitz} + displays a ratio of these fluxes for each set of synthetic spectra." + Kurucz model spectra do not extend to the cooler effective temperatures of M dwarfs and therefore Marcs and NextGen model spectraare also compared in this way to determine the possible differences in flux prediction for such objects., Kurucz model spectra do not extend to the cooler effective temperatures of M dwarfs and therefore Marcs and NextGen model spectraare also compared in this way to determine the possible differences in flux prediction for such objects. +" At 24 um, the extrapolated fluxes ofKURUCZ and model spectra exhibit good agreement (of approximately 2 %)) for F, G and early K spectral types."," At $24$ $\mu$ m, the extrapolated fluxes of and model spectra exhibit good agreement (of approximately 2 ) for F, G and early K spectral types." +"The trend deviates significantly from unity for cooler late K and early M spectral types with disagreement as high as 15 in and spectra of 3500 K. At 70 um, the flux ratio of andMARCS model spectra is identical to that of 24 wm though it has a larger deviation from unity (approximately 5%)).","The trend deviates significantly from unity for cooler late K and early M spectral types with disagreement as high as $15$ in and spectra of 3500 K. At $70$ $\mu$ m, the flux ratio of and model spectra is identical to that of $24$ $\mu$ m though it has a larger deviation from unity (approximately $5$ )." + This suggests that the long wavelength regions of and synthetic spectra differ in slope and therefore their log-log straight line fits (Eq. 3)), This suggests that the long wavelength regions of and synthetic spectra differ in slope and therefore their log-log straight line fits (Eq. \ref{eq:logf}) ) + diverge with wavelength., diverge with wavelength. +" In comparison, the trend exhibits a higher level of agreement which is consistent with Fig. 2."," In comparison, the trend exhibits a higher level of agreement which is consistent with Fig. \ref{fig:kurng}." +" At 24 um, the flux ratio almost perfectly centres on unity with large disagreement only apparent in the comparison of early M dwarfs."," At $24$ $\mu$ m, the flux ratio almost perfectly centres on unity with large disagreement only apparent in the comparison of early M dwarfs." +" At 70 um, a small deviation from unity is apparent though agreement is still true within 3 for F, G and K spectral types."," At $70$ $\mu$ m, a small deviation from unity is apparent though agreement is still true within $3$ for F, G and K spectral types." +" Similarly,MARCS and model spectra of F, G and K spectral types exhibit good agreement (of approximately 4 %)) at 24 ym, deviating to approximately 8 at 70 um. Again, M dwarfs exhibit the worst agreement with differences as large as 20%."," Similarly, and model spectra of F, G and K spectral types exhibit good agreement (of approximately 4 ) at $24$ $\mu$ m, deviating to approximately $8$ at $70$ $\mu$ m. Again, M dwarfs exhibit the worst agreement with differences as large as $20$." +". The poor agreement of M dwarf model spectra likely arises from the challenges in determining the opacity-relevant effects of molecular species present in such atmospheres (?,, ?,, see also section 2.2 of ?))."," The poor agreement of M dwarf model spectra likely arises from the challenges in determining the opacity-relevant effects of molecular species present in such atmospheres \cite{gustafmols}, \cite{jorgensen03}, see also section 2.2 of \cite{hellinglucas}) )." + Observational studies have noted discrepancies between the observed and synthetic colours of such objects (?))., Observational studies have noted discrepancies between the observed and synthetic colours of such objects \cite{gautier_far-infrared_2007}) ). + 'The possible impact in the use of different model groups in flux prediction of disk observations has so far only been inferred from comparison of the model spectra., The possible impact in the use of different model groups in flux prediction of disk observations has so far only been inferred from comparison of the model spectra. + It is therefore ideal to physically apply using all three model spectra to a set of observations., It is therefore ideal to physically apply using all three model spectra to a set of observations. + A recent publication (?)) analysed the Spitzer MIPS 24 um observations of approximately 70 stars in the Pleiades cluster., A recent publication \cite{sierchio10}) ) analysed the Spitzer MIPS $24$ $\mu$ m observations of approximately 70 stars in the Pleiades cluster. +" UsingKURUCZ model spectra for prediction of the stellar flux at 24 wm, they concluded that 23 of such stars harboured disks."," Using model spectra for prediction of the stellar flux at $24$ $\mu$ m, they concluded that 23 of such stars harboured disks." +" Using a smaller subset of their target sample (due to limitations in the available photometry) this study was reproduced usingKURUCZ, and model spectra."," Using a smaller subset of their target sample (due to limitations in the available photometry) this study was reproduced using, and model spectra." +" Johnson B,V, R, I and 2MASS J, H, Ks photometry of each object was compiled where possible."," Johnson B,V, R, I and 2MASS J, H, Ks photometry of each object was compiled where possible." + Synthetic photometry of all spectra of all three model groups was, Synthetic photometry of all spectra of all three model groups was +abundances between dwarfs and giants of ~0.2 dex for 47 'Tuc.,abundances between dwarfs and giants of $\sim$ 0.2 dex for 47 Tuc. +" A similar offset can be obtained also for NGC 6397, when comparing Na abundances for dwarfs from Lind et al. ("," A similar offset can be obtained also for NGC 6397, when comparing Na abundances for dwarfs from Lind et al. (" +2009) and for giants from Carretta et al. (,2009) and for giants from Carretta et al. ( +2009b).,2009b). +" We investigated the nature of this offset, concluding that it is due to the adopted set of lines, with the doublets 5682— 5688 aand 6154—6160 ((used in Carretta et al.)"," We investigated the nature of this offset, concluding that it is due to the adopted set of lines, with the doublets $-$ 5688 and $-$ 6160 (used in Carretta et al.)" + yielding always higher abundances than the 8183-8194 ffeatures (employed for dwarfs)., yielding always higher abundances than the 8183-8194 features (employed for dwarfs). +" We, in fact, detected the same effect in the Sun (with the same A(Na)~ 0.2 dex)."," We, in fact, detected the same effect in the Sun (with the same $\Delta$ $\sim$ 0.2 dex)." + We propose that the way damping wings are treated is responsible for the observed difference., We propose that the way damping wings are treated is responsible for the observed difference. + The present analysis uses values consistent with the Barklem et al. (, The present analysis uses values consistent with the Barklem et al. ( +"2000) values; however, EWs are extracted using Gaussian profiles, which may result in systematic underestimates of the EWs for very strong lines, like the 8183-8194 ones.","2000) values; however, EWs are extracted using Gaussian profiles, which may result in systematic underestimates of the EWs for very strong lines, like the 8183-8194 ones." +" We then consider abundances from the weaker doublets as more reliable, and we offset our Na abundances for this effect."," We then consider abundances from the weaker doublets as more reliable, and we offset our Na abundances for this effect." +" In general, we conclude that there is a very good agreement between the two distributions as can be clearly seen in Figure 2:: after applying the derived offset in Na abundances, the cumulative [Na/O] functions look very similar, and a Kolmogorov—Smirnov (KS) test indicates that the two distributions cannot be distinguished (the probability from KS being ~14%))."," In general, we conclude that there is a very good agreement between the two distributions as can be clearly seen in Figure \ref{f:ks1}: after applying the derived offset in Na abundances, the cumulative [Na/O] functions look very similar, and a $-$ Smirnov (KS) test indicates that the two distributions cannot be distinguished (the probability from KS being $\sim$ )." +" 'Thanks to the wide sample available, we confirm that evolutionary effects, acting during the red giant branch (RGB) phase (see, e.g., D'Antona Ventura 2007 for M cannot contribute to the Na—O distribution 13),least for the present cluster), since the extent of anticorrelation(at in both giants and dwarfs is essentially the same."," Thanks to the wide sample available, we confirm that evolutionary effects, acting during the red giant branch (RGB) phase (see, e.g., D'Antona Ventura 2007 for M 13), cannot contribute to the $-$ O distribution (at least for the present cluster), since the extent of anticorrelation in both giants and dwarfs is essentially the same." +" Furthermore, following the approach by Carretta et al. ("," Furthermore, following the approach by Carretta et al. (" +"2009b) the fractions of primordial, intermediate (I) and extreme (E) stars computed from unevolved members are 34%+5%,, 6396-E796,, and 3%+1% respectively to be compared with 27964-596,, 69%+8%,, and 4%+2% from giants (see Carretta et al.","2009b) the fractions of primordial, intermediate (I) and extreme (E) stars computed from unevolved members are $\pm$, $\pm$, and $\pm$ respectively to be compared with $\pm$, $\pm$, and $\pm$ from giants (see Carretta et al." + 2009b)., 2009b). +" On the other hand, there is not a one-to-one correlation between Li and O abundances panel of Fig. 3)):"," On the other hand, there is not a one-to-one correlation between Li and O abundances (left-hand panel of Fig. \ref{f:6397}) ):" +" even if some trend might be(left-hand present, there is a considerable scatter, much larger than observational errors."," even if some trend might be present, there is a considerable scatter, much larger than observational errors." +" T'he figure shows that, while the stars with low O values have also low Li content, at higher O abundances, Li can assume a large range values, from 1.54+0.06 to 2.51+0.18, with the most extreme star 085) having log= 2.78+0.08 (this very Li-rich(# star, which appears n(Li)as primordial type according to its O abundances, surely deserves special attention and further high-resolution observations, in order to investigate this extreme behaviour)."," The figure shows that, while the stars with low O values have also low Li content, at higher O abundances, Li can assume a large range values, from $\pm$ 0.06 to $\pm$ 0.18, with the most extreme star 085) having $\log~n{\rm (Li)}=2.78$$\pm$ 0.08 (this very Li-rich star, which appears as primordial type according to its O abundances, surely deserves special attention and further high-resolution observations, in order to investigate this extreme behaviour)." +" In Figure 4 we show, as explicative example, the spectra of three stars with almost the same O abundances; one is star 085 and the two others have intermediate and low If we then focus on the Li—Na diagram (middle panel of Figure 3)), the scatter is even larger withanticorrelation."," In Figure \ref{f:spectra} we show, as explicative example, the spectra of three stars with almost the same O abundances; one is star 085 and the two others have intermediate and low If we then focus on the $-$ Na diagram (middle panel of Figure \ref{f:6397}) ), the scatter is even larger with." +" As further evidence, the linear correlation coefficient is 0.39 (77 stars) and —0.02 (84 stars), respectively, for the Li-O and Li-Na distributions: in the first case, the significance level is >99.5%,, while the second one has no statistical meaning."," As further evidence, the linear correlation coefficient is 0.39 (77 stars) and $-$ 0.02 (84 stars), respectively, for the $-$ O and $-$ Na distributions: in the first case, the significance level is $>$, while the second one has no statistical meaning." +" Our study increases the sample of Li determination in this cluster, completing the previous studies by Pasquini Molaro Li for two and by Bonifacio et al. ("," Our study increases the sample of Li determination in this cluster, completing the previous studies by Pasquini Molaro (1997, Li for two stars) and by Bonifacio et al. (" +"2007), who (1997,proposed a Li—Na stars)anticorrelation on the","2007), who proposed a $-$ Na anticorrelation on the" +the calculated values of qo He between -0.28 and 0.70.,the calculated values of $q_0$ lie between -0.28 and 0.70. + These calculations include none of the intrinsic scatter from simulations., These calculations include none of the intrinsic scatter from simulations. + If we again assume a maximum actual evolution in the gas fraction. the limits change to 20.22«qo0.74 and 20.32 10^{45}$ erg $^{-1}$, though our results are not strongly affected by this selection." +" We include the intrinsic scatter in f, predicted by simulations and verified by observations.", We include the intrinsic scatter in $f_g$ predicted by simulations and verified by observations. + We obtain 20.47—2 from studies of gravitational lensing (Park Gott 1997)., 1998) and the lower limit $q_0>-2$ from studies of gravitational lensing (Park Gott 1997). + We find that the standard closed. flat. and open models for the universe are all within the formal confidence limits. as are some flat Q+A=1 models with non-zero cosmological constant.," We find that the standard closed, flat, and open models for the universe are all within the formal confidence limits, as are some flat $\Omega + \Lambda = 1$ models with non-zero cosmological constant." + We are able to rule out a universe with O=0 and A=|., We are able to rule out a universe with $\Omega = 0$ and $\Lambda=1$. + Our results are consistent with observations of high-redshift Type la supernovae (Perlmutter et al., Our results are consistent with observations of high-redshift Type Ia supernovae (Perlmutter et al. + 1997. Garnavich et al.," 1997, Garnavich et al." + 1998. Riess et al.," 1998, Riess et al." + 1998) as well as with gravitational lensing statistics. which yield A<0.65 (Kochanek 1996) at confidence.," 1998) as well as with gravitational lensing statistics, which yield $\Lambda < 0.65$ (Kochanek 1996) at confidence." +" Determining go from distant cluster gas fractions has the significant advantage of being independent of Hy and the numerical value of f,.", Determining $q_0$ from distant cluster gas fractions has the significant advantage of being independent of $H_0$ and the numerical value of $f_g$. + Systematic effects could be created by calibration offsets. unknown selection effects. non-Gaussian errors. or cooling flows and mergers which are responsible for much of the intrinsic scatter in the gas fraction.," Systematic effects could be created by calibration offsets, unknown selection effects, non-Gaussian errors, or cooling flows and mergers which are responsible for much of the intrinsic scatter in the gas fraction." + We have included the expected intrinsic scatter in our calculations. and the results of Henry (1997) suggest that calibration. offsets between fluxes from and are not very significant.," We have included the expected intrinsic scatter in our calculations, and the results of Henry (1997) suggest that calibration offsets between fluxes from and are not very significant." + The actual cluster gas mass fractions may increase slightly with redshift., The actual cluster gas mass fractions may increase slightly with redshift. + This would be true if the gas 1n nearby clusters has been expelled from the core (e.g.. by shock heating) systematically more than in distant clusters.," This would be true if the gas in nearby clusters has been expelled from the core (e.g., by shock heating) systematically more than in distant clusters." + Simulations suggest that this effect is negligible in both €=1 and Oτρ)ΞΞ0 quoted errors are c.l)"," \ref{curnoeq} (right panel): the parameter are $\sigma_\mathrm{d}$ $^{+62}_{-74}$ km $^{-1}$, $r_{\mathrm{d}}=67^{+16} _{-28}$ arcsecs $P(\tilde{\chi}^2>\tilde{\chi}_0^2)=$ ,quoted errors are c.l.)" + aud the nass distribution is iu Fig. 7.., and the mass distribution is in Fig. \ref{noeqmo}. +" The mass-to-light ratio is AI/Ly—26!SM.EL. within 100"". where the errors refer o the extreme values of the confidence FFollowing Binney Tremaine (1987)). we estimate the injected cherev using the equation where AJ4 ο...aud Ao are the total masses of olNGC 1399 and NGC L101 respectively. bis the impact parameter. V. is the relative velocity. r2 is the squared mean radius of the perturbed system and G is the eravitational constant."," The mass-to-light ratio is $M/L_\mathrm{B}=26^{+8}_{-6} M_{\odot}/L_{\odot}$ within $400''$, where the errors refer to the extreme values of the confidence Following Binney Tremaine \cite{bintr}) ), we estimate the injected energy using the equation where $M_1$ and $M_2$ are the total masses of NGC 1399 and NGC 1404 respectively, $b$ is the impact parameter, $V$ is the relative velocity, $\overline{r^2}$ is the squared mean radius of the perturbed system and $G$ is the gravitational constant." + We initially assuiie a tangential encounter. where b=9 is the projected separation between NGC 1399) and NGC L101. aud the relative velocity is then eiven by the difference of the object svstemic velocities. W=522 kins [du," We initially assume a tangential encounter, where $b=9'$ is the projected separation between NGC 1399 and NGC 1404, and the relative velocity is then given by the difference of the object systemic velocities, $V=522$ km $^{-1}$." + Eq. (8)).," In Eq. \ref{delE}) )," + we adopt M4=1.7«10131. and (232=10 kpe from our mass model., we adopt $M_1=1.7\times10^{12} M_\odot$ and $(\overline{r^2})^{1/2}=40$ kpc from our mass model. +" Mo is computed from NGC LLOL total huninosity Zp=Lal<10!27, (de Vaucouleurs 1901 aud D=17 Mpc) and a coustaut AMiLy-lr Δινι similar to NGC 1399."," $M_2$ is computed from NGC 1404 total luminosity $L_\mathrm{B}=1.84\times10^{10}L_{\odot}$ (de Vaucouleurs \cite{devau91} and D=17 Mpc) and a constant $M/L_\mathrm{B}$ =17 $M_\odot/L_\odot$, similar to NGC 1399." + Finally we obtain AE=9«101AL. kan? 7. which is ~7% of the total Following Aeguilay White (1985)). this is consistent with the cnerey chauge expected in similar fivbv encounters analysed in their work (for our model we obtain 9=0.8 and τίς see rH! model in Fies.," Finally we obtain $\Delta E=9\times10^{15}M_\odot$ $^2$ $^{-2}$, which is $\sim$ of the total Following Aguilar White \cite{agwi85}) ), this is consistent with the energy change expected in similar flyby encounters analysed in their work (for our model we obtain $\beta=$ 0.8 and $p=$ 4, see $r^{1/4}$ model in Figs." + 2 aud Lin Aguilar White (1985)))., 2 and 4 in Aguilar White \cite{agwi85}) )). + The corresponding AAL/AL is about which is well within our M/L uncertainty: this means that our assumption of null mass loss is consistent with our inodel precision.," The corresponding $\Delta M/M$ is about, which is well within our M/L uncertainty: this means that our assumption of null mass loss is consistent with our model precision." + Similar conclusious are fotud bv coluparing our results with Funato Makito (1999)) : iu this case the expected AMM is about (for Vío-3 and νο. —2 for them Heruquis model. Fig.," Similar conclusions are found by comparing our results with Funato Makito \cite{fuma99}) ): in this case the expected $\Delta M/M$ is about (for $V/\sigma$ =3 and $p/v_\mathrm{r}=$ 2 for their Hernquist model, Fig." + 1l c) aud Eq. (8) , 11 c) and Eq. \ref{delE}) ) +is the most direct way to estimate the injected cnerey. but not the most accurate.," is the most direct way to estimate the injected energy, but not the most accurate." +" Aeuilar White (1985)) poiuted out that this ""distaut encounter approximation can overestimate the real amount of energv change for a laree range of impact parameters.", Aguilar White \cite{agwi85}) ) pointed out that this “distant encounter” approximation can overestimate the real amount of energy change for a large range of impact parameters. + From iuspectiou of their Fie., From inspection of their Fig. + L|. however. we can expect some effect for our encounter οσοnetry : 2=0.8 aud p =imply au overestimate of ~0.02 in AE/E.," 4, however, we can expect some effect for our encounter geometry : $\beta=$0.8 and $p=$ 4imply an overestimate of $\sim 0.02$ in $\Delta E/E$." + We will cousider this source of uncertainty in the followine discussion about the error budeoet ο this lu conclusion. we stress that. within the flyby encounter scenario. we have neeleced possible effects of the relative nearby svstem. NGC 1380.," We will consider this source of uncertainty in the following discussion about the error budget of this In conclusion, we stress that, within the flyby encounter scenario, we have neglected possible effects of the relative nearby system, NGC 1380." + This galaxy has a, This galaxy has a + In recent vears. increasing evidence for chemical complexity and multiple stellar populations in several massive Galactic globular clusters (GCs) has emerged (e.g. Gratton et al.," In recent years, increasing evidence for chemical complexity and multiple stellar populations in several massive Galactic globular clusters (GCs) has emerged (e.g. Gratton et al." + 2004. Bedin et al.," 2004, Bedin et al." + 2004. Piotto et al.," 2004, Piotto et al." + 2007. Milone et al.," 2007, Milone et al." + 2008)., 2008). + For some globular clusters (e.g. co CCentauri and NGC 2808) there is evidence that these multiple populations may be due to an enhancement in Helium content (up to Y= 0.4). as deduced from the presence of extremely blue horizontal branches (EHBs) and multiple main sequences (DAntona et al.," For some globular clusters (e.g. $\omega$ Centauri and NGC 2808) there is evidence that these multiple populations may be due to an enhancement in Helium content (up to $Y\simeq 0.4$ ), as deduced from the presence of extremely blue horizontal branches (EHBs) and multiple main sequences (D'Antona et al." + 2005. Lee et al.," 2005, Lee et al." + 2005)., 2005). + The link between occurence of EHBs and He-enhancement is. however. under debate.," The link between occurence of EHBs and He-enhancement is, however, under debate." + EHB stars may also originate directly from fast rotating stars with an enhanced mass loss during the red giant branch (RGB) evolution., EHB stars may also originate directly from fast rotating stars with an enhanced mass loss during the red giant branch (RGB) evolution. + Those stars leave the RGB before the He flash towards the (He-core) white dwarf cooling curve where they ignite Helium and end up on the EHB (Castellani Castellani 1993. DCruz et al.," Those stars leave the RGB before the He flash towards the (He-core) white dwarf cooling curve where they ignite Helium and end up on the EHB (Castellani Castellani 1993, D'Cruz et al." +" 1996, Brown et al."," 1996, Brown et al." + 2001)., 2001). +" This is sometimes called the ""hot-flasher scenario.", This is sometimes called the 'hot-flasher' scenario. + A significant fraction of the EHB stars in «o CCentauri seem to have followed this evolutionary path (Moehler et al., A significant fraction of the EHB stars in $\omega$ Centauri seem to have followed this evolutionary path (Moehler et al. + 2007)., 2007). + It has been shown that EHB stars contribute most of the light in the UV bands (e.g. NGC 2808: Dieball et al., It has been shown that EHB stars contribute most of the light in the UV bands (e.g. NGC 2808: Dieball et al. + 2005)., 2005). + The presence of an EHB in extragalactic - unresolved - GCs reveals itself in the integrated light by a UV-excess compared to GCs with a normal horizontal branch (HB)., The presence of an EHB in extragalactic - unresolved - GCs reveals itself in the integrated light by a UV-excess compared to GCs with a `normal' horizontal branch (HB). + For example. Rey et al. (," For example, Rey et al. (" +2007) find three metal-rich ([Fe/H|» —1) GC candidates in M31 with. significant FUV flux which are thought to be analogs of two peculiar Galactic GCs. NGC 6388 and NGC 6441 (Yoon et al.,"2007) find three metal-rich $>-$ 1) GC candidates in M31 with significant FUV flux which are thought to be analogs of two peculiar Galactic GCs, NGC 6388 and NGC 6441 (Yoon et al." + 2008)., 2008). + Sohn et al. (, Sohn et al. ( +2006) and Kaviraj et al. (,2006) and Kaviraj et al. ( +2007) analysed the UV properties of massive globular clusters associated with M87 in the Virgo cluster. and found that many of them show a UV-excess with respect to canonical stellar population models.,"2007) analysed the UV properties of massive globular clusters associated with M87 in the Virgo cluster, and found that many of them show a UV-excess with respect to canonical stellar population models." + These findings support the idea that EHBs may be à common feature to the most massive compact stellar systems., These findings support the idea that EHBs may be a common feature to the most massive compact stellar systems. + In this Research Note we focus on the UV properties of compact stellar systems in the Fornax cluster., In this Research Note we focus on the UV properties of compact stellar systems in the Fornax cluster. + In contrast to the studies of Sohn et al., In contrast to the studies of Sohn et al. + and Kaviray et al., and Kaviraj et al. + on Virgo GCs. we extend our analysis to compact stellar systems beyond the mass range of GCs (Mx310° Ma). including the so-called ultra-compact dwarf galaxies (UCDs. Drinkwater et al.," on Virgo GCs, we extend our analysis to compact stellar systems beyond the mass range of GCs $M\lesssim 3 +\times 10^6$ $_{\sun}$ ), including the so-called ultra-compact dwarf galaxies (UCDs, Drinkwater et al." + 2003). which cover the mass range up to ΙΟΜο. having Myx-11 mag.," 2003), which cover the mass range up to $\sim10^8$ $_{\sun}$, having $M_V \lesssim -11$ mag." + We analyse how the UV properties of UCDs compare to those of both massive and normal GCs. in order to improve our knowledge of EHB occurence in compact stellar systems.," We analyse how the UV properties of UCDs compare to those of both massive and normal GCs, in order to improve our knowledge of EHB occurence in compact stellar systems." + Throughout this study we adopt (m-M)=31.4 mag (Freedman et al., Throughout this study we adopt (m-M)=31.4 mag (Freedman et al. + 2001) as distance modulus to the Fornax cluster., 2001) as distance modulus to the Fornax cluster. + In order to investigate the UV properties of massive compact stellar systems in Fornax. we retrieved archival FUV and NUV GALEX images from two pointings in the Fornaxcluster!.," In order to investigate the UV properties of massive compact stellar systems in Fornax, we retrieved archival FUV and NUV GALEX images from two pointings in the Fornax." +. One pointing was offset from NGC 1399 by about 0.4° to the west. and had been taken within the Deep Imaging Survey (DIS) with integration time 18000 seconds.," One pointing was offset from NGC 1399 by about $\degr$ to the west, and had been taken within the Deep Imaging Survey (DIS) with integration time 18000 seconds." + The other pointing was centered on NGC 1399. taken within the Near Galaxy Survey (NGS). with integration time 1700 seconds in FUV and NUV.," The other pointing was centered on NGC 1399, taken within the Near Galaxy Survey (NGS), with integration time 1700 seconds in FUV and NUV." + See Fig. 1.., See Fig. \ref{map}. + We subtracted the two giant elliptical galaxies NGC 1399 and NGC 1404 from the archival GALEX images. using the modelling routines and within IRAF.," We subtracted the two giant elliptical galaxies NGC 1399 and NGC 1404 from the archival GALEX images, using the modelling routines and within IRAF." + Then we run SExtractor on the Images to create a source catalog of detections in NUV and FUV., Then we run SExtractor on the images to create a source catalog of detections in NUV and FUV. + For this we required a minimum of 5 adjacent pixels with at least 2σ above the sky noise., For this we required a minimum of 5 adjacent pixels with at least $\sigma$ above the sky noise. + We adopted BBEST as source magnitude. and used the GALEX photometric zero-points given in the image headers.," We adopted BEST as source magnitude, and used the GALEX photometric zero-points given in the image headers." + From artificial star experiments using the same detection parameters we derived completeness limits for scnresolved sources in the DIS images of NUV=24.2 mag. nd νο=24.7 mag.," From artificial star experiments using the same detection parameters we derived completeness limits for unresolved sources in the DIS images of $_0=24.2$ mag, and $_0=24.7$ mag." + The region within ~2’ of the center of GC 1399 showed a considerably brighter completeness limit by 1-2 mag., The region within $\simeq$ $'$ of the center of NGC 1399 showed a considerably brighter completeness limit by 1-2 mag. + The GALEX detections in the output catalogs were then matched with the position of compact Fornax cluster members known from an up-to-date compilation of, The GALEX detections in the output catalogs were then matched with the position of compact Fornax cluster members known from an up-to-date compilation of +"FU)8m(C—JE,)/DCIP). where C is a constant of integration.","$f(J)\approx (\mathcal{C}-JF_J^+)/D(J)$, where $\mathcal{C}$ is a constant of integration." + Weinsist that δε20 since there should not be an incoming flux of planets from infinity., Weinsist that $F_J^+\ge0$ since there should not be an incoming flux of planets from infinity. + Thus the nunerator eventually becomes negative., Thus the numerator eventually becomes negative. + The diffusion coellicient D) is unquestionably positive. so / becomes negative al stuliciently large J.," The diffusion coefficient $D(J)$ is unquestionably positive, so $f$ becomes negative at sufficiently large $J$ ." + But this is absurd. since (ή). is a probability.," But this is absurd, since $f(J)dJ$ is a probability." +" Thus we cannot have both a positive flux aud a positive f at large J in steady-state. aud it follows that #,=0 aud fF,=—JyA."," Thus we cannot have both a positive flux and a positive $f$ at large $J$ in steady-state, and it follows that $F_J^+=0$ and $F_J^-=-J_S\Lambda$." + All the flux generated at the source is accreted through the inner edge of the clisk., All the flux generated at the source is accreted through the inner edge of the disk. + We uow discuss Eq. (11)), We now discuss Eq. \ref{eq:steadystate}) ) + in full. emphasizing behavior at small aud laree J.," in full, emphasizing behavior at small and large $J$." + Let so that exp[yi(/)] is anintegrating factor for Eq. (11))., Let so that $\exp[\mu(J)]$ is anintegrating factor for Eq. \ref{eq:steadystate}) ). + Then As before. the upper (lower) sign on [> aud F7 applies to J>Jy (JJ_S$ $J0.," Normally the mean torque $\bar\Gamma<0$, so that $d \mu/dJ >0$." + Then we can choose the coustaut of integration iu Eq. (15)), Then we can choose the constant of integration in Eq. \ref{eq:mu}) ) + so that po<0 for JxJy and p>0 for J>Js., so that $\mu\le0$ for $J\le J_S$ and $\mu\ge0$ for $J\ge J_S$. + All disks of interest in this paper are clominated yy the mean torque at small radii and by dillusion at large J., All disks of interest in this paper are dominated by the mean torque at small radii and by diffusion at large $J$. + Hence exp[—p(/)] becomes large at stnall J. aud so for a well-behaved solution. the conteuts of the square brackets in Eq. (16))," Hence $\exp[-\mu(J)]$ becomes large at small $J$, and so for a well-behaved solution, the contents of the square brackets in Eq. \ref{eq:fss}) )" + must end to zero as J—0., must tend to zero as $J\to0$. +" This defines a relationship between ως) aud F,.", This defines a relationship between $f(J_S)$ and $F_J^{-}$. +" For J>Js. enlm], so the integral increases at least as [ast as J—Jg."," For $J>J_S$, $e^{\mu(J)}\ge 1$, so the integral increases at least as fast as $J-J_S$." +" As before. if the disk is inclelinitely extended hen we must have #,— 010 prevent f(J) from becoming negative at large J."," As before, if the disk is indefinitely extended then we must have $F^+_J=0$ to prevent $f^+(J)$ from becoming negative at large $J$." + The main conclusion of this discussion is that We have reached this conclusion by cousideriug steady solutions but will assume that it applies generally., The main conclusion of this discussion is that We have reached this conclusion by considering steady solutions but will assume that it applies generally. + The tüne-dependeut problem is more difficult. but we cau determine some general characteristics oL the solution by analytic meaus. most unportantly that Lail.," The time-dependent problem is more difficult, but we can determine some general characteristics of the solution by analytic means, most importantly that ." + For the special caseof the MMSN. where DxJ aud Px—/ 7. this probability declines only as /. 1.," For the special caseof the MMSN, where $D\propto J$ and $\bar\Gamma\propto-J^{-2}$ , this probability declines only as $t^{-1}$ ." + The asymptotic form of the solution at late times is sell-sinilar except near J=0 aud is described explicitly in clitmensiouless units by equation (32))., The asymptotic form of the solution at late times is self-similar except near $J=0$ and is described explicitly in dimensionless units by equation \ref{eq:ssim}) ). +The present analysis can also be used to gain insight into the question of the dark matter content of Pal I4: in the framework of the classical Newtonian dynamics the low observed velocity dispersion implies a dynamical M/L<1.5-2 (for reasonable assumptions on the binary fraction and on the rejection criterion).,The present analysis can also be used to gain insight into the question of the dark matter content of Pal 14: in the framework of the classical Newtonian dynamics the low observed velocity dispersion implies a dynamical $M/L\leq 1.5-2$ (for reasonable assumptions on the binary fraction and on the rejection criterion). + This result. combined with the observation that Pal 14 has significant tidal tails (S11). suggests that dark matter does not contribute substantially to the mass of this remote GC.," This result, combined with the observation that Pal 14 has significant tidal tails (S11), suggests that dark matter does not contribute substantially to the mass of this remote GC." + We warmly thank Andreas Kupper for the helpful discussion and for providing his data., We warmly thank Andreas Kupper for the helpful discussion and for providing his data. + We also thank the anonymous referee for his/her comments and suggestions., We also thank the anonymous referee for his/her comments and suggestions. + A.S is supported by the Istituto Nazionale di Astrofisica (INAF)., A.S is supported by the Istituto Nazionale di Astrofisica (INAF). + C.N. is supported by the MIUR grant PRIN2008., C.N. is supported by the MIUR grant PRIN2008. + We acknowledge the CINECA Awards N. HPIOC2TBYB (2011) and N. HPIOCQFATD (2011) for the availability of high performance computing resources and support., We acknowledge the CINECA Awards N. HP10C2TBYB (2011) and N. HP10CQFATD (2011) for the availability of high performance computing resources and support. +Our primary age indicator for these data is the Lh? index. therefore the uncertainties in this index will rellect heavily on our age estimates for the globular clusters.,"Our primary age indicator for these data is the $\beta$ index, therefore the uncertainties in this index will reflect heavily on our age estimates for the globular clusters." + We calibrate the models to the canonical age we have chosen for the GGCs. which is 12 ανν.," We calibrate the models to the canonical age we have chosen for the GGCs, which is 12 Gyr." + This age for the GOGCSs is consistent with recent work using the latest parallaxes by Carretta (2000). and is convenient since this age-line is directly modelled (Le. not interpolated) by Worthey (1994).," This age for the GGCs is consistent with recent work using the latest parallaxes by Carretta (2000), and is convenient since this age-line is directly modelled (i.e. not interpolated) by Worthey (1994)." + We fit the 12 Gyr line of the models to the Lh? index of the CGOGCs using à x72 procedure., We fit the 12 Gyr line of the models to the $\beta$ index of the GGCs using a $\chi^{2}$ procedure. + The shift implied. in -- is then applied. to our NGC 4472 elobular cluster data., The shift implied in $\beta$ is then applied to our NGC 4472 globular cluster data. + ‘This correction to the models is typically -0.4X... larger than modelling uncertainties. and is cllectively a zero-point calibration.," This correction to the models is typically $\sim$ -0.4, larger than modelling uncertainties, and is effectively a zero-point calibration." + Without this shift. nearly the GGCs would be predicted to have ages zz 15 Gyr.," Without this shift, nearly the GGCs would be predicted to have ages $\ge$ 18 Gyr." + We compare our data to the corrected. models. in Figs., We compare our data to the corrected models in Figs. + (13 16)). each of which consist of two panels: the upper panel over-plots the SSP grids. of Worthey (1994) on to our co-added: data. (filled circles. with bootstrapped uncertainties).," \ref{fig:wor_mg2_hbeta} – \ref{fig:wor_mg2_fe52}) ), each of which consist of two panels: the upper panel over-plots the SSP grids of Worthey (1994) on to our co-added data (filled circles with bootstrapped uncertainties)." + The lower panel compares the combined sample of €iGC€'s to these same models., The lower panel compares the combined sample of GGCs to these same models. + On the whole. the models give a good reproduction of the behaviour of our data. both for the co-added NGC 4472 elobular clusters and the GGCs.," On the whole, the models give a good reproduction of the behaviour of our data, both for the co-added NGC 4472 globular clusters and the GGCs." + The Balmer indices track the isochrones of the models fairly closely. across two decades in metallicity.," The Balmer indices track the isochrones of the models fairly closely, across two decades in metallicity." + Phe new modelling of the cluster LBs shows strikingly similar behaviour to that of our three most moetal-poor cluster bins., The new modelling of the cluster HBs shows strikingly similar behaviour to that of our three most metal-poor cluster bins. + It is apparent that there are small shifts between different metal indices. but these are typically 0.2 aand well within the uncertainties.," It is apparent that there are small shifts between different metal indices, but these are typically 0.2 and well within the uncertainties." + In Fie., In Fig. + 16. we plot Fe5270 against Mg» for our data and the combined sample of GGCs., \ref{fig:wor_mg2_fe52} we plot Fe5270 against $_{2}$ for our data and the combined sample of GGCs. + Por comparison. we also plot the nuclear data of Davies (1993). which we have placed into three radial bins.," For comparison, we also plot the nuclear data of Davies (1993), which we have placed into three radial bins." + Phe spheroid data of Davies, The spheroid data of Davies +the orbital phase dependent change of the pulsar wind bulk Lorentz factor due to the interaction with stellar photons.,the orbital phase dependent change of the pulsar wind bulk Lorentz factor due to the interaction with stellar photons. + More recently. ? modelled the X-ray data obtained with the Suzaku X-ray satellite with a synchrotron and IC radiation model that included orbital phase dependent adiabatic losses.," More recently, \citet{uchiyama} modelled the X-ray data obtained with the Suzaku X-ray satellite with a synchrotron and IC radiation model that included orbital phase dependent adiabatic losses." + Finally. ? suggested that the observed variability of non-thermal fluxes is related to the orbital phase dependence of (1) the pulsar wind bulk Lorentz factor and magnetization parameter. (11) the magnetization parameter and the spectral power law index of shock-accelerated particles.," Finally, \citet{takata} suggested that the observed variability of non-thermal fluxes is related to the orbital phase dependence of (i) the pulsar wind bulk Lorentz factor and magnetization parameter, (ii) the magnetization parameter and the spectral power law index of shock-accelerated particles." + In this last approach. non-radiative losses were not accounted The introduction of orbital phase dependent non-radiative losses accounts for the following physical effects most likely being present in.B1259-63:: (1) the post-shock flow propagating in the confined region formed by the PW and the shocked stellar wind (?) should suffer significant adiabatic losses (2):; (11) the loss rate depends on the hydrodynamics of the interaction and may thus naturally depend on the orbital separation distance and the density of the stellar wind.," In this last approach, non-radiative losses were not accounted The introduction of orbital phase dependent non-radiative losses accounts for the following physical effects most likely being present in: (i) the post-shock flow propagating in the confined region formed by the PW and the shocked stellar wind \citep{bogovalov} should suffer significant adiabatic losses \citep{khangulyan_hepro}; (ii) the loss rate depends on the hydrodynamics of the interaction and may thus naturally depend on the orbital separation distance and the density of the stellar wind." + Moreover. since the pulsar wind is expected to be anisotropic (2).. the adiabatic loss rate could have a rather complicated orbital phase dependence.," Moreover, since the pulsar wind is expected to be anisotropic \citep{bogo&khang}, the adiabatic loss rate could have a rather complicated orbital phase dependence." + Hence. in the following the approach of ? is used. taking into consideration the data obtained with in This paper is organized às follows.," Hence, in the following the approach of \citet{khangulyan} is used, taking into consideration the data obtained with in This paper is organized as follows." + Επί of all. a phenomenological discussion of the lightcurve both in the y--ray and X-ray bands is presented in Sec. 2..," First of all, a phenomenological discussion of the lightcurve both in the -ray and X-ray bands is presented in Sec. \ref{lc}." + A comparison of the expected IC TeV energy flux with the data allows an inference of the non-radiative cooling profile., A comparison of the expected IC TeV energy flux with the data allows an inference of the non-radiative cooling profile. + This ansatz yields results for the prediction of TeV photons from that describe the peculiar drop at periastron. with reasonable accuracy (?).., This ansatz yields results for the prediction of TeV photons from that describe the peculiar drop at periastron with reasonable accuracy \citep{khangulyan}. + In their ?. paper. ?. used the 2004 data in order to calculate the non-radiative cooling coefficients for the orbit.," In their \citeyear{khangulyan} paper, \citet{khangulyan} used the 2004 data in order to calculate the non-radiative cooling coefficients for the orbit." + In Sec., In Sec. + 3. of this article their analysis is redone with the addition of VHE data from the 2007 periastron passage., \ref{model} of this article their analysis is redone with the addition of VHE data from the 2007 periastron passage. + Moreover. three different possible cooling profiles are compared.," Moreover, three different possible cooling profiles are compared." + While y--ray binaries. such as and303.. have been observed over several orbits and thus could be confirmed as periodical VHE emitters (??) this was not possible for so far because of the rather long orbital period. of 3.4 years.," While -ray binaries, such as and, have been observed over several orbits and thus could be confirmed as periodical VHE emitters \citep{5039,LSI2} this was not possible for so far because of the rather long orbital period of 3.4 years." + The overlap between the datasets of 2004 and 2007 is marginal and thus inconclusive in this regard (see top panel in Fig. 1))., The overlap between the datasets of 2004 and 2007 is marginal and thus inconclusive in this regard (see top panel in Fig. \ref{curve}) ). + It is thus up to now unknown whether the TeV lighteurve of this object shows periodicity., It is thus up to now unknown whether the TeV lightcurve of this object shows periodicity. + There is. however. some strong hint that the object indeed behaves periodically in the TeV regime: the lower panel in Fig.," There is, however, some strong hint that the object indeed behaves periodically in the TeV regime: the lower panel in Fig." + 1. shows the energy flux of | TeV photons of as a function of the separation distance r between the pulsar and its companion star., \ref{curve} shows the energy flux of 1 TeV photons of as a function of the separation distance $r$ between the pulsar and its companion star. + The bidaily 2004 energy fluxes for | TeV photons are taken from ? (see their Fig., The bidaily 2004 energy fluxes for 1 TeV photons are taken from \citet{1259} (see their Fig. + 8) whereas the 2007 fluxes are calculated from bolometric fluxes above | TeV assuming the underlying spectral power law as described in ?.., 8) whereas the 2007 fluxes are calculated from bolometric fluxes above 1 TeV assuming the underlying spectral power law as described in \citet{1259new}. + There is an apparent relation between pre and post periastron data obtained in the years 2004 and 2007 by and the orbital distance., There is an apparent relation between pre and post periastron data obtained in the years 2004 and 2007 by and the orbital distance. + The correlation coefficient between the 2007 fluxes shown in time bins of months and the monthly weighted mean of the bidaily 2004 data as a function of r amounts to p=0.89+0.12., The correlation coefficient between the 2007 fluxes shown in time bins of months and the monthly weighted mean of the bidaily 2004 data as a function of $r$ amounts to $\rho=0.89\pm0.12$. + Despite the limited statistics of the TeV data and the fact that firm conclusions can not be drawn at present. this behavior would indicate essentially two things: (1) the TeV flux is symmetric with respect to pertastron and thus mainly a function of the binary separation. (11) the system shows indirect signs of periodicity.," Despite the limited statistics of the TeV data and the fact that firm conclusions can not be drawn at present, this behavior would indicate essentially two things: (i) the TeV flux is symmetric with respect to periastron and thus mainly a function of the binary separation, (ii) the system shows indirect signs of periodicity." + It should be noted that in frameworks of a leptonic scenario this kind of behavior is rather unexpected., It should be noted that in frameworks of a leptonic scenario this kind of behavior is rather unexpected. + Indeed. since any two different orbital positions. which are symmetric with respect to periastron. are characterized by different IC scattering angles (according to the currently accepted orbital elements). one should expect different fluxes in the direction of the observer due to anisotropic IC scattering (??)..," Indeed, since any two different orbital positions, which are symmetric with respect to periastron, are characterized by different IC scattering angles (according to the currently accepted orbital elements), one should expect different fluxes in the direction of the observer due to anisotropic IC scattering \citep{kirk, aharonian}." + The significance of this effect depends on many different factors: the actual locatior of the production region. the y-ray energy band. the slope of the electron spectrum and the temperature of the optical star.," The significance of this effect depends on many different factors: the actual location of the production region, the $\gamma$ -ray energy band, the slope of the electron spectrum and the temperature of the optical star." + Another source of asymmetry in should be Doppler modulation of the post shock flow of relativistic particles., Another source of asymmetry in should be Doppler modulation of the post shock flow of relativistic particles. + The orbital parameters of the system in connectio with expected large Lorentz factors of the bulk flow imply 2£5 strong phase dependence of the related non-thermal emissio (?).., The orbital parameters of the system in connection with expected large Lorentz factors of the bulk flow imply a strong phase dependence of the related non-thermal emission \citep{khangulyan_hepro}. + Taking into account the system orientation with respect tc the observer (?).. this naturally should lead to an asymmetry 1 the observed VHE fluxes.," Taking into account the system orientation with respect to the observer \citep{john92}, this naturally should lead to an asymmetry in the observed VHE fluxes." + In Fig.2 the ratios of the VHE fluxes (integrated betwee 380 GeV and 10 TeV) for the locations of the pulsar symmetric with respect to periastron passage (1e. characterized by the same absolute value of the true anomaly) are shown., In \ref{fig_anisotropy} the ratios of the VHE fluxes (integrated between 380 GeV and 10 TeV) for the locations of the pulsar symmetric with respect to periastron passage (i.e. characterized by the same absolute value of the true anomaly) are shown. + This figure illustrates the dependence of the flux ratio not only on the pulsar orbital location. but also on the star temperature.," This figure illustrates the dependence of the flux ratio not only on the pulsar orbital location, but also on the star temperature." + For the calculations the electron distribution was assumed to be a power law with index 2., For the calculations the electron distribution was assumed to be a power law with index $2$. +" For the currently accepted star temperature 7,=2.3x10°K. the fluxes should differ by a factor of 1.5 at the locations with true anomaly 8~2rad (or 9~1157. r~3xOU em)."," For the currently accepted star temperature $T_*=2.3\times10^4\rm K$, the fluxes should differ by a factor of $1.5$ at the locations with true anomaly $\theta\sim2\rm rad$ (or $\theta\sim115^\circ$, $r\sim3\times10^{13}\rm cm$ )." + Apparently. the observations from these epochs show almost equal fluxes (see Fig.1)) within the limited statistics of the data.," Apparently, the observations from these epochs show almost equal fluxes (see \ref{curve}) ) within the limited statistics of the data." + In case this feature turns out to be significant there are several possible explanations in the IC scenario for such an observational result. (, In case this feature turns out to be significant there are several possible explanations in the IC scenario for such an observational result. ( +i) The ratio of the fluxes strongly depends on the temperature of the star (see Fig.2)).,i) The ratio of the fluxes strongly depends on the temperature of the star (see \ref{fig_anisotropy}) ). + Indeed. if the IC scattering occurs deeper in the Klein-Nishina regime. then the cross section shows a weaker angular dependence.," Indeed, if the IC scattering occurs deeper in the Klein-Nishina regime, then the cross section shows a weaker angular dependence." + Thus. if the star temperature were larger by a factor of 1.5. then the ratio of the fluxes would be consistent with the IC. scenario. considering the relatively large error bars. (," Thus, if the star temperature were larger by a factor of 1.5, then the ratio of the fluxes would be consistent with the IC scenario, considering the relatively large error bars. (" +1) If the VHE emission production site has à size not much smaller than the distance to the optical star. then the IC seattering from each location of the pulsar will be,"ii) If the VHE emission production site has a size not much smaller than the distance to the optical star, then the IC scattering from each location of the pulsar will be" +X-ray. spectra of esType 1 AGNmU are typically. dominated. by a . . . ↓≻∪∖∖⋎∢⊾↓⋅↓⋜↧∖∖⊽≼∼∪⊔⊔⊔⇂⋯⊔↓∪⇂↓≻↓↕∪↿∪⊔↓⊔∠⇂⋖⊾⇀∖↓∿↓⊳↖∖−−≽⋃∖⋜⋯∠∐⋅⋜⊔⋯∠⇂ ∙⇁ PoundsN 1994). with. an ionisedDo. outflow often⋅ imprinting.D. an line. spectrum. in the. soft X-ray D.band (e.g. Ixaspi .~SO 22002. Steenbrugec 22003).,"X-ray spectra of Type 1 AGN are typically dominated by a power law continuum of photon index $\Gamma$$\sim$ 1.8-2 (Nandra and Pounds 1994), with an ionised outflow often imprinting an absorption line spectrum in the soft X-ray band (e.g. Kaspi 2002, Steenbrugge 2003)." + Tvpe 2 AGN. in contrast. are usually heavily absorbed by cold eas (perhaps in the putative: torus: Antonucci 1993). with soft X-rav lines showing up in emission.," Type 2 AGN, in contrast, are usually heavily absorbed by cold gas (perhaps in the putative torus; Antonucci 1993), with soft X-ray lines showing up in emission." + While it is a reasonable assumption that the soft X-rav emission and absorption come from the same ionised outflow (Ixinkhabwala 22002) both components are rarely seen in: the sanie spectrum. since the continuum Lux is generally dominant in Type LAXGN.," While it is a reasonable assumption that the soft X-ray emission and absorption come from the same ionised outflow (Kinkhabwala 2002) both components are rarely seen in the same spectrum, since the continuum flux is generally dominant in Type 1 AGN." + A few cases have been found. however. where a ‘Type 1 AGN in a low flux state exhibits a dominantly emission line spectrum (c.g. Turner 22003. Pounds 22004).," A few cases have been found, however, where a Type 1 AGN in a low flux state exhibits a dominantly emission line spectrum (e.g. Turner 2003, Pounds 2004b)." + The Two Micron All-Sky Survey (2\LASS) has revealed many hiehly recelenec active galaxies (AGN) whose number censity rivals that. of optically selected AGN., The Two Micron All-Sky Survey (2MASS) has revealed many highly reddened active galaxies (AGN) whose number density rivals that of optically selected AGN. + . ⊾↔↓≻⋖⋅≼∙↿↓⋅∪≱∖≼∙∪↓≻⊔∙⇂∪∐∪∖∖⊽−⊔↓≻∪⇂↓⋅∢⋅∠⇂≼⇍⋜⋯∠⇂⊔⇂⋜⋯⋅⊳∖↓⋅∢⊾∖⇁⋖⋅⋜↧↓⊳∖∿⋀⋅↱≻⊀⋅ ⋅ . _ percent are previously. unidentified.u emission-lineD.. AGN. MENwith percent of those. showing the. broad. optical emission. absorptionuu ofs Type ↴⋅1 Sevlert galaxies. and.. QSOs (CutriE ctlines 2001).," Spectroscopic follow-up of red candidates reveals $\sim$ 75 percent are previously unidentified emission-line AGN, with $\sim$ 80 percent of those showing the broad optical emission lines of Type 1 Seyfert galaxies and QSOs (Cutri 2001)." + These objects often have unusually high optical polarization levels. with 10 percent showing 2>3 percent indicating a significant contribution [rom scattered. light (Smith 22002) and suggesting substantial obscuration toward. the nuclear energy source.," These objects often have unusually high optical polarization levels, with $\sim$ 10 percent showing $P>3$ percent indicating a significant contribution from scattered light (Smith 2002) and suggesting substantial obscuration toward the nuclear energy source." + oobservationsvati of a aussamplesnb of οPALASSTu AGN ∢⇁⋅found them. to be. Aeray weal with generally flat. (hard) spectra (Wilkes 22002]., observations of a sample of 2MASS AGN found them to be X-ray weak with generally flat (hard) spectra (Wilkes 2002). + sspectra were recently obtained for a subset of five 2ALASS AGN in an attempt resolve the cllects of absorption from aninfrinsicadly Lat power law spectrum., spectra were recently obtained for a subset of five 2MASS AGN in an attempt resolve the effects of absorption from an flat power law spectrum. + The results of this, The results of this +the Keplerian disk below.,the Keplerian disk below. + Judeing from Figure11.. the differential way be as high as 10-15]aus| if the fall happens at AAU. but less if the fall happens fartler out in the disk.," Judging from Figure\ref{Wind}, the differential may be as high as $\rm km\,s^{-1}$ if the fall happens at AU, but less if the fall happens farther out in the disk." + This is sufficient to eenerate shocks that lav be observable., This is sufficient to generate shocks that may be observable. + Clearly. the parametrized wind model is not based on a detailed treatineut of the uuderlviug bydrodvuamics and radiative transfer.," Clearly, the parametrized wind model is not based on a detailed treatment of the underlying hydrodynamics and radiative transfer." +" Ποπονο, it does represeut a phenomenological structure required to match clearly defined observables."," However, it does represent a phenomenological structure required to match clearly defined observables." + Tt is therefore important to consider he circumstances under which the plivsical aud clemical structure of the wind may differ from the simple model., It is therefore important to consider the circumstances under which the physical and chemical structure of the wind may differ from the simple model. + Oue property of the wind model that does not match he observations is the rotational temperatures of the ines., One property of the wind model that does not match the observations is the rotational temperatures of the lines. + The model predicts lower temperatures than observed., The model predicts lower temperatures than observed. + However. this can likely be explained by the use of LTE level populations in thermal balauce with he dust.," However, this can likely be explained by the use of LTE level populations in thermal balance with the dust." + The eas that forms the wind will be exposed o a strong IR and UV radiation field from the ceutral star and iunermiost disk. and is therefore subject to fuorescencoe pumping as well as collisional excitation oa gas that is heated aud likely partly ionized bx xioto-electrous.," The gas that forms the wind will be exposed to a strong IR and UV radiation field from the central star and innermost disk, and is therefore subject to fluorescence pumping as well as collisional excitation by a gas that is heated and likely partly ionized by photo-electrons." + Balaucing this are the strong cooling ernis offered by the rovibrational molecular cussion. in particular that of CO and water.," Balancing this are the strong cooling terms offered by the rovibrational molecular emission, in particular that of CO and water." + While previous wind models generally predict very high wiud cluperatures (10.000 I&) aud fast winds (LOOkins Ly the existence of significant molecular coolants may. in part ofthe wind flow. maintain the required low temperatures and velocities.," While previous wind models generally predict very high wind temperatures (10,000 K) and fast winds $\rm 100\,km\,s^{-1}$ ), the existence of significant molecular coolants may, in part of the wind flow, maintain the required low temperatures and velocities." + Iu particular the temperatures may be closer to those given by the assunption of equilibrium with the stellar radiation field. as assumed in this paper. than the high temperatures implied by a purely atomic eas.," In particular the temperatures may be closer to those given by the assumption of equilibrium with the stellar radiation field, as assumed in this paper, than the high temperatures implied by a purely atomic gas." + A future detailed heating-cooling balance calculation for the wind model is clearly anu iaportaut next step., A future detailed heating-cooling balance calculation for the wind model is clearly an important next step. + More detailed lydro-dyvnamic modeling i8 essential to fullv assess the muplicatious of slow disk wines., More detailed hydro-dynamic modeling is essential to fully assess the implications of slow disk winds. + What is the wind launching mechanisin?, What is the wind launching mechanism? + Does the wind eventually fall back outo the disk aud at which radi?, Does the wind eventually fall back onto the disk and at which radii? + Tow cau the wind remain. at least in part. im a molecular form. as the material is lofted to altitudes where dust shiclding low and the gas is exposed to a harsh UV radiation field?," How can the wind remain, at least in part, in a molecular form as the material is lofted to altitudes where dust shielding low and the gas is exposed to a harsh UV radiation field?" + While a model of the chemustry of the molecular wind is a study in its own right. if can be noted that the CO column densities required to generate the deep absorption lines seen iu the self-absorbed (nore inclined) sources are likely high cuough to selt-zshield.," While a model of the chemistry of the molecular wind is a study in its own right, it can be noted that the CO column densities required to generate the deep absorption lines seen in the self-absorbed (more inclined) sources are likely high enough to self-shield." + Likewise. the preseuce of water in the flow. at least in AS 205N see Figure 8 will provide additional shicldine against UV photons for a range of niolecular species(?).," Likewise, the presence of water in the flow, at least in AS 205N – see Figure \ref{SA_H2O} – will provide additional shielding against UV photons for a range of molecular species." +. Using spectro-astrometry to image molecular gas at O.1-10AU in a sample of protoplauetziry disks has revealed an intriguing range of structure., Using spectro-astrometry to image molecular gas at AU in a sample of protoplanetary disks has revealed an intriguing range of structure. + Some disks appear to be dominated by eas in WNeplerian rotation about the central star. as expected. while others have a significantsow radial velocity component consistent with a wide-angle disk wind.," Some disks appear to be dominated by gas in Keplerian rotation about the central star, as expected, while others have a significant radial velocity component consistent with a wide-angle disk wind." + The basic observational evidence for a slow wind is the clear presence of It is difficult to eeucrate low velocity σας deep in a potential well. but one simple way of doing so is via angular momentum conservation of an expanding. but initially Weplerian. flow.," The basic observational evidence for a slow wind is the clear presence of It is difficult to generate low velocity gas deep in a potential well, but one simple way of doing so is via angular momentum conservation of an expanding, but initially Keplerian, flow." + While it has long been known that fast atomic winds were conunon in T Tauri stars. we now find that there is a significant molecular conrponeut as well.," While it has long been known that fast atomic winds were common in T Tauri stars, we now find that there is a significant molecular component as well." + Further. it appears that the observed molecular Wind must be launched from the disk surface.," Further, it appears that the observed molecular wind must be launched from the disk surface." + It is not clear whether the gas in the wind reaches escape velocities. and may therefore be re-accreted onto the disk at huger radii.," It is not clear whether the gas in the wind reaches escape velocities, and may therefore be re-accreted onto the disk at larger radii." +" The wind reproducing the CO line spectro-astrometry is much slower than that predicte by X-wiud theorv. which reaches terminal velocities of several LOOkiasDελλ, but is a much better match to photo-evaporative flows that have poloidal velocities similar to the sound speed7)."," The wind reproducing the CO line spectro-astrometry is much slower than that predicted by X-wind theory, which reaches terminal velocities of several $100\,\rm km\,s^{-1}$, but is a much better match to photo-evaporative flows that have poloidal velocities similar to the sound speed." +. The existence of disk winds with high iuass-loss rates lave siguificaut iupliceatious for the availability of material for planot formation in the PFZs of protoplauctary disks. ar av lnit the time available for planet formation.," The existence of disk winds with high mass-loss rates have significant implications for the availability of material for planet formation in the PFZs of protoplanetary disks, and may limit the time available for planet formation." + The potential laree scale οσομις of iuuer disk material as sugeested by the low velocity of the winds will also influence the chemistry of plauct-forming material. for instance by exposing a huge fraction of the disk mass to the strong UV fields at high disk elevations.," The potential large scale cycling of inner disk material as suggested by the low velocity of the winds will also influence the chemistry of planet-forming material, for instance by exposing a large fraction of the disk mass to the strong UV fields at high disk elevations." + Future work will include the development of a model for how slowmolecular winds are launched. as well as a chemical model of the wind that can explain the survivability of. at least. CO. TO and ΟΠ at low optical depths aud at lueh elevatious above the dis-," Future work will include the development of a model for how slow winds are launched, as well as a chemical model of the wind that can explain the survivability of, at least, CO, $_2$ O and OH at low optical depths and at high elevations above the disk." +" This transitional disks is one of the ""cold disks” iuaged at subiuillimeter wavelengths by ?..", This transitional disks is one of the “cold disks” imaged at submillimeter wavelengths by . + The, The +and spectroscopy (Hallidayetal.2004.. Milvang-al.2008)). with a spectroscopic success rate (number of redshifts/number of spectra) at the magnitudes used here.,"and spectroscopy \citealt{halliday04}, , \citealt{milvang-jensen08}) ), with a spectroscopic success rate (number of redshifts/number of spectra) at the magnitudes used here." + We estimate galaxy stellar masses using photo-z fitting total absolute magnitudes (Pellóetal.2009) and the relation between mass-to-light M/Ly ratio and rest-frame (B—V ) color for solar metallicity from Bell&deJongetal.(2001). (logL=—-0.5141.435€8—V )).," We estimate galaxy stellar masses using photo-z fitting total absolute magnitudes \citep{pello09} and the relation between mass-to-light $M/L_B$ ratio and rest-frame $B-V$ ) color for solar metallicity from \cite{bell01}, $ \log \frac{M}{L_B}= -0.51+1.45(B-V)$ )." + The internal accuracy of the measured masses is ~O.15dex., The internal accuracy of the measured masses is $\sim$. + The spectroscopic magnitude limit (7=23 atz20.8 and /=22 at z=0.6) corresponds to à mass limit logMΞ10.5 M.. for galaxies of all colors. and logM.=10.5 M.. for blue galaxies (see below for our red/blue limit).," The spectroscopic magnitude limit $I=23$ at $z=0.8$ and $I=22$ at $z=0.6$ ) corresponds to a mass limit $\log M_{\ast}= 10.8$ $M_{\odot}$ for galaxies of all colors, and $\log M_{\ast}= 10.5$ $M_{\odot}$ for blue galaxies (see below for our red/blue limit)." + To estimate SFRs. we usethe IR luminosities of Finnet (2009).," To estimate SFRs, we usethe IR luminosities of \cite{finn09}." + The IR luminosities are derived fromSpitzer 247m imaging. and the observed 24jim flux is converted to total IR. luminosity using the models of Dale&Helou (2002).," The IR luminosities are derived from $\mu$ m imaging, and the observed $\mu$ m flux is converted to total IR luminosity using the models of \cite{dale02}." +. The IR luminosity is converted to SFR; according to Kennicutt(1998): SERMyr!)=45«1074Lyjteress! ). assuming that the mid-IR emission of the great majority of distant cluster galaxies is powered by starbursts rather than. AGNs. as found by previous studies (Finn et al.," The IR luminosity is converted to $SFR_{IR}$ according to \cite{kennicutt98}: $SFR_{IR}(M_{\odot} \, yr^{-1}) =4.5\times 10^{-44} \times L_{IR}(\rm ergs \, s^{-1})$ , assuming that the mid-IR emission of the great majority of distant cluster galaxies is powered by starbursts rather than AGNs, as found by previous studies (Finn et al." + 2009 and references therein)., 2009 and references therein). + The median IR lummosity error is7%.. and is always less than23%.," The median IR luminosity error is, and is always less than." +. The Λο error associated with estimating the IR luminosity from the observed 24j/ flux ranges from 5 to22%.. depending on the cluster redshiftm (Finn et al.," The $SFR_{IR}$ error associated with estimating the IR luminosity from the observed $\mu$ m flux ranges from 5 to, depending on the cluster redshift (Finn et al." + 2009)., 2009). + The completeness of our Spitzer data stoa SER of ume atz20.6 and ~13 Moy! at comespordsz20.8.," The completeness limit of our Spitzer data corresponds to a $SFR_{IR}$ of at $z=0.6$ and $\sim$ 13 $M_{\odot} \, yr^{-1}$ at $z=0.8$." +" We also use he SFRjoy, (Poggiantieal.2008) from the observed [OII] luminosity using the Kewleyetal.(2004) conversion: SFRyoM.yr!)=1.26«10""Logs), corrected to our IMF."," We also use the $SFR_{[OII]}$ \citep{poggianti08} from the observed [OII] luminosity using the \cite{kewley04} conversion: $SFR_{[OII]} +(M_{\odot} \, yr^{-1}) =1.26\times 10^{41} L_{[OII]}(\rm ergs \, +s^{-1})$, corrected to our IMF." +" The SFRoj, detection lergeslimit. is —0.3M..vir!"," The $SFR_{[OII]}$ detection limit is $\sim$ $M_{\odot} \, yr^{-1}$." + The EDisCS [OIL] detections of even weak lines are very robust. having been confirmed by manual inspection of all 2D spectra.," The EDisCS [OII] detections of even weak lines are very robust, having been confirmed by manual inspection of all 2D spectra." + The SFRo; errors in SFRory range from —O0.05dex to—O.ddex. with a mean error of 7-0.Iden.," The $SFR_{[OII]}$ errors in $SFR_{[OII]}$ range from $\sim$ to$\sim$, with a mean error of $\sim$." +" To account for both obscured and unobscured SE. in galaxies with a 244m detection (all of whichhave lines in their spectra). we use the total SFR,,,=SFRip+SFR without correcting the [OH] estimate for dust extinction."," To account for both obscured and unobscured SF, in galaxies with a $\mu$ m detection (all of whichhave emission-lines in their spectra), we use the total $SFR_{tot}=SFR_{IR}+SFR_{[OII]}$ , without correcting the [OII] estimate for dust extinction." +oy. For galaxies without a 24/:m detection. we use the SFRon corrected for dust.," For galaxies without a $\mu$ m detection, we use the $SFR_{[OII]}$ corrected for dust." + The [OU] extinction correction is estimatedfrom the correlation between the uncorrected SFRow and E(B—V) observed at low-z: 0.1605log(SFRori)ME315 (Fritzetal.2009.. Kewleyetal. 2004).," The [OII] extinction correction is estimatedfrom the correlation between the uncorrected $SFR_{[OII]}$ and $E(B-V)$ observed at low-z: $E(B-V)=0.165 \log(SFR_{[OII]}) +0.315$ \citealt{fritz09}, \citealt{kewley04}) )." +" This E(CB—""V) is derived from the Balmer decrement. thus Is appropriate emission-lines."," This $E(B-V)$ is derived from the Balmer decrement, thus is appropriate for emission-lines." + We adopt the Sudziuset Galactic mean interstellar extinction law for which Fae(1996)0749., We adopt the \cite{sudzius96} Galactic mean interstellar extinction law for which $\frac{A_{3727}}{E(B-V)}=4.749 $. + Using either the total 24;;m+[OIL] or the dust corrected [OLI] SFRs. the SSFRis simply SSFRη.," Using either the total $\micron$ +[OII] or the dust corrected [OII] SFRs, the SSFR is simply $SSFR = \frac{SFR}{M_{\ast}}$." + Galaxies without a 247m detection are further =divfided into red and blue.in order to separate those that can be assumed to be powered by SF (blue) from those that could be strongly contaminated by an AGN (red).," Galaxies without a $\mu$ m detection are further divided into red and blue, in order to separate those that can be assumed to be powered by SF (blue) from those that could be strongly contaminated by an AGN (red)." +" Following (2007a).. the color separation is defined by Willmer (2000):U- Based on visual morphological classifications by Desaietal. (2007).. blue emission-line (BEL) galaxies and Spitzer- galaxies have mostly late-type morphologies (~75% and ~95%, respectively). in agreement with the assumption that they are star-forming."," Following \cite{noeske07a}, the color separation is defined by \cite{willmer06}: Based on visual morphological classifications by \cite{desai07}, blue emission-line (BEL) galaxies and Spitzer-detected galaxies have mostly late-type morphologies $\sim 75\%$ and $\sim 95\%$, respectively), in agreement with the assumption that they are star-forming." + In addition. a fraction of the REL galaxies could have their [OIL] powered by a residual low level of SF. instead of being dominated by an AGN.," In addition, a fraction of the REL galaxies could have their [OII] powered by a residual low level of SF, instead of being dominated by an AGN." + In our dataset. we currently do not have a way to quantify AGN contamination.," In our dataset, we currently do not have a way to quantify AGN contamination." + External estimates can vary significantly: at low-z. Yanetal.(2006) in their SDSS sample found that only ~10% of red galaxies with [OIL] in emission are characterized by SF.," External estimates can vary significantly: at low-z, \cite{yan06} in their SDSS sample found that only $\sim 10 \%$ of red galaxies with [OII] in emission are characterized by SF." + At higher redshifts. Noeskeetal.(2007a) find a higher fraction of probable star formation-dominated REL systems. up to30%.," At higher redshifts, \cite{noeske07a} find a higher fraction of probable star formation-dominated REL systems, up to." +. In broad agreement with this. we find that of our REL galaxies have late-type morphologies. while only are ellipticals.," In broad agreement with this, we find that of our REL galaxies have late-type morphologies, while only are ellipticals." + This suggests that at least a third of galaxies in this class are indeed star-forming., This suggests that at least a third of galaxies in this class are indeed star-forming. + Moreover. analyzing the EDisCS optical spectra. Sanchez-Blazquez et al. (," Moreover, analyzing the EDisCS optical spectra, Sanchez-Blazquez et al. (" +2009) conclude that most of our REL galaxies are dusty and star-forming.,2009) conclude that most of our REL galaxies are dusty and star-forming. + This agrees with the large population of red star-forming cluster galaxies identified at z0.2 (Wolfetal.2009)., This agrees with the large population of red star-forming cluster galaxies identified at $z\sim0.2$ \citep{wolf09}. +. However. since we cannot be certain of exactly how many red objects should be considered star-forming. in our analysis we analyze two different cases: in the first case we assume that the [OIL] emission ina// red galaxies is dominated by an AGN. and we exclude them from our analysis.," However, since we cannot be certain of exactly how many red objects should be considered star-forming, in our analysis we analyze two different cases: in the first case we assume that the [OII] emission in red galaxies is dominated by an AGN, and we exclude them from our analysis." + In the second case. we include REL galaxies.," In the second case, we include REL galaxies." + These cases should bracket the real situation occurring in nature., These cases should bracket the real situation occurring in nature. + We compare our results to those for the field at 0.4—z<0.8 from Noeskeetal.(2007a.b).. who studied the SFR and the SSER in field galaxies from the All-Wavelength Extended Groth Strip International Survey Our method to derive SFRs is similar to theirs.," We compare our results to those for the field at $0.4\leq z \leq 0.8$ from \cite{noeske07a,noeske07b}, who studied the SFR and the SSFR in field galaxies from the All-Wavelength Extended Groth Strip International Survey Our method to derive SFRs is similar to theirs." + For galaxies with robust 24;:m detections. they determined the total SFR by summing the SFR derived from 24j/m data with that derived from the emission lines uncorrected for extinction. as we do.," For galaxies with robust $\mu$ m detections, they determined the total SFR by summing the SFR derived from $\micron$ data with that derived from the emission lines uncorrected for extinction, as we do." +" For galaxies below the 24;j;m detection limit. they estimated extinction-corrected SFRs from emission line fluxes using the observed average Balmer decrement. for à fixed Aj,=1.30 value."," For galaxies below the $\mu$ m detection limit, they estimated extinction-corrected SFRs from emission line fluxes using the observed average Balmer decrement, for a fixed $A_{\rm +H\alpha}=1.30$ value." + This method overestimates the extinction in galaxies with low SFRs (Noeskeetal. 2007a).., This method overestimates the extinction in galaxies with low SFRs \citep{noeske07a}. . + To avoid systematic effects due to a different dust treatment for field and cluster galaxies. we de-corrected the AEGIS emission-line data using their value of extinction. then we applied our own method of dust correction to their datapoints.," To avoid systematic effects due to a different dust treatment for field and cluster galaxies, we de-corrected the AEGIS emission-line data using their value of extinction, then we applied our own method of dust correction to their datapoints." + Our comparison with the field is meaningful only for those galaxies with mass and SFR above the highest between our and AEGIS limits. where we are sure both samples are unbiased.," Our comparison with the field is meaningful only for those galaxies with mass and SFR above the highest between our and AEGIS limits, where we are sure both samples are unbiased." +" These limits are: a) atzc 0.6. M.>10!""8M. when we consider both blue and red galaxies (10!""°M.. when we do not consider red galaxies). and SERjojj,,,212M vr! b) at z> 0.6. M.>10!SM and ΕΛ...&1.65M vr."," These limits are: a) at $z<0.6$ , $M_{\ast} \geq 10^{10.8} M_{\odot}$ when we consider both blue and red galaxies $10^{10.5} M_{\odot}$ when we do not consider red galaxies), and $SFR_{[OII]_{corr}} \geq 1.2 M_{\odot} yr^{-1}$ ; b) at $z>0.6$ , $M_{\ast} \geq 10^{10.8} M_{\odot}$ and $SFR_{[OII]_{corr}} \geq 1.65 M_{\odot} \, yr^{-1}$ ." + Galaxies above our mass limit but below the SF limits will be disregarded inour analysis. as they make a Ro;negligible contribution to the SER census.," Galaxies above our mass limit but below the $SFR_{[OII]}$ limits will be disregarded inour analysis, as they make a negligible contribution to the SFR census." + This leaves us with a final cluster sample of 127 galaxies. and a field sample of 426 galaxies.," This leaves us with a final cluster sample of 127 galaxies, and a field sample of 426 galaxies." + Weshow the SFR-Mass relation in different environments in Fig. 1.. ," Weshow the SFR-Mass relation in different environments in Fig. \ref{SFR}, ," +where only 24j/m and BEL galaxies are considered, where only $\micron$ and BEL galaxies are considered +magnetic islands and secondary vortices.,magnetic islands and secondary vortices. + Ehe generation and decay of these vortices results in further periods of growth in the transverse kinetic energy in the svstem corresponding to periods of decreasing magnetic energy ancl vice-versa., The generation and decay of these vortices results in further periods of growth in the transverse kinetic energy in the system corresponding to periods of decreasing magnetic energy and vice-versa. + “This is clearly demonstrated in figure 9.. where the peaks in each energy are seen to correspond to the troughs in the other.," This is clearly demonstrated in figure \ref{results2_ideal_magE_KEx}, where the peaks in each energy are seen to correspond to the troughs in the other." + ‘This behaviour continues in the ideal ALLIED svstem until the system has reached a somewhat disordered state (see figure 10))., This behaviour continues in the ideal MHD system until the system has reached a somewhat disordered state (see figure \ref{results_2KH_KEx_vmag_later}) ). + In the multilluid case. on the other hand. the subsequent evolution of the KWH instability is quite dillerent.," In the multifluid case, on the other hand, the subsequent evolution of the KH instability is quite different." + The high ambipolar resistivity causes the magnetic field to experience very little wind-up. through decoupling and diffusion.," The high ambipolar resistivity causes the magnetic field to experience very little wind-up, through decoupling and diffusion." + As a result. the WIE vortex. undergoes little or no stretching or expansion as a consequence of the magnetic field.," As a result, the KH vortex undergoes little or no stretching or expansion as a consequence of the magnetic field." + Following the saturation of the instability. the magnetic field is seen to steadily return to its original configuration. and neither the velocity field. nor the magnetic field. undergo a second period of growth: (see figure 113).," Following the saturation of the instability, the magnetic field is seen to steadily return to its original configuration, and neither the velocity field nor the magnetic field undergo a second period of growth (see figure \ref{perturbB_KEx_ideal_ambi}) )." + Instead. the magnetic field eventually stabilises the velocity field. and the plasma returns almost to its original state. with simple laminar Low on either side of a much wider shear laver (see figure 12)).," Instead, the magnetic field eventually stabilises the velocity field, and the plasma returns almost to its original state, with simple laminar flow on either side of a much wider shear layer (see figure \ref{results_1KH_KEx_vmag_later}) )." + This wider shear laver is no longer conducive to the growth of the WIL instability., This wider shear layer is no longer conducive to the growth of the KH instability. + As the vortex is broken cown and the system returns to a stable state. the energy consumed. by the instability Hattens out.," As the vortex is broken down and the system returns to a stable state, the energy consumed by the instability flattens out." + The system has lost some energy. during the initial. growth of the instability due to ambipolar diffusion removing some magnetic energy. but this levels oll at [ater times.," The system has lost some energy during the initial growth of the instability due to ambipolar diffusion removing some magnetic energy, but this levels off at later times." + This is a deviation from the ideal ΑΠΟ case. in which the svstem continues to lose energv as the WIT vortex is broken down through reconnection into disordered decay.," This is a deviation from the ideal MHD case, in which the system continues to lose energy as the KH vortex is broken down through reconnection into disordered decay." + Figure 13. plots the total energies of the ideal ane multilluid ΔΗΤΟ cases. as well as the hyelroclynamic case.," Figure \ref{nonidealHD_KEy} plots the total energies of the ideal and multifluid MHD cases, as well as the hydrodynamic case." + In the hvdrodynamic case. the WIE vortex. remains indefinitely. as there is no magnetic field to lead to its decay.," In the hydrodynamic case, the KH vortex remains indefinitely, as there is no magnetic field to lead to its decay." + For these reasons. the total energies in the multilluid and hivelrodyvnamic cases are seen to level ο. while the ideal MED system continues to lose energy through decay.," For these reasons, the total energies in the multifluid and hydrodynamic cases are seen to level off, while the ideal MHD system continues to lose energy through decay." + AX studs of the KI instability in a molecular cloud. plasma is carried out., A study of the KH instability in a molecular cloud plasma is carried out. + We restrict our attention to the case of a single. transonic. super-Alfyvennic shear layer and. as such. the body modes of the WH instability are not examined.," We restrict our attention to the case of a single, transonic, super-Alfvénnic shear layer and, as such, the body modes of the KH instability are not examined." + The WH instability. in particular the growth of its surface modes. is severely reduced. for high Mach. number lows. while sub-Alfvénnic Lows tend to be stabilised by the presence of the magnetic field.," The KH instability, in particular the growth of its surface modes, is severely reduced for high Mach number flows, while sub-Alfvénnic flows tend to be stabilised by the presence of the magnetic field." + Our choice of an Alfyénn number of 10 for the system. is realistic in terms of that. present in a molecular cloud. ancl means that the growth of the instability. in the ideal. MIID approximation where there is," Our choice of an Alfvénn number of 10 for the system is realistic in terms of that present in a molecular cloud and means that the growth of the instability, in the ideal MHD approximation where there is" +Forty vears after the discovery of quasars there is still much uncertainty about their structure.,Forty years after the discovery of quasars there is still much uncertainty about their structure. +" Phere is. arguably. broad agreement about the basic nature ane overall arrangement of the various components of a ""unified: model for active ealactic nucle: (AGN) (Antonucei1993).. but the details have proved very hard to tie down."," There is, arguably, broad agreement about the basic nature and overall arrangement of the various components of a `unified model' for active galactic nuclei (AGN) \cite{a93}, but the details have proved very hard to tie down." + In particular. the nature of the central engine and. the radiative transfer. processes are the subject of. much debate.," In particular, the nature of the central engine and the radiative transfer processes are the subject of much debate." + Part. of the problem. is the paucity of observations which can elfectively distinguish one model from another., Part of the problem is the paucity of observations which can effectively distinguish one model from another. + Two tvpes of constraint which are of particular interest are the spectral energy. distribution and the observed. variations in [lux., Two types of constraint which are of particular interest are the spectral energy distribution and the observed variations in flux. +" Although one can deduce much about ACN structure from. properties such as the optical/xray Lux ratio (George&Fabian1901) or the so-called. ""big blue bump! (CGondhalekarctal...LOO4).. such measurements are not sullicient to distinguish between competing mocels. let alone refine model parameters."," Although one can deduce much about AGN structure from properties such as the optical/xray flux ratio \cite{g91} or the so-called `big blue bump' \cite{g94}, such measurements are not sufficient to distinguish between competing models, let alone refine model parameters." + Variations in Εαν were detected in quasars shortly after their discovery. and right from the start have plaved a pivotal role in constraining quasar morphology.," Variations in flux were detected in quasars shortly after their discovery, and right from the start have played a pivotal role in constraining quasar morphology." + The early detection of light. Uuetuations on a timescale of months provided a fundamental constraint on the size of the emitting region which has uncerlain all subsequent efforts to model. the structure of quasars., The early detection of light fluctuations on a timescale of months provided a fundamental constraint on the size of the emitting region which has underlain all subsequent efforts to model the structure of quasars. + In. order to obtain a clearer picture of the emitting regions in AGN and the associated emission mechanisms. a number of monitoring programmes have been carried out to measure the spectrum of variations in cillerent wavebanes.," In order to obtain a clearer picture of the emitting regions in AGN and the associated emission mechanisms, a number of monitoring programmes have been carried out to measure the spectrum of variations in different wavebands." + At present there are three basic models for explaining the observed AGN variability., At present there are three basic models for explaining the observed AGN variability. + Phe first involves instabilities in the accretion disc. the central engine poweringthe energy output. (Rees1984).," The first involves instabilities in the accretion disc, the central engine poweringthe energy output \cite{r84}." +. Phe second. postulates that AGN are powered by multiple supernova explosions or starbursts which result in stochastic variations in brightness (Arctxaga&Verlevich 1994)., The second postulates that AGN are powered by multiple supernova explosions or starbursts which result in stochastic variations in brightness \cite{a94}. +. In the third. approach. the observed variations are not intrinsic to the AGN at all. but the result of gravitational microlensing by small compact. bodies or ALACTIIOSs along the line of sight (Llawkins1993).," In the third approach, the observed variations are not intrinsic to the AGN at all, but the result of gravitational microlensing by small compact bodies or MACHOs along the line of sight \cite{h93}." +. In fact. it seems quite likely that two or even all three of these processes are present at some level. and so the task of the observer is to cliscntanele them all in order to draw useful astrophysical conclusions.," In fact, it seems quite likely that two or even all three of these processes are present at some level, and so the task of the observer is to disentangle them all in order to draw useful astrophysical conclusions." + Phere is also the possibility that different mechanisms dominate in dillerent. luminosity regimes. and so in the analysis in this paper we shall divide AGN into two categories. quasars with Alp«23 and Sevlert galaxies with Mg23.," There is also the possibility that different mechanisms dominate in different luminosity regimes, and so in the analysis in this paper we shall divide AGN into two categories, quasars with $M_{B} < -23$ and Seyfert galaxies with $M_{B} > -23$." + Although much effort has been put. into monitoring quasars CIreveseetal.1994:HookCristiani 1996).. both individually and in samples," Although much effort has been put into monitoring quasars \cite{t94,h94,c96,h96}, , both individually and in samples" +Irecquency.,frequency. + Discerning which of these processes is dominant in this region is extremely difficult when a laree spectrum of waves is continually being excited and is bevond (lie scope of (his paper., Discerning which of these processes is dominant in this region is extremely difficult when a large spectrum of waves is continually being excited and is beyond the scope of this paper. + Maxima in the convergence of Revnolds stress deep within the radiative interior (but a significant. distance below the overshoot region) propagate upward (Figure 7) as expected from the nonlinear interaction of low amplitude waves., Maxima in the convergence of Reynolds stress deep within the radiative interior (but a significant distance below the overshoot region) propagate upward (Figure 7) as expected from the nonlinear interaction of low amplitude waves. + In. addition. signilicant interference is seen in the lower radiation zone. which likely comes [rom the interaction of inward propagating and outward reflected waves.," In addition, significant interference is seen in the lower radiation zone, which likely comes from the interaction of inward propagating and outward reflected waves." + While we have not observed a complete reversal ol the angular velocity in the bulk of the radiative region. there is some evidence that one is underway (Figure6)*.," While we have not observed a complete reversal of the angular velocity in the bulk of the radiative region, there is some evidence that one is underway (Figure." +. In the core the mean angular velocity switches [rom retrograde to progerade at nearly (he same time as the tachocline switches from prograde to retrograde., In the core the mean angular velocity switches from retrograde to prograde at nearly the same time as the tachocline switches from prograde to retrograde. + This suggests that the angular velocity of the core is linked to the angular velocity of the Lachocline and hence. of the convection zone.," This suggests that the angular velocity of the core is linked to the angular velocity of the tachocline and hence, of the convection zone." + The link between tachocline angular velocity and that of the core due to selective filtering has been elucidated previously in Talon. Kumar Zahn 2002.," The link between tachocline angular velocity and that of the core due to selective filtering has been elucidated previously in Talon, Kumar Zahn 2002." +" Were we make the link between (he tachocline and (he convection zone ancl propose Chat a self-consistent study. of differential rotation in (he sun must not treat. the raciative and convective regions separately,", Here we make the link between the tachocline and the convection zone and propose that a self-consistent study of differential rotation in the sun must not treat the radiative and convective regions separately. + Despite some similarity between (he convective-radiative interface in (hie sun and the Earth's tropopause. there are several obvious differences.," Despite some similarity between the convective-radiative interface in the sun and the Earth's tropopause, there are several obvious differences." + In (he sun. convection is constantly driving gravity waves everywhere below the overshoot region: whereas (he generation of gravity. waves in the Earth's atmosphere is intermittent in time and space.," In the sun, convection is constantly driving gravity waves everywhere below the overshoot region; whereas the generation of large-amplitude gravity waves in the Earth's atmosphere is intermittent in time and space." + Solar eravily waves travel down into a converging region of increasing density (and therefore. have very little chance of breaking): whereas in the Earth waves travel up into an expanding region ol decreasing density.," Solar gravity waves travel down into a converging region of increasing density (and therefore, have very little chance of breaking); whereas in the Earth waves travel up into an expanding region of decreasing density." + Furthermore. previous numerical simulations of convective penetration in a stratified atmosphere demonstrate a remarkable difference between penetration into an overlving stable region and penetration into an underlying stable region (IIurlburt. Toomre AMassaguer 1986).," Furthermore, previous numerical simulations of convective penetration in a stratified atmosphere demonstrate a remarkable difference between penetration into an overlying stable region and penetration into an underlying stable region (Hurlburt, Toomre Massaguer 1986)." + Penetration into an underlving stable region is characterizecl by thin localized downflows: whereas penetration into an overlving stable region is characterized by larger scale broad upllows., Penetration into an underlying stable region is characterized by thin localized downflows; whereas penetration into an overlying stable region is characterized by larger scale broad upflows. + This asymmetry allows descending plumes to travel farther into an underlving stable region than ascending motions travel into an overlving stable region., This asymmetry allows descending plumes to travel farther into an underlying stable region than ascending motions travel into an overlying stable region. + Therefore. it is likely (hat penetrative convection plavs a more crucial role at the base of," Therefore, it is likely that penetrative convection plays a more crucial role at the base of" +f; and fij ave numerical [actors of order unity we can write Equ.,$f_I$ and $f_W$ are numerical factors of order unity we can write Eqn. +" 1 can then be expressed as: (he subscripts represent normalization in ces units. Όρο, =Orand we expect Chor <ος."," \ref{lum1} can then be expressed as: where the subscripts represent normalization in cgs units, $v_{rot} = \Omega r$ and we expect $v_{rot} \lesssim c_s$." + The timescale for dissipation of the rotational kinetic energy by this MIID Παν is then: These results are sensitive to specilic parameters. especially (he radius aud the ambient density that will vary with position and time. the value of T/|W|. and the amplitude of the oscillation.," The timescale for dissipation of the rotational kinetic energy by this MHD flux is then: These results are sensitive to specific parameters, especially the radius and the ambient density that will vary with position and time, the value of $\tw$, and the amplitude of the oscillation." + Our choice of normalization was guided by the density and radius at which the shear aud magnetic field are maximum ancl the amplitude by numerical simulations (Ottel /rotinst.., Our choice of normalization was guided by the density and radius at which the shear and magnetic field are maximum and the amplitude by numerical simulations \citep{ott05} . + With this choice of normalization we find that for a PNS of radius 50 km the timescale could be rather short even for rather small radial perturbations., With this choice of normalization we find that for a PNS of radius 50 km the timescale could be rather short even for rather small radial perturbations. + Note that T/|W] is bounded by 0.01 and 0.14 in the framework we address here., Note that $\tw$ is bounded by 0.01 and 0.14 in the framework we address here. + For T/|W|&0.01. Ry~5 and or/r~0.1. Eqn.," For $\tw \sim 0.01$, $R_6 \sim 5$ and $\delta r/r \sim 0.1$, Eqn." + 3. gives Linn~2.5xLO” ere 1 and Equ., \ref{lum2} gives $L_{mhd} \sim 2.5\times 10^{50}$ erg $^{-1}$ and Eqn. + 4. gives τω~300 ms. somewhat shorter than the de-leptonization time.," \ref{tau-mhd} gives $\tau_{mhd} \sim 300$ ms, somewhat shorter than the de-leptonization time." + For the same parameters. but with T/|W| near the upper limit. the Iuminosity would be 200 limes larger and «quite competitive wilh neutrino heating rates.," For the same parameters, but with $\tw$ near the upper limit, the luminosity would be 200 times larger and quite competitive with neutrino heating rates." + Note also that these expressions are formally independent of the magnetic field (which enters through Όρη). but that for realistic cases wilh strong gradients in magnetic field and perhaps concentrations of the field on (he rotational axis. (he exact nature of the dependence on the field strength and distribution could be rather more direct.," Note also that these expressions are formally independent of the magnetic field (which enters through $v_{fast}$ ), but that for realistic cases with strong gradients in magnetic field and perhaps concentrations of the field on the rotational axis, the exact nature of the dependence on the field strength and distribution could be rather more direct." + Some of this power could tend to go out the equatorial plane. but significant power could be channeled up the rotation axis.," Some of this power could tend to go out the equatorial plane, but significant power could be channeled up the rotation axis." +,. +" refsmoothing,d..M Ahthenaluralehoices7=ar|37. iM can be evaluated. using Equation (50))."," With the natural choice $\gamma^{2}=\alpha^2+\beta^2$, it can be evaluated using Equation \ref{eq:g_nm}) )." + Figuree 7 shows the how the oealaxy imageὃν of ligure 3. can be smoothed using our. shapelet method., Figure \ref{fig:smooth} shows the how the galaxy image of Figure \ref{fig:hst} can be smoothed using our shapelet method. + The resulting image is indistinguishable from that derive using ordinary convolution in real-space (also shown), The resulting image is indistinguishable from that derived using ordinary convolution in real-space (also shown). + The shapelet method. is however computationally very. efficien when the coclicient matrix is sparse às is the case here (sce Figure 4))., The shapelet method is however computationally very efficient when the coefficient matrix is sparse as is the case here (see Figure \ref{fig:hst_coef}) ). + The effect of smoothing on the shapele coellicients of this galaxy can be seen in Figure 9.., The effect of smoothing on the shapelet coefficients of this galaxy can be seen in Figure \ref{fig:hst_coef_smooth}. + For clarity. the smoothing scale was enhanced to.=4 pixels.," For clarity, the smoothing scale was enhanced to $\beta=4$ pixels." +" Clearly.- convolution amounts to a projection onto the lower order states. as discussed in refsmoothing,d.."," Clearly, convolution amounts to a projection onto the lower order states, as discussed in \\ref{smoothing_1d}." + The cartesian basisfunctions discussed above are separable in the cartesian coordinates .rj and ure., The cartesian basisfunctions discussed above are separable in the cartesian coordinates $x_{1}$ and $x_{2}$. + I ds also useful to construct basis functions which are separable in the polar coordinates .r and og., It is also useful to construct basis functions which are separable in the polar coordinates $x$ and $\varphi$. +" ""These are cigenstates of the Llamiltonian // and of the angular momentum £L simultaneously. and. thus have a number of convenient features."," These are eigenstates of the Hamiltonian $\hat{H}$ and of the angular momentum $\hat{L}$ simultaneously, and thus have a number of convenient features." + In this section. we show how they can be constructed and study some of their properties.," In this section, we show how they can be constructed and study some of their properties." + ‘To construct the polar basis functions. we first define the left and right lowering operators as (see eg.," To construct the polar basis functions, we first define the left and right lowering operators as (see eg." + Cohben-Tannoudji et al., Cohen-Tannoudji et al. + 1971) ↾∐↕⋖⋅⋜↧⊳∖⊳∖⋯⋰↓⋜⋯⊾∠⇂↓⋅⋜↧⊲↓⊳∖⊲↓⊔⋏∙≟∪↓≻∢⊾↓⋅⋜⊔∪↓⋅⊳∖⋜⊔⋅⋖⊾↙↾∣∣↴⋜⋯∠⇂↙↾∣∣⊳ respectively.," 1977) The associated raising operators are $\hat{a}_{l}^{\dagger}$ and $\hat{a}_{r}^{\dagger}$, respectively." + Phe only non-vanishing commutators between these operators are The Hamiltonian (eq. 21]]), The only non-vanishing commutators between these operators are The Hamiltonian (Eq. \ref{eq:hamiltonian_2d}] ]) + and angular momentunm (Eq. 33] , and angular momentum (Eq. \ref{eq:l}] ]) +"operators for the 2-dimensional QUO can be then be written as where the left-handec and right-hanclecd number operators are naturally defined as The operators @,. 67. a. and ἄν can thus be thought of as creating and cestroving Ieft- and right-handed quanta."," operators for the 2-dimensional QHO can be then be written as where the left-handed and right-handed number operators are naturally defined as The operators $\hat{a}_{l}^{\dagger}$ , $\hat{a}_{r}^{\dagger}$, $\hat{a}_{l}$, and $\hat{a}_{r}$ can thus be thought of as creating and destroying left- and right-handed quanta." + Since the operators Ny and Np form a complete set of commuting observables. their eigenstates. [miη) provide a complete basis for our function space.," Since the operators $\hat{N}_{r}$ and $\hat{N_{l}}$ form a complete set of commuting observables, their eigenstates $\vert n_{l},n_{r} +\rangle$ provide a complete basis for our function space." +" These states are defined Nin;no?=oman}. and similarly for N,. for n; n, non-negalive integers."," These states are defined $\hat{N}_{l}\vert n_{l},n_{r} \rangle = n_{l} \vert n_{l},n_{r} +\rangle$ , and similarly for $\hat{N}_{r}$, for $n_{l}$ $n_{r}$ non-negative integers." +" Lheyv can be constructed by applving the raising operators several times on the eround state fay=0.ns—0[n;0.n,Q0)10.0). as From Equation (58)). it is easy to see that We can therefore relabel these states in terms of their energy and angular momentum quantum numbers. nny and m=n,Dp. απ The angular momentum quantum number takes on the D| lvalues given bv mi.n.n|2.....n2.n."," They can be constructed by applying the raising operators several times on the ground state $\vert n_{1}=0,n_{2}=0 \rangle += \vert n_{l}=0,n_{r}=0 \rangle \equiv \vert 0,0 \rangle$, as From Equation \ref{eq:hl_lr}) ), it is easy to see that We can therefore relabel these states in terms of their energy and angular momentum quantum numbers, $n=n_{r}+n_{l}$ and $m=n_{r}-n_{l}$, as The angular momentum quantum number takes on the $n+1$ values given by $m=-n,-n+2,\ldots,n-2,n$." +" Using the representation of éj and ἆν. one can show that the basis functions X,Gr)=ενm) for the angular momentumstates are given hy where ff,Cr) are polynomials. which we call *polw Lermite polynomials’."," Using the $x$ -representation of $\hat{a}_{l}^{\dagger}$ and $\hat{a}_{r}^{\dagger}$ , one can show that the basis functions $\chi_{n_l,n_r}(x,\varphi) \equiv \langle x \vert n_{l},n_{r} \rangle$ for the angular momentumstates are given by where $H_{n_{k},n_{r}}(x)$ are polynomials, which we call `polar Hermite polynomials'." + μον can be computed by noting that flyoGr)=1 and byusing the recursion relation," They can be computed by noting that $H_{0,0}(x)=1$ and byusing the recursion relation" +and LDLs require that either the beam pattern or physical jet openius angle for the N-ray ciuission is lavecr than than for the radio cuuission. e.g.. StockeColottictal. (1993)...,"and LBLs require that either the beam pattern or physical jet opening angle for the X-ray emission is larger than than for the radio emission, e.g., \citet{sto89,urr91,ghi93,cel93}." + Several observed. properties are consistent with this hwpothesis., Several observed properties are consistent with this hypothesis. + Compared to LBLs. IIBLs are more nunerous. their cores are less radio huninous. and they are less optically variable (Januuzietal.1993).," Compared to LBLs, HBLs are more numerous, their cores are less radio luminous, and they are less optically variable \citep{jan93}." +. IIBLEs also cuit less compact radio emission (Perhuau&Stocke1993.1991:Laureut-Muoehlleisenotal. 1993).. contain larger fractions of starlight iu the optical (Morrisctal.1991).. and lave snaller degrees Or: ¢optical polarization. often with a preferred optical »olarization angle. E157 (CJaunuzictal.1991).," HBLs also emit less compact radio emission \citep{per93,per94,lau93}, contain larger fractions of starlight in the optical \citep{mor91}, and have smaller degrees of optical polarization, often with a preferred optical polarization angle, $\pm +15\arcdeg$ \citep{jan94}." +. ITowever. several observed properties which should be iudepeudeut of orientation. e.2.. observed evolution. optical euission-ine strengths and extended radio powers. do not agree tween IIBLs aud LDLs. indicating that oricutation alone is insufficieut to explain the observed distinctions tween the two classes (Rector&Stocke2001).," However, several observed properties which should be independent of orientation, e.g., observed evolution, optical emission-line strengths and extended radio powers, do not agree between HBLs and LBLs, indicating that orientation alone is insufficient to explain the observed distinctions between the two classes \citep{rec01}." +". Iu fact. uauv LBLs appear to be beamed. high-huninosity ER-Ils: aud at least one is a gravitationallv lensed object. he ""uallest Einstein rine” object Lv 0218|357 (ODoaetal. 1992)."," In fact, many LBLs appear to be beamed, high-luminosity FR-IIs; and at least one is a gravitationally lensed object, the “smallest Einstein ring"" object 1Jy 0218+357 \citep{ode92}." +. The picture seenis to be more clear for UBLs. whose properties are very cousisteut with being xuued FR-Is (Rectoretal.2000).," The picture seems to be more clear for HBLs, whose properties are very consistent with being beamed FR-Is \citep{rec00}." +. Several observatious support this picture. e.g.. extended radio huuinositv and morphology (Autouucci&Ulvestad1985:Perlnan&Stocke 1993). host ealaxy huuinositv and uorphologv (Abrahametal.1991:Wurtz1996). and comparative space deusities and Inuuinosityv functions (Dadovani&αν1990:Morrisetal.1991).," Several observations support this picture, e.g., extended radio luminosity and morphology \citep{ant85,per93}, host galaxy luminosity and morphology \citep{abr91,wur96}, and comparative space densities and luminosity functions \citep{pad90,mor91}." + Alternatively. it has also been suggested that the iference between LBLs aud HDBLs des not iu xieutation. but in the higl-energy cutoff in their energy istributious. such that IIDLs and LDLs represent a siuele £unilv of objects with a smooth energy distributio- followed by. a sharp cutoff.," Alternatively, it has also been suggested that the difference between LBLs and HBLs lies not in orientation, but in the high-energy cutoff in their energy distributions, such that HBLs and LBLs represent a single family of objects with a smooth energy distribution followed by a sharp cutoff." + For LBLs this cutoff occurμα in the near-IRfoptical aud for IIDEs it is at UV/X-rav or higher energies (Cdonuui&Padovani199DPadovaui&(οι1995:Sambrunaetal. 1996).," For LBLs this cutoff occurs in the near-IR/optical and for HBLs it is at UV/X-ray or higher energies \citep{gio94,pad95,sam96}." +". Tu this model. hereafter the ""energv-cutoff model. IIDEs have imtriunsieallv lower radio huuinosities than LBLs. and strong selection effects explain why most known BL Lacs are of the IBL variety."," In this model, hereafter the “energy-cutoff"" model, HBLs have intrinsically lower radio luminosities than LBLs, and strong selection effects explain why most known BL Lacs are of the HBL variety." + Observational studies of BL Lacs at radio wavelengths have proven to be an effective test of unification mocels for two reasons., Observational studies of BL Lacs at radio wavelengths have proven to be an effective test of unification models for two reasons. + First. the kpc-scale exteuded radio fiux is Likely uubemued. aud is therefore iudicative of the actual ACN power: and second. the core and parsec-scale extended flux is highly beamed. aud is therefore strouglv depeudent on the orientation and relativistic jiture of the jet.," First, the kpc-scale extended radio flux is likely unbeamed, and is therefore indicative of the actual AGN power; and second, the core and parsec-scale extended flux is highly beamed, and is therefore strongly dependent on the orientation and relativistic nature of the jet." + If IIBEs are seen further off axis than LDLs. radio nuages will reveal several distinct trends.," If HBLs are seen further off axis than LBLs, radio images will reveal several distinct trends." + First. relativistic Doppler boosting aud apparent proper notion are strongly scusitive to the oricutation anele and bulk Lorentz factor of the jet.," First, relativistic Doppler boosting and apparent proper motion are strongly sensitive to the orientation angle and bulk Lorentz factor of the jet." + Thus. if seen close o their jet axis. LBLs should be more core-dominated. show inore instances of superblunimal motion aud have arecr jet to counter-jet briehtuess ratios.," Thus, if seen close to their jet axis, LBLs should be more core-dominated, show more instances of superluminal motion and have larger jet to counter-jet brightness ratios." + Aud if IIBEs aud LBLs share the jue parent population. both should wave simular jet Lorentz factors.," And if HBLs and LBLs share the same parent population, both should have similar jet Lorentz factors." + Second. geometrical xojection effects will cause jets with intrinsically sinall ends to appear highly distorted when seen close to the line of sight.," Second, geometrical projection effects will cause jets with intrinsically small bends to appear highly distorted when seen close to the line of sight." + Thus. the projected jet position angle (PA) in these highly inclined objects is very scusitive to the jet structure.," Thus, the projected jet position angle (PA) in these highly inclined objects is very sensitive to the jet structure." +" It is known that LBLs show a wide range of parsec- and Ispe-scale jet misalignment aneles =[PA;,,PÀ,, j. presumably from a ""knottv or helical jet seen close to the Lue of sight (Nollgaardctal.1992:Conway&Murphy1993:Appletal.1996)."," It is known that LBLs show a wide range of parsec- and kpc-scale jet misalignment angles $\equiv +\vert {\rm PA}_{kpc} - {\rm PA}_{pc} \vert$ ), presumably from a “knotty"" or helical jet seen close to the line of sight \citep{kol92,con93,app96}." +. I£ MBLs are seen further off-axis than LBLs. geometrical projection effects will cause the parsec- aud kpc-scale projected jet PAs of IIBLs to be more aligned than LBLs.," If HBLs are seen further off-axis than LBLs, geometrical projection effects will cause the parsec- and kpc-scale projected jet PAs of HBLs to be more aligned than LBLs." +" If the ""euergv-cutoff model is correct and there is no orientation bias. LDLs aud IIBLs should showsiuilar parsec- and kpe-scale radio structure. sinuülar distributious of parsec- aud kpe-scale jet miusaliguiuent. assundue thev share the same parent population."," If the “energy-cutoff"" model is correct and there is no orientation bias, LBLs and HBLs should showsimilar parsec- and kpc-scale radio structure, similar distributions of parsec- and kpc-scale jet misalignment, assuming they share the same parent population." + But suce LBLs are generallv more huninous than IIDLs (Fossatictal.1998).. their parsec-scale structures nia differ iutrimsically frou IIDLs.," But since LBLs are generally more luminous than HBLs \citep{fos98}, their parsec-scale structures may differ intrinsically from HBLs." + Iu this paper we present deep VLA aud fist-epoch VLBA observations of a sample of fifteen BL Lacs which span the full range of «ποσο iu IIBEs (82)., In this paper we present deep VLA and first-epoch VLBA observations of a sample of fifteen BL Lacs which span the full range of seen in HBLs 2). + These Ενmaps are used to compare the xusec and kpe-scale structure of these objects., These maps are used to compare the parsec and kpc-scale structure of these objects. + In & discuss the results of these observations. compare them ο simular studies of LBLs aud discuss their iuplications or unification models.," In 3 we discuss the results of these observations, compare them to similar studies of LBLs and discuss their implications for unification models." + As these are ouly the first epoch of observations. proper motions of jet commpoucuts are rot vet available: thus we consider ouly the aliguiaicut and structure of the parsec-scale jets.," As these are only the first epoch of observations, proper motions of jet components are not yet available; thus we consider only the alignment and structure of the parsec-scale jets." + Iu §l we prescut he conclusions., In 4 we present the conclusions. + Due to their relative radio faintuess. few IIBEs have been studied with VLBI techniques.," Due to their relative radio faintness, few HBLs have been studied with VLBI techniques." + INolleaardetal.(1996) preseuted tuages of four IIBLs from the bright ΠΑΟ 1I survev (Scluwartzetal.1989).. all of which have vvalues close o the LDBL/IIBL bouudiurv.," \citet{kol96} presented images of four HBLs from the bright HEAO 1 survey \citep{sch89}, all of which have values close to the LBL/HBL boundary." + Couwav et al. (, Conway et al. ( +private. conun.),private comm.) + completed VLBA observations of cight IIBLs fro uthe Medimu Sensitivity Survey (Morrisetal.1991:Rector2000):: however. parsec-scale. extended structure was not detected im inost of these objects. uost likely due to their füutness 25 indy at 5 CGIIz).," completed VLBA observations of eight HBLs from the Medium Sensitivity Survey \citep{mor91,rec00}; however, parsec-scale extended structure was not detected in most of these objects, most likely due to their faintness $f_{core} \approx 25$ mJy at 5 GHz)." + In order to better determine the parsec-scale structure. of IIDBLs. we completed deep VLÀ aud VLBA observatious of a sample of IIDBEs that covers a factor of ~30 iulogCf./f.," In order to better determine the parsec-scale structure of HBLs, we completed deep VLA and VLBA observations of a sample of HBLs that covers a factor of $\sim$ 30 in." +). The initial goal was o determine their morphology and core dominance on VLBI scales as well as to measure the projected alienminent of their parsec- aud kpce-cale radio jets., The initial goal was to determine their morphology and core dominance on VLBI scales as well as to measure the projected alignment of their parsec- and kpc-scale radio jets. + At he tine this project was begun. the availability of shase-reference calibrators for the VLBA was limited. so we chose oulv targets which were likely bright euoughl cor self-calibration (f£.250 Jv at 1961 GIIz).," At the time this project was begun, the availability of phase-reference calibrators for the VLBA was limited, so we chose only targets which were likely bright enough for self-calibration $f_{core} \geq 50$ mJy at 4.964 GHz)." + Since IIBLs are for the most part too radio faint to observe a statisticallycomplete sample without phase referencing. we chose a sample that represcuted the full ranee of vvalues observable in IIBLEs. as shown in Figure 1..," Since HBLs are for the most part too radio faint to observe a statisticallycomplete sample without phase referencing, we chose a sample that represented the full range of values observable in HBLs, as shown in Figure \ref{fig-1}. ." +" Our salple was selected primarily from the ""Slew Survey (LES: Perlnanetal. (1996)3)."," Our sample was selected primarily from the “Slew"" Survey (1ES; \citet{per96}) )." + Objects that are LBL-like (i.c.. pS) werediscarded ," Objects that are LBL-like (i.e., $< -5.5$ ) were discarded." +/ Thissainplewassupplemented wit hthrecob ject., This sample was supplemented with three objects from the RGB BL Lac sample to fill in the +In regards to creation of SÀDs. we offer a plausible scenario in which a log-normal distribution ean be generated with minimal suppositions: Firstly. that the SADs form through patchy reconnection and grow al a rate described bv equation (1).,"In regards to creation of SADs, we offer a plausible scenario in which a log-normal distribution can be generated with minimal suppositions: Firstly, that the SADs form through patchy reconnection and grow at a rate described by equation (1)." + Secondly. that the growth coefficient 4 is approximately uniform for all SADs. while the duration of the growth is normally distributed.," Secondly, that the growth coefficient $k$ is approximately uniform for all SADs, while the duration of the growth is normally distributed." + Although the conjecture of uniform & appears to imply a uniform reconnection rate for all resistive patches in supra-arcade current sheets. (his scenario remains io be tested via numerical simulations of reconnection.," Although the conjecture of uniform $k$ appears to imply a uniform reconnection rate for all resistive patches in supra-arcade current sheets, this scenario remains to be tested via numerical simulations of reconnection." + This work was partially supported by NASA under contract NNMOTADOTC with the IHarvard-Smithsonian Astrophysical Observatory., This work was partially supported by NASA under contract NNM07AB07C with the Harvard-Smithsonian Astrophysical Observatory. + data are provided courtesy of the NASA-supported Legacy Archive at Montana State University., data are provided courtesy of the NASA-supported Legacy Archive at Montana State University. + We eratefullv acknowledge ihe helpful comments of an anonymous referee., We gratefully acknowledge the helpful comments of an anonymous referee. +"The transition from fluxes calculated using the main radiative transfer equations (1,, 3)) and the diffusion approximation (4)) occurs based on the local optical depth (7=rgP/g, taking intoaccount any dependence of «jr with pressure).","The transition from fluxes calculated using the main radiative transfer equations \ref{eqn:sw}, , \ref{eqn:fir}) ) and the diffusion approximation \ref{eqn:fdiff}) ) occurs based on the local optical depth $\tau = \kir P/g$, taking intoaccount any dependence of $\kir$ with pressure)." +" The original radiative scheme begins to fail when the term E=exp(—[1.66/g]fkidP) becomes too small, and so we use this as a criterion for when to begin the implementation of the flux diffusion scheme."," The original radiative scheme begins to fail when the term $E=\exp(-[1.66/g]\int \kir dP)$ becomes too small, and so we use this as a criterion for when to begin the implementation of the flux diffusion scheme." +" Through trial and comparison to the analytic solutions, we determined that the fix should begin at the point where E<0.01, which in our code corresponds to an optical depth 7>nimi;=5.55/(104—10-4), where A is the vertical resolution of the model, A=logj9(Pmaz/Pmin)/NL."," Through trial and comparison to the analytic solutions, we determined that the fix should begin at the point where $E \leq 0.01$, which in our code corresponds to an optical depth $\tau > \tau_{\mathrm{limit}} = 5.55/(10^A-10^{-A})$, where $A$ is the vertical resolution of the model, $A=\log_{10}(P_{max}/P_{min})/NL$." +" For a model whose bottom boundary is atPmax=100 bar, whose upper boundary is P,,5,=1 mbar, and that has NL=30 levels, Τι=7 (=0.56 barin Figure 1))."," For a model whose bottom boundary is at$P_{max}=100$ bar, whose upper boundary is $P_{min}=1$ mbar, and that has $NL=30$ levels, $\tau_{\mathrm{limit}}=7$ $= 0.56$ barin Figure \ref{fig:fdiff}) )." + A model using only 10 vertical levels would have nig;=2 (=0.16 bar in Figure 1))., A model using only 10 vertical levels would have $\tau_{\mathrm{limit}}=2$ $= 0.16$ bar in Figure \ref{fig:fdiff}) ). + This resolution-dependent Τι appropriately fixes the resolution dependence of the problem with the original radiative transfer scheme., This resolution-dependent $\tau_{\mathrm{limit}}$ appropriately fixes the resolution dependence of the problem with the original radiative transfer scheme. +" At optical depths greater than τιμες, the infrared flux is calculated as: Fg(P) ai, where Firrad is the infrared flux calculated fromEquation 3.."," At optical depths greater than $\tau_{\mathrm{limit}}$ , the infrared flux is calculated as: $F_{\mathrm{IR}}(P) = (E^{0.023}) F_{\mathrm{IR,rad}} + (1-E^{0.023}) F_{\mathrm{IR,diff}}$ , where $F_{\mathrm{IR,rad}}$ is the infrared flux calculated fromEquation \ref{eqn:fir}. ." + The transition to, The transition to +are imposed on equation (18)).,are imposed on equation \ref{SE3}) ). +" Equation (18)) is a second-order ordinary differential equation with respect to 7, whereas three boundary conditions (22)) and (23)) are imposed on it."," Equation \ref{SE3}) ) is a second-order ordinary differential equation with respect to $T$, whereas three boundary conditions \ref{BC1}) ) and \ref{BC2}) ) are imposed on it." +" Therefore, it has a solution only when the mass flux j is tuned as an eigenvalue of the solution, and j is expressed as a function of p, (Shchekinov IbátikzmarkmainBodyEnd10037mainBodyStartIO04neez 2001)."," Therefore, it has a solution only when the mass flux $j$ is tuned as an eigenvalue of the solution, and $j$ is expressed as a function of $p_{1}$ (Shchekinov Ib\'a\\tikzmark{mainBodyEnd1003}\~\tikzmark{mainBodyStart1004}neez 2001)." +" In the case of a static front, that is, j=70, equation (18)) can be transformed as follows: Cel'dovich Pikelner 1969, Penston Brown 1970)."," In the case of a static front, that is, $j=v=0$, equation \ref{SE3}) ) can be transformed as follows: (Zel'dovich Pikel'ner 1969, Penston Brown 1970)." + Equation (24)) expresses the balance between cooling and heating inside a static front., Equation \ref{SAT}) ) expresses the balance between cooling and heating inside a static front. + The pressure that allows such a static structure is called thepressure., The pressure that allows such a static structure is called the. +". Substituting equations (6))-(8)) into equation (24)) and solving, we obtain a saturation pressure p./Ay=2612 K * for our choice of cooling function."," Substituting equations \ref{CF1}) \ref{CF3}) ) into equation \ref{SAT}) ) and solving, we obtain a saturation pressure $p_{s}/k_{B}=2612$ K $^{-3}$ for our choice of cooling function." +" If p, is higher (lower) than this pressure, fluid elements that pass through the front experience a net cooling (heating) inside the front."," If $p_{1}$ is higher (lower) than this pressure, fluid elements that pass through the front experience a net cooling (heating) inside the front." +" Thus, such a front becomes a condensation (evaporation) front."," Thus, such a front becomes a condensation (evaporation) front." + We numerically solve equations (16))-(18)) with the boundary conditions of equations (22)) and (23))., We numerically solve equations \ref{SE1}) \ref{SE3}) ) with the boundary conditions of equations \ref{BC1}) ) and \ref{BC2}) ). + We take the CNM to be state 1., We take the CNM to be state 1. +" The dominant contribution to thermal conductivity 1s due to neutral atoms, so we use &=2.5x10*T? eress !K tem ! (Parker 1953)."," The dominant contribution to thermal conductivity is due to neutral atoms, so we use $\kappa=2.5\times 10^{3}\,T^{1/2}$ ergs $^{-1}$ $^{-1}$ $^{-1}$ (Parker 1953)." +" We plot the solutions in the number density-pressure diagram and in terms of temperature structure in Figures | and 2.. respectively, for values p,/Ay of 1500.2000.2612. and 4000 K *."," We plot the solutions in the number density-pressure diagram and in terms of temperature structure in Figures \ref{f1} and \ref{f2}, respectively, for values $p_{1}/k_{\rm B}$ of $1500, 2000, 2612,$ and $ 4000$ K $^{-3}$." +" The structure of the temperature. pressure, number density. and velocity for py/hy=1500 K are plotted in Figure 3.."," The structure of the temperature, pressure, number density, and velocity for $p_{1}/k_{\rm B}=1500$ K $^{-3}$ are plotted in Figure \ref{f3}." + Figures | and 3 show that the structure is almost isobaric., Figures \ref{f1} and \ref{f3} show that the structure is almost isobaric. + That is due to the small Mach number of the flow (typically M.~10. 7)., That is due to the small Mach number of the flow (typically $\mathcal{M}\simeq 10^{-2}$ ). +" From equation (16)) and (17)). the pressure difference between the CNM and WNM is where subscripts w and c denote the values in the WNM and CNM. respectively. c=(5RT/pot7 is the sound speed, and we use the fact that ,> v."," From equation \ref{SE1}) ) and \ref{SE2}) ), the pressure difference between the CNM and WNM is where subscripts $\rm w$ and $\rm c$ denote the values in the WNM and CNM, respectively, $c=(\gamma\,R\,T/\mu)^{1/2}$ is the sound speed, and we use the fact that $v_{\rm w}\gg v_{\rm c}$ ." +where Ar—rsry.,"where $\Delta r= r_c - r_b\,$." +" Similarly as we did for the IXerr case. here we can consider OAL=fhHe(o,) and in view of ()) and ()) write (/=1) oM== The >οὉ − − − ∖∖⊽↥∐↲↕⋅≼↲∖∖⇁≼↲∐≀↧↴∖⇁≼↲∏⋟∖⇁≼↲≼⇂∫↘−↴∿↴≡↽⊰∣⋮∁≀↕↴↕∐⇂≺∢∪∐⋟∖⊽∐⇂≼↲↕⋅≼↲≼⇂⇖∣∣↓∪↕⋅≸↽↔↴↕⋅≀↧↴∖↽∐≀↧↴⊔∪↕⋯↥↕↽≻≼↲∐∏↕⋅∣↽≻≀↧"," Similarly as we did for the Kerr case, here we can consider $\delta M=\hbar Re(\omega_n)\,$ and in view of \ref{modos2}) ) and \ref{surfgrav}) ) write $\hbar=1$ ) M= , where we have used $R^2\sim 3r_b^2 $ and considered $V_0$ for gravitational perturbations." +"↴⊔∪∐⋟∖⊽⋅ variation of the black hole horizon area. Ql — Sarporpe ihen gives us Ql =. for gravitational quasi-normal modes and dl,=Zin)(((+1)--"" otherwise."," The variation of the black hole horizon area, A_b = r_b, then gives us A_b =, for gravitational quasi-normal modes and $\delta A_b = +24\pi\sqrt{\ell(\ell+1)-\frac{1}{4}}$ otherwise." +" Thus we can prescribe (he «quantum. area spectrum for a quasi-Nariai black hole as E nó A078πρpin. where »=1.2..... or. in the case of scalar or electromagnetic perturbations. 122/101,n."," Thus we can prescribe the quantum area spectrum for a quasi-Nariai black hole as = n ^2_P, where $n=1,2,...\,$, or, in the case of scalar or electromagnetic perturbations, $12\pi \sqrt{7}\ell^2_P\,n\,$." + In sunumary. wilh the knowledge of the analvtical «quasi-normal mode spectrum of near extreme Ixerr and near extremeS419 black holes. as given in," In summary, with the knowledge of the analytical quasi-normal mode spectrum of near extreme Kerr and near extremeS-dS black holes, as given in" +The structure ancl evolution of neutron stars depends on the properties of matter al nuclear ancl supranuclear densities.,The structure and evolution of neutron stars depends on the properties of matter at nuclear and supranuclear densities. + Such conditions are not achievable in terrestrial laboratories and the theoretical description of such superdense matter remains uncertain., Such conditions are not achievable in terrestrial laboratories and the theoretical description of such superdense matter remains uncertain. + It has therefore been hoped that neutron stus. ancl in particular those that. are isolated and not complicated by strong accretion or magnetospheric signatures. mieht provide some empirical insights: observations of their masses. radii and cooling characteristics could. in principle. provide useful constraints for the equation of state (EOS) of dense matter LLattimer Prakash 2001 and references therein).," It has therefore been hoped that neutron stars, and in particular those that are isolated and not complicated by strong accretion or magnetospheric signatures, might provide some empirical insights: observations of their masses, radii and cooling characteristics could, in principle, provide useful constraints for the equation of state (EOS) of dense matter Lattimer Prakash 2001 and references therein)." + In a relatively brief period of 109-10* vr. a hot. isolated neutron star (INS) born in a supernova explosion ean cool. cease pulsar activitv and become essentially inactive (see. e.g.. (he review of Treves et 22000).," In a relatively brief period of $10^6$ $10^7$ yr, a hot, isolated neutron star (INS) born in a supernova explosion can cool, cease pulsar activity and become essentially inactive (see, e.g., the review of Treves et 2000)." + Of the estimated 105-10? isolated neutron stars thought to inhabit the Galaxy. only a (nv fraction are therefore expected to be sulliciently voung to remain hot and visible in N-ravs.," Of the estimated $10^8$ $10^9$ isolated neutron stars thought to inhabit the Galaxy, only a tiny fraction are therefore expected to be sufficiently young to remain hot and visible in X-rays." + One possible mechanism capable of sustaining thermal X-ray emission in an older INS is accretion of material [rom the ISM., One possible mechanism capable of sustaining thermal X-ray emission in an older INS is accretion of material from the ISM. + To date. only a handful of these older INS candidates have been found.," To date, only a handful of these older INS candidates have been found." + The soft X-ray source dediscovered by Walter. Wolk Neuhauuser (1996) is the brightest. and probably the closest (xaplan. van Ixerkwijk Anderson 2002) of the INS candidates.," The soft X-ray source discovered by Walter, Wolk Neuhäuuser (1996) is the brightest, and probably the closest (Kaplan, van Kerkwijk Anderson 2002) of the INS candidates." + It was identified with a very [aint (V.o 25.6) optical counterpart bv Walter Matthews (1997). was [ound to have an optical fax about a factor of 2-3 higher (han that predicted by the Baxvleigh-Jeans tail of the ~55 eV blackbody spectrum that represents the low resolution ROSAT PSPC spectrum WWalter et 11996; Campana et 11997. Pons et 22001). aud lies in the line-olsieht toward the dark molecular cloud Ro CrA. However. the exact nature of rremains unknownwhether it is a fairly voung. cooling INS. perhaps uudetected as a pulsar because of unfortunate beam alignment. or an older object reheated by ISM acceretion.," It was identified with a very faint $V\simeq25.6$ ) optical counterpart by Walter Matthews (1997), was found to have an optical flux about a factor of 2-3 higher than that predicted by the Rayleigh-Jeans tail of the $\sim 55$ eV blackbody spectrum that represents the low resolution ROSAT PSPC spectrum Walter et 1996; Campana et 1997, Pons et 2001), and lies in the line-of-sight toward the dark molecular cloud R CrA. However, the exact nature of remains unknown—whether it is a fairly young, cooling INS, perhaps undetected as a pulsar because of unfortunate beam alignment, or an older object reheated by ISM accretion." + Verv Large Telescope (VLT) observations have recently revealed an Hla. nebula round acid a blackbody spectrum through the UV-optical range (wan Ixerkwijk Ixulkarni 2001a.b).," Very Large Telescope (VLT) observations have recently revealed an $\alpha$ nebula round and a blackbody spectrum through the UV-optical range (van Kerkwijk Kulkarni 2001a,b)." + ]lubble Space Telescope (IIST) astrometryv was used by Walter (2001) and Ixaplan et ((2002) to estimate a parallax and proper motion. but with conflicting results (16.52:2.3 mas THe? mas).," Hubble Space Telescope (HST) astrometry was used by Walter (2001) and Kaplan et (2002) to estimate a parallax and proper motion, but with conflicting results $16.5\pm 2.3$ mas $7\pm 2$ mas)." +" Waller (2001) argued that the proper motion points to the 5co-Cen OD associalion and an age of —10"" vr.", Walter (2001) argued that the proper motion points to the Sco-Cen OB association and an age of $\sim 10^6$ yr. + However. Pons et ((2001) failed to detect the expected pulsation signature in ROSAT and. ASCA data.," However, Pons et (2001) failed to detect the expected pulsation signature in ROSAT and ASCA data." + Modelling X-ray. EUV. UV and optical spectra using the Walter (2001) parallax ancl assuming a metal-dominated atmosphere resulted in stellar radii too small for current. EOS and smaller than the Schwarzschild," Modelling X-ray, EUV, UV and optical spectra using the Walter (2001) parallax and assuming a metal-dominated atmosphere resulted in stellar radii too small for current EOS and smaller than the Schwarzschild" +withh common interstellar ice constituents are largely lacking.,h common interstellar ice constituents are largely lacking. +Iu Figure Lis shown the CPR2003 zurvev area. covering a 1.5? x 2° field of view.,"In Figure 4 is shown the CPR2003 survey area, covering a $^{\circ}$ x $^{\circ}$ field of view." + The ceuter of the field is aligned with the ceuter of the star distribution secu for (νο OD2 by IEuóddelseder (2000) using 2\LASS. a=20337105.6|11715.7'.," The center of the field is aligned with the center of the star distribution seen for Cyg OB2 by Knöddelseder (2000) using 2MASS, $\alpha = 20^{h} 33^{m} 10^{s}, \ +\delta= ++41^{\circ} 15.7'$." + The circles correspond to the 120 stars previously ideutified to bo micuhers of the (νο OD2 cluster by AITOL based on UBY colors., The circles correspond to the 120 stars previously identified to be members of the Cyg OB2 cluster by MT91 based on UBV colors. + Asterisks in Figure Llocate a total of 62 new massive star candidates identified by CPR2002., Asterisks in Figure 4 locate a total of 62 new massive star candidates identified by CPR2002. + The asterisk sources include 15 candidate early-type uecmbers (CPR 2002 AL3 is left out since if was previously ideutified as Schulte 16). L1 stars with Br 7 cussion (6 of their 20 Br 5 sources were previously ideutified). and 3 new sources showing CO in emission.," The asterisk sources include 45 candidate early-type members (CPR 2002 A43 is left out since it was previously identified as Schulte 16), 14 stars with Br $\gamma$ emission (6 of their 20 Br $\gamma$ sources were previously identified), and 3 new sources showing CO in emission." + What is first muuediatelv obvious in this nuage is that most of the new sources found by CPR2002 lie well away from the previously ideutified optical cluster stars., What is first immediately obvious in this image is that most of the new sources found by CPR2002 lie well away from the previously identified optical cluster stars. + Ouly near the south and west side of the optical field are new candidate OB members seen to lie in close proximity to previously identified cluster members., Only near the south and west side of the optical field are new candidate OB members seen to lie in close proximity to previously identified cluster members. + This study has confirmed 11 ποτ OB stars in the field. all L1 of which are labeled with CPR2002 identifications in Ll (A20. A23. ete).," This study has confirmed 14 new OB stars in the field, all 14 of which are labeled with CPR2002 identifications in 4 (A20, A23, etc.)." + O£ the 11 now OB stars coufiriied in this study. all lie a siguificaut distance from the previously identified optical cluster of AIT9OL.," Of the 14 new OB stars confirmed in this study, all lie a significant distance from the previously identified optical cluster of MT91." + The reason most of these OB stars were mussed by AIT91 was simply because the field over which AIT91 searched did not exteud to these augular distances., The reason most of these OB stars were missed by MT91 was simply because the field over which MT91 searched did not extend to these angular distances. + From the full sample of 71 (νο OB2 stars with spectral types published in MT91. a subset of 35 stars. listed iu Table 3. was selected to perform specific calibrations of the cluster characteristics.," From the full sample of 71 Cyg OB2 stars with spectral types published in MT91, a subset of 35 stars, listed in Table 3, was selected to perform specific calibrations of the cluster characteristics." + This subset of stars was selected t| have optical spectral types between O7.5 and Bl inclusive. all ave normal dwarf stars. and all have both UDV values as well as 2\LASS JIIINs colors.," This subset of stars was selected to have optical spectral types between O7.5 and B1 inclusive, all are normal dwarf stars, and all have both UBV values as well as 2MASS $_S$ colors." + None of the new OB stars preseuted in this paper were mceludec|l., None of the new OB stars presented in this paper were included. + Usine the intrinsic UDV color terms given by FitzGerald (1970: aud receutlv used by Slesuick. Illeubrand. Massey. 2002) aud. JITI&&. color terms given by Lejeuue Schaerer (2001) for cvarf stars. the extiwction characteristics were determined toward cach star iudepeudoeutly based ou the stars observed s colors.," Using the intrinsic UBV color terms given by FitzGerald (1970; and recently used by Slesnick, Hillenbrand, Massey 2002) and $_S$ color terms given by Lejenue Schaerer (2001) for dwarf stars, the extinction characteristics were determined toward each star independently based on the stars observed $_S$ colors." + This has lead to a well constrained average extinction law towards the cluster as illustrated in Figures 5. 6 and 7.," This has lead to a well constrained average extinction law towards the cluster as illustrated in Figures 5, 6 and 7." + The extinction law created from the fits shown in 55. 6. aud 7 are given in Table .," The extinction law created from the fits shown in 5, 6, and 7 are given in Table 4." + The optical extinction law was previously measured by ALTT9L and Torres-Dodgen ct ((1991)., The optical extinction law was previously measured by MT91 and Torres-Dodgen et (1991). + As seen in these previous studies. the extinction was measured to be consistent with a total to selective extinction ratio. Ry. of 3.0.," As seen in these previous studies, the extinction was measured to be consistent with a total to selective extinction ratio, $R_V$, of 3.0." + The extinction law through the near-intrared matches that given for the general iuterstelay miedimm by Ricke Lebotsky (1985). except for the I& band.," The extinction law through the near-infrared matches that given for the general interstellar medium by Rieke Lebofsky (1985), except for the K band." + The ceutroid of the 2N[ASS Ix band is at 2.16 μπα. while Ricke Lebofsky used Johusou I&-baud filters ceutered at 2.22 pau. This leads to a sligtly lareer extinction ratio in the 2\TASS Ks baud (Alyfy= 0.125) relative to the Rieke Lehofsky (C985) IX baud (AgAy:= 0.112).," The centroid of the 2MASS $_S$ band is at 2.16 $\mu$ m, while Rieke Lebofsky used Johnson K-band filters centered at 2.22 $\mu$ m. This leads to a slightly larger extinction ratio in the 2MASS $_S$ band $A_{K_s}/A_V = 0.125$ ) relative to the Rieke Lebofsky (1985) K band $A_K/A_V = 0.112$ )." + With a well esablished extinction law derived for the cluster. Ay- values for every star with optical spectral types in our full sample of 85 (Fl previously ideutified by MT9OL. plus the L1 uew OB stars confirmed in this study) could be calculated from either ΤΟΝ. & colors. or both depending on what was available.," With a well established extinction law derived for the cluster, $_V$ values for every star with optical spectral types in our full sample of 85 (71 previously identified by MT91, plus the 14 new OB stars confirmed in this study) could be calculated from either UBV, $_S$ colors, or both depending on what was available." + Extinction values for all stars in this study. Guclusive of the 35 dwarf stars also listed in Table 1) are given in Table 5., Extinction values for all stars in this study (inclusive of the 35 dwarf stars also listed in Table 4) are given in Table 5. + Of the 85 stars in our complete sample extinction varied from Ay- = 3.83 up to Ay = 10.70 for the infamous BS supereiaut. IV Cre 112.," Of the 85 stars in our complete sample extinction varied from $_V$ = 3.83 up to $_V$ = 10.70 for the infamous B5 supergiant, IV Cyg 12." + It is worth noting that the average extinction towards the 14 CPR2002 OB stars was uot significantly ercater than that found towards the OB stars previously ideutified in the optical by AIT9L Also. the new OB," It is worth noting that the average extinction towards the 14 CPR2002 OB stars was not significantly greater than that found towards the OB stars previously identified in the optical by MT91 Also, the new OB" +5truciu BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures οί.,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt} + = 12pt" +"as event, single bit (both with 122 us time resolution), and good xenon (1 us time resolution) are considered.","as event, single bit (both with 122 $\mu$ s time resolution), and good xenon (1 $\mu$ s time resolution) are considered." +" Since in these paper we deal with the source properties during its (i.e., non-bursting) emission, we discard 5s of data before each of the seven bursts detected byRXTE,, as well as before the two observed bySwift,, and an interval of variable length depending on the burst properties (~60 s), after."," Since in these paper we deal with the source properties during its (i.e., non-bursting) emission, we discard 5s of data before each of the seven bursts detected by, as well as before the two observed by, and an interval of variable length depending on the burst properties $\sim60$ s), after." + The 1-10 keV Swift//XRT spectra are satisfactorily modelled by an absorbed power law., The 1–10 keV /XRT spectra are satisfactorily modelled by an absorbed power law. + The best-fit value of the absorption column ranges from 2.5 to 3.5x10?? cm”., The best-fit value of the absorption column ranges from 2.5 to $\times10^{22}$ $^{-2}$. +" Since these values are compatible and much less accurate than the estimate given by ?,, nH=(2.87+0.04)x102 cm, we fixed the absorption column to this value in the fitting."," Since these values are compatible and much less accurate than the estimate given by \citet{torres11}, ${\textrm{H}}=(2.87\pm0.04)\times10^{22}$ $^{-2}$, we fixed the absorption column to this value in the fitting." +" The keV absorbed flux is plotted as red circles in panel (a) of Fig. 1,,"," The 2--10 keV absorbed flux is plotted as red circles in panel (a) of Fig. \ref{fig:lc}," + together with a dashed line representing the average flux trend obtained by fitting with a sixth-order polynomial also the flux observed by the RXTE//PCA in the same energy band (blue triangles; see below)., together with a dashed line representing the average flux trend obtained by fitting with a sixth-order polynomial also the flux observed by the /PCA in the same energy band (blue triangles; see below). +" We measured an excess of 2.1(2)x107? erg cm? s! with respect to this trend during the observation starting on 2011 Aug 20.5, a value significantly larger than the average RMS scatter in the flux observed, 3.5x10:11 erg cm? s!."," We measured an excess of $2.1(2)\times10^{-10}$ erg $^{-2}$ $^{-1}$ with respect to this trend during the observation starting on 2011 Aug 20.5, a value significantly larger than the average RMS scatter in the flux observed, $3.5\times10^{-11}$ erg $^{-2}$ $^{-1}$." +" The flux during this observation of Ff"")=(5.8+0.2)x107? erg cm""? s-!, is the peak value observed during the outburst and corresponds to an unabsorbed luminosity of Leet=(5.1+0.2)x1036 di, erg s!, where d7 is the distance to the source in units of 7.6 kpc."," The flux during this observation of $F_{2-10}^{max}=(5.8\pm0.2)\times10^{-10}$ erg $^{-2}$ $^{-1}$, is the peak value observed during the outburst and corresponds to an unabsorbed luminosity of $L_{2-10}^{peak}=(5.1\pm0.2)\times10^{36}$ $_{7.6}^2$ erg $^{-1}$, where $d_{7.6}$ is the distance to the source in units of 7.6 kpc." + An excess of 1.0(2)x107? erg cm? s! is also observed during the observation starting on 2011 Aug 21.5., An excess of $1.0(2)\times10^{-10}$ erg $^{-2}$ $^{-1}$ is also observed during the observation starting on 2011 Aug 21.5. +" By comparing these observations with the nearest ones, a timescale as low as «1000 s is found for the flux variability."," By comparing these observations with the nearest ones, a timescale as low as $\approx1000$ s is found for the flux variability." +" Spectral variability is not observed as the photon index, I', has values that are consistent with those observed during most of the Swift//XRT observations (between 1.7 and 2; see red circles in panel (b) of Fig. 1))."," Spectral variability is not observed as the photon index, $\Gamma$, has values that are consistent with those observed during most of the /XRT observations (between 1.7 and 2; see red circles in panel (b) of Fig. \ref{fig:lc}) )." + A steepening of the power law is instead observed as the transient fades to quiescence., A steepening of the power law is instead observed as the transient fades to quiescence. +" The source was no longer detected after Sep 19; by co-adding the observations performed from Sep 19.4 to 22.7, we obtained an upper limit of 3.2x107! erg cm? s! to the 2-10 keV flux (9 σ.ο. Ι.. assuming a power-law with index I =1.8)."," The source was no longer detected after Sep 19; by co-adding the observations performed from Sep 19.4 to 22.7, we obtained an upper limit of $3.2\times10^{-13}$ erg $^{-2}$ $^{-1}$ to the 2–10 keV flux (3 $\sigma$ c. l., assuming a power-law with index $\Gamma=$ 1.8)." +" The X-ray transient lies very close to the central regions of the Galactic bulge (120.1559?, b=-1.0038°) and the emission of the Galactic ridge and numerous nearby sources contaminate the observations in the field of view of the PCA, which is about 1 by 1 degrees with a hexagonal shape."," The X-ray transient lies very close to the central regions of the Galactic bulge $^{\circ}$, $^{\circ}$ ) and the emission of the Galactic ridge and numerous nearby sources contaminate the observations in the field of view of the PCA, which is about 1 by 1 degrees with a hexagonal shape." + ? estimated a 2-10 keV surface brightness of (8.6+0.5)x107!! erg cm? s! deg? from a nearby field not containing bright sources.," \citet{revnivtsev09} + estimated a 2–10 keV surface brightness of $(8.6\pm0.5)\times10^{-11}$ erg $^{-2}$ $^{-1}$ $^{-2}$ from a nearby field not containing bright sources." +" Moreover, ten sources with 2-12 keV flux exceeding 5x107!! erg cm? s! were found in a region of 1? around the position of in the fifth serendipitous source catalogue (?);; the brightest of these sources is the persistent burster 1A 1742-294 with a 2-10 keV flux between 2 and 4x107!° erg cm""? s!."," Moreover, ten sources with 2–12 keV flux exceeding $5\times10^{-11}$ erg $^{-2}$ $^{-1}$ were found in a region of $1^{\circ}$ around the position of in the fifth serendipitous source catalogue \citep{watson09}; the brightest of these sources is the persistent burster 1A 1742–294 with a 2–10 keV flux between 2 and $\times10^{-10}$ erg $^{-2}$ $^{-1}$." +" To estimate the contamination of the PCA spectra, we considered observations performed between 2011 Sep 20.5 and Sep 22.4, for an exposure of 3.7 ks, when the transient had already faded into quiescence (see above)."," To estimate the contamination of the PCA spectra, we considered observations performed between 2011 Sep 20.5 and Sep 22.4, for an exposure of 3.7 ks, when the transient had already faded into quiescence (see above)." +" The net count-rate observed by the top layer of the PCU2 during these observations was 32.5(2) s! (36.5(2) s, if all the layers are considered) and the absorbed 2-10 keV flux is (3.5+0.1)x10:19 erg cm? s."," The net count-rate observed by the top layer of the PCU2 during these observations was 32.5(2) $^{-1}$ (36.5(2) $^{-1}$, if all the layers are considered) and the absorbed 2–10 keV flux is $(3.5\pm0.1)\times10^{-10}$ erg $^{-2}$ $^{-1}$." + We considered the spectrum obtained during these PCA observations as an additional background to those performed previously., We considered the spectrum obtained during these PCA observations as an additional background to those performed previously. +" After this subtraction, all the PCA spectra could be accurately described by an absorbed power-law, with the value of nH fixed to the estimate."," After this subtraction, all the PCA spectra could be accurately described by an absorbed power-law, with the value of $\textrm{H}$ fixed to the estimate." +" The 2-10 keV fluxes and the best-fit values of the power-law photon index, ranging from 1.8 to 2, are plotted as blue triangles in panel (a) and (b) of Fig. 1,,"," The 2–10 keV fluxes and the best-fit values of the power-law photon index, ranging from 1.8 to 2, are plotted as blue triangles in panel (a) and (b) of Fig. \ref{fig:lc}," + respectively., respectively. + We found that the best-fit models of the simultaneous Swift--XRT and RXTE--PCA spectra are consistent with each other., We found that the best-fit models of the simultaneous -XRT and -PCA spectra are consistent with each other. + The bolometric fluence of the outburst was estimated to be f=(4.1x0.6)x10? τς erg ? by integrating the average trend of the 2-10 keV source flux (dashed line in panel (a) of Fig. 1)), The bolometric fluence of the outburst was estimated to be $\mathcal{F}=(4.1\pm0.6)\times10^{-3}$ $_{7.6}^2$ erg $^{-2}$ by integrating the average trend of the 2–10 keV source flux (dashed line in panel (a) of Fig. \ref{fig:lc}) ) +" over the whole outburst length, and scaling the value obtained by a"," over the whole outburst length, and scaling the value obtained by a" +,. + This scenario—an association of dwarfs falling onto 2008)..the Milky Way—has been found to require a much more compact distribution than is seen in dwarf associations in the local group 2009)., This scenario—an association of dwarfs falling onto the Milky Way—has been found to require a much more compact distribution than is seen in dwarf associations in the local group . +. These bound associations were also unstable when orbiting a larger Galaxy., These bound associations were also unstable when orbiting a larger Galaxy. +" Few dwarfs who would spend their entire undisturbed orbit within the tidal radius remain bound after two pericentre passages, and almost half are lost within 500 Myr of the first pericentre passage."," Few dwarfs who would spend their entire undisturbed orbit within the tidal radius remain bound after two pericentre passages, and almost half are lost within $500$ Myr of the first pericentre passage." +" Here we examine the properties of dwarfs that were bound to the LMC in the past, and whether this scenario could be responsible for some of the dwarf galaxies seen today."," Here we examine the properties of dwarfs that were bound to the LMC in the past, and whether this scenario could be responsible for some of the dwarf galaxies seen today." +" As no dwarfs seen today are bound to the LMC, possibly excluding the SMC, any dwarfs associated in the past with the Magellanic system were likely to have been high in the potential well."," As no dwarfs seen today are bound to the LMC, possibly excluding the SMC, any dwarfs associated in the past with the Magellanic system were likely to have been high in the potential well." +" If there were multiple small dwarfs bound to the LMC, they were unlikely to have interacted, with no difference seen between models which had only one dwarf associated and those with four."," If there were multiple small dwarfs bound to the LMC, they were unlikely to have interacted, with no difference seen between models which had only one dwarf associated and those with four." +" The presence of smaller dwarfs, which possessed insufficient gas to form"," The presence of smaller dwarfs, which possessed insufficient gas to form" +and eU corresponds to each component at each band.,and $\Phi^{(j)}_{\lm}$ corresponds to each component at each band. +" The maps of spectral-index varying signal at each band for each foreground component are Taking into account Eq.(9)) one gets the map of fluctuation where AW=oU—$5,.", The maps of spectral-index varying signal at each band for each foreground component are Taking into account \ref{comp}) ) one gets the map of fluctuation where $\Delta^{(j)}_{\lm}=\Phi^{(j)}_{\lm}-\Phi_{\lm}$. +" The map from Eq.(10)) represents all variation of the phase for all m>1 harmonics of the signal, if AC)«1."," The map from \ref{fluc}) ) represents all variation of the phase for all $m \ge 1$ harmonics of the signal, if $\Delta^{(j)}_{\lm} \ll +1$." +" As one can see, for that map the moduli are lamJA and the phases are the initial phases rotated by the angle 7/2, if AO20 and by the angle 37/2, if AW<0."," As one can see, for that map the moduli are $|\alm^{(j),{\cal S},{\cal F},{\cal D}}||\Delta^{(j)}_{\lm}|$ and the phases are the initial phases rotated by the angle $\pi/2$ , if $\Delta^{(j)}_{\lm}>0$ and by the angle $3\pi/2$, if $\Delta^{(j)}_{\lm} < 0$." +" We implement the method we have developed to extract the peculiar signals for the synchrotron, free-free and dust emission for the frequency bands."," We implement the method we have developed to extract the peculiar signals for the synchrotron, free-free and dust emission for the frequency bands." + We do not include the K band in our analysis due to the same reason as the science team mentions., We do not include the K band in our analysis due to the same reason as the science team mentions. +" The maps for the spectral-index varying signals are grouped in three: synchrotron, free-free and dust emission."," The maps for the spectral-index varying signals are grouped in three: synchrotron, free-free and dust emission." + In Fig.1 we plot the maps for the spectral-index varying signal of the synchrotron emission for the Ka-W bands., In \ref{syn} we plot the maps for the spectral-index varying signal of the synchrotron emission for the Ka-W bands. + The m=0 modes in these spectral-index varying maps have zero amplitude., The $m=0$ modes in these spectral-index varying maps have zero amplitude. + It is the reason why synchrotron maps looks peculiar., It is the reason why synchrotron maps looks peculiar. +" Fig.2 and 3 are the spectral-index varying signals for the free-free and dust emission, respectively."," \ref{free} and \ref{dust} are the spectral-index varying signals for the free-free and dust emission, respectively." + Again the m—0 modes are naturallly excluded., Again the $m=0$ modes are naturallly excluded. + For the dust maps the spectral-index varying signals are relatively weak in comparison with those from the synchrotron and free-free maps., For the dust maps the spectral-index varying signals are relatively weak in comparison with those from the synchrotron and free-free maps. +" However, it is in order of of the amplitude of ILC signal which should be taken into account seriously."," However, it is in order of of the amplitude of ILC signal which should be taken into account seriously." +" In Fig.4 we display the spectral-index varyingsignals, the sum of the synchrotron, free-free and dust emission."," In \ref{sfd} we display the spectral-index varyingsignals, the sum of the synchrotron, free-free and dust emission." + (socalledUltraLwininousIR1996).. (DiMatteoetal., \citep[so called Ultra Luminous IR Galaxies -- ULIRGs;][]{Sanders1996}. \citep{DiMatteo2005}. +2005)... (Saundersetal.1988a.b).. r," $S_{25\mu\mathrm{m}}/S_{60\mu\mathrm{m}}>0.2$ \citep{Sanders1988a,Sanders1988b}. \citep[e.g.][]{Sanders1989, Young1991, Sanders1996}." +esolutiou of sinele-dish telescopes. poor scusitivity of the few interferometric CO maps available aud the lack of higli-resolutiou optical images (e.g. with the IST) for most of these objects. few studies were able to determine the location of the molectlar gas reservoir respect to the powerful QSO.," resolution of single-dish telescopes, poor sensitivity of the few interferometric CO maps available and the lack of high-resolution optical images (e.g. with the HST) for most of these objects, few studies were able to determine the location of the molecular gas reservoir respect to the powerful QSO." + Scovilleetal.(2003) imaged the CO line cluission from a nuniber of the most optically huuniuous PG QSOs. which are thought to be the end-product of the starburst-to-QSO transition.," \citet{Scoville2003} imaged the CO line emission from a number of the most optically luminous PG QSOs, which are thought to be the end-product of the starburst-to-QSO transition." + DIuterestinely. larec amounts of eas. simular to that found in ULIRCs. where found in these objects.," Interestingly, large amounts of gas, similar to that found in ULIRGs, where found in these objects." + The couclusion drawn frou these observations was that. assmuing that the CO cussion aud starburst activity. are well centered around the nuclei. the QSO host galaxies should be Iate-tvpe spirals (Scovilleetal.2003).," The conclusion drawn from these observations was that, assuming that the CO emission and starburst activity are well centered around the nuclei, the QSO host galaxies should be late-type spirals \citep{Scoville2003}." +. However. this coutracdicts the fact that most of these objects are typically found to have eiut elliptical host ealaxies in the optical.," However, this contradicts the fact that most of these objects are typically found to have giant elliptical host galaxies in the optical." + Recently. sensitive high-resolution interferometric CO observations of a template ULIRC-to-QSO transition systema. IIEO150-2958 at 2~0.3. along with IIubble Space Telescope (IST) imaging fouud a merger between a egas-rich spiral aud a gas-poor elliptical. iusteack of au optically huninous QSO hosted by a late-type eas-rich spiral im this svstem (Papadopoulosetal.2008a).," Recently, sensitive high-resolution interferometric CO observations of a template ULIRG-to-QSO transition system, HE0450-2958 at $z\sim0.3$, along with Hubble Space Telescope (HST) imaging found a merger between a gas-rich spiral and a gas-poor elliptical, instead of an optically luminous QSO hosted by a late-type gas-rich spiral in this system \citep{Papadopoulos2008}." +. Tere. the optically huninous QSO liesoutside the molecular gas reservoir. Which is rather ideutified with a massive but obscured companion galaxy. (Papadopoulosetal.2008a:Elbazetal. 2009).," Here, the optically luminous QSO lies the molecular gas reservoir, which is rather identified with a massive but obscured companion galaxy \citep{Papadopoulos2008, Elbaz2009}." +. Iligli-resolution. IR observatious of this object support this assertion. aud sugeest also a more conrplex scenario where the QSO radio jet alters the state of the ISAL aud. possibly induces a starburst in the easvich member of the interaction," High-resolution IR observations of this object support this assertion, and suggest also a more complex scenario where the QSO radio jet alters the state of the ISM and possibly induces a starburst in the gas-rich member of the interaction" +" gaseoussurroundingMilky |Visr| |Visr|>90 Wakker2001)). ((Murphyetal.1995;Wakker&vanWoerden1997;Collins2003)) ((Sembachetal.2003;Collins2004;Fox Wakker1996;Ryansetal.1997;Richter2001)), interpretation. (Shapiro&Field (Wakkeretal.1999;Collins2003;Shulletal.2009),, plane (Blitzet1999), (Tripp2003)). The HVC Complex M lies at the highest Galactic latitude among known HVC b=45? to 70? and longitudes from ¢=complexes,130° to 200°,covering over a velocity range of —125«vga—85kms! (Hulsbosch1968)."," $|V_{\rm LSR}| = 30-90$ $|V_{\rm LSR}| > 90$ \citealt{wak01}) \citealt{mur95, wak97, col03}) \citealt{sem03, col04, fox06, leh10}) \citealt{wak96, rya97, ric01}) \citep{sha76, hou90}, \citep{wak99, col03, shu09}, \citep{bli99, bra99}, \citealt{tri03}) The HVC Complex M lies at the highest Galactic latitude among known HVC complexes, covering $b = 45^\circ$ to $70^\circ$ and longitudes from $\ell = 130^\circ$ to $200^\circ$, over a velocity range of $-1250.5Z_ for the MIII cloud."," Combining a much deeper 21-cm emission limit, $\log N_{\rm HI}<17.43$ from the Jodrell Bank 76m, with absorption measurements by \citet{dan93} along the sight line, \citet{rya97} estimated an oxygen abundance $>0.5 Z_{\odot}$ for the MIII cloud." + Wakker(2001) constrained the metallicity of the MI cloud to be 0.4-1.8 Zo basedonaand eemission data in the core region of MI; the large range arisesfrom uncertainty in the ionization correction., \citet{wak01} constrained the metallicity of the MI cloud to be 0.4–1.8 $Z_\odot$ basedonand emission data in the core region of MI; the large range arisesfrom uncertainty in the ionization correction. +" Because of its short distance and possible high metallicity, Complex M is believed to be part of the IV Arch 2001).."," Because of its short distance and possible high metallicity, Complex M is believed to be part of the IV Arch \citep{kun96, wak01}. ." +fixed to LV. in all models to compare the evolution of cloud with the same mass.,fixed to $1M_\odot$ in all models to compare the evolution of cloud with the same mass. + In addition. we fixed the initial cloud temperature to LOW. Thus. parameter o. and initial cloud density are determined when the initial cloud racius is given.," In addition, we fixed the initial cloud temperature to K. Thus, parameter $\alpha$ and initial cloud density are determined when the initial cloud radius is given." + Note that such treatment changes the gravitational energy ol the cloud. After the eloud radius is fixed with arbitrary à. parameter 923 is determined when the initial angular velocity f2y ds given.," Note that such treatment changes the gravitational energy of the cloud, After the cloud radius is fixed with arbitrary $\alpha$, parameter $\beta$ is determined when the initial angular velocity $\Omega_0$ is given." + The model name. parameters a ancl 2. initial cloud radius. initial angular velocity and initial cloud density are listed in Table 1.," The model name, parameters $\alpha$ and $\beta$, initial cloud radius, initial angular velocity and initial cloud density are listed in Table 1." + Phe initial cloud is modeled with about ut10 000 SPILL particles., The initial cloud is modeled with about 500 000 SPH particles. +" To ealeulate the disk formation several 10%103 vears after the protostar. formation. we adopt a sink particle technique according to the prescription by Bateefαἱ, (1995)."," To calculate the disk formation several $10^3 - 10^4 $ years after the protostar formation, we adopt a sink particle technique according to the prescription by \citet{betal95}." +. Starting from the prestellar core stage. the cloud evolution is calculated. without sink particle.," Starting from the prestellar core stage, the cloud evolution is calculated without sink particle." +" “Phen. we assume the protostar formation and dynamically introduce a sink particle when the gas particle density exceeds. the threshold. density. paar=4510""gem."," Then, we assume the protostar formation and dynamically introduce a sink particle when the gas particle density exceeds the threshold density, $\rho_{\rm sink}=4\times 10^{-9} {\rm g~ cm^{-3}}$." + The threshold. density roughly corresponds to the density at which the second. collapse begins., The threshold density roughly corresponds to the density at which the second collapse begins. + As shown in Larson(2001) and Alasunaga&Inutsuka(2010).. the second collapse begins when the gas density. reaches p10nσοι»7puak at which the gas temperature exceeds Loz210° κ and molecular hydrogen begins to clissociate.," As shown in \citet{larson69} and \citet{mi00}, the second collapse begins when the gas density reaches $\rho \sim 10^{-9 }{\rm g~ cm^{-3}} \sim \rho_{\rm sink}$ at which the gas temperature exceeds $T \gtrsim 2 \times 10^3$ K and molecular hydrogen begins to dissociate." + The protostar orms immediately after the second. collapse., The protostar forms immediately after the second collapse. + Thus. in this xaper. we safely define the protostar formation epoch as that at which the gas density exceeds p7paa ," Thus, in this paper, we safely define the protostar formation epoch as that at which the gas density exceeds $\rho > \rho_{\rm sink}$." +To treat the gas accretion onto the sink particle alter he creation of the sink particle. we set the accretion radius Face=OSDAL.," To treat the gas accretion onto the sink particle after the creation of the sink particle, we set the accretion radius $r_{\rm acc}=0.85 {\rm AU}$." +" Then. within the accretion radius. we allow he gas accretion onto the sink particle when the following condition is fulfilled: (1) the eas particle density exceeds he aceretion density pios=419tleem""S (2) dH ds eravitationally bound to the sink particle and (3) its specific angular momentum is less than that required for it to form a circular orbit at race."," Then, within the accretion radius, we allow the gas accretion onto the sink particle when the following condition is fulfilled: (1) the gas particle density exceeds the accretion density $\rho_{\rm acc}=4 \times 10^{-11} {\rm g~ cm^{-3}}$, (2) it is gravitationally bound to the sink particle and (3) its specific angular momentum is less than that required for it to form a circular orbit at $r_{\rm acc}$." + We did not implement a boundary condition for sink particle., We did not implement a boundary condition for sink particle. + As listed in Table 1. we calculated the cloud evolution for 17 models in total. ancl classified them into four modes as follows: The calculation results and its classification are summarized in Figure L.. Ala," As listed in Table 1, we calculated the cloud evolution for 17 models in total, and classified them into four modes as follows: The calculation results and its classification are summarized in Figure \ref{alpha_beta}." +ssive disk mocle is indicated by the circles in Figure 1.., Massive disk mode is indicated by the circles in Figure \ref{alpha_beta}. + Figures 2 and 32 show the time evolution of the center of the cloud for model S (a=0.6 and 3=710%) that is a typical moclel for massive disk mode., Figures \ref{faceon_massive_disk} and \ref{edgeon_massive_disk} show the time evolution of the center of the cloud for model 8 $\alpha =0.6$ and $\beta=7 \times 10^{-3}$ ) that is a typical model for massive disk mode. + The upper left and upper middle panels in these figures show snapshots before the protostar formation., The upper left and upper middle panels in these figures show snapshots before the protostar formation. + A strong bar-lHike structure appears in the central high-density gas region in the top left panel in Figure 2.., A strong bar-like structure appears in the central high-density gas region in the top left panel in Figure \ref{faceon_massive_disk}. + Vhen. the bar structure cllectively transfers the angular momentum outward. and the high-density gas region shrinks.," Then, the bar structure effectively transfers the angular momentum outward and the high-density gas region shrinks." + As a result. a bimodal structure composed of the central high-density. core ancl its surrounding. disk appears as seen in the top middle panel.," As a result, a bimodal structure composed of the central high-density core and its surrounding disk appears as seen in the top middle panel." + Phese figures clearly garow the clisk formation before the protostar formation., These figures clearly show the disk formation before the protostar formation. + The op right panel shows the snapshot just when the second collapse occurs. (Le. the protostar forms).," The top right panel shows the snapshot just when the second collapse occurs (i.e., the protostar forms)." + The time when 10 protostar forms is 8.6«107 vears from beginning., The time when the protostar forms is $8.6 \times 10^5$ years from beginning. + This roughly. corresponds to the free-falltimescale of the initial loud., This roughly corresponds to the free-falltimescale of the initial cloud. + By this epoch. the spiral arm has developed: around the central object.," By this epoch, the spiral arm has developed around the central object." + Phe bottom left. middle. and right panels show the snapshots L4.107.1.0.10* and 1.0«107 vears after the protostar formation.," The bottom left, middle, and right panels show the snapshots $1.4\times 10^2,~1.0\times 10^3$ and $1.0\times 10^4$ years after the protostar formation." + These figures show that the disk eracually increases its size with time retaining the elobal spiral structure., These figures show that the disk gradually increases its size with time retaining the global spiral structure. + Figure 4. shows the mass evolution of the disk. and protostar., Figure \ref{time_mass} shows the mass evolution of the disk and protostar. + For this model. the disk mass is greater than the protostellar mass for more than LO? vears after the protostar formation.," For this model, the disk mass is greater than the protostellar mass for more than $10^4$ years after the protostar formation." + Such a disk is expected. to be gravitationally unstable., Such a disk is expected to be gravitationally unstable. +" To investigate the disk stability. the contours of ""Toomre's Q parameter at 14107 and 1.0«107 vears after the protostar formation (the same epoch of the bottom left ancl middle panels of Fie. 2))"," To investigate the disk stability, the contours of Toomre's Q parameter at $1.4\times 10^2$ and $1.0\times 10^3$ years after the protostar formation (the same epoch of the bottom left and middle panels of Fig. \ref{faceon_massive_disk}) )" + are plotted in Figure 5.., are plotted in Figure \ref{q_value}. +" The ""Joomre's Q parameter is described as where ὃς. & and X are the sound. velocity ancl epievclic requeney and surface. density of the disk. respectively."," The Toomre's Q parameter is described as where $c_s$ , $\kappa$ and $\Sigma$ are the sound velocity and epicyclic frequency and surface density of the disk, respectively." + For this model. the circumstellar clisk cid not show ragmentation even though the circumstellar disk has the region of Qκ1 at L45107 vears after the protostar ormation.," For this model, the circumstellar disk did not show fragmentation even though the circumstellar disk has the region of $Q<1$ at $1.4 \times 10^2$ years after the protostar formation." + ας is because Gl cannot grow sulliciently Last in the circumstellar disk., This is because GI cannot grow sufficiently fast in the circumstellar disk. +" The characteristic timescale of ""loomre's analysis. 7—2e,/ο.7]. is comparable o the orbital period of the disk. (both are. several housane vears)."," The characteristic timescale of Toomre's analysis, $ \tau=2c_s/[G \Sigma (1-Q^2)^{1/2}] $, is comparable to the orbital period of the disk (both are several thousand years)." + In this case. there are non-linear stabilize mechanisms against Cil.," In this case, there are non-linear stabilize mechanisms against GI." + As seen in the right panel of Figure or bottom middle panel of Figure 2.. the spiral arm elobally redistribute the mass and angular momentum in a short duration. 10 vears Toon )-," As seen in the right panel of Figure \ref{q_value} or bottom middle panel of Figure \ref{faceon_massive_disk}, the spiral arm globally redistribute the mass and angular momentum in a short duration, $\sim 10^3$ years $ \lesssim T_{orbit}$ )." + Furthermore. the clisk-star configuration also dvnanücally changes in a short duration.," Furthermore, the disk-star configuration also dynamically changes in a short duration." + Figure 6 shows the trajectory of the protostar for 8.0.10% vears after the protostar formation., Figure \ref{xy_star} shows the trajectory of the protostar for $8.0 \times 10^3$ years after the protostar formation. + The asterisk indicates the position where the protostar forms., The asterisk indicates the position where the protostar forms. + The central. protostar drifts toward the dense part of the spiral arm due to the gravitational interaction between the protostar ancl spiral arms., The central protostar drifts toward the dense part of the spiral arm due to the gravitational interaction between the protostar and spiral arms. + Since the strength of Keplerian shear is proportional to ΩΣxον its radial dependeney ds very strong and the drift motion increases the shear stress of the dense region and suppresses fragmenting of the disk.," Since the strength of Keplerian shear is proportional to $\frac{d}{dr}(r \Omega^2) \propto r^{-3}$, its radial dependency is very strong and the drift motion increases the shear stress of the dense region and suppresses fragmenting of the disk." + As described in Gammie (2001).. the thermal evolution of the disk. also may playan important role to suppressing/promoting fragmentation.," As described in \citet{gammie01}, , the thermal evolution of the disk also may playan important role to suppressing/promoting fragmentation." + They showed that no fragmentation occurs when the cooling time is much longer than the orbital, They showed that no fragmentation occurs when the cooling time is much longer than the orbital +Inran!. F. Krennrich!. Depl. of Physies & Astronomy. Lowa Stale University. Ames. LA.,"Imran^1, F. Krennrich$^{1}$.}\tikzmark{mainBodyEnd3} +%Short title to print in the headers to the final puplication (Not showed in this print). +%\shortauthors{Imran and Krennrich} +%All the affiliations. +%\afiliations{$^1$ Dept. of Physics \& Astronomy, Iowa State University, Ames, IA, 50011, USA} +\tikzmark{mainBodyStart4}\affil{$^1$ Dept." + 50011. discuss prospects for detecting a spectral break in 5-rav spectra of blazars due to the extragalactic background light (EBL) density falling off between the near and mid-IR.," of Physics & Astronomy, Iowa State University, Ames, IA, 50011, USA}\tikzmark{mainBodyEnd16} + +\tikzmark{mainBodyStart17}\email{imranisuiastate.edu}\tikzmark{mainBodyEnd17} + + +%The abstract. +\tikzmark{mainBodyStart18}\begin{abstract}We discuss prospects for detecting a spectral break in γ-ray spectra of blazars due to the extragalactic background light (EBL) density falling off between the near and mid-IR." + A measurable spectral change in the TeV spectra ad 1 TeV could arise [rom a rapid or slow drop in the EBL density above zz 1 um., A measurable spectral change in the TeV spectra at 1 TeV could arise from a rapid or slow drop in the EBL density above ≈ 1 um. + This ellect is mediated by the ratio of the near to mid-IR density of EBL., This effect is mediated by the ratio of the near to mid-IR density of EBL. + A detection of such a spectral feature could become a clear signature of EBL absorption., A detection of such a spectral feature could become a clear signature of EBL absorption. + A would give a strong observational constraint to the shape of the EBL speclrum., A non-detection would give a strong observational constraint to the shape of the EBL spectrum. + We present calculations estimating the sensiüivitv of TeV telescopes for detecting such a break for blazar observations al different redshifts.," We present calculations estimating the sensitivity of TeV telescopes for detecting such a break for blazar observations at different redshifts. \end{abstract}\tikzmark{mainBodyEnd138} + +%\email{aastex-helpaas.org} +\tikzmark{mainBodyStart139}\keywords{TeV;" + Gamma-ray Astronomy. Extragalactic Dackground Verv high energv 5-rav. beams [rom sources al cosmological distances provide a unique opportunity to probe the intervening medium.," Gamma-ray Astronomy, Extragalactic Background Light}\tikzmark{mainBodyEnd144} + +%%%%%%%%%%%%%%%%%%%% B E G I N D O C U M E N T%%%%%%%%%%%%%%%%%%%%%%% +\tikzmark{mainBodyStart145}\begin{document} Very high energy $\gamma$ -ray beams from sources at cosmological distances provide a unique opportunity to probe the intervening medium." + The interaction is with photons from the extragalactic background light (7.. 2)) vin 52-5—€+e.," The interaction is with photons from the extragalactic background light \cite{gs67}, \cite{sds92}) ) via $\gamma+\gamma \rightarrow e^+ + e^-$." + Direct measurements of the EBL. particularly in the mid-LR. are extremely difficult due to strong foreground emissions. making TeV 5-rav absorption measurements invaluable.," Direct measurements of the EBL, particularly in the mid-IR, are extremely difficult due to strong foreground emissions, making TeV $\gamma$ -ray absorption measurements invaluable." + The task of extracting information about the EBL [rom spectra of TeV οταν sources is complicated by our lack of knowledge about the intrinsic source spectra., The task of extracting information about the EBL from spectra of TeV $\gamma$ -ray sources is complicated by our lack of knowledge about the intrinsic source spectra. +" Attempts to find signatures Irom the EBL in TeV spectra?) were hindered by the possibility (hat cutolls could be intrinsic,", Attempts to find signatures from the EBL in TeV spectra \cite{sds92} were hindered by the possibility that cutoffs could be intrinsic. + As a result. current 5-rav based methods to probe the diffuse background (?.. ?)) necessarily rely on assumptions made about the source spectra and are often founded on a theoretical understanding of particle acceleration ancl emission mechanisms in blazar jets.," As a result, current $\gamma$ -ray based methods to probe the diffuse background \cite{dk2005}, \cite{aha2006}) ) necessarily rely on assumptions made about the source spectra and are often founded on a theoretical understanding of particle acceleration and emission mechanisms in blazar jets." + An, An +asymmetric.,asymmetric. + One can also note that the maximal growth rate of the extraordinary mode exceeds that of the ordinary mode by more than two orders of magnitude., One can also note that the maximal growth rate of the extraordinary mode exceeds that of the ordinary mode by more than two orders of magnitude. + Both for the ordinary and extraordinary modes. there are also amplification regions near higher harmonies of the cyclotron frequency. but with much lower growth rates (they are not shown at the figure).," Both for the ordinary and extraordinary modes, there are also amplification regions near higher harmonics of the cyclotron frequency, but with much lower growth rates (they are not shown at the figure)." + Thus the fundamental extraordinary mode is strongly dominating., Thus the fundamental extraordinary mode is strongly dominating. + Figure 2. shows the electron distribution function. at different times (the chosen time moments correspond to the different stages of the relaxation. process. see comment to Fig. 4)).," Figure \ref{ev_b_V} shows the electron distribution function at different times (the chosen time moments correspond to the different stages of the relaxation process, see comment to Fig. \ref{prof_V}) )." + For some time after the beginning of the simulation. while the wave energy density ts low. the distribution function remains very similar to the initial one (Fig.," For some time after the beginning of the simulation, while the wave energy density is low, the distribution function remains very similar to the initial one (Fig." + 2aa)., \ref{ev_b_V}a a). + When the waves are amplified to a certain eritical level. a effective diffusion of electrons on these waves begins.," When the waves are amplified to a certain critical level, an effective diffusion of electrons on these waves begins." + As a result. the electrons drift along the trajectories of p.=const towards lower values of p.. thus losing energy.," As a result, the electrons drift along the trajectories of $p_z=\textrm{const}$ towards lower values of $p_{\bot}$, thus losing energy." + At the early relaxation stage (Fig., At the early relaxation stage (Fig. + 2bb). this results in formation of a plateau slightly below the maximum of the initial distribution function (with respect to the momentum) and around a=90° (with respect to the pitch angle).," \ref{ev_b_V}b b), this results in formation of a plateau slightly below the maximum of the initial distribution function (with respect to the momentum) and around $\alpha\simeq 90^{\circ}$ (with respect to the pitch angle)." + On the other hand. at the upper and lower boundaries of this plateau (with respect to the momentum). the gradient of the distribution function increases.," On the other hand, at the upper and lower boundaries of this plateau (with respect to the momentum), the gradient of the distribution function increases." + At the middle relaxation stage (Fig., At the middle relaxation stage (Fig. +" 2cc). the ""plateau"" expands with respect both to the momentum and pitch angle. and we can see that this feature is not really flat: while the derivative Of/Óp| in this area approaches zero. the derivative Of/ÓOp.- remains nonzero. so the distribution function gradually decreases with increasing p-"," \ref{ev_b_V}c c), the “plateau” expands with respect both to the momentum and pitch angle, and we can see that this feature is not really flat: while the derivative $\partial f/\partial p_{\bot}$ in this area approaches zero, the derivative $\partial f/\partial p_z$ remains nonzero, so the distribution function gradually decreases with increasing $p_z$." + Nevertheless. since the maser amplification or damping of waves depends mainly on the derivative with respect to the transversal component of the momentum. a contribution of this region of the distribution function into. growth rate is close to zero.," Nevertheless, since the maser amplification or damping of waves depends mainly on the derivative with respect to the transversal component of the momentum, a contribution of this region of the distribution function into growth rate is close to zero." + At the upper boundary (with respect to the momentum). the “plateau” extends beyond the circle p=pp (where the initial distribution furction had a maximum) and the positive slope in p_ disappears: at the lower boundary. this slope is still quite large.," At the upper boundary (with respect to the momentum), the “plateau” extends beyond the circle $p=p_{\mathrm{b}}$ (where the initial distribution function had a maximum) and the positive slope in $p_{\bot}$ disappears; at the lower boundary, this slope is still quite large." + At the late relaxation stage (Fig., At the late relaxation stage (Fig. + 244). the “plateau” expands eve1 further. so now we have," \ref{ev_b_V}d d), the “plateau” expands even further, so now we have" +the Institute for Astronomy.,the Institute for Astronomy. +" For each candidate. we obtained 24"" postage stamps of every exposure from the dropout band and detection band."," For each candidate, we obtained 24"" postage stamps of every exposure from the dropout band and detection band." + We produce weighted mean stacks of these exposures and performed forced photometry on each stacked image., We produce weighted mean stacks of these exposures and performed forced photometry on each stacked image. + Approximately half of all candidates were in small image gaps in the detection band., Approximately half of all candidates were in small image gaps in the detection band. + We automatically eliminated all sources which were not detected in the detection band with less than 0.15 magnitude uncertainty in our postage stamp stacks., We automatically eliminated all sources which were not detected in the detection band with less than 0.15 magnitude uncertainty in our postage stamp stacks. + This cut was judged. by eye. to be complete for real sources.," This cut was judged, by eye, to be complete for real sources." + Approximately half of the candidates were saturation defects not spotted by the PSI pipeline., Approximately half of the candidates were saturation defects not spotted by the PS1 pipeline. + We required that sources be 1.5 magnitudes fainter in the dropout band than in the detection band if they are detected or have a 5o limiting magnitude 1.5 magnitudes greater than the detection magnitude., We required that sources be 1.5 magnitudes fainter in the dropout band than in the detection band if they are detected or have a $\sigma$ limiting magnitude 1.5 magnitudes greater than the detection magnitude. + We also required that sources have of their PSF flux imaged by good pixels to ensure that they are not chip edge or other artifacts., We also required that sources have of their PSF flux imaged by good pixels to ensure that they are not chip edge or other artifacts. + In cases where an object had been imaged in the detection band on two nights. we eliminated sources that were detected one night but not on another night of sufficient depth.," In cases where an object had been imaged in the detection band on two nights, we eliminated sources that were detected one night but not on another night of sufficient depth." + Finally. we examined the stacks and individual exposures of the remaining 3« 10 sources by eye.," Finally, we examined the stacks and individual exposures of the remaining $\times$ $^3$ sources by eye." + At this level. we eliminated cosmic rays that the software missed. marginal detections and artifacts registered as sources.," At this level, we eliminated cosmic rays that the software missed, marginal detections and artifacts registered as sources." + There were approximately 10? candidates over the half of the 37 we examined., There were approximately $^3$ candidates over the half of the $\pi$ we examined. + We prioritized our follow up candidates based on the reliability of the detection. the size of the color difference and observability from the observation site.," We prioritized our follow up candidates based on the reliability of the detection, the size of the color difference and observability from the observation site." + So far. we have performed some follow up on z200 quasars.," So far, we have performed some follow up on $\approx 200$ quasars." + We require more |information than PSI gives to confirm a candidate., We require more information than PS1 gives to confirm a candidate. + In individual exposures. most z=5.7 quasars will be near the PSI detection limit. and it is difficult to reject asteroids which are detected in the detection band but have moved when that area is covered by other bands. so simply confirming the existence of a candidate is important.," In individual exposures, most $z > 5.7$ quasars will be near the PS1 detection limit, and it is difficult to reject asteroids which are detected in the detection band but have moved when that area is covered by other bands, so simply confirming the existence of a candidate is important." +" In addition. brown dwarfs and other red objects can have similar PSI colors to high redshift quasars (?).. so obtaining deeper izv photometry for ip; dropouts and zvJ photometry for zp, dropouts is essential to remove false detections."," In addition, brown dwarfs and other red objects can have similar PS1 colors to high redshift quasars \citep{FAN99}, so obtaining deeper $izy$ photometry for $\ips$ dropouts and $zyJ$ photometry for $\zps$ dropouts is essential to remove false detections." + We confirm our candidates with photometry and spectroscopy from small telescopes before moving on to the more expensive spectroscopy necessary for deeper analysis., We confirm our candidates with photometry and spectroscopy from small telescopes before moving on to the more expensive spectroscopy necessary for deeper analysis. + Initially. we planned to confirm candidates using the Calar Alto 3.5 m telescope and the Omega 2000 camera with the Y and J filters in spring 2011.," Initially, we planned to confirm candidates using the Calar Alto 3.5 m telescope and the Omega 2000 camera with the Y and J filters in spring 2011." + Unfortunately. the telescope was offline due to a mechanical failure for a period of many months that included our observation time.," Unfortunately, the telescope was offline due to a mechanical failure for a period of many months that included our observation time." + We obtained five nights of time. 2011 February 16-20. with MMT SWIRC.," We obtained five nights of time, 2011 February 16-20, with MMT SWIRC." + For each source. we took nine 30 second exposures in Y band.," For each source, we took nine 30 second exposures in Y band." + This initial sample of sources was chosen to aggressively probe very faint sources. allowing for some false detections as aresult of statistical noise.," This initial sample of sources was chosen to aggressively probe very faint sources, allowing for some false detections as a result of statistical noise." + In addition. we did not account for moving solar system objects in our search.," In addition, we did not account for moving solar system objects in our search." + Only 23 of the 100 sources we followed up on were confirmed., Only 23 of the 100 sources we followed up on were confirmed. + This was to some degree expected. as coincident noise peaks and slow-moving objects which can be detected twice on one night are both plentiful in our large dataset.," This was to some degree expected, as coincident noise peaks and slow-moving objects which can be detected twice on one night are both plentiful in our large dataset." + This work helped us understand how to select sources efficiently near our limiting magnitude., This work helped us understand how to select sources efficiently near our limiting magnitude. + We used GROND. a grizJHK simultaneous imager at the 2.2 m telescope in La Silla. to obtain colors of the confirmed candidates from our MMT run and 61 additional candidates.," We used GROND, a $grizJHK$ simultaneous imager at the 2.2 m telescope in La Silla, to obtain colors of the confirmed candidates from our MMT run and 61 additional candidates." + The observations occupied roughly of a ten night observation period. 2011 March 4-13.," The observations occupied roughly of a ten night observation period, 2011 March 4-13." +" Each object was observed using am instrument standard ""8 minute observation block"" in which the infrared images get a total of eight minutes exposure time in the optical bands get slightly more (?).."," Each object was observed using am instrument standard ""8 minute observation block"" in which the infrared images get a total of eight minutes exposure time in the optical bands get slightly more \citep{GREI++08}." + We detected 48 of 62 sources. but found that most of them were less red than they had appeared in PSI.," We detected 48 of 62 sources, but found that most of them were less red than they had appeared in PS1." + This was expected. since our typical PSI colors have uncertainties of a few tenths. and we find many common bluer objects which randomly appear red in our PSI observation.," This was expected, since our typical PS1 colors have uncertainties of a few tenths, and we find many common bluer objects which randomly appear red in our PS1 observation." + We did find one very promising candidate (finding chart in Fig., We did find one very promising candidate (finding chart in Fig. + | and multi-filter imaging in Fig. 2)).," \ref{fig:chart} and multi-filter imaging in Fig. \ref{fig:GROND}) )," +" PSO J215.1512-16.0417 (at J2000 215.1512. -16.0417 or 14/20""36.3°. -16702? 30.2"")."," PSO J215.1512-16.0417 (at J2000 215.1512, -16.0417 or $^h$ $^m$ $^s$, $^\circ$ $^m$ $^s$ )." + It had /Ggowp-zogoup = 2.06 and zogowp-JGkowp = 0.60 (complete photometry in Table 2)., It had $i_{\rm{GROND}}$ $z_{\rm{GROND}}$ = 2.06 and $z_{\rm{GROND}}$ $J_{\rm{GROND}}$ = 0.60 (complete photometry in Table \ref{tab:GROND}) ). + Unfortunately. this source was located near a chip gap in the GROND K detector. preventing us from reducing the K band image and obtaining accurate K photometry.," Unfortunately, this source was located near a chip gap in the GROND K detector, preventing us from reducing the K band image and obtaining accurate K photometry." + Using individual K exposures.we were only able to set a limiting magnitude of approximately K > 17 for this source.," Using individual K exposures,we were only able to set a limiting magnitude of approximately K > 17 for this source." +Markoffetal.(2008).,\citet{metal08}. +.. The discrepancy could be explained by the low signal-to-noise in the estimate from the SED fit or by variability iu the ACN emission: the 870 jin fiux density has been observed to vary by 2s (Markoffetal. 2008)., The discrepancy could be explained by the low signal-to-noise in the estimate from the SED fit or by variability in the AGN emission; the 870 $\mu$ m flux density has been observed to vary by $3\times$ \citep{metal08}. +. Iu the other SEDs. we found that single blackbodies 1nocdifiec with A7 ciissivity funetions could be fit accurately to the 100 yan data without the fit overpredicting the observed 70 sau ueasunrenien. but fits that included the 70 juu data point did not accurately replicate the peak of the SED.," In the other SEDs, we found that single blackbodies modified with $\lambda^{-2}$ emissivity functions could be fit accurately to the $>$ 100 $\mu$ m data without the fit overpredicting the observed 70 $\mu$ m measurement, but fits that included the 70 $\mu$ m data point did not accurately replicate the peak of the SED." + No evidence is found for the excess Cluission at subnmüllimetre waveleugthns sometimes attributed to dust with <10 Ik temperatures or shallow enissivities. although prior results had indicated that this enidssion would be more prominent at 2500 gin (e.g.CalOTalloranetal. 2010)..," No evidence is found for the excess emission at submillimetre wavelengths sometimes attributed to dust with $<10$ K temperatures or shallow emissivities, although prior results had indicated that this emission would be more prominent at $>$ 500 $\mu$ m \citep[e.g.][]{gmjwb05, betal06, zpxkl09, + oetal10}. ." + By applviug to the data for he elobal SED the equation ως=L5.D?[eBiv. Gvhere D is distance. &j is the dust opacity from LiT')]&Draine (2001).. aud Bow.2) is the best fitting modified dackbody). we estimated the elobal dust uass to be ο0.5<10° ML.," By applying to the data for the global SED the equation $M_{dust}=[f_\nu D^2]/[\kappa B(\nu,T)]$ (where $D$ is distance, $\kappa_\nu$ is the dust opacity from \citet{ld01}, and $B(\nu,T)$ is the best fitting modified blackbody), we estimated the global dust mass to be $3.4 \pm 0.5 \times10^7$ $_\odot$." + Given that the atomic eas mass is B.GL4018s10° AL. (Walteretal.2008) aud the uolecular gas mass is negligible iu comparison (Sage1993.Sáuchez-Callegoetal.in prep.).. we estimate that the eas-to-dust ratio is 107d17. which is within the range of 100-200 expected for solar metallicity objects based ou the depletion of metals from the gaseous phase of the interstellar medium or conrparisons of gas coluun density to dust extinction (e.gWhittet2003).," Given that the atomic gas mass is $3.64 \pm 0.18\times10^9$ $_\odot$ \citep{wetal08} and the molecular gas mass is negligible in comparison \citep[][S\'anchez-Gallego et al. in prep.]{s93}, we estimate that the gas-to-dust ratio is $107 \pm 17$, which is within the range of $\sim100$ -200 expected for solar metallicity objects based on the depletion of metals from the gaseous phase of the interstellar medium or comparisons of gas column density to dust extinction \citep[e.g][]{w03}." +. IIence. this simplistic modif&ed blackbody ft may be a fair representation of the oenüssioun from the bulk of the ust nass in M81. although more sophisticated modeling should uot only vield more accurate nasses but also describe the emission from warluer dust components.," Hence, this simplistic modified blackbody fit may be a fair representation of the emission from the bulk of the dust mass in M81, although more sophisticated modeling should not only yield more accurate masses but also describe the emission from warmer dust components." + The SED fits along with the results from Fies., The SED fits along with the results from Figs. + 2 and 5 iuply that the το pau bane traces cust heated by a ifereut source than the dust that primarily cuits in the 160-500 gan bands., \ref{f_img_ratio} and \ref{f_ratiovar} imply that the 70 $\mu$ m band traces dust heated by a different source than the dust that primarily emits in the 160-500 $\mu$ m bands. + Although the 70/160 pau ratio exhibits lot of scatter. the cuhancemeuts in the 70/160 jan ratio oei the spiral arius iurplies that the 70 pau band may be," Although the 70/160 $\mu$ m ratio exhibitsa lot of scatter, the enhancements in the 70/160 $\mu$ m ratio in the spiral arms implies that the 70 $\mu$ m band may be" +the bias factor. for cach of the three approaches described above.,"the bias factor, for each of the three approaches described above." + The dillerent. methods. produce broadly: consistent results. and the best-littine values are in good agreement with those determined. [from the latest measurements of the temperature. fluctuations of the Cosmic Microwave Background radiation (Ixomatsu et 22009).," The different methods produce broadly consistent results, and the best-fitting values are in good agreement with those determined from the latest measurements of the temperature fluctuations of the Cosmic Microwave Background radiation (Komatsu et 2009)." +" The probability contours in Figure 22. display evidence of the well-known degencracy between Oy, and. O,/0,, in the determination of the overall shape of the matter power spectrum. which is exacerbated by the fact that we cannot vet detect the imprint of the barvon acoustic oscillations in our power spectrum measurement."," The probability contours in Figure \ref{figomfbprob} display evidence of the well-known degeneracy between $\Omega_{\rm m}$ and $\Omega_{\rm + b}/\Omega_{\rm m}$ in the determination of the overall shape of the matter power spectrum, which is exacerbated by the fact that we cannot yet detect the imprint of the baryon acoustic oscillations in our power spectrum measurement." + This degeneracy will be broken as the WigeleZ Survey progresses., This degeneracy will be broken as the WiggleZ Survey progresses. + In this paper we have described our method of determining the selection Function of the WigeleZ Dark Energy Survey. and have presented the current measurement. of the larec- galaxy power spectrum using 56.159 redshifts of bright emission-line galaxies spanning redshifts 0.3<2«0.9.," In this paper we have described our method of determining the selection function of the WiggleZ Dark Energy Survey, and have presented the current measurement of the large-scale galaxy power spectrum using $56{,}159$ redshifts of bright emission-line galaxies spanning redshifts $0.3 < z < 0.9$." + This sample constitutes approximately 2555%ο of the final WigeleZ survey., This sample constitutes approximately $25\%$ of the final WiggleZ survey. + We have quantified: and categorized. the redshift blunder rate and determined its effect. on. the power spectrum measurement via. analytical calculations ane detailed simulations., We have quantified and categorized the redshift blunder rate and determined its effect on the power spectrum measurement via analytical calculations and detailed simulations. + We conclude that:, We conclude that: +between the detected. longitudinal magnetic field ancl flux changes anc GOES X-ray flare (his.,between the detected longitudinal magnetic field and flux changes and GOES X-ray flare flux. + Fieure 11. shows scatter plots of the magnetic field intensity changes and the net aud unsigned magnetic [lux changes against the GOES peak X-raw flix., Figure \ref{intfarrays} shows scatter plots of the magnetic field intensity changes and the net and unsigned magnetic flux changes against the GOES peak X-ray flux. +" Table 7 summarizes the correlations between the field and flux chanee and the GOES peak X-ray flux,", Table \ref{fieldfluxinttable} summarizes the correlations between the field and flux change and the GOES peak X-ray flux. + Overall. the field change. the net fIux change. and the unsigned [ιν change all show some weak to moderate correlation with GOES X-ray. [hix (ine 1 of Table 7)).," Overall, the field change, the net flux change, and the unsigned flux change all show some weak to moderate correlation with GOES X-ray flux (line 1 of Table \ref{fieldfluxinttable}) )." + The correlation between field change and GOES X-rav [lux is dominated by A-class flares at the limb (compare the first (vo columns of lines 2. 5. and 8 in Table 7)).," The correlation between field change and GOES X-ray flux is dominated by X-class flares at the limb (compare the first two columns of lines 2, 5, and 8 in Table \ref{fieldfluxinttable}) )." + As discussed in Section 4.. the median value of the field change is higher for X-class flares than for M-class flares and for limb flares than disk-center Wares (Table 3)).," As discussed in Section \ref{fieldchanges}, the median value of the field change is higher for X-class flares than for M-class flares and for limb flares than disk-center flares (Table \ref{minmaxtable}) )." + All this adds up to the conelusion that X-elass limb flares are slightly more likely than other fares to produce strong longitudinal field changes., All this adds up to the conclusion that X-class limb flares are slightly more likely than other flares to produce strong longitudinal field changes. + some correlation between (he change in (he magnetic [αν and the GOES X-ray fIux is expected. as discussed in Section 5.. and the correlation is dominated by the A-class fLIares (compare lines 1 and 2 in Table 7)).," Some correlation between the change in the magnetic flux and the GOES X-ray flux is expected, as discussed in Section \ref{fluxchanges}, and the correlation is dominated by the X-class flares (compare lines 1 and 2 in Table \ref{fieldfluxinttable}) )." + The statistically significant correlation between (he net magnetic [Iux change and the GOES X-ray flux at clisk-center is dominated by the clisk-center X-class [lares (compare (he middle (wo columus of lines 4 and 6 in Table 7))., The statistically significant correlation between the net magnetic flux change and the GOES X-ray flux at disk-center is dominated by the disk-center X-class flares (compare the middle two columns of lines 4 and 6 in Table \ref{fieldfluxinttable}) ). + The statistically significant correlation between the unsigned magnetic [Iux change and the GOES X-ray παν near (he limb is dominated by the limb X-class flares (compare the last (vo columns of lines 5 and 8 in Table 7)). so the N-class flare theme repeats itself. but we do see (o deviations from this theme.," The statistically significant correlation between the unsigned magnetic flux change and the GOES X-ray flux near the limb is dominated by the limb X-class flares (compare the last two columns of lines 5 and 8 in Table \ref{fieldfluxinttable}) ), so the X-class flare theme repeats itself, but we do see two deviations from this theme." + The correlation between the net flux change at the limb and the GOES X-ray flux. (aniddle two columns of line 5) appears to be split amonest X- and M-class flares (lines 8 and 9)., The correlation between the net flux change at the limb and the GOES X-ray flux (middle two columns of line 5) appears to be split amongst X- and M-class flares (lines 8 and 9). + The correlation between the unsigned magnetic flux change and GOES X-ray [ας near clisk-center (last (wo columns of line +) appears to be significant in spite of (he [act (hat the separate M-class ancl X-class correlations are not., The correlation between the unsigned magnetic flux change and GOES X-ray flux near disk-center (last two columns of line 4) appears to be significant in spite of the fact that the separate M-class and X-class correlations are not. + This is because (hese distributions, This is because these distributions +Since the star has only been observed at one epoch we cannot comment on its possiblevariability’.,Since the star has only been observed at one epoch we cannot comment on its possible. +" We have obtained JILIN. photometry of a complete sample of stars to Ix,—16 in a 7.2 aremin square field. centred. on Leo Land in an adjacent. field.", We have obtained $_s$ photometry of a complete sample of stars to $_s$ =16 in a 7.2 arcmin square field centred on Leo I and in an adjacent field. + This sample includes all 21 known carbon stars falling in the imaged area., This sample includes all 21 known carbon stars falling in the imaged area. + Our results show that the top one magnitude or more of the AGB in dv. is populated entirely or almost entirely by. carbon stars., Our results show that the top one magnitude or more of the AGB in $K_{s}$ is populated entirely or almost entirely by carbon stars. + ‘These stars form àsequence in the A.(UJ.IN.) diagram and several of them are variable., These stars form asequence in the $K_{s} - (J-K_{s})$ diagram and several of them are variable. + En addition there are five very red stars. at least three of them variable. which from their magnitudes and. colours are deduced to be AGB tip stars obscurecl by cust shells.," In addition there are five very red stars, at least three of them variable, which from their magnitudes and colours are deduced to be AGB tip stars obscured by dust shells." + Phey are strong candidates for Mira variability., They are strong candidates for Mira variability. + These stars. and at least the brightest unobscured AGB stars. probably belong to the voungest and most metal rich of the significant stellar populations in Leo L Comparison with carbon stars in Alagellanie Cloud clusters suggests ages of about 2 Gyr for these stars in agreement with the age of the voungest major population in this galaxy as derived. in other wavs.," These stars, and at least the brightest unobscured AGB stars, probably belong to the youngest and most metal rich of the significant stellar populations in Leo I. Comparison with carbon stars in Magellanic Cloud clusters suggests ages of about 2 Gyr for these stars in agreement with the age of the youngest major population in this galaxy as derived in other ways." + Surprisingly. in view of the fact that vounger populations are generally more centrally concentrated than others in chwarl spheroidals. one of the obscured stars lies about S arcmin from the centre of the galaxy. compared with a tidal radius of 13 arcmin.," Surprisingly, in view of the fact that younger populations are generally more centrally concentrated than others in dwarf spheroidals, one of the obscured stars lies about 8 arcmin from the centre of the galaxy, compared with a tidal radius of 13 arcmin." + We are grateful to Novivuki Alatsunaga for help at. the telescope., We are grateful to Noriyuki Matsunaga for help at the telescope. + We also thank Yasushi Nakajima for providing the reduction pipeline and for information on the photometric system., We also thank Yasushi Nakajima for providing the reduction pipeline and for information on the photometric system. + The Πο] project was initiated. and. supported bv Nagova University and. the National Astronomical Observatory of Japan. anc we thank Professor Sato. Professor Nagata ancl all others involved in the project," The IRSF project was initiated and supported by Nagoya University and the National Astronomical Observatory of Japan, and we thank Professor Sato, Professor Nagata and all others involved in the project ." +Fie.,Fig. + 2 shows he color-color diagram of the IRAS ποτος ASSOCTATCE with the sample of water lasers., 2 shows the color-color diagram of the IRAS sources associated with the sample of water masers. +" The box ou the upper right corner shows the Wood Churchwell (1989) (hereafter WC) criteria used. to identify οοσα, massive stars and ultracompact III regions.", The box on the upper right corner shows the Wood Churchwell (1989b) (hereafter WC) criteria used to identify embedded massive stars and ultracompact HII regions. +" The stars and circles show the old aud new uethanol maser detections respectively,", The stars and circles show the old and new methanol maser detections respectively. + 113 out of 151 sources satisfy the WC criteria. of which LO sources have uethauol maser cussion.," 113 out of 154 sources satisfy the WC criteria, of which 40 sources have methanol maser emission." + Since 21 sources satistving the WC criteria were rot observed. the detection rate among IRAS sources satisfying WC criteria and hosting ILO uasers is at least ~35%..," Since 21 sources satisfying the WC criteria were not observed, the detection rate among IRAS sources satisfying WC criteria and hosting $_2$ O masers is at least $\sim$." + This detection rate is better han that of a survey based purelv on IRAS sources satistving WC criteria (c.g. see discussion of Elinescu et al., This detection rate is better than that of a survey based purely on IRAS sources satisfying WC criteria (e.g. see discussion of Ellingsen et al. + L996)., 1996). + It is to be cautioned that not all of these cases are true associations. as the TRAS source may point to the brightest far infrared source in the star forming region. and better positious for methanol mascers may preclude sole of the current associations (Elinescu 2006: Paudian Coldsuüth 2007).," It is to be cautioned that not all of these cases are true associations, as the IRAS source may point to the brightest far infrared source in the star forming region, and better positions for methanol masers may preclude some of the current associations (Ellingsen 2006; Pandian Goldsmith 2007)." + There are also 12 methanol masers whose IRAS colors do not satisfy WC criteria., There are also 12 methanol masers whose IRAS colors do not satisfy WC criteria. + It can also be secu from Fie., It can also be seen from Fig. + 2 that there is no distinction between the IRAS sources associated with the new cetectious. aud those associated with the previous detectious (which are brighter). nor is there any distinction between the colors of sources with aud without methanol mascrs.," 2 that there is no distinction between the IRAS sources associated with the new detections, and those associated with the previous detections (which are brighter), nor is there any distinction between the colors of sources with and without methanol masers." + Thus. the 1yw detection rate in our survey (11 1) is not due to auy systematic differences vetween in the imfrarecl properties of the sources iu our survey (versus the sources associated with previous cetections of methanol masers).," Thus, the low detection rate in our survey (11 ) is not due to any systematic differences between in the infrared properties of the sources in our survey (versus the sources associated with previous detections of methanol masers)." + The lack of distinction of the IRAS source properties of bright versus faut methanol masers is also consistent with the observation of Paudian Coldsuith (2007)., The lack of distinction of the IRAS source properties of bright versus faint methanol masers is also consistent with the observation of Pandian Goldsmith (2007). + There is only one detection with a peak fux density less than 1 Js. (this is also the onlv such source in the eutire sample incliding previous detections).," There is only one detection with a peak flux density less than 1 Jy, (this is also the only such source in the entire sample including previous detections)." + It should be noted that our saauple is uot from an unbiased survey. and heuce it is nof possible to diseuss the implications of this in the context of the methanol maser population in the Calaxy.," It should be noted that our sample is not from an unbiased survey, and hence it is not possible to discuss the implications of this in the context of the methanol maser population in the Galaxy." + However. we note that this is cousisteut with the results of the simulation of van der Walt (2005) iid the results of the Pancian et al. (," However, we note that this is consistent with the results of the simulation of van der Walt (2005) and the results of the Pandian et al. (" +2007).,2007). + vau der Walt (2005) using Monte Carlo simulations determined the completeness of surveys as a unction of their flux densities. while the observational results of Poaudiui et al. (," van der Walt (2005) using Monte Carlo simulations determined the completeness of surveys as a function of their flux densities, while the observational results of Pandian et al. (" +2007) corroborate the theoretical analysis with regard to the total nunmiber of methanol mascrs iu the Calaxyv.,2007) corroborate the theoretical analysis with regard to the total number of methanol masers in the Galaxy. + Moreover. Paucian et al. (," Moreover, Pandian et al. (" +2007) fou that the distribution of peak flux deusities drops at flux densities below ~ 1 Jv.,2007) found that the distribution of peak flux densities drops at flux densities below $\sim$ 1 Jy. + This could be one of the reasous why we didu't detect many sources below 1 Jy., This could be one of the reasons why we didn't detect many sources below 1 Jy. + Fig., Fig. + 3a (left pancl) shows the huninosity distributions for both maser tvpes as a function of the infrared luminosity of the host IRAS sources and Fie., 3a (left panel) shows the luminosity distributions for both maser types as a function of the infrared luminosity of the host IRAS sources and Fig. + 3b (aight paucl) shows the the maser huninositics of the two species plotted against cach other., 3b (right panel) shows the the maser luminosities of the two species plotted against each other. + Ouly sources that show euission in both species are shown in Fig., Only sources that show emission in both species are shown in Fig. + 3., 3. + The iufrared flux Fyyy (used to determine the infrared huuinositv £y7) is calculated using the formula below (Casoli ot al., The infrared flux $F_{IR}$ (used to determine the infrared luminosity $L_{IR}$ ) is calculated using the formula below (Casoli et al. + 1986)., 1986). + where Fio. Fos. Foy aud Fà4oo refer2 to the IRAS fluxes iu 12. 25. G0 and 100. pau respectively.," where $F_{12}$, $F_{25}$, $F_{60}$ and $F_{100}$ refer to the IRAS fluxes in 12, 25, 60 and 100 $\mu$ m respectively." + The distances are aken from the literature., The distances are taken from the literature. + For sources with no published distance. the near kinematic distance. computed from he peak velocity of 6.7 GIIz eunission using the galactic rotation curve of Wouterloot Braud (1989). asuniug Ry = 8.5 kpc aud Oy = 220 aus +. is adopted.," For sources with no published distance, the near kinematic distance, computed from the peak velocity of 6.7 GHz emission using the galactic rotation curve of Wouterloot Brand (1989), assuming $R_{0}$ = 8.5 kpc and $\Theta_{0}$ = 220 km $^{-1}$, is adopted." + The ucar kinematic distance is used vecause it secs realistic (Sobolev et al., The near kinematic distance is used because it seems realistic (Sobolev et al. + 2005)., 2005). + Fig., Fig. + Ja shows that there is reasonably eood correlation seen between the infrared bpgunuinuositv aud that of both IIO (Correlation coefficient R= 0.61. Probability p« 0.0001) aud CIT;OIT mascrs (R= 0.56. p« 0.00013.," 3a shows that there is reasonably good correlation seen between the infrared luminosity and that of both $_{2}$ O (Correlation coefficient R = 0.64, Probability $p <$ 0.0001) and $_{3}$ OH masers (R = 0.56, $p <$ 0.0001)." + This correlation has been found in the past by a muuber of eroups (c.g. Wouterloot Wahlusley 1986: Szviuczak ct al., This correlation has been found in the past by a number of groups (e.g. Wouterloot Walmsley 1986; Szymczak et al. + 2005). aud the vertical scatter is normally attributed to the variabilitv of the nasers.," 2005), and the vertical scatter is normally attributed to the variability of the masers." + Tlowever. it is not clear as to whether this correlation is physically nieaniusful.," However, it is not clear as to whether this correlation is physically meaningful." + Ou the oue hand. both maser types are spatially separated and have very different excitation requirements.," On the one hand, both maser types are spatially separated and have very different excitation requirements." + TO masers are collisionally pumped aud occur in shocks aloug outflows. while ΠΟΠ masers produced by radiative pimping aud originate from circumstellar disk: or envelopes.," $_{2}$ O masers are collisionally pumped and occur in shocks along outflows, while $_{3}$ OH masers produced by radiative pumping and originate from circumstellar disks or envelopes." + Thus. it is not clear whether the correlation seen in Fie.," Thus, it is not clear whether the correlation seen in Fig." + 3a arises from a plivsical connection between he far-infrared bhunünositv aud maser Dmuuinositv., 3a arises from a physical connection between the far-infrared luminosity and maser luminosity. + , Fig. +3b shows that there is also a good correlation betweeu uethauol aud water maser luminosities (R= 0.63. p« 0001).," 3b shows that there is also a good correlation between methanol and water maser luminosities (R = 0.63, $p <$ 0.0001)." + Since there is no physical connection. between je two quantities if is possible that the correlations are just a distance squared effect. as suggested by Palla et al. ," Since there is no physical connection between the two quantities, it is possible that the correlations are just a distance squared effect, as suggested by Palla et al. (" +1991) for the correlation between the water maser aud ie infrared Imiuinositv.,1991) for the correlation between the water maser and the infrared luminosity. + It is also curious that the water Ποο in our salple (that are associated with methanel nascrs} are an order of magnitude more bhuuinous thaw 15 ones associated with the methanol maser sample of Szviuczak et al. (, It is also curious that the water masers in our sample (that are associated with methanol masers) are an order of magnitude more luminous than the ones associated with the methanol maser sample of Szymczak et al. ( +2005).,2005). + Some methanol masers detected oe rour survey have low luminosities with the faiutest source waving a maser huuinmositv of only 109 Lo, Some methanol masers detected in our survey have low luminosities with the faintest source having a maser luminosity of only $10^{-9}$ $L_{\odot}$. +However. the oeifrared. luminosities of all sources auge from 107 to 10 £... indicating that they are associated with massive star ornuation.," However, the infrared luminosities of all sources range from $10^{3}$ to $10^{6}$ $L_{\odot}$, indicating that they are associated with massive star formation." + A survey for 6.7 GIIz Πο ΟΙ masers was carried out toward 89 water niasers aud LO new sources were detected. five of which are located bevoud the solu circle.," A survey for 6.7 GHz $_{3}$ OH masers was carried out toward 89 water masers and 10 new sources were detected, five of which are located beyond the solar circle." + A uil detection rate frou low-mass star forming regions chhances the couchision that 6.7 Cz methanol masers are ouly associated with massive star formune regions., A nil detection rate from low-mass star forming regions enhances the conclusion that 6.7 GHz methanol masers are only associated with massive star forming regions. + There, There +"approximately given by p2mim form,<300.",approximately given by $\rho\simeq n_{\rm b} m$ for $n_{\rm b} < 3 n_0$. +" MI forces predict the appearance ofmuons at m,o0.12 fim or pex2.Lol 7).", All forces predict the appearance ofmuons at $n_{\rm b}\simeq0.12$ $^{-3}$ or $\rho\simeq 2\times 10^{14}$ $^{-3}$ ). + The forces LNS and. NRAPR. vield similar composition., The forces LNS and NRAPR yield similar composition. + T'hev both predict a slightly larger (resp., They both predict a slightly larger (resp. + smaller) proton fraction than the force SEy4 above (resp., smaller) proton fraction than the force SLy4 above (resp. + below) po., below) $\rho_0$. + Vhis can be understood by remarking that Eq. (88)), This can be understood by remarking that Eq. \ref{eq.beta.equi}) ) + can be approximately written as (7) where the symmetry energy Simi defined by represents the cost in (nuclear) energy. per particle to replace protons by neutrons in svmmetrie nuclear matter.," can be approximately written as \citep{muether-87} + where the symmetry energy ${\cal S}\{n_{\rm b}\}$ defined by represents the cost in (nuclear) energy per particle to replace protons by neutrons in symmetric nuclear matter." + From. Eq. (115)).," From Eq. \ref{eq.muther}) )," + we have As can be seen on Figure 2.. the forces LNS and NRAPR vield a larger (resp.," we have As can be seen on Figure \ref{fig:sym}, the forces LNS and NRAPR yield a larger (resp." + smaller) svnimetry energy than the force SLx4 above (resp., smaller) symmetry energy than the force SLy4 above (resp. +" below) the saturation density ny (note that the svmametry energy coellicient e,2 δη).", below) the saturation density $n_0$ (note that the symmetry energy coefficient $a_s\simeq {\cal S}\{n_0\}$ ). +" Figure 6 shows the static pressure (90) of npergi matter in equilibrium as a function of the mass-energy density p=(ay.""ο.", Figure \ref{fig:eos} shows the static pressure \ref{eq.Peq}) ) of $npe\mu$ matter in equilibrium as a function of the mass-energy density $\rho=U_{\rm ins}/c^2$. + In figures 7.. S. and 9.. we compare the effective masses defined by Eq. (56))," In figures \ref{fig:effmass_SLy4}, \ref{fig:effmass_LNS} and \ref{fig:effmass_NRAPR}, , we compare the effective masses defined by Eq. \ref{eq:effmass}) )" + for the two Skyrme forces., for the two Skyrme forces. + In both cases the, In both cases the +proposed for the ιοτατο (Condolo2000).,proposed for the neutralino \citep{gondolo00}. +. These rely ou the fact that he neutralino is a Majorana particle. aud thus can anuililate with itself.," These rely on the fact that the neutralino is a Majorana particle, and thus can annihilate with itself." + The resultant heavy quarks and eauge and Που bosous produce hadronuic and clectromagueic showers., The resultant heavy quarks and gauge and Higgs bosons produce hadronic and electromagnetic showers. + This leads to a primary antiprotou colpolicut to the cosmic-ravs., This leads to a primary antiproton component to the cosmic-rays. + The autiprotou component has ]oen discussed mo imaanwo papers aud. searched for iu uanv experiments., The antiproton component has been discussed in many papers and searched for in many experiments. +" It is difficult to distinguish the primary antiproton component from the secondary component produced in cosmic-ray iuteractions in the iuterstellar medium refiutro,barbelow)."," It is difficult to distinguish the primary antiproton component from the secondary component produced in cosmic-ray interactions in the interstellar medium \\ref{intro_pbar} + below)." + Bothlincandcontin ΕΠΗ vay signatures have been proposed as a 1162218 to search for the ueutralino with GLAST., Both line and continuum $\gamma$ -ray signatures have been proposed as a means to search for the neutralino with GLAST. + Iu addition. it has been proposed to search for the neutring signature produced when ucutralinos aunihilate iu the gravitational potential well of the su- (Andrésctal.1999).," In addition, it has been proposed to search for the neutrino signature produced when neutralinos annihilate in the gravitational potential well of the sun \citep{amanda99}." +. The promise of iudirect detection techniques to search for the neutralino has changed markedly in the last vear., The promise of indirect detection techniques to search for the neutralino has changed markedly in the last year. + Theoretical calculations predict a flux of primary autideuterous dn the cosmuic-ravs due to the aunibilatio- of the neutralino (Donatoetal.2000)., Theoretical calculations predict a flux of primary antideuterons in the cosmic-rays due to the annihilation of the neutralino \citep{donato00}. +. Like the welknown primary autiproton signal. the autideuteron signal is produced when WIAIPS annihilate to heavy quarks and eauge and Iiees bosons that fragment to cosmiüc-orav antiprotous and antineutrons.," Like the well-known primary antiproton signal, the antideuteron signal is produced when WIMPs annihilate to heavy quarks and gauge and Higgs bosons that fragment to cosmic-ray antiprotons and antineutrons." + This flux is laree enough that the GAPS technique. when cuploved in a modest space-based experiment. has competitive and possibly superior sensitivitv to as vet unrealized 3rd generation direct detection experiments.," This flux is large enough that the GAPS technique, when employed in a modest space-based experiment, has competitive and possibly superior sensitivity to as yet unrealized 3rd generation direct detection experiments." + Indeed the indirect detection of the neutralino via the autidleuteron provides an ideal complementary techuique to the direct detection experiments because its background source is not neutrous (sce below)., Indeed the indirect detection of the neutralino via the antideuteron provides an ideal complementary technique to the direct detection experiments because its background source is not neutrons (see below). + Figure d shows the projected seusitivitv of CDAIS II. a state-ofthe-art direct detection experiueut. through the vear 2001.," Figure \ref{sensitivity1} shows the projected sensitivity of CDMS II, a state-of-the-art direct detection experiment, through the year 2004." +" Also shown is the projected. sensitivity of GENIUS, a proposed 3rd generation experiment based ou ~1 Tou Cermmanimn."," Also shown is the projected sensitivity of GENIUS, a proposed 3rd generation experiment based on $\sim1$ Ton Germanium." + The third ecucration experiments will iuuprove on the 2ud generation experiuents by abou 3 orders of magnitude., The third generation experiments will improve on the 2nd generation experiments by about 3 orders of magnitude. + The dots represent the eusenible of SUSY models parameterized by their spiududepeudenu cross-section and neutralino mass., The dots represent the ensemble of SUSY models parameterized by their spin-independent cross-section and neutralino mass. + A similar plot is shown in fieure 2 for a modest MIDEX class satellite experimen (described in more detail in refappaber)).," A similar plot is shown in figure \ref{sensitivity2} + for a modest MIDEX class satellite experiment (described in more detail in \\ref{app_dbar}) )." +Thesensitivitgealeulationisall inclusivetineludisigllweysr agyy earginggcomagnetiecutof fandsolarmodulation), The sensitivity calculation is all-inclusive (including the effects of orbit-varying geomagnetic cutoff and solar modulation). + Thesepsitiο 1H); aE diseaseV;DG rofing 2e, The sensitivity for this (unoptimized) experiment is much more than an order of magnitude better than AMS for detecting the antideuteron. +vcperimenthasdetectedamearginal(2/50) discrepancy in the anomalous maguctic moment for the muon| (Brownetal. 2001)., Recently a g--2 experiment has detected a marginal $\sigma$ ) discrepancy in the anomalous magnetic moment for the muon \citep{brown01}. +. If this discrepancy is due to supersviuuuetric corrections to loop diagrams producing the maguetic moment. then the range of possible SUSY models is severely constrained. as shown by the ereen circles in fieures 1.. 2. (Baltz&Condolo2001).," If this discrepancy is due to supersymmetric corrections to loop diagrams producing the magnetic moment, then the range of possible SUSY models is severely constrained, as shown by the green circles in figures \ref{sensitivity1}, \ref{sensitivity2} \citep{baltz01}." +. Uulike the AMS experiment on ISS. the GAPS experiment on a small satellite can be as scusitive as a 3rd generation experiment and will access nearly the cutive allowed SUSY parameter space as restricted by the ο2 results.," Unlike the AMS experiment on ISS, the GAPS experiment on a small satellite can be as sensitive as a 3rd generation experiment and will access nearly the entire allowed SUSY parameter space as restricted by the g–2 results." + The source of background in a primary autideuteron search is the secondary autideuterous produced m cosnmic-rav interactions., The source of background in a primary antideuteron search is the secondary antideuterons produced in cosmic-ray interactions. + The situation is reminiscent of the primary antiproton searches. where the backeround is due to secondary and tertiary autiprotous (Simonctal.1998:Berestromctal.1999).," The situation is reminiscent of the primary antiproton searches, where the background is due to secondary and tertiary antiprotons \citep{simon98, bergstrom99}." +. ILowever the situation is much better for a primary autideuteron search., However the situation is much better for a primary antideuteron search. + The secoudary antideuterons cut off at wich lieher kinetic cuerey than iu the case of secondary aud tertiary autiprotons (figure 3))., The secondary antideuterons cut off at much higher kinetic energy than in the case of secondary and tertiary antiprotons (figure \ref{dbar_flux}) ). + If primary anticdeuterons are searched for at low enough energies the probability of contamination by secondary antideuterons can be made neelieible. iu coutradistinction to the primary autixoton case.," If primary antideuterons are searched for at low enough energies the probability of contamination by secondary antideuterons can be made negligible, in contradistinction to the primary antiproton case." + The autideuterou search provides a nice complement to the direct detection experiments seeking the neutralimo., The antideuteron search provides a nice complement to the direct detection experiments seeking the neutralino. + With their very differeut sources of background thev can together provide a convincing case for the nueutralino detection., With their very different sources of background they can together provide a convincing case for the neutralino detection. + In addition there are WIAIP models in which the autideutcron signal would be present but a nicasurable sigual in a direct detection experiment would not be obtained., In addition there are WIMP models in which the antideuteron signal would be present but a measurable signal in a direct detection experiment would not be obtained. + The antiproton spectrum has been the subject of nunerous theoretical and observational papers., The antiproton spectrum has been the subject of numerous theoretical and observational papers. + This is a vast subject and we restrict our conuuents to those areas where CAPS represeuts a significant improvement over curent techuiques and where the discovery space js substantial, This is a vast subject and we restrict our comments to those areas where GAPS represents a significant improvement over current techniques and where the discovery space is substantial. + An example is the use of GAPS on an interstellar probe to characterize the ultralow cucrey antiproton spectrum., An example is the use of GAPS on an interstellar probe to characterize the ultralow energy antiproton spectrum. + At comparable mass. volunue and power constunption CAPS has almost an order of maenitude more grasp (AQ product) than alternatives. can probe to lower autiproton energies aud can do so with superior discrinunatory power agaiust false detectious rofappybar] ).," At comparable mass, volume and power consumption GAPS has almost an order of magnitude more grasp $A\Omega$ product) than alternatives, can probe to lower antiproton energies and can do so with superior discriminatory power against false detections \\ref{app_pbar}) )." + The secondary antiprotous are produced through plop>p|X veactious aud the kincmatic suppression of the secondary autiprotous due to the requirement of 3 protons in the final state. combined with the decreasing primary protou spectrum. provides a very characteristic shape for the secondary autiproton spectrum.," The secondary antiprotons are produced through $p+p\rightarrow \bar{p}+X$ reactions and the kinematic suppression of the secondary antiprotons due to the requirement of 3 protons in the final state, combined with the decreasing primary proton spectrum, provides a very characteristic shape for the secondary antiproton spectrum." + This has been probed iu imany balloon flights aud will be measured by AMS on ISS., This has been probed in many balloon flights and will be measured by AMS on ISS. + The very sharp suppression of the secondary antiproton flux at low energies provides au opportunity to test subdominant contributions to the antiproton flux (Simonctal.1998:Berestromet1999:Donatoctal 2001).," The very sharp suppression of the secondary antiproton flux at low energies provides an opportunity to test subdominant contributions to the antiproton flux \citep{simon98, bergstrom99, donato01}. ." + These processes include ate protons with heavier nuclei (uaiuly ήpe ARG osaBored durimg propagation (producing the tertiary antiprotonus coniponent)., These processes include collisions of primary protons with heavier nuclei (mainly helium) and energy losses of the secondary antiprotons during propagation (producing the tertiary antiprotons component). + These separate conmiponents are shown iu ure L., These separate components are shown in figure \ref{pbar_flux}. +" The effect of these subdominant componucuts is marked below ~ 150 MeV. But the ability to probe these coniponents is τος, by the effects of solar modulation and the ecomaeguctic regiditv cutoff iuhereut iun low earth orbit mussious.", The effect of these subdominant components is marked below $\sim$ 150 MeV. But the ability to probe these components is limited by the effects of solar modulation and the geomagnetic rigidity cutoff inherent in low earth orbit missions. + The modulation preveuts autiprotous with energies of less than order the solar potential ( 500 MeV) from reaching the vicinity of the earth., The modulation prevents antiprotons with energies of less than order the solar potential $\sim$ 500 MeV) from reaching the vicinity of the earth. + Iu order to surmount this difficulty it has been proposed to seud a probe out of the heliosphere (Wellsetal.1999)., In order to surmount this difficulty it has been proposed to send a probe out of the heliosphere \citep{wells99}. +". In refapp, bar... weshowhowal gearobsercationwith GAP Sousucha pr Several sources of primaryantiprotons could be even larger than the secondary and tertiary autiproton signal."," In \\ref{app_pbar}, we show how a 1-year observation with GAPS on such a probe can detect secondary and tertiary antiprotons down to 40 MeV. Several sources of primaryantiprotons could be even larger than the secondary and tertiary antiproton signal." + Autiprotous are produced in the ueutralino aunihlilatiou and dominate over the secondary aud tertiary compoucuts, Antiprotons are produced in the neutralino annihilation and dominate over the secondary and tertiary components +J.M. and A.M. acknowledge financial support from the Prodex-ESA Contract Prodex 8 COROT (C90199) and FNRS.,J.M. and A.M. acknowledge financial support from the Prodex-ESA Contract Prodex 8 COROT (C90199) and FNRS. + The authors thank M.A. Dupret for useful suggestions concerning oscillation frequency computations., The authors thank M.A. Dupret for useful suggestions concerning oscillation frequency computations. +the Gaussian window has large short range correlations and therefore a wider kernel is also valid for The kernel Aο.) which mixes the £ and D modes on the cut sky is plotted as à dashed line in figures (7)) and (8)),"the Gaussian window has large short range correlations and therefore a wider kernel is also valid for The kernel $K_{-2}(\ell,\ell')$ which mixes the $E$ and $B$ modes on the cut sky is plotted as a dashed line in figures \ref{fig:polcutg}) ) and \ref{fig:polcutth}) )." + ]t is much smaller than the three other kernels and the shape seems to differ as well., It is much smaller than the three other kernels and the shape seems to differ as well. + Note that the height of the mixing kernel relative to the other kernels is lower for the 15 degree window than for t10 5- degree window., Note that the height of the mixing kernel relative to the other kernels is lower for the $15$ degree window than for the $5$ degree window. + That the size of the mixing kernel relative to the other kernels is dropping when the size of the window is Increasing was to be expected since in the limit of full sky. coverage the £-2 mixing disappears and the mixing kernel mus go lo In figure (9)) a slice at {5200 of the temperature kernel and the mixirig kernel is shown for the 5 and 15 degree ENIM Gaussian Gabor window., That the size of the mixing kernel relative to the other kernels is dropping when the size of the window is increasing was to be expected since in the limit of full sky coverage the $E$ $B$ mixing disappears and the mixing kernel must go to In figure \ref{fig:km2cutg}) ) a slice at $\ell=200$ of the temperature kernel and the mixing kernel is shown for the $5$ and $15$ degree FWHM Gaussian Gabor window. + Phe kernels are normalised to one at the peak so tiat the shapes can be compared., The kernels are normalised to one at the peak so that the shapes can be compared. + For the Gaussian window. the shapes of the kernels still seem to be the same.," For the Gaussian window, the shapes of the kernels still seem to be the same." + But the kernes for the corresponding tophat windows shown in figure (10)) does not have a Gaussian shape and clillers significantlv from tie other Since the kernels for the polarisation power spectra have a shape similar to that of he temperature power spectrum the ellect of a Gabor window on the shape of the power spectrum should also be similar., But the kernels for the corresponding tophat windows shown in figure \ref{fig:km2cutth}) ) does not have a Gaussian shape and differs significantly from the other Since the kernels for the polarisation power spectra have a shape similar to that of the temperature power spectrum the effect of a Gabor window on the shape of the power spectrum should also be similar. + This can be seen in figure (11)) and (12))., This can be seen in figure \ref{fig:pcle}) ) and \ref{fig:pclc}) ). + The figures show the full sky polarisation power spectra (dashed. line) C£ (figure 11)) and C (ligure 12)) for a standard CDM. model., The figures show the full sky polarisation power spectra (dashed line) $C_\ell^E$ (figure \ref{fig:pcle}) ) and $C_\ell^C$ (figure \ref{fig:pclc}) ) for a standard CDM model. + In this model the 2 component of polarisation is zero., In this model the $B$ component of polarisation is zero. + On op of the ful skv power spectra we have plotted the polarisation pseudo power spectra for a 5 and 15 degree Gaussian Gabor window (upper and lower plots respectively) normalised so that it can be compared to the full sky spectrum., On top of the full sky power spectra we have plotted the polarisation pseudo power spectra for a $5$ and $15$ degree Gaussian Gabor window (upper and lower plots respectively) normalised so that it can be compared to the full sky spectrum. + The pseudo spectra for the corresponding tophat windows are plotted as dotted lines., The pseudo spectra for the corresponding tophat windows are plotted as dotted lines. + As expected the shape of the polarisation pseuco spectra relative to the full sky spectra is similar to that for the temperature spectrum shown in LICL., As expected the shape of the polarisation pseudo spectra relative to the full sky spectra is similar to that for the temperature spectrum shown in HGH. + One dillerence is tha the polarisaion pseudo spectra for the Gaussian window do not have the characteristic extra peak at low multipole which is seen in the temperature pseudo spectrum., One difference is that the polarisation pseudo spectra for the Gaussian window do not have the characteristic extra peak at low multipole which is seen in the temperature pseudo spectrum. + This peak in the temperature spectrum arose due to the steep 1//(£|1) fall-oIL of the tem»epature spectrum at low multipolo., This peak in the temperature spectrum arose due to the steep $1/\ell(\ell+1)$ fall-off of the temperature spectrum at low multipole. + The polarisation spectra do not have this steep Fall-olf and for this reason here is no extra Because of the mixing of £ and D modes there is also à. L polarisation component C. for the pseudo spectrum even when the input full sky CP were zero., The polarisation spectra do not have this steep fall-off and for this reason there is no extra Because of the mixing of $E$ and $B$ modes there is also a $B$ polarisation component $\tilde C^B_\ell$ for the pseudo spectrum even when the input full sky $C^B_\ell$ were zero. + This is shown in figure (13)) where we have plotted the full sky spectrum CT and the pseudo spectra C7“bp foros the 5 and 15 degree EFWHIAL Gaussian]. Gabor] windows. and corresponding. tophat windows., This is shown in figure \ref{fig:pclb}) ) where we have plotted the full sky spectrum $C^E_\ell$ and the pseudo spectra $\tilde C_\ell^B$ for the $5$ and $15$ degree FWHM Gaussian Gabor windows and corresponding tophat windows. +. rpsPhe pseudo spectra are normalised so that they can be compared directly to the full sky spectrum., The pseudo spectra are normalised so that they can be compared directly to the full sky spectrum. + The dashed lines show the pseudo, The dashed lines show the pseudo +The criterion for significant improvement between two modelfits was developed using a ratio of reduced y parameters where the subseripts refer to the two modelfits compared.,The criterion for significant improvement between two modelfits was developed using a ratio of reduced $\chi^2$ parameters where the subscripts refer to the two modelfits compared. + The order is defined by the number of degrees of freedom n of the individual modelfits with the condition ny)- 3., The order is defined by the number of degrees of freedom $n$ of the individual modelfits with the condition $n_12TOAL.. (hese stars may conclude bv implosions to intermediate-mass black holes without giving out much metals to the surroundings.," For example, in the most extreme case where all Pop-III stars are more massive than, say, $\ge 270\msun$, these stars may conclude by implosions to intermediate-mass black holes without giving out much metals to the surroundings." + However. exactly how massive Pop III stars are is uncertain.," However, exactly how massive Pop III stars are is uncertain." + While simulations have suggested that Pop III stus may be more massive than 100M. (covery massive star. VAIS: Abeletal.2000:Brommοἱ 2001a)). Tan&Melee.(2004) lind that stellar feedback processes mav limit the mass of the Pop HI stus to the range 30—100 M...," While simulations have suggested that Pop III stars may be more massive than $100\,\msun$ (“very massive star”, VMS; \citealt{abe00,bro01}) ), \citet{tan04} find that stellar feedback processes may limit the mass of the Pop III stars to the range $30-100\,\msun$ ." + Observationallv. (he VMS picture is advocated by Obetal.(2001) and Wasserburg (2002).. based on an analvsis of metal viekld patterns from pair-instability supernova (PISN) explosion of VAIS progenitors (Ileger&Wooslev|2002).. al. (2004).. Daigneetal... (2004).," Observationally, the VMS picture is advocated by \cite{ohn01} and \cite{qia02}, based on an analysis of metal yield patterns from pair-instability supernova (PISN) explosion of VMS progenitors \citep{heg02}. \cite{tum04}, \cite{dai04}," +. Umeda Nomoto (2003.2005) and (2003).. on the other hand. argue (that the general pattern in metal-poor halo stars. in the Lya forest and cosmic star formation history. is more consistent with the vield pattern of Type HI supernovae (SNII) perhaps with a lower cutoll of 10....," Umeda Nomoto (2003,2005) and \cite{ven03}, on the other hand, argue that the general pattern in metal-poor halo stars, in the $\alpha$ forest and cosmic star formation history, is more consistent with the yield pattern of Type II supernovae (SNII) perhaps with a lower cutoff of $\msun$." + Clearly. the metallicity of gas out of which stars are formed is critically important.," Clearly, the metallicity of gas out of which stars are formed is critically important." + The conventional picture that is often. adopted goes as follows: formed stars will eject metals into the IGM and eventually raise the metallicity of the IGM to above the threshold for the Pop-III to Pop-II transition., The conventional picture that is often adopted goes as follows: formed stars will eject metals into the IGM and eventually raise the metallicity of the IGM to above the threshold for the Pop-III to Pop-II transition. + A somewhat refined version of this takes into account that the metallicityv enrichment process of the IGM is unlikely to be synchronous for different regions (e.g.. Furlanetto&Loeb. 2005)).," A somewhat refined version of this takes into account that the metallicity enrichment process of the IGM is unlikely to be synchronous for different regions (e.g., \citealt{fl05}) )." + Ilere. we point out a possibly large difference between the metallidtv of the IGM and the metallicity of the eas in minihalos.," Here, we point out a possibly large difference between the metallicity of the IGM and the metallicity of the gas in minihalos." + Since minihalos collapse ab very high redshift (e... Wvithe&Cen 2007)). the large amount of dense gas in minihalos (hus may provide a primary [uel for subsequent star formation. when eventually (μον are incorporated into large svstems where efficient atomic cooling allows gas to condense to form slars.," Since minihalos collapse at very high redshift (e.g., \citealt{wc07}) ), the large amount of dense gas in minihalos thus may provide a primary fuel for subsequent star formation, when eventually they are incorporated into large systems where efficient atomic cooling allows gas to condense to form stars." + To quanüfv. this possible difference between the metallicity of minihalo gas and that ol the IGM. we study the stability and metal enrichment of minihalos subject to metal-rich shockwaves launched by supernovae explosions from large galaxies.," To quantify this possible difference between the metallicity of minihalo gas and that of the IGM, we study the stability and metal enrichment of minihalos subject to metal-rich shockwaves launched by supernovae explosions from large galaxies." + We will treat an idealized situation where a minihalo is subject to shock waves enriched with a chosen metallicity. and we investigate how gas inside it may be contaminated by metals.," We will treat an idealized situation where a minihalo is subject to shock waves enriched with a chosen metallicity, and we investigate how gas inside it may be contaminated by metals." + We will assume that there has been no star formation hence no sellnetal-enrichunent in minihalos. because of the lack of adequate coolants: molecular hydrogen is assumed to have long been destroyed. byLvman-Werner photons produced by earlier stars elsewhere.," We will assume that there has been no star formation hence no self-metal-enrichment in minihalos, because of the lack of adequate coolants; molecular hydrogen is assumed to have long been destroyed byLyman-Werner photons produced by earlier stars elsewhere." + Because gas in minihalos is, Because gas in minihalos is +of values achieved by primordial collapse models shows the inability of these models to reproduce the observed. central line-strengths for both «Lez and Ales features.,of values achieved by primordial collapse models shows the inability of these models to reproduce the observed central line-strengths for both $<$ $>$ and $_{2}$ features. + This result is confirmed in fies 5. and 6.., This result is confirmed in figs \ref{FeHb} and \ref{Fe4Hb}. + Introduction to models of a biased LME at early epochs can resolve the under-abundance problem but can not simultaneously. explain the high. 1117 values observed in some elliptical galaxies and at least one of our spiral bulges (fig. 5))., Introduction to models of a biased IMF at early epochs can resolve the under-abundance problem but can not simultaneously explain the high ${\beta}$ values observed in some elliptical galaxies and at least one of our spiral bulges (fig. \ref{FeHb}) ). + We might also expect to see an Ales excess with respect to solar in the biased EME scenario., We might also expect to see an $_{2}$ excess with respect to solar in the biased IMF scenario. + ‘There is no evidence for this excess in our bulge data., There is no evidence for this excess in our bulge data. + While direct evidence for primordial collapse is not observed. examples of ongoing galaxy mergers are.," While direct evidence for primordial collapse is not observed, examples of ongoing galaxy mergers are." + Indeed. Schweizer Seitzer (1992) suggest that. based. on the number of ealaxies exhibiting on-going merecrs or the fine structure indicative of a recent event. ~ of field cllipticals have undergone a merger event in the last 7 Gaver.," Indeed, Schweizer Seitzer \shortcite{SS92} suggest that, based on the number of galaxies exhibiting on-going mergers or the fine structure indicative of a recent event, $\sim$ of field ellipticals have undergone a merger event in the last 7 Gyr." + This would seen to be supported by the fact that ~ of the elliptical ancl SO sample shown in fig., This would seem to be supported by the fact that $\sim$ of the elliptical and S0 sample shown in fig. + 5. show LL? values that lic the 8S Gyr SSP line., \ref{FeHb} show ${\beta}$ values that lie the 8 Gyr SSP line. + In merger models. galaxy formation proceeds by coalescence of fragments that have undergone SE prior to merger.," In merger models, galaxy formation proceeds by coalescence of fragments that have undergone SF prior to merger." + Such models can achieve high central line-streneths as the period. of SE prior to merger pre-enriches the ESAT from which the bull of the population is formed (Sansom&Proctor1998).., Such models can achieve high central line-strengths as the period of SF prior to merger pre-enriches the ISM from which the bulk of the population is formed \cite{SP98a}. + It. should be noted that both primordial collapse and merger models of galaxy formation predict short bursts of SE due to the extremely rapid. inllow of gas in both scenarios (Theisetal.1992:Barnes&IHernquist. 1996).," It should be noted that both primordial collapse and merger models of galaxy formation predict short bursts of SF due to the extremely rapid inflow of gas in both scenarios \cite{TBH92,BH96}." +. Therelore. the excess Ale observed in elliptical galaxies is predicted. by both of hese models. without the need for the assumption of a jased IME.," Therefore, the excess Mg observed in elliptical galaxies is predicted by both of these models, without the need for the assumption of a biased IMF." + “Phe modelling of spiral bulges. using merger models. is constrained by their lack of Ales excess.," The modelling of spiral bulges, using merger models, is constrained by their lack of $_{2}$ excess." + As the ime-scale of eas inflow during an interaction is extremely rapid. large merger induced: star-bursts will result. in an Ales excess.," As the time-scale of gas inflow during an interaction is extremely rapid, large merger induced star-bursts will result in an $_{2}$ excess." + As this is not seen in our spiral bulges. if xilee. formation is dominated. by accretions/mergers. the SE bursts must have been small and numerous.," As this is not seen in our spiral bulges, if bulge formation is dominated by accretions/mergers, the SF bursts must have been small and numerous." + Εις is consistent with. the presence. of the dise which is highly unstable to mergers of more than a few percent of the total galaxy mass (Voth&Ostriker1992)., This is consistent with the presence of the disc which is highly unstable to mergers of more than a few percent of the total galaxy mass \cite{TO92}. +. While we can construct single. burst merger. models that reproduce the «pec. Ld and Ales indices observed in the bulges. detailed modelling of merger scenarios has not been carried out. as the large parameter space implied by multiple short bursts makes these models highly degenerate.," While we can construct single burst merger models that reproduce the $<$ $>$, ${\beta}$ and $_{2}$ indices observed in the bulges, detailed modelling of merger scenarios has not been carried out as the large parameter space implied by multiple short bursts makes these models highly degenerate." + In the limiting case. where interactions are so frequent that the induced. SE is cllectively continuous. we expect merger models converge to extended inflow," In the limiting case, where interactions are so frequent that the induced SF is effectively continuous, we expect merger models converge to extended inflow" +so that the formation length in a medium characterized by j& and A becomes ,so that the formation length in a medium characterized by $\mu$ and $\lambda$ becomes z_c. +For the validity of ((6.43)). the mean free path has to be larger than (he interaction range of the centers. ie. A>pet.," For the validity of \ref{9e}) ), the mean free path has to be larger than the interaction range of the centers, i.e., $\lambda > \mu^{-1}$." +" The enerev loss of the passing color charge is now determined by the relative scales of the process,", The energy loss of the passing color charge is now determined by the relative scales of the process. +" If A>z,.we have incoherence. while for A<2, there is coherent scattering with destructive interference."," If $\lambda >z_c$,we have incoherence, while for $\lambda < z_c$ there is coherent scattering with destructive interference." + In both cases. we have assumed that the thickness £ of the medium is larger (han all other scales.," In both cases, we have assumed that the thickness $L$ of the medium is larger than all other scales." +" When the coherence length reaches the size of the svstem. 2,—£L. elfeclively only one gluon can be emitted."," When the coherence length reaches the size of the system, $z_c = L$, effectively only one gluon can be emitted." +" This delines a critical thickness L.(E)ο» ab fixed incident energv. E. or equivalently a critical E,=1?L?/A for lixed thickness L: for L2Lo there is bulk LPAI-behavior. below £, there are finite-s1ze corrections."," This defines a critical thickness $L_c(E)=(E \lambda / \mu^2)^{1/2}$ at fixed incident energy $E$ , or equivalently a critical $E_c=\mu^2 L^2 /\lambda$ for fixed thickness $L$; for $L > L_c$, there is bulk LPM-behavior, below $L_c$ there are finite-size corrections." + We are thus left with three regimes for radiative energy loss., We are thus left with three regimes for radiative energy loss. +" In case of incoherence. τμ, (here is (he classical radiative lossL— where o, is (he strong coupling."," In case of incoherence, $z_c < \mu^{-1}$, there is the classical radiative loss, where $\alpha_s$ is the strong coupling." +" In the coherent region. A> z,. the energy loss is given by theLPM bulk expression when L>L. |[66].."," In the coherent region, $\lambda >z_c$ the energy loss is given by theLPM bulk expression when $L > L_c$\cite{Baier}, ," +magnetized regions as suggested by Lindsey&Braun(2005a).,magnetized regions as suggested by \citet{lin05a}. +". The second-skip time-distance experiment also convincingly demonstrates that the double-skip acoustic travel times, measured without using signals inside active regions, are in nice agreement with the mean single-skip acoustic travel times obtained with using signals inside active regions, which indicates that the solar oscillation signals inside sunspots are useful for time-distance helioseismology measurements."," The second-skip time-distance experiment also convincingly demonstrates that the double-skip acoustic travel times, measured without using signals inside active regions, are in nice agreement with the mean single-skip acoustic travel times obtained with using signals inside active regions, which indicates that the solar oscillation signals inside sunspots are useful for time-distance helioseismology measurements." + We believe that the numerical studies of the wave interactions with the magnetic field will help us better understand local helioseismological measurements., We believe that the numerical studies of the wave interactions with the magnetic field will help us better understand local helioseismological measurements. + We thank Drs., We thank Drs. +" Tom Duvall, Doug Braun and Charlie Lindsey for useful discussions and comments on some parts of this research, and we also thank them for thoroughly reading this manuscript and providing valuable comments."," Tom Duvall, Doug Braun and Charlie Lindsey for useful discussions and comments on some parts of this research, and we also thank them for thoroughly reading this manuscript and providing valuable comments." + We also thank an anonymous referee for some constructive comments to improve the quality of this paper., We also thank an anonymous referee for some constructive comments to improve the quality of this paper. + This research is partly supported by “Living With a Star” TR&TT program of NASA., This research is partly supported by “Living With a Star” T program of NASA. + The project is supported by NASA erant NAG5-10483 to Stanford University., The project is supported by NASA grant NAG5-10483 to Stanford University. + is a project of international cooperation between ESA and NASA., is a project of international cooperation between ESA and NASA. +Another feature which reacts to the changing clisk fraction is the shock touching the boundary. in the upper right hand quadrant.,Another feature which reacts to the changing disk fraction is the shock touching the boundary in the upper right hand quadrant. + It becomes more inclined towards the center of the disk and increases in length with increasing fa. raising the concern that it might interact with other features in the disk.," It becomes more inclined towards the center of the disk and increases in length with increasing $\rm f_{\rm d}$, raising the concern that it might interact with other features in the disk." + Lt is hard to discount this shock as artificial because Figure 2. indicates that there is a minimum in the potential in the upper quadrants of the grid., It is hard to discount this shock as artificial because Figure \ref{Potential} indicates that there is a minimum in the potential in the upper quadrants of the grid. + However it is likely that whatever structure forms in that area of the erid. mav be allectec by the outer boundary conditions.," However it is likely that whatever structure forms in that area of the grid, may be affected by the outer boundary conditions." + Because it is thought that the interstellar cloud: medium can be crudely approximated. by an isothermal gas if the clouds have an equilibrium mass spectrum. (Cowie 1980) maintained by supernovac which both destroy ancl create gas clouds. most simulations of eas [lows in disk galaxies treat the eas as isothermal where the sound speed represents the rms velocity of the interstellar clouds.," Because it is thought that the interstellar cloud medium can be crudely approximated by an isothermal gas if the clouds have an equilibrium mass spectrum (Cowie 1980) maintained by supernovae which both destroy and create gas clouds, most simulations of gas flows in disk galaxies treat the gas as isothermal where the sound speed represents the rms velocity of the interstellar clouds." + Simulations treating the gas as multi-phase are starting to be run (Colina Wada 2000. Wacla Ixoda 2001. Slvz et al.," Simulations treating the gas as multi-phase are starting to be run (Colina Wada 2000, Wada Koda 2001, Slyz et al." + 2003)., 2003). + Given the caveats in modeling a multi-phase interstellar medium. we find it prudent to keep the simple assumption of a uniform ISAL for these global. disk: simulations. since. as already remarked in the Introduction. for our study in Paper E we are," Given the caveats in modeling a multi-phase interstellar medium, we find it prudent to keep the simple assumption of a uniform ISM for these global disk simulations, since, as already remarked in the Introduction, for our study in Paper I we are" +a recent review of the short-duration (<<18) bursts of gravitational waves in core-bounce. more Closely related to Type II supernovae. see (Frver.Holz&Hughes2004) and references iherein.,"a recent review of the short-duration $<<1$ s) bursts of gravitational waves in core-bounce, more closely related to Type II supernovae, see \citep{fry04} and references therein." + On account of (7--8)}. core-collapse compact can produce hieh-mass. rapidly. spinning black holes in centered. nucleation. whose rotational enerev can reach about one-half the maximal spin-energv of a Ixerr black hole.," On account of \ref{EQN_AA1}- \ref{EQN_AA2}) ), core-collapse compact can produce high-mass, rapidly spinning black holes in centered nucleation, whose rotational energy can reach about one-half the maximal spin-energy of a Kerr black hole." + In a suspended accretion state. these black holes spin-down in the process of emitting a long-duration burst of tens of seconds in gravitational waves (vanPuttenetal.2004).," In a suspended accretion state, these black holes spin-down in the process of emitting a long-duration burst of tens of seconds in gravitational waves \citep{mvp04}." +. This long duration burst comes as a second burst. alter the short burst of gravitational radiation in centered nucleation.," This long duration burst comes as a second burst, after the short burst of gravitational radiation in centered nucleation." + To conclude. Type Ib/c supernovae produce a short. single burst of gravitational radiation ab birth of a low-mass black hole.," To conclude, Type Ib/c supernovae produce a short, single burst of gravitational radiation at birth of a low-mass black hole." + The sub-population of GRB-supernovae produce a subsequent long burst of gravitational radiation representing spin-down of the black hole., The sub-population of GRB-supernovae produce a subsequent long burst of gravitational radiation representing spin-down of the black hole. + The second burst tales place alter a quiescent or subluminous (Mineshige2002) surge of the black hole into a high-imass object., The second burst takes place after a quiescent or subluminous \citep{min02} surge of the black hole into a high-mass object. + The author (hanks D. Saulson. J. Bekenstein and (he releree for constructive comments.," The author thanks P. Saulson, J. Bekenstein and the referee for constructive comments." + This research was completed at a joint APCTP-TPI meeting at ihe University of Alberta. ancl is supported by the LIGO Observatories. constructed. by Caltech and MIT. with finding from NSF under cooperative agreement PIIY 9210038.," This research was completed at a joint APCTP-TPI meeting at the University of Alberta, and is supported by the LIGO Observatories, constructed by Caltech and MIT with funding from NSF under cooperative agreement PHY 9210038." + The LIGO Laboratory operates under cooperative agreement PIIY-0107417., The LIGO Laboratory operates under cooperative agreement PHY-0107417. + This paper has been assigned LIGO document number LIGO-DP040014-00-R., This paper has been assigned LIGO document number LIGO-P040014-00-R. +The scalar constant vector & should have values between 0.5 and. 1.0 in order to achieve second order of accuracy.,The scalar constant vector $\kappa$ should have values between $0.5$ and $1.0$ in order to achieve second order of accuracy. + Following suggestions of ?.. value 0.5 should be used for both pressure and velocity. and 1.0 for both density and magnetic field: however. we find no problems while using 1.0 for all Duid quantities.," Following suggestions of \cite{2004ApJS..151..149B}, value $0.5$ should be used for both pressure and velocity, and $1.0$ for both density and magnetic field; however, we find no problems while using $1.0$ for all fluid quantities." + Phe frame velocity at uri; is approximated as a;;=(a;|aj)/2.," The frame velocity at $x_{ij}$ is approximated as ${\bf a}_{ij} = ({\bf a}_i + {\bf + a}_j)/2$." + Finally. the reconstructed Ieft and right states. the frame velocity a;;. and the unit vector n;; are used to obtain the Hux from the 1D Riemann problem.," Finally, the reconstructed left and right states, the frame velocity ${\bf + a}_{ij}$, and the unit vector ${\bf n}_{ij}$ are used to obtain the flux from the 1D Riemann problem." + Insteacl of a linear. a piecewise parabolic reconstruction can also be used to achieve third-order spatial accuracy.," Instead of a linear, a piecewise parabolic reconstruction can also be used to achieve third-order spatial accuracy." + In Appencix ??.. we describe parabolic reconstruction of a scalar field q(x./).," In Appendix \ref{sect:ppm_reconstruction}, we describe parabolic reconstruction of a scalar field $q(\bfx,t)$." + Due to large operation count. this reconstruction is presented only for purpose of completeness. and in the test that will follow later. only linear reconstruction is used.," Due to large operation count, this reconstruction is presented only for purpose of completeness, and in the test that will follow later, only linear reconstruction is used." + The smoothing length in our scheme is a property of the particle distribution and. in contrast to SPILL does not depend on the Laid state.," The smoothing length in our scheme is a property of the particle distribution and, in contrast to SPH, does not depend on the fluid state." + In principle. a constant smoothing length can be used throughout the whole space and time domain.," In principle, a constant smoothing length can be used throughout the whole space and time domain." + In practice however this cause dillieulties due to the possible development of wide range in particle number densities as the simulation progresses., In practice however this cause difficulties due to the possible development of wide range in particle number densities as the simulation progresses. + Similarly to SPLL this can lead to under- or oversampling in low and high particle density regions respectively.," Similarly to SPH, this can lead to under- or oversampling in low and high particle density regions respectively." + The approach used here is inspired by conservative SPL formulations (?7).. ," The approach used here is inspired by conservative SPH formulations \citep{2002MNRAS.335..843M, + 2002MNRAS.333..649S}." +Phe idea is to constrain the smoothing length of a particle ἐς h;= h(x;). to the particle number density at this location.n;= n(x;). i.c. This tends to maintain approximately Niue number of neighbours for cach particle: here ξ1. a and 42/3 for D—1.2 and 3 dimensions respectively. and. n(x;)=L£w(xi). where «w(x;) is defined in3.," The idea is to constrain the smoothing length of a particle $i$, $h_i = h(\bfx_i)$ , to the particle number density at this location,$n_i = n(\bfx_i)$ , i.e. This tends to maintain approximately $N_{\rm ngb}$ number of neighbours for each particle; here $C = 1$ , $\pi$ and $4\pi/3$ for $D=1$, $2$ and $3$ dimensions respectively, and $n(\bfx_i) = 1/w(\bfx_i)$, where $w(\bfx_i)$ is defined in." +.. As in conservative SPLE equations. /; is obtained by iteratively solving15.. for example via Newton-Raphson method (e.g. 2)).," As in conservative SPH equations, $h_i$ is obtained by iteratively solving, for example via Newton-Raphson method (e.g. \citealp{1992nrca.book.....P}) )." + One might be also tempted to use the continuity equation to compute time evolution of the smoothing length. from its initial value., One might be also tempted to use the continuity equation to compute time evolution of the smoothing length from its initial value. + This. however. is undesirable for two main reasons: a) the result depends on the functional form of the divergence operator. and b) in discontinuous Hows the τα may be undefined at some points. which can result in unexpected behaviour.," This, however, is undesirable for two main reasons: a) the result depends on the functional form of the divergence operator, and b) in discontinuous flows the $\nabla\cdot{\bf a}$ may be undefined at some points, which can result in unexpected behaviour." + As a result. in our tests we chose to iteratively solve15.. but we use the dillerential form to predict f(x) as à first guess to an iterative solver.," As a result, in our tests we chose to iteratively solve, but we use the differential form to predict $h(\bfx)$ as a first guess to an iterative solver." + Finally. knowledge of smoothing length permits calculation of the rest of geometric quantities. such as effective volume of a particle. Vi.," Finally, knowledge of smoothing length permits calculation of the rest of geometric quantities, such as effective volume of a particle, $V_i$." + Ht is possible to use numerical quadrature to evaluate fc;(x)dx with a desired accuracy. however we find that defining V;—w(xi) works fine for our purpose. and therefore we decided not to perform more accurate volume estimates.," It is possible to use numerical quadrature to evaluate $\int \psi_i(\bfx) \,d\bfx$ with a desired accuracy, however we find that defining $V_i = w(\bfx_i)$ works fine for our purpose, and therefore we decided not to perform more accurate volume estimates." + Particle regularity is an important aspect of the scheme., Particle regularity is an important aspect of the scheme. + Lf particles are randomly. sampled within a domain. there is non-zero probability that. particles smoothing length. P. will diller significantly from the average f in its neighbourhood.," If particles are randomly sampled within a domain, there is non-zero probability that particle's smoothing length, $h$, will differ significantly from the average $h$ in its neighbourhood." + Furthermore. the resulting Zr-distribution will not be a smooth function of position. and therefore will not be dilferentiable.," Furthermore, the resulting $h$ -distribution will not be a smooth function of position, and therefore will not be differentiable." + This will break the approximation which lead to10., This will break the approximation which lead to. +. Namely. the variation of within the neighbour sphere will be large enough that the estimate in will result in intolerable errors which. produces unexpected behaviour. such as negative values of density or pressure.," Namely, the variation of $h$ within the neighbour sphere will be large enough that the estimate in will result in intolerable errors which produces unexpected behaviour, such as negative values of density or pressure." + To avoid these situations. the particle distribution must be first regularised.," To avoid these situations, the particle distribution must be first regularised." + Lf the initial particle distribution is regular. it will maintain its regularity during the simulation except in the regions where particle velocity Ποιά. a. is cliscontinuous. e.g. across shock waves (22)..," If the initial particle distribution is regular, it will maintain its regularity during the simulation except in the regions where particle velocity field, ${\bf a}$, is discontinuous, e.g. across shock waves \citep{VILA:1999, 1404789}." + Phe criteria which determines regularity of the particle distribution depends on the approximations of4., The criteria which determines regularity of the particle distribution depends on the approximations of. +. Expanding f(x) to the first order. gives The first term is f;V;. and we can rewrite the integral in the second term in the following form where in the right hand. side we changed: variables from xt0 y=x σα.," Expanding $f(\bfx)$ to the first order, gives The first term is $f_i V_i$, and we can rewrite the integral in the second term in the following form where in the right hand side we changed variables from $\bfx$to $\bfy = \bfx - +\bfx_i$ ." +" Ifwe require that w(x,|yj)dy;9C' isapproximately constant in the neighbourhood of an /-particle. we can diseretise the integral on the right hand side to obtain"," Ifwe require that $w(\bfx_i + \bfy_j) d\bfy_j \approx C_i$ isapproximately constant in the neighbourhood of an $i$ -particle, we can discretise the integral on the right hand side to obtain" +We now plan to introduce the ellipsoidal-collapse model into the approach presented by ? to improve the prediction of the X-ray temperature function for galaxy clusters based on the gravitational potential rather than on the density contrast.,We now plan to introduce the ellipsoidal-collapse model into the approach presented by \citet{Angrick2009} to improve the prediction of the X-ray temperature function for galaxy clusters based on the gravitational potential rather than on the density contrast. + Here we compare our results for the evolution equations of the collapsing ellipsoid with those presented by ? for a flat ACDM and an OCDM model., Here we compare our results for the evolution equations of the collapsing ellipsoid with those presented by \citet{Monaco1997} for a flat $\Lambda$ CDM and an OCDM model. +" Starting from Eq.(6),"," Starting from Eq.," +", we can replace E(a) and E’(a) for a flat ACDM model using since O4=1—Ωμ and the curvature parameter Q,=0.", we can replace $E(a)$ and $E'(a)$ for a flat $\Lambda$ CDM model using since $\Omega_\Lambda=1-\Omega_\mm$ and the curvature parameter $\Omega_\mathrm{k}=0$. + This gives This equation differs from Eq. (, This gives This equation differs from Eq. ( +B11) of ? in the second and third term: a factor a? in the denominator of both terms was omitted.,B11) of \citet{Monaco1997} in the second and third term: a factor $a^2$ in the denominator of both terms was omitted. +" Additionally, the vacuum term οςpa as well as a factor 3 were not included in the nominator of the third term."," Additionally, the vacuum term $\propto \rho_\Lambda$ as well as a factor $3$ were not included in the nominator of the third term." +" For an OCDM model, we have since O4=0 and Q,=(1—Ωμα”2."," For an OCDM model, we have since $\Omega_\Lambda=0$ and $\Omega_\mathrm{k}=(1-\Omega_\mm)a^{-2}$." + Inserting this again into Eq., Inserting this again into Eq. + yields Equation (B12) of ? is again slightly different: The factor 3 in the last term was omitted., yields Equation (B12) of \citet{Monaco1997} is again slightly different: The factor $3$ in the last term was omitted. + There is one last difference concerning the initial conditions: Comparing Eq. (, There is one last difference concerning the initial conditions: Comparing Eq. ( +B17) of ? with Eq.,B17) of \citet{Monaco1997} with Eq. +" of this paper, one can find an additional factor αρ in front of A;(ao) which should be dropped."," of this paper, one can find an additional factor $a_0$ in front of $\lambda_i(a_0)$ which should be dropped." +~4«10°M.. (Reidtherein)...,"$\sim4\times10^6~M_\odot$ \citep[and references + therein]{reid2009}." + ~8 pas. making the apparent size of its event horizon the largest that we know of.," $\sim8~$ as, making the apparent size of its event horizon the largest that we know of." + VLBI at (sub)millimeter wavelengths is ideally suited to observing Ser A* on these angular scales., VLBI at (sub)millimeter wavelengths is ideally suited to observing Sgr A* on these angular scales. +" Previous 1.3 mm VLBI detections of Ser A* on a Hawatt-Arizona baseline established the existence of coherent structures on scales of a few Rs, (Doelemanetal.2008).", Previous 1.3 mm VLBI detections of Sgr A* on a Hawaii-Arizona baseline established the existence of coherent structures on scales of a few $R_\mathrm{Sch}$ \citep{doeleman2008}. +. Current 1.3 mm VLBI observations can be used to address two fundamental questions concerning the nature of Sgr A*., Current 1.3 mm VLBI observations can be used to address two fundamental questions concerning the nature of Sgr A*. +" The first is whether the accretion flow surrounding Ser A* exhibits an expected ""shadow"" feature that occurs due to the strong gravitational lensing near the black hole.", The first is whether the accretion flow surrounding Sgr A* exhibits an expected “shadow” feature that occurs due to the strong gravitational lensing near the black hole. + Emission from the accretion flow ts preferentially lensed onto the last photon orbit. resulting in a relatively dim central region encircled by a brighter annulus (Falckeetal.2000).," Emission from the accretion flow is preferentially lensed onto the last photon orbit, resulting in a relatively dim central region encircled by a brighter annulus \citep{falcke2000}." +. A second question is whether the flaring behavior exhibited by Ser A* has its origins 1n compact structures that arise near the black hole event horizon., A second question is whether the flaring behavior exhibited by Sgr A* has its origins in compact structures that arise near the black hole event horizon. + Broadband flares on timescales ranging from minutes to hours are well-documented (Marroneetal.2008:Yusef-Zadehetal.2009:Dodds-Eden2009) and imply time-variable structures in the innermost accretion region.," Broadband flares on timescales ranging from minutes to hours are well-documented \citep{marrone2008,yusefzadeh2009,doddseden2009} and imply time-variable structures in the innermost accretion region." + If small-scale variable structures are present. 1.3 mm VLBI can sensitively monitor the changing morphology of Ser A* using non-imaging techniques with time resolutions of tens of seconds (Doelemanetal.2009;Fish2009b).," If small-scale variable structures are present, 1.3 mm VLBI can sensitively monitor the changing morphology of Sgr A* using non-imaging techniques with time resolutions of tens of seconds \citep{doeleman2009,fish2009b}." +. We report on new 1.3 mm VLBI observations of Sgr A* using à four-telescope array., We report on new 1.3 mm VLBI observations of Sgr A* using a four-telescope array. + These observations confirm event horizon scale structure within Ser A*. impose new constraints on accretion models for Sgr A*. and reveal dependent variability on scales of a few Rs.," These observations confirm event horizon scale structure within Sgr A*, impose new constraints on accretion models for Sgr A*, and reveal time-dependent variability on scales of a few $R_\mathrm{Sch}$." + Ser A* and several calibrator sources were observed with four telescopes at three observatories: the James Clerk Maxwell Telescope (JCMT: henceforth also J) on Mauna Kea, Sgr A* and several calibrator sources were observed with four telescopes at three observatories: the James Clerk Maxwell Telescope (JCMT; henceforth also J) on Mauna Kea +ower than BAO. the correlation function becomes negative in the line-of-sight direction. creating a better contrast. in he BAO position. easier to detect than in real space.,"lower than BAO, the correlation function becomes negative in the line-of-sight direction, creating a better contrast in the BAO position, easier to detect than in real space." + Also. non-linearities. magnification and bias can boost the peak (sce GCL and Tian et al 2010 for further details).," Also, non-linearities, magnification and bias can boost the peak (see GCH and Tian et al 2010 for further details)." + GCLL presented. (wo wavs to analyze the BAO data: he peak and the shape method., GCH presented two ways to analyze the BAO data: the peak and the shape method. + In the peak method thev ind the location of the peak ancl use it as standard. ruler o measure //(z)., In the peak method they find the location of the peak and use it as standard ruler to measure $H(z)$. + In the shape method they use à x it to the full shape of the correlation and find the best shift in the distance (22/10., In the shape method they use a $\chi^2$ fit to the full shape of the correlation and find the best shift in the distance $H(z)/H_0$. + The shape method was also used to test i£ the data was compatible with the shape of he correlation expected in zoCDM., The shape method was also used to test if the data was compatible with the shape of the correlation expected in $\omega$ CDM. + They compare cilferent classes of models: the stancarcd BAO ωςΝΤ model. a similar class of models without BAO (so called. no-wigele model in Eisenstein Llu 1998) and a model with zero correlation £=0.," They compare different classes of models: the standard BAO $\omega$ CDM model, a similar class of models without BAO (so called no-wiggle model in Eisenstein Hu 1998) and a model with zero correlation $\xi=0$." + The no-BAO model has Ay?=10 with respect to the best fitting ωςΔΙ model while a model with £=0 has Ay?=4., The no-BAO model has $\Delta \chi^2=10$ with respect to the best fitting $\omega$ CDM model while a model with $\xi=0$ has $\Delta \chi^2=4$. + lxazin ct al (2010b) did an independent analysis of the SDSS catalog ancl found similar results for the correlation measurements anc errors., Kazin et al (2010b) did an independent analysis of the SDSS catalog and found similar results for the correlation measurements and errors. + In their interpretation they clic not explore the parameter space of wCDAL but conclude tha there is no convincing evidence for radial BAO because the €—0 model fit the data better than wCDAL., In their interpretation they did not explore the parameter space of $\omega$ CDM but conclude that there is no convincing evidence for radial BAO because the $\xi=0$ model fit the data better than $\omega$ CDM. + They argue tha there are no parameters in the £=0 model wμαrile for «xLLe several parameters where fitted in GCTLI., They argue that there are no parameters in the $\xi=0$ model while for $\omega$ CDM several parameters where fitted in GCH. + After including the penalty for adding parameters. they find that «CDM is no significantly better than £=0.," After including the penalty for adding parameters, they find that $\omega$ CDM is not significantly better than $\xi=0$." + 3ut a similar argument could be extended to the BAO monopole measurements., But a similar argument could be extended to the BAO monopole measurements. + For example. if one fits a constan correlation to the LB correlation function in Fig.17 of Sanchez etal (2009) to scales larger than 70 Mpce/h one finds that this model can not be distinguished. [rom a ωςDA model with free. parameters.," For example, if one fits a constant correlation to the LRG correlation function in Fig.17 of Sanchez etal (2009) to scales larger than 70 Mpc/h one finds that this model can not be distinguished from a $\omega$ CDM model with free parameters." + The original Eisenstein cta (2005) results can also be well fitted. with a power-law niodelt., The original Eisenstein etal (2005) results can also be well fitted with a power-law $^1$. + Docs this mean that the BAO feature has not been detected at all?, Does this mean that the BAO feature has not been detected at all? + These are important points to clarify as it is common practice to include BAO measurements when fitting cosmological mocdels to provide evidence for dark energy models (eg Sanchez et al 2009: Ixomatsu et al 2010: Ixazin et al 2010a: Ciaztanaga. ΠΟΙΟ Sanchez 2009).," These are important points to clarify as it is common practice to include BAO measurements when fitting cosmological models to provide evidence for dark energy models (eg Sanchez et al 2009; Komatsu et al 2010; Kazin et al 2010a; Gaztanaga, Miquel Sanchez 2009)." + Other recent studies seem to reach a similar conclusion. that the BAO feature has not been detected. but using an argument that seems to go in the opposite direction.," Other recent studies seem to reach a similar conclusion, that the BAO feature has not been detected, but using an argument that seems to go in the opposite direction." + Rather than finding that data is too noisy and. compatible with featureless models. they find that the data is not consistent with ωςΟΝΕ (eg see Labini ct al 2009. Labatie ct al 2010).," Rather than finding that data is too noisy and compatible with featureless models, they find that the data is not consistent with $\omega$ CDM (eg see Labini et al 2009, Labatie et al 2010)." + Also see Martinez et al 2009 for a study of peak detection using DRT monopole., Also see Martinez et al 2009 for a study of peak detection using DR7 monopole. + We will investigate this here to find. as in previous analysis (eg GCL. Sanchez et al 2009. Ixazin et al 2010a) that data is in good. agreement with w DAL although we should stress that this statement will depend on the specific test we use.," We will investigate this here to find, as in previous analysis (eg GCH, Sanchez et al 2009, Kazin et al 2010a) that data is in good agreement with $\omega$ CDM although we should stress that this statement will depend on the specific test we use." + We will argue that there are two separate questions mixed up in the above line of argumentation: model selection and parameter fitting., We will argue that there are two separate questions mixed up in the above line of argumentation: model selection and parameter fitting. + We will find that while current data can not be used. to select οςDAL. one can still constrain the parameters of eCDAL if this model is assumed.," We will find that while current data can not be used to select $\omega$ CDM, one can still constrain the parameters of $\omega$ CDM if this model is assumed." + To show this. we will set out to address two main questions: 1) can we use current BAO data to favor wCDAL?," To show this, we will set out to address two main questions: 1) can we use current BAO data to favor $\omega$ CDM?" + In other words: is the volume of current data large enough to pass a null detection test to choose wC DAL over some other model?, In other words: is the volume of current data large enough to pass a null detection test to choose $\omega$ CDM over some other model? + 2) can we constrain the parameters of the ως ΕΝ model. and in particular the BAO position with current cata?," 2) can we constrain the parameters of the $\omega$ CDM model, and in particular the BAO position with current data?" + We will investigate these points with a set of 216 mock ealaxy catalogs extracted from. AICETGSO (see Fosalba οἱ al 2008. Crocce et al 2009). one of the largest volume dark matter simulation run to date.," We will investigate these points with a set of 216 mock galaxy catalogs extracted from MICE7680 (see Fosalba et al 2008, Crocce et al 2009), one of the largest volume dark matter simulation run to date." + Phe mocks are made to match the SDSS LRG DRG sample and should therefore provide a good representation of biased «CDM realizations., The mocks are made to match the SDSS LRG DR6 sample and should therefore provide a good representation of biased $\omega$ CDM realizations. + We will use these mocks to explore the peak and the shape method applied to the monopole., We will use these mocks to explore the peak and the shape method applied to the monopole. + We use the monopole here (rather than racial BAO) for several reasons: shape measurements have larger signal-to-noise. theoretical modeling of monopole is better understood. (sce GCL) and the monopole BAO has been more widely used to test. cosmological mocels.," We use the monopole here (rather than radial BAO) for several reasons: shape measurements have larger signal-to-noise, theoretical modeling of monopole is better understood (see GCH) and the monopole BAO has been more widely used to test cosmological models." + Rather than comparing the ος ΟΝΕ with some adcd-hoc correlation (power-law. Constant or sone combination) we choose to focus on comparing BAO ancl no-BAO mocels.," Rather than comparing the $\omega$ CDM with some add-hoc correlation (power-law, constant or some combination) we choose to focus on comparing BAO and no-BAO models." + This has the advantage of being a well defined procedure (quite standard in the literature) where we have the same number of parameters in each case. which simplifies the interpretation of the statistical significance when comparing two cdillerent. models with different number of parameters (ee see Liddle 2009).," This has the advantage of being a well defined procedure (quite standard in the literature) where we have the same number of parameters in each case, which simplifies the interpretation of the statistical significance when comparing two different models with different number of parameters (eg see Liddle 2009)." +" Throughout we assume a standard cosmological moclel. with O3;= 0.25.04=0.75. O1,=0.044. ης=0.95. ox=O18 and h=fof(100kms‘Alpe‘y=."," Throughout we assume a standard cosmological model, with $\Omega_{\rm M}=0.25$ $\Omega_{\Lambda}=0.75$, $\Omega_{\rm b}=0.044$, $n_s=0.95$, $\sigma_8=0.8$ and $h\equiv H_{0}/(100\,{\rm km\,s}^{-1}{\rm Mpc}^{-1})=0.7$." + Appendix A in Cabré CGaztanaga 2009 (ς(109 from now on) describes how our mocks were built anc also how the correlation. function is estimated? We include both bias ane redshift distortions in the mocks., Appendix A in Cabré Gaztanaga 2009 (CG09 from now on) describes how our mocks were built and also how the correlation function is $^1$ We include both bias and redshift distortions in the mocks. + We will focus here on the monopole correlation for halo z=O0 mocks with a bias bo2. similar to LRG galaxies.," We will focus here on the monopole correlation for halo z=0 mocks with a bias $b\simeq 2$, similar to LRG galaxies." + The correlation function for our 216 mocks. its mean and errors are displaved in Fig.1..," The correlation function for our 216 mocks, its mean and errors are displayed in \ref{fig:correlation}." + Vhese mocks are realistic as they cover similar volume. densities and bias as the real LARC galaxies. but they have some limitations.," These mocks are realistic as they cover similar volume, densities and bias as the real LRG galaxies, but they have some limitations." + In general. one needs first to explore the xwameters in wCDAL (and bias model) to ect a good match o data.," In general, one needs first to explore the parameters in $\omega$ CDM (and bias model) to get a good match to data." +" Our simulations have 3=.f(0,,)/b0.25 and >=0. which are different [rom the values in real data jc0.34d0.03 and z=0.35 (the cdillerence in 3 comes rom the dillerence in redshift. as bias is similar. see CCGO9)."," Our simulations have $\beta\equiv +f(\Omega_m)/b \simeq 0.25$ and $z=0$, which are different from the values in real data $\beta \simeq 0.34 \pm 0.03$ and $z=0.35$ (the difference in $\beta$ comes from the difference in redshift, as bias is similar, see CG09)." + Depending on the test used. this could result in a poor fit of models to data.," Depending on the test used, this could result in a poor fit of models to data." + Despite these limitations. we will find below a good fit of data to the mocks when we allow the amplitude o vary in the fit.," Despite these limitations, we will find below a good fit of data to the mocks when we allow the amplitude to vary in the fit." + This indicates that our mocks provide à eood representation of the data. given. the errors. at. least or the questions we want to address here.," This indicates that our mocks provide a good representation of the data, given the errors, at least for the questions we want to address here." + In our analysis we will pretend that cach mock is a realization of the real LRG data., In our analysis we will pretend that each mock is a realization of the real LRG data. + Our mocks are close enough o the real data to provide a realistic representation of how much variation there is from one realization of real data to he other., Our mocks are close enough to the real data to provide a realistic representation of how much variation there is from one realization of real data to the other. +" Indeed the jack-knife (JIN) errors (ancl covariance matrix) in the real data are similar to the JI, errors in our mocks and to the ensemble variation from mock to mock.", Indeed the jack-knife (JK) errors (and covariance matrix) in the real data are similar to the JK errors in our mocks and to the ensemble variation from mock to mock. + ‘This was shown in €€GO9 and can also be seen in Fig.l where we compare the ensemble variation in mocks (short dashed lines) to the JIx errors in the DRG SDSS LAG measurements, This was shown in CG09 and can also be seen in \ref{fig:correlation} where we compare the ensemble variation in mocks (short dashed lines) to the JK errors in the DR6 SDSS LRG measurements +and emplov a time-dependent. generalized I-correction (Iximetal.1996) that utilizes the spectra of SN 1998bw from Patatetal.(2001) and the photometry of Galamaetal.(1993)..,"and employ a time-dependent, generalized K-correction \citep{Kim+96} + that utilizes the spectra of SN 1998bw from \cite{Patat+01} and the photometry of \cite{Galama+98}. ." + The observed /-band light curve of SN 1998bw atl 2=0.49 is shown as a curve in (he inset of Figure 1., The observed $I$ -band light curve of SN 1998bw at $z=0.49$ is shown as a curve in the inset of Figure 1. + The SN associated with GRD 091127 evolves faster (han SN 1993bw. and reaches a sliehtly cdimmer peak magnitude.," The SN associated with GRB 091127 evolves faster than SN 1998bw, and reaches a slightly dimmer peak magnitude." + This peak magnitude could be brighter if the SN was been reddened by its host galaxy: (he 36 upper Ilimit on reddening is ly)<0.5 mag and. therefore. extinction is unlikely to alter (he peak magnitude by more than a few tenths of a naenitucde.," This peak magnitude could be brighter if the SN has been reddened by its host galaxy; the $3\sigma$ upper limit on reddening is $A_V<0.5$ mag and, therefore, extinction is unlikely to alter the peak magnitude by more than a few tenths of a magnitude." + Given the resemblance between SN 19983bw and the extra component of late-time light in GRB 091127. allernatives to the SN explanation for the source of this light are clifficult to support.," Given the resemblance between SN 1998bw and the extra component of late-time light in GRB 091127, alternatives to the SN explanation for the source of this light are difficult to support." +" While it was initially speculated that some late-time GRD optical alterelow rebrightenings might be attributed (ο ""dust echos” (e.g..Waxman&Draine2000).. later analvsis concluded that these models could not fit the data and SNe were much more natural explanations (Reichart2001)."," While it was initially speculated that some late-time GRB optical afterglow rebrightenings might be attributed to “dust echos” \citep[e.g.,][]{WD00}, later analysis concluded that these models could not fit the data and SNe were much more natural explanations \citep{Reichart01}." +. Furthermore. similar d “bumps” in the OAG light curvesof other GRBs (e.g.. GRD021211. DellaValleetal.2003::SNe. GRB 050525a. 2006a)) have been shown spectroscopically to be GRDB-," Furthermore, similar late-time “bumps” in the OAG light curvesof other GRBs (e.g., GRB 021211, \citealt{DellaValle+03}; GRB 050525a, \citealt{DellaValle+06a}) ) have been shown spectroscopically to be GRB-SNe." + Ilence. we consider our observations to be an extremely strong photometric case for a SN associated with GRD 091127.," Hence, we consider our observations to be an extremely strong photometric case for a SN associated with GRB 091127." + We compare the absolute V-band light curve of SN 2009nz with other GRB-SNe whose SN light eurves can be separated from their OACGs (SN ANM 980425. SN 2003dh/GRD 030329. SNe 2003hw/GRD031203. and SN and 2006aj/GBRD060213: --see Fie.," We compare the absolute $V$ -band light curve of SN 2009nz with other GRB-SNe whose SN light curves can be separated from their OAGs (SN 1998bw/GRB 980425, SN 2003dh/GRB 030329, SN 2003lw/GRB 031203, and SN 2006aj/GRB 060218; see Fig." + 4)., 4). + The GRD-5Ne are bal very similarin terms of rise times peak , The GRB-SNe are globally very similar in terms of rise times and peak magnitudes. +The GRB-SNe cluster fairly Gehtly in peak brightness. (though SN20031w appears to be somewhat brighter than the others.," The GRB-SNe cluster fairly tightly in peak brightness, though SN 2003lw appears to be somewhat brighter than the others." + The exact peak magnitude of SN2003hw. however. depends on a M and uncertain amount of Galactic and host-galaxyv extinction (e.g..Malesanietal.2004).," The exact peak magnitude of SN 2003lw, however, depends on a large and uncertain amount of Galactic and host-galaxy extinction \citep[e.g.,][]{Malesani+04}." +. Depending on the reddening values assumed. SN 2000 may be up (ο 0.5 mag dimmer (han shown in Figure 4. thus making its peak brightness more in line with the other GRB-SNe.," Depending on the reddening values assumed, SN 2003lw may be up to 0.5 mag dimmer than shown in Figure 4, thus making its peak brightness more in line with the other GRB-SNe." + The lieht curve of SN 2003dh is also subject to some uncertainty because of the difficulty of separating ihe SN component of GRD 030329 from its verv bright OAG (Dengetal.2005)., The light curve of SN 2003dh is also subject to some uncertainty because of the difficulty of separating the SN component of GRB 030329 from its very bright OAG \citep{Deng+05}. +. A significant variation among the GRB-SNe is their rise times. with SN 2006aj peaking (he fastest and SN 2003Iw taking the longest time to peak.," A significant variation among the GRB-SNe is their rise times, with SN 2006aj peaking the fastest and SN 2003lw taking the longest time to peak." + There appears tobe a trend towarel brighter GRB-SNe evolving more slowly than fainter GRB-SNe (Bloometal. 2002b).., There appears tobe a trend toward brighter GRB-SNe evolving more slowly than fainter GRB-SNe \citep{Bloom+02b}. . + For, For +calculated radial abundance profiles or the hydrocarbons ΟΠ (1=2.1.0).,"calculated radial abundance profiles for the hydrocarbons $_n$ H $n=2,4,6$ )." + Comparisou with shows the inipact of tlie cleusity-enhancer shells on these species., Comparison with shows the impact of the density-enhanced shells on these species. + A prominent elfect of the shells is o raise of the abundauces rela]ve o the surrouudiug CSE due to the lucreasec eas density., A prominent effect of the shells is to raise of the abundances relative to the surrounding CSE due to the increased gas density. + The photon-iuduced hydrocarbon: €lelnistry ds suppressed. very lear to the star by the dust. shell at a radius of r=1” which provides additional shieding of CoH» [rom photocdissociation., The photon-induced hydrocarbon chemistry is suppressed very near to the star by the dust shell at a radius of $r=1''$ which provides additional shielding of $_2$ $_2$ from photodissociation. + The abundances all reach a peak in thTT she al p=15”., The abundances all reach a peak in the shell at $r=15''$. +" However. this is not wherTT CoH reaches its greatest abundauce. whic1 OCCIs in the thirda deusity-enhanced. shell atr=929""."," However, this is not where $_6$ H reaches its greatest abundance, which occurs in the third density-enhanced shell at $r=29''$." +" As shown in the middle )alie| olLL. HC4N aud HC3N both Teach heir [n]greatest abuudauces in the 15"" shell."," As shown in the middle panel of, $_3$ N and $_5$ N both reach their greatest abundances in the $15''$ shell." + C'osmic-ray-lMnduced. chemistry also results iu he svuhesis of a significant amount of HC4N in the innermost (r=1”) shell (throug the 'eactiol HCN + CRPHOT — CN 4+ H. ollowec by CN + CoH»— HC;N + H).," Cosmic-ray-induced chemistry also results in the synthesis of a significant amount of $_3$ N in the innermost $r=1''$) shell (through the reaction HCN + CRPHOT $\longrightarrow$ CN + H, followed by CN + $_2$ $_2 \longrightarrow$ $_3$ N + H)." +" The anions C4H. . CsyH and ΟΠ (shown iu do not reach their maximum abuncdawes in the 15” shell: C,H peaks at a similar radius to the model with no shells whereas ΟΠ and C.H peak in the 29"" shell"," The anions $_4$ $^-$, $_6$ $^-$ and $_8$ $^-$ (shown in ), do not reach their maximum abundances in the $15''$ shell; $_4$ $^-$ peaks at a similar radius to the model with no shells whereas $_6$ $^-$ and $_8$ $^-$ peak in the $29''$ shell." +" Molecular abuudauces tend to peak within he cleusitv-eunhanced shells because the increased density raises the aounudauces of chemical 'eagents which drives he chemistry at a faster ""ale.", Molecular abundances tend to peak within the density-enhanced shells because the increased density raises the abundances of chemical reagents which drives the chemistry at a faster rate. +" ]t is not always the case. however. tliat his ""alses the abundauces of daughter species. as can be seeu iu where the CoH abtdance is reduced in the r=29"" shell «ue ο the increase densities of atoms and ions (iuclidling C. and N). that it 'eacts with."," It is not always the case, however, that this raises the abundances of daughter species, as can be seen in where the $_2$ H abundance is reduced in the $r=29''$ shell due to the increased densities of atoms and ions (including C, $^+$ and N), that it reacts with." + A comparison of the abuudauce profiles in tie. wwodels with aud without cleusity-enhancer shells shows that. in general. the lucreasec shielding of the CSE from interstellar UV by the dust shells (which inhibitsthe photochemistry). causes photocdissociation of parent species to be less efficient iu the iuner regions aud causes the daughter abuucdauxes to rise more slowly with radius. moving tlie profile nuaxima outwards.," A comparison of the abundance profiles in the models with and without density-enhanced shells shows that, in general, the increased shielding of the CSE from interstellar UV by the dust shells (which inhibitsthe photochemistry), causes photodissociation of parent species to be less efficient in the inner regions and causes the daughter abundances to rise more slowly with radius, moving the profile maxima outwards." +" The calculated emission intensities for CoH. C4H. ΟΠ. CoH and HC4N. (shown in the lower panels of Figures 3.. | aud 2.. respectively). are greatest within lie r=15"" deusity-enhanced shell."," The calculated emission intensities for $_2$ H, $_4$ H, $_6$ H, $_6$ $^-$ and $_3$ N (shown in the lower panels of Figures \ref{fig:CnH}, \ref{fig:cyano} and \ref{fig:anions}, respectively), are greatest within the $r=15''$ density-enhanced shell." +" C;H reaches maximum intensity near i=δη,", $_4$ $^-$ reaches maximum intensity near $r=8''$. + The dillerences between the abundauce profiles and the emission profiles for CoH aud ΟΠ are particularly notable., The differences between the abundance profiles and the emission profiles for $_6$ H and $_6$ $^-$ are particularly notable. + Because the 3 nuu emission [rom these species originates Lrn a high rotational level (around -30). lie strength of the emission is highly. dependeut on the rate of collisional excitation. and therefore the censity.," Because the 3 mm emission from these species originates from a high rotational level (around $J=30$ ), the strength of the emission is highly dependent on the rate of collisional excitation, and therefore the density." + Thus. inside tlie cleusity-enhanced shells the lower J levels teud to become depopulated in favour of the higher levels.," Thus, inside the density-enhanced shells the lower $J$ levels tend to become depopulated in favour of the higher levels." +" For CoH. CH. CoH aud their correspoucdiug anious. two-dimensioual emission maps have ,)een constructed. from the radial. emission ooliles by iueeration along (pencil-beam) ines of sight through the CSE."," For $_2$ H, $_4$ H, $_6$ H and their corresponding anions, two-dimensional emission maps have been constructed from the radial emission profiles by integration along (pencil-beam) lines of sight through the CSE." + This calculalou asstumes spherical symmetry of t1ο CSE and herefore canuot show any of the aziuimlal structure in observed emission maps., This calculation assumes spherical symmetry of the CSE and therefore cannot show any of the azimuthal structure in observed emission maps. + Neverheless. hese maps (shown in 6)). provide a iseful ineaus for comparing the main featJes in the modeled aud observed molecular emisSIOLL.," Nevertheless, these maps (shown in ), provide a useful means for comparing the main features in the modeled and observed molecular emission." +" CoH and ΟΠ show a πιο, lariNW emission ring centered on 15”. in excellent agreement with observed maps of Cuéliuetal. (1999).."," $_2$ H and $_6$ H show a strong, narrow emission ring centered on $15''$, in excellent agreement with observed maps of \citet{gue99}. ." +" In addition to the observed 15"" ring. he modeled CH emission map shows a thic strong ring at around r= 8’."," In addition to the observed $15''$ ring, the modeled $_4$ H emission map shows a thick, strong ring at around $r=8'$ ." +" The patter or ΟΠ | and CoH are similar to their σαοί neutrals whereas CoH παν| different: it has a centrally-peakec emissi1l uap because it is produced. precdomiuantN ""€ the reaction of with C54H» lie", The patterns for $_4$ $^-$ and $_6$ $^-$ are similar to their parent neutrals whereas $_2$ $^-$ is markedly different: it has a centrally-peaked emission map because it is produced predominantly by the reaction of $^-$ with $_2$ $_2$ — the +"lower value for s, compared to the one obtaine« usine T -—sO000 EK. This low value of à»; mdicates a rather low ionization. which could be argued for also by the nou-cdetection of the interstellar line at 1206.5A.","lower value for $n_e$ compared to the one obtained using $T=$ 8000 K. This low value of $n_e$ indicates a rather low ionization, which could be argued for also by the non-detection of the interstellar line at 1206.5." +. The Sirius A photospheric liue appears near 0 bbut no interstellar liue is siguificautlv. detected ou any of our four spectra in that spectral region. toward Sirius A or Sirius D with high aud πουπια spectral resolution.," The Sirius A photospheric line appears near 0 but no interstellar line is significantly detected on any of our four spectra in that spectral region, toward Sirius A or Sirius B with high and medium spectral resolution." + The lower limiting detectable equivalent width at 370 found. obtaine ou Sinus D spectra (sce Fig. 11)).," The lower limiting detectable equivalent width at $3\sigma$ found, obtained on Sirius B spectra (see Fig. \ref{siiii}) )," + is Wainm23mA... fromwhich we derive the upper limit Nur (Sim) <1.5tot Jasstuning fui=1.669 (Morton 19913].," is $W_{lim}\simeq 3$, fromwhich we derive the upper limit $N_{\mathrm{LIC}}$ ) $\le 1.5\times 10^{11}$ $^{-2}$ [assuming $f_{\mathrm{\ion{Si}{iii}}}=1.669$ (Morton \cite{morton}) )]." + We thus obtained: Thus uou-cdetection of the line at 1206.5 lis surprising because this line was detected in the LIC by (ασ et al. (1995)), We thus obtained: This non-detection of the line at 1206.5 is surprising because this line was detected in the LIC by Gry et al. \cite{gry95}) ) + toward e CMa which is located only aswav frou Sirius., toward $\epsilon$ CMa which is located only away from Sirius. + Thew derivect ιο cobluun deusitv Nur (Sill)22.0+£0.21013 which is a value more than 10 times huger than our upper limit!, They derived the column density $N_{\mathrm{LIC}}($ $)=2.0\pm0.2 \times 10^{12}$ which is a value more than 10 times larger than our upper limit! + Tf the line detected by. Cay et al. (1995)), If the line detected by Gry et al. \cite{gry95}) ) + is actually caused by the LIC aud uot by another more distant cloud whose racdia velocity is bv coiucideuce confused with the LIC one. this may imean that the lonization in the LIC varies over very short distances.," is actually caused by the LIC and not by another more distant cloud whose radial velocity is by coincidence confused with the LIC one, this may mean that the ionization in the LIC varies over very short distances." + This non-detection may confirm the won-detection of in the LIC already reported toward 6191-D2D by VidalAladjar et al. (19983)., This non-detection may confirm the non-detection of in the LIC already reported toward G191-B2B by Vidal-Madjar et al. \cite{avm98}) ). + Moreover. Holbereg et al. (19993) ," Moreover, Holberg et al. \cite{holberg99}) )" +claiued that it is quite doubtful that the ISM absorption line that they detected toward REJ 1032-532 is produced in the LIC., claimed that it is quite doubtful that the ISM absorption line that they detected toward REJ 1032-532 is produced in the LIC. + Thus it secius to favour the idea that another cloud iu the lone line of sight toward e CMa is by coincidence at a radial velocity similar to the LIC one., Thus it seems to favour the idea that another cloud in the long line of sight toward $\epsilon$ CMa is by coincidence at a radial velocity similar to the LIC one. + Note that Cav et al. (1995)), Note that Gry et al. \cite{gry95}) ) +" do not detected in their “component- 2. in agreement with our nou-detection of that ion iu. ""DC toward Sirius. which is identified as the same componcut."," do not detected in their “component 2”, in agreement with our non-detection of that ion in “BC” toward Sirius, which is identified as the same component." +" Tn addition. Dupin Gav (1998)) detected a saturated line at 1206.5 Hu their componeut ""D toward > CMS which is located at less than ffrom Sirius."," In addition, Dupin Gry \cite{dupin98}) ) detected a saturated line at 1206.5 in their component “D” toward $\beta$ CMa, which is located at less than from Sirius." +" They derived the colui deusity |(S111) (L5.10)«Lot 2.72,", They derived the column density $N($ $)=(1.5 - 10) \times 10^{14}$ 2. +" Sincee the velocity. of. that component does iof correspond to the LIC. this huge cohunu density could be iuterpreted as a sign that the component ""D'. detected by Dupin Cav (1998)) toward ij CMa is xobablv located bevoud Simus aud may explain some absorption iu the e CMa line of sight. for istance at the LIC velocity."," Since the velocity of that component does not correspond to the LIC, this huge column density could be interpreted as a sign that the component “D”, detected by Dupin Gry \cite{dupin98}) ) toward $\beta$ CMa, is probably located beyond Sirius and may explain some absorption in the $\epsilon$ CMa line of sight, for instance at the LIC velocity." + Our cevaluation ismade assuming the three following mainhypotheses:, Our evaluation ismade assuming the three following mainhypotheses: +Our best-fit period for the combined datasets. 5.5908. + 0.0001. cd is identical to well within the standard: errors with the GB period. of 5.59974 + 0.00008 d. and our Tu. or epoch of inferior conjunction. agrees with the prediction of the GB ephemeris to within 0.014. phase. or 0.078 cl. Since the uncertainty in the periods vields an uncertainty in the GB prediction of To of + 0.12 days at this epoch. this is excellent. agreement.,"Our best-fit period for the combined datasets, 5.5998 $\pm$ 0.0001 d is identical to well within the standard errors with the GB period of 5.59974 $\pm$ 0.00008 d, and our $_0$, or epoch of inferior conjunction, agrees with the prediction of the GB ephemeris to within 0.014 phase, or 0.078 d. Since the uncertainty in the periods yields an uncertainty in the GB prediction of $_0$ of $\pm$ 0.12 days at this epoch, this is excellent agreement." + Thus our results confirm the ephemeris of CD and refute suggestions of period variation by NWY., Thus our results confirm the ephemeris of GB and refute suggestions of period variation by NWY. + Why. then. did NWY's result show such a discrepancy and suggest a change in period?," Why, then, did NWY's result show such a discrepancy and suggest a change in period?" + They. reported. that. the period. determined. from their data. alone was 5.60172 + 0.00003 d. differing hy 20 σ from the period. determined from all previous observations.," They reported that the period determined from their data alone was 5.60172 $\pm$ 0.00003 d, differing by 20 $\sigma$ from the period determined from all previous observations." + We suggest. several sources for this error., We suggest several sources for this error. + Fist of all. we performed. our own. period. searches on the data published. by NWY: the best fit we find is at 5.6002 d. or only 2 & greater than the GB value. so we may be looking at much ado about a tvpographical error.," First of all, we performed our own period searches on the data published by NWY; the best fit we find is at 5.6002 d, or only 2 $\sigma$ greater than the GB value, so we may be looking at much ado about a typographical error." + In addition. there is excellent phase agreement between the NWY data and the CB ephemeris. again suggesting no real period. discrepancy.," In addition, there is excellent phase agreement between the NWY data and the GB ephemeris, again suggesting no real period discrepancy." + Finally. it seems that the error estimates for both the NWY period and their period determined from. historical data are too small by as much as an order of magnituce.," Finally, it seems that the error estimates for both the NWY period and their period determined from historical data are too small by as much as an order of magnitude." + This is primarily because the formal error calculations used. to determine these error estimates are based on the assumption of a very good. fit. of the model to the data. Le. that AZ. 1.," This is primarily because the formal error calculations used to determine these error estimates are based on the assumption of a very good fit of the model to the data, i.e. that $\chi^2_\nu\sim$ 1." + This condition is met by any of the data sets and. fits used. in this work. presumably because the estimates of the uncertainties in the velocities were too small. although perhaps because. of variability in the source.," This condition is met by any of the data sets and fits used in this work, presumably because the estimates of the uncertainties in the velocities were too small, although perhaps because of variability in the source." + We recaleulated. the fits. trying larger estimates for the velocity uncertainties until the reduced chi-square criterion was satisfied.," We recalculated the fits, trying larger estimates for the velocity uncertainties until the reduced chi-square criterion was satisfied." + We found that the period uncertainties then were about an order of magnitude larger than reported. bv the original authors., We found that the period uncertainties then were about an order of magnitude larger than reported by the original authors. + For example. treating NWY's data in this wav vields a best-fit period of 5.6002 + 0.0003 d. and the cliserepaney with GB disappears.," For example, treating NWY's data in this way yields a best-fit period of 5.6002 $\pm$ 0.0003 d, and the discrepancy with GB disappears." + An additional source of unelerestimatec error uneertainty is the inclusion. by both NAWY ane Bolton (1975) of two velocities obtained. by Seyfert ancl Popper (1941). ostensibly to improve the precision of the period determinations.," An additional source of underestimated error uncertainty is the inclusion by both NWY and Bolton (1975) of two velocities obtained by Seyfert and Popper (1941), ostensibly to improve the precision of the period determinations." + For example. Bolton (1975). uses. these points to decrease his uncertainty estimate by a factor of 10: NWY do not discuss the effect of including these points on their uncertainty.," For example, Bolton (1975) uses these points to decrease his uncertainty estimate by a factor of 10; NWY do not discuss the effect of including these points on their uncertainty." + Popper (1996. personal communication) suggests that these velocities are “very weak reeds on which to hang significant conclusions’. the velocities having considerable uncertainties and being based. on averaging velocities from lines of several dillerent species.," Popper (1996, personal communication) suggests that these velocities are “very weak reeds on which to hang significant conclusions”, the velocities having considerable uncertainties and being based on averaging velocities from lines of several different species." +" Because of he problems with hvdrogen-line velocities discussed above. inclusion of these points is therefore unlikely to improve the »eriod. GB also introduced. “velocity corrections"" to many of heir velocities. shifting spectra to fit a mean interstellar Ix-line. velocity. due to instabilities in. their spectrograph."," Because of the problems with hydrogen-line velocities discussed above, inclusion of these points is therefore unlikely to improve the period GB also introduced “velocity corrections” to many of their velocities, shifting spectra to fit a mean interstellar K-line velocity due to instabilities in their spectrograph." + lt is not unlikely that this introduced. uncertainties larger han the mean errors they We have carried out a programme of radial velocity determinations for the black hole binary (νο αγ]. and jwe combined these data with data used. previously to determine the period. to provide a new orbital ephemeris for he source.," It is not unlikely that this introduced uncertainties larger than the mean errors they We have carried out a programme of radial velocity determinations for the black hole binary Cyg X-1, and have combined these data with data used previously to determine the period, to provide a new orbital ephemeris for the source." + A critical consideration of the errors associated with previous work has shown these to be uncderestimated., A critical consideration of the errors associated with previous work has shown these to be underestimated. + Based on this. our main conclusion is that there is no evidence for a change in orbital period. as suggested: by dinkov et al.," Based on this, our main conclusion is that there is no evidence for a change in orbital period as suggested by Ninkov et al." + Finally. our new ephemeris allows the orbital hase calculation for €vg X-1 with an error that is much reduced. compared. with the error that. would be attached o extrapolating the Cies and Bolton ephemeris with its quoted accuracy to the present. We are very grateful to the La Palma support astronomers. and particularly Don Pollacco. who operate the Service Programme. and to those astronomers who allowed the (νο X-l1 observations to be taken during their own time.," Finally, our new ephemeris allows the orbital phase calculation for Cyg X-1 with an error that is much reduced compared with the error that would be attached to extrapolating the Gies and Bolton ephemeris with its quoted accuracy to the present We are very grateful to the La Palma support astronomers, and particularly Don Pollacco, who operate the Service Programme, and to those astronomers who allowed the Cyg X-1 observations to be taken during their own time." + The Isaac Newton Group of telescopes is operated on the island of La Palma by the Roval Greenwich: Observatory in the Spanish Observatorio del Itoque de Los Muchachos of the Instituto ce issica de Canarias., The Isaac Newton Group of telescopes is operated on the island of La Palma by the Royal Greenwich Observatory in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de sica de Canarias. + JLS wishes gratefully. to acknowledge the following sources of partial support for his participation in this work: the Margaret Cullinan Wray Charitable Lead Annuity Trust (through the AAS Small Grants Program): the NASA JOVIS program: a Theodore Dunham. Jr.. Grant of the Fund for Astrophysical Itesearch: the International Astronomical Union. Exchange of Astronomers Program: and the Department of Astrophysies of the University of Oxford.," JLS wishes gratefully to acknowledge the following sources of partial support for his participation in this work: the Margaret Cullinan Wray Charitable Lead Annuity Trust (through the AAS Small Grants Program); the NASA JOVE program; a Theodore Dunham, Jr., Grant of the Fund for Astrophysical Research; the International Astronomical Union Exchange of Astronomers Program; and the Department of Astrophysics of the University of Oxford." +nucleus is generated. then star-star relaxation in (he central regions may also become a significant. cause of dvnamical evolution.,"nucleus is generated, then star-star relaxation in the central regions may also become a significant cause of dynamical evolution." + All of the above are specific mechanisms that are expected to make elliptical galaxies evolve in spite of their very long (vpical star-star relaxation time., All of the above are specific mechanisms that are expected to make elliptical galaxies evolve in spite of their very long typical star-star relaxation time. + Most of these processes are hard to model and to ealeulate in detail., Most of these processes are hard to model and to calculate in detail. + As for the evolution of other complex many-hocly svslenms. it is hoped Chat thermodyvnamieal arguments may help us identify general trends characterizing such evolution.," As for the evolution of other complex many-body systems, it is hoped that thermodynamical arguments may help us identify general trends characterizing such evolution." + This is the basic physical scenario in which the caleulations presented in (his paper are expected to be of interest for real elliptical galaxies., This is the basic physical scenario in which the calculations presented in this paper are expected to be of interest for real elliptical galaxies. +" Let us consider the standard Boltzmann entropy S=—f1nfdved*e and look for functions that extremize its value under the constraint that the total energy Ej,=(1/3)f.Efedi. the total mass A=ffeed?v. and the additional quantity are taken to be constant."," Let us consider the standard Boltzmann entropy $S = - \int f \ln{f} d^3x d^3v$ and look for functions that extremize its value under the constraint that the total energy $E_{tot} = (1/3)\int E f d^3x d^3v$, the total mass $M = \int f d^3x d^3v$, and the additional quantity are taken to be constant." +" Here the functions E and J? represent specilic energy and specific angular momentum square of a single star subject to a spherically svaunetric meanpotential (rr),", Here the functions $E$ and $J^2$ represent specific energy and specific angular momentum square of a single star subject to a spherically symmetric meanpotential $\Phi(r)$. +" As shown elsewhere (Stiavelliand.Bertin1937).. this extremization process leads to the following family of distribution functions where «. ο, and d are positive real constants."," As shown elsewhere \citep{sti87}, this extremization process leads to the following family of distribution functions where $a$, $A$, and $d$ are positive real constants." +" One may think of these constants as providing two dimensional scales (for example. Af and (Q) and one dimensionless parameter: (he dimensionless parameter can be taken to be >.=ad?""/(4aGyef/A)."," One may think of these constants as providing two dimensional scales (for example, $M$ and $Q$ ) and one dimensionless parameter; the dimensionless parameter can be taken to be $\gamma = ad^{2/\nu}/(4 +\pi GA)$." + In principle. v is any positive real number: in practice. we will locus on values of vzz 1.," In principle, $\nu$ is any positive real number; in practice, we will focus on values of $\nu \approx 1$ ." +" The f"" non-truncated models are constructed by taking this form of the distribution function flor σ0. a vanishing distribution function lor £>0. and by integrating (he relevant Poisson equation under the condition that the potential ? be regular at the origin andbehaves like —C/M/r at large radii."," The $f^{(\nu)}$ non-truncated models are constructed by taking this form of the distribution function for $E \leq 0$, a vanishing distribution function for $E>0$, and by integrating the relevant Poisson equation under the condition that the potential $\Phi$ be regular at the origin andbehaves like $- G M/r$ at large radii." + This integration leads to an eigenvalue problem (see Appendix) for which a value of 5 is determined bv the choice of the centraldimensionless potential. ;= 7(W). with Y=—adb(r= 0).," This integration leads to an eigenvalue problem (see Appendix) for which a value of $\gamma$ is determined by the choice of the centraldimensionless potential, $\gamma = \gamma (\Psi)$ , with $\Psi = - a \Phi (r=0)$ ." +"the scaling for the density. poxd.7°. we estimate the optical depth in the boundary laver as stre, 1/3),sar e1. where ag,=0/01 and similarly for other parameters.","the scaling for the density, $\rho\propto d^{-2/5}$, we estimate the optical depth in the boundary layer as s^2 <1, where $\alpha_{0.1}=\alpha/0.1$ and similarly for other parameters." + Hence. eas is optically thin to electron scattering for reasonable accretion parameters.," Hence, gas is optically thin to electron scattering for reasonable accretion parameters." +" TheCompton y-parameter. L6(e,,/0) n. caleulated for the boundary laver should match that of the hot settling Low at the transitiondistance."," TheCompton $y$ -parameter, $y=16(c_{se}/c)^4\tau_{\rm es}$ , calculated for the boundary layer should match that of the hot settling flow at the transitiondistance." +" Using the result of Medvedev&Naravan(2001) and that οἳxd, we estimate fd) /di."," Using the result of \citet{MN01} and that $c_{se}^2\propto d^{1/5}$, we estimate ) )." +)(56) The effect of Comptonization is important in the high-temperature region of the boundary laver where yZ1. which occurs at distances larger or comparable toI," The effect of Comptonization is important in the high-temperature region of the boundary layer where $y\ga1$, which occurs at distances larger or comparable to." +so Therefore. we conclude that Comptonization is not important deep inside the boundary laver. d«d. ancl our one-temperature sell-similar solution is accurate there.," Therefore, we conclude that Comptonization is not important deep inside the boundary layer, $d 0$ because the changing size of the beam does encompass a varying amount of the starburst ring with frequency (i.e. we expect a frequency dependence for the relative fraction of coupling to the ring). + Finally. we note that the core/jet cimission makes ouly a small contribution to the overall continuum. but it docs affect he shape of the continuam aud especially improves our fit at the higher cud of our baud: without it. we would ikcly overestimate the CS flux bv overθ," Finally, we note that the core/jet emission makes only a small contribution to the overall continuum, but it does affect the shape of the continuum and especially improves our fit at the higher end of our band; without it, we would likely overestimate the CS flux by over." +"ά, In stummary. this model adequately fits our continuun spectruni with reasonable physical »uwanmeters."," In summary, this model adequately fits our continuum spectrum with reasonable physical parameters." + The resulting nicasureieuts are eiven in Table 1.., The resulting measurements are given in Table \ref{table:fit}. + This fit had a reduced 4? of 5.1 with 110 deerees of freedom., This fit had a reduced $\chi^2$ of 5.1 with 140 degrees of freedom. + As can be secu in the bottom panel of Figure LL. a large percentage of the total 47 comes from the CO line. which is not well fit by a sinele-component Caussian.," As can be seen in the bottom panel of Figure \ref{fig:spectrum}, a large percentage of the total $\chi^2$ comes from the CO line, which is not well fit by a single-component Gaussian." + We do not iive the resolution to be able to better model this line. whether its assvinetry is due to kinematic structure or lending of other lines.," We do not have the resolution to be able to better model this line, whether its assymetry is due to kinematic structure or blending of other lines." + If we exclude the bius coutainiug he CO line. the total \? is « 3.," If we exclude the bins containing the CO line, the total $\chi^2$ is $<$ 3." + Hosvever. we do not use CO in our radiative transfer analysis. so its poor fit is rot problematic for the rest of our results.," However, we do not use CO in our radiative transfer analysis, so its poor fit is not problematic for the rest of our results." + Our fit includes one unidentified spectral feature at a rest frequency of approximately 290 GIIz., Our fit includes one unidentified spectral feature at a rest frequency of approximately 290 GHz. +" This requency nay correspond to CIT4CCTII oor IbCO J=ly,>394. but we cannot identify other features of these molecules that might be in our ud."," This frequency may correspond to $_3$ CCH or $_2$ CO $\rm J\eqq4_{04}\too3_{03}$, but we cannot identify other features of these molecules that might be in our band." + Likely. this feature is a combination of eiuissiou eatures that we cannot resolve. and is therefore left as unidentified.," Likely, this feature is a combination of emission features that we cannot resolve, and is therefore left as unidentified." +" Though other features may be present at he upper eud of the spectrum. the channelto-chamucl variation mnereases siguificantly above the CS transition due to imperfect atmospheric subtraction. so we do uot attempt to define spectral features above this yequeney,"," Though other features may be present at the upper end of the spectrum, the channel-to-channel variation increases significantly above the CS transition due to imperfect atmospheric subtraction, so we do not attempt to define spectral features above this frequency." + SIO ccould possibly be identified iu this range. but because we cannot ideutify the two lower-J transitions im our αμα. we do not fit this feature either.," SiO could possibly be identified in this range, but because we cannot identify the two lower-J transitions in our band, we do not fit this feature either." + Below this requency range. there are a few other features of note hat are not fitted.," Below this frequency range, there are a few other features of note that are not fitted." + The first is a possible 3-sigia οσο at approximately 281 (11: given our inability o know the exact line center aud no particularly strong rausition expected that at waveleneth (though there are a few transitions of mcthanol. ΟΠ. around that requency). we do not fit this Lue.," The first is a possible 3-sigma feature at approximately 284 GHz; given our inability to know the exact line center and no particularly strong transition expected that at wavelength (though there are a few transitions of methanol, $_3$ OH, around that frequency), we do not fit this line." + Though the same difficulties apply to the unidentified line at 290 Πε. its sienificance was twice that of this line. and warranted inclusion in the ft.," Though the same difficulties apply to the unidentified line at 290 GHz, its significance was twice that of this line, and warranted inclusion in the fit." + The apparent features at 200 and 260 GIIz are not lines. but part of the continua model. having been passed through our measured line profiles which included the iustruimnental sidelobes of the CÓ ttrausition.," The apparent features at 200 and 260 GHz are not lines, but part of the continuum model, having been passed through our measured line profiles which included the instrumental sidelobes of the CO transition." + Future use of Z-Spec will include modification of the line profiles to exclude these artifacts., Future use of Z-Spec will include modification of the line profiles to exclude these artifacts. +packages are traced in random directions from random points of absorption within a cell and Eq.,packages are traced in random directions from random points of absorption within a cell and Eq. + 1 is integrated along the paths., \ref{radtran} is integrated along the paths. +" Summing over all photons, the mean radiation field J, is obtained for the cell."," Summing over all photons, the mean radiation field $J_\nu$ is obtained for the cell." +" In our implementation, the source model is not mapped onto a regular grid of cells."," In our implementation, the source model is not mapped onto a regular grid of cells." +" Instead we use a random set of points which represents the local environment (density, temperature, populations, etc.)."," Instead we use a random set of points which represents the local environment (density, temperature, populations, etc.)." +" The points are distributed in three-dimensional space, and thus we are able to use three-dimensional source models whereas in, for instanceRATRAN,, even though photons propagate in three-dimensional space, the source model needs to be rotational symmetric around the second axis and mirror symmetric around the first axis."," The points are distributed in three-dimensional space, and thus we are able to use three-dimensional source models whereas in, for instance, even though photons propagate in three-dimensional space, the source model needs to be rotational symmetric around the second axis and mirror symmetric around the first axis." +" Our points are placed randomly throughout the entire computational domain, however with a probability that is weighted by a source model dependent function."," Our points are placed randomly throughout the entire computational domain, however with a probability that is weighted by a source model dependent function." + This approach is similar to the one described by ?.., This approach is similar to the one described by \citet{ritzerveld2006}. +" We choose to use the molecular density profile of the source model as a probability distribution for the grid points, so that we end up with a point distribution that has particularly interesting properties from a radiation transfer point of view, namely, that the average distance from a point to its neighbors becomes inversely proportional to the density and proportional to the local mean free path, since the mean free path |=(vp)!."," We choose to use the molecular density profile of the source model as a probability distribution for the grid points, so that we end up with a point distribution that has particularly interesting properties from a radiation transfer point of view, namely, that the average distance from a point to its neighbors becomes inversely proportional to the density and proportional to the local mean free path, since the mean free path $l = (\alpha _\nu \rho)^{-1}$." +" If we at first consider continuum radiation transfer only, where the absorption coefficient is independent of the radiation field, a, is constant and the mean free path depends on density alone."," If we at first consider continuum radiation transfer only, where the absorption coefficient is independent of the radiation field, $\alpha _\nu$ is constant and the mean free path depends on density alone." + We can thus obtain a grid point distribution where the expectation value of the neighbor point separation equals the local mean free path by adjusting the number of grid points in accordance to the dust opacity κ»., We can thus obtain a grid point distribution where the expectation value of the neighbor point separation equals the local mean free path by adjusting the number of grid points in accordance to the dust opacity $\kappa _\nu$. + Figure 1 shows that the average neighbor distance is proportional to the density over two orders of magnitude., Figure \ref{mfp} shows that the average neighbor distance is proportional to the density over two orders of magnitude. + The arbitrary offset between the mean free path graph and the point separation graph scales with the total number of grid points., The arbitrary offset between the mean free path graph and the point separation graph scales with the total number of grid points. + The point separations are seen to deviate from proportionality at radii smaller than 10? m (=7 AU)., The point separations are seen to deviate from proportionality at radii smaller than $10^{12}$ m $\approx 7$ AU). + This is because we impose the constraint that a certain number of points should be present a the largest scales and thus it would take an unfeasible number of points to follow proportionality with the mean free path down to 0.1 AU., This is because we impose the constraint that a certain number of points should be present a the largest scales and thus it would take an unfeasible number of points to follow proportionality with the mean free path down to 0.1 AU. + The point distribution in Fig., The point distribution in Fig. + 1 consists of 40000 points., \ref{mfp} consists of 40000 points. +" offers several different options for sampling the density, depending on the geometry of the input model, such as uniform sampling in a rectangular box or logarithmic radial sampling in a sphere."," offers several different options for sampling the density, depending on the geometry of the input model, such as uniform sampling in a rectangular box or logarithmic radial sampling in a sphere." +" It is also possible to use a fixed set of points, for instance the cell centers of a tabulated input model or the particles of an SPH simulation."," It is also possible to use a fixed set of points, for instance the cell centers of a tabulated input model or the particles of an SPH simulation." +" In this case, the resulting point distribution may not, of course, scale with the mean free path."," In this case, the resulting point distribution may not, of course, scale with the mean free path." + In other cases it may not be desirable to grid according to the molecular density., In other cases it may not be desirable to grid according to the molecular density. +" If, for instance, the user is interested only in the very high J-lines of a molecule, it can be useful to grid according to the temperature distribution, or if the model involves shocks or outflows, the velocity gradients."," If, for instance, the user is interested only in the very high $J$ -lines of a molecule, it can be useful to grid according to the temperature distribution, or if the model involves shocks or outflows, the velocity gradients." +" In that case however, the grid does not describe the opacity well, but rather ensures that certain spatial region are well sampled."," In that case however, the grid does not describe the opacity well, but rather ensures that certain spatial region are well sampled." +" It is possible to logically OR point distributions, so that a grid may be based on both the temperature and the density, in which case the opacity is also sampled."," It is possible to logically OR point distributions, so that a grid may be based on both the temperature and the density, in which case the opacity is also sampled." +" In fact, point distributions for each individual opacity source (e.g., gas and dust) should always be OR’ed to form a single grid."," In fact, point distributions for each individual opacity source (e.g., gas and dust) should always be OR'ed to form a single grid." +" If we now consider line radiation transfer, the local absorption coefficient αν depends on the current level population through Eq. 3.."," If we now consider line radiation transfer, the local absorption coefficient $\alpha_\nu$ depends on the current level population through Eq. \ref{alpha_gas}." +" The local mean free path thus changes with the radiation field and no longer scales simply with the density, but rather with the population dependent opacity."," The local mean free path thus changes with the radiation field and no longer scales simply with the density, but rather with the population dependent opacity." +" Furthermore, the opacity varies across the line, so photons at different frequencies will have a different mean free path, and therefore the local photon mean free path is not a well defined property."," Furthermore, the opacity varies across the line, so photons at different frequencies will have a different mean free path, and therefore the local photon mean free path is not a well defined property." +" Despite of this, gridding according to density turns out to be the best way to form the grid for line radiation transfer too, simply because it results in a grid that describes the spatial distribution of the molecules very well."," Despite of this, gridding according to density turns out to be the best way to form the grid for line radiation transfer too, simply because it results in a grid that describes the spatial distribution of the molecules very well." +" When the point distribution has been obtained, the points are connected by Delaunay triangulation, using the public available library (?).."," When the point distribution has been obtained, the points are connected by Delaunay triangulation, using the public available library \citep{barber1996}." +" In 2D, the Delaunay triangulation is constructed by connecting any three points that defines an empty circumcircle, meaning that no other points can lie inside the circle defined by a Delaunay triangle."," In 2D, the Delaunay triangulation is constructed by connecting any three points that defines an empty circumcircle, meaning that no other points can lie inside the circle defined by a Delaunay triangle." + The definition is valid for all higher dimensions and in 3D the Delaunay triangulation forms tetrahedra out of four vertices., The definition is valid for all higher dimensions and in 3D the Delaunay triangulation forms tetrahedra out of four vertices. + Figure shows a random point distribution (in 2D) in the left panel with its Delaunay triangulation shown in the center panel., Figure \ref{random} shows a random point distribution (in 2D) in the left panel with its Delaunay triangulation shown in the center panel. +" Also shown, to the right, in Fig."," Also shown, to the right, in Fig." + 2 is the corresponding Voronoi diagram., \ref{random} is the corresponding Voronoi diagram. + The Voronoi diagram is the topological dual of the Delaunay triangulation and one can be constructed from the other., The Voronoi diagram is the topological dual of the Delaunay triangulation and one can be constructed from the other. +" For a discrete set of generating points P, a Voronoi cell is defined as the region surrounding the site s€P which contain points that lie closer to s than to any other generating sites in P."," For a discrete set of generating points $P$ , a Voronoi cell is defined as the region surrounding the site $s \in P$ which contain points that lie closer to $s$ than to any other generating sites in $P$." +" The physical properties of the grid points (density, temperature, excitation, etc.)"," The physical properties of the grid points (density, temperature, excitation, etc.)" + thus represent the entire Voronoi cell associated with that point and therefore the Voronoicell can be considered similar to the cells in traditional codes., thus represent the entire Voronoi cell associated with that point and therefore the Voronoicell can be considered similar to the cells in traditional codes. +(2010).,. +. We show that there has been significant evolution between (he two epochs in L'. the characteristic emission-line luminosity of the Schechter(1976). function. o. the integrated number densitv of bright LAEs. and iei. the e-folding scale length of the rest-frame equivalent width distribution.," We show that there has been significant evolution between the two epochs in $L^*$, the characteristic emission-line luminosity of the \citet{schechter} function, $\phi$, the integrated number density of bright LAEs, and $w_0$, the e-folding scale length of the rest-frame equivalent width distribution." + In 85. we examine the Λος) star-lormation rates. using both (heir rest-Irame UV emission aud Lya. and in 86. we compare (he star-lormation rate density οἱ the LAE population with that of the universe as a whole.," In 5, we examine the LAEs' star-formation rates, using both their rest-frame UV emission and $\alpha$, and in 6, we compare the star-formation rate density of the LAE population with that of the universe as a whole." + We conclude by stummarizing our results and arguing that LAEs represent the extreme low-metallicitv. low-extinetion. [aint-end tail of the high-redshift star-forming galaxy. population.," We conclude by summarizing our results and arguing that LAEs represent the extreme low-metallicity, low-extinction, faint-end tail of the high-redshift star-forming galaxy population." + For this paper. we assume a ACDAM cosmology. with O4=0.7. Q4;=0.3 and km ' f.," For this paper, we assume a $\Lambda$ CDM cosmology, with $\Omega_{\Lambda} = 0.7$, $\Omega_M = 0.3$ and $H_0 = 70$ km $^{-1}$ $^{-1}$." + The luminosity function ancl equivalent width distribution of :=3.1 LAEs is fairl: well-known from the narrow-band surveys of Gronwalletal.(2007.hereafterGrOT)| and Ouchiοἱal.(2008)., The luminosity function and equivalent width distribution of $z=3.1$ LAEs is fairly well-known from the narrow-band surveys of \citet[][hereafter Gr07]{g+07} and \citet{ouchi+08}. +. However these observations. which have identified more than 200 LAE candidates with little contamination from [oreground objects. suffer from larger than normal photometric uncertainties due to (he Gaussian-like transmission profiles of their narrow-bancl filters.," However these observations, which have identified more than 200 LAE candidates with little contamination from foreground objects, suffer from larger than normal photometric uncertainties due to the Gaussian-like transmission profiles of their narrow-band filters." + To confirm these results. and to increase the survey sample al 2e3.1. we extended the GrOT study by re-imaging the ECDF-S. this time with a 57 [full-widtbh-hall-maximum (FWIIM) nearly top-hat filler centered near 5010null.," To confirm these results, and to increase the survey sample at $z \sim 3.1$, we extended the Gr07 study by re-imaging the ECDF-S, this time with a 57 full-width-half-maximum (FWHM) nearly top-hat filter centered near 5010." + As with GrO7. the data were collected with the MOSAIC II CCD camera on the CTIO Blanco 4-m telescope. and consisted of a set of 47 images taken in 171 seeing for a total narrow-band exposure time of 15.67 hr.," As with Gr07, the data were collected with the MOSAIC II CCD camera on the CTIO Blanco 4-m telescope, and consisted of a set of 47 images taken in $1\farcs 1$ seeing for a total narrow-band exposure time of 15.67 hr." + A log of the observations is given in Table 1: a ligure showing our fillers transmission curve. compared to (that used by Gi07. appears in Figure 1..," A log of the observations is given in Table \ref{obslog}; a figure showing our filter's transmission curve, compared to that used by Gr07, appears in Figure \ref{o3_filters}." + The procedures used to reduce the data. identify line emitters. and measure LAE brightnesses were identical to those used by (ος ancl discussed in detail by (2003)..," The procedures used to reduce the data, identify line emitters, and measure LAE brightnesses were identical to those used by Gr07 and discussed in detail by \citet{ipn2}." + After de-biasing. flat-lielding. ancl aligning the data. we co-added our frames to create a master image (hat was clipped of cosmic ravs.," After de-biasing, flat-fielding, and aligning the data, we co-added our narrow-band frames to create a master image that was clipped of cosmic rays." + This frame was then compared to a deep DV continuum image provided by (he MUSYC collaboration 2006b).. and the routines of DAOPILOT were used to create a color-magnitude diagram ol all sources [ound on the narrow-band image.," This frame was then compared to a deep $B$ $V$ continuum image provided by the MUSYC collaboration \citep{musyc}, and the routines of DAOPHOT were used to create a color-magnitude diagram of all sources found on the narrow-band image." + Objects with narrow-band minus continuum colors less than 0.93 mag in the AB svstem were flagged as possible emission-line sources (see Figure 2))., Objects with narrow-band minus continuum colors less than 0.93 mag in the AB system were flagged as possible emission-line sources (see Figure \ref{cmd}) ). + Then. to detect those LAEs whose photometry was compronmised by object blending. skv gradients. and/or source confusion. we re-ran our detection algorithm on a," Then, to detect those LAEs whose photometry was compromised by object blending, sky gradients, and/or source confusion, we re-ran our detection algorithm on a" +The pressure external to the shell is exerted. by. the surrounding hot background (i.e. Por = Py in Ίσα. 7)),The pressure external to the shell is exerted by the surrounding hot background (i.e. $_{ext}$ = $_h$ in Eq. \ref{eq:Newton2_HPB}) ) + and is therefore assumed to be constant in time., and is therefore assumed to be constant in time. + This pressure will stronely decelerate the shell as. illustrated below., This pressure will strongly decelerate the shell as illustrated below. + Numerical resolution of Eqs., Numerical resolution of Eqs. + (5. - 8)) provides. /2.(/) and thereby Vo) and oo(/).," \ref{eq:bubble_nrj_HPB} + - \ref{eq:mass_sh_HPB}) ) provides $R_s(t)$ and thereby $V_s(t)$ and $\sigma _0(t)$." +" The initial conditions are those at the time /,4,;,. Le. when the shell crosses the interface between the cloud anc the surrounding background: the mass and radius of the shell are those of the pressure-bound cloud (2,(0,.,,)=B. MiGUS,)= M). the velocity of the shell is determined. by its former propagation at. constant speed V through the cloud. (see Paper 1. Eq."," The initial conditions are those at the time $t_{em}$, i.e. when the shell crosses the interface between the cloud and the surrounding background: the mass and radius of the shell are those of the pressure-bound cloud $R_s(t_{em})=R$, $M_s(t_{em})=M$ ), the velocity of the shell is determined by its former propagation at constant speed $V$ through the cloud (see Paper I, Eq." +" 19). that is Vo= απά vl,Ξ0."," 13), that is $V_s=V$ and $A_s=0$." +" Figure 1. shows the evolution with time of the shell radius for 200SSNeLL. Le. the maximum number of supernovae that a PGCC can sustain (disruption criterion. Paper 1]. and for 3 different values of the hot. protogalactic background pressure. Le.. £4 = 5.10HO q07""I and 5.10Üddvneem 7."," Figure \ref{fig:RsHPB} shows the evolution with time of the shell radius for SNeII, i.e. the maximum number of supernovae that a PGCC can sustain (disruption criterion, Paper I), and for 3 different values of the hot protogalactic background pressure, i.e. $P_h$ = $\times 10^{-11}$, $^{-10}$ and $\times 10^{-10}$ $^{-2}$." + The SN rate being the same in the three cases. the shells propagate at the same velocity in the cold. phase (eq.," The SN rate being the same in the three cases, the shells propagate at the same velocity in the cold phase (Eq." + 13 in Paper D., 13 in Paper I). + Their expansions begin to differ once they have crossed the interface between their respective POCC and. the hot background. in which the atter is embedded. this time being indicated by an arrow in Fig. 1..," Their expansions begin to differ once they have crossed the interface between their respective PGCC and the hot background in which the latter is embedded, this time being indicated by an arrow in Fig. \ref{fig:RsHPB}." + Obviously. the propagation of the shell through he cloud is much shorter than its propagation through he background.," Obviously, the propagation of the shell through the cloud is much shorter than its propagation through the background." + A significant part of the shell expansion hrough the background takes place at carly time., A significant part of the shell expansion through the background takes place at early time. + Indeed. alter a transient phase curing which the velocity of the shell does not diller markedly from its velocity inside the cloud (Vig. 19).," Indeed, after a transient phase during which the velocity of the shell does not differ markedly from its velocity inside the cloud (Fig. \ref{fig:RsHPB}) )," + the overall expansion slows clown and the racius of he shell scales roughly as (47%., the overall expansion slows down and the radius of the shell scales roughly as $t^{1/3}$. +" ""his average expansion can x' obtained from Eqs.", This average expansion can be obtained from Eqs. + (5. - S)) assuming that M.(/)=0. rellecting thereby that the temporal evolution of the shell radius does not depend strongly on the mass (Brown et al.," \ref{eq:bubble_nrj_HPB} + - \ref{eq:mass_sh_HPB}) ) assuming that $M_s(t)=0$, reflecting thereby that the temporal evolution of the shell radius does not depend strongly on the mass (Brown et al." + 1995): ligure 2. shows the good. agreement between Iq., 1995): Figure \ref{fig:RsHPBt1/3} shows the good agreement between Eq. + 9 and the result. of the numerical integration over time of Eqs., \ref{eq:RsHPBt1/3} and the result of the numerical integration over time of Eqs. + (5. - 8)., \ref{eq:bubble_nrj_HPB} - \ref{eq:mass_sh_HPB}) ). + Equation 9. shows that. during the lone- evolution. the expansion rates of two shells having the same (ΛΑ). ratio are similar.," Equation \ref{eq:RsHPBt1/3} shows that, during the long-term evolution, the expansion rates of two shells having the same $(N/P_h)$ ratio are similar." +" Figure 2 illustrates this elfect for two sets of values. namely AN=LOO and D,25. 10t+dedsne.cm 7 (plain curve) and N=200) and P,=10P 27 (dashed-dotted. curve)."," Figure \ref{fig:RsHPBt1/3} illustrates this effect for two sets of values, namely $N$ =100 and $P_h$ $\times 10^{-11}$ $^{-2}$ (plain curve) and $N$ =200 and $P_h$ $10^{-10}$ $^{-2}$ (dashed-dotted curve)." + In order to assess whether the shell transverse collapse proceeds successfully or not. we now numerically integrate over time Ίσα». αμα 2 in order to derive the temporal evolutions of the perturbed and unperturbed surface densities. σι({) ancl συ(1). respectively.," In order to assess whether the shell transverse collapse proceeds successfully or not, we now numerically integrate over time \ref{eq:per_cont} and \ref{eq:per_motion} in order to derive the temporal evolutions of the perturbed and unperturbed surface densities, $\tilde{\sigma} _1(t)$ and $\sigma _0(t)$, respectively." + Assuming that the perturbed quantities follow a complex exponential of the angular position © along the shell. we ect: and In these equations. AO represents the phase dilference between the perturbed surface density σι and the perturbed velocity c.," Assuming that the perturbed quantities follow a complex exponential of the angular position $\phi$ along the shell, we get: and In these equations, $\Delta \phi$ represents the phase difference between the perturbed surface density $\sigma _1$ and the perturbed velocity $v$." + 5g is the angular wavenumber and is related to the spatial wavenumber & by: where A is the wavelength of the perturbation. namely the average clistance between forming fragments.the sites of future star. formation.," $\eta$ is the angular wavenumber and is related to the spatial wavenumber $k$ by: where $\lambda$ is the wavelength of the perturbation, namely the average distance between forming fragments,the sites of future star formation." + Therefore. 7 is the number. of forming clumps along a shell cireumference and. as such. yomust be an integer.," Therefore, $\eta$ is the number of forming clumps along a shell circumference and, as such, $\eta$ must be an integer." + Moreover. any realistic perturbation must fit inside a fraction of the shell circumference. say. A0.7Mg ," In the group 3 set of $N$ -body simulations, 52 of the 161 planets ) had final masses $>0.7M_{\rm Earth}$." +In the perfect merge Moute Carlo simulatiou. 50 of 200 planets (25% reach fina masses >(07ALRat: however. in eroup A. )})the uunber of large plaucts drops to only 15 )).," In the perfect merging Monte Carlo simulation, 50 of 200 planets ) reach final masses $>0.7M_{\rm Earth}$; however, in group A, the number of large planets drops to only 15 )." + When hit-aud-run return impacts are considered (eroup D). the fina lass distribution of planets is between perfect mereiue and eroup A. In this case. 31 large plaucts are produce )).," When hit-and-run return impacts are considered (group B), the final mass distribution of planets is between perfect merging and group A. In this case, 34 large planets are produced )." + During collisional growth and fragmentation. materia is preferentially lost from the silicate mautle. thus raising the core mass fraction (Figure. 7zDD.E).," During collisional growth and fragmentation, material is preferentially lost from the silicate mantle, thus raising the core mass fraction (Figure \ref{fig:montecarlo}D D,E)." + Iu. simulation eroups A and D. the iiaxiuun core mass fractions are 0.87 and 0.96. respectively. im bodies that experienced catastrophic impact events.," In simulation groups A and B, the maximum core mass fractions are 0.87 and 0.96, respectively, in bodies that experienced catastrophic impact events." +" Such core-domiünated bodies are rare. and most )) final core mass fractious fall in the range of 0.33 to 0.1,"," Such core-dominated bodies are rare, and most ) final core mass fractions fall in the range of 0.33 to 0.4." + In other words. most of the irou οσοι! is within of the initial value of feore.," In other words, most of the iron enrichment is within of the initial value of $f_{\rm core}$." +" Towever., as a group. the largest planets are more likely to be enriched in core mass fraction compared to saller planets."," However, as a group, the largest planets are more likely to be enriched in core mass fraction compared to smaller planets." + In both eroup A aud B simmlations. about 2/3 of the largest plancts have core mass fractions greater than of the initial value. compared to about 1/3 of all planets (Table 2)).," In both group A and B simulations, about 2/3 of the largest planets have core mass fractions greater than of the initial value, compared to about 1/3 of all planets (Table \ref{tab:mcoutcomes}) )." + The largest planets expericuce a larger προ of collisions which results im more cumulative erosion of the uautle., The largest planets experience a larger number of collisions which results in more cumulative erosion of the mantle. + The mass of debris produced during plauetarv erowth bv giant impacts can be significant., The mass of debris produced during planetary growth by giant impacts can be significant. + While there were plauets that suffered only mereie collisions that produced negligible debris (31 planets in group A and 25 iu eroup D). they all had. final masses of less tha 0.38Magy and an average of oulv 2 giaut impacts.," While there were planets that suffered only merging collisions that produced negligible debris (34 planets in group A and 25 in group B), they all had final masses of less than $0.38M_{\rm Earth}$ and an average of only 2 giant impacts." +" For conrparison. the mean nuuber of eiut impacts was 7 aud 9 for all planets in eroups A and D. respectively,"," For comparison, the mean number of giant impacts was 7 and 9 for all planets in groups A and B, respectively." + During the growth of large plancts. debris production averaged of the final planet mass in group A and in eroup D (Figure 7EEF.C).," During the growth of large planets, debris production averaged of the final planet mass in group A and in group B (Figure \ref{fig:montecarlo}F F,G)." + The mass of debris reported in Fieure ? only includes debris from gjiaut impacts: ylanctesimal collisions would also have contributed to the debris durius planet growth., The mass of debris reported in Figure \ref{fig:montecarlo} only includes debris from giant impacts; planetesimal collisions would also have contributed to the debris during planet growth. + Iu group A. the growth sequence that produced. the uost debris (0.28 gau) suffered a penultimate erosive ejut nupact on a planet with final mass of oulv 122Meaty.," In group A, the growth sequence that produced the most debris $0.28 +M_{\rm Earth}$ ) suffered a penultimate erosive giant impact on a planet with final mass of only $0.22M_{\rm Earth}$." + The most debris produced from oue of the argest plancts was of a 191ga plauct.," The most debris produced from one of the largest planets was of a $1.31 M_{\rm + Earth}$ planet." +" Notably. here is a case of à l.2Mga4, planet iu group D that xoduced 0.833gas of debris duiug its erowth."," Notably, there is a case of a $1.2M_{\rm Earth}$ planet in group B that produced $0.83M_{\rm Earth}$ of debris during its growth." + In some cases. the erowth sequence meludes a step where the argest relat is stualler than the initial eiibrvo.," In some cases, the growth sequence includes a step where the largest remnant is smaller than the initial embryo." + Such destructive sequences occured for | planets in eroup A and 7 planets in eroup D. Ax average of 12 eiaut impacts erew the largest plauets in eroup A. With the inclusion of hit-and-run return events. an average of 16 elaut impacts erew the largest anets in eroup D. Iu eroup D. the largest umber laut maupacts for any plancts was 26 (au ultimately SOME planet). iu contrast to the maxim of I8 ymant impacts in group A. HHit-aud-arun return collisions often led to multiple re-iupact events before the final nereine or cistuption of the projectile.," Such destructive sequences occured for 4 planets in group A and 7 planets in group B. An average of 12 giant impacts grew the largest planets in group A. With the inclusion of hit-and-run return events, an average of 16 giant impacts grew the largest planets in group B. In group B, the largest number of giant impacts for any planets was 26 (an ultimately $0.89M_{\rm Earth}$ planet), in contrast to the maximum of 18 giant impacts in group A. Hit-and-run return collisions often led to multiple re-impact events before the final merging or disruption of the projectile." +" The uuuber of excess @lant iupacts iu eroup D is shown in Figure ὃν,", The number of excess giant impacts in group B is shown in Figure \ref{fig:numhr}. + The ican uuuber of extra collisions ou the largest auets was laud ranged from 0 to 8., The mean number of extra collisions on the largest planets was 4 and ranged from 0 to 8. + This work demonstrates that the final. stochastic stage of terrestrial plauet formation cacolpasscs a diversity of collision outcomes.," This work demonstrates that the final, stochastic stage of terrestrial planet formation encompasses a diversity of collision outcomes." + All types of collisions. from siper- disruption to perfect mereie. are possible.," All types of collisions, from super-catastrophic disruption to perfect merging, are possible." +(phe).,(phe). + The correction is applied according to the following forma: Applving this correction. obviouslyT non-detected showers cannot be recovered. but the SIZE distributions are πο affected sienificautly for au atmospheric absorption up to data Guchiding absorption). the SIZE distributious agree well after applving the correction for an absorption smaller than of higher absorption. a more detailed Moute Carlo study js required. and a more couples. correction nüeght be considered.," The correction is applied according to the following formula: Applying this correction, obviously non-detected showers cannot be recovered, but the SIZE distributions are not affected significantly for an atmospheric absorption up to data (including absorption), the SIZE distributions agree well after applying the correction for an absorption smaller than of higher absorption, a more detailed Monte Carlo study is required, and a more complex correction might be considered." + Frthermore. the fiuctuations in signals. such as those ποια night-skv backeround elt. increase.," Furthermore, the fluctuations in signals, such as those from night-sky background light, increase." + Comparing corrected dark-time observations with data taken in strong mooulight (?).. the fluctuations after correction are found to remain well below those for extreme lieht conditions.," Comparing corrected dark-time observations with data taken in strong moonlight \citep{moon}, the fluctuations after correction are found to remain well below those for extreme light conditions." + By includiug arrival-time information iu the nuage cleaning. it could also be shown (7) that even data with strong fluctuations are properly handled.," By including arrival-time information in the image cleaning, it could also be shown \citep{time} that even data with strong fluctuations are properly handled." + ence. no further correction is necessary to account for this effect if the correction is applied to data taken uuder normal dieit conditious.," Hence, no further correction is necessary to account for this effect if the correction is applied to data taken under normal light conditions." + Consequently. the calculated nuage parameters are not skewed by the increase im the amplitude of the fluctuations and therefore do not influence the efficiencies obtained from simulated showers.," Consequently, the calculated image parameters are not skewed by the increase in the amplitude of the fluctuations and therefore do not influence the efficiencies obtained from simulated showers." + To check the method. a source of coustaut fiux is ideally used.," To check the method, a source of constant flux is ideally used." + However. no affected MAGIC data of a steady source are available.," However, no affected MAGIC data of a steady source are available." + Data affected by the SAL are difficult o schedule. suce these raro weather conditions are iaxdly predictable aud difficult to identify for the support astronolniers.," Data affected by the SAL are difficult to schedule, since these rare weather conditions are hardly predictable and difficult to identify for the support astronomers." + In July 2006. the MAGIC. telescope observed he Active Galactic Nucleus 11553|113 contemporaneously with the N-vav satellite Suzaku. he TACT array iud the optical telescope KVA diving a MWL campaign.," In July 2006, the MAGIC telescope observed the Active Galactic Nucleus 1553+113 contemporaneously with the X-ray satellite Suzaku, the IACT array and the optical telescope KVA during a MWL campaign." + Due to the SAL. the absorption or the suele nights from July 1579 to July 287 varied νοποσα correction was applied to the MAGIC data.," Due to the SAL, the absorption for the single nights from July ${\rm ^{th}}$ to July ${\rm ^{th}}$ varied between correction was applied to the MAGIC data." +" With the atmospheric ΕΙ j-1 determined frou, the preseuted. ineasurenients comparableo results were achieved for the cight nights of observation of 11553|113 in July 2006 (Fie. 2))."," With the atmospheric transmission $\frac{I}{I_0}$ determined from the presented measurements, comparable results were achieved for the eight nights of observation of 1553+113 in July 2006 (Fig. \ref{extinction}) )." + From the MAGIC data. the trausiission was determined only for the welts iu which data of 11553|113 were available.," From the MAGIC data, the transmission was determined only for the nights in which data of 1553+113 were available." + During some nights. the atmospheric transmission was changing. as ποσα both by the CAIT aud NWA.," During some nights, the atmospheric transmission was changing, as seen both by the CMT and KVA." + The KVA reports considerable changes even within a few minutes., The KVA reports considerable changes even within a few minutes. + Consequently. the different micasuremeuts agree less than for nights with stable extinction. since they were probably acquired not precisely simultaucously.," Consequently, the different measurements agree less than for nights with stable extinction, since they were probably acquired not precisely simultaneously." + Custable couditious diving the observations worsened the accuracy of the correction., Unstable conditions during the observations worsened the accuracy of the correction. + The remaining differences between the values roni the NWA aud the CAIT can be explained by the fact hat the intrinsic errors in imaguitude for the comparison stars are larger in the case of NVA., The remaining differences between the values from the KVA and the CMT can be explained by the fact that the intrinsic errors in magnitude for the comparison stars are larger in the case of KVA. + Deviatious of the SIZE nay come from the Iinüited accuracy of the method., Deviations of the SIZE may come from the limited accuracy of the method. +" For he nmon measurements, the svstematic uncertainties in he values are larger due to the strong dependence on the vertical distribution of the saud-dust in the SAL."," For the muon measurements, the systematic uncertainties in the values are larger due to the strong dependence on the vertical distribution of the sand-dust in the SAL." + Apart roni αμα. deviations aud the differences im he nights with variable extinction. the iieasuremoents agree well.," Apart from small deviations and the differences in the nights with variable extinction, the measurements agree well." + Since the CNET measurements are the most accurate. μον were used for the calculation of the correction factors.," Since the CMT measurements are the most accurate, they were used for the calculation of the correction factors." + As explained in Sect. 2.1..," As explained in Sect. \ref{iact}," + the atimospleric extinction iuffuences mainly the SIZE of the showers., the atmospheric extinction influences mainly the SIZE of the showers. + Figure 3. shows he SIZE distributions for the range used for the analvsis fore (left) aud after (aight) applviug the correction with he values from the CAIT., Figure \ref{sizedistr} shows the SIZE distributions for the range used for the analysis before (left) and after (right) applying the correction with the values from the CMT. +" For the shown distributions. special cuts were applied to remove nou-physical anc unon events,"," For the shown distributions, special cuts were applied to remove non-physical and muon events." + Each curve corresponds to data of one nieht., Each curve corresponds to data of one night. + Before the correction. the SIZE distributions spreac )etween aai aat 2OO0pple.," Before the correction, the SIZE distributions spread between and at phe." + After the correction. the Spread was reduced to the interva ICTWCOLL aand aapar roni one outher. correspouding to one nieht of variable extinction (rec dotted line. 22.7.2006).," After the correction, the spread was reduced to the interval between and apart from one outlier, corresponding to one night of variable extinction (red dotted line, 22.7.2006)." + Apart from this and a seco curve (black dotted ine. 17.72006) with a deviation at around pple. the SIZE distributions agree well after the correction for pphe. iiu the range used iu the analysis.," Apart from this and a second curve (black dotted line, 17.7.2006) with a deviation at around phe, the SIZE distributions agree well after the correction for phe, in the range used in the analysis." + The cuts for the background suppression mentioned iu Sect., The cuts for the background suppression mentioned in Sect. + 2.1 include an iutriusic lower cut iu SIZE. ceveuts with small SIZE are removed.," \ref{iact} + include an intrinsic lower cut in SIZE, events with small SIZE are removed." + Consequently. eveuts with reduced SIZEs due to atmospheric absorption are cut away. resulting ina lower significance of the signal if the same standard cuts are applied.," Consequently, events with reduced SIZEs due to atmospheric absorption are cut away, resulting in a lower significance of the signal if the same standard cuts are applied." + For 11553]113. a significant nuniber of eveuts are expected at low euergies due to the measured steep spectrum) of the source.," For 1553+113, a significant number of events are expected at low energies due to the measured steep spectrum of the source." + The expected effect of reduced significance due to the SAL is observed. for data takeu in July 2006: Without correction. a sigual is obtained with 3.20 sienificance. inproviug to 5.06 with correction. using identical cuts for the backeround suppression iu both cases.," The expected effect of reduced significance due to the SAL is observed for data taken in July 2006: Without correction, a signal is obtained with $\sigma$ significance, improving to $\sigma$ with correction, using identical cuts for the background suppression in both cases." +flor the whole nebula. from the neutral (1). to. the highly ionized ions (VIL. for all species. are respectively 1O0.2004200Kk. 10.0502: 1501Ix.. 10.050-E850Ix. 1140041050. 12.6002: T00Ix.. 10042008 and 12.650728 1.3004x Our model results for aand ccompare well with the many. estimates available from the literature: in particular aand for the rim. can be compared to the values of Hvung&(1098):Luoetal.(2001):Sabbadin(2004). that cluster around: 10.0001x. forolii. while values between 9.0001. and. 12.800Ix.. peaking around. 10.5501. were found for bv Hvung&Aller(1995a.b):IxwitterHenryCGoncalvesetal. (2003).,"for the whole nebula, from the neutral (I) to the highly ionized ions (VII), for all species, are respectively $\pm$ 200K, $\pm$ 150K, $\pm$ 850K, $\pm$ 1050K, $\pm$ 700K, $\pm$ 200K and $\pm$ 1,300K. Our model results for and compare well with the many estimates available from the literature; in particular and for the rim, can be compared to the values of \citet{b022,b023,b031,b026,b029,b039} that cluster around 10,000K for, while values between 9,000K and 12,800K, peaking around 10,550K, were found for by \citet{b022,b023,b026,b017}." +.. As for the outer knots. aand wwere found as being S.LOOW and 11200 by Balickοἱal. (1994).. 9.300Ix and 9.1001 bv Ixwitter&Henry(1998). and 11.350 and 10.0001Ix. by Goncalvesctal.(2003).," As for the outer knots, and were found as being 8,100K and 11,500K by \citet{b06}, 9,300K and 9,100K by \citet{b026} and 11,350 and 10,000K by \citet{b017}." +.. tesults for the fractional ionic abundances are shown in ‘Table 5., Results for the fractional ionic abundances are shown in Table 5. + Hydrogen. and helium are Lully at least sinely-ionized in lt. Ix. and. NEB. ancl significant fractions of the reavy elements are in higher ionization stages in the rim as well as in the nebula as a whole (NEB).," Hydrogen and helium are fully at least singly-ionized in R, K and NEB, and significant fractions of the heavy elements are in higher ionization stages in the rim as well as in the nebula as a whole (NEB)." + We also note 1e lower ionization of the knots., We also note the lower ionization of the knots. + An important issue that ga1ould. be noted here is the ratio being higher than 10 ratio by a factor of 1.39 in the knots. 1.66 rim απο 1.61 in the total nebula.," An important issue that should be noted here is the $^+$ ratio being higher than the $^+$ ratio by a factor of 1.39 in the knots, 1.66 rim and 1.61 in the total nebula." + Vhis result is at variance with we (Ikingsburgh&Barlow1994:Perinottoetal.2004b) generally assumed by theef method. with he consequent errors on empirically derived total elemental abuncdances. like those in1.," This result is at variance with the $^+$ $^+$ \citep{b025,b034} generally assumed by the method, with the consequent errors on empirically derived total elemental abundances, like those in." +. We note from Table 5. that. only a small fraction (K.64.. and for Re Ix and NEB. respectively) ol the total nitrogen in the nebula is in the form of N° and No.," We note from Table 5, that only a small fraction (, and for R, K and NEB, respectively) of the total nitrogen in the nebula is in the form of $^0$ and $^+$." + Xs only lines from these ions were observed. (see ‘Table 3 of 1)). the nitrogen abundance determination is particularly uncertain.," As only lines from these ions were observed (see Table 3 of ), the nitrogen abundance determination is particularly uncertain." + Sulfur abundances also sulfer from similar problems., Sulfur abundances also suffer from similar problems. + Combining the values in Table 5 with those. for the total elemental abundances used by our. model (Table 2). fractional ionic abundances relative to Ll are readily. available.," Combining the values in Table 5 with those for the total elemental abundances used by our model (Table 2), fractional ionic abundances relative to H are readily available." +" The total abundance that we have used. for all regions modelec returns ionic abundances. for Ro and Ix respectivelv. of — 0.091 ancl 0.111: = L17.10 and δι 7 = 7 and 3.64.10 4) 7 = and 10.: and finally 7 = 4300.10 "" and ""."," The total abundance that we have used for all regions modeled returns ionic abundances, for R and K respectively, of $^+$ = 0.091 and 0.111; $^+$ = $\times$ $^{-6}$ and $\times$ $^{-6}$; $^{+2}$ = $\times$ $^{-4}$ and $\times$ $^{-4}$; $^{+2}$ = $\times$ $^{-5}$ and $\times$ $^{-5}$; and finally $^{+2}$ = $\times$ $^{-6}$ and $\times$ $^{-6}$." + These whieh are the most important ions of the optical range for determining the total abundances are comparable to the ionic abundances derived from the observations— inI. with an agreement etter than for all of the above ions. except the 7/1 of It. whose discrepancy reachesτον.," These —which are the most important ions of the optical range for determining the total abundances— are comparable to the ionic abundances derived from the observations in, with an agreement better than for all of the above ions, except the $^{+2}$ /H of R, whose discrepancy reaches." +.. In Figure 1. we show the ionic abundance profiles of he model. as well as the electron density and temperature xofiles along the axis which includes the knots.," In Figure \ref{IonProf} we show the ionic abundance profiles of the model, as well as the electron density and temperature profiles along the axis which includes the knots." + Phe top-left xil in this Figure. rellects the ((continuous line) and ((dashed. line) variations through the long axis of the nebula.," The top-left panel in this Figure, reflects the (continuous line) and (dashed line) variations through the long axis of the nebula." + It shows that peaks at the innermost region of theZt-component. having a mean value through the component of 4.100 7," It shows that peaks at the innermost region of the, having a mean value through the component of 4,100 $^{-3}$." +" The as well as the have mean oof 1385 cm"" and 1640 respectively. while somewhat smoothed profiles are present at. the edges."," The as well as the have mean of 1385 $^{-3}$ and 1640 $^{-3}$, respectively, while somewhat smoothed profiles are present at the edges." + The electron. density profile is a result. of the ionization structure combined with the density. distribution πα in Section 2.3.3., The electron density profile is a result of the ionization structure combined with the density distribution assumed in Section 2.3.3. + As for the pprotiles. although varving somewhat within the components. have mean values that are in close agreement with the values measured inL. see numbers quoted in the previous subsection.," As for the profiles, although varying somewhat within the components, have mean values that are in close agreement with the values measured in, see numbers quoted in the previous subsection." + Vhis will be discussed further in Section 4., This will be discussed further in Section 4. + ligure 1 also highlights the strong dependence of the ionisation level on the ecometry and density distribution of the gas., Figure 1 also highlights the strong dependence of the ionisation level on the geometry and density distribution of the gas. + Lt is therefore clear that an apparent overabundance of Nin the knots can be produced by providing the correct gas opacity to screen this region from the direct. stellar photons., It is therefore clear that an apparent overabundance of $^+$ in the knots can be produced by providing the correct gas opacity to screen this region from the direct stellar photons. + We should add at this point that an cven larger abunclanee can be obtained by further enhancing the eas density at the rim-jet interlace. without significantly changing the ο u] density ratio in theR-component.," We should add at this point that an even larger $^+$ abundance can be obtained by further enhancing the gas density at the rim-jet interface, without significantly changing the [S ] density ratio in the." + NGC 7009 has been observed with the£57 ΛΕΡΟΣ with filters centred in the 11]A5007 anc UJAG5S3 emission lines (see Section 2.1)., NGC 7009 has been observed with the WFPC2 with filters centred in the $\lambda$ 5007 and $\lambda$ 6583 emission lines (see Section 2.1). + These archive images. already published in1. are compared to the model predicted emission. maps in Figure 2..," These archive images, already published in, are compared to the model predicted emission maps in Figure \ref{EmisMap}." + The maps were produced. at an inclination of S4° with respect to the line of sight. as indicated by the kinematies of the PN polar axis Atherton 1985).. for ((right top panel) and ((lower right. panel) emission lines.," The maps were produced at an inclination of $^\circ$ with respect to the line of sight, as indicated by the kinematics of the PN polar axis \citep{b037}, for (right top panel) and (lower right panel) emission lines." +" First of all we call the readers attention to the fact that thebubble. which appear in the£57 image. at fainter intensity levels. as an extension of theshelf, ancl also the inner. pair of knots. anclAY were not considered in our modelling."," First of all we call the readers attention to the fact that the, which appear in the image, at fainter intensity levels, as an extension of the, and also the inner pair of knots, and were not considered in our modelling." + Thus. excluding the polar bubble and the inner knots. the images and our maps are at least qualitatively in good agreement (note that a photometric comparison is beyond the scope of this paper).," Thus, excluding the polar bubble and the inner knots, the images and our maps are at least qualitatively in good agreement (note that a photometric comparison is beyond the scope of this paper)." + From the maps we note the higher excitation of the equatorial axis of the PN as compared to the polar one. because of the higher density of the rim. and. following the pattern known from previous studies. as stated in the Introduction.," From the maps we note the higher excitation of the equatorial axis of the PN as compared to the polar one, because of the higher density of the rim, and following the pattern known from previous studies, as stated in the Introduction." + One also clearly sees that the mmap is more extended than the oone. as expected. from a nebula excited by a central star.," One also clearly sees that the map is more extended than the one, as expected from a nebula excited by a central star." + Finally. one notes that the knots are fainter (as compared," Finally, one notes that the knots are fainter (as compared" +wwith redshift via luuinosity densities.,with redshift via luminosity densities. + Ia particular we can compare the value of Jj defined aud measured by Ποσο(2002) as well as other measurements of the variation of the comoving SFR density with redshift (e.g.Lillyet1996:Madauetal. 1996).," In particular we can compare the value of $\beta$ defined and measured by \citet{Hogg02} as well as other measurements of the variation of the comoving SFR density with redshift \citep[e.g.][]{LLHC96,madau96}." +. The total amount of star formation (r7) between 2= Sand 2=O as a fraction of the mass available was normalized to a range of values from kr=0.35 tor=1.1 (the SER normalization)., The total amount of star formation $r$ ) between $z=5$ and $z=0$ as a fraction of the mass available was normalized to a range of values from $r=0.3$ to $r=1.4$ (the SFR normalization). + Iu other words. the mass of gas available for star formation is unitv aud the r is the total lnass of stars formed simce igi.," In other words, the mass of gas available for star formation is unity and the $r$ is the total mass of stars formed since $\zform$." + Pls can be greater than nuity because of recycling of material back iuto the inter-stellar uedimm., This can be greater than unity because of recycling of material back into the inter-stellar medium. + Higher + values result in higher average metallicity because the fusion products released iuto the ISAL by supernovae are more abundant relative to the rendus eas., Higher $r$ values result in higher average metallicity because the fusion products released into the ISM by supernovae are more abundant relative to the remaining gas. + The ddata were divided iuto 114 redshift bius between 2=0.025 and 2=0.25. cach containing about 120000 spectra.," The data were divided into 14 redshift bins between $z=0.025$ and $z=0.25$, each containing about 000 spectra." + Πα the redshift bins were below 2=0.11 (the median redshift of the survey)., Half the redshift bins were below $z=0.11$ (the median redshift of the survey). + The lower and higher groups of 7 redshift bins were considered separately aud together to test the robustuess to varving aperture and selection effects (sec Section 5. for a further discussion of this)., The lower and higher groups of 7 redshift bins were considered separately and together to test the robustness to varying aperture and selection effects (see Section \ref{sec:biases} for a further discussion of this). + For cach redshift biu. the spectra were divided iuto en positional bius based ou their coordinates (1 reeious in the NCP aud 6 in the SCP).," For each redshift bin, the spectra were divided into ten positional bins based on their coordinates (4 regions in the NGP and 6 in the SGP)." + A normalized average spectruni was calculated aud the positional bius were used o estimate the uucertaiuties., A normalized average spectrum was calculated and the positional bins were used to estimate the uncertainties. + This spectrmu represcuts the otal optical emission of all galaxies in the volume of the redshift shell down to the umaenitude luit., This spectrum represents the total optical emission of all galaxies in the volume of the redshift shell down to the magnitude limit. + The absolute magnitude uit is fainter han or about AL” out to a redshift of 0.2 (the depth is discussed further iu Section 5))., The absolute magnitude limit is fainter than or about $M^*$ out to a redshift of 0.2 (the depth is discussed further in Section \ref{sec:biases}) ). + To fiux-calibrate the spectra they were divided bv the 2dF response function of Lewisetal.(2002)— before coadding the fluxes at their rest waveleugths., To flux-calibrate the spectra they were divided by the 2dF response function of \citet{lewis02} before coadding the fluxes at their rest wavelengths. +" Spectra contribute to the final spectrum in proportion to their Thuninosity,", Spectra contribute to the final spectrum in proportion to their luminosity. + Iu addition. the averaged spectra were sanoothed and resampled to match approximately the πιο lower resohition of the spectral library (Lejeuue.Cuisiuier.Duser1997) used by the populatiou-svuthesis code.," In addition, the averaged spectra were smoothed and resampled to match approximately the much lower resolution of the spectral library \citep*{LCB97} used by the population-synthesis code." + To evaluate the ‘goodness of fit between a formation scenario aud the ddata. we compare the spectrum from cach redshift bin with the appropriate model spectrum (at the same age) from the scenario.," To evaluate the `goodness of fit' between a star-formation scenario and the data, we compare the spectrum from each redshift bin with the appropriate model spectrum (at the same age) from the scenario." + Fiber spectra are kuown to be dificult to flux accurately so it is desirable to develop methods which are insensitive to Να] spectrophotometric unicertaimties., Fiber spectra are known to be difficult to flux accurately so it is desirable to develop methods which are insensitive to small spectrophotometric uncertainties. + The first method we used was to allow for the possibility of spectrophotometric calibration. crrors by including a correction function before evaluating the ft., The first method we used was to allow for the possibility of spectrophotometric calibration errors by including a correction function before evaluating the fit. + This was to account for spectrophotometric discrepancies between the 2dF respouse curve used to calculate the average spectra and the true average rrespouse., This was to account for spectrophotometric discrepancies between the 2dF response curve used to calculate the average spectra and the true average response. + We used a fourth order polynomial withobserved waveleugth for this spectrophotometric correction. the coefficients being determined by ratioiug the model aud data spectra (excluding the strongest cussion lines as per the fitting).," We used a fourth order polynomial with wavelength for this spectrophotometric correction, the coefficients being determined by ratioing the model and data spectra (excluding the strongest emission lines as per the fitting)." + An important point is that the correction is constrained to be the same function at all redshifts. thus the degeneracy between the spectrophotometric correction aud the model fitting is partially broken because of the range of redshift covered (0.030.25).," An important point is that the correction is constrained to be the same function at all redshifts, thus the degeneracy between the spectrophotometric correction and the model fitting is partially broken because of the range of redshift covered (0.03–0.25)." + Typically iu our fitting we find this spectrophotometric correction to be of the order change in the response fuuctiou of Lewisetal. ffor the best-üttiug models Qvithin 30)., Typically in our fitting we find this spectrophotometric correction to be of the order change in the response function of \citeauthor{lewis02} for the best-fitting models (within $\sigma$ ). + These values represcut the RAIS relative differcuce over the wavelcueth ranec between the polvuondal correction aud a constant value (represeutiug changes iu the relative. not absolute. spectrophotometry).," These values represent the RMS relative difference over the wavelength range between the polynomial correction and a constant value (representing changes in the relative, not absolute, spectrophotometry)." + Since the response fuuction was, Since the response function was +has additional variability at lower energies.,has additional variability at lower energies. +" This component is clearly hotter than the soft. excess seen in the mean spectrum. and the reality of this as an additional component is supported by it lagging behind the 2-10 keV variability by 310 s. This lag could be produced by reprocessing. in which case it corresponds to a light crossing distance of 3042, for a 2.JO""AZ. black bole."," This component is clearly hotter than the soft excess seen in the mean spectrum, and the reality of this as an additional component is supported by it lagging behind the 2-10 keV variability by 370 s. This lag could be produced by reprocessing, in which case it corresponds to a light crossing distance of $30R_g$ for a $2\times 10^6 M_\odot$ black hole." + This new information on the QPO spectral shape puls some constraints on models., This new information on the QPO spectral shape puts some constraints on models. + For example. a radial perturbation. of the Compton torus leads to απ olfset geometry Lc. to elliptical orbits whose perihelion precesses.," For example, a radial perturbation of the Compton torus leads to an offset geometry i.e. to elliptical orbits whose perihelion precesses." + llowever. there is no change in illumination of the disc during the azimuthal precession so it is hard to incorporate a soft lag from reprocessing into this model.," However, there is no change in illumination of the disc during the azimuthal precession so it is hard to incorporate a soft lag from reprocessing into this model." + Conversely. a vertical oscillation or coupled vertical-radial oscillation clearly changes the cise illumination (CXbramowicz Ixluzniak 2005: Blaes ct al 2007).," Conversely, a vertical oscillation or coupled vertical-radial oscillation clearly changes the disc illumination (Abramowicz Kluzniak 2005; Blaes et al 2007)." + An alternative set. of models incorporate a transonic shock rather than a global mode., An alternative set of models incorporate a transonic shock rather than a global mode. + Phe shock could occur in a hot. very low angular momentuni How. and its racial position can oscillate (Das Czerny 2010).," The shock could occur in a hot, very low angular momentum flow, and its radial position can oscillate (Das Czerny 2010)." + The maximum in hare X-ray [ux is where this shock radius is largest. which leads also to stronger illumination of the disc. so these models can also produce a soft lag (rom reprocessing.," The maximum in hard X-ray flux is where this shock radius is largest, which leads also to stronger illumination of the disc, so these models can also produce a soft lag from reprocessing." + The QPO spectrum is also clearly not alfected by strong absorption features., The QPO spectrum is also clearly not affected by strong absorption features. + An absorption origin for the QPO is also ruled out by the ROS. spectrum which shows that the atomic features (which are present in the spectrum as claimed in AMaitra Aliller 2010) are narrow and. not strongly Doppler shifted., An absorption origin for the QPO is also ruled out by the RGS spectrum which shows that the atomic features (which are present in the spectrum as claimed in Maitra Miller 2010) are narrow and not strongly Doppler shifted. + The small cistances required. for periodic obscuration by an orbiting clump of material to produce the QPO would imply much larger velocities., The small distances required for periodic obscuration by an orbiting clump of material to produce the QPO would imply much larger velocities. + The periodic change in absorption seen by Maitra Miller (2010) maw instead simply be the wind at large distances changing in ionisation in response to the changing illuminating Lux., The periodic change in absorption seen by Maitra Miller (2010) may instead simply be the wind at large distances changing in ionisation in response to the changing illuminating flux. + None of the remaining observations show any significant excess of power over the red noise at the QDPO frequency., None of the remaining observations show any significant excess of power over the red noise at the QPO frequency. + The one with the most power at this frequeney. is Obsth. which. along with Obsda. has a fairly similar short timescale covariance spectrum to that of the QPO which may indicate a similar variablitv process was occuring although not as dominant as in Obs2.," The one with the most power at this frequency is Obs4b, which, along with Obs4a, has a fairly similar short timescale covariance spectrum to that of the QPO which may indicate a similar variablity process was occuring although not as dominant as in Obs2." + Thus the QPO is transient. and there is no clear trigecr [or its emergence.," Thus the QPO is transient, and there is no clear trigger for its emergence." + One potential way forward is. instead to assume that this is similar to the 671Iz QPO in CIUS 1915|105 (e.g. Morgan. Hemillard Creiner 1997) and use the substantially [larger dataset on CRS 1915|105 to search for the trigeer of the QPO in the stellar mass black hole.," One potential way forward is instead to assume that this is similar to the 67Hz QPO in GRS 1915+105 (e.g. Morgan, Remillard Greiner 1997) and use the substantially larger dataset on GRS 1915+105 to search for the trigger of the QPO in the stellar mass black hole." + This has not vet been done. but may. prove to be illuminating.," This has not yet been done, but may prove to be illuminating." + lu J1034|396 is one of the most extreme and important AGN detected thus far as its timing properties resemble those of the highest luminosity BIIBs., RE J1034+396 is one of the most extreme and important AGN detected thus far as its timing properties resemble those of the highest luminosity BHBs. + Follow-up observations show that the PDS no longer contains the strong QPO that characterised the lightcurve in. the 2008 detection., Follow-up observations show that the PDS no longer contains the strong QPO that characterised the lightcurve in the 2008 detection. + Such a change in the intrinsic variability properties indicates that the PDS is non-stationary., Such a change in the intrinsic variability properties indicates that the PDS is non-stationary. + We use covariance spectra to get better signal to noise on the spectrum of the variability., We use covariance spectra to get better signal to noise on the spectrum of the variability. + This reveals new features in the QPO itself., This reveals new features in the QPO itself. + Phere is a soft component in addition to the power law tail which contributes to the QPO signal., There is a soft component in addition to the power law tail which contributes to the QPO signal. + Folding the lighteurve on the QPO timescale over dillerent energy. bands indicates that this component lags behind the hard. emission., Folding the lightcurve on the QPO timescale over different energy bands indicates that this component lags behind the hard emission. +" This implies a size scale of ~304, if this is produced. by reprocessing of the hard QPO spectrum. though we caution that the lag could. also be caused by a more complex. interaction between the isc and corona. rather than by reprocessing."," This implies a size scale of $\sim +30R_g$ if this is produced by reprocessing of the hard QPO spectrum, though we caution that the lag could also be caused by a more complex interaction between the disc and corona, rather than by reprocessing." + Llowever. C reprocessing origin puts some constraints on the QPO mechanism. since this requires a changing illumination of 1e disce.," However, a reprocessing origin puts some constraints on the QPO mechanism, since this requires a changing illumination of the disc." + “Phis probably rules out models where the QPO is from a racial perturbation precessing around the black hole. as here there is no change in disc illumination.," This probably rules out models where the QPO is from a radial perturbation precessing around the black hole, as here there is no change in disc illumination." + Lastcac this could. be produced. by a vertical or coupled: vertical-radial (breathing mode) mode (CXbramowicz IxIluzniak 2005: Blaes et al 2007). or the oscillating shock model of Das Czerny (2010).," Instead this could be produced by a vertical or coupled vertical-radial (breathing mode) mode (Abramowicz Kluzniak 2005; Blaes et al 2007), or the oscillating shock model of Das Czerny (2010)." +" We rule out. occultation models. [rom an. orbiting cloud. from the RGS data. which show that the ionisec absorbed has narrow features at low velocity. unlike those expected from material within 202, as required by the QPO imescale."," We rule out occultation models from an orbiting cloud from the RGS data, which show that the ionised absorbed has narrow features at low velocity, unlike those expected from material within $20R_g$ as required by the QPO timescale." + None of the other 4 datasets show the QPO despite 3 of hese showing rather similar spectra and 2 of these showing a rather similar covariance spectrum on short. timescales., None of the other 4 datasets show the QPO despite 3 of these showing rather similar spectra and 2 of these showing a rather similar covariance spectrum on short timescales. + ‘Thus there is no clear trigger we can identify for the QPO rom these data., Thus there is no clear trigger we can identify for the QPO from these data. + We suggest instead. that it may be useful o search the much more extensive datasets in. black hole jnaries for the trigger of their transient high. frequency QPOs., We suggest instead that it may be useful to search the much more extensive datasets in black hole binaries for the trigger of their transient high frequency QPOs. +where (2) is the growth factor computed fron E,where $D(z)$ is the growth factor computed from an $E(z)=H(z)/H_0$. +rrors on the power spectrum are due to two factors: sample variance. ic. the fact that not all A modes are measured. ancl shot-noise which is the elective. noise on the measurement of an individual mode.," Errors on the power spectrum are due to two factors: sample variance, i.e. the fact that not all $k$ modes are measured, and shot-noise which is the effective noise on the measurement of an individual mode." + The total error op on the measurementof the power spectrum. P(A.z). for a given & with logarithmic bin width (log&) can be expressed as (Feldmanetal.1994:Tegmoark1997) where 2=P(k.z) and ο=n(z) is the number density of galaxies which are detected (making n7? dimensionless) and Viar(A) is the effective survey volume probed for a particular A-mocde For definiteness. we will consider a survey taking two vears performed. by the FAST telescope with a focal plane array with ay=100 and fon.=6005 per instantaneous FoV. Quaml00aremin?.," The total error $\sigma_{\rm P}$ on the measurementof the power spectrum, $P(k,z)$, for a given $k$ with logarithmic bin width $\Delta(\log k)$ can be expressed as \citep{FKP,Tegmark1997} + where $P=P(k,z)$ and $n=n(z)$ is the number density of galaxies which are detected (making $nP$ dimensionless) and $V_{\rm eff}(k)$ is the effective survey volume probed for a particular $k$ -mode For definiteness, we will consider a survey taking two years performed by the FAST telescope with a focal plane array with $n_{\rm B}=100$ and $t_{\rm obs}=600\,s$ per instantaneous FoV, $\Omega_{\rm inst}\approx 1000\,{\rm arcmin}^2$." +" The choice of £i,=600 is simply the required survey time for scanning the full sky in 2 vears and hence is the most. οποίο use of the telescopes resources."," The choice of $t_{\rm obs}=600\,s$ is simply the required survey time for scanning the full sky in 2 years and hence is the most efficient use of the telescopes resources." + The justification for such an observation strategy is the simple fact that the area covered is inversely. linear in integration time per field while the depth attained. goes as the square root. of the integration time: the most cosmic volume is attained from full sky surveys., The justification for such an observation strategy is the simple fact that the area covered is inversely linear in integration time per field while the depth attained goes as the square root of the integration time; the most cosmic volume is attained from full sky surveys. + We have also calculated the etfect of probing dillerent barvonic acoustic modes in the sky with varving observation strategies and determined that the simplemaxim. of ‘wicle-shallow’ is always preferable to narrow-deep! in large-scale galaxy surveys., We have also calculated the effect of probing different baryonic acoustic modes in the sky with varying observation strategies and determined that the simplemaxim of `wide-shallow' is always preferable to `narrow-deep' in large-scale galaxy surveys. + Using the methods of section 3.3. we have estimated that such a survey will find ~LO galaxies with S/N=4. the vast majority of which are spatially unresolved.," Using the methods of section \ref{inclination} we have estimated that such a survey will find $\sim 10^{7}$ galaxies with $S/N=4$ , the vast majority of which are spatially unresolved." + The expected. errors. on. the power spectrum are presented in Fig., The expected errors on the power spectrum are presented in Fig. + 8. for A(log&)=0.04. which should be sullicienthy [large to ensure the errors are uncorrelated. according to a simple prescription detailed in Meiskin(1999).," \ref{fig:powersp} for $\Delta(\log k)=0.04$, which should be sufficiently large to ensure the errors are uncorrelated, according to a simple prescription detailed in \cite{MeiskinWhitePeacock1999}." +. Phe errors increase at low & due to sample variance and. would also increase at high. & due to shot noise were it not for our choice of a logarithmic binning: that is. the bins do not contain an equal number of &-modes.," The errors increase at low $k$ due to sample variance and would also increase at high $k$ due to shot noise were it not for our choice of a logarithmic binning; that is, the bins do not contain an equal number of $k$ -modes." + We have also divided the power spectrum by a model with no barvons which illustrates the acoustic features in the spectrum., We have also divided the power spectrum by a model with no baryons which illustrates the acoustic features in the spectrum. + The average redshift £2220.15 will prevent much cosmological information being eleaned from the acoustic scale. and jerefore we will not use it explicitly in our estimates of the 'osmological parameters., The average redshift $\langle z\rangle\approx 0.15$ will prevent much cosmological information being gleaned from the acoustic scale and therefore we will not use it explicitly in our estimates of the cosmological parameters. + Iis clear. however. from Fig.," It is clear, however, from Fig." + N ju the detection of the baryonie features would be possible with these data., \ref{fig:powersp} that the detection of the baryonic features would be possible with these data. + Lt is now interesting to compare the characteristics of 16 proposed. FAST survey with those presently available., It is now interesting to compare the characteristics of the proposed FAST survey with those presently available. +" The ellective volume of the proposed FAST survey evaluated at the &=ky0.075hAlpe! scale of the acoustic peak in Ίο power spectrum. is Vor=0.82πο,7Mpe."," The effective volume of the proposed FAST survey evaluated at the $k=k_{\rm A}=0.075h\,{\rm Mpc}^{-1}$ scale of the acoustic peak in the power spectrum, is $V_{\rm eff}=0.82\times 10^{9} h^{-3}\,{\rm Mpc}^{3}$." + This is shown in Fig., This is shown in Fig. + 9. where the effective volume probed. as well as the galaxy number count. of a variety of optical survey schemes are given. namely the SDSS main and SDSS LRG results as well as 2dEGIU. in comparison with FAST rp=19 for both fn.=1205 and fon.=6005 survey mocles as well as our proposed version with np=100 and fo.=600s.," \ref{fig:effvol} where the effective volume probed, as well as the galaxy number count, of a variety of optical survey schemes are given, namely the SDSS main and SDSS LRG results as well as 2dFGRS, in comparison with FAST $n_{\rm B}=19$ for both $t_{\rm obs}=120\,s$ and $t_{\rm obs}=600\,s$ survey modes as well as our proposed version with $n_{\rm B}=100$ and $t_{\rm obs}=600\,s$." + In the previous section we have shown that a survey using the FAST with np100 would find z10° galaxies., In the previous section we have shown that a survey using the FAST with $n_{\rm B}=100$ would find $\approx 10^{7}$ galaxies. + Lt is interesting to determine the improvement that this would bring to cosmological parameter estimation through the accurate sampling of the galactic power spectrum relative to current large-scale optical surveys: 2dbEGIU and SDSS., It is interesting to determine the improvement that this would bring to cosmological parameter estimation through the accurate sampling of the galactic power spectrum relative to current large-scale optical surveys; 2dFGRS and SDSS. + Since the EAST survey will have similar redshift coverage. but in a different wavebancl. this would bring more than just an improvement in signal-to-noise.," Since the FAST survey will have similar redshift coverage, but in a different waveband, this would bring more than just an improvement in signal-to-noise." + For the 2dkPGRS surveys we use the data presented in (Coleetal.2005)., For the 2dFGRS survey we use the data presented in \citep{Cole}. +. We select 32 bandpowers in the range 0.022OCIO !9)-OC107). permeating extracluster voids (222)..," Recent observations of radiation from blazars implies a lower limit in the extra-galactic medium of $B\gtrsim\mathcal{O}(10^{-16})$ $\mathcal{O}(10^{-15})$, permeating extracluster voids \citep{Neronov:1900zz,Tavecchio:2010ja,Dolag:2010ni}." + The presence of fields on such fields implies either a primordial origin or an efficient transfer of fields from within galaxies deep into the intergalactic medium., The presence of fields on such fields implies either a primordial origin or an efficient transfer of fields from within galaxies deep into the intergalactic medium. + The precise origin of fields on such large scales remains debated but magnetogenesis scenarios exist which were viable in the extremely early universe., The precise origin of fields on such large scales remains debated but magnetogenesis scenarios exist which were viable in the extremely early universe. + Such scenarios can be produced directly during inflation (????2?)999999) or at," Such scenarios can be produced directly during inflation \citep{Turner:1987bw,Bassett:2000aw,Prokopec:2004au,Giovannini:2007rh,Campanelli:2007cg,Bamba:2008my} or at" +position!,! + his is not a problem since the torque. formula contains a d-funetion at the resonance., This is not a problem since the torque formula contains a $\delta$ -function at the resonance. + Thus we see that a pure gauge perturbation leads to zero contribution to &'shed al resonance. and the resonant torque is gauge-invariant.," Thus we see that a pure gauge perturbation leads to zero contribution to ${\cal S}^{(m)}$ at resonance, and the resonant torque is gauge-invariant." + There is an alternative wav of writing the resonant amplitude &nd that will be better suited to computation in the Schwarzschild and. Kerr spacetimes., There is an alternative way of writing the resonant amplitude ${\cal S}^{(m)}$ that will be better suited to computation in the Schwarzschild and Kerr spacetimes. +" We will argue in this section that S7""nid is related to a particular integral of the metric perturbation along the world line of a test particle on an orbit with very small cecentricity.", We will argue in this section that ${\cal S}^{(m)}$ is related to a particular integral of the metric perturbation along the world line of a test particle on an orbit with very small eccentricity. + This formulation has some utility in the Newtonian case. but it will be shown to be very powerful in Paper Ll where we will relate it to the eravitational waveform. emitted. by a test. particle on such an orbit.," This formulation has some utility in the Newtonian case, but it will be shown to be very powerful in Paper II, where we will relate it to the gravitational waveform emitted by a test particle on such an orbit." + Ht will thus allow computation of S'D using standard methocls for computing waveforms. without explicit evaluation of the metric perturbations.," It will thus allow computation of ${\cal S}^{(m)}$ using standard methods for computing waveforms, without explicit evaluation of the metric perturbations." + Our starting point is to consider a particle on an unperturbed orbit (ic. traveling according to £0) oscillating between r=2c and B|¢., Our starting point is to consider a particle on an unperturbed orbit (i.e. traveling according to $H_0$ ) oscillating between $r=R-\epsilon$ and $R+\epsilon$. + To first order in e. its trajectory is given Now we consider the integral of the metric perturbation over the test. particle world line where the range of integration is over any epicyclic period. i.e. from £4<=Ib446 kms + and eο...0.5530.09 dex (mean errors) for this thick-clisk sample are in concordance with the mean values given in the literature. such as in Schuster et al. (," Other values, $ = 154 \pm 6$ km $^{-1}$ and $<[M/H]> = -0.55 \pm 0.03$ dex (mean errors) for this thick-disk sample are in concordance with the mean values given in the literature, such as in Schuster et al. (" +(1993).,1993). + Our thick-cisk sample defined by the range. 21 6. is given in Table 3 together with the kinematic and abundance data.," Our thick-disk sample defined by the range, $-21 \leq X \leq -6$ , is given in Table 3 together with the kinematic and abundance data." + The a-clement and. spectroscopic Fe/LI] abundances of some stars have been found in the literature., The $\alpha$ -element and spectroscopic [Fe/H] abundances of some stars have been found in the literature. +" It can be seen from ""Table 3 that. spectroscopic Ve/LI] abundances are in good agreement with the photometric ones.", It can be seen from Table 3 that spectroscopic [Fe/H] abundances are in good agreement with the photometric ones. + The mean <ας> values of seven thick-clisk stars. except LID 16623 are constant at a level of 0.27 dex. which are overabundant relative to thin clisk stars. over the »ectroscopic mictallicity range from -0.45 to -0.84 dex (See ο.," The mean $<[\alpha/Fe]>$ values of seven thick-disk stars, except HD 16623 are constant at a level of 0.27 dex, which are overabundant relative to thin disk stars, over the spectroscopic metallicity range from -0.45 to -0.84 dex (See Fig." + Ld in Nissen 2004. Fig.," 1.4 in Nissen 2004, Fig." + 4 in Nissen Schuster 1997. ie.," 4 in Nissen Schuster 1997, Fig." + 13 in Benshy ct 22003. and Fig.," 13 in Bensby et 2003, and Fig." + S in Benshy et , 8 in Bensby et 2005). [ +Meg/Fe] abundances of stars with thickedisk kinematics in Table 3. which fall in the range. |0.19AlgíPFe]|0.43 dex are similar to those of the thick disk found in the literature.,"Mg/Fe] abundances of stars with thick-disk kinematics in Table 3, which fall in the range $+0.19 \leq [Mg/Fe] \leq+0.43$ dex are similar to those of the thick disk found in the literature." + The trend. of a-capture elements like Ale. Si. Ca. and Ti with photometric M/LM] (or spectroscopic FefM]) abundances of thick-disk stars in Table 3 agrees well with the findings of Nissen Schuster (1997) and Aoensbv et al. (," The trend of $\alpha$ -capture elements like Mg, Si, Ca, and Ti with photometric [M/H] (or spectroscopic [Fe/H]) abundances of thick-disk stars in Table 3 agrees well with the findings of Nissen Schuster (1997) and Bensby et al. (" +2005).,2005). + Also. the a-clement abuncances of thick-clisk stars. which are available in Table 3. support," Also, the $\alpha$ -element abundances of thick-disk stars, which are available in Table 3, support" +effects.,effects. + The BAO features in particular are at the degree angular scale on the sky and thus ean be resolved easily with a rather modest size radio instrument (diameter D<100m).," The BAO features in particular are at the degree angular scale on the sky and thus can be resolved easily with a rather modest size radio instrument (diameter $D \lesssim 100 \, \mathrm{m}$ )." +" The specific BAO clustering scale (&pg30) can be measured both in the transverse plane (angular correlation function. (45,05) or along the longitudinal Cline of sight or redshift (4),Il4) direction."," The specific BAO clustering scale $k_{\mathrm{BAO}}$ ) can be measured both in the transverse plane (angular correlation function, $k_{\mathrm{BAO}}^\perp$ ) or along the longitudinal (line of sight or redshift $k_{\mathrm{BAO}}^\parallel$ ) direction." + A direct measurement of the Hubble parameter H(z) can be obtained by comparing the longitudinal and transverse BAO scales., A direct measurement of the Hubble parameter $H(z)$ can be obtained by comparing the longitudinal and transverse BAO scales. + A reasonably good redshift resolution ὃςx0.01 is needed to resolve longitudinal BAO clustering. which is a challenge for photometric optical surveys.," A reasonably good redshift resolution $\delta z \lesssim 0.01$ is needed to resolve longitudinal BAO clustering, which is a challenge for photometric optical surveys." + In order to obtain a measurement of the LSS power spectrum with small enough statistical uncertainties (sample or cosmic variance). a large volume of the universe should be observed. typically few Gpe*.," In order to obtain a measurement of the LSS power spectrum with small enough statistical uncertainties (sample or cosmic variance), a large volume of the universe should be observed, typically few $\mathrm{Gpc^3}$." + Moreover. stringent constraint on DE parameters can only be obtained when comparing the distance or Hubble parameter measurements with DE models as a function of redshift. which requires a significant survey depth Az>I.," Moreover, stringent constraint on DE parameters can only be obtained when comparing the distance or Hubble parameter measurements with DE models as a function of redshift, which requires a significant survey depth $\Delta z \gtrsim 1$." + Radio instruments intended for BAO surveys must thus have large instantaneous field of view (FOV >10 deg) and large bandwidth (Av= 100MHz) to explore large redshift domains.," Radio instruments intended for BAO surveys must thus have large instantaneous field of view (FOV $\gtrsim 10 \, \mathrm{deg^2}$ ) and large bandwidth $\Delta \nu \gtrsim 100 \, \mathrm{MHz}$ ) to explore large redshift domains." + Although the application of 21 cm radio survey to cosmology. i particular LSS mapping has been discussed in length in the framework of large future instruments. such as the SKA (e.g SKA.Science.. Abdalla&Rawlings (2005))). the method envisaged has been mostly through the detection of galaxies as compact sources.," Although the application of 21 cm radio survey to cosmology, in particular LSS mapping has been discussed in length in the framework of large future instruments, such as the SKA (e.g \cite{ska.science}, \cite{abdalla.05}) ), the method envisaged has been mostly through the detection of galaxies as compact sources." + However. extremely large radio telescopes are required to detected sources at cosmological distances.," However, extremely large radio telescopes are required to detected sources at cosmological distances." +" The sensitivity (or detection threshold) limit Sj, for the total power from the two polarisations of a radio instrument characterized by an effective collecting area A. and system temperature 7,,, can be written as where fj, 1s the total integration time and ὃν ts the detection frequency band."," The sensitivity (or detection threshold) limit $S_{lim}$ for the total power from the two polarisations of a radio instrument characterized by an effective collecting area $A$, and system temperature $\Tsys$ can be written as where $t_{int}$ is the total integration time and $\delta \nu$ is the detection frequency band." + In table ] (left) we have computed the sensitivity for 6 different sets of instrument effective area and system temperature. with a total integration time of 86400 seconds (1 day) over a frequency band of 1 MHz.," In table \ref{slims21} (left) we have computed the sensitivity for 6 different sets of instrument effective area and system temperature, with a total integration time of 86400 seconds (1 day) over a frequency band of 1 MHz." +" The width of this frequency band is well adapted to detection of source with an intrinsic velocity dispersion of few 100 km/s. These detection limits should be compared with the expected 21 em brightness S5, of compact sources which can be computed using the expression below (e.g.Binney&Merrifield (1998))) where Mj, is the neutral hydrogen mass. dj(z) Is the luminosity distance and o, is the source velocity dispersion."," The width of this frequency band is well adapted to detection of source with an intrinsic velocity dispersion of few 100 km/s. These detection limits should be compared with the expected 21 cm brightness $S_{21}$ of compact sources which can be computed using the expression below \cite{binney.98}) ): where $ M_{H_I} $ is the neutral hydrogen mass, $\dlum(z)$ is the luminosity distance and $\sigma_v$ is the source velocity dispersion." +" In table 1 (right). we show the 21 em brightness for compact objects with a total mass of IO'""M and an intrinsic velocity dispersion of 200km/s."," In table \ref{slims21} (right), we show the 21 cm brightness for compact objects with a total mass of $10^{10} M_\odot$ and an intrinsic velocity dispersion of $200 \, \mathrm{km/s}$." + The luminosity distance is computed for the standard WMAP universe., The luminosity distance is computed for the standard WMAP universe. + 10?—10'°M.. of neutral gas mass is typical for large galaxies (Lahetal.(2009))., $10^9 - 10^{10} M_\odot$ of neutral gas mass is typical for large galaxies \citep{lah.09}. +. It is clear that detection of sources at cosmological distances would require collecting area in. the range of 109m., It is clear that detection of sources at cosmological distances would require collecting area in the range of $10^6 \mathrm{m^2}$. + Intensity mapping has been suggested as an alternative and economie method to map the 3D distribution of neutral hydrogen by (Changetal.(2008)) and further studied by (Ansarietal.(2008)) (Seoetal(2010))., Intensity mapping has been suggested as an alternative and economic method to map the 3D distribution of neutral hydrogen by \citep{chang.08} and further studied by \citep{ansari.08} \citep{seo.10}. +. In this approach. sky brightness map with angular resolution ~10—30are.min is made for a wide range of frequencies.," In this approach, sky brightness map with angular resolution $\sim 10-30 \, \mathrm{arc.min}$ is made for a wide range of frequencies." + Each 3D pixel (2 angles 6. frequency v or wavelength .t) would correspond to a cell with a volume of -10Mpe?. containing ten to hundred galaxies and a total mass ~107M4.," Each 3D pixel (2 angles $\vec{\Theta}$, frequency $\nu$ or wavelength $\lambda$ ) would correspond to a cell with a volume of $\sim 10^3 \mathrm{Mpc^3}$, containing ten to hundred galaxies and a total mass $ \sim 10^{12} M_\odot$." + If we neglect local velocities relative to the Hubble flow. the observed frequency v would be translated to the emission redshift z through the well known relation: The large scale distribution of the neutral hydrogen. down to angular scales of ~IOare.min can then be observed without the detection of individual compact sources. using the set of sky brightness map as a function of frequency (3D-brightness map) Bx (O.2).," If we neglect local velocities relative to the Hubble flow, the observed frequency $\nu$ would be translated to the emission redshift $z$ through the well known relation: The large scale distribution of the neutral hydrogen, down to angular scales of $\sim 10 \mathrm{arc.min}$ can then be observed without the detection of individual compact sources, using the set of sky brightness map as a function of frequency (3D-brightness map) $B_{21}(\vec{\Theta},\lambda)$ ." +" The sky brightness B», (radiation power/unit solid angle/unit surface/unit frequency) can be converted to brightness temperature using the well known black body Rayleigh-Jeans approximation: In the absence of any foreground or background radiation. the brightness temperature for a given direction and wavelength T,(O.EN1) would be proportional to the local number density nj(À.5) through the relation: whereAs=2.851076ss""! (Lang(1999)) is the spontaneous 2] cem emission coeflicient. /7 is the Planck"," The sky brightness $B_{21}$ (radiation power/unit solid angle/unit surface/unit frequency) can be converted to brightness temperature using the well known black body Rayleigh-Jeans approximation: In the absence of any foreground or background radiation, the brightness temperature for a given direction and wavelength $\TTlam$ would be proportional to the local number density $\etaHI(\vec{\Theta},z)$ through the relation: where$A_{21}=2.85 \, 10^{-15} \mathrm{s^{-1}}$ \citep{astroformul} is the spontaneous 21 cm emission coefficient, $h$ is the Planck" +comprise à minimum of 20 ents (mean EPIC/pn spectrum: 30 ents).,comprise a minimum of 20 cnts (mean EPIC/pn spectrum: 30 cnts). + Photon arrival times were corrected to the barycenter of the solar system via the task., Photon arrival times were corrected to the barycenter of the solar system via the task. + In the soft energy regime below kkeV. where the calibration is known to be least precise (??).. we use the isolated neutron star to calibrate the EPIC spectra.," In the soft energy regime below keV, where the calibration is known to be least precise , we use the isolated neutron star to calibrate the EPIC spectra." + JJ1856.4—3754 was established as a low-energy calibration target for missions such as Chandra. Suzaku. Swift. and and exhibits a high soft X-ray and low optical flux.," $-$ 3754 was established as a low-energy calibration target for missions such as Chandra, Suzaku, Swift, and and exhibits a high soft X-ray and low optical flux." + Its spectrum is free from prominent line features and described well by two black bodies(?)., Its spectrum is free from prominent line features and described well by two black bodies. +. We compare archival XMM-Newton EPIC data of RXJJ1856.4—3754. which span more than five years. with the nodel spectra of and carefully adjust the instrumental effective areas.," We compare archival XMM-Newton EPIC data of $-$ 3754, which span more than five years, with the model spectra of and carefully adjust the instrumental effective areas." + In this approach. we assume that the energy redistribution is independent of the incident energy when considering only objects with very soft X-ray spectra.," In this approach, we assume that the energy redistribution is independent of the incident energy when considering only objects with very soft X-ray spectra." + The discrepancies between data and model remain mostly below 556. with larger excesses up to 20% for EPIC/MOS2.," The discrepancies between data and model remain mostly below $5\,\%$, with larger excesses up to $20\,\%$ for EPIC/MOS2." + A first XMM-Newton observation of AI Tri on August 15. 2005 in the same configuration as described above resulted in partially corrupteddata (observation ID 0306840901) due to technical problems.," A first XMM-Newton observation of AI Tri on August 15, 2005 in the same configuration as described above resulted in partially corrupted data (observation ID 0306840901) due to technical problems." + During 1.1 to kksec (0.3 to hhrs). EPIC. RGS (Ist order). and OM data are usable.," During 1.1 to ksec (0.3 to hrs), EPIC, RGS (1st order), and OM data are usable." + We apply the same data reduction steps as applied to the data acquired on August 22. 2005.," We apply the same data reduction steps as applied to the data acquired on August 22, 2005." + With peak count rates of 21etss! collected by EPIC/pn and l.4etss! by the RGS detectors. the source flux was considerably higher than one week later.," With peak count rates of $21\,\mathrm{cts\,s}^{-1}$ collected by EPIC/pn and $1.4\,\mathrm{cts\,s}^{-1}$ by the RGS detectors, the source flux was considerably higher than one week later." + Therefore. we extended the EPIC/pn aperture to aaresec. excising the innermost aarcsec.," Therefore, we extended the EPIC/pn aperture to arcsec, excising the innermost arcsec." + The EPIC spectra were rebinned to at least 20 counts per bin., The EPIC spectra were rebinned to at least 20 counts per bin. + In addition. we used unpublished ROSAT archival. data obtained between January 15 and February 5. 1998 with the HRI detector.," In addition, we used unpublished ROSAT archival data obtained between January 15 and February 5, 1998 with the HRI detector." + The total integration time of kksec hhrs) consisted. of nine observation intervals., The total integration time of ksec hrs) consisted of nine observation intervals. + The individual light curves were extracted with standard tasks of the software packages. corrected to the barycenter. and combined to à common light curve profile.," The individual light curves were extracted with standard tasks of the software packages, corrected to the barycenter, and combined to a common light curve profile." + At the Gótttüngen SOcem. the Potsdam 70cem. the Monet//North (Texas) 1.2mm. and the Tübbingen 80cem telescopes. we carried out optical V-band and white-light," At the Götttingen cm, the Potsdam cm, the /North (Texas) m, and the Tübbingen cm telescopes, we carried out optical $V\!$ -band and white-light" +hat both ideuti&catious of Vil with X99 aud V22 with X119 are due to chance is nou-neslieible.,that both identifications of 1 with 9 and 2 with 19 are due to chance is non-negligible. + For the noment we conclude that our suggested ideutifications are yosstble. bu not secure.," For the moment we conclude that our suggested identifications are possible, but not secure." + If we asstune that 11 and 22 mav be ideutifiec with X99 aud 119. respectively. we learn from Fie.," If we assume that 1 and 2 may be identified with 9 and 19, respectively, we learn from Fig." + 1 hat their ratio of N-rav to optical flux is rather biel if hey are cataclysmic variables. but as expected for soft X-rav transicuts in quiescence.," \ref{fcvs} that their ratio of X-ray to optical flux is rather high if they are cataclysmic variables, but as expected for soft X-ray transients in quiescence." + The X-ray couutrates of the cataclysunic variables in Fig., The X-ray countrates of the cataclysmic variables in Fig. + Lo have not been correctec or interstellar absorption: the correction is expected to ve staal for most svstenis. but not necessarily for all.," \ref{fcvs} + have not been corrected for interstellar absorption; the correction is expected to be small for most systems, but not necessarily for all." + For ypical X-ray spectra of cataclysimic variables. the vista Hux is affected more stronely by interstellar absorption han the N-vay couutrate. aud thus it is not expecte hat correction for absorption will increase the ratio of X-rav to optical flux for cataclysmic variables.," For typical X-ray spectra of cataclysmic variables, the visual flux is affected more strongly by interstellar absorption than the X-ray countrate, and thus it is not expected that correction for absorption will increase the ratio of X-ray to optical flux for cataclysmic variables." + We conclude hat Fig., We conclude that Fig. + L provides another illustration of he argument originally made bv Verbunt et al. (, \ref{fcvs} provides another illustration of the argument originally made by Verbunt et al. ( +1981) tha sole of he dim N-vay sources in the cores of elobular clusters are oo bright to be cataclvsiuic variables.,1984) that some of the dim X-ray sources in the cores of globular clusters are too bright to be cataclysmic variables. + The N-rav flux of 99 is variable: that of 119 may or nay not be variable., The X-ray flux of 9 is variable; that of 19 may or may not be variable. + The range of variability iu 99 is not unprecedented im soft X-ray trausieuts in quiescence: the variatious im the flux of Cen N- bin quiescence. reported by Campana et (01997) aud shown iu Fie. L.," The range of variability in 9 is not unprecedented in soft X-ray transients in quiescence: the variations in the flux of Cen X-4 in quiescence, reported by Campana et (1997) and shown in Fig. \ref{fcvs}," + is of a simular uaenuitude as that observed iu X99., is of a similar magnitude as that observed in 9. + Such variations iu a quiescent soft N-rav transicut are not expected to be accompanied bv detectable optical variations. and thus he absence of optical variation in nuueed not be in couflic with the suegeestedOO identification.," Such variations in a quiescent soft X-ray transient are not expected to be accompanied by detectable optical variations, and thus the absence of optical variation in need not be in conflict with the suggested identification." + I may be voted that simular variations in the N-rav flux without acconmpanuving variations in the optical are probably also oossible in cataclysmic variables., It may be noted that similar variations in the X-ray flux without accompanying variations in the optical are probably also possible in cataclysmic variables. + For example. the dwarf Ίωνα VW. πα was brighter in quiescence when observed with ROSAT in Nov 1990 than when observed with ENOSAT several vears earlier (Wheatley et 11996. heir Fie.," For example, the dwarf nova VW Hyi was brighter in quiescence when observed with ROSAT in Nov 1990 than when observed with EXOSAT several years earlier (Wheatley et 1996, their Fig." + 22 has been detected at a level about £ magnitudes above its quicsceut level twice: this magnitude difference Is more duclicative of a dwarf nova than of a soft N-rav transient. as noted by Paresce DDe Marchi (1991) and by Shara et ((1996).," 2 has been detected at a level about 4 magnitudes above its quiescent level twice; this magnitude difference is more indicative of a dwarf nova than of a soft X-ray transient, as noted by Paresce De Marchi (1994) and by Shara et (1996)." + The two coustaut N-rayv sources X55 aud N77 in the core of hhave no sueeested optical counterparts., The two constant X-ray sources 5 and 7 in the core of have no suggested optical counterparts. + The level aud the constancy of their N-rav fluxes are compatible with them beius radio pulsars., The level and the constancy of their X-ray fluxes are compatible with them being radio pulsars. + For example. 15212[ in globular cluster M28 aud J0218|1232. at comparable distances as ((5.5 and 5.7 kpe. respectively compared to 1.6 kpc for Tuc). have ROSAT PSPC couutrates of the same order of imaeuitude as X55 aud N77.," For example, $\,$ $\,1821-24$ in globular cluster $\,$ 28 and $\,$ $\,0218+4232$, at comparable distances as (5.5 and $>$ 5.7 kpc, respectively compared to 4.6 kpc for ), have ROSAT PSPC countrates of the same order of magnitude as 5 and 7." + Whether X55 or TT. or any of the four X-ray sources just outside the core. cau be ideutifiec with any of the 11 radio pulsars in aawaits further study of the radio pulsus. m particular determination of their positfious. and of their period derivatives (so hat the N-rav data cau be folded. on a known period).," Whether 5 or 7, or any of the four X-ray sources just outside the core, can be identified with any of the 11 radio pulsars in awaits further study of the radio pulsars, in particular determination of their positions, and of their period derivatives (so that the X-ray data can be folded on a known period)." + More accurate pinpoiuting of the N-rav positions will be possible with ANAF., More accurate pinpointing of the X-ray positions will be possible with AXAF. + Considering the large nubers ofpotential optical counterparts. optical or ultraviolet monitoring of the iuncr region of ssluultanecous with the N-ray observations would be very useful. as detection of sinultaneous N-rav and optical variability would streughteu auv identification based ou )ositional coincidence ouly.," Considering the large numbers of potential optical counterparts, optical or ultraviolet monitoring of the inner region of simultaneous with the X-ray observations would be very useful, as detection of simultaneous X-ray and optical variability would strenghten any identification based on positional coincidence only." + To summarize. we find possible optical counterparts or three of the five N-rav sources in the core ofTuc.. nit note that all could be chance positional coincideuces.," To summarize, we find possible optical counterparts for three of the five X-ray sources in the core of, but note that all could be chance positional coincidences." + The N-rav lIuninuosities of 55. 77 and X99 are rather Πο] for these to be cataclvsimie variables. but compatible with soft A-rav trausicuts in quiescence.," The X-ray luminosities of 5, 7 and 9 are rather high for these to be cataclysmic variables, but compatible with soft X-ray transients in quiescence." + 99 is a variable A-rayv source. and its X-ray to optical flux ratio suggests hat it is a soft N-rav transient. hitherto always observed in quiescence.," 9 is a variable X-ray source, and its X-ray to optical flux ratio suggests that it is a soft X-ray transient, hitherto always observed in quiescence." + The steadier sources X55 and X77 wav © either soft A-ray trausieuts or recveled radio pulsars., The steadier sources 5 and 7 may be either soft X-ray transients or recycled radio pulsars. +" The sources 119 im the core. and Ll. X66. 111 aud X113. outside but near the core. have X-ray Ihuniuosities Lx< dUTerg/s. compatible with them being sot Nouv trausicuts. cataclvsimic variables. or recveled radio mulsars,"," The sources 19 in the core, and 4, 6, 11 and 13, outside but near the core, have X-ray luminosities $L_{\rm X}<10^{32}$ erg/s, compatible with them being soft X-ray transients, cataclysmic variables, or recycled radio pulsars." + If 22 is indeed a cataclysinic variable. it is probably the best candidate counterpart hitherto sugeested for au source in Tuc..," If 2 is indeed a cataclysmic variable, it is probably the best candidate counterpart hitherto suggested for an X-ray source in ." +Asano.Ix.. Kobavashi. 5. 2002. in preparation.,"Asano,K., Kobayashi, S. 2002, in preparation." + Deloborodov.A.M. 2000. ApJ. 539. Deloborodov.A.M.. Stern.D.E. Svensson.R. 2000. ApJ. 535. Fenimore.E.. Ramirez-Raiz. E. 2000. Submitted to ApJ. Frail. D. 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Woosley,S. 1999, ApJ, 524, Mésszárros, P., Rees,M.J. 2000 ApJ, 530," +Now let us consider a different question ancl compare seven different simulations. in each of which one of the above seven configurations is present.,"Now let us consider a different question and compare seven different simulations, in each of which one of the above seven configurations is present." + Since now the scaling can be applied independentIy to each of the configurations. in order to compare these cases between them we need. to use the weighted: versions of the AZSE definition and softening.," Since now the scaling can be applied independently to each of the configurations, in order to compare these cases between them we need to use the weighted versions of the $MASE$ definition and softening." + Since the total mass of all the configurations is the same. the only factor that is changing from one configuration to another is the half mass radius. which takes respectively the values 0.13. 0.14. 0.18. 0.45. 0.97. 1.18 ancl 1.30.," Since the total mass of all the configurations is the same, the only factor that is changing from one configuration to another is the half mass radius, which takes respectively the values 0.13, 0.14, 0.18, 0.45, 0.97, 1.18 and 1.30." + Now the result of the least cleonse (ep= 1) and most dense (ep= 0.1) configuration are of course identical., Now the result of the least dense $a_P=1$ ) and most dense $a_P=0.1$ ) configuration are of course identical. + This simply reflects the fact that the densest Plummer sphere can be represented as well as the least dense one. provided one uses appropriately weighted: softening values.," This simply reflects the fact that the densest Plummer sphere can be represented as well as the least dense one, provided one uses appropriately weighted softening values." +" This is clear also also. [rom Figure 4. which shows AZ.1S45,, and cop) as a function of the percentage of mass in the least. dense component.", This is clear also also from Figure \ref{twoplum_eps2} which shows $MASE_{opt}$ and $\epsilon_{opt}$ as a function of the percentage of mass in the least dense component. + ‘This ligureD also shows that. from the configurations5 analysed here. the largest error corresponds to the case with of the particles in the more concentrated Plummer sphere.," This figure also shows that, from the configurations analysed here, the largest error corresponds to the case with of the particles in the more concentrated Plummer sphere." +" Εις is also the configuration for which c, is mininium.", This is also the configuration for which $\epsilon_{opt}$ is minimum. + We have so far considered the case of a Plummer sphere. a mass distribution Lrequenthy used in astrophivsies.," We have so far considered the case of a Plummer sphere, a mass distribution frequently used in astrophysics." + In this section we will consider two other censity distributions. a truncated homogeneous sphere anc a Dehnen sphere (Dehnen 1993).," In this section we will consider two other density distributions, a truncated homogeneous sphere and a Dehnen sphere (Dehnen 1993)." +" The former is less centrally concentrated than the Plummer sphere and the latter more. so that. by comparing the respective AZLSFE or ALASL we can test the οσοι of central concentration on the optimal « and on the corresponding accuracy,"," The former is less centrally concentrated than the Plummer sphere and the latter more, so that by comparing the respective $MISE$ or $MASE$ we can test the effect of central concentration on the optimal $\epsilon$ and on the corresponding accuracy." + Since both Plummer aud. Dehnen spheres extend to infinity. we have introduced in both cases a cut-olf radius. taken so that the mass within that radius is equal to 0.999 times the total mass.," Since both Plummer and Dehnen spheres extend to infinity, we have introduced in both cases a cut-off radius, taken so that the mass within that radius is equal to 0.999 times the total mass." + The density profile of the homogeneous sphere is where 2 is its outer racius anc Ady its total mass., The density profile of the homogeneous sphere is where $R$ is its outer radius and $M_T$ its total mass. + For the Dehnen sphere we have, For the Dehnen sphere we have +the larger database it now becomes evident that this relation represents an averaged approximation to the X-ray efficiency rather than a fixed correlation.,the larger database it now becomes evident that this relation represents an averaged approximation to the X-ray efficiency rather than a fixed correlation. + This was already suggested by Becker Triimmper (1997) and may be due to the fact that ROSAT with its limited sensitivity was able to detect essentially only the brightest pulsars., This was already suggested by Becker Trümmper (1997) and may be due to the fact that ROSAT with its limited sensitivity was able to detect essentially only the brightest pulsars. + With the higher sensitivity of XMM-Newton and Chandra more faint pulsars could be detected in which e.g. the orientation of their magnetic/rotational axes to the observers line of sight might not have been optimal., With the higher sensitivity of XMM-Newton and Chandra more faint pulsars could be detected in which e.g. the orientation of their magnetic/rotational axes to the observers line of sight might not have been optimal. +" As no beaming correction can be applied to the observed luminosities the X-ray efficiency of those pulsars appears to be smaller, even though their spin-down energy might be comparable to more efficient emitters."," As no beaming correction can be applied to the observed luminosities the X-ray efficiency of those pulsars appears to be smaller, even though their spin-down energy might be comparable to more efficient emitters." + As far as the X-ray efficiency trom the globular cluster millisecond pulsars is concerned it can be seen from Figure 19 that their X-ray luminosities are well within the scatter of other data points at this spin-down energy level., As far as the X-ray efficiency from the globular cluster millisecond pulsars is concerned it can be seen from Figure \ref{figure19} that their X-ray luminosities are well within the scatter of other data points at this spin-down energy level. + Within the uncertainties of the deduced X-ray luminosities it is therefore not justified to conclude that these pulsars have an X-ray efficiency which is different from the one observed for c.g. field millisecond pulsars., Within the uncertainties of the deduced X-ray luminosities it is therefore not justified to conclude that these pulsars have an X-ray efficiency which is different from the one observed for e.g. field millisecond pulsars. + Millisecond pulsars in the galactie plane and in globular clusters thus appear to show no distinet differences in their X-ray emission propertics., Millisecond pulsars in the galactic plane and in globular clusters thus appear to show no distinct differences in their X-ray emission properties. +During the last decade there has been an increasing observational effort to understand the nature of the HCN emission from galaxies.,During the last decade there has been an increasing observational effort to understand the nature of the HCN emission from galaxies. + This includes studies of HCN emission in nearby AGN and starbursts (Kohnoetal..2001;Kohno.2005:Kohnoetal.2008;Krips2007.2008) às well as luminous and ultraluminous galaxies (Graciá-Carpioetal..2006. 2008).," This includes studies of HCN emission in nearby AGN and starbursts \citep{koh01,koh05,koh08,kri07,kri08} as well as luminous and ultraluminous galaxies \citep{gra06,gra08}." +". One result is that HCN line emission is enhanced with respect to CO in at least some AGN compared with starbursts (Kohno,2005;Kohnoetal..2008)."," One result is that HCN line emission is enhanced with respect to CO in at least some AGN compared with starbursts \citep{koh05,koh08}." +. The high HCN/CO intensity ratios could be due to high molecular gas densities near the AGN. and/or high HCN/CO abundance ratios that might be due to elevated X-ray tonisation and heating rates near the accreting black holes.," The high HCN/CO intensity ratios could be due to high molecular gas densities near the AGN, and/or high HCN/CO abundance ratios that might be due to elevated X-ray ionisation and heating rates near the accreting black holes." + For example. in an early study. Sternbergetal.(1994) concluded that the large HCN/CO intensity ratio observed in the nuclear (<100 pe) region in the Seyfert-2 galaxy NGC 1068 indicates a high HCN/CO abundance ratio ~1077 near the AGN.," For example, in an early study, \cite{ste94} concluded that the large HCN/CO intensity ratio observed in the nuclear $< 100$ pc) region in the Seyfert-2 galaxy NGC 1068 indicates a high HCN/CO abundance ratio $\sim 10^{-2}$ near the AGN." + Lepp&Dalgarno(1996) and Useroetal.(2004) argued that elevated HCN/CO abundance ratios are signatures of high X-ray tonisation rates (Maloneyetal..1996;Metjerink&Spaans.2005:BogerSternberg.2005:Meijerinketal. 2007).," \cite{lep96} and \cite{use04} argued that elevated HCN/CO abundance ratios are signatures of high X-ray ionisation rates \citep{mal96,mei05,bog05,mei07}." +. High gas densities also likely play a role in boosting the HCN line intensity (Kripsetal.. 2008)., High gas densities also likely play a role in boosting the HCN line intensity \citep{kri08}. +. In this paper we present high resolution observations of CO (2-1) and HCN (1-0) rotational line emissions in. the inner regions of 33227. à nearby (D=17MMpe: Ι”- ppc) Seyfert galaxy for which detailed studies have been made of the stellar (Daviesetal..2006.2007) and gaseous (Schinnereretal..2000:Hicks2009) content of its central regions.," In this paper we present high resolution observations of CO (2-1) and HCN (1-0) rotational line emissions in the inner regions of 3227, a nearby Mpc; $\sim$ pc) Seyfert galaxy for which detailed studies have been made of the stellar \citep{dav06,dav07} and gaseous \citep{sch00,hic09} content of its central regions." + We analyze the data using large-velocity-gradient (LVG) computations., We analyze the data using large-velocity-gradient (LVG) computations. + For this galaxy we again find a significant enhancement in the HCN/CO intensity ratio close to the active nucleus., For this galaxy we again find a significant enhancement in the HCN/CO intensity ratio close to the active nucleus. + The observed nuclear intensity ratio is consistent with optically thick thermalized emission in dense (=10° em) gas., The observed nuclear intensity ratio is consistent with optically thick thermalized emission in dense $\gtrsim 10^5$ $^{-3}$ ) gas. + Alternatively. and especially in comparison with similar data in NGC 1068 and NGC 6951. the nuclear emissions could be tracing optically thinner emission m which the HCN/CO abundance ratio is large.," Alternatively, and especially in comparison with similar data in NGC 1068 and NGC 6951, the nuclear emissions could be tracing optically thinner emission in which the HCN/CO abundance ratio is large." + The analysis in this paper is based on subaresecond resolution observations of the CO(2-1) 230.5GGHz and HCN(I-0) GGHz lines., The analysis in this paper is based on subarcsecond resolution observations of the CO(2-1) GHz and HCN(1-0) GHz lines. +" The CO(2-1) data. for which the beam ts0.6"".. were previously presented by Schinnereretal.(2000)."," The CO(2-1) data, for which the beam is, were previously presented by \cite{sch00}." +" New 3mmm HCN(1-0) data. with a 0.9"" bbeam. were obtained during February 2009 in the A configuration mm baseline) of the six 15-meter antennas of the IRAM Plateau de Bure Interferometer."," New mm HCN(1-0) data, with a $\times$ beam, were obtained during February 2009 in the A configuration m baseline) of the six 15-meter antennas of the IRAM Plateau de Bure Interferometer." + The HCN(I- 0) line at GGHz and the HCN(I-0) line at GGHz were observed together. using a single polarisation. for each GGHz bandwidth segment.," The $^{12}$ CN(1-0) line at GHz and the $^{13}$ CN(1-0) line at GHz were observed together, using a single polarisation for each GHz bandwidth segment." + The system temperature was KK. Atmospheric conditions were moderate. with winds and ~ Smmm precipitable water vapour.," The system temperature was K. Atmospheric conditions were moderate, with winds and $\sim5$ mm precipitable water vapour." + Phase and amplitude variations were calibrated out by interleaving reference observations of standard calibration sources., Phase and amplitude variations were calibrated out by interleaving reference observations of standard calibration sources. + The data were processed and calibrated using the CLIC program in the IRAM GILDAS package. and binned spectrally to a resolution of 50kkm7! to increase the signal to noise.," The data were processed and calibrated using the CLIC program in the IRAM GILDAS package, and binned spectrally to a resolution of $^{-1}$ to increase the signal to noise." + The kinematics of the HCN(1-0) line emission in 33227 are analysed by Sanietal.(2011) together with several other galaxies., The kinematics of the HCN(1-0) line emission in 3227 are analysed by \cite{san11} together with several other galaxies. + It is remarkable that despite the similar beam sizes. the CO(2-1) map clearly shows the cireumnuelear ring at a radius of ppe (1.7. while the HCN map shows emission from only the central region. within a few tens of parsecs from the nucleus.," It is remarkable that despite the similar beam sizes, the CO(2-1) map clearly shows the circumnuclear ring at a radius of pc ), while the HCN map shows emission from only the central region, within a few tens of parsecs from the nucleus." + This can be seen clearly in Fig., This can be seen clearly in Fig. + | and is reflected in the line fluxes given in Table. 1l.., \ref{fig:obs} and is reflected in the line fluxes given in Table. \ref{tab:data}. +" In the nuclear region. which we define here to be the central (ie. r<4O ppc). the flux ratio is Frcsico/Fcos-4120.11: on the other hand in the circumnuclear ring. for which we take an annulus2—4"".. we find Fyj¢-a)—o/Feo2_)=0.01. an order of magnitude less."," In the nuclear region, which we define here to be the central (i.e. $r<40$ pc), the flux ratio is $_{HCN1-0}$ $_{CO2-1}$ =0.11; on the other hand in the circumnuclear ring, for which we take an annulus, we find $_{HCN1-0}$ $_{CO2-1}$ =0.01, an order of magnitude less." + Since the emission Is spatially resolved in both cases. this difference cannot be due to differing beam dilution effects.," Since the emission is spatially resolved in both cases, this difference cannot be due to differing beam dilution effects." + Instead it is likely to be due to differences in either molecular abundance — e.g.. as a result of a distance dependent X-ray tonisation rate — or differences in excitation efficiencies — e.g.. due to higher nuclear gas densities favoring HCN. (," Instead it is likely to be due to differences in either molecular abundance – e.g., as a result of a distance dependent X-ray ionisation rate – or differences in excitation efficiencies – e.g., due to higher nuclear gas densities favoring HCN. (" +The,The +"we choose to centre the flux ring along the separator (alr. =y.2,0) ancl take the parameters ¢= 1/2. /21 and by=20 giving the particular [Iux ring We add this flix ring to the potential field in à smooth manner. (aking a time evolution satisfving Faradays law. Specifically we set with 7=1 so that the time evolution takes place in 04x1. (","we choose to centre the flux ring along the separator (at $x_{c}=y_{c}=z_{c}=0$ ) and take the parameters $a=1/2$ , $l=1$ and $b_{1}=20$ giving the particular flux ring We add this flux ring to the potential field in a smooth manner, taking a time evolution satisfying Faraday's law, Specifically we set with $\tau=1$ so that the time evolution takes place in $0 \leq t \leq 1$. (" +Note that the gradient of a scalar could also be added to the electric field which could allow for the superimposition of a stationary ideal How.,Note that the gradient of a scalar could also be added to the electric field which could allow for the superimposition of a stationary ideal flow. + We have. for simplicity. neglected this possibility.)," We have, for simplicity, neglected this possibility.)" + Similar evolutions can be obtained for the addition of the more general [αν ring to the potential field(2)., Similar evolutions can be obtained for the addition of the more general flux ring to the potential field. +. The addition of the magnetic flux ring creates a localised region of twist in the centre of the domain and we now wish (o determine whether and how the magnetic field topology is changed., The addition of the magnetic flux ring creates a localised region of twist in the centre of the domain and we now wish to determine whether and how the magnetic field topology is changed. + In order to do so first notce that the flux ring is sufficiently. localised that the magnetic field at the null points remains unchanged during the time evolution., In order to do so first notice that the flux ring is sufficiently localised that the magnetic field at the null points remains unchanged during the time evolution. + Accordingly for each magnetic null point we may (race magnetic field lines in the fan surface in the neighbourhood of (he null point and out into the volume., Accordingly for each magnetic null point we may trace magnetic field lines in the fan surface in the neighbourhood of the null point and out into the volume. + This method allows us (o determine how the fan surfaces are deformed by the reconnection and to locate any intersections of these surfaces. ie. separators.," This method allows us to determine how the fan surfaces are deformed by the reconnection and to locate any intersections of these surfaces, i.e. separators." + We describe our findings on the field topology in thefollowing section., We describe our findings on the field topology in thefollowing section. + Water molecules play an essential role in the physics and chemistry of the dense interstellar medium (ISM)., Water molecules play an essential role in the physics and chemistry of the dense interstellar medium (ISM). + Water is, Water is +are not populated at room temperature.,are not populated at room temperature. + To make our line lists complete we have inserted all WITRAN lines with an intensity above LxLO7? em/molecule at each temperature., To make our line lists complete we have inserted all HITRAN lines with an intensity above $1\times10^{-22}$ cm/molecule at each temperature. + As some of the observed emission lines are due to these IIETRAN lines. the observed lines have been removed to avoid the same line appearing (wice.," As some of the observed emission lines are due to these HITRAN lines, the observed lines have been removed to avoid the same line appearing twice." + Table G lists the number of lines in each file broken down into added LUTRAN lines and observed lines (the total number of observed lines starts to decrease above 1100 °C because of NII; decomposition in the cell)., Table \ref{tab6} lists the number of lines in each file broken down into added HITRAN lines and observed lines (the total number of observed lines starts to decrease above 1100 $^{\circ}$ C because of $_{3}$ decomposition in the cell). + The consequence of this procedure can be seen [rom a lower state energv plot of the 10007 C* line list (Figure 3))., The consequence of this procedure can be seen from a lower state energy plot of the $^{\circ}$ C line list (Figure \ref{fig8}) ). + The 12 line lists at each temperature have been amaleamatled into one table which is available in a machine readable version online., The 12 line lists at each temperature have been amalgamated into one table which is available in a machine readable version online. + A sample of this final line list forall temperatures is provided in Table 7.., A sample of this final line list forall temperatures is provided in Table \ref{tab7}. . +an iutceration time of 2-3 seconds per sample.,an integration time of 2-3 seconds per sample. + Strips of constant declination were spaced by 37., Strips of constant declination were spaced by $\arcmin$. + Corresponding maps were made by moving the telescope in right ascension to form a “basket weave pattern over the region., Corresponding maps were made by moving the telescope in right ascension to form a `basket weave' pattern over the region. + Total integration time was approximately 58 hours for CVn L {τν hours for NGC 672. and Ll hours for NGC 15.," Total integration time was approximately 58 hours for CVn I, 47 hours for NGC 672, and 41 hours for NGC 45." + Tables 10 through 12. eive a sunnuuw of the observations. iuncludiug the RAIS noise figures.," Tables \ref{canes1obs} through \ref{n45obs} give a summary of the observations, including the RMS noise figures." + The CBT data were reduced. in the standard manner using the GDTIDL and dat: reduction packages., The GBT data were reduced in the standard manner using the GBTIDL and data reduction packages. +" Iu order to match our velocity resolution to the expected linewidths of IIT clouds in the group. spectra were smoothed to a channel spacing of .2L1I kIIz. correspouding⋅⋡ to a velocity∙ resolution∙ of 5.2 Ein sο,"," In order to match our velocity resolution to the expected linewidths of HI clouds in the group, spectra were smoothed to a channel spacing of 24.4 kHz, corresponding to a velocity resolution of 5.2 km $^{-1}$." + A reference spectrmu for cach of the observation sessions was made using an observation of an cuuission-free region. usally roni the map edges.," A reference spectrum for each of the observation sessions was made using an observation of an emission-free region, usually from the map edges." + The reference spectrum was hen used to perform a (signalreference)/refereuce calibration of cach pixel., The reference spectrum was then used to perform a (signal-reference)/reference calibration of each pixel. + The calibrated spectra were scaled by the system temperature. corrected or atmosphere opacity and GBT efficiency.," The calibrated spectra were scaled by the system temperature, corrected for atmospheric opacity and GBT efficiency." + We adopted the GBT efficiency equation (1) roni Laneston&Turner(2007) with a zenith atinospheric opacity 7 = 0.009., We adopted the GBT efficiency equation (1) from \citet{lang07} with a zenith atmospheric opacity $\tau_{0}$ = 0.009. + The frequency. range observed was relatively vee of REL with less than of all spectra adversely affected.," The frequency range observed was relatively free of RFI, with less than of all spectra adversely affected." + The spectra exhibiting RET were identified bv tabulating the RAIS noise level iu channels free of neutral hydrogen ΟΙΒΙΟΙ., The spectra exhibiting RFI were identified by tabulating the RMS noise level in channels free of neutral hydrogen emission. + Spectra that showed lieh RAIS noise across many channels were fagecd aud removed., Spectra that showed high RMS noise across many channels were flagged and removed. + Observations were eridded using the AIPS task SDIAIG. which also averages polavizations.," Observations were gridded using the AIPS task SDIMG, which also averages polarizations." + After amplitude calibration and exidding. a lst-order polvnomial was fit to line-free regions of the spectra and subtracted from the eridded spectra using the AIPS task IMLIN.," After amplitude calibration and gridding, a 1st-order polynomial was fit to line-free regions of the spectra and subtracted from the gridded spectra using the AIPS task IMLIN." + Oulv channels in high uceative velocity ranges. where few or no sources are expected. were used for the fit.," Only channels in high negative velocity ranges, where few or no sources are expected, were used for the fit." +" This simple baseclue fit was extrapolated to the positive velocity ranec. ""where galaxies make a baselime fit unreliable."," This simple baseline fit was extrapolated to the positive velocity range, where galaxies make a baseline fit unreliable." + This baseline velocity range yielded a fat baseline for areas free of strong continmiu radio sources. which is true of the majority of the region.," This baseline velocity range yielded a flat baseline for areas free of strong continuum radio sources, which is true of the majority of the region." + The effective aneular resolution. determined from. maps of 3C286. is 915+0.," The effective angular resolution, determined from maps of 3C286, is $\pm$." +05'.. To couvert to units of flux denusitv. we observed the calibration source 3C286. whose flux deusitv is 157 + 0.91 Jy at 1.1158 νε (Ottetal.199D.," To convert to units of flux density, we observed the calibration source 3C286, whose flux density is 14.57 $\pm$ 0.94 Jy at 1.418 GHz \citep{ott94}." +.. The calibration frou I< to Jv was derived by mapping 3C286 in the sale way that the WI maps were produced., The calibration from K to Jy was derived by mapping 3C286 in the same way that the HI maps were produced. + After all corrections for the GBT cficiency and the inappiug process. the scale factor frou IX/Deuu to Jv/Beam images is 0.13. + 0.03.," After all corrections for the GBT efficiency and the mapping process, the scale factor from K/Beam to Jy/Beam images is 0.43 $\pm$ 0.03." + Exror estimates are difficult to obtain. given the wide range iu RATS2N noisejap valuesowλα overror theB maps.," Error estimates are difficult to obtain, given the wide range in RMS noise values over the maps." +;: However.“OVO the5 dominant error coutribution is the approximately wnecrtainty du the absolute calibration for these observations.," However, the dominant error contribution is the approximately uncertainty in the absolute calibration for these observations." +"rvation The mass detection thresholds were calculated assuming that clouds would be unresolved in the GBT beam, using the relation: where D is the distance in Mpc. σε is the RAIS raise in one channel. AV is the channel width. and N ds the number of chamnels required for a secure detection."," The mass detection thresholds were calculated assuming that clouds would be unresolved in the GBT beam, using the relation: where $D$ is the distance in Mpc, $\sigma_s$ is the RMS noise in one channel, $\Delta V$ is the channel width, and $N$ is the number of channels required for a secure detection." + We required a cloud. candidate ο be visible in at least N=2 chanucls. therefore he lowest velocity width that could be detecte was LO kins .," We required a cloud candidate to be visible in at least $N=2$ channels, therefore the lowest velocity width that could be detected was 10 km $^{-1}$." + Mass detection thresholds are listed im Tables 10 through 12.., Mass detection thresholds are listed in Tables \ref{canes1obs} through \ref{n45obs}. + IIT cloud. candidates were fone by visual iuspection of cach channel of the bascline subtracted spectral line cube., HI cloud candidates were found by visual inspection of each channel of the baseline subtracted spectral line cube. + Cloud. candidates are spatially distinct frou eroup galaxies and tida streams and coherent iu velocity over more than oue chanucl., Cloud candidates are spatially distinct from group galaxies and tidal streams and coherent in velocity over more than one channel. + For each EHI cloud candidate. we produced spectra Gutensity versus velocity) usimg the AIPS task ISPEC.," For each HI cloud candidate, we produced spectra (intensity versus velocity) using the AIPS task ISPEC." + Ow observations cover more than c 700 km πι respect to the systemic velocity of aux eroup galaxy., Our observations cover more than $\pm$ 700 km $^{-1}$ with respect to the systemic velocity of any group galaxy. + Iu principle. this allows us to detect clouds associated with any of the mechauisus that create IIT clouds. all of: which: predict: clouds to be within 300 kins + of the ealaxvs velocity," In principle, this allows us to detect clouds associated with any of the mechanisms that create HI clouds, all of which predict clouds to be within 300 km $^{-1}$ of the galaxy's velocity" +From the previous equations we can extract an important conclusion.,From the previous equations we can extract an important conclusion. + As tvpicallv o15000 K) and electron densities >10"" em? are required to reach emission in this line (2)..", High temperatures $> 15000$ K) and electron densities $> 10^{\rm 14}$ $^{\rm -3}$ are required to reach emission in this line \citep{1983ApJ...271..832F}. + Nanoflare heating has been proposed as the main heating mechanism of the stellar outer atmospheres., Nanoflare heating has been proposed as the main heating mechanism of the stellar outer atmospheres. + The energy distribution of flares has been found to be a power law (22). of the 4N/dE=KE.," The energy distribution of flares has been found to be a power law \citep{1974SoPh...39..155D,1984ApJ...283..421L} of the ${dN}/{dE}=kE^{-\alpha}$." + ? concluded that very weak flares are expected to occur much more frequently than those observed in that work (>0.71 flares/hour). in the sense that the quiescent emission of the UV Ceti-type stars in the upper branch may be the result of à superposition of multiple small flares (named nanoflares) following the distribution law given above.," \cite{2006A&A...452..987C} concluded that very weak flares are expected to occur much more frequently than those observed in that work $> 0.71$ flares/hour), in the sense that the quiescent emission of the UV Ceti-type stars in the upper branch may be the result of a superposition of multiple small flares (named nanoflares) following the distribution law given above." + In this work. we present empirical flux—flux power. law relationships between the most important chromospheric activity indicators for a large sample of main-sequence F. G. K. and T stars.," In this work, we present empirical flux–flux power law relationships between the most important chromospheric activity indicators for a large sample of main-sequence F, G, K, and M stars." + In addition. we obtain relations between X-ray and chromospheric surface fluxes for ditferent chromospheric lines.," In addition, we obtain relations between X-ray and chromospheric surface fluxes for different chromospheric lines." + These new relationships will be useful for comparing classical and oresent/future data of magnetic activity., These new relationships will be useful for comparing classical and present/future data of magnetic activity. + For the first time. we have proved the non-universality of some Hux—flux relations between chromospheric indicators.," For the first time, we have proved the non-universality of some flux–flux relations between chromospheric indicators." + Genera »ower laws hold for the majority of the stars. but some late-K and T dwarf stars deviate from the general trend when He is used as a chromospheric activity diagnostic.," General power laws hold for the majority of the stars, but some late-K and M dwarf stars deviate from the general trend when $\alpha$ is used as a chromospheric activity diagnostic." + We have also contirmec hat this different behaviour persists when X-ray fluxes are usec instead of Ha ones., We have also confirmed that this different behaviour persists when X-ray fluxes are used instead of $\alpha$ ones. + Therefore. late-type stars follow two differen yower law flux-flux relationships when X-raysorHa:are used as Magnetic activity indicators.," Therefore, late-type stars follow two different power law flux–flux relationships when X-raysor$\alpha$are used as magnetic activity indicators." + We have quantitied. for the firs," We have quantified, for the first" +obtained hy Wood et a. (,obtained by Wood et al. ( +1992).,1992). + First. it is not clear wmat is the seuse of a procedure in which oue first fits intensity maps to ecipse curves by using MEM. then. iu a second step. ο1e fits the plavsical paraietcrs to he intensities (ITorue 1993: Vriehuauu 1997).," First, it is not clear what is the sense of a procedure in which one first fits intensity maps to eclipse curves by using MEM, then, in a second step, one fits the physical parameters to the intensities (Horne 1993; Vrielmann 1997)." +" Second. the status of the so-callec ""Physical Parameter Eclipse Mapping? proposed by Vrielinann (1997) is rot well established aud its application to TT Cas produced results which are In coutraclicticn both with Wood et al. ("," Second, the status of the so-called `Physical Parameter Eclipse Mapping' proposed by Vrielmann (1997) is not well established and its application to HT Cas produced results which are in contradiction both with Wood et al. (" +1992) and the fuudamenutal assuniptini of he DIAL.,1992) and the fundamental assumption of the DIM. + lu any case using the SW codo for tιο Physical Parameter Eclio»e Mappiug! would require a prolibitive amouut of computer time., In any case using the SW code for the `Physical Parameter Eclipse Mapping' would require a prohibitive amount of computer time. + We adopted. therefore. a simple aud pragmatic approach aud just red ο find the range of accretion rates and values of t1ο Viscosity paraneter whicen eives the best description of the observed properties of the quiescent disc in WT Cas.," We adopted, therefore, a simple and pragmatic approach and just tried to find the range of accretion rates and values of the viscosity parameter which gives the best description of the observed properties of the quiescent disc in HT Cas." + We used as a guide tlic| total disc colours which are not determine by t1ο AIEM fitting procedure (13t they are model depeideut)., We used as a guide the total disc colours which are not determined by the MEM fitting procedure (but they are model dependent). + We tried ο το]xoduce flux ratios of the U.D.V ane B waveleneths (foldec through baudpaSSCS LOSPOLSC functions of the Sticuning photometer).," We tried to reproduce flux ratios of the U,B,V and R wavelengths (folded through bandpasses response functions of the Stienning photometer)." + This prc)cedure is incdepeicleu oft 10 distance to IIT. Cas., This procedure is independent of the distance to HT Cas. + Tn this wav we fud a rauge of M and a valies which correspond to flux ratios of both the total disc eudsson and the xeconstructed radial distiuilution., In this way we find a range of $\dot M$ and $\alpha$ values which correspond to flux ratios of both the total disc emission and the reconstructed radial distribution. + Our maij adu was to ¢heck if observed properties of the quicsceif cise du IIT Cas are consisteut wit1i the general assunrations of accretion cise models., Our main aim was to check if observed properties of the quiescent disc in HT Cas are consistent with the general assumptions of accretion disc models. + Results of pr'evijous studies (Wood et al., Results of previous studies (Wood et al. + 1992: Vi3eliuaun 1997) wereiu à flagrant contradictioji with the staidard disc model (not only with the DIA so that constraints «)btained on criica teniperatures ec.," 1992; Vrielmann 1997) were in a flagrant contradiction with the standard disc model (not only with the DIM, so that constraints obtained on critical temperatures etc." + do not have much meaniug)., do not have much meaning). +" Tere we tric«d to see if an improved model of the dise vertical structiPO Wan help to recowile models aud oservatioIs,", Here we tried to see if an improved model of the disc vertical structure may help to reconcile models and observations. + The tota cise fluxes in UBVR (whic Lare jus slightly differcut ferua Jcousons standarcds) i LOT Cas are (Woo dot al., The total disc fluxes in UBVR (which are just slightly different form Johnson's standards) in HT Cas are (Wood et al. + 1992): Fr-=0.71d E0.02. Ευ=0.5]=~0.03. FY=0.90.05. Fg=0.8£0.05 (Gn uilijuuskvs).," 1992): $F_U=0.71\pm +0.02$ , $F_B=0.51\pm 0.03$, $F_V=0.5\pm 0.05$, $F_R=0.8 \pm 0.05$ (in millijanskys)." + Clearly the Balmer jump 1s 1n enulss1on uud Fr>Fp.Py confirus that the continue is οuitted by an optically thin ΕΠΕ," Clearly the Balmer jump is in emission and $F_R > F_B, +F_V$ confirms that the continuum is emitted by an optically thin medium." + Ρ lines apparently contribute ~3C to the R enission. but even with this coityibutk)1 subtracted. the R emission is still hie conrpared with fluxes in shorter wavecheths.," Emission lines apparently contribute $\sim 30\%$ to the $R$ emission, but even with this contribution subtracted, the $R$ emission is still high compared with fluxes in shorter wavelengths." + The Huxes eivon above assiunie E(BVy)=0 but since the reddening to TT Cas is not. well decrnüued. we have also used E(5VP)=0.2 which. probarly. is t1ο αμα value alleοι by observatious (Wood et al.," The fluxes given above assume $E(B-V)=0$ but since the reddening to HT Cas is not well determined, we have also used $E(B-V)=0.2$ which, probably, is the maximum value allowed by observations (Wood et al." + 1992)., 1992). +" First. we studied the disc flux ratios at eiven radius as a fuiction o| fhe accretioi rate for a given a,"," First, we studied the disc flux ratios at given radius as a function of the accretion rate for a given $\alpha$." + An example is srown on Fies. (, An example is shown on Figs. ( +2) iux l3) for DRwp.,2) and (3) for $R=5R_{\rm WD}$ . + We asstuned that. the dise effective temperaure is constant. paralcl to the critical effective temperature (we can neglect in Eq.," We assumed that, the disc effective temperature is constant, parallel to the critical effective temperature (we can neglect in Eq." + 3 the weaςdepenucence on R aud a). so that in the disc M~R? (," 3 the weakdependence on $R$ and $\alpha$ ), so that in the disc $\dot M \sim R^3$. (" +Iu what follows we use CR/9Rwp)).,In what follows we use $\dot M = \dot M_0 \left(R/9R_{\rm WD}\right)$ ). + This is a good approximation of the cluperature profiles obtained in the framework of the DIM., This is a good approximation of the temperature profiles obtained in the framework of the DIM. +" Oue cau see that the U fluxes ratios all lave a muiniuu nat accretion rates Mg~10h1016 & &1,", One can see that the U fluxes ratios all have a minimum at accretion rates $\dot M_0 \sim 10^{15}-10^{16} $ g $^{-1}$. + (My ix the accretion rate corresponding to a steady disc. the real aceretion rate iu this case is 7 timeslarger - see 3.1.," $\dot M_0$ is the accretion rate corresponding to a steady disc, the real accretion rate in this case is 7 timeslarger - see 3.1." + Eq., Eq. + 5)., 5). + This feature is aliiost iudepeudeut of the value of a., This feature is almost independent of the value of $\alpha$ . + At, At +redshift. it is important to appreciate that a given redshift corresponds to an cntirely cillerent dynamical epoch in different: cosmologies.,"redshift, it is important to appreciate that a given redshift corresponds to an entirely different dynamical epoch in different cosmologies." +" Given the same Llubble parameter. the age of the Universe is a sensitive function of the cosmic density parameter 8, and even more so of the cosmological constant."," Given the same Hubble parameter, the age of the Universe is a sensitive function of the cosmic density parameter $\Omega_{m}$ and even more so of the cosmological constant." + As for the latter. we have to realize that the change in cosmic time as a function of the cosmological constant is the most important influence of A.," As for the latter, we have to realize that the change in cosmic time as a function of the cosmological constant is the most important influence of $\Lambda$." + To give an appreciation of the dillerences in cosmic time for a given redshift in the different cosmologies. we refer to Table 2..," To give an appreciation of the differences in cosmic time for a given redshift in the different cosmologies, we refer to Table \ref{table:ct}." + We have probed the scaling relations over a range of redshifts from z=4 to z=0 and over a range of cosmic look-back time going from I to 10 Civr., We have probed the scaling relations over a range of redshifts from $z=4$ to $z=0$ and over a range of cosmic look-back time going from $1$ to $10$ Gyr. + The evolution of the fitted scaling parameters as a function of redshift is shown in the left column of Fig. 10.., The evolution of the fitted scaling parameters as a function of redshift is shown in the left column of Fig. \ref{fig:sr_z}. + Phe corresponding evolution as a function of cosmic look-back time can be found in the right hand. column., The corresponding evolution as a function of cosmic look-back time can be found in the right hand column. + The Ixormends parameter e is shown in the top panels. the Faber-Jackson parameter b in the center panels and the EP? parameters e and d in the bottom panels.," The Kormendy parameter $a$ is shown in the top panels, the Faber-Jackson parameter $b$ in the center panels and the FP parameters $c$ and $d$ in the bottom panels." + Each different cosmology is represented by a cillerent linestvle. listed in the insert at the top left hand frame.," Each different cosmology is represented by a different linestyle, listed in the insert at the top left hand frame." + For all cosmologies the evolution of the Kormencly relation is marginal at best., For all cosmologies the evolution of the Kormendy relation is marginal at best. + In the case of the low Ὁ ACDALO2 cosmologv we can not discern anv significant change of the parameter e. (this may. in part be due to the large uncertainties in the calculated parameter resulting from the low number of halos in this simulation).," In the case of the low $\Omega_{m}$ $\Lambda$ CDMO2 cosmology we can not discern any significant change of the parameter $a$, (this may in part be due to the large uncertainties in the calculated parameter resulting from the low number of halos in this simulation)." + In the case of the other cosmologies we find no noticeable change of e before a recishift z2. followed by a mild increase from ezz0.3 to ae025 at zom0.," In the case of the other cosmologies we find no noticeable change of $a$ before a redshift $z\approx 2$, followed by a mild increase from $a \approx 0.3$ to $a\approx 0.38$ at $z \approx 0$." + This is also clearly visible when assessing the evolution in terms of cosmic time. as can be seen in the top right panel.," This is also clearly visible when assessing the evolution in terms of cosmic time, as can be seen in the top right panel." + Evolutionary trends for the Faber-Jackson relation are comparable to that seen in the [Ixormendy. relation., Evolutionary trends for the Faber-Jackson relation are comparable to that seen in the Kormendy relation. + No discernible trends ave found in the open cosmology. while all of the other high density Universes do show a mild decrease from 6ez0.35 at z2 to bzz0.32 at 2&0.," No discernible trends are found in the open cosmology, while all of the other high density Universes do show a mild decrease from $b\approx 0.35$ at $z\approx 2$ to $b\approx 0.32$ at $z \approx 0$." + When assessing in terms of cosmic time (center right panel). we observe a near uniform increase of b over the last S Civr.," When assessing in terms of cosmic time (center right panel), we observe a near uniform increase of $b$ over the last 8 Gyr." + In most studied cosmologies. with the possible exception of the ACDAIO2 cosmology. we find a marginal trend of the Fundamental Plane parameter e to decrease for 2o2. more or less in the past ~ 6-7 Cir.," In most studied cosmologies, with the possible exception of the $\Lambda$ CDMO2 cosmology, we find a marginal trend of the Fundamental Plane parameter $c$ to decrease for $z <2$, more or less in the past $\sim$ 6-7 Gyr." + At earlier epochs such a trend. is entirely. absent., At earlier epochs such a trend is entirely absent. + No significant evolution of the FP parameter d can be observed in Fig. 10.., No significant evolution of the FP parameter $d$ can be observed in Fig. \ref{fig:sr_z}. + o significant evolution has been found for the Fundamental lane parameters e and d (see Fig. 10..," No significant evolution has been found for the Fundamental Plane parameters $c$ and $d$ (see Fig. \ref{fig:sr_z}," + lower panels)., lower panels). + Evolution of the Fundamental Plane mainly concerns. its hickness., Evolution of the Fundamental Plane mainly concerns its thickness. + In Fig., In Fig. + 11 we show the development of the FP thickness as a [function of cosmic expansion factor αν)=τα|2) or four cosmological models. and in Figs.," \ref{fig:spreadcosmo} we show the development of the FP thickness as a function of cosmic expansion factor $a_{exp}(t)=1/(1+z)$ for four cosmological models, and in Figs." + 13. and 12. we show the evolution of the spread of points with the FP as a 'unction of redshift in the ACDAIP2 model., \ref{fig:SCDMplanes} and \ref{fig:Lambdaplanes} we show the evolution of the spread of points with the FP as a function of redshift in the $\Lambda$ CDMF2 model. + We see à systematic increase of FP thickness over the, We see a systematic increase of FP thickness over the +is reported in Fig. 5..,is reported in Fig. \ref{compr-ratio}. +" As expected from the previous considerations, the gas in the WHIM phase has a larger value of the compressive ratio throughout the simulation, with respect to the ICM phase, indicating a higher contribution from compressional modes in filaments and cluster peripheries."," As expected from the previous considerations, the gas in the WHIM phase has a larger value of the compressive ratio throughout the simulation, with respect to the ICM phase, indicating a higher contribution from compressional modes in filaments and cluster peripheries." + A more detailed analysis on the T—6 plane at z=0 (Fig. 6)), A more detailed analysis on the $T-\delta$ plane at $z = 0$ (Fig. \ref{compr-ratio-t-rho}) ) +" shows that the compressive ratio is low at high densities and temperatures (the ICM), while it is significantly higher elsewhere."," shows that the compressive ratio is low at high densities and temperatures (the ICM), while it is significantly higher elsewhere." +" The compressive ratio is particularly high also at the extrema of the overdensity distribution, resulting either from strong rarefactions or compressions."," The compressive ratio is particularly high also at the extrema of the overdensity distribution, resulting either from strong rarefactions or compressions." + A similar conclusion can be drawn from the visual inspection of the projection in Fig. 7::, A similar conclusion can be drawn from the visual inspection of the projection in Fig. \ref{compr-projection}: +" rc is generally lower in clusters, except for localised regions (for example, in the cluster at the centre of the projected volume), likely to be associated with weak shocks in the ICM."," $r_{\rmn{cs}}$ is generally lower in clusters, except for localised regions (for example, in the cluster at the centre of the projected volume), likely to be associated with weak shocks in the ICM." + The role of the turbulence SGS model in our large-scale structure simulations and the consistency of the energy budget in this framework is further investigated with a comparison between the simulation using and an adiabatic reference run., The role of the turbulence SGS model in our large-scale structure simulations and the consistency of the energy budget in this framework is further investigated with a comparison between the simulation using and an adiabatic reference run. +" In these simulations the flow is mostly subsonic, and the energy content of the SGS turbulence is globally almost negligible(?).."," In these simulations the flow is mostly subsonic, and the energy content of the SGS turbulence is globally almost negligible." +" Quantitatively, it means that, for every baryon phase, the sum of kinetic and thermal energy should be approximately equal in the adiabatic and the run (in the latter case, the sum is extended to the SGS turbulent energy)."," Quantitatively, it means that, for every baryon phase, the sum of kinetic and thermal energy should be approximately equal in the adiabatic and the run (in the latter case, the sum is extended to the SGS turbulent energy)." +" In fact, good agreement (mostly within 2%) is found on the global gas properties of WHIM and ICM (mass fractions, energy content and their time evolution)."," In fact, good agreement (mostly within $2\%$ ) is found on the global gas properties of WHIM and ICM (mass fractions, energy content and their time evolution)." +" As a more sensitive diagnostic for the detailed energy budget in the ICM and WHIM, for the different phases we study the evolution of the total energies where ex,; is the value of the specific energy ex in the celli (the index ’k’ refers to eint or et; cf."," As a more sensitive diagnostic for the detailed energy budget in the ICM and WHIM, for the different phases we study the evolution of the total energies where $e_{\rmn{k},i}$ is the value of the specific energy $e_{\rmn{k}}$ in the cell $i$ (the index 'k' refers to $e_{\rmn{int}}$ or $e_{\rmn{t}}$ cf." + Fig. 4)), Fig. \ref{energy-z}) ) + and piV; is the baryon mass in the cell i., and $\rho_i V_i$ is the baryon mass in the cell $i$. +" The sum is performed on the cells belonging to a same baryon phase, either WHIM or ICM."," The sum is performed on the cells belonging to a same baryon phase, either WHIM or ICM." + In Fig., In Fig. +" 8 we compare F4 with AFin, the difference of Ei, between the adiabatic and simulations."," \ref{energy-x-omega} we compare $E_{\rmn{t}}$ with $\Delta E_{\rmn{int}}$, the difference of $E_{\rmn{int}}$ between the adiabatic and simulations." +" In both phases, Fint (not in the plot) is 40 times or more larger than £4."," In both phases, $E_{\rmn{int}}$ (not in the plot) is 40 times or more larger than $E_{\rmn{t}}$." +" We observe that E, and AEi are of the same order of magnitude during the simulation, both for the ICM and WHIM, indicating that the SGS turbulent energy acts as an energy buffer between the resolved and unresolved scales."," We observe that $E_{\rmn{t}}$ and $\Delta E_{\rmn{int}}$ are of the same order of magnitude during the simulation, both for the ICM and WHIM, indicating that the SGS turbulent energy acts as an energy buffer between the resolved and unresolved scales." +" In other words, the global decrease of Ei; in the run is partly balanced by FA, so that the global energy budget is nearly unaffected."," In other words, the global decrease of $E_{\rmn{int}}$ in the run is partly balanced by $E_{\rmn{t}}$, so that the global energy budget is nearly unaffected." +" Further physical interpretations of this energy budget are difficult, because of the high complexity of the flow in cosmological simulations;we refer the reader to to more tests in simplified setups."," Further physical interpretations of this energy budget are difficult, because of the high complexity of the flow in cosmological simulations;we refer the reader to to more tests in simplified setups." +" Another caveat, however,"," Another caveat, however," +in à larger macroscopic scale than the scale of turbulence e&enerated in the accretion disk.,in a larger macroscopic scale than the scale of turbulence generated in the accretion disk. + Such [large scale magnetic field should. be amplified by the aceretion., Such large scale magnetic field should be amplified by the accretion. + The accretion plasma carries the frozen. magnetic. field. into the inner magnetosphere and compresses it., The accretion plasma carries the frozen magnetic field into the inner magnetosphere and compresses it. + Against this process. small but finite resistivity clissipates the magnetic feld.," Against this process, small but finite resistivity dissipates the magnetic field." + Then the saturated level of the magnetic field strength is determined by the equilibrium of the compression ancl the dissipation., Then the saturated level of the magnetic field strength is determined by the equilibrium of the compression and the dissipation. + Unfortunately. this problem has not been solved vet as in the next subsection.," Unfortunately, this problem has not been solved yet as in the next subsection." + Hence we have assumed that Bo depends on the DII mass m like equation (6)) because the accretion rate seems to depen on nm., Hence we have assumed that $B_0$ depends on the BH mass $m$ like equation \ref{eq:B0}) ) because the accretion rate seems to depend on $m$. + Aqmbiguities are still remained. on the estimation of the power of the Us-wheel activity mainly due to the following two reasons., Ambiguities are still remained on the estimation of the power of the fly-wheel activity mainly due to the following two reasons. + The first is due to some theoretical ambiguities of the estimation ofthe magnetic field strength near the DIL., The first is due to some theoretical ambiguities of the estimation of the magnetic field strength near the BH. + The second is ambiguity of the innermost magnetospheric structure of the Bll-aceretion disk: svstems. especially whether the Ποιά lines threading the horizon (or the innermost region of the accretion disk) are open toward the infinity or closed to be loop-like one.," The second is ambiguity of the innermost magnetospheric structure of the BH-accretion disk systems, especially whether the field lines threading the horizon (or the innermost region of the accretion disk) are open toward the infinity or closed to be loop-like one." + The poloidal magnetic field. strength is. traditionally estimated. by an intuition of a principle of equipartition oetween the magnetic energy density and the gravitational one or the thermal one (sec. e$. Shakra Sunvaev. 1973).," The poloidal magnetic field strength is traditionally estimated by an intuition of a principle of equipartition between the magnetic energy density and the gravitational one or the thermal one (see, e.g., Shakra Sunyaev 1973)." + tecent numerical studies based. on nonlinear evolutionary oocess Of the resistive MIID. seem to support. the result rom the equipartition., Recent numerical studies based on nonlinear evolutionary process of the resistive MHD seem to support the result from the equipartition. + For example. Matsumoto ct al. (," For example, Matsumoto et al. (" +1997) conclude that predominantly toroidal magnetic field is amplified by a differential rotation of the disk and the asma «ναμις of 3~10 can be achieved.,1997) conclude that predominantly toroidal magnetic field is amplified by a differential rotation of the disk and the plasma $\beta$ -value of $\beta \sim 10$ can be achieved. +" LE there is significant magnitude of the poloidal magnetic field. the saturation level will be more large and 3~1 might be achieved,"," If there is significant magnitude of the poloidal magnetic field, the saturation level will be more large and $\beta \sim 1$ might be achieved." + While this conjecture of equipartition is now widely accepted. there is still room for a disagreement about his point.," While this conjecture of equipartition is now widely accepted, there is still room for a disagreement about this point." + Recently Livio ct al. (, Recently Livio et al. ( +1999) critically assess he efliciency of the Blancforcd-Znajek (BZ) process (the magnetically dominated. case of the BIL Uv-wheel niceim comparing with other disk activities.,1999) critically assess the efficiency of the Blandford-Znajek (BZ) process (the magnetically dominated case of the BH fly-wheel model) comparing with other disk activities. + They. reconsider the 101 strength in the innermost region οἱ DlI-disk svstem., They reconsider the field strength in the innermost region of BH-disk system. + In their result. power of the BZ process is dominated. by he Ενος or the fuel (viscous heating) power of the innermost region of the accretion disk.," In their result, power of the BZ process is dominated by the fly-wheel or the fuel (viscous heating) power of the innermost region of the accretion disk." + “Phe problem of the saturated strength. of the poloidal magnetic field is still an open question., The problem of the saturated strength of the poloidal magnetic field is still an open question. + llowever we should note that the energetics of the ]|v-wheel process depend not only on the strength. of he magnetic field. but. also on the inner magnetospheric structure of the DIH-cdisκ svstenis., However we should note that the energetics of the fly-wheel process depend not only on the strength of the magnetic field but also on the inner magnetospheric structure of the BH-disk systems. + The extracted Povnting enerey [lux due to the Dv-wheel process is carried along the xoloidal magnetic field lines. and. will be converted to the kinetic energy of plasma outflow at some distant region from he horizon.," The extracted Poynting energy flux due to the fly-wheel process is carried along the poloidal magnetic field lines, and will be converted to the kinetic energy of plasma outflow at some distant region from the horizon." + Hence only open magnetic field lines can take place to the energy extraction toward. very distant. region., Hence only open magnetic field lines can take place to the energy extraction toward very distant region. + For example. Nitta ct al. (," For example, Nitta et al. (" +1991). give schematic Ligure for the innermost magnetospheric structure (see figure 3 of that paper).,1991) give schematic figure for the innermost magnetospheric structure (see figure 3 of that paper). + In their result. the magnetic field lines connecting to the innermost region of the disk are closed. (à. loop-like structure connecting the DII and the disk). and do not contribute to the energy. extraction.," In their result, the magnetic field lines connecting to the innermost region of the disk are closed (a loop-like structure connecting the BH and the disk), and do not contribute to the energy extraction." + Open field. lines. are emanated [from a high. latitude region of the DII and the outer part of the disk., Open field lines are emanated from a high latitude region of the BH and the outer part of the disk. + In this case. the discussion of Livio et al. (," In this case, the discussion of Livio et al. (" +1999) should be altered.,1999) should be altered. + Thus cllicieney of the. Ενπου process is. closely combined with πο disk dynamo process anc the magnetospheric structure of the innermost region., Thus efficiency of the fly-wheel process is closely combined with the disk dynamo process and the magnetospheric structure of the innermost region. + These are very important but still open questions in the current state. and to argue this point would carry us too far away [rom the purpose of this paper.," These are very important but still open questions in the current state, and to argue this point would carry us too far away from the purpose of this paper." + As discussed in section 4. in the [lv-wheel model. we can only estimate the total output power of the engine. and we cannot discuss the spectrum. of resultant radiation.," As discussed in section 4, in the fly-wheel model, we can only estimate the total output power of the engine, and we cannot discuss the spectrum of resultant radiation." +" llence the only wav ο distinguish QSOsS/AGNSs. from normal galaxies is setting a criterion. sav Ly;,,. on the xlometrie Luminosity."," Hence the only way to distinguish QSOs/AGNs from normal galaxies is setting a criterion, say $L_{lim}$, on the bolometric luminosity." +" Here we suppose that entire released energy is perfectly converted to radiation. and suppose that he engines having the luminosity greater than Lj, can of (treated. as QSOS/AGNs."," Here we suppose that entire released energy is perfectly converted to radiation, and suppose that the engines having the luminosity greater than $L_{lim}$ can be treated as QSOs/AGNs." + This simplified: procedure. is obviously far from the actual QSO number counting studies., This simplified procedure is obviously far from the actual QSO number counting studies. + In future study. the problem of the resultant spectrum of he radiation should. be solved.," In future study, the problem of the resultant spectrum of the radiation should be solved." + This is possible only if we solve the physics of plasma outllows being generated by the ]v-wheel engine., This is possible only if we solve the physics of plasma outflows being generated by the fly-wheel engine. + This is. needless to sav. one of the most difficult open questions in the magnetospheric astrophysics.," This is, needless to say, one of the most difficult open questions in the magnetospheric astrophysics." +" From figure 7.. the locus of the peak of population stronely depends on the criterion Ly;,,,."," From figure \ref{fig:pop1}, the locus of the peak of population strongly depends on the criterion $L_{lim}$." + Lowe set the smaller Lis. the peak shifts to the smaller +.," If we set the smaller $L_{lim}$, the peak shifts to the smaller $z$." + This means that if we survey AGNs in more deep. we will find more and more faint AGINs including low mass DII.," This means that if we survey AGNs in more deep, we will find more and more faint AGNs including low mass BH." + These may corresponc to Sevlerts., These may correspond to Seyferts. + However we should note if the mass of centra Bll is too small. the nucleus activity is dominated by its host galaxy.," However we should note if the mass of central BH is too small, the nucleus activity is dominated by its host galaxy." + Such objects may not be classified as QSOs/ACGNSs., Such objects may not be classified as QSOs/AGNs. +" In this meaning. the criterion Ly;,,,1077or 1077WW adopted in this paper might be plausible. because these values dominate the typical luminosity of normal galaxies 10** WY] CXadromeda galaxy)."," In this meaning, the criterion $L_{lim}=10^{38.9} \ \mbox{or}\ 10^{37.7}$ [W] adopted in this paper might be plausible, because these values dominate the typical luminosity of normal galaxies $10^{37}$ [W] (Andromeda galaxy)." + Similarity among all kines of AGNs ds. widely accepted from the observational point of view., Similarity among all kinds of AGNs is widely accepted from the observational point of view. + The spectral energy distribution. (SED) of radio-loud ACINs. ancl raclio-quiet AGNs are quit similar except. the radio range (see. e.g. Elvis et al.," The spectral energy distribution (SED) of radio-loud AGNs and radio-quiet AGNs are quit similar except the radio range (see, e.g., Elvis et al." + 1994)., 1994). + We also cannot. find any intrinsic difference in the evolution of the spatial number. density of the optically selected QSOs. the Iat-and-steep spectrum sources and racdio-oud QSOs (see Shaver et al.," We also cannot find any intrinsic difference in the evolution of the spatial number density of the optically selected QSOs, the flat-and-steep spectrum sources and radio-loud QSOs (see Shaver et al." + 1996)., 1996). + These, These +The current baseline mission is four satellites that are carried in pairs on either two Atlas V or Delta TV launchers.,The current baseline mission is four satellites that are carried in pairs on either two Atlas V or Delta IV launchers. + The interval between the two launches will be ~ lL vear. with the first launch in the 2010 timeframe.," The interval between the two launches will be $\sim$ 1 year, with the first launch in the 2010 timeframe." + A L2 orbit will facilitate high observing efficiency. provide an euvironimnent optimal for exrogenic cooling. aud siuplifv the spacecraft design.," A L2 orbit will facilitate high observing efficiency, provide an environment optimal for cyrogenic cooling, and simplify the spacecraft design." + The telescope collecting area is sized. assunidug ~ observing efficiency. which maximizes the observing program for a nininmu 5 vear mission lifetime (with all satellites operating).," The telescope collecting area is sized assuming $\sim$ observing efficiency, which maximizes the observing program for a minimum 5 year mission lifetime (with all satellites operating)." +" To set the long term goals; NASA has put ou the road map two ""vision missions” for the 22015 timeframe Cioneration-X is designed to observe the high redshift (5-20) Universe to observe A-rav endsson frou the first black holes aud starburst galaxies at redshift aud to observe the N-ray evolution of galaxies over all τουςτς,"," To set the long term goals, NASA has put on the road map two ""vision missions"" for the $>$ 2015 timeframe Generation-X is designed to observe the high redshift (5-20) Universe to observe X-ray emission from the first black holes and starburst galaxies at redshift 5-20, and to observe the X-ray evolution of galaxies over all redshifts." + These science objectives require that the mission has 50-150 ii? collecting area at 1 keV. combined with Chaudra-like augular resolution of 0.1 to 1.0 arc sec resolution., These science objectives require that the mission has 50-150 $^2$ collecting area at 1 keV combined with Chandra-like angular resolution of 0.1 to 1.0 arc sec resolution. + This resolution Is necessary to provide the necessary detection scusitivity aud avoid source confusion., This resolution is necessary to provide the necessary detection sensitivity and avoid source confusion. + The large collecting area would be achieved by developing precision liebt. weight N-ray optics. with a mass per unit collecting area similar to the Astro-E optics. xit with a factor of 100 improved angular resolution.," The large collecting area would be achieved by developing precision light weight X-ray optics, with a mass per unit collecting area similar to the Astro-E optics, but with a factor of 100 improved angular resolution." + As currently cuvisioned the wission would cousist of 3-6 identical satellites. cach carrving a fraction of the collecting area.," As currently envisioned the mission would consist of 3-6 identical satellites, each carrying a fraction of the collecting area." + Deplovable optics would be used to maximize the collecting area o launch vehicle., Deployable optics would be used to maximize the collecting area per launch vehicle. + The focal leugth of 25 to 50 ui would be achieved by using au extendible mast., The focal length of 25 to 50 m would be achieved by using an extendible mast. + The mission would be placed at L2 to provicle a stable thermal environment aud to maximize the viewing cficicucy., The mission would be placed at L2 to provide a stable thermal environment and to maximize the viewing efficiency. + The enabling technology for lis mission is Leltweieht. precision. grazius incidence optics aud the mission requirements feed into NÀSAs lone term technology program.," The enabling technology for this mission is lightweight, precision, grazing incidence optics and the mission requirements feed into NASA's long term technology program." + The Micro-Aresecoud. N-rav Tagine Mission (NLANIM) will have the angular resolutiou of 0.1 to l nücro arc secoud required to resolve the event horizon of accreting black holes at the ceuter of nearby galaxies (e.g. AIST)., The Micro-Arcsecond X-ray Imaging Mission (MAXIM) will have the angular resolution of 0.1 to 1 micro arc second required to resolve the event horizon of accreting black holes at the center of nearby galaxies (e.g. M87). + MANIM will cluplov for the first time N-ray interferometry aud in doing so will achieve a spectacular 10 million times increase in augular resolution compared to Chanclra., MAXIM will employ for the first time X-ray interferometry and in doing so will achieve a spectacular 10 million times increase in angular resolution compared to Chandra. + The basic technique has recently been demonstrated iu the laboratory., The basic technique has recently been demonstrated in the laboratory. + To obtain 0.1 nücro arcsec requires a 1060 mi to 1000 ii baseline., To obtain 0.1 micro arcsec requires a 100 m to 1000 m baseline. + The mission is beiue studied by NASA’s Tustitute for Advanced Concepts (NIAC, The mission is being studied by NASA's Institute for Advanced Concepts (NIAC). + It involves up to 3l spacecraft flving in formation. with precision metrology and tolerances at the nano-nueter level.," It involves up to 34 spacecraft flying in formation, with precision metrology and tolerances at the nano-meter level." + Ou orbit metrology and stability requirements are similar to TPF/Darwin., On orbit metrology and stability requirements are similar to TPF/Darwin. + A two spacecraft Pathfinder mission is being studied that will have a lin baseline ceiving 0.1 miulli-are second imiaeme., A two spacecraft Pathfinder mission is being studied that will have a 1 m baseline giving 0.1 milli-arc second imaging. + This will provide the required demonstration of X-ray interferometer in space and at the same time give a 1.000," This will provide the required demonstration of X-ray interferometer in space and at the same time give a 1,000" +Llowever. the authors of the discovery. paper argue that this is likely a disrupted: reevelecd pulsar.,"However, the authors of the discovery paper argue that this is likely a disrupted recycled pulsar." + For this reason we do not include it to our interpulse database., For this reason we do not include it to our interpulse database. + “Phe global computing technique should. result in more pulsar discoveries in the near future and we hope that some of them will contain the interpulse The main results and. conclusions of this paper can be summarized as follows: This work is partially supported by the Cuant 1: D03D 015 29 of the Polish State Committee for Scientific Research and by Polish. Research Grants NN. 203 2738 33 and NN 203 3919 34., The global computing technique should result in more pulsar discoveries in the near future and we hope that some of them will contain the interpulse The main results and conclusions of this paper can be summarized as follows: This work is partially supported by the Grant 1 P03D 015 29 of the Polish State Committee for Scientific Research and by Polish Research Grants NN 203 2738 33 and NN 203 3919 34. + We thank I.N. Manchester for invitation of IX.M. to Australia. support and access to the ATNE pulsar data.," We thank R.N. Manchester for invitation of K.M. to Australia, support and access to the ATNF pulsar data." + We also thank AL. Kramer for sharing with us unpublished results concerning new interpulse cases., We also thank M. Kramer for sharing with us unpublished results concerning new interpulse cases. + We thank M. Wolocdzicjezvk for linguistic help., We thank M. Kolodziejczyk for linguistic help. + We also thank the anonymous referee for useful comments., We also thank the anonymous referee for useful comments. +In the upper part of table | we list the detected elements in AM CVn stars.,In the upper part of table \ref{tab:abundances} we list the detected elements in AM CVn stars. + Observationally. their optical spectra fall in two categories. emission line spectra for the longer period systems (plus ES Cet) and absorption line spectra in the shorter period systems.," Observationally, their optical spectra fall in two categories, emission line spectra for the longer period systems (plus ES Cet) and absorption line spectra in the shorter period systems." + The absorption line systems CAM CVn and HP Lib and the outbursting systems in their high states) typically hardly show any elements other than He. with the exception of cjuite weak Mg and Si lines in AM CVn.," The absorption line systems (AM CVn and HP Lib and the outbursting systems in their high states) typically hardly show any elements other than He, with the exception of quite weak Mg and Si lines in AM CVn." + More promising are the emission line systems. in which N lines. in addition to the very srong He lines. are always detected if the appropriate spectral range is observed.," More promising are the emission line systems, in which N lines, in addition to the very strong He lines, are always detected if the appropriate spectral range is observed." + In particular GP Com has been studied in detail. with strong limits found on the presence of C and O from the absence of C lines and weakness of the O lines in the optical spectra(2)... yielding estimates of N/Cc100 and N/Oz50.," In particular GP Com has been studied in detail, with strong limits found on the presence of C and O from the absence of C lines and weakness of the O lines in the optical spectra, yielding estimates of $\rm N/C > 100$ and $\rm N/O \approx 50$." + report the discovery of C in the UV spectrum of GP Com and. scaling the line flux ratios to those observed in CVs. they estimate NC=10.," report the discovery of C in the UV spectrum of GP Com and, scaling the line flux ratios to those observed in CVs, they estimate $\rm N/C \approx 10$." + However. they comment on the fact that this is incompatible with earlier optical results and suggest the UV may underestimate the N abundance.," However, they comment on the fact that this is incompatible with earlier optical results and suggest the UV may underestimate the N abundance." + For CE 315(V396 Hya). a similar conclusion can be drawn because the system is very similar to GP Com ?).," For CE 315 (V396 Hya), a similar conclusion can be drawn because the system is very similar to GP Com ." +. From UV spectra derived a flux ratio of 714.5 in agreement with CNO, From UV spectra derived a flux ratio of $> 14.5$ in agreement with CNO +"By equating (7) and (8)) and using (1) and (2) to eliminate £, we obtain the following differential equation for the radial velocity dispersion, where the function ~ is defined by Clearly, w is determined directly from the X-ray observables andthe «-profile, which we discuss in section ??","By equating \ref{eq:je}) ) and \ref{eq:he}) ) and using \ref{eq:be}) ) and \ref{eq:trl}) ) to eliminate $\beta$, we obtain the following differential equation for the radial velocity dispersion, where the function $\psi$ is defined by Clearly, $\psi$ is determined directly from the X-ray observables andthe $\kappa$ -profile, which we discuss in section \ref{sec:simtrl}." + 'The differential equation (9)) is solved by finding an integrating factor which yields The dark matter density is determined as usual through ppm=Ptot—µπιητιε., The differential equation \ref{eq:rd}) ) is solved by finding an integrating factor which yields The dark matter density is determined as usual through $\rho_{\mathrm{DM}}=\rho_{\mathrm{tot}}-\mu m_H n_e$. +" With the radial velocity dispersion profile determined, the velocity anisotropy is easily recovered from either the temperature relation (2) or the Jeans equation (2). Obviously these two expressions should be equal."," With the radial velocity dispersion profile determined, the velocity anisotropy is easily recovered from either the temperature relation \ref{eq:trl}) ) or the Jeans equation \ref{eq:je}) ), Obviously these two expressions should be equal." + This can be used as a consistency check on whether numerical issues related to the differentiations and integration involved are kept under control., This can be used as a consistency check on whether numerical issues related to the differentiations and integration involved are kept under control. +" To summarize, the assumed relation (B)) between the effective dark matter temperature and the gas temperature, along with the mass estimate from (8), allows us to solve the dark matter dynamics directly from X-ray data, and determine both the radial velocity dispersion and the velocity anisotropy as functions of radius."," To summarize, the assumed relation \ref{eq:trl}) ) between the effective dark matter temperature and the gas temperature, along with the mass estimate from \ref{eq:he}) ), allows us to solve the dark matter dynamics directly from X-ray data, and determine both the radial velocity dispersion and the velocity anisotropy as functions of radius." +" We use numerical simulations of the formation of galaxy clusters in the ACDM cosmology to investigate the validity and shape of the temperature relation (2)), and to test the method for determining the velocity anisotropy."," We use numerical simulations of the formation of galaxy clusters in the $\Lambda$ CDM cosmology to investigate the validity and shape of the temperature relation \ref{eq:trl}) ), and to test the method for determining the velocity anisotropy." + In order to check systematic effects we take samples from two different simulations based on two completely independent numerical codes., In order to check systematic effects we take samples from two different simulations based on two completely independent numerical codes. +" We first consider a sample of 67 clusters taken from the CLEF simulation (?), details of which are briefly summarized here."," We first consider a sample of 67 clusters taken from the CLEF simulation \citep{Kay:2006iz}, , details of which are briefly summarized here." +" The CLEF simulation was run with the GADGET2 N-body/SPH code (?) and followed the evolution of large-scale structure within a box of comoving length, 200k~'Mpc."," The CLEF simulation was run with the GADGET2 $N$ -body/SPH code \citep{2005MNRAS.364.1105S} and followed the evolution of large-scale structure within a box of comoving length, $200 h^{-1}{\rm Mpc}$." +" The following cosmological parameters were assumed: Ομ,=0.3;Q40.7;=0.0486;h0.7;n5σε 09.", The following cosmological parameters were assumed: $\Omega_{\rm m}=0.3; \Omega_{\Lambda}=0.7; \Omega_{\rm b}=0.0486; h=0.7; n_{\rm s}=1; \sigma_8=0.9$ . + Here the value of the Hubble constant is written as 100hkms~!Mpc! and σε is the rms mass fluctuation at the present epoch in a sphere of radius 8h~!Mpc.," Here the value of the Hubble constant is written as $100 \, h\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ and $\sigma_8$ is the rms mass fluctuation at the present epoch in a sphere of radius $8\,h^{-1} \mathrm{Mpc}$." +" The number of particles was set to 428? for each of the gas and dark matter species, thus determining the particle masses to be mpm=7.1x10)ΤΜΟ and meas=1.4x10957!Mo respectively."," The number of particles was set to $428^3$ for each of the gas and dark matter species, thus determining the particle masses to be $m_{\rm DM}=7.1\times 10^{9}h^{-1}{\rm M}_{\odot}$ and $m_{\rm gas}=1.4\times 10^{9}h^{-1}{\rm M}_{\odot}$ respectively." + The equivalent Plummer softening length was set to 20h-!kpc and held fixed at all times in comoving co-ordinates.," The equivalent Plummer softening length was set to $20\,h^{-1}\,$ kpc and held fixed at all times in comoving co-ordinates." + Pressure forces were calculated using the standard GADGET2 entropy-conserving version of SPH with an artificial viscosity to convert kinetic energy into thermal energy where the flow was convergent., Pressure forces were calculated using the standard GADGET2 entropy-conserving version of SPH with an artificial viscosity to convert kinetic energy into thermal energy where the flow was convergent. +" The gas could cool radiatively assuming a fixed metallicity, Z=0.3Z."," The gas could cool radiatively assuming a fixed metallicity, $Z=0.3Z_{\odot}$." +" Cold (T«10°K) gas with ny>10-?cm-? either formed stars or was heated by an entropy, AS=1000keVcm?."," Cold $T<10^{5}$ K) gas with $n_{\rm H}>10^{-3}{\rm cm}^{-3}$ either formed stars or was heated by an entropy, $\Delta S=1000\, {\rm keV \, cm}^2$." +" This choice was determined stochastically by selecting a random number, r, from the unit interval and heating the particle if r«0.1, i.e. a 10 per cent probability of being heated."," This choice was determined stochastically by selecting a random number, $r$, from the unit interval and heating the particle if $r<0.1$, i.e. a 10 per cent probability of being heated." + 'This high level of feedback was necessary to reproduce the observed excess entropy in clusters (see ? for further details)., This high level of feedback was necessary to reproduce the observed excess entropy in clusters (see \citet{Kay:2006iz} for further details). +" To select the cluster sample, we first consider all clusters at z=0 with X-ray temperatures, kT>2keV; this produces 95 objects, with virial masses, Myir>1.3x1014571Mg >15,000 dark matter particles)."," To select the cluster sample, we first consider all clusters at $z=0$ with X-ray temperatures, $kT>2\, {\rm keV}$ ; this produces 95 objects, with virial masses, $M_{\rm vir}>1.3\times 10^{14}h^{-1}{\rm M}_{\odot}$ (correspondingly, $> 15,000$ dark matter particles)." +" We then(correspondingly, select those clusters with 3D substructure statistic, s<0.05."," We then select those clusters with 3D substructure statistic, $s<0.05$." +" The substructure statistic (7) measures the displacement of the centre of mass from the potential minimum of the cluster (taken to be its centre), relative to rsoo, which is the scale radius within which the mean total density is 500 times the critical density."," The substructure statistic \citep{1998MNRAS.296.1061T} measures the displacement of the centre of mass from the potential minimum of the cluster (taken to be its centre), relative to $r_{500}$, which is the scale radius within which the mean total density is $500$ times the critical density." +" By making this cut, we therefore exclude all clusters that show significant signs of dynamical activity, i.e. major mergers."," By making this cut, we therefore exclude all clusters that show significant signs of dynamical activity, i.e. major mergers." + 'The second sample is a subsample of the one presented in ?| which we refer to as V06., The second sample is a subsample of the one presented in \citet{2006NewA...12...71V} which we refer to as V06. + These simulations assumed a concordance flat ACDM with the same cosmological parameters as for the CLEF simulation., These simulations assumed a concordance flat $\Lambda$ CDM with the same cosmological parameters as for the CLEF simulation. + The simulation ensemble of galaxy clusters was constructed according to a procedure described in (?)., The simulation ensemble of galaxy clusters was constructed according to a procedure described in \citep{2008arXiv0808.1111P}. + Here we briefly summarize the most important aspects., Here we briefly summarize the most important aspects. + The hydrodynamic simulations were run using an entropy-conserving multistep TREESPH code for a sample of 153 clusters spanning a range from ~1.5x101?5h-!Mg down to Myr~1.5x101h-1Me., The hydrodynamic simulations were run using an entropy-conserving multistep TREESPH code for a sample of 153 clusters spanning a range from $\simeq 1.5 \times 10^{15} h^{-1} M_{\odot}$ down to $M_{vir}\simeq 1.5 \times 10^{14} h^{-1} M_{\odot}$. + The initial conditions (z;;= 49) were extracted from a set of purely N-body cosmological simulations in which clusters of galaxies were identified from the particle distribution at z=0 using a friends-of-friends algorithm., The initial conditions $z_{in}=49$ ) were extracted from a set of purely N-body cosmological simulations in which clusters of galaxies were identified from the particle distribution at $z=0$ using a friends–of–friends algorithm. +" In order to investigate the effect of the implemented gas processes on the energy equipartition between gas end dark matter particles, we performed both adiabatic and radiative simulations."," In order to investigate the effect of the implemented gas processes on the energy equipartition between gas end dark matter particles, we performed both adiabatic and radiative simulations." +" The radiative simulations are of course more realistic than the adiabatic ones, because they additionally take into account radiative cooling, star formation, energy and metal feedback (?).."," The radiative simulations are of course more realistic than the adiabatic ones, because they additionally take into account radiative cooling, star formation, energy and metal feedback \citep{2003MNRAS.339.1117V}." + More details concerning the simulation technique and the implementation of physical processes of the gas are given in ?.. , More details concerning the simulation technique and the implementation of physical processes of the gas are given in \citet{2006NewA...12...71V}. . +"In order to avoid contamination from dynamically perturbed clusters, we select the 20 most relaxed objects at z— 0."," In order to avoid contamination from dynamically perturbed clusters, we select the 20 most relaxed objects at $z=0$ ." +" The selection is based on the power ratiomethod, which measures the amount of substructure in X-ray surface brightness maps."," The selection is based on the power ratiomethod, which measures the amount of substructure in X-ray surface brightness maps." + The map sources a, The map sources a + (C'atelaui[m]2009)., \citet{mc09} \citep{mc09}. +. trose in Oo-I/II systems., those in Oo-I/II systems. +" The LMC is an ideal place for tdis study because of the large umber of Oo-int clusters tii it contains (Bonoetal.1991:Catclan2009): of t1ο twelve LAIC elobular clusters that contain at least 5 RRab variables. five of these clusters are Oo-int (NCC 1166. NGC 1853, NGC 2019. NGC 2210. and NGC 2257)."," The LMC is an ideal place for this study because of the large number of Oo-int clusters that it contains \citep{bo94,mc09}; of the twelve LMC globular clusters that contain at least $5$ RRab variables, five of these clusters are Oo-int (NGC 1466, NGC 1853, NGC 2019, NGC 2210, and NGC 2257)." + Iu this paper we identify. classify. aud discuss the variable stars found in the LMC elobular cluster NGC 1166," In this paper we identify, classify, and discuss the variable stars found in the LMC globular cluster NGC 1466." + Subsequent papers will focus on the variable stairs in other LAIC elobular clusters., Subsequent papers will focus on the variable stars in other LMC globular clusters. + NGC 1166 is au old globular cluster that is located relatively far from the center of the LAIC., NGC 1466 is an old globular cluster that is located relatively far from the center of the LMC. + It has a nietal abundauce of |Fe/TII| =1.60. see discussion in section L1. aud is uot very reddened. E(B-V) = 0.09+40.02 (Walker1992)..," It has a metal abundance of [Fe/H] $\approx -1.60$, see discussion in section \ref{sec:abprop}, and is not very reddened, E(B-V) = $0.09\pm0.02$ \citep{wa92b}." + Johusonetal.(1999) used. color-magnitude diagrams obtained with the Dubble Space Telescope to determine that the age of NCC 1166 within 1 Gyr of the ages of the Alilky Way elobular clusters M3 (NGC 5272) and M92 (NGC 6311)., \citet{jj99} used color-magnitude diagrams obtained with the Hubble Space Telescope to determine that the age of NGC 1466 is within $1$ Gyr of the ages of the Milky Way globular clusters M3 (NGC 5272) and M92 (NGC 6341). + NGC 1166 features a well-populated horizoutal brauch that extends through the instability strip(sce Figure 5 iu Walker 1992): thus it is expected to coutain a significant uunber of RR Lyrae stars., NGC 1466 features a well-populated horizontal branch that extends through the instability strip (see Figure 5 in Walker 1992); thus it is expected to contain a significant number of RR Lyrae stars. + RR Lvrae stars were first found in NGC 1166 bv Thackeray&Wesselink(1953).. aud additional RR Lyrae were discovered by. Wesselink. (1971).," RR Lyrae stars were first found in NGC 1466 by \citet{tw53}, and additional RR Lyrae were discovered by \citet{we71}." +. The most receut study of variables in NCC 1166 was conducted by Walker(1992).. who found 12 RR Lyrae stars: 25 RRab and 17 RRe stars.," The most recent study of variables in NGC 1466 was conducted by \citet{wa92b}, who found $42$ RR Lyrae stars; $25$ RRab and $17$ RRc stars." + Due to the density of uuresolved stars in the chister core. Walker did not perform photometry of stars within a radius of 13 aresec from the cluster center. suggesting that there are probably additional RR Lyrac stars that could uot be detected in his study.," Due to the density of unresolved stars in the cluster core, Walker did not perform photometry of stars within a radius of $13$ arcsec from the cluster center, suggesting that there are probably additional RR Lyrae stars that could not be detected in his study." + The core radius of NGC 1166 is 10.7EOLL aresec. as measured by Mackey&Calmore(2003) using tuages from the IIubble Space Telescope. which is entirely within the region of the cluster where Walker was unable to perform photometry.," The core radius of NGC 1466 is $10.7\pm0.4$ arcsec, as measured by \citet{mg03} using images from the Hubble Space Telescope, which is entirely within the region of the cluster where Walker was unable to perform photometry." + Advances in instrument resolution and imuage-subtractiou techniques now inake it easier for us to search for variable stars in, Advances in instrument resolution and image-subtraction techniques now make it easier for us to search for variable stars in +order to separate the quiescent contribution from the flaring emission. we modeled the spectra with an absorbed 3T-plasma.,"order to separate the quiescent contribution from the flaring emission, we modeled the spectra with an absorbed 3T-plasma." + The parameters of the first two components (representing the quiescent emission) were frozen to the values derived by simultaneously fitting four spectra during the quiescent phase 00201. 0401. 0601. 0701. 0801).," The parameters of the first two components (representing the quiescent emission) were frozen to the values derived by simultaneously fitting four spectra during the quiescent phase 0201, 0401, 0601, 0701, 0801)." + The values for the third component (the flaring emission) were then fitted., The values for the third component (the flaring emission) were then fitted. + The results for this component are summarized in Table 3.., The results for this component are summarized in Table \ref{tab:v827_flare}. + To derive the flare’s physical parameters we used the approach initially discussed by Realeetal.(1997) and since then applied to a variety of stellar flares., To derive the flare's physical parameters we used the approach initially discussed by \citet{rbp+97} and since then applied to a variety of stellar flares. + The calibration of the method for the ddetectors. and a detailed explanation of the physics behind it can be found in Realeetal.(2004).. to which the reader is referred.," The calibration of the method for the detectors, and a detailed explanation of the physics behind it can be found in \citet{rgp+2004}, to which the reader is referred." + This approach allowed us to account properly for the presence of sustained heating during the flare decay. using the slope ¢ of the flare decay in the log7. vs. logVEM diagram.," This approach allowed us to account properly for the presence of sustained heating during the flare decay, using the slope $\zeta$ of the flare decay in the $\log T$ vs. $\log \sqrt{E\!M}$ diagram." +" The semi-length of the flaring loop in this formulation is given by where «a3.7x0enr!s!K'Z, re is the l/e folding time of the light curve decay. and Z4, 1s the peak temperature of the plasma in the flaring loop."," The semi-length of the flaring loop in this formulation is given by where $\alpha = 3.7 \times 10^{-4} {\rm cm^{-1} s^{-1} K^{1/2}}$, $\tau_{\rm LC}$ is the $1/e$ folding time of the light curve decay, and $T_{\rm max}$ is the peak temperature of the plasma in the flaring loop." +" Then. F(Z) and the relationship between 7,4, and the best-fit peak temperature Top, are both functions that need to be separately determined for each X-ray detector. depending on its spectral response."," Then, $F(\zeta)$ and the relationship between $T_{\rm max}$ and the best-fit peak temperature $T_{\rm obs}$ are both functions that need to be separately determined for each X-ray detector, depending on its spectral response." +" For the EPIC PN. where c,=0.51+ 0.03. Z,=0.350.01. and gy= 1.36x0.18."," For the EPIC PN, where $c_a =0.51 \pm 0.03$ , $\zeta_a = 0.35 \pm 0.01$, and $q_a = 1.36 +\pm 0.18$ ." + The range of validity corresponds to an impulsively heated flare (6 1.66) and to very slow decays (strong sustained heating) corresponding tothe locus of statics loops, The range of validity corresponds to an impulsively heated flare $\zeta = 1.66$ ) and to very slow decays (strong sustained heating) corresponding tothe locus of statics loops +stay formation rate.,star formation rate. + The ‘elective’ vield (p.;;) determines the constant of proportionality. c-(p/p.rr)— 1.," The `effective' yield $_{eff}$ ) determines the constant of proportionality, $_{eff}$ $-1$." + If chemical evolution is suddenly halted before all of the gas is exhausted. a discontinuity occurs in (he metallicity distribution of stars formed as well as in the lost gas. leaving a reservoir of gas with uniform composition available for later star formation.," If chemical evolution is suddenly halted before all of the gas is exhausted, a discontinuity occurs in the metallicity distribution of stars formed as well as in the lost gas, leaving a reservoir of gas with uniform composition available for later star formation." + The stellar metalliityv. distribution can be described. mathematically as the undisturbed. distribution multipliel bx a complementary IHeaviside unit step function., The stellar metallicity distribution can be described mathematically as the undisturbed distribution multiplied by a complementary Heaviside unit step function. +" "" je step function (or gas starvation function. E) is replaced with one distributed in metallicity (i.e. we round the corners of the step function). then the one zone model appears as though it contains many individually evolving boxes."," If the step function (or gas starvation function, f) is replaced with one distributed in metallicity (i.e. we round the corners of the step function), then the one zone model appears as though it contains many individually evolving boxes." + In HO04. lor example. (he complementary error Iunction replaces the Heaviside ΠΟΙΟ to be consistent wilh the Gaussian distribution ol stoppages assumed to occur as a result of collisions among the numerous individual clumps.," In H04, for example, the complementary error function replaces the Heaviside function to be consistent with the Gaussian distribution of stoppages assumed to occur as a result of collisions among the numerous individual clumps." + To provide more context for the model we give a brief summary of its application in 1104., To provide more context for the model we give a brief summary of its application in H04. + There. by confining attention (to a representative volume of the universe. the chemical evolution and star formation history associated with galaxy formation and evolution is derived from observations of stus and clusters in (he Galaxy and in M31.," There, by confining attention to a representative volume of the universe, the chemical evolution and star formation history associated with galaxy formation and evolution is derived from observations of stars and clusters in the Galaxy and in M31." + The picture considers (he anisotropic collapse of a number of star forming clumps., The picture considers the anisotropic collapse of a number of star forming clumps. + The gas in these clumps is assumed (ο have been enriched by a previous generation of star formation., The gas in these clumps is assumed to have been enriched by a previous generation of star formation. +" The first collapse. perpendicular to the eventual rotation axis. results in collisions between low angular momentum clunmps (Mig, ) which terminates the star formation and is assumed to create the metal poor (blue) elobular clusters."," The first collapse, perpendicular to the eventual rotation axis, results in collisions between low angular momentum clumps $_{t,blue}$ ) which terminates the star formation and is assumed to create the metal poor (blue) globular clusters." +" The stars already formed. (M,pe) then constitute the extended metal poor halo and the gas released in (he collisions (Mts) falls to the center to form the bulge."," The stars already formed $_{s,blue}$ ) then constitute the extended metal poor halo and the gas released in the collisions $_{ml,blue}$ ) falls to the center to form the bulge." + The hieher angular momentum clumps (M; 4) continue to form stars and become more metal rich until they too begin to collide as they fall along the rotation axis.," The higher angular momentum clumps $_{t,red}$ ) continue to form stars and become more metal rich until they too begin to collide as they fall along the rotation axis." + These collisions again terminate star formation and give rise to the metal rich (red) globular clusters., These collisions again terminate star formation and give rise to the metal rich (red) globular clusters. + The stars already formed (Al...) ave released to form a metal rich spheroid population. and the gas (ΝΕ) dissipates to form the disk.," The stars already formed $_{s,red}$ ) are released to form a metal rich spheroid population, and the gas $_{ml,red}$ ) dissipates to form the disk." + literestinely. in (his picture only ~20% of the available barvons are required to provide an acceptable fit to the observed cosmic star formation rate clensity.," Interestingly, in this picture only $\sim20$ of the available baryons are required to provide an acceptable fit to the observed cosmic star formation rate density." + Further. before collisions terminate star formation within the clumps. approximately half of these baryons are returned (o the IGM by supernova driven winds (designated. (MiΙΕΜι ΕΛΠΕ) in H04 but renamed here Mecca. the cireum-galactie medium (CGM) component).," Further, before collisions terminate star formation within the clumps, approximately half of these baryons are returned to the IGM by supernova driven winds (designated $_{WHIM,blue}$ $_{WHIM,red}$ ) in H04 but renamed here $_{CGM}$, the circum-galactic medium (CGM) component)." + Accounting for the ‘leftover’ of the barvons provided one of the main motivations for the present work., Accounting for the `leftover' of the baryons provided one of the main motivations for the present work. + lere we assume there are a large number of star forming clamps approaching the transition to Pop II as the carbon and oxygen abundances approach |C-O/I]o-—De, Here we assume there are a large number of star forming clumps approaching the transition to Pop II as the carbon and oxygen abundances approach $\sim-3$. + Al (his point the gas can cool more elliciently which in turn allows low-mass Pop lI stars to, At this point the gas can cool more efficiently which in turn allows low-mass Pop II stars to +3.,3. + Combining the reddened distance moduli in the J and Ix bands obtained in (his paper with those obtained in Paper Lin the V and I bands we derive a total reddening of the WLM Cepheids of E(D-V) = 0.082 4 0.02. and a absorption corrected. (rue distance modulus Lor WLAM of 24.92 + 0.04 mag (random error) zc 0.06 mag (svstematic error).," Combining the reddened distance moduli in the J and K bands obtained in this paper with those obtained in Paper I in the V and I bands we derive a total reddening of the WLM Cepheids of E(B-V) = 0.082 $\pm$ 0.02, and a absorption corrected, true distance modulus for WLM of 24.92 $\pm$ 0.04 mag (random error) $\pm$ 0.06 mag (systematic error)." + 4., 4. + We report on an error in Paper I where we had confused the distance modulus in the V band with the one in the Wesenheit band., We report on an error in Paper I where we had confused the distance modulus in the V band with the one in the Wesenheit band. + For our present distance determination. we have obviously used the correct value of the τοσο distance modulus in V. as obtained from the data in Paper I. The true distauce modulus from the Wesenheit magnitude obtained in that paper must read 25.014 + 0.036 mag. rather (han the erroneosly given. value of 25.144 mag.," For our present distance determination, we have obviously used the correct value of the reddened distance modulus in V as obtained from the data in Paper I. The true distance modulus from the Wesenheit magnitude obtained in that paper must read 25.014 $\pm$ 0.036 mag, rather than the erroneosly given value of 25.144 mag." + 5., 5. + The WLM distance derived from the mulliwaveleneth VIJIx Cepheicl analvsis in this paper is in excellent agreement with the various determinations of the WLM distance from the [ρα lip of the red giant. branch method and from other techniques which have been reported in the literature., The WLM distance derived from the multiwavelength VIJK Cepheid analysis in this paper is in excellent agreement with the various determinations of the WLM distance from the I-band tip of the red giant branch method and from other techniques which have been reported in the literature. + 6., 6. + With the completion of the Cepheid mulliwaveleneth distance determination Lor WLM there are now six late-tvpe galaxies in the Araucaria Project for which such distance determinations have been carried out (WLAL IC 1613. NGC 3109 and NGC 6822 in the Local Group and NGC 300 and NGC 55 in the Sculptor Group: see references in the Introduction).," With the completion of the Cepheid multiwavelength distance determination for WLM there are now six late-type galaxies in the Araucaria Project for which such distance determinations have been carried out (WLM, IC 1613, NGC 3109 and NGC 6822 in the Local Group and NGC 300 and NGC 55 in the Sculptor Group; see references in the Introduction)." + Corresponding work for two more Sculptor Group galaxies. NGC 247 anc NGC 7793. is underway.," Corresponding work for two more Sculptor Group galaxies, NGC 247 and NGC 7793, is underway." + A comparison of these distances with those derived for the same galaxies from the other techniques we are using in our project will be conducted in due time ancl is expected {ο lead to an improved determination of the metallicity dependence of the different techiiques., A comparison of these distances with those derived for the same galaxies from the other techniques we are using in our project will be conducted in due time and is expected to lead to an improved determination of the metallicity dependence of the different techniques. + This will finally vield a set of very accurate distances to a number of nearby galaxies in the 0.054 Mpc range which can be used to calibrate more accurately other techniques which reach out to distances large enough for an improved determination of the Hubble constant., This will finally yield a set of very accurate distances to a number of nearby galaxies in the 0.05-4 Mpc range which can be used to calibrate more accurately other techniques which reach out to distances large enough for an improved determination of the Hubble constant. + WG. GP and DM gratefully. acknowledge financial support for this work [rom the Chilean Center lor Astrophysics FONDAP 15010003. and from the BASAL Centro de Astrolisica. v Teenologias Alines (CATA).," WG, GP and DM gratefully acknowledge financial support for this work from the Chilean Center for Astrophysics FONDAP 15010003, and from the BASAL Centro de Astrofisica y Tecnologias Afines (CATA)." + Support [rom the Polish grant. N203 002 31/046 and the FOCUS subsidy of the Fundation for Polish Science (FNP) is also acknowledged., Support from the Polish grant N203 002 31/046 and the FOCUS subsidy of the Fundation for Polish Science (FNP) is also acknowledged. + It is a eveal pleasure to thank the support astronomers al ESO-La Silla aud at Las Campanas Observatory for their expert help in (he observations., It is a great pleasure to thank the support astronomers at ESO-La Silla and at Las Campanas Observatory for their expert help in the observations. + We also thank the ESO OPC and CNTAC for allotting generous amounts of observing time to this project., We also thank the ESO OPC and CNTAC for allotting generous amounts of observing time to this project. + HHelpful comments of a referee on a previous version of (his paper are appreciated., Helpful comments of a referee on a previous version of this paper are appreciated. +"as well as their spectrum, implies that the detections of prompt photons are most likely to have been dominated by the high-energy tail of the synchrotron emission; i.e., 7)©Ίνα in Figure 2((top).","as well as their spectrum, implies that the detections of prompt photons are most likely to have been dominated by the high-energy tail of the synchrotron emission; i.e., $\eta +\approx \eta_{\rm syn}$ in Figure \ref{fig:mu_sig}( )." +" In fact, simply extrapolating synchrotron tail of many BATSE bursts up to ~100 MeV regime, using inferred values for their and o», a value of ry, which is consistent with the 14,,one obtained giveshere for the prompt phase."," In fact, simply extrapolating synchrotron tail of many BATSE bursts up to $\sim$ 100 MeV regime, using inferred values for their $\nu_{\rm syn}$ and $\alpha_2$ , gives a value of $\eta_{\rm syn}$ which is consistent with the one obtained here for the prompt phase." +" The harder IC prompt emission, however, can still have as much as 10 times larger fluence than that of the synchrotron emission in EGRET window, without being detected."," The harder IC prompt emission, however, can still have as much as 10 times larger fluence than that of the synchrotron emission in EGRET window, without being detected." +" Therefore, this figure also sets an upper limit on the ratio of the IC and synchrotron components of nic<0.6, as larger 1c gives enough photon fluence detectable by EGRET."," Therefore, this figure also sets an upper limit on the ratio of the IC and synchrotron components of $\eta_{\rm IC} \lesssim 0.6$, as larger $\eta_{\rm IC}$ gives enough photon fluence detectable by EGRET." +" As we showed in 2.1,, theoretically we predict mjc&1.2 (for EGRET) with a canonical set of parameters."," As we showed in \ref{sub:prompt}, theoretically we predict $\eta_{\rm IC} \approx +1.2$ (for EGRET) with a canonical set of parameters." +" Although this appears to imply that the current bound from EGRET already excludes the canonical model, we cannot make such a strong statement given the current uncertainties of many relevant "," Although this appears to imply that the current bound from EGRET already excludes the canonical model, we cannot make such a strong statement given the current uncertainties of many relevant parameters." +"Therefore, a more conservative statement would beparameters. that the current EGRET bound is barely consistent with the predictions of the SSC within the internal shock model."," Therefore, a more conservative statement would be that the current EGRET bound is barely consistent with the predictions of the SSC within the internal shock model." +" We may interpret the bound τις<0.6 as constraints on €,/eg and Ym, which is shown in Figure 5((a)."," We may interpret the bound $\eta_{\rm IC} \lesssim 0.6$ as constraints on $\epsilon_e / +\epsilon_B$ and $\gamma_m$, which is shown in Figure \ref{fig:const}( (a)." +" As theKlein-Nishina suppression (£kw) becomes significant for large , We have only modest limit on €,/eg in such a regime."," As theKlein-Nishina suppression $\xi_{\rm KN}$ ) becomes significant for large $\gamma_m$, we have only modest limit on $\epsilon_e / \epsilon_B$ in such a regime." +" However, one should keep in mind that these are order of magnitude constraints, which may farther vary with other parameters, such as 7,,4,0? and I’."," However, one should keep in mind that these are order of magnitude constraints, which may farther vary with other parameters, such as $\nu_{\rm syn}, \alpha_2$ and $\Gamma_b$." +" Much better constraint plot is expected with the futureGLAST data, where hopefully, mc will be measured for many individual bursts."," Much better constraint plot is expected with the future data, where hopefully, $\eta_{\rm IC}$ will be measured for many individual bursts." +" During the afterglow the synchrotron emission is much softer than during the prompt phase, and therefore, the IC component is expected to dominate EGRET observations also near its lower energy-band limit."," During the afterglow the synchrotron emission is much softer than during the prompt phase, and therefore, the IC component is expected to dominate EGRET observations also near its lower energy-band limit." +" Moreover, the fact that the number of bursts detected by EGRET during the afterglow is higher than the number detected during the prompt emission suggests that here EGRET is likely to have detected the actual IC component of the afterglow."," Moreover, the fact that the number of bursts detected by EGRET during the afterglow is higher than the number detected during the prompt emission suggests that here EGRET is likely to have detected the actual IC component of the afterglow." +" The spectral index of the GeV afterglow in EGRET window during the first 200 s is expected to be a= 1.5-2, implying that the evaluation of yw in the bottom panel of Figure 2,, which assumes a spectral index of —2.4, might be larger by at most a small factor (~2-3)."," The spectral index of the GeV afterglow in EGRET window during the first 200 s is expected to be $\alpha = 1.5$ –2, implying that the evaluation of $\mu$ in the bottom panel of Figure \ref{fig:mu_sig}, which assumes a spectral index of $-2.4$, might be larger by at most a small factor $\sim$ 2–3)." +" Thus, for the afterglow, ηις~0.01—0.1."," Thus, for the afterglow, $\eta_{\rm IC} \sim +0.01$ $0.1$." + We then compare this result with the theoretical expectation of nc in equation (2))., We then compare this result with the theoretical expectation of $\eta_{\rm IC}$ in equation \ref{eq:eta_IC}) ). +" But first we need to estimate the value of /Fuev. where F;y, is measured during the first 200 s followingF,y, Too and Fev is the prompt emission fluence.", But first we need to estimate the value of $F_{\rm syn}/F_{\rm MeV}$ where $F_{\rm syn}$ is measured during the first 200 s following $T_{90}$ and $F_{\rm MeV}$ is the prompt emission fluence. +" We use the Swift GRB which provides X-ray afterglow fluences several tens to several hundreds of seconds after the bursts, as well as the prompt MeV fluences."," We use the GRB which provides X-ray afterglow fluences several tens to several hundreds of seconds after the bursts, as well as the prompt MeV fluences." +" Using only bursts where the X-ray observation starts after Τορ but no more than 300 s after the burst we find a distribution of F;;/Fwev that ranges from 10? to 0.1, with the central value of 102."," Using only bursts where the X-ray observation starts after $T_{90}$ but no more than $300$ s after the burst we find a distribution of $F_{\rm syn} / F_{\rm MeV}$ that ranges from $10^{-3}$ to $0.1$, with the central value of $\sim$ $^{-2}$." +" Thus afterglow theory with canonical parameters predicts mic10? with a large spread, consistent with EGRET constraints."," Thus afterglow theory with canonical parameters predicts $\eta_{\rm IC} \sim +10^{-2}$ with a large spread, consistent with EGRET constraints." + Figure 5((b) shows the interpretation of EGRET constraint on mc (Fig. 2)), Figure \ref{fig:const}( (b) shows the interpretation of EGRET constraint on $\eta_{\rm IC}$ (Fig. \ref{fig:mu_sig}) ) +" as that for e,/eg and 7, assuming canonical parameters and Fyn/Fmev=102."," as that for $\epsilon_e / \epsilon_B$ and $\gamma_m$ , assuming canonical parameters and $F_{\rm syn} / F_{\rm MeV} = 10^{-2}$." +" Although this allowed region may change with other model one cannot have too large value of γι because of the parameters,Klein-Nishinaagain suppression factor EKN."," Although this allowed region may change with other model parameters, again one cannot have too large value of $\gamma_m$ because of the Klein-Nishina suppression factor $\xi_{\rm KN}$." + We now move on to discussions on implications forGLAST using the obtained constraints on 7 in the previous section., We now move on to discussions on implications for using the obtained constraints on $\eta$ in the previous section. +" Firstwe estimate the sensitivity of LAT on board GLAST for and GeV emission, based on its published promptsensitivity to steady afterglowpoint whichis 4x10? cm? s! above 100 MeV at 5c with a power-law index of—2."," Firstwe estimate the sensitivity of LAT on board for prompt and afterglow GeV emission, based on its published sensitivity to steady point whichis $4 +\times 10^{-9}$ $^{-2}$ $^{-1}$ above 100 MeV at $5\sigma$ with a power-law index of$-2$." + This sensitivity is obtained by a one-year all-sky survey during, This sensitivity is obtained by a one-year all-sky survey during +"similar spectral type to HD 189733, but it is considerably fainter, with a J-band magnitude of 9.94 (c.f.","similar spectral type to HD 189733, but it is considerably fainter, with a J-band magnitude of 9.94 (c.f." + 6.07 for HD 189733)., 6.07 for HD 189733). +" The transit was observed over five half orbits, consisting of 279 spectra in total, each with an exposure time of 40 seconds."," The transit was observed over five half orbits, consisting of 279 spectra in total, each with an exposure time of 40 seconds." +" The first, second and fifth orbit cover the of-transit part of the light curve, and consist of 56, 56 and 55 spectra, respectively."," The first, second and fifth orbit cover the out-of-transit part of the light curve, and consist of 56, 56 and 55 spectra, respectively." +" The third orbit covers the ingress with 56 spectra, and the fourth covers mid-transit, consisting of 55 spectra."," The third orbit covers the ingress with 56 spectra, and the fourth covers mid-transit, consisting of 55 spectra." +" XO-1 has a longer transit duration than HD 189733 or GJ-436, hence two consecutive orbits cover in-transit data."," XO-1 has a longer transit duration than HD 189733 or GJ-436, hence two consecutive orbits cover in-transit data." +" Again, some exposures were taken prior to the first orbit to set the position for wavelength calibration."," Again, some exposures were taken prior to the first orbit to set the position for wavelength calibration." + The images were treated and the light curves extracted using the techniques described in Sects., The images were treated and the light curves extracted using the techniques described in Sects. + 2.2 and 3.2.., \ref{sect:HD189733_analysis} and \ref{sect:GJ436_analysis}. + The 1D spectra were extracted along 90 pixel columns of width 16 pixels., The 1D spectra were extracted along 90 pixel columns of width 16 pixels. + The background was estimated from a column strip above each wavelength channel., The background was estimated from a column strip above each wavelength channel. +" We also experimented with flat-fielding and global background corrections, but neither significantly affects the final results."," We also experimented with flat-fielding and global background corrections, but neither significantly affects the final results." +" Fig.21 shows typical 1D spectra extracted for in-transit and out-of-transit observations, with the number of electrons collected per image per pixel column ranging from approximately 11600000 to 4400"," \ref{fig:XO1_1D_spectra} shows typical 1D spectra extracted for in-transit and out-of-transit observations, with the number of electrons collected per image per pixel column ranging from approximately 000 to 000." +0000., Fig. +" Fig. 23 shows the light curves extracted for each of the 18 wavelength channels, after binning into 5 pixel bins."," \ref{fig:XO1_normalised_lightcurves} shows the light curves extracted for each of the 18 wavelength channels, after binning into 5 pixel bins." + Fig., Fig. +" 22 shows the resulting white light curve, extracted over 110 pixel columns."," \ref{fig:XO1_wlc} shows the resulting white light curve, extracted over 110 pixel columns." +" The first few points in each orbit exhibit strong variation in flux, and are thus excluded from the subsequent analysis."," The first few points in each orbit exhibit strong variation in flux, and are thus excluded from the subsequent analysis." + The white light curve shows much larger systematics than either the HD 189733 and GJ-436 light curves., The white light curve shows much larger systematics than either the HD 189733 and GJ-436 light curves. +" Consequently, the light curves for each wavelength channel suffer from significant levels of correlated noise."," Consequently, the light curves for each wavelength channel suffer from significant levels of correlated noise." +" The decorrelation parameters were extracted as for HD 189733 and GJ-436, and are plotted in Fig. 24.."," The decorrelation parameters were extracted as for HD 189733 and GJ-436, and are plotted in Fig. \ref{fig:XO1_decorr_parameters}." +" Given the large amount of systematics, one would like to apply the decorrelation used for HD 189733 and GJ-436 on these data."," Given the large amount of systematics, one would like to apply the decorrelation used for HD 189733 and GJ-436 on these data." +" However, it is clear from Fig. 24,,"," However, it is clear from Fig. \ref{fig:XO1_decorr_parameters}," +" that for the in-transit orbits (3 and 4), we must extrapolate if we are to use corrections for AX, AY and 0."," that for the in-transit orbits (3 and 4), we must extrapolate if we are to use corrections for $\Delta X$, $\Delta Y$ and $\theta$." + We therefore must exclude these decorrelation parameters from the procedure., We therefore must exclude these decorrelation parameters from the procedure. +" An example of the decorrelation procedure using only W, T, ox and $7;, is shown in Fig. 25.."," An example of the decorrelation procedure using only $W$, $T$, $\phi_H$ and $\phi_H^2$, is shown in Fig. \ref{fig:XO1_decorr_eg}." + The large residuals show the decorrelation process does not provide a more satisfactory correction., The large residuals show the decorrelation process does not provide a more satisfactory correction. + The decorrelated light curves are shown in Fig. 26.., The decorrelated light curves are shown in Fig. \ref{fig:XO1_decorr_lightcurves}. . +result is not surprising if we consider that onlv a small fraction of the observed U-baud fux is expected to be scattered light (thus polarized): most of it is plotospleric cnussion from the central star. or thermal emission frou the disk.,"result is not surprising if we consider that only a small fraction of the observed H-band flux is expected to be scattered light (thus polarized); most of it is photospheric emission from the central star, or thermal emission from the disk." + Qur model indicates that the CO baudhead emission is consistent with cussion from CO eas which has a eniperature of IIS aud which is located iu the disk S i ⋝⋠↾↖↖⋂∐∩∩≺∖⋯⋠⊓∎↓≱≚≚↕↕↕⋅↭⋯↾↕↓⋠∖≼⋡⋠∖∐∏⋅⋠, Our model indicates that the CO bandhead emission is consistent with emission from CO gas which has a temperature of K and which is located in the disk between 0.08 and AU from the central star. +↕↕∖↴↾⋠∐⋅⋅↗AAU al star. 7 ound that in outburst there is a dust-free inner hole iu he system within AAT., \citet{juhasz2010} found that in outburst there is a dust-free inner hole in the system within AU. + Thus. the CO eas we observe rere should mostly be located iu this dust-free region.," Thus, the CO gas we observe here should mostly be located in this dust-free region." +" ? also derived the properties and distribution of he CO eas uxiug the fundamental vibrational lines iu he 5,nuu wavelength range.", \citet{goto2011} also derived the properties and distribution of the CO gas using the fundamental vibrational lines in the $\mu$ m wavelength range. +" They found that the dmudamental lines: are the superposition2. of"" a narrow (FWOAM=H50Man s 2) and a broad (FWZI-ID0 lan 1) component.", They found that the fundamental lines are the superposition of a narrow km $^{-1}$ ) and a broad (FWZI=150 km $^{-1}$ ) component. + The broad compoucut comes frou gas ovbitine rationalthe central star at 0.LAAT. and has a vil temperature between 1500 aud 00011. These paramicters are very similar to those we obtained from the overtouc baudhead features.," The broad component comes from gas orbiting the central star at AU, and has a vibrational temperature between 1800 and K. These parameters are very similar to those we obtained from the overtone bandhead features." + Thus the eas cnutting the overtone aud the fundiainental lines are co-located and are very likely plysically the same material., Thus the gas emitting the overtone and the fundamental lines are co-located and are very likely physically the same material. + ↽↙∏↕⋠∖≼⊲↻↴⋝⋮↕↕⋠∐∐∖⋯↕↕≽⋠∖⋮↕⋂⋯∖↕↕↕⊏∑↕↕↕↕↴≽⋠↧↕⋝↴≽↕⋮↴⋝↽⋝ sjeuificaut temporal variabilitv: if was m absorption iu quiescence (2)... very strong enission in February 2008. weals chussion in May 2008 (2)... and also weal: emission in July 2008 (this works).," The CO bandhead feature in Lup displays significant temporal variability: it was in absorption in quiescence \citep{sipos2009,herbig2001}, very strong emission in February 2008, weak emission in May 2008 \citep{aspin2010}, and also weak emission in July 2008 (this work)." + ? the variability of observedtle CO baudhead feature iu several other ENors., \citet{lorenzetti2009} observed the variability of the CO bandhead feature in several other EXors. + They claim that CO absorption is associated with quiescent periods. when the accretion rate is low aud the stellar photosphere (of an M-tyvpe cdwiuf) is visible.," They claim that CO absorption is associated with quiescent periods, when the accretion rate is low and the stellar photosphere (of an M-type dwarf) is visible." + According to them. CO cluission∙∙ is∙ associated∙ with. more active. periods.. when the accretion rate is higher. UV radiation is higher as well. thus the CO eas in the immer disk is heated ancl is producing CO bauchead emission.," According to them, CO emission is associated with more active periods, when the accretion rate is higher, UV radiation is higher as well, thus the CO gas in the inner disk is heated and is producing CO bandhead emission." + The general behavior of the CO bandhead feature in LLup is cousisteut with this picture., The general behavior of the CO bandhead feature in Lup is consistent with this picture. + There are several scenarios described in the literature to explain the origin of CO bandhead emission in YSOs., There are several scenarios described in the literature to explain the origin of CO bandhead emission in YSOs. + Based ou observations of low-mass YSOs iudicating significant CO bandhead emission variability ou timescales as short as a few davs. 7? considered the disk. stellar/disk wind. aud funnel flows as the origin of CO enmissiou.," Based on observations of low-mass YSOs indicating significant CO bandhead emission variability on timescales as short as a few days, \citet{biscaya1997} considered the disk, stellar/disk wind, and funnel flows as the origin of CO emission." + Although our observations are cousisteut with the inner disk origin (Fig. 7)).," Although our observations are consistent with the inner disk origin (Fig. \ref{fig:co}) )," +" we cannot exclude the fuunel- flow∙ origin either:""Deqavn the fieure4 in?7 ayco suggestsnetu that fuunel flows cau produce CO bandhlead profiles very simular to those we observed.", we cannot exclude the funnel flow origin either: the figure in \citet{martin1997} suggests that funnel flows can produce CO bandhead profiles very similar to those we observed. + 7 areued against the funnel flow origin based ou the lack of systematic recdwaurd absorption in the fundamental CO lines., \citet{goto2011} argued against the funnel flow origin based on the lack of systematic redward absorption in the fundamental CO lines. + IHowever. oue ↸⊳⋜⋯↕⊔⋜↧∶↴∙⊾∐∐∖⋜↧↴∖↴↕↑∏⋜↧⊓∪∐↖↖⇁↕∐∖∐≼⊔∐∖↑∪↑∐↸∖∐∐⊳∐∐⋜↧⊓∪∐:. :⋅ ⋅⋅⋅ ot. the syste Πιο funnel. flows do not Cross the liuc-.of-iel fowar the hot spot on the stellar surface. thus. absorp. 15 not expected to he seen.," However, one can imagine a situation when – due to the inclination of the system – the funnel flows do not cross the line-of-sight toward the hot spot on the stellar surface, thus, absorption is not expected to be seen." +" Ne note that CO can survive without dissociation only in the outer parts fuel flows, MM M 2 n disk. Mpp. ÁPere TS uo Coscutuvs ο. pDerweena -manelB flow τονand an. ner;EN diskfol. origin."," We note that CO can survive without dissociation only in the outer parts of the funnel flows, close to the inner edge of the disk, thus, there is no essential physical difference between a funnel flow and an inner disk origin." +303 Iu order to test whether the heating of the CO eas ix related to accrchou. atcifferent epochs we he streneth of the CO handhead feature with correlatedthe visual rightuess of the star (which is supposed to be accretion unuuositv) aud with the Bre line fux (another usual accretion rate tracer).," In order to test whether the heating of the CO gas is related to accretion, at different epochs we correlated the strength of the CO bandhead feature with the visual brightness of the star (which is supposed to be accretion luminosity) and with the $\gamma$ line flux (another usual accretion rate tracer)." + Using the spline-smoothed version of the light curve presented in 2.. we estimated a visual xiehtuess of niunag in February. πας in Max. and unas in⋅ July 2008.," Using the spline-smoothed version of the light curve presented in \citet{juhasz2010}, we estimated a visual brightness of mag in February, mag in May, and mag in July 2008." +". Assuniug⋅ that the V. EK color 10.2of the Was .. at these epochs fo the mcastired in SOULEEApril 2008 manag. ?)). the Dr? line valnefixes by a factor of (2.051.9 between February aud May, and a decreasedfactor of 25 between February and July."," Assuming that the $-$ K color of the source was similar at these epochs to the value measured in April 2008 mag, \citealt{juhasz2010}) ), the $\gamma$ line fluxes decreased by a factor of 1.9 between February and May, and a factor of 2.3 between February and July." +" We caleulated. the EWs of the CO bandhead by integrating the spectra between. 2.2925 and. jnu. aud oltained tor February. ⋟⋅"" M yar sRR Dor July 2008."," We calculated the EWs of the CO bandhead by integrating the spectra between 2.2925 and $\,\mu$ m, and obtained $-$ for February, $-$ for May, and $-$ for July 2008." +" ""AAssuming. agam. a constant VK7 color. the fux of the CO bandhead bya factor of 10 between February aud May. aud a decreasedfactor of 13 aud. July."," Assuming again a constant $-$ K color, the flux of the CO bandhead decreased by a factor of 10 between February and May, and a factor of 12 between February and July." + strength of the CO betweenbandheac Februaryfeature. the optical Thus.brightnessthe of the star. aud the strength of the Br feature seems to be changing in the same direction. although> not exactly with the same," Thus, the strength of the CO bandhead feature, the optical brightness of the star, and the strength of the $\gamma$ feature seems to be changing in the same direction, although not exactly with the same" +available data.,available data. + However. a discussion of this point would bring us away from the main objective of this paper.," However, a discussion of this point would bring us away from the main objective of this paper." + The correlation coefheient for the entire sample is 0.96., The correlation coefficient for the entire sample is $r_{h-R_{\Omega}} = 0.96$ . + It is thus interesting to note that the same correlation applies to both HSB and LSB galaxies., It is thus interesting to note that the same correlation applies to both HSB and LSB galaxies. + The correlation provides additional support to a conspiracy argument. because it shows that even in the inner region of approximately linear growth of the rotation curve the dark matter distribution must be in tune with the distribution of the visible mass.," The correlation provides additional support to a conspiracy argument, because it shows that even in the inner region of approximately linear growth of the rotation curve the dark matter distribution must be in tune with the distribution of the visible mass." + Note that. this is not necessarily in favor of the maximum-disk hypothesis. but rather it suggests that the relative distribution of visible and dark matter in spiral galaxies is homologous among different objects.," Note that this is not necessarily in favor of the maximum-disk hypothesis, but rather it suggests that the relative distribution of visible and dark matter in spiral galaxies is homologous among different objects." + Such homology could also be at the basis of observed correlations such as the Tully-Fisher (1977) relation (van Albada Sancisi 1986)., Such homology could also be at the basis of observed correlations such as the Tully-Fisher (1977) relation (van Albada Sancisi 1986). + In addition. this result will allow us to make a significant (although preliminary) test of the models developed in this paper on a simple idealized prototypical case that incorporates the observed correlation. without the need for separate tests on several observed objects.," In addition, this result will allow us to make a significant (although preliminary) test of the models developed in this paper on a simple idealized prototypical case that incorporates the observed correlation, without the need for separate tests on several observed objects." + We refer to standare cylindrical coordinates (R. 2.4). so that r=VRi42 represents the spherical radius.," We refer to standard cylindrical coordinates $(R, z, \theta)$ , so that $r = \sqrt{R^2+z^2}$ represents the spherical radius." +" We assume that the rotation curve V(R) of the disk galaxy. for which we want to construct à mass model. is known (1.e.. it has been ""observed""): as a mathematical boundary condition. we assume that the rotation curve remains flat at V4 out to infinite radii."," We assume that the rotation curve $V(R)$ of the disk galaxy, for which we want to construct a mass model, is known (i.e., it has been “observed""); as a mathematical boundary condition, we assume that the rotation curve remains flat at $V_{\infty}$ out to infinite radii." + In order to make a fit to the observed rotation curve. we wish to construct axisymmetric equilibrium models made of two mass components: the visible disk and the dark halo.," In order to make a fit to the observed rotation curve, we wish to construct axisymmetric equilibrium models made of two mass components: the visible disk and the dark halo." + For simplicity. we imagine the disk to be made only of stars. with known surface brightness profile a(R). and 1enore the contribution of other visible components.," For simplicity, we imagine the disk to be made only of stars, with known surface brightness profile $\mu(R)$, and ignore the contribution of other visible components." + It will soon be clear that the contributions from a gaseous disk and from a spheroidal bulge with given structure could be easily incorporated. 1f desired.," It will soon be clear that the contributions from a gaseous disk and from a spheroidal bulge with given structure could be easily incorporated, if desired." + The visible disk is deseribed as a zero-thickness disk: in a follow-up paper. we will address the studv of a self-consistent finite-thickness disk as a generalization of the present model.," The visible disk is described as a zero-thickness disk; in a follow-up paper, we will address the study of a self-consistent finite-thickness disk as a generalization of the present model." + The dark halo ts taken to be characterized by a Maxwellian. isothermal distribution function.," The dark halo is taken to be characterized by a Maxwellian, isothermal distribution function." + The choice of the dark matter distribution function is justified by an argument of physical simplicity., The choice of the dark matter distribution function is justified by an argument of physical simplicity. + With the minimum number of free parameters. 1t guarantees the flatness of the outer parts of the rotation curve.," With the minimum number of free parameters, it guarantees the flatness of the outer parts of the rotation curve." + The procedure that we are going to describe can be easily adapted to study dark halos characterized by other physically justified distribution functions. if so desired (e.g.. see Bertin. Saglia. and Stiavelli (1992) and Bertin (2000)).," The procedure that we are going to describe can be easily adapted to study dark halos characterized by other physically justified distribution functions, if so desired (e.g., see Bertin, Saglia, and Stiavelli (1992) and Bertin (2000))." +" In conclusion. for the dark matter halo we take the isotropic distribution function: where E=v7/2+Φ is the specific energy of dark matter particles and D, ts the gravitational potential."," In conclusion, for the dark matter halo we take the isotropic distribution function: where $E = v^2/2 + \Phi_T$ is the specific energy of dark matter particles and $\Phi_T$ is the gravitational potential." + In our model Φ is determined by the dark matter halo by the disk: The density distribution associated with the distribution function (5)) is where we have made it explicit that. in general. it is not spherically symmetric. because of the presence of the disk.," In our model $\Phi_T$ is determined by the dark matter halo by the disk: The density distribution associated with the distribution function \ref{fiso}) ) is where we have made it explicit that, in general, it is not spherically symmetric, because of the presence of the disk." + At large radii. the gravitational contribution of the disk becomes vanishingly small. so that the total gravitational potential eventually approaches the natural spherical symmetry of the self-consistent isolated isothermalsp/iere.," At large radii, the gravitational contribution of the disk becomes vanishingly small, so that the total gravitational potential eventually approaches the natural spherical symmetry of the self-consistent isolated isothermal." +. The dimensional free scales of the distribution funetion in Eq. (5)), The dimensional free scales of the distribution function in Eq. \ref{fiso}) ) + are the central density Phy and the (constant) velocity dispersion c., are the central density $\rho_{DM}^{0}$ and the (constant) velocity dispersion $\sigma$. +" We identify the quantity p?,,DM) with the central dark matter density. because we impose the condition In other words. we will only consider models that are regular at the center."," We identify the quantity $\rho_{DM}^{0}$ with the central dark matter density, because we impose the condition In other words, we will only consider models that are regular at the center." + The velocity dispersion ο is uniquely fixed by the value V4 of the rotation curve at large radit. so that the central dark matter density p0 is the only remaining free dimensional scale for the adopted dark matter density distribution.," The velocity dispersion $\sigma$ is uniquely fixed by the value $V_{\infty}$ of the rotation curve at large radii, so that the central dark matter density $\rho_{DM}^{0}$ is the only remaining free dimensional scale for the adopted dark matter density distribution." + In fact. at large distances from the center. where the system is almost spherically symmetric. matching with the observed rotation curve requires which. inserted in the Poisson equation. gives We thus see that thescale length ro of the dark matter density distribution appearing in Eq. (9))," In fact, at large distances from the center, where the system is almost spherically symmetric, matching with the observed rotation curve requires which, inserted in the Poisson equation, gives We thus see that thescale length $r_0$ of the dark matter density distribution appearing in Eq. \ref{asypot}) )" + is not a free length. because," is not a free length, because" +. where ht corresponds to the right-moving cosmic rays and fj is for left-moving cosmic rays.,", where $f_1^+$ corresponds to the right-moving cosmic rays and $f_1^-$ is for left-moving cosmic rays." + 0).k are the wave frequency and the wave number.," $\omega, k$ are the wave frequency and the wave number." + Q=Ωμ/Υ 1s the relativistic Larmor frequency. Qo—qB/mfc. mis the proton mass.," $\Omega=\Omega_0/\gamma_L$ is the relativistic Larmor frequency, $\Omega_0=qB/m/c$, $m$ is the proton mass." + From the Maxwell equations. one can obtain where By is the current density arising from the perturbed distribution fi.," From the Maxwell equations, one can obtain where d^3v is the current density arising from the perturbed distribution $f_1$." + Then. the dispersion relation can be obtained through eqs.(11..12..13)) =.0n-0 and the perturbed part of dielectric tensor [dpag where the subscript ] refers to different species.," Then, the dispersion relation can be obtained through \ref{linearf}, \ref{maxwell}, \ref{current}) ) _j )=0 and the perturbed part of dielectric tensor d^3p ], where the subscript `j' refers to different species." + For 6<< Q. Κὺ=EE representing MHD waves parallel to the magnetic field with Ωμ=Avy.," For $\omega\ll \Omega$ , $K^0=c^2/v_A^2$, representing MHD waves parallel to the magnetic field with $\omega_0=kv_A$." +" Insert ©=@)|0, into the above equation, one can find the growth rate corresponding to the imaginary part of the perturbed K;. RUND The growth rate of the gyroresonance instability can. be easily derived from this equation: where 7 is the gas number density. ©,=y‘Anne?fim is the proton plasma frequency. 1,e«p!7* is the number density of cosmic rays. and (see e.g.. LBO6) Q- πτπαγγσπασταipe. in which ry 1s the gyro-radius of IGeV particles. Br represents a beta function (see?).."," Insert $\omega=\omega_0+\omega_1$ into the above equation, one can find the growth rate corresponding to the imaginary part of the perturbed $K_j$ , ) The growth rate of the gyroresonance instability can be easily derived from this equation: where $n$ is the gas number density, $\omega_p=\sqrt{4\pi n e^2/m}$ is the proton plasma frequency, $n_{cr}\propto p^{1-\alpha}$ is the number density of cosmic rays, and (see e.g., LB06) Q = -1), in which $r_0$ is the gyro-radius of 1GeV particles, $Bt$ represents a beta function \citep[see][]{Math_handbook}." +" The sign of [,, determines whether the wave grows C) or damps (-"").", The sign of $\Gamma_{gr}$ determines whether the wave grows ('+') or damps ('-'). + It depends on the bracketed expression in Eq.(15)). which is a derivative of f along a circle centered at p-—Ηλpy=O (see?).. The wave grows if there are more and more particles along the way it propagates.," It depends on the bracketed expression in \ref{dielectric}) ), which is a derivative of $f$ along a circle centered at $p_z = m v_A, p_\bot = 0$ \citep[see][]{Kulsrudbook}, The wave grows if there are more and more particles along the way it propagates." + Unlike with shifted distribution (streaming instability). only circularly polarized waves can be excited by the gyroresonance instability.," Unlike with shifted distribution (streaming instability), only circularly polarized waves can be excited by the gyroresonance instability." + First we decide the directions of wave vector resonant with right and left moving cosmic rays. respectively.," First we decide the directions of wave vector resonant with right and left moving cosmic rays, respectively." + Then we determine the polarization of the waves bearing in mind that CR protons always rotate clockwise with respect to the magnetic field., Then we determine the polarization of the waves bearing in mind that CR protons always rotate clockwise with respect to the magnetic field. +" For an oblate distribution of particles with p,>p. the left moving. right circularlypolarized wave can resonate with the right moving CRs (with superscript ) and gain energy from them as it encounters more particles in the wave propagation direction (see Fig.lright)."," For an oblate distribution of particles with $p_\bot>p_\|$, the left moving, right circularlypolarized wave can resonate with the right moving CRs (with superscript `+') and gain energy from them as it encounters more particles in the wave propagation direction (see \ref{vel_dist}{ )." + So do the right moving. left circularly polarized waves with the left moving CRs (with superscript -.," So do the right moving, left circularly polarized waves with the left moving CRs (with superscript `-')." + For a prolate distribution. the opposite is true.," For a prolate distribution, the opposite is true." + They are illustrated by 1.., They are illustrated by \ref{vel_dist}. + In this section we shall provide a rigorous study of the suppression of the growth of the instability., In this section we shall provide a rigorous study of the suppression of the growth of the instability. + The wave-particle interaction was treated using the second order theory (SOT) in?) for bi-Maxwellian distribution of thermal particles., The wave-particle interaction was treated using the second order theory (SOT) in \citet{GaryTokar} for bi-Maxwellian distribution of thermal particles. + These particles have Maxwellian distribution characterized by Tj «Τι. two different temperatures parallel and perpendicular," These particles have Maxwellian distribution characterized by $T_\|, T_\bot$ , two different temperatures parallel and perpendicular" + , +the SSTS geueralized zeta Tiuctious cau be written iu the form: The diagonal Seeley coefficients [e](4G) of the IX-heat function high-T expansion (resp.,the SSTS generalized zeta functions can be written in the form: The diagonal Seeley coefficients $[c_n]_{AA}(K)$ of the K-heat function high-T expansion (resp. +" the Seeley coellicients e,(4A €)) are the integrals over the whole plane of the Seeley densities [cs]vaGEFd) which arise in the associated IW-heat kernel expansion (resp.the Seeley densities ejCr.d:AC)): Neelecting the entire part aud setting a large but fiuite No. the SSTS Casimir energies are regularized where the Lf zero mocles have been subtracted: the zero-point vacuum renormalization amounts to ruline out the contribution"" of+ the ejA-CA) aud ejACNMN€) coefficients."," the Seeley coefficients $c_n(K^G)$ ) are the integrals over the whole plane of the Seeley densities $[c_n]_{AA}(\vec{x},\vec{x};K)$ which arise in the associated K-heat kernel expansion (resp.the Seeley densities $c_n(\vec{x},\vec{x};K^G)$ ): Neglecting the entire part and setting a large but finite $N_0$, the SSTS Casimir energies are regularized as where the $4l$ zero modes have been subtracted: the zero-point vacuum renormalization amounts to ruling out the contribution of the $c_0(K)$ and $c_0(K^G)$ coefficients." +"nan Also. AMT> is"" regularized"" tu"" a similar"" way The physical limits fes=—4 for AALrey ud s=+ for MALE are regular points of the zeta functions."," Also, $\Delta M_{\rm TS}^R$ is regularized in a similar way The physical limits $s=-{1\over 2}$ for $\Delta M_{\rm TS}^C$ and $s={1\over 2}$ for $\Delta M_{\rm TS}^R$ are regular points of the zeta functions." + The contribution of the first coelficieut of the asyiuptotic expansion is not compensated by the coutributiou of the mass renormalization couuter-ternmis: Massless particles spoil the large mass subtraction criterion. see [1]. . and we finally obtain the one-loop SSTS mass shift formula:," The contribution of the first coefficient of the asymptotic expansion is not compensated by the contribution of the mass renormalization counter-terms: Massless particles spoil the large mass subtraction criterion, see \cite{BRvNV}, , and we finally obtain the high-temperature one-loop SSTS mass shift formula:" +we use a inodified version of the one-dimensional lydrodvuaumiics code VIEL by ?.. which is publiclyablet.,"we use a modified version of the one-dimensional hydrodynamics code VH-1 by \cite{Blondin1993}, which is publicly." +. VIEL is based on the piecewise parabolic inethod (?2).. and uses a Lagrange-Remap approach to solve the Euler equations: where the primary variables are the mass density p. gas pressure P. aud fluid velocity u.," VH-1 is based on the piece-wise parabolic method \citep{Colella1984}, and uses a Lagrange-Remap approach to solve the Euler equations: where the primary variables are the mass density $\rho$ , gas pressure $P$ , and fluid velocity $\textbf{u}$." + Iu our implementation. the acceleration feld a includes both eravity and radiative pressure forces. and JP iud C are heating aud cooling source ternis arising from radiative feedback.," In our implementation, the acceleration field $\textbf{a}$ includes both gravity and radiative pressure forces, and $H$ and $C$ are heating and cooling source terms arising from radiative feedback." + The total euergv per uuit mass £ ds the sua of the kinetic energy and the internal enerexy e: and the iuterual energy is related to the pressure through the equation of state for au ideal gas for a given aciabatic index 5., The total energy per unit mass $E$ is the sum of the kinetic energy and the internal energy $e$: and the internal energy is related to the pressure through the equation of state for an ideal gas for a given adiabatic index $\gamma$. + The modifications we made to VIT-T include two main aspects., The modifications we made to VH-1 include two main aspects. + The first one is the straightforward chanee of a nuiform radial erid iu spherical geometry to a logaritlanic ouc., The first one is the straightforward change of a uniform radial grid in spherical geometry to a logarithmic one. + This is to ensure sufficieutly lieh resolition near the central DIT while covering a large spherical region with a reasonable number of eid. cells., This is to ensure sufficiently high resolution near the central BH while covering a large spherical region with a reasonable number of grid cells. + The second one involves a detailed treatiment of radiative feedback., The second one involves a detailed treatment of radiative feedback. + Specifically. we added the heating aud cooling terms iu the energv conservation equation. and the radiative pressure forces in the momentum aud euergy conscrvation equations.," Specifically, we added the heating and cooling terms in the energy conservation equation, and the radiative pressure forces in the momentum and energy conservation equations." + The radiative feedback is modeled by formulating the cooling. heating. and radiation pressure with two parameters: the ionization parameter © and eas temperature ©.," The radiative feedback is modeled by formulating the cooling, heating, and radiation pressure with two parameters: the ionization parameter $\xi$ and gas temperature $T$." + We asstune that the photo-ionized region around the DII cau be fully described by © aud 7., We assume that the photo-ionized region around the BH can be fully described by $\xi$ and $T$. + The ionization parameter © is defined as: where Lor) is the local luminosity. aud ate} is the hydrogen 1νο deusity at radius kc.," The ionization parameter $\xi$ is defined as: where $L(r)$ is the local luminosity, and $n(r)$ is the hydrogen number density at radius $r$." +" The DIT luninesity L(0) is assmued to have a power law spectrum. L,~vy > and the atteuuation of the luminosity is described by where a!) is the radiative acceleration due to photo-absorption. and ο is the speed of light."," The BH luminosity $L(0)$ is assumed to have a power law spectrum, $L_{\nu}\sim \nu^{-3/2}$ , and the attenuation of the luminosity is described by where $a^r_{abs}$ is the radiative acceleration due to photo-absorption, and $c$ is the speed of light." +" Iu solving Equation 7.. we ake another simplifving assumption that the spectral shape of L(r) is the same as the original £(0). so that the heating. cooling. aud radiation acceleration at any radius can be obtained frou computed tables of the £-T. exid. where the scaling on the local hwdrosen deusitv is explicitly factored out. aud ay, is the radiation acceleration mainly due to resonant Lya lue scattering."," In solving Equation \ref{eq:rt}, we make another simplifying assumption that the spectral shape of $L(r)$ is the same as the original $L(0)$, so that the heating, cooling, and radiation acceleration at any radius can be obtained from pre-computed tables of the $\xi$ $T$ grid, where the scaling on the local hydrogen density is explicitly factored out, and $a^{r}_{line}$ is the radiation acceleration mainly due to resonant $\rm {Ly\alpha}$ line scattering." + We compute these two dimensional tables using the photo-ionization code CLOUDY version 08.00 (?).. assundue a primordial clemental abuudance. and a yower-law input spectrmm with index 1.5 in the cuerev range of 13.6 eV to 100 keV. Tn the lycockwnamics update of the momentum and energy conservation equations. the heating. cooling. aud radiation forces are hen interpolated from these tables. in conjunction with he solution of Equation 7..," We compute these two dimensional tables using the photo-ionization code CLOUDY version 08.00 \citep{Ferland1998}, assuming a primordial elemental abundance, and a power-law input spectrum with index $-1.5$ in the energy range of 13.6 eV to 100 keV. In the hydrodynamics update of the momentum and energy conservation equations, the heating, cooling, and radiation forces are then interpolated from these tables, in conjunction with the solution of Equation \ref{eq:rt}." +" Iun addition to photo-absorption and resonant line scattering. Thomsou scattering also contributes to the radiation pressure force. which is treated separately as Cone=aEODLoqu(r). where a?(r) and L;44 are the gravitational(nr) acceleration aud Eddingtoun Iuninosity of the DII. respectively,"," In addition to photo-absorption and resonant line scattering, Thomson scattering also contributes to the radiation pressure force, which is treated separately as $a^r_{cont} = -a^g(r)L(0)/L_{edd}(r)$, where $a^g(r)$ and $L_{edd}$ are the gravitational acceleration and Eddington luminosity of the BH, respectively." + We note that the unattenuated DII huuinositv. L(0). is used iu calculating «4. as the absorbed bhuuinuositv is assuniexd to be re-ciitted at energies below the ionization threshold. which also contributes to Thomson scatteriug.," We note that the unattenuated BH luminosity, $L(0)$, is used in calculating $a^r_{cont}$, as the absorbed luminosity is assumed to be re-emitted at energies below the ionization threshold, which also contributes to Thomson scattering." +" Our feedback method is an improvement to those previously used (e... 7?7?7)) in that it computes the heating. cooling. and radiation pressure forces more accurately, aud applies to a temperature range of Tox108 WW. much larger than the previous range 10+>© (Watson 1981)).," The 2D approximation neglects the radial displacements which can be expected as small in stably stratified radiative shells where the buoyancy frequency $N$ is much higher than the rotation rate, $N \gg \Omega$ (Watson \cite{W81}) )." + This condition ts not fulfilled in stellar convection zones., This condition is not fulfilled in stellar convection zones. + The present paper overcomes the 2D approximation by allowance for radial displacements., The present paper overcomes the 2D approximation by allowance for radial displacements. + Poloidal motions and entropy disturbances are thus included., Poloidal motions and entropy disturbances are thus included. + Our formulation contains the 2D approximation as a special limit. of large parameter 42£N/GQ)o»D: where £ is the radial scale of the disturbances and ris the radius.," Our formulation contains the 2D approximation as a special limit of large parameter $\hat{\lambda} = \ell N/(r\Omega ) +\gg 1$; where $\ell$ is the radial scale of the disturbances and $r$ is the radius." + We shall see that the most unstable modes have so small radial scales that | and this condition is by far not fulfilled., We shall see that the most unstable modes have so small radial scales that $}1$ and this condition is by far not fulfilled. + The minimum amount of differential rotation for onset of the instability 1s considerably reduced compared to the 2D case., The minimum amount of differential rotation for onset of the instability is considerably reduced compared to the 2D case. + More important is that the instability does not exist in the limit of No-0. so that differential rotation is stable in convection zones with their almost adiabatic stratification.," More important is that the instability does not exist in the limit of $N\rightarrow 0$, so that differential rotation is stable in convection zones with their almost adiabatic stratification." + The instability may. however. switch on in the region of penetrative convection near the base of the convection zone.," The instability may, however, switch on in the region of penetrative convection near the base of the convection zone." + Such a near-base instability may be the reason for the difference in latitudinal profiles of angular velocity between the top and the bottom of the solar convection zone (Charbonneau et al. 1999))., Such a near-base instability may be the reason for the difference in latitudinal profiles of angular velocity between the top and the bottom of the solar convection zone (Charbonneau et al. \cite{CDG99}) ). + If this is the case. transequatorial vortices (unstable S1 modes) should be present near the base.," If this is the case, transequatorial vortices (unstable S1 modes) should be present near the base." + The rates of (retrograde) drift of the vortices are similar to that of the r-modes signatures inferred by Knaack et al. (2005)), The rates of (retrograde) drift of the vortices are similar to that of the r-modes signatures inferred by Knaack et al. \cite{KSB05}) ) + from solar magnetograms., from solar magnetograms. + The latitudinal dependence of the angular velocity Q on the sun can be approximated by an expression including cos?8 and cos0 terms so that Here Ωμ is the equatorial angular velocity. « is the normalized equator-pole difference in the rotation rate. and f is the fraction of the cos?6 term contribution to that differential rotation.," The latitudinal dependence of the angular velocity $\Omega$ on the sun can be approximated by an expression including $\cos^2\theta$ and $\cos^4\theta$ terms so that Here $\Omega_0$ is the equatorial angular velocity, $a$ is the normalized equator-pole difference in the rotation rate, and $f$ is the fraction of the $\cos^4\theta$ term contribution to that differential rotation." + The rotation is assumed slow enough not to deform the spherical symmetry of the star., The rotation is assumed slow enough not to deform the spherical symmetry of the star. +aud ou the SN Ta ejecta’s interaction with a donor (Marietta2011:Nugentetal.Bloomct2012). severely istrain the red giant donor chaunclbs contribution to the SN Ia population.,"and on the SN Ia ejecta's interaction with a donor \citep{mbf00,kase10,hayd10,bian11,nuge11,bloo12} severely constrain the red giant donor channel's contribution to the SN Ia population." + The double detonation scenario has received iore attention recently due to the prediction of He detouatious in- prc-AM CV systems (Bildstenetal.2007:FinkSimetal.2010:Woosley&Ixaseun 2011).," The double detonation scenario has received more attention recently due to the prediction of He detonations in pre-AM CVn systems \citep{bild07,fhr07,fink10,sb09b,shen10,sim10,wk11}." + However. while many features of this scenario are attractive. it is not clear how the ILe-detonation products on the outside of the core will skew observatious away from SN Ta-like events.," However, while many features of this scenario are attractive, it is not clear how the He-detonation products on the outside of the core will skew observations away from SN Ia-like events." + Even a sinall amount of surface irou-eroup clements created during UWe-burning. especially Ti aud Cr. can significautly impact the colors of the SN at peak light.," Even a small amount of surface iron-group elements created during He-burning, especially Ti and Cr, can significantly impact the colors of the SN at peak light." + The UV Lue blanketing due to these elements causes the predicted spectra near peak light to be much redder than observed (IKromieretal.2010:Simetal.2011).," The UV line blanketing due to these elements causes the predicted spectra near peak light to be much redder than observed \citep{krom10,sim11}." +.. Furthermore. the Ho detonation will eject radioactive isotopes at hieh velocities. a feature that las never been observed ia SNe Ia. The double degenerate scenario involves the dynamical coalescence of two C/O WDs.," Furthermore, the He detonation will eject radioactive isotopes at high velocities, a feature that has never been observed in SNe Ia. The double degenerate scenario involves the dynamical coalescence of two C/O WDs." + The predicted merecr rate id delay time distribution (Brauchetal.1995:Nele-mansetal.2001:Ruiter2009). ancl observatious of progenitor systems (albeit with large error bars Nelemansetal.2005:Geier2010a.b:Toviassiauetal.2010:Rodrfguez-Cal 2010)) are pronuisiuelv consistent with the observed SN Ia rate aud delay. time distribution (Maozetal.2010.2011:παν2011).," The predicted merger rate and delay time distribution \citep{bran95,nele01a,rbf09} and observations of progenitor systems (albeit with large error bars; \citealt{nele05b,geie10a,geie10b,tovm10,rodr10}) ) are promisingly consistent with the observed SN Ia rate and delay time distribution \citep{msg10,maoz11,grau11}." +. ILowever. previous theoretical studies have found that the morecr of two WDs instead trigecrs an accretion induced collapse. vielding a faint explosion and a neutron star remnant iustead of à SN Ia (Nomoto&Όροι1985:Iiaetal.1987:Sato&Nomoto200 1).," However, previous theoretical studies have found that the merger of two WDs instead triggers an accretion induced collapse, yielding a faint explosion and a neutron star remnant instead of a SN Ia \citep{ni85,ksn87,sn04}." +". These studies assumued that the less massive WD is disrupted iuto a Weplerian disk from which the more massive WD accretes at a constant rate near the gravitational Eddington limit of 10.7AL.vr+ for ~10"" vr.", These studies assumed that the less massive WD is disrupted into a Keplerian disk from which the more massive WD accretes at a constant rate near the gravitational Eddington limit of $10^{-5} \smpy$ for $\sim 10^5$ yr. + In coutrast. smoothed particle hydrodvuamical (SPIT) studies of the mereimg process (Deuzetal.1990:RasioDanetal.2011:Raskin2011) find that the tically disrupted WD is instead converted into material that is supported against eravity bv a combination of thermal pressure frou shock heating in regions close to the more massive WD and centrifugal support iu the optically thick outer regions.," In contrast, smoothed particle hydrodynamical (SPH) studies of the merging process \citep{benz90,rs95,scm97,ggi04,lore05,lig09,ypr07,dan11,rask11} find that the tidally disrupted WD is instead converted into material that is supported against gravity by a combination of thermal pressure from shock heating in regions close to the more massive WD and centrifugal support in the optically thick outer regions." + Until the work of Yoonctal.(2007) and vanIerkwijketal.(2010).. these important features of the merged coufiguration were lareelv neglected iu studies of the long-terii evolution of niereer roninauts.," Until the work of \cite{ypr07} and \cite{vcj10}, these important features of the merged configuration were largely neglected in studies of the long-term evolution of merger remnants." + Oue couclusion reached from consideration of this more detailed merger cud-state is that the viscous evolution of the ditfercutially rotating lavers ist be taken iuto account before the secular thermal evolution of the iuerger remnant can be calculated., One conclusion reached from consideration of this more detailed merger end-state is that the viscous evolution of the differentially rotating layers must be taken into account before the secular thermal evolution of the merger remnant can be calculated. + Tn particular. if maguetically-governed processes sucli as the maeuctorotational instability (Balbus&Taw-lov1991:Tawley&Balbus2003)— aud the Tavler-Spruit dynamo (TavlerL973:Spruit1999.2002) operate cficicutly. augular monentuni will be redistributed throughout the remmant mach more rapidly than heat can be raciated away.," In particular, if magnetically-governed processes such as the magnetorotational instability \citep{bh91,hb91,balb03} and the Tayler-Spruit dynamo \citep{tayl73,spru99,spru02} operate efficiently, angular momentum will be redistributed throughout the remnant much more rapidly than heat can be radiated away." + Tn this paper. we present an updated physical model for the evolutiou of unequal mass double WD ierecrs.," In this paper, we present an updated physical model for the evolution of unequal mass double WD mergers." + Dynamical aud viscous processes. acting on timescales much shorter than the thermal timescale. convert the majority of the less massive WD iuto a hot radially extended envelope surrounding the more massive WD.," Dynamical and viscous processes, acting on timescales much shorter than the thermal timescale, convert the majority of the less massive WD into a hot radially extended envelope surrounding the more massive WD." + Little mass remains ceutrifugallvy-supported following the viscous evolution., Little mass remains centrifugally-supported following the viscous evolution. + While the eutire renmaut has a inass essentiallv equal to the total mass of the initial binary and may be larger than the Chandrasckhar mass. the hot envelope is extended aud docs not exert considerable pressure ou the degenerate core.," While the entire remnant has a mass essentially equal to the total mass of the initial binary and may be larger than the Chandrasekhar mass, the hot envelope is extended and does not exert considerable pressure on the degenerate core." + Substantial heat is generated diving the dyiamical aud viscous phases of evolution aud may lead to convective C-burning at the interface between the hot envelope and degenerate core duriug or directly after the viscous evolution., Substantial heat is generated during the dynamical and viscous phases of evolution and may lead to convective C-burning at the interface between the hot envelope and degenerate core during or directly after the viscous evolution. + If iustead the maxima temperature is too low or munuediate convective C-burning prior to siguificaut hermal transport. the iuuer part of the cuvelope will undergo a Welvin-Wehuholtz coutraction on a thermal nuescale of 107—107 xx. which is set by the Eddingtou iuimositv of the elant euvelope.," If instead the maximum temperature is too low for immediate convective C-burning prior to significant thermal transport, the inner part of the envelope will undergo a Kelvin-Helmholtz contraction on a thermal timescale of $10^3- 10^4$ yr, which is set by the Eddington luminosity of the giant envelope." + The hot noucotatiug euvelope radiates near the Eddington limit. cooling aud colpressing the base of the cuvelope relatively rapidly. ist as the base of the accreted cuvelope is compressed im studies assunuiug disk accretion such as Nomoto&Όροι (1985).," The hot non-rotating envelope radiates near the Eddington limit, cooling and compressing the base of the envelope relatively rapidly, just as the base of the accreted envelope is compressed in studies assuming disk accretion such as \cite{ni85}." +. This contraction proceeds on a shorter timescale iu the iuward thermal diffusion timescale mto the degenerate core of ~1089 xy. so that a temperature inversion is formed aud a convective C-burning shell is )oru well away from the ceuter.," This contraction proceeds on a shorter timescale than the inward thermal diffusion timescale into the degenerate core of $\sim 10^6$ yr, so that a temperature inversion is formed and a convective C-burning shell is born well away from the center." + Thus. it appears unavoidable that double C/O WD nerecrs ignite C-burniug well away from the mereecr relmnaut’s center.," Thus, it appears unavoidable that double C/O WD mergers ignite C-burning well away from the merger remnant's center." + This off-ceuter ignition allows the convective laver to expand. aud the necessary conditions or a Violent deflagration and/or detonation are uot reached.," This off-center ignition allows the convective layer to expand, and the necessary conditions for a violent deflagration and/or detonation are not reached." + Under the assmuptioun of heat transport bv hermal conduction. the burning shell moves slowly inwards at a speed of ~0.01curs+. reaches the ceuter in ~104 yr. and eventually converts the previously C/O WD into an O/Ne WD (Timesetal.1991:Saio&Nomoto 1998).," Under the assumption of heat transport by thermal conduction, the burning shell moves slowly inwards at a speed of $\sim 0.01 \cgsv$, reaches the center in $\sim 10^{4}$ yr, and eventually converts the previously C/O WD into an O/Ne WD \citep{twt94,sn98}." + Tf the rommant mass is lareer than the Chandrasekhar mass. envelope material can coutinue to contract and compress the O/Ne WD until it collapses into a neutron star. acconipauied by a weak explosion.," If the remnant mass is larger than the Chandrasekhar mass, envelope material can continue to contract and compress the O/Ne WD until it collapses into a neutron star, accompanied by a weak explosion." + While such events will not viell SNe Ta. they may eive rie to fast transicuts and contribute to r-process enrichineut. and are certainly of astrophysical interest (Dessartetal.2006:Moetzeer2009a.b:Darbhact 2010)..," While such events will not yield SNe Ia, they may give rise to fast transients and contribute to $r$ -process enrichment, and are certainly of astrophysical interest \citep{dess06,mpq09a,mpq09b,darb10}. ." + Although this chain of eveuts represents an updated description of double WD inerger evolution. the final," Although this chain of events represents an updated description of double WD merger evolution, the final" +Although we focussed primarily on instability with radial wave numbers 1 corresponding to hall a wavelength across the laver. our instability equations allow modes of any racial wavenumber p». and we have explored some cases wilh »=10 and »=100 (plots nol presented).,"Although we focussed primarily on instability with radial wave numbers 1 corresponding to half a wavelength across the layer, our instability equations allow modes of any radial wavenumber $n$, and we have explored some cases with $n=10$ and $n=100$ (plots not presented)." + In general the higher the » chosen. the shorter are the radial displacements.," In general the higher the $n$ chosen, the shorter are the radial displacements." + Shorter displacements imply reduced resistance bv any negative buovancy force., Shorter displacements imply reduced resistance by any negative buoyancy force. + For overshoot tachoclines the low effective gravity implies (here is little buovant resistance to vertical motions., For overshoot tachoclines the low effective gravity implies there is little buoyant resistance to vertical motions. +" So the growth rate of unstable modes is nearly independent ol η,", So the growth rate of unstable modes is nearly independent of $n$. + For radiative tachoclines. the strong negative buovancy due to the high effective gravity C suppresses the radial motions.," For radiative tachoclines, the strong negative buoyancy due to the high effective gravity $G$ suppresses the radial motions." + So it becomes easier to excite unstable modes with higher n. because modes with higher » contain smaller radial displacements. aud hence should feel less resistance [rom the strong negative buovancy.," So it becomes easier to excite unstable modes with higher $n$, because modes with higher $n$ contain smaller radial displacements, and hence should feel less resistance from the strong negative buoyancy." + Therefore they could be more unstable. or be unstable for parameter values for which »=1 modes are stable.," Therefore they could be more unstable, or be unstable for parameter values for which $n=1$ modes are stable." + Our results lor radiative tachoclines in E. C. and Ix stars represent (he minimum amount ol instability in the svstem which is for n=1 there could be even more lor ηz1.," Our results for radiative tachoclines in F, G, and K stars represent the minimum amount of instability in the system which is for $n=1$ – there could be even more for $n>1$." + If diffusion were included in the model. which is certainly. present in stellar tachoclines. modes with higher » would become less unstable or even stable.," If diffusion were included in the model, which is certainly present in stellar tachoclines, modes with higher $n$ would become less unstable or even stable." + Higher » modes will also be less unstable if the toroidal bands are (twisted (Fisheretal1999)., Higher $n$ modes will also be less unstable if the toroidal bands are twisted \citep{fllfp1999}. +. From analvses of global MIID instabilities in 3D thin-shell models of the solar/stellar Lachoclines. we find that solar-like and antisolar (wpe Iatitudinal differential rotations with coexisting toroidal bands are unstable.," From analyses of global MHD instabilities in 3D thin-shell models of the solar/stellar tachoclines, we find that solar-like and antisolar type latitudinal differential rotations with coexisting toroidal bands are unstable." + Antisolar differential rotation is. in general. more unstable (han a solar-like one in all F. G and Ix stis. (he pole rotating one or (vo percent faster than (he equator can make (he latitudinal differential rotation unstable in weakly maegneltized overshoot tachoclines. although it requires much stronger magnetic fields to be unstable in the radiative tachoclines in G and IX stars.," Antisolar differential rotation is, in general, more unstable than a solar-like one in all F, G and K stars – the pole rotating one or two percent faster than the equator can make the latitudinal differential rotation unstable in weakly magnetized overshoot tachoclines, although it requires much stronger magnetic fields to be unstable in the radiative tachoclines in G and K stars." + llieh effective eravily in the radiative tachoclines largely. suppreses (he radial motions bv the negative magnete buovancy and therefore. it is diffieult to grow the perturbations.," High effective gravity in the radiative tachoclines largely suppreses the radial motions by the negative magnetic buoyancy and therefore, it is difficult to grow the perturbations." + By contrast. low effective gravity allows the radial motions to grow. and more so when the variation in differential rotation in latitude is smaller.," By contrast, low effective gravity allows the radial motions to grow, and more so when the variation in differential rotation in latitude is smaller." + Thus antsolar (wpe differential rotation becomes more unstable (han solar tvpe ones. because less JxD force is needed {ο overcome (he perturbation centrifugal force Chat tries to stabilize the displacement.," Thus antisolar type differential rotation becomes more unstable than solar type ones, because less $J\times B$ force is needed to overcome the perturbation centrifugal force that tries to stabilize the displacement." +few vears) variability has also been reported (Pellegrinietal.2000:Ishisaki&Wang 2001).,"few years) variability has also been reported \citep{pelle,ishi,imm}." +. No spectral variability has been reported: however. a full study of the spectral behaviour using the wealth of data collected from the nucleus of M31 has not been done so far.," No spectral variability has been reported; however, a full study of the spectral behaviour using the wealth of data collected from the nucleus of M81 has not been done so far." + In the present paper we revisit the soft. X-ray emission of the nucleus of M81 through the observations of ROSAT instruments concentrating on variability. and compare these data with those from ASCA. BeppoSAX and.," In the present paper we revisit the soft X-ray emission of the nucleus of M81 through the observations of ROSAT instruments concentrating on variability, and compare these data with those from ASCA, BeppoSAX and." +.. In particular. the ROSAT/PSPC data eive us the opportunity to study anv spectral variation of soft X-ray emission that occurred during the extensive ROSAT coverage of M81.," In particular, the ROSAT/PSPC data give us the opportunity to study any spectral variation of soft X-ray emission that occurred during the extensive ROSAT coverage of M81." + This paper is structured as follows: Section illustrates the data aud their reduction: in Section 3. we describe the source variability: section 4 is devoted to spectral analvsis; our results are discussed in Section 5.., This paper is structured as follows: Section \ref{data} illustrates the data and their reduction; in Section \ref{time} we describe the source variability; Section \ref{spec} is devoted to spectral analysis; our results are discussed in Section \ref{disc}. + A log of all the observations of M81 is given in Table 1.., A log of all the observations of M81 is given in Table \ref{log}. + M81 was observed 22 times with ROSAT in a period of seven vears from 1991 to 1998: 12 times with the PSPC (PositionPlellermannetal.LOST) and 10 times with the IIRI (Llieh 1996).., M81 was observed 22 times with ROSAT in a period of seven years from 1991 to 1998: 12 times with the PSPC \citep[Position Sensitive Proportional Counter;][]{pfef} and 10 times with the HRI \citep[High Resolution Imager;][]{david}. + This frequent coverage is mainly due to the monitoring of the supernova SN1993J (Zimmermannοἱal.1994).. 2.7. south of the nucleus of M81. whose evolution was followed with roughly one observation every six months.," This frequent coverage is mainly due to the monitoring of the supernova SN1993J \citep{zim}, 2.7' south of the nucleus of M81, whose evolution was followed with roughly one observation every six months." + The large field ol view of the PSPC (2° diameter) and of the ILRI (30. diameter) ensures that the nucleus is included in every observation of $N1993J. The data have been processed using the IRAE(v., The large field of view of the PSPC $2^{\circ}$ diameter) and of the HRI (30' diameter) ensures that the nucleus is included in every observation of SN1993J. The data have been processed using the IRAF(v. + 2.11)/PROS (v. 2.5) software svstem (Tody1986;Worralletal.," 2.11)/PROS (v. 2.5) software system \citep{tody,wor}." +1992).. The radius for source photon selection for the PSPC depends on the position of the source on (he detector plane. because the radius of the Point Spread Function (PSF) increases with the distance from the center of the field of view (FOV) (Boese2000):: for the on-axis observations we used a source radius of 3°. which includes of the emission at all energies and an annular background region with inner and outer radi 3° and 7 respectively.," The radius for source photon selection for the PSPC depends on the position of the source on the detector plane, because the radius of the Point Spread Function (PSF) increases with the distance from the center of the field of view (FOV) \citep{boese}; for the on-axis observations we used a source radius of 3', which includes of the emission at all energies and an annular background region with inner and outer radii 3' and 7' respectively." + For the off-axis observations the source position and radius were evaluated with the processing (Damianietal1997) applied to each observation and from the ROSAT/PSPC point spread function description (Boese2000):: the radius is 5 aud 6. for M81 nucleus positions of 10 and 36° (o 42°. respectively.," For the off-axis observations the source position and radius were evaluated with the processing \citep{dami} applied to each observation and from the ROSAT/PSPC point spread function description \citep{boese}: the radius is 5' and 6', for M81 nucleus off-axis positions of 16' and 36' to 42', respectively." + We have excluded. any. part of the selected region obscured by the PSPC window supporting ribs., We have excluded any part of the selected region obscured by the PSPC window supporting ribs. + The background was extracted from an annular region with outer and inner radii 12° and G respectively. after subtraction of the contribution of point sources.," The background was extracted from an annular region with outer and inner radii 12' and 6' respectively, after subtraction of the contribution of point sources." + For convenience of reference. we designate the PSPC pointings D1-P12 in time order.," For convenience of reference, we designate the PSPC pointings P1-P12 in time order." + The ten IRI observations pointed on M81 (111-1110) have a total exposure time of 177, The ten HRI observations pointed on M81 (H1-H10) have a total exposure time of 177 +"calibrate the individual exposures taken ou the 2018,",calibrate the individual exposures taken on the $^{\rm{th}}$. + No fringe subtraction was done for the I band images., No fringe subtraction was done for the I band images. + Surface photometry for IKIK98 250 was doue using the ellipse fitting algorithm of Deuder&Mólleuloff(1987)., Surface photometry for KK98 250 was done using the ellipse fitting algorithm of \cite{bender87}. +. Ellipse fitting in the I band was restricted to the imner reeions of the galaxy. since the outer low surface brightuess cnussion is affected by fringing.," Ellipse fitting in the I band was restricted to the inner regions of the galaxy, since the outer low surface brightness emission is affected by fringing." + The average ellipticity was fouud to be 0.72£0.02 (correspouding to an inclination of ~ for an intrinsic thickuess ratio qu=0.2).," The average ellipticity was found to be $0.72\pm0.02$ (corresponding to an inclination of $\sim 79^\circ$, for an intrinsic thickness ratio $q_0 =0.2$ )." + The position angle. measured between the north direction on the sky aud the uajor axis of he receding half of the ealaxv (see Sect. 3.3)).," The position angle, measured between the north direction on the sky and the major axis of the receding half of the galaxy (see Sect. \ref{ssec:rotcur}) )," + was found to be ~270°, was found to be $\sim 270^\circ$. + The surface brightucss profiles obtained from the ellipse fitting in V and I bands are well described byexponcutial disk with the scale leneth of 11.07 (1.1 kpc) aud 62.07 (1.7 kpc) respectively., The surface brightness profiles obtained from the ellipse fitting in V and I bands are well described byexponential disk with the scale length of ${41.0''}$ $\sim$ 1.1 kpc) and ${62.0''}$ $\sim$ 1.7 kpc) respectively. + The average «x τσ color is —1.2. with little variation with radius.," The average $<$ $>$ color is $\sim$ 1.2, with little variation with radius." + The total maeuitude after correcting for galactic extinction(using . [NI]. MSH]. (OI. [NI]. ΤΟΠ. and Iel. Figure Saa shows the central line profiles towards the IRAS source 05173.0555.," Emission lines which \citet{coh} detects in this source include $\alpha$, $\beta$, $\gamma$ , [NII], [SII], [OI], [NI], [OIII], and HeI. Figure \ref{sfoxvi_xviii_profiles}a a shows the central line profiles towards the IRAS source 05173–0555." + The vertical line indicates the best fit velocity of the 0) hyperfine ensemble., The vertical line indicates the best fit velocity of the ) hyperfine ensemble. + Both the CO 0) and the CO 1) lines show wings., Both the CO ) and the CO ) lines show wings. + These wings often indicate the presence of outflows., These wings often indicate the presence of outflows. + The 0) line. however appears to have a fairly gaussian shape.," The ) line, however appears to have a fairly gaussian shape." + The ]line profiles. shown in Figure Saa. are a bit more eniematic.," The line profiles, shown in Figure \ref{sfoxvi_xviii_profiles}a a, are a bit more enigmatic." + The 2) and 2) lines seem fairly well centered on the Viag. but the 0) shows a pronounced asvmmetrv.," The ) and ) lines seem fairly well centered on the $V_{\rm LSR}$, but the ) shows a pronounced asymmetry." + This asymmetric profile is not sharedbv the 0), This asymmetric profile is not sharedby the ) +"the adiabatic phase, has been subtracted from the energy of each supernova explosion when computing the injection of mechanical energy.","the adiabatic phase, has been subtracted from the energy of each supernova explosion when computing the injection of mechanical energy." +" A more detailed description of our models is provided in Cervifio,Mas-Hesse,&Kunth(2002).", A more detailed description of our models is provided in \citet{Cervino02}. +. The contribution of the stellar atmospheres to the soft X- emission was neglected because it is expected to be two orders of magnitude lower than the emission from the diffuse gas., The contribution of the stellar atmospheres to the soft X-ray emission was neglected because it is expected to be two orders of magnitude lower than the emission from the diffuse gas. + The contribution of high-mass X-ray binaries to the soft X-ray emission has in addition been neglected in this work., The contribution of high-mass X-ray binaries to the soft X-ray emission has in addition been neglected in this work. + Mas-Hesse&Cervifio(1999) discussed the properties of the HMXB population expected to form during a massive star-formation burst., \citet{MasHesse99a} discussed the properties of the HMXB population expected to form during a massive star-formation burst. +" Binary systems become X-ray emitters when the primary collapses into a black hole or neutron star, the atmosphere of the secondary has started to expand, and the secondary is sufficiently close to the collapsed primary for mass transfer to begin."," Binary systems become X-ray emitters when the primary collapses into a black hole or neutron star, the atmosphere of the secondary has started to expand, and the secondary is sufficiently close to the collapsed primary for mass transfer to begin." +" Mass is accreted onto the surface of the compact object and emits X-rays with a typical 109? s-!,, peaking at energies between 5 and 10 keV (Persic&Rephaeli2002)."," Mass is accreted onto the surface of the compact object and emits X-rays with a typical $\sim +10^{38}$ , peaking at energies between $5$ and $10$ keV \citep{Persic02}." +". In all cases, the total contribution of HMXB, to the soft X-ray emission, remains 15% for IB and 10% for EB."," In all cases, the total contribution of HMXB, to the soft X-ray emission, remains $15$ for IB and $10$ for EB." +" Only if one or a few of these HMXB develop into an ultraluminous X-ray source (ULX), with ~10 (Miniuttietal.2006),, could the X-ray emission, from soft to hard X-rays, of the entire galaxy, be dominated by the emission of HMXB, compared to that of the diffuse gas."," Only if one or a few of these HMXB develop into an ultraluminous X-ray source (ULX), with $\sim 10^{40}$ \citep{Miniutti06}, could the X-ray emission, from soft to hard X-rays, of the entire galaxy, be dominated by the emission of HMXB, compared to that of the diffuse gas." +" Concerning the FIR emission, a thermal equilibrium of dust is assumed, implying that all the energy absorbed by dust, mostly originating from the UV continuum of the massive stars, is reemitted in the FIR range."," Concerning the FIR emission, a thermal equilibrium of dust is assumed, implying that all the energy absorbed by dust, mostly originating from the UV continuum of the massive stars, is reemitted in the FIR range." +" The evolution of both aand ppredicted by the models are shown in Fig. 1,,"," The evolution of both and predicted by the models are shown in Fig. \ref{lumin}," + while their ratio iis presented/ in Fig. 2.., while their ratio is presented in Fig. \ref{ratio}. +" For IB models, the luminosities are shown scaled to 1 oof gas transformed into stars at the onset of the starburst."," For IB models, the luminosities are shown scaled to $1$ of gas transformed into stars at the onset of the starburst." +" In the case of EBmodels, the luminosities arenormalized to == 1Moyr i."," In the case of EBmodels, the luminosities arenormalized to = $1 \, M_{\sun} \, yr^{-1}$ ." +"The most up-to-date conductive opacities are those of Itohetal.(1983,hereinafterI83)..",The most up-to-date conductive opacities are those of \citet[hereinafter I83]{ito83}. + We consider an ion mixture consisting of n species of nuclei., We consider an ion mixture consisting of $n$ species of nuclei. + The conductive opacity κο for temperature Tg (units of 105 K) and density pg (units of 106 g cm?) is taken from eq. (, The conductive opacity $\kappa_{c}$ for temperature $T_{8}$ (units of $10^{8}$ K) and density $\rho_{6}$ (units of $10^{6}$ g $^{-3}$ ) is taken from eq. ( +"7) in 183, where () denotes the average over the nuclear species and Z;, X;, and A; are the atomic number, the mass fraction, and the atomic mass number of i* nucleus.","7) in I83, where $\langle \rangle$ denotes the average over the nuclear species and $Z_{i}$, $X_{i}$, and $A_{i}$ are the atomic number, the mass fraction, and the atomic mass number of $i^{\rm th}$ nucleus." + The average value is taken as The quantities 5.1); and (S41); are calculated with eqs. (, The average value is taken as The quantities $\ave{S_{-1}}_{i}$ and $\ave{S_{+1}}_{i}$ are calculated with eqs. ( +"8) and (9) in 183 and with the parameters according to eq.(19) of Itohetal.(2004):: where iis the Coulomb coupling constant for the i* nucleus, a, the electron-sphere radius defined as a,=(3/A4nn,)!/? with the electron number density n,, and r, the electron density parameter.","8) and (9) in I83 and with the parameters according to eq.(19) of \citet{ito04}: where is the Coulomb coupling constant for the $i^{\rm th}$ nucleus, $a_{e}$ the electron-sphere radius defined as $a_{e} = (3 / 4 \pi n_{e})^{1/3}$ with the electron number density $n_{e}$, and $r_{s}$ the electron density parameter." +" 'The expressions for various mixtures are to be be considered as first approximations, compared with the formulae in I83 which are for pure compositions and are accurate solutions."," The expressions for various mixtures are to be be considered as first approximations, compared with the formulae in I83 which are for pure compositions and are accurate solutions." +" In particular, the approximation for a mixture of elements with very different Z's (e.g., !H and ?9Fe) is not very accurate; however, the exact solution for such mixtures is not presently attainable."," In particular, the approximation for a mixture of elements with very different $Z$ 's (e.g., $\nucm{1}{H}$ and $\nucm{56}{Fe}$ ) is not very accurate; however, the exact solution for such mixtures is not presently attainable." +" For mixtures of elements of comparable Z's (e.g., !?C and 160), the approximation is fairly accurate."," For mixtures of elements of comparable $Z$ 's (e.g., $\nucm{12}{C}$ and $\nucm{16}{O}$ ), the approximation is fairly accurate." +" The I83 results are strictly applicable only for T€Tr, where Tp is the Fermi temperature defined by eq. ("," The I83 results are strictly applicable only for $T \leq T_{F}$, where $T_{F}$ is the Fermi temperature defined by eq. (" +1) in I83.,1) in I83. +" In this work, κο as defined by 183 and κε as defined by Iben(1975) are interpolated with one other over the range 0.5€T/Tr<2.0 using a sin squared algorithm."," In this work, $\kappa_{c}$ as defined by I83 and $\kappa_{c}$ as defined by \citet{ibe75} are interpolated with one other over the range $0.5 \leq T / T_{F} \leq 2.0$ using a sin squared algorithm." + Another algorithm is used to extrapolate I83 results for values of l' outside the region defined by 160., Another algorithm is used to extrapolate I83 results for values of $\Gamma$ outside the region defined by $2 \leq \Gamma \leq 160$ . +" Both (S_1) and (S44) are constrained by (S1)€(S1),lim and (S41)€(S41),,,,lim? where the upper limits are calculated by demanding that, in eq. ("," Both $\ave{S_{-1}}$ and $\ave{S_{+1}}$ are constrained by $\ave{S_{-1}} \leq \ave{S_{-1}}_{\rm lim}$ and $\ave{S_{+1}} \leq +\ave{S_{+1}}_{\rm lim}$, where the upper limits are calculated by demanding that, in eq. (" +"6) in I83, where kyr is the Thomas-Fermi wavenumber.","6) in I83, where $k_{\rm TF}$ is the Thomas-Fermi wavenumber." + The first condition assumes that interactions between ions can be neglected and the second condition expresses the Thomas-Fermi approximation for electron screening., The first condition assumes that interactions between ions can be neglected and the second condition expresses the Thomas-Fermi approximation for electron screening. + These conditions give for the upper limits:, These conditions give for the upper limits: +In Bernardinietal.(2011) we showed that the decoupling of the evolution of the peak luminosity of late-time flares from the underlying continuum allows the detection of only the brightest flares.,In \citet{2011A&A...526A..27B} we showed that the decoupling of the evolution of the peak luminosity of late-time flares from the underlying continuum allows the detection of only the brightest flares. +" Comparing the average luminosity of the present sample with the one calculated for the continuum underlying the late-time flares analysed in Bernardinietal. (2011), we observe that their temporal behaviour is similar, and it traces the flare detection threshold luminosity calculated in Marguttietal.(2011).."," Comparing the average luminosity of the present sample with the one calculated for the continuum underlying the late-time flares analysed in \citet{2011A&A...526A..27B}, we observe that their temporal behaviour is similar, and it traces the flare detection threshold luminosity calculated in \citet{2011MNRAS.410.1064M}." + We analysed 64 long GRB X-ray light curves observed by XRT with redshift measurement that do not exhibit flaring activity., We analysed $64$ long GRB X-ray light curves observed by XRT with redshift measurement that do not exhibit flaring activity. + This allowed us to characterise the morphology and energetics of the sample in order to constrain the mechanism that produces the X-ray continuum., This allowed us to characterise the morphology and energetics of the sample in order to constrain the mechanism that produces the X-ray continuum. +" The light curves of the sample can be divided into four morphological Types, with similarities between different parts."," The light curves of the sample can be divided into four morphological Types, with similarities between different parts." +" When necessary, we compared our sample with the one considered in Marguttietal.(2011) of 44 GRBs that exhibit flaring activity."," When necessary, we compared our sample with the one considered in \citet{2011MNRAS.410.1064M} of $44$ GRBs that exhibit flaring activity." + We found that The magnetar model is able to explain the different morphologies of the X-ray continuum and the properties of the shallow decay., We found that The magnetar model is able to explain the different morphologies of the X-ray continuum and the properties of the shallow decay. + The main limit in the accretion model is the difficulty of achieving very long timescales as observed in Type Ib shallow decay., The main limit in the accretion model is the difficulty of achieving very long timescales as observed in Type Ib shallow decay. +" The behaviour of the steep decay and the suggested connection with the flaring activity (seealsoBarniolDuran&Kumar2009;Marguttietal.2010,2011) indicates that the steep decay may not be viewed as simply the tail of the prompt emission."," The behaviour of the steep decay and the suggested connection with the flaring activity \citep[see also][]{2009MNRAS.395..955B,giantflares10,2011MNRAS.410.1064M} indicates that the steep decay may not be viewed as simply the tail of the prompt emission." + We thank the referee for her/his very useful comments and suggestions., We thank the referee for her/his very useful comments and suggestions. +" This work is supported by ASI grant SWIFT 1/011/07/0, by the Ministry of University and Research of Italy (PRIN MIUR 2007TNYZXL), by MAE, and by the University of Milano Bicocca (Italy)."," This work is supported by ASI grant SWIFT I/011/07/0, by the Ministry of University and Research of Italy (PRIN MIUR 2007TNYZXL), by MAE, and by the University of Milano Bicocca (Italy)." +coefficients from a representative simulation (Run TO4).,coefficients from a representative simulation (Run T04). + In order to do this. we use the test-field method. introduced in the geodynamo context by ο and currently available in the (e.g.??)..," In order to do this, we use the test-field method, introduced in the geodynamo context by \cite{Schrinner+etal_05,Schrinner+etal_07} and currently available in the \citep[e.g.][]{B05,BRRK08}." + In mean-field theory. the electromotive force E=u.B governs the evolution of the large-scale magnetic field (?)..," In mean-field theory, the electromotive force $\memf=\mean{\bm{u}\times\bm{B}}$ governs the evolution of the large-scale magnetic field \citep[]{KR80}." + Under the assumption that the mean field varies smoothly in space and time. and that there is no small scale dynamo action. the electromotive force may be written in terms of the large-scale magnetic field: Considering large-scale fields that depend only on : we need four independent test fields in order to compute the 4--4 components of ;; and ο (seeadetaileddescriptionofmethodin ?)..," Under the assumption that the mean field varies smoothly in space and time, and that there is no small scale dynamo action, the electromotive force may be written in terms of the large-scale magnetic field: Considering large-scale fields that depend only on $z$ we need four independent test fields in order to compute the 4+4 components of $\alpha_{ij}$ and $\eta_{ijk}$ \citep[see a detailed description of +the method in][]{BRRK08}." + The novel feature of the test field method is that the test fields do not act back on the flow and that the turbulent diffusivity can also be computed. thus avoiding many of the problems that plaque other methods (cf.?)..," The novel feature of the test field method is that the test fields do not act back on the flow and that the turbulent diffusivity can also be computed, thus avoiding many of the problems that plaque other methods \citep[cf.][]{KKB10}." + We discuss our resultsin terms of the following quantities: which represent the inductive (n). diffusive GR). and pumping (5) effects of turbulence. respectively.," We discuss our resultsin terms of the following quantities: which represent the inductive $\alpha$ ), diffusive $\etat$ ), and pumping $\gamma$ ) effects of turbulence, respectively." + In Fig., In Fig. + 10. we show the vertical profiles of the kinetic helicity (uc). where =V «uisthe vorticity. and the turbulent transport coefficients of Eqs. (20)}-(22)).," \ref{fig:tfcoeff} we show the vertical profiles of the kinetic helicity $\mean{\bm{u}\cdot\bm{\omega}}$ ), where $\bm=\bm\nabla\times\bm{u}$ is the vorticity, and the turbulent transport coefficients of Eqs. \ref{eq:tca}) \ref{eq:tcg}) )," + normalized with the first order smoothing approximation (FOSA) quantities: For computing the coefficients in Fig., normalized with the first order smoothing approximation (FOSA) quantities: For computing the coefficients in Fig. + 10. we use Run ΤΟΝ in the purely hydrodynamic state., \ref{fig:tfcoeff} we use Run T04 in the purely hydrodynamic state. + The magnetic diffusivity considered for the test fields is one order of magnitude larger that that used for the magnetic field in the original run., The magnetic diffusivity considered for the test fields is one order of magnitude larger that that used for the magnetic field in the original run. + However. the magnetic Reynolds number (Rinz 1) ts still sufficiently large to yield reasonable results (?)..," However, the magnetic Reynolds number $\Rm\approx4$ ) is still sufficiently large to yield reasonable results \citep{Kapyla+etal_09b}." + We find that certain amount of helicity is generated in the system. but that it is still statistically consistent with zero.," We find that certain amount of helicity is generated in the system, but that it is still statistically consistent with zero." + The coefficient αν. despite large fluctuations. has a negative sign.," The coefficient $\alpha_{xx}$, despite large fluctuations, has a negative sign." + This component of à contributes to amplifying the y component of the magnetic field. but its contribution is likely negligible when compared with that of the shear in the present models.," This component of $\alpha$ contributes to amplifying the $y$ component of the magnetic field, but its contribution is likely negligible when compared with that of the shear in the present models." +" The component o,, shows a zero mean value. but its variance has a large amplitude. especially in the middle of the convection zone."," The component $\alpha_{yy}$ shows a zero mean value, but its variance has a large amplitude, especially in the middle of the convection zone." + According to ?.. an incoherent « effect. zero in average but with finite variance. may generate enough inductive effects to sustain the dynamo.," According to \cite{vish+bran_97}, an incoherent $\alpha$ effect, zero in average but with finite variance, may generate enough inductive effects to sustain the dynamo." +" This suggest that the incoherent « effect may be the mechanism sustaining the dynamo,", This suggest that the incoherent $\alpha$ effect may be the mechanism sustaining the dynamo. + The shear-current effect. arising from the inhomogeneity of the turbulence and the mean shear flow. may also result in the generation of a mean field (??)..," The shear-current effect, arising from the inhomogeneity of the turbulence and the mean shear flow, may also result in the generation of a mean field \citep{rog+kleo_03,rog+kleo_04}." + The existence of this effect has been studied with models of forced turbulence and latitudinal shear by (??).. but no conclusive evidence has been found.," The existence of this effect has been studied with models of forced turbulence and latitudinal shear by \citep{BRRK08, Mitra+etal_09}, but no conclusive evidence has been found." + Similar results have also been found from convection with horizontal shear (?).., Similar results have also been found from convection with horizontal shear \citep{Kapyla+etal_09b}. + In the case presented here. with vertical shear. the relevant coefficient for this effect would be ia. Which is not captured by the current version of the test- method with only :-dependent test fields.," In the case presented here, with vertical shear, the relevant coefficient for this effect would be $\eta_{13}$, which is not captured by the current version of the test-field method with only $z$ -dependent test fields." + Thus. we leave the study of the shear-current effect in turbulent convection with vertical shear for a forthcoming work.," Thus, we leave the study of the shear-current effect in turbulent convection with vertical shear for a forthcoming work." + The turbulent diffusivity. jjj. is roughly four times larger than the FOSA estimate.," The turbulent diffusivity, $\eta_t$ , is roughly four times larger than the FOSA estimate." + When compared with the molecular diffusivity. it is also four times larger oof the same order as Rin μή).," When compared with the molecular diffusivity, it is also four times larger of the same order as $\Rm \sim \etat/\eta$ )." + This result agrees with previously computed turbulent diffusivity for convection (?).., This result agrees with previously computed turbulent diffusivity for convection\citep{Kapyla+etal_09b}. . + The vertical profile of i. differs somewhat from previous results. indicating the action of the radial shear on the turbulent diffusion.," The vertical profile of $\etat$ differs somewhat from previous results, indicating the action of the radial shear on the turbulent diffusion." +" Anotherinteresting point is that e,, is not closeto zero. as in ?.."," Anotherinteresting point is that $\epsilon_{\eta}$ is not closeto zero, as in \cite{Kapyla+etal_09b}. ." + This, This +The discovery. of millisecond pulsars (AISPs) was reported by Backeretal.(1982)..,The discovery of millisecond pulsars (MSPs) was reported by \cite{bac82}. + Their origin was suggested to be due to spin-up by accretion torques of a binary companion, Their origin was suggested to be due to spin-up by accretion torques of a binary companion +The total inteusitv map of the IIO iuasers aroun VY CMa is shown in Fie. 10...,The total intensity map of the $_2$ O masers around VY CMa is shown in Fig. \ref{vycma}. + Circular polarization has oen detected on 7? out of 10 of the brightest maser eatures down to Pyz0.24., Circular polarization has been detected on 7 out of 10 of the brightest maser features down to $P_{\rm V}\approx 0.2\%$. + Similar to the values foun or S Per we fux a maenuetie Ποια of z200 iC usingc» he LTE Zeeman analvsis or z175 wwe using the NW uodels.," Similar to the values found for S Per we find a magnetic field of $\approx +200$ mG using the LTE Zeeman analysis or $\approx 175$ mG using the NW models." + The maguetic field poiuts toward us for most of he sources., The magnetic field points toward us for most of the sources. + suffers from blending with nearby uaser spots which made accurate fitting iniposside. this can also explain the change of sign.," suffers from blending with nearby maser spots which made accurate fitting impossible, this can also explain the change of sign." +" Diamoud et al.(1987) give the radius of the Ποο mascr reeion for VY C'Ma to be z150 mas. corresponding to 5,220 AU."," Diamond et al.(1987) give the radius of the $_2$ O maser region for VY CMa to be $\approx 150$ mas, corresponding to $\approx 220$ AU." + The 1612 MIIz ΟΠ maser radius is shown to be z2100 AU in observations by Reid ct al.(1981)., The 1612 MHz OH maser radius is shown to be $\approx 2400$ AU in observations by Reid et al.(1981). + We have ouly been able to detect a few IIOmascr features around NAIL Cye. which are shown in Fig. 11..," We have only been able to detect a few $_2$ Omaser features around NML Cyg, which are shown in Fig. \ref{nmlcyg}." + We find circular polarization frou 0.62%., We find circular polarization from $0.6 - 2\%$. + The spectra forb aud ave shown in the same Figure., The spectra for and are shown in the same Figure. + The V-spectrum fora ds shown in Fig. 12., The V-spectrum for is shown in Fig. \ref{sp4}. + The circular polarization spectrum seenis to indicate that this features actually consists of 2 heavily bleuded. features of zz30 Jv., The circular polarization spectrum seems to indicate that this features actually consists of 2 heavily blended features of $\approx 30$ Jy. + The magnetic fidd. streugt ion this feature has been estimated using this simple uodel., The magnetic field strength on this feature has been estimated using this simple model. + Both the interpretations mdicate he magnetic field strength to be zzHOO an. higher thau or bo LS Per and VY CMa.," Both the interpretations indicate the magnetic field strength to be $\approx 500$ mG, higher than for both S Per and VY CMa." + The ΠΟ Waser region extent is m195 unas. corresponding to z210 AU (Johustou et al.," The $_2$ O maser region extent is $\approx 195$ mas, corresponding to $\approx 240$ AU (Johnston et al." + 1985)., 1985). + Diunond et al.(1981) eive for he 1612 MIIz ΟΠ mascers a animextent of z35 arcsec., Diamond et al.(1984) give for the 1612 MHz OH masers a maximumextent of $\approx 3-5$ arcsec. + The total intensity map for the HT2O masers around U Ter is shown in Fie. 13.., The total intensity map for the $_2$ O masers around U Her is shown in Fig. \ref{uher}. + U Wer is the only Mira. variable star du our sample aud shows significantly weaker TO masers., U Her is the only Mira variable star in our sample and shows significantly weaker $_2$ O masers. + However as seen in the figure. we do detect circular polarization of up to zz10%.," However as seen in the figure, we do detect circular polarization of up to $\approx +10\%$." + The field strength iu the ΠΟ maser region of U Ier is higher than those observed for the supereiant stars in our sample., The field strength in the $_2$ O maser region of U Her is higher than those observed for the supergiant stars in our sample. + We find streneths of zz2.5 CG using the LTE Zeeman analysis or z1.5 C using the non-LTE models., We find strengths of $\approx 2.5$ G using the LTE Zeeman analysis or $\approx 1.5$ G using the non-LTE models. + While the features aud, While the features and + While the features aud , While the features and + While the features aud b, While the features and +"Because the curvature radii. δὲ> of the open field lines. assuming a dipole configuration. originating from the polar cap rim near (,,.στALCSVIENH4.)) are smaller than those originating at smaller polar angles (at the magnetic pole Ro»cx and no curvature emission can be produced) the initial CR 5-ray emission spectrum (x.ΤΠ) is most pronounced and hardest (maximum of CR-spectrum is reached at uaeC20.209.xD?/ RP) near the polar rim resulting in à hollow cone emission pattern.","Because the curvature radii $R_{cr}$ of the open field lines, assuming a dipole configuration, originating from the polar cap rim near $\theta_{pc} \simeq \arcsin(\sqrt(R_{ns}/R_{lc}))$ are smaller than those originating at smaller polar angles (at the magnetic pole $R_{cr} \rightarrow \infty$ and no curvature emission can be produced) the initial CR $\gamma$ -ray emission spectrum $\propto 1/ R_{cr}$ ) is most pronounced and hardest (maximum of CR-spectrum is reached at $\omega_{\max} \simeq 0.29 \cdot \omega_c \propto \Gamma^3 / R_{cr}$ ) near the polar rim resulting in a hollow cone emission pattern." + The mostly developed cascades originate near the polar rim which in turn soften the input most efficiently., The mostly developed cascades originate near the polar rim which in turn soften the input CR-spectrum most efficiently. + This means that a distant observer not only sees a double peaked profile when the hollow -ray emission cone passes his line of sight. but also a soft-hard-soft variation of the emission is expected. because the CR-emission emanating nearer the magnetic pole is less softened by cascading.," This means that a distant observer not only sees a double peaked profile when the hollow $\gamma$ -ray emission cone passes his line of sight, but also a soft-hard-soft variation of the emission is expected, because the CR-emission emanating nearer the magnetic pole is less softened by cascading." + Grazing through the 5-ray emission cone will result in a single pulse profile highly softened by cascade processes., Grazing through the $\gamma$ -ray emission cone will result in a single pulse profile highly softened by cascade processes. + The last situation may be applicable for PSR B1509-58 requiring clear constraints on the geometrical aspects of both the system and the observer., The last situation may be applicable for PSR B1509-58 requiring clear constraints on the geometrical aspects of both the system and the observer. + In particular. it demands that the pulsar spin axis / line-of-sight angle ¢ should approximately be equal to the sum of the magnetic inclination angle © and the >-ray cone semi-angle 0. (beam radius).," In particular, it demands that the pulsar spin axis / line-of-sight angle $\zeta$ should approximately be equal to the sum of the magnetic inclination angle $\alpha$ and the $\gamma$ -ray cone semi-angle $\theta_{\gamma}$ (beam radius)." + However. the large duty cycle of the single pulse of ~0.L poses an additional constraint. namely ¢ should then be smaller than a|0..," However, the large duty cycle of the single pulse of $\sim 0.4$ poses an additional constraint, namely $\zeta$ should then be smaller than $\alpha+\theta_{\gamma}$." + This can be estimated using the following equation: which can be derived in the rotating vector model (e.g. Rankin 1993)., This can be estimated using the following equation: which can be derived in the rotating vector model (e.g. Rankin 1993). + Ad is the duty cycle of the pulse. while ./ is the impact parameter defined as 3=¢—o.," $\Delta\Phi$ is the duty cycle of the pulse, while $\beta$ is the impact parameter defined as $\beta\equiv\zeta-\alpha$." + Radio-polarization data yield in the context of this rotating vector model (Crawford et al., Radio-polarization data yield in the context of this rotating vector model (Crawford et al. + 1997; private communication 1999) a~18!15 degree and jc20!30 degree., 1997; private communication 1999) $\alpha\simeq 18^{+18}_{-13}$ degree and $\beta\simeq 20^{+20}_{-20}$ degree. + If we use the best fit parameters. then 0.— 36.," If we use the best fit parameters, then $\theta_{\gamma} \simeq 36\degr$ ." + Eventhough the uncertainties are large. the emitting rim must be very broad to explain the broad single pulse.," Eventhough the uncertainties are large, the emitting rim must be very broad to explain the broad single pulse." + The CRPC model also predicts a spectral cutoff in the --ray spectrum at several GeV. Another interesting feature is that a lower cutoff energy is expected for those pulsars with a higher magnetic field. because the softening by cascade processes is more efficient in. these cases.," The CRPC model also predicts a spectral cutoff in the $\gamma$ -ray spectrum at several GeV. Another interesting feature is that a lower cutoff energy is expected for those pulsars with a higher magnetic field, because the softening by cascade processes is more efficient in these cases." + Some of these general trends are indeed observed in some 5-ray pulsars (Thompsonetal. 1997))., Some of these general trends are indeed observed in some $\gamma$ -ray pulsars \cite{thompson4}) ). + The current implementation of geometrical and physical aspects. however. predicts lightecurves with a high degree of symmetry.," The current implementation of geometrical and physical aspects, however, predicts lightcurves with a high degree of symmetry." + This symmetry 1s a problem for e.g. the Vela pulsar high-energy lighteurve (Grenieretal.1988:: Kanbachetal. 1994)) which shows rather asymmetric bridge emission., This symmetry is a problem for e.g. the Vela pulsar high-energy lightcurve \cite{grenier}; \cite{kanbach}) ) which shows rather asymmetric bridge emission. + For PSR B15309-58 this CRPC model explain the observed spectral cutoff energy occuring between 10 and 30 MeV. However. the (very) strong polar surface magnetic field strength of ~3.1«LO! likely triggers another more exotic attenuation process to be active in the vicinity of the magnetic pole. namely B>ar|o besides attenuation by magnetic. pair production.," For PSR B1509-58 this CRPC model explain the observed spectral cutoff energy occuring between 10 and 30 MeV. However, the (very) strong polar surface magnetic field strength of $\sim 3.1\times10^{13}$ likely triggers another more exotic attenuation process to be active in the vicinity of the magnetic pole, namely $\gamma\stackrel{B}{\rightarrow}\gamma\prime + \gamma\prime\prime$, besides attenuation by magnetic pair production." +" Hardingetal.(1997) showed that the photo splitting attenuation lengths can be shorter than the attenuatio lengths for pair production for magnetic field strenghts B20.3B,, with D,mele=Ες«10775 G. This means that photon splitting acts as the dominant attenuatio process for such strong magnetic fields and can suppress the emission of high-energy photons.", \cite{harding} showed that the photon splitting attenuation lengths can be shorter than the attenuation lengths for pair production for magnetic field strenghts $B \ga 0.3 B_{cr}$ with $B_{cr} = m_e c^3 / e\hbar = 4.413\times 10^{13}$ G. This means that photon splitting acts as the dominant attenuation process for such strong magnetic fields and can suppress the emission of high-energy photons. + Contrary to the attenuatio by magnetic pair production. photon splitting has energy threshold and can degrade the photon energy also below the magnetic pair production threshold (ω2οsiaOpp). fp is the angle between photon propagation direction and local magnetic field).," Contrary to the attenuation by magnetic pair production, photon splitting has energy threshold and can degrade the photon energy also below the magnetic pair production threshold $\omega\ge 2m_ec^2/\sin(\theta_{kB})$ , $\theta_{kB}$ is the angle between photon propagation direction and local magnetic field)." + Depending on the splitting mode. partial and full splitting cascades are addressed. Hardingetal.(1997) calculate the high-energy spectrum of PSR B1509-58 for various values of the model parameters 7; and 60. the magnetic co-latitude angle. assuming that the mitial high-energy photon emission originates from the neutron star surface in a polar rim at co-latitude 0.," Depending on the splitting mode, partial and full splitting cascades are addressed, \cite{harding} calculate the high-energy spectrum of PSR B1509-58 for various values of the model parameters $\theta_{kB}$ and $\theta$, the magnetic co-latitude angle, assuming that the initial high-energy photon emission originates from the neutron star surface in a polar rim at co-latitude $\theta$." + Our new medium-energy >-ray data and in particular the spectrum of the main pulse severely constrain the magnetic co-latitude of the emission rim. irrespective of the splitting mode.," Our new medium-energy $\gamma$ -ray data and in particular the spectrum of the main pulse severely constrain the magnetic co-latitude of the emission rim, irrespective of the splitting mode." +" A co-latitude of ~2”. close to the ""classical"" radius of the polar cap @,,,.. appears to be required in the model calculations to be consistent with the evident spectral break between 10 and 30 MeV in the combined COMPTEL-EGRET spectrum."," A co-latitude of $\sim 2\degr$, close to the “classical” radius of the polar cap $\theta_{pc}$ , appears to be required in the model calculations to be consistent with the evident spectral break between 10 and 30 MeV in the combined COMPTEL-EGRET spectrum." + No detailed model calculations have been performed for PSR B1509-58 in the inverse Compton induced Polar Cap cascade scenario (Sturner&Dermer1994:; Sturneretal.1995 and Sturner 1995)). although some interesting. qualitative statements have been made.," No detailed model calculations have been performed for PSR B1509-58 in the inverse Compton induced Polar Cap cascade scenario \cite{sturner1}; \cite{sturner2} and \cite{sturner3}) ), although some interesting qualitative statements have been made." + In particular. if 2.107 G and the neutron star surface temperature T>3109 K the Lorentz factors of the electrons are limited to <107. which might explain the low cutoff energy in the spectrum of PSR B1509-38 (Sturner 1995)).," In particular, if $B > 10^{13}$ G and the neutron star surface temperature $T > 3\cdot 10^6$ K the Lorentz factors of the electrons are limited to $\la 10^3$ , which might explain the low cutoff energy in the spectrum of PSR B1509-58 \cite{sturner3}) )." + However. this type of PC-model also suffers from predicting too symmetric. lighteurves.," However, this type of PC-model also suffers from predicting too symmetric lightcurves." + The model requirement of a nearly aligned rotator (a~0.x5 57) can formally not be excluded for the estimates of the magnetic inclination a~18!m degree (Crawford et al., The model requirement of a nearly aligned rotator $\alpha \sim \theta_{\gamma} \la 5\degr$ ) can formally not be excluded for the estimates of the magnetic inclination $\alpha\simeq 18^{+18}_{-13}$ degree (Crawford et al. + 1997) and 0.z-3622 degree., 1997) and $\theta_{\gamma} \simeq 36^{+32}_{-30}$ degree. + In outer gap scenarios (see e.g. Chengetal.1986a.. Chengetal.1986b and Ho 1989)) it is believed that stable vacuum gaps (Holloway 1973)) can be formed in the outer magnetosphere along the boundary of the last closed field lines which extend from the null-charge surface to the light cylinder.," In outer gap scenarios (see e.g. \cite{chenga}, \cite{chengb} and \cite{ho}) ) it is believed that stable vacuum gaps \cite{holloway}) ) can be formed in the outer magnetosphere along the boundary of the last closed field lines which extend from the null-charge surface to the light cylinder." + Voltage drops of typically ~1077 V can be obtained across the gaps and accelerate (+. ereated either in the gap or flowing in from beyond the light cylinder and from across the null-charge surface. to energies limited by curvature radiation and to a lesser extent inverse Compton scattering (off the ambient bath of lower energy photons).," Voltage drops of typically $\sim 10^{13}$ V can be obtained across the gaps and accelerate $e^{\pm}$, created either in the gap or flowing in from beyond the light cylinder and from across the null-charge surface, to energies limited by curvature radiation and to a lesser extent inverse Compton scattering (off the ambient bath of lower energy photons)." +" A geometrical calculationof the high-energy emission (beamed along the local magnetic field inthe outer gap resulting in a ""fan? beam) from an outer gap region was successfull in reproducing qualitatively the observed 2-ray lightcurves of theknown", A geometrical calculationof the high-energy emission (beamed along the local magnetic field inthe outer gap resulting in a “fan” beam) from an outer gap region was successfull in reproducing qualitatively the observed $\gamma$ -ray lightcurves of theknown +each observation represents the quict Sun at different times and in different regions of the solar surface.,each observation represents the quiet Sun at different times and in different regions of the solar surface. + The comparison of the polarization amplitudes of different data sets is not straightforward., The comparison of the polarization amplitudes of different data sets is not straightforward. +" As stated in MartínezGonzálezetal.(2008a)., the presence of noise introduces some systematic effects in the weak polarization tails of polarization amplitude histograms."," As stated in \cite{marian_andres_08}, the presence of noise introduces some systematic effects in the weak polarization tails of polarization amplitude histograms." +" In addition to purely instrumental errors, Stokes V profiles are affected by asymmetries in the line profile, thus making it difficult to estimate the amplitude."," In addition to purely instrumental errors, Stokes $V$ profiles are affected by asymmetries in the line profile, thus making it difficult to estimate the amplitude." + We propose a method based on principal component analysis (PCA) to overcome all these issues and end up with sensible comparisons between the polarization amplitudes of different data sets., We propose a method based on principal component analysis (PCA) to overcome all these issues and end up with sensible comparisons between the polarization amplitudes of different data sets. + Figure 1. shows the first (solid line) and second (dashed line) principal components (PC) of the Stokes V (upper panel) and Stokes Q and U (lower panel).," Figure \ref{principal_components} + shows the first (solid line) and second (dashed line) principal components (PC) of the Stokes $V$ (upper panel) and Stokes $Q$ and $U$ (lower panel)." +" In the case of Stokes V, the first PC (containing the vast majority of variance of the data set) 1s a typical antisymmetric Zeeman profile."," In the case of Stokes $V$, the first PC (containing the vast majority of variance of the data set) is a typical antisymmetric Zeeman profile." +" For Stokes Q and U, the first PC is à typical symmetric Zeeman profile."," For Stokes $Q$ and $U$, the first PC is a typical symmetric Zeeman profile." +" The rest of the PC's contain information about velocity shifts, broadenings, asymmetries, etc. (Skumanich&LópezAriste2002)."," The rest of the PC's contain information about velocity shifts, broadenings, asymmetries, etc. \citep{skumanich_02}." +". Consequently, if we describe our data sets using only the first PC, we fundamentally filter out all contributions except the one related to the amplitude of the profiles."," Consequently, if we describe our data sets using only the first PC, we fundamentally filter out all contributions except the one related to the amplitude of the profiles." +" With this procedure, the contribution of noise and asymmetries is also strongly reduced."," With this procedure, the contribution of noise and asymmetries is also strongly reduced." + The amplitude of circular polarization (Ay) is computed as follows., The amplitude of circular polarization $A_V$ ) is computed as follows. + We calculate the projection of the complete Stokes V data set onto the first PC., We calculate the projection of the complete Stokes $V$ data set onto the first PC. +" Then. since the first PC is antisymmetric, we define the amplitude of the Stokes V profiles as the semi-difference between the amplitudes of the blue and red lobes."," Then, since the first PC is antisymmetric, we define the amplitude of the Stokes $V$ profiles as the semi-difference between the amplitudes of the blue and red lobes." +" On the other hand, the linear polarization amplitude (A;) is defined as the maximum value of the quantity (Qr+ U7)'. Οἱ and U, being the projection of the data set in the first PC of Stokes Q and U, respectively."," On the other hand, the linear polarization amplitude $A_L$ ) is defined as the maximum value of the quantity $(Q_1^2+U_1^2)^{1/2}$ , $Q_1$ and $U_1$ being the projection of the data set in the first PC of Stokes $Q$ and $U$ , respectively." +" Interestingly, this simple exercise allows us to extract an important conclusion from the Stokes ο and U PC's."," Interestingly, this simple exercise allows us to extract an important conclusion from the Stokes $Q$ and $U$ PC's." + Figure 1. shows that the first and second PC’s for Stokes Q and U are nearly indistinguishable., Figure \ref{principal_components} shows that the first and second PC's for Stokes $Q$ and $U$ are nearly indistinguishable. +" Morcover, higher PCs having a significant variance (not shown inthe figure) behave similarly."," Moreover, higher PC's having a significant variance (not shown inthe figure) behave similarly." + This indicates thatthe the, This indicates thatthe the +correlation is found lor the Ny—Mc relation which has a chance correlation probability over 604.,correlation is found for the $N_{0}-M_{\rm GC}$ relation which has a chance correlation probability over $60\%$. + As this choice of huninositw threshold is arbitrary. we further check (the robustness of the correlation analvsis results by repeating the investigation with different thiresholds.," As this choice of luminosity threshold is arbitrary, we further check the robustness of the correlation analysis results by repeating the investigation with different thresholds." +" We have repeated (he analvsis by adopting NV(Lyicy,>0.5) in Table 2.. which provide the estimates for the number of MSPs with Lyjog,>0.5 mJv kpc?."," We have repeated the analysis by adopting $N\left(L_{\rm 1.4 GHz}>0.5\right)$ in Table \ref{gc_lf_par}, which provide the estimates for the number of MSPs with $L_{\rm 1.4 GHz}>0.5$ mJy $^{2}$." + Almost all the MSPs in GCs considered in this investigation have their radio luminosities above this threshold., Almost all the MSPs in GCs considered in this investigation have their radio luminosities above this threshold. + With these new values. the correlations of the MSP number versus D. [Fe/H]. Mc. and vou (or ay) are found at the confidence levels of 99.4756. 92.3154. 26.76% and 84.56% respectively.," With these new values, the correlations of the MSP number versus $\Gamma_{\rm c}$, [Fe/H], $M_{\rm GC}$, and $v_{\rm escape}$ (or $\sigma_{0}$ ) are found at the confidence levels of $99.47\%$, $92.31\%$, $26.76\%$ and $84.56\%$ respectively." +" For a further test of the robustness. by using the best-fit CLFs in Table 2.. we have also repeated the analvsis for a minimum luminosity cut-off of Lyyap,72 mJv kpc?."," For a further test of the robustness, by using the best-fit CLFs in Table \ref{gc_lf_par}, we have also repeated the analysis for a minimum luminosity cut-off of $L_{\rm 1.4 GHz}>2$ mJy $^{2}$." + In this case. (he correlations with P. [Fe/IJ. Moe. and Coscape (or ση) are confident at the levels of 08.3254. 98.68%. 40.08% and 92.94% respectively.," In this case, the correlations with $\Gamma_{\rm c}$, [Fe/H], $M_{\rm GC}$, and $v_{\rm escape}$ (or $\sigma_{0}$ ) are confident at the levels of $98.32\%$, $98.68\%$, $40.03\%$ and $92.94\%$ respectively." + Therefore. the degrees of correlation for the tested «quantities are found to be insensitive to the choice of the threshold.," Therefore, the degrees of correlation for the tested quantities are found to be insensitive to the choice of the threshold." + We conclude that the correlation between E. and the MSP number is the most robust among all the tested quanilies. which have a confidence level >98% regardless of the chosen threshold.," We conclude that the correlation between $\Gamma_{\rm c}$ and the MSP number is the most robust among all the tested quanities, which have a confidence level $>98\%$ regardless of the chosen threshold." + The CLFs of nine GCs. each containing a population of MSPs has been examined.," The CLFs of nine GCs, each containing a population of MSPs has been examined." + Upon comparison of the MSP population in GCs with that in the Galactic field. it has been found that the slopes of the CLFs inferred in these (wo populations significantly differ.," Upon comparison of the MSP population in GCs with that in the Galactic field, it has been found that the slopes of the CLFs inferred in these two populations significantly differ." + It is natural to speculate that the CLF is somehow related to the magnetic field and spin of the MSPs., It is natural to speculate that the CLF is somehow related to the magnetic field and spin of the MSPs. + Wane. Jiang Chene (2005) have compared the distributions of the spin period aud the dipolar surface magnetic fiekl for both cluster and disk populations (cL.," Wang, Jiang Cheng (2005) have compared the distributions of the spin period and the dipolar surface magnetic field for both cluster and disk populations (cf." + Fig., Fig. + 2 and Fig., 2 and Fig. + 3 in their paper)., 3 in their paper). + Despite Cae broader distribution for the disk population. their mean values are nol clissimilar in both populations aud therefore cannot solely explain (he difference of CLFEs.," Despite the broader distribution for the disk population, their mean values are not dissimilar in both populations and therefore cannot solely explain the difference of CLFs." + Apart from the radio huninosity functions. the X-ray emission properties of the MSPs in the GCs are also founcl to be very different [rom those in the Galactic field.," Apart from the radio luminosity functions, the X-ray emission properties of the MSPs in the GCs are also found to be very different from those in the Galactic field." + While the MSPs in the Galactic field generally require a hot polar cap component plus a non-thermal power-law tail to model their X-ray spectra (cL., While the MSPs in the Galactic field generally require a hot polar cap component plus a non-thermal power-law tail to model their X-ray spectra (cf. + Zavlin 2006). the N-ravs from a majority of the MSPs in GCs are purely thermal in nature (see IIui et al.," Zavlin 2006), the X-rays from a majority of the MSPs in GCs are purely thermal in nature (see Hui et al." + 2009 and (he references (herein lor a recent review)., 2009 and the references therein for a recent review). + Cheng Taam (2003) suggest the absence of non-thermal X-ray [rom the cluster MSPs can be possibly related to the complicated magnetic field structure., Cheng Taam (2003) suggest the absence of non-thermal X-ray from the cluster MSPs can be possibly related to the complicated magnetic field structure. + Since (he stellar, Since the stellar +The hierarchical. clustering model for the formation of structure in the universe precicts that dark matter halos should. be scaled versions of each (7)...,The hierarchical clustering model for the formation of structure in the universe predicts that dark matter halos should be scaled versions of each \cite{navarro95a}. + While some energv transler between cark matter and gas is possible through gravitational interaction and shock heating. simulations suggest that the eas and. dark matter halos will be almost self-ximilar in the absence of additional heating or cooling processes (?)..," While some energy transfer between dark matter and gas is possible through gravitational interaction and shock heating, simulations suggest that the gas and dark matter halos will be almost self-similar in the absence of additional heating or cooling processes \cite{eke98a}." + Comparison of the structure of real galaxy systems with this predicted: scll-similarity provides an excellent. probe of extra. physical processes that may be taking place in galaxy clusters and eroups., Comparison of the structure of real galaxy systems with this predicted self-similarity provides an excellent probe of extra physical processes that may be taking place in galaxy clusters and groups. + ]t has been suggested. that specific energy. in. cluster cores is higher than expected from gravitational collapse aud that this may be due to energy injected by supernova-driven protogalactic winds (7:7)..," It has been suggested that specific energy in cluster cores is higher than expected from gravitational collapse and that this may be due to energy injected by supernova-driven protogalactic winds \cite{white91a,david91a}." + 7 studied the entropy in a small sample of galaxy systems and sugeested that the entropy in their cores had. been fattened due to energy. injection., \scite{david96a} studied the entropy in a small sample of galaxy systems and suggested that the entropy in their cores had been flattened due to energy injection. + ? have recently. shown that the surface brightness profiles of clusters and groups co not. follow the predicted: sel-similar scaling., \scite{ponman98a} have recently shown that the surface brightness profiles of clusters and groups do not follow the predicted self-similar scaling. + Surface brightness profiles of galaxy groups are observed to be significantly Hatter than those of clusters. indicating differences in the gas distribution.," Surface brightness profiles of galaxy groups are observed to be significantly flatter than those of clusters, indicating differences in the gas distribution." + In order to explore this ellect further. it is necessary to study the properties of the eas in these systems in greater," In order to explore this effect further, it is necessary to study the properties of the gas in these systems in greater" +" 0.1 7. 0 ~ 0, 2(6)=6(Essμι)LN,7AS""f £s» 10°-ergs. n, em. p~2.4 (77171?frequencies#74.Wesuggestasphericalthat >~0. 1/5 "," $0.1$ $\gamma$ $\theta _{0}$ $\gamma $ $\theta _{0}^{-1}$ $\gamma (t)\approx 6 (E_{52}/n_{1})^{1/8}t_{{\rm day}}^{-3/8}$ $E_{52}$ $10^{52} +$ $n_1$ $^{-3}$ $p\sim 2.4$ $t^{-1.1-1.3}$ $\gamma \sim \theta_{0}^{-1}$ $1/\gamma $ " +sources in reftab:Ix. for which a spectral analysis was possible. the X-ray luminosity given here compares well with the values derived from the spectral fits.,"sources in \\ref{tab:lx} for which a spectral analysis was possible, the X-ray luminosity given here compares well with the values derived from the spectral fits." + Among the cluster members. most of the sources (21) are concentrated at the main sequence turn-off in the CMD ana have masses around 1.3 and 1.5 solar masses.," Among the cluster members, most of the sources (21) are concentrated at the main sequence turn-off in the CMD and have masses around 1.3 and 1.5 solar masses." + Most of these sources have a similar X-ray luminosity. between 0.1 and 0.7x10°?sv: the exceptions. with Lx210°?s7!.. are the two binary systems (DLM94). 113 and 204. the fast rotators (DLM94) 28onn and μι (this last one is also a binary system). and δν.," Most of these sources have a similar X-ray luminosity, between 0.1 and $0.7 \times 10^{29}$; the exceptions, with $L_{\rm X}\ga 10^{29}$, are the two binary systems (DLM94), 113 and 204, the fast rotators (DLM94) $_{\rm xmm}$ and $_{\rm + xmm}$ (this last one is also a binary system), and $_{\rm + xmm}$." + The two cluster members at the stage of core heltum burning (115 and 124) have the same X-ray luminosity., The two cluster members at the stage of core helium burning (115 and 124) have the same X-ray luminosity. +" There are only six sources within the mass range of our interest (0.8—1.2 Mg) among the likely cluster members: of these. five sources have luminosity in the range 0.1-0.4 x107? the other one. source 42,4,,,. is significantly brighter."," There are only six sources within the mass range of our interest $0.8-1.2~M_{\sun}$ ) among the likely cluster members; of these, five sources have luminosity in the range 0.1-0.4 $\times 10^{29}$; the other one, source $_{\rm xmm}$, is significantly brighter." +" This star does not show evidence of being a close binary nor a fast rotator, vandenBerg&Verbunt(2001). classified it as F5-F7 and report that no H&KK are visible in the low-resolution spectra.", This star does not show evidence of being a close binary nor a fast rotator; \cite{bv2001} classified it as $-$ F7 and report that no K are visible in the low-resolution spectra. + For source 93. the X-ray luminosity derived from the ddata is ~6 times lower than that derived from the ddata. however. this sources light curve shows evidence that the source was caught by dduring the decay phase of a flare.," For source 93, the X-ray luminosity derived from the data is $\sim 6$ times lower than that derived from the data, however, this source's light curve shows evidence that the source was caught by during the decay phase of a flare." + In reftab:Ix we also provide an estimate of the X-ray luminosity of 11 sources which have no counterpart among the cluster members listed in DLM94. but which have 2MASS colours and proper motion (in. Nowap) compatible with cluster membership: in addition their X-ray spectrum or hardness ratio (HR) is consistent with the source being a star.," In \\ref{tab:lx} we also provide an estimate of the X-ray luminosity of 11 sources which have no counterpart among the cluster members listed in DLM94, but which have 2MASS colours and proper motion (in ) compatible with cluster membership; in addition their X-ray spectrum or hardness ratio (HR) is consistent with the source being a star." + These 11 cluster member candidates have all a lower mass than those from DLM?94. with their position in the IR CMD consistent with masses <0.8Mp.," These 11 cluster member candidates have all a lower mass than those from DLM94, with their position in the IR CMD consistent with masses $< 0.8 M_{\sun}$." + In reffig:LxLbol the value of Lx{οι from the table are plotted against a star's bolometric magnitude. Mj).," In \\ref{fig:LxLbol} the value of $L_{\rm X}/L_{\rm bol}$ from the table are plotted against a star's bolometric magnitude, $M_{\rm + bol}$." + This plot can be directly compared with the plot of Ly/Lpo vs My for the Hyades in figure 15 of Sternetal.(1995).," This plot can be directly compared with the plot of $L_{\rm + X}/L_{\rm bol}$ vs $M_{\rm bol}$ for the Hyades in figure 15 of \cite{ssk95}." +. The comparison shows that for stars with bolometric magnitude Mp<8 (corresponding to M2 0.5Mo) the sensitivity of the oobservation in terms Lx/Ly is such that we do not expect to lose a significant fraction of the cluster population within the FFOV (possibly a couple of members). consistent with a ddetection rate of88%.," The comparison shows that for stars with bolometric magnitude $M_{\rm bol} < 8$ (corresponding to $M\ga 0.5 M_{\sun}$ ) the sensitivity of the observation in terms $L_{\rm X}/L_{\rm + bol}$ is such that we do not expect to lose a significant fraction of the cluster population within the FOV (possibly a couple of members), consistent with a detection rate of." +. From the comparison of our reffig:LxLbol and Fig., From the comparison of our \\ref{fig:LxLbol} and Fig. + 15 in Sternetal.(1995).. the deficiency of low mass stars with respect to cluster members at the main-sequence turn-off in NGC 752 is again apparent.," 15 in \cite{ssk95}, the deficiency of low mass stars with respect to cluster members at the main-sequence turn-off in NGC 752 is again apparent." + Comparison of the two figures shows also that this is not an effect of the sensitivity of the oobservation., Comparison of the two figures shows also that this is not an effect of the sensitivity of the observation. + This result and the fact that eross-matehing with the 2MASS catalogue did not identify any new candidate members with M.»0.8Me beside those already listed in DLM?94. confirms that (within the FFOV where our sensitivity is higher) the sample by DLM94," This result and the fact that cross-matching with the 2MASS catalogue did not identify any new candidate members with $M > 0.8~M_{\sun}$ beside those already listed in DLM94, confirms that (within the FOV where our sensitivity is higher) the sample by DLM94" + I first seek a solution of the radiative transfer problem for theincoming radiationvisible., I first seek a solution of the radiative transfer problem for the radiation. +" This is a long-standing problem in planetary atmospheres, one for which the scattering of the incoming light by atmospheric particules is crucial in determining the fraction of flux that is absorbed ????)."," This is a long-standing problem in planetary atmospheres, one for which the scattering of the incoming light by atmospheric particules is crucial in determining the fraction of flux that is absorbed ." +". For giant exoplanets orbiting close to solar-type stars (i.e. with orbital periods shorter than 10 days), the fraction of the irradiation that is reflected back is generally very low, of order or less, both from theoretical calculations and from observations ???)."," For giant exoplanets orbiting close to solar-type stars (i.e. with orbital periods shorter than 10 days), the fraction of the irradiation that is reflected back is generally very low, of order or less, both from theoretical calculations and from observations ." +". For simplicity, I hence choose to neglect scattering: yyΑ΄Ky."," For simplicity, I hence choose to neglect scattering: $\chi_\nu\approx \kappa_\nu$." +" I integrate the moments of the radiation field in the visible: Similarly, I define a mean opacity: It is interesting to note that since the visible radiation field is set by the stellar irradiation, x, can be calculated p"," I integrate the moments of the radiation field in the visible: Similarly, I define a mean opacity: It is interesting to note that since the visible radiation field is set by the stellar irradiation, $\kapv$ can be calculated ." +"riori. that B,0 for v in the visible.", $B_\nu\sim 0$ for $\nu$ in the visible. +" The equations (4)) and (5)) can hence be simplified by integrating over visible wavelengths: Following Eddington, I write µ.= VKy/Jy."," The equations \ref{eq:H}) ) and \ref{eq:K}) ) can hence be simplified by integrating over visible wavelengths: Following Eddington, I write $\mu_*\equiv \sqrt{\Kv/\Jv}$." +" Note that this approach is valid in two extremecases: for isotropic irradiation?),, for which µ.=1/v3, or in the case of collimated visible irradiation ?),, in which case οο5θ.."," Note that this approach is valid in two extremecases: for isotropic irradiation, for which $\mu_*=1/\sqrt{3}$, or in the case of collimated visible irradiation , in which case $\mu_*=cos\theta_*$ ." +" Equations (10)) and (11)) then write: Because both J, and Ην vanish at great depths co), therefore Furthermore, eq. (10))"," Equations \ref{eq:Hv}) ) and \ref{eq:Kv}) ) then write: Because both $\Jv$ and $\Hv$ vanish at great depths $m\rightarrow\infty$ ), therefore Furthermore, eq. \ref{eq:Hv}) )" +" implies that: In the case of an incoming radiation flux that is considered as fully isotropic, there is an inconsistency as we should have H,(0)=—J,(0)/2."," implies that: In the case of an incoming radiation flux that is considered as fully isotropic, there is an inconsistency as we should have $\Hv(0)=-\Jv(0)/2$." + This inconsistency is at the heart of the Eddington approximation however., This inconsistency is at the heart of the Eddington approximation however. + It is due to the fact that the incoming irradiation flux cannot remain fully isotropic because of the larger absorption of grazing rays., It is due to the fact that the incoming irradiation flux cannot remain fully isotropic because of the larger absorption of grazing rays. + Only an approximate solution can be found by neglecting the dependence on direction., Only an approximate solution can be found by neglecting the dependence on direction. +" In the collimated beam case, the solution is exact in the limit of no scattering."," In the collimated beam case, the solution is exact in the limit of no scattering." + Let us now consider the thermal part of the radiation field., Let us now consider the thermal part of the radiation field. +" As previously, we obtain average quantities by integration over thermal wavelengths: As previously for the mean visible opacity, Κιν is a function of temperature that can be calculatedpriorifield."," As previously, we obtain average quantities by integration over thermal wavelengths: As previously for the mean visible opacity, $\kapth$ is a function of temperature that can be calculated." +" The system of equations (4)) to (6)) is integrated over wavelengths with the hypothesis thatKy: We can combine eqs. (13)), (10) "," The system of equations \ref{eq:H}) ) to \ref{eq:rad eq}) ) is integrated over wavelengths with the hypothesis that: We can combine eqs. \ref{eq:Jv Hv}) ),\ref{eq:Hth}) )" +"and (19)) to find by integration in m: Separately, integrating(1 eq. (18)))"," and \ref{eq:rad eq th}) ) to find by integration in $m$: Separately, integrating eq. \ref{eq:Kth}) )" + over column mass and using eq. (20)), over column mass and using eq. \ref{eq:dHth}) ) +" yields: Equations (7)) and (14)) implythatΗι(0)=H+ p.J\(0), whichallows integrating the above equation to find Using the firstEddingtoncoefficient for the thermal radiation field, Ian=Ky /Jin, we obtain the mean intensity:"," yields: Equations \ref{eq:Htot}) ) and \ref{eq:Hv0}) ) implythat$\Hth(0)=H+\mu_* \Jv(0)$ , whichallows integrating the above equation to find Using the firstEddingtoncoefficient for the thermal radiation field, $\fKth\equiv \Kth/\Jth$ we obtain the mean intensity:" +when the scale factor. e. of the Universe was 0.55 times its current size.,"when the scale factor, $a$, of the Universe was 0.55 times its current size." + At any given redshift in Fig., At any given redshift in Fig. + 6. the average ratio of the mass of a halo to its final mass (tat >=0) is calculated for all eligible haloes., \ref{aadfig7} the average ratio of the mass of a halo to its final mass (at $z\!=\!0$ ) is calculated for all eligible haloes. + The error is represented by the standard error on the mean. Le. afSAEVN. where o is the standard deviation of the original distribution and jV is the sample size.," The error is represented by the standard error on the mean, i.e. $\sigma/\sqrt{N}$, where $\sigma$ is the standard deviation of the original distribution and $N$ is the sample size." + The same was done for both sets of control groups., The same was done for both sets of control groups. + The original sample of fossils was divided into two subsamples. of low mass and high mass groups (see Fig.," The original sample of fossils was divided into two subsamples, of low mass and high mass groups (see Fig." + 6bb and Fig., \ref{aadfig7}b b and Fig. + 6οο). such that both subsamples have equal numbers of groups.," \ref{aadfig7}c c), such that both subsamples have equal numbers of groups." + The boundary between the two subsamples corresponds to the median present-day mass 1055 !M..," The boundary between the two subsamples corresponds to the median present-day mass $\sim 3.34 \times 10^{13}\,h^{-1}\,$ $_{\odot}$ ." + Fig., Fig. + 6aa shows that at a scale factor of QS ἐς~ 0.24). the fossil groups have already attained ~90¢% of their final mass while. at the same redshift. the fraction of assembled mass of the extreme non-fossil groups is about ~77% of their final mass.," \ref{aadfig7}a a shows that at a scale factor of 0.8 $z\sim 0.24$ ), the fossil groups have already attained $\sim$ of their final mass while, at the same redshift, the fraction of assembled mass of the extreme non-fossil groups is about $\sim$ of their final mass." + The intermediate control group gives intermediate values., The intermediate control group gives intermediate values. + The fossil groups have almost all their mass in place by a redshift of +~0.1. and show no evidence of recent major mergers. while the fossils seem to be assembling mass even at the present day.," The fossil groups have almost all their mass in place by a redshift of $z\! \sim\! 0.1$, and show no evidence of recent major mergers, while the non-fossils seem to be assembling mass even at the present day." + These results suggest an early formation and consequent higher mass concentration in fossil groups. in comparison to normal groups. particularly for the more massive fossils.," These results suggest an early formation and consequent higher mass concentration in fossil groups, in comparison to normal groups, particularly for the more massive fossils." + As Figs., As Figs. + 6bb and. 6ce show. the difference in mass assembly is larger in more massive haloes than haloes with lower mass.," \ref{aadfig7}b b and \ref{aadfig7}c c show, the difference in mass assembly is larger in more massive haloes than haloes with lower mass." + The decreased distinction in the assembly history for our lower mass fossil systems probably results from the fact there is a large fraction of “statistical fossils” in this category: groups which achieve Anjo:2 due to random chance. because of the small number of members.," The decreased distinction in the assembly history for our lower mass fossil systems probably results from the fact there is a large fraction of “statistical fossils” in this category: groups which achieve $\Delta m_{12} \geq 2\,$ due to random chance, because of the small number of members." + As can be seen in Fig. 3..," As can be seen in Fig. \ref{aadfig3}," + — of optical fossil groups with masses less than ~3.3.1017 4M. are expected to fall into this “statistical fossil” category.," $\sim$ of optical fossil groups with masses less than $\sim 3.3 \times 10^{13}\,h^{-1}\,$ $_{\odot}$ are expected to fall into this “statistical fossil” category." + Various observational properties (Ponmanetal.1994:Khosroshahietal.2006:Khosroshahi.Ponman&Jones2007) have suggested an early formation epoch for fossils.," Various observational properties \citep{b130,b65,b75,b167,b80,b85} have suggested an early formation epoch for fossils." + D'Onghiaetal.(2005). and Sommer-Larsen(2006) used a set of twelve high-resolution numerical simulations in the XCDM cosmology to study the formation of fossil groups. and found a correlation for the magnitude gap between the brightest and second-brightest galaxies and the halo formation epoch. with fossils accreting half of their final dark matter mass at >2:1.," \citet{b50} and \citet{b147} used a set of twelve high-resolution numerical simulations in the $\Lambda$ CDM cosmology to study the formation of fossil groups, and found a correlation for the magnitude gap between the brightest and second-brightest galaxies and the halo formation epoch, with fossils accreting half of their final dark matter mass at $z\geq 1$." +" Such an early assembly of fossil haloes leaves enough time for L, galaxies to merge into the central one by dynamical friction. resulting in the observed magnitude gap at z=0."," Such an early assembly of fossil haloes leaves enough time for $_{\ast}$ galaxies to merge into the central one by dynamical friction, resulting in the observed magnitude gap at $z=0$." + Fig., Fig. + 7. shows the history of mass assembly of a typical example of a massive fossil group (right panel) and a control group (left panel) from the Millennium Gas Simulation from redshift >= L0to >0., \ref{aadfig9} shows the history of mass assembly of a typical example of a massive fossil group (right panel) and a control group (left panel) from the Millennium Gas Simulation from redshift $z=1.0$ to $z=0$. + The dimension of each image is LO.10 Mpc. centred around the central halo.," The dimension of each image is $10 \times 10$ Mpc, centred around the central halo." + It ean be seen that at 2=0.3. the X-ray fossil group has already largely been assembled. while the control group has considerable substructure even at a later epoch.," It can be seen that at $z=0.3$, the X-ray fossil group has already largely been assembled, while the control group has considerable substructure even at a later epoch." + We studied the history of the mass assembly of fossil groups. selected using the usual observational criteria at 2= 0. from a redshift +=O.S to the present day. within the Millennium simulation.," We studied the history of the mass assembly of fossil groups, selected using the usual observational criteria at $z\!=\!0$ , from a redshift $z\!=\!0.8$ to the present day, within the Millennium simulation." + A sample of X-ray fossil groups was defined from the Millennium simulations and associated gas and galaxy catalogues. according to the usualcriteria: (a) the difference between the /?- magnitudes of the first and second ranked galaxies. within half the projected radius enclosing 200 times the meandensity of material C?»99. is nj»22 magnitudes. and (b) The bolometric X-ray luminosity of the group is Lxasa20.25.107. Zerg +.," A sample of X-ray fossil groups was defined from the Millennium simulations and associated gas and galaxy catalogues, according to the usualcriteria: (a) the difference between the $R$ -band magnitudes of the first and second ranked galaxies, within half the projected radius enclosing 200 times the meandensity of material $R_{200}$ ), is $\Delta m_{12}\!\geq\! 2$ magnitudes, and (b) The bolometric X-ray luminosity of the group is $L_{\rm X,bol} \geq 0.25 \times 10^{42} h^{-2}$ erg $^{-1}$ ." + While optical fossil groups fulfill just the first condition. fossilssatisfy both criteria.," While optical fossil groups fulfill just the first condition, X-ray fossilssatisfy both criteria." + Our main results are as follows:, Our main results are as follows: +ie physical temperatures of the absorbing clouds.,the physical temperatures of the absorbing clouds. + The dnetic temperatures of the first two compoucuts are iweer than those of coll clouds in the Milkv Way Braun&Walterbos 1992)). while the temperature of ιο third (T5. TG00. IS) is in excellent agreenmienut with estinates of the temperature of the ΝΑΙ (~σουSOOO Ts: EI&ulkarii Teiles 1988. απ et al.," The kinetic temperatures of the first two components are larger than those of cold clouds in the Milky Way \cite{braun92}) ), while the temperature of the third $T_k\sim $ 7600 K) is in excellent agreement with estimates of the temperature of the WNM $\sim 5000 - 8000$ K; Kulkarni Heiles 1988, Carilli et al." + 1998)., 1998). + Note that recent Arecibo observatious of the WNM in the Milkv Wav have found some evideuce forlower temperatures than the above. with Tj;2000 Is UTeiles&Troland2000.ITe3les 2001)). although these results are still iu preliminary form.," Note that recent Arecibo observations of the WNM in the Milky Way have found some evidence for temperatures than the above, with $T_k \sim 2000$ K \cite{heiles00,heiles01}) ), although these results are still in preliminary form." + These estimates of the kinetic teniperature can be used in equation (3)) to obtain tie HIT column densities of he different compoucuts., These estimates of the kinetic temperature can be used in equation \ref{eqn:nh-ts}) ) to obtain the HI column densities of the different components. + This vields Αι)=1.740.21.107 aid μι)=2.41.0&1029 for he Wo Marrow COnporents. and (ο)=1.260.19<1pi for tjo wick' conipoueut.," This yields $\NHI (1) = 1.7 \pm 0.24 \times 10^{20}$ and $\NHI (2) = 2.1 \pm 1.0 \times 10^{19}$ for the two narrow components, and $\NHI (3) = 1.26 \pm 0.49 \times 10^{21}$ for the wide component." + The total colunu deusitv in all three conmponenuts is ΑΗ=1.15£0.19ον larger han (but. eivoen the errors. stil ln agreenieut with) he value of ..7.9E.1.1«1079 obtained from the La ine (Rao&TTsιο 19983).," The total column density in all three components is $\NHI = 1.45 \pm 0.49$, larger than (but, given the errors, still in agreement with) the value of $7.9 \pm 1.4 \times 10^{20}$ obtained from the $\alpha$ line \cite{rao98}) )." + Cüven tvat the οσα Nyy neasurements are. strictly speasine. upper lits. since here may be nou-thermal contributions to the line width. hne agreement beween the coinn deusities obtainied rou the 21-cu profile aud the Lxauau-o. profile is qiite eood.," Given that the 21-cm $\NHI$ measurements are, strictly speaking, upper limits, since there may be non-thermal contributions to the line width, the agreement between the column densities obtained from the 21-cm profile and the $\alpha$ profile is quite good." + Thus. the 21-an profile of this absorber agrees fairly well with what would be expected from an absorber with a iuulti-phase medium ach like that of the Galaxy (at least. im terius of the of the two pliases).," Thus, the 21-cm profile of this absorber agrees fairly well with what would be expected from an absorber with a multi-phase medium much like that of the Galaxy (at least, in terms of the of the two phases)." + It should be noted that uou-thermal motious of a eiven maenitude will make a larger difference to narrow lines than to wide lines., It should be noted that non-thermal motions of a given magnitude will make a larger difference to narrow lines than to wide lines. + It is therefore likely that the column deusitv in the narrow componcuts Ovhich we ideutifv wih the CNAD) are iore severely over-estimate., It is therefore likely that the column density in the narrow components (which we identify with the CNM) are more severely over-estimated. +" The total contribution of the ΟΝΑΤ to the QD column densitv is NuiΝΔ1.9025«10?""2. Le, at inost of the total coluun density obtained frou the line (Rao&Turusick 1998))."," The total contribution of the CNM to the HI column density is $\NHI ({\rm CNM}) \le 1.9 \pm 0.25 \times 10^{20}$, i.e. at most of the total column density obtained from the line \cite{rao98}) )." +" Of course. it is possible that the wide compment also las a low kinetic cluperature and that its aree width is prinarily due o non-therual motious of the absorbing eas,"," Of course, it is possible that the wide component also has a low kinetic temperature and that its large width is primarily due to non-thermal motions of the absorbing gas." + For exiuuple. this coid be due to t16 blending of a nunber of narrow C'NÀ lines of low optical depth. rather than due to absorXon bv the WNAL," For example, this could be due to the blending of a number of narrow CNM lines of low optical depth, rather than due to absorption by the WNM." + Even in such a situation. however. he total contribution of such clouds to the ITI columim density would be very low. leavi18o unaccounuted a substanlal fraction of the column density. which must Le in a sti] hotter component.," Even in such a situation, however, the total contribution of such clouds to the HI column density would be very low, leaving unaccounted a substantial fraction of the column density, which must lie in a still hotter component." +" Fe0 exanpο,5 if we asstune that the hypothetical blended cold clouds have kinetic tempecratiwes Tj~100 Ts. then the total III column density iu the wide component is ucelieib AquLF«101?72."," For example, if we assume that the hypothetical blended cold clouds have kinetic temperatures $T_k \sim 100$ K, then the total HI column density in the wide component is negligible, $\NHI \sim 1.7\times 10^{19}$." + The bulk of the eas seen iu Lyuuura profile would hence still be required to be in : ase Whose temperature is sufficieutlv large to make Lem optical deoth lower than our detection threshol, The bulk of the gas seen in the $\alpha$ profile would hence still be required to be in a phase whose temperature is sufficiently large to make the 21-cm optical depth lower than our detection threshold. +" lius. regardless «of whether or not the wide componern entified with the WNAL one requires ~76% (or possil) evel, more} of the III to be coutained in the WNAL"," Thus, regardless of whether or not the wide component is identified with the WNM, one requires $\sim 76\%$ (or possibly, even more) of the HI to be contained in the WNM." + Iudeed. the mere fact that we observe components iu absorption profile whose kinetic temperatures are suiall," Indeed, the mere fact that we observe components in the absorption profile whose kinetic temperatures are smaller" +The X-ray transient XTE J1752—223 was discovered by the (RXTE)) on 2009 October 23.,The X-ray transient XTE $-$ 223 was discovered by the ) on 2009 October 23. +" The 2010 outburst of XTE J1752—223 was monitored by the (Shaposhnikovetal.2010), the (MAXI,2010), and (Curranetal.2010) in the X-ray domain."," The 2010 outburst of XTE $-$ 223 was monitored by the \citep{sha10}, the \citep[\emph{MAXI}, and \citep{cur10} in the X-ray domain." + The outburst exhibited an evolving behavior in agreement with what would be expected from stellar mass black hole binary., The outburst exhibited an evolving behavior in agreement with what would be expected from a stellar mass black hole binary. +" In the preceding alow-hard X-ray state, the radio counterpart was identified by the ATCA (Australia Telescope Compact Array) with a flux density of ~2 mJy and a flat spectrum consistent with that of a compact jet (Brocksoppetal.2009)."," In the preceding low-hard X-ray state, the radio counterpart was identified by the ATCA (Australia Telescope Compact Array) with a flux density of $\sim$ 2 mJy and a flat spectrum consistent with that of a compact jet \citep{bro09}." +. XTE J1752—223 started to transit toward a high-soft X-ray state around 2010 January 20 (e.g.Shaposhnikovetal.2010)., XTE $-$ 223 started to transit toward a high-soft X-ray state around 2010 January 20 \citep[e.g.][]{sha10}. +. A 10-fold increase of radio flux density and a flat spectrum were observed by the ATCA on 2010 January 21 (Brocksoppetal.2010)., A 10-fold increase of radio flux density and a flat spectrum were observed by the ATCA on 2010 January 21 \citep{bro10}. +". The increased flux density suggested that a major ejection was imminent (Brocksoppetal.2010) and, indeed, a transient jet was detected by the rapid-response EVN (European VLBI Newtork) observations on 2010 February 11."," The increased flux density suggested that a major ejection was imminent \citep{bro10} and, indeed, a transient jet was detected by the rapid-response EVN (European VLBI Newtork) observations on 2010 February 11." +" The transitions from a low-hard X-ray state toward a high-soft X-ray state are in fact, commonly associated with discrete ejection events (Corbeletal.2004;Fender2004,2009)."," The transitions from a low-hard X-ray state toward a high-soft X-ray state are in fact, commonly associated with discrete ejection events \citep{cor04, fen04, fen09}." +". Together with follow-up VLBA (Very Long Baseline Array) observations in 2010 February, the transient jet was found to show significant deceleration, possibly due to the jet interaction with the surrounding medium (Yangetal.2010,hereafterPaper I).."," Together with follow-up VLBA (Very Long Baseline Array) observations in 2010 February, the transient jet was found to show significant deceleration, possibly due to the jet interaction with the surrounding medium \citep[][hereafter Paper~I]{yan10}." + In this paper we present results from the additional three epochs that show a new transient ejection event and later a stationary feature which we identify as the core., In this paper we present results from the additional three epochs that show a new transient ejection event and later a stationary feature which we identify as the core. +Fig.,Fig. + 3 shows the agreement between our NEAR. MID. and FAR. power spectra and the nmeasurenienis presented in ?..," \ref{fig:pktegcomparech4} shows the agreement between our NEAR, MID, and FAR power spectra and the measurements presented in \citet{tegmark/etal:2006}." +" We used this comparison (o set by eve the large scale bias of our mockcatalogs through 01,44;. the width of Αν} in Eqn. 27.."," We used this comparison to set by eye the large scale bias of our mockcatalogs through $\sigma_{\log M}$, the width of $N_{cen}(M)$ in Eqn. \ref{NcenM}." +" The small discrepancy between the normalizations of the FAR and other catalogs at small & could be eliminated with a slight variation in 91,43717e."," The small discrepancy between the normalizations of the FAR and other catalogs at small $k$ could be eliminated with a slight variation in $\sigma_{\log M,FAR}$." + However. the FAR sample clearly has a different shape. and is consistent with trends in Fig.," However, the FAR sample clearly has a different shape, and is consistent with trends in Fig." + 6 of ?.. though in the SDSS sample the signilicance of (hese trends is less clear.," 6 of \citet{tegmark/etal:2006}, though in the SDSS sample the significance of these trends is less clear." + Our FAR sample has ~3% more power at &=0.09 and ~LOY more power al 7:=0.2 than the NEAR and MID llaviung established the agreement between our mock catalogs and the ?/— observed Prpe(h). we now attempt toisolate the sources of nonlinearity in our catalogs and demonstrate that the power spectrum of (he reconstructed halo clensity field is the best tracer of the underlving linear spectrwm.," Our FAR sample has $\sim 3\%$ more power at $k=0.09$ and $\sim 10\%$ more power at $k=0.2$ than the NEAR and MID Having established the agreement between our mock catalogs and the \citet{tegmark/etal:2006} observed $P_{LRG}(k)$, we now attempt to isolate the sources of nonlinearity in our catalogs and demonstrate that the power spectrum of the reconstructed halo density field is the best tracer of the underlying linear spectrum." + In Fie., In Fig. + 7 we analyze in detail the MID sample. while Fies.," \ref{fig:LRGratMIDall} we analyze in detail the MID sample, while Figs." + and 9 show that the NEAR. and FAR. sample behave similarly., \ref{fig:LRGratNEAR} and \ref{fig:LRGratFAR} show that the NEAR and FAR sample behave similarly. + The first major result is that there is no detectable deviation lrom a constant bias between the central LRGs aud the dark matter in real space for &<0.1. and the deviation at f=0.2 is <2% [or the MID and FAR subsamples: the discrepaney for the NEAR sample is ~1% at &=0.1 and ab hk=0.2 (solid curves with the lowest amplitude as &— 0)., The first major result is that there is no detectable deviation from a constant bias between the central LRGs and the dark matter in real space for $k \leq 0.1$ and the deviation at $k=0.2$ is $\leq 2\%$ for the MID and FAR subsamples; the discrepancy for the NEAR sample is $\sim 1\%$ at $k=0.1$ and at $k=0.2$ (solid curves with the lowest amplitude as $k \rightarrow 0$ ). + The lower left panel of Fig., The lower left panel of Fig. + 7 demonstrates (hat the main effect of using redshift space coordinates for the central LRGs is the further damping of the BAO signatures., \ref{fig:LRGratMIDall} demonstrates that the main effect of using redshift space coordinates for the central LRGs is the further damping of the BAO signatures. + There is also a nonmonotonie but smooth variation that is <4 between &=0 and /=0.4., There is also a nonmonotonic but smooth variation that is $\leq 4\%$ between $k=0$ and $k=0.4$. + In the /0.2h ! regime. the direction of the deviation is opposite of that between (he real space central LRGs ancl underlving dark matter. so that the redshift space central LRG power spectrum is nearly linearly related to the real space matter power spectrum at A—0.25Mpe.|. The inclusion of satellite LRGs in real space has (wo effects.," In the $k \leq 0.2 \; h$ $^{-1}$ regime, the direction of the deviation is opposite of that between the real space central LRGs and underlying dark matter, so that the redshift space central LRG power spectrum is nearly linearly related to the real space matter power spectrum at $k \leq 0.2 h \; {\rm Mpc}^{-1}$ The inclusion of satellite LRGs in real space has two effects." + The linear bias is increased because (he satellites upwelelt only the most massive. more highlv biased halos traced by the LRGs.," The linear bias is increased because the satellites upweight only the most massive, more highly biased halos traced by the LRGs." + Secondly. (he satellite galaxies add a shot noise given bv Equ. 8..," Secondly, the satellite galaxies add a shot noise given by Eqn. \ref{onehaloterm}. ." + The upper right panel of Fie., The upper right panel of Fig. +" 7 shows that the difference between the (7) including satellites and ΙΛ} of the central LRGs only is well described by these (wo effects. with a relative bias 5,,;=1.042 and PIzz1460 (h1 Mpcy*."," \ref{fig:LRGratMIDall} shows that the difference between the $P(k)$ including satellites and $P(k)$ of the central LRGs only is well described by these two effects, with a relative bias $b_{rel} = 1.042$ and $P^{1h} \approx 1460$ $h^{-1}$ $^3$ ." + This latter value is in good agreement with 1480 (5. Mpc)*.the value computed directly from Equ.," This latter value is in good agreement with 1480 $h^{-1}$ $^3$ ,the value computed directly from Eqn." + & using our input LOD parameters., \ref{onehaloterm} using our input HOD parameters. + As —0.4.the amplitude of the difference slightly diminishes due to the width of the satellite LRG density," As $k \rightarrow 0.4$,the amplitude of the difference slightly diminishes due to the width of the satellite LRG density" +suppressed due to the low accretion rate of atomic hydrogen. which is depleted by two orders of magnitude.,"suppressed due to the low accretion rate of atomic hydrogen, which is depleted by two orders of magnitude." + In the molecular environment. the formation of water in either dust or ga:u phase is inefficient through neutral-neutral reactions. and 101molecule reactions will also contribute significantly or even dominate. through the chain O7+H:OH +H.OH+H:H:O -H.H;O+H:—H;O+H. followed by recombination HiO+e-Π.Ο--Η.," In the molecular environment, the formation of water in either dust or gas phase is inefficient through neutral-neutral reactions, and ion-molecule reactions will also contribute significantly or even dominate, through the chain $\rm O^+ + H_2 \rightarrow OH^+ +H$, $\rm +OH^+ + H_2 \rightarrow H_2O^+ +H$ , $\rm H_2O^+ + H_2 \rightarrow +H_3O^+ +H$, followed by recombination $\rm H_3O^+ + e^- \rightarrow +H_2O + H$." +" The inner regions of active galaxies from. e.g.. Mrk 231. which are highly exposed to X-rays. are likely to exhibit enhanced formation of HO on dust grains: (1) Dust temperatures are expected to be moderate. Z4,~20—40 K. as the heating of dust is less efficient than by UV: (1) The dynamical timescales are not very long and shocks are expected to be present. and therefore dust particles are not expected to be or stay covered with ice: (111) Shocks may even be able to break up grains into smaller particles. therefore enlarging the effective surface of dust. where water is expected to form."," The inner regions of active galaxies from, e.g., Mrk 231, which are highly exposed to X-rays, are likely to exhibit enhanced formation of $_2$ O on dust grains: (i) Dust temperatures are expected to be moderate, $T_{\rm dust}\sim 20-40$ K, as the heating of dust is less efficient than by UV; (ii) The dynamical timescales are not very long and shocks are expected to be present, and therefore dust particles are not expected to be or stay covered with ice; (iii) Shocks may even be able to break up grains into smaller particles, therefore enlarging the effective surface of dust, where water is expected to form." + In Fig. 8..," In Fig. \ref{XDRapplication}," + the chemical abundances of H. Hs. OH and H:O and temperatures of an XDR model is shown with density 107? em? Fy=160 erg em? s7!. and Solar metallicity. Ζω ," the chemical abundances of H, $_2$, OH and $_2$ O and temperatures of an XDR model is shown with density $n=10^{5.5}$ $^{-3}$, $F_X=160$ erg $^{-2}$ $^{-1}$, and Solar metallicity, $Z = Z_\odot$ ." +"Three different cases for the formation of OH and H:O are considered: To summarize. we find that the warm H»O colunmn density is enhanced by apprimately an order of magnitude over a column Ny~5-1077 em"". when including H:O formation on dust."," Three different cases for the formation of OH and $_2$ O are considered: To summarize, we find that the warm $_2$ O colunmn density is enhanced by apprimately an order of magnitude over a column $N_{\rm H}\sim +5\cdot 10^{22}$ $^{-2}$, when including $_2$ O formation on dust." + At larger column densities. where temperatures decrease and the gas becomes molecular. the formation on dust grains does not impact the abundance of H:O. The OH abundance is only indirectly affected by the higher H» formation rate on dust when using the distribution with the higher dust crosssection.," At larger column densities, where temperatures decrease and the gas becomes molecular, the formation on dust grains does not impact the abundance of $_2$ O. The OH abundance is only indirectly affected by the higher $_2$ formation rate on dust when using the distribution with the higher dust crosssection." + The role and importance of OH and H:Oformation on dust is investigated., The role and importance of OH and $_2$ Oformation on dust is investigated. + We use both Monte Carlo as well as rate equation, We use both Monte Carlo as well as rate equation +line. and further distorted. by complex absorption.,"line, and further distorted by complex absorption." + The intrinsic enuüssion is required. to be a multi.temperature plasma. and the cooling components are significantly detected in the data.," The intrinsic emission is required to be a multi–temperature plasma, and the cooling components are significantly detected in the data." + Parameters for both the expected a=1 cooling model and the better fitting model where a is [ree are given in Table 1., Parameters for both the expected $\alpha=1$ cooling model and the better fitting model where $\alpha$ is free are given in Table 1. + The best fit single temperature model (including rellection and complex absorption) is also tabulated for comparison. but is a worse lit by AY?=20 as the data contain significant iron L line emission which cannot be fit bv the single temperature mocoels.," The best fit single temperature model (including reflection and complex absorption) is also tabulated for comparison, but is a worse fit by $\Delta\chi^2=20$ as the data contain significant iron L line emission which cannot be fit by the single temperature models." + This is the first. observational confirmation of the theoretically expected cooling of the shocked plasma in polars. although the distribution of cool components with temperature. 1s marginally inconsistent with the predicted a=," This is the first observational confirmation of the theoretically expected cooling of the shocked plasma in polars, although the distribution of cool components with temperature is marginally inconsistent with the predicted $\alpha=1$." + AIL 3 GINGA spectra give a lower flux than the ASCA data. even in the overlapping 2.10 keV band.," All 3 GINGA spectra give a lower flux than the ASCA data, even in the overlapping 2–10 keV band." + Ratios of these spectra with the best [it ASC'A model are given in Figure 4., Ratios of these spectra with the best fit ASCA model are given in Figure 4. + All the spectra are also systematically dillerent in shape compared to the SCA data. being eencrally softer.," All the spectra are also systematically different in shape compared to the ASCA data, being generally softer." + Thus rere are significant spectral as well as intensity changes between the GINGA and ASCA observations., Thus there are significant spectral as well as intensity changes between the GINGA and ASCA observations. + We first fit the GINGA [ow ancl high pulse state ala. where the inclination angle to the eclipsing spot 1s changing with phase.," We first fit the GINGA low and high pulse state data, where the inclination angle to the eclipsing spot is changing with phase." + We fit the two datasets simultaneously. constraining the interstellar absorption. plasma temperature and abundances to be the same.," We fit the two datasets simultaneously, constraining the interstellar absorption, plasma temperature and abundances to be the same." + Ishida et al (1991) show that complex absorption is required by the data. and model this ον partial covering.," Ishida et al (1991) show that complex absorption is required by the data, and model this by partial covering." + X single temperature plasma mocel with »wlial covering gives V7=37/51., A single temperature plasma model with partial covering gives $\chi^2=37/51$. + Phe low state spectrum is significantly softer than the high state at low energies. and in fact does not require any absorption.," The low state spectrum is significantly softer than the high state at low energies, and in fact does not require any absorption." + Constraining he two partial coverers to the be same gives à much worse it with 47=r56/53., Constraining the two partial coverers to the be same gives a much worse fit with $\chi^2=56/53$. + Replacing the partial coverer by the vower law columncovering fraction model used for the ASCA data gives an equally &ood fit. showing that the wider ASCA bandpass is needed to properly constrain the complex absorption properties.," Replacing the partial coverer by the power law column–covering fraction model used for the ASCA data gives an equally good fit, showing that the wider ASCA bandpass is needed to properly constrain the complex absorption properties." + We use the power law absorber for consistency with the ASCA results. but since Iguus ane 3 are strongly correlated and poorly determined we constrain Στο be equal across all the datasets.," We use the power law absorber for consistency with the ASCA results, but since $N_{\rm H, max}$ and $\beta$ are strongly correlated and poorly determined we constrain $\beta$ to be equal across all the datasets." + ueThis gives. V52=35/52. [or 32LOLEOOS. Nae;—5.0' Ευσος ? for the low and high state spectra. respectively.," This gives $\chi^2_\nu=35/52$ for $\beta=-1.01\pm 0.08$, $N_{H,max}=5.0^{+9.0}_{-4.5}$ and $770^{+\infty}_{-690}\times 10^{22}$ $^{-2}$ for the low and high state spectra, respectively." + Again the residuals clearly indicate structure around the iron line and edge energies so we [fit a rellection continuum spectrum and 6.4 keV iron lluorescence Dine., Again the residuals clearly indicate structure around the iron line and edge energies so we fit a reflection continuum spectrum and 6.4 keV iron fluorescence line. + This gives a significant improvement in the fit with Az= 28/50., This gives a significant improvement in the fit with $\chi^2_\nu=28/50$ . + The continuum was then replaced. with the multitemperature à=1 emission. model., The continuum was then replaced with the multi--temperature $\alpha=1$ emission model. + This did not give a significantly better fit to thedata. showing that the 220 keV GINGA bandpass is not sullicient to distinguish between single and multitemperature emission mocels.," This did not give a significantly better fit to the data, showing that the 2–20 keV GINGA bandpass is not sufficient to distinguish between single and multi–temperature emission models." + Llowever. we chose this model for further study. for ease of comparison with the ASCA fits.," However, we chose this model for further study, for ease of comparison with the ASCA fits." + The flaring state spectrum is then also fit. with this model. and the results detailed in. Table 2.," The flaring state spectrum is then also fit with this model, and the results detailed in Table 2." + Error ranges on the absorber are not given since this quantity is unconstrained by the data., Error ranges on the absorber are not given since this quantity is unconstrained by the data. + The harder spectrum seen in the high state can equally well be described by a larger contribution from the rellection continuum as by more absorption., The harder spectrum seen in the high state can equally well be described by a larger contribution from the reflection continuum as by more absorption. + The complex absorption is clearly à major component in the spectrum. giving a smooth hardening at energies lower than 4 keV which cannot be described by complete covering by material of a single ionization parameter.," The complex absorption is clearly a major component in the spectrum, giving a smooth hardening at energies lower than $\sim 4$ keV which cannot be described by complete covering by material of a single ionization parameter." + The lack of the standard absorption sm.enatures (strong low energy cutoll or ionised edges) means that it is not always obvious that this component is present in the spectrum., The lack of the standard absorption signatures (strong low energy cutoff or ionised edges) means that it is not always obvious that this component is present in the spectrum. + In BY Cam its main signature is that. the derived. temperature for the ASCA spectrum becomes unphysically high without it., In BY Cam its main signature is that the derived temperature for the ASCA spectrum becomes unphysically high without it. + We caution that where this complex absorption is present. the observed," We caution that where this complex absorption is present, the observed" +11998) mass-huninosity (M-L) relations.,1998) mass-luminosity (M-L) relations. + For the lowest-mass stars aud brown dwarfs (AD 0.1: AL.) im regious of space. aud asstuuine no evolution of the star-forming process over time (although its rate can change). the IAIF is identical to the PDMPE and can be referred to simply as the Mass Function (AIF).," For the lowest-mass stars and brown dwarfs (M $\lesssim 0.1$ $_{\sun}$ ) in well-defined regions of space, and assuming no evolution of the star-forming process over time (although its rate can change), the IMF is identical to the PDMF and can be referred to simply as the Mass Function (MF)." + While this technique is suitable for low-mass stellar populations. substellar ME determinations are hindered by their thermal evolution.," While this technique is suitable for low-mass stellar populations, substellar MF determinations are hindered by their thermal evolution." + A brown dif with au observed luminosity and/or effective teniperature CT 55) has a wide range of possible iiasses depending ou its age., A brown dwarf with an observed luminosity and/or effective temperature $_{eff}$ ) has a wide range of possible masses depending on its age. + This mass-age degeneracy is not critical for vouug cluster brown dwiuf populations. where members are asstuued to be approximately coeval (e.8.. White Chez 2001).," This mass-age degeneracy is not critical for young cluster brown dwarf populations, where members are assumed to be approximately coeval (e.g., White Ghez 2001)." + In the Galactic disk. however. stars and brown οστάτς eau span a fairly broad range of ages. from a few teus of Myr to ~ 10 Cyr.," In the Galactic disk, however, stars and brown dwarfs can span a fairly broad range of ages, from a few tens of Myr to $\sim$ 10 Gyr." + In other words. there is no single ALL relation that can be used to convert the LF iuto the ME for brown cawarts in the field.," In other words, there is no single M-L relation that can be used to convert the LF into the MF for brown dwarfs in the field." + Field brown dwarfs are also generally older than heir voune cluster counterparts. so that the lowest mass field objects can be exceedingly faint. requiring deep and/or wide area surveys to detect sufficicnt ummbers.," Field brown dwarfs are also generally older than their young cluster counterparts, so that the lowest mass field objects can be exceedingly faint, requiring deep and/or wide area surveys to detect sufficient numbers." + Nevertheless. the plivsical properties of evolved own dwiirfs are better understood than their vouuger counterparts. without the complications of vouthful accretion or rapid evolution.," Nevertheless, the physical properties of evolved brown dwarfs are better understood than their younger counterparts, without the complications of youthful accretion or rapid evolution." + Furthermore. the nearby population of stars is not affected by reddening: cau j nore easily followed-rp with spectroscopic. parallactic. aud high-resolution Πασάς observatious (to derive physical characteristics and inultiplicitv): aud. assuming that it is well-inixed. is eeucrallv devoid of oreground or background contamination.," Furthermore, the nearby population of stars is not affected by reddening; can be more easily followed-up with spectroscopic, parallactic, and high-resolution imaging observations (to derive physical characteristics and multiplicity); and, assuming that it is well-mixed, is generally devoid of foreground or background contamination." + This article is the first of a two-part scrics investieatiug the substellar ME in the Solar Neighborhood. * cColmparing simulated LFs to a maguitude-limited sample of T. dwarts (Bureasseretal.2003a) identified in the Two Micron. All Sky Survey (Cutrietal.200:.hereafter2MASS)..," This article is the first of a two-part series investigating the substellar MF in the Solar Neighborhood, by comparing simulated LFs to a magnitude-limited sample of T dwarfs \citep{me03a} identified in the Two Micron All Sky Survey \citep[hereafter 2MASS]{cut03}." +" T dwarfs are a spectroscopic class of brown durs that exhibit CIT, absorption (Dreasscretal.2002b:Ceballe2002).. implying ToreZ1300 I& (Iirkpatrieketal.2000:Colimowskict2000).."," T dwarfs are a spectroscopic class of brown dwarfs that exhibit $_4$ absorption \citep{me02a,geb02}, implying $_{eff} \lesssim 1300$ K \citep{kir00,gol04}." + Di this article. Monte Carlo simulations of the field μαυροβαν ME. are examined. and dependencies ou. various mput parameters are vestigated.," In this article, Monte Carlo simulations of the field substellar MF are examined, and dependencies on various input parameters are investigated." + These simulations are comparable to those of Allenetal.(2001)... who constrain the substellar ME. through Bavesian techuiques.," These simulations are comparable to those of \citet{all04}, who constrain the substellar MF through Bayesian techniques." + The implementation of the simulations presented here is described in 5 2. which iucludes discussion ofthe variousinput distributions aud evolutionary models used.," The implementation of the simulations presented here is described in $\S$ 2, which includes discussion of the variousinput distributions and evolutionary models used." +" An in-depth analysis of the derived LF and T,.,,; distributious aud their features is given in 5] 3.", An in-depth analysis of the derived LF and $_{eff}$ distributions and their features is given in $\S$ 3. + Iu 5 Ll. the seusitivitv of these distributious between the evolutionary models eniploved. different birth rates. different age and mass τς. and the influence of uesolved multiple svstenis is explored.," In $\S$ 4, the sensitivity of these distributions between the evolutionary models employed, different birth rates, different age and mass limits, and the influence of unresolved multiple systems is explored." + Surface deusitv predictions based on the simulatious are derived for both shallow aud deep maguitude-limited survevs in 5 5., Surface density predictions based on the simulations are derived for both shallow and deep magnitude-limited surveys in $\S$ 5. + Results are sumunarized iu 8 6., Results are summarized in $\S$ 6. + The purpose of these simulations is to create a statistical link between the ALF and LF. or more eoncrally a luk between the fundamental properties of brown dwarfs mass. age. and ictallicitv — and their observables — (T.5; aud luminosity.," The purpose of these simulations is to create a statistical link between the MF and LF, or more generally a link between the fundamental properties of brown dwarfs – mass, age, and metallicity – and their observables – $_{eff}$ and luminosity." + This link is mace through evolutionary models coupled to uou-grev model atinosphleres., This link is made through evolutionary models coupled to non-grey model atmospheres. + In this study. we assume that all brown dwarfs are described by a single distribution for cach of their fundamental paraucters. denoted Pr). where e is the fuudiuuental property in question.," In this study, we assume that all brown dwarfs are described by a single distribution for each of their fundamental parameters, denoted $P(x)$, where $x$ is the fundamental property in ." + The fundamental distributions examined are summarized in Table 1 and described iu detail below., The fundamental distributions examined are summarized in Table 1 and described in detail below. +a 3-climensional. time-dependent model of the eas aud dust in the envelope would be required). but to permit the study of the eeneral effects on the chemical moclel of the addition of denusity-enhanced gas and dust shells.,"a 3-dimensional, time-dependent model of the gas and dust in the envelope would be required), but to permit the study of the general effects on the chemical model of the addition of density-enhanced gas and dust shells." + The radial H» gas deusity clistribution used in the model is shown in2., The radial $_2$ gas density distribution used in the model is shown in. +. The H» is assumed to be completely sell-shielded in the regions of interest iu the CSE so that ngQr)u(r)., The $_2$ is assumed to be completely self-shielded in the regions of interest in the CSE so that $n_{H_2}(r)\approx n(r)$. + The adopted temperature profile is based on an empirical fit to the gas kinetic temperature profile derived by Crosas&Menten.(1997).. and takes the form with a lower limit of 10 Ik. to prevent the temperature becoming uurealistically low in the outer envelope.," The adopted temperature profile is based on an empirical fit to the gas kinetic temperature profile derived by \citet{cro97}, and takes the form with a lower limit of 10 K to prevent the temperature becoming unrealistically low in the outer envelope." + Parent species (with ibundauces shown in 1)) are injected into the model at the inner radius of 7;=1010 u. where the gas deusity is 8.6xLO’ ciuo3," Parent species (with abundances shown in ) are injected into the model at the inner radius of $r_i=10^{15}$ cm, where the gas density is $8.6\times10^7$ $^{-3}$." + At this radius the eas kinetic temperature is Ότο kk and the interstellar radiation fiekl is attenuated by an ellective radial extinction ol IY maguitudes in the V. band., At this radius the gas kinetic temperature is 575 K and the interstellar radiation field is attenuated by an effective radial extinction of 47 magnitudes in the $V$ band. + Initial abundauces are the same as in Millar (2000).. with the adcition of Mg (see 3.3)). and with C»H» and HCN abuudauces taken from the recent measurements by Fonfriaetal.(2008).," Initial abundances are the same as in \citet{mil00}, , with the addition of Mg (see ), and with $_2$ $_2$ and HCN abundances taken from the recent measurements by \citet{fon08}." +. The standard interstellar radiation field (DraineLOTS) is assumed to impiuge on the outside of the circumstellar envelope from all directions., The standard interstellar radiation field \citep{dra78} is assumed to impinge on the outside of the circumstellar envelope from all directions. + The extinction is calculated [or the underlying 1/7? density. distribution of the CSE using the approach of Jura&Mor-, The extinction is calculated for the underlying $1/r^2$ density distribution of the CSE using the approach of \citet{jur81}. + Additional terms are added to the extinction due to the contributions of the cdeusity-enliauced shells (lorfurtherdetailsofdust.shells.seeBrown&Millar 2003).," Additional terms are added to the extinction due to the contributions of the density-enhanced shells \citep[for further details of the extinction calculation in the presence of dust shells, see][]{bro03}." +. The chemical reaction network is based ou that used by Petrieetal.(20059) aud Millaretal.(2007)., The chemical reaction network is based on that used by \citet{pet03} and \citet{mil07}. +. The reaction rates lave been updated to be consistent with those in the (dipole-enhauced) RATEOG database (Woodalletal.2007)., The reaction rates have been updated to be consistent with those in the (dipole-enhanced) RATE06 database \citep{wood07}. +.‘honeAdditional new reactious from RATEOG for species in the Petrieetal.(2003) model have also been adde., Additional new reactions from RATE06 for those species in the \citet{pet03} model have also been added. +" The following reactious were deleted from the reaction network in order to increase computational speed. withx ueelieible effect ou the chemistry of the species of interest in tliis study: those with activation energies greater than 300 Ix. those reactions involving H40 as a reagent (except lor HzO + € ). those with Hs as a reagent (except lor Ho + € and H, + Hs). aud any reactions Involving .5 .CO . . CoH,. and CaHs."," The following reactions were deleted from the reaction network in order to increase computational speed, with negligible effect on the chemistry of the species of interest in this study: those with activation energies greater than 300 K, those reactions involving $_3$ $^+$ as a reagent (except for $_3$ $^+$ + $e^-$ ), those with $_2^+$ as a reagent (except for $_2^+$ + $e^-$ and $_2^+$ + $_2$ ), and any reactions involving $^-$, $^-$, $^+$, $^+$ , $_2$ $_6^+$ , and $_2$ $_5$ ." + Carbou-chain species. bydrocarbous. cyanopolyvues and their associated. auions and catious are oL principal importance for the chemistry of this studs.," Carbon-chain species, hydrocarbons, cyanopolyynes and their associated anions and cations are of principal importance for the chemistry of this study." +"The following species are amoue those included in the chemical model: carbon chains C, (0= 1—23). C,ul (0=1— 23). C, (n—3 23): οS (1= 1-3): HC»,1S fv=1-: η. hydrocarbons C,H' Gn=2— 23). CH, (n=1 23). C, Ha fy=1— I). C,H, C.H (n=1— 23). C,,Hy fn=1— 3). vanopolyynes(n= 1-9) Cos (η= 2—9): and ¢ Ca, 1N! fey= 1-11). HC», 4N (n=1— 12).","The following species are among those included in the chemical model: carbon chains $_n$ $n=1-23$ ), $_n^+$ $n=1-23$ ), $_n^-$ $n=3-23$ ); $_{2n-1}^{(+)}$S $n=1-3$ ); $_{2n-1}$S $n=1-3$ ); hydrocarbons $_n$$^{(+/-)}$ $n=2-23$ ), $_n$ $_2^{(+)}$ $n=1-23$ ), $_n$ $_3$ $n=1-4$ ), $_n$ $_3^{+}$ $n=1-23$ ), $_n$ $_4$ $n=1-3$ ), $_n$ $_4^{+}$ $n=1-9$ ), $_n$ $_5^{+}$ $n=2-9$ ); and cyanopolyynes $_{2n-1}$ $^{(+/-)}$ $n=1-11$ ), $_{2n-1}$ N $n=1-12$ )," +Laboratory (USA). Rutherforc Appleton Laboratory (Ulx). and the Universities of Florence (Italv) and Cambridge (Ulx).,"Laboratory (USA), Rutherford Appleton Laboratory (UK), and the Universities of Florence (Italy) and Cambridge (UK)." +The highly filamentary morphology. of molecular clouds (AICS) and their observed non-thermal line-wicths »oint to MC's being highly dynamical objects.,The highly filamentary morphology of molecular clouds (MCs) and their observed non-thermal line-widths point to MCs being highly dynamical objects. + Observational evidence suggests that star formation in local MC's such as ‘Taurus is rapid once molecular gas is available. anc that he parental clouds are short-lived (???).," Observational evidence suggests that star formation in local MCs such as Taurus is rapid once molecular gas is available, and that the parental clouds are short-lived ." +. Phe dynamical. or turbulent. nature of ALC's is assumed to play a crucial role in the process of star formation via turbulent fragmentation 7?7.. lor a summary of the effects. and interpretation of turbulence inMC's).," The dynamical, or turbulent, nature of MCs is assumed to play a crucial role in the process of star formation via turbulent fragmentation , for a summary of the effects and interpretation of turbulence in." + Because of the rapid onset of star formation. the cloud.formelion process needs to. provide the MC with he observed. turbulence. anc substructure.," Because of the rapid onset of star formation, the cloud process needs to provide the MC with the observed turbulence and substructure." + Moreover. elobal geometry ancl gravity considerations mandate hat this substructure be non-linear. (7)... ie. a physical oocess is needed that can imprint non-linear density verturbations in the proto-clouclformation.," Moreover, global geometry and gravity considerations mandate that this substructure be non-linear , i.e. a physical process is needed that can imprint non-linear density perturbations in the proto-cloud." + These requirements have lec to the scenario of [ow-driven cloud. formation. where molecular clouds are assembled w large-scale) converging Lows of atomic hydrogen corresponding to the warm neutral medium.," These requirements have led to the scenario of flow-driven cloud formation, where molecular clouds are assembled by large-scale converging flows of atomic hydrogen corresponding to the warm neutral medium ." + The rapid fragmentation is driven bv a combination of strong thermal and cyvnamical instabilities. dominated: by the thermal instability for a cüscussion oftimescales).," The rapid fragmentation is driven by a combination of strong thermal and dynamical instabilities, dominated by the thermal instability for a discussion of." + Large-scale gas Lows are ubiquitous in the Galaxy., Large-scale gas flows are ubiquitous in the Galaxy. + They might be driven locally by supernova explosions or elobally by shear motions in the Galactic disk. by global," They might be driven locally by supernova explosions or globally by shear motions in the Galactic disk, by global" +predictions of this much simpler approach with results [ron the Halo Mocel.,predictions of this much simpler approach with results from the Halo Model. + The paper is organized as follows., The paper is organized as follows. + In the next section. we outline the methodology for the fitting function method.," In the next section, we outline the methodology for the fitting function method." + Following that in Section 3.. the models are compared. to recent data ancl the best-fitting values of the free parameters are extracted and. compared.," Following that in Section \ref{SECpoint2}, the models are compared to recent data and the best-fitting values of the free parameters are extracted and compared." + In Section 4... we conclude with a summary.," In Section \ref{SECcon}, we conclude with a summary." + A model for the angular correlation function. of galaxies basically involves ai model for the. thiree-cümensional clustering of galaxies as a function of epoch (i.e. redshift 2) combined with a machinery (derived from a model of the background cosmology) for projecting this information down the observer's light conc., A model for the angular correlation function of galaxies basically involves a model for the three-dimensional clustering of galaxies as a function of epoch (i.e. redshift $z$ ) combined with a machinery (derived from a model of the background cosmology) for projecting this information down the observer's light cone. + The observed. angularὃν correlation function. i(6). is calculated from the spatial power spectrum. Az(A.z). using: where A2) is the normalized. distribution of galaxies over redshift. G2)=ποt+where (z) ids the comoving distance to redshift z. the separation η0.2)=VIb.)02 Apello and £(rc) ds the two-point (ealaxv-galaxy) correlation function where. The galaxy power spectrum can be approximated using different methods such as those described below.," The observed angular correlation function, $\omega_\textsuperscript{obs} (\theta)$, is calculated from the spatial power spectrum, $\Delta^2_{\rm g}(k,z)$, using: where $\mathcal{N}(z)$ is the normalized distribution of galaxies over redshift, $G(z) = (dx/dz)^{-1}$where $x(z)$ is the comoving distance to redshift $z$, the separation $r(u,\theta,z) = \sqrt{u^2 + x^2(z)\theta^2}$ $h^{-1}$, and $\xi(r,z)$ is the two-point (galaxy-galaxy) correlation function where, The galaxy power spectrum can be approximated using different methods such as those described below." + The Halo Model estimate for the galaxy power spectrum represents Ht as arising from two distinct components: The first term represents contributions from. galaxies residing within the same dark matter halo. while the second is generated by contributions from galaxies in separate halos.," The Halo Model estimate for the galaxy power spectrum represents it as arising from two distinct components: The first term represents contributions from galaxies residing within the same dark matter halo, while the second is generated by contributions from galaxies in separate halos." + Phe one-halo term models. small-scale highly. non-linear clustering using a recipe that involves a number of dilferent. components. including the dark matter profile of the halos. the mass function. of halos. and the halo occupation distribution (LOD): the two-halo term depends on the underlving matter power-spectrum as well as the bias of galaxy clustering relative to mass clustering.," The one-halo term models small-scale highly non-linear clustering using a recipe that involves a number of different components, including the dark matter profile of the halos, the mass function of halos, and the halo occupation distribution (HOD); the two-halo term depends on the underlying matter power-spectrum as well as the bias of galaxy clustering relative to mass clustering." + In this paper the dark matter halo density. profile is approximated using the NEW. profile suggested. by Navarro.Erenk.&White (1997)., In this paper the dark matter halo density profile is approximated using the NFW profile suggested by \cite{Navarro1997}. +. The mass function is elfectivelv the number densitv of halos at a given mass and for this we use the approximation found by Sheth& Tormen.(1999)., The mass function is effectively the number density of halos at a given mass and for this we use the approximation found by \cite{Sheth1999}. +.. The Lalo Occupation. Distribution (IIOD) is a simple way of relating the clistribution of galaxies from the dark matter distribution. bv estimating how many galaxies are expected within a dark matter halo of given mass.," The Halo Occupation Distribution (HOD) is a simple way of relating the distribution of galaxies from the dark matter distribution, by estimating how many galaxies are expected within a dark matter halo of given mass." + This is split into two estimates - the number of central galaxies (which would either be 1 or 0) and the number of satellite galaxies: a summary of the procedure can be found in Ross(2009)., This is split into two estimates - the number of central galaxies (which would either be 1 or 0) and the number of satellite galaxies; a summary of the procedure can be found in \cite{Ross2009}. +. Phere are extensions to the model (c.g. Cil-Marín.Jimenez.&Verde2010)) but we just consider the basic version here., There are extensions to the model (e.g. \citealt{Gil-Marin2010}) ) but we just consider the basic version here. + Cooray&Sheth(2002)— provide a. detailed review of the Halo Model. so we will not &o into any further cetails.," \cite{Cooray2002} provide a detailed review of the Halo Model, so we will not go into any further details." + The linear matter power spectrumcan be calculated as: where the transfer function. ἆμι). and the growing mode of linear perturbations. Z2.(2). can be approximated as described by Eisenstein&Llu(1999).," The linear matter power spectrumcan be calculated as: where the transfer function, $T(k_\textsuperscript{lin})$, and the growing mode of linear perturbations, $D_{+}(z)$ , can be approximated as described by \cite{Eisenstein1999}." +. The non-linear power spectrum. (Aup) is known [or extreme values of the wavenumber & (ie. at small &. Af. and at large f. AS)ονAK). the latter derived using the so-called stable clusteringensalz.," The non-linear power spectrum $\Delta_\textsuperscript{nl}^2$ ) is known for extreme values of the wavenumber $k$ (i.e. at small $k$, $\Delta_\textsuperscript{nl}^2 \simeq \Delta_\textsuperscript{lin}^2$ , and at large $k$, $\Delta_\textsuperscript{nl}^2 \sim \Delta_\textsuperscript{lin}^3$ ), the latter derived using the so-called stable clustering." +. In the light of these two asymptotic regimes a fitting. function. was. proposed to extrapolate AS)1L. at all other & directly. [rom the linear counterpart: where Aw=Ana|ASQ.," In the light of these two asymptotic regimes a fitting function was proposed to extrapolate $\Delta_\textsuperscript{nl}^2$ at all other $k$ directly from the linear counterpart: where $k_\textsuperscript{nl} = k_\textsuperscript{lin} [1 + \Delta_\textsuperscript{nl}^2(k_\textsuperscript{nl},z) ]^{\frac{1}{3}}$." +SES Peacock&Docles found a fit ford this for low density Universes with cold dark matter and a cosmological constant: A This method can be used. to approximate the non-linear. dark matter power spectrum. (Np).," \cite{Peacock1996} found a fit for this for low density Universes with cold dark matter and a cosmological constant: where, This method can be used to approximate the non-linear dark matter power spectrum $\Delta_{\rm DM}^2$ )." + Under. very general conditions. proved. by Coles(1993). this can used to approximate the non-linear galaxy power spectrum. Az. via à simple linear relationship of the form: We use an approximation for the bias proposed by AMoscardinictal. C1998).. which is based on work by Alo& whosuggested the following relation between the bias and mass density [Luctuations:," Under very general conditions, proved by \cite{Coles1993}, this can used to approximate the non-linear galaxy power spectrum, $\Delta_{\rm g}^2$ , via a simple linear relationship of the form: We use an approximation for the bias proposed by \cite{Moscardini1998}, , which is based on work by \cite{Mo1996} whosuggested the following relation between the bias and mass density fluctuations:" +"Figure 16,, which shows the angular momentum enclosed within r=O.6r,; for model RRAN.","Figure \ref{f:angmom_encl_rand}, which shows the angular momentum enclosed within $r = 0.6\rs0$ for model RAN." + The angular momentum is related to the growth of spiral modes amplification(compare with directlyFigure ??))., The angular momentum amplification is directly related to the growth of spiral modes (compare with Figure \ref{f:PE}) ). +" By the time integration stops, is still growing, so L, may increase even more in magnitude."," By the time integration stops, $Y_1^1$ is still growing, so $L_y$ may increase even more in magnitude." +Y] The fact that the spin-up along the z-axis is (in contrast to models HHR and LLI11P2c) positiveis a consequence of the random LLI1.initial relative phase between the corresponding sloshing modes., The fact that the spin-up along the z-axis is positive (in contrast to models HR and L11P2c) is a consequence of the random initial relative phase between the corresponding sloshing modes. + The spherical symmetry of the problem implies that changing the sign of in equation (12)) leads to angular momentum redistribution with the opposite sign., The spherical symmetry of the problem implies that changing the sign of $\Phi$ in equation \ref{eq:trigger_eqn}) ) leads to angular momentum redistribution with the opposite sign. +" The order-of-magnitude of the maximum angular momentum redistribution, Mr, can be understood if at saturation, the azimuthal velocity vg is close to the upstream velocity νι."," The order-of-magnitude of the maximum angular momentum redistribution, $\dot{M}\rs0^2$, can be understood if at saturation, the azimuthal velocity $v_\phi$ is close to the upstream velocity $v_1$." +" From linear theory (A.1)), this follows for shock displacements of order unity, which is indeed the case for /=1 modes."," From linear theory \ref{s:background}) ), this follows for shock displacements of order unity, which is indeed the case for $\ell=1$ modes." +" Not so straightforward to explain is the size of the fluctuations in the saturated state, which involves interference between modesfully with different amplitudes and phases."," Not so straightforward to explain is the size of the fluctuations in the fully saturated state, which involves interference between modes with different amplitudes and phases." +" The basic behavior of the spin-up during the exponential growth phase agrees with what was seen by ? (their Figure 7), although they did not quantify their results in terms of fundamental physical quantities."," The basic behavior of the spin-up during the exponential growth phase agrees with what was seen by \citet{blondin07b} (their Figure 7), although they did not quantify their results in terms of fundamental physical quantities." + Our results agree to within a factor of a few with those of ?.., Our results agree to within a factor of a few with those of \citet{blondin07a}. +" They report typical spin-ups of 2.5x1077 at 250 ms (72tgo for M=1.2Me and reo=230/1.5153 km, where 1.5 is our approximate average shock radius in units of rg and 230 km their quoted shock position)."," They report typical spin-ups of $2.5\times 10^{47}$ at 250 ms $\tff0$ for $M=1.2M_\sun$ and $\rs0 = 230/1.5 = 153$ km, where 1.5 is our approximate average shock radius in units of $\rs0$ and $230$ km their quoted shock position)." +" At similar times, we find 0.6Mr,j?~10""km? g cm? sl."," At similar times, we find $0.6\dot{M}\rs0^2 \simeq 10^{47}(\dot{M}/0.36\,M_\sun~{\rm s}^{-1})(\rs0/153~{\rm km})^2$ g $^2$ $^{-1}$." +" The differences could(M/0.36Mc be causeds)(9/153 by several factors: (1) their absorbing boundary condition with no cooling, which causes the shock to expand with time (e.g., ?)), and (ii) resolution, which we have already shown to affect the long term behavior of the system."," The differences could be caused by several factors: (i) their absorbing boundary condition with no cooling, which causes the shock to expand with time (e.g., \citealt{BM03}) ), and (ii) resolution, which we have already shown to affect the long term behavior of the system." +" Assuming that all of the angular momentum enclosed within the radius where /,(r) changes sign is accreted onto the neutron star, and that the latter has a moment of inertia Ius=ysx109 g cm?, one can write the minimum period due to spiral modes as where famp is the fraction of Mr? achieved during the phase of exponential growth."," Assuming that all of the angular momentum enclosed within the radius where $l_z(r)$ changes sign is accreted onto the neutron star, and that the latter has a moment of inertia $I_{\rm NS} = I_{45}\times 10^{45}$ g $^2$, one can write the minimum period due to spiral modes as where $f_{\rm amp}$ is the fraction of $\dot{M}\rs0^2$ achieved during the phase of exponential growth." +" If no exponentially growing spiral mode takes place, one can still expect to achieve fampS0.1 from stochastic fluctuations, in which case the spin period P2,500 ms."," If no exponentially growing spiral mode takes place, one can still expect to achieve $f_{\rm amp}\lesssim 0.1$ from stochastic fluctuations, in which case the spin period $P\gtrsim 500$ ms." +" Figure 17 shows the evolution of the spin period for a few representative modes, taking into account the three components of the angular momentum, ΡΞ2π]νς/α[L2UD, with the L; measured at the radius at which/,(r) changes sign."," Figure \ref{f:periods_combined} shows the evolution of the spin period for a few representative modes, taking into account the three components of the angular momentum, $P = 2\pi I_{\rm NS} / \sqrt{L_x^2+L_y^2+L_z^2}$, with the $L_i$ measured at the radius at which$l_z(r)$ changes sign." + This simplistic picture is bound to change when more realistic physics is included., This simplistic picture is bound to change when more realistic physics is included. +" First, because it is not clear yet that spiral modes can easily develop in a convective gain region (e.g., ?)), but also because both the neutrinosphere radius, the mass accretion rate, and the shock radius change as a function of time."," First, because it is not clear yet that spiral modes can easily develop in a convective gain region (e.g., \citealt{iwakami08}) ), but also because both the neutrinosphere radius, the mass accretion rate, and the shock radius change as a function of time." +" The onset of explosion further the as the mass accretion is cut off and the complicatespostshock flow picture,expands."," The onset of explosion further complicates the picture, as the mass accretion is cut off and the postshock flow expands." +" Still, anisotropic cold and fast downflows piercing the convective region are expected to impart stochastic torques to the forming neutron star (?),, an"," Still, anisotropic cold and fast downflows piercing the convective region are expected to impart stochastic torques to the forming neutron star \citep{thompson00}, , an" +wimarilv due to spiral shocks or cloud coagulations (?)..,primarily due to spiral shocks or cloud coagulations \citep{Dobbsetal2006}. + La such cases. self-gravity need not. play an important role in he formation process and clouds can be formed. without »ing gravitationallv bound.," In such cases, self-gravity need not play an important role in the formation process and clouds can be formed without being gravitationally bound." +" Cloud formation from external collisions or compression implies an increasing contribution {ο the cloud's eravitational potential,", Cloud formation from external collisions or compression implies an increasing contribution to the cloud's gravitational potential. + During formation. the cloud evolves from a state where self-gravitv is unimportant to one where self-eravity has a significant effect on the clouds dynamics.," During formation, the cloud evolves from a state where self-gravity is unimportant to one where self-gravity has a significant effect on the cloud's dynamics." + Once the gravitational energy is within a [actor of a few of the kinetic energy. then star formation proceeds in local regions that become bound due to the clouds internal cdvnamics (2)).," Once the gravitational energy is within a factor of a few of the kinetic energy, then star formation proceeds in local regions that become bound due to the cloud's internal dynamics \citealt*{ClaBonKle2008}) )." + Phis local star formation will occur as parts of the cloud. are still being assembled as the local timescale is much shorter than the overall dynamical time [or the cloud or its precursor., This local star formation will occur as parts of the cloud are still being assembled as the local timescale is much shorter than the overall dynamical time for the cloud or its precursor. + Star formation would then proceed. until either. the local gas reservoir is depleted. or until the gas reservolr is removed. by the cllects of feedback. [rom voung stars.," Star formation would then proceed until either the local gas reservoir is depleted, or until the gas reservoir is removed by the effects of feedback from young stars." + The tidal shear from leaving the spiral armi potential could also limit the lifetime of the elouds (2).., The tidal shear from leaving the spiral arm potential could also limit the lifetime of the clouds \citep{Dobbsetal2006}. + Phe majority of the cloud need never become gravitationally bound before the cloud is dispersed resulting in inellicient star formation process that is still occurring on a fast civnamical timescale., The majority of the cloud need never become gravitationally bound before the cloud is dispersed resulting in inefficient star formation process that is still occurring on a fast dynamical timescale. + Star formation in realistic GAICS will proceed. from. a varietv of physical conditions. spanning regions that are eravitationally bound to parts or whole clouds which are eravitationally unbound.," Star formation in realistic GMCs will proceed from a variety of physical conditions, spanning regions that are gravitationally bound to parts or whole clouds which are gravitationally unbound." + Star formation will occur as long as the local conditions are. close to being eravitationally bound but the properties of the voung stellar population can depend strongly on these conditions., Star formation will occur as long as the local conditions are close to being gravitationally bound but the properties of the young stellar population can depend strongly on these conditions. + Regions that are bound produce bound stellar clusters and a stellar population that follows the full initial mass function from brown cdwarfs to high-niass stars., Regions that are bound produce bound stellar clusters and a stellar population that follows the full initial mass function from brown dwarfs to high-mass stars. + ltegions that are unbound are likely to produce a somewhat skewed EME biased towards the local Jeans mass in the gas and with significant lack of lower-mass stars. such as is seen in Taurus (?)..," Regions that are unbound are likely to produce a somewhat skewed IMF biased towards the local Jeans mass in the gas and with significant lack of lower-mass stars, such as is seen in Taurus \citep{Luhman2004b}." + The star formation cllicicney is also a product. of the local physical conditions with bound regions resulting in a relatively high star. formation. cllicieney of order 10. or more per free-[all time., The star formation efficiency is also a product of the local physical conditions with bound regions resulting in a relatively high star formation efficiency of order 10 or more per free-fall time. + Regions that are unbound can have drastically reduced efficiencies of order 1% or less por free-fall time., Regions that are unbound can have drastically reduced efficiencies of order 1 or less per free-fall time. + Thus clustered star formation should occur in regions of higher local star formation elliciencies that more distributed populations., Thus clustered star formation should occur in regions of higher local star formation efficiencies that more distributed populations. + Estimates of low star formation efIiiciencies are equally consistent with fast cvnamical star. formation as slow quasistatic star formation provided that one relaxes the condition that GAIC's are globally bound long-lived entities., Estimates of low star formation effiiciencies are equally consistent with fast dynamical star formation as slow quasistatic star formation provided that one relaxes the condition that GMCs are globally bound long-lived entities. + Including the pre-star formation timeperiods where clouds are being assembled. global estimates of depletion timescales or star formation rates per free-fall time will appear to be low even while local regions are undergoing Last star formation at high elliciencies.," Including the pre-star formation timeperiods where clouds are being assembled, global estimates of depletion timescales or star formation rates per free-fall time will appear to be low even while local regions are undergoing fast star formation at high efficiencies." + Finally. realistic GAIC'S are likely to be constructed fron a mix of physical conditions such that a fraction of the cloud is bound. producing stellar clusters at high elliciencies whereas the majority of the cloud is unbound: producing a more distributed population at. low star. formation elliciencies before. the cloud. is unbound by. feedback. or alternativo process.," Finally, realistic GMCs are likely to be constructed from a mix of physical conditions such that a fraction of the cloud is bound producing stellar clusters at high efficiencies whereas the majority of the cloud is unbound producing a more distributed population at low star formation efficiencies before the cloud is unbound by feedback or alternative process." + Such a scenario is consistent. with a model where GMCS are not formed due to their sell-gravity but rather to an external process such as spiral shocks (??)..," Such a scenario is consistent with a model where GMCs are not formed due to their self-gravity but rather to an external process such as spiral shocks \citep{Dobbsetal2006, Dobbs2008}." +-].0cm Stellar isochrones are commonly used to predict or interpret the properties of. distant. stellar. systems.,-1.0cm Stellar isochrones are commonly used to predict or interpret the properties of distant stellar systems. + Pwo popular uses are to derive ages ancl metallicities of resolved. stellar populations (such as open and globular clusters) ancl to determine the evolutionary state anc ages of unresolved systems using the integrated. light anc svnthetic stellar population models (see e.g. Stetson. VandenDerg Bolte 1996: Sarajedini. Chabover Demarque L997: Jimenez. Ενας Ixotoneva 1998: Carraro. Girardi Chiosi 1999: Chabover. Green Liebert 1999: Liu Chabover 2000: Jimenez 1999).," Two popular uses are to derive ages and metallicities of resolved stellar populations (such as open and globular clusters) and to determine the evolutionary state and ages of unresolved systems using the integrated light and synthetic stellar population models (see e.g. Stetson, VandenBerg Bolte 1996; Sarajedini, Chaboyer Demarque 1997; Jimenez, Flynn Kotoneva 1998; Carraro, Girardi Chiosi 1999; Chaboyer, Green Liebert 1999; Liu Chaboyer 2000; Jimenez 1999)." + Phe agreement. between stellar theoretical models and the Sun is outstanding (e.g Baheall ct al 2001). but. comparisons of models to cata for other metallicities anc masses. is still an arduous task.," The agreement between stellar theoretical models and the Sun is outstanding (e.g Bahcall et al 2001), but comparisons of models to data for other metallicities and masses is still an arduous task." + Comparisons of this type have been restricted in the past to open ancl globular clusters (e.g. Westera et al 9005. Cassisi et al 2000," Comparisons of this type have been restricted in the past to open and globular clusters (e.g. Westera et al 2002, Cassisi et al 2000), but in both cases distances and luminosities are a source of considerable uncertainty." +," Nevertheless, good agreement has been found between isochrones and data from globular clusters, i.e. isochrones at low metallicity are good." +, Much more difficult to check is the accuracy of metal rich isochrones ([Fe/H] $ \ga -1$ ). +," Our aim in this paper is to make such a comparison for stars on the lower main sequence (K dwarfs), using the accurate distances (and thus luminosities) provided by the ESA Hipparcos mission." +).," The width of the lower main sequence has long been held to be a consequence of the metallicities of the stars (for a review see e.g. Reid, 1999)." + but in bot," However, this has been difficult to test without having precise parallaxes and metallicities and furthermore the ability to remove multiple stars." +h cases , The Hipparcos catalogue makes this possible for the first time. +of WW cbwarfs of a given colour as a function of metallicity and compare these luminosities to isochrones from the literature.," In this paper we use Hipparcos parallaxes of a sample of 213 nearby K dwarfs (in the absolute magnitude range $5.5 < M_V < 7.3$, or broadly G8 to K3), for which photometric metallicities are available from Kotoneva and Flynn (2002), to calibrate the luminosity of K dwarfs of a given colour as a function of metallicity and compare these luminosities to isochrones from the literature." + The paper is organised as follows., The paper is organised as follows. + In section 2 we describe the sample., In section 2 we describe the sample. + ln section 3 we compare cillerent isochrone sets. from the literature to stars of similar metallicity in the sample., In section 3 we compare different isochrone sets from the literature to stars of similar metallicity in the sample. + Having found that no isochrone set is able to fit the whole range of metallicities in the data. we construct an empirical calibration of the main sequence luminosity with the metallicity in section 4.," Having found that no isochrone set is able to fit the whole range of metallicities in the data, we construct an empirical calibration of the main sequence luminosity with the metallicity in section 4." + Comparing with the original sample of spectroscopically anabysecl Ix. cdwarts. the relation turns out to be surprisingly precise. ancl we discuss applications of this calibration in section 5.," Comparing with the original sample of spectroscopically analysed K dwarfs, the relation turns out to be surprisingly precise, and we discuss applications of this calibration in section 5." + We draw our conclusions in section 6., We draw our conclusions in section 6. + We have chosen all stars in the survey part of the Llipparcos output catalogue in the absolute magnitude AA range 5.5po. il is no longer possible to maintain INI since RixNS ,"When the particle density becomes large, $\rho_{\rm p} \gg \rho_{\rm +g}$, it is no longer possible to maintain KHI since $Ri \propto +\Sigma_{\rm p}^2$." +While the buovancy is relatively constant (as long as we can still ignore sell-gravitv). the shear actually decreases with added mass. διὃςx(Opy/0z)p?Xp. because the velocity. contrast is diminished as more of the material rotates al speeds closer to Ixeplerian.," While the buoyancy is relatively constant (as long as we can still ignore self-gravity), the shear actually decreases with added mass, $\partial v_\phi/\partial z \propto (\partial +\rho_{\rm p}/\partial z)\rho^{-2} \propto \Sigma_{\rm p}^{-1}$, because the velocity contrast is diminished as more of the material rotates at speeds closer to Keplerian." +" From this simplified analvsis one finds that the maxinium X, which can be supported by the III is: Xy,cVΠορω. in agreement with the detailed result except [or 1ο sell-gravitational correction faetor."," From this simplified analysis one finds that the maximum $\Sigma_{\rm p}$ which can be supported by the KHI is: $\Sigma_{\rm p,c} \sim \sqrt{Ri_{\rm c}} \eta r \rho_{\rm +g}$, in agreement with the detailed result except for the self-gravitational correction factor." + As already hinted upon. saturation does not lead to GI of the entire particle laver unless 1e gas disk is already sell-gravitating: Qj©O2Hu/(3GYX5)~Qe.," As already hinted upon, saturation does not lead to GI of the entire particle layer unless the gas disk is already self-gravitating: $Q_{\rm p} \approx \Omega^2 +H_{\rm p,c}/(\pi G\Sigma_{\rm p,c}) \sim Q_{\rm g}$." + Thus. only the unstirred —yarlicles in excess of X; should undergo GI initially.," Thus, only the unstirred particles in excess of $\Sigma_{\rm p,c}$ should undergo GI initially." + Sell-gravityv is important largely [or je (ο) factor., Self-gravity is important largely for the $s(\psi)$ factor. +" If we were to take i—0. which can be shown to be equivalent to setting g.=Oz> al the outset. then as a high. density. cusp develops. pj(0).Z9po. one finds. (ha Vpx In(p,(0))."," If we were to take $\psi \rightarrow 0$, which can be shown to be equivalent to setting $g_z = \Omega^2 z$ at the outset, then as a high density cusp develops, $\rho_{\rm p}(0) \gg \rho_{\rm g}$, one finds that $\Sigma_{\rm +p} \propto \ln(\rho_{\rm p}(0))$ ." + Thus. an infinite density cusp no longer corresponds to a finite X.," Thus, an infinite density cusp no longer corresponds to a finite $\Sigma_{\rm p,c}$." + Ignoring sell-gravitv entirely would have caused us to miss the saturation effect in Sekiva's detailed solutions., Ignoring self-gravity entirely would have caused us to miss the saturation effect in Sekiya's detailed solutions. + The fact that midplane shear can only stir a finite amount of solids is only relevant if the salvation point can be reached., The fact that midplane shear can only stir a finite amount of solids is only relevant if the saturation point can be reached. +" Let us compare X, to the surface density available ad cosmic abundances: where we use X,4ci2dp,re,/vy: and g~Lote,""yJe).9− "," Let us compare $\Sigma_{\rm p,c}$ to the surface density available at cosmic abundances: where we use $\Sigma_{\rm g} \simeq 2.4 \rho_{\rm g} r c_{\rm g} / +v_{\rm K}$ and $\eta \simeq 1.6 (c_{\rm g} / v_{\rm K})^2$." +Sabluration requires that the thinness of the particulate laver. {1 Πν~ονSiκc1/30. equalize the space densities (p) of particles and gas.," Saturation requires that the thinness of the particulate layer, $H_{\rm p}/H_{\rm g} \sim c_{\rm g}/v_{\rm K} \sim 1/30$, equalize the space densities $\rho$ ) of particles and gas." +" Our estimate indicates that saturation may be possible at cosmic abundances (ie. Xj,5\times10^{11} M_{\odot}$ $M_{stellar}>10^{10} M_{\odot}$ ) make up roughly $\sim60\%$ (RMS $=5\%$ ) of its GC system." + This percentage increases in. lower mass galaxies so bv AlancLOPAL. most GC. systems have ~90% metal-poor GCs., This percentage increases in lower mass galaxies so by $M_{stellar}\sim10^{9} M_{\odot}$ most GC systems have $\sim90\%$ metal-poor GCs. + However. the halo masses of these lower mass galaxies are poorly constrained. thus we currenthy cannot determine whether the metal-poor GCs show a closer relationship to its host halo.," However, the halo masses of these lower mass galaxies are poorly constrained, thus we currently cannot determine whether the metal-poor GCs show a closer relationship to its host halo." + We have presented evidence for a direct correlation between the total GC system mass and the host galaxy halo mass., We have presented evidence for a direct correlation between the total GC system mass and the host galaxy halo mass. + While this result appears to be robust for intermeciate-to-massive galaxies (and possibly galaxy clusters). the halo masses of low-mass galaxies are not well-constrained. anc thus the correlation at low galaxy masses must be confirme with better halo mass estimates.," While this result appears to be robust for intermediate-to-massive galaxies (and possibly galaxy clusters), the halo masses of low-mass galaxies are not well-constrained, and thus the correlation at low galaxy masses must be confirmed with better halo mass estimates." + The direct. correlation implies CC svstem masses can be used to directly measure the total halo mass of individual galaxies., The direct correlation implies GC system masses can be used to directly measure the total halo mass of individual galaxies. + This technique has the acvantage tha it can be applied irrespective. of the host. galaxy tvpe and environment., This technique has the advantage that it can be applied irrespective of the host galaxy type and environment. + Lt is relatively inexpensive in terms of observing time. requiring only wide-field. imaging under reasonable observing conditions (e.g. Spitler et al.," It is relatively inexpensive in terms of observing time, requiring only wide-field imaging under reasonable observing conditions (e.g. Spitler et al." + 2008)., 2008). + A few examples have been demonstrated here. to. help illustrate the promising astrophysical applications of this new technique., A few examples have been demonstrated here to help illustrate the promising astrophysical applications of this new technique. + We thank IW. Dekki. dx. Glazebrook. A. Graham. d. Mancdelbaum. J. Strader. and A. Romanowsky for reviewing a draft of the manuscript.," We thank K. Bekki, K. Glazebrook, A. Graham, R. Mandelbaum, J. Strader, and A. Romanowsky for reviewing a draft of the manuscript." + We are grateful for useful discussions with lt. Alancdelbaum and T. Alendel., We are grateful for useful discussions with R. Mandelbaum and T. Mendel. + We also thank A. Graham for use of his supermassive black hole catalogue., We also thank A. Graham for use of his supermassive black hole catalogue. + DAF acknowledges the ARC for financial support., DAF acknowledges the ARC for financial support. + The referee. D. Moore. provided. a number. of comments that enhanced the discussion.," The referee, B. Moore, provided a number of comments that enhanced the discussion." +"When the hot gas particles are in thermal equilibrium. P=X. and the pressure is given by: where By=(1keV)749,No and div=22/7keV).","When the hot gas particles are in thermal equilibrium, $\tilde{\Gamma}= +\tilde{\Lambda}$, and the pressure is given by: where $P_0=(1~{\rm keV})^{1/2}k \tilde{\Gamma_0}/ \tilde{\Lambda_0}$ and $T_{{\rm keV}}=T_e/(1~ \rm keV)$." + Fig. (, Fig. ( +2) shows the relation between 2 and 7; by using the mean metallicity within 20 pe (Munoetal.2004).,2) shows the relation between $P$ and $T_e$ by using the mean metallicity within 20 pc \citep{Muno}. +.. We notice that for some values of P there are (wo dillerent values of 1)., We notice that for some values of $P$ there are two different values of $T_e$. + By putting the heating and cooling rates into Eq. (, By putting the heating and cooling rates into Eq. ( +11). we get the criterion for stable solutions: where 3;=22;/A7).,"11), we get the criterion for stable solutions: where $\beta_i=2I_i/kT_i$." + We impose a [free parameter jr such that 7)=yl., We impose a free parameter $\mu$ such that $T_e= \mu T_i$. + We define 4 and B to be the expressions on the left and right hand. sides of the inequality in σαι (, We define $A$ and $B$ to be the expressions on the left and right hand sides of the inequality in Eq. ( +15) respectively.,15) respectively. + La Fig. , In Fig. ( +3). we plot A—D against 7; for two values of yr.,"3), we plot $A-B$ against $T_e$ for two values of $\mu$." + When p=3.2 and jp=6.9. OS keV. «T.κ 4 keV and L8 keV 0$." + We also indicate the unstable regions in Fig. (, We also indicate the unstable regions in Fig. ( +"3). and we notice that a two-temperature phase may exist. with 7,>S keV and 1;0.5. keV. for 3.2xp6.9.","3), and we notice that a two-temperature phase may exist with $T_e \ge 8$ keV and $T_e \le 0.8$ keV for $3.2 \le \mu \le +6.9$." + In Fig. (, In Fig. ( +2). we can see that if there are less large-Z metal ions (especially iron) in the hot gas. more hot eas particles will shift to the lower temperature phase and only one equilibrium solution may be obtained.,"2), we can see that if there are less $Z$ metal ions (especially iron) in the hot gas, more hot gas particles will shift to the lower temperature phase and only one equilibrium solution may be obtained." + Clearly. our model can account for the two-tempoerature structure of the hot gas near the Milky Way center.," Clearly, our model can account for the two-temperature structure of the hot gas near the Milky Way center." + To explain the origin of the hard component. Munoοἱ make use of magnetic reconnection driven by the turbulence that supernovae generate in the interstellar medium.," To explain the origin of the hard component, \citet{Muno} + make use of magnetic reconnection driven by the turbulence that supernovae generate in the interstellar medium." + Magnetic reconnection can heat the hot gas to KToDLnauaSiny.," Magnetic reconnection can heat the hot gas to $kT \sim B_{\rm center}^2/8 +\pi n_g$." + For ny~0.1 Uo Doa~0.2 mG. KT—S keV. However there is not enough. evidence to support whether this mechanism can maintain the high temperature of the hard component (Munoetal.2004).," For $n_g \sim 0.1$ $^{-3}$, $B_{\rm center} \sim 0.2$ mG, $kT +\sim +8$ keV. However there is not enough evidence to support whether this mechanism can maintain the high temperature of the hard component \citep{Muno}." +". In our model. we have assumed that there exists a sterile neutrino halo with m,=1618 keV in the Milky. Way center. which decay to emit ~ with life-time of cosmological order."," In our model, we have assumed that there exists a sterile neutrino halo with $m_s=16-18$ keV in the Milky Way center, which decay to emit $\gamma$ with life-time of cosmological order." + It provides a large amount of energy to the hot gas and maintains the extremely high temperature., It provides a large amount of energy to the hot gas and maintains the extremely high temperature. + The bound-free collisions provide. enough. energy to. the two cillerent temperature components ancl maintain their temperatures., The bound-free collisions provide enough energy to the two different temperature components and maintain their temperatures. + At the same time. a stable two-tempecrature structure in the hot gas can be explained by this heating mechanism naturally.," At the same time, a stable two-temperature structure in the hot gas can be explained by this heating mechanism naturally." + Phe uniform emission of the soft and hard components suggests that they may come from similar physical processes (Munoetal.2004)., The uniform emission of the soft and hard components suggests that they may come from similar physical processes \citep{Muno}. +. In our mocel. both components indeed. share the same source of energy - the 8-0 keV photons emitted by the decays of sterile neutrinos.," In our model, both components indeed share the same source of energy - the 8-9 keV photons emitted by the decays of sterile neutrinos." + In our model. the sterile neutrinos may not be the major component of dark matter.," In our model, the sterile neutrinos may not be the major component of dark matter." + Pherefore. any bounds on ma assuming thev are the major dark matter candidate does not constrain our model severely.," Therefore, any bounds on $m_s$ assuming they are the major dark matter candidate does not constrain our model severely." + The heating rate in the Milky. Way center is time dependent as there is a decreasing number of sterile neutrinos., The heating rate in the Milky Way center is time dependent as there is a decreasing number of sterile neutrinos. + Vherefore. if two galaxies have similar chemical compositions. the heaing rate Is greater ⋅ Heher laree redshifm one. which has more particles in the higher temperature component.," Therefore, if two galaxies have similar chemical compositions, the heating rate is greater for the large redshift one, which has more particles in the higher temperature component." + We therefore predict. that the hard component of the x-ravs would be stronger for large redshift ancl metal-rich galaxies., We therefore predict that the hard component of the x-rays would be stronger for large redshift and metal-rich galaxies. + Moreover. if a galaxy has lower metallicity. then only a single temperature component may be observed instead of two (see Fig. (," Moreover, if a galaxy has lower metallicity, then only a single temperature component may be observed instead of two (see Fig. (" +2)).,2)). + This work is partially supported. by a grant. from the Research Grant Council of the Ποιος Wong Special Administrative Region. China (Project No.," This work is partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No." + 400805)., 400805). +apertures composed. of a small number of pixels.,apertures composed of a small number of pixels. + For the larger apertures. there was no measurable dillerence in S/N when circular apertures were used. so for consistency. all photometric apertures used. were square.," For the larger apertures, there was no measurable difference in S/N when circular apertures were used, so for consistency, all photometric apertures used were square." + For each image the aperture is placed at the centroid of X-22. known to a fraction of a pixel.," For each image the aperture is placed at the centroid of 2, known to a fraction of a pixel." + The comparison star aperture ds. placed at the (fixed) mean. distance from tlo compensate for. aperture losses., The comparison star aperture is placed at the (fixed) mean distance from to compensate for aperture losses. + We checked that the PSPs of the two stars were similar and not allectec by instrumental cllects., We checked that the PSFs of the two stars were similar and not affected by instrumental effects. + Because every image includes both aand the nearby comparison star. observed simultaneously under. identical observing conditions. differential photometry allows the removal of temporal photometric throughput variations.," Because every image includes both and the nearby comparison star, observed simultaneously under identical observing conditions, differential photometry allows the removal of temporal photometric throughput variations." + We cdo not correct for extinction hence the broad band white light data can be subject to an airmassecorreLlated. variation due to the colour dillerence between aand the comparison star., We do not correct for extinction hence the broad band white light data can be subject to an airmass-correlated variation due to the colour difference between and the comparison star. + However. since all our observations were done at airmass «1.2. with two-thirds of the data taken at airmass < Ld. we feel this will have a negligible influence on the short timescale variability. study.," However, since all our observations were done at airmass $<$ 1.2, with two-thirds of the data taken at airmass $<$ 1.1, we feel this will have a negligible influence on the short timescale variability study." + We ignored images for which the centroiding algorithm rad failed. a cosmic ray had been tagged inside the aperture. or (more Commonly) those images in which the photometric aperture extended outside the unvignettecl slit edges.," We ignored images for which the centroiding algorithm had failed, a cosmic ray had been tagged inside the aperture, or (more commonly) those images in which the photometric aperture extended outside the unvignetted slit edges." + The ickeround in each window of each image was calculated as an average over the window. for pixels more than 10 Pixels (4 aresec) from the window center.," The background in each window of each image was calculated as an average over the window, for pixels more than 10 pixels (4 arcsec) from the window center." + We then computed he signal-to-noise ratio of the flux from N-22 as a 'unction of aperture., We then computed the signal-to-noise ratio of the flux from 2 as a function of aperture. + The maximum: S/N was obtained for an aperture of 7 pixels in white light and 3.3 pixels with he filter., The maximum S/N was obtained for an aperture of $\times$ 7 pixels in white light and $\times$ 3 pixels with the filter. + The comparison star data was extracted. using the same aperture and the [ux ratio computed to correct. for ost flux and. atmospheric variations., The comparison star data was extracted using the same aperture and the flux ratio computed to correct for lost flux and atmospheric variations. + Ehe final lighteurve is therefore the dillerential magnitude between X-22 and the comparison star., The final lightcurve is therefore the differential magnitude between 2 and the comparison star. + The S/N. chosen aperture. total number of measurements and number of measurements kept in each observation sequence can be found in Tab.," The S/N, chosen aperture, total number of measurements and number of measurements kept in each observation sequence can be found in Tab." + 1., 1. + The lighteurves. rebinnecl with 32 s resolution. are shown in Fig.," The lightcurves, rebinned with 32 s resolution, are shown in Fig." + l., 1. + Note that 32 s is an elapsed. time and that the actual exposure time and S/N in cach bin varies with the observational setup., Note that 32 s is an elapsed time and that the actual exposure time and S/N in each bin varies with the observational setup. + “Phe le error for each bin is obtained from the standard deviation of the averaged data points. hence implicitly assuming that the measurements are independent.," The $\sigma$ error for each bin is obtained from the standard deviation of the averaged data points, hence implicitly assuming that the measurements are independent." + Typical error values are given in column 4 of ‘Tab., Typical error values are given in column 4 of Tab. + 2., 2. + To characterise the overall behaviour of X-22 in X-rays. a colour-intensity diagram was plotted. using 32 s Lux averages (Fig.," To characterise the overall behaviour of 2 in X-rays, a colour-intensity diagram was plotted using 32 s flux averages (Fig." + 2)., 2). + This diagram suggests that X-22 was on the normal branch during visits 1 and 2 (Aue 2). on the llaring branch during visit 3 (Aug 2) and on the horizontal branch during the visits of Aug 3 and 4.," This diagram suggests that 2 was on the normal branch during visits 1 and 2 (Aug 2), on the flaring branch during visit 3 (Aug 2) and on the horizontal branch during the visits of Aug 3 and 4." + Power density spectra (PDS. see vanderας 1989)). were then constructed. for each visit using all the detected: photons.," Power density spectra (PDS, see \citealt{vdk}) ) were then constructed for each visit using all the detected photons." + The high frequeney (1 Hz128 Hz) part of the PDS is the average PDS of 1 s long segments with a binsize of 1/256 s. The low frequeney part (~101 1.5 Lz) is computed from. als rebinned lighteurve.," The high frequency (1 Hz–128 Hz) part of the PDS is the average PDS of 1 s long segments with a binsize of 1/256 s. The low frequency part $\sim +10^{-4}$ –0.5 Hz) is computed from a 1 s rebinned lightcurve." + Phe PDS are normalised to units of rms” 3. {fractional variance per unit frequency. and the expected Poisson measurement noise bias was subtracted.," The PDS are normalised to units of $^2$ $^{-1}$, fractional variance per unit frequency, and the expected Poisson measurement noise bias was subtracted." + No corrections were mace for background and PCA dead time. which are negligible.," No corrections were made for background and PCA dead time, which are negligible." + The resulting. PDS confirm that ο. moved through the dillerent. branches of the Z track during the observations., The resulting PDS confirm that 2 moved through the different branches of the Z track during the observations. + On Aug 2. the absence of detectable broad band variability at frequencies above Liz except for a weak QPO at GEL Hz during the second. visit. (1.32:0.2'4 D.ni.)," On Aug 2, the absence of detectable broad band variability at frequencies above 1 Hz except for a weak QPO at $\pm$ 1 Hz during the second visit $\pm0.2$ r.m.s.)" + is typical of the normal/flaring branch., is typical of the normal/flaring branch. + The Aug 34 PDS are tvpical of the horizontal branch with strong broad baud variability peaking around 10 Lz and two QPOs varving between 2434 Tle (3.140.2% to 4440.2% r.nis.), The Aug 3–4 PDS are typical of the horizontal branch with strong broad band variability peaking around 10 Hz and two QPOs varying between $\sim$ 24–34 Hz $\pm$ to $\pm$ r.m.s.) + and 5063 Le (2.2+0.3% to Ες rans)., and $\sim$ 50–63 Hz $\pm$ to $\pm$ r.m.s.). + In addition. low frequeney variability is present in all the observations at frequencies below 0.1 Lz.," In addition, low frequency variability is present in all the observations at frequencies below 0.1 Hz." + These results are in line with previous. more extensive X-ray timing studies of this source (c.g. Wijnandsetal.1997:Ixuulkers.&vanderIxlis1999:Wijnands&vancerIxIis 2001)).," These results are in line with previous, more extensive X-ray timing studies of this source (e.g. \citealt{wijnands,kuulkers,w2001}) )." + We show in Fig., We show in Fig. + 3 some of the logarithmically rebinned X-ray PDS obtained on different nights., 3 some of the logarithmically rebinned X-ray PDS obtained on different nights. + The 32 5 binned optical lightcurves (Fig., The 32 s binned optical lightcurves (Fig. + 1) show variations above the measurement noise on timescales of minutes to jours., 1) show variations above the measurement noise on timescales of minutes to hours. + Quantitativelv. the binned white light. (resp. Lle)," Quantitatively, the binned white light (resp. )" +) iehteurves have standard deviations of up to 0.04 mag (resp., lightcurves have standard deviations of up to 0.04 mag (resp. + 1.06) compared to the measurement noise of 0.003 mag (resp., 0.06) compared to the measurement noise of $\sim$ 0.003 mag (resp. + 0.017: see 822.2)., 0.017; see 2.2). + The values for cach observation are in Tab., The values for each observation are in Tab. + 2., 2. + Plotting the optical luxes against the simultaneous X-ray [luxes. we find no obvious correlations tween the two: but we note that the average white light ux was highest (ον about 0.15 mag. second. night). when 1ο X-ray count rate was also highest (close to the vertex of 16 horizontal branch).," Plotting the optical fluxes against the simultaneous X-ray fluxes, we find no obvious correlations between the two; but we note that the average white light flux was highest (by about 0.15 mag, second night), when the X-ray count rate was also highest (close to the vertex of the horizontal branch)." + PDS were constructed for the optical cata using a gaight modification to the standard. technique used for X-rav timing., PDS were constructed for the optical data using a slight modification to the standard technique used for X-ray timing. + For the optical data. we found the white noise level empirically instead of using Poisson statistics.," For the optical data, we found the white noise level empirically instead of using Poisson statistics." + The data were (fast) Fourier transformed: ancl normalised by, The data were (fast) Fourier transformed and normalised by +siddiqui.Stewart&Johnstone(1998).. who show that no excess absorption is required Lor either single-temperature models or cooling [low models without reheating. but that excess absorption can oceur in the center for a cooling flow model with a partial covering screen.,"\citet{ssj}, who show that no excess absorption is required for either single-temperature models or cooling flow models without reheating, but that excess absorption can occur in the center for a cooling flow model with a partial covering screen." + A somewhat different approach is taken by Allen&Fabian(1997) who use PSPC color maps along with a deprojection technique to fit cooling flows plus internal absorption to nearly all of their galaxy clusters.," A somewhat different approach is taken by \citet{af} + who use PSPC color maps along with a deprojection technique to fit cooling flows plus internal absorption to nearly all of their galaxy clusters." + They can achieve agreement with WFJALA when thev adopt a partial covering moclel lor (he absorption., They can achieve agreement with WFJMA when they adopt a partial covering model for the absorption. + The evidence suggests to us that excess absorption can be accommodated but is not requirecl for successful spectral fits of clusters along lines of sight where the Galactic Vip<5x1077., The evidence suggests to us that excess absorption can be accommodated but is not required for successful spectral fits of clusters along lines of sight where the Galactic $\NHIo \lesssim 5\tenup{20}$. + The situation is different along sight lines with higher Galactic column densities. where excess columns are reported even [or isothermal fits to the data.," The situation is different along sight lines with higher Galactic column densities, where excess columns are reported even for isothermal fits to the data." + Irwin&Sarazin(1995) observed 240335--096. which has a Galactic Vay=1.7x1075 aand found an excess of 0.6—1.2.xL074?.. depending upon the type of fit.," \citet{is} observed 2A0335+096, which has a Galactic $\NHIo = 1.7\tenup{21}$ and found an excess of $0.6-1.2\tenup{21}$, depending upon the type of fit." + A similar result is found by Allenetal.(1993).. who observed Abell 478 and found an excess of 0.7—1.7x107! ccompared to the Galactie Nyy=14xL107!7..," A similar result is found by \citet{afjwdes}, who observed Abell 478 and found an excess of $0.7-1.7\tenup{21}$ compared to the Galactic $\NHIo = 1.4\tenup{21}$." + An important aspect of these studies is that (he excess absorption occurs both inside and outside of the cooling flow core., An important aspect of these studies is that the excess absorption occurs both inside and outside of the cooling flow core. + Of direct relevance to this discussion is our recent study where we used the non-central regions of bright clusters to measure absorption columns for comparison with Galactic Nyy) and Nyy data CArabadjis&Bregman(1999a).. hereafter AB).," Of direct relevance to this discussion is our recent study where we used the non-central regions of bright clusters to measure absorption columns for comparison with Galactic $\NHIo$ and $\NHII$ data \citet{ab_a}, hereafter AB)." + The motivation was that the bright isothermal parts of galaxv clusters. were ideal background light sources with particularly simple spectra. so absorption columns could be determined to high accuracy.," The motivation was that the bright isothermal parts of galaxy clusters were ideal background light sources with particularly simple spectra, so absorption columns could be determined to high accuracy." + We found that for X-ray absorption columns <5x1077.. the only absorption necessary was due to Galactic Ay).," We found that for X-ray absorption columns $< 5\tenup{20}$, the only absorption necessary was due to Galactic $\NHIo$." + However. for (he seven clusters with higher Galactic cohunn densities. excess absorption was detected in every case and we attribute (his excess to ii (he Galaxy. a result that is consistent wilh Copernicus sstdies (Savageetal.LO77).," However, for the seven clusters with higher Galactic column densities, excess absorption was detected in every case and we attribute this excess to in the Galaxy, a result that is consistent with Copernicus studies \citep{sbdb}." +. As part of our investigation. we developed software to incorporate ihe most recent values of the Ile absorption cross section. (ο which the results are are somewhat sensitive.," As part of our investigation, we developed software to incorporate the most recent values of the He absorption cross section, to which the results are are somewhat sensitive." + Ilere we extend (he techniques that we developed to study the centers ol these 20 bright clusters with the goal of determining whether excess absorption is required. and whether it is statistically different than the absorption seen in the non-central parts of galaxy clusters.," Here we extend the techniques that we developed to study the centers of these 20 bright clusters with the goal of determining whether excess absorption is required, and whether it is statistically different than the absorption seen in the non-central parts of galaxy clusters." + For this investigation we use the cluster sample studied in AD (Table 1))., For this investigation we use the cluster sample studied in AB (Table \ref{tab:sample}) ). + These clusters, These clusters +We can now express (he colour (23—V) as a function of the absolute visual magnitude Af and the following formula for (he mass of the star is obtained where WV is the Lambert W-funetion. after Lambert(1758).,"We can now express the colour $(B-V)$ as a function of the absolute visual magnitude $M_{V}$ and the following formula for the mass of the star is obtained where $W$ is the Lambert W-function, after \cite{Lambert_1758}." +".. A test of the previous ↓∪↕⋅∐∐∏≀↧↴≺∢≀↧↴∐∣↽≻≼↲≼⇂∪∐≼↲≀↧↴↥⊔∐↲↥∖∖⇁∪∣↽≻∪∏↕∐⇂≀↕↴↕⋅↕≼↲⋟∖⇁∶∖∖⇁↥∐↲∐⇀∪∖⇁∶−∩⋅↱≻⋖↽∖⋟∣⋅↥∪≸↽↔↴↓∣∣ ⋅ MV=1.63"" against− the calibrated⋅ value log,ENV=16. andwhen M. —11.8. logy,ο.VM=—0.56. against≓⋅ the calibrated value log,is=—0.66. see Table 3.1 in Bowers&Deemine(1984)."," A test of the previous formula can be done at the two boundaries: when $M_V$ =-0.58 , $ \log_{10} \frac {{\mathcal M_S}}{{\mathcal +M}_{\sun}}=1.63$ against the calibrated value $\log_{10} \frac +{{\mathcal M_S}}{{\mathcal M}_{\sun}}=1.6$ andwhen $M_V$ =11.8, $ \log_{10} \frac {{\mathcal M_S}}{{\mathcal M}_{\sun}}=-0.56$ against the calibrated value $\log_{10} \frac {{\mathcal +M_S}}{{\mathcal M}_{\sun}}=-0.66$, see Table 3.1 in \cite{deeming}." +. The mass of a galaxy can be evaluated once the mass luninosity ratio . 2 is given some values of /? are now reported: /2<20 by Ixiang(1961) and Persic&Salucei R=20 by Padmanabhan(1996). 2=5.93 by vanderMarel(1991).," The mass of a galaxy can be evaluated once the mass luminosity ratio , $R$ is given Some values of $R$ are now reported: $ R \leq 20$ by \cite{kiang1961} and \cite{Persic_1992} , $R =20$ by \cite{pad} , $R =5.93 $ by \cite{vandermarel1991}." +. Further on deJongiς (2001).. demonstrated. (amongst others)4 that atV varies. as a function. oftl galaxy colour. and therefore. (wpe.," Further on \cite{Bell2001}, demonstrated (amongst others) that $\frac{\mathcal{M}}{L} $ varies as a function of galaxy colour, and therefore, type." +" If the bright end of the luminosity fancton is dominated by massive.. evolved. red galaxies.. and the faintD. end by low mass. blue galaxies.. then XVxL; (GIANTS II) at the bright end and MxL"" (MAIN SEQUENCE V) at the faint end. see coelficients of Table 1 in Zaninetti(2005)."," If the bright end of the luminosity function is dominated by massive, evolved, red galaxies, and the faint end by low mass, blue galaxies, then $\frac{\mathcal{M}}{L}\propto L^{-0.64}$ (GIANTS III) at the bright end and $\frac{\mathcal{M}}{L}\propto L^{-0.7}$ (MAIN SEQUENCE V) at the faint end, see coefficients of Table 1 in \cite{zaninetti05}." +. Then x will almost certainly not be constant due to different prevailing populations of stars at the boundaries of the Iuminosity function., Then $\frac{\mathcal{M}}{L} $ will almost certainly not be constant due to different prevailing populations of stars at the boundaries of the luminosity function. + The scatter in the models by Bell&deJong(2001) is a starting point when evaluating the validity of assuming a constant at , The scatter in the models by \cite{Bell2001} is a starting point when evaluating the validity of assuming a constant $\frac{\mathcal{M}}{L} $. +Generally. near-intrared M ratios are more constant than optical passband. but still vary. with Iuminositv.," Generally, near-infrared $\frac{\mathcal{M}}{L} $ ratios are more constant than optical passband, but still vary with luminosity." + In our framework. we made J à function of the passhand. in order (ο have (he same results for the masses of the galaxies once the absolute magnitude is given. seeFigure 15..," In our framework, we made $R$ a function of the passband, in order to have the same results for the masses of the galaxies once the absolute magnitude is given, seeFigure \ref{masse}. ." + In ow framework 2 can be expressed as On inserting formula (14)) and formula (20)) in Che previousratio the folowing formula [or M* is found, In our framework $R$ can be expressed as On inserting formula \ref{massamedia}) ) and formula \ref{lmedia}) ) in the previousratio the following formula for ${\mathcal M^*}$ is found +perhaps. occultation events within the dusty. ancl gaseous disks surrounding classical T Tauri stars (CTTS).,"perhaps, occultation events within the dusty and gaseous disks surrounding classical T Tauri stars (CTTS)." + This behavior can persist for as long as 10 My. as (the example of TW Ilva (Alencar&Batalha2002) illustrates., This behavior can persist for as long as $\sim$ 10 My as the example of TW Hya \citep{ab} illustrates. + One also sees variations of tvpically a few tenths of a magnitude or less in weak-line T Tauri stars (WTTS) Chat may be largely or entirely. attributed to cool (magnetic) spots on the stellar surfaces (Ilerbstetal.1994)., One also sees variations of typically a few tenths of a magnitude or less in weak-line T Tauri stars (WTTS) that may be largely or entirely attributed to cool (magnetic) spots on the stellar surfaces \citep{h94}. +.. If the spot patterns persist for many rotations it is often possible to derive rotation periods for the stars by monitoring their photometric variations., If the spot patterns persist for many rotations it is often possible to derive rotation periods for the stars by monitoring their photometric variations. + Recent accounts of (his (wpe of work and its value have been given for the Orion Nebula cluster by Herbstetal.(2002).. lor the larger Orion association by Stassunοἱal.(1999).. Carpenter.(2001) and Rebull (2001).. for the voung cluster IC 348 by and for NGC 2264 by Lammetal.(2003).," Recent accounts of this type of work and its value have been given for the Orion Nebula cluster by \citet{hbj}, for the larger Orion association by \citet{s99}, \citet{chs} and \citet{r01}, , for the young cluster IC 348 by \citet{chw} and for NGC 2264 by \citet{lm03}." +. AIDM 12 (Alagnani.Blitz&Mundy1955). i$ a nearby complex of dark clouds which has given birth to a small number of relatively low mass stars (Luliman known as the MDM 12 association. or MDM 124. The distance was originally thought to be only 65 pe (leartyetal.2000a.b).. which would make MDM 12 the closest known star forming cloud.," MBM 12 \citep{m85} is a nearby complex of dark clouds which has given birth to a small number of relatively low mass stars \citep{l01,o03} known as the MBM 12 association, or MBM 12A. The distance was originally thought to be only 65 pc \citep{h00a,h00b}, which would make MBM 12 the closest known star forming cloud." + Recent studies. however. indicate much larger values near 300 pe (CLuliman2001:Straizvsetal.2002:Andersson2002).," Recent studies, however, indicate much larger values near 300 pc \citep{l01, sckl, a02}." +.. At the larger distance. the stars must be well above the main sequence and. therefore. extremely voung (~1-5 Mx).," At the larger distance, the stars must be well above the main sequence and, therefore, extremely young $\sim$ 1-5 My)." + The recent discovery. of an edge-on disk around an association member (Javawardhanaal.2002:Chauvinet2002) supports Chis view. as does the detection of millimeter wavelength radiation [rom some members (Πίοοἱal.2003).," The recent discovery of an edge-on disk around an association member \citep{j02,c02} supports this view, as does the detection of millimeter wavelength radiation from some members \citep{i03}." +. Our interest in the association came [rom ils inclusion on a list of possible targets lor a Space Interlerometry. Mission (SIM) satellite study to detect extra-solar planets by astrometric means (Beichman2001)., Our interest in the association came from its inclusion on a list of possible targets for a Space Interferometry Mission (SIM) satellite study to detect extra-solar planets by astrometric means \citep{b03}. +. While it may be too distant for that purpose. we have carried out a photometric study of nine of the twelve known members in four fields ancl report the results here.," While it may be too distant for that purpose, we have carried out a photometric study of nine of the twelve known members in four fields and report the results here." + They. provide some new insight into the nature of MDM 124 as well assome information on its members.," They provide some new insight into the nature of MBM 12A as well assome information on its members," +vectors for X ancl O mode photons in the magnetosphere (e.g..?):: where 425 is (he azimuthal angle of the magnetic field projected in a plane perpendicular to the observer line of sight (see below).,"vectors for X and O mode photons in the magnetosphere \citep[e.g.,][]{vanAdelsbergLai06a}: where $\varphi_B$ is the azimuthal angle of the magnetic field projected in a plane perpendicular to the observer line of sight (see below)." + Thus. the photon polarization state depends only on the magnetic field direction.," Thus, the photon polarization state depends only on the magnetic field direction." +" The difference in the eigenvalues corresponding to the X and O polarization states is EAn/(he)e5x10*E,DU(r/R)"" +. where E,=Ef(1keV) is (he photon energv at the NS surface aud i is (the distance between (he photon aud the NS."," The difference in the eigenvalues corresponding to the X and O polarization states is $E \Delta n/(\hbar c)\sim 5\times 10^3\, E_1\, B_{14}^2\, (r/R)^{-6}$ $^{-1}$, where $E_1 = E/(\mbox{1 keV})$ is the photon energy at the NS surface and $r$ is the distance between the photon and the NS." + When r2R. the derivative of the angle for a dipole field is approximately Fl where ry—r/(00km) and s is the affine parameter defined along the j»hoton oeeodesic.," When $r\ga R$, the derivative of the angle for a dipole field is approximately $d \varphi_B/ds \sim r^{-1} = 10^{-6}\, r_{10}^{-1}$ $^{-1}$, where $r_{10} = r/(10\mbox{ km})$ and $s$ is the affine parameter defined along the photon geodesic." + Thus. near the star surface. AnPM/(he)29rjες. and the polarization state evolves acliabatically with the changing direction of the magnetic field.," Thus, near the star surface, $E\Delta n/(\hbar c)\gg d\varphi_B/ds$, and the polarization state evolves adiabatically with the changing direction of the magnetic field." +" As the photoΕν continues to propagate in the magnetosphere. it reaches the polarization limiting radius. ry. where {δηPM(Πο)=de,vdj/ds."," As the photon continues to propagate in the magnetosphere, it reaches the polarization limiting radius, $r_{\rm pl}$, where $E\Delta n/(\hbar c) = d\varphi_B/ds$." + At distances 5greater than rj.pl the polarization state is fixed. and the directions of the mode vectors are constant.," At distances greater than $r_{\rm pl}$, the polarization state is fixed, and the directions of the mode vectors are constant." +" Thus. the measured values of the photoΕν Stokes parameters ave ""Irozen in at rp."," Thus, the measured values of the photon Stokes parameters are “frozen in” at $r_{\rm pl}$." + Far from the NS. μαςeL/ry. where rj=οΩω is the light-cvlinder radius.," Far from the NS, $d\varphi_B/ds\sim 1/r_l$, where $r_l\equiv c/\Omega$ is the light-cylinder radius." + Therefore. ry takes the value: In contrast. if the polarization states of emitted photons were determined near (he NS surface. the observed signal would be greatly reduced.," Therefore, $r_{\rm pl}$ takes the value: In contrast, if the polarization states of emitted photons were determined near the NS surface, the observed signal would be greatly reduced." + In this case. addition of the Stokes parameters for photons emitted [rom regions with distinct magnetic field directions would tend to cancel.," In this case, addition of the Stokes parameters for photons emitted from regions with distinct magnetic field directions would tend to cancel." + Aciahatic evolution of the photon modes to distances lar from the star surface. where the magnetic geometry is uniform. leads (to sienifieant. polarization signals. even when emission occurs over an extended region on the star surface (??)..," Adiabatic evolution of the photon modes to distances far from the star surface, where the magnetic geometry is uniform, leads to significant polarization signals, even when emission occurs over an extended region on the star surface \citep[][]{HeylShaviv02a,Heyletal03a}." + We present calculations for NSs with a pure dipole magnetic field structure., We present calculations for NSs with a pure dipole magnetic field structure. + As discussed above. realistic magnetar models include twisted magnetic field configurations which contain contributions [rom higher-order multipoles.," As discussed above, realistic magnetar models include twisted magnetic field configurations which contain contributions from higher-order multipoles." + Nevertheless. we have argued (hat because the polarization signal is fixed far from the star surface. the dipole component of the field is the most important lor determining (he observed Stokes parameters.," Nevertheless, we have argued that because the polarization signal is fixed far from the star surface, the dipole component of the field is the most important for determining the observed Stokes parameters." + ? performed a detailed analvsis of polarization mode evolution in a strongly magnetized vacuum. and showed that acdiabaticitv can be broken near (he star surface only when the photon (raverses a," \citet[][]{WangLai09a} performed a detailed analysis of polarization mode evolution in a strongly magnetized vacuum, and showed that adiabaticity can be broken near the star surface only when the photon traverses a" +relation (Lully Fisher 1977) were used by a number of eroups to infer the 3-D structure of this cluster.,relation (Tully Fisher 1977) were used by a number of groups to infer the 3-D structure of this cluster. + Lully Shava (1984) and Pierce Tully (1988) found evidence for a significant sample depth along the line of sight. interpreting weir evidence as a presence of infall.," Tully Shaya (1984) and Pierce Tully (1988) found evidence for a significant sample depth along the line of sight, interpreting their evidence as a presence of infall." + Fukugita et al. (, Fukugita et al. ( +1993) used. their. photographic photometry to confirm that. the cluster has a significant depth.,1993) used their photographic photometry to confirm that the cluster has a significant depth. + More recently Yasuda ct al. 9, More recently Yasuda et al. ( +097) re-addressed. the issue. and. concluded that the D. AL and W clouds are at larger distance than Virgo itself.,"1997) re-addressed the issue, and concluded that the B, M and W clouds are at larger distance than Virgo itself." + Feelerspicl. Fammann Sandage (1998) used new B band i0tometry to pursue the issue.," Federspiel, Tammann Sandage (1998) used new B band photometry to pursue the issue." + They agree with Yasucla et al. (, They agree with Yasuda et al. ( +1997) in determining that W and M are distant. clouds.,1997) in determining that W and M are distant clouds. + They confirmed that cluster Bis 0.5 mag further away than Virgo itself. although the mean recessional velocity of this sub-cluster is identical to that of the dominant. cluster A (Bingeeli. Popescu Tammann 1993).," They confirmed that cluster B is 0.5 mag further away than Virgo itself, although the mean recessional velocity of this sub-cluster is identical to that of the dominant cluster A (Binggeli, Popescu Tammann 1993)." + Deside the Cepheids anc the TE relation. other methods have been used to estimate distances {ο the Virgo spirals.," Beside the Cepheids and the TF relation, other methods have been used to estimate distances to the Virgo spirals." + These include the peak of the Iuminosity vs. declining ratio of Novae (Perrarese et. al., These include the peak of the luminosity vs. declining ratio of Novae (Ferrarese et al. + 1996b). the expanding photosphere method for the type LL supernovae (Schmidt et al.," 1996b), the expanding photosphere method for the type II supernovae (Schmidt et al." + 1994). the peak brightness of the Tvpe Ia supernovae (Schank 1997) and the bright stars as standard cancels (Pierce et al.," 1994), the peak brightness of the Type Ia supernovae (Schank 1997) and the bright stars as standard candels (Pierce et al." + 1992) methods., 1992) methods. + The mean distance modulus derived from these methods is 30.92 + Distance estimates to earlv-tyvpe galaxies have been based on the surface brightness Dluctuation method (Tonry. ct al., The mean distance modulus derived from these methods is 30.92 $\pm$ Distance estimates to early-type galaxies have been based on the surface brightness fluctuation method (Tonry et al. + 990: Jensen et al., 1990; Jensen et al. + 1996: Morris Shanks 1998: Ajhar et al., 1996; Morris Shanks 1998; Ajhar et al. + 997). on Novae luminosities (Della Valle Livio 1995). on the globular clusters Iuminosity function (Secker Llarris 903: Whitmore et al.," 1997), on Novae luminosities (Della Valle Livio 1995), on the globular clusters luminosity function (Secker Harris 1993; Whitmore et al." + 1995: van den Bereh 1996). and on he planetary nebulae. luminosity function. (Jacoby et. al.," 1995; van den Bergh 1996), and on the planetary nebulae luminosity function (Jacoby et al." + 990: Ciardullo ct al., 1990; Ciardullo et al. + 1998)., 1998). + These methods give distances in the range 30.31-32.13., These methods give distances in the range 30.31-32.13. +" AIST itself. has been found. at [1,730.8-31.3.", M87 itself has been found at $\mu_o$ =30.8-31.3. +". MAD. poses a. problem. since its distance determination (44, —31.0) is significantly. smaller than the distance estimate to cluster D. (jj,—31.8.. Federspiel ct al."," M49 poses a problem, since its distance determination $\mu_o$ =31.0) is significantly smaller than the distance estimate to cluster B $\mu_o$ =31.8, Federspiel et al." + 1998) to which it is supposed to Altogether there appears to be unanimous consent that galaxies in the Virgo region are not at à unique distance., 1998) to which it is supposed to Altogether there appears to be unanimous consent that galaxies in the Virgo region are not at a unique distance. + The W. M and B clouds are found further away than A. and evidence for infall has been reported.," The W, M and B clouds are found further away than A, and evidence for infall has been reported." + In this paper we make a further step in the direction of unveiling the structure of the Virgo cluster. with two main improvements over previous works.," In this paper we make a further step in the direction of unveiling the structure of the Virgo cluster, with two main improvements over previous works." + Firstly. we combine distances to spirals obtained with the TE method. with distances to I2/8S0s obtained with the Fundamental. Plane (FP) method. (Djorgovski Davis 1987: Dressler οἱ al.," Firstly, we combine distances to spirals obtained with the TF method with distances to E/S0s obtained with the Fundamental Plane (FP) method (Djorgovski Davis 1987; Dressler et al." + 1987). thus increasing the statistical significance of the determination.," 1987), thus increasing the statistical significance of the determination." + Secondly. for both of these methods we rely on LE band surface photometry.," Secondly, for both of these methods we rely on H band surface photometry." + Phe advantages of using near-intrared (NUR) photometry over the Bo band one are that ΔΙ magnitudes are [less sensitive to recent episodes of star formation. and they are less allected by internal extinetion. thus they better trace the luminous matter in galaxies (Gavazzi. Pierini Doselli 1996b).," The advantages of using near-infrared (NIR) photometry over the B band one are that NIR magnitudes are less sensitive to recent episodes of star formation, and they are less affected by internal extinction, thus they better trace the luminous matter in galaxies (Gavazzi, Pierini Boselli 1996b)." + Also. spiral disks have a smoother appearance in the NI. and this makes it easier to fit photometric profiles to. derive the ealaxy total magnitude. and the clisk inclination.," Also, spiral disks have a smoother appearance in the NIR, and this makes it easier to fit photometric profiles to derive the galaxy total magnitude, and the disk inclination." + Both these factors should contribute to a reduction in the overall uncertainty with which distance determinations are The remainder of this paper is organized as follows., Both these factors should contribute to a reduction in the overall uncertainty with which distance determinations are The remainder of this paper is organized as follows. + In Section 2 we illustrate the sample selected. for the present analysis., In Section 2 we illustrate the sample selected for the present analysis. + The Ll band imaging observations and the new spectroscopy are brielly. summarized. in Section 3., The H band imaging observations and the new spectroscopy are briefly summarized in Section 3. + The cosmological assumptions. and the derivation of the PE and FP templates are described in Section 4.," The cosmological assumptions, and the derivation of the TF and FP templates are described in Section 4." + Our new distance estimates. and a comparison with other estimates. from the literature are. presented in Section 5. together with a discussion on the structure of the Virgo cluster as delineated bv these new measurements.," Our new distance estimates, and a comparison with other estimates from the literature are presented in Section 5, together with a discussion on the structure of the Virgo cluster as delineated by these new measurements." + Our main conclusions are summarized in Section 6., Our main conclusions are summarized in Section 6. + Galaxies analyzed in this work are selected from the 220 Virgo Cluster Catalog (VCC: Dinggeli. Sancage ‘Temmann.," Galaxies analyzed in this work are selected from the 220 Virgo Cluster Catalog (VCC; Binggeli, Sandage Tammann." + 1985) objects with D.«14.0., 1985) objects with $B<14.0$. + We ade to this sample 13 objects. slightly fainter than this limit. that were taken from the COGCCG. catalogue (Zwicky et al.," We add to this sample 13 objects, slightly fainter than this limit, that were taken from the CGCG catalogue (Zwicky et al." + 1961-68). because distance estimates are readily available for them.," 1961-68), because distance estimates are readily available for them." + For cach galaxy a membership estimate is given in the VCC (revised. by Dingecli. Popescu “Tamumann 1993).," For each galaxy a membership estimate is given in the VCC (revised by Binggeli, Popescu Tammann 1993)." + Cluster A coincides. with the X-ray cluster associated with AIST., Cluster A coincides with the X-ray cluster associated with M87. + The subeluster B is centered. on ΔΙ)., The subcluster B is centered on M49. + Other ageregates include the AL Wo and. W clouds. anc the Southern extension.," Other aggregates include the M, W and W' clouds and the Southern extension." + Galaxies with Vyc3000£ms+ are treated as background objects. ancl are excluded from the present Both the availability of the photometric and spectroscopic data necessary to. build. the TE and FP relation. and inclination restrictions that apply to any Th sample plav a role in limiting the number of galaxies for which we can obtain distance estimates.," Galaxies with $V_{hel}>3000~km~s^{-1}$ are treated as background objects, and are excluded from the present Both the availability of the photometric and spectroscopic data necessary to build the TF and FP relation, and inclination restrictions that apply to any TF sample play a role in limiting the number of galaxies for which we can obtain distance estimates." + We have obtained NIR H1 or WO band images of 200 out of the 233. selected ealaxies (these observations are described in Section 3)., We have obtained NIR H or K' band images of 200 out of the 233 selected galaxies (these observations are described in Section 3). + Of the SO carly-twpc galaxies. imaged. 48 have central velocity dispersion measurements available in the literature (AleElroy 1995).," Of the 89 early-type galaxies imaged, 48 have central velocity dispersion measurements available in the literature (McElroy 1995)." + To these we add. Ll new measurements of the central velocity. dispersion. obtained at ΟΠΗ (see Section 3.4)., To these we add 11 new measurements of the central velocity dispersion obtained at OHP (see Section 3.4). +" Of the 111 spiral galaxies imaged. 75 match the criteria for the inclusion in the TE sample. je: a) have the correct inclination (7> 307) (see Section 4.2): b) have high signal-to-noise 2lem LL line profiles (or Z4, rotation curves) and. c) meet the additional requirement that. the"," Of the 111 spiral galaxies imaged, 75 match the criteria for the inclusion in the TF sample, i.e.: a) have the correct inclination $i > 30^{\circ}$ ) (see Section 4.2); b) have high signal-to-noise 21cm HI line profiles (or $H_{\alpha}$ rotation curves) and, c) meet the additional requirement that the" +used as an estimation of the orbital angular velocity at the mass-shedding limit for neutron stars in a relativistic binary system.,used as an estimation of the orbital angular velocity at the mass-shedding limit for neutron stars in a relativistic binary system. +" As we stated in Section 1, one of the primary purposes for constructing quasi-equilibrium states is to provide initial data for inspiral and merger simulations in numerical relativity."," As we stated in Section 1, one of the primary purposes for constructing quasi-equilibrium states is to provide initial data for inspiral and merger simulations in numerical relativity." +" It will be quite useful for numerical relativity community, if we provide quantities with which they can compare the results of simulations in the inspiral phase."," It will be quite useful for numerical relativity community, if we provide quantities with which they can compare the results of simulations in the inspiral phase." + One of the quantities derived from quasi-equilibrium results is the time evolution of the orbital angular velocity., One of the quantities derived from quasi-equilibrium results is the time evolution of the orbital angular velocity. +" To obtain the orbital angular velocity as a function of time, we adopt a similar method introduced by Boyleetal.(2007)."," To obtain the orbital angular velocity as a function of time, we adopt a similar method introduced by \citet{boy07}." +". Assuming the quasi-stationary adiabatic evolution of the inspiral orbit, we may write the time derivative of the orbital angular velocity as This equation is the same as Equation (55) in Uryüetal.(2009)."," Assuming the quasi-stationary adiabatic evolution of the inspiral orbit, we may write the time derivative of the orbital angular velocity as This equation is the same as Equation (55) in \citet{ury09}." +". For the temporal change in the binding energy of the binary neutron stars, dE/dt, we use the 3.5PN equation shown in Blanchet(2006)."," For the temporal change in the binding energy of the binary neutron stars, $dE/dt$, we use the 3.5PN equation shown in \citet{bla06}." +". On the other hand, we estimate the change in the binding energy, dE/dQ, as follows: we write the binding energy as where r=(Mo)?/%, and (E)aspw denotes the binding energy through 3.5PN order."," On the other hand, we estimate the change in the binding energy, $dE/d\Omega$, as follows: we write the binding energy as where $x \equiv (M_0 \Omega)^{2/3}$, and $(E)_{\rm 3.5PN}$ denotes the binding energy through 3.5PN order." +" The constants, a, b, and c, are determined by numerically fitting the obtained sequences."," The constants, $a$, $b$, and $c$, are determined by numerically fitting the obtained sequences." +" Then we calculate the change in the binding energy by taking the derivative with respect to the orbital angular velocity as By numerically integrating Equation (67)), we obtain the orbital angular velocity as a function of time, Here CQ; is the initial orbital angular velocity at which the time is defined to be zero, and Cg, is the final orbital angular velocity."," Then we calculate the change in the binding energy by taking the derivative with respect to the orbital angular velocity as By numerically integrating Equation \ref{eq:dodt}) ), we obtain the orbital angular velocity as a function of time, Here $\Omega_{\rm ini}$ is the initial orbital angular velocity at which the time is defined to be zero, and $\Omega_{\rm fin}$ is the final orbital angular velocity." +" For Ώρα, we use the orbital angular velocity at the mass-shedding limit obtained in Section 4.3.."," For $\Omega_{\rm fin}$, we use the orbital angular velocity at the mass-shedding limit obtained in Section \ref{sec:endpoint}." + Figure 23 shows the orbital angular velocity as a function of time for three piecewise polytropes with I;=3.0., Figure \ref{fig23} shows the orbital angular velocity as a function of time for three piecewise polytropes with $\Gamma_1=3.0$. +" The thick (red) dashed, thick (blue) dot-dashed, and thick (green) dot-dot-dashed curves denote the results for ΊοσδιρΓι=13.95 (PwPoly30-1395), 13.45 (PwPoly30-1345), and 13.15 (PwPoly30-1315), respectively."," The thick (red) dashed, thick (blue) dot-dashed, and thick (green) dot-dot-dashed curves denote the results for $\log_{10} P_1=13.95$ (PwPoly30-1395), 13.45 (PwPoly30-1345), and 13.15 (PwPoly30-1315), respectively." +" All of them are calculated by using the equal-mass sequences of MNBl,=ΜΑΡ1.35Mo.", All of them are calculated by using the equal-mass sequences of $M_{\rm ADM}^{\rm NS1}=M_{\rm ADM}^{\rm NS2}=1.35 M_{\odot}$. + We also show two reference curves of TaylorT1 and TaylorT4 introduced by Boyleetal.(2007)., We also show two reference curves of TaylorT1 and TaylorT4 introduced by \citet{boy07}. +. The initial orbital angular velocity is set to MopQini=0.03., The initial orbital angular velocity is set to $M_0 \Omega_{\rm ini}=0.03$. +" It is found that the curve of the most compact neutron stars (the dot-dot-dashed curve, PwPoly30-1315) is the closest to that of TaylorT4 among all the models."," It is found that the curve of the most compact neutron stars (the dot-dot-dashed curve, PwPoly30-1315) is the closest to that of TaylorT4 among all the models." + This is reasonable, This is reasonable +For the purpose of the present paper. we have decided (o use the conditional median as our measure of the effective distance of galaxies with a eiven flux.,"For the purpose of the present paper, we have decided to use the conditional median as our measure of the effective distance of galaxies with a given flux." + This particular choice is somewhat arbitrary and influences scalings of top axes in 4.. 6. 7..," This particular choice is somewhat arbitrary and influences scalings of top axes in \\ref{Fig:growth.r}, , \ref{Fig:misal}, \ref{Fig:predicted} \ref{Fig:g_m and v_c}." + However. since the difference between the conditional mean and median is verv small (about 5%)). this choice has a negligible impact on general conclusions aud results of (his paper.," However, since the difference between the conditional mean and median is very small (about ), this choice has a negligible impact on general conclusions and results of this paper." + Relating the flux to the Amagnitude via (14). (?)..," Relating the flux to the $K$magnitude via \ref{eq:S_i}) \citep{6dF_Fi}," +a mean photon energy ~1 keV: llere. we assume that each X-ray photon produces 12 hvdrogen ionizations. primarily through secondary ionizatious Irom X-ray photoelectrons (Shull van Steenberg 1985; VGS01).,"a mean photon energy $\sim1$ keV: Here, we assume that each X-ray photon produces $\sim 12$ hydrogen ionizations, primarily through secondary ionizations from X-ray photoelectrons (Shull van Steenberg 1985; VGS01)." + In the partially ionized IGM. the free electrons come from I. Le. and trace 7.," In the partially ionized IGM, the free electrons come from $^+$, $^+$, and trace $^{+2}$." + We assume that the clumping factor (ος) and escape fraction (f...) are roughly unity for N-rays. given (heir high penetrating power relative to UV photons.," We assume that the clumping factor $c_L$ ) and escape fraction $f_{\rm esc}$ ) are roughly unity for X-rays, given their high penetrating power relative to UV photons." + Figure 2 shows the allowed additional optical depth. analogous to the constraints of Figure 1. for X-ray efficiency in both Lya--cooled halos and minihalos.," Figure 2 shows the allowed additional optical depth, analogous to the constraints of Figure 1, for X-ray efficiency in both -cooled halos and minihalos." +" Evidently. N-ravs from black holes located in high-redshilt minihalos can produce Az,20.02. with a substantial ionizing elliciency. eyzz100. that rivals that of Pop II star formation."," Evidently, X-rays from black holes located in high-redshift minihalos can produce $\Delta \tau_e \approx 0.02$, with a substantial ionizing efficiency, $\epsilon_X \approx 100$, that rivals that of Pop II star formation." +" In summary. we have shown that the revised (WMAP-5) values of CMD optical depth. 7T,=0.084+0.016. lead (o a more constrained picture of early reionization of the IGM."," In summary, we have shown that the revised (WMAP-5) values of CMB optical depth, $\tau_e = 0.084 \pm 0.016$, lead to a more constrained picture of early reionization of the IGM." + Approximately half of the observed 7. comesfrom a fully ionized IGM back to £z 67., Approximately half of the observed $\tau_e$ comesfrom a fully ionized IGM back to $\approx$ 6–7. + The additional At. al 2> pprobably arises [rom the [ist massive stus and from accretion onto early black holes., The additional $\Delta \tau_e$ at $z >$ probably arises from the first massive stars and from accretion onto early black holes. +" Some ol the observed 7, may come from scattering [rom residual electrons left from recombination: inaccuracies in computing (his ionization historv add svstematic uncertaintv to the CMD inlerred signal.", Some of the observed $\tau_e$ may come from scattering from residual electrons left from recombination; inaccuracies in computing this ionization history add systematic uncertainty to the CMB inferred signal. +" We have assumed extra scattering. Az,=0.032:0.02 ad z> and used this to constrain (he elliciencies for production and escape of ionizing photons. either by ultraviolet photons from (he first massive stars 11) or by N-ravs Irom accretion onto early black holes 22)."," We have assumed extra scattering, $\Delta \tau_e = 0.03 \pm 0.02$ at $z >$ and used this to constrain the efficiencies for production and escape of ionizing photons, either by ultraviolet photons from the first massive stars 1) or by X-rays from accretion onto early black holes 2)." + In both cases. the picture is of a partially ionized IGM at redshifts 2=6—20.," In both cases, the picture is of a partially ionized IGM at redshifts $z = 6-20$." + For X-ray pre-onization by early black holes. equation (6) can be used to provide an estimate of the effects of partial reionization.," For X-ray pre-ionization by early black holes, equation (6) can be used to provide an estimate of the effects of partial reionization." +" Belween redshifis το220 and 2,26. an IGM with ionized fraction r4=0.1 (Ricotti 2005) would produce (Az)=(0.018)Cr4/0.1). which is a sienificant contribution to the observed τ,=0.084+0.016."," Between redshifts $z_2 \approx 20$ and $z_1 \approx 6$, an IGM with ionized fraction $x_{e,0} = 0.1$ (Ricotti 2005) would produce $(\Delta \tau_e) = (0.018) (x_{e,0} / 0.1)$, which is a significant contribution to the observed $\tau_e = 0.084 \pm 0.016$." +" Ricotti (2005) suggested a large .r,£0.1—0.6 and pushed their black-hole space densities and accretion rates to large values in order to reach the WALAP-1 estimates of 7.=0.17.", Ricotti (2005) suggested a large $x_e \approx 0.1-0.6$ and pushed their black-hole space densities and accretion rates to large values in order to reach the WMAP-1 estimates of $\tau_e = 0.17$. +" Because such large values of 7, are no longer required. (he black hole densities and IGM ionization [fractions are likely to be considerably less."," Because such large values of $\tau_e$ are no longer required, the black hole densities and IGM ionization fractions are likely to be considerably less." + All these constraints depend heavily on uncertain parameterizations of the efficiency. of star formation and ionizing photon production., All these constraints depend heavily on uncertain parameterizations of the efficiency of star formation and ionizing photon production. + The most sensitive of these parameters is oy. although the details of the clumping [actor are comparably portant.," The most sensitive of these parameters is $\sigma_8$ , although the details of the clumping factor are comparably important." + With more precise, With more precise +The acceleration of each star relative to that on the center of mass of the perturbed body ts where V is the interaction potential between the perturber and the victim. A/ is the mass of the victim. and the integral is over the density profile of this object.,"The acceleration of each star relative to that on the center of mass of the perturbed body is where $\Psi$ is the interaction potential between the perturber and the victim, $M$ is the mass of the victim, and the integral is over the density profile of this object." + Expand VW about the origin in a Taylor series using After algebra. taking into account that the origin 1s located at the center of mass of the victim. the &-th component of theacceleration becomes where /7;;=Ij/M and Dj; is the moment of inertia tensor (Binney&Tremaine1987): For simplicity. treat the force on each star in the disk from the perturber as that from a point mass.," Expand $\nabla \Psi$ about the origin in a Taylor series using After algebra, taking into account that the origin is located at the center of mass of the victim, the $k$ -th component of theacceleration becomes where $H_{jl} \equiv I_{jl} / M$ and $I_{jl}$ is the moment of inertia tensor \citep{BT87}: For simplicity, treat the force on each star in the disk from the perturber as that from a point mass." + Then. the interaction potential Is Performing the derivatives required in the above expression. we obtain the acceleration of a particular star at a given time.," Then, the interaction potential is Performing the derivatives required in the above expression, we obtain the acceleration of a particular star at a given time." + The velocity impulse delivered by the encounter can then be obtained by integrating over time., The velocity impulse delivered by the encounter can then be obtained by integrating over time. + Thus. the leading term in the series 1s (Binney&Tremaine1987) Likewise. the next order correction term can be written In principle. this procedure can be extended to even higher order terms in the series.," Thus, the leading term in the series is \citep{BT87} + Likewise, the next order correction term can be written In principle, this procedure can be extended to even higher order terms in the series." + Note that the terms m this last equation are all ~Ον} since the elements in the matrix H involve integrals over squares of theinternal coordinates of the victim. while the terms in eq. (9) ," Note that the terms in this last equation are all $\sim O (r^2)$ since the elements in the matrix ${\bf H}$ involve integrals over squares of theinternal coordinates of the victim, while the terms in eq. \ref{impulse}) )" +are ~O(r)., are $\sim O (r)$. + In what follows. we will employ eq. (9))," In what follows, we will employ eq. \ref{impulse}) )" + as the starting point for our analysis., as the starting point for our analysis. + Unlike as in the usual impulse approximation we will allow both R(t) i(f) to vary in time., Unlike as in the usual impulse approximation we will allow both $\overrightarrow{R}(t)$ $\overrightarrow{r}(t)$ to vary in time. + We will. however. assume that the trajectory of the interaction. specified by Π(f). is prescribed (i.e. orbital decay is not accounted for). and that the orbital motion within the victim. set by i(7). is such that the stars follow their unperturbed motions throughout the course of the interaction.," We will, however, assume that the trajectory of the interaction, specified by $\overrightarrow{R}(t)$, is prescribed (i.e. orbital decay is not accounted for), and that the orbital motion within the victim, set by $\overrightarrow{r}(t)$, is such that the stars follow their unperturbed motions throughout the course of the interaction." + To illustrate our approach. we begin by considering a coplanar interaction between a perfectly thin. rotating disk of stars and à passing perturber.," To illustrate our approach, we begin by considering a coplanar interaction between a perfectly thin, rotating disk of stars and a passing perturber." + As noted earlier. the origin of the coordinate system will be at the center of mass of the victim and the coordinate system will be oriented so that the disk lies in the.e4 plane.," As noted earlier, the origin of the coordinate system will be at the center of mass of the victim and the coordinate system will be oriented so that the disk lies in the $x-y$ plane." + While not general. this case suffices to characterize the dynamies of such encounters: we will generalize to non-coplanar collisions later.," While not general, this case suffices to characterize the dynamics of such encounters; we will generalize to non-coplanar collisions later." + Denote the mass of the victim disk by 1 and that of the perturber by 3M., Denote the mass of the victim disk by $M$ and that of the perturber by $M_{\rm{pert}}$. + The case of a perturber moving along a straight line relative to the victim 15 the simplest one to analyze and is appropriate for high-speed encounters. as in clusters of galaxies.," The case of a perturber moving along a straight line relative to the victim is the simplest one to analyze and is appropriate for high-speed encounters, as in clusters of galaxies." +" For definiteness. take the orbit path to be where. as indicated in Figure 2.. / is the distance of closest approach (the impact parameter). which occurs at time 7=0, and T ts the velocity of the encounter. which ts constant for a straight-line trajectory."," For definiteness, take the orbit path to be where, as indicated in Figure \ref{Stripstraight}, $b$ is the distance of closest approach (the impact parameter), which occurs at time $t=0$, and $V_{sl}$ is the velocity of the encounter, which is constant for a straight-line trajectory." + The internal motions of the disk particles are given by eq. (2)), The internal motions of the disk particles are given by eq. \ref{vicorb}) ) + with where O the internal angular frequency of the victim and oy is the phase at the mmimum distance from the perturber at f= 0., with where $\Omega$ the internal angular frequency of the victim and $\phi_0$ is the phase at the minimum distance from the perturber at $t=0$ . + Note that while 2 is assumed to be constant in time. it can vary spatially according to Q=O (i). depending on the shape of," Note that while $\Omega$ is assumed to be constant in time, it can vary spatially according to $\Omega = \Omega(r)$ , depending on the shape of" +increase the total number of GRBs te.g.. Virgili et al.,"increase the total number of GRBs (e.g., Virgili et al." + 2011)., 2011). + These models might be distinguished by the future observations., These models might be distinguished by the future observations. + We are very grateful to the referee for helpful comments and suggestions., We are very grateful to the referee for helpful comments and suggestions. + We also thank David Wanderman. Andrew Hopkins. Hansan Yükksel and Matthew Kistler for making their data available. and Yizhong Fan and Bing Zhang for helpful discussion and suggestions.," We also thank David Wanderman, Andrew Hopkins, Hansan Yükksel and Matthew Kistler for making their data available, and Yizhong Fan and Bing Zhang for helpful discussion and suggestions." + This work was supported in part by the National Natural Science Foundation of China (grants 10973041. 10921063 and 11163003).," This work was supported in part by the National Natural Science Foundation of China (grants 10973041, 10921063 and 11163003)." + F.-W.Z. acknowledges the support by the China Postdoctoral Science Foundation funded. project (No., F.-W.Z. acknowledges the support by the China Postdoctoral Science Foundation funded project (No. + 20110490139). the Guangxi Natural Science Foundation (No.," 20110490139), the Guangxi Natural Science Foundation (No." + 2010GXNSFBO1I3050) and the doctoral research foundation of Guilin University of Technology., 2010GXNSFB013050) and the doctoral research foundation of Guilin University of Technology. +ligh particle/solar background (a significant issue in the second epoch observation).,high particle/solar background (a significant issue in the second epoch observation). + For those observations when the EPIC cata were in ‘ull frame mode. we excluded events [rom the central core of the psf (using an aperture of in radius) in. order hat pile-up was not significant.," For those observations when the EPIC data were in full frame mode, we excluded events from the central core of the psf (using an aperture of $^{''}$ in radius) in order that pile-up was not significant." + We did not extract spectra rom the timing moce data since the spectral calibration is not as well defined as for the other modes., We did not extract spectra from the timing mode data since the spectral calibration is not as well defined as for the other modes. + For the RCS data. we extracted. spectra which included the source and ickeground. and a background: spectrum. separately.," For the RGS data, we extracted spectra which included the source and background, and a background spectrum separately." + We erouped the EPIC spectra so that cach bin had a minimum of 40 counts., We grouped the EPIC spectra so that each bin had a minimum of 40 counts. + Since the RCS spectra from the individual epochs were relatively low. we co-added the spectra from the 1GS51 and HGS2 detectors obtained using the 3rd and 4th epoch observations (the first two epochs hac much shorter OXPOSULES)," Since the RGS spectra from the individual epochs were relatively low, we co-added the spectra from the RGS1 and RGS2 detectors obtained using the 3rd and 4th epoch observations (the first two epochs had much shorter exposures)." + We used the task and then eroupec each spectrum so that each bin of each spectrum rack a minimum of 20 counts per bin., We used the task and then grouped each spectrum so that each bin of each spectrum had a minimum of 20 counts per bin. + To determine the observed N-rav tux at cach epoch. we used data taken using the EPIC pn detector.," To determine the observed X-ray flux at each epoch, we used data taken using the EPIC pn detector." + We fitted he integrated. X-ray. spectra using an absorbed: blackbody xus broad. emission line., We fitted the integrated X-ray spectra using an absorbed blackbody plus broad emission line. + We show the integrated observed lux in the 0.2IO0keV energy band using in Table 1. (the observed [lux is only weakly sensitive to the mocoel used)., We show the integrated observed flux in the 0.2–10keV energy band using in Table \ref{log} (the observed flux is only weakly sensitive to the model used). + This shows that the observed Uux varied. by between he 4 observation epochs., This shows that the observed flux varied by between the 4 observation epochs. +" The X-ray. data folded on the 569 see period shows a distinctive ""onolf behaviour. with the X-ray [lux being olf for approximately half the 569 see period (Cropper et al 1998)."," The X-ray data folded on the 569 sec period shows a distinctive `on–off' behaviour, with the X-ray flux being off for approximately half the 569 sec period (Cropper et al 1998)." + There is a sharp rise in Hux which is followed by a slower decline from maximum brightness., There is a sharp rise in flux which is followed by a slower decline from maximum brightness. + Ramsay et al (2005) showed evidence using the two shorter duration observations that the spectrum. gets softer. curing this declino phase., Ramsay et al (2005) showed evidence using the two shorter duration observations that the spectrum gets softer during this decline phase. + Using the 3rd. and 4th longer series of observations we confirm this finding., Using the 3rd and 4th longer series of observations we confirm this finding. + Therefore. we have obtained a spectrum which covers the ‘bright phase’ which we define to be ó-0.080.38 where ó6-0.0 is defined as the start of the sharp rise in N-rav Εαν., Therefore we have obtained a spectrum which covers the `bright phase' which we define to be $\phi$ =0.08–0.38 where $\phi$ =0.0 is defined as the start of the sharp rise in X-ray flux. + We extracted RGS spectra from the bright phase using the 3rd and 4th epoch observations., We extracted RGS spectra from the bright phase using the 3rd and 4th epoch observations. + In fitting the spectra. we used a blackbody. a blackbody plus a Ciaussian component both in absorption and emission and a multi-temperature thermal plasma plus edge model.," In fitting the spectra, we used a blackbody, a blackbody plus a Gaussian component both in absorption and emission and a multi-temperature thermal plasma plus edge model." + In the work of Ramsay et al (2005. 2006). the absorption model which was used was the ‘wa’ neutral absorption model found. in. the [fitting package (Arnaucl 1996).," In the work of Ramsay et al (2005, 2006), the absorption model which was used was the ' neutral absorption model found in the fitting package (Arnaud 1996)." + Here. we use the 'Pübbingen.Boulder absorption LSAT mocdel and abundances (Wilms. Allen AleCray 2000) which incorporates advances in atomic cross-sections and other physical parameters compared to the model (Morrison AleCammon 1983).," Here, we use the Tübbingen–Boulder absorption ISM model and abundances (Wilms, Allen McCray 2000) which incorporates advances in atomic cross-sections and other physical parameters compared to the model (Morrison McCammon 1983)." + We used this model implemented. intoXSPEC as the model (which. assumes an interstellar medium. of solar xiuxdance) and the model (which allows the xindance of cach element to vary)., We used this model implemented into as the model (which assumes an interstellar medium of solar abundance) and the model (which allows the abundance of each element to vary). + We show the goodness of fit to the RCS spectrum using he different models in Table 2..., We show the goodness of fit to the RGS spectrum using the different models in Table \ref{rgsfits}. + As was found by Ramsay al (2005) a simple absorbed blackbody model gives à very »oor fit., As was found by Ramsay et al (2005) a simple absorbed blackbody model gives a very poor fit. + Ramsay ct al (2006) found that a low temperature rermal plasma plus edge. model gave a good fit to the μα»ectrum obtained. using the EPIC pn detector., Ramsay et al (2006) found that a low temperature thermal plasma plus edge model gave a good fit to the spectrum obtained using the EPIC pn detector. + Using the tC data we can rule this model out., Using the RGS data we can rule this model out. + The temperature of 1e plasma determined. using the EPLC pn detector is very ow. (< 1keV). which would result in strong X-ray emission ines these lines are not detected in the RCS data.," The temperature of the plasma determined using the EPIC pn detector is very low, $<1$ keV), which would result in strong X-ray emission lines – these lines are not detected in the RGS data." + This leaves three models a blackbody. with either an absorption or emission component. or a blackbody with an absorption component which has abundance dillerent to solar composition.," This leaves three models – a blackbody with either an absorption or emission component, or a blackbody with an absorption component which has abundance different to solar composition." + We show the ROS spectrum. together with the best fit using an absorbed blackbody. where the absorptioncomponent has variable abundances. in Figure l..," We show the RGS spectrum together with the best fit using an absorbed blackbody, where the absorptioncomponent has variable abundances, in Figure \ref{spectra}. ." +power-law part. ancl a spectral peak in between in the sub-MeV range (Bandetal.1993).,"power-law part, and a spectral peak in between in the sub-MeV range \citep{ban93}." +. IIowever. the Large Area Telescope (LAT) onboard the Fermi Ganuna-Ray Space Telescope (Ferma) recently detected an additional. haud spectral component above ~0.1 GeV in the prompt phase of the short GRD 090510 (Abdoetal.2009b:Ackermann2010).," However, the Large Area Telescope (LAT) onboard the Fermi Gamma-Ray Space Telescope ) recently detected an additional, hard spectral component above $\sim 0.1$ GeV in the prompt phase of the short GRB 090510 \citep{abd09b,ack10}." +. Notwithstanding alternative models (Granot2010:Dermer2010).. if the GRB accelerated ultra-high-energy protons with isotropic-equivalent luminosity Lj2LO” erg/s. svnehrotvon and inverse Compton (IC) emission from an electron-positron pair cascade (riggered by photopion interactions of the protons with low-energv photons (Bottcher&DermerGupta&Zhang.2007;AsanoInoue2007) can account for this GeV emission al. 2009b).," Notwithstanding alternative models \citep{gra10,der10}, if the GRB accelerated ultra-high-energy protons with isotropic-equivalent luminosity $L_{\rm p} \gtrsim 10^{55}$ $/$ s, synchrotron and inverse Compton (IC) emission from an electron-positron pair cascade triggered by photopion interactions of the protons with low-energy photons \citep{boe98,gup07,asa07} + can account for this GeV emission \citep{asa09b}." +. Interestingly. in this same burst. theFermi Gamma-rayBurst Monitor (GDM) observed a further. soft excess leature below ~20 keV. which appears to lie on a continuation of the hard. GeV power-law.," Interestingly, in this same burst, the Gamma-rayBurst Monitor (GBM) observed a further, soft excess feature below $\sim 20$ keV, which appears to lie on a continuation of the hard, GeV power-law." + A similar. even clearer X-ray excess. as well as a GeV excess was also reported for the prompt emission of the long GR 090902D (Abdoetal.2009c).," A similar, even clearer X-ray excess, as well as a GeV excess was also reported for the prompt emission of the long GRB 090902B \citep{abd09c}." +. Evidence of extra low-energv Components was also reported in about ~15% of BATSE bursts 1996)., Evidence of extra low-energy components was also reported in about $\sim 15$ of BATSE bursts \citep{pre96}. +. In the optical bancl. several GRBs have exhibited prompt optical fluxes (hat are brighter Caan expected from simple extrapolations of their low-enerev Dand spectra 2007;Panaileseu 2003).," In the optical band, several GRBs have exhibited prompt optical fluxes that are brighter than expected from simple extrapolations of their low-energy Band spectra \citep{yos07,pan08}." +. One of the most impressive cases was (he extremely. luminous optical emission of the “nakec-eve” GRD 080319D(Racusinetal.2003).. Despite alternative explanations such as an early onset of the aflerelow (GhiselliniKamar&Duran2009) or upscattering of external/photospheric photons (Toma2010:Peeretal. 2010).. the emission from hadronic pair cascades can also potentially account for the excess components in the X-ray or even optical band. owing to the generally verv wide distribution in energv of (he secondary pairs and their resultant radiation.," One of the most impressive cases was the extremely luminous optical emission of the “naked-eye” GRB 080319B\citep{rac08}. Despite alternative explanations such as an early onset of the afterglow \citep{ghis09,kum09} + or upscattering of external/photospheric photons \citep{tom09,tom10,pee10}, the emission from hadronic pair cascades can also potentially account for the excess components in the X-ray or even optical band, owing to the generally very wide distribution in energy of the secondary pairs and their resultant radiation." + In addition to hieh-enerey gamma-rays. prompt X-ray. ancl optical emission may thus prove to be valuable observational signatures of VITECR acceleration in GRBs.," In addition to high-energy gamma-rays, prompt X-ray and optical emission may thus prove to be valuable observational signatures of UHECR acceleration in GRBs." + Here we demonstrate this through Monte Carlo spectral modeling. focusing on the two remarkable cases of GRB 090902D and GRB 080319D. Our Monte Carlo code self-consistently calculates the photon and. neutrino spectra corresponding to individual pulses in (he GID prompt emission in a one-zone approximation. including all relevant leptonie and hadronie processes (Asanoetal. 2009b)..," Here we demonstrate this through Monte Carlo spectral modeling, focusing on the two remarkable cases of GRB 090902B and GRB 080319B. Our Monte Carlo code self-consistently calculates the photon and neutrino spectra corresponding to individual pulses in the GRB prompt emission in a one-zone approximation, including all relevant leptonic and hadronic processes \citep{asa09b}. ." + More detailed descriptions of the code can be found in a series of previous publications (Asano2005: 2009). ," More detailed descriptions of the code can be found in a series of previous publications \citep{asa05,asa06,asa07,asa09}. ." +In this work.," In this work," +5.,. +" In order to produce the dashed: curves. representative values. estimated from the simmlatious. were nserted for the eradients Vlup and Vlu é44,. namely 1.5 and 1.0 in the unstable laver. and 1.0 and =23.5 in the stable laver (Fig.3"," In order to produce the dashed curves, representative values, estimated from the simulations, were inserted for the gradients $\na\ln\rho$ and $\na\ln u_{\rms}$ , namely $1.5$ and $-1.0$ in the unstable layer, and $1.0$ and $-3.5$ in the stable layer (Fig.," +. row L)., row 4). + For a given Tavlor uumuber. the same value of Co was used for both the unstable laver aud the stable laver. ie the turnover time. ττε{(aus. Was assunied to be the same.," For a given Taylor number, the same value of $\mb{Co}$ was used for both the unstable layer and the stable layer, i.e. the turnover time, $\tau\approx\ell/u_{\rms}$, was assumed to be the same." + This is motivated * the fact that both the effective thickness. ἐν aud μι. for the stable laver are sanaller bv a factor 31 compared to their values in the unstable laver.," This is motivated by the fact that both the effective thickness, $\ell$, and $u_{\rms}$ for the stable layer are smaller by a factor 3–4 compared to their values in the unstable layer." + Secondly. the temporal variatious of the flow are very similar in both lavers (Fig.2," Secondly, the temporal variations of the flow are very similar in both layers (Fig.," +. bottom)., bottom). + After ividing Eqs. (32), After dividing Eqs. ) + and (33) by day... a factor ΤΕ rouains oe1i front which can be assume to be iudepeudoeu of Co.," and ) by $u_{\rms}$, a factor $\tau u_{\rms}$ remains in front which can be assumed to be independent of $\mb{Co}$." + ILloever. it was fouud tha setting this factor to rug=f overestimates the amplitude of a.," However, it was found that setting this factor to $\tau u_{\rms}=\ell$ overestimates the amplitude of $\alpha$." + For the dashecοον VArown in Fig.5," For the dashedcurves shown in Fig.," +. it was replaced by a suitable uniform scaling factor. namely 0.19 for ay aud 0.01 for ayy.," it was replaced by a suitable uniform scaling factor, namely $0.19$ for $\alpha_{\rm V}$ and $0.01$ for $\alpha_{\rm H}$." + Thus. our simulations produce much sinaller a coefficieuts thui oxedieted by (32) aud (33). especially ay which is smaller o» two orders of magnitude.," Thus, our simulations produce much smaller $\alpha$ coefficients than predicted by ) and ), especially $\alpha_{\rm H}$ which is smaller by two orders of magnitude." + Ou the other haud. the uain poiut is the agreement with regard to the rotational dependence.," On the other hand, the main point is the agreement with regard to the rotational dependence." + Except for the sien of ay in the unstable aver. the rotational quenching is reproduced. including he position of the maxima.," Except for the sign of $\alpha_{\rm V}$ in the unstable layer, the rotational quenching is reproduced, including the position of the maxima." + For weak rotation. oyzmLev. so that the coutribution of Vlay... dominates. while for Co£2 the deusitv eradicut dominates: in both cases the neau-field formula vields the wrong negative sign.," For weak rotation, $\psi_{\rm V}^u\approx 4\psi_{\rm V}^{\rho}$, so that the contribution of $\na\ln u_{\rms}$ dominates, while for $\mb{Co}\ga 2$ the density gradient dominates; in both cases the mean-field formula yields the wrong negative sign." + Clearly. he sien of ay as predicted by Eq. (32)," Clearly, the sign of $\alpha_{\rm V}$ as predicted by Eq. )" + can have both values in principle. aud. depends in a delicate wav on the relative importance of the two gradients:O even a slighto change of the c coefficients can generate a sign chauco.," can have both values in principle, and depends in a delicate way on the relative importance of the two gradients; even a slight change of the $\psi$ coefficients can generate a sign chance." + With regard to αμ. we confiii the saturation predicted by Eq. (33)," With regard to $\alpha_{\rm H}$, we confirm the saturation predicted by Eq. )" + only iu the stably stratified laver. but not (vet) in the nustable laver (Fig.," only in the stably stratified layer, but not (yet) in the unstable layer (Fig." +5. bottom)., bottom). + Apart fro this. the eeneral trend as well as the correct sigus are reproduced by (33) in both lavers.," Apart from this, the general trend as well as the correct signs are reproduced by ) in both layers." + Due to the shape of the functions cm. this feature should be rather robust.," Due to the shape of the functions $\psi_{\rm H}^{\rho,u}$, this feature should be rather robust." + Tn order to shed further Leht ou the infiuence of rotation. Fig.," In order to shed further light on the influence of rotation, Fig." + shows snapshots of the vertical velocity for two παπαΊος with different rotation rates., shows snapshots of the vertical velocity for two simulations with different rotation rates. + Clearly. strouser rotation causes the eddies to have a πα diameter in the horizoutal plane G.c. perpendicular to the rotation axis).," Clearly, stronger rotation causes the eddies to have a smaller diameter in the horizontal plane (i.e. perpendicular to the rotation axis)." + Uence the umber of eddies within the simulation domain iucreases with therotation rate. aud this leads to a more accurate result for à. as ds obvious from the length of the error bars in Fig. 5," Hence the number of eddies within the simulation domain increases with therotation rate, and this leads to a more accurate result for $\alpha$ , as is obvious from the length of the error bars in Fig. ," +.taking,taking +The kinematic parameters were determined [or the entire sample of 340 GCs. as well as the subpopulations of 178 metal-poor and 158 metal-rich GCs (four clusters have unknown metalliitv).,"The kinematic parameters were determined for the entire sample of 340 GCs, as well as the subpopulations of 178 metal-poor and 158 metal-rich GCs (four clusters have unknown metallicity)." + The kinematic results lor the entire population of GC's are shown in Table 2.. reproduced almost in full from Woodley(2006).. while the restuts for the metal-poor and metal-rich clusters ave shown in Tables 3. 4... respectively.," The kinematic results for the entire population of GCs are shown in Table \ref{tab:all_GC}, reproduced almost in full from \cite{w06}, while the results for the metal-poor and metal-rich clusters are shown in Tables \ref{tab:MP_GC} + \ref{tab:MR_GC}, respectively." + The columns give the radial bin. the mean projected radius in the bin. (he radius of the oulermost cluster. (he number of clusters in the bin. (he rotation amplitude. the rotation axis. aud the velocity dispersion. with associated uncertainties.," The columns give the radial bin, the mean projected radius in the bin, the radius of the outermost cluster, the number of clusters in the bin, the rotation amplitude, the rotation axis, and the velocity dispersion, with associated uncertainties." + These are followed by the mass correction. tlie pressure-supported mass. (he rotationally supported mass. and (he (total mass in units of solar mass (see 5 for the mass discussion).," These are followed by the mass correction, the pressure-supported mass, the rotationally supported mass, and the total mass in units of solar mass (see \ref{sec:dyn} for the mass discussion)." + The results for (he alternate (wo methods. using an equal number of GCs per bin aud (the exponentially weighted GCs. are not shown in tabular form but are included in all of the figures.," The results for the alternate two methods, using an equal number of GCs per bin and the exponentially weighted GCs, are not shown in tabular form but are included in all of the figures." + Figure 4 shows the sine fit of Equ., Figure \ref{fig:kin_plot} shows the sine fit of Eqn. + 1. for the total population and for the metal-poor and metal-rieh. subpopulations., \ref{eqn:kin} for the total population and for the metal-poor and metal-rich subpopulations. + All three populations show rotation about a similar axis., All three populations show rotation about a similar axis. + As diseussed in 3.1.. the metal-poor population has more members with low velocities (V.<300 km !) than the metal-rich population. suggesting possible contamination of Milky Way foreground stars in the sample.," As discussed in \ref{sec:velfield}, the metal-poor population has more members with low velocities $V_r \leq 300$ km $^{-1}$ ) than the metal-rich population, suggesting possible contamination of Milky Way foreground stars in the sample." + Figures 5 6 show the rotation amplitude results for the entire population aud for the metal-poor ancl metal-rich subpopulations. respectively.," Figures \ref{fig:rotamp_final} \ref{fig:rotamp_metal} show the rotation amplitude results for the entire population and for the metal-poor and metal-rich subpopulations, respectively." + The three kinematic methods. described in Section 3.2.1.. appear lo agree relatively well for all (νου populations ofclusters.," The three kinematic methods, described in Section \ref{sec:math}, appear to agree relatively well for all three populations of clusters." + While there appears {ο be no extreme cliflerence in rotation amplitude between (he cluster populations. the metal-poor subpopulation of clusters has lower rotation in the inner 5 kpc ol NGC 5128 than the metalrich subpopulation.," While there appears to be no extreme difference in rotation amplitude between the cluster populations, the metal-poor subpopulation of clusters has lower rotation in the inner 5 kpc of NGC 5128 than the metal-rich subpopulation." + The weighted average of (he 0-5 kpe radial bin and the innermost ecqual-iumbered bin. shows that the entire population has a rotation amplitude of OR231z17km |. while the metal-poor population has OA=17+26 km stand the metal-rich population has QR=57+22 kins +.," The weighted average of the 0-5 kpc radial bin and the innermost equal-numbered bin, shows that the entire population has a rotation amplitude of $\Omega R = 31\pm17$km $^{-1}$, while the metal-poor population has $\Omega R = 17\pm26$ km $^{-1}$ and the metal-rich population has $\Omega R = 57\pm22$ km $^{-1}$." + Peng. show in (heir study. that the metal-poor population has very little rotation in the central regions. Completely consistent wilh our findings.," \cite{pff04II} show in their study that the metal-poor population has very little rotation in the central regions, completely consistent with our findings." + The rotation amplitude does not appear to differ between the (vo populations outside of 5 kpe., The rotation amplitude does not appear to differ between the two populations outside of 5 kpc. + The results of the rotation axis solutions are shown in Figures 7 &.. again for the entire population and for the metal-poor and metalrich subpopulations.," The results of the rotation axis solutions are shown in Figures \ref{fig:rotaxis_final} \ref{fig:rotaxis_metal}, , again for the entire population and for the metal-poor and metal-rich subpopulations." + The solution [or, The solution for +This expression sets the effective temperature of the star and its cooling rate Fy as functions of AL. Ry and opacity behavior.,"This expression sets the effective temperature of the star and its cooling rate $F_0$ as functions of $M_\star$, $R_\star$ and opacity behavior." + Iu particular. for # typical at temperatures below 5000 I& one finds using equation (60)) that 1200 RHÜ.," In particular, for $\kappa$ typical at temperatures below $5000$ K one finds using equation \ref{eq:K_3_2}) ) that 1200 ." + This is considerably znaller than Τετ2000|£000 Ts typical for au isolated fully convective star on the Hayashi track that one obtains with detailed nunerical stellar structure calculations (Siess 2000)., This is considerably smaller than $T_{eff}\approx 3000-4000$ K typical for an isolated fully convective star on the Hayashi track that one obtains with detailed numerical stellar structure calculations (Siess 2000). + We ascribe this difference to our adoption of fixed 5 throughout the whole star aud the neglect of superadiabaticitv iu the outer parts of the couvective region. see 85.2..," We ascribe this difference to our adoption of fixed $\gamma$ throughout the whole star and the neglect of superadiabaticity in the outer parts of the convective region, see \ref{sect:complications}." +" At the sale time equation (63)) captures the main property of the Tavashi track = extremely weak seusitivitv of 7j to R, aud. consequently. stellar Iuninosity."," At the same time equation \ref{eq:Hayashi}) ) captures the main property of the Hayashi track – extremely weak sensitivity of $T_0$ to $R_\star$ and, consequently, stellar luminosity." + Tf we now eo back to equation (55)) one can easily see that it can be rewritten asὃν or. with equation (15)). as CST," If we now go back to equation \ref{eq:F_in}) ) one can easily see that it can be rewritten as, or, with equation \ref{eq:balance}) ), as )^4." + This result together with (58)) once again vividly ilustrates the inhibition of stellar cooling bv external radiation aud specifies the magnitude of this effect., This result together with \ref{eq:4xi}) ) once again vividly illustrates the inhibition of stellar cooling by external irradiation and specifies the magnitude of this effect. +" Using equations (53)) aud (61)) we can also writex which shows that VjLo when stellar surface is strongly irradiated (2,4,2 Ty). tlus confirming equation (17))."," Using equations \ref{eq:nab_ph}) ) and \ref{eq:Fin}) ) we can also write, which shows that $\nabla_{ph}\ll 1$ when stellar surface is strongly irradiated $T_{ph}\gtrsim T_0$ ), thus confirming equation \ref{eq:nabla_cond}) )." +" Note the stroug depeudence of Vj, ou Typ/To: with our power-law auzatz for opacity &©13/2 and =13 below and above 5000 I& correspoucinely. see equations (329) and (31))."," Note the strong dependence of $\nabla_{ph}$ on $T_{ph}/T_0$: with our power-law anzatz for opacity $\xi\approx 13/2$ and $\approx 13$ below and above $5000$ K correspondingly, see equations \ref{eq:low_T}) ) and \ref{eq:high_T}) )." + Iu Appendix D.sve determine the circumstances under which the results of 83.1. hold tzue., In Appendix \ref{ap:1D_validity} we determine the circumstances under which the results of \ref{sect:1D} hold true. + We show there that the coudition of the validity of 1D approximation cau be expressed as where Ly is a characteristic scale in 0 direction over which the external boundary couditiou jin our case Tih(0 experiences variation., We show there that the condition of the validity of 1D approximation can be expressed as where $L_\theta$ is a characteristic scale in $\theta$ direction over which the external boundary condition [in our case $T_{ph}(\theta)$ ] experiences variation. + Equation (5)) aud Figure 2 demonstrate that in the case of radiation by accretion disk Ly~R.., Equation \ref{eq:irr_flux}) ) and Figure \ref{fig:irr_flux} demonstrate that in the case of irradiation by accretion disk $L_\theta\sim R_\star$. +" Then equations (53)) and (61)) allow us to rewrite the condition (67)) as (assumuine that Zy aud Tj, ave i the suue opacity regine) where Hyρου(gry) is the photosphienrie scale heightin the absence of raciation."," Then equations \ref{eq:nab_ph}) ) and \ref{eq:Fin}) ) allow us to rewrite the condition \ref{eq:validity}) ) as (assuming that $T_0$ and $T_{ph}$ are in the same opacity regime) , where $H_0=k_B T_0/(\mu g)$ is the photospheric scale heightin the absence of irradiation." +" Caven that Ree ART, we nav conclude that LD approximation should be rather accurate even it Zn, exceeds Tj by a factor of several (c.g. Ty,Z1T for Tτς5000 Is).", Given that 10^3 M_1 we may conclude that 1D approximation should be rather accurate even if $T_{ph}$ exceeds $T_0$ by a factor of several (e.g. $T_{ph}\lesssim 7 T_0$ for $T\lesssim 5000$ K). + Whenever the condition (67)) is violated the redistribution of cuerey in @-direction within the radiative laver becomes iniportaut., Whenever the condition \ref{eq:validity}) ) is violated the redistribution of energy in $\theta$ -direction within the radiative layer becomes important. + Iu this case oue needs to solve the full two-dimensional equation (21)) without assunudne that radiative flux iu 0 direction is small., In this case one needs to solve the full two-dimensional equation \ref{eq:rad_tran}) ) without assuming that radiative flux in $\theta$ direction is small. + A sinular situation arises at stellar equator where a lot of cherev is released iu a boundary laver that is uot very extended in 0 direction. (Popham 1993)., A similar situation arises at stellar equator where a lot of energy is released in a boundary layer that is not very extended in $\theta$ direction (Popham 1993). +" As a result. at equator LyR, aud the coudition (67)) can be violated there even though at all other latitudes 1D approxituation works fine."," As a result, at equator $L_\theta\ll R_\star$ and the condition \ref{eq:validity}) ) can be violated there even though at all other latitudes 1D approximation works fine." +" We are now iu position to calculate the iutegrated lutrinsic Duumositv £ (due to stellar contraction and interior cooling) of a couvective star that is mradiated by a cmeunmstellar disk: £;,(00)). where £;,(0) is given bv the expression (55))iu the iradiated part of the stellar surface. for 0Z 0;,,. while FU)xoTi in the weakly inadiated polar regious. for Oy. O"," We are now in position to calculate the integrated intrinsic luminosity $L$ (due to stellar contraction and interior cooling) of a convective star that is irradiated by a circumstellar disk: ), where $F_{in}(\theta)$ is given by the expression \ref{eq:F_in}) )in the irradiated part of the stellar surface, for $\theta\gtrsim\theta_{irr}$ , while $F_{in}(\theta)\approx +\sigma T_0^4$ in the weakly irradiated polar regions, for $\theta\lesssim\theta_{irr}$ ." +SConvective objects can exhibit different modes of cooling which is best illustrated by considering the limit Din ACAc9 1)., Convective objects can exhibit different modes of cooling which is best illustrated by considering the limit $\theta_{irr}\ll 1$ $\Lambda\gg 1$ ). + Tn this limit the contribution of polar caps tothe total Iuninositv is IxFjf, In this limit the contribution of polar caps tothe total luminosity is F_0 + Tn this limit the contribution of polar caps tothe total Iuninositv is IxFjfü, In this limit the contribution of polar caps tothe total luminosity is F_0 + Tn this limit the contribution of polar caps tothe total Iuninositv is IxFjfüu, In this limit the contribution of polar caps tothe total luminosity is F_0 + Tn this limit the contribution of polar caps tothe total Iuninositv is IxFjfüul, In this limit the contribution of polar caps tothe total luminosity is F_0 +as are many of the close gas giants that have been discovered recently around nearby stars.,as are many of the close gas giants that have been discovered recently around nearby stars. + We construct a dynamical model of the ONC. implemented using Aarseth’s code (Aarscth2000).. consisting of 4000 stars. and starting from a density. distribution going as r7.," We construct a dynamical model of the ONC, implemented using Aarseth's code \cite{Aar00}, consisting of 4000 stars, and starting from a density distribution going as $r^{-2}$." + Except where stated otherwise (in the discussion of Figure 3)). the results shown refer to a cluster in. virial equilibrium. with a half-mass radius of ~1 pc. and in all cases the initial conditions are chosen to match the appearance of the ONC after an evolution time of 23 Myr (a [ow crossing times).," Except where stated otherwise (in the discussion of Figure \ref{F:coldfrac}) ), the results shown refer to a cluster in virial equilibrium with a half-mass radius of $\sim 1$ pc, and in all cases the initial conditions are chosen to match the appearance of the ONC after an evolution time of 2–3 Myr (a few crossing times)." + Phe mass function used is that of Ixroupa. Tout Cilmore (1093).. and the three most massive stars are assigned the UV Ilux parameters specified in the previous section («b;= 2.6. 0.2 and 0.05).," The mass function used is that of Kroupa, Tout Gilmore \shortcite{KroTouGil93}, and the three most massive stars are assigned the UV flux parameters specified in the previous section $\Phi_{\mathrm{i}} =$ 2.6, 0.2 and 0.05)." + Of these. the most massive is placed at the cluster centre. while the other two are given random initial locations.," Of these, the most massive is placed at the cluster centre, while the other two are given random initial locations." + Several random realisations of this setup were generated and run. but no statistically significant variations were found. and the results presented here for one particular model are characteristic of all those generated.," Several random realisations of this setup were generated and run, but no statistically significant variations were found, and the results presented here for one particular model are characteristic of all those generated." + To model photoevaporation. we run two series of simulations.," To model photoevaporation, we run two series of simulations." + In the first we are interested in the distribution of proplves (in the FUV-dominated. region) and for every star in the cluster. so we keep track of three things during the course of the simulation: We then use the first two of these in (1) and. (2) to evaluate the total mass lost by cach star cue to photoevaporation during its life in the cluster by assuming a fixed disk radius for all the svstems throughout - which we take to be 100 AU.," In the first we are interested in the distribution of proplyds (in the FUV-dominated region) and for every star in the cluster, so we keep track of three things during the course of the simulation: We then use the first two of these in (1) and (2) to evaluate the total mass lost by each star due to photoevaporation during its life in the cluster by assuming a fixed disk radius for all the systems throughout - which we take to be 100 AU." + The assumption that the disk radii remain [fixed throughout is a simplification. since in reality it is likely that the disks will decrease in size as they lose mass through evaporation.," The assumption that the disk radii remain fixed throughout is a simplification, since in reality it is likely that the disks will decrease in size as they lose mass through evaporation." + This would in turn lead to a reduction in the mass loss rate. which scales with the disk radius r4 in both the EUV and EUM regimes. as shown in (1) and (2).," This would in turn lead to a reduction in the mass loss rate, which scales with the disk radius $r_{\mathrm{d}}$ in both the EUV and FUV regimes, as shown in (1) and (2)." + Johnstone. Hollenbach Bally (1998) calculate. the implied. variation with time / (at a fixed distance from the ionising star) as rax/ (EUV) and rax£? (PUY) fora clisk whose surface density goes as ri. and assuming that the disk is unable to replenish the outer regions from which material evaporates.," Johnstone, Hollenbach Bally \shortcite{JohHolBal98} + calculate the implied variation with time $t$ (at a fixed distance from the ionising star) as $r_{\mathrm{d}} \propto t^{-1}$ (EUV) and $r_{\mathrm{d}} \propto t^{-2}$ (FUV) for a disk whose surface density goes as $r^{-3/2}$, and assuming that the disk is unable to replenish the outer regions from which material evaporates." + Direct measurements of disk radii are dillicult to make. and to a certain extent depend. on the wavelength one observes at.," Direct measurements of disk radii are difficult to make, and to a certain extent depend on the wavelength one observes at." + However. estimates for various proplyds in the ONC (Johnstone.Hollenbach&Bally1998). vary from. 20 το SO AU. and are in agreement with the mocdoel's predictions taking into account the size of the ionisation front stancd-olf and the distance to tin each case (Stórzer&Lollenbach1999).," However, estimates for various proplyds in the ONC \cite{JohHolBal98} vary from 20 to 80 AU, and are in agreement with the model's predictions taking into account the size of the ionisation front stand-off and the distance to in each case \cite{StoHol99}." +. Civen this. and the possibility that the disks might have been much leer in the past if they have already sullered a long period. of photoevaporation. we take a fixed. value of 10) AU for these objects as a simplifving assumption which wi underestimate the total mass evaporated to date.," Given this, and the possibility that the disks might have been much larger in the past if they have already suffered a long period of photoevaporation, we take a fixed value of 100 AU for these objects as a simplifying assumption which will underestimate the total mass evaporated to date." + Le woul of course be possible to repeat our calculations while also keeping track of the disk size for cach svstem. but this would necessitate making an assumption about their initia size as well as incorporating the assumption that there is no viscous replenishment of the outer disk.," It would of course be possible to repeat our calculations while also keeping track of the disk size for each system, but this would necessitate making an assumption about their initial size – as well as incorporating the assumption that there is no viscous replenishment of the outer disk." + This woul seem to be unwarranted in the light of our finding (later in this section) that the mass loss assumption already. implies unacceptably large initial clisk massses for the proplyds., This would seem to be unwarranted in the light of our finding (later in this section) that the mass loss assumption already implies unacceptably large initial disk massses for the proplyds. + 1n the second. series of simulations we are interested in mass loss from the planet-forming region of the disk. i.c. the inner 10 AU.," In the second series of simulations we are interested in mass loss from the planet-forming region of the disk, i.e. the inner $\sim$ 10 AU." + We assume that there is no FUV-driven mass loss [rom this region. which is true for any star more massive than ~0.2 ((more than 60 per cent of cluster stars) πο that for each star we only need to keep track of the time-integratecl value of Vdfd? for all three UV. sources., We assume that there is no FUV-driven mass loss from this region – which is true for any star more massive than $\sim 0.2$ (more than 60 per cent of cluster stars) – so that for each star we only need to keep track of the time-integrated value of $\sqrt{\Phi_{\mathrm{i}} / d^2}$ for all three UV sources. + This is converted to à mass loss in (2) by setting ry=LOA.," This is converted to a mass loss in (2) by setting $r_{\mathrm{d}} = 10\,\mbox{AU}$." + Once again the fixed disk raclius assumption is a simplification. which in this case will overestimate the mass loss [rom the disk region we are interested in. (," Once again the fixed disk radius assumption is a simplification, which in this case will overestimate the mass loss from the disk region we are interested in. (" +We assume that the existence of disk material at radii greater than LO AU does not increase the mass loss rate within that raclius.),We assume that the existence of disk material at radii greater than 10 AU does not increase the mass loss rate within that radius.) + Figure | shows a histogram of mass loss due to photocvaporation after 2.89. Myr (roughly the ONC's current age) in the case where the disks are LOO AU in radius., Figure \ref{F:phothist100AU} shows a histogram of mass loss due to photoevaporation after 2.89 Myr (roughly the ONC's current age) in the case where the disks are 100 AU in radius. + We see that almost all svstems have lost. more than 0.01AL... The rightmost bin contains svstems which have spent heir whole time in Ori's EUV dominated region.," We see that almost all systems have lost more than 0.01, The rightmost bin contains systems which have spent their whole time in 's FUV domimated region." + ligure 2. shows. at various times during the life ofOri.. the percentage ofstars in the central projected 1.15 pe of the cluster which are proplvels. as a function of the initial clisk mass (assuming all disks are equal initially).," Figure \ref{F:propfrac} shows, at various times during the life of, the percentage of stars in the central projected 0.15 pc of the cluster which are proplyds, as a function of the initial disk mass (assuming all disks are equal initially)." + A »oplvd in this context is a star in an FUV-dominated region with some circumstellar disk: matter remaining (ancl recall hat the racius of EUV-dominated region is 0.3 2ο)., A proplyd in this context is a star in an FUV-dominated region with some circumstellar disk matter remaining (and recall that the radius of s FUV-dominated region is 0.3 pc). +" At the start of the simulation (or immediately after the massive stars formed if that were dillerent). all stars in the central 0.3 pe (in 3D) would be proplyvels. corresponding to zNÜ per cent of the stars within 0.15 pc in projection. given 16 ONC'""s density distribution."," At the start of the simulation (or immediately after the massive stars formed if that were different), all stars in the central 0.3 pc (in 3D) would be proplyds, corresponding to $\ga 80$ per cent of the stars within 0.15 pc in projection, given the ONC's density distribution." + But low mass disks are very dickly destroyed. and to mateh the observed. distribution X proplvds at the ONC's present age requires a high initial isk mass 0.6NL; in Figure 2)) for these stars. (," But low mass disks are very quickly destroyed, and to match the observed distribution of proplyds at the ONC's present age requires a high initial disk mass $0.6\,\msol$ in Figure \ref{F:propfrac}) ) for these stars. (" +Note iu these initial disc masses would have to be even higher -- Save were to include the effect of evaporation reducing the isk rac and mass loss rates.),Note that these initial disc masses would have to be even higher if we were to include the effect of evaporation reducing the disk radii and mass loss rates.) +he probability. distributions iu 3-D paramcter space. selecting all the cases for which 4?Gu«cd (lo confidence level).,"the probability distributions in 3-D parameter space, selecting all the cases for which $\chi^2 -\chi_{min}^2< 1$ $\sigma$ confidence level)." + To eusure a reliable estimate of hese errors we ueed enoueh triplets satisfvius the 4? condition., To ensure a reliable estimate of these errors we need enough triplets satisfying the $\chi^2$ condition. + After many tests we decided to sample the xuanmeter space with 16 million poiuts: 100 fay « 100 (3) s 1600 (5)., After many tests we decided to sample the parameter space with 16 million points: 100 $\alpha$ ) $\times$ 100 $\beta$ ) $\times$ 1600 $\gamma$ ). + This way. for cach fit. we suuple the > yaraeter space with au average bin of 0.001ς101* erg tem 7 aud we obtain ~LOO triplets satisfying the X7. with a minium of 15 (for the QSO BR 1033.0327).," This way, for each fit, we sample the $\gamma$ parameter space with an average bin of $0.001\times 10^{-17}$ erg $^{-1}$ $^{-2}$ and we obtain $\sim 100$ triplets satisfying the $\chi^2$, with a minimum of 15 (for the QSO BR $1033-0327$ )." + This condition is not satisfied for JO8030019À.17): iu this case the nunuajor features are severcly affected by the telluric absorptions. resulting iu a weaker coustraiut outhe template normalization which is in any case consistent with 0 (see Tab. 3)).," This condition is not satisfied for $0303-0019$: in this case the major features are severely affected by the telluric absorptions, resulting in a weaker constraint onthe template normalization which is in any case consistent with 0 (see Tab. \ref{tab_fit}) )." + Iu Fig., In Fig. + 3.1 we show two examples of the 3D \?-cube projections aud of the relative probability distribution for the teiiplate norinalization (simular plots for all sources discussed here are shown iu the online Appenclix)., \ref{fig_fit_errors} we show two examples of the 3D $\chi^2$ -cube projections and of the relative probability distribution for the template normalization (similar plots for all sources discussed here are shown in the online Appendix). + The \P-amaps are overall regular (non-pateliv). implying he absence of secondary local minima.," The $\chi^2$ -maps are overall regular (non-patchy), implying the absence of secondary local minina." + The degeueracy )etwoeen power-law slope aud intercept is evident from he bottom-right plots in the two paucls., The degeneracy between power-law slope and intercept is evident from the bottom-right plots in the two panels. + The fitted components are then subtracted and we xoceed to ft the eemussion line., The fitted components are then subtracted and we proceed to fit the emission line. + The Tine fit ix performed with a least-squares procedure., The line fit is performed with a least-squares procedure. + Since 16 ddoublet is not resolved in the majority of our spectra. we model the emission line as a simple Cussiau (three free parameters: central wavelength. width aud πολλασαΠοια).," Since the doublet is not resolved in the majority of our spectra, we model the emission line as a simple Gaussian (three free parameters: central wavelength, width and normalization)." + If there was a siguificaut narrow second conrponeut that we do not resolve. this would lead to a slight uuderestinate of the black-hole mass.," If there was a significant narrow second component that we do not resolve, this would lead to a slight underestimate of the black-hole mass." + Exaiples of the spectral decomposition are shown iu Fie. 3.L., Examples of the spectral decomposition are shown in Fig. \ref{fig_new}. + The results of the fit aud relative \? maps for the literature suuple are shown in the ouline Appcucix., The results of the fit and relative $\chi^2$ maps for the literature sample are shown in the online Appendix. + The fitted parineters are listed in Tab. 3.., The fitted parameters are listed in Tab. \ref{tab_fit}. + Even if we do not overcome the degeneracy between the power-law slope aud intercept. we cau compare the distribution of our local slope estimates with those in the literature.," Even if we do not overcome the degeneracy between the power-law slope and intercept, we can compare the distribution of our local slope estimates with those in the literature." + We obtain à mean value à=1.5+1.2 which is iu agreement within the uncertainties with both the local slope estimate by and with the elobal oue by(2010)., We obtain a mean value $\alpha=-1.5\pm1.2$ which is in agreement within the uncertainties with both the local slope estimate by and with the global one by. +. We estimate. the using scaling relations. calibrated om local ACNs. that are based. ou broad Cluission line widths aud coutiunuai buwinosities.," We estimate the using scaling relations, calibrated on local AGNs, that are based on broad emission line widths and continuum luminosities." + Uuder the assumnuption that the dvuamics of the broad line region is donunated bv the eravitv of the central DII. the virial theorem states: where dis the black hole mass. Πρες is the characteristic radius of the BER aud ορ7 is the orbital velocity of the clouds cimitting at Rppr.," Under the assumption that the dynamics of the broad line region is dominated by the gravity of the central BH, the virial theorem states: where is the black hole mass, $R_{BLR}$ is the characteristic radius of the BLR and $v_{BLR}$ is the orbital velocity of the clouds emitting at $R_{BLR}$ ." + The cloud velocity can be obtained from the width of the broad Cluission lines: epre=foBVITAL. where f is a ecolctrical factor that accounts for the de-projection of eprg frou the line of sight2008).. and PWOIAL is the full width at half maxima of the line profile.," The cloud velocity can be obtained from the width of the broad emission lines: $v_{BLR} = f \cdot +FWHM$, where $f$ is a geometrical factor that accounts for the de-projection of $v_{BLR}$ from the line of sight, and FWHM is the full width at half maximum of the line profile." + Even if the DER. size cannot be directly measured by sinele epoch spectra. it can still be evaluated since it is strongly correlated with the coutimmun luminosity of the AGN2000).," Even if the BLR size cannot be directly measured by single epoch spectra, it can still be evaluated since it is strongly correlated with the continuum luminosity of the AGN." +. It is then possible to estimate for high-redshift QSOs using a single spectrum covering the blended Hine doublet (A=2795.2803. À)) and the redward contiuuuau (A=3000 Aj).," It is then possible to estimate for high-redshift QSOs using a single spectrum covering the blended line doublet $\lambda=2795,2803$ ) and the redward continuum $\lambda=3000$ )." + Iu particular for Πρι we use the relation provided by(2002): and for the ecolmctrical actor the value provided by(2008):: FOAL W=1.6. obtainedassumingthatthe aandI -eauittine regious have a similar geometry.," In particular for $R_{BLR}$ we use the relation provided by: and for the geometrical factor the value provided by: $f($ $)=1.6$, obtained assuming that the and -emitting regions have a similar geometry." + All these relations are based on low redshift objects (2<0.3). and the underline assuuptiou here is that they are still valid at hielivedshift.," All these relations are based on low redshift objects $z<0.3$ ), and the underlying assumption here is that they are still valid at high-redshift." + Using relation (1)) reproduced obtained with the full reverberation mapping method with au accuracy of 0.1 dex., Using relation \ref{eq_mass_1}) ) reproduced obtained with the full reverberation mapping method with an accuracy of 0.4 dex. + This intrinsic scatter of the estimator dominates the measurement uncertaiuties., This intrinsic scatter of the estimator dominates the measurement uncertainties. + To compare our resultswith the ones published iu previous works on :~6 sources2009).. we also estimate wusing the relation obtained by 1):: froii a suuple of 17 low redshift ACNs (20.7). with Iuiinosities comparable to those of high-z QSOs (ALA>10H eve 1).," To compare our resultswith the ones published in previous works on $z\sim6$ sources, we also estimate using the relation obtained by : from a sample of 17 low redshift AGNs $z<0.7$ ), with luminosities comparable to those of high-z QSOs $\lambda L_\lambda> 10^{44} $ erg $^{-1}$ )." +" Frou the estimated we compute the QSO Eddington ratios defined as the ratio between the measured bolometric Wuuinesity L5, aud the theoretical Eddington hunuinositv Lg. as Compted from theMp."," From the estimated we compute the QSO Eddington ratios defined as the ratio between the measured bolometric luminosity $L_{bol}$ and the theoretical Eddington luminosity $L_{Edd}$, as computed from the." + We obtain the observed monochronmatic luuinosity ALAGOOQDA) from the continu compoueut of the fit fx\(B000A) aud from the luuinosity «istance Dry as: Since L(3000A) is only a. fracion of the total electromagnetic huuinositv come ron the QSO. we apply the bolometric correction bv to obtain L4: The Eddingtou luminosity is defiuc vas the maxima huuinosity attaimable. at which the radiation pressure acting ou the eas counterbalances the eravitational attraction of the DII: The obtained aud the relativeQSO Eddington ratios are listed in Tab. L..," We obtain the observed monochromatic luminosity $\lambda L_\lambda(3000 \rm{\AA})$ from the continuum component of the fit $f_\lambda(3000 \rm{\AA})$ and from the luminosity distance $D_L$ as: Since $L(3000 \rm{\AA})$ is only a fraction of the total electromagnetic luminosity coming from the QSO, we apply the bolometric correction by to obtain $L_{bol}$: The Eddington luminosity is defined as the maximum luminosity attainable, at which the radiation pressure acting on the gas counterbalances the gravitational attraction of the BH: The obtained and the relativeQSO Eddington ratios are listed in Tab. \ref{tab_mass}. ." + Thetwo relations. Eq.," Thetwo relations, Eq." + 1 and Eq. 5..," \ref{eq_mass_1} and Eq. \ref{eq_mass_2}, ," + lead to a difference in the mass estimates, lead to a difference in the mass estimates +For this paper. we needed to estimate the probability of finding seven DIID stars in a restricted portion of 1b.Vase.go parameter space.,"For this paper, we needed to estimate the probability of finding seven BHB stars in a restricted portion of $l,b,V_{\mbox{\it gsr}},g_0$ parameter space." + In this appendix. we present a solution to the more general. problem of determining the probability of finding A of N data points in a small portion ofa d-dimensional space.," In this appendix, we present a solution to the more general problem of determining the probability of finding $K$ of $N$ data points in a small portion of a $d$ -dimensional space." + Suppose one analyses of a set of JN. data points in a large d-cdimensional hypercube 2h).Bi]0sssooaBu]. and finds a small. axis-alignecl. d-dimensional hypercube ay.bi]--‘ayba] that has A2 data points in it.," Suppose one analyses of a set of $N$ data points in a large $d$ -dimensional hypercube $[A_1, B_1] \times \ldots \times [A_d, B_d]$, and finds a small, axis-aligned, $d$ -dimensional hypercube $[a_1, b_1] \times \ldots +\times [a_d, b_d]$ that has $K \ge 2$ data points in it." + The naturalquestion is whether this “clump” of A data points is statistically significant. or whether even random data would vield such a clump.," The natural question is whether this “clump” of $K$ data points is statistically significant, or whether even random data would yield such a clump." + Here we precisely estimate an {εναιο for the expected number of clumps. thus providing an upper bound to the probability that. random. data would somewhere have A or more data points within an axis-aligned. d-dimensional hypercube with dimensions TNπι)(οιaye...byag).," Here we precisely estimate an $E$ -value for the expected number of clumps, thus providing an upper bound to the probability that random data would somewhere have $K$ or more data points within an axis-aligned, $d$ -dimensional hypercube with dimensions $(w_1, \ldots, +w_d) = (b_1 - a_1, \ldots, b_d - a_d)$." + We start with the simple case where a full data set of NV points lies within a dimensional unit hypercube 0.1]..," We start with the simple case where a full data set of $N$ points lies within a $d$ -dimensional unit hypercube $[0,1]^d$." + We further assume that a random (or null) model would distribute these No points uniformly. within the hypercube., We further assume that a random (or null) model would distribute these $N$ points uniformly within the hypercube. +" Additionally, we assume that the hypercube is not periodic/toroidal."," Additionally, we assume that the hypercube is not periodic/toroidal." + We relax these simplifving assumptions in subsequent sections., We relax these simplifying assumptions in subsequent sections. +" We sav that an axis-aligned. d-dimensional hypercube contained within 0.1]"" is aa. Me say that a set of A2bor ofthe IN. points is a if there exists a box that contains the A points without containing any of the remaining ;Vdv points."," We say that an axis-aligned, $d$ -dimensional hypercube contained within $[0,1]^d$ is a. We say that a set of $K \ge 2$ of the $N$ points is a if there exists a box that contains the $K$ points without containing any of the remaining $N-K$ points." + We define the lor a ἐν-boxed set as the intersection of all boxes that contain the A. points., We define the for a $K$ -boxed set as the intersection of all boxes that contain the $K$ points. + A box of dimensions (t4.....wy) or smaller with A or more points exists only if there is a A-boxed set that has a minimal box with climensions not greater than (ij...ονWa).," A box of dimensions $(w_1, \ldots, w_d)$ or smaller with $K$ or more points exists only if there is a $K$ -boxed set that has a minimal box with dimensions not greater than $(w_1, \ldots, w_d)$." + ‘Thus. we aim to compute the expected number of the latter.," Thus, we aim to compute the expected number of the latter." + We use as an integrancl the probability density that a box will be a minimal box for aset of A points. and we integrate over all applicable boxes.," We use as an integrand the probability density that a box will be a minimal box for aset of $K$ points, and we integrate over all applicable boxes." + Consider a box fi.gi]Jada] with dimensions ο...fy=(fiqefaga) and hypervolume lt will be a (non-minimal) box indicating that a set of dv points is a Av-boxed set if exactly A points fall within it.," Consider a box $[f_1, g_1] \times \ldots \times [f_d, g_d]$ with dimensions $(l_1, \ldots, l_d) = (f_1 - g_1, \ldots, f_d - g_d)$ and hypervolume It will be a (non-minimal) box indicating that a set of $K$ points is a $K$ -boxed set if exactly $K$ points fall within it." + Thus the probability that it indicates a A-boxed set is llowever. it is our goaln points.caleulate the probability density for a box for to," Thus the probability that it indicates a $K$ -boxed set is However, it is our goal to calculate the probability density for a box for $K$ points." + This box is minimal only if. for every dimension index ἐν we have that f; is the minimum of the A points’ ith coordinate values ancl g; is the maximum of these coordinate. values.," This box is minimal only if, for every dimension index $i$ , we have that $f_i$ is the minimum of the $K$ points' $i$ th coordinate values and $g_i$ is the maximum of these coordinate values." + Thus. for each dimension. we must. have one of the fy points achieve the minimum and one of the remaining A/—1 points achieve the maximum.," Thus, for each dimension, we must have one of the $K$ points achieve the minimum and one of the remaining $K-1$ points achieve the maximum." + The remaining δν2 coordinate values can be anvwhere in the range Cfi.g;). (," The remaining $K-2$ coordinate values can be anywhere in the range $(f_i, g_i)$. (" +Note that the possibility of having multiple points exactly achieve the minimum or maximum is an event that has a probability density of zero and thus is safely. ignored.),Note that the possibility of having multiple points exactly achieve the minimum or maximum is an event that has a probability density of zero and thus is safely ignored.) + Thus. the th dimension contributes a factor of Avy1357 to the probability density.," Thus, the $i$ th dimension contributes a factor of $K(K-1){l_i}^{K-2}$ to the probability density." + “Phe probability density for the event that the box is a minimal box for a AxX-boxed set is We note that a box with climensions (/4.....li) can have its minimum corner (fy.....fi) anywhere in 0.1./4] taj.," The probability density for the event that the box is a minimal box for a $K$ -boxed set is We note that a box with dimensions $(l_1, \ldots, l_d)$ can have its minimum corner $(f_1, \ldots, f_d)$ anywhere in $[0, 1-l_1] \times +\ldots \times [0, 1-l_d]$ ." + When we restrict attention to minimal boxes with dimensions notgreater than(ey.....wy) the expected number of A-boxed sets is," When we restrict attention to minimal boxes with dimensions notgreater than $(w_1, \ldots, w_d)$ the expected number of $K$ -boxed sets is" +suggesting that outflows are an almost ubiquitous feature of central black hole activity (Ixing 2010b).,suggesting that outflows are an almost ubiquitous feature of central black hole activity (King 2010b). + Although supermassive black holes (S5MDIIS) in galaxy centres frequently accrete at the IEddington rate. accretion at significantly higher rates requires extreme conditions (cf Wine. 2010a).," Although supermassive black holes (SMBHs) in galaxy centres frequently accrete at the Eddington rate, accretion at significantly higher rates requires extreme conditions (cf King, 2010a)." + Accordingly we consider cases where the accretion rate far from the SMBILE only mildIy exceeds Alpaa. and both the central aceretion rate anc the outflowrate Mu are cMaa.," Accordingly we consider cases where the accretion rate far from the SMBH only mildly exceeds $\me$, and both the central accretion rate and the outflowrate $\mo$ are $\simeq \me$." + Then the outllow has scattering optical depth ~1. and the photons driving it typically scatter only once before escaping.," Then the outflow has scattering optical depth $\sim 1$, and the photons driving it typically scatter only once before escaping." + The front.back symmetry of electron scattering means that the outllow momentum must be of the same order as the original photon momoentum. i.e. so that the outflow: velocity ye. where a0.1 is the accretion elliciency. (eig. Wing Pounds 2003: Kine 2010a).," The front–back symmetry of electron scattering means that the outflow momentum must be of the same order as the original photon momentum, i.e. so that the outflow velocity $v \sim \eta c$, where $\eta \sim 0.1$ is the accretion efficiency (e.g. King Pounds 2003; King 2010a)." + Phe wind Lows with essentially constant velocity ο until it shocks against the interstellar gas of the host galaxy. driving a second shock outwards into this ambient medium and sweeping its up into a shell.," The wind flows with essentially constant velocity $v$ until it shocks against the interstellar gas of the host galaxy, driving a second shock outwards into this ambient medium and sweeping its up into a shell." +" A simple representation of the interstellar density is the isothermal distribution where f, is the gas fraction. and m is the velocity dispersion."," A simple representation of the interstellar density is the isothermal distribution where $f_g$ is the gas fraction, and $\sigma$ is the velocity dispersion." + The average cosmological value of fy is f.20.16., The average cosmological value of $f_g$ is $f_c\simeq 0.16$. + Within this model. then. in galaxies with large a2150 kam *. Eddington outllows tend to sweep the vicinity of the hole clear of gas of density. (2)) ancl prevent further accretion and growth. establishing the AJ@ relation [or the black hole mass (xing 2003: 2005).," Within this model, then, in galaxies with large $\sigma \simgt 150$ km $^{-1}$, Eddington outflows tend to sweep the vicinity of the hole clear of gas of density \ref{rho}) ) and prevent further accretion and growth, establishing the $M - \sigma$ relation for the black hole mass (King 2003; 2005)." + At smaller. values of σ. anv cllect of this kind. is outdone bv the ellects. of mass loss from nuclear star clusters.," At smaller values of $\sigma$, any effect of this kind is outdone by the effects of mass loss from nuclear star clusters." + These sweep out the eas (MeLaughlin et al..," These sweep out the gas (McLaughlin et al.," + 2006: Navakshin ct al..," 2006; Nayakshin et al.," + 2009) and establish an olfset AZ 0 relation between the total cluster mass and the bulge velocity dispersion (Ferrarese ct al., 2009) and establish an offset $M$ – $\sigma$ relation between the total cluster mass and the bulge velocity dispersion (Ferrarese et al. + 2006. Fie.," 2006, Fig." + 2. middle panel).," 2, middle panel)." + Phe Milky Way is probably a member of this starcluster dominated class of galaxies. ancl indeed its SAIBLE mass lies significantly below the value predicted from the AZ o relation (see. e.g. Greene et al.," The Milky Way is probably a member of this star–cluster dominated class of galaxies, and indeed its SMBH mass lies significantly below the value predicted from the $M$ $\sigma$ relation (see, e.g. Greene et al." + 2010. Fig.," 2010, Fig." + 9)., 9). + The double shock pattern caused by the impact of an Iddington outllow on the host interstellar medium must move racially outwards from the vicinity of the black hole., The double shock pattern caused by the impact of an Eddington outflow on the host interstellar medium must move radially outwards from the vicinity of the black hole. + The nature of this motion depends crucially on whether or not the shocked. wind cools within the How time., The nature of this motion depends crucially on whether or not the shocked wind cools within the flow time. + Lf cooling is cHeetive. most of the energy injection rate is lost. to radiation. and onlv the ram pressure of the outflow is communicated. to the host. ISM.," If cooling is effective, most of the energy injection rate is lost to radiation, and only the ram pressure of the outflow is communicated to the host ISM." + This is a momentum.οίνος How., This is a momentum–driven flow. + Lo instead. the Low does not cool. the shocked wind expands acliabatically. doing Pd work against the sweptup interstellar medium.," If instead the flow does not cool, the shocked wind expands adiabatically, doing $P{\rm d}V$ work against the swept–up interstellar medium." + This is an energydriven Dow. which expancds faster through the ISM than a momentumdriven one.," This is an energy--driven flow, which expands faster through the ISM than a momentum–driven one." + The gammarav. lobes observeck by the LAL instrument are very wide features that we shall first consider approximately quasi-spherical., The gamma–ray lobes observed by the –LAT instrument are very wide features that we shall first consider approximately quasi-spherical. +" For the present clay Milky Wav and directions well out of the Galactic plane. we expect fy to be significantly less than {ων so we parametrize f, as fy=1.6:10Pfuoi. where four~1 ds a dimensionless [ree parameter of the model."," For the present day Milky Way and directions well out of the Galactic plane, we expect $f_g$ to be significantly less than $f_c$, so we parametrize $f_g$ as $f_g = +1.6 \cdot 10^{-3} f_{0.01}$ , where $f_{0.01} \sim 1$ is a dimensionless free parameter of the model." + We now ask if the shocked gas cools in. conditions appropriate for the outburst., We now ask if the shocked gas cools in conditions appropriate for the outburst. +" The outflow speed ο50.1e implies a shock temperature 7;=(3m,1όκηce1.6102 Ix. μις is much higher than the Compton temperature ~101 Ix of the SMDBLLE aceretion How. so when the shock is sulliciently close to the hole. Compton cooling hy the central radiation [eld is very elective. and. enforces momentunirdriven flow."," The outflow speed $v \simeq 0.1c$ implies a shock temperature $T_s += (3m_p/16k)\eta^2c^2 \simeq 1.6 \times 10^{10}$ K. This is much higher than the Compton temperature $\sim 10^7$ K of the SMBH accretion flow, so when the shock is sufficiently close to the hole, Compton cooling by the central radiation field is very effective and enforces momentum--driven flow." +" As the shock reaches a critical radius Lea, the radiation field becomes too dilute to cool it.", As the shock reaches a critical radius $R_{\rm en}$ the radiation field becomes too dilute to cool it. + Also. the shocked wind has far too low a density to cool elfectively by atomic or free processes. so the Dow becomes energydriven (xing 2003: Wing ct al.," Also, the shocked wind has far too low a density to cool effectively by atomic or free–free processes, so the flow becomes energy--driven (King 2003; King et al." + 2011)., 2011). + For the parameters ol Ser A*® (mass Apuc45LOPAL.. velocity. dispersion oc100kms.+) the transition to energy.driven How occurs at a radius (cf eqs S - 10 of Wing 2003).," For the parameters of Sgr A* (mass $M_{\rm BH} \simeq 4\times 10^6\msun$, velocity dispersion $\sigma +\simeq 100~{\rm km\, s^{-1}})$ the transition to energy–driven flow occurs at a radius (cf eqs 8 - 10 of King 2003)." + Even at the cosmological eas fraction (fou.=100) the estimate (4)) is so small compared. with the size of the gammarav lobes that we can regard the οιμον as essentially always energy.cleiven in directions away from the Galactic plane., Even at the cosmological gas fraction $f_{0.01} = 100$ ) the estimate \ref{rcool}) ) is so small compared with the size of the gamma–ray lobes that we can regard the outflow as essentially always energy–driven in directions away from the Galactic plane. + In. an energy.driven. outflow. the shocked wind density driving the expansion is always much lower ian the density of the swept:up interstellar mecdium outside it.," In an energy–driven outflow, the shocked wind density driving the expansion is always much lower than the density of the swept–up interstellar medium outside it." + This makes the shock interface inherently Havleigh‘Tavlor unstable (c£ Ixing 2010b)., This makes the shock interface inherently Rayleigh--Taylor unstable (cf King 2010b). + Phe hot shocked gas mixes =vith cool dense interstellar eas throughout the [low in directions away from the Galactic plane., The hot shocked gas mixes with cool dense interstellar gas throughout the flow in directions away from the Galactic plane. + This mixture is clearly a promising site for ganuuaray emission., This mixture is clearly a promising site for gamma–ray emission. + Within the Galactic plane the eas density is far higher. ancl we expect little expansion (see also 84).," Within the Galactic plane the gas density is far higher, and we expect little expansion (see also 4)." + This kind of outtlow ius naturally produces the main qualitative features. of je LAT gammaray map: extensive ganaray emitting lobes placed: svnunetrically on cach side of the Galactic plane. with a narrow waist inthe plane.," This kind of outflow thus naturally produces the main qualitative features of the –LAT gamma–ray map: extensive gamma–ray emitting lobes placed symmetrically on each side of the Galactic plane, with a narrow waist inthe plane." + ]inergvdriven outllows rapidly attain a constant speed in the bulge of a galaxy. (Ixing 2005)., Energy–driven outflows rapidly attain a constant speed in the bulge of a galaxy (King 2005). +" Here the factor b2-1 allows for some collimation of the outflow. Ad, is the predicted: value of the SMBIL mass in the Milky Way from the AM@ relation and AJoO.2AL, is the mass of A*."," Here the factor $b \la 1$ allows for some collimation of the outflow, $M_{\sigma}$ is the predicted value of the SMBH mass in the Milky Way from the $M - \sigma$ relation and $M \simeq 0.2 M_\sigma$ is the mass of ." +. For the rest of this Section we model the outllow away from the dise plane as a sector of a spherical Dow., For the rest of this Section we model the outflow away from the disc plane as a sector of a spherical flow. + Lf theEddington accretion phase lasts for a time face. the shock reaches radius when the quasar phase ends.," If theEddington accretion phase lasts for a time $t_{\rm acc}$ , the shock reaches radius when the quasar phase ends." + However the shocked wind, However the shocked wind +"uncertainties are whether the merger rate is sufficiently high to produce the required growth. and whether a realistic treatment of the dark matter and orbital configurations retains the high efficiency of minor mergers to “puff up"" a galaxy.","uncertainties are whether the merger rate is sufficiently high to produce the required growth, and whether a realistic treatment of the dark matter and orbital configurations retains the high efficiency of minor mergers to “puff up” a galaxy." +" Whatever the dominant physical mechanism turns out to be. we find that o2 if the relation between size growth and mass growth is parameterized as 43/7)=(Mus/Mj)""."," Whatever the dominant physical mechanism turns out to be, we find that $\alpha \gtrsim 2$ if the relation between size growth and mass growth is parameterized as $r_{1+2}/r_1 = (M_{1+2}/M_1)^{\alpha}$." + Inside-out formation via mergers predicts that stars in the central regions of a nearby elliptical galaxy are qualitatively different from stars at larger radii., Inside-out formation via mergers predicts that stars in the central regions of a nearby elliptical galaxy are qualitatively different from stars at larger radii. + Elliptical galaxies do have color- and metallicity gradients. which could reflect differences in stellar populations between stars formed in-situ and those accreted from other systems (e.g..Peletier 1990).," Elliptical galaxies do have color- and metallicity gradients, which could reflect differences in stellar populations between stars formed in-situ and those accreted from other systems (e.g., 1990)." + While it is not yet clear whether these gradients are consistent with such aceretion scenarios. it may be difficult to reconcile them with an expansion model alone (see. e.g.. 2008).," While it is not yet clear whether these gradients are consistent with such accretion scenarios, it may be difficult to reconcile them with an expansion model alone (see, e.g., 2008)." + It is tempting to identify kinematically decoupled cores (e.g.. 1988: 1988) with the descendants of the compact galaxies. but the scales of these features are typically a few 100 pe rather than ~ Ikkpe.," It is tempting to identify kinematically decoupled cores (e.g., 1988; 1988) with the descendants of the compact galaxies, but the scales of these features are typically a few 100 pc rather than $\sim 1$ kpc." + More information on color gradients and the inner ~1 kkpe of the compact high redshift galaxies will provide important additional constraints., More information on color gradients and the inner $\sim 1$ kpc of the compact high redshift galaxies will provide important additional constraints. + Our determinations of stellar density profiles and masses can be improved., Our determinations of stellar density profiles and masses can be improved. + The calculated density profiles and integrated masses are based on Sersic profile fits to the galaxy light distributions. not on the actual light profiles themselves.," The calculated density profiles and integrated masses are based on Sersic profile fits to the galaxy light distributions, not on the actual light profiles themselves." + Furthermore. for the high redshift galaxies the profiles within ~] kkpe are extrapolations. as the galaxies are not resolved on smaller scales.," Furthermore, for the high redshift galaxies the profiles within $\sim 1$ kpc are extrapolations, as the galaxies are not resolved on smaller scales." + The conversion from light to mass is also very uncertain., The conversion from light to mass is also very uncertain. + The conversion for the local samples ignores scatter in the M/L versus L relation. and ignores gradients in M/L ratio.," The conversion for the local samples ignores scatter in the $M/L$ versus $L$ relation, and ignores gradients in $M/L$ ratio." + The mass estimates of the high redshift galaxies are based on stellar population models and are very sensitive to the assumed IMF and to possible contributions from dark matter., The mass estimates of the high redshift galaxies are based on stellar population models and are very sensitive to the assumed IMF and to possible contributions from dark matter. + As noted in .I1. bottom-light IMFs would change the masses and alter the required amount of size- and mass evolution to bring the galaxies to local relations.," As noted in 1, bottom-light IMFs would change the masses and alter the required amount of size- and mass evolution to bring the galaxies to local relations." + Measurements of absorption-line kinematics of high redshift compact galaxies would provide a direct test of the IMF. and of several of the other assumptions that enter the analysis (see. e.g.. 2008).," Measurements of absorption-line kinematics of high redshift compact galaxies would provide a direct test of the IMF, and of several of the other assumptions that enter the analysis (see, e.g., 2008)." + van der Wel et ((2008) find that the observed size evolution at 0«z| is similar when dynamical masses rather than photometric masses are used. but this needs to be verified at higher redshifts.," van der Wel et (2008) find that the observed size evolution at $00.8""vr! ). are so restrictive that only a small (1%) fraction of the halo white dwarf population can be found in the selection zone."," It is also worth noting that the applied selection criteria, in particular the proper motion cut $\mu>0.8''\, {\rm yr^{-1}}$ ), are so restrictive that only a small $1\%$ ) fraction of the halo white dwarf population can be found in the selection zone." + As already mentioned. the thick disk ts characterized by higher velocity distributions and a larger scale height than those of the thin disk.," As already mentioned, the thick disk is characterized by higher velocity distributions and a larger scale height than those of the thin disk." + Several studies on halo white dwarfs have considered the thick disk population as a possible source of contamination (Oppenheimer et al., Several studies on halo white dwarfs have considered the thick disk population as a possible source of contamination (Oppenheimer et al. + 2001: Reid et al., 2001; Reid et al. + 2001: Torres et al., 2001; Torres et al. + 2002). but a comprehensive theoretical study remains to be done.," 2002), but a comprehensive theoretical study remains to be done." + Accordingly we evaluate in this section the Joint contribution of thick disk white dwarfs and red dwarfs to the microlensing optical depth., Accordingly we evaluate in this section the joint contribution of thick disk white dwarfs and red dwarfs to the microlensing optical depth. + We do that for both the MACHO and EROS experiments in the same way as for the halo simulations presented in the previous section., We do that for both the MACHO and EROS experiments in the same way as for the halo simulations presented in the previous section. + The model of spectral evolutior of white dwarfs adopted for this study 1s our model B. which we consider to be the most realistic one.," The model of spectral evolution of white dwarfs adopted for this study is our model B, which we consider to be the most realistic one." + Before starting the discussion of our results. we would like to emphasize that the calculation of the microlensing optical depth involves the addition of individual contributions. which are proportional to the Einstein crossing time corrected by the efficiency function — see Eq. (," Before starting the discussion of our results, we would like to emphasize that the calculation of the microlensing optical depth involves the addition of individual contributions, which are proportional to the Einstein crossing time corrected by the efficiency function — see Eq. (" +3).,3). + The efficiency function in turn depends on the crossing time. which ts directly proportional to the Einstein radius and inversely proportional to the velocity perpendicular to the observer.," The efficiency function in turn depends on the crossing time, which is directly proportional to the Einstein radius and inversely proportional to the velocity perpendicular to the observer." + For a thick disk object the average distance is smaller than that of a typical halo object., For a thick disk object the average distance is smaller than that of a typical halo object. + Thus there are two competing effects. smaller distances clearly imply smaller individual contributions to the optical depth.," Thus there are two competing effects, smaller distances clearly imply smaller individual contributions to the optical depth." + However. thick disk stars have also lower velocities than those of the halo. thus implying more important individual contributions.," However, thick disk stars have also lower velocities than those of the halo, thus implying more important individual contributions." + The precise balance between these two effects determines the final contribution., The precise balance between these two effects determines the final contribution. + The results of these simulations are shown in Fig., The results of these simulations are shown in Fig. + 4 and Table 3., 4 and Table 3. + In the top panels of Fig., In the top panels of Fig. + 4 we show the contribution of the different populations under study to the optical depth derived by the MACHO experiment for both the canonical thick disk — left panels — and the metal-weak thick disk of Carollo et al. (, 4 we show the contribution of the different populations under study to the optical depth derived by the MACHO experiment for both the canonical thick disk — left panels — and the metal-weak thick disk of Carollo et al. ( +2009) — right panels.,2009) — right panels. + It is interesting to realize that in both cases DÀ and non-DA white dwarfs contribute by roughly the same amount., It is interesting to realize that in both cases DA and non-DA white dwarfs contribute by roughly the same amount. + Additionally. the contribution of red dwarfs quickly decreases anc becomes almost negligible for realistic magnitude cuts. while that of white dwarfs decreases only slightly.," Additionally, the contribution of red dwarfs quickly decreases and becomes almost negligible for realistic magnitude cuts, while that of white dwarfs decreases only slightly." +" Consequently. for realistic magnitude cuts — say mL,>20"" — the contributions to the microlensing optical depth of both DA and non-DA white dwarfs are much more significant than that of red dwarfs."," Consequently, for realistic magnitude cuts --- say $m_v > 20^{\rm mag}$ — the contributions to the microlensing optical depth of both DA and non-DA white dwarfs are much more significant than that of red dwarfs." + In the bottom panels of Fig., In the bottom panels of Fig. + 4 we show the contribution of the entire population to the microlensing optical depth for both thick disk models., 4 we show the contribution of the entire population to the microlensing optical depth for both thick disk models. +" We obtain that in the case of the MACHO experiment and for a typical magnitude cut of 22.5""** the contribution of the populations of the canonical thick disk white dwarfs and red dwarfs to the optical depth can be as large as 30%. which is slightly more than that of the metal-weak thick disk model. which ts on the order of 20%."," We obtain that in the case of the MACHO experiment and for a typical magnitude cut of $22.5^{\rm +mag}$ the contribution of the populations of the canonical thick disk white dwarfs and red dwarfs to the optical depth can be as large as $30\%$, which is slightly more than that of the metal-weak thick disk model, which is on the order of $20\%$." + At first glance. this result may seem to be in contrast with other recent estimates.," At first glance, this result may seem to be in contrast with other recent estimates." + For instance. Aleock et al. (," For instance, Alcock et al. (" +2000) estimated the contribution of thick disk stars to be ~2% of the observed optical depth.,2000) estimated the contribution of thick disk stars to be $\sim 2\%$ of the observed optical depth. + This agrees with our model if we only consider the red dwarf population. for which we obtain a contribution to the optical depth of ~3%. à value very similar to that obtained by Alcock et al. (," This agrees with our model if we only consider the red dwarf population, for which we obtain a contribution to the optical depth of $\sim 3\%$, a value very similar to that obtained by Alcock et al. (" +2000).,2000). + On the contrary. when thick disk white dwarfs are taken into account. the contribution of the thick disk is as large as that of the halo.," On the contrary, when thick disk white dwarfs are taken into account, the contribution of the thick disk is as large as that of the halo." +" A more detailed analysis of the thick disk population can be done and reveals that in the case of the canonical thick disk the possible microlensing events have an Einstein crossing time f;x170 days for a magnitude cut of 22.5"", while for the case of the metal-weak thick disk the average Einstein crossing time amounts to £j;=120 days."," A more detailed analysis of the thick disk population can be done and reveals that in the case of the canonical thick disk the possible microlensing events have an Einstein crossing time $t_{\rm +E}\approx\,170$ days for a magnitude cut of $22.5^{\rm mag}$ , while for the case of the metal-weak thick disk the average Einstein crossing time amounts to $t_{\rm E}\approx\,120$ days." + Both values are considerably higher than that of the halo population., Both values are considerably higher than that of the halo population. + Moreover. as can be seen in Table 3. the mean average tangential velocity is ~80kms! for both models — which is what we would expect for a thick disk population. but the mean average distance of the lenses is ~4+ kpe — which ts comparable to that obtained for the halo population.," Moreover, as can be seen in Table 3, the mean average tangential velocity is $\sim 80\;{\rm km\;s^{-1}}$ for both models — which is what we would expect for a thick disk population, but the mean average distance of the lenses is $\sim 4$ kpc — which is comparable to that obtained for the halo population." + This can be easily understood in terms of the selection criteria we use to decide when a star can be considered responsible of a microlensing event., This can be easily understood in terms of the selection criteria we use to decide when a star can be considered responsible of a microlensing event. + In particular. we only consider as reliable microlensing events those in which the lens is dimmer than a certain magnitude cut and. given that the thick population is intrinsically brighter than the halo population. we only select those thick disk lenses which are far enough away.," In particular, we only consider as reliable microlensing events those in which the lens is dimmer than a certain magnitude cut and, given that the thick population is intrinsically brighter than the halo population, we only select those thick disk lenses which are far enough away." + In any case. as can be seen in Table 3. our simulations show that the thick disk populations can produce at most one microlensing event.," In any case, as can be seen in Table 3, our simulations show that the thick disk populations can produce at most one microlensing event." + We emphasize that the results obtained using the canonical thick disk model appear to provide an upper limit for the contribution to the total microlensing optical depth — see Fig., We emphasize that the results obtained using the canonical thick disk model appear to provide an upper limit for the contribution to the total microlensing optical depth — see Fig. + 4., 4. + We have also estimated the contribution to the optical depth of the thick disk populations in the case of the EROS experiment., We have also estimated the contribution to the optical depth of the thick disk populations in the case of the EROS experiment. + The results are shown in Table 4., The results are shown in Table 4. +" For a realistic magnitude cut of 22.577, |+ microlensing event is expected ata Ic confidence level."," For a realistic magnitude cut of $22.5^{\rm +mag}$, $1\pm1$ microlensing event is expected at a $1\sigma$ confidence level." + The confirmation of this microlensing event would increase the value of the optical depth measured by the EROS team by ~40%., The confirmation of this microlensing event would increase the value of the optical depth measured by the EROS team by $\sim 40\%$. + However. we point out that given the poor statistics. the number of microlensing events obtained in our simulations agrees reasonably well with theobservations of the EROS team. who found none.," However, we point out that given the poor statistics, the number of microlensing events obtained in our simulations agrees reasonably well with theobservations of the EROS team, who found none." +To study timing ancl spectral characteristies of NMMU J031747.5-663010. we used the cata of 2004 November 23 observation of NGC 1919 field. with three European Photon Imaging Camera (ePIC) instruments (MOSI. MOS2 and pn)(Turneretal.2001:Strucclerctal. 2001).. and the Optical Monitor (OM) telescope (Mason et al.,"To study timing and spectral characteristics of XMMU J031747.5-663010, we used the data of 2004 November 23 observation of NGC 1313 field with three European Photon Imaging Camera (EPIC) instruments (MOS1, MOS2 and pn)\citep{Turner01,Strueder01}, and the Optical Monitor (OM) telescope (Mason et al." + 2O0L\(Lable 1))., 2001)(Table \ref{obslog}) ). + We also. used several 2000-2006 (Smithetal.2007). and 2002-2003. observations of the same field to obtain upper limits on the source [lux when the source was not detected., We also used several 2000-2006 \citep{Smith07} and 2002-2003 observations of the same field to obtain upper limits on the source flux when the source was not detected. + We reduced.NALA data. using Science Analysis System (SAS ν Before generating X-ray images. and source spectra ane lighteurves. we performed stancard screening of the original event files to exelucle time intervals with high background. levels. applying an upper count rate threshold. of above average background evel.," We reduced data using Science Analysis System (SAS v. Before generating X-ray images, and source spectra and lightcurves, we performed standard screening of the original event files to exclude time intervals with high background levels, applying an upper count rate threshold of above average background level." + The standard SAS toolbaryeen was used to perform xwvcentrie correction on the original EPIC event files used or timing analysis., The standard SAS tool was used to perform barycentric correction on the original EPIC event files used for timing analysis. + We generated EPIC-pn ancl MOS images of NGC 1313 ield in the 0.3-7.0 keV energy band. ancl used. the SAS standard maximum likelihood (ML) source detection script to detect and localize point sources.," We generated EPIC-pn and MOS images of NGC 1313 field in the 0.3-7.0 keV energy band, and used the SAS standard maximum likelihood (ML) source detection script to detect and localize point sources." + We used sight X-ray sources with known counterparts from USNO-3 catalog (Monetetal.2003). ancl source lists to correct EPIC image astrometry., We used bright X-ray sources with known counterparts from USNO-B catalog \citep{Monet03} and source lists to correct EPIC image astrometry. + The astrometric correction was also applied to the OM images. using cross-correlation with USNO-D catalog.," The astrometric correction was also applied to the OM images, using cross-correlation with USNO-B catalog." +" After correction. we estimate residual systematic error in the source positions to be of the order ~1"" for both EPIC and OM."," After correction, we estimate residual systematic error in the source positions to be of the order $\sim 1\arcsec$ for both EPIC and OM." +" To extract EPIC-pn source lighteurves. and. spectra during the 2004 November 23 observation. we used the elliptical region with semi-axes of 22"" and. 1s” and position angle of 407."," To extract EPIC-pn source lightcurves and spectra during the 2004 November 23 observation, we used the elliptical region with semi-axes of $\arcsec$ and $\arcsec$ and position angle of $^{\circ}$." + Due to the source. proximity to the edge of EPIC-\MIOS CCD. the source counts were extracted. [rom the elliptical region with scmi-axes of 20” ancl 107. including τοις of the source energy Hux.," Due to the source proximity to the edge of EPIC-MOS CCD, the source counts were extracted from the elliptical region with semi-axes of $\arcsec$ and $\arcsec$, including $\sim 70\%$ of the source energy flux." + The adjacent source-[ree regions were used to extract background spectra and lighteurves., The adjacent source-free regions were used to extract background spectra and lightcurves. + The source and background spectra were then renormalized by ratio of the detector areas., The source and background spectra were then renormalized by ratio of the detector areas. + For spectral analysis. we used data in the 0.3T keV energy iid.," For spectral analysis, we used data in the $0.3 - 7$ keV energy band." + In this analvsis we use valid pn events with pattern | (single and double) and pattern 0-12 (single-cquacdruple) events for MOS cameras., In this analysis we use valid pn events with pattern 0-4 (single and double) and pattern 0-12 (single-quadruple) events for MOS cameras. + To svachronize both source and xickeround lighteurves from individual EPIC detectors. we used the identical time filtering criteria based on Mission telative Time CLIE). following the procedure described in Barnardetal.(2007)..," To synchronize both source and background lightcurves from individual EPIC detectors, we used the identical time filtering criteria based on Mission Relative Time (MRT), following the procedure described in \cite{Robin_timing}." +. Phe background lighteurves were not subtracted from the source lighteurves. but were used later o estimate the background. contribution in the calculation of the source pulsed fractions.," The background lightcurves were not subtracted from the source lightcurves, but were used later to estimate the background contribution in the calculation of the source pulsed fractions." + The EPIC spectra were grouped to contain a mininimum of 20 counts per spectral bin in order to allow X7 statistics. and fit to analytic models using the NSPEC fitting package (ArnauclL99," The EPIC spectra were grouped to contain a minimum of 20 counts per spectral bin in order to allow $\chi^{2}$ statistics, and fit to analytic models using the XSPEC fitting package \citep{arnaud96}." +G).. ΕΙρα. MOSI ancl MOS2 spectra were fitted simultaneously. but with normalizations varving independently.," EPIC-pn, MOS1 and MOS2 spectra were fitted simultaneously, but with normalizations varying independently." + For timing analysis we used standard XANADU/XRONOS tasks., For timing analysis we used standard XANADU/XRONOS tasks. + The data of observations was processed. using the CLAO threads., The data of observations was processed using the CIAO threads. + We performed. standard screening of the data to exclude time intervals with hieh background. levels., We performed standard screening of the data to exclude time intervals with high background levels. + For cach observation. we generated: X-rav images in the 0.3-7. keV energy. band. ancl used. CLAO wavelet detection routineweedefee! to detect point sources.," For each observation, we generated X-ray images in the 0.3-7 keV energy band, and used CIAO wavelet detection routine to detect point sources." +" To estimate upper limits on the quiescent source luminosities. the ChandrafACITS and. NALALZAEPIC count rates were converted into encrey [luxes in the 0.3-7 keV energv range using WebPLALMIS.. assuming an absorbed power law spectral shape with photon index EP—1.5r and Galactic foreground absorbing column Ng 23.6«107"" 2"," To estimate upper limits on the quiescent source luminosities, the /ACIS and /EPIC count rates were converted into energy fluxes in the 0.3-7 keV energy range using Web, assuming an absorbed power law spectral shape with photon index $\Gamma = 1.5$ and Galactic foreground absorbing column $_{\rm H}$ $3.6\times10^{20}$ $^{-2}$." + 1n the following analvsis we assume a distance of 4.1 Alpe for NGC 1313 (Méndezetal.2002)., In the following analysis we assume a distance of 4.1 Mpc for NGC 1313 \citep{Mendez02}. +.. ALL parameter errors quoted are (10) confidence limits., All parameter errors quoted are $1\sigma$ ) confidence limits. + A new X-ray source NMMU. J031747.5-663010. has. been discovered. in the data of the 2004 November 23 observation of the Νας 1313. fiel. (CLable 13)., A new X-ray source XMMU J031747.5-663010 has been discovered in the data of the 2004 November 23 observation of the NGC 1313 field (Table \ref{obslog}) ). + The estimated. source luminosity was 1.6 10% eres assuming the distance of 4.1 Alpe.," The estimated source luminosity was $\sim$ $\times 10^{39}$ ergs $^{-1}$, assuming the distance of 4.1 Mpc." +" We measure the position of NMMU J031747.5-663010 to be a=O3""1747.59.856G30'10.2"" (J2000 equinox) with an uncertainty of ~1.07 (Fig. 1))."," We measure the position of XMMU J031747.5-663010 to be $\alpha = 03^{h} 17^{m} 47.59^{s}, +\delta = -66^{\circ} 30\arcmin 10.2\arcsec$ (J2000 equinox) with an uncertainty of $\sim 1.0\arcsec$ (Fig. \ref{image_general}) )." + The projected galactocentric distance of NMMU J031747.5-663010 is ~3 or ~3.6 kpe at 4.1 Mpc., The projected galactocentric distance of XMMU J031747.5-663010 is $\sim 3\arcmin$ or $\sim 3.6$ kpc at 4.1 Mpc. + The analysis of other archival observations of the same field with and. did not vield source detection with an upper limit (20) ranging from ~210% to 23.10 eres + (or ~ SO-SOO times lower than outburst luminosity). depending on the duration of the observation and instrument used (Table 1)).," The analysis of other archival observations of the same field with and did not yield source detection with an upper limit $\sigma$ ) ranging from $\sim 2\times 10^{36}$ to $\sim 2\times 10^{37}$ ergs $^{-1}$ (or $\sim$ 80-800 times lower than outburst luminosity), depending on the duration of the observation and instrument used (Table \ref{obslog}) )." + The search for the optical counterparts using the deep images of NGC 1313 from Las Campanas Observatory 2.5m du Pont telescope (Ixuchinskictal.2000) did. not viel stellar-like objects brighter than ~21 mag in V and ~20 mae in D band within the 30 error circle of NMMU. JO81747.5-663010., The search for the optical counterparts using the deep images of NGC 1313 from Las Campanas Observatory 2.5m du Pont telescope \citep{Kuchinski00} did not yield stellar-like objects brighter than $\sim 21$ mag in V and $\sim 20$ mag in B band within the $\sigma$ error circle of XMMU J031747.5-663010. + We also used the cata of the 2004 November 23 NALA/-NewlonfOAL observation to search for optical/UV. counterparts to the source. during its N-rav outburst (Fig. 1))., We also used the data of the 2004 November 23 /OM observation to search for optical/UV counterparts to the source during its X-ray outburst (Fig. \ref{image_general}) ). + We did not detect any stellar counterparts to NMMU J031747.5-663010 in the OM images down to the limit of —20 mag in the V and U bands., We did not detect any stellar counterparts to XMMU J031747.5-663010 in the OM images down to the limit of $\sim 20$ mag in the V and U bands. + We performed timing analysis of NMMU JO031747.5-663010 using the 2004 November 23 data from all three NewlonfEPlC detectors in the 0.3-7 keV energy band., We performed timing analysis of XMMU J031747.5-663010 using the 2004 November 23 data from all three /EPIC detectors in the 0.3-7 keV energy band. + After a barvcentric correction of the photon arrival times in the original event Lists. we performed a Fast. Fourier Transform (FET) analysis using standard XIONOS task poispec. in," After a barycentric correction of the photon arrival times in the original event lists, we performed a Fast Fourier Transform (FFT) analysis using standard XRONOS task , in" +Finally. this is converted into an estimate of amount of AGN energv available via cx=(AlgaO00)e7.,"Finally, this is converted into an estimate of amount of AGN energy available via $E_{\rm AGN} = \epsilon M_{\rm BH}(r_{500}) c^2$." + In Figure 3. we present a comparison of the minimum.specifie energy. required. to resolve. the cluster vs. CALB discrepaney with the energy available to be tapped in black oles. C," In Figure 3, we present a comparison of the minimum energy required to resolve the cluster vs. CMB discrepancy with the energy available to be tapped in black holes. (" +lo facilitate comparison with the observations. we calculate the specific energy. by dividing the total required enerev by the tvpicalobserved mass of gas within r500.,"To facilitate comparison with the observations, we calculate the specific energy by dividing the total required energy by the typical mass of gas within r500." + In particular. we assume Adv.(soo)=0.12Msoo: see 11.).," In particular, we assume $M_{\rm gas}(r_{500}) = 0.12 M_{500}$; see 1.)." + In order to explain the most massive systems. we calculate hat à minimum energy of 10 keV. per particle is required.," In order to explain the most massive systems, we calculate that a minimum energy of $\sim 10$ keV per particle is required." + It one adopts an ellicieney ofe=0.1. which is approximately he ellicieney predicted by. standard: racliatively eflicient accretion disk models (e.g. Shakura Sunvaev 1973). there is potentially just enough. energy. available in black holes distributed throughout. rsoo. to account. for the observed eas mass fractions. (," If one adopts an efficiency of $\epsilon=0.1$, which is approximately the efficiency predicted by standard radiatively efficient accretion disk models (e.g., Shakura Sunyaev 1973), there is potentially just enough energy available in black holes distributed throughout $r_{500}$ to account for the observed gas mass fractions. (" +We use the term ‘potentially’ since we remind the reader that we have calculated the enerev required. and. furthermore have made optimistic assumptions about the mass of black holes available to heat the LOCAL.),We use the term `potentially' since we remind the reader that we have calculated the energy required and furthermore have made optimistic assumptions about the mass of black holes available to heat the ICM.) + ‘Phis result agrees quite well with the more detailed: calculations of Bode et (2007) (that. include. e.g.. the effects of asphericity ancl substructure). when one normalises their estimated required total energy to the same total mass of gas assumed above.," This result agrees quite well with the more detailed calculations of Bode et (2007) (that include, e.g., the effects of asphericity and substructure), when one normalises their estimated required total energy to the same total mass of gas assumed above." + llowever. modelling of .AGIN-blown X-ray cavities sugeests the typical cluster black hole cllicieney is actually much lower than 0.1.," However, modelling of AGN-blown X-ray cavities suggests the typical cluster black hole efficiency is actually much lower than $0.1$." + The most energetic AGN outbursts known. in Lereules A (Nulsen et 22005) ancl M80735.6|7421 (AleNamara et 22005). have mean vowers of &L6—LT«10/5 eres ," The most energetic AGN outbursts known, in Hercules A (Nulsen et 2005) and MS0735.6+7421 (McNamara et 2005), have mean powers of $\approx 1.6-1.7 \times 10^{46}$ ergs $^{-1}$." +The typical age of such outbursts is zz LOO Myr. corresponding to a total energy of few times 1095 ores or a specilie energy. of a few enths of a keV. per particle (see the thick clashed line in 33).," The typical age of such outbursts is $\approx$ 100 Myr, corresponding to a total energy of few times $10^{61}$ ergs or a specific energy of a few tenths of a keV per particle (see the thick dashed line in 3)." + This falls nearly two orders of magnitude short of he requirecl minimum to reduce a massive cluster's barvon raction from the universalWALAP value to the observed raction., This falls nearly two orders of magnitude short of the required minimum to reduce a massive cluster's baryon fraction from the universal value to the observed fraction. + Therefore. even if a tvpical cluster experiences 10 such powerful outbursts over its lifetime (sav. once per Civr over 10 Gyr) the energy. injected. into the ICM still falls short of the minimum required energy by up to an order of maenituce.," Therefore, even if a typical cluster experiences 10 such powerful outbursts over its lifetime (say, once per Gyr over 10 Gyr) the energy injected into the ICM still falls short of the minimum required energy by up to an order of magnitude." + We therefore conclude that AGN heating is a highly implausible. but perhaps not impossible. solution to the cluster vs. CAB diserepaney.," We therefore conclude that AGN heating is a highly implausible, but perhaps not impossible, solution to the cluster vs. CMB discrepancy." +. In. addition to. the exceptionally large energy. requirements. we point out that the heating must be distributed. in just such a way as to explain the convergence trend in 22 and the facet that the ICM properties at large racii in massive clusters follow thegravilalional scll-similar scalings(MeCarthy et 22007).," In addition to the exceptionally large energy requirements, we point out that the heating must be distributed in just such a way as to explain the convergence trend in 2 and the fact that the ICM properties at large radii in massive clusters follow the self-similar scalings(McCarthy et 2007)." + The observed. gas fractious are proportional to P.07. while theWALAP constraint is independent of 5.," The observed gas fractions are proportional to $h^{-1.5}$, while the constraint is independent of $h$." + Εις. adopting a lower value of zz0.55 would bring these two results into agreement.," Thus, adopting a lower value of $h\approx 0.55$ would bring these two results into agreement." + Indeed. this is why similar analyses by. Roussel et al. (," Indeed, this is why similar analyses by Roussel et al. (" +2000) ancl Sadat et al. (,2000) and Sadat et al. ( +2005). who adopt f=0.5. find higher gas fractions than we have shown here.,"2005), who adopt $h=0.5$, find higher gas fractions than we have shown here." + However. the large body of independent evidence in favour of h>0.6 (e.g. York et al.," However, the large body of independent evidence in favour of $h>0.6$ (e.g. York et al." + 2005: Jones ct al., 2005; Jones et al. + 2005: Riess ct al., 2005; Riess et al. + 2005: Ngeow Ixanbur 2006) makes this solution seen unlikely., 2005; Ngeow Kanbur 2006) makes this solution seem unlikely. +" We can use the observed. barvon content of clusters to reverse-cneinecr the universal total matter density. £2,,. via: where bate(rsoo) is the barvon depletion factor within rsoo and bysr is the observational bias introduced by assuming strict LISE (Le. ignores pressure support dueto turbulent motions). both of which can be estimated using gascdvnamic cosmological simulations."," We can use the observed baryon content of clusters to reverse-engineer the universal total matter density, $\Omega_m$, via: where $b_{\rm dep}(r_{500})$ is the baryon depletion factor within $r_{500}$ and $b_{\rm HSE}$ is the observational bias introduced by assuming strict HSE (i.e., ignores pressure support dueto turbulent motions), both of which can be estimated using gasdynamic cosmological simulations." + Adopting the barvon density. of Ορ—0.0223oes (which is in good. agreement. with the latest QSO constraints: sce O'Meara et 22006). bse.(reson)=0.05—0.05. (kravisov et al.," Adopting the baryon density of $\Omega_b h^2 = +0.0223^{+0.0007}_{-0.0009}$ (which is in good agreement with the latest QSO constraints; see O'Meara et 2006), $b_{\rm +dep}(r_{500}) = 0.95 \pm 0.05$ (Kravtsov et al." + 2005: Ettori et 22006: Crain et 22006). busez0.9 (Nagai et 22007). Moarl(rsu)L(AbeTESrsu0)=O10+0.05 (see∖ 59.1). and 5 ⇠∕≒∣∆∖↿∖∣⋮↽∣∩∩⊐∶∪⋅⊔⋅↱≻∶∶∪⋅∪↓↱↿∖≱∖⋖⋅⋖⋅↓⊲↝↓⋏∙≟⊳⊔−⊔∪↿∢⊾⇂↓⋯⇂⇂↓↕⊀↓⊳∖⊳∖↓≻⋜⋯⊳∖ both the Chandraand. results at σου). we lind: This is larger than the best-fit HAAZAP 3-xear value of," 2005; Ettori et 2006; Crain et 2006), $b_{\rm HSE} \approx 0.9$ (Nagai et 2007), $M_{star}(r_{500})/M_{\rm gas}(r_{500}) = 0.10 +\pm 0.05$ (see 3.1), and $f_{\rm gas}(r_{500}) = 0.115 \pm +0.015$ (see 1 - note that this spans both the and results at $r_{500}$ ), we find: This is larger than the best-fit 3-year value of" +parameters are gathered in Table 4..,parameters are gathered in Table \ref{tab:events}. + The events light curve along with the best fit model is shown in Fig. 4.., The event's light curve along with the best fit model is shown in Fig. \ref{fig:events}. + From the multi-band fit we were able to derive. the source maenituce and colour of /;=19.18+0.10 mae and (V£)s=1.050.05 mae., From the multi-band fit we were able to derive the source magnitude and colour of $\IS=19.18\pm0.10$ mag and $\VIS=1.05\pm0.05$ mag. + This places the source on the red eiant branch of the CMD (Pig. 2)).," This places the source on the red giant branch of the CMD (Fig. \ref{fig:cmd}) )," + indicating the source intrinsically belongs to the LM., indicating the source intrinsically belongs to the LMC. + Field LMC122. in which OGLE-LMC-03 is located. is one of the sparsest according to its stellar density (see Table 13).," Field LMC122, in which OGLE-LMC-03 is located, is one of the sparsest according to its stellar density (see Table \ref{tab:fields}) )." + At that density and magnitude level. there is about 9 per cent ofstars being blended with another one (see Section 5)). therefore we can safely assume the entire remaining light in the blend constituting the baseline of the event comes from a single star - the lens.," At that density and magnitude level, there is about 9 per cent of stars being blended with another one (see Section \ref{sec:blending}) ), therefore we can safely assume the entire remaining light in the blend constituting the baseline of the event comes from a single star - the lens." + Another constraint comes from the astrometric measurements of the DLA residuals around the peak of the event., Another constraint comes from the astrometric measurements of the DIA residuals around the peak of the event. + They clearly indicate lack of any shift of the centroid during the microlensing magnification. which suggests the additional Dux sits exactly on top of the source star.," They clearly indicate lack of any shift of the centroid during the microlensing magnification, which suggests the additional flux sits exactly on top of the source star." + The blending parameters in both pass-bands obtained in the light curve fitting indicate the lens is very similar to the source in terms of the brightness and colour., The blending parameters in both pass-bands obtained in the light curve fitting indicate the lens is very similar to the source in terms of the brightness and colour. + Hence. the lens mayalso be an LMC red giant (see Fig.6)).," Hence, the lens mayalso be an LMC red giant (see \ref{fig:cmdlenses}) )." + This relatively bright red. star (17.3 mag) shows an event of small amplitude (50.5 mag) just at the beginning of the OGLEUL observations in Nov 2001 (the peak occurred on 1JD=2452 227.9)., This relatively bright red star (17.3 mag) shows an event of small amplitude $\sim$ 0.5 mag) just at the beginning of the OGLE–III observations in Nov 2001 (the peak occurred on $HJD=2\;452\;227.9$ ). + Us light curve is shown in Fig. +.., Its light curve is shown in Fig. \ref{fig:events}. + There was no V-band OGLE data available during the course of the event. but 37 V-band data points after the event allowed a derivation of the colour of the blend.," There was no $V$ -band OGLE data available during the course of the event, but 37 $V$ -band data points after the event allowed a derivation of the colour of the blend." + A standard microlensing model fit to the Z-band data shown in Fig., A standard microlensing model fit to the $I$ -band data shown in Fig. +" 4. (solid line) is best described with the time-scale of oyepOLD . ∣⊏∶⇀∫≻−≽⋅⋔⊥⊐⊽↴⊤∠⇂⋜↧∙∖⇁⊳∖⊳⋜↧⊔↓⋜∟∖↓⊔∐⋯↓⋜⋯↓↓≻↓↓∐≼⇍⋜∐↓∪⊔∪⇂⇀↨∶↓⋅≟⋅↱≻le. and the blending: parameter fs,:=0.70Las5,5."," \ref{fig:events} (solid line) is best described with the time-scale of $\te=32.76^{+9.12}_{-12.57}$ days, a maximum amplification of $A=1.45$ and the blending parameter $\fsi=0.70^{+2.98}_{-0.35}$." + Dlending. less than 1 indicates there is an additional light present in the overall flux of the object., Blending less than 1 indicates there is an additional light present in the overall flux of the object. + The source magnitude can be calculated. from the model as Z4=17.65+0.02 mag. but the colour can be only assumed. to be equal to. the blends. (V{λα~Ld.," The source magnitude can be calculated from the model as $\IS=17.65\pm0.02$ mag, but the colour can be only assumed to be equal to the blend's, $(V-I)_{\rm S}\sim 1.1$." + Even with these values and their uncertainties. the CMD location of the source can be linked to the LMC stars locus at the red giant branch. just above the Red Clump (see Fig. 2)).," Even with these values and their uncertainties, the CMD location of the source can be linked to the LMC stars locus at the red giant branch, just above the Red Clump (see Fig. \ref{fig:cmd}) )." + ΙΓ all additional light within a blend. comes from the lens (also hinted by zero-shift of the light centroid) its brightness can be calculated. however because there were no 1 -band data during the event we could not derive its colour.," If all additional light within a blend comes from the lens (also hinted by zero-shift of the light centroid) its brightness can be calculated, however because there were no $V$ -band data during the event we could not derive its colour." + The estimated location of the lens in this scenario is shown on Fig. 6.., The estimated location of the lens in this scenario is shown on Fig. \ref{fig:cmdlenses}. + We note the large positive error on. the. blending parameter. which might indicate that the stanclarc microlensing model is in fact not favoured. for this event.," We note the large positive error on the blending parameter, which might indicate that the standard microlensing model is in fact not favoured for this event." + ]ts relatively bright baseline ancl small aniplification may also suggest the brightness bump is caused by sonic kine of a variable star. for example a “Blue Bumper” blende with a red star to move its colour towards the red. part of the CAID.," Its relatively bright baseline and small amplification may also suggest the brightness bump is caused by some kind of a variable star, for example a “Blue Bumper” blended with a red star to move its colour towards the red part of the CMD." + Moreover. the light. curve indicates some smal asvnunetry around the peak. which can be reproduced with a microlensed binary source (clashed line in Fig.4)) with the goodness of fit ανμμ=1.52.," Moreover, the light curve indicates some small asymmetry around the peak, which can be reproduced with a microlensed binary source (dashed line in \ref{fig:events}) ) with the goodness of fit $\chi/N_\mathrm{dof}=1.52$." + However. that mode has very little constraints and the “wigele” around the peak could be as well caused by instrumental inaccuracies.," However, that model has very little constraints and the “wiggle” around the peak could be as well caused by instrumental inaccuracies." + Further photometric observations of this star are necessary as “Blue Bumpers” usually have secondary brightenings alter a decade or so., Further photometric observations of this star are necessary as “Blue Bumpers” usually have secondary brightenings after a decade or so. + This event was not detected in our regular search. procedure described above. because its baseline magnitude (21.22 mag) was well below our threshold (20.4 mag).," This event was not detected in our regular search procedure described above, because its baseline magnitude (21.22 mag) was well below our threshold (20.4 mag)." + It was found when the search. lor events was conducted: with magnitude cut removed. (see Table 3)). which means it would pass through the pipeline if the magnitude cut was cillerent.," It was found when the search for events was conducted with magnitude cut removed (see Table \ref{tab:conditions}) ), which means it would pass through the pipeline if the magnitude cut was different." + The microlensing model fit to its Z- and Y-band light curves (shown in Fig. 4)), The microlensing model fit to its $I$ - and $V$ -band light curves (shown in Fig. \ref{fig:events}) ) +" vielded the time-scale of fe=347417s days and πο=0.0705+0.0447 with blending parameters of fs,=0.2512+0.1643 and [ως=0.46180.3460.", yielded the time-scale of $\te=347\pm178$ days and $\u0=0.0705\pm0.0447$ with blending parameters of $\fsi=0.2512\pm0.1643$ and $\fsv=0.4618\pm0.3460$. + Lhe &oodness of fit to miulti-band. cata was \o/dof=0.749. whereas when only. Z-band data were used it was V7/dof=0.676.," The goodness of fit to multi-band data was $\chi^2/dof=0.749$, whereas when only $I$ -band data were used it was $\chi^2/dof= 0.676$ ." +" The single passbancl model returned. also a relatively long time-scale of fp=2244115 days with wy=0.12010.0820 and. fs,=0.4366+0.3201.", The single passband model returned also a relatively long time-scale of $\te=224\pm115$ days with $\u0=0.1201\pm0.0820$ and $\fsi=0.4366\pm0.3201$. + From the blended multi-colour models we were able to estimate the magnitude and colour of the source as fs=22.62£0.13 mag and (V1);=O0.5140.22. which locates he source on the blue end of the main sequence of the LALC (sce Fig. 2)).," From the blended multi-colour models we were able to estimate the magnitude and colour of the source as $\IS=22.62\pm0.13$ mag and $\VIS=0.51\pm0.22$, which locates the source on the blue end of the main sequence of the LMC (see Fig. \ref{fig:cmd}) )." + Severe blending indicates there is a lot of additional ight within the seeing disk of the object with the event., Severe blending indicates there is a lot of additional light within the seeing disk of the object with the event. + Judging from the sparse stellar density of the field LALC159 containing the event. we could assume all the remaining light xlongs to the lens.," Judging from the sparse stellar density of the field LMC159 containing the event, we could assume all the remaining light belongs to the lens." + Astrometry of the centroid from the DIA indicates no shift compared to the baseline template »osition., Astrometry of the centroid from the DIA indicates no shift compared to the baseline template position. +" ""his also supports the assumption that there is no additional light taking part in the event except the source and the lens.", This also supports the assumption that there is no additional light taking part in the event except the source and the lens. +" This places the lens at Vi,=23.00+0.40 mag and (VoZ)y=1.35+0.43. which is far from the main LAIC locus (see Fig. 6))."," This places the lens at $V_{\rm L}=23.00\pm0.40$ mag and $(V-I)_{\rm L}=1.35\pm0.43$, which is far from the main LMC locus (see Fig. \ref{fig:cmdlenses}) )." + Hs €MD location in the vicinity of the two NACLIO events caused by thick-disk lenses suggests this could be another example of a Galactic lens towards the LMC., Its CMD location in the vicinity of the two MACHO events caused by thick-disk lenses suggests this could be another example of a Galactic lens towards the LMC. + This. however. is relatively dillicult to confirm with a follow-up using currently. available instruments given the very faint magnitudes of both the source and the lens and large uncertainties of events parameters.," This, however, is relatively difficult to confirm with a follow-up using currently available instruments given the very faint magnitudes of both the source and the lens and large uncertainties of event's parameters." + This candidate was also not detected by the regular search pipeline. but was visually found in the data when inspecting large signal to noise ratio light curves.," This candidate was also not detected by the regular search pipeline, but was visually found in the data when inspecting large signal to noise ratio light curves." + Is light curve exhibits asvmmetrie bump with amplitude of about 3 mag. but the peak is covered. very. sparsely by the OGLIS observations.," Its light curve exhibits asymmetric bump with amplitude of about 3 mag, but the peak is covered very sparsely by the OGLE observations." + Llowever. single lens model does not. reproduce the light curve.," However, single lens model does not reproduce the light curve." + “Lhe simplest static binary source model is doing a much better job (see Fie. 4)).," The simplest static binary source model is doing a much better job (see Fig. \ref{fig:events}) )," + however due to insullicient number of datapoints we can not exclude numerous possible binary lens models here., however due to insufficient number of datapoints we can not exclude numerous possible binary lens models here. + Phe binary source model gave time- of about 27 days ancl amplifications of 3 ancl 137 on each of the components with y/Nao= 1.51. compared to αι=3.55 for a standard single source single lens moclel.," The binary source model gave time-scale of about 27 days and amplifications of 3 and 137 on each of the components with $\chi/N_\mathrm{dof}=1.51$ , compared to $\chi/N_\mathrm{dof}=3.55$ for a standard single source single lens model." + The lack of a sensible model for the event prevents a, The lack of a sensible model for the event prevents a +of LBGs. although the substantial box size ellects in their analysis introduced some uncertainty.,"of LBGs, although the substantial box size effects in their analysis introduced some uncertainty." + More recently. LBGs have also been studied in the near infrared (IR) (Sawicki&Yee1998:Papovich.Dickinson.nicketal. 2001).," More recently, LBGs have also been studied in the near infrared (IR) \citep*{Sawicki98, Papovich01, Pettini01, Sha01, Rudnick01}." +. Near LR observations are Less alfected by dust. obseuration and clirecthy probe the rest-frame optica xoperties of LBGs at z=3., Near IR observations are less affected by dust obscuration and directly probe the rest-frame optical properties of LBGs at $z=3$. + Pherefore. they allow a more reliable derivation of the stellar masses of LBGs.," Therefore, they allow a more reliable derivation of the stellar masses of LBGs." + Based on hese observations. it has been suggested that the value of he extinction lies in the range (D.V)00.0.3 with a median value of 0.15. and that a significant old. stellar »opulation exists in LBCGs at z=23. with a stellar mass of xLOA. (Papovichetal.2001:Shapley2001).," Based on these observations, it has been suggested that the value of the extinction lies in the range $E(B-V)\approx 0.0-0.3$ with a median value of 0.15, and that a significant old stellar population exists in LBGs at $z=3$, with a stellar mass of $\approx 10^{10}\Msun$ \citep{Papovich01, Sha01}." +. The existence of such a stellar component would again sugges hat LBGs are embedded in massive clark matter halos which inve continuously formed. stars over an extended.period of roughly one Cyr up {ος=3., The existence of such a stellar component would again suggest that LBGs are embedded in massive dark matter halos which have continuously formed stars over an extendedperiod of roughly one Gyr up to $z=3$. + These systems would then most likely evolve into elliptical galaxies at the present day. or into the spheroidal components of massive spiral galaxies.," These systems would then most likely evolve into elliptical galaxies at the present day, or into the spheroidal components of massive spiral galaxies." + llowever. in a competing model. LBCs have been suggested. to. be. merecr-induced starbursting systems associated with low-mass halos (Lowenthaletal.1997:Saw-icki&Yee199s:Somerville.Primack.Faber 2001).. and in some cases merecr-induced starbursts are given a crucial role even when LDBCGs are the most massive galaxies at their time (Somervilleetal.2001).," However, in a competing model, LBGs have been suggested to be merger-induced starbursting systems associated with low-mass halos \citep*{Lowenthal97, Sawicki98, Som01}, and in some cases merger-induced starbursts are given a crucial role even when LBGs are the most massive galaxies at their time \citep{Som01}." +. Given that the merger rate is expected to be quite high at z23. these scenarios provide an interesting alternative to the more conventional picture which associates LBGs with the most massive svstenis.," Given that the merger rate is expected to be quite high at $z\simeq 3$, these scenarios provide an interesting alternative to the more conventional picture which associates LBGs with the most massive systems." + Self-consistent. hvdrodyvnamic simulations are an ideal tool for trving to clistinguish between these. dilferent scenarios for the nature of LBGs., Self-consistent hydrodynamic simulations are an ideal tool for trying to distinguish between these different scenarios for the nature of LBGs. + Davéetal.(1999). and Weinberg.Hernequist&Katz(2002) were the first to employ smoothed particle hvdrodvnamics (SPILL) simulations to this end., \citet{Dave99} and \citet{Wei02} were the first to employ smoothed particle hydrodynamics (SPH) simulations to this end. + However. their box size o£ 11.15.+Mpe represented an inportant limitation. because the space-density of LBCs is so low that only a few of them canbe found in a volume of this size. às we will discuss further in Section 4..," However, their box size of $11.1\,\himpc$ represented an important limitation, because the space-density of LBGs is so low that only a few of them canbe found in a volume of this size, as we will discuss further in Section \ref{section:color-color}." + Therefore. simulations with a larger box size are desirable to obtain larger samples of simulated LBGs.," Therefore, simulations with a larger box size are desirable to obtain larger samples of simulated LBGs." +" Nagamine(2002). used an Eulerian hydrodynamic simulation with a box size of Li,25h! Mpe. tracing the merger history of galaxies from Stor—0."," \citet{Nag02} used an Eulerian hydrodynamic simulation with a box size of $\Lbox=25\,\himpc$ , tracing the merger history of galaxies from $z=5$ to $z=0$." + The results of these earlier numerical studies were consistent with each other. and agreed reasonably well with the observations. within the uncertainties.," The results of these earlier numerical studies were consistent with each other, and agreed reasonably well with the observations, within the uncertainties." + In. particular. the median stellar masses of LBGs were predicted to be ~10/7AFAL. and the simulated galaxies were experiencing significant star formation rates (230M. /vr) for extended periods of time (=1 Cir).," In particular, the median stellar masses of LBGs were predicted to be $\sim 10^{10}\himsun$ , and the simulated galaxies were experiencing significant star formation rates $>30\,\Msun/\yr$ ) for extended periods of time $\ge 1$ Gyr)." + In this paper. we improve on the earlier. numerical studies of LDCGs. by using à new set. of. high-resolution numerical simulations.," In this paper, we improve on the earlier numerical studies of LBGs by using a new set of high-resolution numerical simulations." + These simulations are based. on a novel model for the physies of star formation and feedback. and they use a more accurate implementation of SPL.," These simulations are based on a novel model for the physics of star formation and feedback, and they use a more accurate implementation of SPH." + For the first time. we also systematically study the clleets of resolution and box size in the context of simulated. LBC ealaxies.," For the first time, we also systematically study the effects of resolution and box size in the context of simulated LBG galaxies." + The treatment of star formation and feedback. we use is based on a sub-resolution multi-phase description of the dense. steu-Lforming interstellar medium (LSAL). and a phenomenological model for strong feedback hy galactic winds. as recently proposecl by(2003a).," The treatment of star formation and feedback we use is based on a sub-resolution multi-phase description of the dense, star-forming interstellar medium (ISM), and a phenomenological model for strong feedback by galactic winds, as recently proposed by." +. This model has been shown to provide converged star formation rates lor well-resolved galaxies. with a cosmic star formation history consistent with recent observations (Springel&Lcrnquist2003b:LernquistSpringel2003).," This model has been shown to provide converged star formation rates for well-resolved galaxies, with a cosmic star formation history consistent with recent observations \citep{SH03b, Her03}." +..” ‘Phe inclusion of winds was motivated by the realisation hat galactic outllows at high redshift (Pettinietal.2002) likely play à. key vole in distributing metals into the intergalactic medium (c.g.Aguirreetal.2001a.b).. as well as cing important for the regulation of star formation activity.," The inclusion of winds was motivated by the realisation that galactic outflows at high redshift \citep{Pet02} likely play a key role in distributing metals into the intergalactic medium \citep[e.g.][]{Aguirre01a, Aguirre01b}, as well as being important for the regulation of star formation activity." + In fact. winds may also alter the distribution of neutral eas around galaxies CXdelbergerctal.2003).. although the details of how this process may happen remain unclear (e.g.Croftctal.2002:Ixollmeier2003:al.2003).," In fact, winds may also alter the distribution of neutral gas around galaxies \citep{Ade03}, , although the details of how this process may happen remain unclear \citep[e.g.][]{Croft02, Kol03, Bruscoli}." +. In passing. we note that both Desjaccquesetal.(2003) and. Masellictal.(2003). have. found that the Lyman-a transmissivity close to 112615. as measured by Adelbergeretal.(2003).. is better reproduced if LBCs are identified as dwarf starbursting galaxies as proposed in Somervilleetal.(2001) and Weatherley&Warren(2003).," In passing, we note that both \citet{Des} and \citet{Maselli} have found that the $\alpha$ transmissivity close to LBGs, as measured by \citet{Ade03}, is better reproduced if LBGs are identified as dwarf starbursting galaxies as proposed in \citet{Som01} and \citet{WW}. ." +. We will ciscuss the work of Weatherley&Warren(2003) in Section &.., We will discuss the work of \citet{WW} in Section \ref{section:discussion}. + ‘Together with the increase in numerical resolution provided by our simulations. it is of interest to sce row our refined physical modelling mocifies the predictions or LBC properties within the ACDAL scenario.," Together with the increase in numerical resolution provided by our simulations, it is of interest to see how our refined physical modelling modifies the predictions for LBG properties within the $\Lambda$ CDM scenario." + This paper is organised. as follows., This paper is organised as follows. + In Section 2.. we ielly introduce the numerical parameters of our simulation set.," In Section \ref{section:simulation}, we briefly introduce the numerical parameters of our simulation set." + In Section. 3... we then describe. our. method. for computing spectra of simulated: galaxies both in the and the observed frame.," In Section \ref{section:method}, we then describe our method for computing spectra of simulated galaxies both in the rest-frame and the observed frame." + In Sections 4 and 5.. we show he colour-colour diagrams ancl colour-magnitude diagrams of simulated: galaxies. and we discuss the number density of colour-selected LBGs. as well as the stellar masses of LBGs at 2=3.," In Sections \ref{section:color-color} and \ref{section:colour-magnitude}, we show the colour-colour diagrams and colour-magnitude diagrams of simulated galaxies, and we discuss the number density of colour-selected LBGs, as well as the stellar masses of LBGs at $z=3$." + We then investigate the rest-[rame 1- band. luminosity function and observed. ραπ Iuminosity function in Section 6.. followed by an analysis of the star formation histories of LBCGs in Section 7..," We then investigate the rest-frame $V$ -band luminosity function and observed $R$ -band luminosity function in Section \ref{section:lf}, followed by an analysis of the star formation histories of LBGs in Section \ref{section:sf}." + Finally. we sumumarise and discuss the implications of our work in Section δὲ.," Finally, we summarise and discuss the implications of our work in Section \ref{section:discussion}." + We analyse a large set of cosmological SPL simulations with varving box size. mass resolution ancl feedback. strength. as summarised in Table 1..," We analyse a large set of cosmological SPH simulations with varying box size, mass resolution and feedback strength, as summarised in Table \ref{table:sim}." + Our box size ranges from. 10 to 1004+Alpe on a side. with particle numbers. between 2.TA and 2486°. giving gaseous mass resolutions in the range 3.35107 to 3.331075.ΑΝ.," Our box size ranges from 10 to $100\,\himpc$ on a side, with particle numbers between $2\times 144^3$ and $2\times 486^3$, giving gaseous mass resolutions in the range $3.3 \times 10^5$ to $3.3\times 10^8\himsun$ ." + These simulations are partly taken from astudy of the cosmic star formation history by Springel&Llernquist(2003b).. supplemented by additional runs with weaker or no galactic winds.," These simulations are partly taken from astudy of the cosmic star formation history by \citet{SH03b}, , supplemented by additional runs with weaker or no galactic winds." +" A similar set of simulations was used by Nagamine.Springel.&Llern-to studs the properties of damped Lyman-a absorbers. but here we analyse the C6-run whieh has higher resolution than the ""Cd-run used in the previous studies."," A similar set of simulations was used by \citet{Nag03a, Nag03b} to study the properties of damped $\alpha$ absorbers, but here we analyse the `G6'-run which has higher resolution than the `G4'-run used in the previous studies." +Paper 1. but still statistically consistent (at the 1.5o level) with the previous result.,"Paper 1, but still statistically consistent (at the $\sigma$ level) with the previous result." + LE we attempt to split the SN host ealaxy| sample into spirals (and. irregulars) ancl ellipticals. xwed on the available data on the host galaxy morphologies (largely LIST. images). whilst still excluding the two strong detections. we find a similar average Iux for the two classes of object (0.40 £0.29 for spirals/irregulars. and 0.69 xk 0.46 or ellipticals).," If we attempt to split the SN host galaxy sample into spirals (and irregulars) and ellipticals, based on the available data on the host galaxy morphologies (largely HST images), whilst still excluding the two strong detections, we find a similar average flux for the two classes of object (0.40 $\pm$ 0.29 for spirals/irregulars, and 0.69 $\pm$ 0.46 for ellipticals)." + H>y consideration of the local SLUGs 850j/m Luminosity unction (Dunne et al.," By consideration of the local SLUGs $\mu$ m luminosity function (Dunne et al.," + 2000 - though see also. Vlahakis et al.," 2000 - though see also Vlahakis et al.," + 2005) combined with appropriate& corrections from he cirrus model of Efstathiou Rowan-Robinson (2003). and tje assumption that the submillimetre emission. from. ellipticals is negligible. Paper 1. predicted. that the mean observied frame. οὔθμαι Hux of à z-0.5 galaxy would. be 0.56 d ΕΙ mJy if there is no evolution in the amount of dust in normal galaxies [from z=0 to z=0.5.," 2005) combined with appropriate corrections from the cirrus model of Efstathiou Rowan-Robinson (2003), and the assumption that the submillimetre emission from ellipticals is negligible, Paper 1 predicted that the mean observed frame $\mu$ m flux of a z=0.5 galaxy would be 0.56 $\pm$ 0.1 mJy if there is no evolution in the amount of dust in normal galaxies from z=0 to z=0.5." + Our result. is thus c'onsistent. with there being at most. only moderate, Our result is thus consistent with there being at most only moderate +and for aciabatic fast-cooliug. (Sarietal. 1998)).,"and for adiabatic fast-cooling, \cite{sari98}) )." + For slow-cooliug the spectral energy flux is (Sarictal. 1998))., For slow-cooling the spectral energy flux is \cite{sari98}) ). +" Note that a simple relation exists between the temporal and spectral iudices through the value of the electron iudex p for theligh-cucrey spectral slopes (7> ve) aud the spectral slope below v, in the slow- regine.", Note that a simple relation exists between the temporal and spectral indices through the value of the electron index $p$ for thehigh-energy spectral slopes $\nu > \nu_{\rm c}$ ) and the spectral slope below $\nu_{\rm c}$ in the slow-cooling regime. + Defining the low-enerev spectral slopeas o and the hieli-energv spectral slope as 6. the following relations between the temporal aud spectral iudices for a spherical blast wave are established (Sarictal. 1998)): The αμΊσα value of p is readilv determined from the measured ligh-cucrey spectral slope. p= 2a’.," Defining the low-energy spectral slopeas $\alpha$ and the high-energy spectral slope as $\alpha^{\prime}$, the following relations between the temporal and spectral indices for a spherical blast wave are established \cite{sari98}) ): The numerical value of $p$ is readily determined from the measured high-energy spectral slope, $p = -2 \alpha^{\prime}$ ." + Lone wavelength afterglow measurements eive typical electron indices in the range 2.0πpx2.5., Long wavelength afterglow measurements give typical electron indices in the range $2.0 \le p \le 2.5$. + Although the nature of the emission in this model is always svuchrotrou radiation with its characteristic slopes aud breaks. the time dependence of the breaks are affected by the details of the ecoletry and dvuaiiics.," Although the nature of the emission in this model is always synchrotron radiation with its characteristic slopes and breaks, the time dependence of the breaks are affected by the details of the geometry and dynamics." + The relatious m equation 6 are only valid iu the case of a splierical blast wave euncouuterimeg a coustaut density medium., The relations in equation 6 are only valid in the case of a spherical blast wave encountering a constant density medium. + Rhoads (1999) considered the adiabatic evolution of a collimated or jet-like outflow in which the cjecta are confined to a conical volune with a half opening anele 0.., Rhoads (1999) considered the adiabatic evolution of a collimated or jet-like outflow in which the ejecta are confined to a conical volume with a half opening angle $\theta_{c}$. + As the outflow eucouuters the external iuediui. the bulk Lorentz factor of the dow. D. decreases with radius and time as a power-law (ee sce Huangctal. 1999)).," As the outflow encounters the external medium, the bulk Lorentz factor of the flow, $\Gamma$, decreases with radius and time as a power-law (e.g., see \cite{huang99}) )." +" ILowever. the hwdrodyvnuauucal evolution of the shock changes from a power-law to an exponential regime when 60,=T!~@. (Rhoads1999.. Sarietal. 19993)."," However, the hydrodynamical evolution of the shock changes from a power-law to an exponential regime when $\theta_{b} \equiv \Gamma^{-1} \simeq \theta_{c}$ \cite{rhoads99}, \cite{sari99b}) )." + The observer is able to discern that the flow is confined to an expanding cone rather than a sphere because less radiation is observed., The observer is able to discern that the flow is confined to an expanding cone rather than a sphere because less radiation is observed. + Iu consequence. a break in the light curve to a FfoU behavior is observed as the ejecta sweep up a larger amount of mass.," In consequence, a break in the light curve to a $F_{\nu} \sim t^{-p}$ behavior is observed as the ejecta sweep up a larger amount of mass." + For adiabatic evolution of a jet. MyXF7. XP= const. and the peak flix scales as FoaaxsXt+ (Rhoads1999.. Sariotal. 1999}).," For adiabatic evolution of a jet, $\nu_{\rm m} \propto t^{-2}$, $\nu_{\rm c} \propto t^{0} =$ const, and the peak flux scales as $F_{\nu,{\rm max}} \propto t^{-1}$ \cite{rhoads99}, \cite{sari99b}) )." +" Thus the spectral flux for an aciabatic jet in the fast-cooliug regine 1s given by The jet geoinetry can therefore be tested by the simple relation 3=δα.2—p. mrespoective of whether the spectrum is fast or slow-cooling. provided that 1WMaN(Me.My,)- "," Thus the spectral flux for an adiabatic jet in the fast-cooling regime is given by and for slow-cooling, The jet geometry can therefore be tested by the simple relation $\beta = 2\alpha^{\prime} = -p$ , irrespective of whether the spectrum is fast or slow-cooling, provided that $\nu > {\rm max}(\nu_{\rm c},\nu_{\rm m})$ ." +We examine the properties of extended decay emission in GRBs in the energy rauge ~25-2000 keV using data from DATSE. a iuulti-detector all-sky moniter iustriunuenut onboard theObservatory (CGRO).," We examine the properties of extended decay emission in GRBs in the energy range $\sim 25$ -2000 keV using data from BATSE, a multi-detector all-sky monitor instrument onboard the (CGRO)." + DATSE consisted of eight identical detector modules placed at the corners of the CCRO in the form of au octahedrou (Fishinanotal.1989))., BATSE consisted of eight identical detector modules placed at the corners of the CGRO in the form of an octahedron \cite{fishman89}) ). + Each module contains a Large Area Detector (LAD) composed of a ποται iodide crystal scintillator that continuously recorded comut rates in 1.021 aud 2.018 second time intervals with four and sixteen cucrey channels. respectively (known as the DISCLA aud CONT data types).," Each module contains a Large Area Detector (LAD) composed of a sodium iodide crystal scintillator that continuously recorded count rates in 1.024 and 2.048 second time intervals with four and sixteen energy channels, respectively (known as the DISCLA and CONT data types)." + Nominally. a burst προς is declared when the count rates in two or more LADs exceed the backeround count rate by at least 5.50.," Nominally, a burst trigger is declared when the count rates in two or more LADs exceed the background count rate by at least $5.5\sigma$." + Various burst data types are then acciunulated. inchiding the four channel high time resolution (6 1125) discriminator science data (DISCSC).," Various burst data types are then accumulated, including the four channel high time resolution (64 ms) discriminator science data (DISCSC)." +" The DISCSC and DISCLA rates cover four broad energy chaunels in the 25-2000 keV range (25-50. 50-100. L00-300, >300 keV)."," The DISCSC and DISCLA rates cover four broad energy channels in the 25-2000 keV range (25-50, 50-100, 100-300, $> 300$ keV)." + The CONT data span roughly the same cucrey range. but with sixteen energv channels aud 2.018 s time resolution.," The CONT data span roughly the same energy range, but with sixteen energy channels and 2.048 s time resolution." + Our dataset was collected by visually selecting eveuts from the cureut BATSE catalog with extended decay features. using DISCSC time histories in the 25-2000 keV ranec.," Our dataset was collected by visually selecting events from the current BATSE catalog with extended decay features, using DISCSC time histories in the 25-2000 keV range." + Tune listorics used in this search had a time resolution of 61 is or lounger. therefore our scan was not sensitive to the selection of eveuts from the short class of bursts in the bimodal duration distribution (Ikouveliotoual. 1993a)).," Time histories used in this search had a time resolution of 64 ms or longer, therefore our scan was not sensitive to the selection of events from the short class of bursts in the bimodal duration distribution \cite{kouveliotou93a}) )." + A study of decay. ciission iu short CRBs will not be included in this analysis but will be the subject of future work., A study of decay emission in short GRBs will not be included in this analysis but will be the subject of future work. + Our search resulted in a sample of 10 bursts. 17 with a FRED-like profile aud 23 that exhibit a period of variability followed bv a smooth decaving enission tail.," Our search resulted in a sample of 40 bursts, 17 with a FRED-like profile and 23 that exhibit a period of variability followed by a smooth decaying emission tail." + We erouped events iuto three categories based on the characteristic time history of the bursts: (1) pure FREDs (PF). (2) FREDs with initial variability mainly during the peak (EV). aud (3) bursts with a period of variability followed by au emission tail (V|T).," We grouped events into three categories based on the characteristic time history of the bursts: (1) pure FREDs (PF), (2) FREDs with initial variability mainly during the peak (FV), and (3) bursts with a period of variability followed by an emission tail (V+T)." + Note that lis categorization onlv serves as a descriptive guideline or this analysis aud does not imply a robust temporal classification scheme., Note that this categorization only serves as a descriptive guideline for this analysis and does not imply a robust temporal classification scheme. + Our analysis uses cdiscrinüuator (DISCSC and DISCLA) aud continuous (CONT) data rom the DATSE LADs., Our analysis uses discriminator (DISCSC and DISCLA) and continuous (CONT) data from the BATSE LADs. + The source count rates in the ‘th time biu aud the jth οπσον channel. 5;;. were obtained by subtracting he background model rates. D;;. fron) tle bust time ustoryv.," The source count rates in the $i{\rm th}$ time bin and the $j{\rm th}$ energy channel, $S_{i,j}$, were obtained by subtracting the background model rates, $B_{i,j}$, from the burst time history." +" The backeround model rates in the jth euergv channel were generated by modeling pre aud post-burst vackevound intervals appropriate for cach burst with a )bvnonüdal of order η, where 1zx5x L "," The background model rates in the $j{\rm th}$ energy channel were generated by modeling pre and post-burst background intervals appropriate for each burst with a polynomial of order $n$ , where $1 \le n \le 4$ ." +Post-burst intervals werechosen at sufficicutly late times bevoud the ail ofthe burst. since the time when the tail cussion disappears into the backeround is somewhat uucertain.," Post-burst intervals werechosen at sufficiently late times beyond the tail ofthe burst, since the time when the tail emission disappears into the background is somewhat uncertain." + This method was adequate for bursts with durations less, This method was adequate for bursts with durations less +"Lavine explained the spin pulse in outburst we can ""urther explain the slight rise in hardness ratio at. pulse maximum.",Having explained the spin pulse in outburst we can further explain the slight rise in hardness ratio at pulse maximum. + Some of the N-ravs from the shock will be reflected by the white cdwarl and these will have a iarder spectrum. since the softer photons are preferentially. absorbed in the white cwarlatmosphere (e.g. Done. Osborne BBeardmore 1995).," Some of the X-rays from the shock will be reflected by the white dwarf and these will have a harder spectrum, since the softer photons are preferentially absorbed in the white dwarf atmosphere (e.g. Done, Osborne Beardmore 1995)." + Phe reflected. component. will be seen oeferentiallv when the accretion area is face on. that is at spin maximum. and so produce the increase in. hardness ratio.," The reflected component will be seen preferentially when the accretion area is face on, that is at spin maximum, and so produce the increase in hardness ratio." + The same elfect is seen in AAL Ler stars when the accretion region [aces us (Bearcmore 11995)., The same effect is seen in AM Her stars when the accretion region faces us (Beardmore 1995). + In addition to explaining the enhanced spin pulse during outburst the above picture also accounts for the increased absorption., In addition to explaining the enhanced spin pulse during outburst the above picture also accounts for the increased absorption. + There is substantial observational evidence that disces in DNe thicken during outburst. producing absorbing along lines-of-sight at angles up to aabove the plane (e.g. Mason 11988).," There is substantial observational evidence that discs in DNe thicken during outburst, producing absorbing along lines-of-sight at angles up to above the plane (e.g. Mason 1988)." + At the high inclination of XY Ari this ensures that the Hux from the upper accretion region will encounter the extra absorption seen in the spectra., At the high inclination of XY Ari this ensures that the flux from the upper accretion region will encounter the extra absorption seen in the spectra. + ‘To check the plausibility of the interpretation we can make order of magnitude estimates of the accretion Low.AL.," To check the plausibility of the interpretation we can make order of magnitude estimates of the accretion flow,." + At the peak of the outburst the accretion rate is 24 times that in quiescence (scaling it by the normalisations of the X-ray spectral fits. ancl assuming that only the upper pole is seen in outburst).," At the peak of the outburst the accretion rate is 24 times that in quiescence (scaling it by the normalisations of the X-ray spectral fits, and assuming that only the upper pole is seen in outburst)." + The increased tthrough the inner disc means that the ram. pressure (x AL) overwhelms the magnetic. pressure at. the original magnetosphere., The increased through the inner disc means that the ram pressure $\propto$ ) overwhelms the magnetic pressure at the original magnetosphere. + Thus only a fraction of the increased material accretes inumeciately (he X-ray normalisations rise by a factor 4: Fig 6) and most of it pushes the clise inwards [rom 9 (ιο 4 wwhere the magnetic pressure (x or?) ds sullicient to establish a new equilibrium., Thus only a fraction of the increased material accretes immediately (the X-ray normalisations rise by a factor 4; Fig 6) and most of it pushes the disc inwards from 9 to 4 where the magnetic pressure $\propto r^{-6}$ ) is sufficient to establish a new equilibrium. + Here. the Dow from the inner disc again matches the Low into it and the luminosity reaches 24 times the quiescent. value.," Here, the flow from the inner disc again matches the flow into it and the luminosity reaches 24 times the quiescent value." + The delay of 0.82 d (Fig., The delay of 0.3–2 d (Fig. + 1) is the time taken to fill the disc between 99 and 74Raa., 1) is the time taken to fill the disc between 9 and 4. + With a quiescent accretion rate of (Warner 1997) it implies a mass of ee for this section of disc., With a quiescent accretion rate of (Warner 1997) it implies a mass of g for this section of disc. + Using an outer disc radius of 660 ((Allan 11996). and assuming a constant surface density. the total mass of the dise is eo. Further. again scaling from the X-ray luminosities. the total mass accreted over the 5 days of outburst is oo For comparison. the theoretical disc by Ichikawa OOsaki (1992). adjusted for the parameters of U Cem. has a total mass of ee and deposits ee onto the white dwarf cach outburst.," Using an outer disc radius of 60 (Allan 1996), and assuming a constant surface density, the total mass of the disc is g. Further, again scaling from the X-ray luminosities, the total mass accreted over the 5 days of outburst is g. For comparison, the theoretical disc by Ichikawa Osaki (1992), adjusted for the parameters of U Gem, has a total mass of g and deposits g onto the white dwarf each outburst." + X. model by Cannizzo. Wheeler PPolidan (1986) has a total mass of ee and again deposits ee per outburst.," A model by Cannizzo, Wheeler Polidan (1986) has a total mass of g and again deposits g per outburst." + Phese values agree with our values to within the observational uncertainties., These values agree with our values to within the observational uncertainties. + We summarise the above as follows., We summarise the above as follows. + In quiescence the disc is disrupted at ~99 Pea. allowing a clear view of the white dwarf.," In quiescence the disc is disrupted at 9 $R$, allowing a clear view of the white dwarf." + Aceretion occurs roughly equally onto both poles., Accretion occurs roughly equally onto both poles. + The appearance‘disappearance of one pole. compensates or the disappearance/appearance of the opposite pole. producing a low-amplitude pulse as the white cwarf spins.," The appearance/disappearance of one pole compensates for the disappearance/appearance of the opposite pole, producing a low-amplitude pulse as the white dwarf spins." + Dav 1: A disc instability occurs somewhere in the disc. ceeding material towards the magnetosphere at an increased rate.," Day 1: A disc instability occurs somewhere in the disc, feeding material towards the magnetosphere at an increased rate." + The magnetosphere shrinks and the inner disc occults 16 lower pole., The magnetosphere shrinks and the inner disc occults the lower pole. + Left alone. the upper pole now produces a aree amplitude spin pulse as it evcles from the visible face o the hidden face.," Left alone, the upper pole now produces a large amplitude spin pulse as it cycles from the visible face to the hidden face." + Some of the increased. mass How reaches 1e white ενας and the intrinsic X-ray emission increases by vfactor 4., Some of the increased mass flow reaches the white dwarf and the intrinsic X-ray emission increases by a factor 4. + However. since we are no longer seeing the lower vole. and since the upper pole sullers increased. absorption. 16 observed. count rate drops.," However, since we are no longer seeing the lower pole, and since the upper pole suffers increased absorption, the observed count rate drops." + The material accretes onto xwt of the ring around the white dwarf. and at some spin ohases the accreting region is entirely on the visible face. xoducing a Hat topped spin pulse.," The material accretes onto part of the ring around the white dwarf, and at some spin phases the accreting region is entirely on the visible face, producing a flat topped spin pulse." + Dav 2: The mass flow onto the white ciwarf increases dramatically. producing a 24-fold increase in X-ray emission over quiescence.," Day 2: The mass flow onto the white dwarf increases dramatically, producing a 24-fold increase in X-ray emission over quiescence." + Thus. even with the increased absorption.," Thus, even with the increased absorption," +(?) andIIr.,\citep{2007A&A...468..951K} and. + Thus. the origins of the shallowine of the lags iu NGC 1211 aud NGC 891 may bo different.," Thus, the origins of the shallowing of the lags in NGC 4244 and NGC 891 may be different." + Also displaving radial variation in the lag is the DIC in one quadrant of NGC 1302 (2)... but the treud found in that galaxv was opposite from what we detect in the dn NGC 1211.," Also displaying radial variation in the lag is the DIG in one quadrant of NGC 4302 \citep{2007ApJ...663..933H}, but the trend found in that galaxy was opposite from what we detect in the in NGC 4244." + NGC 1302 displaved a substantial steepening of the lag. eoiug from approximately 23 kin tkpe ttoahnost 60luns ! bat radii outward of 1.25 kpc.," NGC 4302 displayed a substantial steepening of the lag, going from approximately $-$ 23 km $^{-1}$ $^{-1}$ to almost $-$ 60 km $^{-1}$ $^{-1}$ at radii outward of 4.25 kpc." + Ultimatelv. a larger sample of galaxies where this phenomenon is observed aud modeled will ereatlv aid in determining its cause and nature.," Ultimately, a larger sample of galaxies where this phenomenon is observed and modeled will greatly aid in determining its cause and nature." + There is substautial evidence against the existence of an extended halo in NCC 1211. most notably the alure of the addition of a second vertical componcut w itself or accompanied by a warp along the line of sight to improve the fit of the vertical profile (Figure 5)). aud that the appearance of Figure 1. docs rot differ substantially from the 104 shallower Olliug data.," There is substantial evidence against the existence of an extended halo in NGC 4244, most notably the failure of the addition of a second vertical component by itself or accompanied by a warp along the line of sight to improve the fit of the vertical profile (Figure \ref{fig5}) ), and that the appearance of Figure \ref{fig1} does not differ substantially from the $\times$ shallower Olling data." + Furthermore. a second componcut added to the warp model vields uo overall improvement to the by ots or channel maps aud adds au unnecessary degree of complexity.," Furthermore, a second component added to the warp model yields no overall improvement to the bv plots or channel maps and adds an unnecessary degree of complexity." + The significance of the lack of au ido has vet to be determined., The significance of the lack of an halo has yet to be determined. + Tavine such a sinall ΠΠΟΙ of galaxies observed to this depth and modeled using these methods makes it impossible to extract anv reliable treuds., Having such a small number of galaxies observed to this depth and modeled using these methods makes it impossible to extract any reliable trends. + This will be remedied iu the near ture via the TALOCAS survey aud EVLA observations involving some WALOCAS team members., This will be remedied in the near future via the HALOGAS survey and EVLA observations involving some HALOGAS team members. + For now. we can only compare the results for NGC 1211 with those of previously modeled galaxies.," For now, we can only compare the results for NGC 4244 with those of previously modeled galaxies." + Extended neutral halos have been detected im several ealaxies listed below., Extended neutral halos have been detected in several galaxies listed below. + The full resolution lo riis noise per channel for cach external galaxy is given in Jy |., The full resolution $\sigma$ rms noise per channel for each external galaxy is given in mJy $^{-1}$. +" An extended neutral halo is seen iu the Milkv Wav (?).. with a scale height of 1.6 kpe (2) NGC 891 (2: 0.09 1iJs- 1.23.4167 resolution). with a scale height of 1.25- kpe (?).. NGC 1559 with a maxima scale height of L kpe (7: 0.52 ταν 1 12.24.21.5"" resolution). as well as UGC 7321 (2) with a EWIIM of 3.2 kpe: 0.36- mJy !. 16.2415.77. resolution 7))."," An extended neutral halo is seen in the Milky Way \citep{2008ApJ...679.1288L}, , with a scale height of 1.6 kpc \citep{2010arXiv1010.3563M} NGC 891 \citealt{1997ApJ...491..140S}; 0.09 mJy $^{-1}$, $\times$ 16"" resolution), with a scale height of 1.25-2.5 kpc \citep{2007AJ....134.1019O}, NGC 4559 with a maximum scale height of 4 kpc \citealt{2005A&A...439..947B}; 0.52 mJy $^{-1}$, $\times$ 24.5"" resolution), as well as UGC 7321 \citep{2003ApJ...593..721M} with a FWHM of 3.3 kpc; 0.36-0.40 mJy $^{-1}$, $\times$ 15.7"" resolution \citealt{2003AJ....125.2455U}) )." + These are all substantially eveater than our estimated scale height for NCC 1211 of 565 pe. although that is only for a thickened disk. rather than a disk-halo combination as seen in those galaxies listed above.," These are all substantially greater than our estimated scale height for NGC 4244 of 565 pc, although that is only for a thickened disk, rather than a disk-halo combination as seen in those galaxies listed above." + NGC 1559 and CGC 7321 are discussed below., NGC 4559 and UGC 7321 are discussed below. +" NGC 1559 has a star formation rate: 0.69 M, vet (?).. approximately 5 times that of NGC. 1211."," NGC 4559 has a star formation rate; 0.69 $_{\odot}$ $^{-1}$ \citep{2011A&A...526A.118H}, approximately 5 times that of NGC 4244." + Roughly 1054 of the total mass is contained in its halo (?).., Roughly $\%$ of the total mass is contained in its halo \citep{2005A&A...439..947B}. + If halos are due to star formation. then this would be consistent with NGC 121L having a simaller halo. or as found in this work. none at all.," If halos are due to star formation, then this would be consistent with NGC 4244 having a smaller halo, or as found in this work, none at all." + UGC 7321 is also a galaxy with low star formation. with a rate of (0.15 ML. wri.," UGC 7321 is also a galaxy with low star formation, with a rate of 0.15 $_{\odot}$ $^{-1}$." + This rate of star formation is comparable to that of NGC 121L. aud vet a halo is detected iu UGC 7321. but not NGC 1211.," This rate of star formation is comparable to that of NGC 4244, and yet a halo is detected in UGC 7321, but not NGC 4244." + At first glance. the two galaxies appear quite siuular.," At first glance, the two galaxies appear quite similar." + Both display thickened disks with warps iuIli. aud bv comparing with results for UGC 7321 im ?.. thei rotation curves indicate simular masses. and thus similar eravitational potentials.," Both display thickened disks with warps in, and by comparing with results for UGC 7321 in \citet{2010A&A...515A..63O}, their rotation curves indicate similar masses, and thus similar gravitational potentials." + Finally. neither has close companion salaxies.," Finally, neither has close companion galaxies." + Du spite of these similarities. extended wing structures are seen dn the vertical profiles shown iu Figures 2 and 5 of 7.. which are absent in analogous plots of NGC. 1211 (not. shown). drawing a clear and fundamental distinctiou between the morplologics of the two.," In spite of these similarities, extended wing structures are seen in the vertical profiles shown in Figures 2 and 5 of \citet{2003ApJ...593..721M}, which are absent in analogous plots of NGC 4244 (not shown), drawing a clear and fundamental distinction between the morphologies of the two." + The presence of a halo in UCC 7321. a galaxy with a comparable star formation rate to that of NGC 1211. indicates that halos necessarily due solely to star formation.," The presence of a halo in UGC 7321, a galaxy with a comparable star formation rate to that of NGC 4244, indicates that halos necessarily due solely to star formation." + It is uot the primary intent of this paper to perform an exhaustive study of suiall-scale features., It is not the primary intent of this paper to perform an exhaustive study of small-scale features. + NGC [2Lb is nearly devoid of promunent. enersetieIDL shells as well as expanding features akin to those seen iu iore actively star fornüng galaxies.," NGC 4244 is nearly devoid of prominent, energetic shells as well as expanding features akin to those seen in more actively star forming galaxies." + IElowever. a small umber of notable features are detected (85) aud will be discussed.," However, a small number of notable features are detected 5) and will be discussed." + Firstly. we cousider the shell-like feature in the approaching halt.," Firstly, we consider the shell-like feature in the approaching half." + This feature is above aud slightly offset racially from a region of star formation (Figure 11)). which extends between 3.5° aud 1.6 along the major axis in the Πα and 21 an data.," This feature is above and slightly offset radially from a region of star formation (Figure \ref{fig11}) ), which extends between 3.5' and 4.6' along the major axis in the $\alpha$ and 24 $\mu$ m data." + The feature’s proximity to a region of star formation as well as the lack of nearby external features iudicate an internal origin., The feature's proximity to a region of star formation as well as the lack of nearby external features indicate an internal origin. + To estimate the energy required to produce it. the number density must first be found.," To estimate the energy required to produce it, the number density must first be found." + For the caleulatious below we assume this feature is indeed a shell created by multiple supernovae in the disk., For the calculations below we assume this feature is indeed a shell created by multiple supernovae in the disk. + Following the approach taken by 2. we measure the peals flux in the limbs of the prestuued shell to acquire a colui density.," Following the approach taken by \citet{1993AJ....105.2098R}, we measure the peak flux in the limbs of the presumed shell to acquire a column density." + To obtain the uumuber density. we then consider the path length along the line of sight (7) to be: Where d is the shell wall thickness aud + is the mner radius of the shell.," To obtain the number density, we then consider the path length along the line of sight $l$ ) to be: Where $d$ is the shell wall thickness and $r$ is the inner radius of the shell." + Since the shell walls are not well resolved. we set d equal to the beam resolution parallel to the disk of about 17.," Since the shell walls are not well resolved, we set $d$ equal to the beam resolution parallel to the disk of about 17""." + From this. a value of 1280 pc is obtained for /. which vields a παπανο density of 0.15 cm? ," From this, a value of 1280 pc is obtained for $l$, which yields a number density of 0.15 $^{-3}$ ." +Now using Figure 12.. au estimate for the expausion velocity (Voy) is 25 lan s1," Now using Figure \ref{fig12}, an estimate for the expansion velocity $V_{\rm exp}$ ) is 25 km $^{-1}$." + Together with the estimate for the shells radius iu parsecs GaiTHO pc) aud assundue a constant expansion. its age is approxiuatelv 2.0ς10* vers.," Together with the estimate for the shell's radius in parsecs $R_{\rm shell}=750$ pc) and assuming a constant expansion, its age is approximately $2.9\times10^{7}$ years." + We now calculate the cucrey required to produce sucli a shell from ? where my is the umber deustv iu c;P. Roya is the radius of the shell iu parsecs. and Va is in kin Las described above: Given these estimates. we find that a single burst of energv of roughly 5.1.1075 eres orthe equivaleut of 510 supernovae would be required to produce this shell. (," We now calculate the energy required to produce such a shell from \citet{1974ApJ...188..501C} where $n_{\rm 0}$ is the number density in $^{-3}$, $R_{\rm shell}$ is the radius of the shell in parsecs, and $V_{\rm exp}$ is in km $^{-1}$ as described above: Given these estimates, we find that a single burst of energy of roughly $5.4\times10^{53}$ ergs orthe equivalent of 540 supernovae would be required to produce this shell. (" +assuning an euerev of 1075 eres per supernova) Lf the shell iustead formed frou a coutiuuous supply of energv as described iu ?:: where tr[ is the age iu units of LOS voars. thiswould ouly require1.7«10 eres or 170 superuovac.,"assuming an energy of $^{51}$ ergs per supernova) If the shell instead formed from a continuous supply of energy as described in \citet{1987ApJ...317..190M}: : where $t_{\rm 7}$ is the age in units of $10^7$ years, thiswould only require$1.7\times10^{53}$ ergs or 170 supernovae." +Thus. at the lowest order in Z7. the Doussinesq equations reduce to the Navier-Stokes equation: together with the incompressibility condition. At this order. the dynamical aud. thermal equations are decoupled.,"Thus, at the lowest order in $P_e$, the Boussinesq equations reduce to the Navier-Stokes equation: together with the incompressibility condition, At this order, the dynamical and thermal equations are decoupled." +" The coupling is recovered at the first order in D: Solutions à=ug|Pu4.0042.0, valid up to the first order in £7. must satisfv the above system of equations G3). (9). 09). (00)). (109). (12)."," The coupling is recovered at the first order in $P_e$ : Solutions ${\bf \hat{u} }= {\bf u_0} + P_e {\bf u_1}, \hat{\theta} = \theta_0 + +P_e \theta_1$ valid up to the first order in $P_e$ must satisfy the above system of equations \ref{eq:temp0}) ), \ref{eq:vel0}) ), \ref{eq:div0}) ), \ref{eq:vel2}) ), \ref{eq:temp2}) ), \ref{eq:div2}) )." + We note that the Lagraugiau derivative of temperature deviations docs not appear iu the heat equation of this system., We note that the Lagrangian derivative of temperature deviations does not appear in the heat equation of this system. + Thus. at the first order in {ιν one would have found the same system of equations for ug. uy. Oy. (4 if the Tavlor series had been introduced iu the following equations: Therefore. if u aud 0 actually behave as Taylor series for sinall Pécclet πανους. the solution of the above equations is ideutica to the solution of the Doussinesq equations up to the first order in 2...," Thus, at the first order in $P_e$ , one would have found the same system of equations for ${\bf u_0}$, ${\bf u_1}$, $\theta_0$ , $\theta_1$ if the Taylor series had been introduced in the following equations: Therefore, if ${\bf u}$ and $\theta$ actually behave as Taylor series for small Pécclet numbers, the solution of the above equations is identical to the solution of the Boussinesq equations up to the first order in $P_e$." + The unique difference with the Boussinesq equations conies from the heat equation., The unique difference with the Boussinesq equations comes from the heat equation. + Physically. the process leading to the balance Paw=πό can be described as follows: For luge values of the thermal diffusivity. the temperature fluctuations are expected to be small and the mean temperature stratification to remain unchanged by the mechanical heat fiux.," Physically, the process leading to the balance $P_e w = \nabla ^2 \theta$ can be described as follows: For large values of the thermal diffusivity, the temperature fluctuations are expected to be small and the mean temperature stratification to remain unchanged by the mechanical heat flux." + IHosvever. vertical motions advecting fud parcels against 1c Incan tempcrature eradient always produce temperature deviations aud. uulike the non-linear advection term u.V0. this eencration process does not depend on the amplitude of the temperature deviations.," However, vertical motions advecting fluid parcels against the mean temperature gradient always produce temperature deviations and, unlike the non-linear advection term ${\bf u}. \nabla \theta$, this generation process does not depend on the amplitude of the temperature deviations." + As fluid parcels eo up (or down) in a nean tempcrature eraclicut. the amplitude of the temperature deviations tends to increase continuously," As fluid parcels go up (or down) in a mean temperature gradient, the amplitude of the temperature deviations tends to increase continuously." +Iu the meantime. thermal diffusion teudsto reduce these temperature deviations.,"In the meantime, thermal diffusion tendsto reduce these temperature deviations." + Taspection of the heat Eq., Inspection of the heat Eq. +clusters have been used to study the iuflueuce of the CN band streneths ou the Stromaineren metallicity.,clusters have been used to study the influence of the CN band strengths on the Strömmgren metallicity. + The observations were performed during the mights 21-2] April 1995 with the Danish 1.5lu telescope at ESO/La Silla., The observations were performed during the nights 21-24 April 1995 with the Danish 1.54m telescope at ESO/La Silla. + The CCD in use was a Tektronix chip with 1051 pixels., The CCD in use was a Tektronix chip with $\times$ 1024 pixels. + The f/8.5 beam of the telescope provides a scale of 15/77 πα. aud with a pixel size of 21 ja the total field is 6/3«673.," The $f$ /8.5 beam of the telescope provides a scale of $15\farcs7$ /mm, and with a pixel size of 24 $\mu$ m the total field is $6\farcm3 \times +6\farcm3$." + The observations aud data reduction of the M22 and M55 inages have beeu preseuted by Richter et al. (1999)., The observations and data reduction of the M22 and M55 images have been presented by Richter et al. \cite{richp}) ). + Iu x Cen. 20 fields were observed caving the third nieht of the run through the Strónmmneren ybe filters (Danish set of maging filters).," In $\omega$ Cen, 20 fields were observed during the third night of the run through the Strömmgren $ybv$ filters (Danish set of imaging filters)." + Table 1. gives a log of the field positions.," Table \ref{log} + gives a log of the field positions." + In Fig., In Fig. + 1. all fields are plotted ina coordinate system centered on w Cen.," 1, all fields are plotted in a coordinate system centered on $\omega$ Cen." + The exposure times were 70. 120. aud 210 seconds for jy. b aud e. respectively.," The exposure times were 70, 120, and 240 seconds for $y$, $b$ and $v$, respectively." + All nights had photometricconditious. and the seeing. measured frou the PWIIAL of stellar images. was in the range 1072—175.," All nights had photometricconditions, and the seeing, measured from the FWHM of stellar images, was in the range $1\farcs2 - 1\farcs5$." + The CCD frames were processed with staudard IRAF routines., The CCD frames were processed with standard IRAF routines. + Tustramental magnitudes were derived using DAO- PIIOT II (Stetson 1987.. 1992)).," Instrumental magnitudes were derived using DAO- PHOT II (Stetson \cite{stet87}, \cite{stet92}) )." + For the coluparison with the standard stars. aperturePSF shifts have been determined i all fields.," For the comparison with the standard stars, aperture–PSF shifts have been determined in all fields." + The romaine nucertainty of this shift is iu the order of 0.01 mae in all filters., The remaining uncertainty of this shift is in the order of 0.01 mag in all filters. + The corrected magnitudes of the stars belougine to overlapping areas of two adjacent fields agree very well and have been avaraged for the final photometry file., The corrected magnitudes of the stars belonging to overlapping areas of two adjacent fields agree very well and have been avaraged for the final photometry file. + The calibration equations and cocticicuts for the third night[um are given in Richter et al. (1999))., The calibration equations and coefficients for the third night are given in Richter et al. \cite{richp}) ). + After the photometric reduction and calibration oftlic magnitudes. the average photometric errors for the red ejauts used in the metallicity calibration are 0.015 mae for V. 0.016 mae for (by) and 0.02[ mag for ny.," After the photometric reduction and calibration of the magnitudes, the average photometric errors for the red giants used in the metallicity calibration are 0.015 mag for $V$ , 0.016 mag for $(b-y)$ and 0.024 mag for $m_1$ ." +erain models and the amounts of these elements available in the diffuse ISM. when recent depletion measurements ancl B-star reference abundances are combined (Snow Wilt 1996).,"grain models and the amounts of these elements available in the diffuse ISM, when recent depletion measurements and B-star reference abundances are combined (Snow Witt 1996)." + On the other hand. it also does not solve this problem: it simply shifts more of the needed mass into larger grains.," On the other hand, it also does not solve this problem; it simply shifts more of the needed mass into larger grains." + The full discussion of this problem goes bevond the scope of (his paper. and we refer to Frisch et al. (," The full discussion of this problem goes beyond the scope of this paper, and we refer to Frisch et al. (" +1999) for further details.,1999) for further details. + A serious problem does arise with respect to the NMBN distribution when one considers its impact on (he wavelength dependence of extinction., A serious problem does arise with respect to the XMRN distribution when one considers its impact on the wavelength dependence of extinction. + The original MIUN distribution (Mathis et al., The original MRN distribution (Mathis et al. + 1977) was constructed with the constraint that the average Galactic extinction law will 4 = 3.2 as well as (he canonical ratio of the extinction optical depth per hydrogen atom would be matched., 1977) was constructed with the constraint that the average Galactic extinction law with $R_{V}$ = 3.2 as well as the canonical ratio of the extinction optical depth per hydrogen atom would be matched. +" By shifting most of the dust mass into grains with larger sizes. we find that the NAIRN distribution leads to an extinction curve with 2, — 6.1 and an A, /N(II) ratio of only half the canonical value of 5.3x10.77 eni?"," By shifting most of the dust mass into grains with larger sizes, we find that the XMRN distribution leads to an extinction curve with $R_{V}$ = 6.1 and an ${_{_V}}$ /N(H) ratio of only half the canonical value of $\times 10^{-22}$ $^{2}$." + By contrast. the extinction for NMBRN Iongward of | jan is greatly enhanced over that expected for the standard MBN distribution.," By contrast, the extinction for XMRN longward of 1 $\mu$ m is greatly enhanced over that expected for the standard MRN distribution." +" The extinction law toward Nova Cygni 1992 is not known specifically, ancl a value of δν = 6.1 would suggest a peculiar grain size distribution (hat differs from that in the average ISM towards that line of sight."," The extinction law toward Nova Cygni 1992 is not known specifically, and a value of $R_{V}$ = 6.1 would suggest a peculiar grain size distribution that differs from that in the average ISM towards that line of sight." + A more likely solution to the present dilemma seems (to be in the high probabilitw that neither MIN nor NMBRN with their assuniptions of chemically homogeneous. spherical solid particles are the correct descriptions of interstellar grains and their size distribution.," A more likely solution to the present dilemma seems to be in the high probability that neither MRN nor XMRN with their assumptions of chemically homogeneous, spherical solid particles are the correct descriptions of interstellar grains and their size distribution." + The apparent incompatibility between the constraints arising from the X-ray halo of Nova Cvgni 1992 and the Galactic exGinelion law simply illustrates again the incompleteness of current grain models. (Witt 1999). which will not be resolved here.," The apparent incompatibility between the constraints arising from the X-ray halo of Nova Cygni 1992 and the Galactic extinction law simply illustrates again the incompleteness of current grain models (Witt 1999), which will not be resolved here." + We have demonstrated with the example of Nova Cveni 1992 Chat the line-ol-sight density distribution of the scattering dust is also a critical [actor in determining the shape ol the seattering halo., We have demonstrated with the example of Nova Cygni 1992 that the line-of-sight density distribution of the scattering dust is also a critical factor in determining the shape of the scattering halo. + We suggest. based on Nova Cvgni 1992's height above the Galactic," We suggest, based on Nova Cygni 1992's height above the Galactic" +done. including establishing whether spots disappear at rotation periods of 2-3 hours. (hus providing a natural explanation for (he CV period-gap.,"done, including establishing whether spots disappear at rotation periods of 2-3 hours, thus providing a natural explanation for the CV period-gap." + CV secondaries al these periods are themselves M-tvpe stars and so the mere detection of TiO bands will not be sufficient to prove the presence of starspols., CV secondaries at these periods are themselves M-type stars and so the mere detection of TiO bands will not be sufficient to prove the presence of starspots. + The Isaac Newton Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrolisica de Canarias., The Isaac Newton Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. + This work made use of Peter van Hoofs Atomic Line List (http://www.pa.uky.edu/ peter/aton, This work made use of Peter van Hoof's Atomic Line List (http://www.pa.uky.edu/ peter/atomic). + The majority of this work was carried out when NAW was supported by a PPARC studentship at Keele University. ancl TN was in receipt of a PPARC Advanced Fellowship at the same institute.," The majority of this work was carried out when NAW was supported by a PPARC studentship at Keele University, and TN was in receipt of a PPARC Advanced Fellowship at the same institute." + We are grateful to Steve Saar for comments on an earlier version of (his paper., We are grateful to Steve Saar for comments on an earlier version of this paper. +The classical Algol-ivpe binaries are composed. of a B or A spectral-tv main-sequence hotter. primary star and an EF or later-Gpe. giant. or subgiant cooler secondary. star.,The classical Algol-type binaries are composed of a B or A spectral-type main-sequence hotter primary star and an F or later-G giant or subgiant cooler secondary star. + They are semi-detached interacting binary svstems in which the evolved. less massive secondary components have filled their corresponding Roche lobes., They are semi-detached interacting binary systems in which the evolved less massive secondary components have filled their corresponding Roche lobes. + Therefore. the material on the loss massive secondary star is transferring onto the hot main-sequence primaries.," Therefore, the material on the less massive secondary star is transferring onto the hot main-sequence primaries." + The classical Algols are. in general. in a slow stage of mass transfer.," The classical Algols are, in general, in a slow stage of mass transfer." + The evolution of the semi-detached: binaries is mostly. interpreted. in the framework of the Roche model, The evolution of the semi-detached binaries is mostly interpreted in the framework of the Roche model. + A number. of. implicit assumptions are made for its application., A number of implicit assumptions are made for its application. + These assumptions are ordered as follows: 1) the components are point masses. they are co-rotating with the orbital motion and 2) the most importanthy the total mass and. angular momentum are conserved.," These assumptions are ordered as follows: 1) the components are point masses, they are co-rotating with the orbital motion and 2) the most importantly the total mass and angular momentum are conserved." + Llowever. these restrictions are not so. valid for the evolved. binary systems.," However, these restrictions are not so valid for the evolved binary systems." + Glazunova et al. (, Glazunova et al. (