ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Also clear is the large discrepancy relative to a regular écchelle spectrum around 1000Hz., Also clear is the large discrepancy relative to a regular écchelle spectrum around $1000\:{\rm{\mu Hz}}$.3 The only mode present in the and not detected with the EACF is the mixed mode at 695.75uHz., The only mode present in the and not detected with the EACF is the mixed mode at $695.75\:{\rm{\mu Hz}}$.4 This peak appears as supernumerary when compared to the regular agency of the modes., This peak appears as supernumerary when compared to the regular agency of the modes.5 The EACF makes it possible to derive the large separation one radial order further than does peak-bagging., The EACF makes it possible to derive the large separation one radial order further than does peak-bagging.6 Results for KIC 10920273 are given in Fig. [[3.., Results for KIC 10920273 are given in Fig. \ref{fig_autodeltanuridge_10920273}.7 The lower SNR is counterbalanced by using a broader filter when computing the EACF., The lower SNR is counterbalanced by using a broader filter when computing the EACF.8" Again, the analysis is not conclusive for one mixed mode at low frequency, but it is able to recover the /21 ridge."," Again, the analysis is not conclusive for one mixed mode at low frequency, but it is able to recover the $l\!=\!1$ ridge."9 We note that the even ridge is affected by the proximity of mixed modes., We note that the even ridge is affected by the proximity of mixed modes.10" As opposed to the case of KIC 10273246, the EACF does not provide any further modes."," As opposed to the case of KIC 10273246, the EACF does not provide any further modes."11" Stellar rotation removes the (2/+1)-fold degeneracy of the frequencies of non-radial modes, allowing for a direct measurement of the stellar angular velocity averaged over the regions probed by these modes, as conveyed by Eq. A]. "," Stellar rotation removes the $(2l + 1)$ -fold degeneracy of the frequencies of non-radial modes, allowing for a direct measurement of the stellar angular velocity averaged over the regions probed by these modes, as conveyed by Eq. \ref{ledoux}. ."12Using the radii and masses computed from model-grid-based methods by Creevey et al. (, Using the radii and masses computed from model-grid-based methods by Creevey et al. (13"in preparation) together with the estimates of P,o, we have computed the ratio of the surface angular velocity to the Keplerian break-up velocity, i.e., Ω/~GM/R>, which returned a value of approximately for both stars, indicating that these are most likely slow rotators.","in preparation) together with the estimates of $P_{\rm{rot}}$, we have computed the ratio of the surface angular velocity to the Keplerian break-up velocity, i.e., $\Omega/\sqrt{GM/R^3}$, which returned a value of approximately for both stars, indicating that these are most likely slow rotators."14" In view of this and given the precision achievable from the spectra, we have thus decided not to include any second-order effects on the rotational splitting."," In view of this and given the precision achievable from the spectra, we have thus decided not to include any second-order effects on the rotational splitting."15" The overall profile of a non-radial multiplet thus consists of the sum of 2/+1 Lorentzian profiles regularly spaced in frequency, and scaled in height according to the 5j,(i) factors (222): where i is the inclination angle between the direction of the stellar rotation axis and the line of sight, and P/""(x) are the associated Legendre functions."," The overall profile of a non-radial multiplet thus consists of the sum of $2l + 1$ Lorentzian profiles regularly spaced in frequency, and scaled in height according to the $\mathscr{E}_{l m}(i)$ factors \citep[][]{Dz77,DzG85,GS03}: where $i$ is the inclination angle between the direction of the stellar rotation axis and the line of sight, and $P_l^m(x)$ are the associated Legendre functions."16" Note that 26imn(@)=1, meaning that the &;,,(i) factors represent the relative power contained in the modes within a multiplet."," Note that $\sum_m \mathscr{E}_{l m}(i) \! = \! 1$, meaning that the $\mathscr{E}_{l m}(i)$ factors represent the relative power contained in the modes within a multiplet."17" While we are not able to robustly constrain the rotational splitting and inclination for both stars, we are however in a position to impose loose constraints on these parameters."," While we are not able to robustly constrain the rotational splitting and inclination for both stars, we are however in a position to impose loose constraints on these parameters."18" Figures [[4] and [[5] map the two-dimensional posterior probability distributions of these parameters respectively for KIC 10273246 and KIC 10920273, based on the samples from a MCMC analysis of the ten-month-long time series by IAS.OOB."," Figures \ref{inc_splt_M} and \ref{inc_splt_S} map the two-dimensional posterior probability distributions of these parameters respectively for KIC 10273246 and KIC 10920273, based on the samples from a MCMC analysis of the ten-month-long time series by OB."19" We have overlaid each of these correlation maps withcurves representing the estimate of P,.¢ given in Sect.", We have overlaid each of these correlation maps withcurves representing the estimate of $P_{\rm{rot}}$ given in Sect.20" ?? and the P,(i) relation ofCreevey et al. (", \ref{rotmod} and the $P_{\rm{rot}}(i)$ relation ofCreevey et al. (21"in preparation),","in preparation),"22"Explaining the IHubble acceleration. the ""dark energv. is one of the main challenges to cosinologists.","Explaining the Hubble acceleration, the “dark energy,” is one of the main challenges to cosmologists."23 Weak gravitational lensing (WL) has perhaps the most potential to constrain dark enerev parameters of any observational window. but is a newly developed technique which could be badly degraded by systematic errors (Albrecht et al 2005).," Weak gravitational lensing (WL) has perhaps the most potential to constrain dark energy parameters of any observational window, but is a newly developed technique which could be badly degraded by systematic errors (Albrecht et al 2005)."24 A WL survey requires an estimate of the shape and the redshift of cach source: dominant observational svsteniatie errors are expected to be errors in galaxy shape due to the uncorrected influcuce of the point spread function (PSF) aud errors iu estimation of redshift distributions if they are determined by photometric redshifts (photo-z«)., A WL survey requires an estimate of the shape and the redshift of each source; dominant observational systematic errors are expected to be errors in galaxy shape due to the uncorrected influence of the point spread function (PSF) and errors in estimation of redshift distributions if they are determined by photometric redshifts (photo-z's).25 Interpretation of WL data could also be systematically incorrect due to errors in the theory of the non-linear matter power spectrum or intrinsic alieumoeuts of ealaxies., Interpretation of WL data could also be systematically incorrect due to errors in the theory of the non-linear matter power spectrum or intrinsic alignments of galaxies.26 Iu this paper we present a new and more general analysis of the effect of photo-z calibration errors aud of the size of the spectroscopic survey required to reduce photo-z errors to a desired level., In this paper we present a new and more general analysis of the effect of photo-z calibration errors and of the size of the spectroscopic survey required to reduce photo-z errors to a desired level.27 Recent work has addressed imauv of these potential systematic errors in WL data aud theory: from the conrputation of the nonlinear matter power spectrui (Vale&White2003:Vale2001:Ποιαoet 2007): from barvouic cooling aud pressure forces on the distribution of large-scale structures (White2001:Zhanueretal. 2008): approximations in iuferrius the shear from the maps2006): aud the presence of dust (Valeetal.2001).," Recent work has addressed many of these potential systematic errors in WL data and theory: from the computation of the nonlinear matter power spectrum \citep{Vale_White, White_Vale, LosAlamos, Huterer_Takada, Hagan_Ma_Kravtsov,28Linder05, Ma06, Francis07}; from baryonic cooling and pressure forces on the distribution of large-scale structures \citep{White_baryons, Zhan_Knox, Jing06, Rudd07, Zentner07}; approximations in inferring the shear from the maps; and the presence of dust \citep{Vale_Hoekstra}."29". The promise aud problems of WL have stimulated work on how to improve the PSF reconstruction (Jarvis&Jain200 Εν, estimate shear from noisv nuages (Berustein&Jarvis2002:ID-Nakajima&Derusteiu2007:Masseyetal. 2007).. aud protect against errors iu the theoretical power spectrum at siiall scales (ITuterer&White2005)."," The promise and problems of WL have stimulated work on how to improve the PSF reconstruction \citep{Jarvis_Jain}, , estimate shear from noisy images \citep{Bernstein_Jarvis,Hirata_Seljak,Hoekstra04,Heymans06,30Nakajima06,STEP2_07}, and protect against errors in the theoretical power spectrum at small scales \citep{nulling}."31. For visible-NIR WL galaxw surveys. the dounünaut systematic error is likely to be inaccuracies in the ploto-z calibration.," For visible-NIR WL galaxy surveys, the dominant systematic error is likely to be inaccuracies in the photo-z calibration."32 The effect of photo-z calibration on weal: chsing is studied by Alaetal.(2006):IIuterer(2006):Jainetal.(2007):Abdalla (2007): and Dile&ing(2007).," The effect of photo-z calibration on weak lensing is studied by \cite{Ma05, Huterer05_wlsys, Jain06, Abdalla07}; and \cite{Bridle07}."33. The distributions of photo-z errors assuned for these studies are. however. much simpler hau will exist iu real surveys (Dahlenetal.2007:Ovaizuotal.2007:WittmanetStabenau2007 )..," The distributions of photo-z errors assumed for these studies are, however, much simpler than will exist in real surveys \citep{Dahlen07,Oyaizu07,Wittman07,Stabenau07}. ."34 IIutereretal.(2006). assumed that photo-z errors take he form of simple shifts (a bias that varies with :). while Maetal.(2006) assume the photo-z error distribution is a Gaussian. with a biasend dispersion that are functions of +.," \citet{Huterer05_wlsys} assumed that photo-z errors take the form of simple shifts (a bias that varies with $z$ ), while \cite{Ma05} assume the photo-z error distribution is a Gaussian, with a bias dispersion that are functions of $z$."35 These studies find that dark cucrey constraints are very scusitive to the uncertainties of photo-z parameters., These studies find that dark energy constraints are very sensitive to the uncertainties of photo-z parameters.36 A spectroscopic calibration sample of galaxies on t order of 10? is required to liave less than 50% degradation ou dark euergv constramts., A spectroscopic calibration sample of galaxies on the order of $10^5$ is required to have less than $50\%$ degradation on dark energy constraints.37 In this work we relax f Gaussian assuniptionu. presenting a method to evaluate the degradation of dark energv paranueter accuracy versus the size of the spectroscopic calibration survey. for the case of a photo-z eror distribution described by any paralucterized function.," In this work we relax the Gaussian assumption, presenting a method to evaluate the degradation of dark energy parameter accuracy versus the size of the spectroscopic calibration survey, for the case of a photo-z error distribution described by any parameterized function."38 We then apply this to a modelin which the core of the photo-z error distribution is the stun of multiple Gaussians. igunoriugfor uow the effect of," We then apply this to a modelin which the core of the photo-z error distribution is the sum of multiple Gaussians, ignoringfor now the effect of"39Another interesting issue is whether the extra freedom in the dark energy fluid will affect the constraints on the other parameters in our cosmological model.,Another interesting issue is whether the extra freedom in the dark energy fluid will affect the constraints on the other parameters in our cosmological model.40" That is, are the parameter constraints in the ACDM model robust to changes in c2;, and c?,,,."," That is, are the parameter constraints in the $\Lambda$ CDM model robust to changes in $\cvis$ and $\clam$."41" This was also studied in (?),, where they found that a,:, did not change the constraints in the other cosmological parameters significantly, but that varying Gam Shifted the other parameter ranges slightly."," This was also studied in \citep{ichiki:2007}, where they found that $\avis$ did not change the constraints in the other cosmological parameters significantly, but that varying $\clam$ shifted the other parameter ranges slightly."42" In Figure 8 we have plotted the marginalized likelihoods for different cosmological parameters in the case of a 7 parameter model with free w but with avis=0 and cZ,,=1.", In Figure \ref{fig:1D} we have plotted the marginalized likelihoods for different cosmological parameters in the case of a 7 parameter model with free $w$ but with $\avis = 0$ and $\clam=1$.43" We compare this to a model where ayis is allowed to vary freely in the interval (—20,20) (the same model as shown in Figure 4))."," We compare this to a model where $\avis$ is allowed to vary freely in the interval $\{-20,20\}$ (the same model as shown in Figure \ref{fig:alpha_w}) )."44" Also shown is a model with Qvis=0 and c2,,,=0.", Also shown is a model with $\avis=0$ and $\clam = 0$.45 We see that the extra freedom in the Qyis parameter does not change the other parameter distributions significantly., We see that the extra freedom in the $\avis$ parameter does not change the other parameter distributions significantly.46" We do however get a slight shift in the parameter distributions by changing c7,,, from 1 to 0.", We do however get a slight shift in the parameter distributions by changing $\clam$ from 1 to 0.47 This is consistent with the results from (?).., This is consistent with the results from \citep{ichiki:2007}.48" The most notable effect of changing from a model with Gam=1 to a model with c2,,,=0, is that the probability distributionfor w becomes narrower in the latter case."," The most notable effect of changing from a model with $\clam=1$ to a model with $\clam=0$, is that the probability distributionfor $w$ becomes narrower in the latter case."49" For a model with c2,,,=1 we find w=(—1.47,—0.57} at CL, while this range changes to w={—1.26,—0.52} for a model with c2,,,= 0."," For a model with $\clam=1$ we find $w=\{-1.47,-0.57\}$ at CL, while this range changes to $w=\{-1.26,-0.52\}$ for a model with $\clam=0$ ."50" For the other parameters, the effect of changing c2,,, is not very notable."," For the other parameters, the effect of changing $\clam$ is not very notable."51" As we have seen, only weak constraints can be found on the c2,,, Qvis and c7,,, parameters using present data."," As we have seen, only weak constraints can be found on the $\cvis$, $\avis$ and $\clam$ parameters using present data."52" We have also argued that the effect of includingother types of data sets, like LSS and SNIa, would not be very helpful, as such kinds of data sets are not affected significantly by these parameters."," We have also argued that the effect of includingother types of data sets, like LSS and SNIa, would not be very helpful, as such kinds of data sets are not affected significantly by these parameters."53" Also, unless w is significantly below -1, they will not serve to break parameter degeneracies for the parameters studied here."," Also, unless $w$ is significantly below -1, they will not serve to break parameter degeneracies for the parameters studied here."54 Will it then be possible to improve our constraints with future CMB data?, Will it then be possible to improve our constraints with future CMB data?55" To answer this question we have simulated a “perfect” CMB temperature data set, where the error bars are defined only from cosmic variance (CV) around a power spectrum generated from the best-fit ACDM model (with w=—1, Cà;,=0 and Cy,= 1) from WMAP data."," To answer this question we have simulated a “perfect” CMB temperature data set, where the error bars are defined only from cosmic variance (CV) around a power spectrum generated from the best-fit $\Lambda$ CDM model (with $w=-1$, $\cvis=0$ and $\clam=1$ ) from WMAP data."56 The likelihood part of CosmoMC has been modified to use this perfect data instead of the WMAP measurements., The likelihood part of CosmoMC has been modified to use this perfect data instead of the WMAP measurements.57" The likelihood is calculated as in (?):: For this mock data set we have used multipoles from |=2 to l=2000 in our analysis, and also here we have added the same prior on Ho and age as earlier."," The likelihood is calculated as in \citep{verde:2003}: For this mock data set we have used multipoles from $l=2$ to $l=2000$ in our analysis, and also here we have added the same prior on $H_0$ and age as earlier."58 A completely noise-free data set is of course not realistic., A completely noise-free data set is of course not realistic.59" However, it is an interesting case to study, sinceeffects that cannot be seen here, will never be possible to see using a real CMB temperature experiment."," However, it is an interesting case to study, sinceeffects that cannot be seen here, will never be possible to see using a real CMB temperature experiment."60" Note that, when using this mock data set, we do not include any polarization data in our analysis."," Note that, when using this mock data set, we do not include any polarization data in our analysis."61" In Figure 9 we show the constraints in the a,;s-w plane in a model with c7,,,=1 and avis<0.", In Figure \ref{fig:alpha_w_p} we show the constraints in the $\avis$ $w$ plane in a model with $\clam=1$ and $\avis<0$.62" This is compared with the results from using WMAP data alone, as also shown in Figure 4.."," This is compared with the results from using WMAP data alone, as also shown in Figure \ref{fig:alpha_w}."63" As we can see, even in this idealized case, we do not see any major improvement in our constraints on Qyis."," As we can see, even in this idealized case, we do not see any major improvement in our constraints on $\avis$ ."64 In this case the lower limit increases from ayis>—0.23 (from WMAP data) to avis>—0.22., In this case the lower limit increases from $\avis>-0.23$ (from WMAP data) to $\avis>-0.22$.65" In Figure 10 we have used the CV limited mock data to redo one the most interesting case from the analysis with WMAP data, namely the constraints in the c2;,-w plane with w«—1 and c2;,« 0, as shown inFigure 3.."," In Figure \ref{fig:cvis_w_p} we have used the CV limited mock data to redo one the most interesting case from the analysis with WMAP data, namely the constraints in the $\cvis$ $w$ plane with $w<-1$ and $\cvis<0$ , as shown inFigure \ref{fig:cvis_w}. ."66" We see that the constraints in this area improve slightly, but not very significantly."," We see that the constraints in this area improve slightly, but not very significantly."67" Using the CV-limited mockdata we find c2;,> —17.5, compared to c2;,>19.5 using WMAP data."," Using the CV-limited mockdata we find $\cvis>-17.5$ , compared to $\cvis>19.5$ using WMAP data."68used to explain the rapid damping of kink oscillations (see. e.g. Ofman and Aschwanden 2002. Ruderman and Roberts 2002. Ruderman 2008. ete).,"used to explain the rapid damping of kink oscillations (see, e.g. Ofman and Aschwanden 2002, Ruderman and Roberts 2002, Ruderman 2008, etc)."69 Equation (3)) implies that the eigenfunctions. v. are driven by particular forms of e&(z). through the particular profile of the quantities that make up the kink speed (density. magnetic field).," Equation \ref{eq:2.3}) ) implies that the eigenfunctions, $v_r$, are driven by particular forms of $c_K(z)$, through the particular profile of the quantities that make up the kink speed (density, magnetic field)."70 Inspired from the eigenvalue problem of Rayleigh-Ritz procedure. McEwan et al. (," Inspired from the eigenvalue problem of Rayleigh-Ritz procedure, McEwan et al. ("712008) used a variational principle that allows the calculation of eigenvalues. c. - a method that is employed by our analysis.,"2008) used a variational principle that allows the calculation of eigenvalues, $\omega$, - a method that is employed by our analysis."72" Let us multiply the above equation by v; and integrate from the apex to the footpoint of the loop as Using integration by parts in the first integral (taking into account that for the fundamental mode vL)=dv(0)/dz0 and for the first harmonic v,(0)=vl) 0). the above equation simplifies to which Cu)results into theV equation derived earlier by McEwan et al. ("," Let us multiply the above equation by $v_r$ and integrate from the apex to the footpoint of the loop as Using integration by parts in the first integral (taking into account that for the fundamental mode $v_r(L)=dv_r(0)/dz=0$ and for the first harmonic $v_r(0)=v_r(L)=0$ ), the above equation simplifies to which results into the equation derived earlier by McEwan et al. ("73"2008) where In order to express the eigenvalueCR) of such problem. we consider some trial functions for v, that satisfy the boundary conditions imposed at the footpoints and the apex of the loop.","2008) where In order to express the eigenvalue of such problem, we consider some trial functions for $v_r$ that satisfy the boundary conditions imposed at the footpoints and the apex of the loop."74 Since we are interested only in the characteristics. of fundamental mode of kink oscillations and its first harmonic. we will assume that v(z) will be proportional to coscrz/2) for the fundamental mode and sinGzz/L) for the first harmonic.," Since we are interested only in the characteristics of fundamental mode of kink oscillations and its first harmonic, we will assume that $v_r(z)$ will be proportional to $\cos(\pi z/2L)$ for the fundamental mode and $\sin(\pi z/L)$ for the first harmonic."75 It is obvious that these choices for eigenfunctions correspond to the homogeneous plasma. however - as we show in the Appendix - the corrections to the eigenfunction due to density stratification are rather small.," It is obvious that these choices for eigenfunctions correspond to the homogeneous plasma, however - as we show in the Appendix - the corrections to the eigenfunction due to density stratification are rather small."76 The problem of how the kink speed depends on the longitudinal coordinate. z. is a rather delicate problem and only simplified cases can be solved analytically.," The problem of how the kink speed depends on the longitudinal coordinate, $z$, is a rather delicate problem and only simplified cases can be solved analytically."77" For simplicity. let us consider that the magnetic field inside and outside of the coronal loop are identical and homogeneous. while the density varies exponentially according to where o;(0) and p,(0) are the densities inside and outside the loop at z=0. re. at the the loop apex and H; and H, are the density scale-heights inside and outside the loop."," For simplicity, let us consider that the magnetic field inside and outside of the coronal loop are identical and homogeneous, while the density varies exponentially according to where $\rho_i(0)$ and $\rho_e(0)$ are the densities inside and outside the loop at $z=0$, i.e. at the the loop apex and $H_i$ and $H_e$ are the density scale-heights inside and outside the loop."78 Obviously the choice of density reflects a simplified description of the coronal loop model where plasma ts tsothermal and other further effects are neglected. however. this density profile allows us to obtain analytical results.," Obviously the choice of density reflects a simplified description of the coronal loop model where plasma is isothermal and other further effects are neglected, however, this density profile allows us to obtain analytical results."79 A realistic deseription would require taking into account that the plasma is not isothermal (inside and outside the loop). the loop is curved and the density can depend on other coordinates. as well.," A realistic description would require taking into account that the plasma is not isothermal (inside and outside the loop), the loop is curved and the density can depend on other coordinates, as well."80 This form of density dependence on the coordinate was earlier used by. e.g. Verth et al.," This form of density dependence on the $z$ coordinate was earlier used by, e.g. Verth et al."81 2007. McEwan et al.," 2007, McEwan et al."82 2008. Morton and Erdéllyi 2009. Morton and Ruderman 2011. Morton et al.," 2008, Morton and Erdéllyi 2009, Morton and Ruderman 2011, Morton et al."83 2011., 2011.84 With our chosen density profiles. the kink speed given by Eq. (2))," With our chosen density profiles, the kink speed given by Eq. \ref{eq:2.2}) )"85" becomes where Bo 1s the magnitude of the magnetic field. v4,(0) 18 the Alfvénn speed at the apex of the loop. and & is the density ratio. Le. o;(0)/p,(0)."," becomes where $B_0$ is the magnitude of the magnetic field, $v_{Ai}(0)$ is the Alfvénn speed at the apex of the loop, and $\xi$ is the density ratio, i.e. $\rho_i(0)/\rho_e(0)$."86 Since the density outside the coronal loop is smaller than inside. we will consider that &>1.," Since the density outside the coronal loop is smaller than inside, we will consider that $\xi\geq 1$."87" The quantities H; and H, are the density scale-heights and they are proportional to the temperature of the plasma.", The quantities $H_i$ and $H_e$ are the density scale-heights and they are proportional to the temperature of the plasma.88" Here we denoted y=H,/H;.", Here we denoted $\chi=H_e/H_i$.89 Since the temperature of the loop is higher than its environment. we will take y<l. so that the value y=| corresponds to an identical density variation with height inside and outside the loop and identical temperatures. y—co resulting in a constant density 1n the environment of the loop. while the limit y-O0 represents a case when the plasma inside the loop is homogeneous.," Since the temperature of the loop is higher than its environment, we will take $\chi\leq 1$, so that the value $\chi=1$ corresponds to an identical density variation with height inside and outside the loop and identical temperatures, $\chi\rightarrow \infty$ resulting in a constant density in the environment of the loop, while the limit $\chi\rightarrow 0$ represents a case when the plasma inside the loop is homogeneous."90" Using the particular form of v, for the fundamental mode and its first harmonic. we obtain that in the case of the fundamental mode where we introduced the dimensionless variable v=L/zH;. f(xy) is the modified Bessel function of order v. LG is the modified Struve function of order v. and the index f stands for the fundamental mode."," Using the particular form of $v_r$ for the fundamental mode and its first harmonic, we obtain that in the case of the fundamental mode where we introduced the dimensionless variable $y=L/\pi H_i$, $I_\nu(x)$ is the modified Bessel function of order $\nu$, $L_\nu(x)$ is the modified Struve function of order $\nu$, and the index $f$ stands for the fundamental mode."91 For the first harmonic we obtain that where the superscript 1 in the expressions of iu and vi stands for the first harmonic., For the first harmonic we obtain that where the superscript $1$ in the expressions of $\Psi_1^1$ and $\Psi_2^1$ stands for the first harmonic.92 Now using Eq. (6)), Now using Eq. \ref{eq:2.6}) )93" for both modes we obtain that Inspectingthe above relations we can see that the period ratio P,/Ps does not depend on Alfvénn speed or loop length (they cancel out when calculating Eq. 11)).", for both modes we obtain that Inspecting the above relations we can see that the period ratio $P_1/P_2$ does not depend on Alfvénn speed or loop length (they cancel out when calculating Eq. \ref{eq:2.12}) ).94 For coronal conditions we plot the period ratio given by Eq. (110 , For coronal conditions we plot the period ratio given by Eq. \ref{eq:2.12}) )95for €=2 with the variable v varying between O and 10. although the larger values of v are rather unrealistic since v=10 would correspond to a scale-height of 30 times shorter than the loop," for $\xi=2$ with the variable $y$ varying between 0 and 10, although the larger values of $y$ are rather unrealistic since $y=10$ would correspond to a scale-height of 30 times shorter than the loop"96and 6 cin radio continu observations are presented i Sec.,and 6 cm radio continuum observations are presented in Sec.97 6 aud 7.., \ref{sec:molecular} and \ref{sec:radiocontinuum}.98 The distribution of the polarized radio continui eniüsson is compared to MIID simulations iu Sec. 7.3.., The distribution of the polarized radio continuum emission is compared to MHD simulations in Sec. \ref{sec:mhd}. .99 The peculiar Πα aud UV emission distributions of NGC L330 are compared to the model iu Sec., The peculiar $\alpha$ and UV emission distributions of NGC 4330 are compared to the model in Sec.100 8 aud 9.. followed bv the overall picture of the rin pressure stripping event (Sec. 10)).," \ref{sec:starformation}101 and \ref{sec:sfr100}, followed by the overall picture of the ram pressure stripping event (Sec. \ref{sec:overall}) )."102 The stellar age distributions of the gas-free parts of galactic disk are preseuted in Sec. 11.., The stellar age distributions of the gas-free parts of galactic disk are presented in Sec. \ref{sec:sfrhist}. .103 Finally. we eive our conclusions in Sec. 12..," Finally, we give our conclusions in Sec. \ref{sec:conclusions}."104 We use the N-body code described. iu Volhuer ct al. (, We use the N-body code described in Vollmer et al. (1052001) which consists of two conmonents a uon-collisional comiponenut that simulates the stellar bulge/cdisk and the dark halo. and a collisional component that simulates the ISAL,"2001) which consists of two components: a non-collisional component that simulates the stellar bulge/disk and the dark halo, and a collisional component that simulates the ISM."106 A new scheme for star formation las been aplemented. where stars are formed during cloud collisions and are then evolved as nou-collisional particles.," A new scheme for star formation has been implemented, where stars are formed during cloud collisions and are then evolved as non-collisional particles."107 The uoncollisional conmponeut consists. of 819920 particles. which simulate the galactic halo. bulge. aud disk.," The non–collisional component consists of 920 particles, which simulate the galactic halo, bulge, and disk."108 The characteristics of the different galactic compoucuts are shown iu Table ], The characteristics of the different galactic components are shown in Table \ref{tab:param}.109 The resultingC» rotation velocity is 7180 ! and the rotation curve becomes flat at a radius of about 5 kpc., The resulting rotation velocity is $\sim$ 180 $^{-1}$ and the rotation curve becomes flat at a radius of about 5 kpc.110 We have adopted a uodoel where the ISM is simulated as a collisional component. ic. as discrete particles which possess a miss and a radius aud which can have inelastic collisions (sticky ouwticles).," We have adopted a model where the ISM is simulated as a collisional component, i.e. as discrete particles which possess a mass and a radius and which can have inelastic collisions (sticky particles)."111 Since the ISM 3s a turbulent and fractal medium (see e.g.àY Ehucercen Falearone 1996). it is neither continuous nor discrete.," Since the ISM is a turbulent and fractal medium (see e.g. Elmegreen Falgarone 1996), it is neither continuous nor discrete."112 The volume filling factor of the wari aud cold plases is aller than one., The volume filling factor of the warm and cold phases is smaller than one.113 The wari neutral aud ionized eas fill about 30HOM of the volume. whereas cold neutral eas has a volume ülline factor simaller than (Boulares Cox 1990).," The warm neutral and ionized gas fill about $30-50\%$ of the volume, whereas cold neutral gas has a volume filling factor smaller than (Boulares Cox 1990)."114 Tt is not clear how this fraction changes. when au external oressure ds applied.," It is not clear how this fraction changes, when an external pressure is applied."115 Iu contrast to smoothed particles ivdrodyvianudes (SPT). which ds ao quas continuous approach and where the particles cannot penetrate cach other. our approach allows a finite penetration leneth. which is given by the mass-racius relation of the particles.," In contrast to smoothed particles hydrodynamics (SPH), which is a quasi continuous approach and where the particles cannot penetrate each other, our approach allows a finite penetration length, which is given by the mass-radius relation of the particles."116 Both methods have their advantages aud their limits., Both methods have their advantages and their limits.117 The advantage of our approach is that ram pressure can be iuchided easily as au additional acceleration on particles that are not protected bv other particles (see Volliner et al., The advantage of our approach is that ram pressure can be included easily as an additional acceleration on particles that are not protected by other particles (see Vollmer et al.118 2001)., 2001).119 The 200000 particles of the collisional componeut represent gas cloud complexes which are evolving iu the eravitational potential of the galaxy., The 000 particles of the collisional component represent gas cloud complexes which are evolving in the gravitational potential of the galaxy.120 The total assumed. gas mass ix AT=1310? XL. which correspouds to the total neutral eas mass before stripping. ic. to an deleficicncy of 0. which is defined as the logarithi of the ratio between the cconteut of a feld galaxy of same morphological type aud diameter and the observed nunass.," The total assumed gas mass is $M_{\rm gas}^{\rm tot}=4.3\,10^{9}$ $_{\odot}$, which corresponds to the total neutral gas mass before stripping, i.e. to an deficiency of 0, which is defined as the logarithm of the ratio between the content of a field galaxy of same morphological type and diameter and the observed mass."121 To each particle a radius is attributed depeuding on its mass., To each particle a radius is attributed depending on its mass.122 During the disk evolution the particles can have inelastic collisions. the outcome of which (coalescence. mass exchange. or fragmentation) is siuplified following Wicecl (1991).," During the disk evolution the particles can have inelastic collisions, the outcome of which (coalescence, mass exchange, or fragmentation) is simplified following Wiegel (1994)."123 This results iu an effective gas viscosity in the disk., This results in an effective gas viscosity in the disk.124 As the galaxy moves through the ICAL its clouds are accelerated by rn pressure.," As the galaxy moves through the ICM, its clouds are accelerated by ram pressure."125 Within the galaxys inertial system its clouds are exposed to a wind coming roni a direction opposite to that of the ealaxys motion hrough the ICAL, Within the galaxy's inertial system its clouds are exposed to a wind coming from a direction opposite to that of the galaxy's motion through the ICM.126 The temporal ram pressure profile was the form of a Lorentzian. which is realistic for ealaxies on highly eccentric orbits within the Virgo cluster (Vollmer et al.," The temporal ram pressure profile has the form of a Lorentzian, which is realistic for galaxies on highly eccentric orbits within the Virgo cluster (Vollmer et al."127 2001)., 2001).128 The effect of ram. pressure ou he clouds is simulated by an additional force on the clouds in the wind direction., The effect of ram pressure on the clouds is simulated by an additional force on the clouds in the wind direction.129 Ouly clouds which are not wotected by other clouds against the wind are affected., Only clouds which are not protected by other clouds against the wind are affected.130 Since the eas cannot develop instabilities. the influence of turbulence ou the stripped eas is not included in the uodel.," Since the gas cannot develop instabilities, the influence of turbulence on the stripped gas is not included in the model."131 The mixing of the intracluster medium iuto the ISM is very crudely approximated by a finite penctration cheth of the intracluster medimm iuto the ISM. ic. until lis peuetration leneth the clouds undergo au additional acceleration due to ram pressure.," The mixing of the intracluster medium into the ISM is very crudely approximated by a finite penetration length of the intracluster medium into the ISM, i.e. until this penetration length the clouds undergo an additional acceleration due to ram pressure."132 The article trajectories are inteerated using au adaptive timestep for cach particle., The particle trajectories are integrated using an adaptive timestep for each particle.133 This method is described in Springel et al. (, This method is described in Springel et al. (1342001).,2001).135 The following criterion for an individual timestep is applied: where e; is the acceleration of the particle i. The nonin value of f; defines the global timestep used for the BurlischStoer inteerator that integrates the collisional component., The following criterion for an individual timestep is applied: where $a_{i}$ is the acceleration of the particle i. The minimum value of $t_{\rm i}$ defines the global timestep used for the Burlisch–Stoer integrator that integrates the collisional component.136 It is typically a few 104 vr., It is typically a few $10^{4}$ yr.137 We assune that the star formation rate is proportional to the cloud collision rate., We assume that the star formation rate is proportional to the cloud collision rate.138 Diving the simulations stars are formed in cloud-cloud collisions., During the simulations stars are formed in cloud-cloud collisions.139 At each collision a collisionless particle is created which is added to the eusenible of collisional aud collisionless particles., At each collision a collisionless particle is created which is added to the ensemble of collisional and collisionless particles.140 The newly created collisionless particles have zero mass (theyare test particles) aud the positions aud velocitics of the colliding clouds after the collision., The newly created collisionless particles have zero mass (theyare test particles) and the positions and velocities of the colliding clouds after the collision.141 Theseparticles are then, Theseparticles are then142Althoueh a large f‘action of nearby stars occur in multiple systetis. direct detection exoplauet searches has'e generally selected against binary targets because a secolary star complicates observations al limits the detectior sensitiviy.,"Although a large fraction of nearby stars occur in multiple systems, direct detection exoplanet searches have generally selected against binary targets because a secondary star complicates observations and limits the detection sensitivity."143 Iu acclition to olervational complications. binary systems were traclitionally asstumect >| ye a hostile e1virouruent for the formation and evolution of planetary s¥stelus.," In addition to observational complications, binary systems were traditionally assumed to be a hostile environment for the formation and evolution of planetary systems."144 He»wvever. direc1 linagine of st:us kuown to harbor panets detected radial. velocities has revealed several bihary star systelis OT.," However, direct imaging of stars known to harbor planets detected by radial velocities has revealed several binary star systems \mycitep{Pat02, Egg09}."145 Protoplanetary disks. which form the material basis for planet formaion. are observed in both circumstella circumbinary. configurations in binary systems (?? uid the growh and settling of dus Sl:o]ulls is COLL iu ary star systems (?)..," Protoplanetary disks, which form the material basis for planet formation, are observed in both circumstellar and circumbinary configurations in binary systems \mycitep{Rod96, Tri07}, and the growth and settling of dust grains is common in binary star systems \mycitep{Pas08}."146 Theoreical uumerical simulatious successfully node the evoluu of protoplanets (?).. terrestrlal planets (?)..? giant jxlauets (/2) and bfowl dwars (0) in circumbinary disks.," Theoretical numerical simulations successfully model the evolution of protoplanets \mycitep{Pie07}, terrestrial planets \mycitep{Qui06}, giant planets \mycitep{Pie08} and brown dwarfs \mycitep{Jia04} in circumbinary disks."147 Furthermore. theoretical models also permit planet [ortiallol through graviational instability iu binary systems.," Furthermore, theoretical models also permit planet formation through gravitational instability in binary systems."148 Planes forued iu 11is way have large separaious from their sals aud are therefore particularly importa largets for direct imaele., Planets formed in this way have large separations from their stars and are therefore particularly important targets for direct imaging.149 The intheeuce of a secondary star cau i some Cases prevel ita collapse th‘ough tical heating (?) Or 1Ἰσορ) he collapse for au otherwise stable clisk (?).. leaviug a calacteristic iiiprint ou t edemographics of planets in binary systems. the observation oL which weuld xovide au invaluable test for R9]planet formation theory.," The influence of a secondary star can in some cases prevent a collapse through tidal heating \mycitep{May05} or trigger the collapse for an otherwise stable disk \mycitep{Bos06}, leaving a characteristic imprint on the demographics of planets in binary systems, the observation of which would provide an invaluable test for planet formation theory."150 A secondary star can alsO act as a sjurce of angular nometum for : 'cumbinary planet and either scatter or tidaly pus ithe planet ino wider orljts. ths enrichi ie expected population of wide-orbit stars (227?)..," A secondary star can also act as a source of angular momentum for a circumbinary planet and either scatter or tidally push the planet into wider orbits, thus enriching the expected population of wide-orbit stars \mycitep{Nel03, Ver04, Hol99, Kle00}."151 Di‘ect cleection tecμιαles are critical for iivestigating extrasolar planets οi large (> 10 AU) orbital separations. and the first clirect detectious of extrasoar planets have confiriued that planets do exist iu these orbits (e.g.. ?2??)).," Direct detection techniques are critical for investigating extrasolar planets on large $>$ 10 AU) orbital separations, and the first direct detections of extrasolar planets have confirmed that planets do exist in these orbits (e.g., \mycitealt{Mar08,Kal08,Lag09}) )."152 High contrast instrumeration aud didirect detection techniques are beiig develo»ed to probe planet fonaljon aud the evolitiou of planeary systens., High contrast instrumentation and direct detection techniques are being developed to probe planet formation and the evolution of planetary systems.153" In order to achieve high courast (> 10°) at smal alglar sep:uations (« 1""). one must controI the diffracted ight [rom the host star in the image dlane."," In order to achieve high contrast $>$ $^{-6}$ ) at small angular separations $<$ $\arcsec$ ), one must control the diffracted light from the host star in the image plane."154" Howe,rer. the uajoriiy of coonagrapls are designed o remove light roni siiele host stars."," However, the majority of coronagraphs are designed to remove light from single host stars."155" Ie secondary star lies close to ilthe taget star and it is 101 suppressed. the secxdary stars light. will ove""wlielia he sienal [roi1 ahy allI conmpatlOlis."," If the secondary star lies close to the target star and it is not suppressed, the secondary star's light will overwhelm the signal from any faint companions."156 The peak of the G dwar. comipaniou cisribution is near 30 AU [y. and wlile also accountii& lor 'andoim orbital inclinatiius and phases ou tle sky. he vast ajo‘ity of nearyw biuary stars uw 100 0€) targetec by high conFast imaging stt'veys woul benelit from having a specialized corouag'apli.," The peak of the G dwarf companion distribution is near 30 AU \mycitep{Duq91}, and while also accounting for random orbital inclinations and phases on the sky, the vast majority of nearby binary stars $<$ 100 pc) targeted by high contrast imaging surveys would benefit from having a specialized coronagraph."157 Coronaeraphis capadle of simultanecsusly blockug the light from binary stars can be grouped luto two caegorles: COromagraphs with inear mask:s. aud coronagraplis with dual circular masks.," Coronagraphs capable of simultaneously blocking the light from binary stars can be grouped into two categories: coronagraphs with linear masks, and coronagraphs with dual circular masks."158 Each type las advantagees aud cdisadvaitages: in tie. following. we preseut examples of each aud discuss thei performance in the presence ola typical low-order wavelrout uoise following au adaptive Oplles systeur," Each type has advantages and disadvantages; in the following, we present examples of each and discuss their performance in the presence of a typical low-order wavefront noise following an adaptive optics system."159 Iu particular. we present adwabinask design based on an APLC which allows [or a simall inier working :iuele aud a large «liSCOVeI “space even for au obstructed aperture. and which miniulzes cross-talk between the masks.," In particular, we present a dual-mask design based on an APLC which allows for a small inner working angle and a large discovery space even for an obstructed aperture, and which minimizes cross-talk between the masks."160 We also address manulacturiug and implementation COLLCELLIS slch as obstrueed apertures. liekl rotation. manulacturing. and mask placement. and," We also address manufacturing and implementation concerns such as obstructed apertures, field rotation, manufacturing, and mask placement, and"161 A*  A* (~10* 101. , $^*$ $\sim $ $^*$ $\sim 10^3$ $10^4 M_{\odot}$ 162of the Hubble radius at EoR and has an amplitude proportional to T.,of the Hubble radius at EoR and has an amplitude proportional to $\tau$.163 Any model of reionization must reproduce the observed value of optical depth., Any model of reionization must reproduce the observed value of optical depth.164 For a forecast on anticipated improvements of observational estimation of 7. please see (Colombo&Pierpaoli 2009)..," For a forecast on anticipated improvements of observational estimation of $\tau$, please see \citep{2009NewA...14..269C}."165 The reionization history depends on the star formation history of he universe. which in the simplified models is closely related to he halo formation history.," The reionization history depends on the star formation history of the universe, which in the simplified models is closely related to the halo formation history."166 The IMF of stars and the escape fraction or ionizing photons then give us the number of ionizing photons hat are available as a function of time., The IMF of stars and the escape fraction for ionizing photons then give us the number of ionizing photons that are available as a function of time.167 These can then be used to compute the evolution of the neutral or ionized fraction of gas in he universe., These can then be used to compute the evolution of the neutral or ionized fraction of gas in the universe.168 As mentioned above. we assume that star formation is triggered during formation of haloes.," As mentioned above, we assume that star formation is triggered during formation of haloes."169 As most time scales of interest are longer than the dynamical time scale over which the bulk of star formation takes place. we assume star formation to be instantaneous in our model.," As most time scales of interest are longer than the dynamical time scale over which the bulk of star formation takes place, we assume star formation to be instantaneous in our model."170 We consider a global averaged evolution of ionized fractio= instead of following evolution of HII regions around haloes. the approach used in most studies (Chiu&Ostriker2000:Sethi 2005).," We consider a global averaged evolution of ionized fraction instead of following evolution of HII regions around haloes, the approach used in most studies \citep{2000ApJ...534..507C,1712005MNRAS.363..818S}."172 Further. we assume that during reionization. a region is either neutral or completely ionized.," Further, we assume that during reionization, a region is either neutral or completely ionized."173 With these assumptions. the evolution of the ionized fraction evolves as: Here .r is the fractional volume that is ionized. and y is the number of ionizing photons per baryon.," With these assumptions, the evolution of the ionized fraction evolves as: Here $x$ is the fractional volume that is ionized, and $y$ is the number of ionizing photons per baryon."174" c, denotes the effective cross-section of photoionization. àg is the recombination coefficient. for all levels except the ground state of neutral hydrogen. and m, denotes the mass of a proton."," $\sigma_{p}$ denotes the effective cross-section of photoionization, $\alpha_{B}$ is the recombination coefficient for all levels except the ground state of neutral hydrogen, and $m_p$ denotes the mass of a proton."175 The first term on the right hand side of equation (50) describes recombination., The first term on the right hand side of equation \ref{xtoy}) ) describes recombination.176 C is the clumping factor defined as C=nuling ?.," ${\mathcal C}$ is the clumping factor defined as ${\mathcal C}^2 =177{\langle}n_{H}^2{\rangle}/{\langle}n_H{\rangle}^2$ ."178 This term usually involves square of the ionized fraction but in our model we assume that the ionized fraction is either unity or zero., This term usually involves square of the ionized fraction but in our model we assume that the ionized fraction is either unity or zero.179 This. when used in volume averaging over the universe with an additional assumption that the clumping is the same in ionized and neutral regions. leads to a linear dependence.," This, when used in volume averaging over the universe with an additional assumption that the clumping is the same in ionized and neutral regions, leads to a linear dependence."180 In the process of averaging. the meaning of . changes from the ionized fraction to the volume filling fraction of the ionized regions.," In the process of averaging, the meaning of $x$ changes from the ionized fraction to the volume filling fraction of the ionized regions."181" We can express this in terms of equations: We have assumed that the clumping factor is the same in all parts of the universe. this allows us to take {73,) outside the integral."," We can express this in terms of equations: We have assumed that the clumping factor is the same in all parts of the universe, this allows us to take $\langle n_{H}^2\rangle$ outside the integral."182 The third equality in equation (7) follows from the definition of .r as a filling fraction., The third equality in equation \ref{eqls}) ) follows from the definition of $x$ as a filling fraction.183 We also expect C to change with the evolution of clustering., We also expect ${\mathcal C}$ to change with the evolution of clustering.184 Wetake this dependence to be of the form (Tlievetal.2007) Sources of ionizing radiation are represented in the last term of equation (63). Pb being related to the formation rate of collapsed haloes.," Wetake this dependence to be of the form \citep{2007MNRAS.376..534I}185 Sources of ionizing radiation are represented in the last term of equation \ref{ytoy}) ), $\dot{F}$ being related to the formation rate of collapsed haloes."186 This is obtained from the Press-Schechter formalism as described above., This is obtained from the Press-Schechter formalism as described above.187 ;V. denotes the number of photons produced per unit mass of star formation., $N_{\gamma}$ denotes the number of photons produced per unit mass of star formation.188 Ionization of neutral hydrogen is described in the last term on the right hand side of equation (53)., Ionization of neutral hydrogen is described in the last term on the right hand side of equation \ref{xtoy}) ).189 This term occurs in both equations., This term occurs in both equations.190 We neglect the contribution of collisional ionization., We neglect the contribution of collisional ionization.191 We solve these equations numerically for different cosmological models., We solve these equations numerically for different cosmological models.192 The system of equations (59) and. (6)) is “stiff since (ως=O.y0) is a stable point and time scales for evolution of . and y are very different.," The system of equations \ref{xtoy}) ) and \ref{ytoy}) ) is “stiff,” since $(x=0,y=0)$ is a stable point and time scales for evolution of $x$ and $y$ are very different."193 Further. ας is bounded from above (by unity) while y is not.," Further, $x$ is bounded from above (by unity) while $y$ is not."194 Thus the usual forward differencing methods do not give accurate solutions easily., Thus the usual forward differencing methods do not give accurate solutions easily.195 We bypass this problem by noting that during the process of reionization almost every ionizing photon will be immediately absorbed by themedium’., We bypass this problem by noting that during the process of reionization almost every ionizing photon will be immediately absorbed by the.196. This means that the two terms in the right hand side of the second equation are of the same order till a becomes nearly equal to 1. whereas the left hand side is much smaller and may be assumed to be zero.," This means that the two terms in the right hand side of the second equation are of the same order till $x$ becomes nearly equal to $1$, whereas the left hand side is much smaller and may be assumed to be zero."197 This reduces the system of equations to a single equation. which ean now be solved using forward differencing methods.," This reduces the system of equations to a single equation, which can now be solved using forward differencing methods."198 Note that this approximation is not valid when . approaches |. although in practice the approximate solution is fairly accurate up tour 0.9.," Note that this approximation is not valid when $x$ approaches 1, although in practice the approximate solution is fairly accurate up to $x \sim 0.9$."199 Indeed. if we use the approximation up to.r —1.0 then we make an error in estimation of of less than 54.," Indeed, if we use the approximation up to $x=1.0$ then we make an error in estimation of $\tau$ of less than $5\%$."200 We take ap=1.0104%envtsee+. ignoring its dependence on temperature.," We take $\alpha_{\mathrm B} = 1.0 \times 10^{-13} \; \mathrm{cm^3} \,201\mathrm{sec^{-1}}$, ignoring its dependence on temperature."202 This dependence is fairly weak at temperatures of interest., This dependence is fairly weak at temperatures of interest.203" We use oa,=6.30.10.DPcm.", We use $\sigma_p = 6.30 \times 10^{-18}\;\mathrm{cm^2}$.204? We thus assume that most of the ionizing radiation is around the Lyman limit., We thus assume that most of the ionizing radiation is around the Lyman limit.205 The number of ionizing photons released per baryon of stars formed. denoted by ;V.. depends on the initial mass function (IMF) of the stars.," The number of ionizing photons released per baryon of stars formed, denoted by $N_{\gamma}$, depends on the initial mass function (IMF) of the stars."206 We obtain this number from the stellar population synthesis code (Leithereretal.therer 2005).," We obtain this number from the stellar population synthesis code \citep{1999ApJS..123....3L, 2005ApJ...621..695V}."207 Our aim here is to study a variety of models with varying cosmological parameters as well as parameters related to star formation and enrichment., Our aim here is to study a variety of models with varying cosmological parameters as well as parameters related to star formation and enrichment.208 We consider a random subset of fla ACDM models allowed by WMAPS (Komatsuetal.2008:Dunkleyetal. 2008)..," We consider a random subset of flat $\Lambda$ CDM models allowed by WMAP5 \citep{2008arXiv0803.0547K, 2008arXiv0803.0586D}."209 We do not consider models with massive neutrinos or a non-vanishing tensor component. or models where the primordia yower spectrum deviates from a pure power law.," We do not consider models with massive neutrinos or a non-vanishing tensor component, or models where the primordial power spectrum deviates from a pure power law."210 We use only WMAP constraints for limiting cosmological parameters., We use only WMAP constraints for limiting cosmological parameters.211 We used he MCMC chains made available by the WMAP team /)., We used the MCMC chains made available by the WMAP team ).212 We considered a random subse of all models allowed with a confidence level of GS% from the ICMC chains., We considered a random subset of all models allowed with a confidence level of $68\%$ from the MCMC chains.213 We studied a handful of models for parameters related to star formation: details of these are given in Table (1)., We studied a handful of models for parameters related to star formation; details of these are given in Table \ref{sfmodels}) ).214" The table lists the IMFs used in our study"".", The table lists the IMFs used in our .215.. We have also listed he amount of ionizing photons produced per baryon in stars.and," We have also listed the amount of ionizing photons produced per baryon in stars,and"216" rg M, (V~ος). 26. rover. these Nrirag=0.9Vie/tsFl) [1IS-requioverr and [15]."," $r_p$ $M_\ast$ $V_w\sim\cs$ $2\cs$ $r_{\rm over}$ $\Delta r_{\rm over}/\Delta\rarm=0.5\,(V_w/\cs\mp1)$ r] and \ref{equ:del1}] ])."217" In cool AGB envelopes. the wind is usually much faster than the souud speed (Vi.29 σι). makiug Are, relatively large."," In cool AGB envelopes, the wind is usually much faster than the sound speed $V_w\gg\cs$ ), making $\Delta r_{\rm over}$ relatively large."218" For instauce. with Vi,=10e, which is easily found for ACB stars. the outer aud iuner arm boundaries can meet only alter five turis."," For instance, with $V_w=10\cs$, which is easily found for AGB stars, the outer and inner arm boundaries can meet only after five turns."219 For the case of an observational detection of ouly parts of the spiral. especially when the partial spiral is expected over the distance of Arvey. a more careful analysis is required to avoid misideutifyiug the outer aud inner boundaries.," For the case of an observational detection of only parts of the spiral, especially when the partial spiral is expected over the distance of $\Delta r_{\rm over}$, a more careful analysis is required to avoid misidentifying the outer and inner boundaries."220 We have also provided an empirical formula (eq. [12]]), We have also provided an empirical formula (eq. \ref{equ:jump}] ])221" for the arm-interarm density contrast. α=6p/py. along a normalized distance r/ry as a function of Vip/e;. Vi/e; aud rgr,y=GMy/(2r,)."," for the arm-interarm density contrast, $\alpha=\delta\rho/\rho_w$, along a normalized distance $r/r_p$ as a function of $V_w/\cs$, $V_p/\cs$, and $r_B/r_p=GM_p/(\cs^2r_p)$."222" Usiug this empirical formula. we estimate the properties of a Jupiter wake in the stellar wind when ¢u Stun becomes a giant of size AAU (AL,=0.8sun. AL,=2*«107spy.. Z4=3000/0: according to Hurleyetal. 2000))."," Using this empirical formula, we estimate the properties of a Jupiter wake in the stellar wind when our Sun becomes a giant of size AU $M_\ast=0.8$, $\dot{M_\ast}=2\times10^{-7}$, $T_\ast=3000K$; according to \citealp{hur00}) )."223" The wind speed V, is set to be ~ Pbasecd on the trend. between the mass-Ioss rate aud the envelope expausion speed 2006).. and tlie sonic speed c; is assumed to beanps."," The wind speed $V_w$ is set to be $\sim$ based on the trend between the mass-loss rate and the envelope expansion speed \citep[see Fig.~16 in][]{fon06}, and the sonic speed $\cs$ is assumed to be."224". The estimated orbital speed V,=(GM,/rj)? of Jupiter in situ (rp—9 AAU) isaups.. corresponding to the aruriuterarimn deusity contrast of only. contrast does not significantly depend ou the orbital cistauce. ie.. detect the gravitational wake of a Jupiter mass object with the current observatioual linitatious of sensitivity aud augular resolution."," The estimated orbital speed $V_p=(GM_\ast/r_p)^{1/2}$ of Jupiter in situ $r_p=5$ AU) is, corresponding to the arm-interarm density contrast of only contrast does not significantly depend on the orbital distance, i.e., detect the gravitational wake of a Jupiter mass object with the current observational limitations of sensitivity and angular resolution."225 In the same rauge of orbital distance. a 10 Jupiter mass object can create a gravitational wake with the deusity contrast of aud for a brown dwarf mass Msun)). the contrast increases to performauce of the Atacama Large Millimeter/submillimeter Array (ALALA).," In the same range of orbital distance, a 10 Jupiter mass object can create a gravitational wake with the density contrast of and for a brown dwarf mass ), the contrast increases to performance of the Atacama Large Millimeter/submillimeter Array (ALMA)."226" We note that these uunmerical values are lower limits since the peak deusity contrast at the arm boundary can be higher with a realistic size of the object much smaller than >0.1 AAU employed in this study: but the effect of the object size ry is uot significant uuless the size is comparable to the accretion raclius ry.Therequiredspatial resolution to distinguish the arm pattern separation is AAU depending on the orbital distance (rj,= 3-30AAU).", We note that these numerical values are lower limits since the peak density contrast at the arm boundary can be higher with a realistic size of the object much smaller than $\geq0.1$ AU employed in this study; but the effect of the object size $r_s$ is not significant unless the size is comparable to the accretion radius $r_B$.Therequiredspatial resolution to distinguish the arm pattern separation is AU depending on the orbital distance $r_p=3$ AU).227 On a larger scale. a distancecorresponding to 5 times," On a larger scale, a distancecorresponding to 5 times"228Three binary svstems containing a massive star and a compact object 5039.. and have been clearly detected in TeV energy baud (see lor the updated information).,"Three binary systems containing a massive star and a compact object –, and – have been clearly detected in TeV energy band (see for the updated information)."229 While the nature of the compact companion in and is not vet. establishecl 2005a.b:;Sartyetal. 2011).. the detection of the pulsed radio emission Irom indicates the presence of a 47.7 ms pulsar in (he svstem (Johnstonetal.1992).," While the nature of the compact companion in and is not yet established \citep{casares05a,casares05b,sarty11}, the detection of the pulsed radio emission from indicates the presence of a 47.7 ms pulsar in the system \citep{johnston92}."230". The pulsar orbits a luminous star in a very eccentric orbit with the following orbital parameters: eccentricity e=0.87. period 2,=1237 d. and semi-major axis e»=6.9AU (seeNegueru-elaetal.2011.andreferences therein).."," The pulsar orbits a luminous star in a very eccentric orbit with the following orbital parameters: eccentricity $e=0.87$, period $P_{{\rm orb}}= 1237$ d, and semi-major axis $a_{\rm 2}=6.9\rm \, AU$ \citep[see][and references231therein]{negueruela10}."232 The svstem displavs variable broadband nonthermal radio. X-ray and TeV gama ray. emission close {ο periastron passage (Johnstonetal.2005: 2009).. which currently lacks successful multiwavelength interpretations.," The system displays variable broadband nonthermal radio, X-ray and TeV gamma ray emission close to periastron passage \citep{johnston05,uchiyama09,masha09,grove95,aharonian05,aharonian09}, which currently lacks successful multiwavelength interpretations."233 Moreover. (heFermi LAT observations of periastron passage in December 2010 have shown that in general the GeV [lux level [rom the svstem is quite low. although a short intensive [lare was detected as well (seee.g.Tamοἱal.2011:Abdoet2011).," Moreover, the LAT observations of periastron passage in December 2010 have shown that in general the GeV flux level from the system is quite low, although a short intensive flare was detected as well \citep[see e.g.][]{tam11,abdo11}."234". Recently. optical observations with discovered that the optical star corresponds to a late O-star and has a significantly higher luminositv of L,=2.3x10""ergs.! than previously thought (Negueruelaetal.2011)."," Recently, optical observations with discovered that the optical star corresponds to a late O-star and has a significantly higher luminosity of $L_*=2.3\times10^{38}\rm235\, erg\,s^{-1}$ than previously thought \citep{negueruela10}."236. Because of [ast rotation thestar is significantly oblated with equatorial radius of Log=9.72. and the polar radius of Aj= 5.142..," Because of fast rotation thestar is significantly oblated with equatorial radius of $R_{\rm eq}=9.7 R_\sun$ and the polar radius of $R_{\rm237 pole}=8.1 R_\sun$ ."238" This leads as well to a strong gradient of the star surface temperature with 7,=27500 lk and Έρως=34000 IX. The star rotation axis is inclined by 7,33° in respect to the Hne-ofsielt (Negueruelaetal.2011)."," This leads as well to a strong gradient of the star surface temperature with $T_{\rm eq}=27\,500$ K and $T_{\rm239 pole}=34\,000$ K. The star rotation axis is inclined by $i_*\simeq33^\circ$ in respect to the line-of-sight \citep{negueruela10}."240. The distance to (he svstem is now estimated to be 2.3+40.4kpc.," The distance to the system is now estimated to be $2.3\pm0.4\,\rm241kpc$."242 Moreover. the observations favored an orbital inclination value of /~25. which is remarkably smaller than the previously obtained value ol e35? (Johnstonetal. 1994)..," Moreover, the observations favored an orbital inclination value of $i\simeq25^\circ$, which is remarkably smaller than the previously obtained value of $\sim35^\circ$ \citep{johnston94}. ."243 Allthese new parameters together should have an importaat impact on (the multiwavelength properties of (his svstem., Allthese new parameters together should have an important impact on the multiwavelength properties of this system.244ransit window. itis now larecly dominated by the transit duration. which is expected to be ~3.0 davs as shown in Table 2..,"transit window, it is now largely dominated by the transit duration, which is expected to be $\sim 3.0$ days as shown in Table \ref{probdepdur}."245 Eveu so. attempts to obtain full coverage of je transit window from the eround will require a niulti-ongitudinal campaign during which oue can only hope ⋅cooperative weather.," Even so, attempts to obtain full coverage of the transit window from the ground will require a multi-longitudinal campaign during which one can only hope for cooperative weather."246: The complete. observation of. au $3 or ceress durius a single night is a substantially ; achievable goal under such circumstances., The complete observation of an ingress or egress during a single night is a substantially more achievable goal under such circumstances.247 However. 200 still must contend with the challenge of mecting Date photometric precision requirenieuts for à successful fie. etection.," However, one still must contend with the challenge of meeting the photometric precision requirements for a successful detection."248 SIMDAD refers to ( Dra as a variable star based ou its citation as NSV 7077 iu the (Ixulguwkiunetal.1982)., SIMBAD refers to $\iota$ Dra as a variable star based on its citation as NSV 7077 in the \citep{kuk82}.249. The NSV eutry is based on the photometric study of Jackisch(1963)... who reported a magnitude range of 0.09 mae.," The NSV entry is based on the photometric study of \citet{jac63}, who reported a magnitude range of 0.09 mag."250 Later. Percy(1993) included. 7 Dra in his search for photometric variability in [KW giants chosen from the (loffeit&Jaschek1991) and found the star to be coustant to a limit of 0.01 mae.," Later, \citet{per93} included $\iota$ Dra in his search for photometric variability in K giants chosen from the \citep{hof91} and found the star to be constant to a limit of 0.01 mag."251 We investigated the photometric stability of ; Dra musing newer observations., We investigated the photometric stability of $\iota$ Dra using newer observations.252 The satellite observed the star diving its three-year mission ac acquired a photometric data set consisting of 10 lucasurements spanning a period of 1100 davs (Perrvinanetal. 1997)., The satellite observed the star during its three-year mission and acquired a photometric data set consisting of 104 measurements spanning a period of 1160 days \citep{per97}.253. The scatter of the 10147 Dra measurements 15is (0.005 mag. while the rauge of the observations. defined in terms of the 5th aud 95th perceutiles of their distribution. is 0.02 mae.," The scatter of the 104 $\iota$ Dra measurements is 0.005 mag, while the range of the observations, defined in terms of the 5th and 95th percentiles of their distribution, is 0.02 mag."254 The scatter is roughly consistent with the expected unucertaintv of a single observation. but the rauge is roughly twice that expecος fromi a coustaut star.," The scatter is roughly consistent with the expected uncertainty of a single observation, but the range is roughly twice that expected from a constant star."255" Cousequenuth. the Catalogue (Permvinanetal.L997) lists the variability type for ; Dra as a blank. indicating that the star ""couk uot be classified as variable or constant.”"," Consequently, the Catalogue \citep{per97} lists the variability type for $\iota$ Dra as a blank, indicating that the star “could not be classified as variable or constant.”"256 We performed a Fourier analysis of the data. plotted in Figure 5.. and confined the abseuce of any significant periodic variability.," We performed a Fourier analysis of the data, plotted in Figure \ref{phot_hip}, and confirmed the absence of any significant periodic variability."257 We also acquired new Joliusou £2 aud V. observations with the Τὸ 0.1 mi Automatic Photoclectric Telescope (APT) located at Fairboru Observatory iu the Patagonia Mountains of southern Arizona., We also acquired new Johnson $B$ and $V$ observations with the T3 0.4 m Automatic Photoelectric Telescope (APT) located at Fairborn Observatory in the Patagonia Mountains of southern Arizona.258 Between 2010 Jauuuv and May. T3 observed + Dra cifferentially with respect to a nearby comparison star iu the following sequence. termed a eroup observation:V.C.S. where Sis a sky reading. C ds the comparison star ID 110δι = 0 Dra (V Lol 8V0.53. Fs IV). and V ds the program (variable?)," Between 2010 January and May, T3 observed $\iota$ Dra differentially with respect to a nearby comparison star in the following sequence, termed a group observation:, where $S$ is a sky reading, $C$ is the comparison star HD 144284 = $\theta$ Dra $V=4.01$ , $B-V=0.53$, F8 IV), and $V$ is the program (variable?)"259 star ; Dra (V 520. DBV— 1.17. A2 ΠΠ).," star $\iota$ Dra $V=3.29$ , $B-V=1.17$ , K2 III)."260 A 2.5 mag neutral-density filter was used iu combination with the B aud V filters to attenuate the signal aud so minimize the deadtine correction for the two bright stars., A 2.3 mag neutral-density filter was used in combination with the $B$ and $V$ filters to attenuate the signal and so minimize the deadtime correction for the two bright stars.261 Three C differcutial maenitudesOo in both B and V were computed frou cach sequence and averaged to creacB and V. eroup nieaus., Three $V-C$ differential magnitudes in both $B$ and $V$ were computed from each sequence and averaged to create $B$ and $V$ group means.262 Croup mean differeutial maeuitudes with internal standard deviatious greater than 0.01 mae were rejected to eliminate observations taken uider nou-photometric conditions., Group mean differential magnitudes with internal standard deviations greater than 0.01 mag were rejected to eliminate observations taken under non-photometric conditions.263 The surviving eroup leas were corrected for differential extinction with niehtlv extinction coefficieits. transformed to the Johnson system with vearly-ean transformation cocficicuts. ancl treated as single Oservations thereafter.," The surviving group means were corrected for differential extinction with nightly extinction coefficients, transformed to the Johnson system with yearly-mean transformation coefficients, and treated as single observations thereafter."264 The tvvical precision of a single eroup-uean observation from T3. as micasured for pairs o: constant stars. ds ~0.00L0.005 mae (Πανetal.2000).," The typical precision of a single group-mean observation from T3, as measured for pairs of constant stars, is $\sim$ 0.004–0.005 mag \citep{hen00}."265. The APT acquired one or two group observations each clear nigit except for three full nights when the star was oserved at a much ueher cadence of LO eroup observations TOS 10r., The APT acquired one or two group observations each clear night except for three full nights when the star was observed at a much higher cadence of $\sim~10$ group observations per hour.266 The APT collected a total of 221 B iux 220 V ex nposervations., The APT collected a total of 224 $B$ and 220 $V$ group observations.267 Further details ou the automatic oweraloli ¢ft tus telescope. the observing procedures. aud he¢ata 1°cduetion process ean be found in Παινeal.(2000) alu references therein.," Further details on the automatic operation of this telescope, the observing procedures, and the data reduction process can be found in \citet{hen00} and references therein."268 The complete. reduced Johnson 2B data set is plotted in the top panel of Figure 6: tie bottou panel prescuts just the high-cadewe B photometry roin one of the three monitoring welts.," The complete, reduced Johnson $B$ data set is plotted in the top panel of Figure \ref{phot_apt}; the bottom panel presents just the high-cadence $B$ photometry from one of the three monitoring nights."269 The data in thi paucls scatter about their means with a standard deviajon of 0.0011 mag. after a half dozei outliers are removed im cach case.," The data in both panels scatter about their means with a standard deviation of 0.0041 mag, after a half dozen outliers are removed in each case."270 Resultsfor theV. observatious are essentially ideutical (0.0013 mae)., Resultsfor the$V$ observations are essentially identical (0.0043 mag).271" This, our observatious sueecstOO that + Dra. as well as its comparison star theta Dra. are both constant to a Dini of approxinatelv 0.00£ mae."," Thus, our observations suggest that $\iota$ Dra, as well as its comparison star $theta$ Dra, are both constant to a limit of approximately 0.004 mag."272data. the power-law fitting vields a scaling of divine~510 UD. where the units are pe.,"data, the power-law fitting yields a scaling of $d_{\rm min,pc}\sim 5\times 10^{-5}D_{\rm pc}^{0.7}$ , where the units are pc."273 This arguably reflects the uistory of how the filamentary turbulence evolves as the jet propagates. increasing the width.," This arguably reflects the history of how the filamentary turbulence evolves as the jet propagates, increasing the width."274 The physical implication can be revealed by translating a quantity DAU.παν 48 he upper limit of the numberof outer-scale. filaments. CNNaimax:," The physical implication can be revealed by translating a quantity $\la D^{2}/d_{\rm min}^{2}$ as the upper limit of the numberof outer-scale filaments, $(N_{\lambda\sim d})_{\rm max}$."275 Fig. 4((, Fig. \ref{fig:4}( (276b) plots the values of (Nydias (=D>fd. or convenience) as a function of the deprojected. length of jets L.,"b) plots the values of $(N_{\lambda\sim d})_{\rm max}$ $=D^{2}/d_{\rm min}^{2}$, for convenience) as a function of the deprojected length of jets $L$."277 Interpolating them. vields the scaling GN\y-dues Lee. indicating the trend that the capacity of outer- filaments increases as £ increases (shaded area).," Interpolating them yields the scaling $(N_{\lambda\sim d})_{\rm max}\sim 10^{9}L_{\rm kpc}^{0.6}$ , indicating the trend that the capacity of outer-scale filaments increases as $L$ increases (shaded area)."278 In order to see the significance. we recall à promising scenario in which jets having large-scale magnetic fields are necessarily accompanied by huge currents in the bulk plasmas (Appl&Camenzinc 1992).. the kinetic energy of which is dissipated only a little during the transport from the cores to the lobes (Tashiro&Isobe2004).," In order to see the significance, we recall a promising scenario in which jets having large-scale magnetic fields are necessarily accompanied by huge currents in the bulk plasmas \citep{appl92}, the kinetic energy of which is dissipated only a little during the transport from the cores to the lobes \citep{tashiro04}."279.. As a whole. this is compatible with he superconductivity of plasmas.," As a whole, this is compatible with the superconductivity of plasmas."280 For example. let us consider thewell-confirmed samples AIST and AA. the nuclei of which have the supermassive Mack holes with mass 10A4; (Alaechettoetal.1997) and (107LOYAL. (Marconietal.2006)... respectively.," For example, let us consider thewell-confirmed samples M87 and A, the nuclei of which have the supermassive black holes with mass $\sim 10^{9}M_{\sun}$ \citep{macchetto97} and $(10^{7}-10^{8})M_{\sun}$ \citep{marconi06}, respectively."281 According to the arguments of Appl&Camoenzind(1992).. heir central engines. incorporated with their accretion disces. ought to have the potential to drive a current of the order of magnitude of £101A and ~1077AL respectively.," According to the arguments of \citet{appl92}, their central engines, incorporated with their accretion discs, ought to have the potential to drive a current of the order of magnitude of $I\sim 10^{19}~{\rm A}$ and $\sim 10^{18}~{\rm A}$, respectively."282 Such a huge current could not be transported. by a single uniform column. on account of the current inhibition (Lloncla 2007).," Such a huge current could not be transported by a single uniform column, on account of the current inhibition \citep{honda07}."283. One possible solution is to allow for the presence of many filaments that each carry a current. [limited by ig~(me?fe)5E; (onda2000)., One possible solution is to allow for the presence of many filaments that each carry a current limited by $i_{0}\sim (mc^{3}/e)\beta_{j}\Gamma_{j}$ \citep{honda00}.284. It is noted that the value of fy is independent of A (Llondactal.2000).., It is noted that the value of $i_{0}$ is independent of $\lambda$ \citep{honda00b}.285 Phe number of current filaments can then be estimated as NC4/74)~10477 and 107. respeetivelv.," The number of current filaments can then be estimated as $N(\sim I/i_{0})\sim 10^{15}$ and $\sim 10^{14}$, respectively."286 Note that these values are just in the expected ranges of (Nyoadias for AIST and AA (cf., Note that these values are just in the expected ranges of $(N_{\lambda\sim d})_{\rm max}$ for M87 and A (cf.287 Fig., Fig.288 4bb)., \ref{fig:4}b b).289 The outcome suggests that. if the actual capacity of the outer-scale filaments reaches the level ~(Nymax: the filament cluster. which consists of the smaller filaments with size A«d. would not be closely. packed. in the jet.," The outcome suggests that, if the actual capacity of the outer-scale filaments reaches the level $\sim (N_{\lambda\sim d})_{\rm max}$, the filament cluster, which consists of the smaller filaments with size $\lambda<d$, would not be closely packed in the jet."290 This seems to be qualitatively amenable to the observed appearance of the non-uniformlvy. filled features in the jets of AIST (Direttaοἱal.1991:Marshallet2002)and AA (Ixraftetal.2002:Hardcastle2007).," This seems to be qualitatively amenable to the observed appearance of the non-uniformly filled features in the jets of M87 \citep{biretta91,marshall02} and A \citep{kraft02,hardcastle07}."291". As for the BLLLac object 4421. the black hole mass of which is considered to be ~10""AZ; (Xieetal.1908) or more. one anticipates a current of /Lor A."," As for the Lac object 421, the black hole mass of which is considered to be $\sim 10^{6}M_{\sun}$ \citep{xie98}292 or more, one anticipates a current of $I\ga 10^{17}~{\rm A}$ ."293 ltegarding the strongly beaming low with a narrow viewing angle in which 6~by. we lind the order of fy~1018A (in the regime. also note the scaling £4.οο). in equation NJ).," Regarding the strongly beaming flow with a narrow viewing angle in which $\delta\sim\Gamma_{j}$, we find the order of $i_{0}\sim 10^{4}\delta~{\rm A}$ (in the regime, also note the scaling $\nu_{c}\sim b(i_{0}/e)$ in equation \ref{eq:8}) )."294 For ax: 100. we accordingly have IN= 104. which is much larger than (Nvdias~107 (rie.," For $\delta\leq 100$ , we accordingly have $N\ga 10^{11}$ , which is much larger than $(N_{\lambda\sim d})_{\rm max}\sim 10^{8}$ (Fig."295 4bb)., \ref{fig:4}b b).296 The relation INENN uas: Which is in contrast to IN~GNLudusFor the aforementioned LL sources. can also be found in other LLaes (Mrk5501. for example).," The relation $N\gg (N_{\lambda\sim d})_{\rm max}$ , which is in contrast to $N\sim (N_{\lambda\sim d})_{\rm max}$for the aforementioned I sources, can also be found in other Lacs 501, for example)."297 Le is thus ensured. that the jets accompanying these compact objects have many, It is thus ensured that the jets accompanying these compact objects have many298also been studied using optical as well as near-L data ane found that it is normal in the direction of both the clusters.,also been studied using optical as well as near-IR data and found that it is normal in the direction of both the clusters.299 Colour-colour diagram gives the colour excess LJN) = 0.30-E0.20 mag and AAVA) = 1.6040.20 mag for Basel 4 and (J.A )-0.400.20 mag and L(VA) = 2.10+0.20 mag for NGC 7067. (, Colour-colour diagram gives the colour excess $E(J-K)$ = $\pm$ 0.20 mag and $E(V-K)$ = $\pm$ 0.20 mag for Basel 4 and $E(J-K)$ $\pm$ 0.20 mag and $E(V-K)$ = $\pm$ 0.20 mag for NGC 7067. (300ii) Basel 4 and NGC 7067 are located at a clistance of 3.040.2 and 3.60.2 IXpe respectively.,ii) Basel 4 and NGC 7067 are located at a distance of $\pm$ 0.2 and $\pm$ 0.2 Kpc respectively.301 The corresponding ages are 200450 and 10024525. Alves respectively., The corresponding ages are $\pm$ 50 and $\pm$ 25 Myrs respectively.302 They are determined by fitting the isochrones of Schaerer et al. (, They are determined by fitting the isochrones of Schaerer et al. (3031993) for Z = 0.008 in Basel 4 and of Schaller et al. (,1993) for Z $=$ 0.008 in Basel 4 and of Schaller et al. (3041992) for Z = 0.02 in NGC 7067.,1992) for Z $=$ 0.02 in NGC 7067.305 Using the 2ALASS data we also derived the distance and age of both the clusters and they are in agreement with those derived using optical data. (, Using the 2MASS data we also derived the distance and age of both the clusters and they are in agreement with those derived using optical data. (306iii) The radial density profiles show that the radius of Basel 4 and NGC 7067 are LS and 37.0 respectively which indicate that the clusters under study are compact.,iii) The radial density profiles show that the radius of Basel 4 and NGC 7067 are $^{\prime}$ .8 and $^{\prime}$ .0 respectively which indicate that the clusters under study are compact.307 At the cluster distance. they correspond to linear radius of  1.6 and 3.2 pe respectively. (," At the cluster distance, they correspond to linear radius of $\sim$ 1.6 and 3.2 pc respectively. ("308iv) The values of ME slope are 1.55+0.25. and L.68+0.47 for Basel 4 and NGC 7067 respectively.,iv) The values of MF slope are $1.55\pm0.25$ and $\pm0.47$ for Basel 4 and NGC 7067 respectively.309 They are determined. by applying the corrections of data incompleteness and field star contamination and are in agreement with the Salpeter (1955) value. (, They are determined by applying the corrections of data incompleteness and field star contamination and are in agreement with the Salpeter (1955) value. (310v) Mass segregation is observed in both Basel + and NGC 7067 in the sense that massive stars tend. to lio near the cluster. center.,v) Mass segregation is observed in both Basel 4 and NGC 7067 in the sense that massive stars tend to lie near the cluster center.311 The. cynamical relaxation time indicate that both the clusters are dynamically relaxed., The dynamical relaxation time indicate that both the clusters are dynamically relaxed.312 “Thus mass segregation might have occurred. due to dynamical evolution. or imprint of star formation or We thank the referee for. valuable comments which have improved the quality of this paper.," Thus mass segregation might have occurred due to dynamical evolution, or imprint of star formation or We thank the referee for valuable comments which have improved the quality of this paper."313 We are grateful to Dr. Vijay Mohan for helping in data reduction., We are grateful to Dr. Vijay Mohan for helping in data reduction.314 This study mace use of 2ALASS and WEDDA., This study made use of 2MASS and WEBDA.315older populations) increases significantly with age.,older populations) increases significantly with age.316 Actually. 1e time structure is essentially lost for all ages greater than 10 Gyr. corresponding to the first 5 yrs in the history of jese systems. in the axis shown in Figure 1.," Actually, the time structure is essentially lost for all ages greater than 10 Gyr, corresponding to the first 5 Gyrs in the history of these systems, in the axis shown in Figure 1."317 Also. given 1ο total cessation of star forming activity after a strong ealactic¢ wind which we are assuming. the time structure of S.Rae was slightly. mocified. ancl re-normalized. to give 16 observed. present. day total Iuminosities.," Also, given the total cessation of star forming activity after a strong galactic wind which we are assuming, the time structure of $SFR_{HGV}$ was slightly modified and re-normalized to give the observed present day total luminosities."318 As it can be seen from the large number of parameters needed to specify a particular model. our knowledge of the detailed: structure and. evolution of dSph's remains quite poor.," As it can be seen from the large number of parameters needed to specify a particular model, our knowledge of the detailed structure and evolution of dSph's remains quite poor."319 We hence perform an exploration of parameter space. looking for results which are robust with respect to the details of the model. and. seeking correlations between the model parameters. which rellect the underlving physics of these galaxies.," We hence perform an exploration of parameter space, looking for results which are robust with respect to the details of the model, and seeking correlations between the model parameters, which reflect the underlying physics of these galaxies."320 We have tuned. the gas accretion parameters of the generic model by requiring that given the SET(tU inferred by LGV for cach galaxy. galactic winds fully clear the svstemis of gas only once the luminous galaxy has formed.," We have tuned the gas accretion parameters of the generic model by requiring that given the SFR(t) inferred by HGV for each galaxy, galactic winds fully clear the systems of gas only once the luminous galaxy has formed."321 The results of LGV can be divided into two groups. with Leo LE and Ursa Minor showing a single episode of star forming activity.," The results of HGV can be divided into two groups, with Leo II and Ursa Minor showing a single episode of star forming activity."322 One expects tha the DAL halo of these galaxies manages to retain their gas only up to the onset of a galactic wind. which ends all SE activity.," One expects that the DM halo of these galaxies manages to retain their gas only up to the onset of a galactic wind, which ends all SF activity."323 A second eroup is formed by Carina ancl Leo Lo which show extended and. repeated episodes of star forming activity.," A second group is formed by Carina and Leo I, which show extended and repeated episodes of star forming activity."324 In these Last wo cases. the wind criterion can only be satisfied by the inclusion of at least a second episode of eas infall.," In these last two cases, the wind criterion can only be satisfied by the inclusion of at least a second episode of gas infall."325 Finally. for he case of the more nearby Carina and Ursa Minor galaxies. he results of LGV. refer striethy only to the portion of the galaxy seumpled. by the observations. local variations might exist which would make this different from the average over he whole galaxy.," Finally, for the case of the more nearby Carina and Ursa Minor galaxies, the results of HGV refer strictly only to the portion of the galaxy sampled by the observations, local variations might exist which would make this different from the average over the whole galaxy."326 ‘Table 1 gives the values of the input parameters of 4 models calculated for Leo Ll and. Ursa Minor., Table 1 gives the values of the input parameters of 4 models calculated for Leo II and Ursa Minor.327 The first row shows a model where we have tuned the dark matter halo of the ealaxy so that no ealactic wind develops until the maximum of the inferred SELL is reached. ουμα.," The first row shows a model where we have tuned the dark matter halo of the galaxy so that no galactic wind develops until the maximum of the inferred SFH is reached, leoii.dm."328 The value of τ. the parameter which describes the accretion of gas. is fixed. by the inferred. onset of the SE episode of this galaxy.," The value of $\tau$, the parameter which describes the accretion of gas, is fixed by the inferred onset of the SF episode of this galaxy."329 Since ~—0. all the energy ancl metals of all the SNae are mixed into the gaseous content of the galaxy. pu.," Since $\gamma =0$, all the energy and metals of all the SNae are mixed into the gaseous content of the galaxy. $f_{DM}$,"330 the factor v which the tical racius is multiplied to give the core radius of the dark matter halo in this case. must be fitted to 1.28.," the factor by which the tidal radius is multiplied to give the core radius of the dark matter halo in this case, must be fitted to 1.28."331 In this wav. assuming the SPR) inferred by HOGV. we find that we require a dark halo slightly larger than the tidal radius of this galaxy. i£ we want to form the stars it formed in the ime it formed. them.," In this way, assuming the SFR(t) inferred by HGV, we find that we require a dark halo slightly larger than the tidal radius of this galaxy, if we want to form the stars it formed in the time it formed them."332 The details of the accretion formula are largely unimportant. any other infall prescription having he duration required bv the SEI(0) inferences. would give xwicallv the same result.," The details of the accretion formula are largely unimportant, any other infall prescription having the duration required by the SFR(t) inferences, would give basically the same result."333" Since a core radius lareer han the tidal radius was required. we can conclude that not all the energy associated with SE can have participa in heating the ISM. or that estimates of Z2, are oll by or Leo LL. not terribly unlikeA"," Since a core radius larger than the tidal radius was required, we can conclude that not all the energy associated with SF can have participated in heating the ISM, or that estimates of $R_{t}$ are off by for Leo II, not terribly unlikely."334 To put this in perspective. the second row of the Leo 11 models has Ξ0. fox=1. and v calibrated. to ensure that the wind does no start before the maximum in he SET) is reached. model Ieoi.sfr.," To put this in perspective, the second row of the Leo II models has $\gamma=0$, $f_{DM} =1$, and $\nu$ calibrated to ensure that the wind does not start before the maximum in the SFR(t) is reached, model leoii.sfr."335 ie. we decrease the mocel SETt with respec to that inferred by LIGV. to see how zw olf we end up.," i.e., we decrease the model SFR with respect to that inferred by HGV, to see how far off we end up."336 The value of v required in this case is 0.24., The value of $\nu$ required in this case is 0.24.337" ""This means that the inferred SERCO) would have to be olf by a [actor of 4. for the tically limited dark halo of this galaxy o retain the eas long enough to explain the age spread. of stars in Leo LL."," This means that the inferred SFR(t) would have to be off by a factor of 4, for the tidally limited dark halo of this galaxy to retain the gas long enough to explain the age spread of stars in Leo II."338 Since the SEBR(G) of HIGV. was normalizec using the otal observed. Luminosity of these galaxies. such a arge error is not possible. the disagreement of model Τουαι cannot be explained within the uncertainties of the inferrec SER.," Since the SFR(t) of HGV was normalized using the total observed luminosity of these galaxies, such a large error is not possible, the disagreement of model leo.dm cannot be explained within the uncertainties of the inferred SFR."339 The third model for Leo LE. ουνα. is caleulated by taking fow= 1.05=1.0. and optimizing  so that the win starts not before the maximum in the SER is reached.," The third model for Leo II, leoii.wind, is calculated by taking $f_{DM}=1.0$ $\nu =1.0$, and optimizing $\gamma$ so that the wind starts not before the maximum in the SFR is reached."340 In this, In this341shear measurement demands shear statistics such as n-point correlation functions to be measured in an unconventional way as well. but with little additional cost.,"shear measurement demands shear statistics such as n-point correlation functions to be measured in an unconventional way as well, but with little additional cost."342 The author acknowledges Gary Bernstein. Toshifumi Futamase. Yi Mao. Pengjie Zhang for helpful discussions. and Shanghai Astronomical Observatory (SILXO). National Astronomical Observatories of China (NAOC) for their Yospitalitv.," The author acknowledges Gary Bernstein, Toshifumi Futamase, Yi Mao, Pengjie Zhang for helpful discussions, and Shanghai Astronomical Observatory (SHAO), National Astronomical Observatories of China (NAOC) for their hospitality."343 In particular. JZ would like to thank Cary Bernstein for pointing out a mistake in the proof for the nonexistence of CSEs in the presence of PSE in the previous version of this manuscript.," In particular, JZ would like to thank Gary Bernstein for pointing out a mistake in the proof for the nonexistence of CSEs in the presence of PSF in the previous version of this manuscript."344" JZ is currently. supported. by he PCC Fellowship of Texas Cosmology Center of the University of Texas at Austin. ancl was previously supported w the PAC Fellowship of the ""Theoretical Astrophysics Center of UC Berkeley. where part of this work was done."," JZ is currently supported by the TCC Fellowship of Texas Cosmology Center of the University of Texas at Austin, and was previously supported by the TAC Fellowship of the Theoretical Astrophysics Center of UC Berkeley, where part of this work was done."345 LEW is supported in part by NSE grants AST-0807649 and IY-0758153 anc NASA grant NNXOSALA3C lem Under a clockwise coordinate rotation of angle 6. the cosmic shear components transform according to the following rule: Using the chain rule. we then find:," EK is supported in part by NSF grants AST-0807649 and PHY-0758153 and NASA grant NNX08AL43G. 1cm Under a clockwise coordinate rotation of angle $\theta$, the cosmic shear components transform according to the following rule: Using the chain rule, we then find:"346freeze-out timescale is afower limit and. would be larger if the sticking coefficient. were less than unity. or if (as would seem likely) the cores have condensed from a less dense state.,"freeze-out timescale is a limit and would be larger if the sticking coefficient were less than unity, or if (as would seem likely) the cores have condensed from a less dense state."347 We may therefore conclude that the level of CO depletion may provide a sensitive indicator of the age of cores relative to their free-fall times and that a CHO survey of sources at various (carly) stages of evolution could provide a powerful chagnostic of their dynamical status., We may therefore conclude that the level of CO depletion may provide a sensitive indicator of the age of cores relative to their free-fall times and that a $^{17}$ O survey of sources at various (early) stages of evolution could provide a powerful diagnostic of their dynamical status.348 We thank the referee. for a prompt report that. led. to an improved paper., We thank the referee for a prompt report that led to an improved paper.349 We thank W-EF.D. Thi for useful discussions., We thank W-F.D. Thi for useful discussions.350 AIPR ancl DIN are supported by PPARC., MPR and DJN are supported by PPARC.351 We thank the stall of the JCAIT lor their excellent assistance during the observations., We thank the staff of the JCMT for their excellent assistance during the observations.352 The JCAL is operated bv the JAC. Hawai. on behalf of the UK PPARC. the Netherlands NWO. and the Canadian NIC.," The JCMT is operated by the JAC, Hawaii, on behalf of the UK PPARC, the Netherlands NWO, and the Canadian NRC."353 We have mace use of the ΛΕΡ data archive at the CADC. which is operated by the Dominion Astrophysical Observatory for the National Research Council of Canada's Herzberg Institute of Astrophysics.," We have made use of the JCMT data archive at the CADC, which is operated by the Dominion Astrophysical Observatory for the National Research Council of Canada's Herzberg Institute of Astrophysics."354reflected back to the surface from a single stratum that is also equally flat.,reflected back to the surface from a single stratum that is also equally flat.355 This has been schematically represented in Fig. |.., This has been schematically represented in Fig. \ref{f1}.356 In this simple situation it is possible to set down the geometrical locus for the physical raypath in the .(—£ plane. with e defining the source-to-receiver position. and with the receiver itself gathering reflected signals after an interval of time. f.," In this simple situation it is possible to set down the geometrical locus for the physical raypath in the $x$ $t$ plane, with $x$ defining the source-to-receiver position, and with the receiver itself gathering reflected signals after an interval of time, $t$."357 To that end the Pythagoras theorem may be applied to the triangle MDR in Fig. ]..," To that end the Pythagoras theorem may be applied to the triangle $\overline{\mrm{MDR}}$ in Fig. \ref{f1},"358 under the prescription that MIR=2/2. MD=4 (the vertical depth of the reflecting interface from the surface of the earth). and DR=c£/2 (with e being the constant velocity of the waves propagating through the subsurface).," under the prescription that $\overline{\mrm{MR}} = x/2$, $\overline{\mrm{MD}} = d$ (the vertical depth of the reflecting interface from the surface of the earth), and $\overline{\mrm{DR}} = vt/2$ (with $v$ being the constant velocity of the waves propagating through the subsurface)."359 Followed by some simple algebraic manipulations. this exercise will deliver the .—£ locus corresponding to the actual raypath. known also as the (Lowrie1997).. as which is an expression that very recognisably bears the canonical form of a hyperbola. with the parameter fj having been defined as ty=2d/c.," Followed by some simple algebraic manipulations, this exercise will deliver the $x$ $t$ locus corresponding to the actual raypath, known also as the \citep{lowrie}, as which is an expression that very recognisably bears the canonical form of a hyperbola, with the parameter $t_0$ having been defined as $t_0 = 2d/v$."360 The solution given by Eq. (1)), The solution given by Eq. \ref{hyper1}) )361 has been geometrically depicted by the continuous curve in Fig. 2.., has been geometrically depicted by the continuous curve in Fig. \ref{f15}.362 From the plot it may also be appreciated that different values of d. as a parameter in Eq. (1)).," From the plot it may also be appreciated that different values of $d$, as a parameter in Eq. \ref{hyper1}) ),"363 will yield a family of hyperbolae (assuming that ο retains the same constant value all through)., will yield a family of hyperbolae (assuming that $v$ retains the same constant value all through).364 The turning points. the maxima in this case. of this family of hyperbolae (represented by the single continuous curve in Fig. 2)).," The turning points, the maxima in this case, of this family of hyperbolae (represented by the single continuous curve in Fig. \ref{f15})),"365 obtained under the condition d£αι=0. will correspond to the coordinate (0.10) in the ..—-f plane.," obtained under the condition ${\mrm d}t/{\mrm d}x = 0$, will correspond to the coordinate $(0, t_0)$ in the $x$ $t$ plane."366 And for any fixed value of win the .—t plane. the entire range of points along the ¢ axis (with £ customarily having been scaled along the vertical direction). cutting down the entire family of hyperbolae. will define what i$ known in seismic processing terms as a (Maretal. 1999).," And for any fixed value of $x$ in the $x$ $t$ plane, the entire range of points along the $t$ axis (with $t$ customarily having been scaled along the vertical direction), cutting down the entire family of hyperbolae, will define what is known in seismic processing terms as a \citep{mgc}. ."367 Recast in a slightly different form. Eq. (1))," Recast in a slightly different form, Eq. \ref{hyper1}) )"368 will read as, will read as369(Qameastred or estimated) iu the two lower redshift clusters would have been casily detectedecisted.,(measured or estimated) in the two lower redshift clusters would have been easily detected.370 To emphasize the disparity between the three clusters. we conpare their halfheht radi to iuterual velocity dispersions iu Fie. 77:," To emphasize the disparity between the three clusters, we compare their half-light radii to internal velocity dispersions in Fig. \ref{rh_lognsigma};"371 neither of these parameters is expected to evolve significantly within the redshift auge covered here., neither of these parameters is expected to evolve significantly within the redshift range covered here.372 For comparison. we also include E|A’s from Coma using velocity dispersious from ? and halt-leh radii from ?..," For comparison, we also include E+A's from Coma using velocity dispersions from \citet{caldwell:96} and half-light radii from \citet{scodeggio:98}."373 The halflieht radii aud dispersions of E|As at τ=0.83 are comparable to those of the massive carlyype members iu all three clusters., The half-light radii and dispersions of E+A's at $z=0.83$ are comparable to those of the massive early-type members in all three clusters.374 Iu. contrast. noue of he E]A’s at 2=0.33 nor in Coma could be cousidere a cluster giaut.," In contrast, none of the E+A's at $z=0.33$ nor in Coma could be considered a cluster giant."375 It is apparent that the progenitors of he lower redshift E|A’s are very different from those a >=0.83., It is apparent that the progenitors of the lower redshift E+A's are very different from those at $z=0.83$.376 As with their huninositv. the E|As with the ehest internal velocity dispersions are found in our nios distant cluster.," As with their luminosity, the E+A's with the highest internal velocity dispersions are found in our most distant cluster."377 Another key result from our analvsis is that iu the owest redshift cluster. we fud no counterparts to the xieht. high σ late-tvpes found at 2=0.83.," Another key result from our analysis is that in the lowest redshift cluster, we find no counterparts to the bright, high $\sigma$ late-types found at $z=0.83$."378 The a>200 galaxies iu MS105L include SO/a-Sa’s. E|A’s. spirals. aud mergers while the only galaxies in CLI358 with such high dispersions are E-SO’s (Fies. 2???)).," The $\sigma>200$ galaxies in MS1054 include S0/a-Sa's, E+A's, spirals, and mergers while the only galaxies in CL1358 with such high dispersions are E-S0's (Figs. \ref{nsigma_hist}379\ref{rh_lognsigma}) )."380 If we assume that. eiven their similar cluster dispersions (Table ο). CL1358 (2= 0.33) is an evolved. version of MS1051 (2= 0.83). then the wide mis of hieh o svstenis in MS105£ iust be morphologically transformed iuto E-SOs within ~2.5 Gar.," If we assume that, given their similar cluster dispersions (Table \ref{clusters}) ), CL1358 $z=0.33$ ) is an evolved version of MS1054 $z=0.83$ ), then the wide mix of high $\sigma$ systems in MS1054 must be morphologically transformed into E-S0's within $\sim2.5$ Gyr."381 The E|A phase may be an iuteeral step in this process., The E+A phase may be an integral step in this process.382 The οΑν in our sample arc found at Πρες of ~1ου9005 kpe (Fie. ??3)., The E+A's in our sample are found at $R_{BCG}$ of $\sim100-900$ kpc (Fig. \ref{dzsigma_Rbcg}) ).383 Like D99. we find that E|A’s tend to avoid the 3uner cluster core (Προς=1005 kpcj.," Like D99, we find that E+A's tend to avoid the inner cluster core $R_{BCG}\lesssim100$ kpc)."384" At.Ξ0:50, three of the eight E|A’s are associated with a large subcluster (220members:?).. while at =0.58 the E|Αν are found in both the main cluster and massive subcluster (Fig. ??.."," At $z=0.83$, three of the eight E+A's are associated with a large subcluster \citep[$>20$ members;][]{tran:02}, while at $z=0.58$ the E+A's are found in both the main cluster and massive subcluster (Fig. \ref{dzsigma_Rbcg},"385 muddle right)., middle right).386 This sueeests that ~30% of E|Als. if not more. are associated with the eroups that are being accreted by the clusters.," This suggests that $\sim30$ of E+A's, if not more, are associated with the groups that are being accreted by the clusters."387 Iu the following section. we atteiipt to form a colerent picture of the cluster E|A population at intermediate redshifts.," In the following section, we attempt to form a coherent picture of the cluster E+A population at intermediate redshifts."388 Usiug the plysical properties detailed in ll. we determine if E|A’s would be equally as nuuerous iu aidnass selected sample aud test if EÀs are drawn frou the same parent population as regular clustermembers’. and establish a connection between the progenitors and descendauts of these systeuis.," Using the physical properties detailed in 4, we determine if E+A's would be equally as numerous in a mass selected sample and test if E+A's are drawn from the same parent population as regular cluster, and establish a connection between the progenitors and descendants of these systems."389 As in ΕΙ. we only consider cluster mienibers brighter than Mp.=19.1Slogh.. aud E|A’s that satisfy our strict selection criteria (833.2).," As in 4, we only consider cluster members brighter than $M_{Be}=-19.1$, and E+A's that satisfy our strict selection criteria 3.2)."390 One possible concern is how the varving richness of the three clusters affects the couclusious drawn frou these data., One possible concern is how the varying richness of the three clusters affects the conclusions drawn from these data.391 Wowever. we cluphasize it is the relative uunuber of spectra that is iurportaut.," However, we emphasize it is the relative number of spectra that is important."392 Our large sample of confined cluster members (> 120/cluster) combined with the extensive spectroscopic and photometric properties we have gathered allows us to make a 1ieauimeful analysis of the cluster E|A population., Our large sample of confirmed cluster members $>120$ /cluster) combined with the extensive spectroscopic and photometric properties we have gathered allows us to make a meaningful analysis of the cluster E+A population.393 We find the fraction of E|A galaxies in intermediate redshift clusters ranges from 7.13% (Table ??))., We find the fraction of E+A galaxies in intermediate redshift clusters ranges from $7-13$ (Table \ref{eafractions}) ).394 However. we note our spectroscopic survey is magnitude lited.," However, we note our spectroscopic survey is magnitude limited."395 From refbrieht.. we know E|As can be brightened by as uch as AATp.~1.25mae. aud so the E|A fraction in aselected cluster sample might be lower.," From \\ref{bright}, we know E+A's can be brightened by as much as $\Delta M_{Be}\sim1.25$mag, and so the E+A fraction in a cluster sample might be lower."396 Tere we determine the influence of brighteniug on the ΕΙA fraction and estimate a mass selected fraction., Here we determine the influence of brightening on the E+A fraction and estimate a mass selected fraction.397" We first use the Schechter Iuuinositv fiction (7) to populate cluster menmbers as a function of magnitude: at DomO83. Mj,19.5 imag aud à=1 (7)."," We first use the Schechter luminosity function \citep{schechter:76} to populate cluster members as a function of magnitude; at $z=0.83$, $M_{Be}^{\ast}=-19.5$ mag and $\alpha=-1$ \citep{hoekstra:00}."398" Since E|As are brightened by <AMοιτις0.25 mag (SEC rofbxieht)). they follow a Iuninuosity fuuctiou with M5,=19.75 mag."," Since E+A's are brightened by $<\Delta M_{Be}>_{med}=0.25$ mag (see \\ref{bright}) ), they follow a luminosity function with $M_{Be}^{\ast}=-19.75$ mag."399 By combining the two luminosity fuuctious. we can estimate approximately how biased a luminosity selected sample is (Fig. 2?)).," By combining the two luminosity functions, we can estimate approximately how biased a luminosity selected sample is (Fig. \ref{lumfunc}) )."400 Note this approach assumes 1) all E|A’s are brightened by 0.25 maes aud 2) E|Avs wave the same à as regular cluster menibers., Note this approach assumes 1) all E+A's are brightened by $0.25$ mags and 2) E+A's have the same $\alpha$ as regular cluster members.401" If of he members are E|Avs. ie. if the total chister Iuuinositv ""unction conprises reenlar and brightened. we estimate the E|A yaction in a luminosity selected sample (Mp,—zx19.1 5logh)) is ~1/3 larger than that of a ass selected suuple."," If of the members are E+A's, i.e. if the total cluster luminosity function comprises regular and brightened, we estimate the E+A fraction in a luminosity selected sample $M_{Be}\leq-19.1$ ) is $\sim1/3$ larger than that of a mass selected sample."402 Depending ou the magnitude limit. the E|A Traction dn a mass selected siuuple can differ bv ~30% conrpared to a maguitude selected fraction.," Depending on the magnitude limit, the E+A fraction in a mass selected sample can differ by $\sim30$ compared to a magnitude selected fraction."403"Iu Coma. known E|Às are low luminosity (L«ο,LL""). low dispersion (a«150 iy svstenis that are uulikely to evolve into massive carly-type members (??7)..","In Coma, known E+A's are low luminosity $L<0.4L^{\ast}$ ), low dispersion $\sigma<150$ ) systems that are unlikely to evolve into massive early-type members \citep{caldwell:96,caldwell:99,poggianti:03}."404 Towever. we find this is not the case at 2>0.3.," However, we find this is not the case at $z>0.3$."405 From Fies., From Figs.406 ?7 TUS we see that at 2=0.33. E-SQO's aud SO/a-Sa’s are the onlv logical descendauts of the high cispersion (o>1950 ')) BE]A’s at 2=O83.," \ref{nsigma_hist} \ref{rh_lognsigma}, we see that at $z=0.33$, E-S0's and S0/a-Sa's are the only logical descendants of the high dispersion $\sigma>150$ ) E+A's at $z=0.83$."407" The EJA phase lay signify the trausforiiationu of earlv-tvpoe spirals iuto Τομ, and stronely star-forming spirals iuto SO/a-Sas."," The E+A phase may signify the transformation of early-type spirals into E-S0's, and strongly star-forming spirals into S0/a-Sa's."408" The voune stellar ages implied by the E|A phase may seein to conflict with the old stellar ages (:,> 2) derived from studies usine the FP and absorption liue streneths (2773.."," The young stellar ages implied by the E+A phase may seem to conflict with the old stellar ages $z_f>2$ ) derived from studies using the FP and absorption line strengths \citep{kelson:97,vandokkum:98b,kelson:01}."409 However. these ages represent the mean epoch of star formation aud do not preclude activity at Doc2.," However, these ages represent the mean epoch of star formation and do not preclude activity at $z<2$."410 Furthermore. it is not clear whether alb salaxies uudergo the E|A phase.," Furthermore, it is not clear whether all galaxies undergo the E+A phase."411 Also note that the total starburst population cau be as little as of the galaxy’s final stellar imuass (7). , Also note that the total starburst population can be as little as of the galaxy's final stellar mass \citep{barger:96}. .412Assuming the majority of their stars formed at zy> 2. even eaxbv-tyvpe members eau be E|As.," Assuming the majority of their stars formed at $z_f>2$ , even early-type members can be E+A's."413 The connection between E|A progenitors and descendants aerees very well with the concept of “progenitor bias” introduced by ?.., The connection between E+A progenitors and descendants agrees very well with the concept of “progenitor bias” introduced by \citet{vandokkum:01}.414 Du this scenario. as manyas of present dav early-type members are transformed from (later) galaxy types at :< 1l.," In this scenario, as manyas of present day early-type members are transformed from (later) galaxy types at $z<1$ ."415 This morphological evolution is strouely supported by the likely transformation of the IE]À's at 2=0.83 to early-type members by i= 0:33., This morphological evolution is strongly supported by the likely transformation of the E+A's at $z=0.83$ to early-type members by $z=0.33$ .416Much corroborating evidence is presented for this conclusion is presented in the literature.,Much corroborating evidence is presented for this conclusion is presented in the literature.417 A particularly distinctive feature of the YH GCs is their distribution of core radii 2004;; see also Mackey&vandenBergh 2005))., A particularly distinctive feature of the YH GCs is their distribution of core radii \citeauthor{Mackey04} \citeyear{Mackey04}; ; see also \citeauthor{MackeyvdB05} \citeyear{MackeyvdB05}) ).418" The core radii (r.) of the YH GCs shows a very long tail to very large radii (all but one GC with r,>9 pc resides in the Mackey&Gilmore grouping of GCs associated with the outer halo GCs).", The core radii $r_c$ ) of the YH GCs shows a very long tail to very large radii (all but one GC with $r_c > 9$ pc resides in the \citeauthor{Mackey04} grouping of GCs associated with the outer halo GCs).419" Furthermore, the Το distribution of these GCs shows no statistical difference to that observed from a compilation of GCs from the LMC, Fornax and Sagittarius dwarf galaxies (Mackey&Gilmore2003).."," Furthermore, the $r_c$ distribution of these GCs shows no statistical difference to that observed from a compilation of GCs from the LMC, Fornax and Sagittarius dwarf galaxies \citep{Mackey03b}."420" Together with the similarity in morphology of the horizontal branch between the external GCs and the YH GC grouping, this evidence leads Mackey&Gilmore(2004) to propose that all the YH GCs are accreted."," Together with the similarity in morphology of the horizontal branch between the external GCs and the YH GC grouping, this evidence leads \citet{Mackey04} to propose that all the YH GCs are accreted."421 The implications of the size distribution for an accreted origin of the outer halo GCs are elucidated in the study of Hurley&Mackey(2010)., The implications of the size distribution for an accreted origin of the outer halo GCs are elucidated in the study of \citet{Hurley10}.422". In this study, the authors use simulations of star clusters in a tidal field to investigate the conditions required to produce and sustain a GC of large core radius."," In this study, the authors use N-body simulations of star clusters in a tidal field to investigate the conditions required to produce and sustain a GC of large core radius."423" Hurley&Mackey show that clusters may be born with a range of r, governed by how much the cluster fills its initial tidal radius.", \citeauthor{Hurley10} show that clusters may be born with a range of $r_c$ governed by how much the cluster fills its initial tidal radius.424 When a cluster completely fills its natal tidal radius an extended GC can result (τε>10 pc)., When a cluster completely fills its natal tidal radius an extended GC can result $r_c > 10$ pc).425 Conditions for a cluster to completely fill its tidal radius at birth are optimal in regions where background tidal forces are low: such conditions are best satisfied at large distances from MW-like galaxies and in dwarf systems (see discussion in Elmegreen 2008 and 2009))., Conditions for a cluster to completely fill its tidal radius at birth are optimal in regions where background tidal forces are low: such conditions are best satisfied at large distances from MW-like galaxies and in dwarf systems (see discussion in \citeauthor{Elmegreen08} \citeyear{Elmegreen08} and \citeauthor{DaCosta09} \citeyear{DaCosta09}) ).426 This again argues for the accretion of the outer halo GCs to the MW., This again argues for the accretion of the outer halo GCs to the MW.427 The timing of the delivery of the outer Young Halo GCs through accretion is not constrained by the physical parameters of the GCs., The timing of the delivery of the outer Young Halo GCs through accretion is not constrained by the physical parameters of the GCs.428" Gnedin(1997) describe the stability of the MW's GCs against two-body relaxation, tidal truncation, and tidal shocks due to passage through the disk and due to close proximity to the bulge."," \citet{Gnedin97} describe the stability of the MW's GCs against two-body relaxation, tidal truncation, and tidal shocks due to passage through the disk and due to close proximity to the bulge."429" With the exception of two clusters (Pal 1 and Pal 13), GCs of R >10 kpc are expected to be long-lived, with lifetimes of between 5 and 100 Hubble times."," With the exception of two clusters (Pal 1 and Pal 13), GCs of R $> 10$ kpc are expected to be long-lived, with lifetimes of between 5 and 100 Hubble times."430" Hence, by this criterion, these systems could have been accreted into the MW at any stage over the last Hubble time."," Hence, by this criterion, these systems could have been accreted into the MW at any stage over the last Hubble time."431 We can ask the question: how many satellites of a given mass are required to contribute the observed (conservative) 22 Young Halo GCs at R >10 kpc., We can ask the question: how many satellites of a given mass are required to contribute the observed (conservative) 22 Young Halo GCs at R $>10$ kpc.432" Given the specific frequency of GCs (Sy)as a function of host galaxy luminosity (first introduced by Harris&vandenBergh 1981,, and ddiscussed recently by Georgievetal. 2010)), we find this would require for example, approximately 2 Magellanic-like (My~—18 with GC Sy~ 1) systems or 22 systems with Sculptor-like luminosities (My—11 with GC Sy~ 70)."," Given the specific frequency of GCs $S_{N}$ )as a function of host galaxy luminosity (first introduced by \citeauthor{Harris81} \citeyear{Harris81}, , and discussed recently by \citeauthor{Georgiev10} \citeyear{Georgiev10}) ), we find this would require for example, approximately 2 Magellanic-like $_{V} \sim -18$ with GC $S_{N} \sim 1$ ) systems or 22 systems with Sculptor-like luminosities $_{V} \sim -11$ with GC $S_{N} \sim 70$ )."433 If we then consider that the number of accreted clusters islikely to besupplemented by 10-12 OH clusters (Mackey&Gilmore2004) we estimate that the MW may have experienced mergers with 3 Magellanic-like to 30, If we then consider that the number of accreted clusters islikely to besupplemented by 10-12 OH clusters \citep{Mackey04} we estimate that the MW may have experienced mergers with 3 Magellanic-like to 30434There were two approaches we considered in estimating the metallicities of the NGC 524 GCs from our integrated spectra.,There were two approaches we considered in estimating the metallicities of the NGC 524 GCs from our integrated spectra.435 The empirical calibration of Brodie&Lluchra (1990) was specifically designed to estimate metallicitics for extragalactic GCs from. low-resolution. ancl potentially low S/N spectra.," The empirical calibration of \citeANP{Brodie90} (1990) was specifically designed to estimate metallicities for extragalactic GCs from low-resolution, and potentially low S/N spectra."436 Alternatively. stellar population models may be emploved to derive metallicities either by assuming an age for the GCs (necessary due to the agemetallicity degeneracy). or by allowing age cliscrimination to come from Balmer indices.," Alternatively, stellar population models may be employed to derive metallicities either by assuming an age for the GCs (necessary due to the age–metallicity degeneracy), or by allowing age discrimination to come from Balmer indices."437 The former technique ids tied to Alilky Way and Andromeda GC calibrators with independently derived, The former technique is tied to Milky Way and Andromeda GC calibrators with independently derived438In Figure 3 we show a histogram of compact radio source monochromatic 18cm power [or M32. and for each of the two nuclei of Arp 220.,"In Figure 3 we show a histogram of compact radio source monochromatic 18cm power for M82, and for each of the two nuclei of Arp 220."439 The detection threshold for Arp 220 is ~LOM OW |! while that for M82 is ~LON W |.," The detection threshold for Arp 220 is $\sim 10^{19.6}$ W $^{-1}$, while that for M82 is $\sim 10^{18.0}$ W $^{-1}$."440 It is notable that only one of the AIS2 sources [alls above the Arp 220 luminosity detection threshold., It is notable that only one of the M82 sources falls above the Arp 220 luminosity detection threshold.441 If the supernova rate in M32 is 50 times lower than in Arp 220. consistent with the ratio of FIR luminosities. we expect only one RSN in M32 of comparable vouth to the 50 that we have detected in Arp 220.," If the supernova rate in M82 is 50 times lower than in Arp 220, consistent with the ratio of FIR luminosities, we expect only one RSN in M82 of comparable youth to the 50 that we have detected in Arp 220."442 In fact. the last RSN to appear in M82 was ~40 vears ago. so another is somewhat overdue.," In fact, the last RSN to appear in M82 was $\sim$ 40 years ago, so another is somewhat overdue."443 The bright M32 source 41.95+57.5 is decaving al δις νε. and while it may be a plausible candidate for a voung RSN. there is strong evidence (hat this object is alwpical. may not be an RSN. and may be much older (Pedlar et al.," The bright M82 source 41.95+57.5 is decaying at $\sim$ /yr, and while it may be a plausible candidate for a young RSN, there is strong evidence that this object is atypical, may not be an RSN, and may be much older (Pedlar et al."444 1999. MeDonald et al.," 1999, McDonald et al."445 2001. Beswick et al.," 2001, Beswick et al."446 2006 submitted)., 2006 submitted).447 The hypothesis that the starburst in M32 is a scaled-down version of the same phenomenon occurring in Arp 220 is thus attractive. and supported by the data.," The hypothesis that the starburst in M82 is a scaled-down version of the same phenomenon occurring in Arp 220 is thus attractive, and supported by the data."448 Based on (his. we can make an estimate of the number and strength of supernova remnants. similar to those observed in M32. that lie below our detection threshold in Arp 220.," Based on this, we can make an estimate of the number and strength of supernova remnants, similar to those observed in M82, that lie below our detection threshold in Arp 220."449 This number should scale with the FIR huminosity. and the resulting total flix density from 1500 SNRs is 11 mJy. comparable to the total [Iux density in (he 49 detected sources.," This number should scale with the FIR luminosity, and the resulting total flux density from 1500 SNRs is $\sim$ 11 mJy, comparable to the total flux density in the 49 detected sources."450 Based on the observed sizes of (he M82 sources (e.g. Muxlow et al., Based on the observed sizes of the M82 sources (e.g. Muxlow et al.451 1994. \leDonald οἱ al.," 1994, McDonald et al."452 2001). the SNRs will have a volume filling factor of up to a few percent in the Arp 220 nuclei.," 2001), the SNRs will have a volume filling factor of up to a few percent in the Arp 220 nuclei."453 The predicted Ll mJy will contribute to the apparently diffuse emission from the Arp 220 nuclei. but the Πας density will actually reside in angularly compact but undetectably weak supernova renimant(s.," The predicted 11 mJy will contribute to the apparently diffuse emission from the Arp 220 nuclei, but the flux density will actually reside in angularly compact but undetectably weak supernova remnants."454 This is in addition to the 12 mJv of the nuclear flux density that resides in the detected sources., This is in addition to the $\sim$ 12 mJy of the nuclear flux density that resides in the detected sources.455 Together. these total ~12% of the nuclear aud ~s% of the total LSem flux density in Arp 220.," Together, these total $\sim$ of the nuclear and $\sim$ of the total 18cm flux density in Arp 220."456 This constitutes a measure of the number of relativistic electrons (hat remain trapped in hiel-emissivily regions of supernova renmantis. and that have not vet diffused into the lower emissivity environment of the general ISA.," This constitutes a measure of the number of relativistic electrons that remain trapped in high-emissivity regions of supernova remnants, and that have not yet diffused into the lower emissivity environment of the general ISM."457 This conclusion must be tempered by (he realization (hat (he evolution of older supernova remnants in the dense Arp 220 environment may differ svstematically from Chat occurring in M82., This conclusion must be tempered by the realization that the evolution of older supernova remnants in the dense Arp 220 environment may differ systematically from that occurring in M82.458 While the hypothesized weak SNRs may be undetectable in continuum emission. it is possible (hat they. will contribute compact spots of enhanced continuum brightness. which may exhibit OLI maser amplification to detectable levels.," While the hypothesized weak SNRs may be undetectable in continuum emission, it is possible that they will contribute compact spots of enhanced continuum brightness, which may exhibit OH maser amplification to detectable levels."459 Interpretation of OII maser properties ol galaxies such as Arp 220 should take this possibility into account., Interpretation of OH maser properties of galaxies such as Arp 220 should take this possibility into account.460pure starbursts.,pure starbursts.461 This result can be seen in Figure 1 of Desaietal.(2007) which compares the average starburst spectrum from Drandletal.(2006) (o the average spectrum of heavily absorbed ULIBRGs., This result can be seen in Figure 1 of \citet{des07} which compares the average starburst spectrum from \citet{bra06} to the average spectrum of heavily absorbed ULIRGs.462 The to ratio is approximately 1.0 in both cases. even though the feature is within the silicate absorption so should be suppressed i£ it is obscured by (he same silicate absorption (hat obscures the buried source.," The to ratio is approximately 1.0 in both cases, even though the feature is within the silicate absorption so should be suppressed if it is obscured by the same silicate absorption that obscures the buried source."463 The average absorbed ULIRG shown in Desaietal.(2007) has a silicate optical depth of 1.5., The average absorbed ULIRG shown in \citet{des07} has a silicate optical depth of 1.5.464 For (his absorption. the feature is extincted by 1.1 mag compared to 0.48 mag of extinction for the feature. using the extinction curve of DraineandLi.(2001).," For this absorption, the feature is extincted by 1.1 mag compared to 0.48 mag of extinction for the feature, using the extinction curve of \citet{dra01}."465. This differential extinction would imply that the observed to ratio would be 0.56 for an intrinsic ratio of 1.0., This differential extinction would imply that the observed to ratio would be 0.56 for an intrinsic ratio of 1.0.466 That such a lower ratio is not observed in the absorbed ULIRGs is evidence that their starbursts are not extincted by the same dust that produces the silicate absorption., That such a lower ratio is not observed in the absorbed ULIRGs is evidence that their starbursts are not extincted by the same dust that produces the silicate absorption.467 This reasoning justifies treating ULIRG starbursts the same as other starbursts regarding exGinelion corrections., This reasoning justifies treating ULIRG starbursts the same as other starbursts regarding extinction corrections.468" Therefore. we do not apply exGuelion corrections to the ULIRGs and will apply the same transformation between PAI] luminosities and L;, to the ULIRG starbursts as to the other starbursts."," Therefore, we do not apply extinction corrections to the ULIRGs and will apply the same transformation between PAH luminosities and $L_{ir}$ to the ULIRG starbursts as to the other starbursts."469 The plotted. values and [fitted envelope in Figure 3 derive strictly. [roii observed. data. with no assumptions regarding templates or spectral shapes for starburst galaxies.," The plotted values and fitted envelope in Figure 3 derive strictly from observed data, with no assumptions regarding templates or spectral shapes for starburst galaxies."470" The only assumption is that the values of pL, μη) arise purely [rom a starburst. with no contribution from an AGN."," The only assumption is that the values of $\nu$ $_{\nu}$ $\mu$ m) arise purely from a starburst, with no contribution from an AGN."471 As discussed above. the sample was chosen in order to tse only pure starbursts with no evidence that the PAIL complex is diluted by an AGN. or to use sources with published Inminosities of individual PAIL features for the starburst component when there is evidence of an AGN.," As discussed above, the sample was chosen in order to use only pure starbursts with no evidence that the PAH complex is diluted by an AGN, or to use sources with published luminosities of individual PAH features for the starburst component when there is evidence of an AGN."472" The pL, μαι) in Figure 3 can be transformed to bolometric luminosities (L;.) and star formation rates (SFR) using empirically determined conversions.", The $\nu$ $_{\nu}$ $\mu$ m) in Figure 3 can be transformed to bolometric luminosities $L_{ir}$ ) and star formation rates (SFR) using empirically determined conversions.473 Such conversions ancl their relevant uncertainties are subject to further refinement. but this would not affect the data shown in Figure 3.," Such conversions and their relevant uncertainties are subject to further refinement, but this would not affect the data shown in Figure 3."474 For further discussion. the conversions which are adopted are those," For further discussion, the conversions which are adopted are those"475the intensity in the region below the Lyman edge.,the intensity in the region below the Lyman edge.476 We will describe this in more detail in section 3 below., We will describe this in more detail in section 3 below.477 This approach requires the observations to be obtained through an aperture that encloses the bulk of the starburst’s emission (so that a global constraint is obtained)., This approach requires the observations to be obtained through an aperture that encloses the bulk of the starburst's emission (so that a global constraint is obtained).478 It also requires that the width of instrumental spectral line-spread function is significantly smaller than the characteristic velocity dispersion in the starburst (so that the interstellar absorption lines are well resolved)., It also requires that the width of instrumental spectral line-spread function is significantly smaller than the characteristic velocity dispersion in the starburst (so that the interstellar absorption lines are well resolved).479" Finally, the data need to have a high signal-to-noise ratio in the far- UV continuum so that useful constraints are derived."," Finally, the data need to have a high signal-to-noise ratio in the far- UV continuum so that useful constraints are derived."480" Based on these considerations, we will consider two data sets in this paper."," Based on these considerations, we will consider two data sets in this paper."481 The first consists of the sample of eighteen galaxies studied by H01 and G09., The first consists of the sample of eighteen galaxies studied by H01 and G09.482 These are local starburst or star-forming galaxies observed with the Far-Ultraviolet Spectroscopic Explorer (FUSE - Moos et al., These are local starburst or star-forming galaxies observed with the Far-Ultraviolet Spectroscopic Explorer (FUSE - Moos et al.483" 2000), each having signal-to-noise better than 4.6 per 0.078 25 km spectral element in the FUSE LiF1A channel(~ (see s!)"," 2000), each having signal-to-noise better than 4.6 per 0.078 $\sim$ 25 km $^{-1}$ ) spectral element in the FUSE LiF1A channel (see G09)."484 The observations and properties of this sample are G09).described in Table 1., The observations and properties of this sample are described in Table 1.485 Three of these galaxies are in fact LBAs without a DCO: Mrk 54 (Deharveng et al., Three of these galaxies are in fact LBAs without a DCO: Mrk 54 (Deharveng et al.486 Haro 11 (Grimes et al.," 2001), Haro 11 (Grimes et al."487" 2007), and VV 114 et "," 2007), and VV 114 (Grimes et al."488"2001),al.", 2006).489" However, most of these galaxies have (Grimesconsiderably 2006).lower UV luminosities and star-formation rates than the LBAs."," However, most of these galaxies have considerably lower UV luminosities and star-formation rates than the LBAs."490" They also span a much broader range in galaxy mass and metallicity (see G09 and O09, and compare Table 1 and 2)."," They also span a much broader range in galaxy mass and metallicity (see G09 and O09, and compare Table 1 and 2)."491 The second is a sample of eight LBAs observed with the Cosmic Origins Spectrograph Green 2009) on the Hubble Space Telescope (Froning 11727: PI T. Heckman)., The second is a sample of eight LBAs observed with the Cosmic Origins Spectrograph (Froning Green 2009) on the Hubble Space Telescope (Program 11727: PI T. Heckman).492 These are members of a (Programsample of 31 LBAs with HST UV images discussed by O09 and were selected for spectroscopy based on a high UV flux through the COS aperture and a compact UV size (so that the COS line-spread function is not significantly degraded)., These are members of a sample of 31 LBAs with HST UV images discussed by O09 and were selected for spectroscopy based on a high UV flux through the COS aperture and a compact UV size (so that the COS line-spread function is not significantly degraded).493 These observations and the properties of this sample are listed in Table 2 and HST images are shown in Figure 1., These observations and the properties of this sample are listed in Table 2 and HST images are shown in Figure 1.494 In the discussion to follow we will refer to the eight LBAs with HST COS data and the three LBAs with FUSE data as the LBA sample., In the discussion to follow we will refer to the eight LBAs with HST COS data and the three LBAs with FUSE data as the LBA sample.495 We will refer to the other fifteen galaxies with FUSE data as the local starburst sample., We will refer to the other fifteen galaxies with FUSE data as the local starburst sample.496 The observations and data reduction of the FUSE sample have been described in detail in HO1 and G09., The observations and data reduction of the FUSE sample have been described in detail in H01 and G09.497 We refer the reader to these papers., We refer the reader to these papers.498" All the data were obtained through the 30 x 30 arcsec LWRS aperture, except for the cases of NGC 5253 and NGC 7714 (which used the 4 x 20 arcsec MDRS aperture)."," All the data were obtained through the 30 x 30 arcsec LWRS aperture, except for the cases of NGC 5253 and NGC 7714 (which used the 4 x 20 arcsec MDRS aperture)."499 As shown by G09 these apertures encompass most or all of the starburst in the far-UV., As shown by G09 these apertures encompass most or all of the starburst in the far-UV.500 These spectra cover the observed wavelength range from 905 to 1187 Table 1 for the corresponding range in the rest-((see, These spectra cover the observed wavelength range from 905 to 1187 (see Table 1 for the corresponding range in the rest-frame).501" Depending on the angular size of the starburst in the frame).far-UV, the instrumental spectral resolution is R~ 5000 to 14,000, corresponding to a velocity dispersion of ac 9 to 25 km s-! "," Depending on the angular size of the starburst in the far-UV, the instrumental spectral resolution is $R \sim$ 5000 to 14,000, corresponding to a velocity dispersion of $\sigma \sim$ 9 to 25 km $^{-1}$ (G09)."502In all cases the interstellar absorption lines in the (G09).starbursts are well resolved., In all cases the interstellar absorption lines in the starbursts are well resolved.503 For the HST-COS sample we have used the COS G130M and G160M gratings to obtain spectra of our eight targets., For the HST-COS sample we have used the COS G130M and G160M gratings to obtain spectra of our eight targets.504" As can be seen in Figure 1, the COS aperture encompasses most or all of the galaxy."," As can be seen in Figure 1, the COS aperture encompasses most or all of the galaxy."505 We have retrieved these data from the HST MAST archive after they have been processed through the standard COS pipeline., We have retrieved these data from the HST MAST archive after they have been processed through the standard COS pipeline.506 The merged spectra cover a range from about 1160 to 1780 with the corresponding range in the rest- frame, The merged spectra cover a range from about 1160 to 1780 with the corresponding range in the rest- frame507of <2 mCrab in bothdetections!.,of $<2$ mCrab in both.508. Analysing all ppublic data and using the data available on the public page of the GGalactic Bulge program!. ? discovered a likely period of ~185 days as the source was detected by aat a level of z5c for a few days during March and September each year between 2003-2007.," Analysing all public data and using the data available on the public page of the Galactic Bulge $^{1}$, \citet{Zuritaal07} discovered a likely period of $\sim185$ days as the source was detected by at a level of $\gtrsim 5 \sigma$ for a few days during March and September each year between 2003–2007."509 Following this announcement. pperformed a target of opportunity (ToO) observation of 5 ks on March 30. 2007 (?)s7!..," Following this announcement, performed a target of opportunity (ToO) observation of 5 ks on March 30, 2007 \citep{Romanoal07a}."510". They detected a brightsource at the position R.A. (2000) =1749'""06.8 and Dec. =—27°3230.6” (6:93 at confidence). 51"" away from the pposition-."," They detected a brightsource at the position R.A. (2000) $=\ra{17}{49}{06.8}$ and Dec. $=\dec{-27}{32}{30.6}$ $\arcsec$ at confidence), $51\arcsec$ away from the ."511. Its spectrum could be fitted with an absorbed power-law (Ny=23x42-4107ο. FPΞ 2.577%) and the observed 2-10 keV flux is ~107!!ergsem77s7!.," Its spectrum could be fitted with an absorbed power-law $\nh=23_{-10}^{+14}\times10^{22}\ \unit{cm}{-2}$, $\Gamma=2.5_{-1.7}^{+2.0}$ ) and the observed 2–10 keV flux is $\sim10^{-11}\ \ecms$."512 The Swift//UVOT telescope did not detect any optical counterpart with a 3c upper limit of V=20.67 mag., The /UVOT telescope did not detect any optical counterpart with a $3\sigma$ upper limit of $V=20.67$ mag.513 Within the error circle. ? report three 2MASS candidate counterparts whose infrared (HR) magnitudes in the JHK bands suggest a strong optical extinction of 20 mag.," Within the error circle, \citet{Romanoal07a} report three 2MASS candidate counterparts whose infrared (IR) magnitudes in the JHK bands suggest a strong optical extinction of 20 mag."514 Only one candidate is compatible with a supergiant., Only one candidate is compatible with a supergiant.515 Thus. the nature of rremains a mystery.," Thus, the nature of remains a mystery."516 aalso performed a ToO observation of the source during the expected outburst of 2007 March., also performed a ToO observation of the source during the expected outburst of 2007 March.517 From this observation. reported the discovery of a pulsation of ~132 s. The pulse profile displays a double-peak structure with a pulse fraction of ~30% in the 2-10 keV energy range.," From this observation, \citet{Karaseval07,Karaseval08} reported the discovery of a pulsation of $\sim132$ s. The pulse profile displays a double-peak structure with a pulse fraction of $\sim30$ in the 2–10 keV energy range."518 They also detected a pulsation during the outburst detected by oon Sept. 8-10. 2003 in the 20-60 keV energy range with a higher pulse fraction of50G.," They also detected a pulsation during the outburst detected by on Sept. 8–10, 2003 in the 20–60 keV energy range with a higher pulse fraction of."519. Here we report multiwavelength observations performed on wwithJNTEGRAL..XMM-Newton... and. the ESO/NTT telescope.," Here we report multiwavelength observations performed on with, and the ESO/NTT telescope."520 In Sect. ??..," In Sect. \ref{secObs},"521 we first describe the observations and the data analysis of each instrument., we first describe the observations and the data analysis of each instrument.522 Then. we present the results in Sect. ??..," Then, we present the results in Sect. \ref{secRes}."523 Finally. we finish with a discussion and the conclusion on the nature of the source in Sect. ??..," Finally, we finish with a discussion and the conclusion on the nature of the source in Sect. \ref{secDis}."524 The present work is based on data of two high-energy space missions. citepWinkleral03 and citepJansenalO!.. of the European Space Agency (ESA).," The present work is based on data of two high-energy space missions, \\citep{Winkleral03} and \\citep{Jansenal01}, of the European Space Agency (ESA)."525 Multi- follow-up observations were also performed with the 3.5 m New Technology Telescope (NTT) at La Silla Observatory. Chile.," Multi-wavelength follow-up observations were also performed with the 3.5 m New Technology Telescope (NTT) at La Silla Observatory, Chile."526 The INTErnational Gamma-Ray Astrophysics Laboratory TEGRAL)) is a hard X-ray and sspacecraft (S/C) laboratory operating since Oct. 2002., The INTErnational Gamma-Ray Astrophysics Laboratory ) is a hard X-ray and spacecraft (S/C) laboratory operating since Oct. 2002.527 The scientific payload is composed of four instruments., The scientific payload is composed of four instruments.528 However. only data from the hard X-ray and soft ccoded-mask imager IBIS/ISGRI (15 keV-1 MeV) (??) are going to be considered in this work.," However, only data from the hard X-ray and soft coded-mask imager IBIS/ISGRI (15 keV–1 MeV) \citep{Ubertinial03,Lebrunal03} are going to be considered in this work."529 The imager possesses a wide field of view (FOV) of 29° square with a spatial resolution of 12’., The imager possesses a wide field of view (FOV) of $\degr$ square with a spatial resolution of $\arcmin$.530 The source is located near the galactic centre at a distance of 1.67., The source is located near the galactic centre at a distance of $\degr$.531 As the galactic centre is one of the major scientific goals ofINTEGRAL.. the source's field has been extensively observed.," As the galactic centre is one of the major scientific goals of, the source's field has been extensively observed."532 All public data available in March 2007 for hhave been considered in this work., All public data available in March 2007 for have been considered in this work.533 Only pointings where the source is located less than 14 from the FOV centre and whose time exposure is longer than 600 s are kept., Only pointings where the source is located less than $\degr$ from the FOV centre and whose time exposure is longer than 600 s are kept.534 In total. we collected 4759 pointings distributed in 129 revolutions of the S/C that goes from Feb. 2003 (revolution 46. MJD 52698.0) to Oct. 2005 (revolution 370. MJD 53670.1).," In total, we collected 4759 pointings distributed in 129 revolutions of the S/C that goes from Feb. 2003 (revolution 46, MJD 52698.0) to Oct. 2005 (revolution 370, MJD 53670.1)."535 The total exposure time on the source is 10.8 Ms 125.4 days) spanning 2.5 years of observations., The total exposure time on the source is 10.8 Ms 125.4 days) spanning 2.5 years of observations.536 They are not equally. distributed along this period for scheduling reasons., They are not equally distributed along this period for scheduling reasons.537 The ISGRI data were reduced using the Offline Scientific Analysis (OSA)) version 6.0 software that is publicly released by the SScience Data Centre (ISDC) (?).., The ISGRI data were reduced using the Offline Scientific Analysis ) version 6.0 software that is publicly released by the Science Data Centre (ISDC) \citep{Courvoisieral03}.538 Individual sky images for each pointing were produced in the energy band 22-50 keV. Sky mosaics with longer exposures were built combining pointings in which the source is not detected at a δ.σ level or higher in individual pointings., Individual sky images for each pointing were produced in the energy band 22–50 keV. Sky mosaics with longer exposures were built combining pointings in which the source is not detected at a $\sigma$ level or higher in individual pointings.539 The light curves were built using the imaging products., The light curves were built using the imaging products.540 The source count rate was extracted with help of the tool (version 1.4) that is part of the OSA package., The source count rate was extracted with help of the tool (version 1.4) that is part of the OSA package.541 Detections of the source in mosaics are considered at a 6c level or higher., Detections of the source in mosaics are considered at a $\sigma$ level or higher.542 We extracted à spectrum of the source during the first bright flare detected with ISGRI., We extracted a spectrum of the source during the first bright flare detected with ISGRI.543 The spectral extraction was performed using the recently released OSA version 7.0., The spectral extraction was performed using the recently released OSA version 7.0.544 The source spectrum was extracted with within OSA for each pointing., The source spectrum was extracted with within OSA for each pointing.545 Then. each individual spectra was summed to build one single spectrum of the source using the OSA toolpick.," Then, each individual spectra was summed to build one single spectrum of the source using the OSA tool."546 The redistribution matrix. file (RMF) was rebinned into 5channels spread between 15 and 80 keV. Light curves with a binning of 10 s of the first bright flare observed with ISGRI were also extracted with, The redistribution matrix file (RMF) was rebinned into 5channels spread between 15 and 80 keV. Light curves with a binning of 10 s of the first bright flare observed with ISGRI were also extracted with547excellent performance is independent of whether the Edclington approximation. diffusion approximation. or flux-Iimited dilfusion approximation is emploved for the cloud. as well as of the optical depth assumed.,"excellent performance is independent of whether the Eddington approximation, diffusion approximation, or flux-limited diffusion approximation is employed for the cloud, as well as of the optical depth assumed."548 Considering that tvpical disk instability caleulations with the diffusion approximation last [or only ~10? vr. the fact that these models show that the radiative (ransler scheme is highly accurate over (ime scales of al least ~109 vr is reassuring for the mechanism of giant planet formation by disk instability.," Considering that typical disk instability calculations with the diffusion approximation last for only $\sim 10^3$ yr, the fact that these models show that the radiative transfer scheme is highly accurate over time scales of at least $\sim 10^6$ yr is reassuring for the mechanism of giant planet formation by disk instability."549 These moclels presented here test only the raciative (ransfer routines and other (hermodvnamical aspects of the Boss codes. not the coupling between these processes and the hyedrodynanmies (hat occurs in full disk instability models.," These models presented here test only the radiative transfer routines and other thermodynamical aspects of the Boss codes, not the coupling between these processes and the hydrodynamics that occurs in full disk instability models."550 Ideally. one would test the full radiative hydrodynamics codes against analytical solutions.," Ideally, one would test the full radiative hydrodynamics codes against analytical solutions."551 In the absence of such solutions. one can test the codes with respect to their ability (ο represent convective motions. which do involve a coupling of hvedrodsnamies and thermodsyvnamies.," In the absence of such solutions, one can test the codes with respect to their ability to represent convective motions, which do involve a coupling of hydrodynamics and thermodynamics."552 Boss (2004) analvzed in detail the convective stability oL his disk instability models. and founda good agreement between where transient. upwellings and downwellings occurred ancl where the Schwarzschild criterion for convection was met.," Boss (2004) analyzed in detail the convective stability of his disk instability models, and found a good agreement between where transient, convective-like upwellings and downwellings occurred and where the Schwarzschild criterion for convection was met."553 Bolev et al. (, Boley et al. (5542007b) presented the results of several tests for convection in (heir codes. finding that convection occurred when it should have ancl did not occur when it should nol have.,"2007b) presented the results of several tests for convection in their codes, finding that convection occurred when it should have and did not occur when it should not have."555 Convection and convective-like motions thus appear to be appropriately modeled by both the Boss and Boley et al., Convection and convective-like motions thus appear to be appropriately modeled by both the Boss and Boley et al.556 codes., codes.557 Boss Avhill (1992) described a variety of other Cests to which the code has been subjected. including the standard nonisothermal test case for protostellar collapse (tested on two different codes by Myhill Boss 1993). whose results have since been confirmed by Whitehouse Bate (2006).," Boss Myhill (1992) described a variety of other tests to which the code has been subjected, including the standard nonisothermal test case for protostellar collapse (tested on two different codes by Myhill Boss 1993), whose results have since been confirmed by Whitehouse Bate (2006)."558 Further tests of the Boss ΔΙΝΕΙ (1992) code have been presented as follows: spatial resolution (Boss 2000. 2005): gravitational potential solver (Boss 2000. 2001. 2005). artificial viscosity (Boss 2006a): and radiative transfer (Boss 2001. 2007. 2008).," Further tests of the Boss Myhill (1992) code have been presented as follows: spatial resolution (Boss 2000, 2005); gravitational potential solver (Boss 2000, 2001, 2005), artificial viscosity (Boss 2006a); and radiative transfer (Boss 2001, 2007, 2008)."559 Given (he ongoing theoretical debate over the viability of disk instability for giant planet formation. it will continue to be important for other workers to conduct their own tests of these key numerical issues.," Given the ongoing theoretical debate over the viability of disk instability for giant planet formation, it will continue to be important for other workers to conduct their own tests of these key numerical issues."560 The r analvtical solution was derived while I was a lecturer al the Winter School on Exoplanets at the Theoretical Institute for Advanced Research in Astrophysics (TIARA) of the National Tsing Hua. University. in [IIsinehu. Taiwan.," The $r$ analytical solution was derived while I was a lecturer at the Winter School on Exoplanets at the Theoretical Institute for Advanced Research in Astrophysics (TIARA) of the National Tsing Hua University, in Hsinchu, Taiwan."561 | thank the Acting Director of TIARA. Ronald Taam. for making possible my visit to TIARA.," I thank the Acting Director of TIARA, Ronald Taam, for making possible my visit to TIARA."562 The 9 analytical solution was derived in part while I was a visitor at the Roval Observatory. Edinburgh and at St Andrews University in Scotland.," The $\theta$ analytical solution was derived in part while I was a visitor at the Royal Observatory, Edinburgh and at St Andrews University in Scotland."563 I thank [νου Rice and lan Bonnell for making those visits possible. and the referee for promplting me to imvestigate this second lest case as well as for other good advice.," I thank Ken Rice and Ian Bonnell for making those visits possible, and the referee for prompting me to investigate this second test case as well as for other good advice."564 E also thank Saucy Weiser [or computer svstems support at DTM., I also thank Sandy Keiser for computer systems support at DTM.565 This research was supported in part by NASA Planetary Geology ancl Geophysics grant, This research was supported in part by NASA Planetary Geology and Geophysics grant566more than three hundred cool Ap stars from which we also found. several stars with very strong magnetic fields.,more than three hundred cool Ap stars from which we also found several stars with very strong magnetic fields.567 The strongest. Geld of ΚΚ was found in 775049., The strongest field of kG was found in 75049.568 Most probably this value is close to a physical limit for the observed magnetic field in cool Ap stars., Most probably this value is close to a physical limit for the observed magnetic field in cool Ap stars.569 DWI and. WOE acknowledge support for this work from the Science and Technology Facilities Council (ος)., DWK and VGE acknowledge support for this work from the Science and Technology Facilities Council (STFC).570 This research has made use of SIMDBAD database. operated. at CDS. Strasbourg. France.," This research has made use of SIMBAD database, operated at CDS, Strasbourg, France."571"outermost zones (Αι=115""— 155""). containing 33890 measured stars.","outermost zones $R_{gc} =572115''-155''$ ), containing 33890 measured stars."573 The RGB spans a broad color range. suggesting a large range in metallicity. or very large internal photometric scatter. or both.," The RGB spans a broad color range, suggesting a large range in metallicity, or very large internal photometric scatter, or both."574 Our ability to see the true metallicity spread of the RGB tip is limited by the F606W exposures. which set the very distinet red-edge cutoff to the data at Vx30 (for similar cases. see the NGC 3379 or NGC 5128 studies of Harris et al. 2002..," Our ability to see the true metallicity spread of the RGB tip is limited by the $F606W$ exposures, which set the very distinct red-edge cutoff to the data at $V \lesssim 30$ (for similar cases, see the NGC 3379 or NGC 5128 studies of Harris et al. \cite{har02},"575 2007b where the most metal-rich part of the population is cut off)., \cite{har07} where the most metal-rich part of the population is cut off).576 A more specific demonstration of this point is shown in Figure 4.. where the combined photometry for the two outermost annuli is plotted along with fiducial tracks for 12-Gyr-old RGB stars over the metallicity range [Fe/H] =—-2.3 to +0.4.," A more specific demonstration of this point is shown in Figure \ref{cmd_fiducials}, where the combined photometry for the two outermost annuli is plotted along with fiducial tracks for 12-Gyr-old RGB stars over the metallicity range [Fe/H] $= -2.3$ to $+0.4$."577 These tracks are the same ones used in previous studies of NGC 3128 and NGC 3379 (Harris et al. 2002. 2007b))," These tracks are the same ones used in previous studies of NGC 5128 and NGC 3379 (Harris et al. \cite{har02,har07}) )"578 and are drawn primarily from the model library of VandenBerg et al. (2000))., and are drawn primarily from the model library of VandenBerg et al. \cite{vdb00}) ).579 At the right-hand edge of the CMD. the detection limits set by the V filter prevent us from measuring any stars more metal-rich than [m/H] =—0.2 (i.e. stars in the range of the three reddest tracks in the model grid).," At the right-hand edge of the CMD, the detection limits set by the $V$ filter prevent us from measuring any stars more metal-rich than [m/H] $\simeq -0.2$ (i.e. stars in the range of the three reddest tracks in the model grid)."580 In addition. at levels I>27.6 the increasing photometric measurement uncertainties produce an scatter in the observed colors: objects measured too blue by random errors fall well to the blue side of the most," In addition, at levels $I \gtrsim 27.6$ the increasing photometric measurement uncertainties produce an scatter in the observed colors: objects measured too blue by random errors fall well to the blue side of the most"581Long Gamina Ray Bursts (CRBs) are intrinsically linked to core collapse supernovae.,Long Gamma Ray Bursts (GRBs) are intrinsically linked to core collapse supernovae.582 This conclusion comes frou the detection of Type le supernovae nearly coincident with loug GRBs (??)..," This conclusion comes from the detection of Type Ic supernovae nearly coincident with long GRBs \citep{smg+03,Hjorth}."583 [t is also confirmed by studies of the host galaxies of long GRBs. which turued out to be actively star-lormine (?)..," It is also confirmed by studies of the host galaxies of long GRBs, which turned out to be actively star-forming \citep{Djorgovski}."584 The leadiug mocel of long GRBs is a collapsar model (??).. which postttlates that a comyact central source (a black bole or rapidly. rotating citelsov92 Oorms inside the collapsing core.," The leading model of long GRBs is a collapsar model \citep{1999ApJ...524..262M,2008MNRAS.385L..28B}, which postulates that a compact central source (a black hole or rapidly rotating \\cite{Usov92}) ) forms inside the collapsing core."585 The ceural engine generates a collimated out!OW. which upo reaking out of tlie star reaches relativisic velocities and eventually produces 75-1:vs.," The central engine generates a collimated outflow, which upon breaking out of the star reaches relativistic velocities and eventually produces $\gamma$ -rays."586 Moder uodels of neutrino-driven SN explosior are uot. OstableO. in a sense that cifeent eroups do 1 agree with each other aid the role of dierent ing‘eclieut is not settled (e.g.?)..," Modern models of neutrino-driven SN explosion are not ÒstableÓ, in a sense that different groups do not agree with each other and the role of different ingredient is not settled \citep[\eg][]{2009AIPC.1171..273B}."587 The Mlapsar 110€el assumes that in αποτοι to the conveional ueutrino-cdriven SN explosion. tle'e Is 1 additio lxjirce of energy. the GRB ceutral eugiue.," The collapsar model assumes that in addition to the conventional neutrino-driven SN explosion, there is an addition source of energy, the GRB central engine."588 ]t is possible that depencling on the dealled 'operties of he pre-collapse core (like angular momeuim. initialfielcl.. sinall differences COMPOSποu etc). the two euergy sources that tay potentially lead to the explosion. convection and the GRB central engine. may cotribute different amount of euergy. restilting," It is possible that depending on the detailed properties of the pre-collapse core (like angular momentum, initial, small differences in composition etc), the two energy sources that may potentially lead to the explosion, neutrino-driven convection and the GRB central engine, may contribute different amount of energy, resulting"589technique and compared the model to the data by eye.,technique and compared the model to the data by eye.590" This method yields (at best) a model that is consistent with the data, but it cannot provide errors of the parameters, and different models could fit as well."," This method yields (at best) a model that is consistent with the data, but it cannot provide errors of the parameters, and different models could fit as well."591 The three-dimensional radiative-transfer code was used to compute the radiation that a model emits., The three-dimensional radiative-transfer code was used to compute the radiation that a model emits.592" It allows adaptive mesh refinement, following user-defined criteria."," It allows adaptive mesh refinement, following user-defined criteria."593" Dust properties and the dust density distribution as well as location, surface temperature and radius of stars are given as input."," Dust properties and the dust density distribution as well as location, surface temperature and radius of stars are given as input."594 The program then computes the dust temperature by tracing photon packets which are randomly emitted by the stars., The program then computes the dust temperature by tracing photon packets which are randomly emitted by the stars.595" Additional inputs are density and temperature of ionized gas, the velocity field, fundamental molecular data, and the molecular abundance."," Additional inputs are density and temperature of ionized gas, the velocity field, fundamental molecular data, and the molecular abundance."596"Alultiple-component sources only alfect the first term in this expression. producing an olfset in the Cy spectrum jut Ju,=<Yos?owAO from equation Ἐν, ancl this expression simplifies to an ollset independent of f£: Alost multiple-component sources in the NVSS catalogue are double radio sources.","Multiple-component sources only affect the first term in this expression, producing an offset in the $C_\ell$ spectrum But $J_{\ell m} = <|Y_{\ell m}|^2> \Delta \Omega$ from equation \ref{eqjlm}, and this expression simplifies to an offset independent of $\ell$: Most multiple-component sources in the NVSS catalogue are double radio sources."597 Let a fraction e<1 of the radio galaxies be doubles., Let a fraction $e \ll 1$ of the radio galaxies be doubles.598 Phen e=1|¢ ance?=11356. thus the constant olfset may be written We can deduce ο=0.07x0.005. from the form of the NVSS angular correlation function w(8) at small angles 0«0.1. where double sources dominate the close pairs (seco Blake Wall 2002a ancl also Section. 4.2)).," Then $\overline{c} = 1 + e$ and $\overline{c^2} = 1 + 3e$, thus the constant offset may be written We can deduce $e = 0.07 \pm 0.005$ from the form of the NVSS angular correlation function $w(\theta)$ at small angles $\theta < 0.1^\circ$, where double sources dominate the close pairs (see Blake Wall 2002a and also Section \ref{secalm}) )."599 This correction was applied to the measured NVSS C spectrum and successfully removed the small systematic olfset in 6 al high f£., This correction was applied to the measured NVSS $C_\ell$ spectrum and successfully removed the small systematic offset in $C_\ell$ at high $\ell$.600 A sophisticated suite of analytical tools has been developed bv the CAIB community. for deriving the angular power spectra of the observed CMD temperature and. polarization maps., A sophisticated suite of analytical tools has been developed by the CMB community for deriving the angular power spectra of the observed CMB temperature and polarization maps.601 These methods can also be exploited. to. analyze galaxy data (see for example Efstathiou Moody. 2001. lluterer. Ixnox Nichol 2001 and Tegmark et al.," These methods can also be exploited to analyze galaxy data (see for example Efstathiou Moody 2001, Huterer, Knox Nichol 2001 and Tegmark et al."602 2002)., 2002).603 In this approach the power spectrum is determined. using an iterative maximum likelihood analysis. in contrast to the direct estimator ciscussed in Section 3.," In this approach the power spectrum is determined using an iterative maximum likelihood analysis, in contrast to the direct estimator discussed in Section \ref{secestharm}."604 Phe likelihood is a fundamental statistical quantity. and this analysis method permits straightforward control of such issues as edge cllects. noise correlations and svstematic errors.," The likelihood is a fundamental statistical quantity, and this analysis method permits straightforward control of such issues as edge effects, noise correlations and systematic errors."605 The starting point for maximum likelihood estimation (AILE) is Bayes’ theorem where à. are the parameters one is trying determine. D is the data ancl Z is the additional information describing the problem.," The starting point for maximum likelihood estimation (MLE) is Bayes' theorem where $\alpha$ are the parameters one is trying determine, $D$ is the data and $I$ is the additional information describing the problem."606 The quantity ία) is the likelihood. i.c. the probability of the data given a specifie set of parameters. while the left-hand side is the posterior. i.e. the probability of the parameters given the data.," The quantity $P(\alpha|I)$ is the likelihood, i.e. the probability of the data given a specific set of parameters, while the left-hand side is the posterior, i.e. the probability of the parameters given the data."607 We will assume that the sky is a realization of a stationary Gaussian process. with an angular power spectrumCy.," We will assume that the sky is a realization of a stationary Gaussian process, with an angular power spectrum $C_\ell$."608 We assume no cosmological information abou the distribution of the €., We assume no cosmological information about the distribution of the $C_\ell$.609 The rendition of the sky wil be a pixelized. map. created. by binning the galaxy. data in equal-area cells such that the count in the ;/th. eel is n;. cllectively constructing a “temperature map” of galaxy surface density.," The rendition of the sky will be a pixelized map, created by binning the galaxy data in equal-area cells such that the count in the $i$ th cell is $n_i$, effectively constructing a “temperature map” of galaxy surface density."610 We performec this task using the IHIZALDPLIN. software. package (Gorksi. Hivon. Wanelel 1900: http://www.eso.org/science/healpix).," We performed this task using the HEALPIX software package (Gorksi, Hivon Wandelt 1999; )."611 We chose the HISALPIN. pixelization scheme rig.=382. which corresponds to 12.288 pixels over a full sky.," We chose the HEALPIX pixelization scheme $n_{\rm side} = 32$, which corresponds to 12,288 pixels over a full sky."612 Phe angular power spectrum may be safely extracted to multipole 20 page., The angular power spectrum may be safely extracted to multipole $\ell_{\rm max} \approx 2 \times n_{\rm side}$ .613 We then defined a data vector: where 7 is the mean count per pixel., We then defined a data vector: where $\overline{n}$ is the mean count per pixel.614 Figure 3 demonstrates that the data vector e; For the NVSS sample is well-approximated by a Gaussian distribution. as assumed in a maximum likelihood analvsis.," Figure \ref{fighist} demonstrates that the data vector $x_i$ for the NVSS sample is well-approximated by a Gaussian distribution, as assumed in a maximum likelihood analysis."615 The covariance matrix CL due ο primordial Iluctuations is given by where 2 is the Legendre polvnomial anc 6 is the angle between pixel pair (7.7).," The covariance matrix $C^T_{ij}$ due to primordial fluctuations is given by where $P_\ell$ is the Legendre polynomial and $\theta_{ij}$ is the angle between pixel pair $(i,j)$."616 In order to apply a likelihood analvsis we must also specify a noise covariance matrix CN., In order to apply a likelihood analysis we must also specify a noise covariance matrix $C^N_{ij}$.617 We mocellecd the noise as a Gaussian random. process with variance l/m. uncorrelated between pixels. such that Ch=(1/7)δι.," We modelled the noise as a Gaussian random process with variance $1/\overline{n}$, uncorrelated between pixels, such that $C^N_{ij} =618(1/\overline{n}) \, \delta_{ij}$."619 The likelihood of the map. with a particular power spectrum C'. is given by The goal of ALLE is to maximize this function. and the astest general method is to use Newton-Raphson iteration o find the zeroes of the derivatives in InP(C|]x) with respect to C.," The likelihood of the map, with a particular power spectrum $C_\ell$, is given by The goal of MLE is to maximize this function, and the fastest general method is to use Newton-Raphson iteration to find the zeroes of the derivatives in $\ln P(C_{\ell}|{\bf x})$ with respect to $C_\ell$."620 We used the ALADCAP package (Borrill 1999: http://www.nersc.gov/--borrill/cmb/madcap) to «derive he maximum likelihood. handed angular power spectrum. rom the pixelized galaxy map and noise matrix., We used the MADCAP package (Borrill 1999; ) to derive the maximum likelihood banded angular power spectrum from the pixelized galaxy map and noise matrix.621 NLADC'ATP is a parallel implementation of the Bond. Jalle Knox (JOOS) maximunm-likelihood algorithms for the analysis of CAMB datasets.," MADCAP is a parallel implementation of the Bond, Jaffe Knox (1998) maximum-likelihood algorithms for the analysis of CMB datasets."622 We ran the analysis software on the supercomputer Seaborg. administered. by the National Enereyv Research Scientific Computing Centre (NERSC) at Lawrence Berkeley National Laboratory. California.," We ran the analysis software on the supercomputer Seaborg, administered by the National Energy Research Scientific Computing Centre (NERSC) at Lawrence Berkeley National Laboratory, California."623 We again applied equation. 12 to the ALADCADP results to correct the measured. power spectrum for the inlluence of multiple-component sources., We again applied equation \ref{eqcldoub} to the MADCAP results to correct the measured power spectrum for the influence of multiple-component sources.624 Boughn Crittenden (2002) also. performed. a HEALPIX analysis of the NVWSS as. part. of a. cross- analysis with the CAIB searching for evidence, Boughn Crittenden (2002) also performed a HEALPIX analysis of the NVSS as part of a cross-correlation analysis with the CMB searching for evidence625Thus our results Irom [mode frequencies which effectively measure (he solar radius in the subsurface lavers. are probably not inconsistent. with these measurements.,"Thus our results from f-mode frequencies which effectively measure the solar radius in the subsurface layers, are probably not inconsistent with these measurements."626 This work utilizes data obtained by the Solar Oscillations Investigation / Michelson Doppler Luager on the Solar and IHeliospherie Observatory (SOIIO)., This work utilizes data obtained by the Solar Oscillations Investigation / Michelson Doppler Imager on the Solar and Heliospheric Observatory (SOHO).627" SOILO is a project of internalional cooperation between ESA and NASA,", SOHO is a project of international cooperation between ESA and NASA.628A search in the Geneva photometry database revealed that several Cepheids already had a substantial number of measurements.,A search in the Geneva photometry database revealed that several Cepheids already had a substantial number of measurements.629 These data could constitute a basis for expanding Bersier et al., These data could constitute a basis for expanding Bersier et al.630's (1997) efforts to determine Period-Raclius ancl Period-Liuninosityv. relations via the Baacle-Wesselink method.,'s (1997) efforts to determine Period-Radius and Period-Luminosity relations via the Baade-Wesselink method.631 I present these old unpublished together with new data obtained in several runs curing 1996 and 1997., I present these old unpublished together with new data obtained in several runs during 1996 and 1997.632 Like the data eiven in Bersier.Durki.&Burnet(1994).. the measurements are in the Geneva 7-color svstem (Golav 1980. Rutener 1988) and most have been obtained with the 70-cm Swiss telescope al La Sila Observatory.," Like the data given in \citet{ber94a}, the measurements are in the Geneva 7-color system (Golay 1980, Rufener 1988) and most have been obtained with the 70-cm Swiss telescope at La Silla Observatory."633 The instrument used is a photometer (Burnet1976). that measures each filler several times per second: (he exposure is stopped alter a mininunm signal-to noise ratio has been reached in each filter: the integration time was at least three minutes., The instrument used is a photometer \citep{b76} that measures each filter several times per second; the exposure is stopped after a minimum signal-to noise ratio has been reached in each filter; the integration time was at least three minutes.634 Given that most of our stars are brighter Chan my=10 the uncertainty is better than Q.01' for virtually all measurements., Given that most of our stars are brighter than $m_V = 10$ the uncertainty is better than $0.01^m$ for virtually all measurements.635 Furthermore all measurements have been obtained in photometric conditions., Furthermore all measurements have been obtained in photometric conditions.636 Table 1. lists all 62 Cepheids that have data.," Table \ref{tbl_nph}637 lists all 62 Cepheids that have data."638 The 1250 inclivicual measurements in seven colors are given in Table 2p.harvard.edu/pub/cdbersier/., The 1250 individual measurements in seven colors are given in Table \ref{tbl_ph}.639. Forty-three stars have more (han 20 measurements., Forty-three stars have more than 20 measurements.640 Figure 1. presents examples of light aad color curves for well-observecl Cepheids., Figure \ref{fig_lc} presents examples of light and color curves for well-observed Cepheids.641 Most observations were obtained in several runs on the 1.5 meter Danish telescope at ESO La Silla in 1996 and 1997. hence these data are contemporaneous with most of the photometry presented above.," Most observations were obtained in several runs on the 1.5 meter Danish telescope at ESO La Silla in 1996 and 1997, hence these data are contemporaneous with most of the photometry presented above."642 I used the CORAVEL spectrograph. described in detail in Daranne.Mavor&DPoncet(1979).," I used the CORAVEL spectrograph, described in detail in \citet{bmp79}."643. The instrument. was optimized to vield accurate radial velocities through a cross-correlation method., The instrument was optimized to yield accurate radial velocities through a cross-correlation method.644 The light is dispersed and (hen goes through a mask (based on the spectrum of Arcturus) before being detected by a photomultiplier., The light is dispersed and then goes through a mask (based on the spectrum of Arcturus) before being detected by a photomultiplier.645 An are spectrum is obtained just before ancl just after each star exposure. to provide a eood wavelength solution.," An arc spectrum is obtained just before and just after each star exposure, to provide a good wavelength solution."646 The observing setup is such (hat the cross-correlation function (CCF) is viewed in real-time., The observing setup is such that the cross-correlation function (CCF) is viewed in real-time.647 This allows to stop the exposure when the CCF has a sufficient signal-to-noise., This allows to stop the exposure when the CCF has a sufficient signal-to-noise.648 A Gaussian is fitted to the observed. eross-correlation function to vield the, A Gaussian is fitted to the observed cross-correlation function to yield the649cosmological gas. and the approximations that are mace in.,"cosmological gas, and the approximations that are made in."650. To facilitate comparison with other radiative transfer codes we review some of the other approximations which can be mace., To facilitate comparison with other radiative transfer codes we review some of the other approximations which can be made.651 1n what follows. we use Roman numerals to indicate the ionization state of an element (HLLIo) in the standard wav.," In what follows, we use Roman numerals to indicate the ionization state of an element (H,He) in the standard way."652 Elements without Roman numerals refer to the nuclei of atoms (or all ionization states)., Elements without Roman numerals refer to the nuclei of atoms (or all ionization states).653 A subscripted η refers to the number density of an clement (or a specific ionization state of an element)., A subscripted $n$ refers to the number density of an element (or a specific ionization state of an element).654 A subscripted a refers to the ratio of the number density of a specific ionization state to the number density of all nuclei of that clement., A subscripted $x$ refers to the ratio of the number density of a specific ionization state to the number density of all nuclei of that element.655" A subsceripted y refers to the ratio of the number density of the subscripted species to the number density of LE nuclei. for example. The 3-D radiative transfer equation in a frame comoving with the expansion of the Universe can be written (c.g.?).. where ce, and 5, are the emission and extinction coefficients respectively. Lf=6/0 ds the Hubble parameter. a—afa; is the scale factor at time £ divided bv the scale [actor at time ἐν (when the photons in the ray were emitted). and J,=(κ.i.9.1) is the specific intensity."," A subscripted $y$ refers to the ratio of the number density of the subscripted species to the number density of H nuclei, for example, The 3-D radiative transfer equation in a frame comoving with the expansion of the Universe can be written \citep[e.g.][]{1998MmSAI..69..455N}, where $ \epsilon_{\nu} $ and $ \kappa_{\nu} $ are the emission and extinction coefficients respectively, $H = \dot{a}/a$ is the Hubble parameter, $\bar{a} =656a / a_e $ is the scale factor at time $t$ divided by the scale factor at time $t_e$ (when the photons in the ray were emitted), and $I_{\nu} = I657({\mathbf {\vec{x}}}, {\mathbf {\hat{n}}}, \nu, t) $ is the specific intensity."658" For photons with à mean free path Aj, much. less than the Horizon size c/44. the classical radiative transfer equation is a valid approximation."," For photons with a mean free path $\lambda_{\rm mfp}$ much less than the Horizon size $c/H$, the classical radiative transfer equation is a valid approximation."659 This local approximation holds fairly well before the percolation stage of reionization when the growing ionization bubbles are still insulated. (rom each other by the optically thick ICM., This local approximation holds fairly well before the percolation stage of reionization when the growing ionization bubbles are still insulated from each other by the optically thick IGM.660 Care must be taken once the majority of the ICM. is reionized and becomes optically thin allowing photons to travel distances greater than the simulation box length., Care must be taken once the majority of the IGM is reionized and becomes optically thin allowing photons to travel distances greater than the simulation box length.661 The ellect of these background fluxes from outside the simulation volume must be taken into account. especially for. high enerev photons which have longer mean free paths and the potential to tonize and heat the IGM after being redshifted.," The effect of these background fluxes from outside the simulation volume must be taken into account, especially for high energy photons which have longer mean free paths and the potential to ionize and heat the IGM after being redshifted."662 The treatment of these non-local Duxes should be tailored to the specific problem at hand and so were not hardewired into., The treatment of these non-local fluxes should be tailored to the specific problem at hand and so were not 'hard-wired' into.663. For the test cases presented in £4 they were not necessary., For the test cases presented in 4 they were not necessary.664 Another caveat to using the classical equation. as explained in ?).. is that it is only valid when [gdfe]< and hence only for continuum radiation.," Another caveat to using the classical equation, as explained in \cite{1999ApJ...523...66A}, is that it is only valid when $ |\nu \partial665I_{\nu} / \partial \nu| \leq I_{\nu} $ and hence only for continuum radiation."666 However. the classical equation can still be used for line radiation if the redshiltec absorption (photo-ionization) cross-sections are used when determining By.," However, the classical equation can still be used for line radiation if the redshifted absorption (photo-ionization) cross-sections are used when determining $\kappa_{\nu}$."667" Ife, and s, can be approximated as constant. a time independent RV equation can be used."," If $\epsilon_{\nu}$ and $\kappa_{\nu}$ can be approximated as constant, a time independent RT equation can be used."668 This is à good approximation for individual SPL particles over a sulliciently. short time. however (asisalsodiscussedin2). ijt breaks down close to sources ancl allows the possibility of ionization. fronts that travel faster than the speed. of light.," This is a good approximation for individual SPH particles over a sufficiently short time, however \citep[as is also discussed in][]{1999ApJ...523...66A} it breaks down close to sources and allows the possibility of ionization fronts that travel faster than the speed of light."669 his can be quantified by examining the ionization front jump conclition for a single point source ionizing a uniform density. constant temperature. Livclrogen eas. where. ry is the distance to the ionization front from the source. A is the number of photons per second emitted by the source. and ag is the recombination rate.," This can be quantified by examining the ionization front jump condition for a single point source ionizing a uniform density, constant temperature, Hydrogen gas, where, $r_{I}$ is the distance to the ionization front from the source, $\dot{N}$ is the number of photons per second emitted by the source, and $\alpha_{\rm H}$ is the recombination rate."670 An upper limit on the radius. 7 within which the ionization front has a speed greater than c is. Within this region. use of the time independent equation breaks down.," An upper limit on the radius, $r_c$ within which the ionization front has a speed greater than c is, Within this region, use of the time independent equation breaks down."671 In à ravtracing scheme. this can be avoided by stopping rays once they have reached a distance (d—clos where £o) is the amount of time the source has been on.," In a raytracing scheme, this can be avoided by stopping rays once they have reached a distance $d = ct_{on}$ where $t_{on}$ is the amount of time the source has been on."672 The photons that were in the ray can be saved and traced from the stopping point once cnough time has elapsed., The photons that were in the ray can be saved and traced from the stopping point once enough time has elapsed.673 Ln practice this is not always necessary., In practice this is not always necessary.674" For example. the first test presented in 8&4 has rr,=6.9.105 where the Strommeren radius. r,=5.4 kpe. In.. the diffuse component of the radiation field is modeled using the on-the-spot (OLS) approximation. Or às à set of many point sources and so for all calculations we can set ce,=0 along the rav. further simplifving the ICE equation. which has the analytic solution. where In principle. &, should include contributions [rom every process that removes. photons from. the rav. under consideration (photo absorption. Thomson scattering. dust. etc)."," For example, the first test presented in 4 has $r_c/r_s = 6.9675\times 10^{-3}$ where the Strömmgren radius, $r_s = 5.4$ kpc, In, the diffuse component of the radiation field is modeled using the on-the-spot (OTS) approximation, or as a set of many point sources and so for all calculations we can set $\epsilon_{\nu}=0$ along the ray, further simplifying the RT equation, which has the analytic solution, where In principle, $\kappa_{\nu}$ should include contributions from every process that removes photons from the ray under consideration (photo absorption, Thomson scattering, dust, etc.)."676 For the tests presented. here. we consider only photo absorption. however it would be straightforward. το add terms to account for other processes.," For the tests presented here, we consider only photo absorption, however it would be straightforward to add terms to account for other processes."677 In this section we review the equations that determine the time cevelopment of the ionization fractions., In this section we review the equations that determine the time development of the ionization fractions.678 They represent the contributions from photo-ionization. collisional ionization and recombination.," They represent the contributions from photo-ionization, collisional ionization and recombination."679 Analytic and time averaged solutions in the case of constant rates are derived for use in an iterative solution scheme which relaxes the stringent constraints on the time step., Analytic and time averaged solutions in the case of constant rates are derived for use in an iterative solution scheme which relaxes the stringent constraints on the time step.680(121) right))-e, ) -.681 As compared with Eq.(76)). the new exponcutial factor ef js que to the discontinuitv of As atq. associated with shell crossing within the ‘sticky model.," As compared with \ref{Psc-def1}) ), the new exponential factor $e^{-\ii k f q \mu}$ is due to the discontinuity of $\Delta\vs$ at, associated with shell crossing within the “sticky model”."682 The factors (1|f£) that uniltiply the longitudinal wavenuuuber & could be expected from Eqs.(108))-(113))., The factors $(1+f)$ that multiply the longitudinal wavenumber $k$ could be expected from \ref{ks-sticky1}) \ref{ks-sticky2}) ).683 As for the reabspace Fig. l..," As for the real-space Fig. \ref{fig_lDk},"684 we show in Fig., we show in Fig.685 b. our uuuerncal results for the redshift-space loganritlinie power. for longitudinal waveuunibers k. defined as Lah? PUO.," \ref{fig_lsDk} our numerical results for the redshift-space logarithmic power, for longitudinal wavenumbers $\vk$, defined as (k) = k^3 (k)."686 We use the same defiuitiou (77)). even though Pith) ouly holds aloug the lougitucinal direction and Py(kh)}(=P(k)) holds along the two trausverse directions (so that using a factor Jl iustead of A? would be more uatural here). to make the comparison with Fig.," We use the same definition \ref{Delta2def}) ), even though $P^s_{\parallel}(k)$ only holds along the longitudinal direction and $P^s_{\perp}(k) (=P(k))$ holds along the two transverse directions (so that using a factor $k$ instead of $k^3$ would be more natural here), to make the comparison with Fig."687 1. easier., \ref{fig_lDk} easier.688 In particular.," In particular,"689Ou the other haud. the thermodynamics require the black hole eutropy has to be normalized. to the Bekenstein-Tawking- expression.- ic.. 9*=SpyA(77).,"On the other hand, the thermodynamics require the black hole entropy has to be normalized to the Bekenstein-Hawking expression, i.e., $S=S_{BH}=A/(4l_p^2)$."6902 Then.d we obtain the ummber NV as follows Tn the next section. we will show that the result of (75)) is not only valid for the Schwarzschild black hole. it is also right for all static spherical black holes.," Then, we obtain the number $N$ as follows In the next section, we will show that the result of \ref{NN}) ) is not only valid for the Schwarzschild black hole, it is also right for all static spherical black holes."691 To reveal the physical ucaning of the brick wall thickness / introduced by t IHooft. we calculate the statistical average value of A(e) Comparing eq.(76)) with (27)). we find where a=N'z?2/(080003)) is a constant.," To reveal the physical meaning of the brick wall thickness $h$ introduced by 't Hooft, we calculate the statistical average value of $\Delta(\omega)$ Comparing \ref{ad}) ) with \ref{h}) ), we find where $\alpha= N'\pi^2/(1080\zeta(3))$ is a constant."692 Therefore we conclude. the “brick wall thickness  represcuts the statistical average effects of the quantum horizon spread rauge A(uw).," Therefore we conclude the ""brick wall"" thickness $h$ represents the statistical average effects of the quantum horizon spread range $\Delta(\omega)$."693 Finally in this section. we argue that the effects of Q(£?) in eq.C607)) raise the effective temperature of the hole as it radiates;," Finally in this section, we argue that the effects of $\mathcal{O}(\xi^2)$ in \ref{xi}) ) raise the effective temperature of the hole as it radiates."694 Namely. the £-depeudeucy in the eq.(67)}) should be thought as its thermal statistical average €dependeucy.," Namely, the $\xi$ -dependency in the \ref{xi}) ) should be thought as its thermal statistical average $\overline{\xi}$ -dependency."695 like eq.(76)). (fray)/ Lothen the effective temperature] for the hole is where the Ley is Tawkine temperature aud the second terii in the rigbit-haud-side represents a correction to the temperature duc to the space-time non-conmmiutative property near the eveut horizon.," like \ref{ad}) ), $\overline{\xi^2}=l_p^4\overline{\omega^2}/(4r_H^2)=1/160\times(l_p/r_H)^4$ , then the effective temperature for the hole is where the $T_{BH}$ is Hawking temperature and the second term in the right-hand-side represents a correction to the temperature due to the space-time non-commutative property near the event horizon."696 Obviously. this correction to the Το is tuy as ry2P. aud houce it can be ignored indeed.," Obviously, this correction to the $T_{BH}$ is tiny as $r_H\gg697l_p$, and hence it can be ignored indeed."698 The corrections of O(£*) with No>2 can be analyzed likewise aud they are also ignorable as τμ2»1)., The corrections of $\mathcal{O}(\xi^N)$ with $N>2$ can be analyzed likewise and they are also ignorable as $r_H\gg l_p$.699 Iu this section. we study our OFT inodel with quanti horizou for general static black holes.," In this section, we study our QFT model with quantum horizon for general static black holes."700 The static spherical black holes metric ecnerically cau be written as the eq.(33)). and the Sclavarzschild black hole is a special case of this metric.," The static spherical black hole's metric generically can be written as the \ref{metric}) ), and the Schwarzschild black hole is a special case of this metric."701 The calculation process is similar to the previous section. except the metric is different.," The calculation process is similar to the previous section, except the metric is different."702 As discussed in above. the nonconmuutative rauee near the horizon is not bieeero0 than the Plauck leneth.," As discussed in above, the noncommutative range near the horizon is not bigger than the Planck length."703 Heuce. to the metric near the horizon the function D(r) in 219 (33)) can be approximately written as follows," Hence, to the metric near the horizon the function $D(r)$ in \ref{metric}) ) can be approximately written as follows"704of our simulation.,of our simulation.705" Also, we are unable to count all of the most massive clusters due to our limited simulation volume."," Also, we are unable to count all of the most massive clusters due to our limited simulation volume."706" However, we can estimate the magnitude of these effects in a simple way."," However, we can estimate the magnitude of these effects in a simple way."707" By extrapolating our mass function, we estimate that we are missing ~40 clusters with M,>1.2x101?5-7!Mg in our simulation volume."," By extrapolating our mass function, we estimate that we are missing $\sim$ 40 clusters with $M_v > 1.2 \times 10^{15} \hmsol$ in our simulation volume."708" We can use the fits to the Pi.4anz—M, relation to find the radio power of these missing halos, which for all models leads to P414>3x10245WHz! for the missing clusters."," We can use the fits to the $\pmvir$ relation to find the radio power of these missing halos, which for all models leads to $P_{1.4} > 3 \times 10^{24} h_{70}^{-1} \whz$ for the missing clusters."709" We assign radio halosd to of these most massive clusters, which gives us an additional 12 halos."," We assign radio halos to of these most massive clusters, which gives us an additional 12 halos."710" If we assume that these clusters are evenly distributed within a 1 Gpc volume, then even the least luminous radio halo has flux = 100 mJy, so essentially all of these radio halos contribute to the number counts."," If we assume that these clusters are evenly distributed within a $\sim$ 1 Gpc volume, then even the least luminous radio halo has flux $\gtrsim$ 100 mJy, so essentially all of these radio halos contribute to the number counts."711" This increases our 1.4 GHz number counts to ~12 objects above the 10 mJy flux limit, roughly in line with known observations (???).."," This increases our 1.4 GHz number counts to $\sim$ 12 objects above the 10 mJy flux limit, roughly in line with known observations \citep{GIOVANNINI1999, Cassano2006, Cassano2010}."712" Since we expect these high-mass objects to host roughly the same proportion of 150 MHz radio halos, a similar number contributes to our 150 MHz number counts."," Since we expect these high-mass objects to host roughly the same proportion of 150 MHz radio halos, a similar number contributes to our 150 MHz number counts."713" While the model trends continue from the above analysis, we find that at high flux limits (>100 mJy) and high frequencies, we have too few radio halos to strongly distinguish several models, even those with large discrepancies in either assumed average magnetic field or scalings with virial mass or total turbulent pressure."," While the model trends continue from the above analysis, we find that at high flux limits $>100$ mJy) and high frequencies, we have too few radio halos to strongly distinguish several models, even those with large discrepancies in either assumed average magnetic field or scalings with virial mass or total turbulent pressure."714" This is due to the suppression of radio halos at high redshift, meaning that the integrated counts depend most strongly on high-luminosity objects, where the counts are nearly the same."," This is due to the suppression of radio halos at high redshift, meaning that the integrated counts depend most strongly on high-luminosity objects, where the counts are nearly the same."715" At 150 MHz and an assumed LOFAR sensitivity limit of 30 mJy, we find that although some models, such as Model Sets 2A and 2B, produce an almost factor of two difference in the total counts, the large uncertainties preclude any clean distinction."," At $150$ MHz and an assumed LOFAR sensitivity limit of $30$ mJy, we find that although some models, such as Model Sets 2A and 2B, produce an almost factor of two difference in the total counts, the large uncertainties preclude any clean distinction."716 In we show the total counts of radio halos within redshift z«0.2 at 1.4GHz and 150MHz., In we show the total counts of radio halos within redshift $z<0.2$ at $1.4 \ghz$ and $150 \mhz$.717 This redshift range fits largely within our computational volume without the need for periodic replication of the domain and is more easily accessible to observers., This redshift range fits largely within our computational volume without the need for periodic replication of the domain and is more easily accessible to observers.718" Although we find little degradation in the total number counts in the LOFAR-accessible regime (>30 mJy), the models remain indistinguishable."," Although we find little degradation in the total number counts in the LOFAR-accessible regime $>30$ mJy), the models remain indistinguishable."719" While we could in principle produce mock sky maps within any frequency range, we choose LOFAR-like parameters since low-frequency instruments are able to survey large portions of the sky and hence collect many halo images for use in statistical comparison."," While we could in principle produce mock sky maps within any frequency range, we choose LOFAR-like parameters since low-frequency instruments are able to survey large portions of the sky and hence collect many halo images for use in statistical comparison."720 We generate raw mock sky maps in the 20—240 MHz LOFAR bandpass by following a similar strategy of interpolating and redshift-correcting clusters as used above.," We generate raw mock sky maps in the $20721- 240$ MHz LOFAR bandpass by following a similar strategy of interpolating and redshift-correcting clusters as used above."722 Appropriate cosmological dimming and redshift are then applied to determine the contribution of the slice to the sky observed at z=0., Appropriate cosmological dimming and redshift are then applied to determine the contribution of the slice to the sky observed at $z = 0$.723" We generate a radio image for each cluster by projecting its density and turbulent pressure onto the sky map and computing the relevant radio intensity using a given set of radio model parameters, ensuring that the integrated radio power across the projected cluster is equal to the value obtained using M, and Ἐν in the above sections."," We generate a radio image for each cluster by projecting its density and turbulent pressure onto the sky map and computing the relevant radio intensity using a given set of radio model parameters, ensuring that the integrated radio power across the projected cluster is equal to the value obtained using $M_v$ and $\Gamma_v$ in the above sections."724" We only project gas values within R,.", We only project gas values within $R_v$.725" For halos not within the high-resolution sample, we identify the nearest high-resolution cluster in mass and copy that high-resolution image to the location of the low-resolution halo."," For halos not within the high-resolution sample, we identify the nearest high-resolution cluster in mass and copy that high-resolution image to the location of the low-resolution halo."726" Also, since we do not have imaging information for missing high-mass halos due to our limited simulation volume, these are not included in the mock skies."," Also, since we do not have imaging information for missing high-mass halos due to our limited simulation volume, these are not included in the mock skies."727" While this procedure is admittedly somewhat crude, it does allow us to explore some of the observational consequences of these models and demonstrates a method of generating radio maps in the future using more sophisticated and realistic simulated data."," While this procedure is admittedly somewhat crude, it does allow us to explore some of the observational consequences of these models and demonstrates a method of generating radio maps in the future using more sophisticated and realistic simulated data."728" shows the entire radio sky containing our simulated clusters at 120 arcsec resolution assuming no background (i.e., a threshold sensitivity of 0 mJy)."," shows the entire radio sky containing our simulated clusters at $120$ arcsec resolution assuming no background (i.e., a threshold sensitivity of $0$ mJy)."729 This resolution best approximates the LOFAR beam at an average frequency of ~120 MHz and a longest baseline of L~2 km., This resolution best approximates the LOFAR beam at an average frequency of $\sim 120$ MHz and a longest baseline of $L \sim 2$ km.730 For this example we have chosen Model Set A1., For this example we have chosen Model Set A1.731" This map particularly highlights the paucity of radio halos in the universe, even at low sensitivity thresholds, but it is useful for providing a mock all-sky map for linking simulations to observations."," This map particularly highlights the paucity of radio halos in the universe, even at low sensitivity thresholds, but it is useful for providing a mock all-sky map for linking simulations to observations."732" highlights a region of the sky 6 degrees on a side at a resolution of 10 arcsec, representing the high-resolution capability between 20 and 240 MHz at the longest baseline configuration of LOFAR."," highlights a region of the sky $6$ degrees on a side at a resolution of $10$ arcsec, representing the high-resolution capability between $20$ and $240$ MHz at the longest baseline configuration of LOFAR."733" We also draw contour levels at varying sensitivities: 1, 10, and 30 mJy."," We also draw contour levels at varying sensitivities: $1$, $10$, and $30$ mJy."734 These sensitivities represent different configurations of the LOFAR array., These sensitivities represent different configurations of the LOFAR array.735" At high resolution and peak sensitivity, we are able to clearly distinguish several substructures and features within the two radio halos, indicating that LOFAR may be able to cleanly distinguish various radio power models based on their dependence on local gas density or local turbulent pressure, which can have different characteristic structures in the cluster atmosphere (Figure 3))."," At high resolution and peak sensitivity, we are able to clearly distinguish several substructures and features within the two radio halos, indicating that LOFAR may be able to cleanly distinguish various radio power models based on their dependence on local gas density or local turbulent pressure, which can have different characteristic structures in the cluster atmosphere (Figure \ref{fig:rh_projgamma}) )."736" At lower sensitivities, we can still distinguish features in the cluster cores, and early LOFAR images of nearby and bright radio halos may also provide useful distinguishing results."," At lower sensitivities, we can still distinguish features in the cluster cores, and early LOFAR images of nearby and bright radio halos may also provide useful distinguishing results."737" We will present a detailed radio morphological study, which requires knowledge of the spatial dependence of the magnetic field, in a future paper."," We will present a detailed radio morphological study, which requires knowledge of the spatial dependence of the magnetic field, in a future paper."738 shows the same region of the sky as above with a much lower resolution of 240 arcsec., shows the same region of the sky as above with a much lower resolution of $240$ arcsec.739 The contours are the same as above., The contours are the same as above.740" While we lose significant information about distant and small clusters, some larger clusters, such as the one shown, still show significant structure even at lower resolutions."," While we lose significant information about distant and small clusters, some larger clusters, such as the one shown, still show significant structure even at lower resolutions."741" We see that we can still identify substructure within the large cluster, and the effects of higher sensitivity thresholds are limited to distant clusters and the outer regions of nearby objects."," We see that we can still identify substructure within the large cluster, and the effects of higher sensitivity thresholds are limited to distant clusters and the outer regions of nearby objects."742" 'These results are encouraging, since they indicate that LOFAR may be able to give detailed radio maps of many radio halos."," These results are encouraging, since they indicate that LOFAR may be able to give detailed radio maps of many radio halos."743 We have introduced the first set of radio halo statistics derived entirely from large-scale cosmological simulation., We have introduced the first set of radio halo statistics derived entirely from large-scale cosmological simulation.744 Our radio power model is sufficiently broad to encompass many viable and more realistic models of CR generation and synchrotron emission in clusters of galaxies., Our radio power model is sufficiently broad to encompass many viable and more realistic models of CR generation and synchrotron emission in clusters of galaxies.745" Our approach demonstrates the viability of using large-scale simulation to bridge simulations and observations, both by deriving radio halo statistics from the simulated"," Our approach demonstrates the viability of using large-scale simulation to bridge simulations and observations, both by deriving radio halo statistics from the simulated"746the star to star abundance at low metallicities is strongly needed.,the star to star abundance at low metallicities is strongly needed.747 Gravitational waves seem interesting in this respec (seco Talon Charbonnel 2003). but we still wait for ful metallicity dependent computations.," Gravitational waves seem interesting in this respect (see Talon Charbonnel 2003), but we still wait for full metallicity dependent computations."748 We should. recall at this. point that. our. stancare chemical evolution models refer to. large-scale. long-term phenomena and cannot account for small-scale. short-term variations.," We should recall at this point that our standard chemical evolution models refer to large-scale, long-term phenomena and cannot account for small-scale, short-term variations."749 Lf we want to reproduce also the observed spreac in the abundances of the light elements. as observed. [or instance. by in the local ISM (6g... Moos et al.," If we want to reproduce also the observed spread in the abundances of the light elements, as observed, for instance, by in the local ISM (e.g., Moos et al."750 2002). or for Πο across the Galactic disce (Dania et al.," 2002), or for$^3$ He/H across the Galactic disc (Bania et al."751 2002). we should also take into account the possible inhomogencitics in the chemical enrichment of cach region and the cllects of possible orbital diffusion of the stars.," 2002), we should also take into account the possible inhomogeneities in the chemical enrichment of each region and the effects of possible orbital diffusion of the stars."752 ALY. is) particularly grateful. to Corinne Charbonnel. Johannes Geiss. and Ceorge Gloeckler of the LOLA-CI team for the enlightening discussions at the International Space Science Institute in Berne (611).," M.T. is particularly grateful to Corinne Charbonnel, Johannes Geiss, and George Gloeckler of the LOLA-GE team for the enlightening discussions at the International Space Science Institute in Berne (CH)."753 Dana Balser. Tom Dania. and Bob Rood are warmly thanked for always being ready to share updated: values of the ο abundances.," Dana Balser, Tom Bania, and Bob Rood are warmly thanked for always being ready to share updated values of the $^3$ He abundances."754 We also thank Daniele Calli and Cary Steigman for their useful comments., We also thank Daniele Galli and Gary Steigman for their useful comments.755 Exil Jenkins. Warren Moos and νο Viclal-Aladjar are gratefully acknowledged for elarifving what is the range o£ LISM D/L values which should be quoted according to the most reliable data.," Ed Jenkins, Warren Moos and Alfred Vidal-Madjar are gratefully acknowledged for clarifying what is the range of LISM D/H values which should be quoted according to the most reliable data."756 This work has been partially supported by the through grant HULII301ZAM., This work has been partially supported by the through grant 11301ZAM.757ppc. and (i)m most of these sources show only modest variability at GGllIz on timescales of 13 vears.,"pc, and (ii) most of these sources show only modest variability at GHz on timescales of 1–3 years."758 The opticalp counterpart' of this radio| source is |a member of PLSa compact group of galaxies (Figure 3))., The optical counterpart of this radio source is a member of a compact group of galaxies (Figure \ref{fig:J031010-573041_optical}) ).759 No redshift has been measured for the host galaxy (object A in Figure 3)). so we adopt the measured 6dE665 redshift of z=0.082 for the companion galaxy as the redshift of the whole eroup.," No redshift has been measured for the host galaxy (object A in Figure \ref{fig:J031010-573041_optical}) ), so we adopt the measured 6dFGS redshift of $z=0.082$ for the companion galaxy as the redshift of the whole group."760 None of the other galaxies in this group has a redshift measurement., None of the other galaxies in this group has a redshift measurement.761" ThiVhis source""Co wasOWE detectedποσο ini the PPAIN. surveyOON (Grillithvilli et Eal.", This source was detected in the PMN survey (Griffith et al.762 1994) with a [lux density of 534511 mmJv in the aarcmin Parkes beam at 1., 1994) with a flux density of $\pm$ mJy in the arcmin Parkes beam at 4.8GHz.763 This is significantly lower than the Αθ value of 92x94 mnmiJy. (in a L5aaresee beam). suggesting that the source may be variable.," This is significantly lower than the AT20G value of $\pm$ mJy (in a arcsec beam), suggesting that the source may be variable."764 Phe 041 spectrum shows absorption lines twpical of an carbtvpe galaxy but no obvious optical emission lines., The 6dFGS spectrum shows absorption lines typical of an early–type galaxy but no obvious optical emission lines.765 The 6dEGS spectrum shows absorption lines together with possible weak ILLI] emission., The 6dFGS spectrum shows absorption lines together with possible weak III] emission.766 There is a faint NVSS source associated with this object (see Table 2)). but it lies below the limit of the MMIIz SUAISS catalogue.," There is a faint NVSS source associated with this object (see Table \ref{table:sumss_nvss}) ), but it lies below the limit of the MHz SUMSS catalogue."767ratios of ~0.01 ./L. (neglecting dust).,ratios of $\sim$ $_{\odot}$ $_{\odot}$ (neglecting dust).768 Thus the stellar mass of these structures is probably ~10*.—107M .. similar to globular clusters.," Thus the stellar mass of these structures is probably $\sim10^4-10^5$ $_\odot$, similar to globular clusters."769 From their Ha fluxes. we estimate the star-formation rates to be AZ. vr.1. and hence their star-formation time-scales are « I.0GGyr.," From their $\alpha$ fluxes, we estimate the star-formation rates to be $\,{M_\odot}$ $^{-1}$, and hence their star-formation time-scales are $<$ Gyr."770 The tireball masses are similar to those estimated for the TDGs in Arp 305 by Hancock et al. (, The fireball masses are similar to those estimated for the TDGs in Arp 305 by Hancock et al. (7712009).,2009).772 For TDGs in interacting field galaxies. it is a matter of dispute whether they will eventually become independent of the galaxies which originally hosted their gas.," For TDGs in interacting field galaxies, it is a matter of dispute whether they will eventually become independent of the galaxies which originally hosted their gas."773 By contrast. in the case of ram-pressure stripped cluster galaxies. the ultimate detachment of the clumps from the host galaxy seems quite likely. and if they survive as bound systems they may evolve into stellar systems resembling intra-cluster globular clusters or compact dwarf galaxies.," By contrast, in the case of ram-pressure stripped cluster galaxies, the ultimate detachment of the clumps from the host galaxy seems quite likely, and if they survive as bound systems they may evolve into stellar systems resembling intra-cluster globular clusters or compact dwarf galaxies."774 Similar objects have been noted in simulations of ram-pressure stripping by Kapferer et al. (, Similar objects have been noted in simulations of ram-pressure stripping by Kapferer et al. (7752008). who term them “stripped baryonic dwarfs”.,"2008), who term them “stripped baryonic dwarfs”."776 Finally. we consider the destiny of the galaxies themselves after stripping is completed.," Finally, we consider the destiny of the galaxies themselves after stripping is completed."777 It has been known for a long time that cluster spirals are deficient in neutral gas. relative to their counterparts in the field (e.g. Haynes Giovanelli 1984).," It has been known for a long time that cluster spirals are deficient in neutral gas, relative to their counterparts in the field (e.g. Haynes Giovanelli 1984)."778 In Coma. Gavazzi et al. (," In Coma, Gavazzi et al. ("7792006) tind that a significant average HI deficiency extends from the cluster core out to ~2 MMpc. the gas content becoming consistent with a field reference sample at ~3 MMpc. (,"2006) find that a significant average HI deficiency extends from the cluster core out to $\sim2$ Mpc, the gas content becoming consistent with a field reference sample at $\sim$ Mpc. ("780A similar trend is seen for Virgo. e.g. Cayatte et al.,"A similar trend is seen for Virgo, e.g. Cayatte et al."781 19943., 1994).782 The HI detficieney data for Coma show an apparently sharp transition at a radius of ο MMpe. within which nearly all cluster members are gas-poor compared to field spirals.," The HI deficiency data for Coma show an apparently sharp transition at a radius of $\sim$ Mpc, within which nearly all cluster members are gas-poor compared to field spirals."783 Figure 4. compares the Gavazzi et., Figure \ref{fig:stripfrac} compares the Gavazzi et.784 al., al.785 HI-deficient fraction to the incidence of ongoing stripping events identified in this paper., HI-deficient fraction to the incidence of ongoing stripping events identified in this paper.786" For this test. the galaxies are flagged as gas-deficient if they have Defy,>0.64. corresponding to the 95th percentile of Defi among galaxies beyond 3MMpe from the Coma core."," For this test, the galaxies are flagged as gas-deficient if they have $_{\rm HI}>0.64$, corresponding to the 95th percentile of $_{\rm HI}$ among galaxies beyond Mpc from the Coma core."787 It is notable that a similar characteristic radius of 1 MMpe seems to apply to both phenomena., It is notable that a similar characteristic radius of $\sim$ Mpc seems to apply to both phenomena.788 On the other hand we found no ongoing stripping events. with the uncertain exception of GMP 5422. beyond MMpe. where pper cent of spirals are HI-deficient.," On the other hand we found no ongoing stripping events, with the uncertain exception of GMP 5422, beyond Mpc, where per cent of spirals are HI-deficient."789 This result can be understood in terms of a “backsplash” population (Sanchis et al., This result can be understood in terms of a “backsplash” population (Sanchis et al.790 2002: Gill. Knebe Gibson 2004): although stripping itself is only effective within -1 MMpe. HI-deficient galaxies can be observed at larger radit after the initial stripping event is complete and the galaxy has passed through the cluster core.," 2002; Gill, Knebe Gibson 2004): although stripping itself is only effective within $\sim$ Mpc, HI-deficient galaxies can be observed at larger radii after the initial stripping event is complete and the galaxy has passed through the cluster core."791 This is contirmed by Figure 7.. which shows that our simple stripping model. tuned to reproduce the fraction of GSE galaxies. also produces a post-stripping population consistent with the observed HI-deficient galaxy fraction.," This is confirmed by Figure \ref{fig:millengse}, which shows that our simple stripping model, tuned to reproduce the fraction of GSE galaxies, also produces a post-stripping population consistent with the observed HI-deficient galaxy fraction."792 We have used UV and optical imaging to identify a sample of candidate gaseous stripping events in the Coma cluster., We have used UV and optical imaging to identify a sample of candidate gaseous stripping events in the Coma cluster.793 The stripped galaxies are characterised by tails or trails of UV-bright debris. which we interpret as young stars formed within gas stripped by ram pressure from the intra-cluster medium.," The stripped galaxies are characterised by tails or trails of UV-bright debris, which we interpret as young stars formed within gas stripped by ram pressure from the intra-cluster medium."794 Some of these cases have been noted as peculiar in previous work. in a variety of wavebands (Vollmer et al.," Some of these cases have been noted as peculiar in previous work, in a variety of wavebands (Vollmer et al."795 2001: Finoguenov et al., 2001; Finoguenov et al.796 2004: Yagi et al., 2004; Yagi et al.797 2007: Yoshida et al., 2007; Yoshida et al.798 2008: Miller et al., 2008; Miller et al.799 2009). while others are newly identitied here as possible stripping events.," 2009), while others are newly identified here as possible stripping events."800 The trails are predominantly oriented away from the cluster centre. indicating that he galaxies are falling into the cluster for the first time. along fairy radial orbits. and that the stripping events are completed rapidly compared to the orbital time-scale.," The trails are predominantly oriented away from the cluster centre, indicating that the galaxies are falling into the cluster for the first time, along fairly radial orbits, and that the stripping events are completed rapidly compared to the orbital time-scale."801 All but one uncertain case lie :it projected radit of kkpe from the cluster centre., All but one uncertain case lie at projected radii of kpc from the cluster centre.802 The racial distribution of these galaxies is much more centrally concentrated than the distribution of blue galaxies from which they were selected. and more similar to the distribution of passive galaxies.," The radial distribution of these galaxies is much more centrally concentrated than the distribution of blue galaxies from which they were selected, and more similar to the distribution of passive galaxies."803 Wihin MMpe projected radius. some pper cent of blue galaxies are currently undergoing stripping. a fraction which is compatible with a -500 MMyr time-scale for the stripping events.," Within Mpc projected radius, some per cent of blue galaxies are currently undergoing stripping, a fraction which is compatible with a $\sim$ Myr time-scale for the stripping events."804 The radius within which UV trails are observed corresponds to an. ICM density of ~107'ggeem . in agreement with simulations which show significant star formation in the stripped wake in this density regime for infall velocities ~ ((Kapferer et al.," The radius within which UV trails are observed corresponds to an ICM density of $\sim10^{-27}$ $^{-3}$, in agreement with simulations which show significant star formation in the stripped wake in this density regime for infall velocities $\sim$ (Kapferer et al."805 2009)., 2009).806 There are hints that some stripping events are associated with local enhancements in the ICM density. e.g. the western structure and the NGC 4839 group. but a firm link can not be concluded from the present data.," There are hints that some stripping events are associated with local enhancements in the ICM density, e.g. the western structure and the NGC 4839 group, but a firm link can not be concluded from the present data."807 We propose an interpretation of these objects as a stage in ram-pressure stripping that is subsequent to the HI gas-tail phase (Chung et al., We propose an interpretation of these objects as a stage in ram-pressure stripping that is subsequent to the HI gas-tail phase (Chung et al.808 2007). and occurring at higher ambient densities.," 2007), and occurring at higher ambient densities."809 The star formation triggered in the stripping events may add mass to the galaxy bulge. if newly-formed stars fall back into the source galaxy.," The star formation triggered in the stripping events may add mass to the galaxy bulge, if newly-formed stars fall back into the source galaxy."810 Alternatively they may escape. forming intra-cluster stellar systems that could evolve into objects resembling globular clusters or compact dwarf galaxies.," Alternatively they may escape, forming intra-cluster stellar systems that could evolve into objects resembling globular clusters or compact dwarf galaxies."811 After the initial stripping. the infalling galaxies will remain as gas-deficient spirals before fading slowly into SOs as they exhaust their remaining gas.," After the initial stripping, the infalling galaxies will remain as gas-deficient spirals before fading slowly into S0s as they exhaust their remaining gas."812 As stressed by Sun et al. (, As stressed by Sun et al. (8132010). a fuller understanding of the relationship between different manifestations of gas stripping (HI deficiency. and tails in HI. UV. Ha and. X-ray) will be made possible by improving the overlap between observations in the various wavebands. for the same galaxy cluster.,"2010), a fuller understanding of the relationship between different manifestations of gas stripping (HI deficiency, and tails in HI, UV, $\alpha$ and X-ray) will be made possible by improving the overlap between observations in the various wavebands, for the same galaxy cluster."814 Our work has assembled a comorehensive wide-tield optical. UV. Ha and spectroscopic dataset or Coma. complemented by archival XMM imaging and the radio continuum survey of Miller et al. (," Our work has assembled a comprehensive wide-field optical, UV, $\alpha$ and spectroscopic dataset for Coma, complemented by archival XMM imaging and the radio continuum survey of Miller et al. ("8152009).,2009).816 A key missing element is high-sensitivity 21em HI mapping of a large sample of Coma member galaxies. which should be possible in the next few years using tye Expanded Very Large Array.," A key missing element is high-sensitivity 21cm HI mapping of a large sample of Coma member galaxies, which should be possible in the next few years using the Expanded Very Large Array."817 We are grateful to Stephen Gwyn for generating a custom stack of the Adami deep v-band data for our use. to Masafumi Yagi for communicating the Subaru Πα results in advance of submission. and to Neal Miller for helpful comments on this paper.," We are grateful to Stephen Gwyn for generating a custom stack of the Adami deep $u$ -band data for our use, to Masafumi Yagi for communicating the Subaru $\alpha$ results in advance of submission, and to Neal Miller for helpful comments on this paper."818 RJS was supported for this work by STFC Rolling Grant PP/C301568/1 “Extragalactic Astronomy and Cosmology at Durham 2008—20137., RJS was supported for this work by STFC Rolling Grant PP/C501568/1 “Extragalactic Astronomy and Cosmology at Durham 2008–2013”.819 This work is based on observations made with the NASA(GALEX)., This work is based on observations made with the NASA.820GALEX is a NASA Small Explorer. developed in cooperation with the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and Technology.," is a NASA Small Explorer, developed in cooperation with the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and Technology."821 This work is based on observations obtained with MegaPrime/MegaCam. a joint project of CFHT and CEA/DAPNIA. at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada. the Institute National des Sciences de l'Univers. of the Centre National de la Recherche Scientitique of France. and the University of Hawaii.," This work is based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada–France–Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institute National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii."822 The work has made use of data, The work has made use of data823Lt is possible to model several dillerent twpes of galaxy and compare the isophotal magnitude and the total magnitude as calculated in $4 with the “true” magnitude.,It is possible to model several different types of galaxy and compare the isophotal magnitude and the total magnitude as calculated in 4 with the “true” magnitude.824 Phe moclels are simple. assuming a face on circular galaxy. composed of a bulge . witha ce Vaucouleurs. 77n law (de .Vaucouleurs 1948) and a disk with an exponential profile (see Eqn. SN)).," The models are simple, assuming a face on circular galaxy, composed of a bulge with a de Vaucouleurs $r^{\frac{1}{4}}$ law (de Vaucouleurs 1948) and a disk with an exponential profile (see Eqn. \ref{eq:exp}) )."825 where rs ds the hall-light radius of the bulge. (5. is the ellective surface brightness of the bulge.," where $r_e$ is the half-light radius of the bulge, $\mu_e$ is the effective surface brightness of the bulge."826 Llere we define it as the mean surface brightness within r5., Here we define it as the mean surface brightness within $r_e$.827 However. it is more useful to define galaxies in terms of their Iuminosities and bulge-to-disk ratios than their elective radii or disk scale-lengths.," However, it is more useful to define galaxies in terms of their luminosities and bulge-to-disk ratios than their effective radii or disk scale-lengths."828 The magnitude of a galaxy and the bulge-disk ratio can be found in terms of the above parameters. by: where D is the magnitude of the bulge and. D is the magnitude of the disk.," The magnitude of a galaxy and the bulge-disk ratio can be found in terms of the above parameters, by: where $B$ is the magnitude of the bulge and $D$ is the magnitude of the disk."829 6/7 is the bulge-to-total ratio., $B/T$ is the bulge-to-total ratio.830 Given the parameters AZ. DBZT. p and pi. a galaxy’s light profile is Cully defined.," Given the parameters $M$, $B/T$, $\mu_e$ and $\mu_o$, a galaxy's light profile is fully defined."831 To caleulate the difference between the total ancl the isophotal magnitude it is necessary to find the fraction of light lost. below the isophote., To calculate the difference between the total and the isophotal magnitude it is necessary to find the fraction of light lost below the isophote.832 Since the intrinsic detection isophote varies with the redshift. this dilference will he a Function of redshift.," Since the intrinsic detection isophote varies with the redshift, this difference will be a function of redshift."833 Fora varietv of redshifts from z=0.001 to 2=0.201. the fraction of light under the isophote was calculated. by first converting the above magnitudes to apparent magnitudes. the intrinsic surface brightnesses to apparent surface brightnesses and then caleulating the scale- as above.," For a variety of redshifts from $z=0.001$ to $z=0.201$, the fraction of light under the isophote was calculated, by first converting the above magnitudes to apparent magnitudes, the intrinsic surface brightnesses to apparent surface brightnesses and then calculating the scale-lengths as above."834 The conversions [rom absolute to apparent properties are given in Eqn., The conversions from absolute to apparent properties are given in Eqn.835 17. and Eqn. I8.., \ref{eq:absmag} and Eqn. \ref{eq:absmu}.836" Using jay,= 24.67mag aresec7. the isophotal radii of the disk and bulge are calculated."," Using $\mu_{lim}=24.67$ mag $^{-2}$, the isophotal radii of the disk and bulge are calculated."837 The fraction of light) above the isophote is then calculated using the equation below., The fraction of light above the isophote is then calculated using the equation below.838 where 7 is the de Vaucouleur's parameter. which is 1 fora disk and 4 for a bulge.," where $\beta$ is the de Vaucouleur's parameter, which is 1 for a disk and 4 for a bulge."839 g=7.67(—y in bulges and g=— in disks., $g=7.67(\frac{r}{r_e})^{1/4}$ in bulges and $g=\frac{r}{\alpha}$ in disks.840 The isophotal magnitude and isophotal radius of the galaxy can now be calculated., The isophotal magnitude and isophotal radius of the galaxy can now be calculated.841"the evolution of active regions (AR), which are structures with filling factors larger than 89.1 ppm (Class IV).","the evolution of active regions (AR), which are structures with filling factors larger than 89.1 ppm (Class IV)."842" The brown and black lines show the evolution of the sunspots penumbrae and umbrae, respectively."," The brown and black lines show the evolution of the sunspots penumbrae and umbrae, respectively."843" Note that for a better visualization, the filling factors of penumbrae and umbrae were multiplied by a factor of five (5)."," Note that for a better visualization, the filling factors of penumbrae and umbrae were multiplied by a factor of five (5)."844 We find that the filling factors of Classes I and II structures do not present trends during the period considered., We find that the filling factors of Classes I and II structures do not present trends during the period considered.845" However, an increase of the filling factors of Class I structures in relation to the average value is observed from 29-Oct-2010 to 07-Mar-2011."," However, an increase of the filling factors of Class I structures in relation to the average value is observed from 29-Oct-2010 to 07-Mar-2011."846 Changes of the filling factors of Class Π structures are observed near the boundaries of this interval., Changes of the filling factors of Class II structures are observed near the boundaries of this interval.847 These changes appear as decreases of the filling factors of Class II structures from 29-Oct-2010 to 10-Nov-2010 and from 15-Feb-2011 to 07-Mar-2011., These changes appear as decreases of the filling factors of Class II structures from 29-Oct-2010 to 10-Nov-2010 and from 15-Feb-2011 to 07-Mar-2011.848 We speculate that these variations are due to small changes in the calibration of the magnetograms or the mapping of the quicklook images., We speculate that these variations are due to small changes in the calibration of the magnetograms or the mapping of the quicklook images.849" In this interval, we did not observe any such discontinuity in the filling factors of Classes III and IV structures."," In this interval, we did not observe any such discontinuity in the filling factors of Classes III and IV structures."850 We, We851of 107. which covers part of the disc and thus increasing the observed mass transfer rate necessary to match the [ux level of the system.,"of $10^{\circ}$, which covers part of the disc and thus increasing the observed mass transfer rate necessary to match the flux level of the system."852 During the decline. we believe that a cooling front. as described in \lineshige&Osaki(1985).. moves inward reducing the disc temperature and at least for the duration of the eclipses the dise behaves in a steady state manner.," During the decline, we believe that a cooling front, as described in \scite{Mineshige85}, moves inward reducing the disc temperature and at least for the duration of the eclipses the disc behaves in a steady state manner."853 Also. Mineshige(1901). showed that for the case of Z Cha. for the disc temperature to decrease with time it is necessary for the dise to behave like. or at least be very close to. steady state.," Also, \scite{Mineshige91} showed that for the case of Z Cha, for the disc temperature to decrease with time it is necessary for the disc to behave like, or at least be very close to, steady state."854 Conversely. models by Cannizzo(1994). on the decline of the optical [Luxes during outbursts of dwarf novae require the accretion disc to be departing from steady state mocels.," Conversely, models by \scite{Cannizzo94} on the decline of the optical fluxes during outbursts of dwarf novae require the accretion disc to be departing from steady state models."855 Clearly this is not the case that we observe. since our steacky state models for the eclipses during the late decline are in eood agreement with the observed data.," Clearly this is not the case that we observe, since our steady state models for the eclipses during the late decline are in good agreement with the observed data."856 Comparing the results from the eruption of LET Cas with other outbursts of SU UMa systems we see many similarities., Comparing the results from the eruption of HT Cas with other outbursts of SU UMa systems we see many similarities.857 In the case of OY Car. eclipse light curves observed by Vogt(1983) and later reexamined by Ruttenetal.(1992). show the same kind of behavior as the outburst eclipses of LEE Cas.," In the case of OY Car, eclipse light curves observed by \scite{Vogt83} and later re–examined by \scite{Rutten92} show the same kind of behavior as the outburst eclipses of HT Cas."858 Both systems are slowly eparting [rom their quiescent eclipse shape. moving towards a more symmetric shape with a distinct flat eclipse bottom during the carly rise.," Both systems are slowly departing from their quiescent eclipse shape, moving towards a more symmetric shape with a distinct flat eclipse bottom during the early rise."859" οσο results are also in extreme contrast with the results of Webbetal.(1999). for the ""insideout” outburst of the U Gem. system IP Poe.", These results are also in extreme contrast with the results of \scite{Webb99} for the “inside–out” outburst of the U Gem system IP Peg.860" A hot transition front of material. which is moving towards the centre of the disc. is suggested by the preference of the modelling code to place a hole (or non-Iuminous material) with a radius of about 472, from the centre of the accretion disc during the rising phase of the outburst."," A hot transition front of material, which is moving towards the centre of the disc, is suggested by the preference of the modelling code to place a hole (or non-luminous material) with a radius of about $4R_{wd}$ from the centre of the accretion disc during the rising phase of the outburst."861 Lt is unclear as to whether the dise is truncated or not when at the peak of the outburst. as the [are angle of the disc grows to 15 and so the innermost parts of the disc are hidden from. view.," It is unclear as to whether the disc is truncated or not when at the peak of the outburst, as the flare angle of the disc grows to $15^{\circ}$ and so the innermost parts of the disc are hidden from view."862 During the decline from outburst the truncation radius is ZOLO., During the decline from outburst the truncation radius is zero.863 Several theories have been put forward in. order. to explain the delay in the rise of the ultraviolet Hux as opposed o the optical., Several theories have been put forward in order to explain the delay in the rise of the ultraviolet flux as opposed to the optical.864 For example. Wing(1997) proposed that he inner parts of the dise remain void of material during cuiescence due to irradiation from the white dwarf.," For example, \scite{King97} proposed that the inner parts of the disc remain void of material during quiescence due to irradiation from the white dwarf."865 Similarly Livio&Pringle(1992) emploved a weak magnetic field to runeate the disc. in the same manner as in intermediate »olar svstenmis.," Similarly \scite{Livio92} employed a weak magnetic field to truncate the disc, in the same manner as in intermediate polar systems."866 Also. Mever(1990) suggested that a “siphon” coronal mass [low was responsible for emptving the inner wis of the accretion disc.," Also, \scite{Meyer90} suggested that a “siphon” coronal mass flow was responsible for emptying the inner parts of the accretion disc."867 Lrraciation of the inner parts of the accretion disc by à hot corona that lies above the cool quiescent disc. leads to the evaporation of material in those inner disc regions.," Irradiation of the inner parts of the accretion disc by a hot corona that lies above the cool quiescent disc, leads to the evaporation of material in those inner disc regions."868 Material from the dise joins the hot corona above and then is accreted onto the white dwarf leaving the inner parts of the accretion dise relatively empty., Material from the disc joins the hot corona above and then is accreted onto the white dwarf leaving the inner parts of the accretion disc relatively empty.869 Llowever. the fact that LP Cas shows X-ray eclipses (Wood 1995: Mukai 1997) does not support the wory of a hot X-ray. producing corona. but instead suggests jiu the X-ray emitting regions in LEE Cas are very close to 1ο white dwactl.," However, the fact that HT Cas shows X-ray eclipses (Wood 1995; Mukai 1997) does not support the theory of a hot X-ray producing corona, but instead suggests that the X-ray emitting regions in HT Cas are very close to the white dwarf."870 There has been previous observational evidence for 1e truncation of accretion discs in non-magnetic dwarf nova svstems., There has been previous observational evidence for the truncation of accretion discs in non-magnetic dwarf nova systems.871 LaDous.Mever&AleverHofmoeister(1996) ound evidence of truncated accretion dises for at least four iferent. svstenis., \scite{ladous96} found evidence of truncated accretion discs for at least four different systems.872 They. compared. the ratio of UV. Duxes xoduced by white chwarts and accretion cdises as predicted w the evaporation theory of Mever ancl Meyer.Hofmoeister (1989) and Alever(1990).," They compared the ratio of UV fluxes produced by white dwarfs and accretion discs as predicted by the evaporation theory of Meyer and Meyer–Hofmeister \shortcite{Meyer89}873 and \scite{Meyer90}."874. 1n all three scenarios outlined above. the delay of the UV [lux arises because of the time it takes for the inner vats of the dise to be filled by material in outburst that is moving inwards.," In all three scenarios outlined above, the delay of the UV flux arises because of the time it takes for the inner parts of the disc to be filled by material in outburst that is moving inwards."875 Unfortunately we do not possess any UV data for this outburst in order to confirm that our model results are compatible with the above theories., Unfortunately we do not possess any UV data for this outburst in order to confirm that our model results are compatible with the above theories.876 However. Wheatleyetal.(1996). and Navlor(1997). speculate that the delay in the UV Dux observed in the VW. Livi svsteni. which was observed simultaneously in the X-ray. UV. and optical parts of the spectrum during an eruption. could be explained by such a mechanism.," However, \scite{Wheatley96} and \scite{Naylor97} speculate that the delay in the UV flux observed in the VW Hyi system, which was observed simultaneously in the X-ray, UV and optical parts of the spectrum during an eruption, could be explained by such a mechanism."877 Our data appear to show such a gap being filled., Our data appear to show such a gap being filled.878 There is substantial evidence that the cise is highly. Dared hroughout the outburst. especially near the peak of the eruption.," There is substantial evidence that the disc is highly flared throughout the outburst, especially near the peak of the eruption."879 The semi-opening angle of the disc is seen to expand rom LO” during the rise to 15 at the peak and then starts o decrease again during the decline., The semi-opening angle of the disc is seen to expand from $10^{\circ}$ during the rise to $15^{\circ}$ at the peak and then starts to decrease again during the decline.880" This could. possibly o» explained. by the ""avalanche"" ellect that Mineshige&Osaki(1985). see in their model caleulations.", This could possibly be explained by the “avalanche” effect that \scite{Mineshige85} see in their model calculations.881 As the hot pont travels towards the inner parts ofthe cisc. it causes 10 viscosity of the material that has just. gone through 10 heating front to rise sharply.," As the hot front travels towards the inner parts of the disc, it causes the viscosity of the material that has just gone through the heating front to rise sharply."882 Therefore as the front moves inwards. material that is now in outburst. is piled up behind the hot front. perhaps thickening the disc.," Therefore as the front moves inwards, material that is now in outburst, is piled up behind the hot front perhaps thickening the disc."883 As 10 outburst. declines. a cooling front that moves inwarcs makes the material at the outer parts of the dise return to ein quiescent cold state.," As the outburst declines, a cooling front that moves inwards makes the material at the outer parts of the disc return to their quiescent cold state."884 Again. as the cooling front travels inwards the disc is seen to decrease in size both racdiallv and vertically.," Again, as the cooling front travels inwards the disc is seen to decrease in size both radially and vertically."885 Evidence that accretion disces thicken during outburst has been observed by others., Evidence that accretion discs thicken during outburst has been observed by others.886 In. particular. in the case of another two SU UMa svstems. OY Car and Z Cha.," In particular, in the case of another two SU UMa systems, OY Car and Z Cha."887 For the case of OY Car Navloretal.(1987). were confronted with a similar problem of not being able to fit the outburst eclipses with a steady state model and they speculate that this could be due to a rim wall shadowing the inner parts of the disc., For the case of OY Car \scite{Naylor87} were confronted with a similar problem of not being able to fit the outburst eclipses with a steady state model and they speculate that this could be due to a rim wall shadowing the inner parts of the disc.888 Also. Navloretal.(1988) found evidence of a rim wall for OY Car by studying the UV. and Xray lux of the 1985 Alay superoutburst of OY Car.," Also, \scite{Naylor88} found evidence of a rim wall for OY Car by studying the UV and X–ray flux of the 1985 May superoutburst of OY Car."889 They suggest that the lack ofan Xray eclipse during the superoutburst. the existence of an orbital modulation of the UV ux and the observation that the UV. spectra show emission. lines which become," They suggest that the lack of an X–ray eclipse during the superoutburst, the existence of an orbital modulation of the UV flux and the observation that the UV spectra show emission lines which become"890"where 7.; is the cooling Irequency. ej; and e; are the fractions of the shock energy given to magnetic field and electrons at the shock. y=(p-2)/(p—1). Ex=E/10? eres. nj=n/l proton em*. gas=veο Lz. and here /; is the observer's time in unit of day. Dox is the huninosity distance in unit of 1075 em. a, is a correction [actor to the extinction along the line of sight to the burst.","where $\nu_{c,f}$ is the cooling frequency, $\epsilon_B$ and $\epsilon_e$ are the fractions of the shock energy given to magnetic field and electrons at the shock, $g=(p-2)/(p-1)$ , $E_{52}=E/10^{52}$ ergs, $n_0=n/1$ proton $^{-3}$, $\nu_{R,15}=\nu_R/10^{15}$ Hz, and here $t_d$ is the observer's time in unit of day, $D_{28}$ is the luminosity distance in unit of $10^{28}$ cm, $a_\nu$ is a correction factor to the extinction along the line of sight to the burst."891" Assuming (hat the re-brightening with the peak liminosityv of ~1 mJy around ~0.1 day is caused by this peak. we get the following formulae for e, ancl iy as functions of eg and other known parameters."," Assuming that the re-brightening with the peak luminosity of $\sim 1$ mJy around $\sim 0.1$ day is caused by this peak, we get the following formulae for $\epsilon_e$ and $n_0$ as functions of $\epsilon_B$ and other known parameters."892 Holland et al. (, Holland et al. (8932002a) claim the extinction ;ly.=0.26mag. which implies a ~20% correction in (he hR-band.,"2002a) claim the extinction $A_V=0.26$mag, which implies a $\sim 20 \%$ correction in the R-band."894 The slope ~—1.05 of the optical afterglow at late (nme implies p2.4., The slope $\sim -1.05$ of the optical afterglow at late time implies $p\sim2.4$.895 However. there is still some debate about the value of p (Sako Harrison 2002: llollauxd et al.," However, there is still some debate about the value of $p$ (Sako Harrison 2002; Holland et al."896 2002a; Pandey et al., 2002a; Pandey et al.897 2002)., 2002).898 We will discuss (wo cases p=2.2 and 2.4., We will discuss two cases $p=2.2$ and $2.4$.899 The evolution of reverse shocks is classified into two cases (IXobavashi 2000)., The evolution of reverse shocks is classified into two cases (Kobayashi 2000).900" If the initial Lorentz factor of the shell 7 is larger than a critical value jj.=(3E/32znmjc.NT) where m,P is (he mass of proton. the reverse shock becomes relativistic in the frame of unshockecl shell material during crossing the shell. and drastically decelerates the shell (thick shell case)."," If the initial Lorentz factor of the shell $\eta$ is larger than a critical value $\eta_c= (3E/32\pi n m_p c^2 \Delta_0^3)^{1/8}$ where $m_p$ is the mass of proton, the reverse shock becomes relativistic in the frame of unshocked shell material during crossing the shell, and drastically decelerates the shell (thick shell case)."901 Ifa<n. the reverse shock can not decelerate the shell effectively (thin shell case).," If $\eta< \eta_c$, the reverse shock can not decelerate the shell effectively (thin shell case)."902 According io the internal shock model. the initial width of the shell Ag is given by the intrinsic duration of the GRD ~ef£/(142) (Ixobavashi. Piran Sari 1997).," According to the internal shock model, the initial width of the shell $\Delta_0$ is given by the intrinsic duration of the GRB $\sim cT/(1+z)$ (Kobayashi, Piran Sari 1997)."903" TheLorentz factor at the shock crossing time is given given by 5,min[y. 7]."," TheLorentz factor at the shock crossing time is given given by $\gamma_\times \sim \min[\eta, \eta_c]$ ."904" The shock crossing time is /,~σαη)T (Sari Piran 1999a: IKobavashi 2000).", The shock crossing time is $t_\times \sim (\gamma_\times/\eta_c)^{-8/3}T$ (Sari Piran 1999a; Kobayashi 2000).905Labels at the bottom of the various panels of Fig.,Labels at the bottom of the various panels of Fig.906 show then-sihü fractions for discs in cach age bin. as well as the the fraction of dise stellar mass in that age bin (quantities in parenthesis).," \ref{disk_structure} show the fractions for discs in each age bin, as well as the the fraction of disc stellar mass in that age bin (quantities in parenthesis)."907" We find thataff disc stars vounger than 9 Car formedκα, and that even the oldest disc stars (representing between 30 and 50% of the total disc mass) have relatively highzn-sihu fractions."," We find that disc stars younger than $9$ Gyr formed, and that even the oldest disc stars (representing between $30$ and $50\%$ of the total disc mass) have relatively high fractions."908 The overall [ractions for simulated. disces are shown in Table 4.., The overall fractions for simulated discs are shown in Table \ref{table_insitu}.909 The fractions for disces are fo0.85 for all simulated ealaxies., The fractions for discs are $f> 0.85$ for all simulated galaxies.910 We note that although the bulk of disc stars are formedtesta. a non-neglieible fraction. of stars (<= 15%) can be contributed by disrupted satellites that come in on nearly coplanar orbits. as is the case for Ag-l-5. but. in general these bring relatively old stars to the final disc.," We note that although the bulk of disc stars are formed, a non-negligible fraction of stars $\le 15\%$ ) can be contributed by disrupted satellites that come in on nearly coplanar orbits, as is the case for Aq-E-5, but in general these bring relatively old stars to the final disc."911 This latter result is very similar to that obtained by Abacdi et al. (, This latter result is very similar to that obtained by Abadi et al. (9122003h). who also found that debris from disrupted satellites can be found in z—0 thin/thick disc components.,"2003b), who also found that debris from disrupted satellites can be found in $z=0$ thin/thick disc components."913 We find very good. agreement. of the overallsiu fractions for disces in Aq-C-6 and Adq-I-6b compared to Aq-C-5 and Aq-E-5. with changes of 54 and 34. respectively (Table 43).," We find very good agreement of the overall fractions for discs in Aq-C-6 and Aq-E-6b compared to Aq-C-5 and Aq-E-5, with changes of $5\%$ and $3\%$, respectively (Table \ref{table_insitu}) )."914 In the case of λαγό. the diseon-sihut fraction is 17% lower than in Aq-E-5. (," In the case of Aq-E-6, the disc fraction is $17\%$ lower than in Aq-E-5. ("915Note that the disc/spheroid decomposition can also introduce some cdillerences since. as explained in SOO. Aq-E has a rotating bulge and the decomposition is dillicult.),"Note that the disc/spheroid decomposition can also introduce some differences since, as explained in S09, Aq-E has a rotating bulge and the decomposition is difficult.)"916 The fractions for stars of given age (in particular for the three stellar age bins used above) show small dillerences with varving resolution., The fractions for stars of given age (in particular for the three stellar age bins used above) show small differences with varying resolution.917 The largest cilferences CS 10%) are found. for the oldest. stellar populations., The largest differences $\lesssim 10\%$ ) are found for the oldest stellar populations.918 For stars vounger than 9 Civr. we recover the result. from the level 5 simulations: all such stars formedbn-siit.," For stars younger than $9$ Gyr, we recover the result from the level 5 simulations: all such stars formed."919 The motion of stars in the simulated clises are dominated by the tangential velocity component., The motion of stars in the simulated discs are dominated by the tangential velocity component.920 In Fig., In Fig.921" 7 we show the mean tangential velocity V7, as a function of pacdius (fillecl circles). as well as V,860,,/2. where o,, is the dispersion in V2, in the corresponding radial bin."," \ref{vtita_vs_r} we show the mean tangential velocity $V_\phi$ as a function of radius (filled circles), as well as $V_\phi\pm \sigma_\phi/2$, where $\sigma_\phi$ is the dispersion in $V_\phi$ in the corresponding radial bin."922 For each simulation. we divided stars in the three age bins we used to analyse the disc structure.," For each simulation, we divided stars in the three age bins we used to analyse the disc structure."923 Young stars (f<9 Cir) usually have higher tangential velocities than older stars. particularly at large radii. and lower tangential velocity," Young stars $t\le 9$ Gyr) usually have higher tangential velocities than older stars, particularly at large radii, and lower tangential velocity"924include both grain opacities aid an improved TiO line list. although incompleteness in the Πο) line list leads to inaccuracies a uear-iutrared waveleneths (Chabrier. priv.,"include both grain opacities and an improved TiO line list, although incompleteness in the $_2$ O line list leads to inaccuracies at near-infrared wavelengths (Chabrier, priv."925 comm..," comm.,"926 2001: see also Reid Cruz. 2002. for comparison agalust iufrared data for late-ty‘pe dwarts).," 2001; see also Reid Cruz, 2002, for comparison against infrared data for late-type dwarfs)."927 The BCAH models are a closest to the empirical main seqence iu the (My. (1-J)) plane. albeit to some exter| smoothinD>oO over the break at Mj~10.5.," The BCAH models are a closest to the empirical main sequence in the $_I$, (I-J)) plane, albeit to some extent smoothing over the break at $_I \sim 10.5$."928 TIe extremely red colours at low ltuninosities reflect the absence oL graiu opacities in those moclels: the DUSTY moclels are clearly a better match to t1ο data., The extremely red colours at low luminosities reflect the absence of grain opacities in those models; the DUSTY models are clearly a better match to the data.929 A optical wavelengths. the BCAH 1iodels show poorer agreement. fallit& below the main sequence at My~10 and remaining 0.5 to ] magnitudes fainter than the obse'valions at lower Again. the DUSTY modes are better match the data. rellecine the more extensive TiO lineliss. but these modes still iniss the M3/M1 break iu (Aly. (V-I). while the mismatch at wavelengths refects tle HeO opacity deficietcles.," At optical wavelengths, the BCAH models show poorer agreement, falling below the main sequence at $_V \sim 10$ and remaining 0.5 to 1 magnitudes fainter than the observations at lower Again, the DUSTY models are better match the data, reflecting the more extensive TiO linelists, but these models still miss the M3/M4 break in $_V$, (V-I)), while the mismatch at near-infrared wavelengths reflects the $_2$ O opacity deficiencies."930 Bedin (2001) point oi similar discrej»ancles between theory aud observation at Owera bundanuces., Bedin (2001) point out similar discrepancies between theory and observation at lower abundances.931 As the latter authors emphasine. resolving those discrepatcies is important both iu interpreting colowr-maguituce diagrams. aud iu establishing reliable theoretical mass-Iuminositv translprimallous.," As the latter authors emphasise, resolving those discrepancies is important both in interpreting colour-magnitude diagrams, and in establishing reliable theoretical mass-luminosity transformations."932 h teris of the present survey. structure i1 the main sectrence has two consequences: first. systematic uuiscalibration. if the colour-iagulttde relation we aclopt fails to follow the empirical distributio> second. higher Malimquist bias. au a consequent inc'eased contamination from more distant star*. at colours where the main-sequence is steepest.," In terms of the present survey, structure in the main sequence has two consequences: first, systematic miscalibration, if the colour-magnitude relation we adopt fails to follow the empirical distribution; second, higher Malmquist bias, and a consequent increased contamination from more distant stars, at colours where the main-sequence is steepest."933 Bot1 of these biases are likely to be inost signiicant near the break at My— 12:10 1£( 52«(V—KKuw2.6. 1.15«(1—J) 1.65).," Both of these biases are likely to be most significant near the break at $_V =12$ to 14 ( $5 < (V-K) < 5.6$, $1.45 < (I-J) < 1.65$ )."934 These effecs will be taken Cully into account in statistical aualvsis of the nearby star sauple., These effects will be taken fully into account in statistical analysis of the nearby star sample.935 For present pu‘poses. we siniply uote the increased uncertainty in plooimetric parallax for stars of the appropriate colours.," For present purposes, we simply note the increased uncertainty in photometric parallax for stars of the appropriate colours."936 We have used the SINIBAD database to cross-'elereuce the NLTT sample agaiust the published iterature. checking all potential uaued couuterpars within 1 areuinute of the 2MLASS position.," We have used the SIMBAD database to cross-reference the NLTT sample against the published literature, checking all potential named counterparts within 1 arcminute of the 2MASS position."937 The alter step is essential since SINIBAD cloes not iuclude cross-refe'euces to all of the LP uaumes cited in the NLTT. while some stars apyear twice (or 1jore) with clilerent uames aud slightly different j»ositions.," The latter step is essential since SIMBAD does not include cross-references to all of the LP names cited in the NLTT, while some stars appear twice (or more) with different names and slightly different positions."938 Moreover. a significant 1umber of stars in the NLTT «atalogue have no associated uaime - a deliberate choice ou Luyteu's part.," Moreover, a significant number of stars in the NLTT catalogue have no associated name - a deliberate choice on Luyten's part."939 The overwlelinine majority oftlese stars are actually from he Lowell Observatory proper moion survey (Ci‘las. Burnham Thomas. 1971).," The overwhelming majority of these stars are actually from the Lowell Observatory proper motion survey (Giclas, Burnham Thomas, 1971)."940 Over 100 stars in the sample as a whole prove to lave either ploOluetric Or asrometric observatious available in, Over 400 stars in the sample as a whole prove to have either photometric or astrometric observations available in941"Relevant invariants introduced in AppendixA have the following values in the primed frame. implied by A=(0.0.0.0). in=(0.0.0.0):(2p, Omegall’,gamma, μμ”. where we assume A?=0?—[KP>0 and write i!—55*.","Relevant invariants introduced in Appendix\ref{sect:covariant} have the following values in the primed frame, implied by $K^{\mu'}=(\Omega',0,0,0)$, $K_D^{\mu'}=(0,0,0,\Omega')$:, t', u', where we assume $K^2=\Omega^2-|{\bi K}|^2>0$ and write $u'=\gamma'\beta'$."942 The electric field. E(x). is an invariant. and has the same form in all frames.," The electric field, $E(\chi)$, is an invariant, and has the same form in all frames."943 The equation of motion max be written in (wo equivalent forms:," The equation of motion may be written in two equivalent forms: u', ."944eround-based telescopes find (hat (he configuration of the magnetic field plavs an important role in the solar eruptive events. lLe.. Coronal Mass Ejections (CME) and solar flares (?)..,"ground-based telescopes find that the configuration of the magnetic field plays an important role in the solar eruptive events, i.e., Coronal Mass Ejections (CME) and solar flares \citep[]{canfield1999}."945 It is thus of great importance to study the building up of the magnetic field in the solar ab(mosphere. as il rises [rom (he convection zone.," It is thus of great importance to study the building up of the magnetic field in the solar atmosphere, as it rises from the convection zone."946 ILowever. the study of the transport οἱ magnetic flux and energv has been hampered by the invisibility of subsurface structures.," However, the study of the transport of magnetic flux and energy has been hampered by the invisibility of subsurface structures."947 With (the time-distance helioseismic analvsis. ? and ? provide a view on the horizontal and vertical flow velocities on the subsurface lavers under sunspots and identify shear flows and rotation of the sunspots underneath the surface. which may build up the enerev aud helicity in the atmosphere.," With the time-distance helioseismic analysis, \cite{sasha1996} and \cite{zhao2003} provide a view on the horizontal and vertical flow velocities on the subsurface layers under sunspots and identify shear flows and rotation of the sunspots underneath the surface, which may build up the energy and helicity in the atmosphere."948 Over the past decades. the development of numerical models have also ereatly improved our understanding of the cvnamics ancl energetics of magnetic flux emergence.," Over the past decades, the development of numerical models have also greatly improved our understanding of the dynamics and energetics of magnetic flux emergence."949 ? describes a two-dimensional magnetohvdrodvnamic (ATID) simulation on the emergence of a horizontal magnetic [lux rope from the photosphere into the chromosphere using a iwo-lavered atmosphere., \cite{shibata1989} describes a two-dimensional magnetohydrodynamic (MHD) simulation on the emergence of a horizontal magnetic flux rope from the photosphere into the chromosphere using a two-layered atmosphere.950 ? and ?/— carry oul sets of anelastic MIID simulations on the buovant rise of the magnetic flux tube Irom the base of convection zone to near the top. respectively.," \cite{fan2008} and \cite{jouve2009} carry out sets of anelastic MHD simulations on the buoyant rise of the magnetic flux tube from the base of convection zone to near the top, respectively."951 In particular. ? shows the rotation of the flux tube driven by the Lorentz force ab the two ends while the twisted tube is bent.," In particular, \cite{fan2008} shows the rotation of the flux tube driven by the Lorentz force at the two ends while the twisted tube is bent."952 ? suggested Chat shearing motion driven bv the Lorentz force draws (he magnetic field parallel to the Polarity Inversion Line (PIL). which was demonstrated in simulations of emereiug flux ropes (???7?777)..," \cite{manchester2000} suggested that shearing motion driven by the Lorentz force draws the magnetic field parallel to the Polarity Inversion Line (PIL), which was demonstrated in simulations of emerging flux ropes \citep[]{fan2001,magara2003,abbett2003,manchester2004,archontis2008,mactaggart2009}."953 ?. [ound that during emergence. energy flix through the photosphere is first dominated bv the vertical flows while horizontal flows dominate the later phase.," \cite{magara2003} found that during emergence, energy flux through the photosphere is first dominated by the vertical flows while horizontal flows dominate the later phase."954 The energy. Wausport of shear flows naturally provides an energv source for CMESs (??)..," The energy transport of shear flows naturally provides an energy source for CMEs \citep[]{manchester2007,manchester2008}."955 Simulations have also revealed (hat shear [lows driven by the Lorentz lorce can produce eruptions in both magnetic arcacles and emerging flux ropes (2???) providing further evidence of a mechanism for CMESs. flares and filament eruptions.," Simulations have also revealed that shear flows driven by the Lorentz force can produce eruptions in both magnetic arcades \citep[]{manchester2003} and emerging flux ropes \citep[]{manchester2004,archontis2008,mactaggart2009} providing further evidence of a mechanism for CMEs, flares and filament eruptions."956" +0d ot = 2,(foA0 2⋅ 242(2.1) 2⋅⊾ 4 Ilere ιν D, = spectrum . of Higgs.» of mass i » . particle > massconsis",The fluctuation operator is defined in general form as where $\psi_i$ denotes the fluctuating fields and $\psi_i^{cl}$ the “classical” background field configuration; here these will be the instanton and the vacuum configurations.957"tsmq> 72 -B bosonsHiggsvector andbosons gaugemj, dilute gas approximationand be describedas separateobjects wit"," If the fields are expanded around the background configuration as $\psi_i = \psi_i^{cl} + \phi_i$ and if the Lagrange density is expanded accordingly, then the fluctuation operator is related to the second order Lagrange density via In terms of the fluctuation operators $\calm$ on the instanton and $\calm^0$ on the vacuum backgrounds, the effective action is defined as For our specific model we expand as In order to eliminate the gauge degrees of freedom we introduce, as in Ref. \cite{Kripfganz:1989vm},"958"h topological chargebyq= +1. Αα).zen"" (y (2.3)", the background gauge function which leads in the Feynman background gauge to the gauge-fixing Lagrange density959Magnetic ‘fields may play au iuportant dynamical role iu the CRB outflows (e.g.??)..,"Magnetic fields may play an important dynamical role in the GRB outflows \cite[\eg][]{LyutikovJPh,Lyutikov:2009}."960 They may power the rel:uivistic outflow through? process (e.g.2).. aud contribute to particle acceleration iu the emission reeious.," They may power the relativistic outflow through\cite{BlandfordZnajek} process \citep[\eg][]{Komissarov05}, and contribute to particle acceleration in the emission regions."961 Iu this p:iper we discuss the dynamics of the relativistic. strongly magnetized ejecta.," In this paper we discuss the dynamics of the relativistic, strongly magnetized ejecta."962 The ‘estults are based Oh an exact solution of a one-dimensional Riemann problem of expausion of a cold. strongly iuagnetized into vacuum aud into external inedium of clensity pos (Lyutikov. stbinitted): they are reviewed in 82..," The results are based on an exact solution of a one-dimensional Riemann problem of expansion of a cold, strongly magnetized into vacuum and into external medium of density $\rho_{\rm ex}$ (Lyutikov, submitted); they are reviewed in \ref{Riemann}."963 In application to GRBs. àve assumes that the central engine produces jet with density po aud nagnelizatio 10 (c=BiJgpo: iis normalized by li). moving with Lorentz factor οZ91l.," In application to GRBs, we assumes that the central engine produces jet with density $\rho_{0}$ and magnetization $\sigma$ $\sigma=B_0^2/\rho_{0}$; is normalized by $\sqrt{4 \pi} $ ), moving with Lorentz factor $\gamma_w\gg 1$."964 Du fact. parzaiueters ο aud σ are 100 always idependent quantities: at παπα radii. when the motion of the ejecta is subsonic. they should be deermined together with the motionof the boundary. see 83.3..," In fact, parameters $\gamma_w$ and $\sigma$ are not always independent quantities: at small radii, when the motion of the ejecta is subsonic, they should be determined together with the motionof the boundary, see \ref{subsonic}."965 Ln a supersonic regime. ‘elation between ον and σ cdeyends ou the details of the flow acceleration iin conical flows we expect ri Vo).," In a supersonic regime, relation between $\gamma_w$ and $\sigma$ depends on the details of the flow acceleration in conical flows we expect $\gamma_w \sim \sqrt{\sigma}$ )."966 For generality. we do uot assume any relatiouship between σ aud η.," For generality, we do not assume any relationship between $\sigma$ and $\gamma_w$ ."967 The ejecta is moviο into external density. pos., The ejecta is moving into external density $\rho_{\rm ex}$ .968and Ac.=0.,and $\Delta v_z=0$.969 In these expressions. for the terms with Xx or + symbols the upper and lower signs correspond to prograde and retrograde cases. respectively.," In these expressions, for the terms with $\mp$ or $\pm$ symbols the upper and lower signs correspond to prograde and retrograde cases, respectively."970 These integrals can be evaluated in terms of the modified Bessel functions. Ay and A» (Abramowitz&Stegun1972)., These integrals can be evaluated in terms of the modified Bessel functions $K_1$ and $K_2$ \citep{AS72}.971 Employing the recursion relation we arrive at where the upper and lower signs are for prograde and retrograde encounters. respectively. and Av.=0 for coplanar collisions.," Employing the recursion relation we arrive at where the upper and lower signs are for prograde and retrograde encounters, respectively, and $\Delta$ $_{z}$ =0 for coplanar collisions."972" The structure of the expressions in terms of the modified Bessel functions Ay and Jv, is reminiscent of the results describing the perturbations of orbits of stars within disks owing to passing molecular clouds (Julian&Toomre1966).", The structure of the expressions in terms of the modified Bessel functions $K_0$ and $K_1$ is reminiscent of the results describing the perturbations of orbits of stars within disks owing to passing molecular clouds \citep{JT66}.973. It is of interest to consider various limiting cases for these expressions., It is of interest to consider various limiting cases for these expressions.974 When ©»0. corresponding to a slowly rotating system. the Bessel functions asymptote to Aya)~—Ino and Ay(a)~1/0 (Abramowitz&Stegun1972).. and we find which can be obtained from the usual result for the impulse approximation (eq.(7-54)inBinney&Tremaine1987).. as this limit describes the situation when the stars in the disk remain nearly stationary during the collision.," When $\alpha \rightarrow 0$ , corresponding to a slowly rotating system, the Bessel functions asymptote to $K_0 (\alpha) \sim- \ln \alpha$ and $K_1(\alpha) \sim 1/ \alpha \ $ \citep{AS72}, and we find which can be obtained from the usual result for the impulse approximation \citep[eq. (7-54) in][]{BT87}, as this limit describes the situation when the stars in the disk remain nearly stationary during the collision."975 Note that this limit is insensitive to the sign of O and hence does not distinguish between prograde and retrograde encounters., Note that this limit is insensitive to the sign of $\Omega$ and hence does not distinguish between prograde and retrograde encounters.976 The limita>x to an interaction where the response should be weak because. for example. the encounter is a distant one or the spin and correspondsorbital frequencies are highly mismatched.," The limit $\alpha \rightarrow \infty$ corresponds to an interaction where the response should be weak because, for example, the encounter is a distant one or the spin and orbital frequencies are highly mismatched."977 Employing the asymptotic expansion for the Bessel functions (Abramowitz&Stegun1972).. where j/=I. we find for the prograde and retrograde cases separately We note that the response is exponentially suppressed in the limita5ox. which demonstrates explicitly that the perturbed system is protected by adiabatic invariance.," Employing the asymptotic expansion for the Bessel functions \citep{AS72}, where $\mu=4\nu^2$, we find for the prograde and retrograde cases separately: We note that the response is exponentially suppressed in the limit $\alpha \rightarrow \infty$, which demonstrates explicitly that the perturbed system is protected by adiabatic invariance."978 It is also interesting that in this limit the prograde and retrograde cases are simply related: and for the y-component: Thus. the prograde response diverges relative to the retrograde one. by a factor of à. and. for a given à the magnitude in the velocity perturbation is exactly a factor of four larger.," It is also interesting that in this limit the prograde and retrograde cases are simply related: and for the y-component: Thus, the prograde response diverges relative to the retrograde one, by a factor of $\alpha$, and, for a given $\alpha$ the magnitude in the velocity perturbation is exactly a factor of four larger."979 From the above expressions. thechange in the energy of the perturbed system can be determined from:," From the above expressions, thechange in the energy of the perturbed system can be determined from:"980"where D,,0( and Bo, ave the upstream and downstream magnetic field strengths in units of iG. In the second step. we assumed that Bo/By=(paf/py)""o"". where w=1 corresponds to Boxp implied by the diffusion model in Equation (4)). Figure 6 shows {σοι} ala. =107. and (Jo/J4)os)=Jo)/sy(v) ad v=280 AMIIz for By= μα and ic=1 for the cases considered in Figure 5.","where $B_{0,\mu{\rm G}}$ and $B_{2,\mu{\rm G}}$ are the upstream and downstream magnetic field strengths in units of $\mu$ G. In the second step, we assumed that $B_2/B_0 = (\rho_2/\rho_0)^w = \sigma^w$ , where $w=1$ corresponds to $B \propto \rho$ implied by the diffusion model in Equation \ref{diffcoef}) ), Figure 6 shows $f_{e,0}(\gamma_e)/f_{e,2}(\gamma_e)$ at $\gamma_e=10^4$, and $(J_2/J_1)_{280} \equiv J_2({\nu}) / J_0({\nu})$ at $\nu = 280$ MHz for $B_0 = 1 \mu$ G and $w = 1$ for the cases considered in Figure 5."981 Ilere. we assume that Nesp is (he same for both the pre-existing aud injected populations.," Here, we assume that $K_{e/p}$ is the same for both the pre-existing and injected populations."982" Since the electron cutoff momentum is 44c10 for the shock parameters considered here. the choice of 4,=10! and v=280 MllIz (see Equation(18))) as the representative values should be safe."," Since the electron cutoff momentum is $\gamma_{\rm cut}\sim 10^8$ for the shock parameters considered here, the choice of $\gamma_e=10^4$ and $\nu = 280$ MHz (see \ref{peaknu}) )) as the representative values should be safe."983 As shown in Figure 5. for MS3. the downstream CR proton pressure can absorb typically only a few to of the shock ram pressure even [or /2=0.05.," As shown in Figure 5, for $M \la 3$, the downstream CR proton pressure can absorb typically only a few to of the shock ram pressure even for $R=0.05$."984 Yet. (he acceleration of CI. electrons can result in a substantial enhancement in svnchrotron radiation across the shock.," Yet, the acceleration of CR electrons can result in a substantial enhancement in synchrotron radiation across the shock."985 Our estimation indicates that the enhancement factor. (Jo/4)oso9. can be up to several al shocks with M1.5. up to several 10s for M.~ 2. and up (o several 1008 for M.~3.," Our estimation indicates that the enhancement factor, $(J_2/J_1)_{280}$, can be up to several at shocks with $M \sim 1.5$, up to several 10s for $M \sim 2$ , and up to several 100s for $M \sim 3$."986 This is partly due to the large enhancement of the electron population across the shock. {οfio. which is ἐνρισα]]ν an order of magnitude smaller than the ratio (Js/4)»s).," This is partly due to the large enhancement of the electron population across the shock, $f_{e,2}/f_{e,0}$ , which is typically an order of magnitude smaller than the ratio $(J_2/J_0)_{280}$."987 Additionalenhancement comes from the amplification of magnetic fields across the shock. οD.," Additionalenhancement comes from the amplification of magnetic fields across the shock, $B_2/B_0$."988 We note that for the compression ofa uniform magnetic field. Boxp?. that is. ie=2/3.," We note that for the compression of a uniform magnetic field, $B \propto \rho^{2/3}$, that is, $w=2/3$."989" With this scaling. (J5/Ju)os, should be a bit smaller (han that in Figure 6."," With this scaling, $(J_2/J_0)_{280}$ should be a bit smaller than that in Figure 6."990 However. it is also «quite plausible that the downstream magnetic field is stronger Chan (that expected for simple compression.," However, it is also quite plausible that the downstream magnetic field is stronger than that expected for simple compression."991 lt has been suggested (hat at shocks. especially at strong shocks. the downstream magnetic field is amplifiecl by plasma instabilities (see.e.g..Dell 2004).. although the existence of such instabilities has not been fully explored [or weak shocks.," It has been suggested that at shocks, especially at strong shocks, the downstream magnetic field is amplified by plasma instabilities \citep[see, e.g.,][]{lucek00,bell04}, although the existence of such instabilities has not been fully explored for weak shocks."992 Moreover. (he magnetic field can be further amplified by the turbulence that is induced through cascade of the vorticity generated behind shocks (GiacaloneΊναetal. 2008).," Moreover, the magnetic field can be further amplified by the turbulence that is induced through cascade of the vorticity generated behind shocks \citep{giacal07,ryuetal08}."993. In such cases. the ratio (J5/.Jg)os; could be larger than that in Figure 6.," In such cases, the ratio $(J_2/ J_0)_{280}$ could be larger than that in Figure 6."994 In that sense. our estimate for the svnchrotron enhancement factor may be considered. as conservalive one.," In that sense, our estimate for the synchrotron enhancement factor may be considered as conservative one."995 We also note that wilh s>r in Equation (21)). Js(»)/Ju(i) is larger al hieher lrequencies. but smaller with larger Bp.," We also note that with $s \geq r$ in Equation \ref{emirat2}) ), $J_2({\nu}) / J_0({\nu})$ is larger at higher frequencies, but smaller with larger $B_0$."996 The above enhancement in svnchrotron emissionacross (he shock can be compared (o ihe enhancement in Dremsstrahling X-ray., The above enhancement in synchrotron emissionacross the shock can be compared to the enhancement in Bremsstrahlung X-ray.997 The Bremsstrahling X-ray emissivity isgiven asJyX(Pv> T. so the ratioB of. the downstream to upstream emissivity. can be written. as," The Bremsstrahlung X-ray emissivity isgiven as$J_X \propto \rho^2\sqrt{T}$ , so the ratio of the downstream to upstream emissivity can be written as"998starting with up to Nox32000 stars and. dillerent binary fractions. density distributions. ry and Z4; values.,"starting with up to $N \simeq 32\,000$ stars and different binary fractions, density distributions, $r_{\rm h}$ and $R_{\rm gc}$ values."999 Our nmocels extend this work to include a distribution of stellar masses and stellar evolution for N=100000.," Our models extend this work to include a distribution of stellar masses and stellar evolution for $N = 100\,000$."1000 In doing so we confirm the findings of Ixüppper. Ixroupa Baumegardt (2008).," In doing so we confirm the findings of Küppper, Kroupa Baumgardt (2008)."1001 The common sequence shows a mfr ratio that starts in the range of 0.15.—0.2 and increases slightlv with decreasing mass., The common sequence shows a $r_{\rm h} / r_{\rm t}$ ratio that starts in the range of $0.15 - 0.2$ and increases slightly with decreasing mass.1002 Relatecl to this the same authors found that clusters in a tidal field show an equilibrium half-mass radius after core-collapse., Related to this the same authors found that clusters in a tidal field show an equilibrium half-mass radius after core-collapse.1003 This was 2 pe for their standard set of models. noting that the particular value will increase for higher initial mass and larger Aue.," This was $2\,$ pc for their standard set of models, noting that the particular value will increase for higher initial mass and larger $R_{\rm gc}$."1004 Our models MI and A2 have a similar tidal tidal field. but [arger initial mass., Our models M1 and M2 have a similar tidal tidal field but larger initial mass.1005 οσο moels also show an ecuilibrium half-mass racius and as expectecL it is larger. im 21xc. with the inclusion of stellar evolution ikely contributing to some of the increase.," These models also show an equilibrium half-mass radius and as expected it is larger, $\sim 5\,$ pc, with the inclusion of stellar evolution likely contributing to some of the increase."1006 This COLPLPCSPOHls to a projected wil-light radius of about 3 pc which fits with the tvpical value observed for compact CC's in the Milky Way (Daumgardt et al.," This corresponds to a projected half-light radius of about $3\,$ pc which fits with the typical value observed for compact GCs in the Milky Way (Baumgardt et al."1007 2010) and. M31. and indeed almost all galaxies where we see GC's (Da Costa οἱ al.," 2010) and M31, and indeed almost all galaxies where we see GCs (Da Costa et al."1008 2009. for example).," 2009, for example)."1009 Of our models in the weaker tidal field only NI gets close to core-collapse and. indeed has a larger half-miass radius at this point. 10 pc. but in this case appears to still be rising.," Of our models in the weaker tidal field only N1 gets close to core-collapse and indeed has a larger half-mass radius at this point, $\sim 10\,$ pc, but in this case appears to still be rising."1010 Using a direct N-body code we have Followed the evolution of star clusters with cilferent initial sizes in a tidal field appropriate for a ealaxy such as the cdwarl irregular 6822 or the Large Magellanic Cloud.," Using a direct $N$ -body code we have followed the evolution of star clusters with different initial sizes in a tidal field appropriate for a galaxy such as the dwarf irregular $\,6822$ or the Large Magellanic Cloud."1011 We also looked at the clleet of increasing the galaxy mass by a factor of ten. appropriate for larger galaxies such as M31 and the Milky Way. on the evolution of clusters which initially fill. their tidal racii.," We also looked at the effect of increasing the galaxy mass by a factor of ten, appropriate for larger galaxies such as M31 and the Milky Way, on the evolution of clusters which initially fill their tidal radii."1012 Our main findings can be summarised as: We are indebted to Sverre Aarseth ancl Weigo Nitadori for creating and maintaining the GPU library forNBODY6., Our main findings can be summarised as: We are indebted to Sverre Aarseth and Keigo Nitadori for creating and maintaining the GPU library for.1013 JRIL also wishes to thank Ben Darsdell anc David. Barnes [or assistance with GPU usage at Swinburne. as well as Annic llughes for informative discussions regarding molecular clouds.," JRH also wishes to thank Ben Barsdell and David Barnes for assistance with GPU usage at Swinburne, as well as Annie Hughes for informative discussions regarding molecular clouds."1014 We also thank the referee for a number of insightul comments., We also thank the referee for a number of insightful comments.1015MOND requires dark. matter of some form.,MOND requires dark matter of some form.1016 As discussed in Angusetal.(2008) there appears to be a scale at which MOND begins to poorly describe the dynamics of astrophysical systems., As discussed in \cite{afb} there appears to be a scale at which MOND begins to poorly describe the dynamics of astrophysical systems.1017 Εις is highlighted by RomanowskyO'Sullivanetal.(2007) which show that no dark matter is necessary to explain the detailed: cdvnamies of relatively low mass groups of galaxies ancl svstems smaller.," This is highlighted by \cite{romanowsky03,milgrom03,aftcz,osullivan08} which show that no dark matter is necessary to explain the detailed dynamics of relatively low mass groups of galaxies and systems smaller."1018 This is expected for sterile neutrino dark matter because Ht would have a free streaming length greater significantly larger than a typical galaxy (~50kpe for the Milky: Way., This is expected for sterile neutrino dark matter because it would have a free streaming length greater significantly larger than a typical galaxy $\sim$ 50kpc for the Milky Way.1019 However. just as numerical simulations of clusters of cold dark matter were necessary to show that the CDAL halos are a poor match to observed galaxies (cleBlok&MeGaugh1998:Gilmorectal. 2007)). the equilibrium distribution of the sterile neutrino DM must be checked to be consistent. with eroups and clusters of galaxies (see Sanders 2007)).," However, just as numerical simulations of clusters of cold dark matter were necessary to show that the CDM halos are a poor match to observed galaxies \citealt{deblok98,mcgaughdeblok,gnedin02,gentile04,gilmore07}) ), the equilibrium distribution of the sterile neutrino DM must be checked to be consistent with groups and clusters of galaxies (see \citealt{sanders07}) )."1020" On the other hand. the three active neutrinos should oobablve have masses well below 0.5eV. Otherwise it. will »come cillieult to match the CMDB power spectrum because he angular scale of the peaks prefers O57=0.117. while QO,xm»."," On the other hand, the three active neutrinos should probably have masses well below 0.5eV. Otherwise it will become difficult to match the CMB power spectrum because the angular scale of the peaks prefers $\Omega_{\nu}h^2=0.117$ while $\Omega_{\nu}\propto m_{\nu}$."1021 Increasing the mass of another neutrino reduces he mass of the sterile neutrino and. the amplitude of the hire peak of the CAIB diminishes due to the rapidly decreasing maximum clensity (p.Μεταx ml)., Increasing the mass of another neutrino reduces the mass of the sterile neutrino and the amplitude of the third peak of the CMB diminishes due to the rapidly decreasing maximum density $\rho_{\nu}^{max}\propto m_{\nu}^4$ ).1022 Certain analyses of neutrino mixing experiments seen ο require an additional. sterile neutrino with a mass in the range 4eV«η<ISeV.," Certain analyses of neutrino mixing experiments seem to require an additional, sterile neutrino with a mass in the range $4eV<m_{\nu_s}<18eV$."1023 Llere E took the that there is à fourth. sterile neutrino of LleV mass and that MOND ellects are not important at cosmological scales.," Here I took the that there is a fourth, sterile neutrino of 11eV mass and that MOND effects are not important at cosmological scales."1024 L showed that its contribution to the dynamics of galaxies. would be negligible. but that it could solve all problems MOND has with the dynamics of clusters of galaxies ancl it can match the angular power spectrum of the CALB.," I showed that its contribution to the dynamics of galaxies would be negligible, but that it could solve all problems MOND has with the dynamics of clusters of galaxies and it can match the angular power spectrum of the CMB."1025 The matter power spectrum needs to be recalculated because ALOND eravity is crucial to the formation of these smaller structures and because of the increased dominance of barvons at hese scales over DM. hydrodynamics cannot be avoided as in CDM simulations.," The matter power spectrum needs to be recalculated because MOND gravity is crucial to the formation of these smaller structures and because of the increased dominance of baryons at these scales over DM, hydrodynamics cannot be avoided as in CDM simulations."1026 Hf experiments can indeed. pinpoint he existence of a sterile neutrino with mass 1I1eV this would be a significant advance for the Mocified Newtonian Dynamics., If experiments can indeed pinpoint the existence of a sterile neutrino with mass $\sim$ 11eV this would be a significant advance for the Modified Newtonian Dynamics.1027Assundug a Keplerian dik. with average rotation speed of (hep)IlzGYMd. the terminal velocity can be writtenas ὃς=lyr.l)jconeQ Which yields a value c42m for Ty=1.,"Assuming a Keplerian disk, with average rotation speed of $\langle v_{c,kep} \rangle \sim1028{1 \over 2} \sqrt{\pi G \Sigma d}$, the terminal velocity can be writtenas $1029v_{\infty}=4(\sqrt{\frac{\pi\Gamma_0}{2}-1}) \langle v_{c,kep} \rangle$, which yields a value $v_{\infty}\simeq\ 3 \langle v_{c,kep} \rangle $, for $\Gamma_0=1$."1030 But these results will change with Diese).the proper inclusion of bulge aud dark latter halo., But these results will change with the proper inclusion of bulge and dark matter halo.1031 Iu this paper. we discuss steady. rotating wind in which dust is propelled outwards bv radiation pressure and drags the eas with it.," In this paper, we discuss steady, rotating wind in which dust is propelled outwards by radiation pressure and drags the gas with it."1032 We ignore magnetic forces and treat the wind as a single-phase fiuid. which is mareinally optically thick (ATQTO05).," We ignore magnetic forces and treat the wind as a single-phase fluid, which is marginally optically thick (MQT05)."1033 Although our results are valid for all temperatures. in practice the model allows for onlv cold flows (as observed n Nal aud Mel lines (c.e. Martin 2005)) for the following reasons.," Although our results are valid for all temperatures, in practice the model allows for only cold flows (as observed in NaI and MgII lines (e.g. Martin 2005)) for the following reasons."1034 The sputtering radius for graius over a wind timescale of LO Myr Qwhich we derive below) is e~5«Ue A for To10° K (Tielens 199D. which Προς that only erains smaller than 5 A are destroved. without changing the opacity.," The sputtering radius for grains over a wind timescale of 10 Myr (which we derive below) is $a \sim 50 \times \frac{n}{0.1/cc}$ $\AA$ for $T \sim 10^5$ K (Tielens 1994), which implies that only grains smaller than $5$ $\AA$ are destroyed, without changing the opacity."1035 But the radiative cooling time is small (<21 Avr). so for adiabatic approximation to be valid. the adiabatic-cooliug time scale should be shorter than the radiative-cooliug timescale. which limits the temperature <104 Is. Also the timescale for heating is ~LO Myr andcan be neglected.," But the radiative cooling time is small $\le 1$ Myr), so for adiabatic approximation to be valid, the adiabatic-cooling time scale should be shorter than the radiative-cooling timescale, which limits the temperature $\le 10^4$ K. Also the timescale for dust-heating is $\sim10$ Myr andcan be neglected."1036 Secondly. we improve upon the previous estimates of the required value of Py needed to drive a wind. by taking iuto account the eravity of bulee aud halo.," Secondly, we improve upon the previous estimates of the required value of $\Gamma_0$ needed to drive a wind, by taking into account the gravity of bulge and halo."1037 Clearly the relation between ex of the wind aud c. i which the rotation speed is estimated frou a kepleriau disk is not relevant for disk galaxies. because the rotation speed must be calculated from the dark matter halo.," Clearly the relation between $v_\infty$ of the wind and $v_{c}$ in which the rotation speed is estimated from a keplerian disk is not relevant for disk galaxies, because the rotation speed must be calculated from the dark matter halo."1038 We cousider a disk with coustaut surface deusitv (X) and surface brightuess (2). of radius 4. aud which is embedded in a bulge aud a halo.," We consider a disk with constant surface density $\Sigma$ ) and surface brightness $I$ ), of radius $d$, and which is embedded in a bulge and a halo."1039 We assmue a spherical mass distribution iu the bulee aud the halo., We assume a spherical mass distribution in the bulge and the halo.1040 For the bulee. we assunie a total mass of AM inside a radius Γραςid.," For the bulge, we assume a total mass of $M_b$ inside a radius $r_b \ll d$."1041" For the halo. we consider a. Navarro-Frenk-Wlite (NEW) profile. with total mass Mj, characterized bv a concentration parameter e=rfr. (Navarre. Frenk. White 1997)."," For the halo, we consider a Navarro-Frenk-White (NFW) profile, with total mass $M_h$ characterized by a concentration parameter $c=r_{vir}/r_s$ (Navarro, Frenk, White 1997)."1042" We fx the total halo mass for a given disk mass (M,= ad?S). by the ratio Mj/AM,~1/0.05. as deteriuned by Mo. Mao White (1998) (referred to as MMWS?OS hereafter)."," We fix the total halo mass for a given disk mass $M_d=\pi d^2 \Sigma$ ), by the ratio $M_h/M_d\sim 1/0.05$, as determined by Mo, Mao White (1998) (referred to as MMW98 hereafter)."1043 We use the prescription of AIAIW9s for the disk exponential scale-leneth Ry~⋖↓∖∕−≽⋟∕∖∫↿⋟⊐⋃⋃⋅↗↳↙↽≓⊽⊥⊐⊽ : : ⊀∙⊀⋅∙⊀ ⋅↗↳∫⋣⊳∙∏↴∖↴↕∐∶↴∙⊾↑∐↸∖∐⋅↸∖≺∣∐↴∖↴−≽⋅≩∙−⋗∢≽∙⋅≩−⋗∙⋜⋯≼↧ ∏↴∖↴↸∖↙∕∶∫↿⋟∣∣∖∕⊇∙↴∖↴↕∐∩∖↑∐↸∖↑∪↑⋜↕↕⋯⋜↧↴∖∷∖↴↸∖↴∖↴↕∐↑∐↸∖↸⊳⋜↧↴∖↴↸∖ of uniformi density and expoucutial disk are given bv AM=πιοsE» ," We use the prescription of MMW98 for the disk exponential scale-length $R_d \sim (1/\sqrt{2}) \lambda R_{200}1044f_c^{-1/2} f_R$ , using their eqns 23, 26, 32, and use $d=R_d/\sqrt{2}$ , since the total masses in the case of uniform density and exponential disk are given by $M=\pi d^2 \Sigma=2 \pi 1045\Sigma_0 R_d^2$."1046Thed rotationB speed nuplied. by the NEW profile peaks 22M.at a racius r2r;. iver by. VOU3l 2 where Ες is the scale radius of NEW profile aud μυ is the rotation speed at the virial radius.," The rotation speed implied by the NFW profile peaks at a radius $r\sim 2 r_s$, given by, v_c ^2, where $r_s$ is the scale radius of NFW profile and $v_{200}$ is the rotation speed at the virial radius."1047 We choose this value of the mui rotation speed to represcut the ce. of the disk galaxy. since Figure 2 of MMW98 shows that the value of c. from the flat part of the total rotation curve does not differ much from the peak of the rotation curve from halo oulv.," We choose this value of the maximum rotation speed to represent the $v_c$ of the disk galaxy, since Figure 2 of MMW98 shows that the value of $v_c$ from the flat part of the total rotation curve does not differ much from the peak of the rotation curve from halo only."1048" We also use Γροἱ~0.1. aud AL,/ALy~0.5. consistent. with observed rauge of huninositv ratio between bulge aud disk (Binney Ἀ[οππποα 1998)."," We also use $r_b/d\sim 0.1$ , and $M_b/M_d \sim 0.5$, consistent with observed range of luminosity ratio between bulge and disk (Binney Merrifield 1998)."1049 To determine the terminal speed of the wind. we use the fact that the Bernoulli function is preserved along a streamline. assmniue that a streamline extends frou the base to iufiuitv.," To determine the terminal speed of the wind, we use the fact that the Bernoulli function is preserved along a streamline, assuming that a streamline extends from the base to infinity."1050 In an isothermal wind the terminal speed tends to mfnitv as the wind maintains coustaut sound speed., In an isothermal wind the terminal speed tends to infinity as the wind maintains constant sound speed.1051 It is however more reasonable to assiune a polvtropic equation of state., It is however more reasonable to assume a polytropic equation of state.1052 Oue can write the Bernoulli equation for a polvtropic eas (with adiabatic index 5) along a streamline: +|—4[ο=E. where ej is the sound speed. o is the potential aud £ is à coustaut.," One can write the Bernoulli equation for a polytropic gas (with adiabatic index $\gamma$ ) along a streamline: ${v^2 \over 2} + {c_s^2 \over \gamma -1} + \phi= E$ , where $c_s$ is the sound speed, $\phi$ is the potential and $E$ is a constant."1053 Equating the values at the base and infinity. we have where ο is the wind speed at the base (2=0). ον Is the souud speed at the base. and esis the sound speed at infinity. which is negligible.," Equating the values at the base and infinity, we have + _b, where $v_b$ is the wind speed at the base $z=0$ ), $c_{s,b} $ is the sound speed at the base, and $c_{s,\infty}$ is the sound speed at infinity, which is negligible."1054 The poteutial is. Tere the first term denotes a pseudo-poteutial due o radiation pressure.," The potential is, Here the first term denotes a pseudo-potential due to radiation pressure."1055 The second terii refers to the eravitational potential of the disk. aud here we have assumed for analytical simplicity that eas stavs near the ole. so these forces are eiven by equ(2).," The second term refers to the gravitational potential of the disk, and here we have assumed for analytical simplicity that gas stays near the pole, so these forces are given by $(\ref{eq:fg})$."1056 The third teri. is the potential due to the outward ceutiüfueal force of the rotating eas in the wind. and the last two terms deuote he effect of the bulee aud halo gravity.," The third term is the potential due to the outward centrifugal force of the rotating gas in the wind, and the last two terms denote the effect of the bulge and halo gravity."1057 We also assiuue hat the bulec exerts a negligible radiation pressure. since he donunaut bulee stellar population is old aud red aud he mean opacity & of dust eraius in these waveleugthlis is sinaller than in blue baud.," We also assume that the bulge exerts a negligible radiation pressure, since the dominant bulge stellar population is old and red and the mean opacity $\kappa$ of dust grains in these wavelengths is smaller than in blue band."1058 The ceutrifugal force at the base of the rotating wind should be equal to eravitational force due to the 1ass insidee. the racial distauce at the base.," The centrifugal force at the base of the rotating wind should be equal to gravitational force due to the mass inside$a$, the radial distance at the base."1059 We assume that a Dong. the bulee radius. while beiug much siualler thu d. the disk radius.," We assume that $a \ge r_b$ , the bulge radius, while being much smaller than $d$ , the disk radius."1060" Hence the centrifugal force is written as, The first tex onRUS is due to the bulge. aud the second term. due to the dark matter halo."," Hence the centrifugal force is written as, The first term onRHS is due to the bulge, and the second term, due to the dark matter halo."1061" For e« r,. the second terii can be approximated: as 3 which is much"," For $a \ll r_s$ , the second term can be approximated as $\frac{G M_s}{2 r_s^{2}}$ which is much"1062For the 29 observed galaxies in the D95 area. we would have preditod 6.7 should have ]ος part of the velocity field of the cluster.,"For the 29 observed galaxies in the B95 area, we would have predicted 6.7 should have been part of the velocity field of the cluster."1063 The large error bar ou this prediction docs not prohibit a conclusive statement about the errors in the 2D statistical background. subtraction method., The large error bar on this prediction does not prohibit a conclusive statement about the errors in the 2D statistical background subtraction method.1064 However. it is very nmuportaut fc| check this result with more redshifts since the 2D statistical subtraction of backgrouud galaxies is now standard practice for coustructing cluster Iuninositv functions: both distant aud neurbyv.," However, it is very important to check this result with more redshifts since the 2D statistical subtraction of background galaxies is now standard practice for constructing cluster luminosity functions; both distant and nearby."1065 One of the su-chuups mentioned in section 2 is coincident with the recsüft peak at zzz0.5 ideutified above., One of the sub-clumps mentioned in section 2 is coincident with the redshift peak at $\simeq$ 0.5 identified above.1066 The spatial extension of this structure is 110 kpe (Ily 2100, The spatial extension of this structure is 110 kpc $_0$ =1001067"One important observation that supports the existence of showerglass effect is that the phase shift, measured from helioseismic holography ingression and egression correlations (corresponding to double-skip travel time measurements of time-distance helioseismology) when the holography focus plane is at the solar surface and located inside a sunspot. is different from the sum of phase shifts measured trom the local ingression and eeression control correlations.","One important observation that supports the existence of showerglass effect is that the phase shift, measured from helioseismic holography ingression and egression correlations (corresponding to double-skip travel time measurements of time-distance helioseismology) when the holography focus plane is at the solar surface and located inside a sunspot, is different from the sum of phase shifts measured from the local ingression and egression control correlations."1068 Measurements using a second-skip time-distance technique showed similar diserepancies (Braun1997)., Measurements using a second-skip time-distance technique showed similar discrepancies \citep{bra97}.1069". These observations supported the argument that acoustic signals observed inside sunspot may cause outgoing and ingoing travel time asymmetries, or introduce uncertainties to time-distance measured travel times."," These observations supported the argument that acoustic signals observed inside sunspot may cause outgoing and ingoing travel time asymmetries, or introduce uncertainties to time-distance measured travel times."1070" To avoid the use of pixels located inside the sunspot region as the central point in traditional time-distance measurement (refer to Figure 6)). Hughes,Rajaguru.&Thompson(2005). used the second-skip time-distance measurements and performed inversions, from which they obtained sound-speed perturbations beneath sunspots similar to the results obtained from the traditional time-distance measurements in the deep interior (Kosovichev,Duvall,&Scherrer2000:Zhao&Kosovichev 2003).."," To avoid the use of pixels located inside the sunspot region as the central point in traditional time-distance measurement (refer to Figure \ref{fg6}) ), \citet{hug05} used the second-skip time-distance measurements and performed inversions, from which they obtained sound-speed perturbations beneath sunspots similar to the results obtained from the traditional time-distance measurements in the deep interior \citep{kos00, zha03}."1071 A disagreement between their second-skip analysis with the traditional one-skip analysis near the surface may be due to the lack of near surface measurements when, A disagreement between their second-skip analysis with the traditional one-skip analysis near the surface may be due to the lack of near surface measurements when1072redshift evolution.,redshift evolution.1073 Note that the clumping will generally be a [function of both redshift and neutral fraction., Note that the clumping will generally be a function of both redshift and neutral fraction.1074" In the model of MILIROO.. the recombination rate in an inhomogeneous Universe is related. to the uniform recombination rate Z2, bv By itself. this formalism. would. underestimate the cllective clumping. since reionization proceeds via the »ercolation of ionized bubbles. which are produced by highly nasecl sources."," In the model of , the recombination rate in an inhomogeneous Universe is related to the uniform recombination rate $R_u$ by By itself, this formalism would underestimate the effective clumping, since reionization proceeds via the percolation of ionized bubbles, which are produced by highly biased sources."1075 This mav be accounted for by calculating he recombination rate inside cach bubble and averaging over the distribution of bubble sizes., This may be accounted for by calculating the recombination rate inside each bubble and averaging over the distribution of bubble sizes.1076 We do this following 3. , We do this following \ref{fig:zeta_history} 1077explain the observations of these bursts.,explain the observations of these bursts.1078 The true CRB rate as a function of redshift is difficult to establish from the current CRB sample., The true GRB rate as a function of redshift is difficult to establish from the current GRB sample.1079 It is eenerallv sugeested that the CRB rate follows the star formation vate., It is generally suggested that the GRB rate follows the star formation rate.1080 Various imocdels of the star formation rate are presented in the literature., Various models of the star formation rate are presented in the literature.1081 Whether or not the model of the star formation rate affects our results?, Whether or not the model of the star formation rate affects our results?1082" We use a iociel of the observed GRB rate suggested by Bloom (2003). who constructed a correction factor of D,7 when 2>1l."," We use a model of the observed GRB rate suggested by Bloom (2003), who constructed a correction factor of $D_L^{-2}$ when $z>1$."1083 This factor leads to the observed GBD rate deeply decay when :>l1., This factor leads to the observed GRB rate deeply decay when $z>1$.1084 Thus. different models of the star formation rate may eive almost the sue observed GRD rate (Bloom 2003). aud then the model of the star formation rate does not significantly affect our results.," Thus, different models of the star formation rate may give almost the same observed GRB rate (Bloom 2003), and then the model of the star formation rate does not significantly affect our results."1085 In fact. we focus ou the comparison of both results ou theoretical bases aud on the observational bases.," In fact, we focus on the comparison of both results on theoretical bases and on the observational bases."1086 The results of the comparison should not be greatly affected by the model of star formation rate (Liang. Wu Dai 2001).," The results of the comparison should not be greatly affected by the model of star formation rate (Liang, Wu Dai 2004)."1087 Our empirical results are derived by the GCGL-relation., Our empirical results are derived by the GGL-relation.1088 This relationship depends on cosmological parameters., This relationship depends on cosmological parameters.1089" Iu this work we adopt O3,=0.5 and O4=(0.7.", In this work we adopt $\Omega_M=0.3$ and $\Omega_{\Lambda}=0.7$.1090 We check if the cosimological parameters siguificautlv affect the results of the comparisous between our empirical results aud model predictions., We check if the cosmological parameters significantly affect the results of the comparisons between our empirical results and model predictions.1091" We take Qa,=0.5 and Q4= 0.5.", We take $\Omega_M=0.5$ and $\Omega_{\Lambda}=0.5$ .1092 In this case. the CCL-relation becomes L.ου=(0.90+0.12)pLEton for a CRB sample presented by Au et al. (," In this case, the GGL-relation becomes $E_{\gamma,50}=(0.90\pm0.12) E_{\rm p}^{1.42\pm 0.10}$ for a GRB sample presented by Xu et al. ("10932005).,2005).1094" We show the comparison between the PMO) based on this relationship and Phy predicted by the power-law jet model iu the cosmology model with Q5,=0.5 and O4=0.5 in Figure 6.", We show the comparison between the $P^{\rm em}(\theta)$ based on this relationship and $P^{\rm th}(\theta)$ predicted by the power-law jet model in the cosmology model with $\Omega_M=0.5$ and $\Omega_{\Lambda}=0.5$ in Figure 6.1095 The I&-S test for the two distributions shows Pys=0.123. confidently: sugecsting that they are consistent.," The K-S test for the two distributions shows $P_{K-S}=0.123$, confidently suggesting that they are consistent."1096 Comparing the results shown in Figure 6 to that shown in the left panel of Figure 3. one can find that cosmological parameters do uot significantly affect our results.," Comparing the results shown in Figure 6 to that shown in the left panel of Figure 3, one can find that cosmological parameters do not significantly affect our results."1097 We should clarity that our empirical approach aud theoretical model are independent without toutologv., We should clarify that our empirical approach and theoretical model are independent without toutology.1098 The model predictions are statistical distributions. while the clupirical results are based ou the relationships related to the spectral properties aud energy release of CRBs.," The model predictions are statistical distributions, while the empirical results are based on the relationships related to the spectral properties and energy release of GRBs."1099 The enipirical approach and theoretical model are intrinsically different., The empirical approach and theoretical model are intrinsically different.1100 Our enpirical results are roughly consistent with the results from currently 0-known CRB sample., Our empirical results are roughly consistent with the results from currently $\theta$ -known GRB sample.1101 This is a selt-consistent result because the GOGL-relation was discovered w this CRB sample., This is a self-consistent result because the GGL-relation was discovered by this GRB sample.1102 For the bursts in this sample their oeakk energies. teniporal breaks of optical afterglow light curves. and redshifts are well measured.," For the bursts in this sample their peak energies, temporal breaks of optical afterglow light curves, and redshifts are well measured."1103 Such a sample uust suffers ercatly observational biases and sample selection. effects. especially when the completeness at low Huxes and the bias of redshift micasurement are considered.," Such a sample must suffers greatly observational biases and sample selection effects, especially when the completeness at low fluxes and the bias of redshift measurement are considered."1104 Daud Preece (2005) argued that the GGL-velation may © an artifact of the selection effects. aud these selection effects may favor sub-populations of CRBs.," Band Preece (2005) argued that the GGL-relation may be an artifact of the selection effects, and these selection effects may favor sub-populations of GRBs."1105 If it is really he case. the selection effects should affect our empirical results.," If it is really the case, the selection effects should affect our empirical results."1106 We thauk the anonuvinious referee for his/her valuable sugecstions and conunents., We thank the anonymous referee for his/her valuable suggestions and comments.1107 We also thank Diug Zhaug. Zieno Dai. and Yiping Qiu for their helpful discussious.," We also thank Bing Zhang, Zigao Dai, and Yiping Qin for their helpful discussions."1108 This work was supported by the National Natural Scieuce Foundation of China (Cwauts10163001)., This work was supported by the National Natural Science Foundation of China (Grants10463001).1109The presence of the solar atmosphere will result also in the de-Iocusing of the coherent raciation. (hus worsening the quality of (he solar gravitational lens.,"The presence of the solar atmosphere will result also in the de-focusing of the coherent radiation, thus worsening the quality of the solar gravitational lens."1110 To analvze this influence let us estimate (he optical distance for the (wo sources affecting the light propagation in the solar vicinity. namely gravitv and plasma.," To analyze this influence let us estimate the optical distance for the two sources affecting the light propagation in the solar vicinity, namely gravity and plasma."1111 One may expect that the beginning of the interference zone will be shifted further away from the Sun., One may expect that the beginning of the interference zone will be shifted further away from the Sun.1112 For estimation purposes we will consider here only the steadi-state part of the plasma model., For estimation purposes we will consider here only the steady-state part of the plasma model.1113 The beginning of the interference zone (e.q., The beginning of the interference zone (e.q.1114" the effective optical distance) in this case may be determined from This expression ngives the effective optical distance for the svstem nleravilv+plasma. JF,grpl>0: One may note (hat. lor any given impact parameter b there is a critical frequency rogi such (hat the denominator in (he expression (15)) vanishes ancl (he effective optical distance Ferpi becomes infinitive.", the effective optical distance) in this case may be determined from This expression gives the effective optical distance for the system gravity+plasma ${\cal F}_{\tt gr+pl}\ge 0$: One may note that for any given impact parameter $b$ there is a critical frequency $\nu_{\tt crit}$ such that the denominator in the expression \ref{eqtot}) ) vanishes and the effective optical distance ${\cal F}_{\tt gr+pl}$ becomes infinitive.1115 This is the case when there is no lensing at all and the solar plasma enlively neutralizes influence of the solar gravity., This is the case when there is no lensing at all and the solar plasma entirely neutralizes influence of the solar gravity.1116 This critical frequency is given as follows: Dased on the estimates [or Fgx presented in the Table 1. and. [rom the practical considerations for the solar gravity lens mission. one will have to limit the range of possible impact parameters to those in the interval b/R...ε|1.05.1.35]. which correspond to the optical distance Ferpi€|601.1000|. AU.," This critical frequency is given as follows: Based on the estimates for ${\cal F}_{\tt gr}$ presented in the Table \ref{tab66} and from the practical considerations for the solar gravity lens mission, one will have to limit the range of possible impact parameters to those in the interval $ {b}/{{\cal R}_\odot } \in [1.05, 1.35]$, which correspond to the optical distance ${\cal F}_{\tt gr+pl} \in [601, 1000[$ AU."1117 For this range of impact parameter. (he main contribution comes from the term ~(R.pn»).," For this range of impact parameter, the main contribution comes from the term $\sim1118\big({{\cal R}_\odot / b}\big)^{15}$."1119 Therefore. approximating to the sufficient order. we will have the critical frequency wilh Merit=ανν...)120Gllz or. equivalently. 2.5 mim.," Therefore, approximating to the sufficient order, we will have the critical frequency with $\nu_{0\,\tt crit}\equiv\nu_{\tt crit}({\cal R}_\odot )=120~{\rm GHz}$ or, equivalently, 2.5 mm."1120 As a result of this analvsis we find that the effective optical distance for the svstem gravitv-plasma will be determined from the following expression:, As a result of this analysis we find that the effective optical distance for the system gravity+plasma will be determined from the following expression:1121"Optical imaging of the RA 02:30 hy field of the ΗΠΑΏου) Survey was obtained on 22 October 2001 UT using the prime focus dmager Suprime-Cam (Mivazakietal.1998) ou the Subaru 8.2-11. Telescope on Mama Wea. Πανάς,","Optical imaging of the RA 02:30 hr field of the IfA-Deep Survey was obtained on 22 October 2001 UT using the prime focus imager Suprime-Cam \citep{1998SPIE.3355..363M} on the Subaru 8.2-m Telescope on Mauna Kea, Hawaii."1122 The instrument is a mosaic of ten contiguous 1006 AITT/Liucolu Lab phase 2 and 3 CCDs with a total field of view of 31/«27'.., The instrument is a mosaic of ten contiguous $\times$ 4096 MIT/Lincoln Lab phase 2 and 3 CCDs with a total field of view of $\times$.1123 Conditions were photometric with O’s8 FWHAL seeing., Conditions were photometric with 8 FWHM seeing.1124 We tmaged two adjacent fields with a total area of 0.5 ddeerees., We imaged two adjacent fields with a total area of 0.5 degrees.1125 DitheredR..£.. z/—baud observations were obtained with iuteerations of 560 x. GI5 s. and 960 s per filter per pointing. respectively.," Dithered, -band observations were obtained with integrations of 560 s, 645 s, and 960 s per filter per pointing, respectively."1126 The aad F--lband filter are Cousins filters., The and -band filter are Cousins filters.1127 The falter has an effective wavelength of 9195 aad a FWOAL of 10A.. very similar to that used by the SDSS survey (Fukueitaetal.1996)..," The filter has an effective wavelength of 9195 and a FWHM of 1410, very similar to that used by the SDSS survey \citep{1996AJ....111.1748F}."1128 huages were flattened. defringed. warped onto a cohbunon sky coordinate svsteun. registered. aud cleaned of cosunic rays.," Images were flattened, defringed, warped onto a common sky coordinate system, registered, and cleaned of cosmic rays."1129 A preliminary photometric calibration of the πω ddata was done using optical Πασάς previously obtained from smaller telescopes. which was calibrated with standards from Landolt(1992)..," A preliminary photometric calibration of the and data was done using optical imaging previously obtained from smaller telescopes, which was calibrated with standards from \citet{1992AJ....104..340L}."1130 For the ddata. the preliminary calibration was done by comparing the ccolors of stars in the Suprime-Cam data with the stellar locus.," For the data, the preliminary calibration was done by comparing the colors of stars in the Suprime-Cam data with the stellar locus."1131 The latter was svuthesized from the spectral enerey distributions of Camu&Stryker(19835) and the instrumental (filter|detectoratumospliere) transmission profiles., The latter was synthesized from the spectral energy distributions of \citet{1983ApJS...52..121G} and the instrumental (filter+detector+atmosphere) transmission profiles.1132 The resulting maguitudes in Table 1 are Vega-based., The resulting magnitudes in Table 1 are Vega-based.1133 We identified an extremely red stellar object at RA(2000) = 02:26:37.6. DEC(2000) = 00:51:51.7 in the I aud 2/--baud imaging.," We identified an extremely red stellar object at RA(2000) = 02:26:37.6, DEC(2000) = 00:51:54.7 in the $I$ and -band imaging."1134 We refer to it as “IEA 0230-Z17 hereinafter., We refer to it as “IfA 0230-Z1” hereinafter.1135 We obtained J aud ZI-baud photometry ou 06 November 2001 UT using the facility spectrograph Spex (Πανetal.1998).., We obtained $J$ and $H$ -band photometry on 06 November 2001 UT using the facility spectrograph Spex \citep{1998SPIE.3354..468R}.1136 Spex has a slitiewing camera. which uses a 5124512 InSb array from Ravtheou-SBRC and has a pixel scale of 071118Ἐ," Spex has a slit-viewing camera, which uses a $\times$ 512 InSb array from Raytheon-SBRC and has a pixel scale of 118."1137"ν, Conditious were photometric with QO/ss5 FWTIAL secing.", Conditions were photometric with 85 FWHM seeing.1138 We obtained a total of 18 nuu aud 10 min of iutegration at J and 1 - respectively., We obtained a total of 18 min and 10 min of integration at $J$ and $H$ -band respectively.1139 The Spex filters were purchased as part of the Mauna hea Filter Cousortimm (Simons&TokunagaWw01:Tokunagaetal. 2001).. and hence will be common to most of the current major infrared telescopes.," The Spex filters were purchased as part of the Mauna Kea Filter Consortium \citep{mkofilters1, mkofilters2}, and hence will be common to most of the current major infrared telescopes."1140 We obtained inages of the standard star $J 9105 frou Perssonctal.(1098) imuneciately after observing HA 0230-Z1., We obtained images of the standard star SJ 9105 from \citet{1998AJ....116.2475P} immediately after observing IfA 0230-Z1.1141 The resulting maeguitudes i Table 1 are Vega-based., The resulting magnitudes in Table 1 are Vega-based.1142 We obtained an Z-baud spectrmm of ΠΔ 0230-Z1 on LO November 2001 UT with the Neck Telescope aud. the facility spectrograplh NIRSPEC (MeLeanetal.1995)., We obtained an $H$ -band spectrum of IfA 0230-Z1 on 10 November 2001 UT with the Keck Telescope and the facility spectrograph NIRSPEC \citep{1998SPIE.3354..566M}.1143 NIRSPEC uses a 102141021 InSh ALADDIN: detector from: Ravtheou-SBRC., NIRSPEC uses a $\times$ 1024 InSb ALADDIN detector from Raytheon-SBRC.1144 A total of 30 min of integration was obtained in low resolution mode using the NIRSPEC-5 blocking filter and the 07776 «lit., A total of 30 min of integration was obtained in low resolution mode using the NIRSPEC-5 blocking filter and the 76 slit.1145 Conditious were very nou-plotometric due to high thick cirrus., Conditions were very non-photometric due to high thick cirrus.1146 The object was dithered on the slit between exposures., The object was dithered on the slit between exposures.1147" The slit PA was set to T3766 cast of north. so that the bright object D/665 away (""object AT} was also on the slit for all the exposures."," The slit PA was set to 6 east of north, so that the bright object 65 away (“object A”) was also on the slit for all the exposures."1148 This provided a well-detected reference for registering the frames. and also a check on the resulting spectrophotometry (see below).," This provided a well-detected reference for registering the frames, and also a check on the resulting spectrophotometry (see below)."1149 A nearby AOV star was observed inmuediately afterward to calibrate the tellurc and iustrmucutal throughput., A nearby A0V star was observed immediately afterward to calibrate the telluric and instrumental throughput.1150 The spectra were reduced using custom IDL scripts., The spectra were reduced using custom IDL scripts.1151 The raw images on the NIRSPEC detector are curved iu both the spectral aud spatial directions., The raw images on the NIRSPEC detector are curved in both the spectral and spatial directions.1152" After subtracting a dark frame and dividing bv a flat field. the individual Huages were cleaned of outlier pixels aud rectified using traces of the arc lamp lines and the object spectra,"," After subtracting a dark frame and dividing by a flat field, the individual images were cleaned of outlier pixels and rectified using traces of the arc lamp lines and the object spectra."1153 Pairs of images taken at successive nods were subtracted to remove the sky cussion., Pairs of images taken at successive nods were subtracted to remove the sky emission.1154 huages were then registered. shifted. and stacked to form a final 2-d mosaic of the spectrum.," Images were then registered, shifted, and stacked to form a final 2-d mosaic of the spectrum."1155" Extractions of I-d spectra frou, the mosaic were done in a manner to produce reliable errors based ou photon counting (Poisson) statistics.", Extractions of 1-d spectra from the mosaic were done in a manner to produce reliable errors based on photon counting (Poisson) statistics.1156 Details will be presented in a future paper., Details will be presented in a future paper.1157 We divided the extracted spectra bv the spectra of the AOV. calibrator star and then multiplied bv a 9720 IK blackbody to restore the true shape ofthe coutimuun., We divided the extracted spectra by the spectra of the A0V calibrator star and then multiplied by a 9720 K blackbody to restore the true shape of the continuum.1158 Uvdrogen absorption features in thecalibrator were removed by linear interpolation., Hydrogen absorption features in thecalibrator were removed by linear interpolation.1159 Wavelength calibration was done with spectra of argou and ueon lamps., Wavelength calibration was done with spectra of argon and neon lamps.1160 The spectral resolution (A/AA) of the original extracted spectra was Ro=1610 (9.7 Aj): nuum of the telluric OI ciission lines are well-separated from each other., The spectral resolution $\lambda/\Delta{\lambda}$ ) of the original extracted spectra was $R=1640$ (9.7 ); many of the telluric OH emission lines are well-separated from each other.1161 The resulting S/N was only zL35. so we xin!oothed the spectra with a 32 pixel EWIINME Gaussian. with proper weighting accounting for the measurement errors. and rebiuued the data to 2 pixels per spectral resolution clement.," The resulting S/N was only $\approx1\!-\!3$, so we smoothed the spectra with a 32 pixel FWHM Gaussian, with proper weighting accounting for the measurement errors, and rebinned the data to 2 pixels per spectral resolution element."1162 The final spectra have a resolution of R=150 and are plotted in Figure L.., The final spectra have a resolution of $R=180$ and are plotted in Figure \ref{fig-spectra}.1163" The zpJ bendeolorsoffA 0230. Zlarceatremelyrcd, whilethe]- IIeolorsarceclatieclgbluc."," The $J$ -band colors of IfA 0230-Z1 are extremely red, while the $J-H$ colors are relatively blue."1164Sucheolorsaveuniquelgeharacteristicof., Such colors are uniquely characteristic of T dwarfs.1165 Zlhasi-J-2.r120.15 mae (Vega). comparable to the reddest known T dwarfs.," IfA 0230-Z1 has $\zp-J=2.74\pm0.15$ mag (Vega), comparable to the reddest known T dwarfs."1166 Its J)II color of 0.312:0.05 indicate a spectral type of ΤὸTl (Leeecttetal. 2002).., Its $J-H$ color of $\pm$ 0.05 indicate a spectral type of T3–T4 \citep{leg01}. .1167 Figure | shows the Ieck/NIRSPEC spectra of I£A 0230-Zl and object A. which were observed simultaneously aud reduced in an identical fashion.," Figure \ref{fig-spectra} shows the Keck/NIRSPEC spectra of IfA 0230-Z1 and object A, which were observed simultaneously and reduced in an identical fashion."1168 The spectrum of object A shows a featureless continumn fy~AP. cousisteut with the near-IR continu of a low redshift galaxy C(Manunuuccietal. 2001)..," The spectrum of object A shows a featureless continuum $f_\lambda\sim\lambda^{-0.7}$, consistent with the near-IR continuum of a low redshift galaxy \citep{2001MNRAS.326..745M}."1169 On the other hand. IA 0230-Z1 shows a peak iu its conutimmun around 1.58 ;42.," On the other hand, IfA 0230-Z1 shows a peak in its continuum around 1.58 ."1170. The continu is depressed in the blue aud the red around the peak. indicating the presence of aud aabsorption. respectively.," The continuum is depressed in the blue and the red around the peak, indicating the presence of and absorption, respectively."1171 Since object A's spectrum docs not show anv such features. we conclude that thesefeatures," Since object A's spectrum does not show any such features, we conclude that thesefeatures"1172up to 100 days.,up to 100 days.1173 Exposures were acquired in pairs to be later summed. except when bad weather conditions forced us to stop observations after the first frame.," Exposures were acquired in pairs to be later summed, except when bad weather conditions forced us to stop observations after the first frame."1174 We thus collected fourteen epochs of data over 2.5 months., We thus collected fourteen epochs of data over 2.5 months.1175 The log of the observations is given in Table |.. where each exposure is identified with a unique ID. and the epoch at the middle of the acquisition period is indicated. along with the exposure time and the observing mode (v=Vvisitor. s=service).," The log of the observations is given in Table \ref{t_obs}, where each exposure is identified with a unique ID, and the epoch at the middle of the acquisition period is indicated, along with the exposure time and the observing mode (v=visitor, s=service)."1176 Data were reduced with the dedicated CPL-based pipeline available at the ESO web site., Data were reduced with the dedicated CPL-based pipeline available at the ESO web site.1177 Because of the extremely low signal collected for the hottest targets. we performed many trial reductions to find the choices and parameter sets that maximized the output quality.," Because of the extremely low signal collected for the hottest targets, we performed many trial reductions to find the choices and parameter sets that maximized the output quality."1178 The frames were de-biased and flat-fielded with standard procedures based on the frames collected within the standard calibration plan., The frames were de-biased and flat-fielded with standard procedures based on the frames collected within the standard calibration plan.1179 The dark current was found to be non-negligible only along the top edge of the CCD. not used in our work. and no dark correction was applied to avoid the corresponding decrease in S/N by10-15%.," The dark current was found to be non-negligible only along the top edge of the CCD, not used in our work, and no dark correction was applied to avoid the corresponding decrease in S/N by."1180. We gave particular attention to. the wavelength calibration (wle). whose defects can easily affect the radial velocity (RV) measurements.," We gave particular attention to the wavelength calibration (wlc), whose defects can easily affect the radial velocity (RV) measurements."1181 The goodness of the wle was checked by analyzing the spectra of the lamp fibers acquired simultaneously with target stars., The goodness of the wlc was checked by analyzing the spectra of the lamp fibers acquired simultaneously with target stars.1182 This reduction step was particularly problematic. because we found that running the complete wle routine resulted in an incorrect solution. with a deviation from the correct one that increased with wavelength and fiber number. up to 10-15 km s'.," This reduction step was particularly problematic, because we found that running the complete wlc routine resulted in an incorrect solution, with a deviation from the correct one that increased with wavelength and fiber number, up to 10-15 km $^{-1}$."1183 We therefore adopted the standard solution for the H7A setup. included in the instrumental package downloadable from the GIRAFFE web site. allowing the pipeline to use the lamp fibers to find rigid shifts and changes in the spectral geometry on the chip.," We therefore adopted the standard solution for the H7A setup, included in the instrumental package downloadable from the GIRAFFE web site, allowing the pipeline to use the lamp fibers to find rigid shifts and changes in the spectral geometry on the chip."1184 After the final extraction. the lamp fibers showed only small random deviations from laboratory wavelengths (0.3 km rms).," After the final extraction, the lamp fibers showed only small random deviations from laboratory wavelengths (0.3 km $^{-1}$ rms)."1185 RVThis wle error is small compared to uncertainties in the measurement. and can be safely neglected in the final error budget.," This wlc error is small compared to uncertainties in the RV measurement, and can be safely neglected in the final error budget."1186 Finally. science spectra were extracted using both an optimum algorithm and a simple sum.," Finally, science spectra were extracted using both an optimum algorithm and a simple sum."1187 We found that these two methods were in general equivalent and the choice did not alter the results. but in some noisy spectra one or the other returned more precise measurements.," We found that these two methods were in general equivalent and the choice did not alter the results, but in some noisy spectra one or the other returned more precise measurements."1188 This was probably due to small cosmetic. defects or noise spikes being treated differently by the two algorithms., This was probably due to small cosmetic defects or noise spikes being treated differently by the two algorithms.1189 We therefore preferred optimum-extracted spectra. but we opted for a simple sum in the few cases in which this clearly returned smaller RV errors.," We therefore preferred optimum-extracted spectra, but we opted for a simple sum in the few cases in which this clearly returned smaller RV errors."1190 The background flux was estimated by averaging nine fibers allocated to the sky and. after subtracting their mean spectrum from those of the targets. we checked that the weak interstellar emission in the core of the Πρ line had been effectively removed.," The background flux was estimated by averaging nine fibers allocated to the sky and, after subtracting their mean spectrum from those of the targets, we checked that the weak interstellar emission in the core of the $_\beta$ line had been effectively removed."1191 The spectra were then trimmed to retain only the central region (1780-4930 ). and we normalized them fitting a linear relation to the continuum on both sides of the Hy line.," The spectra were then trimmed to retain only the central region (4780-4930 ), and we normalized them fitting a linear relation to the continuum on both sides of the $_\beta$ line."1192 We verified that a higher order polynomial was not required in the normalization. as there was no appreciable change in either the fitted function and or the results.," We verified that a higher order polynomial was not required in the normalization, as there was no appreciable change in either the fitted function and or the results."1193 As a final step of the reduction. the spectra forming à pair of exposures (see Table 1)) were added.," As a final step of the reduction, the spectra forming a pair of exposures (see Table \ref{t_obs}) ) were added."1194 Some example spectra are shown in Figure 2.. for two stars at the edge of the temperature range 7700 and 2200 K) and one of intermediate temperature. plus the star #337345. discussed later.," Some example spectra are shown in Figure \ref{f_spectra}, for two stars at the edge of the temperature range 700 and 200 K) and one of intermediate temperature, plus the star 37345, discussed later."1195 The presented spectra are the sum of all the spectra collected for each star. after shifting them to laboratory wavelengths.," The presented spectra are the sum of all the spectra collected for each star, after shifting them to laboratory wavelengths."1196 The observed HB was fitted with the zero-age HB model (ZAHB) of with. metallicity [Fe/H]=-1.10 to derive a temperature scale along the HB., The observed HB was fitted with the zero-age HB model (ZAHB) of with metallicity $-$ 1.10 to derive a temperature scale along the HB.1197 The procedure was not straightforward using the (U— color. and uncertainties remained in the determination of the required distance modulus and reddening.," The procedure was not straightforward using the $U-V$ ) color, and uncertainties remained in the determination of the required distance modulus and reddening."1198 These problems could be due to the use of the, These problems could be due to the use of the1199with zero slope. although it is fair to say that there is evidence for a slight positive correlation.,"with zero slope, although it is fair to say that there is evidence for a slight positive correlation."1200 On the other hand. his correlation is largely. driven by the rare clusters which ormed at very high redshifts: most of these objects formed ab αρ0.0 and are evenly distributed about the mean mass-emperature relationship.," On the other hand, this correlation is largely driven by the rare clusters which formed at very high redshifts; most of these objects formed at $z_f < 0.6$ and are evenly distributed about the mean mass-temperature relationship."

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